YES 3.642 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 b, Ord a) => Either b a  ->  Either b a  ->  Bool) :: (Ord a, Ord b) => Either b a  ->  Either b 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 b, Ord a) => Either b a  ->  Either b a  ->  Bool) :: (Ord a, Ord b) => Either b a  ->  Either b 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 b, Ord a) => Either a b  ->  Either a b  ->  Bool) :: (Ord b, Ord a) => Either a b  ->  Either a b  ->  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 b, Ord a) => Either b a  ->  Either b a  ->  Bool) :: (Ord b, Ord a) => Either b a  ->  Either b 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

compare0 x y True = GT

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

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

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 b, Ord a) => Either a b  ->  Either a b  ->  Bool) :: (Ord b, Ord a) => Either a b  ->  Either a b  ->  Bool)

module Main where
  import qualified Prelude


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

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

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

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

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

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

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

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

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



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

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

module Main where
  import qualified Prelude


Haskell To QDPs


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

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

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

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

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



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

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

new_primPlusNat(Succ(vwx6100), Succ(vwx400000)) → new_primPlusNat(vwx6100, vwx400000)

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

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



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

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

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

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

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



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

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

new_primCmpNat(Succ(vwx2400), Succ(vwx2500)) → new_primCmpNat(vwx2400, vwx2500)

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

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

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



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

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

new_ltEs1(@2(vwx240, vwx241), @2(vwx250, vwx251), df, app(app(ty_@2, ea), eb)) → new_ltEs1(vwx241, vwx251, ea, eb)
new_ltEs0(Just(vwx240), Just(vwx250), app(app(app(ty_@3, dc), dd), de)) → new_ltEs3(vwx240, vwx250, dc, dd, de)
new_ltEs3(@3(vwx240, vwx241, vwx242), @3(vwx250, vwx251, vwx252), baf, app(ty_Maybe, bcc), bcb) → new_lt0(vwx241, vwx251, bcc)
new_compare0(:(vwx240, vwx241), :(vwx250, vwx251), ba) → new_primCompAux(vwx240, vwx250, new_compare(vwx241, vwx251, ba), ba)
new_ltEs2(Left(vwx240), Left(vwx250), app(app(app(ty_@3, ha), hb), hc), gc) → new_ltEs3(vwx240, vwx250, ha, hb, hc)
new_lt3(vwx240, vwx250, fg, fh, ga) → new_compare23(vwx240, vwx250, new_esEs7(vwx240, vwx250, fg, fh, ga), fg, fh, ga)
new_ltEs1(@2(vwx240, vwx241), @2(vwx250, vwx251), app(ty_Maybe, cc), fa) → new_compare20(vwx240, vwx250, new_esEs4(vwx240, vwx250, cc), cc)
new_ltEs3(@3(vwx240, vwx241, vwx242), @3(vwx250, vwx251, vwx252), baf, app(ty_[], bca), bcb) → new_lt(vwx241, vwx251, bca)
new_ltEs3(@3(vwx240, vwx241, vwx242), @3(vwx250, vwx251, vwx252), baf, app(app(ty_Either, bcf), bcg), bcb) → new_lt2(vwx241, vwx251, bcf, bcg)
new_ltEs1(@2(vwx240, vwx241), @2(vwx250, vwx251), df, app(ty_Maybe, dh)) → new_ltEs0(vwx241, vwx251, dh)
new_ltEs3(@3(vwx240, vwx241, vwx242), @3(vwx250, vwx251, vwx252), app(ty_[], bdc), bag, bcb) → new_lt(vwx240, vwx250, bdc)
new_compare0(:(vwx240, vwx241), :(vwx250, vwx251), ba) → new_compare0(vwx241, vwx251, ba)
new_ltEs2(Left(vwx240), Left(vwx250), app(app(ty_Either, gg), gh), gc) → new_ltEs2(vwx240, vwx250, gg, gh)
new_ltEs3(@3(vwx240, vwx241, vwx242), @3(vwx250, vwx251, vwx252), baf, bag, app(ty_[], bah)) → new_ltEs(vwx242, vwx252, bah)
new_compare2(vwx240, vwx250, fb, fc) → new_compare21(vwx240, vwx250, new_esEs5(vwx240, vwx250, fb, fc), fb, fc)
new_ltEs2(Right(vwx240), Right(vwx250), hd, app(app(ty_@2, hg), hh)) → new_ltEs1(vwx240, vwx250, hg, hh)
new_ltEs2(Right(vwx240), Right(vwx250), hd, app(ty_[], he)) → new_ltEs(vwx240, vwx250, he)
new_ltEs0(Just(vwx240), Just(vwx250), app(ty_Maybe, ce)) → new_ltEs0(vwx240, vwx250, ce)
new_compare3(vwx240, vwx250, fd, ff) → new_compare22(vwx240, vwx250, new_esEs6(vwx240, vwx250, fd, ff), fd, ff)
new_ltEs3(@3(vwx240, vwx241, vwx242), @3(vwx250, vwx251, vwx252), baf, bag, app(ty_Maybe, bba)) → new_ltEs0(vwx242, vwx252, bba)
new_ltEs3(@3(vwx240, vwx241, vwx242), @3(vwx250, vwx251, vwx252), baf, app(app(ty_@2, bcd), bce), bcb) → new_lt1(vwx241, vwx251, bcd, bce)
new_ltEs2(Right(vwx240), Right(vwx250), hd, app(ty_Maybe, hf)) → new_ltEs0(vwx240, vwx250, hf)
new_ltEs(:(vwx240, vwx241), :(vwx250, vwx251), ba) → new_primCompAux(vwx240, vwx250, new_compare(vwx241, vwx251, ba), ba)
new_primCompAux(vwx240, vwx250, vwx82, app(ty_[], bb)) → new_compare0(vwx240, vwx250, bb)
new_ltEs3(@3(vwx240, vwx241, vwx242), @3(vwx250, vwx251, vwx252), app(app(ty_Either, bdg), bdh), bag, bcb) → new_lt2(vwx240, vwx250, bdg, bdh)
new_compare21(vwx240, vwx250, False, fb, fc) → new_ltEs1(vwx240, vwx250, fb, fc)
new_ltEs1(@2(vwx240, vwx241), @2(vwx250, vwx251), app(app(ty_@2, fb), fc), fa) → new_compare21(vwx240, vwx250, new_esEs5(vwx240, vwx250, fb, fc), fb, fc)
new_ltEs2(Right(vwx240), Right(vwx250), hd, app(app(ty_Either, baa), bab)) → new_ltEs2(vwx240, vwx250, baa, bab)
new_ltEs3(@3(vwx240, vwx241, vwx242), @3(vwx250, vwx251, vwx252), app(app(ty_@2, bde), bdf), bag, bcb) → new_lt1(vwx240, vwx250, bde, bdf)
new_ltEs0(Just(vwx240), Just(vwx250), app(ty_[], cd)) → new_ltEs(vwx240, vwx250, cd)
new_ltEs2(Left(vwx240), Left(vwx250), app(ty_Maybe, gd), gc) → new_ltEs0(vwx240, vwx250, gd)
new_ltEs3(@3(vwx240, vwx241, vwx242), @3(vwx250, vwx251, vwx252), baf, bag, app(app(app(ty_@3, bbf), bbg), bbh)) → new_ltEs3(vwx242, vwx252, bbf, bbg, bbh)
new_ltEs1(@2(vwx240, vwx241), @2(vwx250, vwx251), app(app(ty_Either, fd), ff), fa) → new_compare22(vwx240, vwx250, new_esEs6(vwx240, vwx250, fd, ff), fd, ff)
new_primCompAux(vwx240, vwx250, vwx82, app(app(ty_@2, bd), be)) → new_compare2(vwx240, vwx250, bd, be)
new_ltEs(:(vwx240, vwx241), :(vwx250, vwx251), ba) → new_compare0(vwx241, vwx251, ba)
new_ltEs3(@3(vwx240, vwx241, vwx242), @3(vwx250, vwx251, vwx252), baf, bag, app(app(ty_@2, bbb), bbc)) → new_ltEs1(vwx242, vwx252, bbb, bbc)
new_ltEs3(@3(vwx240, vwx241, vwx242), @3(vwx250, vwx251, vwx252), app(app(app(ty_@3, bea), beb), bec), bag, bcb) → new_lt3(vwx240, vwx250, bea, beb, bec)
new_primCompAux(vwx240, vwx250, vwx82, app(ty_Maybe, bc)) → new_compare1(vwx240, vwx250, bc)
new_primCompAux(vwx240, vwx250, vwx82, app(app(ty_Either, bf), bg)) → new_compare3(vwx240, vwx250, bf, bg)
new_ltEs1(@2(vwx240, vwx241), @2(vwx250, vwx251), df, app(ty_[], dg)) → new_ltEs(vwx241, vwx251, dg)
new_ltEs1(@2(vwx240, vwx241), @2(vwx250, vwx251), app(app(app(ty_@3, fg), fh), ga), fa) → new_compare23(vwx240, vwx250, new_esEs7(vwx240, vwx250, fg, fh, ga), fg, fh, ga)
new_ltEs1(@2(vwx240, vwx241), @2(vwx250, vwx251), app(ty_[], eh), fa) → new_compare0(vwx240, vwx250, eh)
new_ltEs3(@3(vwx240, vwx241, vwx242), @3(vwx250, vwx251, vwx252), baf, app(app(app(ty_@3, bch), bda), bdb), bcb) → new_lt3(vwx241, vwx251, bch, bda, bdb)
new_ltEs0(Just(vwx240), Just(vwx250), app(app(ty_@2, cf), cg)) → new_ltEs1(vwx240, vwx250, cf, cg)
new_compare1(vwx240, vwx250, cc) → new_compare20(vwx240, vwx250, new_esEs4(vwx240, vwx250, cc), cc)
new_lt(vwx240, vwx250, eh) → new_compare0(vwx240, vwx250, eh)
new_ltEs0(Just(vwx240), Just(vwx250), app(app(ty_Either, da), db)) → new_ltEs2(vwx240, vwx250, da, db)
new_lt1(vwx240, vwx250, fb, fc) → new_compare21(vwx240, vwx250, new_esEs5(vwx240, vwx250, fb, fc), fb, fc)
new_ltEs3(@3(vwx240, vwx241, vwx242), @3(vwx250, vwx251, vwx252), baf, bag, app(app(ty_Either, bbd), bbe)) → new_ltEs2(vwx242, vwx252, bbd, bbe)
new_ltEs2(Left(vwx240), Left(vwx250), app(app(ty_@2, ge), gf), gc) → new_ltEs1(vwx240, vwx250, ge, gf)
new_ltEs2(Left(vwx240), Left(vwx250), app(ty_[], gb), gc) → new_ltEs(vwx240, vwx250, gb)
new_ltEs1(@2(vwx240, vwx241), @2(vwx250, vwx251), df, app(app(app(ty_@3, ee), ef), eg)) → new_ltEs3(vwx241, vwx251, ee, ef, eg)
new_lt2(vwx240, vwx250, fd, ff) → new_compare22(vwx240, vwx250, new_esEs6(vwx240, vwx250, fd, ff), fd, ff)
new_lt0(vwx240, vwx250, cc) → new_compare20(vwx240, vwx250, new_esEs4(vwx240, vwx250, cc), cc)
new_compare22(vwx240, vwx250, False, fd, ff) → new_ltEs2(vwx240, vwx250, fd, ff)
new_compare4(vwx240, vwx250, fg, fh, ga) → new_compare23(vwx240, vwx250, new_esEs7(vwx240, vwx250, fg, fh, ga), fg, fh, ga)
new_ltEs2(Right(vwx240), Right(vwx250), hd, app(app(app(ty_@3, bac), bad), bae)) → new_ltEs3(vwx240, vwx250, bac, bad, bae)
new_compare20(vwx240, vwx250, False, cc) → new_ltEs0(vwx240, vwx250, cc)
new_primCompAux(vwx240, vwx250, vwx82, app(app(app(ty_@3, bh), ca), cb)) → new_compare4(vwx240, vwx250, bh, ca, cb)
new_compare23(vwx240, vwx250, False, fg, fh, ga) → new_ltEs3(vwx240, vwx250, fg, fh, ga)
new_ltEs3(@3(vwx240, vwx241, vwx242), @3(vwx250, vwx251, vwx252), app(ty_Maybe, bdd), bag, bcb) → new_lt0(vwx240, vwx250, bdd)
new_ltEs1(@2(vwx240, vwx241), @2(vwx250, vwx251), df, app(app(ty_Either, ec), ed)) → new_ltEs2(vwx241, vwx251, ec, ed)

The TRS R consists of the following rules:

new_esEs4(Just(vwx300), Just(vwx400), app(ty_Maybe, cfa)) → new_esEs4(vwx300, vwx400, cfa)
new_lt19(vwx241, vwx251, ty_Float) → new_lt6(vwx241, vwx251)
new_lt16(vwx240, vwx250, ty_Bool) → new_lt15(vwx240, vwx250)
new_compare17(Char(vwx240), Char(vwx250)) → new_primCmpNat0(vwx240, vwx250)
new_lt4(vwx240, vwx250) → new_esEs8(new_compare5(vwx240, vwx250), LT)
new_esEs4(Just(vwx300), Just(vwx400), ty_Ordering) → new_esEs8(vwx300, vwx400)
new_esEs27(vwx241, vwx251, app(ty_[], bca)) → new_esEs16(vwx241, vwx251, bca)
new_lt15(vwx240, vwx250) → new_esEs8(new_compare16(vwx240, vwx250), LT)
new_ltEs4(EQ, GT) → True
new_esEs25(vwx300, vwx400, app(ty_[], cfd)) → new_esEs16(vwx300, vwx400, cfd)
new_esEs21(vwx301, vwx401, ty_Float) → new_esEs14(vwx301, vwx401)
new_lt19(vwx241, vwx251, app(app(app(ty_@3, bch), bda), bdb)) → new_lt8(vwx241, vwx251, bch, bda, bdb)
new_esEs23(vwx301, vwx401, ty_Integer) → new_esEs19(vwx301, vwx401)
new_ltEs17(@3(vwx240, vwx241, vwx242), @3(vwx250, vwx251, vwx252), baf, bag, bcb) → new_pePe(new_lt20(vwx240, vwx250, baf), new_asAs(new_esEs28(vwx240, vwx250, baf), new_pePe(new_lt19(vwx241, vwx251, bag), new_asAs(new_esEs27(vwx241, vwx251, bag), new_ltEs19(vwx242, vwx252, bcb)))))
new_ltEs19(vwx242, vwx252, app(ty_[], bah)) → new_ltEs9(vwx242, vwx252, bah)
new_esEs27(vwx241, vwx251, app(ty_Ratio, dbh)) → new_esEs18(vwx241, vwx251, dbh)
new_ltEs18(vwx241, vwx251, ty_Float) → new_ltEs15(vwx241, vwx251)
new_esEs28(vwx240, vwx250, ty_Float) → new_esEs14(vwx240, vwx250)
new_compare([], :(vwx250, vwx251), ba) → LT
new_compare16(vwx240, vwx250) → new_compare24(vwx240, vwx250, new_esEs17(vwx240, vwx250))
new_esEs9(vwx301, vwx401, ty_@0) → new_esEs13(vwx301, vwx401)
new_esEs4(Nothing, Just(vwx400), cdg) → False
new_esEs4(Just(vwx300), Nothing, cdg) → False
new_lt20(vwx240, vwx250, app(app(app(ty_@3, bea), beb), bec)) → new_lt8(vwx240, vwx250, bea, beb, bec)
new_esEs28(vwx240, vwx250, ty_Integer) → new_esEs19(vwx240, vwx250)
new_ltEs6(Nothing, Just(vwx250), bee) → True
new_esEs9(vwx301, vwx401, ty_Char) → new_esEs15(vwx301, vwx401)
new_esEs7(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), bhe, bhf, bhg) → new_asAs(new_esEs22(vwx300, vwx400, bhe), new_asAs(new_esEs21(vwx301, vwx401, bhf), new_esEs20(vwx302, vwx402, bhg)))
new_compare8(vwx240, vwx250, app(ty_Ratio, bed)) → new_compare11(vwx240, vwx250, bed)
new_esEs27(vwx241, vwx251, ty_Bool) → new_esEs17(vwx241, vwx251)
new_lt19(vwx241, vwx251, ty_Int) → new_lt4(vwx241, vwx251)
new_primMulNat0(Zero, Zero) → Zero
new_esEs21(vwx301, vwx401, ty_Int) → new_esEs12(vwx301, vwx401)
new_esEs10(vwx300, vwx400, ty_@0) → new_esEs13(vwx300, vwx400)
new_lt11(vwx240, vwx250, cfb) → new_esEs8(new_compare11(vwx240, vwx250, cfb), LT)
new_compare(:(vwx240, vwx241), [], ba) → GT
new_esEs26(vwx240, vwx250, app(ty_[], eh)) → new_esEs16(vwx240, vwx250, eh)
new_esEs6(Left(vwx300), Left(vwx400), app(app(app(ty_@3, che), chf), chg), cgf) → new_esEs7(vwx300, vwx400, che, chf, chg)
new_esEs25(vwx300, vwx400, app(app(ty_Either, cfe), cff)) → new_esEs6(vwx300, vwx400, cfe, cff)
new_compare27(vwx240, vwx250, False, cc) → new_compare113(vwx240, vwx250, new_ltEs6(vwx240, vwx250, cc), cc)
new_esEs20(vwx302, vwx402, app(ty_Maybe, cba)) → new_esEs4(vwx302, vwx402, cba)
new_ltEs12(Right(vwx240), Right(vwx250), hd, ty_Double) → new_ltEs16(vwx240, vwx250)
new_esEs21(vwx301, vwx401, ty_Bool) → new_esEs17(vwx301, vwx401)
new_lt20(vwx240, vwx250, ty_Float) → new_lt6(vwx240, vwx250)
new_ltEs18(vwx241, vwx251, ty_Integer) → new_ltEs5(vwx241, vwx251)
new_esEs25(vwx300, vwx400, app(ty_Ratio, cga)) → new_esEs18(vwx300, vwx400, cga)
new_esEs25(vwx300, vwx400, ty_Bool) → new_esEs17(vwx300, vwx400)
new_esEs26(vwx240, vwx250, ty_Char) → new_esEs15(vwx240, vwx250)
new_lt7(vwx240, vwx250) → new_esEs8(new_compare10(vwx240, vwx250), LT)
new_ltEs18(vwx241, vwx251, app(ty_[], dg)) → new_ltEs9(vwx241, vwx251, dg)
new_compare8(vwx240, vwx250, app(app(app(ty_@3, bh), ca), cb)) → new_compare18(vwx240, vwx250, bh, ca, cb)
new_compare29(vwx240, vwx250, False, fd, ff) → new_compare114(vwx240, vwx250, new_ltEs12(vwx240, vwx250, fd, ff), fd, ff)
new_ltEs7(vwx24, vwx25) → new_not(new_esEs8(new_compare9(vwx24, vwx25), GT))
new_esEs10(vwx300, vwx400, ty_Int) → new_esEs12(vwx300, vwx400)
new_compare8(vwx240, vwx250, ty_Float) → new_compare7(vwx240, vwx250)
new_esEs21(vwx301, vwx401, ty_Integer) → new_esEs19(vwx301, vwx401)
new_esEs17(True, True) → True
new_ltEs19(vwx242, vwx252, ty_@0) → new_ltEs7(vwx242, vwx252)
new_esEs27(vwx241, vwx251, ty_Char) → new_esEs15(vwx241, vwx251)
new_compare8(vwx240, vwx250, ty_@0) → new_compare9(vwx240, vwx250)
new_ltEs18(vwx241, vwx251, ty_Char) → new_ltEs14(vwx241, vwx251)
new_esEs22(vwx300, vwx400, app(app(ty_@2, ccg), cch)) → new_esEs5(vwx300, vwx400, ccg, cch)
new_compare8(vwx240, vwx250, app(app(ty_@2, bd), be)) → new_compare13(vwx240, vwx250, bd, be)
new_esEs21(vwx301, vwx401, app(app(app(ty_@3, cbh), cca), ccb)) → new_esEs7(vwx301, vwx401, cbh, cca, ccb)
new_ltEs13(True, False) → False
new_compare8(vwx240, vwx250, app(ty_Maybe, bc)) → new_compare12(vwx240, vwx250, bc)
new_esEs6(Left(vwx300), Left(vwx400), ty_Float, cgf) → new_esEs14(vwx300, vwx400)
new_compare8(vwx240, vwx250, ty_Ordering) → new_compare15(vwx240, vwx250)
new_ltEs8(vwx24, vwx25, dcb) → new_not(new_esEs8(new_compare11(vwx24, vwx25, dcb), GT))
new_esEs21(vwx301, vwx401, app(app(ty_Either, cbc), cbd)) → new_esEs6(vwx301, vwx401, cbc, cbd)
new_esEs6(Left(vwx300), Left(vwx400), ty_Bool, cgf) → new_esEs17(vwx300, vwx400)
new_ltEs12(Left(vwx240), Left(vwx250), ty_Ordering, gc) → new_ltEs4(vwx240, vwx250)
new_esEs26(vwx240, vwx250, app(ty_Maybe, cc)) → new_esEs4(vwx240, vwx250, cc)
new_esEs22(vwx300, vwx400, app(ty_Ratio, cda)) → new_esEs18(vwx300, vwx400, cda)
new_ltEs6(Just(vwx240), Just(vwx250), ty_Int) → new_ltEs11(vwx240, vwx250)
new_ltEs6(Just(vwx240), Just(vwx250), ty_@0) → new_ltEs7(vwx240, vwx250)
new_ltEs12(Left(vwx240), Left(vwx250), ty_Int, gc) → new_ltEs11(vwx240, vwx250)
new_esEs6(Left(vwx300), Left(vwx400), ty_Int, cgf) → new_esEs12(vwx300, vwx400)
new_pePe(False, vwx81) → vwx81
new_esEs4(Just(vwx300), Just(vwx400), ty_Int) → new_esEs12(vwx300, vwx400)
new_compare8(vwx240, vwx250, ty_Bool) → new_compare16(vwx240, vwx250)
new_esEs6(Right(vwx300), Right(vwx400), daa, ty_@0) → new_esEs13(vwx300, vwx400)
new_esEs25(vwx300, vwx400, ty_Double) → new_esEs11(vwx300, vwx400)
new_esEs28(vwx240, vwx250, ty_@0) → new_esEs13(vwx240, vwx250)
new_esEs26(vwx240, vwx250, ty_@0) → new_esEs13(vwx240, vwx250)
new_esEs24(vwx300, vwx400, ty_Integer) → new_esEs19(vwx300, vwx400)
new_compare8(vwx240, vwx250, ty_Integer) → new_compare10(vwx240, vwx250)
new_lt19(vwx241, vwx251, app(app(ty_Either, bcf), bcg)) → new_lt9(vwx241, vwx251, bcf, bcg)
new_compare11(:%(vwx240, vwx241), :%(vwx250, vwx251), ty_Int) → new_compare5(new_sr(vwx240, vwx251), new_sr(vwx250, vwx241))
new_esEs22(vwx300, vwx400, ty_Ordering) → new_esEs8(vwx300, vwx400)
new_esEs20(vwx302, vwx402, app(app(ty_@2, cac), cad)) → new_esEs5(vwx302, vwx402, cac, cad)
new_compare19(vwx240, vwx250, True) → LT
new_primCmpNat0(Zero, Succ(vwx2500)) → LT
new_esEs27(vwx241, vwx251, app(app(app(ty_@3, bch), bda), bdb)) → new_esEs7(vwx241, vwx251, bch, bda, bdb)
new_compare113(vwx240, vwx250, True, cc) → LT
new_ltEs19(vwx242, vwx252, ty_Float) → new_ltEs15(vwx242, vwx252)
new_primCompAux0(vwx240, vwx250, vwx82, ba) → new_primCompAux00(vwx82, new_compare8(vwx240, vwx250, ba))
new_ltEs12(Left(vwx240), Left(vwx250), app(ty_Maybe, gd), gc) → new_ltEs6(vwx240, vwx250, gd)
new_esEs6(Right(vwx300), Left(vwx400), daa, cgf) → False
new_esEs6(Left(vwx300), Right(vwx400), daa, cgf) → False
new_ltEs13(False, True) → True
new_esEs8(LT, LT) → True
new_esEs25(vwx300, vwx400, ty_Ordering) → new_esEs8(vwx300, vwx400)
new_esEs24(vwx300, vwx400, ty_Int) → new_esEs12(vwx300, vwx400)
new_lt10(vwx240, vwx250) → new_esEs8(new_compare15(vwx240, vwx250), LT)
new_ltEs6(Just(vwx240), Just(vwx250), ty_Bool) → new_ltEs13(vwx240, vwx250)
new_pePe(True, vwx81) → True
new_primEqNat0(Zero, Zero) → True
new_compare29(vwx240, vwx250, True, fd, ff) → EQ
new_lt16(vwx240, vwx250, app(ty_Maybe, cc)) → new_lt17(vwx240, vwx250, cc)
new_esEs6(Right(vwx300), Right(vwx400), daa, app(app(ty_Either, dac), dad)) → new_esEs6(vwx300, vwx400, dac, dad)
new_lt20(vwx240, vwx250, ty_Integer) → new_lt7(vwx240, vwx250)
new_ltEs12(Right(vwx240), Right(vwx250), hd, ty_Bool) → new_ltEs13(vwx240, vwx250)
new_lt16(vwx240, vwx250, ty_Float) → new_lt6(vwx240, vwx250)
new_esEs17(False, False) → True
new_esEs17(False, True) → False
new_esEs17(True, False) → False
new_ltEs12(Left(vwx240), Left(vwx250), app(app(ty_@2, ge), gf), gc) → new_ltEs10(vwx240, vwx250, ge, gf)
new_ltEs6(Just(vwx240), Just(vwx250), ty_Integer) → new_ltEs5(vwx240, vwx250)
new_esEs6(Right(vwx300), Right(vwx400), daa, ty_Bool) → new_esEs17(vwx300, vwx400)
new_esEs15(Char(vwx300), Char(vwx400)) → new_primEqNat0(vwx300, vwx400)
new_esEs9(vwx301, vwx401, ty_Double) → new_esEs11(vwx301, vwx401)
new_sr(vwx300, vwx400) → new_primMulInt(vwx300, vwx400)
new_esEs20(vwx302, vwx402, ty_Char) → new_esEs15(vwx302, vwx402)
new_esEs28(vwx240, vwx250, app(app(ty_Either, bdg), bdh)) → new_esEs6(vwx240, vwx250, bdg, bdh)
new_esEs9(vwx301, vwx401, app(app(app(ty_@3, bfg), bfh), bga)) → new_esEs7(vwx301, vwx401, bfg, bfh, bga)
new_esEs9(vwx301, vwx401, app(ty_[], bfa)) → new_esEs16(vwx301, vwx401, bfa)
new_ltEs12(Left(vwx240), Left(vwx250), ty_Bool, gc) → new_ltEs13(vwx240, vwx250)
new_esEs26(vwx240, vwx250, ty_Ordering) → new_esEs8(vwx240, vwx250)
new_esEs4(Just(vwx300), Just(vwx400), ty_Bool) → new_esEs17(vwx300, vwx400)
new_esEs26(vwx240, vwx250, ty_Int) → new_esEs12(vwx240, vwx250)
new_esEs8(GT, GT) → True
new_compare113(vwx240, vwx250, False, cc) → GT
new_primPlusNat0(Succ(vwx610), vwx40000) → Succ(Succ(new_primPlusNat1(vwx610, vwx40000)))
new_lt19(vwx241, vwx251, app(ty_Ratio, dbh)) → new_lt11(vwx241, vwx251, dbh)
new_esEs20(vwx302, vwx402, app(app(app(ty_@3, caf), cag), cah)) → new_esEs7(vwx302, vwx402, caf, cag, cah)
new_compare13(vwx240, vwx250, fb, fc) → new_compare26(vwx240, vwx250, new_esEs5(vwx240, vwx250, fb, fc), fb, fc)
new_esEs20(vwx302, vwx402, ty_Bool) → new_esEs17(vwx302, vwx402)
new_esEs8(LT, GT) → False
new_esEs8(GT, LT) → False
new_esEs23(vwx301, vwx401, ty_Int) → new_esEs12(vwx301, vwx401)
new_ltEs12(Right(vwx240), Right(vwx250), hd, ty_Int) → new_ltEs11(vwx240, vwx250)
new_lt16(vwx240, vwx250, app(app(app(ty_@3, fg), fh), ga)) → new_lt8(vwx240, vwx250, fg, fh, ga)
new_lt16(vwx240, vwx250, ty_Ordering) → new_lt10(vwx240, vwx250)
new_esEs4(Just(vwx300), Just(vwx400), app(ty_Ratio, cee)) → new_esEs18(vwx300, vwx400, cee)
new_primEqInt(Neg(Succ(vwx3000)), Neg(Succ(vwx4000))) → new_primEqNat0(vwx3000, vwx4000)
new_compare25(vwx240, vwx250, True) → EQ
new_lt20(vwx240, vwx250, app(ty_Ratio, dca)) → new_lt11(vwx240, vwx250, dca)
new_ltEs19(vwx242, vwx252, app(app(ty_@2, bbb), bbc)) → new_ltEs10(vwx242, vwx252, bbb, bbc)
new_esEs20(vwx302, vwx402, ty_Ordering) → new_esEs8(vwx302, vwx402)
new_esEs6(Right(vwx300), Right(vwx400), daa, app(app(app(ty_@3, dah), dba), dbb)) → new_esEs7(vwx300, vwx400, dah, dba, dbb)
new_ltEs6(Just(vwx240), Just(vwx250), app(app(ty_Either, da), db)) → new_ltEs12(vwx240, vwx250, da, db)
new_compare8(vwx240, vwx250, ty_Double) → new_compare6(vwx240, vwx250)
new_esEs28(vwx240, vwx250, ty_Char) → new_esEs15(vwx240, vwx250)
new_primPlusNat1(Succ(vwx6100), Zero) → Succ(vwx6100)
new_primPlusNat1(Zero, Succ(vwx400000)) → Succ(vwx400000)
new_esEs21(vwx301, vwx401, ty_Char) → new_esEs15(vwx301, vwx401)
new_lt18(vwx240, vwx250) → new_esEs8(new_compare6(vwx240, vwx250), LT)
new_esEs26(vwx240, vwx250, app(app(app(ty_@3, fg), fh), ga)) → new_esEs7(vwx240, vwx250, fg, fh, ga)
new_lt19(vwx241, vwx251, ty_Char) → new_lt14(vwx241, vwx251)
new_esEs28(vwx240, vwx250, app(ty_Maybe, bdd)) → new_esEs4(vwx240, vwx250, bdd)
new_lt20(vwx240, vwx250, ty_Int) → new_lt4(vwx240, vwx250)
new_lt16(vwx240, vwx250, ty_Double) → new_lt18(vwx240, vwx250)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_lt13(vwx240, vwx250) → new_esEs8(new_compare9(vwx240, vwx250), LT)
new_esEs26(vwx240, vwx250, ty_Integer) → new_esEs19(vwx240, vwx250)
new_ltEs19(vwx242, vwx252, app(ty_Ratio, dbg)) → new_ltEs8(vwx242, vwx252, dbg)
new_esEs27(vwx241, vwx251, ty_Int) → new_esEs12(vwx241, vwx251)
new_ltEs19(vwx242, vwx252, ty_Ordering) → new_ltEs4(vwx242, vwx252)
new_esEs9(vwx301, vwx401, ty_Int) → new_esEs12(vwx301, vwx401)
new_compare112(vwx240, vwx250, False, fb, fc) → GT
new_ltEs12(Right(vwx240), Right(vwx250), hd, app(app(app(ty_@3, bac), bad), bae)) → new_ltEs17(vwx240, vwx250, bac, bad, bae)
new_compare10(Integer(vwx240), Integer(vwx250)) → new_primCmpInt(vwx240, vwx250)
new_primEqInt(Neg(Zero), Neg(Succ(vwx4000))) → False
new_primEqInt(Neg(Succ(vwx3000)), Neg(Zero)) → False
new_ltEs12(Left(vwx240), Left(vwx250), ty_Double, gc) → new_ltEs16(vwx240, vwx250)
new_esEs8(EQ, EQ) → True
new_compare26(vwx240, vwx250, True, fb, fc) → EQ
new_esEs4(Just(vwx300), Just(vwx400), ty_@0) → new_esEs13(vwx300, vwx400)
new_esEs22(vwx300, vwx400, ty_Integer) → new_esEs19(vwx300, vwx400)
new_esEs6(Right(vwx300), Right(vwx400), daa, app(ty_[], dab)) → new_esEs16(vwx300, vwx400, dab)
new_esEs10(vwx300, vwx400, app(app(app(ty_@3, bha), bhb), bhc)) → new_esEs7(vwx300, vwx400, bha, bhb, bhc)
new_ltEs12(Right(vwx240), Right(vwx250), hd, app(ty_Ratio, dbf)) → new_ltEs8(vwx240, vwx250, dbf)
new_ltEs12(Left(vwx240), Left(vwx250), ty_Char, gc) → new_ltEs14(vwx240, vwx250)
new_esEs22(vwx300, vwx400, ty_Int) → new_esEs12(vwx300, vwx400)
new_compare([], [], ba) → EQ
new_compare12(vwx240, vwx250, cc) → new_compare27(vwx240, vwx250, new_esEs4(vwx240, vwx250, cc), cc)
new_ltEs18(vwx241, vwx251, ty_Double) → new_ltEs16(vwx241, vwx251)
new_ltEs18(vwx241, vwx251, ty_Ordering) → new_ltEs4(vwx241, vwx251)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_ltEs4(EQ, LT) → False
new_ltEs19(vwx242, vwx252, ty_Bool) → new_ltEs13(vwx242, vwx252)
new_esEs6(Left(vwx300), Left(vwx400), app(ty_Ratio, chd), cgf) → new_esEs18(vwx300, vwx400, chd)
new_ltEs18(vwx241, vwx251, app(app(ty_@2, ea), eb)) → new_ltEs10(vwx241, vwx251, ea, eb)
new_esEs26(vwx240, vwx250, ty_Double) → new_esEs11(vwx240, vwx250)
new_primCmpNat0(Succ(vwx2400), Succ(vwx2500)) → new_primCmpNat0(vwx2400, vwx2500)
new_esEs22(vwx300, vwx400, app(ty_Maybe, cde)) → new_esEs4(vwx300, vwx400, cde)
new_lt16(vwx240, vwx250, ty_Integer) → new_lt7(vwx240, vwx250)
new_esEs25(vwx300, vwx400, app(ty_Maybe, cge)) → new_esEs4(vwx300, vwx400, cge)
new_ltEs12(Right(vwx240), Right(vwx250), hd, ty_Ordering) → new_ltEs4(vwx240, vwx250)
new_primEqInt(Pos(Succ(vwx3000)), Pos(Succ(vwx4000))) → new_primEqNat0(vwx3000, vwx4000)
new_esEs21(vwx301, vwx401, ty_Double) → new_esEs11(vwx301, vwx401)
new_ltEs15(vwx24, vwx25) → new_not(new_esEs8(new_compare7(vwx24, vwx25), GT))
new_lt19(vwx241, vwx251, app(app(ty_@2, bcd), bce)) → new_lt12(vwx241, vwx251, bcd, bce)
new_esEs4(Just(vwx300), Just(vwx400), app(app(ty_Either, cea), ceb)) → new_esEs6(vwx300, vwx400, cea, ceb)
new_esEs4(Just(vwx300), Just(vwx400), app(app(ty_@2, cec), ced)) → new_esEs5(vwx300, vwx400, cec, ced)
new_compare24(vwx240, vwx250, False) → new_compare19(vwx240, vwx250, new_ltEs13(vwx240, vwx250))
new_lt5(vwx240, vwx250, eh) → new_esEs8(new_compare(vwx240, vwx250, eh), LT)
new_esEs6(Right(vwx300), Right(vwx400), daa, app(ty_Maybe, dbc)) → new_esEs4(vwx300, vwx400, dbc)
new_primEqNat0(Succ(vwx3000), Succ(vwx4000)) → new_primEqNat0(vwx3000, vwx4000)
new_esEs27(vwx241, vwx251, ty_Ordering) → new_esEs8(vwx241, vwx251)
new_lt19(vwx241, vwx251, ty_@0) → new_lt13(vwx241, vwx251)
new_esEs6(Right(vwx300), Right(vwx400), daa, app(app(ty_@2, dae), daf)) → new_esEs5(vwx300, vwx400, dae, daf)
new_lt14(vwx240, vwx250) → new_esEs8(new_compare17(vwx240, vwx250), LT)
new_compare111(vwx240, vwx250, True, fg, fh, ga) → LT
new_primCompAux00(vwx86, LT) → LT
new_ltEs4(GT, EQ) → False
new_ltEs12(Right(vwx240), Right(vwx250), hd, ty_@0) → new_ltEs7(vwx240, vwx250)
new_esEs6(Left(vwx300), Left(vwx400), ty_Double, cgf) → new_esEs11(vwx300, vwx400)
new_esEs9(vwx301, vwx401, app(app(ty_Either, bfb), bfc)) → new_esEs6(vwx301, vwx401, bfb, bfc)
new_compare114(vwx240, vwx250, True, fd, ff) → LT
new_primCmpInt(Neg(Succ(vwx2400)), Neg(vwx250)) → new_primCmpNat0(vwx250, Succ(vwx2400))
new_ltEs12(Right(vwx240), Right(vwx250), hd, ty_Char) → new_ltEs14(vwx240, vwx250)
new_esEs28(vwx240, vwx250, ty_Double) → new_esEs11(vwx240, vwx250)
new_esEs22(vwx300, vwx400, ty_Char) → new_esEs15(vwx300, vwx400)
new_esEs28(vwx240, vwx250, ty_Ordering) → new_esEs8(vwx240, vwx250)
new_ltEs12(Right(vwx240), Right(vwx250), hd, app(ty_[], he)) → new_ltEs9(vwx240, vwx250, he)
new_esEs8(LT, EQ) → False
new_esEs8(EQ, LT) → False
new_primEqInt(Pos(Zero), Pos(Succ(vwx4000))) → False
new_primEqInt(Pos(Succ(vwx3000)), Pos(Zero)) → False
new_esEs10(vwx300, vwx400, ty_Char) → new_esEs15(vwx300, vwx400)
new_ltEs4(EQ, EQ) → True
new_ltEs19(vwx242, vwx252, app(ty_Maybe, bba)) → new_ltEs6(vwx242, vwx252, bba)
new_ltEs6(Just(vwx240), Nothing, bee) → False
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(vwx2400), Zero) → GT
new_esEs21(vwx301, vwx401, ty_@0) → new_esEs13(vwx301, vwx401)
new_primCmpInt(Neg(Zero), Pos(Succ(vwx2500))) → LT
new_compare19(vwx240, vwx250, False) → GT
new_compare9(@0, @0) → EQ
new_esEs6(Right(vwx300), Right(vwx400), daa, ty_Integer) → new_esEs19(vwx300, vwx400)
new_ltEs4(GT, LT) → False
new_esEs22(vwx300, vwx400, ty_Double) → new_esEs11(vwx300, vwx400)
new_esEs4(Just(vwx300), Just(vwx400), ty_Float) → new_esEs14(vwx300, vwx400)
new_sr0(Integer(vwx2500), Integer(vwx2410)) → Integer(new_primMulInt(vwx2500, vwx2410))
new_primPlusNat1(Succ(vwx6100), Succ(vwx400000)) → Succ(Succ(new_primPlusNat1(vwx6100, vwx400000)))
new_primEqInt(Neg(Succ(vwx3000)), Pos(vwx400)) → False
new_primEqInt(Pos(Succ(vwx3000)), Neg(vwx400)) → False
new_ltEs5(vwx24, vwx25) → new_not(new_esEs8(new_compare10(vwx24, vwx25), GT))
new_ltEs19(vwx242, vwx252, ty_Double) → new_ltEs16(vwx242, vwx252)
new_ltEs12(Left(vwx240), Right(vwx250), hd, gc) → True
new_esEs25(vwx300, vwx400, ty_@0) → new_esEs13(vwx300, vwx400)
new_compare(:(vwx240, vwx241), :(vwx250, vwx251), ba) → new_primCompAux0(vwx240, vwx250, new_compare(vwx241, vwx251, ba), ba)
new_compare7(Float(vwx240, vwx241), Float(vwx250, vwx251)) → new_compare5(new_sr(vwx240, vwx250), new_sr(vwx241, vwx251))
new_ltEs6(Just(vwx240), Just(vwx250), ty_Float) → new_ltEs15(vwx240, vwx250)
new_ltEs6(Just(vwx240), Just(vwx250), app(ty_Maybe, ce)) → new_ltEs6(vwx240, vwx250, ce)
new_esEs6(Left(vwx300), Left(vwx400), app(ty_Maybe, chh), cgf) → new_esEs4(vwx300, vwx400, chh)
new_esEs22(vwx300, vwx400, ty_Float) → new_esEs14(vwx300, vwx400)
new_esEs6(Left(vwx300), Left(vwx400), ty_@0, cgf) → new_esEs13(vwx300, vwx400)
new_esEs16(:(vwx300, vwx301), :(vwx400, vwx401), cfc) → new_asAs(new_esEs25(vwx300, vwx400, cfc), new_esEs16(vwx301, vwx401, cfc))
new_primEqInt(Neg(Zero), Pos(Succ(vwx4000))) → False
new_primEqInt(Pos(Zero), Neg(Succ(vwx4000))) → False
new_esEs13(@0, @0) → True
new_primCompAux00(vwx86, EQ) → vwx86
new_primCmpInt(Pos(Zero), Pos(Succ(vwx2500))) → new_primCmpNat0(Zero, Succ(vwx2500))
new_compare24(vwx240, vwx250, True) → EQ
new_esEs10(vwx300, vwx400, ty_Double) → new_esEs11(vwx300, vwx400)
new_lt19(vwx241, vwx251, app(ty_[], bca)) → new_lt5(vwx241, vwx251, bca)
new_esEs8(EQ, GT) → False
new_esEs8(GT, EQ) → False
new_ltEs12(Right(vwx240), Right(vwx250), hd, ty_Integer) → new_ltEs5(vwx240, vwx250)
new_esEs10(vwx300, vwx400, app(ty_[], bgc)) → new_esEs16(vwx300, vwx400, bgc)
new_esEs26(vwx240, vwx250, app(app(ty_@2, fb), fc)) → new_esEs5(vwx240, vwx250, fb, fc)
new_esEs5(@2(vwx300, vwx301), @2(vwx400, vwx401), beg, beh) → new_asAs(new_esEs10(vwx300, vwx400, beg), new_esEs9(vwx301, vwx401, beh))
new_esEs21(vwx301, vwx401, app(app(ty_@2, cbe), cbf)) → new_esEs5(vwx301, vwx401, cbe, cbf)
new_ltEs12(Left(vwx240), Left(vwx250), ty_Integer, gc) → new_ltEs5(vwx240, vwx250)
new_esEs9(vwx301, vwx401, ty_Ordering) → new_esEs8(vwx301, vwx401)
new_ltEs18(vwx241, vwx251, app(ty_Ratio, dbd)) → new_ltEs8(vwx241, vwx251, dbd)
new_esEs9(vwx301, vwx401, ty_Float) → new_esEs14(vwx301, vwx401)
new_compare114(vwx240, vwx250, False, fd, ff) → GT
new_not(False) → True
new_esEs6(Left(vwx300), Left(vwx400), app(app(ty_Either, cgh), cha), cgf) → new_esEs6(vwx300, vwx400, cgh, cha)
new_esEs28(vwx240, vwx250, app(ty_[], bdc)) → new_esEs16(vwx240, vwx250, bdc)
new_lt20(vwx240, vwx250, ty_Bool) → new_lt15(vwx240, vwx250)
new_lt16(vwx240, vwx250, app(app(ty_@2, fb), fc)) → new_lt12(vwx240, vwx250, fb, fc)
new_primPlusNat0(Zero, vwx40000) → Succ(vwx40000)
new_primCmpInt(Pos(Succ(vwx2400)), Pos(vwx250)) → new_primCmpNat0(Succ(vwx2400), vwx250)
new_ltEs19(vwx242, vwx252, app(app(ty_Either, bbd), bbe)) → new_ltEs12(vwx242, vwx252, bbd, bbe)
new_ltEs12(Right(vwx240), Right(vwx250), hd, app(app(ty_Either, baa), bab)) → new_ltEs12(vwx240, vwx250, baa, bab)
new_esEs19(Integer(vwx300), Integer(vwx400)) → new_primEqInt(vwx300, vwx400)
new_esEs22(vwx300, vwx400, ty_Bool) → new_esEs17(vwx300, vwx400)
new_esEs26(vwx240, vwx250, app(ty_Ratio, cfb)) → new_esEs18(vwx240, vwx250, cfb)
new_ltEs12(Left(vwx240), Left(vwx250), app(app(app(ty_@3, ha), hb), hc), gc) → new_ltEs17(vwx240, vwx250, ha, hb, hc)
new_lt16(vwx240, vwx250, app(ty_[], eh)) → new_lt5(vwx240, vwx250, eh)
new_ltEs12(Right(vwx240), Left(vwx250), hd, gc) → False
new_esEs20(vwx302, vwx402, ty_Float) → new_esEs14(vwx302, vwx402)
new_lt17(vwx240, vwx250, cc) → new_esEs8(new_compare12(vwx240, vwx250, cc), LT)
new_esEs28(vwx240, vwx250, app(app(ty_@2, bde), bdf)) → new_esEs5(vwx240, vwx250, bde, bdf)
new_lt20(vwx240, vwx250, app(ty_Maybe, bdd)) → new_lt17(vwx240, vwx250, bdd)
new_esEs27(vwx241, vwx251, app(app(ty_Either, bcf), bcg)) → new_esEs6(vwx241, vwx251, bcf, bcg)
new_lt16(vwx240, vwx250, app(ty_Ratio, cfb)) → new_lt11(vwx240, vwx250, cfb)
new_esEs22(vwx300, vwx400, app(app(app(ty_@3, cdb), cdc), cdd)) → new_esEs7(vwx300, vwx400, cdb, cdc, cdd)
new_primCmpInt(Pos(Succ(vwx2400)), Neg(vwx250)) → GT
new_esEs6(Left(vwx300), Left(vwx400), ty_Integer, cgf) → new_esEs19(vwx300, vwx400)
new_esEs22(vwx300, vwx400, app(ty_[], ccd)) → new_esEs16(vwx300, vwx400, ccd)
new_compare11(:%(vwx240, vwx241), :%(vwx250, vwx251), ty_Integer) → new_compare10(new_sr0(vwx240, vwx251), new_sr0(vwx250, vwx241))
new_ltEs6(Just(vwx240), Just(vwx250), app(app(app(ty_@3, dc), dd), de)) → new_ltEs17(vwx240, vwx250, dc, dd, de)
new_lt19(vwx241, vwx251, ty_Ordering) → new_lt10(vwx241, vwx251)
new_compare18(vwx240, vwx250, fg, fh, ga) → new_compare28(vwx240, vwx250, new_esEs7(vwx240, vwx250, fg, fh, ga), fg, fh, ga)
new_primMulInt(Pos(vwx3000), Pos(vwx4000)) → Pos(new_primMulNat0(vwx3000, vwx4000))
new_ltEs12(Left(vwx240), Left(vwx250), app(ty_[], gb), gc) → new_ltEs9(vwx240, vwx250, gb)
new_esEs9(vwx301, vwx401, app(ty_Ratio, bff)) → new_esEs18(vwx301, vwx401, bff)
new_esEs28(vwx240, vwx250, app(app(app(ty_@3, bea), beb), bec)) → new_esEs7(vwx240, vwx250, bea, beb, bec)
new_esEs6(Left(vwx300), Left(vwx400), app(app(ty_@2, chb), chc), cgf) → new_esEs5(vwx300, vwx400, chb, chc)
new_primMulInt(Neg(vwx3000), Neg(vwx4000)) → Pos(new_primMulNat0(vwx3000, vwx4000))
new_compare110(vwx240, vwx250, True) → LT
new_compare8(vwx240, vwx250, ty_Int) → new_compare5(vwx240, vwx250)
new_primEqNat0(Zero, Succ(vwx4000)) → False
new_primEqNat0(Succ(vwx3000), Zero) → False
new_lt20(vwx240, vwx250, app(app(ty_@2, bde), bdf)) → new_lt12(vwx240, vwx250, bde, bdf)
new_compare110(vwx240, vwx250, False) → GT
new_ltEs18(vwx241, vwx251, app(app(app(ty_@3, ee), ef), eg)) → new_ltEs17(vwx241, vwx251, ee, ef, eg)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs20(vwx302, vwx402, ty_Double) → new_esEs11(vwx302, vwx402)
new_esEs4(Nothing, Nothing, cdg) → True
new_lt19(vwx241, vwx251, app(ty_Maybe, bcc)) → new_lt17(vwx241, vwx251, bcc)
new_esEs6(Right(vwx300), Right(vwx400), daa, ty_Float) → new_esEs14(vwx300, vwx400)
new_compare111(vwx240, vwx250, False, fg, fh, ga) → GT
new_ltEs18(vwx241, vwx251, ty_@0) → new_ltEs7(vwx241, vwx251)
new_esEs25(vwx300, vwx400, ty_Int) → new_esEs12(vwx300, vwx400)
new_esEs20(vwx302, vwx402, app(app(ty_Either, caa), cab)) → new_esEs6(vwx302, vwx402, caa, cab)
new_esEs27(vwx241, vwx251, app(app(ty_@2, bcd), bce)) → new_esEs5(vwx241, vwx251, bcd, bce)
new_ltEs12(Left(vwx240), Left(vwx250), app(app(ty_Either, gg), gh), gc) → new_ltEs12(vwx240, vwx250, gg, gh)
new_esEs16([], :(vwx400, vwx401), cfc) → False
new_esEs16(:(vwx300, vwx301), [], cfc) → False
new_compare28(vwx240, vwx250, True, fg, fh, ga) → EQ
new_ltEs12(Left(vwx240), Left(vwx250), ty_@0, gc) → new_ltEs7(vwx240, vwx250)
new_ltEs6(Just(vwx240), Just(vwx250), app(ty_[], cd)) → new_ltEs9(vwx240, vwx250, cd)
new_esEs10(vwx300, vwx400, app(app(ty_@2, bgf), bgg)) → new_esEs5(vwx300, vwx400, bgf, bgg)
new_lt20(vwx240, vwx250, ty_Char) → new_lt14(vwx240, vwx250)
new_esEs27(vwx241, vwx251, app(ty_Maybe, bcc)) → new_esEs4(vwx241, vwx251, bcc)
new_ltEs4(LT, GT) → True
new_ltEs9(vwx24, vwx25, ba) → new_not(new_esEs8(new_compare(vwx24, vwx25, ba), GT))
new_primCmpInt(Neg(Zero), Neg(Succ(vwx2500))) → new_primCmpNat0(Succ(vwx2500), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(vwx2500))) → GT
new_lt19(vwx241, vwx251, ty_Integer) → new_lt7(vwx241, vwx251)
new_esEs6(Left(vwx300), Left(vwx400), ty_Ordering, cgf) → new_esEs8(vwx300, vwx400)
new_compare5(vwx24, vwx25) → new_primCmpInt(vwx24, vwx25)
new_esEs12(vwx30, vwx40) → new_primEqInt(vwx30, vwx40)
new_compare6(Double(vwx240, vwx241), Double(vwx250, vwx251)) → new_compare5(new_sr(vwx240, vwx250), new_sr(vwx241, vwx251))
new_lt20(vwx240, vwx250, ty_Double) → new_lt18(vwx240, vwx250)
new_esEs4(Just(vwx300), Just(vwx400), app(ty_[], cdh)) → new_esEs16(vwx300, vwx400, cdh)
new_esEs11(Double(vwx300, vwx301), Double(vwx400, vwx401)) → new_esEs12(new_sr(vwx300, vwx400), new_sr(vwx301, vwx401))
new_ltEs19(vwx242, vwx252, ty_Int) → new_ltEs11(vwx242, vwx252)
new_esEs20(vwx302, vwx402, app(ty_Ratio, cae)) → new_esEs18(vwx302, vwx402, cae)
new_ltEs19(vwx242, vwx252, ty_Char) → new_ltEs14(vwx242, vwx252)
new_esEs9(vwx301, vwx401, ty_Bool) → new_esEs17(vwx301, vwx401)
new_lt16(vwx240, vwx250, ty_Int) → new_lt4(vwx240, vwx250)
new_esEs21(vwx301, vwx401, app(ty_Maybe, ccc)) → new_esEs4(vwx301, vwx401, ccc)
new_esEs10(vwx300, vwx400, ty_Float) → new_esEs14(vwx300, vwx400)
new_esEs4(Just(vwx300), Just(vwx400), ty_Integer) → new_esEs19(vwx300, vwx400)
new_ltEs18(vwx241, vwx251, ty_Int) → new_ltEs11(vwx241, vwx251)
new_compare8(vwx240, vwx250, app(app(ty_Either, bf), bg)) → new_compare14(vwx240, vwx250, bf, bg)
new_esEs9(vwx301, vwx401, app(app(ty_@2, bfd), bfe)) → new_esEs5(vwx301, vwx401, bfd, bfe)
new_esEs10(vwx300, vwx400, ty_Integer) → new_esEs19(vwx300, vwx400)
new_esEs14(Float(vwx300, vwx301), Float(vwx400, vwx401)) → new_esEs12(new_sr(vwx300, vwx400), new_sr(vwx301, vwx401))
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_ltEs4(LT, EQ) → True
new_esEs6(Right(vwx300), Right(vwx400), daa, ty_Char) → new_esEs15(vwx300, vwx400)
new_ltEs6(Just(vwx240), Just(vwx250), app(app(ty_@2, cf), cg)) → new_ltEs10(vwx240, vwx250, cf, cg)
new_ltEs6(Just(vwx240), Just(vwx250), app(ty_Ratio, bef)) → new_ltEs8(vwx240, vwx250, bef)
new_lt20(vwx240, vwx250, ty_@0) → new_lt13(vwx240, vwx250)
new_esEs20(vwx302, vwx402, app(ty_[], bhh)) → new_esEs16(vwx302, vwx402, bhh)
new_asAs(False, vwx53) → False
new_esEs18(:%(vwx300, vwx301), :%(vwx400, vwx401), cdf) → new_asAs(new_esEs24(vwx300, vwx400, cdf), new_esEs23(vwx301, vwx401, cdf))
new_primMulInt(Neg(vwx3000), Pos(vwx4000)) → Neg(new_primMulNat0(vwx3000, vwx4000))
new_primMulInt(Pos(vwx3000), Neg(vwx4000)) → Neg(new_primMulNat0(vwx3000, vwx4000))
new_primMulNat0(Zero, Succ(vwx40000)) → Zero
new_primMulNat0(Succ(vwx30000), Zero) → Zero
new_compare26(vwx240, vwx250, False, fb, fc) → new_compare112(vwx240, vwx250, new_ltEs10(vwx240, vwx250, fb, fc), fb, fc)
new_esEs21(vwx301, vwx401, ty_Ordering) → new_esEs8(vwx301, vwx401)
new_ltEs12(Right(vwx240), Right(vwx250), hd, app(ty_Maybe, hf)) → new_ltEs6(vwx240, vwx250, hf)
new_ltEs12(Left(vwx240), Left(vwx250), ty_Float, gc) → new_ltEs15(vwx240, vwx250)
new_esEs9(vwx301, vwx401, app(ty_Maybe, bgb)) → new_esEs4(vwx301, vwx401, bgb)
new_lt12(vwx240, vwx250, fb, fc) → new_esEs8(new_compare13(vwx240, vwx250, fb, fc), LT)
new_esEs6(Right(vwx300), Right(vwx400), daa, app(ty_Ratio, dag)) → new_esEs18(vwx300, vwx400, dag)
new_lt19(vwx241, vwx251, ty_Double) → new_lt18(vwx241, vwx251)
new_esEs6(Left(vwx300), Left(vwx400), ty_Char, cgf) → new_esEs15(vwx300, vwx400)
new_esEs10(vwx300, vwx400, app(ty_Ratio, bgh)) → new_esEs18(vwx300, vwx400, bgh)
new_esEs27(vwx241, vwx251, ty_@0) → new_esEs13(vwx241, vwx251)
new_ltEs12(Right(vwx240), Right(vwx250), hd, ty_Float) → new_ltEs15(vwx240, vwx250)
new_esEs27(vwx241, vwx251, ty_Integer) → new_esEs19(vwx241, vwx251)
new_esEs9(vwx301, vwx401, ty_Integer) → new_esEs19(vwx301, vwx401)
new_esEs6(Right(vwx300), Right(vwx400), daa, ty_Double) → new_esEs11(vwx300, vwx400)
new_ltEs11(vwx24, vwx25) → new_not(new_esEs8(new_compare5(vwx24, vwx25), GT))
new_lt19(vwx241, vwx251, ty_Bool) → new_lt15(vwx241, vwx251)
new_esEs25(vwx300, vwx400, ty_Integer) → new_esEs19(vwx300, vwx400)
new_lt16(vwx240, vwx250, ty_@0) → new_lt13(vwx240, vwx250)
new_ltEs12(Right(vwx240), Right(vwx250), hd, app(app(ty_@2, hg), hh)) → new_ltEs10(vwx240, vwx250, hg, hh)
new_ltEs6(Nothing, Nothing, bee) → True
new_esEs20(vwx302, vwx402, ty_Integer) → new_esEs19(vwx302, vwx402)
new_ltEs19(vwx242, vwx252, ty_Integer) → new_ltEs5(vwx242, vwx252)
new_esEs25(vwx300, vwx400, app(app(app(ty_@3, cgb), cgc), cgd)) → new_esEs7(vwx300, vwx400, cgb, cgc, cgd)
new_ltEs13(True, True) → True
new_ltEs13(False, False) → True
new_esEs28(vwx240, vwx250, ty_Bool) → new_esEs17(vwx240, vwx250)
new_esEs25(vwx300, vwx400, ty_Char) → new_esEs15(vwx300, vwx400)
new_ltEs6(Just(vwx240), Just(vwx250), ty_Double) → new_ltEs16(vwx240, vwx250)
new_esEs16([], [], cfc) → True
new_ltEs4(LT, LT) → True
new_lt9(vwx240, vwx250, fd, ff) → new_esEs8(new_compare14(vwx240, vwx250, fd, ff), LT)
new_ltEs18(vwx241, vwx251, ty_Bool) → new_ltEs13(vwx241, vwx251)
new_esEs26(vwx240, vwx250, ty_Bool) → new_esEs17(vwx240, vwx250)
new_esEs25(vwx300, vwx400, app(app(ty_@2, cfg), cfh)) → new_esEs5(vwx300, vwx400, cfg, cfh)
new_esEs20(vwx302, vwx402, ty_Int) → new_esEs12(vwx302, vwx402)
new_ltEs16(vwx24, vwx25) → new_not(new_esEs8(new_compare6(vwx24, vwx25), GT))
new_ltEs18(vwx241, vwx251, app(app(ty_Either, ec), ed)) → new_ltEs12(vwx241, vwx251, ec, ed)
new_ltEs18(vwx241, vwx251, app(ty_Maybe, dh)) → new_ltEs6(vwx241, vwx251, dh)
new_esEs22(vwx300, vwx400, app(app(ty_Either, cce), ccf)) → new_esEs6(vwx300, vwx400, cce, ccf)
new_ltEs19(vwx242, vwx252, app(app(app(ty_@3, bbf), bbg), bbh)) → new_ltEs17(vwx242, vwx252, bbf, bbg, bbh)
new_lt6(vwx240, vwx250) → new_esEs8(new_compare7(vwx240, vwx250), LT)
new_esEs6(Right(vwx300), Right(vwx400), daa, ty_Int) → new_esEs12(vwx300, vwx400)
new_ltEs14(vwx24, vwx25) → new_not(new_esEs8(new_compare17(vwx24, vwx25), GT))
new_compare27(vwx240, vwx250, True, cc) → EQ
new_compare8(vwx240, vwx250, app(ty_[], bb)) → new_compare(vwx240, vwx250, bb)
new_esEs10(vwx300, vwx400, ty_Ordering) → new_esEs8(vwx300, vwx400)
new_esEs28(vwx240, vwx250, ty_Int) → new_esEs12(vwx240, vwx250)
new_esEs22(vwx300, vwx400, ty_@0) → new_esEs13(vwx300, vwx400)
new_esEs26(vwx240, vwx250, app(app(ty_Either, fd), ff)) → new_esEs6(vwx240, vwx250, fd, ff)
new_lt20(vwx240, vwx250, ty_Ordering) → new_lt10(vwx240, vwx250)
new_primPlusNat1(Zero, Zero) → Zero
new_compare15(vwx240, vwx250) → new_compare25(vwx240, vwx250, new_esEs8(vwx240, vwx250))
new_asAs(True, vwx53) → vwx53
new_esEs26(vwx240, vwx250, ty_Float) → new_esEs14(vwx240, vwx250)
new_compare112(vwx240, vwx250, True, fb, fc) → LT
new_compare28(vwx240, vwx250, False, fg, fh, ga) → new_compare111(vwx240, vwx250, new_ltEs17(vwx240, vwx250, fg, fh, ga), fg, fh, ga)
new_primMulNat0(Succ(vwx30000), Succ(vwx40000)) → new_primPlusNat0(new_primMulNat0(vwx30000, Succ(vwx40000)), vwx40000)
new_lt16(vwx240, vwx250, app(app(ty_Either, fd), ff)) → new_lt9(vwx240, vwx250, fd, ff)
new_esEs10(vwx300, vwx400, app(app(ty_Either, bgd), bge)) → new_esEs6(vwx300, vwx400, bgd, bge)
new_esEs28(vwx240, vwx250, app(ty_Ratio, dca)) → new_esEs18(vwx240, vwx250, dca)
new_ltEs6(Just(vwx240), Just(vwx250), ty_Ordering) → new_ltEs4(vwx240, vwx250)
new_ltEs6(Just(vwx240), Just(vwx250), ty_Char) → new_ltEs14(vwx240, vwx250)
new_esEs4(Just(vwx300), Just(vwx400), ty_Char) → new_esEs15(vwx300, vwx400)
new_ltEs10(@2(vwx240, vwx241), @2(vwx250, vwx251), df, fa) → new_pePe(new_lt16(vwx240, vwx250, df), new_asAs(new_esEs26(vwx240, vwx250, df), new_ltEs18(vwx241, vwx251, fa)))
new_compare25(vwx240, vwx250, False) → new_compare110(vwx240, vwx250, new_ltEs4(vwx240, vwx250))
new_compare14(vwx240, vwx250, fd, ff) → new_compare29(vwx240, vwx250, new_esEs6(vwx240, vwx250, fd, ff), fd, ff)
new_esEs27(vwx241, vwx251, ty_Float) → new_esEs14(vwx241, vwx251)
new_lt20(vwx240, vwx250, app(ty_[], bdc)) → new_lt5(vwx240, vwx250, bdc)
new_esEs4(Just(vwx300), Just(vwx400), app(app(app(ty_@3, cef), ceg), ceh)) → new_esEs7(vwx300, vwx400, cef, ceg, ceh)
new_ltEs4(GT, GT) → True
new_ltEs12(Left(vwx240), Left(vwx250), app(ty_Ratio, dbe), gc) → new_ltEs8(vwx240, vwx250, dbe)
new_lt8(vwx240, vwx250, fg, fh, ga) → new_esEs8(new_compare18(vwx240, vwx250, fg, fh, ga), LT)
new_compare8(vwx240, vwx250, ty_Char) → new_compare17(vwx240, vwx250)
new_primCompAux00(vwx86, GT) → GT
new_esEs25(vwx300, vwx400, ty_Float) → new_esEs14(vwx300, vwx400)
new_esEs21(vwx301, vwx401, app(ty_[], cbb)) → new_esEs16(vwx301, vwx401, cbb)
new_esEs6(Right(vwx300), Right(vwx400), daa, ty_Ordering) → new_esEs8(vwx300, vwx400)
new_esEs6(Left(vwx300), Left(vwx400), app(ty_[], cgg), cgf) → new_esEs16(vwx300, vwx400, cgg)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs20(vwx302, vwx402, ty_@0) → new_esEs13(vwx302, vwx402)
new_lt16(vwx240, vwx250, ty_Char) → new_lt14(vwx240, vwx250)
new_esEs4(Just(vwx300), Just(vwx400), ty_Double) → new_esEs11(vwx300, vwx400)
new_esEs27(vwx241, vwx251, ty_Double) → new_esEs11(vwx241, vwx251)
new_esEs10(vwx300, vwx400, app(ty_Maybe, bhd)) → new_esEs4(vwx300, vwx400, bhd)
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_esEs10(vwx300, vwx400, ty_Bool) → new_esEs17(vwx300, vwx400)
new_lt20(vwx240, vwx250, app(app(ty_Either, bdg), bdh)) → new_lt9(vwx240, vwx250, bdg, bdh)
new_esEs21(vwx301, vwx401, app(ty_Ratio, cbg)) → new_esEs18(vwx301, vwx401, cbg)
new_primCmpInt(Neg(Succ(vwx2400)), Pos(vwx250)) → LT
new_not(True) → False

The set Q consists of the following terms:

new_esEs6(Right(x0), Right(x1), x2, ty_Float)
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs24(x0, x1, ty_Integer)
new_esEs10(x0, x1, ty_Char)
new_esEs13(@0, @0)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs6(Just(x0), Just(x1), app(ty_Maybe, x2))
new_ltEs18(x0, x1, ty_Bool)
new_lt20(x0, x1, app(ty_[], x2))
new_ltEs12(Right(x0), Right(x1), x2, ty_@0)
new_ltEs12(Right(x0), Right(x1), x2, ty_Integer)
new_ltEs19(x0, x1, ty_Bool)
new_esEs28(x0, x1, ty_Float)
new_pePe(False, x0)
new_lt20(x0, x1, ty_Bool)
new_ltEs6(Just(x0), Just(x1), ty_@0)
new_esEs27(x0, x1, app(ty_[], x2))
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs12(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs10(x0, x1, ty_@0)
new_pePe(True, x0)
new_lt19(x0, x1, ty_Bool)
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs9(x0, x1, app(app(ty_@2, x2), x3))
new_esEs9(x0, x1, app(ty_Ratio, x2))
new_ltEs12(Right(x0), Right(x1), x2, ty_Int)
new_ltEs12(Right(x0), Right(x1), x2, ty_Char)
new_compare25(x0, x1, False)
new_esEs26(x0, x1, ty_Int)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_esEs5(@2(x0, x1), @2(x2, x3), x4, x5)
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_lt19(x0, x1, ty_@0)
new_ltEs12(Right(x0), Right(x1), x2, ty_Double)
new_ltEs18(x0, x1, app(ty_[], x2))
new_esEs4(Just(x0), Just(x1), ty_Ordering)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs9(x0, x1, ty_Float)
new_esEs21(x0, x1, ty_Float)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs6(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_ltEs19(x0, x1, ty_Int)
new_esEs8(GT, GT)
new_esEs10(x0, x1, app(app(ty_@2, x2), x3))
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_ltEs17(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs6(Right(x0), Right(x1), x2, ty_Bool)
new_esEs28(x0, x1, ty_Integer)
new_esEs4(Just(x0), Just(x1), ty_Char)
new_esEs26(x0, x1, ty_Double)
new_esEs26(x0, x1, ty_@0)
new_esEs22(x0, x1, ty_Bool)
new_ltEs18(x0, x1, ty_Double)
new_ltEs19(x0, x1, ty_Ordering)
new_ltEs12(Left(x0), Right(x1), x2, x3)
new_ltEs12(Right(x0), Left(x1), x2, x3)
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_ltEs6(Nothing, Just(x0), x1)
new_primPlusNat1(Succ(x0), Zero)
new_esEs14(Float(x0, x1), Float(x2, x3))
new_esEs6(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs8(LT, LT)
new_esEs26(x0, x1, ty_Integer)
new_esEs17(False, False)
new_lt20(x0, x1, ty_Char)
new_ltEs6(Just(x0), Just(x1), ty_Char)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_ltEs12(Left(x0), Left(x1), ty_Ordering, x2)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_ltEs18(x0, x1, ty_Float)
new_esEs20(x0, x1, ty_Bool)
new_esEs21(x0, x1, ty_Int)
new_ltEs12(Left(x0), Left(x1), ty_Integer, x2)
new_esEs27(x0, x1, ty_Float)
new_compare8(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs18(x0, x1, ty_Int)
new_esEs23(x0, x1, ty_Integer)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_lt19(x0, x1, ty_Float)
new_esEs25(x0, x1, ty_Int)
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_lt16(x0, x1, app(app(ty_Either, x2), x3))
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs16([], :(x0, x1), x2)
new_primCompAux0(x0, x1, x2, x3)
new_sr(x0, x1)
new_esEs26(x0, x1, app(ty_[], x2))
new_compare24(x0, x1, True)
new_esEs4(Just(x0), Just(x1), app(ty_[], x2))
new_esEs9(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs5(x0, x1)
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_esEs20(x0, x1, ty_Char)
new_esEs28(x0, x1, app(ty_[], x2))
new_esEs10(x0, x1, ty_Bool)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primEqNat0(Zero, Zero)
new_ltEs6(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs6(Right(x0), Right(x1), x2, ty_Double)
new_esEs4(Just(x0), Just(x1), ty_Bool)
new_primMulInt(Pos(x0), Pos(x1))
new_ltEs6(Nothing, Nothing, x0)
new_ltEs6(Just(x0), Just(x1), ty_Float)
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs22(x0, x1, ty_Char)
new_compare112(x0, x1, True, x2, x3)
new_ltEs6(Just(x0), Just(x1), ty_Bool)
new_lt19(x0, x1, ty_Double)
new_esEs25(x0, x1, ty_Ordering)
new_esEs6(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_lt12(x0, x1, x2, x3)
new_primMulNat0(Zero, Zero)
new_compare8(x0, x1, app(ty_[], x2))
new_esEs16([], [], x0)
new_ltEs12(Left(x0), Left(x1), ty_Double, x2)
new_compare113(x0, x1, False, x2)
new_ltEs11(x0, x1)
new_esEs27(x0, x1, ty_@0)
new_esEs9(x0, x1, ty_Int)
new_primCmpNat0(Succ(x0), Succ(x1))
new_lt19(x0, x1, app(ty_Ratio, x2))
new_lt9(x0, x1, x2, x3)
new_lt20(x0, x1, ty_Ordering)
new_esEs22(x0, x1, ty_Int)
new_esEs27(x0, x1, ty_Ordering)
new_lt16(x0, x1, app(ty_Ratio, x2))
new_ltEs14(x0, x1)
new_ltEs6(Just(x0), Just(x1), ty_Double)
new_ltEs4(GT, GT)
new_compare10(Integer(x0), Integer(x1))
new_lt16(x0, x1, ty_Char)
new_lt4(x0, x1)
new_esEs22(x0, x1, ty_@0)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_compare25(x0, x1, True)
new_ltEs18(x0, x1, app(app(ty_@2, x2), x3))
new_esEs15(Char(x0), Char(x1))
new_lt10(x0, x1)
new_esEs22(x0, x1, app(ty_[], x2))
new_esEs21(x0, x1, ty_Integer)
new_esEs26(x0, x1, ty_Char)
new_compare24(x0, x1, False)
new_esEs25(x0, x1, ty_Float)
new_compare113(x0, x1, True, x2)
new_esEs28(x0, x1, ty_Bool)
new_compare17(Char(x0), Char(x1))
new_primMulNat0(Zero, Succ(x0))
new_esEs6(Right(x0), Right(x1), x2, ty_@0)
new_sr0(Integer(x0), Integer(x1))
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, ty_Int)
new_primCompAux00(x0, EQ)
new_lt16(x0, x1, ty_Bool)
new_ltEs12(Left(x0), Left(x1), ty_Bool, x2)
new_esEs6(Left(x0), Left(x1), ty_Char, x2)
new_ltEs12(Left(x0), Left(x1), ty_@0, x2)
new_esEs27(x0, x1, ty_Double)
new_ltEs9(x0, x1, x2)
new_compare8(x0, x1, ty_Integer)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs4(Just(x0), Nothing, x1)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs22(x0, x1, ty_Integer)
new_esEs24(x0, x1, ty_Int)
new_compare112(x0, x1, False, x2, x3)
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_esEs6(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs27(x0, x1, ty_Char)
new_compare8(x0, x1, ty_Int)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs6(Left(x0), Left(x1), ty_Integer, x2)
new_lt16(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primPlusNat0(Zero, x0)
new_esEs27(x0, x1, ty_Bool)
new_compare5(x0, x1)
new_esEs9(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs28(x0, x1, ty_Double)
new_compare(:(x0, x1), :(x2, x3), x4)
new_esEs9(x0, x1, ty_Bool)
new_lt16(x0, x1, ty_Ordering)
new_primEqNat0(Succ(x0), Zero)
new_ltEs12(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs21(x0, x1, ty_Bool)
new_primPlusNat1(Zero, Zero)
new_ltEs18(x0, x1, ty_Ordering)
new_ltEs13(True, True)
new_esEs7(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs10(x0, x1, ty_Ordering)
new_lt7(x0, x1)
new_esEs27(x0, x1, ty_Integer)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_ltEs19(x0, x1, ty_Char)
new_lt19(x0, x1, app(ty_[], x2))
new_ltEs12(Right(x0), Right(x1), x2, ty_Ordering)
new_ltEs12(Left(x0), Left(x1), ty_Char, x2)
new_ltEs6(Just(x0), Just(x1), ty_Int)
new_esEs25(x0, x1, ty_Char)
new_esEs28(x0, x1, ty_Char)
new_ltEs6(Just(x0), Nothing, x1)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_ltEs13(False, False)
new_compare(:(x0, x1), [], x2)
new_compare27(x0, x1, False, x2)
new_esEs10(x0, x1, app(ty_[], x2))
new_compare114(x0, x1, False, x2, x3)
new_compare([], :(x0, x1), x2)
new_ltEs4(EQ, EQ)
new_esEs4(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs25(x0, x1, ty_Double)
new_esEs6(Left(x0), Left(x1), ty_Double, x2)
new_ltEs12(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_ltEs13(False, True)
new_ltEs13(True, False)
new_ltEs12(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs6(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs21(x0, x1, ty_Char)
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs9(x0, x1, ty_Double)
new_ltEs4(EQ, LT)
new_ltEs4(LT, EQ)
new_esEs28(x0, x1, ty_Ordering)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_compare28(x0, x1, True, x2, x3, x4)
new_esEs9(x0, x1, ty_Ordering)
new_asAs(True, x0)
new_ltEs12(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs22(x0, x1, ty_Float)
new_compare8(x0, x1, ty_Ordering)
new_primCmpNat0(Succ(x0), Zero)
new_lt5(x0, x1, x2)
new_esEs20(x0, x1, ty_Float)
new_ltEs8(x0, x1, x2)
new_primEqInt(Neg(Zero), Pos(Zero))
new_primEqInt(Pos(Zero), Neg(Zero))
new_lt18(x0, x1)
new_lt16(x0, x1, ty_Integer)
new_ltEs12(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs6(Just(x0), Just(x1), ty_Ordering)
new_ltEs6(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs20(x0, x1, ty_Int)
new_esEs9(x0, x1, app(ty_[], x2))
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_lt19(x0, x1, ty_Integer)
new_esEs6(Right(x0), Right(x1), x2, ty_Char)
new_ltEs19(x0, x1, ty_@0)
new_compare8(x0, x1, ty_@0)
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_esEs25(x0, x1, ty_@0)
new_lt16(x0, x1, ty_Double)
new_esEs6(Right(x0), Right(x1), x2, ty_Ordering)
new_compare8(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_ltEs18(x0, x1, app(ty_Ratio, x2))
new_ltEs6(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_compare111(x0, x1, True, x2, x3, x4)
new_primEqInt(Neg(Zero), Neg(Zero))
new_compare8(x0, x1, app(ty_Maybe, x2))
new_esEs22(x0, x1, ty_Double)
new_compare28(x0, x1, False, x2, x3, x4)
new_esEs10(x0, x1, app(ty_Maybe, x2))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_ltEs4(LT, LT)
new_lt16(x0, x1, app(ty_[], x2))
new_compare6(Double(x0, x1), Double(x2, x3))
new_esEs9(x0, x1, ty_Char)
new_ltEs6(Just(x0), Just(x1), app(ty_[], x2))
new_esEs26(x0, x1, ty_Float)
new_ltEs19(x0, x1, ty_Float)
new_lt13(x0, x1)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_compare8(x0, x1, ty_Bool)
new_ltEs6(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs27(x0, x1, ty_Int)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs6(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_lt16(x0, x1, app(app(ty_@2, x2), x3))
new_lt19(x0, x1, ty_Ordering)
new_esEs4(Nothing, Nothing, x0)
new_primCompAux00(x0, GT)
new_esEs4(Just(x0), Just(x1), ty_Integer)
new_esEs10(x0, x1, ty_Double)
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_lt19(x0, x1, ty_Char)
new_ltEs16(x0, x1)
new_esEs28(x0, x1, ty_@0)
new_esEs6(Right(x0), Left(x1), x2, x3)
new_esEs6(Left(x0), Right(x1), x2, x3)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_ltEs19(x0, x1, ty_Integer)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Left(x0), Left(x1), ty_Bool, x2)
new_ltEs18(x0, x1, ty_@0)
new_esEs8(GT, EQ)
new_esEs8(EQ, GT)
new_compare111(x0, x1, False, x2, x3, x4)
new_esEs20(x0, x1, ty_Ordering)
new_esEs10(x0, x1, ty_Float)
new_compare8(x0, x1, ty_Float)
new_ltEs7(x0, x1)
new_compare27(x0, x1, True, x2)
new_primCmpNat0(Zero, Zero)
new_lt16(x0, x1, ty_Float)
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs6(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs20(x0, x1, ty_Double)
new_compare114(x0, x1, True, x2, x3)
new_esEs25(x0, x1, ty_Bool)
new_esEs6(Left(x0), Left(x1), ty_Float, x2)
new_lt20(x0, x1, ty_Double)
new_esEs9(x0, x1, ty_Integer)
new_lt20(x0, x1, ty_Int)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs12(Left(x0), Left(x1), ty_Int, x2)
new_compare11(:%(x0, x1), :%(x2, x3), ty_Int)
new_esEs6(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs20(x0, x1, ty_Integer)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, ty_Ordering)
new_compare29(x0, x1, True, x2, x3)
new_esEs22(x0, x1, ty_Ordering)
new_compare12(x0, x1, x2)
new_ltEs12(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_ltEs12(Right(x0), Right(x1), x2, ty_Float)
new_lt19(x0, x1, ty_Int)
new_esEs10(x0, x1, ty_Integer)
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_lt20(x0, x1, ty_@0)
new_esEs4(Nothing, Just(x0), x1)
new_esEs20(x0, x1, ty_@0)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_esEs10(x0, x1, ty_Int)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primEqNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs6(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs16(:(x0, x1), [], x2)
new_ltEs12(Left(x0), Left(x1), app(ty_[], x2), x3)
new_ltEs18(x0, x1, ty_Integer)
new_lt6(x0, x1)
new_esEs6(Left(x0), Left(x1), ty_Int, x2)
new_lt16(x0, x1, ty_Int)
new_primMulNat0(Succ(x0), Zero)
new_compare9(@0, @0)
new_esEs11(Double(x0, x1), Double(x2, x3))
new_primMulNat0(Succ(x0), Succ(x1))
new_compare8(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs15(x0, x1)
new_ltEs12(Right(x0), Right(x1), x2, app(ty_[], x3))
new_compare26(x0, x1, True, x2, x3)
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs12(x0, x1)
new_ltEs12(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_asAs(False, x0)
new_primCompAux00(x0, LT)
new_lt14(x0, x1)
new_lt16(x0, x1, app(ty_Maybe, x2))
new_lt20(x0, x1, ty_Float)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, app(ty_Maybe, x2))
new_ltEs4(EQ, GT)
new_ltEs4(GT, EQ)
new_compare29(x0, x1, False, x2, x3)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_compare14(x0, x1, x2, x3)
new_not(True)
new_esEs4(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs6(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs25(x0, x1, app(ty_[], x2))
new_lt11(x0, x1, x2)
new_compare15(x0, x1)
new_ltEs12(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_lt20(x0, x1, app(ty_Ratio, x2))
new_esEs9(x0, x1, ty_@0)
new_compare([], [], x0)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_compare13(x0, x1, x2, x3)
new_not(False)
new_compare19(x0, x1, False)
new_esEs6(Left(x0), Left(x1), ty_@0, x2)
new_compare8(x0, x1, ty_Char)
new_esEs16(:(x0, x1), :(x2, x3), x4)
new_lt17(x0, x1, x2)
new_ltEs12(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_compare19(x0, x1, True)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_lt20(x0, x1, ty_Integer)
new_primEqNat0(Succ(x0), Succ(x1))
new_ltEs6(Just(x0), Just(x1), ty_Integer)
new_esEs25(x0, x1, ty_Integer)
new_primPlusNat0(Succ(x0), x1)
new_lt15(x0, x1)
new_esEs21(x0, x1, app(ty_[], x2))
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_compare7(Float(x0, x1), Float(x2, x3))
new_compare110(x0, x1, False)
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs8(EQ, LT)
new_esEs8(LT, EQ)
new_esEs4(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs10(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs4(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs18(:%(x0, x1), :%(x2, x3), x4)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs21(x0, x1, ty_Double)
new_compare8(x0, x1, app(ty_Ratio, x2))
new_esEs4(Just(x0), Just(x1), ty_@0)
new_lt19(x0, x1, app(ty_Maybe, x2))
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_ltEs18(x0, x1, ty_Char)
new_compare11(:%(x0, x1), :%(x2, x3), ty_Integer)
new_esEs9(x0, x1, app(ty_Maybe, x2))
new_esEs10(x0, x1, app(app(ty_Either, x2), x3))
new_esEs4(Just(x0), Just(x1), ty_Float)
new_esEs17(False, True)
new_esEs17(True, False)
new_ltEs12(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs18(x0, x1, app(ty_Maybe, x2))
new_compare18(x0, x1, x2, x3, x4)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_compare8(x0, x1, ty_Double)
new_esEs4(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_esEs6(Right(x0), Right(x1), x2, ty_Int)
new_esEs21(x0, x1, ty_Ordering)
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt8(x0, x1, x2, x3, x4)
new_esEs21(x0, x1, ty_@0)
new_ltEs19(x0, x1, ty_Double)
new_compare26(x0, x1, False, x2, x3)
new_esEs10(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Pos(Zero), Pos(Zero))
new_esEs17(True, True)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_compare110(x0, x1, True)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_esEs28(x0, x1, ty_Int)
new_ltEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs4(Just(x0), Just(x1), ty_Int)
new_esEs4(Just(x0), Just(x1), ty_Double)
new_ltEs10(@2(x0, x1), @2(x2, x3), x4, x5)
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_compare16(x0, x1)
new_primCmpNat0(Zero, Succ(x0))
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_esEs20(x0, x1, app(ty_[], x2))
new_ltEs4(GT, LT)
new_ltEs4(LT, GT)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_primPlusNat1(Zero, Succ(x0))
new_ltEs18(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs12(Left(x0), Left(x1), ty_Float, x2)
new_ltEs19(x0, x1, app(ty_[], x2))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_esEs6(Right(x0), Right(x1), x2, ty_Integer)
new_esEs26(x0, x1, ty_Bool)
new_esEs19(Integer(x0), Integer(x1))
new_esEs6(Left(x0), Left(x1), app(ty_[], x2), x3)
new_lt16(x0, x1, ty_@0)

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: