YES 4.409 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
  ((maximum :: Ord a => [Maybe a ->  Maybe a) :: Ord a => [Maybe a ->  Maybe 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
  ((maximum :: Ord a => [Maybe a ->  Maybe a) :: Ord a => [Maybe a ->  Maybe a)

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
  ((maximum :: Ord a => [Maybe a ->  Maybe a) :: Ord a => [Maybe a ->  Maybe a)

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
  ((maximum :: Ord a => [Maybe a ->  Maybe a) :: Ord a => [Maybe a ->  Maybe a)

module Main where
  import qualified Prelude



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

is transformed to
compare x y = compare3 x y

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
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
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
  ((maximum :: Ord a => [Maybe a ->  Maybe a) :: Ord a => [Maybe a ->  Maybe a)

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

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

reduce2D vwv vww = gcd 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' x zx = gcd0Gcd'2 x zx
gcd0Gcd' x y = gcd0Gcd'0 x y

gcd0Gcd'0 x y = gcd0Gcd' y (x `rem` y)

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

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



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

mainModule Main
  ((maximum :: Ord a => [Maybe a ->  Maybe a) :: Ord a => [Maybe a ->  Maybe 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
  (maximum :: Ord a => [Maybe a ->  Maybe 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
                              ↳ QDP

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

new_primEqNat(Succ(vwx2900), Succ(vwx3000)) → new_primEqNat(vwx2900, vwx3000)

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
                              ↳ QDP

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

new_primPlusNat(Succ(vwx5900), Succ(vwx31001000)) → new_primPlusNat(vwx5900, vwx31001000)

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
                              ↳ QDP

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

new_primMulNat(Succ(vwx300000), Succ(vwx3100100)) → new_primMulNat(vwx300000, Succ(vwx3100100))

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
                              ↳ QDP

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

new_esEs3(@3(vwx290, vwx291, vwx292), @3(vwx300, vwx301, vwx302), baf, app(ty_Maybe, bcf), bcc) → new_esEs2(vwx291, vwx301, bcf)
new_esEs(:(vwx290, vwx291), :(vwx300, vwx301), app(app(ty_@2, bb), bc)) → new_esEs0(vwx290, vwx300, bb, bc)
new_esEs2(Just(vwx290), Just(vwx300), app(ty_[], bab)) → new_esEs(vwx290, vwx300, bab)
new_esEs3(@3(vwx290, vwx291, vwx292), @3(vwx300, vwx301, vwx302), baf, bag, app(app(app(ty_@3, bbf), bbg), bbh)) → new_esEs3(vwx292, vwx302, bbf, bbg, bbh)
new_esEs3(@3(vwx290, vwx291, vwx292), @3(vwx300, vwx301, vwx302), baf, bag, app(ty_[], bbe)) → new_esEs(vwx292, vwx302, bbe)
new_esEs3(@3(vwx290, vwx291, vwx292), @3(vwx300, vwx301, vwx302), app(app(ty_@2, bdc), bdd), bag, bcc) → new_esEs0(vwx290, vwx300, bdc, bdd)
new_esEs(:(vwx290, vwx291), :(vwx300, vwx301), app(app(app(ty_@3, bh), ca), cb)) → new_esEs3(vwx290, vwx300, bh, ca, cb)
new_esEs3(@3(vwx290, vwx291, vwx292), @3(vwx300, vwx301, vwx302), app(ty_[], bdh), bag, bcc) → new_esEs(vwx290, vwx300, bdh)
new_esEs1(Left(vwx290), Left(vwx300), app(app(ty_Either, fc), fd), fb) → new_esEs1(vwx290, vwx300, fc, fd)
new_esEs3(@3(vwx290, vwx291, vwx292), @3(vwx300, vwx301, vwx302), baf, app(ty_[], bcg), bcc) → new_esEs(vwx291, vwx301, bcg)
new_esEs1(Right(vwx290), Right(vwx300), gc, app(app(ty_Either, gf), gg)) → new_esEs1(vwx290, vwx300, gf, gg)
new_esEs2(Just(vwx290), Just(vwx300), app(ty_Maybe, baa)) → new_esEs2(vwx290, vwx300, baa)
new_esEs3(@3(vwx290, vwx291, vwx292), @3(vwx300, vwx301, vwx302), app(app(ty_Either, bde), bdf), bag, bcc) → new_esEs1(vwx290, vwx300, bde, bdf)
new_esEs0(@2(vwx290, vwx291), @2(vwx300, vwx301), app(app(ty_Either, ea), eb), dh) → new_esEs1(vwx290, vwx300, ea, eb)
new_esEs3(@3(vwx290, vwx291, vwx292), @3(vwx300, vwx301, vwx302), baf, app(app(ty_@2, bca), bcb), bcc) → new_esEs0(vwx291, vwx301, bca, bcb)
new_esEs0(@2(vwx290, vwx291), @2(vwx300, vwx301), cc, app(ty_[], db)) → new_esEs(vwx291, vwx301, db)
new_esEs(:(vwx290, vwx291), :(vwx300, vwx301), app(ty_Maybe, bf)) → new_esEs2(vwx290, vwx300, bf)
new_esEs3(@3(vwx290, vwx291, vwx292), @3(vwx300, vwx301, vwx302), baf, app(app(ty_Either, bcd), bce), bcc) → new_esEs1(vwx291, vwx301, bcd, bce)
new_esEs2(Just(vwx290), Just(vwx300), app(app(ty_Either, hg), hh)) → new_esEs1(vwx290, vwx300, hg, hh)
new_esEs3(@3(vwx290, vwx291, vwx292), @3(vwx300, vwx301, vwx302), baf, app(app(app(ty_@3, bch), bda), bdb), bcc) → new_esEs3(vwx291, vwx301, bch, bda, bdb)
new_esEs0(@2(vwx290, vwx291), @2(vwx300, vwx301), cc, app(ty_Maybe, da)) → new_esEs2(vwx291, vwx301, da)
new_esEs1(Left(vwx290), Left(vwx300), app(app(ty_@2, eh), fa), fb) → new_esEs0(vwx290, vwx300, eh, fa)
new_esEs(:(vwx290, vwx291), :(vwx300, vwx301), ba) → new_esEs(vwx291, vwx301, ba)
new_esEs0(@2(vwx290, vwx291), @2(vwx300, vwx301), app(app(app(ty_@3, ee), ef), eg), dh) → new_esEs3(vwx290, vwx300, ee, ef, eg)
new_esEs1(Right(vwx290), Right(vwx300), gc, app(app(app(ty_@3, hb), hc), hd)) → new_esEs3(vwx290, vwx300, hb, hc, hd)
new_esEs0(@2(vwx290, vwx291), @2(vwx300, vwx301), app(ty_Maybe, ec), dh) → new_esEs2(vwx290, vwx300, ec)
new_esEs3(@3(vwx290, vwx291, vwx292), @3(vwx300, vwx301, vwx302), baf, bag, app(ty_Maybe, bbd)) → new_esEs2(vwx292, vwx302, bbd)
new_esEs3(@3(vwx290, vwx291, vwx292), @3(vwx300, vwx301, vwx302), app(ty_Maybe, bdg), bag, bcc) → new_esEs2(vwx290, vwx300, bdg)
new_esEs1(Right(vwx290), Right(vwx300), gc, app(app(ty_@2, gd), ge)) → new_esEs0(vwx290, vwx300, gd, ge)
new_esEs1(Left(vwx290), Left(vwx300), app(ty_Maybe, ff), fb) → new_esEs2(vwx290, vwx300, ff)
new_esEs0(@2(vwx290, vwx291), @2(vwx300, vwx301), cc, app(app(ty_Either, cf), cg)) → new_esEs1(vwx291, vwx301, cf, cg)
new_esEs0(@2(vwx290, vwx291), @2(vwx300, vwx301), app(app(ty_@2, df), dg), dh) → new_esEs0(vwx290, vwx300, df, dg)
new_esEs0(@2(vwx290, vwx291), @2(vwx300, vwx301), app(ty_[], ed), dh) → new_esEs(vwx290, vwx300, ed)
new_esEs3(@3(vwx290, vwx291, vwx292), @3(vwx300, vwx301, vwx302), baf, bag, app(app(ty_Either, bbb), bbc)) → new_esEs1(vwx292, vwx302, bbb, bbc)
new_esEs1(Right(vwx290), Right(vwx300), gc, app(ty_[], ha)) → new_esEs(vwx290, vwx300, ha)
new_esEs(:(vwx290, vwx291), :(vwx300, vwx301), app(app(ty_Either, bd), be)) → new_esEs1(vwx290, vwx300, bd, be)
new_esEs1(Left(vwx290), Left(vwx300), app(ty_[], fg), fb) → new_esEs(vwx290, vwx300, fg)
new_esEs2(Just(vwx290), Just(vwx300), app(app(app(ty_@3, bac), bad), bae)) → new_esEs3(vwx290, vwx300, bac, bad, bae)
new_esEs1(Right(vwx290), Right(vwx300), gc, app(ty_Maybe, gh)) → new_esEs2(vwx290, vwx300, gh)
new_esEs1(Left(vwx290), Left(vwx300), app(app(app(ty_@3, fh), ga), gb), fb) → new_esEs3(vwx290, vwx300, fh, ga, gb)
new_esEs0(@2(vwx290, vwx291), @2(vwx300, vwx301), cc, app(app(ty_@2, cd), ce)) → new_esEs0(vwx291, vwx301, cd, ce)
new_esEs3(@3(vwx290, vwx291, vwx292), @3(vwx300, vwx301, vwx302), baf, bag, app(app(ty_@2, bah), bba)) → new_esEs0(vwx292, vwx302, bah, bba)
new_esEs0(@2(vwx290, vwx291), @2(vwx300, vwx301), cc, app(app(app(ty_@3, dc), dd), de)) → new_esEs3(vwx291, vwx301, dc, dd, de)
new_esEs(:(vwx290, vwx291), :(vwx300, vwx301), app(ty_[], bg)) → new_esEs(vwx290, vwx300, bg)
new_esEs3(@3(vwx290, vwx291, vwx292), @3(vwx300, vwx301, vwx302), app(app(app(ty_@3, bea), beb), bec), bag, bcc) → new_esEs3(vwx290, vwx300, bea, beb, bec)
new_esEs2(Just(vwx290), Just(vwx300), app(app(ty_@2, he), hf)) → new_esEs0(vwx290, vwx300, he, hf)

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
                              ↳ QDP

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

new_primCmpNat(Succ(vwx30000), Succ(vwx310000)) → new_primCmpNat(vwx30000, vwx310000)

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

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



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

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

new_ltEs0(Just(vwx3000), Just(vwx31000), app(app(app(ty_@3, dc), dd), de)) → new_ltEs3(vwx3000, vwx31000, dc, dd, de)
new_ltEs1(Left(vwx3000), Left(vwx31000), app(app(ty_@2, ec), ed), dg) → new_ltEs2(vwx3000, vwx31000, ec, ed)
new_ltEs3(@3(vwx3000, vwx3001, vwx3002), @3(vwx31000, vwx31001, vwx31002), baf, app(ty_Maybe, bcc), bcb) → new_lt0(vwx3001, vwx31001, bcc)
new_ltEs3(@3(vwx3000, vwx3001, vwx3002), @3(vwx31000, vwx31001, vwx31002), baf, app(app(ty_Either, bcd), bce), bcb) → new_lt1(vwx3001, vwx31001, bcd, bce)
new_compare0(:(vwx3000, vwx3001), :(vwx31000, vwx31001), ba) → new_primCompAux(vwx3000, vwx31000, new_compare(vwx3001, vwx31001, ba), ba)
new_ltEs1(Left(vwx3000), Left(vwx31000), app(app(ty_Either, ea), eb), dg) → new_ltEs1(vwx3000, vwx31000, ea, eb)
new_lt3(vwx3000, vwx31000, bac, bad, bae) → new_compare23(vwx3000, vwx31000, new_esEs7(vwx3000, vwx31000, bac, bad, bae), bac, bad, bae)
new_ltEs1(Left(vwx3000), Left(vwx31000), app(ty_Maybe, dh), dg) → new_ltEs0(vwx3000, vwx31000, dh)
new_ltEs3(@3(vwx3000, vwx3001, vwx3002), @3(vwx31000, vwx31001, vwx31002), baf, app(ty_[], bca), bcb) → new_lt(vwx3001, vwx31001, bca)
new_ltEs2(@2(vwx3000, vwx3001), @2(vwx31000, vwx31001), gc, app(app(app(ty_@3, hb), hc), hd)) → new_ltEs3(vwx3001, vwx31001, hb, hc, hd)
new_ltEs3(@3(vwx3000, vwx3001, vwx3002), @3(vwx31000, vwx31001, vwx31002), app(ty_[], bdc), bag, bcb) → new_lt(vwx3000, vwx31000, bdc)
new_ltEs1(Right(vwx3000), Right(vwx31000), eh, app(app(ty_@2, ff), fg)) → new_ltEs2(vwx3000, vwx31000, ff, fg)
new_primCompAux(vwx3000, vwx31000, vwx41, app(app(ty_@2, bf), bg)) → new_compare3(vwx3000, vwx31000, bf, bg)
new_compare0(:(vwx3000, vwx3001), :(vwx31000, vwx31001), ba) → new_compare0(vwx3001, vwx31001, ba)
new_ltEs1(Right(vwx3000), Right(vwx31000), eh, app(app(app(ty_@3, fh), ga), gb)) → new_ltEs3(vwx3000, vwx31000, fh, ga, gb)
new_ltEs1(Right(vwx3000), Right(vwx31000), eh, app(ty_[], fa)) → new_ltEs(vwx3000, vwx31000, fa)
new_ltEs2(@2(vwx3000, vwx3001), @2(vwx31000, vwx31001), gc, app(app(ty_Either, gf), gg)) → new_ltEs1(vwx3001, vwx31001, gf, gg)
new_ltEs3(@3(vwx3000, vwx3001, vwx3002), @3(vwx31000, vwx31001, vwx31002), baf, bag, app(ty_[], bah)) → new_ltEs(vwx3002, vwx31002, bah)
new_compare2(vwx3000, vwx31000, hg, hh) → new_compare21(vwx3000, vwx31000, new_esEs5(vwx3000, vwx31000, hg, hh), hg, hh)
new_ltEs0(Just(vwx3000), Just(vwx31000), app(ty_Maybe, ce)) → new_ltEs0(vwx3000, vwx31000, ce)
new_ltEs3(@3(vwx3000, vwx3001, vwx3002), @3(vwx31000, vwx31001, vwx31002), app(app(ty_Either, bde), bdf), bag, bcb) → new_lt1(vwx3000, vwx31000, bde, bdf)
new_compare3(vwx3000, vwx31000, baa, bab) → new_compare22(vwx3000, vwx31000, new_esEs6(vwx3000, vwx31000, baa, bab), baa, bab)
new_ltEs3(@3(vwx3000, vwx3001, vwx3002), @3(vwx31000, vwx31001, vwx31002), baf, bag, app(ty_Maybe, bba)) → new_ltEs0(vwx3002, vwx31002, bba)
new_ltEs(:(vwx3000, vwx3001), :(vwx31000, vwx31001), ba) → new_primCompAux(vwx3000, vwx31000, new_compare(vwx3001, vwx31001, ba), ba)
new_ltEs3(@3(vwx3000, vwx3001, vwx3002), @3(vwx31000, vwx31001, vwx31002), app(app(ty_@2, bdg), bdh), bag, bcb) → new_lt2(vwx3000, vwx31000, bdg, bdh)
new_ltEs1(Left(vwx3000), Left(vwx31000), app(ty_[], df), dg) → new_ltEs(vwx3000, vwx31000, df)
new_primCompAux(vwx3000, vwx31000, vwx41, app(ty_[], bb)) → new_compare0(vwx3000, vwx31000, bb)
new_compare21(vwx3000, vwx31000, False, hg, hh) → new_ltEs1(vwx3000, vwx31000, hg, hh)
new_ltEs2(@2(vwx3000, vwx3001), @2(vwx31000, vwx31001), app(ty_[], he), hf) → new_compare0(vwx3000, vwx31000, he)
new_ltEs1(Right(vwx3000), Right(vwx31000), eh, app(ty_Maybe, fb)) → new_ltEs0(vwx3000, vwx31000, fb)
new_primCompAux(vwx3000, vwx31000, vwx41, app(app(ty_Either, bd), be)) → new_compare2(vwx3000, vwx31000, bd, be)
new_ltEs3(@3(vwx3000, vwx3001, vwx3002), @3(vwx31000, vwx31001, vwx31002), baf, app(app(ty_@2, bcf), bcg), bcb) → new_lt2(vwx3001, vwx31001, bcf, bcg)
new_ltEs3(@3(vwx3000, vwx3001, vwx3002), @3(vwx31000, vwx31001, vwx31002), baf, bag, app(app(ty_@2, bbd), bbe)) → new_ltEs2(vwx3002, vwx31002, bbd, bbe)
new_ltEs2(@2(vwx3000, vwx3001), @2(vwx31000, vwx31001), app(app(app(ty_@3, bac), bad), bae), hf) → new_compare23(vwx3000, vwx31000, new_esEs7(vwx3000, vwx31000, bac, bad, bae), bac, bad, bae)
new_ltEs0(Just(vwx3000), Just(vwx31000), app(ty_[], cd)) → new_ltEs(vwx3000, vwx31000, cd)
new_ltEs2(@2(vwx3000, vwx3001), @2(vwx31000, vwx31001), gc, app(ty_Maybe, ge)) → new_ltEs0(vwx3001, vwx31001, ge)
new_ltEs3(@3(vwx3000, vwx3001, vwx3002), @3(vwx31000, vwx31001, vwx31002), baf, bag, app(app(app(ty_@3, bbf), bbg), bbh)) → new_ltEs3(vwx3002, vwx31002, bbf, bbg, bbh)
new_ltEs2(@2(vwx3000, vwx3001), @2(vwx31000, vwx31001), gc, app(app(ty_@2, gh), ha)) → new_ltEs2(vwx3001, vwx31001, gh, ha)
new_ltEs(:(vwx3000, vwx3001), :(vwx31000, vwx31001), ba) → new_compare0(vwx3001, vwx31001, ba)
new_ltEs3(@3(vwx3000, vwx3001, vwx3002), @3(vwx31000, vwx31001, vwx31002), app(app(app(ty_@3, bea), beb), bec), bag, bcb) → new_lt3(vwx3000, vwx31000, bea, beb, bec)
new_ltEs2(@2(vwx3000, vwx3001), @2(vwx31000, vwx31001), app(app(ty_Either, hg), hh), hf) → new_compare21(vwx3000, vwx31000, new_esEs5(vwx3000, vwx31000, hg, hh), hg, hh)
new_ltEs3(@3(vwx3000, vwx3001, vwx3002), @3(vwx31000, vwx31001, vwx31002), baf, bag, app(app(ty_Either, bbb), bbc)) → new_ltEs1(vwx3002, vwx31002, bbb, bbc)
new_ltEs0(Just(vwx3000), Just(vwx31000), app(app(ty_Either, cf), cg)) → new_ltEs1(vwx3000, vwx31000, cf, cg)
new_primCompAux(vwx3000, vwx31000, vwx41, app(ty_Maybe, bc)) → new_compare1(vwx3000, vwx31000, bc)
new_ltEs2(@2(vwx3000, vwx3001), @2(vwx31000, vwx31001), gc, app(ty_[], gd)) → new_ltEs(vwx3001, vwx31001, gd)
new_ltEs0(Just(vwx3000), Just(vwx31000), app(app(ty_@2, da), db)) → new_ltEs2(vwx3000, vwx31000, da, db)
new_ltEs1(Right(vwx3000), Right(vwx31000), eh, app(app(ty_Either, fc), fd)) → new_ltEs1(vwx3000, vwx31000, fc, fd)
new_ltEs2(@2(vwx3000, vwx3001), @2(vwx31000, vwx31001), app(app(ty_@2, baa), bab), hf) → new_compare22(vwx3000, vwx31000, new_esEs6(vwx3000, vwx31000, baa, bab), baa, bab)
new_ltEs3(@3(vwx3000, vwx3001, vwx3002), @3(vwx31000, vwx31001, vwx31002), baf, app(app(app(ty_@3, bch), bda), bdb), bcb) → new_lt3(vwx3001, vwx31001, bch, bda, bdb)
new_compare1(vwx3000, vwx31000, cc) → new_compare20(vwx3000, vwx31000, new_esEs4(vwx3000, vwx31000, cc), cc)
new_lt(vwx3000, vwx31000, he) → new_compare0(vwx3000, vwx31000, he)
new_lt1(vwx3000, vwx31000, hg, hh) → new_compare21(vwx3000, vwx31000, new_esEs5(vwx3000, vwx31000, hg, hh), hg, hh)
new_lt2(vwx3000, vwx31000, baa, bab) → new_compare22(vwx3000, vwx31000, new_esEs6(vwx3000, vwx31000, baa, bab), baa, bab)
new_lt0(vwx3000, vwx31000, cc) → new_compare20(vwx3000, vwx31000, new_esEs4(vwx3000, vwx31000, cc), cc)
new_compare22(vwx3000, vwx31000, False, baa, bab) → new_ltEs2(vwx3000, vwx31000, baa, bab)
new_compare4(vwx3000, vwx31000, bac, bad, bae) → new_compare23(vwx3000, vwx31000, new_esEs7(vwx3000, vwx31000, bac, bad, bae), bac, bad, bae)
new_compare20(vwx3000, vwx31000, False, cc) → new_ltEs0(vwx3000, vwx31000, cc)
new_ltEs1(Left(vwx3000), Left(vwx31000), app(app(app(ty_@3, ee), ef), eg), dg) → new_ltEs3(vwx3000, vwx31000, ee, ef, eg)
new_primCompAux(vwx3000, vwx31000, vwx41, app(app(app(ty_@3, bh), ca), cb)) → new_compare4(vwx3000, vwx31000, bh, ca, cb)
new_compare23(vwx3000, vwx31000, False, bac, bad, bae) → new_ltEs3(vwx3000, vwx31000, bac, bad, bae)
new_ltEs3(@3(vwx3000, vwx3001, vwx3002), @3(vwx31000, vwx31001, vwx31002), app(ty_Maybe, bdd), bag, bcb) → new_lt0(vwx3000, vwx31000, bdd)
new_ltEs2(@2(vwx3000, vwx3001), @2(vwx31000, vwx31001), app(ty_Maybe, cc), hf) → new_compare20(vwx3000, vwx31000, new_esEs4(vwx3000, vwx31000, cc), cc)

The TRS R consists of the following rules:

new_esEs4(Just(vwx290), Just(vwx300), app(ty_Maybe, cfe)) → new_esEs4(vwx290, vwx300, cfe)
new_lt10(vwx3000, vwx31000, app(app(ty_Either, hg), hh)) → new_lt4(vwx3000, vwx31000, hg, hh)
new_esEs24(vwx291, vwx301, app(app(ty_Either, dab), dac)) → new_esEs5(vwx291, vwx301, dab, dac)
new_esEs21(vwx290, vwx300, app(app(ty_@2, bhf), bhg)) → new_esEs6(vwx290, vwx300, bhf, bhg)
new_esEs21(vwx290, vwx300, ty_Double) → new_esEs20(vwx290, vwx300)
new_ltEs8(False, True) → True
new_lt18(vwx3000, vwx31000) → new_esEs8(new_compare13(vwx3000, vwx31000))
new_esEs5(Right(vwx290), Right(vwx300), cbd, ty_Double) → new_esEs20(vwx290, vwx300)
new_ltEs15(EQ, LT) → False
new_esEs25(vwx290, vwx300, app(ty_[], dbg)) → new_esEs16(vwx290, vwx300, dbg)
new_esEs23(vwx292, vwx302, ty_Ordering) → new_esEs11(vwx292, vwx302)
new_compare30(vwx3000, vwx31000, ty_Ordering) → new_compare13(vwx3000, vwx31000)
new_lt19(vwx3001, vwx31001, app(app(app(ty_@3, bch), bda), bdb)) → new_lt8(vwx3001, vwx31001, bch, bda, bdb)
new_esEs17(Char(vwx290), Char(vwx300)) → new_primEqNat0(vwx290, vwx300)
new_ltEs10(vwx300, vwx3100) → new_not(new_compare7(vwx300, vwx3100))
new_esEs24(vwx291, vwx301, ty_Char) → new_esEs17(vwx291, vwx301)
new_esEs5(Right(vwx290), Right(vwx300), cbd, ty_Int) → new_esEs10(vwx290, vwx300)
new_esEs23(vwx292, vwx302, app(app(ty_Either, cgh), cha)) → new_esEs5(vwx292, vwx302, cgh, cha)
new_compare210(vwx3000, vwx31000, False, bac, bad, bae) → new_compare110(vwx3000, vwx31000, new_ltEs17(vwx3000, vwx31000, bac, bad, bae), bac, bad, bae)
new_compare([], :(vwx31000, vwx31001), ba) → LT
new_compare10(vwx3000, vwx31000, True, hg, hh) → LT
new_esEs4(Just(vwx290), Nothing, cbf) → False
new_esEs4(Nothing, Just(vwx300), cbf) → False
new_esEs24(vwx291, vwx301, app(ty_Maybe, dad)) → new_esEs4(vwx291, vwx301, dad)
new_lt20(vwx3000, vwx31000, app(app(app(ty_@3, bea), beb), bec)) → new_lt8(vwx3000, vwx31000, bea, beb, bec)
new_esEs4(Just(vwx290), Just(vwx300), ty_Char) → new_esEs17(vwx290, vwx300)
new_lt19(vwx3001, vwx31001, app(ty_Ratio, cgd)) → new_lt9(vwx3001, vwx31001, cgd)
new_compare32(@0, @0) → EQ
new_esEs12(vwx291, vwx301, ty_Bool) → new_esEs9(vwx291, vwx301)
new_compare8(Float(vwx3000, vwx3001), Float(vwx31000, vwx31001)) → new_compare6(new_sr0(vwx3000, vwx31000), new_sr0(vwx3001, vwx31001))
new_ltEs6(Nothing, Just(vwx31000), bhb) → True
new_esEs20(Double(vwx290, vwx291), Double(vwx300, vwx301)) → new_esEs10(new_sr0(vwx290, vwx300), new_sr0(vwx291, vwx301))
new_lt19(vwx3001, vwx31001, ty_Double) → new_lt15(vwx3001, vwx31001)
new_esEs4(Just(vwx290), Just(vwx300), app(ty_Ratio, cfg)) → new_esEs19(vwx290, vwx300, cfg)
new_ltEs15(EQ, EQ) → True
new_esEs25(vwx290, vwx300, ty_Char) → new_esEs17(vwx290, vwx300)
new_esEs19(:%(vwx290, vwx291), :%(vwx300, vwx301), cbg) → new_asAs(new_esEs27(vwx290, vwx300, cbg), new_esEs26(vwx291, vwx301, cbg))
new_esEs11(EQ, EQ) → True
new_primMulNat0(Zero, Zero) → Zero
new_esEs6(@2(vwx290, vwx291), @2(vwx300, vwx301), bed, bee) → new_asAs(new_esEs13(vwx290, vwx300, bed), new_esEs12(vwx291, vwx301, bee))
new_compare(:(vwx3000, vwx3001), [], ba) → GT
new_sr(Integer(vwx30000), Integer(vwx310010)) → Integer(new_primMulInt(vwx30000, vwx310010))
new_ltEs16(@2(vwx3000, vwx3001), @2(vwx31000, vwx31001), gc, hf) → new_pePe(new_lt10(vwx3000, vwx31000, gc), vwx3000, vwx31000, new_ltEs18(vwx3001, vwx31001, hf), gc)
new_esEs13(vwx290, vwx300, ty_Integer) → new_esEs14(vwx290, vwx300)
new_lt4(vwx3000, vwx31000, hg, hh) → new_esEs8(new_compare5(vwx3000, vwx31000, hg, hh))
new_lt19(vwx3001, vwx31001, ty_Integer) → new_lt11(vwx3001, vwx31001)
new_esEs22(vwx29, vwx30, ty_Char) → new_esEs17(vwx29, vwx30)
new_esEs25(vwx290, vwx300, ty_Ordering) → new_esEs11(vwx290, vwx300)
new_lt15(vwx3000, vwx31000) → new_esEs8(new_compare14(vwx3000, vwx31000))
new_not(GT) → False
new_esEs23(vwx292, vwx302, app(ty_Maybe, chb)) → new_esEs4(vwx292, vwx302, chb)
new_ltEs4(Left(vwx3000), Left(vwx31000), ty_Float, dg) → new_ltEs5(vwx3000, vwx31000)
new_esEs5(Left(vwx290), Left(vwx300), app(ty_Ratio, cdb), cbe) → new_esEs19(vwx290, vwx300, cdb)
new_ltEs15(GT, LT) → False
new_compare14(Double(vwx3000, vwx3001), Double(vwx31000, vwx31001)) → new_compare6(new_sr0(vwx3000, vwx31000), new_sr0(vwx3001, vwx31001))
new_esEs13(vwx290, vwx300, ty_Char) → new_esEs17(vwx290, vwx300)
new_esEs23(vwx292, vwx302, ty_Bool) → new_esEs9(vwx292, vwx302)
new_ltEs18(vwx3001, vwx31001, app(ty_Ratio, ccc)) → new_ltEs9(vwx3001, vwx31001, ccc)
new_ltEs19(vwx3002, vwx31002, ty_@0) → new_ltEs13(vwx3002, vwx31002)
new_esEs22(vwx29, vwx30, app(ty_Ratio, cbg)) → new_esEs19(vwx29, vwx30, cbg)
new_esEs13(vwx290, vwx300, ty_@0) → new_esEs15(vwx290, vwx300)
new_esEs23(vwx292, vwx302, ty_Double) → new_esEs20(vwx292, vwx302)
new_esEs5(Right(vwx290), Right(vwx300), cbd, ty_Integer) → new_esEs14(vwx290, vwx300)
new_lt10(vwx3000, vwx31000, app(app(app(ty_@3, bac), bad), bae)) → new_lt8(vwx3000, vwx31000, bac, bad, bae)
new_esEs21(vwx290, vwx300, app(app(app(ty_@3, cae), caf), cag)) → new_esEs7(vwx290, vwx300, cae, caf, cag)
new_esEs18(Float(vwx290, vwx291), Float(vwx300, vwx301)) → new_esEs10(new_sr0(vwx290, vwx300), new_sr0(vwx291, vwx301))
new_esEs22(vwx29, vwx30, ty_Double) → new_esEs20(vwx29, vwx30)
new_lt20(vwx3000, vwx31000, app(ty_[], bdc)) → new_lt13(vwx3000, vwx31000, bdc)
new_ltEs18(vwx3001, vwx31001, ty_Float) → new_ltEs5(vwx3001, vwx31001)
new_esEs26(vwx291, vwx301, ty_Integer) → new_esEs14(vwx291, vwx301)
new_ltEs4(Left(vwx3000), Left(vwx31000), app(app(app(ty_@3, ee), ef), eg), dg) → new_ltEs17(vwx3000, vwx31000, ee, ef, eg)
new_compare15(vwx3000, vwx31000, False, cc) → GT
new_lt20(vwx3000, vwx31000, ty_Float) → new_lt17(vwx3000, vwx31000)
new_ltEs6(Just(vwx3000), Just(vwx31000), ty_Int) → new_ltEs11(vwx3000, vwx31000)
new_ltEs4(Left(vwx3000), Left(vwx31000), ty_Double, dg) → new_ltEs14(vwx3000, vwx31000)
new_ltEs4(Right(vwx3000), Right(vwx31000), eh, ty_Double) → new_ltEs14(vwx3000, vwx31000)
new_lt10(vwx3000, vwx31000, ty_Integer) → new_lt11(vwx3000, vwx31000)
new_ltEs19(vwx3002, vwx31002, app(app(ty_Either, bbb), bbc)) → new_ltEs4(vwx3002, vwx31002, bbb, bbc)
new_lt12(vwx3000, vwx31000) → new_esEs8(new_compare31(vwx3000, vwx31000))
new_ltEs19(vwx3002, vwx31002, ty_Ordering) → new_ltEs15(vwx3002, vwx31002)
new_lt10(vwx3000, vwx31000, app(ty_[], he)) → new_lt13(vwx3000, vwx31000, he)
new_ltEs15(EQ, GT) → True
new_esEs5(Left(vwx290), Left(vwx300), ty_Ordering, cbe) → new_esEs11(vwx290, vwx300)
new_esEs13(vwx290, vwx300, app(ty_Maybe, bgd)) → new_esEs4(vwx290, vwx300, bgd)
new_esEs13(vwx290, vwx300, ty_Ordering) → new_esEs11(vwx290, vwx300)
new_esEs22(vwx29, vwx30, ty_@0) → new_esEs15(vwx29, vwx30)
new_esEs21(vwx290, vwx300, app(ty_Ratio, cad)) → new_esEs19(vwx290, vwx300, cad)
new_ltEs6(Just(vwx3000), Just(vwx31000), ty_Bool) → new_ltEs8(vwx3000, vwx31000)
new_ltEs4(Right(vwx3000), Right(vwx31000), eh, app(app(ty_Either, fc), fd)) → new_ltEs4(vwx3000, vwx31000, fc, fd)
new_ltEs4(Left(vwx3000), Left(vwx31000), app(ty_[], df), dg) → new_ltEs12(vwx3000, vwx31000, df)
new_esEs5(Right(vwx290), Right(vwx300), cbd, ty_@0) → new_esEs15(vwx290, vwx300)
new_esEs5(Left(vwx290), Left(vwx300), app(app(ty_@2, ccd), cce), cbe) → new_esEs6(vwx290, vwx300, ccd, cce)
new_esEs14(Integer(vwx290), Integer(vwx300)) → new_primEqInt(vwx290, vwx300)
new_esEs22(vwx29, vwx30, ty_Bool) → new_esEs9(vwx29, vwx30)
new_lt20(vwx3000, vwx31000, app(app(ty_@2, bdg), bdh)) → new_lt7(vwx3000, vwx31000, bdg, bdh)
new_lt20(vwx3000, vwx31000, app(ty_Maybe, bdd)) → new_lt16(vwx3000, vwx31000, bdd)
new_esEs5(Left(vwx290), Left(vwx300), app(ty_Maybe, cch), cbe) → new_esEs4(vwx290, vwx300, cch)
new_ltEs4(Left(vwx3000), Right(vwx31000), eh, dg) → True
new_esEs12(vwx291, vwx301, app(ty_[], bfc)) → new_esEs16(vwx291, vwx301, bfc)
new_lt19(vwx3001, vwx31001, ty_Int) → new_lt5(vwx3001, vwx31001)
new_esEs5(Right(vwx290), Right(vwx300), cbd, ty_Char) → new_esEs17(vwx290, vwx300)
new_esEs23(vwx292, vwx302, app(app(app(ty_@3, che), chf), chg)) → new_esEs7(vwx292, vwx302, che, chf, chg)
new_ltEs15(LT, LT) → True
new_primCmpNat0(Zero, Succ(vwx310000)) → LT
new_esEs25(vwx290, vwx300, ty_Bool) → new_esEs9(vwx290, vwx300)
new_lt10(vwx3000, vwx31000, ty_Double) → new_lt15(vwx3000, vwx31000)
new_esEs25(vwx290, vwx300, app(app(ty_Either, dbd), dbe)) → new_esEs5(vwx290, vwx300, dbd, dbe)
new_esEs25(vwx290, vwx300, app(app(ty_@2, dbb), dbc)) → new_esEs6(vwx290, vwx300, dbb, dbc)
new_ltEs18(vwx3001, vwx31001, ty_@0) → new_ltEs13(vwx3001, vwx31001)
new_lt10(vwx3000, vwx31000, ty_Bool) → new_lt12(vwx3000, vwx31000)
new_ltEs18(vwx3001, vwx31001, ty_Bool) → new_ltEs8(vwx3001, vwx31001)
new_esEs25(vwx290, vwx300, ty_Double) → new_esEs20(vwx290, vwx300)
new_lt20(vwx3000, vwx31000, ty_Int) → new_lt5(vwx3000, vwx31000)
new_lt20(vwx3000, vwx31000, app(ty_Ratio, cge)) → new_lt9(vwx3000, vwx31000, cge)
new_esEs11(GT, GT) → True
new_ltEs4(Left(vwx3000), Left(vwx31000), app(ty_Ratio, cba), dg) → new_ltEs9(vwx3000, vwx31000, cba)
new_compare30(vwx3000, vwx31000, ty_Char) → new_compare7(vwx3000, vwx31000)
new_compare13(vwx3000, vwx31000) → new_compare25(vwx3000, vwx31000, new_esEs11(vwx3000, vwx31000))
new_esEs24(vwx291, vwx301, app(app(ty_@2, chh), daa)) → new_esEs6(vwx291, vwx301, chh, daa)
new_primEqNat0(Zero, Zero) → True
new_esEs5(Right(vwx290), Right(vwx300), cbd, app(app(ty_@2, cdf), cdg)) → new_esEs6(vwx290, vwx300, cdf, cdg)
new_primMulNat0(Succ(vwx300000), Succ(vwx3100100)) → new_primPlusNat1(new_primMulNat0(vwx300000, Succ(vwx3100100)), vwx3100100)
new_compare26(vwx3000, vwx31000, False, cc) → new_compare15(vwx3000, vwx31000, new_ltEs6(vwx3000, vwx31000, cc), cc)
new_esEs5(Right(vwx290), Right(vwx300), cbd, ty_Float) → new_esEs18(vwx290, vwx300)
new_compare27(vwx3000, vwx31000, False) → new_compare16(vwx3000, vwx31000, new_ltEs8(vwx3000, vwx31000))
new_ltEs11(vwx300, vwx3100) → new_not(new_compare6(vwx300, vwx3100))
new_esEs12(vwx291, vwx301, ty_Char) → new_esEs17(vwx291, vwx301)
new_compare30(vwx3000, vwx31000, ty_Bool) → new_compare31(vwx3000, vwx31000)
new_esEs4(Just(vwx290), Just(vwx300), ty_Bool) → new_esEs9(vwx290, vwx300)
new_lt13(vwx3000, vwx31000, he) → new_esEs8(new_compare(vwx3000, vwx31000, he))
new_ltEs18(vwx3001, vwx31001, ty_Char) → new_ltEs10(vwx3001, vwx31001)
new_esEs4(Just(vwx290), Just(vwx300), ty_Double) → new_esEs20(vwx290, vwx300)
new_lt10(vwx3000, vwx31000, ty_@0) → new_lt14(vwx3000, vwx31000)
new_ltEs15(GT, GT) → True
new_ltEs4(Right(vwx3000), Right(vwx31000), eh, ty_Ordering) → new_ltEs15(vwx3000, vwx31000)
new_esEs4(Just(vwx290), Just(vwx300), ty_Integer) → new_esEs14(vwx290, vwx300)
new_esEs23(vwx292, vwx302, app(ty_Ratio, chd)) → new_esEs19(vwx292, vwx302, chd)
new_ltEs19(vwx3002, vwx31002, ty_Char) → new_ltEs10(vwx3002, vwx31002)
new_esEs4(Just(vwx290), Just(vwx300), ty_Ordering) → new_esEs11(vwx290, vwx300)
new_esEs5(Left(vwx290), Left(vwx300), ty_Double, cbe) → new_esEs20(vwx290, vwx300)
new_ltEs6(Just(vwx3000), Just(vwx31000), app(ty_Ratio, bhc)) → new_ltEs9(vwx3000, vwx31000, bhc)
new_compare30(vwx3000, vwx31000, ty_Double) → new_compare14(vwx3000, vwx31000)
new_primEqInt(Neg(Succ(vwx2900)), Neg(Succ(vwx3000))) → new_primEqNat0(vwx2900, vwx3000)
new_compare25(vwx3000, vwx31000, True) → EQ
new_esEs13(vwx290, vwx300, app(ty_Ratio, bgf)) → new_esEs19(vwx290, vwx300, bgf)
new_compare30(vwx3000, vwx31000, ty_Int) → new_compare6(vwx3000, vwx31000)
new_esEs12(vwx291, vwx301, ty_Integer) → new_esEs14(vwx291, vwx301)
new_esEs5(Left(vwx290), Left(vwx300), app(ty_[], cda), cbe) → new_esEs16(vwx290, vwx300, cda)
new_lt20(vwx3000, vwx31000, ty_Char) → new_lt6(vwx3000, vwx31000)
new_lt19(vwx3001, vwx31001, ty_Float) → new_lt17(vwx3001, vwx31001)
new_ltEs8(True, True) → True
new_esEs7(@3(vwx290, vwx291, vwx292), @3(vwx300, vwx301, vwx302), cbh, cca, ccb) → new_asAs(new_esEs25(vwx290, vwx300, cbh), new_asAs(new_esEs24(vwx291, vwx301, cca), new_esEs23(vwx292, vwx302, ccb)))
new_esEs21(vwx290, vwx300, ty_@0) → new_esEs15(vwx290, vwx300)
new_ltEs19(vwx3002, vwx31002, app(ty_Ratio, cgc)) → new_ltEs9(vwx3002, vwx31002, cgc)
new_compare16(vwx3000, vwx31000, True) → LT
new_lt20(vwx3000, vwx31000, app(app(ty_Either, bde), bdf)) → new_lt4(vwx3000, vwx31000, bde, bdf)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs5(Left(vwx290), Left(vwx300), app(app(app(ty_@3, cdc), cdd), cde), cbe) → new_esEs7(vwx290, vwx300, cdc, cdd, cde)
new_ltEs4(Left(vwx3000), Left(vwx31000), ty_Char, dg) → new_ltEs10(vwx3000, vwx31000)
new_ltEs4(Right(vwx3000), Right(vwx31000), eh, ty_Integer) → new_ltEs7(vwx3000, vwx31000)
new_esEs5(Right(vwx290), Right(vwx300), cbd, app(ty_Ratio, ced)) → new_esEs19(vwx290, vwx300, ced)
new_ltEs5(vwx300, vwx3100) → new_not(new_compare8(vwx300, vwx3100))
new_primEqInt(Neg(Zero), Neg(Succ(vwx3000))) → False
new_primEqInt(Neg(Succ(vwx2900)), Neg(Zero)) → False
new_ltEs4(Left(vwx3000), Left(vwx31000), app(app(ty_Either, ea), eb), dg) → new_ltEs4(vwx3000, vwx31000, ea, eb)
new_lt20(vwx3000, vwx31000, ty_Integer) → new_lt11(vwx3000, vwx31000)
new_compare31(vwx3000, vwx31000) → new_compare27(vwx3000, vwx31000, new_esEs9(vwx3000, vwx31000))
new_primPlusNat1(Zero, vwx3100100) → Succ(vwx3100100)
new_compare7(Char(vwx3000), Char(vwx31000)) → new_primCmpNat0(vwx3000, vwx31000)
new_compare24(vwx3000, vwx31000, True, hg, hh) → EQ
new_esEs25(vwx290, vwx300, app(ty_Ratio, dbh)) → new_esEs19(vwx290, vwx300, dbh)
new_ltEs6(Just(vwx3000), Just(vwx31000), app(app(ty_Either, cf), cg)) → new_ltEs4(vwx3000, vwx31000, cf, cg)
new_ltEs6(Just(vwx3000), Just(vwx31000), ty_@0) → new_ltEs13(vwx3000, vwx31000)
new_compare([], [], ba) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_esEs23(vwx292, vwx302, ty_Integer) → new_esEs14(vwx292, vwx302)
new_ltEs15(LT, GT) → True
new_compare6(vwx300, vwx3100) → new_primCmpInt(vwx300, vwx3100)
new_primCmpNat0(Succ(vwx30000), Succ(vwx310000)) → new_primCmpNat0(vwx30000, vwx310000)
new_esEs22(vwx29, vwx30, app(ty_Maybe, cbf)) → new_esEs4(vwx29, vwx30, cbf)
new_esEs25(vwx290, vwx300, app(ty_Maybe, dbf)) → new_esEs4(vwx290, vwx300, dbf)
new_ltEs7(vwx300, vwx3100) → new_not(new_compare17(vwx300, vwx3100))
new_primEqInt(Pos(Succ(vwx2900)), Pos(Succ(vwx3000))) → new_primEqNat0(vwx2900, vwx3000)
new_compare10(vwx3000, vwx31000, False, hg, hh) → GT
new_compare12(vwx3000, vwx31000, bac, bad, bae) → new_compare210(vwx3000, vwx31000, new_esEs7(vwx3000, vwx31000, bac, bad, bae), bac, bad, bae)
new_esEs5(Right(vwx290), Right(vwx300), cbd, ty_Ordering) → new_esEs11(vwx290, vwx300)
new_lt16(vwx3000, vwx31000, cc) → new_esEs8(new_compare29(vwx3000, vwx31000, cc))
new_esEs24(vwx291, vwx301, ty_Double) → new_esEs20(vwx291, vwx301)
new_esEs16(:(vwx290, vwx291), :(vwx300, vwx301), bhe) → new_asAs(new_esEs21(vwx290, vwx300, bhe), new_esEs16(vwx291, vwx301, bhe))
new_esEs23(vwx292, vwx302, ty_Char) → new_esEs17(vwx292, vwx302)
new_compare30(vwx3000, vwx31000, app(app(app(ty_@3, bh), ca), cb)) → new_compare12(vwx3000, vwx31000, bh, ca, cb)
new_esEs5(Right(vwx290), Right(vwx300), cbd, app(app(ty_Either, cdh), cea)) → new_esEs5(vwx290, vwx300, cdh, cea)
new_primEqNat0(Succ(vwx2900), Succ(vwx3000)) → new_primEqNat0(vwx2900, vwx3000)
new_ltEs9(vwx300, vwx3100, bhd) → new_not(new_compare18(vwx300, vwx3100, bhd))
new_ltEs4(Left(vwx3000), Left(vwx31000), ty_Int, dg) → new_ltEs11(vwx3000, vwx31000)
new_esEs12(vwx291, vwx301, ty_@0) → new_esEs15(vwx291, vwx301)
new_ltEs19(vwx3002, vwx31002, ty_Double) → new_ltEs14(vwx3002, vwx31002)
new_esEs4(Just(vwx290), Just(vwx300), ty_Int) → new_esEs10(vwx290, vwx300)
new_primCompAux00(vwx45, LT) → LT
new_lt19(vwx3001, vwx31001, app(ty_[], bca)) → new_lt13(vwx3001, vwx31001, bca)
new_esEs4(Just(vwx290), Just(vwx300), ty_@0) → new_esEs15(vwx290, vwx300)
new_primCmpInt(Neg(Succ(vwx30000)), Neg(vwx31000)) → new_primCmpNat0(vwx31000, Succ(vwx30000))
new_ltEs6(Just(vwx3000), Just(vwx31000), app(app(ty_@2, da), db)) → new_ltEs16(vwx3000, vwx31000, da, db)
new_compare25(vwx3000, vwx31000, False) → new_compare11(vwx3000, vwx31000, new_ltEs15(vwx3000, vwx31000))
new_lt10(vwx3000, vwx31000, ty_Float) → new_lt17(vwx3000, vwx31000)
new_ltEs19(vwx3002, vwx31002, ty_Bool) → new_ltEs8(vwx3002, vwx31002)
new_compare24(vwx3000, vwx31000, False, hg, hh) → new_compare10(vwx3000, vwx31000, new_ltEs4(vwx3000, vwx31000, hg, hh), hg, hh)
new_primEqInt(Pos(Zero), Pos(Succ(vwx3000))) → False
new_primEqInt(Pos(Succ(vwx2900)), Pos(Zero)) → False
new_esEs22(vwx29, vwx30, ty_Ordering) → new_esEs11(vwx29, vwx30)
new_ltEs4(Left(vwx3000), Left(vwx31000), ty_Ordering, dg) → new_ltEs15(vwx3000, vwx31000)
new_compare9(vwx3000, vwx31000, baa, bab) → new_compare28(vwx3000, vwx31000, new_esEs6(vwx3000, vwx31000, baa, bab), baa, bab)
new_ltEs19(vwx3002, vwx31002, app(ty_Maybe, bba)) → new_ltEs6(vwx3002, vwx31002, bba)
new_esEs12(vwx291, vwx301, app(app(app(ty_@3, bfe), bff), bfg)) → new_esEs7(vwx291, vwx301, bfe, bff, bfg)
new_primPlusNat0(Succ(vwx5900), Zero) → Succ(vwx5900)
new_primPlusNat0(Zero, Succ(vwx31001000)) → Succ(vwx31001000)
new_ltEs6(Just(vwx3000), Nothing, bhb) → False
new_compare5(vwx3000, vwx31000, hg, hh) → new_compare24(vwx3000, vwx31000, new_esEs5(vwx3000, vwx31000, hg, hh), hg, hh)
new_primCmpNat0(Zero, Zero) → EQ
new_esEs24(vwx291, vwx301, app(ty_Ratio, daf)) → new_esEs19(vwx291, vwx301, daf)
new_esEs5(Right(vwx290), Right(vwx300), cbd, ty_Bool) → new_esEs9(vwx290, vwx300)
new_esEs13(vwx290, vwx300, ty_Double) → new_esEs20(vwx290, vwx300)
new_primCmpNat0(Succ(vwx30000), Zero) → GT
new_compare30(vwx3000, vwx31000, ty_@0) → new_compare32(vwx3000, vwx31000)
new_esEs22(vwx29, vwx30, ty_Integer) → new_esEs14(vwx29, vwx30)
new_esEs24(vwx291, vwx301, ty_@0) → new_esEs15(vwx291, vwx301)
new_primCmpInt(Neg(Zero), Pos(Succ(vwx310000))) → LT
new_esEs8(LT) → True
new_esEs4(Just(vwx290), Just(vwx300), app(app(ty_Either, cfc), cfd)) → new_esEs5(vwx290, vwx300, cfc, cfd)
new_ltEs4(Right(vwx3000), Right(vwx31000), eh, ty_Char) → new_ltEs10(vwx3000, vwx31000)
new_compare210(vwx3000, vwx31000, True, bac, bad, bae) → EQ
new_ltEs4(Right(vwx3000), Right(vwx31000), eh, app(app(app(ty_@3, fh), ga), gb)) → new_ltEs17(vwx3000, vwx31000, fh, ga, gb)
new_compare30(vwx3000, vwx31000, app(ty_[], bb)) → new_compare(vwx3000, vwx31000, bb)
new_compare28(vwx3000, vwx31000, True, baa, bab) → EQ
new_primEqInt(Neg(Succ(vwx2900)), Pos(vwx300)) → False
new_primEqInt(Pos(Succ(vwx2900)), Neg(vwx300)) → False
new_esEs25(vwx290, vwx300, ty_Int) → new_esEs10(vwx290, vwx300)
new_ltEs18(vwx3001, vwx31001, app(app(ty_Either, gf), gg)) → new_ltEs4(vwx3001, vwx31001, gf, gg)
new_compare(:(vwx3000, vwx3001), :(vwx31000, vwx31001), ba) → new_primCompAux0(vwx3000, vwx31000, new_compare(vwx3001, vwx31001, ba), ba)
new_lt19(vwx3001, vwx31001, app(ty_Maybe, bcc)) → new_lt16(vwx3001, vwx31001, bcc)
new_esEs4(Just(vwx290), Just(vwx300), app(app(ty_@2, cfa), cfb)) → new_esEs6(vwx290, vwx300, cfa, cfb)
new_esEs8(GT) → False
new_lt19(vwx3001, vwx31001, ty_@0) → new_lt14(vwx3001, vwx31001)
new_ltEs6(Just(vwx3000), Just(vwx31000), app(ty_Maybe, ce)) → new_ltEs6(vwx3000, vwx31000, ce)
new_esEs22(vwx29, vwx30, app(app(ty_@2, bed), bee)) → new_esEs6(vwx29, vwx30, bed, bee)
new_compare18(:%(vwx3000, vwx3001), :%(vwx31000, vwx31001), ty_Int) → new_compare6(new_sr0(vwx3000, vwx31001), new_sr0(vwx31000, vwx3001))
new_ltEs4(Right(vwx3000), Right(vwx31000), eh, app(ty_Maybe, fb)) → new_ltEs6(vwx3000, vwx31000, fb)
new_primEqInt(Neg(Zero), Pos(Succ(vwx3000))) → False
new_primEqInt(Pos(Zero), Neg(Succ(vwx3000))) → False
new_esEs24(vwx291, vwx301, ty_Ordering) → new_esEs11(vwx291, vwx301)
new_esEs26(vwx291, vwx301, ty_Int) → new_esEs10(vwx291, vwx301)
new_ltEs14(vwx300, vwx3100) → new_not(new_compare14(vwx300, vwx3100))
new_primCmpInt(Pos(Zero), Pos(Succ(vwx310000))) → new_primCmpNat0(Zero, Succ(vwx310000))
new_primCompAux00(vwx45, EQ) → vwx45
new_esEs21(vwx290, vwx300, ty_Ordering) → new_esEs11(vwx290, vwx300)
new_ltEs4(Left(vwx3000), Left(vwx31000), app(ty_Maybe, dh), dg) → new_ltEs6(vwx3000, vwx31000, dh)
new_ltEs4(Right(vwx3000), Right(vwx31000), eh, app(app(ty_@2, ff), fg)) → new_ltEs16(vwx3000, vwx31000, ff, fg)
new_esEs22(vwx29, vwx30, ty_Float) → new_esEs18(vwx29, vwx30)
new_compare26(vwx3000, vwx31000, True, cc) → EQ
new_compare30(vwx3000, vwx31000, app(ty_Ratio, ceh)) → new_compare18(vwx3000, vwx31000, ceh)
new_ltEs8(True, False) → False
new_esEs21(vwx290, vwx300, ty_Integer) → new_esEs14(vwx290, vwx300)
new_ltEs4(Right(vwx3000), Left(vwx31000), eh, dg) → False
new_ltEs4(Left(vwx3000), Left(vwx31000), app(app(ty_@2, ec), ed), dg) → new_ltEs16(vwx3000, vwx31000, ec, ed)
new_compare30(vwx3000, vwx31000, app(app(ty_@2, bf), bg)) → new_compare9(vwx3000, vwx31000, bf, bg)
new_esEs23(vwx292, vwx302, ty_@0) → new_esEs15(vwx292, vwx302)
new_primCmpInt(Pos(Succ(vwx30000)), Pos(vwx31000)) → new_primCmpNat0(Succ(vwx30000), vwx31000)
new_ltEs19(vwx3002, vwx31002, ty_Float) → new_ltEs5(vwx3002, vwx31002)
new_esEs23(vwx292, vwx302, app(app(ty_@2, cgf), cgg)) → new_esEs6(vwx292, vwx302, cgf, cgg)
new_ltEs12(vwx300, vwx3100, ba) → new_not(new_compare(vwx300, vwx3100, ba))
new_esEs11(GT, LT) → False
new_esEs11(LT, GT) → False
new_esEs23(vwx292, vwx302, ty_Float) → new_esEs18(vwx292, vwx302)
new_ltEs19(vwx3002, vwx31002, app(ty_[], bah)) → new_ltEs12(vwx3002, vwx31002, bah)
new_esEs13(vwx290, vwx300, app(ty_[], bge)) → new_esEs16(vwx290, vwx300, bge)
new_esEs13(vwx290, vwx300, app(app(ty_Either, bgb), bgc)) → new_esEs5(vwx290, vwx300, bgb, bgc)
new_esEs25(vwx290, vwx300, ty_@0) → new_esEs15(vwx290, vwx300)
new_esEs25(vwx290, vwx300, ty_Float) → new_esEs18(vwx290, vwx300)
new_not0True
new_esEs11(EQ, LT) → False
new_esEs11(LT, EQ) → False
new_lt20(vwx3000, vwx31000, ty_Ordering) → new_lt18(vwx3000, vwx31000)
new_esEs9(True, True) → True
new_lt14(vwx3000, vwx31000) → new_esEs8(new_compare32(vwx3000, vwx31000))
new_ltEs4(Right(vwx3000), Right(vwx31000), eh, app(ty_Ratio, cbb)) → new_ltEs9(vwx3000, vwx31000, cbb)
new_lt19(vwx3001, vwx31001, ty_Char) → new_lt6(vwx3001, vwx31001)
new_primCmpInt(Pos(Succ(vwx30000)), Neg(vwx31000)) → GT
new_esEs22(vwx29, vwx30, app(app(app(ty_@3, cbh), cca), ccb)) → new_esEs7(vwx29, vwx30, cbh, cca, ccb)
new_ltEs18(vwx3001, vwx31001, app(app(ty_@2, gh), ha)) → new_ltEs16(vwx3001, vwx31001, gh, ha)
new_ltEs15(LT, EQ) → True
new_ltEs4(Right(vwx3000), Right(vwx31000), eh, ty_Bool) → new_ltEs8(vwx3000, vwx31000)
new_esEs24(vwx291, vwx301, ty_Float) → new_esEs18(vwx291, vwx301)
new_esEs22(vwx29, vwx30, app(ty_[], bhe)) → new_esEs16(vwx29, vwx30, bhe)
new_ltEs6(Just(vwx3000), Just(vwx31000), app(app(app(ty_@3, dc), dd), de)) → new_ltEs17(vwx3000, vwx31000, dc, dd, de)
new_lt20(vwx3000, vwx31000, ty_Double) → new_lt15(vwx3000, vwx31000)
new_primMulInt(Pos(vwx30000), Pos(vwx310010)) → Pos(new_primMulNat0(vwx30000, vwx310010))
new_lt19(vwx3001, vwx31001, ty_Bool) → new_lt12(vwx3001, vwx31001)
new_esEs4(Just(vwx290), Just(vwx300), ty_Float) → new_esEs18(vwx290, vwx300)
new_esEs22(vwx29, vwx30, ty_Int) → new_esEs10(vwx29, vwx30)
new_esEs5(Right(vwx290), Right(vwx300), cbd, app(ty_[], cec)) → new_esEs16(vwx290, vwx300, cec)
new_lt9(vwx3000, vwx31000, cah) → new_esEs8(new_compare18(vwx3000, vwx31000, cah))
new_esEs5(Right(vwx290), Left(vwx300), cbd, cbe) → False
new_esEs5(Left(vwx290), Right(vwx300), cbd, cbe) → False
new_primMulInt(Neg(vwx30000), Neg(vwx310010)) → Pos(new_primMulNat0(vwx30000, vwx310010))
new_lt10(vwx3000, vwx31000, app(app(ty_@2, baa), bab)) → new_lt7(vwx3000, vwx31000, baa, bab)
new_lt20(vwx3000, vwx31000, ty_@0) → new_lt14(vwx3000, vwx31000)
new_primEqNat0(Zero, Succ(vwx3000)) → False
new_primEqNat0(Succ(vwx2900), Zero) → False
new_ltEs8(False, False) → True
new_ltEs4(Right(vwx3000), Right(vwx31000), eh, ty_Int) → new_ltEs11(vwx3000, vwx31000)
new_pePe(False, vwx29, vwx30, vwx31, cbc) → new_asAs(new_esEs22(vwx29, vwx30, cbc), vwx31)
new_primPlusNat0(Zero, Zero) → Zero
new_esEs5(Left(vwx290), Left(vwx300), ty_Integer, cbe) → new_esEs14(vwx290, vwx300)
new_ltEs6(Just(vwx3000), Just(vwx31000), ty_Double) → new_ltEs14(vwx3000, vwx31000)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_ltEs18(vwx3001, vwx31001, app(app(app(ty_@3, hb), hc), hd)) → new_ltEs17(vwx3001, vwx31001, hb, hc, hd)
new_esEs4(Nothing, Nothing, cbf) → True
new_ltEs18(vwx3001, vwx31001, ty_Integer) → new_ltEs7(vwx3001, vwx31001)
new_esEs21(vwx290, vwx300, ty_Bool) → new_esEs9(vwx290, vwx300)
new_esEs12(vwx291, vwx301, app(app(ty_Either, beh), bfa)) → new_esEs5(vwx291, vwx301, beh, bfa)
new_esEs16([], :(vwx300, vwx301), bhe) → False
new_esEs16(:(vwx290, vwx291), [], bhe) → False
new_ltEs17(@3(vwx3000, vwx3001, vwx3002), @3(vwx31000, vwx31001, vwx31002), baf, bag, bcb) → new_pePe(new_lt20(vwx3000, vwx31000, baf), vwx3000, vwx31000, new_pePe(new_lt19(vwx3001, vwx31001, bag), vwx3001, vwx31001, new_ltEs19(vwx3002, vwx31002, bcb), bag), baf)
new_compare29(vwx3000, vwx31000, cc) → new_compare26(vwx3000, vwx31000, new_esEs4(vwx3000, vwx31000, cc), cc)
new_ltEs6(Just(vwx3000), Just(vwx31000), ty_Ordering) → new_ltEs15(vwx3000, vwx31000)
new_pePe(True, vwx29, vwx30, vwx31, cbc) → True
new_primPlusNat1(Succ(vwx590), vwx3100100) → Succ(Succ(new_primPlusNat0(vwx590, vwx3100100)))
new_compare30(vwx3000, vwx31000, app(ty_Maybe, bc)) → new_compare29(vwx3000, vwx31000, bc)
new_lt5(vwx3000, vwx31000) → new_esEs8(new_compare6(vwx3000, vwx31000))
new_esEs21(vwx290, vwx300, ty_Char) → new_esEs17(vwx290, vwx300)
new_primCmpInt(Neg(Zero), Neg(Succ(vwx310000))) → new_primCmpNat0(Succ(vwx310000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(vwx310000))) → GT
new_ltEs6(Just(vwx3000), Just(vwx31000), app(ty_[], cd)) → new_ltEs12(vwx3000, vwx31000, cd)
new_esEs25(vwx290, vwx300, ty_Integer) → new_esEs14(vwx290, vwx300)
new_compare19(vwx3000, vwx31000, True, baa, bab) → LT
new_compare30(vwx3000, vwx31000, app(app(ty_Either, bd), be)) → new_compare5(vwx3000, vwx31000, bd, be)
new_esEs4(Just(vwx290), Just(vwx300), app(ty_[], cff)) → new_esEs16(vwx290, vwx300, cff)
new_sr0(vwx3000, vwx31001) → new_primMulInt(vwx3000, vwx31001)
new_esEs5(Right(vwx290), Right(vwx300), cbd, app(app(app(ty_@3, cee), cef), ceg)) → new_esEs7(vwx290, vwx300, cee, cef, ceg)
new_lt7(vwx3000, vwx31000, baa, bab) → new_esEs8(new_compare9(vwx3000, vwx31000, baa, bab))
new_esEs13(vwx290, vwx300, app(app(ty_@2, bfh), bga)) → new_esEs6(vwx290, vwx300, bfh, bga)
new_ltEs19(vwx3002, vwx31002, ty_Int) → new_ltEs11(vwx3002, vwx31002)
new_compare30(vwx3000, vwx31000, ty_Float) → new_compare8(vwx3000, vwx31000)
new_esEs21(vwx290, vwx300, ty_Float) → new_esEs18(vwx290, vwx300)
new_lt19(vwx3001, vwx31001, app(app(ty_Either, bcd), bce)) → new_lt4(vwx3001, vwx31001, bcd, bce)
new_ltEs4(Left(vwx3000), Left(vwx31000), ty_Integer, dg) → new_ltEs7(vwx3000, vwx31000)
new_esEs13(vwx290, vwx300, ty_Float) → new_esEs18(vwx290, vwx300)
new_esEs21(vwx290, vwx300, app(ty_Maybe, cab)) → new_esEs4(vwx290, vwx300, cab)
new_esEs9(True, False) → False
new_esEs9(False, True) → False
new_esEs5(Left(vwx290), Left(vwx300), ty_Int, cbe) → new_esEs10(vwx290, vwx300)
new_ltEs18(vwx3001, vwx31001, ty_Int) → new_ltEs11(vwx3001, vwx31001)
new_ltEs13(vwx300, vwx3100) → new_not(new_compare32(vwx300, vwx3100))
new_primCompAux0(vwx3000, vwx31000, vwx41, ba) → new_primCompAux00(vwx41, new_compare30(vwx3000, vwx31000, ba))
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs24(vwx291, vwx301, app(app(app(ty_@3, dag), dah), dba)) → new_esEs7(vwx291, vwx301, dag, dah, dba)
new_ltEs4(Right(vwx3000), Right(vwx31000), eh, app(ty_[], fa)) → new_ltEs12(vwx3000, vwx31000, fa)
new_esEs12(vwx291, vwx301, ty_Ordering) → new_esEs11(vwx291, vwx301)
new_esEs24(vwx291, vwx301, ty_Int) → new_esEs10(vwx291, vwx301)
new_esEs15(@0, @0) → True
new_esEs12(vwx291, vwx301, app(ty_Maybe, bfb)) → new_esEs4(vwx291, vwx301, bfb)
new_asAs(False, vwx40) → False
new_primMulInt(Pos(vwx30000), Neg(vwx310010)) → Neg(new_primMulNat0(vwx30000, vwx310010))
new_primMulInt(Neg(vwx30000), Pos(vwx310010)) → Neg(new_primMulNat0(vwx30000, vwx310010))
new_primMulNat0(Succ(vwx300000), Zero) → Zero
new_primMulNat0(Zero, Succ(vwx3100100)) → Zero
new_compare30(vwx3000, vwx31000, ty_Integer) → new_compare17(vwx3000, vwx31000)
new_esEs21(vwx290, vwx300, app(app(ty_Either, bhh), caa)) → new_esEs5(vwx290, vwx300, bhh, caa)
new_esEs13(vwx290, vwx300, ty_Bool) → new_esEs9(vwx290, vwx300)
new_esEs12(vwx291, vwx301, app(ty_Ratio, bfd)) → new_esEs19(vwx291, vwx301, bfd)
new_lt19(vwx3001, vwx31001, ty_Ordering) → new_lt18(vwx3001, vwx31001)
new_compare17(Integer(vwx3000), Integer(vwx31000)) → new_primCmpInt(vwx3000, vwx31000)
new_ltEs4(Left(vwx3000), Left(vwx31000), ty_@0, dg) → new_ltEs13(vwx3000, vwx31000)
new_esEs24(vwx291, vwx301, app(ty_[], dae)) → new_esEs16(vwx291, vwx301, dae)
new_compare110(vwx3000, vwx31000, True, bac, bad, bae) → LT
new_not(EQ) → new_not0
new_ltEs4(Right(vwx3000), Right(vwx31000), eh, ty_@0) → new_ltEs13(vwx3000, vwx31000)
new_compare18(:%(vwx3000, vwx3001), :%(vwx31000, vwx31001), ty_Integer) → new_compare17(new_sr(vwx3000, vwx31001), new_sr(vwx31000, vwx3001))
new_compare27(vwx3000, vwx31000, True) → EQ
new_lt10(vwx3000, vwx31000, app(ty_Maybe, cc)) → new_lt16(vwx3000, vwx31000, cc)
new_esEs5(Left(vwx290), Left(vwx300), ty_@0, cbe) → new_esEs15(vwx290, vwx300)
new_esEs9(False, False) → True
new_compare28(vwx3000, vwx31000, False, baa, bab) → new_compare19(vwx3000, vwx31000, new_ltEs16(vwx3000, vwx31000, baa, bab), baa, bab)
new_esEs24(vwx291, vwx301, ty_Integer) → new_esEs14(vwx291, vwx301)
new_ltEs6(Nothing, Nothing, bhb) → True
new_esEs12(vwx291, vwx301, ty_Int) → new_esEs10(vwx291, vwx301)
new_lt10(vwx3000, vwx31000, ty_Int) → new_lt5(vwx3000, vwx31000)
new_esEs25(vwx290, vwx300, app(app(app(ty_@3, dca), dcb), dcc)) → new_esEs7(vwx290, vwx300, dca, dcb, dcc)
new_lt17(vwx3000, vwx31000) → new_esEs8(new_compare8(vwx3000, vwx31000))
new_esEs5(Right(vwx290), Right(vwx300), cbd, app(ty_Maybe, ceb)) → new_esEs4(vwx290, vwx300, ceb)
new_esEs16([], [], bhe) → True
new_compare11(vwx3000, vwx31000, False) → GT
new_ltEs4(Right(vwx3000), Right(vwx31000), eh, ty_Float) → new_ltEs5(vwx3000, vwx31000)
new_ltEs18(vwx3001, vwx31001, ty_Double) → new_ltEs14(vwx3001, vwx31001)
new_not(LT) → new_not0
new_lt10(vwx3000, vwx31000, ty_Char) → new_lt6(vwx3000, vwx31000)
new_compare11(vwx3000, vwx31000, True) → LT
new_ltEs18(vwx3001, vwx31001, ty_Ordering) → new_ltEs15(vwx3001, vwx31001)
new_esEs5(Left(vwx290), Left(vwx300), app(app(ty_Either, ccf), ccg), cbe) → new_esEs5(vwx290, vwx300, ccf, ccg)
new_ltEs18(vwx3001, vwx31001, app(ty_Maybe, ge)) → new_ltEs6(vwx3001, vwx31001, ge)
new_ltEs19(vwx3002, vwx31002, app(app(app(ty_@3, bbf), bbg), bbh)) → new_ltEs17(vwx3002, vwx31002, bbf, bbg, bbh)
new_lt20(vwx3000, vwx31000, ty_Bool) → new_lt12(vwx3000, vwx31000)
new_ltEs6(Just(vwx3000), Just(vwx31000), ty_Float) → new_ltEs5(vwx3000, vwx31000)
new_lt19(vwx3001, vwx31001, app(app(ty_@2, bcf), bcg)) → new_lt7(vwx3001, vwx31001, bcf, bcg)
new_ltEs19(vwx3002, vwx31002, ty_Integer) → new_ltEs7(vwx3002, vwx31002)
new_esEs24(vwx291, vwx301, ty_Bool) → new_esEs9(vwx291, vwx301)
new_esEs8(EQ) → False
new_primPlusNat0(Succ(vwx5900), Succ(vwx31001000)) → Succ(Succ(new_primPlusNat0(vwx5900, vwx31001000)))
new_esEs23(vwx292, vwx302, app(ty_[], chc)) → new_esEs16(vwx292, vwx302, chc)
new_compare15(vwx3000, vwx31000, True, cc) → LT
new_ltEs19(vwx3002, vwx31002, app(app(ty_@2, bbd), bbe)) → new_ltEs16(vwx3002, vwx31002, bbd, bbe)
new_esEs27(vwx290, vwx300, ty_Integer) → new_esEs14(vwx290, vwx300)
new_lt11(vwx3000, vwx31000) → new_esEs8(new_compare17(vwx3000, vwx31000))
new_asAs(True, vwx40) → vwx40
new_ltEs15(GT, EQ) → False
new_ltEs6(Just(vwx3000), Just(vwx31000), ty_Char) → new_ltEs10(vwx3000, vwx31000)
new_esEs11(LT, LT) → True
new_esEs27(vwx290, vwx300, ty_Int) → new_esEs10(vwx290, vwx300)
new_esEs23(vwx292, vwx302, ty_Int) → new_esEs10(vwx292, vwx302)
new_esEs12(vwx291, vwx301, ty_Double) → new_esEs20(vwx291, vwx301)
new_esEs21(vwx290, vwx300, ty_Int) → new_esEs10(vwx290, vwx300)
new_lt6(vwx3000, vwx31000) → new_esEs8(new_compare7(vwx3000, vwx31000))
new_ltEs18(vwx3001, vwx31001, app(ty_[], gd)) → new_ltEs12(vwx3001, vwx31001, gd)
new_lt10(vwx3000, vwx31000, app(ty_Ratio, cah)) → new_lt9(vwx3000, vwx31000, cah)
new_esEs4(Just(vwx290), Just(vwx300), app(app(app(ty_@3, cfh), cga), cgb)) → new_esEs7(vwx290, vwx300, cfh, cga, cgb)
new_ltEs4(Left(vwx3000), Left(vwx31000), ty_Bool, dg) → new_ltEs8(vwx3000, vwx31000)
new_esEs11(GT, EQ) → False
new_esEs11(EQ, GT) → False
new_esEs5(Left(vwx290), Left(vwx300), ty_Bool, cbe) → new_esEs9(vwx290, vwx300)
new_compare19(vwx3000, vwx31000, False, baa, bab) → GT
new_lt8(vwx3000, vwx31000, bac, bad, bae) → new_esEs8(new_compare12(vwx3000, vwx31000, bac, bad, bae))
new_compare110(vwx3000, vwx31000, False, bac, bad, bae) → GT
new_esEs12(vwx291, vwx301, ty_Float) → new_esEs18(vwx291, vwx301)
new_esEs22(vwx29, vwx30, app(app(ty_Either, cbd), cbe)) → new_esEs5(vwx29, vwx30, cbd, cbe)
new_esEs10(vwx29, vwx30) → new_primEqInt(vwx29, vwx30)
new_primCompAux00(vwx45, GT) → GT
new_esEs13(vwx290, vwx300, app(app(app(ty_@3, bgg), bgh), bha)) → new_esEs7(vwx290, vwx300, bgg, bgh, bha)
new_esEs21(vwx290, vwx300, app(ty_[], cac)) → new_esEs16(vwx290, vwx300, cac)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_ltEs6(Just(vwx3000), Just(vwx31000), ty_Integer) → new_ltEs7(vwx3000, vwx31000)
new_lt10(vwx3000, vwx31000, ty_Ordering) → new_lt18(vwx3000, vwx31000)
new_esEs5(Left(vwx290), Left(vwx300), ty_Float, cbe) → new_esEs18(vwx290, vwx300)
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_esEs12(vwx291, vwx301, app(app(ty_@2, bef), beg)) → new_esEs6(vwx291, vwx301, bef, beg)
new_primCmpInt(Neg(Succ(vwx30000)), Pos(vwx31000)) → LT
new_compare16(vwx3000, vwx31000, False) → GT
new_esEs5(Left(vwx290), Left(vwx300), ty_Char, cbe) → new_esEs17(vwx290, vwx300)
new_esEs13(vwx290, vwx300, ty_Int) → new_esEs10(vwx290, vwx300)

The set Q consists of the following terms:

new_ltEs19(x0, x1, ty_Double)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs4(Just(x0), Nothing, x1)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primPlusNat1(Zero, x0)
new_ltEs18(x0, x1, ty_@0)
new_ltEs6(Nothing, Nothing, x0)
new_esEs5(Left(x0), Left(x1), app(ty_[], x2), x3)
new_ltEs6(Just(x0), Just(x1), app(ty_Ratio, x2))
new_compare110(x0, x1, False, x2, x3, x4)
new_lt8(x0, x1, x2, x3, x4)
new_esEs13(x0, x1, ty_Ordering)
new_esEs21(x0, x1, ty_Ordering)
new_esEs25(x0, x1, app(ty_[], x2))
new_esEs13(x0, x1, ty_Integer)
new_esEs12(x0, x1, app(app(ty_Either, x2), x3))
new_esEs7(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_ltEs19(x0, x1, ty_Int)
new_esEs22(x0, x1, ty_Char)
new_lt10(x0, x1, ty_Int)
new_ltEs19(x0, x1, ty_Integer)
new_ltEs5(x0, x1)
new_lt19(x0, x1, ty_Bool)
new_compare7(Char(x0), Char(x1))
new_esEs12(x0, x1, app(ty_[], x2))
new_esEs27(x0, x1, ty_Integer)
new_primCmpNat0(Succ(x0), Zero)
new_esEs16(:(x0, x1), :(x2, x3), x4)
new_lt10(x0, x1, ty_Ordering)
new_esEs23(x0, x1, ty_Float)
new_esEs4(Just(x0), Just(x1), app(ty_Ratio, x2))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_esEs5(Left(x0), Left(x1), ty_Ordering, x2)
new_compare210(x0, x1, False, x2, x3, x4)
new_esEs4(Just(x0), Just(x1), ty_Char)
new_lt19(x0, x1, ty_Float)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare30(x0, x1, ty_Ordering)
new_primPlusNat0(Zero, Succ(x0))
new_esEs12(x0, x1, app(app(ty_@2, x2), x3))
new_esEs4(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs4(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs5(Right(x0), Right(x1), x2, ty_@0)
new_lt10(x0, x1, ty_Char)
new_esEs5(Left(x0), Right(x1), x2, x3)
new_esEs5(Right(x0), Left(x1), x2, x3)
new_ltEs4(Left(x0), Left(x1), ty_Bool, x2)
new_esEs5(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs24(x0, x1, app(ty_[], x2))
new_esEs8(LT)
new_esEs12(x0, x1, app(ty_Maybe, x2))
new_esEs13(x0, x1, ty_Char)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_esEs24(x0, x1, ty_Integer)
new_compare25(x0, x1, True)
new_esEs13(x0, x1, app(ty_Ratio, x2))
new_ltEs6(Just(x0), Just(x1), ty_Ordering)
new_ltEs18(x0, x1, ty_Char)
new_lt20(x0, x1, ty_Float)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_lt10(x0, x1, ty_Double)
new_esEs5(Left(x0), Left(x1), ty_Bool, x2)
new_primPlusNat1(Succ(x0), x1)
new_lt10(x0, x1, app(ty_Maybe, x2))
new_ltEs6(Just(x0), Just(x1), ty_Float)
new_compare10(x0, x1, False, x2, x3)
new_ltEs8(True, True)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs6(Just(x0), Just(x1), ty_Integer)
new_ltEs4(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_compare19(x0, x1, False, x2, x3)
new_lt18(x0, x1)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_ltEs6(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs24(x0, x1, ty_Ordering)
new_esEs5(Right(x0), Right(x1), x2, app(ty_[], x3))
new_compare(:(x0, x1), :(x2, x3), x4)
new_ltEs6(Just(x0), Just(x1), app(ty_[], x2))
new_compare15(x0, x1, True, x2)
new_ltEs19(x0, x1, ty_Char)
new_lt19(x0, x1, ty_Ordering)
new_ltEs17(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_ltEs4(Right(x0), Right(x1), x2, app(ty_[], x3))
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs11(GT, EQ)
new_esEs11(EQ, GT)
new_ltEs6(Just(x0), Just(x1), ty_Int)
new_esEs13(x0, x1, app(ty_Maybe, x2))
new_ltEs4(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_lt20(x0, x1, app(ty_[], x2))
new_primMulInt(Neg(x0), Neg(x1))
new_primMulNat0(Succ(x0), Zero)
new_lt20(x0, x1, ty_Char)
new_compare19(x0, x1, True, x2, x3)
new_compare12(x0, x1, x2, x3, x4)
new_compare24(x0, x1, True, x2, x3)
new_lt20(x0, x1, ty_Double)
new_ltEs18(x0, x1, ty_Float)
new_compare24(x0, x1, False, x2, x3)
new_primPlusNat0(Succ(x0), Zero)
new_lt10(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs23(x0, x1, ty_Bool)
new_primEqNat0(Zero, Zero)
new_esEs4(Just(x0), Just(x1), ty_Int)
new_esEs5(Left(x0), Left(x1), ty_Integer, x2)
new_lt19(x0, x1, ty_@0)
new_esEs5(Right(x0), Right(x1), x2, ty_Ordering)
new_primCompAux00(x0, LT)
new_lt10(x0, x1, ty_Float)
new_esEs5(Right(x0), Right(x1), x2, ty_Float)
new_esEs4(Just(x0), Just(x1), ty_Bool)
new_esEs12(x0, x1, ty_Double)
new_ltEs6(Just(x0), Just(x1), ty_Double)
new_esEs9(True, True)
new_ltEs4(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs6(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_primCompAux0(x0, x1, x2, x3)
new_esEs8(EQ)
new_ltEs12(x0, x1, x2)
new_compare11(x0, x1, True)
new_primMulNat0(Zero, Zero)
new_esEs22(x0, x1, ty_@0)
new_ltEs4(Left(x0), Left(x1), ty_Char, x2)
new_ltEs6(Just(x0), Just(x1), app(ty_Maybe, x2))
new_ltEs6(Just(x0), Just(x1), ty_@0)
new_compare16(x0, x1, True)
new_sr(Integer(x0), Integer(x1))
new_lt7(x0, x1, x2, x3)
new_ltEs18(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs4(Right(x0), Right(x1), x2, ty_Float)
new_esEs25(x0, x1, ty_Double)
new_esEs22(x0, x1, ty_Ordering)
new_ltEs19(x0, x1, ty_Float)
new_esEs5(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_ltEs4(Right(x0), Right(x1), x2, ty_Int)
new_ltEs18(x0, x1, app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, ty_Int)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_lt10(x0, x1, app(ty_[], x2))
new_esEs12(x0, x1, ty_Ordering)
new_lt13(x0, x1, x2)
new_esEs25(x0, x1, ty_@0)
new_ltEs18(x0, x1, app(ty_Ratio, x2))
new_esEs11(LT, GT)
new_esEs11(GT, LT)
new_compare30(x0, x1, ty_Float)
new_esEs24(x0, x1, ty_Double)
new_ltEs15(GT, EQ)
new_ltEs15(EQ, GT)
new_compare18(:%(x0, x1), :%(x2, x3), ty_Int)
new_esEs13(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_esEs13(x0, x1, ty_Bool)
new_compare210(x0, x1, True, x2, x3, x4)
new_esEs5(Right(x0), Right(x1), x2, ty_Char)
new_compare25(x0, x1, False)
new_esEs13(x0, x1, ty_Double)
new_compare13(x0, x1)
new_compare30(x0, x1, ty_Char)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs21(x0, x1, ty_Float)
new_primPlusNat0(Succ(x0), Succ(x1))
new_asAs(True, x0)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs25(x0, x1, ty_Int)
new_lt9(x0, x1, x2)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs16([], :(x0, x1), x2)
new_esEs5(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_esEs6(@2(x0, x1), @2(x2, x3), x4, x5)
new_ltEs15(LT, GT)
new_ltEs15(GT, LT)
new_ltEs15(GT, GT)
new_primMulNat0(Zero, Succ(x0))
new_esEs11(LT, LT)
new_primEqNat0(Zero, Succ(x0))
new_not0
new_lt19(x0, x1, ty_Double)
new_primPlusNat0(Zero, Zero)
new_lt20(x0, x1, ty_Int)
new_compare30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_compare31(x0, x1)
new_compare32(@0, @0)
new_esEs14(Integer(x0), Integer(x1))
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_lt14(x0, x1)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_lt6(x0, x1)
new_esEs12(x0, x1, ty_Char)
new_esEs5(Right(x0), Right(x1), x2, ty_Double)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs24(x0, x1, ty_Int)
new_esEs5(Left(x0), Left(x1), ty_Double, x2)
new_esEs24(x0, x1, ty_Float)
new_esEs5(Right(x0), Right(x1), x2, ty_Int)
new_esEs21(x0, x1, ty_Int)
new_ltEs15(LT, LT)
new_esEs17(Char(x0), Char(x1))
new_compare26(x0, x1, True, x2)
new_lt10(x0, x1, app(app(ty_@2, x2), x3))
new_compare5(x0, x1, x2, x3)
new_ltEs4(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs18(Float(x0, x1), Float(x2, x3))
new_esEs13(x0, x1, app(app(ty_Either, x2), x3))
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_compare6(x0, x1)
new_ltEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpNat0(Zero, Succ(x0))
new_esEs12(x0, x1, ty_Float)
new_esEs22(x0, x1, ty_Bool)
new_not(GT)
new_pePe(False, x0, x1, x2, x3)
new_ltEs8(False, False)
new_esEs8(GT)
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs18(x0, x1, ty_Integer)
new_ltEs10(x0, x1)
new_esEs22(x0, x1, app(ty_[], x2))
new_esEs20(Double(x0, x1), Double(x2, x3))
new_esEs25(x0, x1, ty_Integer)
new_primEqInt(Neg(Zero), Pos(Zero))
new_primEqInt(Pos(Zero), Neg(Zero))
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs5(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_ltEs8(False, True)
new_ltEs8(True, False)
new_lt20(x0, x1, ty_Ordering)
new_esEs12(x0, x1, ty_Bool)
new_lt4(x0, x1, x2, x3)
new_lt19(x0, x1, ty_Integer)
new_ltEs4(Left(x0), Left(x1), ty_Float, x2)
new_esEs4(Just(x0), Just(x1), app(ty_[], x2))
new_compare28(x0, x1, True, x2, x3)
new_esEs21(x0, x1, ty_Integer)
new_esEs13(x0, x1, app(app(ty_@2, x2), x3))
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_ltEs4(Right(x0), Right(x1), x2, ty_@0)
new_lt10(x0, x1, ty_Integer)
new_compare27(x0, x1, False)
new_esEs11(LT, EQ)
new_esEs11(EQ, LT)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_compare30(x0, x1, app(ty_[], x2))
new_esEs24(x0, x1, ty_Bool)
new_ltEs4(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs26(x0, x1, ty_Int)
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, ty_Ordering)
new_primEqInt(Neg(Zero), Neg(Zero))
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_esEs12(x0, x1, app(ty_Ratio, x2))
new_lt19(x0, x1, ty_Char)
new_ltEs4(Left(x0), Right(x1), x2, x3)
new_ltEs4(Right(x0), Left(x1), x2, x3)
new_ltEs4(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs10(x0, x1)
new_compare28(x0, x1, False, x2, x3)
new_compare30(x0, x1, ty_Double)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_ltEs19(x0, x1, ty_Bool)
new_ltEs16(@2(x0, x1), @2(x2, x3), x4, x5)
new_ltEs4(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs5(Right(x0), Right(x1), x2, ty_Bool)
new_compare9(x0, x1, x2, x3)
new_esEs5(Left(x0), Left(x1), ty_@0, x2)
new_esEs5(Left(x0), Left(x1), ty_Char, x2)
new_esEs12(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt12(x0, x1)
new_esEs13(x0, x1, ty_Int)
new_ltEs18(x0, x1, ty_Bool)
new_ltEs18(x0, x1, ty_Ordering)
new_ltEs4(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_primEqNat0(Succ(x0), Zero)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs4(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs5(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_ltEs4(Right(x0), Right(x1), x2, ty_Char)
new_compare27(x0, x1, True)
new_lt16(x0, x1, x2)
new_ltEs4(Left(x0), Left(x1), ty_Integer, x2)
new_esEs23(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, ty_@0)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_ltEs4(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_compare8(Float(x0, x1), Float(x2, x3))
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs4(Just(x0), Just(x1), app(ty_Maybe, x2))
new_ltEs19(x0, x1, app(ty_[], x2))
new_primCmpNat0(Zero, Zero)
new_lt20(x0, x1, ty_Bool)
new_compare11(x0, x1, False)
new_esEs19(:%(x0, x1), :%(x2, x3), x4)
new_compare29(x0, x1, x2)
new_lt10(x0, x1, ty_@0)
new_ltEs4(Left(x0), Left(x1), ty_Double, x2)
new_esEs13(x0, x1, app(ty_[], x2))
new_lt19(x0, x1, app(ty_[], x2))
new_esEs16([], [], x0)
new_ltEs6(Just(x0), Nothing, x1)
new_esEs23(x0, x1, ty_Double)
new_esEs9(False, False)
new_ltEs9(x0, x1, x2)
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_esEs15(@0, @0)
new_esEs21(x0, x1, ty_@0)
new_esEs24(x0, x1, ty_Char)
new_esEs25(x0, x1, ty_Ordering)
new_esEs5(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_lt19(x0, x1, app(ty_Maybe, x2))
new_compare30(x0, x1, app(app(ty_@2, x2), x3))
new_compare(:(x0, x1), [], x2)
new_primMulNat0(Succ(x0), Succ(x1))
new_esEs4(Just(x0), Just(x1), ty_@0)
new_esEs5(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs21(x0, x1, ty_Double)
new_esEs5(Left(x0), Left(x1), ty_Int, x2)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_esEs16(:(x0, x1), [], x2)
new_lt5(x0, x1)
new_esEs27(x0, x1, ty_Int)
new_compare30(x0, x1, ty_@0)
new_esEs4(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs6(Just(x0), Just(x1), ty_Char)
new_compare10(x0, x1, True, x2, x3)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs4(Nothing, Nothing, x0)
new_esEs5(Left(x0), Left(x1), ty_Float, x2)
new_esEs22(x0, x1, ty_Float)
new_ltEs4(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_esEs11(GT, GT)
new_ltEs4(Right(x0), Right(x1), x2, ty_Integer)
new_esEs4(Nothing, Just(x0), x1)
new_pePe(True, x0, x1, x2, x3)
new_esEs25(x0, x1, ty_Char)
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs5(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs5(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs26(x0, x1, ty_Integer)
new_compare30(x0, x1, app(ty_Maybe, x2))
new_not(EQ)
new_esEs4(Just(x0), Just(x1), ty_Ordering)
new_esEs13(x0, x1, ty_Float)
new_compare([], :(x0, x1), x2)
new_esEs21(x0, x1, ty_Char)
new_primCompAux00(x0, GT)
new_compare30(x0, x1, app(app(ty_Either, x2), x3))
new_compare([], [], x0)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_ltEs18(x0, x1, ty_Int)
new_esEs12(x0, x1, ty_@0)
new_esEs12(x0, x1, ty_Int)
new_ltEs4(Right(x0), Right(x1), x2, ty_Ordering)
new_lt19(x0, x1, ty_Int)
new_esEs22(x0, x1, ty_Int)
new_compare16(x0, x1, False)
new_ltEs18(x0, x1, app(ty_Maybe, x2))
new_esEs22(x0, x1, ty_Integer)
new_esEs21(x0, x1, ty_Bool)
new_ltEs6(Just(x0), Just(x1), ty_Bool)
new_asAs(False, x0)
new_lt15(x0, x1)
new_ltEs14(x0, x1)
new_compare26(x0, x1, False, x2)
new_ltEs4(Left(x0), Left(x1), app(ty_[], x2), x3)
new_ltEs6(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_ltEs15(EQ, LT)
new_ltEs15(LT, EQ)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_ltEs4(Left(x0), Left(x1), ty_Int, x2)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs23(x0, x1, ty_@0)
new_ltEs19(x0, x1, ty_@0)
new_compare30(x0, x1, app(ty_Ratio, x2))
new_ltEs7(x0, x1)
new_compare30(x0, x1, ty_Bool)
new_compare14(Double(x0, x1), Double(x2, x3))
new_lt11(x0, x1)
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs9(False, True)
new_esEs9(True, False)
new_esEs4(Just(x0), Just(x1), ty_Double)
new_ltEs18(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, ty_Integer)
new_ltEs6(Nothing, Just(x0), x1)
new_lt10(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs15(EQ, EQ)
new_esEs25(x0, x1, ty_Float)
new_compare30(x0, x1, ty_Int)
new_esEs4(Just(x0), Just(x1), ty_Integer)
new_lt17(x0, x1)
new_esEs21(x0, x1, app(ty_[], x2))
new_esEs5(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_compare30(x0, x1, ty_Integer)
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs25(x0, x1, ty_Bool)
new_esEs24(x0, x1, ty_@0)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_ltEs4(Left(x0), Left(x1), ty_@0, x2)
new_lt10(x0, x1, app(ty_Ratio, x2))
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs11(x0, x1)
new_compare110(x0, x1, True, x2, x3, x4)
new_esEs22(x0, x1, ty_Double)
new_primEqInt(Pos(Zero), Pos(Zero))
new_esEs11(EQ, EQ)
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_sr0(x0, x1)
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_esEs5(Right(x0), Right(x1), x2, ty_Integer)
new_compare15(x0, x1, False, x2)
new_esEs4(Just(x0), Just(x1), ty_Float)
new_ltEs4(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt19(x0, x1, app(ty_Ratio, x2))
new_esEs12(x0, x1, ty_Integer)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primCmpNat0(Succ(x0), Succ(x1))
new_esEs23(x0, x1, ty_Char)
new_ltEs19(x0, x1, ty_Ordering)
new_ltEs13(x0, x1)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_compare17(Integer(x0), Integer(x1))
new_not(LT)
new_compare18(:%(x0, x1), :%(x2, x3), ty_Integer)
new_esEs23(x0, x1, ty_Integer)
new_ltEs4(Right(x0), Right(x1), x2, ty_Double)
new_ltEs18(x0, x1, ty_Double)
new_lt10(x0, x1, ty_Bool)
new_esEs13(x0, x1, ty_@0)
new_primCompAux00(x0, 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:



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

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

new_foldl(vwx30, :(vwx310, vwx311), ba) → new_foldl(new_max1(vwx30, vwx310, ba), vwx311, ba)

The TRS R consists of the following rules:

new_esEs4(Just(vwx290), Just(vwx300), app(ty_Maybe, cbh)) → new_esEs4(vwx290, vwx300, cbh)
new_lt10(vwx3000, vwx31000, app(app(ty_Either, bb), bc)) → new_lt4(vwx3000, vwx31000, bb, bc)
new_esEs24(vwx291, vwx301, app(app(ty_Either, dac), dad)) → new_esEs5(vwx291, vwx301, dac, dad)
new_esEs21(vwx290, vwx300, app(app(ty_@2, gg), gh)) → new_esEs6(vwx290, vwx300, gg, gh)
new_esEs21(vwx290, vwx300, ty_Double) → new_esEs20(vwx290, vwx300)
new_ltEs8(False, True) → True
new_lt18(vwx3000, vwx31000) → new_esEs8(new_compare13(vwx3000, vwx31000))
new_esEs5(Right(vwx290), Right(vwx300), bda, ty_Double) → new_esEs20(vwx290, vwx300)
new_ltEs15(EQ, LT) → False
new_esEs25(vwx290, vwx300, app(ty_[], dbh)) → new_esEs16(vwx290, vwx300, dbh)
new_max10(vwx8, vwx9, False, dce) → Just(vwx8)
new_esEs23(vwx292, vwx302, ty_Ordering) → new_esEs11(vwx292, vwx302)
new_compare30(vwx3000, vwx31000, ty_Ordering) → new_compare13(vwx3000, vwx31000)
new_lt19(vwx3001, vwx31001, app(app(app(ty_@3, cfb), cfc), cfd)) → new_lt8(vwx3001, vwx31001, cfb, cfc, cfd)
new_ltEs20(vwx300, vwx3100, app(ty_Ratio, ge)) → new_ltEs9(vwx300, vwx3100, ge)
new_esEs17(Char(vwx290), Char(vwx300)) → new_primEqNat0(vwx290, vwx300)
new_ltEs10(vwx300, vwx3100) → new_not(new_compare7(vwx300, vwx3100))
new_esEs24(vwx291, vwx301, ty_Char) → new_esEs17(vwx291, vwx301)
new_esEs5(Right(vwx290), Right(vwx300), bda, ty_Int) → new_esEs10(vwx290, vwx300)
new_esEs23(vwx292, vwx302, app(app(ty_Either, cha), chb)) → new_esEs5(vwx292, vwx302, cha, chb)
new_compare210(vwx3000, vwx31000, False, bf, bg, bh) → new_compare110(vwx3000, vwx31000, new_ltEs17(vwx3000, vwx31000, bf, bg, bh), bf, bg, bh)
new_compare([], :(vwx31000, vwx31001), caa) → LT
new_compare10(vwx3000, vwx31000, True, bb, bc) → LT
new_esEs4(Just(vwx290), Nothing, bdc) → False
new_esEs4(Nothing, Just(vwx300), bdc) → False
new_esEs24(vwx291, vwx301, app(ty_Maybe, dae)) → new_esEs4(vwx291, vwx301, dae)
new_lt20(vwx3000, vwx31000, app(app(app(ty_@3, cgd), cge), cgf)) → new_lt8(vwx3000, vwx31000, cgd, cge, cgf)
new_esEs4(Just(vwx290), Just(vwx300), ty_Char) → new_esEs17(vwx290, vwx300)
new_lt19(vwx3001, vwx31001, app(ty_Ratio, cec)) → new_lt9(vwx3001, vwx31001, cec)
new_compare32(@0, @0) → EQ
new_esEs12(vwx291, vwx301, ty_Bool) → new_esEs9(vwx291, vwx301)
new_compare8(Float(vwx3000, vwx3001), Float(vwx31000, vwx31001)) → new_compare6(new_sr0(vwx3000, vwx31000), new_sr0(vwx3001, vwx31001))
new_ltEs6(Nothing, Just(vwx31000), eh) → True
new_esEs20(Double(vwx290, vwx291), Double(vwx300, vwx301)) → new_esEs10(new_sr0(vwx290, vwx300), new_sr0(vwx291, vwx301))
new_lt19(vwx3001, vwx31001, ty_Double) → new_lt15(vwx3001, vwx31001)
new_esEs4(Just(vwx290), Just(vwx300), app(ty_Ratio, ccb)) → new_esEs19(vwx290, vwx300, ccb)
new_ltEs15(EQ, EQ) → True
new_esEs25(vwx290, vwx300, ty_Char) → new_esEs17(vwx290, vwx300)
new_esEs19(:%(vwx290, vwx291), :%(vwx300, vwx301), bdd) → new_asAs(new_esEs27(vwx290, vwx300, bdd), new_esEs26(vwx291, vwx301, bdd))
new_esEs11(EQ, EQ) → True
new_primMulNat0(Zero, Zero) → Zero
new_esEs6(@2(vwx290, vwx291), @2(vwx300, vwx301), ca, cb) → new_asAs(new_esEs13(vwx290, vwx300, ca), new_esEs12(vwx291, vwx301, cb))
new_compare(:(vwx3000, vwx3001), [], caa) → GT
new_max10(vwx8, vwx9, True, dce) → Just(vwx9)
new_sr(Integer(vwx30000), Integer(vwx310010)) → Integer(new_primMulInt(vwx30000, vwx310010))
new_ltEs16(@2(vwx3000, vwx3001), @2(vwx31000, vwx31001), bdh, bea) → new_pePe(new_lt10(vwx3000, vwx31000, bdh), vwx3000, vwx31000, new_ltEs18(vwx3001, vwx31001, bea), bdh)
new_esEs13(vwx290, vwx300, ty_Integer) → new_esEs14(vwx290, vwx300)
new_lt4(vwx3000, vwx31000, bb, bc) → new_esEs8(new_compare5(vwx3000, vwx31000, bb, bc))
new_lt19(vwx3001, vwx31001, ty_Integer) → new_lt11(vwx3001, vwx31001)
new_esEs22(vwx29, vwx30, ty_Char) → new_esEs17(vwx29, vwx30)
new_esEs25(vwx290, vwx300, ty_Ordering) → new_esEs11(vwx290, vwx300)
new_lt15(vwx3000, vwx31000) → new_esEs8(new_compare14(vwx3000, vwx31000))
new_not(GT) → False
new_esEs23(vwx292, vwx302, app(ty_Maybe, chc)) → new_esEs4(vwx292, vwx302, chc)
new_ltEs4(Left(vwx3000), Left(vwx31000), ty_Float, bab) → new_ltEs5(vwx3000, vwx31000)
new_ltEs20(vwx300, vwx3100, ty_Int) → new_ltEs11(vwx300, vwx3100)
new_esEs5(Left(vwx290), Left(vwx300), app(ty_Ratio, bgc), bdb) → new_esEs19(vwx290, vwx300, bgc)
new_ltEs15(GT, LT) → False
new_compare14(Double(vwx3000, vwx3001), Double(vwx31000, vwx31001)) → new_compare6(new_sr0(vwx3000, vwx31000), new_sr0(vwx3001, vwx31001))
new_esEs13(vwx290, vwx300, ty_Char) → new_esEs17(vwx290, vwx300)
new_esEs23(vwx292, vwx302, ty_Bool) → new_esEs9(vwx292, vwx302)
new_ltEs18(vwx3001, vwx31001, app(ty_Ratio, beb)) → new_ltEs9(vwx3001, vwx31001, beb)
new_ltEs19(vwx3002, vwx31002, ty_@0) → new_ltEs13(vwx3002, vwx31002)
new_esEs22(vwx29, vwx30, app(ty_Ratio, bdd)) → new_esEs19(vwx29, vwx30, bdd)
new_esEs13(vwx290, vwx300, ty_@0) → new_esEs15(vwx290, vwx300)
new_esEs23(vwx292, vwx302, ty_Double) → new_esEs20(vwx292, vwx302)
new_esEs5(Right(vwx290), Right(vwx300), bda, ty_Integer) → new_esEs14(vwx290, vwx300)
new_lt10(vwx3000, vwx31000, app(app(app(ty_@3, bf), bg), bh)) → new_lt8(vwx3000, vwx31000, bf, bg, bh)
new_esEs21(vwx290, vwx300, app(app(app(ty_@3, hf), hg), hh)) → new_esEs7(vwx290, vwx300, hf, hg, hh)
new_esEs18(Float(vwx290, vwx291), Float(vwx300, vwx301)) → new_esEs10(new_sr0(vwx290, vwx300), new_sr0(vwx291, vwx301))
new_esEs22(vwx29, vwx30, ty_Double) → new_esEs20(vwx29, vwx30)
new_lt20(vwx3000, vwx31000, app(ty_[], cff)) → new_lt13(vwx3000, vwx31000, cff)
new_ltEs18(vwx3001, vwx31001, ty_Float) → new_ltEs5(vwx3001, vwx31001)
new_esEs26(vwx291, vwx301, ty_Integer) → new_esEs14(vwx291, vwx301)
new_ltEs4(Left(vwx3000), Left(vwx31000), app(app(app(ty_@3, bbb), bbc), bbd), bab) → new_ltEs17(vwx3000, vwx31000, bbb, bbc, bbd)
new_compare15(vwx3000, vwx31000, False, gd) → GT
new_lt20(vwx3000, vwx31000, ty_Float) → new_lt17(vwx3000, vwx31000)
new_ltEs6(Just(vwx3000), Just(vwx31000), ty_Int) → new_ltEs11(vwx3000, vwx31000)
new_ltEs4(Left(vwx3000), Left(vwx31000), ty_Double, bab) → new_ltEs14(vwx3000, vwx31000)
new_ltEs4(Right(vwx3000), Right(vwx31000), bbe, ty_Double) → new_ltEs14(vwx3000, vwx31000)
new_lt10(vwx3000, vwx31000, ty_Integer) → new_lt11(vwx3000, vwx31000)
new_ltEs19(vwx3002, vwx31002, app(app(ty_Either, cdd), cde)) → new_ltEs4(vwx3002, vwx31002, cdd, cde)
new_lt12(vwx3000, vwx31000) → new_esEs8(new_compare31(vwx3000, vwx31000))
new_ltEs19(vwx3002, vwx31002, ty_Ordering) → new_ltEs15(vwx3002, vwx31002)
new_lt10(vwx3000, vwx31000, app(ty_[], bfd)) → new_lt13(vwx3000, vwx31000, bfd)
new_ltEs15(EQ, GT) → True
new_esEs5(Left(vwx290), Left(vwx300), ty_Ordering, bdb) → new_esEs11(vwx290, vwx300)
new_esEs13(vwx290, vwx300, app(ty_Maybe, eb)) → new_esEs4(vwx290, vwx300, eb)
new_esEs13(vwx290, vwx300, ty_Ordering) → new_esEs11(vwx290, vwx300)
new_esEs22(vwx29, vwx30, ty_@0) → new_esEs15(vwx29, vwx30)
new_esEs21(vwx290, vwx300, app(ty_Ratio, he)) → new_esEs19(vwx290, vwx300, he)
new_ltEs20(vwx300, vwx3100, app(app(ty_Either, bbe), bab)) → new_ltEs4(vwx300, vwx3100, bbe, bab)
new_ltEs6(Just(vwx3000), Just(vwx31000), ty_Bool) → new_ltEs8(vwx3000, vwx31000)
new_ltEs4(Right(vwx3000), Right(vwx31000), bbe, app(app(ty_Either, bca), bcb)) → new_ltEs4(vwx3000, vwx31000, bca, bcb)
new_ltEs4(Left(vwx3000), Left(vwx31000), app(ty_[], bad), bab) → new_ltEs12(vwx3000, vwx31000, bad)
new_esEs5(Right(vwx290), Right(vwx300), bda, ty_@0) → new_esEs15(vwx290, vwx300)
new_esEs5(Left(vwx290), Left(vwx300), app(app(ty_@2, bfe), bff), bdb) → new_esEs6(vwx290, vwx300, bfe, bff)
new_esEs14(Integer(vwx290), Integer(vwx300)) → new_primEqInt(vwx290, vwx300)
new_esEs22(vwx29, vwx30, ty_Bool) → new_esEs9(vwx29, vwx30)
new_lt20(vwx3000, vwx31000, app(app(ty_@2, cgb), cgc)) → new_lt7(vwx3000, vwx31000, cgb, cgc)
new_lt20(vwx3000, vwx31000, app(ty_Maybe, cfg)) → new_lt16(vwx3000, vwx31000, cfg)
new_ltEs20(vwx300, vwx3100, app(ty_[], caa)) → new_ltEs12(vwx300, vwx3100, caa)
new_esEs5(Left(vwx290), Left(vwx300), app(ty_Maybe, bga), bdb) → new_esEs4(vwx290, vwx300, bga)
new_ltEs4(Left(vwx3000), Right(vwx31000), bbe, bab) → True
new_esEs12(vwx291, vwx301, app(ty_[], da)) → new_esEs16(vwx291, vwx301, da)
new_lt19(vwx3001, vwx31001, ty_Int) → new_lt5(vwx3001, vwx31001)
new_esEs5(Right(vwx290), Right(vwx300), bda, ty_Char) → new_esEs17(vwx290, vwx300)
new_esEs23(vwx292, vwx302, app(app(app(ty_@3, chf), chg), chh)) → new_esEs7(vwx292, vwx302, chf, chg, chh)
new_ltEs15(LT, LT) → True
new_primCmpNat0(Zero, Succ(vwx310000)) → LT
new_ltEs20(vwx300, vwx3100, ty_Double) → new_ltEs14(vwx300, vwx3100)
new_esEs25(vwx290, vwx300, ty_Bool) → new_esEs9(vwx290, vwx300)
new_lt10(vwx3000, vwx31000, ty_Double) → new_lt15(vwx3000, vwx31000)
new_ltEs20(vwx300, vwx3100, ty_Bool) → new_ltEs8(vwx300, vwx3100)
new_esEs25(vwx290, vwx300, app(app(ty_Either, dbe), dbf)) → new_esEs5(vwx290, vwx300, dbe, dbf)
new_esEs25(vwx290, vwx300, app(app(ty_@2, dbc), dbd)) → new_esEs6(vwx290, vwx300, dbc, dbd)
new_ltEs18(vwx3001, vwx31001, ty_@0) → new_ltEs13(vwx3001, vwx31001)
new_lt10(vwx3000, vwx31000, ty_Bool) → new_lt12(vwx3000, vwx31000)
new_ltEs18(vwx3001, vwx31001, ty_Bool) → new_ltEs8(vwx3001, vwx31001)
new_esEs25(vwx290, vwx300, ty_Double) → new_esEs20(vwx290, vwx300)
new_lt20(vwx3000, vwx31000, ty_Int) → new_lt5(vwx3000, vwx31000)
new_lt20(vwx3000, vwx31000, app(ty_Ratio, cfe)) → new_lt9(vwx3000, vwx31000, cfe)
new_esEs11(GT, GT) → True
new_ltEs4(Left(vwx3000), Left(vwx31000), app(ty_Ratio, bac), bab) → new_ltEs9(vwx3000, vwx31000, bac)
new_compare30(vwx3000, vwx31000, ty_Char) → new_compare7(vwx3000, vwx31000)
new_compare13(vwx3000, vwx31000) → new_compare25(vwx3000, vwx31000, new_esEs11(vwx3000, vwx31000))
new_esEs24(vwx291, vwx301, app(app(ty_@2, daa), dab)) → new_esEs6(vwx291, vwx301, daa, dab)
new_primEqNat0(Zero, Zero) → True
new_esEs5(Right(vwx290), Right(vwx300), bda, app(app(ty_@2, bgg), bgh)) → new_esEs6(vwx290, vwx300, bgg, bgh)
new_primMulNat0(Succ(vwx300000), Succ(vwx3100100)) → new_primPlusNat1(new_primMulNat0(vwx300000, Succ(vwx3100100)), vwx3100100)
new_compare26(vwx3000, vwx31000, False, gd) → new_compare15(vwx3000, vwx31000, new_ltEs6(vwx3000, vwx31000, gd), gd)
new_esEs5(Right(vwx290), Right(vwx300), bda, ty_Float) → new_esEs18(vwx290, vwx300)
new_compare27(vwx3000, vwx31000, False) → new_compare16(vwx3000, vwx31000, new_ltEs8(vwx3000, vwx31000))
new_ltEs11(vwx300, vwx3100) → new_not(new_compare6(vwx300, vwx3100))
new_esEs12(vwx291, vwx301, ty_Char) → new_esEs17(vwx291, vwx301)
new_compare30(vwx3000, vwx31000, ty_Bool) → new_compare31(vwx3000, vwx31000)
new_esEs4(Just(vwx290), Just(vwx300), ty_Bool) → new_esEs9(vwx290, vwx300)
new_lt13(vwx3000, vwx31000, bfd) → new_esEs8(new_compare(vwx3000, vwx31000, bfd))
new_ltEs18(vwx3001, vwx31001, ty_Char) → new_ltEs10(vwx3001, vwx31001)
new_esEs4(Just(vwx290), Just(vwx300), ty_Double) → new_esEs20(vwx290, vwx300)
new_lt10(vwx3000, vwx31000, ty_@0) → new_lt14(vwx3000, vwx31000)
new_ltEs15(GT, GT) → True
new_ltEs4(Right(vwx3000), Right(vwx31000), bbe, ty_Ordering) → new_ltEs15(vwx3000, vwx31000)
new_esEs4(Just(vwx290), Just(vwx300), ty_Integer) → new_esEs14(vwx290, vwx300)
new_esEs23(vwx292, vwx302, app(ty_Ratio, che)) → new_esEs19(vwx292, vwx302, che)
new_ltEs19(vwx3002, vwx31002, ty_Char) → new_ltEs10(vwx3002, vwx31002)
new_esEs4(Just(vwx290), Just(vwx300), ty_Ordering) → new_esEs11(vwx290, vwx300)
new_esEs5(Left(vwx290), Left(vwx300), ty_Double, bdb) → new_esEs20(vwx290, vwx300)
new_ltEs6(Just(vwx3000), Just(vwx31000), app(ty_Ratio, fa)) → new_ltEs9(vwx3000, vwx31000, fa)
new_compare30(vwx3000, vwx31000, ty_Double) → new_compare14(vwx3000, vwx31000)
new_max1(Nothing, Nothing, ba) → Nothing
new_primEqInt(Neg(Succ(vwx2900)), Neg(Succ(vwx3000))) → new_primEqNat0(vwx2900, vwx3000)
new_compare25(vwx3000, vwx31000, True) → EQ
new_esEs13(vwx290, vwx300, app(ty_Ratio, ed)) → new_esEs19(vwx290, vwx300, ed)
new_compare30(vwx3000, vwx31000, ty_Int) → new_compare6(vwx3000, vwx31000)
new_esEs12(vwx291, vwx301, ty_Integer) → new_esEs14(vwx291, vwx301)
new_esEs5(Left(vwx290), Left(vwx300), app(ty_[], bgb), bdb) → new_esEs16(vwx290, vwx300, bgb)
new_lt20(vwx3000, vwx31000, ty_Char) → new_lt6(vwx3000, vwx31000)
new_lt19(vwx3001, vwx31001, ty_Float) → new_lt17(vwx3001, vwx31001)
new_ltEs8(True, True) → True
new_esEs7(@3(vwx290, vwx291, vwx292), @3(vwx300, vwx301, vwx302), bde, bdf, bdg) → new_asAs(new_esEs25(vwx290, vwx300, bde), new_asAs(new_esEs24(vwx291, vwx301, bdf), new_esEs23(vwx292, vwx302, bdg)))
new_esEs21(vwx290, vwx300, ty_@0) → new_esEs15(vwx290, vwx300)
new_ltEs19(vwx3002, vwx31002, app(ty_Ratio, cda)) → new_ltEs9(vwx3002, vwx31002, cda)
new_compare16(vwx3000, vwx31000, True) → LT
new_lt20(vwx3000, vwx31000, app(app(ty_Either, cfh), cga)) → new_lt4(vwx3000, vwx31000, cfh, cga)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs5(Left(vwx290), Left(vwx300), app(app(app(ty_@3, bgd), bge), bgf), bdb) → new_esEs7(vwx290, vwx300, bgd, bge, bgf)
new_ltEs4(Left(vwx3000), Left(vwx31000), ty_Char, bab) → new_ltEs10(vwx3000, vwx31000)
new_ltEs4(Right(vwx3000), Right(vwx31000), bbe, ty_Integer) → new_ltEs7(vwx3000, vwx31000)
new_esEs5(Right(vwx290), Right(vwx300), bda, app(ty_Ratio, bhe)) → new_esEs19(vwx290, vwx300, bhe)
new_ltEs5(vwx300, vwx3100) → new_not(new_compare8(vwx300, vwx3100))
new_primEqInt(Neg(Zero), Neg(Succ(vwx3000))) → False
new_primEqInt(Neg(Succ(vwx2900)), Neg(Zero)) → False
new_ltEs4(Left(vwx3000), Left(vwx31000), app(app(ty_Either, baf), bag), bab) → new_ltEs4(vwx3000, vwx31000, baf, bag)
new_lt20(vwx3000, vwx31000, ty_Integer) → new_lt11(vwx3000, vwx31000)
new_compare31(vwx3000, vwx31000) → new_compare27(vwx3000, vwx31000, new_esEs9(vwx3000, vwx31000))
new_primPlusNat1(Zero, vwx3100100) → Succ(vwx3100100)
new_compare7(Char(vwx3000), Char(vwx31000)) → new_primCmpNat0(vwx3000, vwx31000)
new_compare24(vwx3000, vwx31000, True, bb, bc) → EQ
new_esEs25(vwx290, vwx300, app(ty_Ratio, dca)) → new_esEs19(vwx290, vwx300, dca)
new_ltEs6(Just(vwx3000), Just(vwx31000), app(app(ty_Either, fd), ff)) → new_ltEs4(vwx3000, vwx31000, fd, ff)
new_ltEs6(Just(vwx3000), Just(vwx31000), ty_@0) → new_ltEs13(vwx3000, vwx31000)
new_compare([], [], caa) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_esEs23(vwx292, vwx302, ty_Integer) → new_esEs14(vwx292, vwx302)
new_ltEs15(LT, GT) → True
new_compare6(vwx300, vwx3100) → new_primCmpInt(vwx300, vwx3100)
new_primCmpNat0(Succ(vwx30000), Succ(vwx310000)) → new_primCmpNat0(vwx30000, vwx310000)
new_esEs22(vwx29, vwx30, app(ty_Maybe, bdc)) → new_esEs4(vwx29, vwx30, bdc)
new_esEs25(vwx290, vwx300, app(ty_Maybe, dbg)) → new_esEs4(vwx290, vwx300, dbg)
new_ltEs7(vwx300, vwx3100) → new_not(new_compare17(vwx300, vwx3100))
new_primEqInt(Pos(Succ(vwx2900)), Pos(Succ(vwx3000))) → new_primEqNat0(vwx2900, vwx3000)
new_compare10(vwx3000, vwx31000, False, bb, bc) → GT
new_compare12(vwx3000, vwx31000, bf, bg, bh) → new_compare210(vwx3000, vwx31000, new_esEs7(vwx3000, vwx31000, bf, bg, bh), bf, bg, bh)
new_esEs5(Right(vwx290), Right(vwx300), bda, ty_Ordering) → new_esEs11(vwx290, vwx300)
new_lt16(vwx3000, vwx31000, gd) → new_esEs8(new_compare29(vwx3000, vwx31000, gd))
new_esEs24(vwx291, vwx301, ty_Double) → new_esEs20(vwx291, vwx301)
new_esEs16(:(vwx290, vwx291), :(vwx300, vwx301), gf) → new_asAs(new_esEs21(vwx290, vwx300, gf), new_esEs16(vwx291, vwx301, gf))
new_esEs23(vwx292, vwx302, ty_Char) → new_esEs17(vwx292, vwx302)
new_compare30(vwx3000, vwx31000, app(app(app(ty_@3, cba), cbb), cbc)) → new_compare12(vwx3000, vwx31000, cba, cbb, cbc)
new_esEs5(Right(vwx290), Right(vwx300), bda, app(app(ty_Either, bha), bhb)) → new_esEs5(vwx290, vwx300, bha, bhb)
new_primEqNat0(Succ(vwx2900), Succ(vwx3000)) → new_primEqNat0(vwx2900, vwx3000)
new_ltEs9(vwx300, vwx3100, ge) → new_not(new_compare18(vwx300, vwx3100, ge))
new_ltEs4(Left(vwx3000), Left(vwx31000), ty_Int, bab) → new_ltEs11(vwx3000, vwx31000)
new_esEs12(vwx291, vwx301, ty_@0) → new_esEs15(vwx291, vwx301)
new_ltEs19(vwx3002, vwx31002, ty_Double) → new_ltEs14(vwx3002, vwx31002)
new_max1(Just(vwx300), Just(vwx3100), ba) → new_max10(vwx300, vwx3100, new_ltEs20(vwx300, vwx3100, ba), ba)
new_esEs4(Just(vwx290), Just(vwx300), ty_Int) → new_esEs10(vwx290, vwx300)
new_primCompAux00(vwx45, LT) → LT
new_lt19(vwx3001, vwx31001, app(ty_[], ced)) → new_lt13(vwx3001, vwx31001, ced)
new_esEs4(Just(vwx290), Just(vwx300), ty_@0) → new_esEs15(vwx290, vwx300)
new_primCmpInt(Neg(Succ(vwx30000)), Neg(vwx31000)) → new_primCmpNat0(vwx31000, Succ(vwx30000))
new_ltEs6(Just(vwx3000), Just(vwx31000), app(app(ty_@2, fg), fh)) → new_ltEs16(vwx3000, vwx31000, fg, fh)
new_compare25(vwx3000, vwx31000, False) → new_compare11(vwx3000, vwx31000, new_ltEs15(vwx3000, vwx31000))
new_lt10(vwx3000, vwx31000, ty_Float) → new_lt17(vwx3000, vwx31000)
new_ltEs19(vwx3002, vwx31002, ty_Bool) → new_ltEs8(vwx3002, vwx31002)
new_compare24(vwx3000, vwx31000, False, bb, bc) → new_compare10(vwx3000, vwx31000, new_ltEs4(vwx3000, vwx31000, bb, bc), bb, bc)
new_primEqInt(Pos(Zero), Pos(Succ(vwx3000))) → False
new_primEqInt(Pos(Succ(vwx2900)), Pos(Zero)) → False
new_esEs22(vwx29, vwx30, ty_Ordering) → new_esEs11(vwx29, vwx30)
new_ltEs4(Left(vwx3000), Left(vwx31000), ty_Ordering, bab) → new_ltEs15(vwx3000, vwx31000)
new_compare9(vwx3000, vwx31000, bd, be) → new_compare28(vwx3000, vwx31000, new_esEs6(vwx3000, vwx31000, bd, be), bd, be)
new_ltEs19(vwx3002, vwx31002, app(ty_Maybe, cdc)) → new_ltEs6(vwx3002, vwx31002, cdc)
new_esEs12(vwx291, vwx301, app(app(app(ty_@3, dc), dd), de)) → new_esEs7(vwx291, vwx301, dc, dd, de)
new_primPlusNat0(Succ(vwx5900), Zero) → Succ(vwx5900)
new_primPlusNat0(Zero, Succ(vwx31001000)) → Succ(vwx31001000)
new_ltEs6(Just(vwx3000), Nothing, eh) → False
new_compare5(vwx3000, vwx31000, bb, bc) → new_compare24(vwx3000, vwx31000, new_esEs5(vwx3000, vwx31000, bb, bc), bb, bc)
new_primCmpNat0(Zero, Zero) → EQ
new_esEs24(vwx291, vwx301, app(ty_Ratio, dag)) → new_esEs19(vwx291, vwx301, dag)
new_esEs5(Right(vwx290), Right(vwx300), bda, ty_Bool) → new_esEs9(vwx290, vwx300)
new_esEs13(vwx290, vwx300, ty_Double) → new_esEs20(vwx290, vwx300)
new_primCmpNat0(Succ(vwx30000), Zero) → GT
new_compare30(vwx3000, vwx31000, ty_@0) → new_compare32(vwx3000, vwx31000)
new_esEs22(vwx29, vwx30, ty_Integer) → new_esEs14(vwx29, vwx30)
new_esEs24(vwx291, vwx301, ty_@0) → new_esEs15(vwx291, vwx301)
new_max1(Nothing, Just(vwx3100), ba) → Just(vwx3100)
new_max1(Just(vwx300), Nothing, ba) → Just(vwx300)
new_primCmpInt(Neg(Zero), Pos(Succ(vwx310000))) → LT
new_esEs8(LT) → True
new_esEs4(Just(vwx290), Just(vwx300), app(app(ty_Either, cbf), cbg)) → new_esEs5(vwx290, vwx300, cbf, cbg)
new_ltEs4(Right(vwx3000), Right(vwx31000), bbe, ty_Char) → new_ltEs10(vwx3000, vwx31000)
new_compare210(vwx3000, vwx31000, True, bf, bg, bh) → EQ
new_ltEs4(Right(vwx3000), Right(vwx31000), bbe, app(app(app(ty_@3, bce), bcf), bcg)) → new_ltEs17(vwx3000, vwx31000, bce, bcf, bcg)
new_compare30(vwx3000, vwx31000, app(ty_[], cac)) → new_compare(vwx3000, vwx31000, cac)
new_compare28(vwx3000, vwx31000, True, bd, be) → EQ
new_primEqInt(Neg(Succ(vwx2900)), Pos(vwx300)) → False
new_primEqInt(Pos(Succ(vwx2900)), Neg(vwx300)) → False
new_esEs25(vwx290, vwx300, ty_Int) → new_esEs10(vwx290, vwx300)
new_ltEs18(vwx3001, vwx31001, app(app(ty_Either, bee), bef)) → new_ltEs4(vwx3001, vwx31001, bee, bef)
new_compare(:(vwx3000, vwx3001), :(vwx31000, vwx31001), caa) → new_primCompAux0(vwx3000, vwx31000, new_compare(vwx3001, vwx31001, caa), caa)
new_lt19(vwx3001, vwx31001, app(ty_Maybe, cee)) → new_lt16(vwx3001, vwx31001, cee)
new_esEs4(Just(vwx290), Just(vwx300), app(app(ty_@2, cbd), cbe)) → new_esEs6(vwx290, vwx300, cbd, cbe)
new_esEs8(GT) → False
new_lt19(vwx3001, vwx31001, ty_@0) → new_lt14(vwx3001, vwx31001)
new_ltEs6(Just(vwx3000), Just(vwx31000), app(ty_Maybe, fc)) → new_ltEs6(vwx3000, vwx31000, fc)
new_esEs22(vwx29, vwx30, app(app(ty_@2, ca), cb)) → new_esEs6(vwx29, vwx30, ca, cb)
new_compare18(:%(vwx3000, vwx3001), :%(vwx31000, vwx31001), ty_Int) → new_compare6(new_sr0(vwx3000, vwx31001), new_sr0(vwx31000, vwx3001))
new_ltEs4(Right(vwx3000), Right(vwx31000), bbe, app(ty_Maybe, bbh)) → new_ltEs6(vwx3000, vwx31000, bbh)
new_primEqInt(Neg(Zero), Pos(Succ(vwx3000))) → False
new_primEqInt(Pos(Zero), Neg(Succ(vwx3000))) → False
new_esEs24(vwx291, vwx301, ty_Ordering) → new_esEs11(vwx291, vwx301)
new_esEs26(vwx291, vwx301, ty_Int) → new_esEs10(vwx291, vwx301)
new_ltEs14(vwx300, vwx3100) → new_not(new_compare14(vwx300, vwx3100))
new_primCmpInt(Pos(Zero), Pos(Succ(vwx310000))) → new_primCmpNat0(Zero, Succ(vwx310000))
new_primCompAux00(vwx45, EQ) → vwx45
new_esEs21(vwx290, vwx300, ty_Ordering) → new_esEs11(vwx290, vwx300)
new_ltEs4(Left(vwx3000), Left(vwx31000), app(ty_Maybe, bae), bab) → new_ltEs6(vwx3000, vwx31000, bae)
new_ltEs4(Right(vwx3000), Right(vwx31000), bbe, app(app(ty_@2, bcc), bcd)) → new_ltEs16(vwx3000, vwx31000, bcc, bcd)
new_ltEs20(vwx300, vwx3100, ty_Ordering) → new_ltEs15(vwx300, vwx3100)
new_esEs22(vwx29, vwx30, ty_Float) → new_esEs18(vwx29, vwx30)
new_compare26(vwx3000, vwx31000, True, gd) → EQ
new_ltEs20(vwx300, vwx3100, ty_Float) → new_ltEs5(vwx300, vwx3100)
new_compare30(vwx3000, vwx31000, app(ty_Ratio, cab)) → new_compare18(vwx3000, vwx31000, cab)
new_ltEs8(True, False) → False
new_esEs21(vwx290, vwx300, ty_Integer) → new_esEs14(vwx290, vwx300)
new_ltEs4(Right(vwx3000), Left(vwx31000), bbe, bab) → False
new_ltEs4(Left(vwx3000), Left(vwx31000), app(app(ty_@2, bah), bba), bab) → new_ltEs16(vwx3000, vwx31000, bah, bba)
new_ltEs20(vwx300, vwx3100, app(app(app(ty_@3, ccf), ccg), cch)) → new_ltEs17(vwx300, vwx3100, ccf, ccg, cch)
new_compare30(vwx3000, vwx31000, app(app(ty_@2, cag), cah)) → new_compare9(vwx3000, vwx31000, cag, cah)
new_esEs23(vwx292, vwx302, ty_@0) → new_esEs15(vwx292, vwx302)
new_primCmpInt(Pos(Succ(vwx30000)), Pos(vwx31000)) → new_primCmpNat0(Succ(vwx30000), vwx31000)
new_ltEs19(vwx3002, vwx31002, ty_Float) → new_ltEs5(vwx3002, vwx31002)
new_esEs23(vwx292, vwx302, app(app(ty_@2, cgg), cgh)) → new_esEs6(vwx292, vwx302, cgg, cgh)
new_ltEs12(vwx300, vwx3100, caa) → new_not(new_compare(vwx300, vwx3100, caa))
new_esEs11(GT, LT) → False
new_esEs11(LT, GT) → False
new_esEs23(vwx292, vwx302, ty_Float) → new_esEs18(vwx292, vwx302)
new_ltEs19(vwx3002, vwx31002, app(ty_[], cdb)) → new_ltEs12(vwx3002, vwx31002, cdb)
new_esEs13(vwx290, vwx300, app(ty_[], ec)) → new_esEs16(vwx290, vwx300, ec)
new_esEs13(vwx290, vwx300, app(app(ty_Either, dh), ea)) → new_esEs5(vwx290, vwx300, dh, ea)
new_esEs25(vwx290, vwx300, ty_@0) → new_esEs15(vwx290, vwx300)
new_esEs25(vwx290, vwx300, ty_Float) → new_esEs18(vwx290, vwx300)
new_not0True
new_esEs11(EQ, LT) → False
new_esEs11(LT, EQ) → False
new_lt20(vwx3000, vwx31000, ty_Ordering) → new_lt18(vwx3000, vwx31000)
new_esEs9(True, True) → True
new_lt14(vwx3000, vwx31000) → new_esEs8(new_compare32(vwx3000, vwx31000))
new_ltEs4(Right(vwx3000), Right(vwx31000), bbe, app(ty_Ratio, bbf)) → new_ltEs9(vwx3000, vwx31000, bbf)
new_lt19(vwx3001, vwx31001, ty_Char) → new_lt6(vwx3001, vwx31001)
new_primCmpInt(Pos(Succ(vwx30000)), Neg(vwx31000)) → GT
new_esEs22(vwx29, vwx30, app(app(app(ty_@3, bde), bdf), bdg)) → new_esEs7(vwx29, vwx30, bde, bdf, bdg)
new_ltEs18(vwx3001, vwx31001, app(app(ty_@2, beg), beh)) → new_ltEs16(vwx3001, vwx31001, beg, beh)
new_ltEs15(LT, EQ) → True
new_ltEs4(Right(vwx3000), Right(vwx31000), bbe, ty_Bool) → new_ltEs8(vwx3000, vwx31000)
new_esEs24(vwx291, vwx301, ty_Float) → new_esEs18(vwx291, vwx301)
new_esEs22(vwx29, vwx30, app(ty_[], gf)) → new_esEs16(vwx29, vwx30, gf)
new_ltEs6(Just(vwx3000), Just(vwx31000), app(app(app(ty_@3, ga), gb), gc)) → new_ltEs17(vwx3000, vwx31000, ga, gb, gc)
new_lt20(vwx3000, vwx31000, ty_Double) → new_lt15(vwx3000, vwx31000)
new_primMulInt(Pos(vwx30000), Pos(vwx310010)) → Pos(new_primMulNat0(vwx30000, vwx310010))
new_lt19(vwx3001, vwx31001, ty_Bool) → new_lt12(vwx3001, vwx31001)
new_esEs4(Just(vwx290), Just(vwx300), ty_Float) → new_esEs18(vwx290, vwx300)
new_esEs22(vwx29, vwx30, ty_Int) → new_esEs10(vwx29, vwx30)
new_esEs5(Right(vwx290), Right(vwx300), bda, app(ty_[], bhd)) → new_esEs16(vwx290, vwx300, bhd)
new_lt9(vwx3000, vwx31000, baa) → new_esEs8(new_compare18(vwx3000, vwx31000, baa))
new_esEs5(Right(vwx290), Left(vwx300), bda, bdb) → False
new_esEs5(Left(vwx290), Right(vwx300), bda, bdb) → False
new_primMulInt(Neg(vwx30000), Neg(vwx310010)) → Pos(new_primMulNat0(vwx30000, vwx310010))
new_lt10(vwx3000, vwx31000, app(app(ty_@2, bd), be)) → new_lt7(vwx3000, vwx31000, bd, be)
new_lt20(vwx3000, vwx31000, ty_@0) → new_lt14(vwx3000, vwx31000)
new_primEqNat0(Zero, Succ(vwx3000)) → False
new_primEqNat0(Succ(vwx2900), Zero) → False
new_ltEs8(False, False) → True
new_ltEs4(Right(vwx3000), Right(vwx31000), bbe, ty_Int) → new_ltEs11(vwx3000, vwx31000)
new_pePe(False, vwx29, vwx30, vwx31, bch) → new_asAs(new_esEs22(vwx29, vwx30, bch), vwx31)
new_primPlusNat0(Zero, Zero) → Zero
new_esEs5(Left(vwx290), Left(vwx300), ty_Integer, bdb) → new_esEs14(vwx290, vwx300)
new_ltEs6(Just(vwx3000), Just(vwx31000), ty_Double) → new_ltEs14(vwx3000, vwx31000)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_ltEs18(vwx3001, vwx31001, app(app(app(ty_@3, bfa), bfb), bfc)) → new_ltEs17(vwx3001, vwx31001, bfa, bfb, bfc)
new_esEs4(Nothing, Nothing, bdc) → True
new_ltEs18(vwx3001, vwx31001, ty_Integer) → new_ltEs7(vwx3001, vwx31001)
new_esEs21(vwx290, vwx300, ty_Bool) → new_esEs9(vwx290, vwx300)
new_esEs12(vwx291, vwx301, app(app(ty_Either, ce), cf)) → new_esEs5(vwx291, vwx301, ce, cf)
new_esEs16([], :(vwx300, vwx301), gf) → False
new_esEs16(:(vwx290, vwx291), [], gf) → False
new_ltEs17(@3(vwx3000, vwx3001, vwx3002), @3(vwx31000, vwx31001, vwx31002), ccf, ccg, cch) → new_pePe(new_lt20(vwx3000, vwx31000, ccf), vwx3000, vwx31000, new_pePe(new_lt19(vwx3001, vwx31001, ccg), vwx3001, vwx31001, new_ltEs19(vwx3002, vwx31002, cch), ccg), ccf)
new_compare29(vwx3000, vwx31000, gd) → new_compare26(vwx3000, vwx31000, new_esEs4(vwx3000, vwx31000, gd), gd)
new_ltEs6(Just(vwx3000), Just(vwx31000), ty_Ordering) → new_ltEs15(vwx3000, vwx31000)
new_pePe(True, vwx29, vwx30, vwx31, bch) → True
new_primPlusNat1(Succ(vwx590), vwx3100100) → Succ(Succ(new_primPlusNat0(vwx590, vwx3100100)))
new_ltEs20(vwx300, vwx3100, app(ty_Maybe, eh)) → new_ltEs6(vwx300, vwx3100, eh)
new_compare30(vwx3000, vwx31000, app(ty_Maybe, cad)) → new_compare29(vwx3000, vwx31000, cad)
new_lt5(vwx3000, vwx31000) → new_esEs8(new_compare6(vwx3000, vwx31000))
new_esEs21(vwx290, vwx300, ty_Char) → new_esEs17(vwx290, vwx300)
new_primCmpInt(Neg(Zero), Neg(Succ(vwx310000))) → new_primCmpNat0(Succ(vwx310000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(vwx310000))) → GT
new_ltEs6(Just(vwx3000), Just(vwx31000), app(ty_[], fb)) → new_ltEs12(vwx3000, vwx31000, fb)
new_esEs25(vwx290, vwx300, ty_Integer) → new_esEs14(vwx290, vwx300)
new_compare19(vwx3000, vwx31000, True, bd, be) → LT
new_compare30(vwx3000, vwx31000, app(app(ty_Either, cae), caf)) → new_compare5(vwx3000, vwx31000, cae, caf)
new_esEs4(Just(vwx290), Just(vwx300), app(ty_[], cca)) → new_esEs16(vwx290, vwx300, cca)
new_sr0(vwx3000, vwx31001) → new_primMulInt(vwx3000, vwx31001)
new_esEs5(Right(vwx290), Right(vwx300), bda, app(app(app(ty_@3, bhf), bhg), bhh)) → new_esEs7(vwx290, vwx300, bhf, bhg, bhh)
new_lt7(vwx3000, vwx31000, bd, be) → new_esEs8(new_compare9(vwx3000, vwx31000, bd, be))
new_esEs13(vwx290, vwx300, app(app(ty_@2, df), dg)) → new_esEs6(vwx290, vwx300, df, dg)
new_ltEs19(vwx3002, vwx31002, ty_Int) → new_ltEs11(vwx3002, vwx31002)
new_compare30(vwx3000, vwx31000, ty_Float) → new_compare8(vwx3000, vwx31000)
new_esEs21(vwx290, vwx300, ty_Float) → new_esEs18(vwx290, vwx300)
new_lt19(vwx3001, vwx31001, app(app(ty_Either, cef), ceg)) → new_lt4(vwx3001, vwx31001, cef, ceg)
new_ltEs4(Left(vwx3000), Left(vwx31000), ty_Integer, bab) → new_ltEs7(vwx3000, vwx31000)
new_esEs13(vwx290, vwx300, ty_Float) → new_esEs18(vwx290, vwx300)
new_esEs21(vwx290, vwx300, app(ty_Maybe, hc)) → new_esEs4(vwx290, vwx300, hc)
new_esEs9(True, False) → False
new_esEs9(False, True) → False
new_esEs5(Left(vwx290), Left(vwx300), ty_Int, bdb) → new_esEs10(vwx290, vwx300)
new_ltEs18(vwx3001, vwx31001, ty_Int) → new_ltEs11(vwx3001, vwx31001)
new_ltEs13(vwx300, vwx3100) → new_not(new_compare32(vwx300, vwx3100))
new_primCompAux0(vwx3000, vwx31000, vwx41, caa) → new_primCompAux00(vwx41, new_compare30(vwx3000, vwx31000, caa))
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs24(vwx291, vwx301, app(app(app(ty_@3, dah), dba), dbb)) → new_esEs7(vwx291, vwx301, dah, dba, dbb)
new_ltEs4(Right(vwx3000), Right(vwx31000), bbe, app(ty_[], bbg)) → new_ltEs12(vwx3000, vwx31000, bbg)
new_esEs12(vwx291, vwx301, ty_Ordering) → new_esEs11(vwx291, vwx301)
new_esEs24(vwx291, vwx301, ty_Int) → new_esEs10(vwx291, vwx301)
new_esEs15(@0, @0) → True
new_esEs12(vwx291, vwx301, app(ty_Maybe, cg)) → new_esEs4(vwx291, vwx301, cg)
new_asAs(False, vwx40) → False
new_primMulInt(Pos(vwx30000), Neg(vwx310010)) → Neg(new_primMulNat0(vwx30000, vwx310010))
new_primMulInt(Neg(vwx30000), Pos(vwx310010)) → Neg(new_primMulNat0(vwx30000, vwx310010))
new_primMulNat0(Succ(vwx300000), Zero) → Zero
new_primMulNat0(Zero, Succ(vwx3100100)) → Zero
new_compare30(vwx3000, vwx31000, ty_Integer) → new_compare17(vwx3000, vwx31000)
new_esEs21(vwx290, vwx300, app(app(ty_Either, ha), hb)) → new_esEs5(vwx290, vwx300, ha, hb)
new_esEs13(vwx290, vwx300, ty_Bool) → new_esEs9(vwx290, vwx300)
new_esEs12(vwx291, vwx301, app(ty_Ratio, db)) → new_esEs19(vwx291, vwx301, db)
new_lt19(vwx3001, vwx31001, ty_Ordering) → new_lt18(vwx3001, vwx31001)
new_ltEs20(vwx300, vwx3100, ty_Integer) → new_ltEs7(vwx300, vwx3100)
new_compare17(Integer(vwx3000), Integer(vwx31000)) → new_primCmpInt(vwx3000, vwx31000)
new_ltEs4(Left(vwx3000), Left(vwx31000), ty_@0, bab) → new_ltEs13(vwx3000, vwx31000)
new_esEs24(vwx291, vwx301, app(ty_[], daf)) → new_esEs16(vwx291, vwx301, daf)
new_compare110(vwx3000, vwx31000, True, bf, bg, bh) → LT
new_not(EQ) → new_not0
new_ltEs4(Right(vwx3000), Right(vwx31000), bbe, ty_@0) → new_ltEs13(vwx3000, vwx31000)
new_compare18(:%(vwx3000, vwx3001), :%(vwx31000, vwx31001), ty_Integer) → new_compare17(new_sr(vwx3000, vwx31001), new_sr(vwx31000, vwx3001))
new_compare27(vwx3000, vwx31000, True) → EQ
new_lt10(vwx3000, vwx31000, app(ty_Maybe, gd)) → new_lt16(vwx3000, vwx31000, gd)
new_esEs5(Left(vwx290), Left(vwx300), ty_@0, bdb) → new_esEs15(vwx290, vwx300)
new_esEs9(False, False) → True
new_compare28(vwx3000, vwx31000, False, bd, be) → new_compare19(vwx3000, vwx31000, new_ltEs16(vwx3000, vwx31000, bd, be), bd, be)
new_esEs24(vwx291, vwx301, ty_Integer) → new_esEs14(vwx291, vwx301)
new_ltEs6(Nothing, Nothing, eh) → True
new_esEs12(vwx291, vwx301, ty_Int) → new_esEs10(vwx291, vwx301)
new_lt10(vwx3000, vwx31000, ty_Int) → new_lt5(vwx3000, vwx31000)
new_esEs25(vwx290, vwx300, app(app(app(ty_@3, dcb), dcc), dcd)) → new_esEs7(vwx290, vwx300, dcb, dcc, dcd)
new_lt17(vwx3000, vwx31000) → new_esEs8(new_compare8(vwx3000, vwx31000))
new_esEs5(Right(vwx290), Right(vwx300), bda, app(ty_Maybe, bhc)) → new_esEs4(vwx290, vwx300, bhc)
new_esEs16([], [], gf) → True
new_compare11(vwx3000, vwx31000, False) → GT
new_ltEs4(Right(vwx3000), Right(vwx31000), bbe, ty_Float) → new_ltEs5(vwx3000, vwx31000)
new_ltEs18(vwx3001, vwx31001, ty_Double) → new_ltEs14(vwx3001, vwx31001)
new_not(LT) → new_not0
new_lt10(vwx3000, vwx31000, ty_Char) → new_lt6(vwx3000, vwx31000)
new_compare11(vwx3000, vwx31000, True) → LT
new_ltEs18(vwx3001, vwx31001, ty_Ordering) → new_ltEs15(vwx3001, vwx31001)
new_esEs5(Left(vwx290), Left(vwx300), app(app(ty_Either, bfg), bfh), bdb) → new_esEs5(vwx290, vwx300, bfg, bfh)
new_ltEs18(vwx3001, vwx31001, app(ty_Maybe, bed)) → new_ltEs6(vwx3001, vwx31001, bed)
new_ltEs19(vwx3002, vwx31002, app(app(app(ty_@3, cdh), cea), ceb)) → new_ltEs17(vwx3002, vwx31002, cdh, cea, ceb)
new_lt20(vwx3000, vwx31000, ty_Bool) → new_lt12(vwx3000, vwx31000)
new_ltEs6(Just(vwx3000), Just(vwx31000), ty_Float) → new_ltEs5(vwx3000, vwx31000)
new_lt19(vwx3001, vwx31001, app(app(ty_@2, ceh), cfa)) → new_lt7(vwx3001, vwx31001, ceh, cfa)
new_ltEs19(vwx3002, vwx31002, ty_Integer) → new_ltEs7(vwx3002, vwx31002)
new_esEs24(vwx291, vwx301, ty_Bool) → new_esEs9(vwx291, vwx301)
new_esEs8(EQ) → False
new_primPlusNat0(Succ(vwx5900), Succ(vwx31001000)) → Succ(Succ(new_primPlusNat0(vwx5900, vwx31001000)))
new_esEs23(vwx292, vwx302, app(ty_[], chd)) → new_esEs16(vwx292, vwx302, chd)
new_compare15(vwx3000, vwx31000, True, gd) → LT
new_ltEs19(vwx3002, vwx31002, app(app(ty_@2, cdf), cdg)) → new_ltEs16(vwx3002, vwx31002, cdf, cdg)
new_esEs27(vwx290, vwx300, ty_Integer) → new_esEs14(vwx290, vwx300)
new_lt11(vwx3000, vwx31000) → new_esEs8(new_compare17(vwx3000, vwx31000))
new_asAs(True, vwx40) → vwx40
new_ltEs15(GT, EQ) → False
new_ltEs6(Just(vwx3000), Just(vwx31000), ty_Char) → new_ltEs10(vwx3000, vwx31000)
new_esEs11(LT, LT) → True
new_esEs27(vwx290, vwx300, ty_Int) → new_esEs10(vwx290, vwx300)
new_esEs23(vwx292, vwx302, ty_Int) → new_esEs10(vwx292, vwx302)
new_esEs12(vwx291, vwx301, ty_Double) → new_esEs20(vwx291, vwx301)
new_esEs21(vwx290, vwx300, ty_Int) → new_esEs10(vwx290, vwx300)
new_lt6(vwx3000, vwx31000) → new_esEs8(new_compare7(vwx3000, vwx31000))
new_ltEs18(vwx3001, vwx31001, app(ty_[], bec)) → new_ltEs12(vwx3001, vwx31001, bec)
new_lt10(vwx3000, vwx31000, app(ty_Ratio, baa)) → new_lt9(vwx3000, vwx31000, baa)
new_esEs4(Just(vwx290), Just(vwx300), app(app(app(ty_@3, ccc), ccd), cce)) → new_esEs7(vwx290, vwx300, ccc, ccd, cce)
new_ltEs4(Left(vwx3000), Left(vwx31000), ty_Bool, bab) → new_ltEs8(vwx3000, vwx31000)
new_esEs11(GT, EQ) → False
new_esEs11(EQ, GT) → False
new_ltEs20(vwx300, vwx3100, ty_@0) → new_ltEs13(vwx300, vwx3100)
new_esEs5(Left(vwx290), Left(vwx300), ty_Bool, bdb) → new_esEs9(vwx290, vwx300)
new_compare19(vwx3000, vwx31000, False, bd, be) → GT
new_lt8(vwx3000, vwx31000, bf, bg, bh) → new_esEs8(new_compare12(vwx3000, vwx31000, bf, bg, bh))
new_compare110(vwx3000, vwx31000, False, bf, bg, bh) → GT
new_esEs12(vwx291, vwx301, ty_Float) → new_esEs18(vwx291, vwx301)
new_ltEs20(vwx300, vwx3100, ty_Char) → new_ltEs10(vwx300, vwx3100)
new_ltEs20(vwx300, vwx3100, app(app(ty_@2, bdh), bea)) → new_ltEs16(vwx300, vwx3100, bdh, bea)
new_esEs22(vwx29, vwx30, app(app(ty_Either, bda), bdb)) → new_esEs5(vwx29, vwx30, bda, bdb)
new_esEs10(vwx29, vwx30) → new_primEqInt(vwx29, vwx30)
new_primCompAux00(vwx45, GT) → GT
new_esEs13(vwx290, vwx300, app(app(app(ty_@3, ee), ef), eg)) → new_esEs7(vwx290, vwx300, ee, ef, eg)
new_esEs21(vwx290, vwx300, app(ty_[], hd)) → new_esEs16(vwx290, vwx300, hd)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_ltEs6(Just(vwx3000), Just(vwx31000), ty_Integer) → new_ltEs7(vwx3000, vwx31000)
new_lt10(vwx3000, vwx31000, ty_Ordering) → new_lt18(vwx3000, vwx31000)
new_esEs5(Left(vwx290), Left(vwx300), ty_Float, bdb) → new_esEs18(vwx290, vwx300)
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_esEs12(vwx291, vwx301, app(app(ty_@2, cc), cd)) → new_esEs6(vwx291, vwx301, cc, cd)
new_primCmpInt(Neg(Succ(vwx30000)), Pos(vwx31000)) → LT
new_compare16(vwx3000, vwx31000, False) → GT
new_esEs5(Left(vwx290), Left(vwx300), ty_Char, bdb) → new_esEs17(vwx290, vwx300)
new_esEs13(vwx290, vwx300, ty_Int) → new_esEs10(vwx290, vwx300)

The set Q consists of the following terms:

new_ltEs19(x0, x1, ty_Double)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primPlusNat1(Zero, x0)
new_ltEs18(x0, x1, ty_@0)
new_ltEs20(x0, x1, app(ty_[], x2))
new_esEs13(x0, x1, ty_Ordering)
new_esEs21(x0, x1, ty_Ordering)
new_lt10(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs20(x0, x1, ty_Float)
new_esEs13(x0, x1, ty_Integer)
new_ltEs19(x0, x1, ty_Int)
new_esEs22(x0, x1, ty_Char)
new_lt10(x0, x1, ty_Int)
new_ltEs19(x0, x1, ty_Integer)
new_ltEs5(x0, x1)
new_lt19(x0, x1, ty_Bool)
new_compare7(Char(x0), Char(x1))
new_ltEs4(Right(x0), Right(x1), x2, ty_Char)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs27(x0, x1, ty_Integer)
new_primCmpNat0(Succ(x0), Zero)
new_esEs5(Left(x0), Left(x1), ty_Double, x2)
new_lt10(x0, x1, ty_Ordering)
new_esEs23(x0, x1, ty_Float)
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_max1(Nothing, Nothing, x0)
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs13(x0, x1, app(ty_Ratio, x2))
new_esEs5(Right(x0), Right(x1), x2, ty_Double)
new_esEs5(Right(x0), Right(x1), x2, ty_Integer)
new_esEs4(Just(x0), Just(x1), ty_Char)
new_lt19(x0, x1, ty_Float)
new_compare210(x0, x1, False, x2, x3, x4)
new_esEs12(x0, x1, app(ty_Maybe, x2))
new_compare30(x0, x1, ty_Ordering)
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_primPlusNat0(Zero, Succ(x0))
new_esEs4(Nothing, Nothing, x0)
new_esEs5(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_lt10(x0, x1, ty_Char)
new_lt19(x0, x1, app(ty_Ratio, x2))
new_ltEs4(Right(x0), Right(x1), x2, ty_Ordering)
new_ltEs4(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs8(LT)
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_esEs24(x0, x1, ty_Integer)
new_esEs13(x0, x1, ty_Char)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_ltEs6(Nothing, Nothing, x0)
new_compare25(x0, x1, True)
new_ltEs6(Just(x0), Just(x1), ty_Ordering)
new_esEs13(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs18(x0, x1, ty_Char)
new_lt20(x0, x1, ty_Float)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_lt8(x0, x1, x2, x3, x4)
new_ltEs4(Left(x0), Left(x1), ty_Float, x2)
new_compare210(x0, x1, True, x2, x3, x4)
new_lt10(x0, x1, ty_Double)
new_primPlusNat1(Succ(x0), x1)
new_esEs5(Left(x0), Left(x1), ty_Int, x2)
new_ltEs6(Just(x0), Just(x1), ty_Float)
new_ltEs8(True, True)
new_compare(:(x0, x1), :(x2, x3), x4)
new_ltEs6(Just(x0), Just(x1), ty_Integer)
new_esEs4(Nothing, Just(x0), x1)
new_esEs4(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_lt18(x0, x1)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs24(x0, x1, ty_Ordering)
new_lt19(x0, x1, ty_Ordering)
new_ltEs19(x0, x1, ty_Char)
new_ltEs6(Nothing, Just(x0), x1)
new_esEs5(Left(x0), Left(x1), ty_Bool, x2)
new_esEs11(GT, EQ)
new_esEs11(EQ, GT)
new_compare28(x0, x1, False, x2, x3)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs6(Just(x0), Just(x1), ty_Int)
new_ltEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt10(x0, x1, app(ty_[], x2))
new_primMulInt(Neg(x0), Neg(x1))
new_primMulNat0(Succ(x0), Zero)
new_ltEs18(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, ty_Char)
new_ltEs18(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_lt20(x0, x1, ty_Double)
new_ltEs18(x0, x1, ty_Float)
new_primPlusNat0(Succ(x0), Zero)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, ty_Bool)
new_primEqNat0(Zero, Zero)
new_esEs4(Just(x0), Just(x1), ty_Int)
new_lt19(x0, x1, ty_@0)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_primCompAux00(x0, LT)
new_lt10(x0, x1, ty_Float)
new_max1(Just(x0), Nothing, x1)
new_esEs13(x0, x1, app(ty_Maybe, x2))
new_esEs4(Just(x0), Just(x1), ty_Bool)
new_ltEs19(x0, x1, app(ty_[], x2))
new_esEs12(x0, x1, ty_Double)
new_ltEs6(Just(x0), Just(x1), ty_Double)
new_esEs9(True, True)
new_esEs5(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_ltEs4(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs4(Just(x0), Just(x1), app(ty_[], x2))
new_esEs8(EQ)
new_ltEs18(x0, x1, app(app(ty_Either, x2), x3))
new_lt16(x0, x1, x2)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_esEs5(Left(x0), Left(x1), ty_Ordering, x2)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_compare11(x0, x1, True)
new_primMulNat0(Zero, Zero)
new_esEs22(x0, x1, ty_@0)
new_esEs4(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_ltEs6(Just(x0), Just(x1), ty_@0)
new_compare16(x0, x1, True)
new_esEs6(@2(x0, x1), @2(x2, x3), x4, x5)
new_sr(Integer(x0), Integer(x1))
new_compare30(x0, x1, app(ty_[], x2))
new_esEs25(x0, x1, ty_Double)
new_compare26(x0, x1, False, x2)
new_esEs22(x0, x1, ty_Ordering)
new_lt10(x0, x1, app(ty_Ratio, x2))
new_ltEs19(x0, x1, ty_Float)
new_esEs5(Right(x0), Right(x1), x2, ty_Float)
new_ltEs6(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_ltEs4(Right(x0), Right(x1), x2, ty_Int)
new_ltEs20(x0, x1, ty_Bool)
new_esEs5(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs5(Left(x0), Left(x1), ty_@0, x2)
new_max1(Just(x0), Just(x1), x2)
new_esEs12(x0, x1, app(ty_[], x2))
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs23(x0, x1, ty_Int)
new_esEs12(x0, x1, ty_Ordering)
new_esEs25(x0, x1, ty_@0)
new_lt9(x0, x1, x2)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs11(LT, GT)
new_esEs11(GT, LT)
new_compare30(x0, x1, ty_Float)
new_esEs24(x0, x1, ty_Double)
new_esEs16(:(x0, x1), [], x2)
new_ltEs15(GT, EQ)
new_ltEs15(EQ, GT)
new_compare18(:%(x0, x1), :%(x2, x3), ty_Int)
new_ltEs4(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs13(x0, x1, ty_Bool)
new_esEs5(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs5(Right(x0), Right(x1), x2, app(ty_[], x3))
new_compare25(x0, x1, False)
new_esEs13(x0, x1, ty_Double)
new_ltEs18(x0, x1, app(ty_Maybe, x2))
new_compare13(x0, x1)
new_compare30(x0, x1, ty_Char)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs21(x0, x1, ty_Float)
new_compare5(x0, x1, x2, x3)
new_primPlusNat0(Succ(x0), Succ(x1))
new_ltEs4(Left(x0), Left(x1), ty_Int, x2)
new_asAs(True, x0)
new_esEs23(x0, x1, app(ty_[], x2))
new_compare30(x0, x1, app(app(ty_@2, x2), x3))
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_ltEs4(Left(x0), Right(x1), x2, x3)
new_esEs25(x0, x1, ty_Int)
new_ltEs4(Right(x0), Left(x1), x2, x3)
new_ltEs16(@2(x0, x1), @2(x2, x3), x4, x5)
new_compare26(x0, x1, True, x2)
new_esEs4(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_primMulInt(Pos(x0), Pos(x1))
new_max1(Nothing, Just(x0), x1)
new_ltEs4(Right(x0), Right(x1), x2, ty_Float)
new_ltEs17(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs4(Left(x0), Left(x1), ty_Double, x2)
new_esEs7(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs12(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs15(LT, GT)
new_ltEs15(GT, LT)
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs15(GT, GT)
new_primMulNat0(Zero, Succ(x0))
new_esEs11(LT, LT)
new_primEqNat0(Zero, Succ(x0))
new_esEs4(Just(x0), Just(x1), app(ty_Ratio, x2))
new_not0
new_lt19(x0, x1, ty_Double)
new_primPlusNat0(Zero, Zero)
new_lt20(x0, x1, ty_Int)
new_compare19(x0, x1, True, x2, x3)
new_compare31(x0, x1)
new_compare9(x0, x1, x2, x3)
new_compare32(@0, @0)
new_esEs14(Integer(x0), Integer(x1))
new_ltEs20(x0, x1, ty_@0)
new_lt14(x0, x1)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_lt6(x0, x1)
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_compare12(x0, x1, x2, x3, x4)
new_esEs12(x0, x1, app(app(ty_Either, x2), x3))
new_esEs12(x0, x1, ty_Char)
new_esEs24(x0, x1, ty_Int)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_esEs24(x0, x1, ty_Float)
new_esEs12(x0, x1, app(app(ty_@2, x2), x3))
new_compare30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, ty_Int)
new_ltEs4(Right(x0), Right(x1), x2, ty_@0)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs15(LT, LT)
new_esEs17(Char(x0), Char(x1))
new_esEs5(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs4(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_ltEs6(Just(x0), Just(x1), app(ty_Ratio, x2))
new_ltEs4(Right(x0), Right(x1), x2, ty_Integer)
new_ltEs4(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_lt19(x0, x1, app(ty_[], x2))
new_esEs5(Right(x0), Right(x1), x2, ty_Int)
new_esEs18(Float(x0, x1), Float(x2, x3))
new_esEs13(x0, x1, app(app(ty_@2, x2), x3))
new_compare15(x0, x1, False, x2)
new_compare([], :(x0, x1), x2)
new_compare6(x0, x1)
new_compare30(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpNat0(Zero, Succ(x0))
new_esEs12(x0, x1, ty_Float)
new_esEs22(x0, x1, ty_Bool)
new_not(GT)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_ltEs8(False, False)
new_esEs8(GT)
new_ltEs18(x0, x1, ty_Integer)
new_ltEs10(x0, x1)
new_esEs25(x0, x1, app(ty_[], x2))
new_esEs12(x0, x1, app(ty_Ratio, x2))
new_esEs20(Double(x0, x1), Double(x2, x3))
new_esEs25(x0, x1, ty_Integer)
new_primEqInt(Neg(Zero), Pos(Zero))
new_primEqInt(Pos(Zero), Neg(Zero))
new_ltEs4(Left(x0), Left(x1), ty_Ordering, x2)
new_ltEs8(False, True)
new_ltEs8(True, False)
new_esEs5(Left(x0), Left(x1), ty_Char, x2)
new_lt20(x0, x1, ty_Ordering)
new_esEs12(x0, x1, ty_Bool)
new_lt19(x0, x1, ty_Integer)
new_esEs16([], :(x0, x1), x2)
new_compare(:(x0, x1), [], x2)
new_ltEs4(Right(x0), Right(x1), x2, ty_Double)
new_esEs5(Right(x0), Right(x1), x2, ty_@0)
new_esEs21(x0, x1, ty_Integer)
new_compare15(x0, x1, True, x2)
new_lt10(x0, x1, ty_Integer)
new_compare27(x0, x1, False)
new_esEs11(LT, EQ)
new_esEs11(EQ, LT)
new_ltEs20(x0, x1, ty_Ordering)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs24(x0, x1, ty_Bool)
new_esEs26(x0, x1, ty_Int)
new_esEs22(x0, x1, app(ty_[], x2))
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, ty_Ordering)
new_primEqInt(Neg(Zero), Neg(Zero))
new_lt19(x0, x1, ty_Char)
new_esEs5(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_compare24(x0, x1, False, x2, x3)
new_esEs10(x0, x1)
new_ltEs12(x0, x1, x2)
new_esEs5(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_compare28(x0, x1, True, x2, x3)
new_compare30(x0, x1, ty_Double)
new_ltEs4(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs4(Just(x0), Just(x1), app(ty_Maybe, x2))
new_ltEs4(Right(x0), Right(x1), x2, ty_Bool)
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs20(x0, x1, ty_Char)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_ltEs19(x0, x1, ty_Bool)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_ltEs4(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs5(Left(x0), Left(x1), ty_Integer, x2)
new_lt12(x0, x1)
new_esEs5(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs13(x0, x1, ty_Int)
new_esEs16(:(x0, x1), :(x2, x3), x4)
new_ltEs18(x0, x1, ty_Bool)
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_lt7(x0, x1, x2, x3)
new_ltEs18(x0, x1, ty_Ordering)
new_primEqNat0(Succ(x0), Zero)
new_compare27(x0, x1, True)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_max10(x0, x1, True, x2)
new_lt20(x0, x1, ty_@0)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_esEs24(x0, x1, app(ty_[], x2))
new_esEs5(Left(x0), Right(x1), x2, x3)
new_esEs5(Right(x0), Left(x1), x2, x3)
new_ltEs4(Left(x0), Left(x1), ty_Integer, x2)
new_ltEs6(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_compare8(Float(x0, x1), Float(x2, x3))
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_primCmpNat0(Zero, Zero)
new_lt20(x0, x1, ty_Bool)
new_compare11(x0, x1, False)
new_ltEs4(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs6(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_lt13(x0, x1, x2)
new_ltEs20(x0, x1, ty_Integer)
new_compare110(x0, x1, False, x2, x3, x4)
new_ltEs9(x0, x1, x2)
new_lt10(x0, x1, ty_@0)
new_esEs23(x0, x1, ty_Double)
new_esEs9(False, False)
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_esEs15(@0, @0)
new_esEs21(x0, x1, ty_@0)
new_lt4(x0, x1, x2, x3)
new_ltEs4(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs24(x0, x1, ty_Char)
new_esEs25(x0, x1, ty_Ordering)
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, ty_Double)
new_compare10(x0, x1, False, x2, x3)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, ty_Int)
new_primMulNat0(Succ(x0), Succ(x1))
new_lt10(x0, x1, app(ty_Maybe, x2))
new_esEs5(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs4(Just(x0), Just(x1), ty_@0)
new_esEs21(x0, x1, ty_Double)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_lt5(x0, x1)
new_compare24(x0, x1, True, x2, x3)
new_ltEs6(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs27(x0, x1, ty_Int)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare30(x0, x1, ty_@0)
new_ltEs6(Just(x0), Just(x1), ty_Char)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs22(x0, x1, ty_Float)
new_esEs16([], [], x0)
new_esEs5(Left(x0), Left(x1), ty_Float, x2)
new_esEs21(x0, x1, app(ty_[], x2))
new_esEs11(GT, GT)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, ty_Char)
new_lt19(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, ty_Integer)
new_primCompAux0(x0, x1, x2, x3)
new_compare30(x0, x1, app(app(ty_Either, x2), x3))
new_compare([], [], x0)
new_not(EQ)
new_esEs4(Just(x0), Just(x1), ty_Ordering)
new_esEs4(Just(x0), Nothing, x1)
new_esEs13(x0, x1, ty_Float)
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_esEs21(x0, x1, ty_Char)
new_compare10(x0, x1, True, x2, x3)
new_primCompAux00(x0, GT)
new_ltEs4(Left(x0), Left(x1), ty_@0, x2)
new_lt10(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_ltEs18(x0, x1, ty_Int)
new_compare29(x0, x1, x2)
new_esEs12(x0, x1, ty_@0)
new_compare19(x0, x1, False, x2, x3)
new_esEs12(x0, x1, ty_Int)
new_esEs5(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_lt19(x0, x1, ty_Int)
new_esEs22(x0, x1, ty_Int)
new_compare16(x0, x1, False)
new_ltEs4(Left(x0), Left(x1), ty_Bool, x2)
new_esEs22(x0, x1, ty_Integer)
new_pePe(False, x0, x1, x2, x3)
new_esEs21(x0, x1, ty_Bool)
new_ltEs6(Just(x0), Just(x1), ty_Bool)
new_asAs(False, x0)
new_esEs5(Right(x0), Right(x1), x2, ty_Ordering)
new_ltEs18(x0, x1, app(ty_Ratio, x2))
new_lt15(x0, x1)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_ltEs14(x0, x1)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs15(EQ, LT)
new_ltEs15(LT, EQ)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_max10(x0, x1, False, x2)
new_esEs23(x0, x1, ty_@0)
new_ltEs19(x0, x1, ty_@0)
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs7(x0, x1)
new_compare30(x0, x1, ty_Bool)
new_compare14(Double(x0, x1), Double(x2, x3))
new_lt11(x0, x1)
new_esEs9(False, True)
new_esEs9(True, False)
new_esEs4(Just(x0), Just(x1), ty_Double)
new_lt20(x0, x1, ty_Integer)
new_esEs5(Right(x0), Right(x1), x2, ty_Char)
new_ltEs15(EQ, EQ)
new_esEs5(Right(x0), Right(x1), x2, ty_Bool)
new_esEs25(x0, x1, ty_Float)
new_ltEs4(Left(x0), Left(x1), ty_Char, x2)
new_compare30(x0, x1, ty_Int)
new_esEs4(Just(x0), Just(x1), ty_Integer)
new_compare30(x0, x1, app(ty_Maybe, x2))
new_lt17(x0, x1)
new_esEs13(x0, x1, app(ty_[], x2))
new_ltEs4(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_lt20(x0, x1, app(ty_[], x2))
new_ltEs6(Just(x0), Just(x1), app(ty_[], x2))
new_compare30(x0, x1, ty_Integer)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs19(:%(x0, x1), :%(x2, x3), x4)
new_esEs25(x0, x1, ty_Bool)
new_esEs24(x0, x1, ty_@0)
new_ltEs11(x0, x1)
new_esEs13(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, ty_Double)
new_primEqInt(Pos(Zero), Pos(Zero))
new_esEs11(EQ, EQ)
new_sr0(x0, x1)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_ltEs4(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_lt10(x0, x1, app(app(ty_@2, x2), x3))
new_esEs4(Just(x0), Just(x1), ty_Float)
new_esEs12(x0, x1, ty_Integer)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primCmpNat0(Succ(x0), Succ(x1))
new_ltEs19(x0, x1, ty_Ordering)
new_esEs23(x0, x1, ty_Char)
new_ltEs6(Just(x0), Nothing, x1)
new_esEs5(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs13(x0, x1)
new_compare110(x0, x1, True, x2, x3, x4)
new_pePe(True, x0, x1, x2, x3)
new_compare17(Integer(x0), Integer(x1))
new_not(LT)
new_compare18(:%(x0, x1), :%(x2, x3), ty_Integer)
new_ltEs4(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs23(x0, x1, ty_Integer)
new_ltEs18(x0, x1, ty_Double)
new_lt10(x0, x1, ty_Bool)
new_esEs13(x0, x1, ty_@0)
new_primCompAux00(x0, 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: