YES 3.489 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, Ord b) => Either a b  ->  Either a b  ->  Bool) :: (Ord b, Ord a) => Either a b  ->  Either a b  ->  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 a, Ord b) => Either b a  ->  Either b a  ->  Bool) :: (Ord b, Ord a) => Either b a  ->  Either b 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 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

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

compare3 x y = compare2 x y (x == y)

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

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

gcd'0 x y = gcd' y (x `rem` y)

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

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

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

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

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

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

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

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

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

is transformed to
absReal x = absReal2 x

absReal0 x True = `negate` x

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

absReal2 x = absReal1 x (x >= 0)

The following Function with conditions
undefined 
 | False
 = undefined

is transformed to
undefined  = undefined1

undefined0 True = undefined

undefined1  = undefined0 False

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

is transformed to
reduce x y = reduce2 x y

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



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

mainModule Main
  (((>) :: (Ord a, Ord b) => 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
reduce2Reduce1 vwv vww x y True = error []
reduce2Reduce1 vwv vww x y False = reduce2Reduce0 vwv vww x y otherwise

reduce2D vwv vww = gcd vwv vww

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

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

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

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

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



↳ 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 b a  ->  Either b 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_primCmpNat(Succ(vwx900), Succ(vwx1000)) → new_primCmpNat(vwx900, vwx1000)

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(vwx5800), Succ(vwx400000)) → new_primPlusNat(vwx5800, 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_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
                              ↳ QDP
                                ↳ QDPSizeChangeProof
                              ↳ QDP

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

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

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

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



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

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

new_lt(vwx90, vwx100, cc, cd) → new_compare2(vwx90, vwx100, new_esEs4(vwx90, vwx100, cc, cd), cc, cd)
new_ltEs1(:(vwx90, vwx91), :(vwx100, vwx101), gc) → new_compare(vwx91, vwx101, gc)
new_compare2(vwx90, vwx100, False, cc, cd) → new_ltEs(vwx90, vwx100, cc, cd)
new_ltEs0(Right(vwx90), Right(vwx100), eh, app(app(app(ty_@3, fh), ga), gb)) → new_ltEs3(vwx90, vwx100, fh, ga, gb)
new_ltEs0(Left(vwx90), Left(vwx100), app(app(app(ty_@3, ee), ef), eg), dh) → new_ltEs3(vwx90, vwx100, ee, ef, eg)
new_ltEs(@2(vwx90, vwx91), @2(vwx100, vwx101), ba, app(ty_[], bf)) → new_ltEs1(vwx91, vwx101, bf)
new_compare5(vwx90, vwx100, dc, dd, de) → new_compare22(vwx90, vwx100, new_esEs7(vwx90, vwx100, dc, dd, de), dc, dd, de)
new_ltEs(@2(vwx90, vwx91), @2(vwx100, vwx101), app(app(ty_Either, cf), cg), ce) → new_compare20(vwx90, vwx100, new_esEs5(vwx90, vwx100, cf, cg), cf, cg)
new_ltEs2(Just(vwx90), Just(vwx100), app(app(ty_Either, hg), hh)) → new_ltEs0(vwx90, vwx100, hg, hh)
new_ltEs(@2(vwx90, vwx91), @2(vwx100, vwx101), ba, app(ty_Maybe, bg)) → new_ltEs2(vwx91, vwx101, bg)
new_ltEs3(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), app(app(ty_@2, bdc), bdd), bag, bcc) → new_lt(vwx90, vwx100, bdc, bdd)
new_compare3(vwx90, vwx100, cf, cg) → new_compare20(vwx90, vwx100, new_esEs5(vwx90, vwx100, cf, cg), cf, cg)
new_compare22(vwx90, vwx100, False, dc, dd, de) → new_ltEs3(vwx90, vwx100, dc, dd, de)
new_ltEs0(Left(vwx90), Left(vwx100), app(ty_[], ec), dh) → new_ltEs1(vwx90, vwx100, ec)
new_ltEs0(Left(vwx90), Left(vwx100), app(app(ty_Either, ea), eb), dh) → new_ltEs0(vwx90, vwx100, ea, eb)
new_primCompAux(vwx90, vwx100, vwx79, app(ty_[], gh)) → new_compare(vwx90, vwx100, gh)
new_ltEs(@2(vwx90, vwx91), @2(vwx100, vwx101), app(ty_[], da), ce) → new_compare(vwx90, vwx100, da)
new_ltEs3(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), app(ty_Maybe, bdh), bag, bcc) → new_lt2(vwx90, vwx100, bdh)
new_ltEs3(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), baf, bag, app(app(ty_Either, bbb), bbc)) → new_ltEs0(vwx92, vwx102, bbb, bbc)
new_ltEs0(Right(vwx90), Right(vwx100), eh, app(app(ty_@2, fa), fb)) → new_ltEs(vwx90, vwx100, fa, fb)
new_lt3(vwx90, vwx100, dc, dd, de) → new_compare22(vwx90, vwx100, new_esEs7(vwx90, vwx100, dc, dd, de), dc, dd, de)
new_ltEs3(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), baf, bag, app(ty_Maybe, bbe)) → new_ltEs2(vwx92, vwx102, bbe)
new_lt0(vwx90, vwx100, cf, cg) → new_compare20(vwx90, vwx100, new_esEs5(vwx90, vwx100, cf, cg), cf, cg)
new_lt2(vwx90, vwx100, db) → new_compare21(vwx90, vwx100, new_esEs6(vwx90, vwx100, db), db)
new_compare20(vwx90, vwx100, False, cf, cg) → new_ltEs0(vwx90, vwx100, cf, cg)
new_ltEs0(Left(vwx90), Left(vwx100), app(app(ty_@2, df), dg), dh) → new_ltEs(vwx90, vwx100, df, dg)
new_ltEs(@2(vwx90, vwx91), @2(vwx100, vwx101), ba, app(app(app(ty_@3, bh), ca), cb)) → new_ltEs3(vwx91, vwx101, bh, ca, cb)
new_ltEs2(Just(vwx90), Just(vwx100), app(ty_[], baa)) → new_ltEs1(vwx90, vwx100, baa)
new_ltEs(@2(vwx90, vwx91), @2(vwx100, vwx101), app(ty_Maybe, db), ce) → new_compare21(vwx90, vwx100, new_esEs6(vwx90, vwx100, db), db)
new_ltEs2(Just(vwx90), Just(vwx100), app(app(app(ty_@3, bac), bad), bae)) → new_ltEs3(vwx90, vwx100, bac, bad, bae)
new_ltEs3(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), baf, bag, app(app(ty_@2, bah), bba)) → new_ltEs(vwx92, vwx102, bah, bba)
new_ltEs0(Right(vwx90), Right(vwx100), eh, app(app(ty_Either, fc), fd)) → new_ltEs0(vwx90, vwx100, fc, fd)
new_lt1(vwx90, vwx100, da) → new_compare(vwx90, vwx100, da)
new_ltEs0(Right(vwx90), Right(vwx100), eh, app(ty_Maybe, fg)) → new_ltEs2(vwx90, vwx100, fg)
new_ltEs3(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), baf, app(app(ty_@2, bca), bcb), bcc) → new_lt(vwx91, vwx101, bca, bcb)
new_ltEs2(Just(vwx90), Just(vwx100), app(app(ty_@2, he), hf)) → new_ltEs(vwx90, vwx100, he, hf)
new_ltEs3(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), baf, bag, app(app(app(ty_@3, bbf), bbg), bbh)) → new_ltEs3(vwx92, vwx102, bbf, bbg, bbh)
new_ltEs3(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), app(ty_[], bdg), bag, bcc) → new_lt1(vwx90, vwx100, bdg)
new_primCompAux(vwx90, vwx100, vwx79, app(app(app(ty_@3, hb), hc), hd)) → new_compare5(vwx90, vwx100, hb, hc, hd)
new_ltEs3(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), app(app(app(ty_@3, bea), beb), bec), bag, bcc) → new_lt3(vwx90, vwx100, bea, beb, bec)
new_ltEs2(Just(vwx90), Just(vwx100), app(ty_Maybe, bab)) → new_ltEs2(vwx90, vwx100, bab)
new_compare(:(vwx90, vwx91), :(vwx100, vwx101), gc) → new_compare(vwx91, vwx101, gc)
new_compare21(vwx90, vwx100, False, db) → new_ltEs2(vwx90, vwx100, db)
new_ltEs0(Left(vwx90), Left(vwx100), app(ty_Maybe, ed), dh) → new_ltEs2(vwx90, vwx100, ed)
new_primCompAux(vwx90, vwx100, vwx79, app(app(ty_Either, gf), gg)) → new_compare3(vwx90, vwx100, gf, gg)
new_compare(:(vwx90, vwx91), :(vwx100, vwx101), gc) → new_primCompAux(vwx90, vwx100, new_compare0(vwx91, vwx101, gc), gc)
new_ltEs(@2(vwx90, vwx91), @2(vwx100, vwx101), ba, app(app(ty_@2, bb), bc)) → new_ltEs(vwx91, vwx101, bb, bc)
new_ltEs0(Right(vwx90), Right(vwx100), eh, app(ty_[], ff)) → new_ltEs1(vwx90, vwx100, ff)
new_ltEs3(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), baf, app(app(app(ty_@3, bch), bda), bdb), bcc) → new_lt3(vwx91, vwx101, bch, bda, bdb)
new_ltEs3(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), baf, app(app(ty_Either, bcd), bce), bcc) → new_lt0(vwx91, vwx101, bcd, bce)
new_compare4(vwx90, vwx100, db) → new_compare21(vwx90, vwx100, new_esEs6(vwx90, vwx100, db), db)
new_primCompAux(vwx90, vwx100, vwx79, app(ty_Maybe, ha)) → new_compare4(vwx90, vwx100, ha)
new_ltEs(@2(vwx90, vwx91), @2(vwx100, vwx101), ba, app(app(ty_Either, bd), be)) → new_ltEs0(vwx91, vwx101, bd, be)
new_ltEs1(:(vwx90, vwx91), :(vwx100, vwx101), gc) → new_primCompAux(vwx90, vwx100, new_compare0(vwx91, vwx101, gc), gc)
new_ltEs(@2(vwx90, vwx91), @2(vwx100, vwx101), app(app(ty_@2, cc), cd), ce) → new_compare2(vwx90, vwx100, new_esEs4(vwx90, vwx100, cc, cd), cc, cd)
new_ltEs3(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), baf, bag, app(ty_[], bbd)) → new_ltEs1(vwx92, vwx102, bbd)
new_ltEs3(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), baf, app(ty_Maybe, bcg), bcc) → new_lt2(vwx91, vwx101, bcg)
new_primCompAux(vwx90, vwx100, vwx79, app(app(ty_@2, gd), ge)) → new_compare1(vwx90, vwx100, gd, ge)
new_ltEs3(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), app(app(ty_Either, bde), bdf), bag, bcc) → new_lt0(vwx90, vwx100, bde, bdf)
new_ltEs3(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), baf, app(ty_[], bcf), bcc) → new_lt1(vwx91, vwx101, bcf)
new_compare1(vwx90, vwx100, cc, cd) → new_compare2(vwx90, vwx100, new_esEs4(vwx90, vwx100, cc, cd), cc, cd)
new_ltEs(@2(vwx90, vwx91), @2(vwx100, vwx101), app(app(app(ty_@3, dc), dd), de), ce) → new_compare22(vwx90, vwx100, new_esEs7(vwx90, vwx100, dc, dd, de), dc, dd, de)

The TRS R consists of the following rules:

new_esEs7(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), cae, caf, cag) → new_asAs(new_esEs24(vwx300, vwx400, cae), new_asAs(new_esEs25(vwx301, vwx401, caf), new_esEs26(vwx302, vwx402, cag)))
new_ltEs10(Left(vwx90), Left(vwx100), app(app(app(ty_@3, ee), ef), eg), dh) → new_ltEs5(vwx90, vwx100, ee, ef, eg)
new_esEs28(vwx300, vwx400, app(ty_[], daa)) → new_esEs13(vwx300, vwx400, daa)
new_compare28(vwx90, vwx100, cc, cd) → new_compare210(vwx90, vwx100, new_esEs4(vwx90, vwx100, cc, cd), cc, cd)
new_esEs24(vwx300, vwx400, app(app(ty_Either, cbf), cbg)) → new_esEs5(vwx300, vwx400, cbf, cbg)
new_lt5(vwx90, vwx100, app(ty_Maybe, bdh)) → new_lt12(vwx90, vwx100, bdh)
new_ltEs15(EQ, LT) → False
new_esEs22(vwx300, vwx400, ty_Ordering) → new_esEs15(vwx300, vwx400)
new_compare15(vwx90, vwx100, True, cf, cg) → LT
new_lt4(vwx91, vwx101, ty_Ordering) → new_lt14(vwx91, vwx101)
new_esEs13([], [], che) → True
new_ltEs10(Left(vwx90), Right(vwx100), eh, dh) → True
new_compare110(vwx90, vwx100, True, cc, cd) → LT
new_esEs23(vwx301, vwx401, app(app(ty_Either, bhf), bhg)) → new_esEs5(vwx301, vwx401, bhf, bhg)
new_esEs23(vwx301, vwx401, app(app(ty_@2, bhh), caa)) → new_esEs4(vwx301, vwx401, bhh, caa)
new_lt20(vwx90, vwx100, app(ty_Ratio, bfc)) → new_lt16(vwx90, vwx100, bfc)
new_esEs28(vwx300, vwx400, ty_Float) → new_esEs14(vwx300, vwx400)
new_esEs23(vwx301, vwx401, ty_Integer) → new_esEs18(vwx301, vwx401)
new_ltEs6(vwx92, vwx102, app(ty_Ratio, bef)) → new_ltEs17(vwx92, vwx102, bef)
new_esEs15(EQ, EQ) → True
new_primCompAux1(vwx90, vwx100, vwx79, gc) → new_primCompAux0(vwx79, new_compare27(vwx90, vwx100, gc))
new_esEs9(vwx91, vwx101, ty_Bool) → new_esEs19(vwx91, vwx101)
new_ltEs15(EQ, EQ) → True
new_esEs22(vwx300, vwx400, ty_Char) → new_esEs12(vwx300, vwx400)
new_ltEs10(Left(vwx90), Left(vwx100), ty_Int, dh) → new_ltEs9(vwx90, vwx100)
new_lt4(vwx91, vwx101, app(ty_Ratio, bee)) → new_lt16(vwx91, vwx101, bee)
new_ltEs10(Left(vwx90), Left(vwx100), ty_Ordering, dh) → new_ltEs15(vwx90, vwx100)
new_ltEs6(vwx92, vwx102, ty_Float) → new_ltEs14(vwx92, vwx102)
new_primMulNat0(Zero, Zero) → Zero
new_esEs28(vwx300, vwx400, ty_Bool) → new_esEs19(vwx300, vwx400)
new_lt20(vwx90, vwx100, ty_@0) → new_lt7(vwx90, vwx100)
new_sr(Integer(vwx1000), Integer(vwx910)) → Integer(new_primMulInt(vwx1000, vwx910))
new_esEs6(Just(vwx300), Just(vwx400), ty_Bool) → new_esEs19(vwx300, vwx400)
new_ltEs6(vwx92, vwx102, app(app(app(ty_@3, bbf), bbg), bbh)) → new_ltEs5(vwx92, vwx102, bbf, bbg, bbh)
new_esEs25(vwx301, vwx401, app(app(ty_@2, cdb), cdc)) → new_esEs4(vwx301, vwx401, cdb, cdc)
new_ltEs13(Nothing, Just(vwx100), beg) → True
new_esEs5(Left(vwx300), Left(vwx400), ty_Char, cef) → new_esEs12(vwx300, vwx400)
new_compare25(vwx90, vwx100, True, db) → EQ
new_lt20(vwx90, vwx100, app(app(app(ty_@3, dc), dd), de)) → new_lt18(vwx90, vwx100, dc, dd, de)
new_esEs25(vwx301, vwx401, ty_Double) → new_esEs16(vwx301, vwx401)
new_esEs5(Right(vwx300), Right(vwx400), cga, ty_Char) → new_esEs12(vwx300, vwx400)
new_ltEs15(GT, LT) → False
new_esEs8(vwx90, vwx100, ty_Int) → new_esEs11(vwx90, vwx100)
new_esEs5(Left(vwx300), Left(vwx400), app(ty_Ratio, cfc), cef) → new_esEs17(vwx300, vwx400, cfc)
new_ltEs10(Left(vwx90), Left(vwx100), ty_@0, dh) → new_ltEs8(vwx90, vwx100)
new_lt5(vwx90, vwx100, ty_Integer) → new_lt17(vwx90, vwx100)
new_esEs5(Right(vwx300), Right(vwx400), cga, ty_Ordering) → new_esEs15(vwx300, vwx400)
new_esEs8(vwx90, vwx100, ty_Double) → new_esEs16(vwx90, vwx100)
new_ltEs19(vwx91, vwx101, ty_Bool) → new_ltEs4(vwx91, vwx101)
new_esEs5(Left(vwx300), Left(vwx400), ty_Ordering, cef) → new_esEs15(vwx300, vwx400)
new_esEs22(vwx300, vwx400, app(ty_Maybe, bgc)) → new_esEs6(vwx300, vwx400, bgc)
new_esEs6(Just(vwx300), Just(vwx400), ty_Ordering) → new_esEs15(vwx300, vwx400)
new_esEs27(vwx90, vwx100, app(ty_Maybe, db)) → new_esEs6(vwx90, vwx100, db)
new_ltEs4(False, True) → True
new_lt10(vwx90, vwx100) → new_esEs15(new_compare14(vwx90, vwx100), LT)
new_esEs23(vwx301, vwx401, ty_Ordering) → new_esEs15(vwx301, vwx401)
new_ltEs12(vwx9, vwx10, gc) → new_not(new_esEs15(new_compare0(vwx9, vwx10, gc), GT))
new_esEs9(vwx91, vwx101, ty_Ordering) → new_esEs15(vwx91, vwx101)
new_ltEs10(Left(vwx90), Left(vwx100), ty_Char, dh) → new_ltEs11(vwx90, vwx100)
new_esEs8(vwx90, vwx100, app(app(ty_@2, bdc), bdd)) → new_esEs4(vwx90, vwx100, bdc, bdd)
new_compare23(vwx90, vwx100, False) → new_compare13(vwx90, vwx100, new_ltEs15(vwx90, vwx100))
new_lt11(vwx90, vwx100, da) → new_esEs15(new_compare0(vwx90, vwx100, da), LT)
new_esEs5(Left(vwx300), Left(vwx400), app(ty_Maybe, cfd), cef) → new_esEs6(vwx300, vwx400, cfd)
new_pePe(False, vwx78) → vwx78
new_ltEs4(True, True) → True
new_ltEs19(vwx91, vwx101, ty_Ordering) → new_ltEs15(vwx91, vwx101)
new_compare27(vwx90, vwx100, ty_Float) → new_compare17(vwx90, vwx100)
new_ltEs6(vwx92, vwx102, ty_Ordering) → new_ltEs15(vwx92, vwx102)
new_esEs23(vwx301, vwx401, ty_Float) → new_esEs14(vwx301, vwx401)
new_compare29(@0, @0) → EQ
new_ltEs15(EQ, GT) → True
new_ltEs10(Right(vwx90), Right(vwx100), eh, app(app(ty_@2, fa), fb)) → new_ltEs7(vwx90, vwx100, fa, fb)
new_ltEs13(Just(vwx90), Just(vwx100), ty_Int) → new_ltEs9(vwx90, vwx100)
new_compare23(vwx90, vwx100, True) → EQ
new_esEs28(vwx300, vwx400, ty_Integer) → new_esEs18(vwx300, vwx400)
new_esEs26(vwx302, vwx402, ty_Char) → new_esEs12(vwx302, vwx402)
new_lt19(vwx90, vwx100) → new_esEs15(new_compare31(vwx90, vwx100), LT)
new_esEs26(vwx302, vwx402, ty_Int) → new_esEs11(vwx302, vwx402)
new_esEs26(vwx302, vwx402, app(ty_Ratio, cdh)) → new_esEs17(vwx302, vwx402, cdh)
new_esEs24(vwx300, vwx400, ty_Float) → new_esEs14(vwx300, vwx400)
new_esEs27(vwx90, vwx100, ty_Ordering) → new_esEs15(vwx90, vwx100)
new_ltEs10(Right(vwx90), Right(vwx100), eh, ty_Int) → new_ltEs9(vwx90, vwx100)
new_esEs22(vwx300, vwx400, app(app(ty_@2, bgf), bgg)) → new_esEs4(vwx300, vwx400, bgf, bgg)
new_esEs26(vwx302, vwx402, ty_Ordering) → new_esEs15(vwx302, vwx402)
new_esEs22(vwx300, vwx400, ty_Int) → new_esEs11(vwx300, vwx400)
new_compare210(vwx90, vwx100, False, cc, cd) → new_compare110(vwx90, vwx100, new_ltEs7(vwx90, vwx100, cc, cd), cc, cd)
new_ltEs10(Left(vwx90), Left(vwx100), app(app(ty_Either, ea), eb), dh) → new_ltEs10(vwx90, vwx100, ea, eb)
new_ltEs6(vwx92, vwx102, app(app(ty_@2, bah), bba)) → new_ltEs7(vwx92, vwx102, bah, bba)
new_lt14(vwx90, vwx100) → new_esEs15(new_compare6(vwx90, vwx100), LT)
new_esEs15(LT, EQ) → False
new_esEs15(EQ, LT) → False
new_esEs5(Left(vwx300), Left(vwx400), ty_Int, cef) → new_esEs11(vwx300, vwx400)
new_esEs5(Right(vwx300), Right(vwx400), cga, app(app(ty_@2, chb), chc)) → new_esEs4(vwx300, vwx400, chb, chc)
new_esEs23(vwx301, vwx401, app(app(app(ty_@3, bgh), bha), bhb)) → new_esEs7(vwx301, vwx401, bgh, bha, bhb)
new_ltEs15(LT, LT) → True
new_primCmpNat0(Zero, Succ(vwx1000)) → LT
new_ltEs13(Just(vwx90), Just(vwx100), app(app(ty_Either, hg), hh)) → new_ltEs10(vwx90, vwx100, hg, hh)
new_esEs27(vwx90, vwx100, app(app(app(ty_@3, dc), dd), de)) → new_esEs7(vwx90, vwx100, dc, dd, de)
new_ltEs13(Nothing, Nothing, beg) → True
new_lt13(vwx90, vwx100) → new_esEs15(new_compare17(vwx90, vwx100), LT)
new_lt4(vwx91, vwx101, app(app(app(ty_@3, bch), bda), bdb)) → new_lt18(vwx91, vwx101, bch, bda, bdb)
new_esEs15(EQ, GT) → False
new_esEs15(GT, EQ) → False
new_esEs25(vwx301, vwx401, app(app(ty_Either, cch), cda)) → new_esEs5(vwx301, vwx401, cch, cda)
new_esEs8(vwx90, vwx100, app(ty_[], bdg)) → new_esEs13(vwx90, vwx100, bdg)
new_esEs27(vwx90, vwx100, ty_@0) → new_esEs10(vwx90, vwx100)
new_esEs28(vwx300, vwx400, ty_Double) → new_esEs16(vwx300, vwx400)
new_ltEs19(vwx91, vwx101, app(app(ty_Either, bd), be)) → new_ltEs10(vwx91, vwx101, bd, be)
new_compare27(vwx90, vwx100, app(app(ty_@2, gd), ge)) → new_compare28(vwx90, vwx100, gd, ge)
new_esEs16(Double(vwx300, vwx301), Double(vwx400, vwx401)) → new_esEs11(new_sr0(vwx300, vwx400), new_sr0(vwx301, vwx401))
new_pePe(True, vwx78) → True
new_compare0([], [], gc) → EQ
new_primEqNat0(Zero, Zero) → True
new_lt5(vwx90, vwx100, ty_Bool) → new_lt19(vwx90, vwx100)
new_esEs6(Just(vwx300), Just(vwx400), app(app(app(ty_@3, dba), dbb), dbc)) → new_esEs7(vwx300, vwx400, dba, dbb, dbc)
new_esEs20(vwx300, vwx400, ty_Int) → new_esEs11(vwx300, vwx400)
new_ltEs17(vwx9, vwx10, bfa) → new_not(new_esEs15(new_compare7(vwx9, vwx10, bfa), GT))
new_ltEs19(vwx91, vwx101, ty_Integer) → new_ltEs18(vwx91, vwx101)
new_ltEs7(@2(vwx90, vwx91), @2(vwx100, vwx101), ba, ce) → new_pePe(new_lt20(vwx90, vwx100, ba), new_asAs(new_esEs27(vwx90, vwx100, ba), new_ltEs19(vwx91, vwx101, ce)))
new_esEs26(vwx302, vwx402, app(ty_Maybe, cea)) → new_esEs6(vwx302, vwx402, cea)
new_ltEs6(vwx92, vwx102, app(app(ty_Either, bbb), bbc)) → new_ltEs10(vwx92, vwx102, bbb, bbc)
new_primMulNat0(Succ(vwx30000), Succ(vwx40000)) → new_primPlusNat1(new_primMulNat0(vwx30000, Succ(vwx40000)), vwx40000)
new_ltEs10(Right(vwx90), Right(vwx100), eh, app(app(app(ty_@3, fh), ga), gb)) → new_ltEs5(vwx90, vwx100, fh, ga, gb)
new_compare18(vwx90, vwx100, dc, dd, de) → new_compare26(vwx90, vwx100, new_esEs7(vwx90, vwx100, dc, dd, de), dc, dd, de)
new_esEs5(Right(vwx300), Right(vwx400), cga, app(ty_Ratio, cgf)) → new_esEs17(vwx300, vwx400, cgf)
new_esEs9(vwx91, vwx101, app(ty_Maybe, bcg)) → new_esEs6(vwx91, vwx101, bcg)
new_esEs27(vwx90, vwx100, ty_Char) → new_esEs12(vwx90, vwx100)
new_compare211(vwx90, vwx100, False) → new_compare10(vwx90, vwx100, new_ltEs4(vwx90, vwx100))
new_esEs19(True, True) → True
new_esEs24(vwx300, vwx400, app(ty_Ratio, cbd)) → new_esEs17(vwx300, vwx400, cbd)
new_esEs6(Just(vwx300), Just(vwx400), ty_Float) → new_esEs14(vwx300, vwx400)
new_esEs25(vwx301, vwx401, ty_Integer) → new_esEs18(vwx301, vwx401)
new_ltEs13(Just(vwx90), Just(vwx100), ty_Integer) → new_ltEs18(vwx90, vwx100)
new_compare110(vwx90, vwx100, False, cc, cd) → GT
new_lt17(vwx90, vwx100) → new_esEs15(new_compare9(vwx90, vwx100), LT)
new_esEs5(Left(vwx300), Left(vwx400), app(ty_[], cfb), cef) → new_esEs13(vwx300, vwx400, cfb)
new_compare12(vwx90, vwx100, True, dc, dd, de) → LT
new_esEs24(vwx300, vwx400, ty_Double) → new_esEs16(vwx300, vwx400)
new_esEs9(vwx91, vwx101, app(app(app(ty_@3, bch), bda), bdb)) → new_esEs7(vwx91, vwx101, bch, bda, bdb)
new_ltEs15(GT, GT) → True
new_esEs24(vwx300, vwx400, ty_Char) → new_esEs12(vwx300, vwx400)
new_ltEs10(Left(vwx90), Left(vwx100), ty_Integer, dh) → new_ltEs18(vwx90, vwx100)
new_ltEs13(Just(vwx90), Just(vwx100), app(app(ty_@2, he), hf)) → new_ltEs7(vwx90, vwx100, he, hf)
new_compare27(vwx90, vwx100, ty_Integer) → new_compare9(vwx90, vwx100)
new_esEs9(vwx91, vwx101, ty_Integer) → new_esEs18(vwx91, vwx101)
new_ltEs10(Right(vwx90), Right(vwx100), eh, ty_Double) → new_ltEs16(vwx90, vwx100)
new_esEs5(Left(vwx300), Left(vwx400), ty_Double, cef) → new_esEs16(vwx300, vwx400)
new_esEs25(vwx301, vwx401, ty_@0) → new_esEs10(vwx301, vwx401)
new_lt20(vwx90, vwx100, ty_Ordering) → new_lt14(vwx90, vwx100)
new_lt7(vwx90, vwx100) → new_esEs15(new_compare29(vwx90, vwx100), LT)
new_lt5(vwx90, vwx100, ty_@0) → new_lt7(vwx90, vwx100)
new_compare17(Float(vwx90, vwx91), Float(vwx100, vwx101)) → new_compare8(new_sr0(vwx90, vwx100), new_sr0(vwx91, vwx101))
new_esEs8(vwx90, vwx100, ty_Char) → new_esEs12(vwx90, vwx100)
new_lt5(vwx90, vwx100, app(ty_Ratio, bed)) → new_lt16(vwx90, vwx100, bed)
new_ltEs13(Just(vwx90), Just(vwx100), ty_Bool) → new_ltEs4(vwx90, vwx100)
new_primEqInt(Neg(Succ(vwx3000)), Neg(Succ(vwx4000))) → new_primEqNat0(vwx3000, vwx4000)
new_compare6(vwx90, vwx100) → new_compare23(vwx90, vwx100, new_esEs15(vwx90, vwx100))
new_esEs26(vwx302, vwx402, app(ty_[], cdg)) → new_esEs13(vwx302, vwx402, cdg)
new_compare16(vwx90, vwx100, True, db) → LT
new_esEs24(vwx300, vwx400, ty_Bool) → new_esEs19(vwx300, vwx400)
new_ltEs19(vwx91, vwx101, app(ty_Ratio, chd)) → new_ltEs17(vwx91, vwx101, chd)
new_compare13(vwx90, vwx100, False) → GT
new_esEs26(vwx302, vwx402, app(app(app(ty_@3, cdd), cde), cdf)) → new_esEs7(vwx302, vwx402, cdd, cde, cdf)
new_compare19(vwx90, vwx100, cf, cg) → new_compare24(vwx90, vwx100, new_esEs5(vwx90, vwx100, cf, cg), cf, cg)
new_ltEs10(Right(vwx90), Right(vwx100), eh, ty_Ordering) → new_ltEs15(vwx90, vwx100)
new_compare27(vwx90, vwx100, ty_Bool) → new_compare31(vwx90, vwx100)
new_esEs5(Left(vwx300), Left(vwx400), app(app(app(ty_@3, ceg), ceh), cfa), cef) → new_esEs7(vwx300, vwx400, ceg, ceh, cfa)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs19(False, False) → True
new_esEs9(vwx91, vwx101, ty_Double) → new_esEs16(vwx91, vwx101)
new_esEs27(vwx90, vwx100, app(app(ty_Either, cf), cg)) → new_esEs5(vwx90, vwx100, cf, cg)
new_esEs5(Left(vwx300), Left(vwx400), ty_@0, cef) → new_esEs10(vwx300, vwx400)
new_compare8(vwx9, vwx10) → new_primCmpInt(vwx9, vwx10)
new_primEqInt(Neg(Succ(vwx3000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(vwx4000))) → False
new_primCompAux0(vwx89, GT) → GT
new_ltEs18(vwx9, vwx10) → new_not(new_esEs15(new_compare9(vwx9, vwx10), GT))
new_primPlusNat1(Zero, vwx40000) → Succ(vwx40000)
new_esEs17(:%(vwx300, vwx301), :%(vwx400, vwx401), bfb) → new_asAs(new_esEs20(vwx300, vwx400, bfb), new_esEs21(vwx301, vwx401, bfb))
new_compare24(vwx90, vwx100, True, cf, cg) → EQ
new_ltEs6(vwx92, vwx102, ty_@0) → new_ltEs8(vwx92, vwx102)
new_esEs21(vwx301, vwx401, ty_Integer) → new_esEs18(vwx301, vwx401)
new_ltEs10(Right(vwx90), Right(vwx100), eh, ty_Bool) → new_ltEs4(vwx90, vwx100)
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_compare14(Char(vwx90), Char(vwx100)) → new_primCmpNat0(vwx90, vwx100)
new_lt20(vwx90, vwx100, ty_Int) → new_lt8(vwx90, vwx100)
new_ltEs15(LT, GT) → True
new_lt4(vwx91, vwx101, ty_Int) → new_lt8(vwx91, vwx101)
new_lt5(vwx90, vwx100, app(app(ty_@2, bdc), bdd)) → new_lt6(vwx90, vwx100, bdc, bdd)
new_primCmpNat0(Succ(vwx900), Succ(vwx1000)) → new_primCmpNat0(vwx900, vwx1000)
new_esEs5(Right(vwx300), Right(vwx400), cga, ty_Integer) → new_esEs18(vwx300, vwx400)
new_esEs6(Nothing, Nothing, dah) → True
new_primEqInt(Pos(Succ(vwx3000)), Pos(Succ(vwx4000))) → new_primEqNat0(vwx3000, vwx4000)
new_esEs26(vwx302, vwx402, ty_Bool) → new_esEs19(vwx302, vwx402)
new_lt4(vwx91, vwx101, app(ty_Maybe, bcg)) → new_lt12(vwx91, vwx101, bcg)
new_esEs28(vwx300, vwx400, ty_Ordering) → new_esEs15(vwx300, vwx400)
new_esEs6(Just(vwx300), Just(vwx400), app(ty_Ratio, dbe)) → new_esEs17(vwx300, vwx400, dbe)
new_esEs5(Right(vwx300), Right(vwx400), cga, app(app(ty_Either, cgh), cha)) → new_esEs5(vwx300, vwx400, cgh, cha)
new_esEs8(vwx90, vwx100, ty_Integer) → new_esEs18(vwx90, vwx100)
new_compare27(vwx90, vwx100, app(app(app(ty_@3, hb), hc), hd)) → new_compare18(vwx90, vwx100, hb, hc, hd)
new_esEs6(Nothing, Just(vwx400), dah) → False
new_esEs6(Just(vwx300), Nothing, dah) → False
new_esEs6(Just(vwx300), Just(vwx400), ty_Int) → new_esEs11(vwx300, vwx400)
new_primEqNat0(Succ(vwx3000), Succ(vwx4000)) → new_primEqNat0(vwx3000, vwx4000)
new_ltEs14(vwx9, vwx10) → new_not(new_esEs15(new_compare17(vwx9, vwx10), GT))
new_lt20(vwx90, vwx100, ty_Integer) → new_lt17(vwx90, vwx100)
new_lt4(vwx91, vwx101, ty_Char) → new_lt10(vwx91, vwx101)
new_esEs28(vwx300, vwx400, ty_Int) → new_esEs11(vwx300, vwx400)
new_primCmpInt(Neg(Succ(vwx900)), Neg(vwx100)) → new_primCmpNat0(vwx100, Succ(vwx900))
new_compare7(:%(vwx90, vwx91), :%(vwx100, vwx101), ty_Int) → new_compare8(new_sr0(vwx90, vwx101), new_sr0(vwx100, vwx91))
new_compare16(vwx90, vwx100, False, db) → GT
new_esEs26(vwx302, vwx402, app(app(ty_@2, ced), cee)) → new_esEs4(vwx302, vwx402, ced, cee)
new_ltEs10(Right(vwx90), Right(vwx100), eh, app(app(ty_Either, fc), fd)) → new_ltEs10(vwx90, vwx100, fc, fd)
new_esEs5(Right(vwx300), Right(vwx400), cga, ty_@0) → new_esEs10(vwx300, vwx400)
new_esEs21(vwx301, vwx401, ty_Int) → new_esEs11(vwx301, vwx401)
new_primEqInt(Pos(Succ(vwx3000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(vwx4000))) → False
new_primPlusNat0(Zero, Succ(vwx400000)) → Succ(vwx400000)
new_primPlusNat0(Succ(vwx5800), Zero) → Succ(vwx5800)
new_esEs24(vwx300, vwx400, ty_@0) → new_esEs10(vwx300, vwx400)
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(vwx900), Zero) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(vwx1000))) → LT
new_esEs19(False, True) → False
new_esEs19(True, False) → False
new_esEs5(Right(vwx300), Right(vwx400), cga, ty_Bool) → new_esEs19(vwx300, vwx400)
new_compare27(vwx90, vwx100, app(ty_[], gh)) → new_compare0(vwx90, vwx100, gh)
new_esEs9(vwx91, vwx101, app(ty_[], bcf)) → new_esEs13(vwx91, vwx101, bcf)
new_esEs5(Left(vwx300), Left(vwx400), ty_Float, cef) → new_esEs14(vwx300, vwx400)
new_compare13(vwx90, vwx100, True) → LT
new_ltEs19(vwx91, vwx101, ty_Double) → new_ltEs16(vwx91, vwx101)
new_primEqInt(Pos(Succ(vwx3000)), Neg(vwx400)) → False
new_primEqInt(Neg(Succ(vwx3000)), Pos(vwx400)) → False
new_esEs28(vwx300, vwx400, app(app(ty_Either, dad), dae)) → new_esEs5(vwx300, vwx400, dad, dae)
new_esEs25(vwx301, vwx401, ty_Bool) → new_esEs19(vwx301, vwx401)
new_esEs24(vwx300, vwx400, app(app(ty_@2, cbh), cca)) → new_esEs4(vwx300, vwx400, cbh, cca)
new_compare11(Double(vwx90, vwx91), Double(vwx100, vwx101)) → new_compare8(new_sr0(vwx90, vwx100), new_sr0(vwx91, vwx101))
new_esEs8(vwx90, vwx100, app(app(ty_Either, bde), bdf)) → new_esEs5(vwx90, vwx100, bde, bdf)
new_ltEs6(vwx92, vwx102, ty_Int) → new_ltEs9(vwx92, vwx102)
new_esEs9(vwx91, vwx101, ty_@0) → new_esEs10(vwx91, vwx101)
new_esEs24(vwx300, vwx400, app(ty_[], cbc)) → new_esEs13(vwx300, vwx400, cbc)
new_esEs25(vwx301, vwx401, ty_Char) → new_esEs12(vwx301, vwx401)
new_esEs9(vwx91, vwx101, app(app(ty_Either, bcd), bce)) → new_esEs5(vwx91, vwx101, bcd, bce)
new_esEs22(vwx300, vwx400, ty_Float) → new_esEs14(vwx300, vwx400)
new_esEs28(vwx300, vwx400, app(ty_Maybe, dac)) → new_esEs6(vwx300, vwx400, dac)
new_ltEs16(vwx9, vwx10) → new_not(new_esEs15(new_compare11(vwx9, vwx10), GT))
new_lt4(vwx91, vwx101, ty_Double) → new_lt15(vwx91, vwx101)
new_primEqInt(Pos(Zero), Neg(Succ(vwx4000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(vwx4000))) → False
new_esEs5(Left(vwx300), Left(vwx400), app(app(ty_@2, cfg), cfh), cef) → new_esEs4(vwx300, vwx400, cfg, cfh)
new_primCmpInt(Pos(Zero), Pos(Succ(vwx1000))) → new_primCmpNat0(Zero, Succ(vwx1000))
new_compare27(vwx90, vwx100, ty_Ordering) → new_compare6(vwx90, vwx100)
new_esEs23(vwx301, vwx401, ty_Bool) → new_esEs19(vwx301, vwx401)
new_esEs8(vwx90, vwx100, ty_@0) → new_esEs10(vwx90, vwx100)
new_esEs22(vwx300, vwx400, ty_Bool) → new_esEs19(vwx300, vwx400)
new_esEs27(vwx90, vwx100, ty_Double) → new_esEs16(vwx90, vwx100)
new_lt4(vwx91, vwx101, ty_Float) → new_lt13(vwx91, vwx101)
new_compare31(vwx90, vwx100) → new_compare211(vwx90, vwx100, new_esEs19(vwx90, vwx100))
new_primCompAux0(vwx89, LT) → LT
new_lt20(vwx90, vwx100, ty_Bool) → new_lt19(vwx90, vwx100)
new_esEs9(vwx91, vwx101, ty_Float) → new_esEs14(vwx91, vwx101)
new_esEs12(Char(vwx300), Char(vwx400)) → new_primEqNat0(vwx300, vwx400)
new_ltEs5(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), baf, bag, bcc) → new_pePe(new_lt5(vwx90, vwx100, baf), new_asAs(new_esEs8(vwx90, vwx100, baf), new_pePe(new_lt4(vwx91, vwx101, bag), new_asAs(new_esEs9(vwx91, vwx101, bag), new_ltEs6(vwx92, vwx102, bcc)))))
new_esEs24(vwx300, vwx400, ty_Integer) → new_esEs18(vwx300, vwx400)
new_not(False) → True
new_esEs11(vwx30, vwx40) → new_primEqInt(vwx30, vwx40)
new_ltEs10(Right(vwx90), Right(vwx100), eh, ty_Float) → new_ltEs14(vwx90, vwx100)
new_compare27(vwx90, vwx100, ty_Char) → new_compare14(vwx90, vwx100)
new_lt20(vwx90, vwx100, app(ty_[], da)) → new_lt11(vwx90, vwx100, da)
new_lt5(vwx90, vwx100, ty_Char) → new_lt10(vwx90, vwx100)
new_esEs8(vwx90, vwx100, app(ty_Maybe, bdh)) → new_esEs6(vwx90, vwx100, bdh)
new_primCmpInt(Pos(Succ(vwx900)), Pos(vwx100)) → new_primCmpNat0(Succ(vwx900), vwx100)
new_compare210(vwx90, vwx100, True, cc, cd) → EQ
new_compare12(vwx90, vwx100, False, dc, dd, de) → GT
new_esEs5(Right(vwx300), Right(vwx400), cga, app(ty_[], cge)) → new_esEs13(vwx300, vwx400, cge)
new_ltEs10(Right(vwx90), Right(vwx100), eh, ty_@0) → new_ltEs8(vwx90, vwx100)
new_ltEs19(vwx91, vwx101, app(ty_[], bf)) → new_ltEs12(vwx91, vwx101, bf)
new_lt4(vwx91, vwx101, app(ty_[], bcf)) → new_lt11(vwx91, vwx101, bcf)
new_ltEs8(vwx9, vwx10) → new_not(new_esEs15(new_compare29(vwx9, vwx10), GT))
new_lt5(vwx90, vwx100, app(app(app(ty_@3, bea), beb), bec)) → new_lt18(vwx90, vwx100, bea, beb, bec)
new_esEs9(vwx91, vwx101, ty_Int) → new_esEs11(vwx91, vwx101)
new_compare0(:(vwx90, vwx91), [], gc) → GT
new_esEs22(vwx300, vwx400, app(ty_[], bga)) → new_esEs13(vwx300, vwx400, bga)
new_esEs26(vwx302, vwx402, app(app(ty_Either, ceb), cec)) → new_esEs5(vwx302, vwx402, ceb, cec)
new_esEs23(vwx301, vwx401, ty_@0) → new_esEs10(vwx301, vwx401)
new_lt12(vwx90, vwx100, db) → new_esEs15(new_compare30(vwx90, vwx100, db), LT)
new_esEs27(vwx90, vwx100, ty_Int) → new_esEs11(vwx90, vwx100)
new_esEs5(Left(vwx300), Left(vwx400), ty_Bool, cef) → new_esEs19(vwx300, vwx400)
new_lt4(vwx91, vwx101, app(app(ty_Either, bcd), bce)) → new_lt9(vwx91, vwx101, bcd, bce)
new_primCmpInt(Pos(Succ(vwx900)), Neg(vwx100)) → GT
new_esEs8(vwx90, vwx100, app(app(app(ty_@3, bea), beb), bec)) → new_esEs7(vwx90, vwx100, bea, beb, bec)
new_esEs22(vwx300, vwx400, app(app(app(ty_@3, bff), bfg), bfh)) → new_esEs7(vwx300, vwx400, bff, bfg, bfh)
new_ltEs19(vwx91, vwx101, ty_Int) → new_ltEs9(vwx91, vwx101)
new_ltEs15(LT, EQ) → True
new_esEs9(vwx91, vwx101, ty_Char) → new_esEs12(vwx91, vwx101)
new_lt4(vwx91, vwx101, ty_@0) → new_lt7(vwx91, vwx101)
new_lt20(vwx90, vwx100, ty_Double) → new_lt15(vwx90, vwx100)
new_esEs26(vwx302, vwx402, ty_@0) → new_esEs10(vwx302, vwx402)
new_primMulInt(Pos(vwx3000), Pos(vwx4000)) → Pos(new_primMulNat0(vwx3000, vwx4000))
new_ltEs13(Just(vwx90), Just(vwx100), ty_@0) → new_ltEs8(vwx90, vwx100)
new_esEs28(vwx300, vwx400, app(app(app(ty_@3, chf), chg), chh)) → new_esEs7(vwx300, vwx400, chf, chg, chh)
new_esEs5(Right(vwx300), Left(vwx400), cga, cef) → False
new_esEs5(Left(vwx300), Right(vwx400), cga, cef) → False
new_primMulInt(Neg(vwx3000), Neg(vwx4000)) → Pos(new_primMulNat0(vwx3000, vwx4000))
new_lt6(vwx90, vwx100, cc, cd) → new_esEs15(new_compare28(vwx90, vwx100, cc, cd), LT)
new_primEqNat0(Succ(vwx3000), Zero) → False
new_primEqNat0(Zero, Succ(vwx4000)) → False
new_primPlusNat0(Zero, Zero) → Zero
new_esEs25(vwx301, vwx401, app(ty_Ratio, ccf)) → new_esEs17(vwx301, vwx401, ccf)
new_lt5(vwx90, vwx100, app(app(ty_Either, bde), bdf)) → new_lt9(vwx90, vwx100, bde, bdf)
new_esEs15(LT, GT) → False
new_esEs15(GT, LT) → False
new_esEs25(vwx301, vwx401, app(ty_Maybe, ccg)) → new_esEs6(vwx301, vwx401, ccg)
new_ltEs10(Right(vwx90), Right(vwx100), eh, ty_Integer) → new_ltEs18(vwx90, vwx100)
new_ltEs6(vwx92, vwx102, ty_Integer) → new_ltEs18(vwx92, vwx102)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_compare24(vwx90, vwx100, False, cf, cg) → new_compare15(vwx90, vwx100, new_ltEs10(vwx90, vwx100, cf, cg), cf, cg)
new_esEs15(LT, LT) → True
new_ltEs9(vwx9, vwx10) → new_not(new_esEs15(new_compare8(vwx9, vwx10), GT))
new_esEs23(vwx301, vwx401, ty_Int) → new_esEs11(vwx301, vwx401)
new_ltEs4(True, False) → False
new_compare30(vwx90, vwx100, db) → new_compare25(vwx90, vwx100, new_esEs6(vwx90, vwx100, db), db)
new_compare26(vwx90, vwx100, False, dc, dd, de) → new_compare12(vwx90, vwx100, new_ltEs5(vwx90, vwx100, dc, dd, de), dc, dd, de)
new_lt18(vwx90, vwx100, dc, dd, de) → new_esEs15(new_compare18(vwx90, vwx100, dc, dd, de), LT)
new_primPlusNat1(Succ(vwx580), vwx40000) → Succ(Succ(new_primPlusNat0(vwx580, vwx40000)))
new_esEs22(vwx300, vwx400, ty_@0) → new_esEs10(vwx300, vwx400)
new_lt5(vwx90, vwx100, app(ty_[], bdg)) → new_lt11(vwx90, vwx100, bdg)
new_esEs28(vwx300, vwx400, app(ty_Ratio, dab)) → new_esEs17(vwx300, vwx400, dab)
new_esEs23(vwx301, vwx401, app(ty_Ratio, bhd)) → new_esEs17(vwx301, vwx401, bhd)
new_esEs9(vwx91, vwx101, app(ty_Ratio, bee)) → new_esEs17(vwx91, vwx101, bee)
new_primCmpInt(Neg(Zero), Neg(Succ(vwx1000))) → new_primCmpNat0(Succ(vwx1000), Zero)
new_esEs5(Right(vwx300), Right(vwx400), cga, ty_Int) → new_esEs11(vwx300, vwx400)
new_primCmpInt(Pos(Zero), Neg(Succ(vwx1000))) → GT
new_ltEs10(Left(vwx90), Left(vwx100), app(ty_Maybe, ed), dh) → new_ltEs13(vwx90, vwx100, ed)
new_ltEs13(Just(vwx90), Just(vwx100), ty_Char) → new_ltEs11(vwx90, vwx100)
new_compare0(:(vwx90, vwx91), :(vwx100, vwx101), gc) → new_primCompAux1(vwx90, vwx100, new_compare0(vwx91, vwx101, gc), gc)
new_esEs5(Right(vwx300), Right(vwx400), cga, app(app(app(ty_@3, cgb), cgc), cgd)) → new_esEs7(vwx300, vwx400, cgb, cgc, cgd)
new_sr0(vwx300, vwx400) → new_primMulInt(vwx300, vwx400)
new_lt8(vwx90, vwx100) → new_esEs15(new_compare8(vwx90, vwx100), LT)
new_compare15(vwx90, vwx100, False, cf, cg) → GT
new_esEs5(Left(vwx300), Left(vwx400), ty_Integer, cef) → new_esEs18(vwx300, vwx400)
new_lt20(vwx90, vwx100, app(app(ty_@2, cc), cd)) → new_lt6(vwx90, vwx100, cc, cd)
new_esEs6(Just(vwx300), Just(vwx400), ty_Double) → new_esEs16(vwx300, vwx400)
new_ltEs11(vwx9, vwx10) → new_not(new_esEs15(new_compare14(vwx9, vwx10), GT))
new_esEs24(vwx300, vwx400, ty_Int) → new_esEs11(vwx300, vwx400)
new_esEs8(vwx90, vwx100, ty_Ordering) → new_esEs15(vwx90, vwx100)
new_esEs6(Just(vwx300), Just(vwx400), app(app(ty_Either, dbg), dbh)) → new_esEs5(vwx300, vwx400, dbg, dbh)
new_ltEs13(Just(vwx90), Just(vwx100), app(ty_Maybe, bab)) → new_ltEs13(vwx90, vwx100, bab)
new_esEs9(vwx91, vwx101, app(app(ty_@2, bca), bcb)) → new_esEs4(vwx91, vwx101, bca, bcb)
new_esEs8(vwx90, vwx100, ty_Bool) → new_esEs19(vwx90, vwx100)
new_lt20(vwx90, vwx100, ty_Char) → new_lt10(vwx90, vwx100)
new_esEs10(@0, @0) → True
new_ltEs13(Just(vwx90), Nothing, beg) → False
new_esEs5(Right(vwx300), Right(vwx400), cga, ty_Float) → new_esEs14(vwx300, vwx400)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs24(vwx300, vwx400, app(app(app(ty_@3, cah), cba), cbb)) → new_esEs7(vwx300, vwx400, cah, cba, cbb)
new_ltEs10(Left(vwx90), Left(vwx100), ty_Float, dh) → new_ltEs14(vwx90, vwx100)
new_ltEs10(Left(vwx90), Left(vwx100), app(app(ty_@2, df), dg), dh) → new_ltEs7(vwx90, vwx100, df, dg)
new_esEs28(vwx300, vwx400, ty_@0) → new_esEs10(vwx300, vwx400)
new_lt4(vwx91, vwx101, app(app(ty_@2, bca), bcb)) → new_lt6(vwx91, vwx101, bca, bcb)
new_compare7(:%(vwx90, vwx91), :%(vwx100, vwx101), ty_Integer) → new_compare9(new_sr(vwx90, vwx101), new_sr(vwx100, vwx91))
new_esEs28(vwx300, vwx400, app(app(ty_@2, daf), dag)) → new_esEs4(vwx300, vwx400, daf, dag)
new_compare9(Integer(vwx90), Integer(vwx100)) → new_primCmpInt(vwx90, vwx100)
new_ltEs19(vwx91, vwx101, app(app(ty_@2, bb), bc)) → new_ltEs7(vwx91, vwx101, bb, bc)
new_asAs(False, vwx49) → False
new_lt4(vwx91, vwx101, ty_Integer) → new_lt17(vwx91, vwx101)
new_primMulInt(Neg(vwx3000), Pos(vwx4000)) → Neg(new_primMulNat0(vwx3000, vwx4000))
new_primMulInt(Pos(vwx3000), Neg(vwx4000)) → Neg(new_primMulNat0(vwx3000, vwx4000))
new_ltEs19(vwx91, vwx101, ty_Char) → new_ltEs11(vwx91, vwx101)
new_primMulNat0(Succ(vwx30000), Zero) → Zero
new_primMulNat0(Zero, Succ(vwx40000)) → Zero
new_esEs22(vwx300, vwx400, ty_Integer) → new_esEs18(vwx300, vwx400)
new_esEs13(:(vwx300, vwx301), [], che) → False
new_esEs13([], :(vwx400, vwx401), che) → False
new_ltEs19(vwx91, vwx101, ty_Float) → new_ltEs14(vwx91, vwx101)
new_esEs6(Just(vwx300), Just(vwx400), app(ty_Maybe, dbf)) → new_esEs6(vwx300, vwx400, dbf)
new_esEs6(Just(vwx300), Just(vwx400), ty_@0) → new_esEs10(vwx300, vwx400)
new_lt5(vwx90, vwx100, ty_Int) → new_lt8(vwx90, vwx100)
new_esEs27(vwx90, vwx100, ty_Integer) → new_esEs18(vwx90, vwx100)
new_lt5(vwx90, vwx100, ty_Float) → new_lt13(vwx90, vwx100)
new_esEs18(Integer(vwx300), Integer(vwx400)) → new_primEqInt(vwx300, vwx400)
new_esEs24(vwx300, vwx400, ty_Ordering) → new_esEs15(vwx300, vwx400)
new_esEs6(Just(vwx300), Just(vwx400), app(app(ty_@2, dca), dcb)) → new_esEs4(vwx300, vwx400, dca, dcb)
new_ltEs6(vwx92, vwx102, app(ty_Maybe, bbe)) → new_ltEs13(vwx92, vwx102, bbe)
new_esEs23(vwx301, vwx401, app(ty_Maybe, bhe)) → new_esEs6(vwx301, vwx401, bhe)
new_ltEs13(Just(vwx90), Just(vwx100), app(ty_[], baa)) → new_ltEs12(vwx90, vwx100, baa)
new_ltEs10(Right(vwx90), Right(vwx100), eh, app(ty_[], ff)) → new_ltEs12(vwx90, vwx100, ff)
new_esEs23(vwx301, vwx401, ty_Char) → new_esEs12(vwx301, vwx401)
new_compare27(vwx90, vwx100, app(app(ty_Either, gf), gg)) → new_compare19(vwx90, vwx100, gf, gg)
new_ltEs4(False, False) → True
new_lt20(vwx90, vwx100, ty_Float) → new_lt13(vwx90, vwx100)
new_esEs23(vwx301, vwx401, ty_Double) → new_esEs16(vwx301, vwx401)
new_ltEs6(vwx92, vwx102, ty_Char) → new_ltEs11(vwx92, vwx102)
new_esEs25(vwx301, vwx401, app(ty_[], cce)) → new_esEs13(vwx301, vwx401, cce)
new_ltEs13(Just(vwx90), Just(vwx100), ty_Ordering) → new_ltEs15(vwx90, vwx100)
new_ltEs10(Right(vwx90), Right(vwx100), eh, app(ty_Ratio, cac)) → new_ltEs17(vwx90, vwx100, cac)
new_ltEs19(vwx91, vwx101, ty_@0) → new_ltEs8(vwx91, vwx101)
new_esEs5(Right(vwx300), Right(vwx400), cga, app(ty_Maybe, cgg)) → new_esEs6(vwx300, vwx400, cgg)
new_esEs4(@2(vwx300, vwx301), @2(vwx400, vwx401), bfd, bfe) → new_asAs(new_esEs22(vwx300, vwx400, bfd), new_esEs23(vwx301, vwx401, bfe))
new_esEs13(:(vwx300, vwx301), :(vwx400, vwx401), che) → new_asAs(new_esEs28(vwx300, vwx400, che), new_esEs13(vwx301, vwx401, che))
new_ltEs19(vwx91, vwx101, app(app(app(ty_@3, bh), ca), cb)) → new_ltEs5(vwx91, vwx101, bh, ca, cb)
new_ltEs6(vwx92, vwx102, app(ty_[], bbd)) → new_ltEs12(vwx92, vwx102, bbd)
new_esEs25(vwx301, vwx401, app(app(app(ty_@3, ccb), ccc), ccd)) → new_esEs7(vwx301, vwx401, ccb, ccc, ccd)
new_esEs27(vwx90, vwx100, app(app(ty_@2, cc), cd)) → new_esEs4(vwx90, vwx100, cc, cd)
new_ltEs19(vwx91, vwx101, app(ty_Maybe, bg)) → new_ltEs13(vwx91, vwx101, bg)
new_ltEs10(Left(vwx90), Left(vwx100), ty_Bool, dh) → new_ltEs4(vwx90, vwx100)
new_esEs6(Just(vwx300), Just(vwx400), app(ty_[], dbd)) → new_esEs13(vwx300, vwx400, dbd)
new_ltEs10(Right(vwx90), Left(vwx100), eh, dh) → False
new_esEs26(vwx302, vwx402, ty_Integer) → new_esEs18(vwx302, vwx402)
new_compare27(vwx90, vwx100, app(ty_Ratio, cad)) → new_compare7(vwx90, vwx100, cad)
new_esEs5(Left(vwx300), Left(vwx400), app(app(ty_Either, cfe), cff), cef) → new_esEs5(vwx300, vwx400, cfe, cff)
new_ltEs6(vwx92, vwx102, ty_Bool) → new_ltEs4(vwx92, vwx102)
new_esEs8(vwx90, vwx100, ty_Float) → new_esEs14(vwx90, vwx100)
new_ltEs6(vwx92, vwx102, ty_Double) → new_ltEs16(vwx92, vwx102)
new_esEs6(Just(vwx300), Just(vwx400), ty_Integer) → new_esEs18(vwx300, vwx400)
new_lt5(vwx90, vwx100, ty_Ordering) → new_lt14(vwx90, vwx100)
new_lt16(vwx90, vwx100, bfc) → new_esEs15(new_compare7(vwx90, vwx100, bfc), LT)
new_esEs14(Float(vwx300, vwx301), Float(vwx400, vwx401)) → new_esEs11(new_sr0(vwx300, vwx400), new_sr0(vwx301, vwx401))
new_esEs22(vwx300, vwx400, app(ty_Ratio, bgb)) → new_esEs17(vwx300, vwx400, bgb)
new_compare27(vwx90, vwx100, ty_@0) → new_compare29(vwx90, vwx100)
new_esEs22(vwx300, vwx400, ty_Double) → new_esEs16(vwx300, vwx400)
new_esEs6(Just(vwx300), Just(vwx400), ty_Char) → new_esEs12(vwx300, vwx400)
new_compare26(vwx90, vwx100, True, dc, dd, de) → EQ
new_primPlusNat0(Succ(vwx5800), Succ(vwx400000)) → Succ(Succ(new_primPlusNat0(vwx5800, vwx400000)))
new_compare27(vwx90, vwx100, ty_Double) → new_compare11(vwx90, vwx100)
new_compare0([], :(vwx100, vwx101), gc) → LT
new_ltEs13(Just(vwx90), Just(vwx100), ty_Float) → new_ltEs14(vwx90, vwx100)
new_ltEs13(Just(vwx90), Just(vwx100), app(ty_Ratio, beh)) → new_ltEs17(vwx90, vwx100, beh)
new_asAs(True, vwx49) → vwx49
new_ltEs15(GT, EQ) → False
new_esEs26(vwx302, vwx402, ty_Float) → new_esEs14(vwx302, vwx402)
new_esEs25(vwx301, vwx401, ty_Int) → new_esEs11(vwx301, vwx401)
new_ltEs10(Right(vwx90), Right(vwx100), eh, app(ty_Maybe, fg)) → new_ltEs13(vwx90, vwx100, fg)
new_esEs27(vwx90, vwx100, app(ty_[], da)) → new_esEs13(vwx90, vwx100, da)
new_lt9(vwx90, vwx100, cf, cg) → new_esEs15(new_compare19(vwx90, vwx100, cf, cg), LT)
new_ltEs13(Just(vwx90), Just(vwx100), ty_Double) → new_ltEs16(vwx90, vwx100)
new_lt4(vwx91, vwx101, ty_Bool) → new_lt19(vwx91, vwx101)
new_compare27(vwx90, vwx100, ty_Int) → new_compare8(vwx90, vwx100)
new_ltEs10(Left(vwx90), Left(vwx100), app(ty_[], ec), dh) → new_ltEs12(vwx90, vwx100, ec)
new_esEs20(vwx300, vwx400, ty_Integer) → new_esEs18(vwx300, vwx400)
new_compare211(vwx90, vwx100, True) → EQ
new_ltEs10(Left(vwx90), Left(vwx100), ty_Double, dh) → new_ltEs16(vwx90, vwx100)
new_ltEs10(Right(vwx90), Right(vwx100), eh, ty_Char) → new_ltEs11(vwx90, vwx100)
new_esEs27(vwx90, vwx100, ty_Float) → new_esEs14(vwx90, vwx100)
new_esEs26(vwx302, vwx402, ty_Double) → new_esEs16(vwx302, vwx402)
new_esEs5(Right(vwx300), Right(vwx400), cga, ty_Double) → new_esEs16(vwx300, vwx400)
new_ltEs13(Just(vwx90), Just(vwx100), app(app(app(ty_@3, bac), bad), bae)) → new_ltEs5(vwx90, vwx100, bac, bad, bae)
new_compare25(vwx90, vwx100, False, db) → new_compare16(vwx90, vwx100, new_ltEs13(vwx90, vwx100, db), db)
new_lt15(vwx90, vwx100) → new_esEs15(new_compare11(vwx90, vwx100), LT)
new_lt5(vwx90, vwx100, ty_Double) → new_lt15(vwx90, vwx100)
new_compare10(vwx90, vwx100, True) → LT
new_esEs24(vwx300, vwx400, app(ty_Maybe, cbe)) → new_esEs6(vwx300, vwx400, cbe)
new_esEs15(GT, GT) → True
new_esEs27(vwx90, vwx100, app(ty_Ratio, bfc)) → new_esEs17(vwx90, vwx100, bfc)
new_ltEs10(Left(vwx90), Left(vwx100), app(ty_Ratio, cab), dh) → new_ltEs17(vwx90, vwx100, cab)
new_compare10(vwx90, vwx100, False) → GT
new_esEs22(vwx300, vwx400, app(app(ty_Either, bgd), bge)) → new_esEs5(vwx300, vwx400, bgd, bge)
new_esEs25(vwx301, vwx401, ty_Float) → new_esEs14(vwx301, vwx401)
new_esEs8(vwx90, vwx100, app(ty_Ratio, bed)) → new_esEs17(vwx90, vwx100, bed)
new_compare27(vwx90, vwx100, app(ty_Maybe, ha)) → new_compare30(vwx90, vwx100, ha)
new_esEs25(vwx301, vwx401, ty_Ordering) → new_esEs15(vwx301, vwx401)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCompAux0(vwx89, EQ) → vwx89
new_lt20(vwx90, vwx100, app(ty_Maybe, db)) → new_lt12(vwx90, vwx100, db)
new_esEs27(vwx90, vwx100, ty_Bool) → new_esEs19(vwx90, vwx100)
new_esEs28(vwx300, vwx400, ty_Char) → new_esEs12(vwx300, vwx400)
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_lt20(vwx90, vwx100, app(app(ty_Either, cf), cg)) → new_lt9(vwx90, vwx100, cf, cg)
new_primCmpInt(Neg(Succ(vwx900)), Pos(vwx100)) → LT
new_esEs23(vwx301, vwx401, app(ty_[], bhc)) → new_esEs13(vwx301, vwx401, bhc)
new_not(True) → False

The set Q consists of the following terms:

new_esEs8(x0, x1, ty_@0)
new_esEs25(x0, x1, ty_Double)
new_esEs24(x0, x1, ty_Integer)
new_ltEs10(Left(x0), Left(x1), ty_Char, x2)
new_compare26(x0, x1, False, x2, x3, x4)
new_esEs5(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs13(:(x0, x1), [], x2)
new_esEs26(x0, x1, ty_Float)
new_esEs27(x0, x1, ty_Char)
new_lt5(x0, x1, ty_Bool)
new_ltEs6(x0, x1, ty_Int)
new_compare27(x0, x1, ty_Bool)
new_esEs8(x0, x1, ty_Int)
new_esEs23(x0, x1, ty_@0)
new_lt4(x0, x1, ty_Double)
new_ltEs6(x0, x1, ty_Integer)
new_compare27(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs13(Just(x0), Just(x1), app(ty_Ratio, x2))
new_lt5(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare28(x0, x1, x2, x3)
new_esEs13(:(x0, x1), :(x2, x3), x4)
new_esEs26(x0, x1, ty_Ordering)
new_esEs9(x0, x1, app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, ty_Float)
new_lt5(x0, x1, app(ty_[], x2))
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_esEs6(Just(x0), Just(x1), ty_Bool)
new_esEs5(Right(x0), Right(x1), x2, ty_@0)
new_esEs5(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs9(x0, x1, ty_@0)
new_ltEs19(x0, x1, ty_Integer)
new_esEs5(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs18(x0, x1)
new_ltEs10(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs10(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_lt15(x0, x1)
new_ltEs6(x0, x1, app(ty_Ratio, x2))
new_esEs5(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_primMulInt(Neg(x0), Neg(x1))
new_lt4(x0, x1, app(ty_Maybe, x2))
new_esEs13([], :(x0, x1), x2)
new_ltEs7(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs27(x0, x1, ty_Integer)
new_ltEs6(x0, x1, app(app(ty_@2, x2), x3))
new_compare27(x0, x1, ty_Int)
new_lt5(x0, x1, app(app(ty_@2, x2), x3))
new_esEs8(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs10(Left(x0), Left(x1), ty_Bool, x2)
new_compare31(x0, x1)
new_compare0(:(x0, x1), [], x2)
new_compare27(x0, x1, app(app(ty_@2, x2), x3))
new_esEs24(x0, x1, ty_Ordering)
new_esEs5(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, ty_Ordering)
new_ltEs5(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs22(x0, x1, ty_Bool)
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_esEs6(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs14(Float(x0, x1), Float(x2, x3))
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_esEs28(x0, x1, ty_Double)
new_esEs23(x0, x1, app(ty_[], x2))
new_compare23(x0, x1, True)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare10(x0, x1, True)
new_esEs28(x0, x1, ty_Bool)
new_esEs24(x0, x1, ty_Float)
new_lt4(x0, x1, app(ty_[], x2))
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_ltEs6(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs10(Left(x0), Left(x1), ty_Double, x2)
new_esEs21(x0, x1, ty_Int)
new_esEs5(Right(x0), Right(x1), x2, ty_Ordering)
new_ltEs10(Right(x0), Left(x1), x2, x3)
new_esEs8(x0, x1, ty_Double)
new_ltEs10(Left(x0), Right(x1), x2, x3)
new_esEs19(True, True)
new_esEs23(x0, x1, ty_Integer)
new_compare0([], [], x0)
new_ltEs10(Right(x0), Right(x1), x2, ty_Double)
new_ltEs10(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_ltEs10(Left(x0), Left(x1), ty_@0, x2)
new_esEs8(x0, x1, ty_Integer)
new_compare29(@0, @0)
new_ltEs6(x0, x1, ty_Float)
new_ltEs10(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_ltEs10(Left(x0), Left(x1), ty_Integer, x2)
new_lt14(x0, x1)
new_primEqNat0(Zero, Zero)
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_esEs8(x0, x1, ty_Ordering)
new_esEs20(x0, x1, ty_Integer)
new_esEs25(x0, x1, ty_Float)
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, ty_Char)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_primMulInt(Pos(x0), Pos(x1))
new_ltEs10(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_ltEs13(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs22(x0, x1, ty_Char)
new_ltEs4(True, True)
new_ltEs13(Just(x0), Just(x1), ty_Bool)
new_ltEs10(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs25(x0, x1, ty_Integer)
new_ltEs19(x0, x1, ty_Ordering)
new_esEs27(x0, x1, ty_Int)
new_lt20(x0, x1, ty_Char)
new_lt20(x0, x1, ty_Double)
new_esEs9(x0, x1, app(ty_Ratio, x2))
new_lt10(x0, x1)
new_primMulNat0(Zero, Zero)
new_ltEs10(Right(x0), Right(x1), x2, ty_Char)
new_esEs8(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs13(Just(x0), Just(x1), ty_Int)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_compare17(Float(x0, x1), Float(x2, x3))
new_esEs22(x0, x1, ty_Int)
new_compare27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt19(x0, x1)
new_lt7(x0, x1)
new_esEs7(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_compare0(:(x0, x1), :(x2, x3), x4)
new_ltEs19(x0, x1, ty_Char)
new_compare27(x0, x1, ty_Integer)
new_pePe(False, x0)
new_esEs22(x0, x1, ty_@0)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_asAs(False, x0)
new_esEs9(x0, x1, ty_Float)
new_ltEs10(Right(x0), Right(x1), x2, ty_Float)
new_esEs6(Nothing, Nothing, x0)
new_compare110(x0, x1, False, x2, x3)
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_ltEs6(x0, x1, ty_Char)
new_ltEs11(x0, x1)
new_esEs21(x0, x1, ty_Integer)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_ltEs19(x0, x1, ty_@0)
new_ltEs15(GT, EQ)
new_ltEs15(EQ, GT)
new_esEs28(x0, x1, ty_Int)
new_primMulNat0(Zero, Succ(x0))
new_esEs28(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, ty_Bool)
new_primPlusNat1(Succ(x0), x1)
new_ltEs4(False, False)
new_ltEs13(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs23(x0, x1, ty_Int)
new_lt20(x0, x1, ty_Float)
new_esEs16(Double(x0, x1), Double(x2, x3))
new_esEs12(Char(x0), Char(x1))
new_esEs5(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_lt5(x0, x1, ty_Double)
new_lt5(x0, x1, ty_Ordering)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs20(x0, x1, ty_Int)
new_ltEs10(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs26(x0, x1, app(ty_[], x2))
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_ltEs13(Just(x0), Just(x1), app(ty_[], x2))
new_esEs24(x0, x1, ty_Int)
new_esEs22(x0, x1, ty_Integer)
new_lt4(x0, x1, app(app(ty_Either, x2), x3))
new_compare23(x0, x1, False)
new_esEs9(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs15(LT, GT)
new_compare16(x0, x1, True, x2)
new_ltEs15(GT, LT)
new_ltEs13(Just(x0), Just(x1), ty_Integer)
new_esEs19(True, False)
new_esEs19(False, True)
new_ltEs15(GT, GT)
new_compare25(x0, x1, False, x2)
new_compare27(x0, x1, ty_@0)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_primEqNat0(Succ(x0), Zero)
new_ltEs10(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_primPlusNat0(Zero, Zero)
new_ltEs9(x0, x1)
new_esEs8(x0, x1, app(ty_[], x2))
new_lt5(x0, x1, ty_@0)
new_lt4(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, ty_Ordering)
new_lt13(x0, x1)
new_esEs23(x0, x1, ty_Bool)
new_primCmpNat0(Succ(x0), Zero)
new_esEs25(x0, x1, ty_Bool)
new_esEs23(x0, x1, ty_Double)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs28(x0, x1, ty_Char)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_compare9(Integer(x0), Integer(x1))
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs13(Just(x0), Just(x1), ty_@0)
new_lt9(x0, x1, x2, x3)
new_lt20(x0, x1, ty_Int)
new_ltEs15(LT, LT)
new_esEs15(LT, LT)
new_lt4(x0, x1, ty_Ordering)
new_esEs5(Left(x0), Left(x1), ty_Integer, x2)
new_esEs5(Left(x0), Left(x1), ty_Char, x2)
new_esEs6(Just(x0), Just(x1), ty_Float)
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_compare25(x0, x1, True, x2)
new_esEs15(EQ, GT)
new_esEs15(GT, EQ)
new_esEs23(x0, x1, ty_Ordering)
new_esEs18(Integer(x0), Integer(x1))
new_esEs24(x0, x1, app(ty_[], x2))
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_ltEs10(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs10(@0, @0)
new_ltEs8(x0, x1)
new_lt4(x0, x1, ty_@0)
new_lt5(x0, x1, ty_Int)
new_esEs26(x0, x1, ty_@0)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_compare210(x0, x1, True, x2, x3)
new_esEs5(Right(x0), Right(x1), x2, ty_Integer)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_lt6(x0, x1, x2, x3)
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_ltEs13(Just(x0), Just(x1), ty_Ordering)
new_primCmpNat0(Succ(x0), Succ(x1))
new_esEs27(x0, x1, ty_Double)
new_compare0([], :(x0, x1), x2)
new_esEs22(x0, x1, ty_Float)
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs9(x0, x1, ty_Ordering)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_compare15(x0, x1, False, x2, x3)
new_ltEs10(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs6(Just(x0), Just(x1), ty_@0)
new_esEs6(Just(x0), Just(x1), ty_Integer)
new_compare11(Double(x0, x1), Double(x2, x3))
new_esEs26(x0, x1, ty_Int)
new_primCompAux0(x0, LT)
new_lt20(x0, x1, ty_Integer)
new_lt4(x0, x1, ty_Integer)
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_esEs6(Nothing, Just(x0), x1)
new_ltEs13(Just(x0), Nothing, x1)
new_esEs9(x0, x1, ty_Bool)
new_ltEs10(Right(x0), Right(x1), x2, ty_Integer)
new_lt4(x0, x1, ty_Int)
new_ltEs10(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs5(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs6(Just(x0), Just(x1), app(ty_Ratio, x2))
new_compare27(x0, x1, ty_Float)
new_lt16(x0, x1, x2)
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs19(False, False)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_compare26(x0, x1, True, x2, x3, x4)
new_ltEs16(x0, x1)
new_lt5(x0, x1, app(app(ty_Either, x2), x3))
new_esEs6(Just(x0), Just(x1), ty_Char)
new_sr(Integer(x0), Integer(x1))
new_primEqInt(Neg(Zero), Neg(Zero))
new_esEs22(x0, x1, ty_Double)
new_esEs17(:%(x0, x1), :%(x2, x3), x4)
new_esEs8(x0, x1, ty_Float)
new_esEs5(Left(x0), Left(x1), app(ty_[], x2), x3)
new_primCompAux0(x0, GT)
new_ltEs13(Nothing, Nothing, x0)
new_compare15(x0, x1, True, x2, x3)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_esEs5(Left(x0), Left(x1), ty_Float, x2)
new_esEs5(Left(x0), Left(x1), ty_@0, x2)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs19(x0, x1, ty_Double)
new_esEs5(Left(x0), Left(x1), ty_Int, x2)
new_esEs27(x0, x1, app(ty_[], x2))
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs5(Right(x0), Right(x1), x2, ty_Double)
new_esEs23(x0, x1, ty_Float)
new_compare12(x0, x1, False, x2, x3, x4)
new_ltEs6(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, ty_Char)
new_lt5(x0, x1, app(ty_Ratio, x2))
new_ltEs10(Right(x0), Right(x1), x2, ty_Int)
new_compare14(Char(x0), Char(x1))
new_esEs5(Left(x0), Left(x1), ty_Double, x2)
new_esEs5(Right(x0), Right(x1), x2, ty_Float)
new_lt20(x0, x1, app(ty_[], x2))
new_esEs24(x0, x1, ty_Bool)
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs17(x0, x1, x2)
new_ltEs13(Nothing, Just(x0), x1)
new_esEs26(x0, x1, ty_Double)
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_compare18(x0, x1, x2, x3, x4)
new_compare7(:%(x0, x1), :%(x2, x3), ty_Integer)
new_esEs9(x0, x1, ty_Integer)
new_ltEs10(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs6(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs10(Left(x0), Left(x1), ty_Float, x2)
new_esEs28(x0, x1, ty_@0)
new_esEs9(x0, x1, ty_Int)
new_esEs9(x0, x1, app(ty_[], x2))
new_esEs8(x0, x1, app(ty_Ratio, x2))
new_ltEs13(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_compare27(x0, x1, ty_Double)
new_primPlusNat1(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_esEs8(x0, x1, ty_Bool)
new_compare8(x0, x1)
new_esEs9(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs27(x0, x1, ty_Bool)
new_compare27(x0, x1, app(ty_[], x2))
new_esEs25(x0, x1, ty_Ordering)
new_compare24(x0, x1, True, x2, x3)
new_compare211(x0, x1, True)
new_lt4(x0, x1, app(ty_Ratio, x2))
new_compare12(x0, x1, True, x2, x3, x4)
new_ltEs10(Left(x0), Left(x1), ty_Ordering, x2)
new_primCmpNat0(Zero, Zero)
new_esEs8(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs6(x0, x1, ty_@0)
new_primPlusNat0(Succ(x0), Succ(x1))
new_ltEs12(x0, x1, x2)
new_ltEs6(x0, x1, ty_Ordering)
new_esEs6(Just(x0), Just(x1), app(ty_[], x2))
new_asAs(True, x0)
new_ltEs4(False, True)
new_ltEs4(True, False)
new_ltEs6(x0, x1, app(ty_[], x2))
new_lt12(x0, x1, x2)
new_lt4(x0, x1, ty_Bool)
new_compare7(:%(x0, x1), :%(x2, x3), ty_Int)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_esEs22(x0, x1, ty_Ordering)
new_ltEs19(x0, x1, ty_Bool)
new_esEs5(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_lt17(x0, x1)
new_esEs28(x0, x1, ty_Ordering)
new_esEs28(x0, x1, ty_Integer)
new_esEs24(x0, x1, ty_Double)
new_esEs15(GT, GT)
new_esEs6(Just(x0), Just(x1), ty_Int)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs5(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs10(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs22(x0, x1, app(ty_[], x2))
new_esEs25(x0, x1, app(ty_[], x2))
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_primEqNat0(Zero, Succ(x0))
new_esEs9(x0, x1, app(ty_Maybe, x2))
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_esEs15(GT, LT)
new_esEs15(LT, GT)
new_esEs6(Just(x0), Just(x1), ty_Ordering)
new_primMulNat0(Succ(x0), Zero)
new_esEs6(Just(x0), Nothing, x1)
new_esEs13([], [], x0)
new_compare27(x0, x1, ty_Char)
new_esEs6(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_primMulNat0(Succ(x0), Succ(x1))
new_compare6(x0, x1)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_esEs26(x0, x1, ty_Char)
new_esEs4(@2(x0, x1), @2(x2, x3), x4, x5)
new_primCompAux1(x0, x1, x2, x3)
new_esEs9(x0, x1, ty_Double)
new_esEs25(x0, x1, ty_@0)
new_ltEs10(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_lt5(x0, x1, ty_Integer)
new_compare16(x0, x1, False, x2)
new_not(True)
new_esEs28(x0, x1, ty_Float)
new_lt4(x0, x1, ty_Float)
new_esEs15(EQ, EQ)
new_esEs5(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_compare19(x0, x1, x2, x3)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_not(False)
new_pePe(True, x0)
new_lt5(x0, x1, app(ty_Maybe, x2))
new_primCmpNat0(Zero, Succ(x0))
new_esEs26(x0, x1, ty_Integer)
new_esEs6(Just(x0), Just(x1), app(ty_Maybe, x2))
new_compare110(x0, x1, True, x2, x3)
new_ltEs6(x0, x1, ty_Double)
new_esEs5(Left(x0), Left(x1), ty_Bool, x2)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_compare27(x0, x1, ty_Ordering)
new_lt5(x0, x1, ty_Char)
new_esEs5(Right(x0), Right(x1), x2, ty_Char)
new_ltEs13(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_ltEs10(Right(x0), Right(x1), x2, ty_@0)
new_primEqNat0(Succ(x0), Succ(x1))
new_ltEs15(EQ, LT)
new_ltEs15(LT, EQ)
new_esEs5(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_lt11(x0, x1, x2)
new_lt4(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs9(x0, x1, ty_Char)
new_lt18(x0, x1, x2, x3, x4)
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_lt20(x0, x1, app(ty_Ratio, x2))
new_compare13(x0, x1, False)
new_ltEs15(EQ, EQ)
new_primCompAux0(x0, EQ)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_ltEs13(Just(x0), Just(x1), ty_Char)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_compare210(x0, x1, False, x2, x3)
new_compare24(x0, x1, False, x2, x3)
new_esEs6(Just(x0), Just(x1), ty_Double)
new_ltEs13(Just(x0), Just(x1), ty_Double)
new_ltEs14(x0, x1)
new_ltEs19(x0, x1, ty_Int)
new_lt20(x0, x1, ty_@0)
new_lt5(x0, x1, ty_Float)
new_esEs8(x0, x1, app(ty_Maybe, x2))
new_compare10(x0, x1, False)
new_esEs26(x0, x1, ty_Bool)
new_esEs5(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs15(EQ, LT)
new_esEs15(LT, EQ)
new_compare13(x0, x1, True)
new_primEqInt(Pos(Zero), Pos(Zero))
new_compare30(x0, x1, x2)
new_primPlusNat0(Zero, Succ(x0))
new_esEs5(Left(x0), Right(x1), x2, x3)
new_esEs5(Right(x0), Left(x1), x2, x3)
new_lt8(x0, x1)
new_esEs24(x0, x1, ty_Char)
new_esEs27(x0, x1, ty_@0)
new_ltEs13(Just(x0), Just(x1), ty_Float)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_compare211(x0, x1, False)
new_esEs8(x0, x1, ty_Char)
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_sr0(x0, x1)
new_ltEs19(x0, x1, ty_Float)
new_lt4(x0, x1, ty_Char)
new_ltEs19(x0, x1, app(ty_[], x2))
new_esEs11(x0, x1)
new_esEs24(x0, x1, ty_@0)
new_compare27(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, ty_Int)
new_esEs5(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_ltEs6(x0, x1, ty_Bool)
new_compare27(x0, x1, app(ty_Ratio, x2))
new_ltEs10(Left(x0), Left(x1), ty_Int, x2)
new_esEs5(Right(x0), Right(x1), x2, ty_Int)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs6(x0, x1, app(app(ty_Either, 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: