YES 3.087 H-Termination proof of /home/matraf/haskell/eval_FullyBlown_Fast/empty.hs
H-Termination of the given Haskell-Program with start terms could successfully be proven:



↳ HASKELL
  ↳ CR

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

module Main where
  import qualified Prelude


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

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



↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ IFR

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

module Main where
  import qualified Prelude


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

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

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

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



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

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

module Main where
  import qualified Prelude


Replaced joker patterns by fresh variables and removed binding patterns.

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

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

module Main where
  import qualified Prelude


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

is transformed to
compare x y = compare3 x y

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

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

compare0 x y True = GT

compare3 x y = compare2 x y (x == y)

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

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

gcd'0 x y = gcd' y (x `rem` y)

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

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

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

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

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

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

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

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

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

is transformed to
absReal x = absReal2 x

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

absReal0 x True = `negate` x

absReal2 x = absReal1 x (x >= 0)

The following Function with conditions
undefined 
 | False
 = undefined

is transformed to
undefined  = undefined1

undefined0 True = undefined

undefined1  = undefined0 False

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

is transformed to
reduce x y = reduce2 x y

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



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

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

module Main where
  import qualified Prelude


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

are unpacked to the following functions on top level
reduce2Reduce0 vwv vww x y True = x `quot` reduce2D vwv vww :% (y `quot` reduce2D vwv vww)

reduce2D vwv vww = gcd vwv vww

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

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

are unpacked to the following functions on top level
gcd0Gcd'1 True x zx = x
gcd0Gcd'1 zy zz vuu = gcd0Gcd'0 zz vuu

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

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

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



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

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

module Main where
  import qualified Prelude


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

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

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

module Main where
  import qualified Prelude


Haskell To QDPs


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

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

new_primPlusNat(Succ(vwx5100), Succ(vwx400000)) → new_primPlusNat(vwx5100, vwx400000)

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

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



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

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

new_primMulNat(Succ(vwx30000), Succ(vwx40000)) → new_primMulNat(vwx30000, Succ(vwx40000))

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

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



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

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

new_primEqNat(Succ(vwx3000), Succ(vwx4000)) → new_primEqNat(vwx3000, vwx4000)

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

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



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

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

new_primCmpNat(Succ(vwx1700), Succ(vwx1800)) → new_primCmpNat(vwx1700, vwx1800)

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

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



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

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

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

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

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



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

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

new_ltEs0(@3(vwx170, vwx171, vwx172), @3(vwx180, vwx181, vwx182), df, app(ty_Maybe, gc), fc) → new_lt3(vwx171, vwx181, gc)
new_lt3(vwx170, vwx180, de) → new_compare22(vwx170, vwx180, new_esEs7(vwx170, vwx180, de), de)
new_lt(vwx170, vwx180, cc, cd) → new_compare2(vwx170, vwx180, new_esEs4(vwx170, vwx180, cc, cd), cc, cd)
new_ltEs1(:(vwx170, vwx171), :(vwx180, vwx181), he) → new_compare(vwx171, vwx181, he)
new_compare2(vwx170, vwx180, False, cc, cd) → new_ltEs(vwx170, vwx180, cc, cd)
new_ltEs(@2(vwx170, vwx171), @2(vwx180, vwx181), app(app(app(ty_@3, cf), cg), da), ce) → new_compare20(vwx170, vwx180, new_esEs5(vwx170, vwx180, cf, cg, da), cf, cg, da)
new_ltEs(@2(vwx170, vwx171), @2(vwx180, vwx181), ba, app(ty_[], bg)) → new_ltEs1(vwx171, vwx181, bg)
new_ltEs3(Just(vwx170), Just(vwx180), app(app(app(ty_@3, bde), bdf), bdg)) → new_ltEs0(vwx170, vwx180, bde, bdf, bdg)
new_ltEs0(@3(vwx170, vwx171, vwx172), @3(vwx180, vwx181, vwx182), app(app(app(ty_@3, gf), gg), gh), dg, fc) → new_lt0(vwx170, vwx180, gf, gg, gh)
new_ltEs2(Left(vwx170), Left(vwx180), app(app(ty_Either, bbf), bbg), bba) → new_ltEs2(vwx170, vwx180, bbf, bbg)
new_ltEs0(@3(vwx170, vwx171, vwx172), @3(vwx180, vwx181, vwx182), df, dg, app(app(ty_@2, dh), ea)) → new_ltEs(vwx172, vwx182, dh, ea)
new_ltEs0(@3(vwx170, vwx171, vwx172), @3(vwx180, vwx181, vwx182), app(app(ty_Either, hb), hc), dg, fc) → new_lt2(vwx170, vwx180, hb, hc)
new_ltEs0(@3(vwx170, vwx171, vwx172), @3(vwx180, vwx181, vwx182), df, app(app(ty_Either, ga), gb), fc) → new_lt2(vwx171, vwx181, ga, gb)
new_ltEs0(@3(vwx170, vwx171, vwx172), @3(vwx180, vwx181, vwx182), app(ty_Maybe, hd), dg, fc) → new_lt3(vwx170, vwx180, hd)
new_ltEs(@2(vwx170, vwx171), @2(vwx180, vwx181), ba, app(app(ty_Either, bh), ca)) → new_ltEs2(vwx171, vwx181, bh, ca)
new_compare5(vwx170, vwx180, de) → new_compare22(vwx170, vwx180, new_esEs7(vwx170, vwx180, de), de)
new_ltEs2(Left(vwx170), Left(vwx180), app(ty_Maybe, bbh), bba) → new_ltEs3(vwx170, vwx180, bbh)
new_ltEs(@2(vwx170, vwx171), @2(vwx180, vwx181), ba, app(ty_Maybe, cb)) → new_ltEs3(vwx171, vwx181, cb)
new_primCompAux(vwx170, vwx180, vwx75, app(ty_[], bac)) → new_compare(vwx170, vwx180, bac)
new_ltEs2(Right(vwx170), Right(vwx180), bca, app(app(app(ty_@3, bcd), bce), bcf)) → new_ltEs0(vwx170, vwx180, bcd, bce, bcf)
new_ltEs(@2(vwx170, vwx171), @2(vwx180, vwx181), app(ty_[], db), ce) → new_compare(vwx170, vwx180, db)
new_compare22(vwx170, vwx180, False, de) → new_ltEs3(vwx170, vwx180, de)
new_ltEs2(Left(vwx170), Left(vwx180), app(app(ty_@2, bag), bah), bba) → new_ltEs(vwx170, vwx180, bag, bah)
new_ltEs3(Just(vwx170), Just(vwx180), app(app(ty_Either, bea), beb)) → new_ltEs2(vwx170, vwx180, bea, beb)
new_ltEs0(@3(vwx170, vwx171, vwx172), @3(vwx180, vwx181, vwx182), df, dg, app(ty_Maybe, eh)) → new_ltEs3(vwx172, vwx182, eh)
new_ltEs0(@3(vwx170, vwx171, vwx172), @3(vwx180, vwx181, vwx182), df, app(app(app(ty_@3, fd), ff), fg), fc) → new_lt0(vwx171, vwx181, fd, ff, fg)
new_compare3(vwx170, vwx180, cf, cg, da) → new_compare20(vwx170, vwx180, new_esEs5(vwx170, vwx180, cf, cg, da), cf, cg, da)
new_lt0(vwx170, vwx180, cf, cg, da) → new_compare20(vwx170, vwx180, new_esEs5(vwx170, vwx180, cf, cg, da), cf, cg, da)
new_ltEs2(Right(vwx170), Right(vwx180), bca, app(ty_[], bcg)) → new_ltEs1(vwx170, vwx180, bcg)
new_primCompAux(vwx170, vwx180, vwx75, app(app(ty_Either, bad), bae)) → new_compare4(vwx170, vwx180, bad, bae)
new_compare21(vwx170, vwx180, False, dc, dd) → new_ltEs2(vwx170, vwx180, dc, dd)
new_ltEs2(Right(vwx170), Right(vwx180), bca, app(app(ty_Either, bch), bda)) → new_ltEs2(vwx170, vwx180, bch, bda)
new_ltEs0(@3(vwx170, vwx171, vwx172), @3(vwx180, vwx181, vwx182), df, dg, app(app(ty_Either, ef), eg)) → new_ltEs2(vwx172, vwx182, ef, eg)
new_ltEs0(@3(vwx170, vwx171, vwx172), @3(vwx180, vwx181, vwx182), app(ty_[], ha), dg, fc) → new_lt1(vwx170, vwx180, ha)
new_ltEs0(@3(vwx170, vwx171, vwx172), @3(vwx180, vwx181, vwx182), df, dg, app(app(app(ty_@3, eb), ec), ed)) → new_ltEs0(vwx172, vwx182, eb, ec, ed)
new_lt1(vwx170, vwx180, db) → new_compare(vwx170, vwx180, db)
new_ltEs0(@3(vwx170, vwx171, vwx172), @3(vwx180, vwx181, vwx182), df, app(app(ty_@2, fa), fb), fc) → new_lt(vwx171, vwx181, fa, fb)
new_ltEs0(@3(vwx170, vwx171, vwx172), @3(vwx180, vwx181, vwx182), df, dg, app(ty_[], ee)) → new_ltEs1(vwx172, vwx182, ee)
new_lt2(vwx170, vwx180, dc, dd) → new_compare21(vwx170, vwx180, new_esEs6(vwx170, vwx180, dc, dd), dc, dd)
new_compare(:(vwx170, vwx171), :(vwx180, vwx181), he) → new_compare(vwx171, vwx181, he)
new_primCompAux(vwx170, vwx180, vwx75, app(app(app(ty_@3, hh), baa), bab)) → new_compare3(vwx170, vwx180, hh, baa, bab)
new_compare(:(vwx170, vwx171), :(vwx180, vwx181), he) → new_primCompAux(vwx170, vwx180, new_compare0(vwx171, vwx181, he), he)
new_ltEs(@2(vwx170, vwx171), @2(vwx180, vwx181), ba, app(app(ty_@2, bb), bc)) → new_ltEs(vwx171, vwx181, bb, bc)
new_ltEs(@2(vwx170, vwx171), @2(vwx180, vwx181), app(app(ty_Either, dc), dd), ce) → new_compare21(vwx170, vwx180, new_esEs6(vwx170, vwx180, dc, dd), dc, dd)
new_ltEs2(Right(vwx170), Right(vwx180), bca, app(app(ty_@2, bcb), bcc)) → new_ltEs(vwx170, vwx180, bcb, bcc)
new_primCompAux(vwx170, vwx180, vwx75, app(ty_Maybe, baf)) → new_compare5(vwx170, vwx180, baf)
new_ltEs2(Right(vwx170), Right(vwx180), bca, app(ty_Maybe, bdb)) → new_ltEs3(vwx170, vwx180, bdb)
new_ltEs1(:(vwx170, vwx171), :(vwx180, vwx181), he) → new_primCompAux(vwx170, vwx180, new_compare0(vwx171, vwx181, he), he)
new_ltEs(@2(vwx170, vwx171), @2(vwx180, vwx181), app(app(ty_@2, cc), cd), ce) → new_compare2(vwx170, vwx180, new_esEs4(vwx170, vwx180, cc, cd), cc, cd)
new_ltEs3(Just(vwx170), Just(vwx180), app(app(ty_@2, bdc), bdd)) → new_ltEs(vwx170, vwx180, bdc, bdd)
new_compare20(vwx170, vwx180, False, cf, cg, da) → new_ltEs0(vwx170, vwx180, cf, cg, da)
new_ltEs2(Left(vwx170), Left(vwx180), app(app(app(ty_@3, bbb), bbc), bbd), bba) → new_ltEs0(vwx170, vwx180, bbb, bbc, bbd)
new_ltEs(@2(vwx170, vwx171), @2(vwx180, vwx181), ba, app(app(app(ty_@3, bd), be), bf)) → new_ltEs0(vwx171, vwx181, bd, be, bf)
new_primCompAux(vwx170, vwx180, vwx75, app(app(ty_@2, hf), hg)) → new_compare1(vwx170, vwx180, hf, hg)
new_compare4(vwx170, vwx180, dc, dd) → new_compare21(vwx170, vwx180, new_esEs6(vwx170, vwx180, dc, dd), dc, dd)
new_ltEs0(@3(vwx170, vwx171, vwx172), @3(vwx180, vwx181, vwx182), df, app(ty_[], fh), fc) → new_lt1(vwx171, vwx181, fh)
new_ltEs(@2(vwx170, vwx171), @2(vwx180, vwx181), app(ty_Maybe, de), ce) → new_compare22(vwx170, vwx180, new_esEs7(vwx170, vwx180, de), de)
new_ltEs3(Just(vwx170), Just(vwx180), app(ty_Maybe, bec)) → new_ltEs3(vwx170, vwx180, bec)
new_ltEs2(Left(vwx170), Left(vwx180), app(ty_[], bbe), bba) → new_ltEs1(vwx170, vwx180, bbe)
new_ltEs3(Just(vwx170), Just(vwx180), app(ty_[], bdh)) → new_ltEs1(vwx170, vwx180, bdh)
new_compare1(vwx170, vwx180, cc, cd) → new_compare2(vwx170, vwx180, new_esEs4(vwx170, vwx180, cc, cd), cc, cd)
new_ltEs0(@3(vwx170, vwx171, vwx172), @3(vwx180, vwx181, vwx182), app(app(ty_@2, gd), ge), dg, fc) → new_lt(vwx170, vwx180, gd, ge)

The TRS R consists of the following rules:

new_esEs25(vwx301, vwx401, app(ty_[], cba)) → new_esEs14(vwx301, vwx401, cba)
new_esEs10(vwx300, vwx400, ty_Integer) → new_esEs12(vwx300, vwx400)
new_esEs22(vwx171, vwx181, ty_Double) → new_esEs17(vwx171, vwx181)
new_esEs7(Just(vwx300), Just(vwx400), app(ty_Maybe, cgg)) → new_esEs7(vwx300, vwx400, cgg)
new_compare17(:%(vwx170, vwx171), :%(vwx180, vwx181), ty_Integer) → new_compare32(new_sr(vwx170, vwx181), new_sr(vwx180, vwx171))
new_esEs26(vwx300, vwx400, app(ty_Ratio, cda)) → new_esEs8(vwx300, vwx400, cda)
new_lt5(vwx170, vwx180) → new_esEs13(new_compare13(vwx170, vwx180), LT)
new_ltEs6(Left(vwx170), Left(vwx180), ty_Char, bba) → new_ltEs10(vwx170, vwx180)
new_esEs25(vwx301, vwx401, ty_Integer) → new_esEs12(vwx301, vwx401)
new_esEs5(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), bha, bhb, bhc) → new_asAs(new_esEs26(vwx300, vwx400, bha), new_asAs(new_esEs25(vwx301, vwx401, bhb), new_esEs24(vwx302, vwx402, bhc)))
new_compare10(vwx170, vwx180, True, cf, cg, da) → LT
new_esEs26(vwx300, vwx400, ty_Bool) → new_esEs18(vwx300, vwx400)
new_esEs23(vwx170, vwx180, ty_Float) → new_esEs20(vwx170, vwx180)
new_esEs24(vwx302, vwx402, app(app(app(ty_@3, bhd), bhe), bhf)) → new_esEs5(vwx302, vwx402, bhd, bhe, bhf)
new_ltEs19(vwx172, vwx182, app(ty_Ratio, bge)) → new_ltEs16(vwx172, vwx182, bge)
new_esEs6(Left(vwx300), Left(vwx400), ty_Ordering, cdd) → new_esEs13(vwx300, vwx400)
new_esEs7(Just(vwx300), Just(vwx400), app(ty_Ratio, chd)) → new_esEs8(vwx300, vwx400, chd)
new_compare15(vwx170, vwx180, True, cc, cd) → LT
new_lt19(vwx171, vwx181, ty_Char) → new_lt4(vwx171, vwx181)
new_esEs23(vwx170, vwx180, app(app(ty_@2, gd), ge)) → new_esEs4(vwx170, vwx180, gd, ge)
new_esEs15(vwx300, vwx400, app(ty_Ratio, bga)) → new_esEs8(vwx300, vwx400, bga)
new_compare23(vwx170, vwx180, False, cf, cg, da) → new_compare10(vwx170, vwx180, new_ltEs5(vwx170, vwx180, cf, cg, da), cf, cg, da)
new_esEs6(Right(vwx300), Right(vwx400), ceg, ty_Double) → new_esEs17(vwx300, vwx400)
new_esEs21(vwx170, vwx180, ty_@0) → new_esEs19(vwx170, vwx180)
new_esEs28(vwx300, vwx400, ty_Char) → new_esEs16(vwx300, vwx400)
new_esEs27(vwx301, vwx401, app(ty_Maybe, dac)) → new_esEs7(vwx301, vwx401, dac)
new_esEs6(Left(vwx300), Left(vwx400), app(ty_Ratio, cef), cdd) → new_esEs8(vwx300, vwx400, cef)
new_lt8(vwx170, vwx180, ty_Ordering) → new_lt7(vwx170, vwx180)
new_lt20(vwx170, vwx180, ty_@0) → new_lt6(vwx170, vwx180)
new_esEs7(Just(vwx300), Just(vwx400), app(app(ty_Either, chb), chc)) → new_esEs6(vwx300, vwx400, chb, chc)
new_primMulNat0(Zero, Zero) → Zero
new_esEs22(vwx171, vwx181, app(ty_Ratio, bgf)) → new_esEs8(vwx171, vwx181, bgf)
new_ltEs17(Just(vwx170), Just(vwx180), ty_Bool) → new_ltEs4(vwx170, vwx180)
new_sr(Integer(vwx1700), Integer(vwx1810)) → Integer(new_primMulInt(vwx1700, vwx1810))
new_esEs25(vwx301, vwx401, app(app(ty_Either, cbe), cbf)) → new_esEs6(vwx301, vwx401, cbe, cbf)
new_ltEs9(GT, LT) → False
new_esEs25(vwx301, vwx401, app(app(ty_@2, cbc), cbd)) → new_esEs4(vwx301, vwx401, cbc, cbd)
new_ltEs17(Just(vwx170), Just(vwx180), app(ty_[], bdh)) → new_ltEs12(vwx170, vwx180, bdh)
new_esEs26(vwx300, vwx400, ty_@0) → new_esEs19(vwx300, vwx400)
new_lt19(vwx171, vwx181, app(app(ty_Either, ga), gb)) → new_lt15(vwx171, vwx181, ga, gb)
new_compare30(vwx170, vwx180, ty_Bool) → new_compare13(vwx170, vwx180)
new_esEs27(vwx301, vwx401, ty_Integer) → new_esEs12(vwx301, vwx401)
new_esEs13(EQ, EQ) → True
new_lt8(vwx170, vwx180, app(ty_[], db)) → new_lt12(vwx170, vwx180, db)
new_compare24(vwx170, vwx180, False, de) → new_compare16(vwx170, vwx180, new_ltEs17(vwx170, vwx180, de), de)
new_compare30(vwx170, vwx180, app(ty_Ratio, bgh)) → new_compare17(vwx170, vwx180, bgh)
new_compare32(Integer(vwx170), Integer(vwx180)) → new_primCmpInt(vwx170, vwx180)
new_esEs27(vwx301, vwx401, app(ty_Ratio, dah)) → new_esEs8(vwx301, vwx401, dah)
new_esEs7(Just(vwx300), Just(vwx400), ty_Float) → new_esEs20(vwx300, vwx400)
new_ltEs6(Left(vwx170), Left(vwx180), app(app(ty_Either, bbf), bbg), bba) → new_ltEs6(vwx170, vwx180, bbf, bbg)
new_compare12(Char(vwx170), Char(vwx180)) → new_primCmpNat0(vwx170, vwx180)
new_esEs15(vwx300, vwx400, app(app(app(ty_@3, beh), bfa), bfb)) → new_esEs5(vwx300, vwx400, beh, bfa, bfb)
new_esEs6(Left(vwx300), Left(vwx400), ty_Int, cdd) → new_esEs11(vwx300, vwx400)
new_lt9(vwx170, vwx180, cc, cd) → new_esEs13(new_compare31(vwx170, vwx180, cc, cd), LT)
new_lt19(vwx171, vwx181, ty_Float) → new_lt13(vwx171, vwx181)
new_esEs15(vwx300, vwx400, app(app(ty_@2, bfe), bff)) → new_esEs4(vwx300, vwx400, bfe, bff)
new_ltEs19(vwx172, vwx182, ty_Bool) → new_ltEs4(vwx172, vwx182)
new_esEs24(vwx302, vwx402, app(ty_Ratio, cae)) → new_esEs8(vwx302, vwx402, cae)
new_lt20(vwx170, vwx180, app(app(ty_@2, gd), ge)) → new_lt9(vwx170, vwx180, gd, ge)
new_ltEs4(False, True) → True
new_esEs7(Just(vwx300), Just(vwx400), app(app(ty_@2, cgh), cha)) → new_esEs4(vwx300, vwx400, cgh, cha)
new_esEs23(vwx170, vwx180, ty_Integer) → new_esEs12(vwx170, vwx180)
new_ltEs9(EQ, GT) → True
new_esEs21(vwx170, vwx180, app(app(ty_Either, dc), dd)) → new_esEs6(vwx170, vwx180, dc, dd)
new_esEs12(Integer(vwx300), Integer(vwx400)) → new_primEqInt(vwx300, vwx400)
new_esEs28(vwx300, vwx400, ty_Integer) → new_esEs12(vwx300, vwx400)
new_esEs22(vwx171, vwx181, app(ty_[], fh)) → new_esEs14(vwx171, vwx181, fh)
new_esEs28(vwx300, vwx400, app(app(app(ty_@3, dba), dbb), dbc)) → new_esEs5(vwx300, vwx400, dba, dbb, dbc)
new_esEs22(vwx171, vwx181, ty_Float) → new_esEs20(vwx171, vwx181)
new_esEs6(Left(vwx300), Left(vwx400), ty_Integer, cdd) → new_esEs12(vwx300, vwx400)
new_ltEs9(LT, EQ) → True
new_lt20(vwx170, vwx180, ty_Char) → new_lt4(vwx170, vwx180)
new_ltEs6(Left(vwx170), Left(vwx180), ty_Double, bba) → new_ltEs15(vwx170, vwx180)
new_pePe(False, vwx74) → vwx74
new_ltEs4(True, True) → True
new_compare28(vwx170, vwx180, False) → new_compare18(vwx170, vwx180, new_ltEs4(vwx170, vwx180))
new_esEs23(vwx170, vwx180, ty_@0) → new_esEs19(vwx170, vwx180)
new_esEs14([], [], beg) → True
new_esEs13(LT, EQ) → False
new_esEs13(EQ, LT) → False
new_esEs15(vwx300, vwx400, ty_Char) → new_esEs16(vwx300, vwx400)
new_esEs6(Left(vwx300), Left(vwx400), app(app(ty_@2, ceb), cec), cdd) → new_esEs4(vwx300, vwx400, ceb, cec)
new_esEs22(vwx171, vwx181, ty_Ordering) → new_esEs13(vwx171, vwx181)
new_esEs21(vwx170, vwx180, ty_Ordering) → new_esEs13(vwx170, vwx180)
new_ltEs17(Just(vwx170), Just(vwx180), ty_Double) → new_ltEs15(vwx170, vwx180)
new_ltEs17(Just(vwx170), Nothing, cdb) → False
new_lt10(vwx170, vwx180) → new_esEs13(new_compare32(vwx170, vwx180), LT)
new_esEs26(vwx300, vwx400, ty_Int) → new_esEs11(vwx300, vwx400)
new_lt14(vwx170, vwx180) → new_esEs13(new_compare6(vwx170, vwx180), LT)
new_ltEs6(Left(vwx170), Left(vwx180), ty_Int, bba) → new_ltEs14(vwx170, vwx180)
new_esEs24(vwx302, vwx402, app(ty_Maybe, bhh)) → new_esEs7(vwx302, vwx402, bhh)
new_lt19(vwx171, vwx181, app(ty_Ratio, bgf)) → new_lt17(vwx171, vwx181, bgf)
new_esEs22(vwx171, vwx181, app(app(ty_@2, fa), fb)) → new_esEs4(vwx171, vwx181, fa, fb)
new_compare14(@0, @0) → EQ
new_esEs22(vwx171, vwx181, ty_Int) → new_esEs11(vwx171, vwx181)
new_esEs22(vwx171, vwx181, ty_Integer) → new_esEs12(vwx171, vwx181)
new_esEs23(vwx170, vwx180, app(ty_Maybe, hd)) → new_esEs7(vwx170, vwx180, hd)
new_compare23(vwx170, vwx180, True, cf, cg, da) → EQ
new_esEs27(vwx301, vwx401, ty_Float) → new_esEs20(vwx301, vwx401)
new_ltEs9(EQ, EQ) → True
new_primCompAux1(vwx170, vwx180, vwx75, he) → new_primCompAux0(vwx75, new_compare30(vwx170, vwx180, he))
new_esEs7(Just(vwx300), Just(vwx400), ty_Bool) → new_esEs18(vwx300, vwx400)
new_ltEs6(Right(vwx170), Right(vwx180), bca, app(ty_[], bcg)) → new_ltEs12(vwx170, vwx180, bcg)
new_ltEs17(Just(vwx170), Just(vwx180), app(app(ty_Either, bea), beb)) → new_ltEs6(vwx170, vwx180, bea, beb)
new_lt12(vwx170, vwx180, db) → new_esEs13(new_compare0(vwx170, vwx180, db), LT)
new_lt8(vwx170, vwx180, ty_Int) → new_lt14(vwx170, vwx180)
new_ltEs6(Left(vwx170), Left(vwx180), ty_Float, bba) → new_ltEs13(vwx170, vwx180)
new_lt19(vwx171, vwx181, app(ty_[], fh)) → new_lt12(vwx171, vwx181, fh)
new_ltEs6(Left(vwx170), Left(vwx180), ty_Ordering, bba) → new_ltEs9(vwx170, vwx180)
new_primCmpNat0(Zero, Succ(vwx1800)) → LT
new_compare27(vwx170, vwx180, False, cc, cd) → new_compare15(vwx170, vwx180, new_ltEs7(vwx170, vwx180, cc, cd), cc, cd)
new_esEs26(vwx300, vwx400, ty_Double) → new_esEs17(vwx300, vwx400)
new_ltEs17(Just(vwx170), Just(vwx180), ty_Float) → new_ltEs13(vwx170, vwx180)
new_esEs20(Float(vwx300, vwx301), Float(vwx400, vwx401)) → new_esEs11(new_sr0(vwx300, vwx400), new_sr0(vwx301, vwx401))
new_esEs6(Left(vwx300), Right(vwx400), ceg, cdd) → False
new_esEs6(Right(vwx300), Left(vwx400), ceg, cdd) → False
new_ltEs6(Left(vwx170), Left(vwx180), app(ty_Maybe, bbh), bba) → new_ltEs17(vwx170, vwx180, bbh)
new_esEs6(Right(vwx300), Right(vwx400), ceg, ty_Integer) → new_esEs12(vwx300, vwx400)
new_esEs6(Left(vwx300), Left(vwx400), ty_Float, cdd) → new_esEs20(vwx300, vwx400)
new_esEs25(vwx301, vwx401, ty_Double) → new_esEs17(vwx301, vwx401)
new_esEs27(vwx301, vwx401, ty_Ordering) → new_esEs13(vwx301, vwx401)
new_ltEs8(vwx17, vwx18) → new_not(new_esEs13(new_compare14(vwx17, vwx18), GT))
new_pePe(True, vwx74) → True
new_compare0([], [], he) → EQ
new_primEqNat0(Zero, Zero) → True
new_esEs6(Right(vwx300), Right(vwx400), ceg, ty_Char) → new_esEs16(vwx300, vwx400)
new_esEs23(vwx170, vwx180, app(app(ty_Either, hb), hc)) → new_esEs6(vwx170, vwx180, hb, hc)
new_primMulNat0(Succ(vwx30000), Succ(vwx40000)) → new_primPlusNat1(new_primMulNat0(vwx30000, Succ(vwx40000)), vwx40000)
new_esEs13(LT, GT) → False
new_esEs13(GT, LT) → False
new_esEs25(vwx301, vwx401, ty_Bool) → new_esEs18(vwx301, vwx401)
new_esEs4(@2(vwx300, vwx301), @2(vwx400, vwx401), che, chf) → new_asAs(new_esEs28(vwx300, vwx400, che), new_esEs27(vwx301, vwx401, chf))
new_esEs6(Right(vwx300), Right(vwx400), ceg, app(app(ty_Either, cfg), cfh)) → new_esEs6(vwx300, vwx400, cfg, cfh)
new_ltEs9(EQ, LT) → False
new_ltEs18(vwx171, vwx181, ty_Char) → new_ltEs10(vwx171, vwx181)
new_lt4(vwx170, vwx180) → new_esEs13(new_compare12(vwx170, vwx180), LT)
new_esEs28(vwx300, vwx400, app(app(ty_Either, dbh), dca)) → new_esEs6(vwx300, vwx400, dbh, dca)
new_esEs24(vwx302, vwx402, ty_Ordering) → new_esEs13(vwx302, vwx402)
new_ltEs19(vwx172, vwx182, ty_Char) → new_ltEs10(vwx172, vwx182)
new_ltEs17(Just(vwx170), Just(vwx180), ty_@0) → new_ltEs8(vwx170, vwx180)
new_esEs6(Left(vwx300), Left(vwx400), ty_Double, cdd) → new_esEs17(vwx300, vwx400)
new_lt19(vwx171, vwx181, app(app(app(ty_@3, fd), ff), fg)) → new_lt11(vwx171, vwx181, fd, ff, fg)
new_esEs23(vwx170, vwx180, ty_Bool) → new_esEs18(vwx170, vwx180)
new_esEs22(vwx171, vwx181, ty_Char) → new_esEs16(vwx171, vwx181)
new_esEs16(Char(vwx300), Char(vwx400)) → new_primEqNat0(vwx300, vwx400)
new_lt8(vwx170, vwx180, ty_@0) → new_lt6(vwx170, vwx180)
new_esEs7(Just(vwx300), Just(vwx400), ty_Integer) → new_esEs12(vwx300, vwx400)
new_esEs26(vwx300, vwx400, ty_Integer) → new_esEs12(vwx300, vwx400)
new_compare30(vwx170, vwx180, app(app(app(ty_@3, hh), baa), bab)) → new_compare7(vwx170, vwx180, hh, baa, bab)
new_compare25(vwx170, vwx180, True) → EQ
new_primEqInt(Neg(Succ(vwx3000)), Neg(Succ(vwx4000))) → new_primEqNat0(vwx3000, vwx4000)
new_esEs24(vwx302, vwx402, ty_Bool) → new_esEs18(vwx302, vwx402)
new_compare30(vwx170, vwx180, app(ty_Maybe, baf)) → new_compare8(vwx170, vwx180, baf)
new_compare30(vwx170, vwx180, ty_Int) → new_compare6(vwx170, vwx180)
new_esEs7(Just(vwx300), Just(vwx400), ty_Double) → new_esEs17(vwx300, vwx400)
new_compare16(vwx170, vwx180, True, de) → LT
new_compare10(vwx170, vwx180, False, cf, cg, da) → GT
new_lt8(vwx170, vwx180, ty_Char) → new_lt4(vwx170, vwx180)
new_lt19(vwx171, vwx181, ty_Integer) → new_lt10(vwx171, vwx181)
new_lt8(vwx170, vwx180, app(app(app(ty_@3, cf), cg), da)) → new_lt11(vwx170, vwx180, cf, cg, da)
new_esEs14([], :(vwx400, vwx401), beg) → False
new_esEs14(:(vwx300, vwx301), [], beg) → False
new_esEs6(Left(vwx300), Left(vwx400), app(ty_[], cdh), cdd) → new_esEs14(vwx300, vwx400, cdh)
new_lt8(vwx170, vwx180, ty_Double) → new_lt16(vwx170, vwx180)
new_esEs6(Right(vwx300), Right(vwx400), ceg, ty_Bool) → new_esEs18(vwx300, vwx400)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_lt20(vwx170, vwx180, app(ty_Maybe, hd)) → new_lt18(vwx170, vwx180, hd)
new_esEs28(vwx300, vwx400, ty_Float) → new_esEs20(vwx300, vwx400)
new_ltEs6(Right(vwx170), Right(vwx180), bca, app(ty_Maybe, bdb)) → new_ltEs17(vwx170, vwx180, bdb)
new_lt20(vwx170, vwx180, ty_Ordering) → new_lt7(vwx170, vwx180)
new_esEs26(vwx300, vwx400, app(ty_[], ccc)) → new_esEs14(vwx300, vwx400, ccc)
new_compare18(vwx170, vwx180, False) → GT
new_lt19(vwx171, vwx181, ty_Double) → new_lt16(vwx171, vwx181)
new_primEqInt(Neg(Succ(vwx3000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(vwx4000))) → False
new_primCompAux0(vwx85, GT) → GT
new_lt8(vwx170, vwx180, ty_Bool) → new_lt5(vwx170, vwx180)
new_compare26(vwx170, vwx180, True, dc, dd) → EQ
new_primPlusNat1(Zero, vwx40000) → Succ(vwx40000)
new_compare30(vwx170, vwx180, ty_Float) → new_compare19(vwx170, vwx180)
new_ltEs17(Just(vwx170), Just(vwx180), ty_Int) → new_ltEs14(vwx170, vwx180)
new_ltEs19(vwx172, vwx182, ty_Int) → new_ltEs14(vwx172, vwx182)
new_esEs6(Right(vwx300), Right(vwx400), ceg, ty_@0) → new_esEs19(vwx300, vwx400)
new_ltEs9(LT, LT) → True
new_esEs28(vwx300, vwx400, app(ty_[], dbd)) → new_esEs14(vwx300, vwx400, dbd)
new_esEs22(vwx171, vwx181, app(app(app(ty_@3, fd), ff), fg)) → new_esEs5(vwx171, vwx181, fd, ff, fg)
new_esEs25(vwx301, vwx401, ty_Char) → new_esEs16(vwx301, vwx401)
new_esEs19(@0, @0) → True
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_compare6(vwx17, vwx18) → new_primCmpInt(vwx17, vwx18)
new_compare7(vwx170, vwx180, cf, cg, da) → new_compare23(vwx170, vwx180, new_esEs5(vwx170, vwx180, cf, cg, da), cf, cg, da)
new_esEs23(vwx170, vwx180, ty_Char) → new_esEs16(vwx170, vwx180)
new_lt8(vwx170, vwx180, app(app(ty_Either, dc), dd)) → new_lt15(vwx170, vwx180, dc, dd)
new_ltEs18(vwx171, vwx181, ty_@0) → new_ltEs8(vwx171, vwx181)
new_ltEs18(vwx171, vwx181, app(ty_Ratio, bgc)) → new_ltEs16(vwx171, vwx181, bgc)
new_primCmpNat0(Succ(vwx1700), Succ(vwx1800)) → new_primCmpNat0(vwx1700, vwx1800)
new_ltEs18(vwx171, vwx181, app(app(ty_Either, bh), ca)) → new_ltEs6(vwx171, vwx181, bh, ca)
new_esEs22(vwx171, vwx181, ty_@0) → new_esEs19(vwx171, vwx181)
new_esEs13(LT, LT) → True
new_primEqInt(Pos(Succ(vwx3000)), Pos(Succ(vwx4000))) → new_primEqNat0(vwx3000, vwx4000)
new_lt20(vwx170, vwx180, app(ty_[], ha)) → new_lt12(vwx170, vwx180, ha)
new_compare27(vwx170, vwx180, True, cc, cd) → EQ
new_esEs6(Left(vwx300), Left(vwx400), app(app(app(ty_@3, cde), cdf), cdg), cdd) → new_esEs5(vwx300, vwx400, cde, cdf, cdg)
new_esEs21(vwx170, vwx180, ty_Float) → new_esEs20(vwx170, vwx180)
new_primEqNat0(Succ(vwx3000), Succ(vwx4000)) → new_primEqNat0(vwx3000, vwx4000)
new_ltEs18(vwx171, vwx181, ty_Bool) → new_ltEs4(vwx171, vwx181)
new_esEs21(vwx170, vwx180, app(ty_[], db)) → new_esEs14(vwx170, vwx180, db)
new_esEs27(vwx301, vwx401, ty_Char) → new_esEs16(vwx301, vwx401)
new_ltEs18(vwx171, vwx181, app(ty_Maybe, cb)) → new_ltEs17(vwx171, vwx181, cb)
new_esEs25(vwx301, vwx401, ty_@0) → new_esEs19(vwx301, vwx401)
new_ltEs5(@3(vwx170, vwx171, vwx172), @3(vwx180, vwx181, vwx182), df, dg, fc) → new_pePe(new_lt20(vwx170, vwx180, df), new_asAs(new_esEs23(vwx170, vwx180, df), new_pePe(new_lt19(vwx171, vwx181, dg), new_asAs(new_esEs22(vwx171, vwx181, dg), new_ltEs19(vwx172, vwx182, fc)))))
new_esEs28(vwx300, vwx400, ty_Int) → new_esEs11(vwx300, vwx400)
new_primCmpInt(Neg(Succ(vwx1700)), Neg(vwx180)) → new_primCmpNat0(vwx180, Succ(vwx1700))
new_lt6(vwx170, vwx180) → new_esEs13(new_compare14(vwx170, vwx180), LT)
new_compare16(vwx170, vwx180, False, de) → GT
new_esEs26(vwx300, vwx400, app(app(ty_@2, cce), ccf)) → new_esEs4(vwx300, vwx400, cce, ccf)
new_lt19(vwx171, vwx181, app(app(ty_@2, fa), fb)) → new_lt9(vwx171, vwx181, fa, fb)
new_esEs27(vwx301, vwx401, app(app(app(ty_@3, chg), chh), daa)) → new_esEs5(vwx301, vwx401, chg, chh, daa)
new_ltEs6(Left(vwx170), Right(vwx180), bca, bba) → True
new_esEs21(vwx170, vwx180, ty_Int) → new_esEs11(vwx170, vwx180)
new_ltEs6(Right(vwx170), Left(vwx180), bca, bba) → False
new_esEs7(Nothing, Nothing, cgb) → True
new_primEqInt(Pos(Succ(vwx3000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(vwx4000))) → False
new_lt20(vwx170, vwx180, app(ty_Ratio, bgg)) → new_lt17(vwx170, vwx180, bgg)
new_esEs27(vwx301, vwx401, ty_@0) → new_esEs19(vwx301, vwx401)
new_ltEs18(vwx171, vwx181, ty_Integer) → new_ltEs11(vwx171, vwx181)
new_primPlusNat0(Zero, Succ(vwx400000)) → Succ(vwx400000)
new_primPlusNat0(Succ(vwx5100), Zero) → Succ(vwx5100)
new_lt7(vwx170, vwx180) → new_esEs13(new_compare9(vwx170, vwx180), LT)
new_ltEs6(Left(vwx170), Left(vwx180), app(app(app(ty_@3, bbb), bbc), bbd), bba) → new_ltEs5(vwx170, vwx180, bbb, bbc, bbd)
new_primCmpNat0(Zero, Zero) → EQ
new_esEs23(vwx170, vwx180, ty_Ordering) → new_esEs13(vwx170, vwx180)
new_esEs6(Right(vwx300), Right(vwx400), ceg, app(ty_Maybe, cfd)) → new_esEs7(vwx300, vwx400, cfd)
new_primCmpNat0(Succ(vwx1700), Zero) → GT
new_lt17(vwx170, vwx180, bgd) → new_esEs13(new_compare17(vwx170, vwx180, bgd), LT)
new_compare18(vwx170, vwx180, True) → LT
new_lt20(vwx170, vwx180, ty_Bool) → new_lt5(vwx170, vwx180)
new_ltEs19(vwx172, vwx182, ty_Ordering) → new_ltEs9(vwx172, vwx182)
new_primCmpInt(Neg(Zero), Pos(Succ(vwx1800))) → LT
new_compare11(vwx170, vwx180, True, dc, dd) → LT
new_esEs21(vwx170, vwx180, ty_Char) → new_esEs16(vwx170, vwx180)
new_esEs28(vwx300, vwx400, app(ty_Ratio, dcb)) → new_esEs8(vwx300, vwx400, dcb)
new_esEs22(vwx171, vwx181, ty_Bool) → new_esEs18(vwx171, vwx181)
new_esEs21(vwx170, vwx180, ty_Double) → new_esEs17(vwx170, vwx180)
new_primEqInt(Pos(Succ(vwx3000)), Neg(vwx400)) → False
new_primEqInt(Neg(Succ(vwx3000)), Pos(vwx400)) → False
new_esEs24(vwx302, vwx402, app(app(ty_@2, caa), cab)) → new_esEs4(vwx302, vwx402, caa, cab)
new_esEs7(Nothing, Just(vwx400), cgb) → False
new_esEs7(Just(vwx300), Nothing, cgb) → False
new_esEs6(Left(vwx300), Left(vwx400), ty_Bool, cdd) → new_esEs18(vwx300, vwx400)
new_lt19(vwx171, vwx181, ty_Bool) → new_lt5(vwx171, vwx181)
new_esEs7(Just(vwx300), Just(vwx400), ty_Char) → new_esEs16(vwx300, vwx400)
new_ltEs6(Right(vwx170), Right(vwx180), bca, ty_Float) → new_ltEs13(vwx170, vwx180)
new_primEqInt(Pos(Zero), Neg(Succ(vwx4000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(vwx4000))) → False
new_primCmpInt(Pos(Zero), Pos(Succ(vwx1800))) → new_primCmpNat0(Zero, Succ(vwx1800))
new_esEs23(vwx170, vwx180, ty_Double) → new_esEs17(vwx170, vwx180)
new_ltEs6(Left(vwx170), Left(vwx180), ty_Bool, bba) → new_ltEs4(vwx170, vwx180)
new_esEs15(vwx300, vwx400, app(ty_Maybe, bfd)) → new_esEs7(vwx300, vwx400, bfd)
new_ltEs14(vwx17, vwx18) → new_not(new_esEs13(new_compare6(vwx17, vwx18), GT))
new_primCompAux0(vwx85, LT) → LT
new_ltEs6(Right(vwx170), Right(vwx180), bca, app(ty_Ratio, bef)) → new_ltEs16(vwx170, vwx180, bef)
new_lt19(vwx171, vwx181, app(ty_Maybe, gc)) → new_lt18(vwx171, vwx181, gc)
new_ltEs17(Just(vwx170), Just(vwx180), ty_Char) → new_ltEs10(vwx170, vwx180)
new_esEs11(vwx30, vwx40) → new_primEqInt(vwx30, vwx40)
new_not(False) → True
new_compare17(:%(vwx170, vwx171), :%(vwx180, vwx181), ty_Int) → new_compare6(new_sr0(vwx170, vwx181), new_sr0(vwx180, vwx171))
new_esEs6(Left(vwx300), Left(vwx400), app(app(ty_Either, ced), cee), cdd) → new_esEs6(vwx300, vwx400, ced, cee)
new_compare24(vwx170, vwx180, True, de) → EQ
new_esEs25(vwx301, vwx401, ty_Float) → new_esEs20(vwx301, vwx401)
new_primCmpInt(Pos(Succ(vwx1700)), Pos(vwx180)) → new_primCmpNat0(Succ(vwx1700), vwx180)
new_esEs24(vwx302, vwx402, app(app(ty_Either, cac), cad)) → new_esEs6(vwx302, vwx402, cac, cad)
new_ltEs9(LT, GT) → True
new_esEs24(vwx302, vwx402, ty_@0) → new_esEs19(vwx302, vwx402)
new_ltEs19(vwx172, vwx182, app(ty_[], ee)) → new_ltEs12(vwx172, vwx182, ee)
new_lt18(vwx170, vwx180, de) → new_esEs13(new_compare8(vwx170, vwx180, de), LT)
new_compare30(vwx170, vwx180, ty_@0) → new_compare14(vwx170, vwx180)
new_esEs24(vwx302, vwx402, app(ty_[], bhg)) → new_esEs14(vwx302, vwx402, bhg)
new_esEs9(vwx301, vwx401, ty_Int) → new_esEs11(vwx301, vwx401)
new_esEs24(vwx302, vwx402, ty_Integer) → new_esEs12(vwx302, vwx402)
new_compare0(:(vwx170, vwx171), [], he) → GT
new_compare28(vwx170, vwx180, True) → EQ
new_esEs27(vwx301, vwx401, app(app(ty_Either, daf), dag)) → new_esEs6(vwx301, vwx401, daf, dag)
new_esEs27(vwx301, vwx401, ty_Int) → new_esEs11(vwx301, vwx401)
new_esEs15(vwx300, vwx400, ty_Ordering) → new_esEs13(vwx300, vwx400)
new_esEs15(vwx300, vwx400, app(app(ty_Either, bfg), bfh)) → new_esEs6(vwx300, vwx400, bfg, bfh)
new_compare11(vwx170, vwx180, False, dc, dd) → GT
new_primCmpInt(Pos(Succ(vwx1700)), Neg(vwx180)) → GT
new_esEs28(vwx300, vwx400, app(ty_Maybe, dbe)) → new_esEs7(vwx300, vwx400, dbe)
new_esEs21(vwx170, vwx180, app(app(app(ty_@3, cf), cg), da)) → new_esEs5(vwx170, vwx180, cf, cg, da)
new_ltEs19(vwx172, vwx182, ty_Float) → new_ltEs13(vwx172, vwx182)
new_esEs21(vwx170, vwx180, app(ty_Maybe, de)) → new_esEs7(vwx170, vwx180, de)
new_primMulInt(Pos(vwx3000), Pos(vwx4000)) → Pos(new_primMulNat0(vwx3000, vwx4000))
new_lt20(vwx170, vwx180, ty_Integer) → new_lt10(vwx170, vwx180)
new_ltEs6(Right(vwx170), Right(vwx180), bca, ty_@0) → new_ltEs8(vwx170, vwx180)
new_esEs21(vwx170, vwx180, app(app(ty_@2, cc), cd)) → new_esEs4(vwx170, vwx180, cc, cd)
new_lt8(vwx170, vwx180, app(ty_Maybe, de)) → new_lt18(vwx170, vwx180, de)
new_esEs23(vwx170, vwx180, app(ty_Ratio, bgg)) → new_esEs8(vwx170, vwx180, bgg)
new_ltEs17(Just(vwx170), Just(vwx180), app(app(app(ty_@3, bde), bdf), bdg)) → new_ltEs5(vwx170, vwx180, bde, bdf, bdg)
new_ltEs17(Nothing, Just(vwx180), cdb) → True
new_primMulInt(Neg(vwx3000), Neg(vwx4000)) → Pos(new_primMulNat0(vwx3000, vwx4000))
new_compare110(vwx170, vwx180, True) → LT
new_esEs13(GT, GT) → True
new_lt20(vwx170, vwx180, app(app(app(ty_@3, gf), gg), gh)) → new_lt11(vwx170, vwx180, gf, gg, gh)
new_primEqNat0(Zero, Succ(vwx4000)) → False
new_primEqNat0(Succ(vwx3000), Zero) → False
new_esEs24(vwx302, vwx402, ty_Char) → new_esEs16(vwx302, vwx402)
new_compare30(vwx170, vwx180, app(app(ty_Either, bad), bae)) → new_compare29(vwx170, vwx180, bad, bae)
new_primPlusNat0(Zero, Zero) → Zero
new_esEs7(Just(vwx300), Just(vwx400), ty_Int) → new_esEs11(vwx300, vwx400)
new_compare110(vwx170, vwx180, False) → GT
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs24(vwx302, vwx402, ty_Float) → new_esEs20(vwx302, vwx402)
new_compare31(vwx170, vwx180, cc, cd) → new_compare27(vwx170, vwx180, new_esEs4(vwx170, vwx180, cc, cd), cc, cd)
new_esEs8(:%(vwx300, vwx301), :%(vwx400, vwx401), bed) → new_asAs(new_esEs10(vwx300, vwx400, bed), new_esEs9(vwx301, vwx401, bed))
new_ltEs17(Nothing, Nothing, cdb) → True
new_ltEs9(GT, GT) → True
new_esEs23(vwx170, vwx180, ty_Int) → new_esEs11(vwx170, vwx180)
new_esEs9(vwx301, vwx401, ty_Integer) → new_esEs12(vwx301, vwx401)
new_ltEs4(True, False) → False
new_ltEs15(vwx17, vwx18) → new_not(new_esEs13(new_compare33(vwx17, vwx18), GT))
new_primPlusNat1(Succ(vwx510), vwx40000) → Succ(Succ(new_primPlusNat0(vwx510, vwx40000)))
new_esEs23(vwx170, vwx180, app(ty_[], ha)) → new_esEs14(vwx170, vwx180, ha)
new_ltEs19(vwx172, vwx182, app(ty_Maybe, eh)) → new_ltEs17(vwx172, vwx182, eh)
new_ltEs18(vwx171, vwx181, app(app(app(ty_@3, bd), be), bf)) → new_ltEs5(vwx171, vwx181, bd, be, bf)
new_ltEs17(Just(vwx170), Just(vwx180), ty_Integer) → new_ltEs11(vwx170, vwx180)
new_primCmpInt(Neg(Zero), Neg(Succ(vwx1800))) → new_primCmpNat0(Succ(vwx1800), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(vwx1800))) → GT
new_lt15(vwx170, vwx180, dc, dd) → new_esEs13(new_compare29(vwx170, vwx180, dc, dd), LT)
new_esEs6(Left(vwx300), Left(vwx400), app(ty_Maybe, cea), cdd) → new_esEs7(vwx300, vwx400, cea)
new_esEs6(Right(vwx300), Right(vwx400), ceg, app(ty_[], cfc)) → new_esEs14(vwx300, vwx400, cfc)
new_compare0(:(vwx170, vwx171), :(vwx180, vwx181), he) → new_primCompAux1(vwx170, vwx180, new_compare0(vwx171, vwx181, he), he)
new_compare8(vwx170, vwx180, de) → new_compare24(vwx170, vwx180, new_esEs7(vwx170, vwx180, de), de)
new_ltEs12(vwx17, vwx18, he) → new_not(new_esEs13(new_compare0(vwx17, vwx18, he), GT))
new_sr0(vwx300, vwx400) → new_primMulInt(vwx300, vwx400)
new_esEs6(Right(vwx300), Right(vwx400), ceg, app(app(ty_@2, cfe), cff)) → new_esEs4(vwx300, vwx400, cfe, cff)
new_compare15(vwx170, vwx180, False, cc, cd) → GT
new_esEs6(Left(vwx300), Left(vwx400), ty_@0, cdd) → new_esEs19(vwx300, vwx400)
new_compare30(vwx170, vwx180, ty_Integer) → new_compare32(vwx170, vwx180)
new_esEs24(vwx302, vwx402, ty_Int) → new_esEs11(vwx302, vwx402)
new_ltEs6(Left(vwx170), Left(vwx180), app(ty_[], bbe), bba) → new_ltEs12(vwx170, vwx180, bbe)
new_lt20(vwx170, vwx180, ty_Double) → new_lt16(vwx170, vwx180)
new_ltEs13(vwx17, vwx18) → new_not(new_esEs13(new_compare19(vwx17, vwx18), GT))
new_ltEs19(vwx172, vwx182, ty_Integer) → new_ltEs11(vwx172, vwx182)
new_esEs25(vwx301, vwx401, app(ty_Maybe, cbb)) → new_esEs7(vwx301, vwx401, cbb)
new_esEs7(Just(vwx300), Just(vwx400), app(app(app(ty_@3, cgc), cgd), cge)) → new_esEs5(vwx300, vwx400, cgc, cgd, cge)
new_ltEs18(vwx171, vwx181, ty_Int) → new_ltEs14(vwx171, vwx181)
new_lt8(vwx170, vwx180, ty_Integer) → new_lt10(vwx170, vwx180)
new_esEs15(vwx300, vwx400, ty_Int) → new_esEs11(vwx300, vwx400)
new_ltEs6(Right(vwx170), Right(vwx180), bca, app(app(ty_Either, bch), bda)) → new_ltEs6(vwx170, vwx180, bch, bda)
new_ltEs6(Right(vwx170), Right(vwx180), bca, app(app(app(ty_@3, bcd), bce), bcf)) → new_ltEs5(vwx170, vwx180, bcd, bce, bcf)
new_esEs6(Right(vwx300), Right(vwx400), ceg, ty_Int) → new_esEs11(vwx300, vwx400)
new_lt19(vwx171, vwx181, ty_Ordering) → new_lt7(vwx171, vwx181)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs6(Right(vwx300), Right(vwx400), ceg, ty_Float) → new_esEs20(vwx300, vwx400)
new_compare30(vwx170, vwx180, app(ty_[], bac)) → new_compare0(vwx170, vwx180, bac)
new_esEs21(vwx170, vwx180, ty_Bool) → new_esEs18(vwx170, vwx180)
new_esEs14(:(vwx300, vwx301), :(vwx400, vwx401), beg) → new_asAs(new_esEs15(vwx300, vwx400, beg), new_esEs14(vwx301, vwx401, beg))
new_ltEs6(Right(vwx170), Right(vwx180), bca, ty_Integer) → new_ltEs11(vwx170, vwx180)
new_esEs28(vwx300, vwx400, app(app(ty_@2, dbf), dbg)) → new_esEs4(vwx300, vwx400, dbf, dbg)
new_asAs(False, vwx43) → False
new_ltEs19(vwx172, vwx182, app(app(ty_@2, dh), ea)) → new_ltEs7(vwx172, vwx182, dh, ea)
new_ltEs18(vwx171, vwx181, ty_Double) → new_ltEs15(vwx171, vwx181)
new_primMulInt(Neg(vwx3000), Pos(vwx4000)) → Neg(new_primMulNat0(vwx3000, vwx4000))
new_primMulInt(Pos(vwx3000), Neg(vwx4000)) → Neg(new_primMulNat0(vwx3000, vwx4000))
new_lt11(vwx170, vwx180, cf, cg, da) → new_esEs13(new_compare7(vwx170, vwx180, cf, cg, da), LT)
new_primMulNat0(Succ(vwx30000), Zero) → Zero
new_primMulNat0(Zero, Succ(vwx40000)) → Zero
new_esEs13(EQ, GT) → False
new_esEs13(GT, EQ) → False
new_esEs25(vwx301, vwx401, app(ty_Ratio, cbg)) → new_esEs8(vwx301, vwx401, cbg)
new_ltEs18(vwx171, vwx181, app(app(ty_@2, bb), bc)) → new_ltEs7(vwx171, vwx181, bb, bc)
new_esEs18(True, True) → True
new_esEs26(vwx300, vwx400, app(ty_Maybe, ccd)) → new_esEs7(vwx300, vwx400, ccd)
new_ltEs18(vwx171, vwx181, ty_Float) → new_ltEs13(vwx171, vwx181)
new_compare30(vwx170, vwx180, ty_Char) → new_compare12(vwx170, vwx180)
new_esEs6(Left(vwx300), Left(vwx400), ty_Char, cdd) → new_esEs16(vwx300, vwx400)
new_esEs28(vwx300, vwx400, ty_@0) → new_esEs19(vwx300, vwx400)
new_esEs27(vwx301, vwx401, ty_Double) → new_esEs17(vwx301, vwx401)
new_esEs28(vwx300, vwx400, ty_Bool) → new_esEs18(vwx300, vwx400)
new_ltEs4(False, False) → True
new_lt20(vwx170, vwx180, ty_Float) → new_lt13(vwx170, vwx180)
new_ltEs7(@2(vwx170, vwx171), @2(vwx180, vwx181), ba, ce) → new_pePe(new_lt8(vwx170, vwx180, ba), new_asAs(new_esEs21(vwx170, vwx180, ba), new_ltEs18(vwx171, vwx181, ce)))
new_esEs10(vwx300, vwx400, ty_Int) → new_esEs11(vwx300, vwx400)
new_ltEs9(GT, EQ) → False
new_ltEs6(Right(vwx170), Right(vwx180), bca, ty_Int) → new_ltEs14(vwx170, vwx180)
new_esEs24(vwx302, vwx402, ty_Double) → new_esEs17(vwx302, vwx402)
new_ltEs19(vwx172, vwx182, ty_@0) → new_ltEs8(vwx172, vwx182)
new_ltEs6(Left(vwx170), Left(vwx180), app(app(ty_@2, bag), bah), bba) → new_ltEs7(vwx170, vwx180, bag, bah)
new_compare25(vwx170, vwx180, False) → new_compare110(vwx170, vwx180, new_ltEs9(vwx170, vwx180))
new_lt8(vwx170, vwx180, app(app(ty_@2, cc), cd)) → new_lt9(vwx170, vwx180, cc, cd)
new_ltEs19(vwx172, vwx182, app(app(app(ty_@3, eb), ec), ed)) → new_ltEs5(vwx172, vwx182, eb, ec, ed)
new_ltEs6(Right(vwx170), Right(vwx180), bca, app(app(ty_@2, bcb), bcc)) → new_ltEs7(vwx170, vwx180, bcb, bcc)
new_esEs21(vwx170, vwx180, app(ty_Ratio, bgd)) → new_esEs8(vwx170, vwx180, bgd)
new_esEs27(vwx301, vwx401, app(app(ty_@2, dad), dae)) → new_esEs4(vwx301, vwx401, dad, dae)
new_compare19(Float(vwx170, vwx171), Float(vwx180, vwx181)) → new_compare6(new_sr0(vwx170, vwx180), new_sr0(vwx171, vwx181))
new_lt8(vwx170, vwx180, ty_Float) → new_lt13(vwx170, vwx180)
new_esEs7(Just(vwx300), Just(vwx400), ty_@0) → new_esEs19(vwx300, vwx400)
new_compare33(Double(vwx170, vwx171), Double(vwx180, vwx181)) → new_compare6(new_sr0(vwx170, vwx180), new_sr0(vwx171, vwx181))
new_ltEs16(vwx17, vwx18, bgb) → new_not(new_esEs13(new_compare17(vwx17, vwx18, bgb), GT))
new_esEs7(Just(vwx300), Just(vwx400), ty_Ordering) → new_esEs13(vwx300, vwx400)
new_ltEs17(Just(vwx170), Just(vwx180), app(app(ty_@2, bdc), bdd)) → new_ltEs7(vwx170, vwx180, bdc, bdd)
new_lt13(vwx170, vwx180) → new_esEs13(new_compare19(vwx170, vwx180), LT)
new_esEs15(vwx300, vwx400, app(ty_[], bfc)) → new_esEs14(vwx300, vwx400, bfc)
new_lt20(vwx170, vwx180, app(app(ty_Either, hb), hc)) → new_lt15(vwx170, vwx180, hb, hc)
new_esEs6(Right(vwx300), Right(vwx400), ceg, ty_Ordering) → new_esEs13(vwx300, vwx400)
new_ltEs6(Right(vwx170), Right(vwx180), bca, ty_Double) → new_ltEs15(vwx170, vwx180)
new_ltEs18(vwx171, vwx181, ty_Ordering) → new_ltEs9(vwx171, vwx181)
new_esEs25(vwx301, vwx401, app(app(app(ty_@3, caf), cag), cah)) → new_esEs5(vwx301, vwx401, caf, cag, cah)
new_esEs22(vwx171, vwx181, app(app(ty_Either, ga), gb)) → new_esEs6(vwx171, vwx181, ga, gb)
new_esEs18(False, True) → False
new_esEs18(True, False) → False
new_compare29(vwx170, vwx180, dc, dd) → new_compare26(vwx170, vwx180, new_esEs6(vwx170, vwx180, dc, dd), dc, dd)
new_compare30(vwx170, vwx180, ty_Double) → new_compare33(vwx170, vwx180)
new_esEs27(vwx301, vwx401, ty_Bool) → new_esEs18(vwx301, vwx401)
new_esEs26(vwx300, vwx400, ty_Float) → new_esEs20(vwx300, vwx400)
new_ltEs6(Left(vwx170), Left(vwx180), ty_@0, bba) → new_ltEs8(vwx170, vwx180)
new_ltEs17(Just(vwx170), Just(vwx180), ty_Ordering) → new_ltEs9(vwx170, vwx180)
new_ltEs19(vwx172, vwx182, ty_Double) → new_ltEs15(vwx172, vwx182)
new_ltEs17(Just(vwx170), Just(vwx180), app(ty_Maybe, bec)) → new_ltEs17(vwx170, vwx180, bec)
new_esEs15(vwx300, vwx400, ty_Float) → new_esEs20(vwx300, vwx400)
new_compare13(vwx170, vwx180) → new_compare28(vwx170, vwx180, new_esEs18(vwx170, vwx180))
new_esEs28(vwx300, vwx400, ty_Double) → new_esEs17(vwx300, vwx400)
new_lt19(vwx171, vwx181, ty_@0) → new_lt6(vwx171, vwx181)
new_primPlusNat0(Succ(vwx5100), Succ(vwx400000)) → Succ(Succ(new_primPlusNat0(vwx5100, vwx400000)))
new_esEs26(vwx300, vwx400, app(app(ty_Either, ccg), cch)) → new_esEs6(vwx300, vwx400, ccg, cch)
new_compare9(vwx170, vwx180) → new_compare25(vwx170, vwx180, new_esEs13(vwx170, vwx180))
new_compare0([], :(vwx180, vwx181), he) → LT
new_esEs15(vwx300, vwx400, ty_Integer) → new_esEs12(vwx300, vwx400)
new_esEs27(vwx301, vwx401, app(ty_[], dab)) → new_esEs14(vwx301, vwx401, dab)
new_ltEs6(Right(vwx170), Right(vwx180), bca, ty_Ordering) → new_ltEs9(vwx170, vwx180)
new_esEs15(vwx300, vwx400, ty_Bool) → new_esEs18(vwx300, vwx400)
new_asAs(True, vwx43) → vwx43
new_esEs15(vwx300, vwx400, ty_Double) → new_esEs17(vwx300, vwx400)
new_esEs25(vwx301, vwx401, ty_Int) → new_esEs11(vwx301, vwx401)
new_esEs28(vwx300, vwx400, ty_Ordering) → new_esEs13(vwx300, vwx400)
new_esEs26(vwx300, vwx400, app(app(app(ty_@3, cbh), cca), ccb)) → new_esEs5(vwx300, vwx400, cbh, cca, ccb)
new_ltEs6(Right(vwx170), Right(vwx180), bca, ty_Bool) → new_ltEs4(vwx170, vwx180)
new_ltEs6(Right(vwx170), Right(vwx180), bca, ty_Char) → new_ltEs10(vwx170, vwx180)
new_esEs17(Double(vwx300, vwx301), Double(vwx400, vwx401)) → new_esEs11(new_sr0(vwx300, vwx400), new_sr0(vwx301, vwx401))
new_ltEs6(Left(vwx170), Left(vwx180), app(ty_Ratio, bee), bba) → new_ltEs16(vwx170, vwx180, bee)
new_esEs7(Just(vwx300), Just(vwx400), app(ty_[], cgf)) → new_esEs14(vwx300, vwx400, cgf)
new_esEs6(Right(vwx300), Right(vwx400), ceg, app(ty_Ratio, cga)) → new_esEs8(vwx300, vwx400, cga)
new_esEs25(vwx301, vwx401, ty_Ordering) → new_esEs13(vwx301, vwx401)
new_lt20(vwx170, vwx180, ty_Int) → new_lt14(vwx170, vwx180)
new_esEs23(vwx170, vwx180, app(app(app(ty_@3, gf), gg), gh)) → new_esEs5(vwx170, vwx180, gf, gg, gh)
new_ltEs18(vwx171, vwx181, app(ty_[], bg)) → new_ltEs12(vwx171, vwx181, bg)
new_esEs15(vwx300, vwx400, ty_@0) → new_esEs19(vwx300, vwx400)
new_esEs26(vwx300, vwx400, ty_Char) → new_esEs16(vwx300, vwx400)
new_lt8(vwx170, vwx180, app(ty_Ratio, bgd)) → new_lt17(vwx170, vwx180, bgd)
new_esEs21(vwx170, vwx180, ty_Integer) → new_esEs12(vwx170, vwx180)
new_lt16(vwx170, vwx180) → new_esEs13(new_compare33(vwx170, vwx180), LT)
new_compare30(vwx170, vwx180, app(app(ty_@2, hf), hg)) → new_compare31(vwx170, vwx180, hf, hg)
new_ltEs11(vwx17, vwx18) → new_not(new_esEs13(new_compare32(vwx17, vwx18), GT))
new_compare26(vwx170, vwx180, False, dc, dd) → new_compare11(vwx170, vwx180, new_ltEs6(vwx170, vwx180, dc, dd), dc, dd)
new_ltEs17(Just(vwx170), Just(vwx180), app(ty_Ratio, cdc)) → new_ltEs16(vwx170, vwx180, cdc)
new_compare30(vwx170, vwx180, ty_Ordering) → new_compare9(vwx170, vwx180)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs6(Right(vwx300), Right(vwx400), ceg, app(app(app(ty_@3, ceh), cfa), cfb)) → new_esEs5(vwx300, vwx400, ceh, cfa, cfb)
new_primCompAux0(vwx85, EQ) → vwx85
new_lt19(vwx171, vwx181, ty_Int) → new_lt14(vwx171, vwx181)
new_ltEs19(vwx172, vwx182, app(app(ty_Either, ef), eg)) → new_ltEs6(vwx172, vwx182, ef, eg)
new_esEs26(vwx300, vwx400, ty_Ordering) → new_esEs13(vwx300, vwx400)
new_ltEs10(vwx17, vwx18) → new_not(new_esEs13(new_compare12(vwx17, vwx18), GT))
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_esEs22(vwx171, vwx181, app(ty_Maybe, gc)) → new_esEs7(vwx171, vwx181, gc)
new_primCmpInt(Neg(Succ(vwx1700)), Pos(vwx180)) → LT
new_not(True) → False
new_ltEs6(Left(vwx170), Left(vwx180), ty_Integer, bba) → new_ltEs11(vwx170, vwx180)
new_esEs18(False, False) → True

The set Q consists of the following terms:

new_esEs25(x0, x1, ty_Double)
new_esEs7(Just(x0), Nothing, x1)
new_compare30(x0, x1, ty_Double)
new_ltEs17(Just(x0), Just(x1), ty_Integer)
new_ltEs6(Left(x0), Left(x1), ty_Char, x2)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare31(x0, x1, x2, x3)
new_lt8(x0, x1, ty_@0)
new_ltEs18(x0, x1, ty_Ordering)
new_ltEs17(Just(x0), Nothing, x1)
new_primCompAux0(x0, GT)
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_esEs15(x0, x1, app(app(ty_Either, x2), x3))
new_lt20(x0, x1, ty_Integer)
new_lt19(x0, x1, app(ty_[], x2))
new_esEs6(Right(x0), Right(x1), x2, ty_Float)
new_lt19(x0, x1, ty_Float)
new_esEs15(x0, x1, ty_Ordering)
new_esEs13(GT, GT)
new_ltEs15(x0, x1)
new_ltEs6(Left(x0), Left(x1), app(ty_[], x2), x3)
new_compare30(x0, x1, ty_Char)
new_esEs20(Float(x0, x1), Float(x2, x3))
new_esEs22(x0, x1, app(ty_[], x2))
new_esEs6(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_compare24(x0, x1, False, x2)
new_esEs6(Right(x0), Right(x1), x2, ty_Integer)
new_esEs24(x0, x1, ty_Bool)
new_primPlusNat1(Succ(x0), x1)
new_lt20(x0, x1, ty_@0)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs15(x0, x1, ty_Integer)
new_lt8(x0, x1, ty_Float)
new_esEs14(:(x0, x1), [], x2)
new_ltEs6(Right(x0), Right(x1), x2, ty_Char)
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs18(x0, x1, app(ty_Maybe, x2))
new_ltEs6(Left(x0), Left(x1), ty_Float, x2)
new_esEs24(x0, x1, ty_@0)
new_compare24(x0, x1, True, x2)
new_esEs6(Left(x0), Left(x1), ty_Double, x2)
new_esEs27(x0, x1, ty_@0)
new_esEs23(x0, x1, ty_Int)
new_ltEs19(x0, x1, ty_Int)
new_lt8(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs7(Just(x0), Just(x1), app(ty_Ratio, x2))
new_compare23(x0, x1, True, x2, x3, x4)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs7(Just(x0), Just(x1), ty_Integer)
new_esEs14(:(x0, x1), :(x2, x3), x4)
new_esEs18(True, True)
new_esEs7(Nothing, Nothing, x0)
new_esEs15(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_esEs14([], :(x0, x1), x2)
new_compare0([], [], x0)
new_compare110(x0, x1, False)
new_lt20(x0, x1, ty_Float)
new_esEs6(Left(x0), Left(x1), ty_@0, x2)
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_esEs15(x0, x1, ty_@0)
new_esEs28(x0, x1, ty_Double)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs28(x0, x1, ty_Bool)
new_esEs27(x0, x1, ty_Int)
new_esEs23(x0, x1, ty_Double)
new_compare26(x0, x1, False, x2, x3)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_compare10(x0, x1, True, x2, x3, x4)
new_primPlusNat0(Succ(x0), Succ(x1))
new_ltEs18(x0, x1, ty_Integer)
new_esEs21(x0, x1, ty_@0)
new_esEs6(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs22(x0, x1, ty_Double)
new_esEs13(LT, GT)
new_esEs13(GT, LT)
new_esEs22(x0, x1, ty_Float)
new_ltEs6(Right(x0), Right(x1), x2, ty_Ordering)
new_ltEs9(EQ, EQ)
new_lt4(x0, x1)
new_compare15(x0, x1, True, x2, x3)
new_lt8(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_esEs24(x0, x1, ty_Char)
new_lt8(x0, x1, ty_Double)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_lt19(x0, x1, ty_Bool)
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_compare10(x0, x1, False, x2, x3, x4)
new_primEqNat0(Zero, Zero)
new_esEs15(x0, x1, ty_Float)
new_compare18(x0, x1, False)
new_esEs6(Left(x0), Left(x1), ty_Char, x2)
new_esEs27(x0, x1, ty_Integer)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs25(x0, x1, ty_Float)
new_ltEs6(Left(x0), Left(x1), ty_Bool, x2)
new_primMulInt(Pos(x0), Pos(x1))
new_lt20(x0, x1, app(ty_Maybe, x2))
new_compare9(x0, x1)
new_ltEs4(True, True)
new_esEs13(GT, EQ)
new_esEs13(EQ, GT)
new_esEs27(x0, x1, ty_Char)
new_esEs25(x0, x1, ty_Integer)
new_compare13(x0, x1)
new_ltEs18(x0, x1, ty_Float)
new_esEs26(x0, x1, ty_Integer)
new_esEs6(Left(x0), Left(x1), ty_Int, x2)
new_esEs6(Right(x0), Right(x1), x2, ty_@0)
new_primMulNat0(Zero, Zero)
new_compare29(x0, x1, x2, x3)
new_esEs21(x0, x1, app(ty_[], x2))
new_ltEs17(Just(x0), Just(x1), app(ty_Ratio, x2))
new_primCmpNat0(Zero, Succ(x0))
new_ltEs11(x0, x1)
new_ltEs16(x0, x1, x2)
new_esEs17(Double(x0, x1), Double(x2, x3))
new_esEs9(x0, x1, ty_Int)
new_ltEs6(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_ltEs19(x0, x1, ty_@0)
new_compare26(x0, x1, True, x2, x3)
new_esEs21(x0, x1, ty_Char)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_compare30(x0, x1, app(ty_Ratio, x2))
new_compare18(x0, x1, True)
new_lt20(x0, x1, ty_Double)
new_ltEs17(Just(x0), Just(x1), ty_Double)
new_compare16(x0, x1, True, x2)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs6(Right(x0), Right(x1), x2, ty_Double)
new_compare17(:%(x0, x1), :%(x2, x3), ty_Int)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_compare30(x0, x1, ty_@0)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, app(ty_[], x2))
new_ltEs17(Just(x0), Just(x1), ty_Int)
new_lt6(x0, x1)
new_esEs13(EQ, EQ)
new_ltEs19(x0, x1, ty_Ordering)
new_esEs28(x0, x1, ty_Int)
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_primMulNat0(Zero, Succ(x0))
new_lt19(x0, x1, ty_Char)
new_compare8(x0, x1, x2)
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_esEs6(Left(x0), Right(x1), x2, x3)
new_esEs6(Right(x0), Left(x1), x2, x3)
new_ltEs4(False, False)
new_esEs23(x0, x1, ty_@0)
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs6(Left(x0), Left(x1), app(ty_[], x2), x3)
new_lt16(x0, x1)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_ltEs18(x0, x1, ty_Double)
new_lt8(x0, x1, ty_Bool)
new_esEs18(False, False)
new_esEs22(x0, x1, ty_Int)
new_ltEs19(x0, x1, ty_Double)
new_lt12(x0, x1, x2)
new_esEs7(Nothing, Just(x0), x1)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_ltEs9(GT, EQ)
new_ltEs9(EQ, GT)
new_compare17(:%(x0, x1), :%(x2, x3), ty_Integer)
new_primPlusNat0(Succ(x0), Zero)
new_lt8(x0, x1, ty_Char)
new_lt19(x0, x1, app(ty_Maybe, x2))
new_lt19(x0, x1, ty_Int)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_compare33(Double(x0, x1), Double(x2, x3))
new_lt9(x0, x1, x2, x3)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primCompAux0(x0, LT)
new_compare12(Char(x0), Char(x1))
new_esEs6(Left(x0), Left(x1), ty_Integer, x2)
new_compare7(x0, x1, x2, x3, x4)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_compare11(x0, x1, False, x2, x3)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_compare15(x0, x1, False, x2, x3)
new_ltEs18(x0, x1, ty_Int)
new_ltEs6(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_ltEs18(x0, x1, app(ty_Ratio, x2))
new_esEs7(Just(x0), Just(x1), ty_Char)
new_primEqNat0(Succ(x0), Zero)
new_esEs21(x0, x1, ty_Bool)
new_lt20(x0, x1, ty_Char)
new_primPlusNat0(Zero, Zero)
new_ltEs6(Left(x0), Left(x1), ty_@0, x2)
new_esEs15(x0, x1, app(ty_Maybe, x2))
new_ltEs19(x0, x1, ty_Integer)
new_ltEs6(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs25(x0, x1, ty_Bool)
new_compare11(x0, x1, True, x2, x3)
new_ltEs6(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs28(x0, x1, ty_Char)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs27(x0, x1, ty_Float)
new_esEs16(Char(x0), Char(x1))
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs17(Just(x0), Just(x1), ty_Ordering)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_compare110(x0, x1, True)
new_ltEs6(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_ltEs17(Nothing, Nothing, x0)
new_ltEs6(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs6(Right(x0), Right(x1), x2, ty_Integer)
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_ltEs6(Left(x0), Left(x1), ty_Integer, x2)
new_lt19(x0, x1, ty_Integer)
new_ltEs6(Right(x0), Right(x1), x2, ty_Bool)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_esEs6(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_primCmpNat0(Succ(x0), Zero)
new_ltEs9(EQ, LT)
new_ltEs9(LT, EQ)
new_esEs6(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_compare19(Float(x0, x1), Float(x2, x3))
new_esEs7(Just(x0), Just(x1), ty_Int)
new_ltEs13(x0, x1)
new_compare6(x0, x1)
new_esEs15(x0, x1, ty_Int)
new_compare30(x0, x1, ty_Int)
new_esEs21(x0, x1, ty_Ordering)
new_lt8(x0, x1, app(ty_Ratio, x2))
new_esEs7(Just(x0), Just(x1), ty_Ordering)
new_ltEs10(x0, x1)
new_esEs26(x0, x1, ty_@0)
new_esEs24(x0, x1, ty_Float)
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_ltEs19(x0, x1, ty_Bool)
new_esEs12(Integer(x0), Integer(x1))
new_lt19(x0, x1, app(ty_Ratio, x2))
new_ltEs18(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, app(ty_[], x2))
new_ltEs6(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_ltEs8(x0, x1)
new_compare30(x0, x1, ty_Ordering)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_primCompAux0(x0, EQ)
new_lt19(x0, x1, ty_Double)
new_ltEs18(x0, x1, app(app(ty_Either, x2), x3))
new_esEs24(x0, x1, app(ty_[], x2))
new_ltEs17(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs25(x0, x1, app(ty_[], x2))
new_compare28(x0, x1, False)
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_ltEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs18(False, True)
new_esEs18(True, False)
new_esEs21(x0, x1, ty_Float)
new_asAs(True, x0)
new_primEqInt(Neg(Zero), Neg(Zero))
new_compare14(@0, @0)
new_compare30(x0, x1, ty_Bool)
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_compare27(x0, x1, False, x2, x3)
new_esEs14([], [], x0)
new_ltEs19(x0, x1, ty_Float)
new_esEs15(x0, x1, ty_Bool)
new_ltEs6(Right(x0), Right(x1), x2, ty_@0)
new_compare27(x0, x1, True, x2, x3)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_esEs15(x0, x1, app(ty_[], x2))
new_lt13(x0, x1)
new_ltEs18(x0, x1, ty_Bool)
new_esEs24(x0, x1, ty_Integer)
new_ltEs6(Right(x0), Right(x1), x2, ty_Int)
new_pePe(True, x0)
new_esEs25(x0, x1, ty_Char)
new_esEs23(x0, x1, ty_Integer)
new_ltEs18(x0, x1, ty_Char)
new_ltEs6(Left(x0), Left(x1), ty_Int, x2)
new_esEs26(x0, x1, app(ty_[], x2))
new_esEs15(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, ty_Int)
new_lt18(x0, x1, x2)
new_esEs22(x0, x1, ty_Bool)
new_ltEs9(LT, LT)
new_lt7(x0, x1)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs28(x0, x1, ty_@0)
new_sr(Integer(x0), Integer(x1))
new_esEs6(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_ltEs6(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_compare16(x0, x1, False, x2)
new_compare30(x0, x1, app(app(ty_Either, x2), x3))
new_primPlusNat1(Zero, x0)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_lt14(x0, x1)
new_ltEs6(Left(x0), Right(x1), x2, x3)
new_ltEs6(Right(x0), Left(x1), x2, x3)
new_esEs25(x0, x1, ty_Ordering)
new_esEs22(x0, x1, ty_Integer)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs4(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_primCmpNat0(Zero, Zero)
new_esEs21(x0, x1, ty_Integer)
new_esEs23(x0, x1, ty_Float)
new_pePe(False, x0)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_compare32(Integer(x0), Integer(x1))
new_lt5(x0, x1)
new_esEs26(x0, x1, ty_Char)
new_esEs8(:%(x0, x1), :%(x2, x3), x4)
new_esEs9(x0, x1, ty_Integer)
new_ltEs4(False, True)
new_ltEs4(True, False)
new_compare28(x0, x1, True)
new_ltEs12(x0, x1, x2)
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(Just(x0), Just(x1), ty_@0)
new_esEs27(x0, x1, app(ty_[], x2))
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs28(x0, x1, ty_Ordering)
new_esEs10(x0, x1, ty_Integer)
new_esEs28(x0, x1, ty_Integer)
new_esEs15(x0, x1, ty_Char)
new_esEs26(x0, x1, ty_Float)
new_ltEs7(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs7(Just(x0), Just(x1), app(ty_[], x2))
new_lt15(x0, x1, x2, x3)
new_esEs10(x0, x1, ty_Int)
new_esEs13(LT, LT)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primEqNat0(Zero, Succ(x0))
new_ltEs17(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs6(Right(x0), Right(x1), x2, ty_Double)
new_compare0(:(x0, x1), [], x2)
new_compare30(x0, x1, ty_Integer)
new_compare30(x0, x1, app(ty_Maybe, x2))
new_compare30(x0, x1, app(app(ty_@2, x2), x3))
new_lt8(x0, x1, app(ty_[], x2))
new_esEs27(x0, x1, ty_Bool)
new_primMulNat0(Succ(x0), Zero)
new_ltEs6(Right(x0), Right(x1), x2, ty_Float)
new_compare0([], :(x0, x1), x2)
new_primMulNat0(Succ(x0), Succ(x1))
new_esEs28(x0, x1, app(ty_[], x2))
new_esEs15(x0, x1, app(app(ty_@2, x2), x3))
new_esEs21(x0, x1, ty_Int)
new_esEs26(x0, x1, ty_Ordering)
new_lt19(x0, x1, ty_Ordering)
new_ltEs9(GT, LT)
new_ltEs9(LT, GT)
new_esEs6(Right(x0), Right(x1), x2, ty_Char)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs17(Just(x0), Just(x1), ty_Char)
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs6(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs25(x0, x1, ty_@0)
new_esEs6(Left(x0), Left(x1), ty_Bool, x2)
new_lt8(x0, x1, ty_Integer)
new_not(True)
new_esEs6(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs28(x0, x1, ty_Float)
new_lt11(x0, x1, x2, x3, x4)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_esEs13(EQ, LT)
new_esEs13(LT, EQ)
new_esEs6(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_lt10(x0, x1)
new_esEs26(x0, x1, ty_Bool)
new_ltEs17(Just(x0), Just(x1), app(ty_Maybe, x2))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_not(False)
new_ltEs5(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs26(x0, x1, ty_Int)
new_esEs6(Right(x0), Right(x1), x2, ty_Int)
new_esEs6(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs24(x0, x1, ty_Ordering)
new_esEs23(x0, x1, ty_Bool)
new_ltEs17(Just(x0), Just(x1), ty_Float)
new_esEs23(x0, x1, ty_Char)
new_compare30(x0, x1, ty_Float)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_ltEs18(x0, x1, app(ty_[], x2))
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_lt8(x0, x1, ty_Int)
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs22(x0, x1, ty_@0)
new_compare25(x0, x1, False)
new_esEs7(Just(x0), Just(x1), ty_Float)
new_compare30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs22(x0, x1, ty_Ordering)
new_esEs6(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs7(Just(x0), Just(x1), ty_Bool)
new_esEs24(x0, x1, ty_Double)
new_lt20(x0, x1, ty_Bool)
new_esEs24(x0, x1, ty_Int)
new_ltEs18(x0, x1, ty_@0)
new_esEs6(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs7(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_compare25(x0, x1, True)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs6(Left(x0), Left(x1), ty_Float, x2)
new_compare30(x0, x1, app(ty_[], x2))
new_lt8(x0, x1, ty_Ordering)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_ltEs9(GT, GT)
new_ltEs19(x0, x1, ty_Char)
new_ltEs17(Just(x0), Just(x1), ty_@0)
new_compare23(x0, x1, False, x2, x3, x4)
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_lt20(x0, x1, ty_Ordering)
new_ltEs19(x0, x1, app(ty_[], x2))
new_esEs27(x0, x1, ty_Double)
new_lt17(x0, x1, x2)
new_esEs7(Just(x0), Just(x1), app(ty_Maybe, x2))
new_ltEs6(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs21(x0, x1, ty_Double)
new_esEs15(x0, x1, ty_Double)
new_esEs23(x0, x1, ty_Ordering)
new_primCompAux1(x0, x1, x2, x3)
new_lt19(x0, x1, ty_@0)
new_esEs6(Right(x0), Right(x1), x2, ty_Bool)
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt8(x0, x1, app(app(ty_@2, x2), x3))
new_asAs(False, x0)
new_esEs5(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_primEqInt(Pos(Zero), Pos(Zero))
new_ltEs6(Left(x0), Left(x1), ty_Double, x2)
new_primPlusNat0(Zero, Succ(x0))
new_esEs7(Just(x0), Just(x1), ty_Double)
new_ltEs6(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs14(x0, x1)
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_sr0(x0, x1)
new_esEs19(@0, @0)
new_esEs26(x0, x1, ty_Double)
new_esEs11(x0, x1)
new_ltEs17(Just(x0), Just(x1), ty_Bool)
new_ltEs6(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs25(x0, x1, ty_Int)
new_ltEs17(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, ty_Ordering)
new_ltEs17(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs17(Nothing, Just(x0), x1)
new_esEs22(x0, x1, ty_Char)
new_compare0(:(x0, x1), :(x2, x3), x4)
new_lt8(x0, x1, app(app(ty_Either, x2), x3))
new_esEs7(Just(x0), Just(x1), app(app(ty_@2, x2), x3))

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: