YES 4.494 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 b a  ->  Either b a  ->  Bool) :: (Ord b, Ord a) => 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 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


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 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


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

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

compare0 x y True = GT

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
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

reduce2D vwv vww = gcd vwv vww

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

are unpacked to the following functions on top level
gcd0Gcd'0 x y = gcd0Gcd' y (x `rem` y)

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

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

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



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

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


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_primPlusNat(Succ(vwx5400), Succ(vwx401000)) → new_primPlusNat(vwx5400, vwx401000)

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

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



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

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

new_primMulNat(Succ(vwx30100), Succ(vwx40100)) → new_primMulNat(vwx30100, Succ(vwx40100))

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

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



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

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

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

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

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



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

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

new_primCmpNat(Succ(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
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                                ↳ QDPSizeChangeProof
                              ↳ QDP

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

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

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_ltEs2(@2(vwx90, vwx91), @2(vwx100, vwx101), app(ty_Maybe, gg), gf) → new_compare2(vwx90, vwx100, new_esEs5(vwx90, vwx100, gg), gg)
new_ltEs(Right(vwx90), Right(vwx100), cd, app(ty_[], da)) → new_ltEs1(vwx90, vwx100, da)
new_ltEs3(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), hf, app(ty_Maybe, bbd), bbc) → new_lt0(vwx91, vwx101, bbd)
new_esEs4(Left(vwx90), Left(vwx100), False, app(app(ty_Either, app(app(ty_@2, bg), bh)), bc), bd) → new_ltEs2(vwx90, vwx100, bg, bh)
new_esEs10(vwx16, vwx17, False, beg, app(app(ty_Either, beh), bfa)) → new_ltEs(vwx16, vwx17, beh, bfa)
new_esEs4(Left(vwx90), Left(vwx100), False, app(app(ty_Either, app(ty_[], bf)), bc), bd) → new_ltEs1(vwx90, vwx100, bf)
new_primCompAux(vwx90, vwx100, vwx79, app(app(ty_Either, bdd), bde)) → new_compare22(vwx90, vwx100, new_esEs8(vwx90, vwx100, bdd, bde), bdd, bde)
new_ltEs(Right(vwx90), Right(vwx100), cd, app(app(ty_Either, ce), cf)) → new_ltEs(vwx90, vwx100, ce, cf)
new_esEs10(vwx16, vwx17, False, beg, app(app(app(ty_@3, bff), bfg), bfh)) → new_ltEs3(vwx16, vwx17, bff, bfg, bfh)
new_esEs4(Just(vwx90), Just(vwx100), False, app(ty_Maybe, app(ty_Maybe, ea)), bd) → new_ltEs0(vwx90, vwx100, ea)
new_compare0(:(vwx90, vwx91), :(vwx100, vwx101), eh) → new_compare0(vwx91, vwx101, eh)
new_lt(Right(vwx30), Right(vwx40), bee, bef) → new_esEs10(vwx30, vwx40, new_esEs11(vwx30, vwx40, bef), bee, bef)
new_esEs4(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), False, app(app(app(ty_@3, hf), hg), app(app(app(ty_@3, baf), bag), bah)), bd) → new_ltEs3(vwx92, vwx102, baf, bag, bah)
new_lt3(vwx90, vwx100, hc, hd, he) → new_compare21(vwx90, vwx100, new_esEs7(vwx90, vwx100, hc, hd, he), hc, hd, he)
new_esEs4(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), False, app(app(app(ty_@3, hf), app(app(app(ty_@3, bbh), bca), bcb)), bbc), bd) → new_lt3(vwx91, vwx101, bbh, bca, bcb)
new_ltEs0(Just(vwx90), Just(vwx100), app(ty_Maybe, ea)) → new_ltEs0(vwx90, vwx100, ea)
new_esEs4(Right(vwx90), Right(vwx100), False, app(app(ty_Either, cd), app(ty_Maybe, cg)), bd) → new_ltEs0(vwx90, vwx100, cg)
new_compare3(vwx90, vwx100, ha, hb) → new_compare20(vwx90, vwx100, new_esEs6(vwx90, vwx100, ha, hb), ha, hb)
new_esEs4(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), False, app(app(app(ty_@3, hf), hg), app(ty_Maybe, bab)), bd) → new_ltEs0(vwx92, vwx102, bab)
new_ltEs3(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), app(app(ty_@2, bcg), bch), hg, bbc) → new_lt2(vwx90, vwx100, bcg, bch)
new_esEs4(Right(vwx90), Right(vwx100), False, app(app(ty_Either, cd), app(app(ty_@2, db), dc)), bd) → new_ltEs2(vwx90, vwx100, db, dc)
new_compare21(vwx90, vwx100, False, hc, hd, he) → new_ltEs3(vwx90, vwx100, hc, hd, he)
new_esEs4(Just(vwx90), Just(vwx100), False, app(ty_Maybe, app(app(ty_Either, dg), dh)), bd) → new_ltEs(vwx90, vwx100, dg, dh)
new_ltEs2(@2(vwx90, vwx91), @2(vwx100, vwx101), app(ty_[], gh), gf) → new_compare0(vwx90, vwx100, gh)
new_esEs4(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), False, app(app(app(ty_@3, hf), app(app(ty_Either, bba), bbb)), bbc), bd) → new_lt(vwx91, vwx101, bba, bbb)
new_ltEs3(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), hf, hg, app(app(ty_@2, bad), bae)) → new_ltEs2(vwx92, vwx102, bad, bae)
new_esEs10(vwx16, vwx17, False, beg, app(ty_Maybe, bfb)) → new_ltEs0(vwx16, vwx17, bfb)
new_compare2(vwx90, vwx100, False, gg) → new_ltEs0(vwx90, vwx100, gg)
new_esEs4(:(vwx90, vwx91), :(vwx100, vwx101), False, app(ty_[], eh), bd) → new_compare0(vwx91, vwx101, eh)
new_esEs4(:(vwx90, vwx91), :(vwx100, vwx101), False, app(ty_[], eh), bd) → new_primCompAux(vwx90, vwx100, new_compare(vwx91, vwx101, eh), eh)
new_lt(Left(vwx30), Left(vwx40), bee, bef) → new_esEs4(vwx30, vwx40, new_esEs9(vwx30, vwx40, bee), bee, bef)
new_esEs4(@2(vwx90, vwx91), @2(vwx100, vwx101), False, app(app(ty_@2, fa), app(app(ty_@2, fg), fh)), bd) → new_ltEs2(vwx91, vwx101, fg, fh)
new_esEs4(@2(vwx90, vwx91), @2(vwx100, vwx101), False, app(app(ty_@2, app(app(ty_Either, gd), ge)), gf), bd) → new_lt(vwx90, vwx100, gd, ge)
new_primCompAux(vwx90, vwx100, vwx79, app(ty_Maybe, bdf)) → new_compare1(vwx90, vwx100, bdf)
new_esEs4(Left(vwx90), Left(vwx100), False, app(app(ty_Either, app(app(ty_Either, ba), bb)), bc), bd) → new_ltEs(vwx90, vwx100, ba, bb)
new_ltEs(Left(vwx90), Left(vwx100), app(ty_Maybe, be), bc) → new_ltEs0(vwx90, vwx100, be)
new_ltEs(Left(vwx90), Left(vwx100), app(app(app(ty_@3, ca), cb), cc), bc) → new_ltEs3(vwx90, vwx100, ca, cb, cc)
new_ltEs2(@2(vwx90, vwx91), @2(vwx100, vwx101), fa, app(ty_[], ff)) → new_ltEs1(vwx91, vwx101, ff)
new_esEs4(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), False, app(app(app(ty_@3, app(app(ty_@2, bcg), bch)), hg), bbc), bd) → new_lt2(vwx90, vwx100, bcg, bch)
new_ltEs3(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), hf, app(app(app(ty_@3, bbh), bca), bcb), bbc) → new_lt3(vwx91, vwx101, bbh, bca, bcb)
new_ltEs1(:(vwx90, vwx91), :(vwx100, vwx101), eh) → new_compare0(vwx91, vwx101, eh)
new_esEs4(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), False, app(app(app(ty_@3, hf), hg), app(app(ty_@2, bad), bae)), bd) → new_ltEs2(vwx92, vwx102, bad, bae)
new_ltEs(Left(vwx90), Left(vwx100), app(ty_[], bf), bc) → new_ltEs1(vwx90, vwx100, bf)
new_esEs4(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), False, app(app(app(ty_@3, app(ty_[], bcf)), hg), bbc), bd) → new_lt1(vwx90, vwx100, bcf)
new_esEs4(@2(vwx90, vwx91), @2(vwx100, vwx101), False, app(app(ty_@2, fa), app(ty_[], ff)), bd) → new_ltEs1(vwx91, vwx101, ff)
new_ltEs3(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), hf, hg, app(ty_[], bac)) → new_ltEs1(vwx92, vwx102, bac)
new_ltEs(Right(vwx90), Right(vwx100), cd, app(ty_Maybe, cg)) → new_ltEs0(vwx90, vwx100, cg)
new_esEs10(vwx16, vwx17, False, beg, app(app(ty_@2, bfd), bfe)) → new_ltEs2(vwx16, vwx17, bfd, bfe)
new_esEs4(Just(vwx90), Just(vwx100), False, app(ty_Maybe, app(app(ty_@2, ec), ed)), bd) → new_ltEs2(vwx90, vwx100, ec, ed)
new_compare20(vwx90, vwx100, False, ha, hb) → new_ltEs2(vwx90, vwx100, ha, hb)
new_esEs4(@2(vwx90, vwx91), @2(vwx100, vwx101), False, app(app(ty_@2, app(app(ty_@2, ha), hb)), gf), bd) → new_compare20(vwx90, vwx100, new_esEs6(vwx90, vwx100, ha, hb), ha, hb)
new_compare1(vwx90, vwx100, gg) → new_compare2(vwx90, vwx100, new_esEs5(vwx90, vwx100, gg), gg)
new_ltEs3(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), hf, hg, app(app(ty_Either, hh), baa)) → new_ltEs(vwx92, vwx102, hh, baa)
new_ltEs2(@2(vwx90, vwx91), @2(vwx100, vwx101), fa, app(app(ty_Either, fb), fc)) → new_ltEs(vwx91, vwx101, fb, fc)
new_ltEs0(Just(vwx90), Just(vwx100), app(app(app(ty_@3, ee), ef), eg)) → new_ltEs3(vwx90, vwx100, ee, ef, eg)
new_compare0(:(vwx90, vwx91), :(vwx100, vwx101), eh) → new_primCompAux(vwx90, vwx100, new_compare(vwx91, vwx101, eh), eh)
new_ltEs(Left(vwx90), Left(vwx100), app(app(ty_Either, ba), bb), bc) → new_ltEs(vwx90, vwx100, ba, bb)
new_esEs4(Right(vwx90), Right(vwx100), False, app(app(ty_Either, cd), app(app(app(ty_@3, dd), de), df)), bd) → new_ltEs3(vwx90, vwx100, dd, de, df)
new_ltEs2(@2(vwx90, vwx91), @2(vwx100, vwx101), fa, app(app(app(ty_@3, ga), gb), gc)) → new_ltEs3(vwx91, vwx101, ga, gb, gc)
new_primCompAux(vwx90, vwx100, vwx79, app(app(ty_@2, bdh), bea)) → new_compare3(vwx90, vwx100, bdh, bea)
new_esEs4(Left(vwx90), Left(vwx100), False, app(app(ty_Either, app(app(app(ty_@3, ca), cb), cc)), bc), bd) → new_ltEs3(vwx90, vwx100, ca, cb, cc)
new_ltEs2(@2(vwx90, vwx91), @2(vwx100, vwx101), app(app(ty_@2, ha), hb), gf) → new_compare20(vwx90, vwx100, new_esEs6(vwx90, vwx100, ha, hb), ha, hb)
new_esEs4(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), False, app(app(app(ty_@3, hf), app(app(ty_@2, bbf), bbg)), bbc), bd) → new_lt2(vwx91, vwx101, bbf, bbg)
new_ltEs2(@2(vwx90, vwx91), @2(vwx100, vwx101), app(app(app(ty_@3, hc), hd), he), gf) → new_compare21(vwx90, vwx100, new_esEs7(vwx90, vwx100, hc, hd, he), hc, hd, he)
new_esEs4(@2(vwx90, vwx91), @2(vwx100, vwx101), False, app(app(ty_@2, app(ty_Maybe, gg)), gf), bd) → new_compare2(vwx90, vwx100, new_esEs5(vwx90, vwx100, gg), gg)
new_ltEs(Right(vwx90), Right(vwx100), cd, app(app(app(ty_@3, dd), de), df)) → new_ltEs3(vwx90, vwx100, dd, de, df)
new_lt0(vwx90, vwx100, gg) → new_compare2(vwx90, vwx100, new_esEs5(vwx90, vwx100, gg), gg)
new_compare4(vwx90, vwx100, hc, hd, he) → new_compare21(vwx90, vwx100, new_esEs7(vwx90, vwx100, hc, hd, he), hc, hd, he)
new_ltEs3(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), hf, hg, app(ty_Maybe, bab)) → new_ltEs0(vwx92, vwx102, bab)
new_esEs4(Right(vwx90), Right(vwx100), False, app(app(ty_Either, cd), app(ty_[], da)), bd) → new_ltEs1(vwx90, vwx100, da)
new_esEs10(vwx16, vwx17, False, beg, app(ty_[], bfc)) → new_ltEs1(vwx16, vwx17, bfc)
new_primCompAux(vwx90, vwx100, vwx79, app(ty_[], bdg)) → new_compare0(vwx90, vwx100, bdg)
new_esEs4(Left(vwx90), Left(vwx100), False, app(app(ty_Either, app(ty_Maybe, be)), bc), bd) → new_ltEs0(vwx90, vwx100, be)
new_ltEs3(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), app(app(ty_Either, bcc), bcd), hg, bbc) → new_lt(vwx90, vwx100, bcc, bcd)
new_ltEs3(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), hf, app(app(ty_Either, bba), bbb), bbc) → new_lt(vwx91, vwx101, bba, bbb)
new_ltEs1(:(vwx90, vwx91), :(vwx100, vwx101), eh) → new_primCompAux(vwx90, vwx100, new_compare(vwx91, vwx101, eh), eh)
new_ltEs2(@2(vwx90, vwx91), @2(vwx100, vwx101), app(app(ty_Either, gd), ge), gf) → new_lt(vwx90, vwx100, gd, ge)
new_ltEs3(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), hf, app(app(ty_@2, bbf), bbg), bbc) → new_lt2(vwx91, vwx101, bbf, bbg)
new_esEs4(@2(vwx90, vwx91), @2(vwx100, vwx101), False, app(app(ty_@2, fa), app(app(app(ty_@3, ga), gb), gc)), bd) → new_ltEs3(vwx91, vwx101, ga, gb, gc)
new_lt1(vwx90, vwx100, gh) → new_compare0(vwx90, vwx100, gh)
new_esEs4(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), False, app(app(app(ty_@3, app(app(ty_Either, bcc), bcd)), hg), bbc), bd) → new_lt(vwx90, vwx100, bcc, bcd)
new_ltEs2(@2(vwx90, vwx91), @2(vwx100, vwx101), fa, app(ty_Maybe, fd)) → new_ltEs0(vwx91, vwx101, fd)
new_ltEs3(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), hf, hg, app(app(app(ty_@3, baf), bag), bah)) → new_ltEs3(vwx92, vwx102, baf, bag, bah)
new_ltEs3(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), app(ty_[], bcf), hg, bbc) → new_lt1(vwx90, vwx100, bcf)
new_ltEs2(@2(vwx90, vwx91), @2(vwx100, vwx101), fa, app(app(ty_@2, fg), fh)) → new_ltEs2(vwx91, vwx101, fg, fh)
new_ltEs3(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), app(app(app(ty_@3, bda), bdb), bdc), hg, bbc) → new_lt3(vwx90, vwx100, bda, bdb, bdc)
new_esEs4(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), False, app(app(app(ty_@3, app(ty_Maybe, bce)), hg), bbc), bd) → new_lt0(vwx90, vwx100, bce)
new_ltEs0(Just(vwx90), Just(vwx100), app(app(ty_@2, ec), ed)) → new_ltEs2(vwx90, vwx100, ec, ed)
new_esEs4(@2(vwx90, vwx91), @2(vwx100, vwx101), False, app(app(ty_@2, fa), app(app(ty_Either, fb), fc)), bd) → new_ltEs(vwx91, vwx101, fb, fc)
new_esEs4(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), False, app(app(app(ty_@3, app(app(app(ty_@3, bda), bdb), bdc)), hg), bbc), bd) → new_lt3(vwx90, vwx100, bda, bdb, bdc)
new_ltEs0(Just(vwx90), Just(vwx100), app(ty_[], eb)) → new_ltEs1(vwx90, vwx100, eb)
new_esEs4(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), False, app(app(app(ty_@3, hf), app(ty_Maybe, bbd)), bbc), bd) → new_lt0(vwx91, vwx101, bbd)
new_ltEs(Right(vwx90), Right(vwx100), cd, app(app(ty_@2, db), dc)) → new_ltEs2(vwx90, vwx100, db, dc)
new_esEs4(@2(vwx90, vwx91), @2(vwx100, vwx101), False, app(app(ty_@2, fa), app(ty_Maybe, fd)), bd) → new_ltEs0(vwx91, vwx101, fd)
new_esEs4(Right(vwx90), Right(vwx100), False, app(app(ty_Either, cd), app(app(ty_Either, ce), cf)), bd) → new_ltEs(vwx90, vwx100, ce, cf)
new_esEs4(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), False, app(app(app(ty_@3, hf), hg), app(app(ty_Either, hh), baa)), bd) → new_ltEs(vwx92, vwx102, hh, baa)
new_esEs4(@2(vwx90, vwx91), @2(vwx100, vwx101), False, app(app(ty_@2, app(ty_[], gh)), gf), bd) → new_compare0(vwx90, vwx100, gh)
new_esEs4(Just(vwx90), Just(vwx100), False, app(ty_Maybe, app(app(app(ty_@3, ee), ef), eg)), bd) → new_ltEs3(vwx90, vwx100, ee, ef, eg)
new_esEs4(Just(vwx90), Just(vwx100), False, app(ty_Maybe, app(ty_[], eb)), bd) → new_ltEs1(vwx90, vwx100, eb)
new_esEs4(@2(vwx90, vwx91), @2(vwx100, vwx101), False, app(app(ty_@2, app(app(app(ty_@3, hc), hd), he)), gf), bd) → new_compare21(vwx90, vwx100, new_esEs7(vwx90, vwx100, hc, hd, he), hc, hd, he)
new_ltEs(Left(vwx90), Left(vwx100), app(app(ty_@2, bg), bh), bc) → new_ltEs2(vwx90, vwx100, bg, bh)
new_esEs4(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), False, app(app(app(ty_@3, hf), app(ty_[], bbe)), bbc), bd) → new_lt1(vwx91, vwx101, bbe)
new_lt2(vwx90, vwx100, ha, hb) → new_compare20(vwx90, vwx100, new_esEs6(vwx90, vwx100, ha, hb), ha, hb)
new_compare22(vwx90, vwx100, False, bdd, bde) → new_ltEs(vwx90, vwx100, bdd, bde)
new_primCompAux(vwx90, vwx100, vwx79, app(app(app(ty_@3, beb), bec), bed)) → new_compare4(vwx90, vwx100, beb, bec, bed)
new_esEs4(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), False, app(app(app(ty_@3, hf), hg), app(ty_[], bac)), bd) → new_ltEs1(vwx92, vwx102, bac)
new_ltEs3(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), hf, app(ty_[], bbe), bbc) → new_lt1(vwx91, vwx101, bbe)
new_ltEs0(Just(vwx90), Just(vwx100), app(app(ty_Either, dg), dh)) → new_ltEs(vwx90, vwx100, dg, dh)
new_ltEs3(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), app(ty_Maybe, bce), hg, bbc) → new_lt0(vwx90, vwx100, bce)

The TRS R consists of the following rules:

new_ltEs19(vwx9, vwx10, app(app(ty_@2, fa), gf)) → new_ltEs5(vwx9, vwx10, fa, gf)
new_ltEs18(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), hf, hg, bbc) → new_pePe(new_lt20(vwx90, vwx100, hf), new_asAs(new_esEs34(vwx90, vwx100, hf), new_pePe(new_lt19(vwx91, vwx101, hg), new_asAs(new_esEs33(vwx91, vwx101, hg), new_ltEs21(vwx92, vwx102, bbc)))))
new_lt6(Right(vwx30), Right(vwx40), bee, bef) → new_esEs26(vwx30, vwx40, new_esEs11(vwx30, vwx40, bef), bee, bef)
new_esEs25(vwx300, vwx400, ty_Int) → new_esEs19(vwx300, vwx400)
new_ltEs4(Right(vwx90), Right(vwx100), cd, ty_Ordering) → new_ltEs9(vwx90, vwx100)
new_compare5(@0, @0) → EQ
new_esEs32(vwx300, vwx400, ty_Int) → new_esEs19(vwx300, vwx400)
new_esEs27(vwx302, vwx402, app(ty_[], cgf)) → new_esEs16(vwx302, vwx402, cgf)
new_esEs23(vwx9, vwx10, True, cba, bd) → new_esEs12(EQ, LT)
new_ltEs4(Right(vwx90), Right(vwx100), cd, app(ty_[], da)) → new_ltEs11(vwx90, vwx100, da)
new_esEs25(vwx300, vwx400, app(ty_[], cdd)) → new_esEs16(vwx300, vwx400, cdd)
new_lt6(Left(vwx30), Right(vwx40), bee, bef) → new_esEs12(new_compare10(Left(vwx30), Right(vwx40), True, bee, bef), LT)
new_lt17(vwx90, vwx100) → new_esEs12(new_compare18(vwx90, vwx100), LT)
new_compare31(vwx90, vwx100, ty_Ordering) → new_compare29(vwx90, vwx100)
new_esEs17(Char(vwx300), Char(vwx400)) → new_primEqNat0(vwx300, vwx400)
new_esEs32(vwx300, vwx400, ty_Float) → new_esEs22(vwx300, vwx400)
new_ltEs4(Left(vwx90), Left(vwx100), app(ty_[], bf), bc) → new_ltEs11(vwx90, vwx100, bf)
new_esEs24(vwx301, vwx401, ty_Char) → new_esEs17(vwx301, vwx401)
new_esEs27(vwx302, vwx402, app(ty_Ratio, cgb)) → new_esEs18(vwx302, vwx402, cgb)
new_lt20(vwx90, vwx100, ty_Char) → new_lt11(vwx90, vwx100)
new_compare10(vwx90, vwx100, True, bdd, bde) → LT
new_compare([], :(vwx100, vwx101), eh) → LT
new_compare16(vwx90, vwx100, False, hc, hd, he) → GT
new_lt20(vwx90, vwx100, app(ty_Ratio, dfc)) → new_lt12(vwx90, vwx100, dfc)
new_esEs11(vwx30, vwx40, app(ty_[], cfd)) → new_esEs16(vwx30, vwx40, cfd)
new_esEs11(vwx30, vwx40, ty_@0) → new_esEs15(vwx30, vwx40)
new_esEs27(vwx302, vwx402, ty_Double) → new_esEs20(vwx302, vwx402)
new_esEs25(vwx300, vwx400, ty_Char) → new_esEs17(vwx300, vwx400)
new_ltEs8(Just(vwx90), Just(vwx100), ty_@0) → new_ltEs10(vwx90, vwx100)
new_primMulNat0(Zero, Zero) → Zero
new_esEs33(vwx91, vwx101, ty_Float) → new_esEs22(vwx91, vwx101)
new_lt20(vwx90, vwx100, ty_Int) → new_lt13(vwx90, vwx100)
new_compare(:(vwx90, vwx91), [], eh) → GT
new_esEs32(vwx300, vwx400, ty_@0) → new_esEs15(vwx300, vwx400)
new_esEs7(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), cee, cef, ceg) → new_asAs(new_esEs29(vwx300, vwx400, cee), new_asAs(new_esEs28(vwx301, vwx401, cef), new_esEs27(vwx302, vwx402, ceg)))
new_ltEs9(GT, LT) → False
new_ltEs8(Just(vwx90), Just(vwx100), app(app(ty_@2, ec), ed)) → new_ltEs5(vwx90, vwx100, ec, ed)
new_esEs13(vwx90, vwx100, ty_Integer) → new_esEs14(vwx90, vwx100)
new_esEs33(vwx91, vwx101, app(app(ty_Either, bba), bbb)) → new_esEs8(vwx91, vwx101, bba, bbb)
new_esEs9(vwx30, vwx40, ty_@0) → new_esEs15(vwx30, vwx40)
new_compare25(vwx90, vwx100, True, gg) → EQ
new_esEs5(Just(vwx300), Just(vwx400), ty_Float) → new_esEs22(vwx300, vwx400)
new_ltEs16(False, True) → True
new_ltEs20(vwx16, vwx17, app(ty_Maybe, bfb)) → new_ltEs8(vwx16, vwx17, bfb)
new_esEs32(vwx300, vwx400, ty_Integer) → new_esEs14(vwx300, vwx400)
new_ltEs12(vwx9, vwx10) → new_not(new_esEs12(new_compare8(vwx9, vwx10), GT))
new_lt20(vwx90, vwx100, app(app(app(ty_@3, bda), bdb), bdc)) → new_lt18(vwx90, vwx100, bda, bdb, bdc)
new_esEs25(vwx300, vwx400, app(ty_Ratio, cch)) → new_esEs18(vwx300, vwx400, cch)
new_compare31(vwx90, vwx100, ty_Int) → new_compare11(vwx90, vwx100)
new_ltEs16(True, False) → False
new_esEs29(vwx300, vwx400, app(app(ty_Either, dah), dba)) → new_esEs8(vwx300, vwx400, dah, dba)
new_esEs13(vwx90, vwx100, ty_Char) → new_esEs17(vwx90, vwx100)
new_ltEs19(vwx9, vwx10, ty_Bool) → new_ltEs16(vwx9, vwx10)
new_lt20(vwx90, vwx100, ty_Double) → new_lt14(vwx90, vwx100)
new_esEs34(vwx90, vwx100, ty_Ordering) → new_esEs12(vwx90, vwx100)
new_esEs12(GT, LT) → False
new_esEs12(LT, GT) → False
new_esEs34(vwx90, vwx100, ty_@0) → new_esEs15(vwx90, vwx100)
new_lt19(vwx91, vwx101, ty_Int) → new_lt13(vwx91, vwx101)
new_esEs13(vwx90, vwx100, ty_@0) → new_esEs15(vwx90, vwx100)
new_esEs27(vwx302, vwx402, ty_Float) → new_esEs22(vwx302, vwx402)
new_ltEs6(vwx91, vwx101, app(app(app(ty_@3, ga), gb), gc)) → new_ltEs18(vwx91, vwx101, ga, gb, gc)
new_esEs5(Just(vwx300), Just(vwx400), app(ty_Maybe, ddh)) → new_esEs5(vwx300, vwx400, ddh)
new_lt15(vwx90, vwx100, ha, hb) → new_esEs12(new_compare7(vwx90, vwx100, ha, hb), LT)
new_ltEs6(vwx91, vwx101, ty_Char) → new_ltEs12(vwx91, vwx101)
new_lt11(vwx90, vwx100) → new_esEs12(new_compare8(vwx90, vwx100), LT)
new_esEs29(vwx300, vwx400, app(app(app(ty_@3, dbc), dbd), dbe)) → new_esEs7(vwx300, vwx400, dbc, dbd, dbe)
new_esEs25(vwx300, vwx400, ty_Bool) → new_esEs21(vwx300, vwx400)
new_ltEs9(EQ, GT) → True
new_ltEs4(Left(vwx90), Left(vwx100), app(ty_Maybe, be), bc) → new_ltEs8(vwx90, vwx100, be)
new_ltEs4(Left(vwx90), Left(vwx100), ty_Char, bc) → new_ltEs12(vwx90, vwx100)
new_esEs11(vwx30, vwx40, app(app(app(ty_@3, cfe), cff), cfg)) → new_esEs7(vwx30, vwx40, cfe, cff, cfg)
new_lt6(Left(vwx30), Left(vwx40), bee, bef) → new_esEs23(vwx30, vwx40, new_esEs9(vwx30, vwx40, bee), bee, bef)
new_compare15(vwx90, vwx100, False) → GT
new_esEs32(vwx300, vwx400, ty_Bool) → new_esEs21(vwx300, vwx400)
new_esEs28(vwx301, vwx401, ty_Bool) → new_esEs21(vwx301, vwx401)
new_lt20(vwx90, vwx100, ty_Float) → new_lt17(vwx90, vwx100)
new_compare29(vwx90, vwx100) → new_compare210(vwx90, vwx100, new_esEs12(vwx90, vwx100))
new_ltEs16(True, True) → True
new_lt9(vwx90, vwx100) → new_esEs12(new_compare29(vwx90, vwx100), LT)
new_ltEs9(LT, EQ) → True
new_esEs9(vwx30, vwx40, ty_Integer) → new_esEs14(vwx30, vwx40)
new_esEs32(vwx300, vwx400, app(app(ty_@2, ddc), ddd)) → new_esEs6(vwx300, vwx400, ddc, ddd)
new_ltEs19(vwx9, vwx10, app(app(ty_Either, cd), bc)) → new_ltEs4(vwx9, vwx10, cd, bc)
new_compare31(vwx90, vwx100, ty_Integer) → new_compare6(vwx90, vwx100)
new_pePe(False, vwx78) → vwx78
new_esEs13(vwx90, vwx100, ty_Ordering) → new_esEs12(vwx90, vwx100)
new_lt5(vwx90, vwx100, ty_Integer) → new_lt7(vwx90, vwx100)
new_esEs9(vwx30, vwx40, app(app(ty_@2, cbd), cbe)) → new_esEs6(vwx30, vwx40, cbd, cbe)
new_ltEs4(Right(vwx90), Right(vwx100), cd, ty_Char) → new_ltEs12(vwx90, vwx100)
new_lt16(vwx90, vwx100) → new_esEs12(new_compare30(vwx90, vwx100), LT)
new_lt19(vwx91, vwx101, ty_Ordering) → new_lt9(vwx91, vwx101)
new_esEs8(Left(vwx300), Left(vwx400), ty_Bool, bgc) → new_esEs21(vwx300, vwx400)
new_esEs34(vwx90, vwx100, ty_Double) → new_esEs20(vwx90, vwx100)
new_ltEs20(vwx16, vwx17, ty_@0) → new_ltEs10(vwx16, vwx17)
new_ltEs8(Just(vwx90), Just(vwx100), ty_Float) → new_ltEs17(vwx90, vwx100)
new_ltEs19(vwx9, vwx10, app(ty_[], eh)) → new_ltEs11(vwx9, vwx10, eh)
new_esEs33(vwx91, vwx101, ty_Bool) → new_esEs21(vwx91, vwx101)
new_ltEs20(vwx16, vwx17, app(app(ty_Either, beh), bfa)) → new_ltEs4(vwx16, vwx17, beh, bfa)
new_compare15(vwx90, vwx100, True) → LT
new_esEs33(vwx91, vwx101, app(app(app(ty_@3, bbh), bca), bcb)) → new_esEs7(vwx91, vwx101, bbh, bca, bcb)
new_lt5(vwx90, vwx100, ty_Ordering) → new_lt9(vwx90, vwx100)
new_esEs28(vwx301, vwx401, ty_@0) → new_esEs15(vwx301, vwx401)
new_esEs22(Float(vwx300, vwx301), Float(vwx400, vwx401)) → new_esEs19(new_sr(vwx300, vwx400), new_sr(vwx301, vwx401))
new_ltEs8(Just(vwx90), Just(vwx100), ty_Bool) → new_ltEs16(vwx90, vwx100)
new_ltEs9(EQ, EQ) → True
new_ltEs4(Right(vwx90), Right(vwx100), cd, app(app(ty_Either, ce), cf)) → new_ltEs4(vwx90, vwx100, ce, cf)
new_esEs8(Right(vwx300), Right(vwx400), bhf, ty_Char) → new_esEs17(vwx300, vwx400)
new_lt7(vwx90, vwx100) → new_esEs12(new_compare6(vwx90, vwx100), LT)
new_esEs31(vwx300, vwx400, ty_Integer) → new_esEs14(vwx300, vwx400)
new_lt5(vwx90, vwx100, app(app(ty_Either, gd), ge)) → new_lt6(vwx90, vwx100, gd, ge)
new_ltEs4(Left(vwx90), Left(vwx100), ty_Double, bc) → new_ltEs15(vwx90, vwx100)
new_lt19(vwx91, vwx101, app(ty_Ratio, dfb)) → new_lt12(vwx91, vwx101, dfb)
new_esEs14(Integer(vwx300), Integer(vwx400)) → new_primEqInt(vwx300, vwx400)
new_esEs32(vwx300, vwx400, ty_Double) → new_esEs20(vwx300, vwx400)
new_esEs8(Left(vwx300), Left(vwx400), ty_Char, bgc) → new_esEs17(vwx300, vwx400)
new_lt13(vwx90, vwx100) → new_esEs12(new_compare11(vwx90, vwx100), LT)
new_ltEs4(Left(vwx90), Right(vwx100), cd, bc) → True
new_esEs27(vwx302, vwx402, ty_Int) → new_esEs19(vwx302, vwx402)
new_primCmpNat0(Zero, Succ(vwx1000)) → LT
new_esEs27(vwx302, vwx402, app(app(app(ty_@3, cgg), cgh), cha)) → new_esEs7(vwx302, vwx402, cgg, cgh, cha)
new_ltEs8(Nothing, Just(vwx100), cbb) → True
new_compare18(Float(vwx90, vwx91), Float(vwx100, vwx101)) → new_compare11(new_sr(vwx90, vwx100), new_sr(vwx91, vwx101))
new_esEs23(vwx9, vwx10, False, cba, bd) → new_esEs12(new_compare10(Left(vwx9), Left(vwx10), new_ltEs19(vwx9, vwx10, cba), cba, bd), LT)
new_compare14(vwx90, vwx100, False) → GT
new_ltEs10(vwx9, vwx10) → new_not(new_esEs12(new_compare5(vwx9, vwx10), GT))
new_esEs33(vwx91, vwx101, app(ty_[], bbe)) → new_esEs16(vwx91, vwx101, bbe)
new_esEs25(vwx300, vwx400, app(app(ty_@2, cdh), cea)) → new_esEs6(vwx300, vwx400, cdh, cea)
new_esEs25(vwx300, vwx400, ty_Double) → new_esEs20(vwx300, vwx400)
new_esEs26(vwx16, vwx17, True, beg, dde) → new_esEs12(EQ, LT)
new_ltEs6(vwx91, vwx101, ty_Ordering) → new_ltEs9(vwx91, vwx101)
new_esEs12(LT, LT) → True
new_esEs11(vwx30, vwx40, ty_Bool) → new_esEs21(vwx30, vwx40)
new_ltEs14(vwx9, vwx10) → new_not(new_esEs12(new_compare11(vwx9, vwx10), GT))
new_esEs8(Right(vwx300), Right(vwx400), bhf, ty_Bool) → new_esEs21(vwx300, vwx400)
new_esEs21(True, True) → True
new_ltEs4(Right(vwx90), Right(vwx100), cd, ty_@0) → new_ltEs10(vwx90, vwx100)
new_pePe(True, vwx78) → True
new_esEs24(vwx301, vwx401, app(app(ty_@2, ccf), ccg)) → new_esEs6(vwx301, vwx401, ccf, ccg)
new_primEqNat0(Zero, Zero) → True
new_compare26(vwx90, vwx100, True) → EQ
new_esEs13(vwx90, vwx100, ty_Int) → new_esEs19(vwx90, vwx100)
new_ltEs21(vwx92, vwx102, ty_@0) → new_ltEs10(vwx92, vwx102)
new_esEs8(Right(vwx300), Right(vwx400), bhf, ty_Int) → new_esEs19(vwx300, vwx400)
new_esEs13(vwx90, vwx100, app(ty_Maybe, gg)) → new_esEs5(vwx90, vwx100, gg)
new_primMulNat0(Succ(vwx30100), Succ(vwx40100)) → new_primPlusNat1(new_primMulNat0(vwx30100, Succ(vwx40100)), vwx40100)
new_compare14(vwx90, vwx100, True) → LT
new_ltEs21(vwx92, vwx102, app(ty_Ratio, dfa)) → new_ltEs13(vwx92, vwx102, dfa)
new_ltEs8(Just(vwx90), Just(vwx100), app(app(app(ty_@3, ee), ef), eg)) → new_ltEs18(vwx90, vwx100, ee, ef, eg)
new_ltEs6(vwx91, vwx101, ty_@0) → new_ltEs10(vwx91, vwx101)
new_lt5(vwx90, vwx100, app(ty_Ratio, bgb)) → new_lt12(vwx90, vwx100, bgb)
new_lt20(vwx90, vwx100, ty_Integer) → new_lt7(vwx90, vwx100)
new_esEs25(vwx300, vwx400, ty_Float) → new_esEs22(vwx300, vwx400)
new_esEs16(:(vwx300, vwx301), :(vwx400, vwx401), ced) → new_asAs(new_esEs32(vwx300, vwx400, ced), new_esEs16(vwx301, vwx401, ced))
new_esEs8(Right(vwx300), Right(vwx400), bhf, app(app(app(ty_@3, cad), cae), caf)) → new_esEs7(vwx300, vwx400, cad, cae, caf)
new_compare31(vwx90, vwx100, ty_Bool) → new_compare30(vwx90, vwx100)
new_ltEs4(Left(vwx90), Left(vwx100), ty_Float, bc) → new_ltEs17(vwx90, vwx100)
new_ltEs9(EQ, LT) → False
new_compare(:(vwx90, vwx91), :(vwx100, vwx101), eh) → new_primCompAux1(vwx90, vwx100, new_compare(vwx91, vwx101, eh), eh)
new_lt19(vwx91, vwx101, app(ty_Maybe, bbd)) → new_lt8(vwx91, vwx101, bbd)
new_compare12(vwx90, vwx100, False, gg) → GT
new_sr(vwx301, vwx401) → new_primMulInt(vwx301, vwx401)
new_esEs5(Just(vwx300), Just(vwx400), ty_Double) → new_esEs20(vwx300, vwx400)
new_esEs5(Just(vwx300), Just(vwx400), ty_Integer) → new_esEs14(vwx300, vwx400)
new_esEs8(Right(vwx300), Right(vwx400), bhf, app(ty_Maybe, bhh)) → new_esEs5(vwx300, vwx400, bhh)
new_ltEs21(vwx92, vwx102, ty_Float) → new_ltEs17(vwx92, vwx102)
new_ltEs4(Left(vwx90), Left(vwx100), app(app(app(ty_@3, ca), cb), cc), bc) → new_ltEs18(vwx90, vwx100, ca, cb, cc)
new_esEs9(vwx30, vwx40, app(ty_[], ced)) → new_esEs16(vwx30, vwx40, ced)
new_esEs9(vwx30, vwx40, app(app(app(ty_@3, cee), cef), ceg)) → new_esEs7(vwx30, vwx40, cee, cef, ceg)
new_ltEs21(vwx92, vwx102, ty_Bool) → new_ltEs16(vwx92, vwx102)
new_esEs11(vwx30, vwx40, ty_Ordering) → new_esEs12(vwx30, vwx40)
new_esEs5(Just(vwx300), Just(vwx400), app(app(ty_Either, dea), deb)) → new_esEs8(vwx300, vwx400, dea, deb)
new_esEs30(vwx301, vwx401, ty_Int) → new_esEs19(vwx301, vwx401)
new_ltEs20(vwx16, vwx17, ty_Bool) → new_ltEs16(vwx16, vwx17)
new_ltEs20(vwx16, vwx17, ty_Int) → new_ltEs14(vwx16, vwx17)
new_ltEs4(Left(vwx90), Left(vwx100), ty_@0, bc) → new_ltEs10(vwx90, vwx100)
new_ltEs4(Left(vwx90), Left(vwx100), ty_Ordering, bc) → new_ltEs9(vwx90, vwx100)
new_compare17(vwx90, vwx100, True, ha, hb) → LT
new_esEs25(vwx300, vwx400, ty_Ordering) → new_esEs12(vwx300, vwx400)
new_esEs26(vwx16, vwx17, False, beg, dde) → new_esEs12(new_compare10(Right(vwx16), Right(vwx17), new_ltEs20(vwx16, vwx17, dde), beg, dde), LT)
new_lt20(vwx90, vwx100, ty_Ordering) → new_lt9(vwx90, vwx100)
new_primEqInt(Neg(Succ(vwx3000)), Neg(Succ(vwx4000))) → new_primEqNat0(vwx3000, vwx4000)
new_compare31(vwx90, vwx100, app(app(ty_@2, bdh), bea)) → new_compare7(vwx90, vwx100, bdh, bea)
new_esEs5(Just(vwx300), Just(vwx400), ty_@0) → new_esEs15(vwx300, vwx400)
new_lt19(vwx91, vwx101, ty_Float) → new_lt17(vwx91, vwx101)
new_esEs8(Right(vwx300), Right(vwx400), bhf, app(app(ty_Either, caa), cab)) → new_esEs8(vwx300, vwx400, caa, cab)
new_esEs8(Right(vwx300), Left(vwx400), bhf, bgc) → False
new_esEs8(Left(vwx300), Right(vwx400), bhf, bgc) → False
new_esEs12(EQ, LT) → False
new_esEs12(LT, EQ) → False
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_compare31(vwx90, vwx100, ty_@0) → new_compare5(vwx90, vwx100)
new_ltEs4(Right(vwx90), Right(vwx100), cd, ty_Integer) → new_ltEs7(vwx90, vwx100)
new_compare31(vwx90, vwx100, app(app(ty_Either, bdd), bde)) → new_compare23(vwx90, vwx100, new_esEs8(vwx90, vwx100, bdd, bde), bdd, bde)
new_ltEs20(vwx16, vwx17, ty_Char) → new_ltEs12(vwx16, vwx17)
new_ltEs4(Left(vwx90), Left(vwx100), app(app(ty_Either, ba), bb), bc) → new_ltEs4(vwx90, vwx100, ba, bb)
new_primEqInt(Neg(Succ(vwx3000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(vwx4000))) → False
new_primCompAux0(vwx83, GT) → GT
new_ltEs19(vwx9, vwx10, ty_Char) → new_ltEs12(vwx9, vwx10)
new_esEs11(vwx30, vwx40, ty_Int) → new_esEs19(vwx30, vwx40)
new_primPlusNat1(Zero, vwx40100) → Succ(vwx40100)
new_lt5(vwx90, vwx100, app(ty_[], gh)) → new_lt4(vwx90, vwx100, gh)
new_lt20(vwx90, vwx100, ty_@0) → new_lt10(vwx90, vwx100)
new_ltEs19(vwx9, vwx10, ty_Int) → new_ltEs14(vwx9, vwx10)
new_esEs27(vwx302, vwx402, app(app(ty_Either, cgd), cge)) → new_esEs8(vwx302, vwx402, cgd, cge)
new_compare24(vwx90, vwx100, True, ha, hb) → EQ
new_esEs32(vwx300, vwx400, app(ty_[], dcg)) → new_esEs16(vwx300, vwx400, dcg)
new_esEs29(vwx300, vwx400, app(ty_[], dbb)) → new_esEs16(vwx300, vwx400, dbb)
new_ltEs9(LT, LT) → True
new_esEs32(vwx300, vwx400, ty_Char) → new_esEs17(vwx300, vwx400)
new_ltEs21(vwx92, vwx102, app(ty_[], bac)) → new_ltEs11(vwx92, vwx102, bac)
new_ltEs21(vwx92, vwx102, app(app(ty_@2, bad), bae)) → new_ltEs5(vwx92, vwx102, bad, bae)
new_ltEs8(Just(vwx90), Just(vwx100), ty_Integer) → new_ltEs7(vwx90, vwx100)
new_compare([], [], eh) → EQ
new_ltEs21(vwx92, vwx102, app(app(ty_Either, hh), baa)) → new_ltEs4(vwx92, vwx102, hh, baa)
new_ltEs21(vwx92, vwx102, ty_Int) → new_ltEs14(vwx92, vwx102)
new_lt18(vwx90, vwx100, hc, hd, he) → new_esEs12(new_compare19(vwx90, vwx100, hc, hd, he), LT)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_esEs34(vwx90, vwx100, app(app(ty_Either, bcc), bcd)) → new_esEs8(vwx90, vwx100, bcc, bcd)
new_ltEs20(vwx16, vwx17, ty_Double) → new_ltEs15(vwx16, vwx17)
new_compare19(vwx90, vwx100, hc, hd, he) → new_compare27(vwx90, vwx100, new_esEs7(vwx90, vwx100, hc, hd, he), hc, hd, he)
new_ltEs20(vwx16, vwx17, app(app(ty_@2, bfd), bfe)) → new_ltEs5(vwx16, vwx17, bfd, bfe)
new_esEs28(vwx301, vwx401, ty_Int) → new_esEs19(vwx301, vwx401)
new_primCmpNat0(Succ(vwx900), Succ(vwx1000)) → new_primCmpNat0(vwx900, vwx1000)
new_ltEs4(Left(vwx90), Left(vwx100), ty_Int, bc) → new_ltEs14(vwx90, vwx100)
new_compare31(vwx90, vwx100, ty_Double) → new_compare28(vwx90, vwx100)
new_primEqInt(Pos(Succ(vwx3000)), Pos(Succ(vwx4000))) → new_primEqNat0(vwx3000, vwx4000)
new_compare24(vwx90, vwx100, False, ha, hb) → new_compare17(vwx90, vwx100, new_ltEs5(vwx90, vwx100, ha, hb), ha, hb)
new_compare10(vwx90, vwx100, False, bdd, bde) → GT
new_esEs6(@2(vwx300, vwx301), @2(vwx400, vwx401), cbd, cbe) → new_asAs(new_esEs25(vwx300, vwx400, cbd), new_esEs24(vwx301, vwx401, cbe))
new_esEs24(vwx301, vwx401, app(app(ty_Either, cbh), cca)) → new_esEs8(vwx301, vwx401, cbh, cca)
new_esEs25(vwx300, vwx400, app(ty_Maybe, cda)) → new_esEs5(vwx300, vwx400, cda)
new_esEs8(Left(vwx300), Left(vwx400), ty_@0, bgc) → new_esEs15(vwx300, vwx400)
new_esEs29(vwx300, vwx400, app(ty_Maybe, dag)) → new_esEs5(vwx300, vwx400, dag)
new_esEs28(vwx301, vwx401, ty_Char) → new_esEs17(vwx301, vwx401)
new_esEs24(vwx301, vwx401, ty_Double) → new_esEs20(vwx301, vwx401)
new_esEs9(vwx30, vwx40, ty_Float) → new_esEs22(vwx30, vwx40)
new_esEs34(vwx90, vwx100, app(app(ty_@2, bcg), bch)) → new_esEs6(vwx90, vwx100, bcg, bch)
new_primEqNat0(Succ(vwx3000), Succ(vwx4000)) → new_primEqNat0(vwx3000, vwx4000)
new_esEs33(vwx91, vwx101, app(ty_Ratio, dfb)) → new_esEs18(vwx91, vwx101, dfb)
new_esEs24(vwx301, vwx401, app(ty_Ratio, cbf)) → new_esEs18(vwx301, vwx401, cbf)
new_esEs33(vwx91, vwx101, app(app(ty_@2, bbf), bbg)) → new_esEs6(vwx91, vwx101, bbf, bbg)
new_esEs8(Left(vwx300), Left(vwx400), app(ty_Maybe, bge), bgc) → new_esEs5(vwx300, vwx400, bge)
new_ltEs19(vwx9, vwx10, app(app(app(ty_@3, hf), hg), bbc)) → new_ltEs18(vwx9, vwx10, hf, hg, bbc)
new_primCmpInt(Neg(Succ(vwx900)), Neg(vwx100)) → new_primCmpNat0(vwx100, Succ(vwx900))
new_ltEs8(Just(vwx90), Nothing, cbb) → False
new_esEs9(vwx30, vwx40, ty_Char) → new_esEs17(vwx30, vwx40)
new_compare28(Double(vwx90, vwx91), Double(vwx100, vwx101)) → new_compare11(new_sr(vwx90, vwx100), new_sr(vwx91, vwx101))
new_esEs12(EQ, EQ) → True
new_esEs33(vwx91, vwx101, ty_Double) → new_esEs20(vwx91, vwx101)
new_esEs34(vwx90, vwx100, app(app(app(ty_@3, bda), bdb), bdc)) → new_esEs7(vwx90, vwx100, bda, bdb, bdc)
new_primEqInt(Pos(Succ(vwx3000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(vwx4000))) → False
new_primPlusNat0(Zero, Succ(vwx401000)) → Succ(vwx401000)
new_primPlusNat0(Succ(vwx5400), Zero) → Succ(vwx5400)
new_ltEs19(vwx9, vwx10, ty_Float) → new_ltEs17(vwx9, vwx10)
new_primCmpNat0(Zero, Zero) → EQ
new_esEs8(Left(vwx300), Left(vwx400), ty_Ordering, bgc) → new_esEs12(vwx300, vwx400)
new_esEs13(vwx90, vwx100, ty_Double) → new_esEs20(vwx90, vwx100)
new_ltEs6(vwx91, vwx101, ty_Double) → new_ltEs15(vwx91, vwx101)
new_primCmpNat0(Succ(vwx900), Zero) → GT
new_ltEs19(vwx9, vwx10, app(ty_Ratio, cbc)) → new_ltEs13(vwx9, vwx10, cbc)
new_ltEs19(vwx9, vwx10, ty_Ordering) → new_ltEs9(vwx9, vwx10)
new_esEs11(vwx30, vwx40, app(app(ty_Either, cfb), cfc)) → new_esEs8(vwx30, vwx40, cfb, cfc)
new_esEs24(vwx301, vwx401, ty_@0) → new_esEs15(vwx301, vwx401)
new_compare31(vwx90, vwx100, app(app(app(ty_@3, beb), bec), bed)) → new_compare19(vwx90, vwx100, beb, bec, bed)
new_esEs8(Right(vwx300), Right(vwx400), bhf, ty_Ordering) → new_esEs12(vwx300, vwx400)
new_primCmpInt(Neg(Zero), Pos(Succ(vwx1000))) → LT
new_compare13(vwx90, vwx100, gg) → new_compare25(vwx90, vwx100, new_esEs5(vwx90, vwx100, gg), gg)
new_compare31(vwx90, vwx100, app(ty_Ratio, dfd)) → new_compare9(vwx90, vwx100, dfd)
new_sr0(Integer(vwx900), Integer(vwx1010)) → Integer(new_primMulInt(vwx900, vwx1010))
new_compare6(Integer(vwx90), Integer(vwx100)) → new_primCmpInt(vwx90, vwx100)
new_compare12(vwx90, vwx100, True, gg) → LT
new_esEs29(vwx300, vwx400, app(ty_Ratio, daf)) → new_esEs18(vwx300, vwx400, daf)
new_esEs32(vwx300, vwx400, app(ty_Maybe, dcd)) → new_esEs5(vwx300, vwx400, dcd)
new_primEqInt(Pos(Succ(vwx3000)), Neg(vwx400)) → False
new_primEqInt(Neg(Succ(vwx3000)), Pos(vwx400)) → False
new_esEs33(vwx91, vwx101, ty_Ordering) → new_esEs12(vwx91, vwx101)
new_compare9(:%(vwx90, vwx91), :%(vwx100, vwx101), ty_Int) → new_compare11(new_sr(vwx90, vwx101), new_sr(vwx100, vwx91))
new_esEs28(vwx301, vwx401, ty_Double) → new_esEs20(vwx301, vwx401)
new_esEs27(vwx302, vwx402, app(ty_Maybe, cgc)) → new_esEs5(vwx302, vwx402, cgc)
new_esEs13(vwx90, vwx100, app(app(ty_Either, gd), ge)) → new_esEs8(vwx90, vwx100, gd, ge)
new_compare210(vwx90, vwx100, False) → new_compare15(vwx90, vwx100, new_ltEs9(vwx90, vwx100))
new_ltEs6(vwx91, vwx101, app(ty_Maybe, fd)) → new_ltEs8(vwx91, vwx101, fd)
new_esEs33(vwx91, vwx101, ty_Integer) → new_esEs14(vwx91, vwx101)
new_primEqInt(Pos(Zero), Neg(Succ(vwx4000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(vwx4000))) → False
new_lt5(vwx90, vwx100, app(app(ty_@2, ha), hb)) → new_lt15(vwx90, vwx100, ha, hb)
new_esEs24(vwx301, vwx401, ty_Ordering) → new_esEs12(vwx301, vwx401)
new_primCmpInt(Pos(Zero), Pos(Succ(vwx1000))) → new_primCmpNat0(Zero, Succ(vwx1000))
new_esEs9(vwx30, vwx40, ty_Ordering) → new_esEs12(vwx30, vwx40)
new_ltEs7(vwx9, vwx10) → new_not(new_esEs12(new_compare6(vwx9, vwx10), GT))
new_esEs20(Double(vwx300, vwx301), Double(vwx400, vwx401)) → new_esEs19(new_sr(vwx300, vwx400), new_sr(vwx301, vwx401))
new_esEs28(vwx301, vwx401, ty_Ordering) → new_esEs12(vwx301, vwx401)
new_esEs11(vwx30, vwx40, app(ty_Ratio, ceh)) → new_esEs18(vwx30, vwx40, ceh)
new_compare17(vwx90, vwx100, False, ha, hb) → GT
new_esEs8(Left(vwx300), Left(vwx400), ty_Double, bgc) → new_esEs20(vwx300, vwx400)
new_primCompAux0(vwx83, LT) → LT
new_ltEs4(Left(vwx90), Left(vwx100), app(ty_Ratio, dbh), bc) → new_ltEs13(vwx90, vwx100, dbh)
new_not(False) → True
new_ltEs4(Right(vwx90), Left(vwx100), cd, bc) → False
new_esEs11(vwx30, vwx40, ty_Float) → new_esEs22(vwx30, vwx40)
new_lt8(vwx90, vwx100, gg) → new_esEs12(new_compare13(vwx90, vwx100, gg), LT)
new_esEs28(vwx301, vwx401, app(ty_[], chh)) → new_esEs16(vwx301, vwx401, chh)
new_primCmpInt(Pos(Succ(vwx900)), Pos(vwx100)) → new_primCmpNat0(Succ(vwx900), vwx100)
new_esEs12(GT, EQ) → False
new_esEs12(EQ, GT) → False
new_esEs8(Right(vwx300), Right(vwx400), bhf, app(ty_[], cac)) → new_esEs16(vwx300, vwx400, cac)
new_ltEs4(Left(vwx90), Left(vwx100), ty_Bool, bc) → new_ltEs16(vwx90, vwx100)
new_ltEs9(LT, GT) → True
new_esEs5(Just(vwx300), Just(vwx400), ty_Bool) → new_esEs21(vwx300, vwx400)
new_esEs13(vwx90, vwx100, app(ty_[], gh)) → new_esEs16(vwx90, vwx100, gh)
new_esEs25(vwx300, vwx400, ty_@0) → new_esEs15(vwx300, vwx400)
new_lt20(vwx90, vwx100, app(app(ty_Either, bcc), bcd)) → new_lt6(vwx90, vwx100, bcc, bcd)
new_lt5(vwx90, vwx100, app(app(app(ty_@3, hc), hd), he)) → new_lt18(vwx90, vwx100, hc, hd, he)
new_esEs8(Left(vwx300), Left(vwx400), ty_Integer, bgc) → new_esEs14(vwx300, vwx400)
new_ltEs21(vwx92, vwx102, ty_Char) → new_ltEs12(vwx92, vwx102)
new_esEs9(vwx30, vwx40, app(ty_Maybe, cec)) → new_esEs5(vwx30, vwx40, cec)
new_esEs34(vwx90, vwx100, ty_Int) → new_esEs19(vwx90, vwx100)
new_esEs34(vwx90, vwx100, app(ty_[], bcf)) → new_esEs16(vwx90, vwx100, bcf)
new_esEs24(vwx301, vwx401, ty_Bool) → new_esEs21(vwx301, vwx401)
new_ltEs6(vwx91, vwx101, app(ty_[], ff)) → new_ltEs11(vwx91, vwx101, ff)
new_compare7(vwx90, vwx100, ha, hb) → new_compare24(vwx90, vwx100, new_esEs6(vwx90, vwx100, ha, hb), ha, hb)
new_compare9(:%(vwx90, vwx91), :%(vwx100, vwx101), ty_Integer) → new_compare6(new_sr0(vwx90, vwx101), new_sr0(vwx100, vwx91))
new_esEs24(vwx301, vwx401, app(ty_Maybe, cbg)) → new_esEs5(vwx301, vwx401, cbg)
new_lt19(vwx91, vwx101, app(ty_[], bbe)) → new_lt4(vwx91, vwx101, bbe)
new_ltEs4(Right(vwx90), Right(vwx100), cd, ty_Double) → new_ltEs15(vwx90, vwx100)
new_esEs28(vwx301, vwx401, ty_Float) → new_esEs22(vwx301, vwx401)
new_esEs8(Left(vwx300), Left(vwx400), app(app(app(ty_@3, bha), bhb), bhc), bgc) → new_esEs7(vwx300, vwx400, bha, bhb, bhc)
new_esEs8(Left(vwx300), Left(vwx400), app(ty_Ratio, bgd), bgc) → new_esEs18(vwx300, vwx400, bgd)
new_esEs8(Right(vwx300), Right(vwx400), bhf, ty_Integer) → new_esEs14(vwx300, vwx400)
new_primCmpInt(Pos(Succ(vwx900)), Neg(vwx100)) → GT
new_esEs27(vwx302, vwx402, ty_@0) → new_esEs15(vwx302, vwx402)
new_esEs33(vwx91, vwx101, ty_Int) → new_esEs19(vwx91, vwx101)
new_ltEs8(Just(vwx90), Just(vwx100), app(ty_Ratio, dcb)) → new_ltEs13(vwx90, vwx100, dcb)
new_compare26(vwx90, vwx100, False) → new_compare14(vwx90, vwx100, new_ltEs16(vwx90, vwx100))
new_esEs11(vwx30, vwx40, app(ty_Maybe, cfa)) → new_esEs5(vwx30, vwx40, cfa)
new_ltEs6(vwx91, vwx101, ty_Integer) → new_ltEs7(vwx91, vwx101)
new_esEs9(vwx30, vwx40, ty_Int) → new_esEs19(vwx30, vwx40)
new_esEs29(vwx300, vwx400, ty_Integer) → new_esEs14(vwx300, vwx400)
new_primMulInt(Pos(vwx3010), Pos(vwx4010)) → Pos(new_primMulNat0(vwx3010, vwx4010))
new_esEs21(False, False) → True
new_esEs34(vwx90, vwx100, ty_Integer) → new_esEs14(vwx90, vwx100)
new_esEs9(vwx30, vwx40, app(ty_Ratio, ceb)) → new_esEs18(vwx30, vwx40, ceb)
new_compare31(vwx90, vwx100, ty_Char) → new_compare8(vwx90, vwx100)
new_esEs28(vwx301, vwx401, app(app(app(ty_@3, daa), dab), dac)) → new_esEs7(vwx301, vwx401, daa, dab, dac)
new_esEs8(Right(vwx300), Right(vwx400), bhf, ty_@0) → new_esEs15(vwx300, vwx400)
new_esEs27(vwx302, vwx402, ty_Char) → new_esEs17(vwx302, vwx402)
new_ltEs13(vwx9, vwx10, cbc) → new_not(new_esEs12(new_compare9(vwx9, vwx10, cbc), GT))
new_ltEs6(vwx91, vwx101, app(app(ty_Either, fb), fc)) → new_ltEs4(vwx91, vwx101, fb, fc)
new_esEs9(vwx30, vwx40, app(app(ty_Either, bhf), bgc)) → new_esEs8(vwx30, vwx40, bhf, bgc)
new_esEs27(vwx302, vwx402, app(app(ty_@2, chb), chc)) → new_esEs6(vwx302, vwx402, chb, chc)
new_ltEs19(vwx9, vwx10, app(ty_Maybe, cbb)) → new_ltEs8(vwx9, vwx10, cbb)
new_primMulInt(Neg(vwx3010), Neg(vwx4010)) → Pos(new_primMulNat0(vwx3010, vwx4010))
new_lt5(vwx90, vwx100, ty_Bool) → new_lt16(vwx90, vwx100)
new_ltEs4(Right(vwx90), Right(vwx100), cd, ty_Bool) → new_ltEs16(vwx90, vwx100)
new_esEs33(vwx91, vwx101, app(ty_Maybe, bbd)) → new_esEs5(vwx91, vwx101, bbd)
new_esEs29(vwx300, vwx400, app(app(ty_@2, dbf), dbg)) → new_esEs6(vwx300, vwx400, dbf, dbg)
new_ltEs20(vwx16, vwx17, ty_Float) → new_ltEs17(vwx16, vwx17)
new_esEs5(Just(vwx300), Just(vwx400), app(ty_Ratio, ddg)) → new_esEs18(vwx300, vwx400, ddg)
new_primEqNat0(Succ(vwx3000), Zero) → False
new_primEqNat0(Zero, Succ(vwx4000)) → False
new_primPlusNat0(Zero, Zero) → Zero
new_ltEs21(vwx92, vwx102, ty_Integer) → new_ltEs7(vwx92, vwx102)
new_ltEs4(Right(vwx90), Right(vwx100), cd, app(app(app(ty_@3, dd), de), df)) → new_ltEs18(vwx90, vwx100, dd, de, df)
new_compare23(vwx90, vwx100, False, bdd, bde) → new_compare10(vwx90, vwx100, new_ltEs4(vwx90, vwx100, bdd, bde), bdd, bde)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs28(vwx301, vwx401, app(app(ty_Either, chf), chg)) → new_esEs8(vwx301, vwx401, chf, chg)
new_compare210(vwx90, vwx100, True) → EQ
new_esEs16([], :(vwx400, vwx401), ced) → False
new_esEs16(:(vwx300, vwx301), [], ced) → False
new_esEs33(vwx91, vwx101, ty_Char) → new_esEs17(vwx91, vwx101)
new_ltEs9(GT, GT) → True
new_ltEs8(Just(vwx90), Just(vwx100), app(app(ty_Either, dg), dh)) → new_ltEs4(vwx90, vwx100, dg, dh)
new_primPlusNat1(Succ(vwx540), vwx40100) → Succ(Succ(new_primPlusNat0(vwx540, vwx40100)))
new_compare16(vwx90, vwx100, True, hc, hd, he) → LT
new_ltEs8(Just(vwx90), Just(vwx100), ty_Int) → new_ltEs14(vwx90, vwx100)
new_lt12(vwx90, vwx100, bgb) → new_esEs12(new_compare9(vwx90, vwx100, bgb), LT)
new_lt5(vwx90, vwx100, ty_Double) → new_lt14(vwx90, vwx100)
new_esEs34(vwx90, vwx100, app(ty_Maybe, bce)) → new_esEs5(vwx90, vwx100, bce)
new_ltEs21(vwx92, vwx102, app(ty_Maybe, bab)) → new_ltEs8(vwx92, vwx102, bab)
new_compare23(vwx90, vwx100, True, bdd, bde) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(vwx1000))) → new_primCmpNat0(Succ(vwx1000), Zero)
new_lt20(vwx90, vwx100, app(app(ty_@2, bcg), bch)) → new_lt15(vwx90, vwx100, bcg, bch)
new_primCmpInt(Pos(Zero), Neg(Succ(vwx1000))) → GT
new_lt19(vwx91, vwx101, ty_Integer) → new_lt7(vwx91, vwx101)
new_esEs25(vwx300, vwx400, ty_Integer) → new_esEs14(vwx300, vwx400)
new_esEs29(vwx300, vwx400, ty_@0) → new_esEs15(vwx300, vwx400)
new_compare31(vwx90, vwx100, app(ty_[], bdg)) → new_compare(vwx90, vwx100, bdg)
new_esEs9(vwx30, vwx40, ty_Double) → new_esEs20(vwx30, vwx40)
new_esEs13(vwx90, vwx100, app(app(ty_@2, ha), hb)) → new_esEs6(vwx90, vwx100, ha, hb)
new_ltEs6(vwx91, vwx101, app(ty_Ratio, bga)) → new_ltEs13(vwx91, vwx101, bga)
new_esEs29(vwx300, vwx400, ty_Int) → new_esEs19(vwx300, vwx400)
new_esEs28(vwx301, vwx401, app(app(ty_@2, dad), dae)) → new_esEs6(vwx301, vwx401, dad, dae)
new_esEs13(vwx90, vwx100, app(ty_Ratio, bgb)) → new_esEs18(vwx90, vwx100, bgb)
new_ltEs4(Left(vwx90), Left(vwx100), ty_Integer, bc) → new_ltEs7(vwx90, vwx100)
new_esEs8(Left(vwx300), Left(vwx400), app(app(ty_Either, bgf), bgg), bgc) → new_esEs8(vwx300, vwx400, bgf, bgg)
new_ltEs6(vwx91, vwx101, app(app(ty_@2, fg), fh)) → new_ltEs5(vwx91, vwx101, fg, fh)
new_esEs19(vwx30, vwx40) → new_primEqInt(vwx30, vwx40)
new_ltEs4(Right(vwx90), Right(vwx100), cd, app(ty_Ratio, dca)) → new_ltEs13(vwx90, vwx100, dca)
new_esEs11(vwx30, vwx40, app(app(ty_@2, cfh), cga)) → new_esEs6(vwx30, vwx40, cfh, cga)
new_ltEs21(vwx92, vwx102, ty_Ordering) → new_ltEs9(vwx92, vwx102)
new_esEs8(Left(vwx300), Left(vwx400), ty_Float, bgc) → new_esEs22(vwx300, vwx400)
new_esEs24(vwx301, vwx401, app(app(app(ty_@3, ccc), ccd), cce)) → new_esEs7(vwx301, vwx401, ccc, ccd, cce)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_ltEs11(vwx9, vwx10, eh) → new_not(new_esEs12(new_compare(vwx9, vwx10, eh), GT))
new_lt14(vwx90, vwx100) → new_esEs12(new_compare28(vwx90, vwx100), LT)
new_primCompAux1(vwx90, vwx100, vwx79, eh) → new_primCompAux0(vwx79, new_compare31(vwx90, vwx100, eh))
new_esEs5(Just(vwx300), Just(vwx400), app(ty_[], dec)) → new_esEs16(vwx300, vwx400, dec)
new_esEs13(vwx90, vwx100, ty_Float) → new_esEs22(vwx90, vwx100)
new_compare30(vwx90, vwx100) → new_compare26(vwx90, vwx100, new_esEs21(vwx90, vwx100))
new_ltEs8(Just(vwx90), Just(vwx100), app(ty_Maybe, ea)) → new_ltEs8(vwx90, vwx100, ea)
new_ltEs4(Right(vwx90), Right(vwx100), cd, app(app(ty_@2, db), dc)) → new_ltEs5(vwx90, vwx100, db, dc)
new_ltEs5(@2(vwx90, vwx91), @2(vwx100, vwx101), fa, gf) → new_pePe(new_lt5(vwx90, vwx100, fa), new_asAs(new_esEs13(vwx90, vwx100, fa), new_ltEs6(vwx91, vwx101, gf)))
new_esEs15(@0, @0) → True
new_asAs(False, vwx45) → False
new_lt20(vwx90, vwx100, ty_Bool) → new_lt16(vwx90, vwx100)
new_primMulInt(Pos(vwx3010), Neg(vwx4010)) → Neg(new_primMulNat0(vwx3010, vwx4010))
new_primMulInt(Neg(vwx3010), Pos(vwx4010)) → Neg(new_primMulNat0(vwx3010, vwx4010))
new_esEs33(vwx91, vwx101, ty_@0) → new_esEs15(vwx91, vwx101)
new_ltEs20(vwx16, vwx17, app(ty_[], bfc)) → new_ltEs11(vwx16, vwx17, bfc)
new_primMulNat0(Zero, Succ(vwx40100)) → Zero
new_primMulNat0(Succ(vwx30100), Zero) → Zero
new_compare27(vwx90, vwx100, False, hc, hd, he) → new_compare16(vwx90, vwx100, new_ltEs18(vwx90, vwx100, hc, hd, he), hc, hd, he)
new_esEs32(vwx300, vwx400, app(app(app(ty_@3, dch), dda), ddb)) → new_esEs7(vwx300, vwx400, dch, dda, ddb)
new_ltEs20(vwx16, vwx17, ty_Integer) → new_ltEs7(vwx16, vwx17)
new_lt5(vwx90, vwx100, ty_@0) → new_lt10(vwx90, vwx100)
new_lt19(vwx91, vwx101, app(app(ty_@2, bbf), bbg)) → new_lt15(vwx91, vwx101, bbf, bbg)
new_esEs24(vwx301, vwx401, app(ty_[], ccb)) → new_esEs16(vwx301, vwx401, ccb)
new_esEs29(vwx300, vwx400, ty_Char) → new_esEs17(vwx300, vwx400)
new_ltEs19(vwx9, vwx10, ty_@0) → new_ltEs10(vwx9, vwx10)
new_lt19(vwx91, vwx101, app(app(app(ty_@3, bbh), bca), bcb)) → new_lt18(vwx91, vwx101, bbh, bca, bcb)
new_lt6(Right(vwx30), Left(vwx40), bee, bef) → new_esEs12(new_compare10(Right(vwx30), Left(vwx40), False, bee, bef), LT)
new_esEs5(Just(vwx300), Just(vwx400), app(app(ty_@2, deg), deh)) → new_esEs6(vwx300, vwx400, deg, deh)
new_ltEs21(vwx92, vwx102, ty_Double) → new_ltEs15(vwx92, vwx102)
new_lt20(vwx90, vwx100, app(ty_[], bcf)) → new_lt4(vwx90, vwx100, bcf)
new_ltEs17(vwx9, vwx10) → new_not(new_esEs12(new_compare18(vwx9, vwx10), GT))
new_ltEs20(vwx16, vwx17, ty_Ordering) → new_ltEs9(vwx16, vwx17)
new_lt19(vwx91, vwx101, ty_Bool) → new_lt16(vwx91, vwx101)
new_ltEs8(Just(vwx90), Just(vwx100), app(ty_[], eb)) → new_ltEs11(vwx90, vwx100, eb)
new_esEs31(vwx300, vwx400, ty_Int) → new_esEs19(vwx300, vwx400)
new_esEs8(Right(vwx300), Right(vwx400), bhf, ty_Float) → new_esEs22(vwx300, vwx400)
new_ltEs20(vwx16, vwx17, app(app(app(ty_@3, bff), bfg), bfh)) → new_ltEs18(vwx16, vwx17, bff, bfg, bfh)
new_esEs11(vwx30, vwx40, ty_Double) → new_esEs20(vwx30, vwx40)
new_esEs34(vwx90, vwx100, app(ty_Ratio, dfc)) → new_esEs18(vwx90, vwx100, dfc)
new_ltEs9(GT, EQ) → False
new_lt5(vwx90, vwx100, ty_Char) → new_lt11(vwx90, vwx100)
new_ltEs6(vwx91, vwx101, ty_Bool) → new_ltEs16(vwx91, vwx101)
new_esEs5(Just(vwx300), Nothing, cec) → False
new_esEs5(Nothing, Just(vwx400), cec) → False
new_ltEs4(Right(vwx90), Right(vwx100), cd, ty_Int) → new_ltEs14(vwx90, vwx100)
new_ltEs15(vwx9, vwx10) → new_not(new_esEs12(new_compare28(vwx9, vwx10), GT))
new_lt5(vwx90, vwx100, ty_Int) → new_lt13(vwx90, vwx100)
new_esEs24(vwx301, vwx401, ty_Integer) → new_esEs14(vwx301, vwx401)
new_compare11(vwx9, vwx10) → new_primCmpInt(vwx9, vwx10)
new_ltEs4(Right(vwx90), Right(vwx100), cd, ty_Float) → new_ltEs17(vwx90, vwx100)
new_esEs25(vwx300, vwx400, app(app(app(ty_@3, cde), cdf), cdg)) → new_esEs7(vwx300, vwx400, cde, cdf, cdg)
new_esEs24(vwx301, vwx401, ty_Float) → new_esEs22(vwx301, vwx401)
new_esEs29(vwx300, vwx400, ty_Float) → new_esEs22(vwx300, vwx400)
new_esEs27(vwx302, vwx402, ty_Bool) → new_esEs21(vwx302, vwx402)
new_esEs34(vwx90, vwx100, ty_Char) → new_esEs17(vwx90, vwx100)
new_esEs16([], [], ced) → True
new_esEs32(vwx300, vwx400, ty_Ordering) → new_esEs12(vwx300, vwx400)
new_esEs8(Right(vwx300), Right(vwx400), bhf, app(app(ty_@2, cag), cah)) → new_esEs6(vwx300, vwx400, cag, cah)
new_ltEs8(Nothing, Nothing, cbb) → True
new_esEs8(Right(vwx300), Right(vwx400), bhf, ty_Double) → new_esEs20(vwx300, vwx400)
new_esEs5(Just(vwx300), Just(vwx400), ty_Ordering) → new_esEs12(vwx300, vwx400)
new_esEs27(vwx302, vwx402, ty_Ordering) → new_esEs12(vwx302, vwx402)
new_esEs5(Nothing, Nothing, cec) → True
new_esEs28(vwx301, vwx401, app(ty_Maybe, che)) → new_esEs5(vwx301, vwx401, che)
new_esEs5(Just(vwx300), Just(vwx400), app(app(app(ty_@3, ded), dee), def)) → new_esEs7(vwx300, vwx400, ded, dee, def)
new_esEs32(vwx300, vwx400, app(ty_Ratio, dcc)) → new_esEs18(vwx300, vwx400, dcc)
new_esEs29(vwx300, vwx400, ty_Double) → new_esEs20(vwx300, vwx400)
new_esEs12(GT, GT) → True
new_ltEs8(Just(vwx90), Just(vwx100), ty_Ordering) → new_ltEs9(vwx90, vwx100)
new_lt10(vwx90, vwx100) → new_esEs12(new_compare5(vwx90, vwx100), LT)
new_ltEs19(vwx9, vwx10, ty_Double) → new_ltEs15(vwx9, vwx10)
new_ltEs6(vwx91, vwx101, ty_Int) → new_ltEs14(vwx91, vwx101)
new_ltEs19(vwx9, vwx10, ty_Integer) → new_ltEs7(vwx9, vwx10)
new_lt19(vwx91, vwx101, ty_Char) → new_lt11(vwx91, vwx101)
new_lt5(vwx90, vwx100, ty_Float) → new_lt17(vwx90, vwx100)
new_lt19(vwx91, vwx101, ty_@0) → new_lt10(vwx91, vwx101)
new_esEs29(vwx300, vwx400, ty_Bool) → new_esEs21(vwx300, vwx400)
new_primPlusNat0(Succ(vwx5400), Succ(vwx401000)) → Succ(Succ(new_primPlusNat0(vwx5400, vwx401000)))
new_lt20(vwx90, vwx100, app(ty_Maybe, bce)) → new_lt8(vwx90, vwx100, bce)
new_ltEs4(Right(vwx90), Right(vwx100), cd, app(ty_Maybe, cg)) → new_ltEs8(vwx90, vwx100, cg)
new_esEs29(vwx300, vwx400, ty_Ordering) → new_esEs12(vwx300, vwx400)
new_esEs18(:%(vwx300, vwx301), :%(vwx400, vwx401), ceb) → new_asAs(new_esEs31(vwx300, vwx400, ceb), new_esEs30(vwx301, vwx401, ceb))
new_ltEs8(Just(vwx90), Just(vwx100), ty_Char) → new_ltEs12(vwx90, vwx100)
new_esEs27(vwx302, vwx402, ty_Integer) → new_esEs14(vwx302, vwx402)
new_esEs34(vwx90, vwx100, ty_Float) → new_esEs22(vwx90, vwx100)
new_asAs(True, vwx45) → vwx45
new_esEs8(Left(vwx300), Left(vwx400), app(ty_[], bgh), bgc) → new_esEs16(vwx300, vwx400, bgh)
new_compare25(vwx90, vwx100, False, gg) → new_compare12(vwx90, vwx100, new_ltEs8(vwx90, vwx100, gg), gg)
new_ltEs4(Left(vwx90), Left(vwx100), app(app(ty_@2, bg), bh), bc) → new_ltEs5(vwx90, vwx100, bg, bh)
new_esEs11(vwx30, vwx40, ty_Char) → new_esEs17(vwx30, vwx40)
new_esEs8(Right(vwx300), Right(vwx400), bhf, app(ty_Ratio, bhg)) → new_esEs18(vwx300, vwx400, bhg)
new_ltEs16(False, False) → True
new_esEs28(vwx301, vwx401, app(ty_Ratio, chd)) → new_esEs18(vwx301, vwx401, chd)
new_esEs24(vwx301, vwx401, ty_Int) → new_esEs19(vwx301, vwx401)
new_compare27(vwx90, vwx100, True, hc, hd, he) → EQ
new_esEs13(vwx90, vwx100, ty_Bool) → new_esEs21(vwx90, vwx100)
new_ltEs21(vwx92, vwx102, app(app(app(ty_@3, baf), bag), bah)) → new_ltEs18(vwx92, vwx102, baf, bag, bah)
new_esEs9(vwx30, vwx40, ty_Bool) → new_esEs21(vwx30, vwx40)
new_esEs21(False, True) → False
new_esEs21(True, False) → False
new_esEs11(vwx30, vwx40, ty_Integer) → new_esEs14(vwx30, vwx40)
new_ltEs6(vwx91, vwx101, ty_Float) → new_ltEs17(vwx91, vwx101)
new_esEs5(Just(vwx300), Just(vwx400), ty_Int) → new_esEs19(vwx300, vwx400)
new_esEs34(vwx90, vwx100, ty_Bool) → new_esEs21(vwx90, vwx100)
new_lt19(vwx91, vwx101, ty_Double) → new_lt14(vwx91, vwx101)
new_esEs8(Left(vwx300), Left(vwx400), ty_Int, bgc) → new_esEs19(vwx300, vwx400)
new_esEs30(vwx301, vwx401, ty_Integer) → new_esEs14(vwx301, vwx401)
new_lt19(vwx91, vwx101, app(app(ty_Either, bba), bbb)) → new_lt6(vwx91, vwx101, bba, bbb)
new_esEs28(vwx301, vwx401, ty_Integer) → new_esEs14(vwx301, vwx401)
new_lt5(vwx90, vwx100, app(ty_Maybe, gg)) → new_lt8(vwx90, vwx100, gg)
new_esEs8(Left(vwx300), Left(vwx400), app(app(ty_@2, bhd), bhe), bgc) → new_esEs6(vwx300, vwx400, bhd, bhe)
new_compare8(Char(vwx90), Char(vwx100)) → new_primCmpNat0(vwx90, vwx100)
new_esEs13(vwx90, vwx100, app(app(app(ty_@3, hc), hd), he)) → new_esEs7(vwx90, vwx100, hc, hd, he)
new_ltEs8(Just(vwx90), Just(vwx100), ty_Double) → new_ltEs15(vwx90, vwx100)
new_compare31(vwx90, vwx100, app(ty_Maybe, bdf)) → new_compare13(vwx90, vwx100, bdf)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCompAux0(vwx83, EQ) → vwx83
new_ltEs20(vwx16, vwx17, app(ty_Ratio, ddf)) → new_ltEs13(vwx16, vwx17, ddf)
new_esEs5(Just(vwx300), Just(vwx400), ty_Char) → new_esEs17(vwx300, vwx400)
new_lt4(vwx90, vwx100, gh) → new_esEs12(new_compare(vwx90, vwx100, gh), LT)
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_compare31(vwx90, vwx100, ty_Float) → new_compare18(vwx90, vwx100)
new_esEs25(vwx300, vwx400, app(app(ty_Either, cdb), cdc)) → new_esEs8(vwx300, vwx400, cdb, cdc)
new_primCmpInt(Neg(Succ(vwx900)), Pos(vwx100)) → LT
new_not(True) → False
new_esEs32(vwx300, vwx400, app(app(ty_Either, dce), dcf)) → new_esEs8(vwx300, vwx400, dce, dcf)

The set Q consists of the following terms:

new_ltEs8(Just(x0), Just(x1), ty_Int)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs4(Right(x0), Right(x1), x2, ty_Int)
new_esEs23(x0, x1, True, x2, x3)
new_esEs5(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_ltEs4(Right(x0), Right(x1), x2, ty_Integer)
new_ltEs21(x0, x1, app(app(ty_Either, x2), x3))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_lt5(x0, x1, ty_Bool)
new_ltEs15(x0, x1)
new_esEs8(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_ltEs16(True, True)
new_primPlusNat1(Zero, x0)
new_esEs8(Right(x0), Right(x1), x2, ty_Bool)
new_esEs8(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs13(x0, x1, ty_Bool)
new_ltEs8(Just(x0), Just(x1), ty_Ordering)
new_primCompAux1(x0, x1, x2, x3)
new_esEs5(Nothing, Just(x0), x1)
new_ltEs4(Left(x0), Left(x1), app(ty_[], x2), x3)
new_ltEs21(x0, x1, ty_Double)
new_compare18(Float(x0, x1), Float(x2, x3))
new_esEs28(x0, x1, ty_Bool)
new_esEs8(Right(x0), Right(x1), x2, app(ty_[], x3))
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs5(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs13(x0, x1, app(ty_Maybe, x2))
new_compare31(x0, x1, ty_Double)
new_esEs33(x0, x1, ty_Float)
new_esEs27(x0, x1, ty_Int)
new_esEs19(x0, x1)
new_esEs8(Left(x0), Left(x1), ty_Bool, x2)
new_ltEs19(x0, x1, app(ty_[], x2))
new_esEs16(:(x0, x1), [], x2)
new_asAs(False, x0)
new_esEs32(x0, x1, ty_Ordering)
new_esEs8(Right(x0), Right(x1), x2, ty_Char)
new_esEs16([], [], x0)
new_compare31(x0, x1, app(app(ty_@2, x2), x3))
new_esEs11(x0, x1, ty_Char)
new_ltEs8(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs8(Left(x0), Left(x1), ty_Float, x2)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_lt5(x0, x1, app(ty_[], x2))
new_esEs33(x0, x1, ty_@0)
new_compare11(x0, x1)
new_ltEs4(Left(x0), Left(x1), ty_Float, x2)
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, ty_@0)
new_compare(:(x0, x1), [], x2)
new_esEs32(x0, x1, ty_Bool)
new_ltEs4(Right(x0), Right(x1), x2, ty_Char)
new_ltEs8(Just(x0), Just(x1), ty_Double)
new_esEs24(x0, x1, app(ty_[], x2))
new_esEs13(x0, x1, app(app(ty_Either, x2), x3))
new_esEs9(x0, x1, ty_Ordering)
new_esEs34(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, ty_Char)
new_ltEs4(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs29(x0, x1, app(ty_[], x2))
new_esEs12(EQ, GT)
new_esEs12(GT, EQ)
new_esEs11(x0, x1, ty_Int)
new_ltEs6(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs21(x0, x1, app(ty_Ratio, x2))
new_compare28(Double(x0, x1), Double(x2, x3))
new_primCompAux0(x0, GT)
new_ltEs6(x0, x1, ty_@0)
new_esEs16(:(x0, x1), :(x2, x3), x4)
new_lt12(x0, x1, x2)
new_esEs29(x0, x1, ty_Double)
new_esEs24(x0, x1, ty_Float)
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_ltEs11(x0, x1, x2)
new_compare31(x0, x1, ty_Integer)
new_esEs27(x0, x1, ty_@0)
new_ltEs10(x0, x1)
new_primPlusNat0(Succ(x0), Succ(x1))
new_ltEs4(Left(x0), Right(x1), x2, x3)
new_ltEs4(Right(x0), Left(x1), x2, x3)
new_esEs12(GT, GT)
new_ltEs4(Right(x0), Right(x1), x2, ty_Double)
new_esEs8(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs34(x0, x1, ty_@0)
new_compare12(x0, x1, True, x2)
new_ltEs19(x0, x1, ty_Float)
new_esEs29(x0, x1, ty_Float)
new_primMulInt(Pos(x0), Pos(x1))
new_compare([], :(x0, x1), x2)
new_ltEs20(x0, x1, ty_Bool)
new_esEs5(Just(x0), Just(x1), ty_Float)
new_ltEs4(Left(x0), Left(x1), ty_@0, x2)
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_esEs32(x0, x1, app(ty_Ratio, x2))
new_esEs29(x0, x1, ty_Int)
new_esEs25(x0, x1, ty_Int)
new_ltEs6(x0, x1, ty_Bool)
new_ltEs21(x0, x1, app(app(ty_@2, x2), x3))
new_compare23(x0, x1, True, x2, x3)
new_esEs8(Left(x0), Left(x1), ty_Double, x2)
new_ltEs5(@2(x0, x1), @2(x2, x3), x4, x5)
new_ltEs21(x0, x1, ty_Float)
new_esEs34(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs9(EQ, EQ)
new_compare5(@0, @0)
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs6(x0, x1, ty_Ordering)
new_compare31(x0, x1, ty_Ordering)
new_esEs34(x0, x1, app(app(ty_@2, x2), x3))
new_lt14(x0, x1)
new_lt5(x0, x1, app(ty_Ratio, x2))
new_lt19(x0, x1, app(ty_Ratio, x2))
new_esEs8(Right(x0), Right(x1), x2, ty_Ordering)
new_compare210(x0, x1, True)
new_ltEs20(x0, x1, ty_Int)
new_primEqNat0(Zero, Zero)
new_compare31(x0, x1, app(ty_Maybe, x2))
new_esEs13(x0, x1, ty_Char)
new_esEs27(x0, x1, ty_Float)
new_esEs33(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare31(x0, x1, ty_Char)
new_ltEs21(x0, x1, app(ty_[], x2))
new_ltEs21(x0, x1, ty_Integer)
new_esEs34(x0, x1, ty_Double)
new_compare([], [], x0)
new_compare14(x0, x1, True)
new_esEs13(x0, x1, ty_@0)
new_compare25(x0, x1, False, x2)
new_esEs25(x0, x1, ty_Ordering)
new_esEs31(x0, x1, ty_Integer)
new_lt20(x0, x1, ty_Char)
new_sr0(Integer(x0), Integer(x1))
new_esEs23(x0, x1, False, x2, x3)
new_lt20(x0, x1, ty_Double)
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_lt10(x0, x1)
new_esEs8(Right(x0), Right(x1), x2, ty_Double)
new_primMulNat0(Zero, Zero)
new_esEs24(x0, x1, ty_Ordering)
new_esEs33(x0, x1, app(app(ty_@2, x2), x3))
new_esEs33(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs4(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs8(Left(x0), Left(x1), ty_Int, x2)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_ltEs6(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs8(Right(x0), Right(x1), x2, ty_Integer)
new_compare26(x0, x1, True)
new_ltEs8(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs6(x0, x1, ty_Int)
new_esEs5(Just(x0), Just(x1), ty_Double)
new_lt7(x0, x1)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_esEs8(Left(x0), Left(x1), ty_Integer, x2)
new_ltEs7(x0, x1)
new_compare16(x0, x1, True, x2, x3, x4)
new_esEs14(Integer(x0), Integer(x1))
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_esEs13(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs8(Just(x0), Just(x1), ty_Char)
new_esEs11(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_pePe(False, x0)
new_lt5(x0, x1, app(app(ty_@2, x2), x3))
new_esEs8(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_compare31(x0, x1, ty_Bool)
new_esEs11(x0, x1, ty_@0)
new_esEs34(x0, x1, ty_Float)
new_esEs9(x0, x1, ty_Char)
new_esEs29(x0, x1, ty_Ordering)
new_ltEs8(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_compare29(x0, x1)
new_ltEs4(Right(x0), Right(x1), x2, ty_@0)
new_esEs29(x0, x1, ty_Integer)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs21(x0, x1, ty_Bool)
new_esEs33(x0, x1, app(ty_Ratio, x2))
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs9(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs25(x0, x1, ty_Float)
new_compare31(x0, x1, app(app(ty_Either, x2), x3))
new_esEs34(x0, x1, app(ty_Maybe, x2))
new_lt20(x0, x1, ty_Bool)
new_ltEs8(Just(x0), Nothing, x1)
new_ltEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, app(ty_Ratio, x2))
new_compare7(x0, x1, x2, x3)
new_lt20(x0, x1, ty_Float)
new_ltEs4(Left(x0), Left(x1), ty_Int, x2)
new_esEs22(Float(x0, x1), Float(x2, x3))
new_lt5(x0, x1, ty_Double)
new_lt5(x0, x1, app(ty_Maybe, x2))
new_lt5(x0, x1, ty_Ordering)
new_esEs8(Right(x0), Right(x1), x2, ty_Int)
new_ltEs4(Left(x0), Left(x1), ty_Char, x2)
new_compare17(x0, x1, False, x2, x3)
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs34(x0, x1, app(ty_Ratio, x2))
new_esEs9(x0, x1, app(ty_Ratio, x2))
new_primMulInt(Neg(x0), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_ltEs9(GT, EQ)
new_ltEs9(EQ, GT)
new_lt19(x0, x1, ty_Bool)
new_esEs25(x0, x1, app(ty_[], x2))
new_esEs5(Just(x0), Just(x1), ty_Char)
new_esEs32(x0, x1, ty_@0)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_ltEs4(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs27(x0, x1, ty_Integer)
new_ltEs4(Left(x0), Left(x1), ty_Integer, x2)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_esEs12(EQ, LT)
new_esEs12(LT, EQ)
new_lt16(x0, x1)
new_compare6(Integer(x0), Integer(x1))
new_compare9(:%(x0, x1), :%(x2, x3), ty_Int)
new_esEs7(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_ltEs8(Just(x0), Just(x1), app(ty_Ratio, x2))
new_primCompAux0(x0, EQ)
new_esEs8(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs8(Just(x0), Just(x1), ty_Float)
new_primEqNat0(Succ(x0), Zero)
new_esEs8(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs28(x0, x1, ty_Integer)
new_esEs30(x0, x1, ty_Integer)
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, ty_Float)
new_compare16(x0, x1, False, x2, x3, x4)
new_esEs5(Just(x0), Nothing, x1)
new_esEs5(Just(x0), Just(x1), app(ty_[], x2))
new_esEs12(EQ, EQ)
new_primPlusNat0(Zero, Zero)
new_esEs34(x0, x1, ty_Ordering)
new_esEs9(x0, x1, ty_Int)
new_esEs34(x0, x1, ty_Char)
new_esEs6(@2(x0, x1), @2(x2, x3), x4, x5)
new_lt5(x0, x1, ty_@0)
new_esEs27(x0, x1, app(ty_[], x2))
new_ltEs4(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_compare31(x0, x1, app(ty_Ratio, x2))
new_ltEs19(x0, x1, ty_Int)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_lt20(x0, x1, ty_Ordering)
new_lt13(x0, x1)
new_esEs25(x0, x1, ty_Char)
new_esEs8(Left(x0), Left(x1), ty_Char, x2)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpNat0(Succ(x0), Zero)
new_esEs28(x0, x1, ty_Ordering)
new_esEs5(Just(x0), Just(x1), ty_Bool)
new_compare210(x0, x1, False)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primMulNat0(Succ(x0), Succ(x1))
new_compare8(Char(x0), Char(x1))
new_ltEs21(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, ty_Double)
new_esEs28(x0, x1, ty_@0)
new_esEs13(x0, x1, ty_Int)
new_lt20(x0, x1, ty_Int)
new_ltEs20(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, app(ty_[], x2))
new_esEs32(x0, x1, ty_Char)
new_primMulNat0(Zero, Succ(x0))
new_compare17(x0, x1, True, x2, x3)
new_esEs33(x0, x1, ty_Char)
new_ltEs6(x0, x1, ty_Float)
new_ltEs17(x0, x1)
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_compare19(x0, x1, x2, x3, x4)
new_primPlusNat0(Zero, Succ(x0))
new_esEs9(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs20(x0, x1, ty_Ordering)
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_esEs24(x0, x1, ty_Char)
new_lt5(x0, x1, ty_Int)
new_lt19(x0, x1, ty_Double)
new_ltEs9(EQ, LT)
new_ltEs9(LT, EQ)
new_lt19(x0, x1, app(ty_[], x2))
new_esEs9(x0, x1, ty_Float)
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpNat0(Succ(x0), Succ(x1))
new_compare27(x0, x1, True, x2, x3, x4)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_lt6(Left(x0), Left(x1), x2, x3)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_esEs5(Just(x0), Just(x1), ty_Ordering)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_compare25(x0, x1, True, x2)
new_lt20(x0, x1, ty_Integer)
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_esEs27(x0, x1, ty_Char)
new_ltEs4(Left(x0), Left(x1), ty_Bool, x2)
new_esEs33(x0, x1, app(ty_[], x2))
new_compare10(x0, x1, False, x2, x3)
new_ltEs8(Just(x0), Just(x1), ty_@0)
new_compare13(x0, x1, x2)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_esEs8(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs33(x0, x1, ty_Double)
new_esEs28(x0, x1, ty_Int)
new_compare24(x0, x1, True, x2, x3)
new_esEs25(x0, x1, ty_@0)
new_esEs34(x0, x1, app(ty_[], x2))
new_primMulNat0(Succ(x0), Zero)
new_ltEs18(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_ltEs4(Left(x0), Left(x1), ty_Double, x2)
new_esEs27(x0, x1, ty_Ordering)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_ltEs6(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt8(x0, x1, x2)
new_esEs32(x0, x1, app(app(ty_@2, x2), x3))
new_primEqInt(Neg(Zero), Neg(Zero))
new_esEs27(x0, x1, ty_Bool)
new_esEs18(:%(x0, x1), :%(x2, x3), x4)
new_esEs24(x0, x1, ty_Double)
new_ltEs20(x0, x1, ty_@0)
new_esEs11(x0, x1, ty_Ordering)
new_esEs5(Just(x0), Just(x1), ty_Int)
new_lt19(x0, x1, ty_@0)
new_lt19(x0, x1, ty_Ordering)
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_compare(:(x0, x1), :(x2, x3), x4)
new_ltEs4(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_lt4(x0, x1, x2)
new_compare12(x0, x1, False, x2)
new_esEs11(x0, x1, ty_Bool)
new_esEs9(x0, x1, app(app(ty_@2, x2), x3))
new_esEs24(x0, x1, ty_Bool)
new_ltEs8(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs9(x0, x1, app(ty_[], x2))
new_ltEs12(x0, x1)
new_esEs11(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, True, x2, x3)
new_esEs8(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_lt6(Right(x0), Left(x1), x2, x3)
new_lt6(Left(x0), Right(x1), x2, x3)
new_lt19(x0, x1, ty_Integer)
new_compare24(x0, x1, False, x2, x3)
new_ltEs9(LT, LT)
new_esEs33(x0, x1, ty_Ordering)
new_ltEs20(x0, x1, ty_Double)
new_ltEs16(False, True)
new_ltEs16(True, False)
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_esEs9(x0, x1, app(ty_Maybe, x2))
new_ltEs13(x0, x1, x2)
new_esEs24(x0, x1, ty_Integer)
new_asAs(True, x0)
new_esEs28(x0, x1, ty_Double)
new_ltEs6(x0, x1, ty_Integer)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_esEs30(x0, x1, ty_Int)
new_ltEs6(x0, x1, app(ty_Maybe, x2))
new_ltEs8(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs8(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_ltEs6(x0, x1, app(app(ty_@2, x2), x3))
new_lt19(x0, x1, ty_Int)
new_primCmpNat0(Zero, Zero)
new_lt11(x0, x1)
new_esEs11(x0, x1, app(ty_[], x2))
new_esEs5(Just(x0), Just(x1), app(ty_Maybe, x2))
new_lt18(x0, x1, x2, x3, x4)
new_esEs25(x0, x1, ty_Bool)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs32(x0, x1, ty_Int)
new_esEs34(x0, x1, ty_Integer)
new_esEs13(x0, x1, ty_Double)
new_ltEs21(x0, x1, ty_Ordering)
new_esEs15(@0, @0)
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs33(x0, x1, ty_Int)
new_esEs32(x0, x1, app(ty_Maybe, x2))
new_lt17(x0, x1)
new_ltEs4(Right(x0), Right(x1), x2, ty_Ordering)
new_primCompAux0(x0, LT)
new_ltEs6(x0, x1, app(ty_[], x2))
new_esEs5(Just(x0), Just(x1), ty_Integer)
new_lt19(x0, x1, ty_Char)
new_ltEs21(x0, x1, ty_Int)
new_esEs32(x0, x1, ty_Integer)
new_esEs32(x0, x1, app(ty_[], x2))
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_ltEs4(Right(x0), Right(x1), x2, ty_Bool)
new_esEs5(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs27(x0, x1, ty_Double)
new_primEqNat0(Zero, Succ(x0))
new_esEs33(x0, x1, ty_Integer)
new_esEs11(x0, x1, app(ty_Ratio, x2))
new_esEs34(x0, x1, ty_Bool)
new_esEs11(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs8(Just(x0), Just(x1), ty_Bool)
new_ltEs19(x0, x1, ty_Double)
new_lt19(x0, x1, app(ty_Maybe, x2))
new_lt6(Right(x0), Right(x1), x2, x3)
new_ltEs4(Left(x0), Left(x1), ty_Ordering, x2)
new_ltEs19(x0, x1, ty_Bool)
new_esEs28(x0, x1, ty_Float)
new_ltEs21(x0, x1, ty_Char)
new_ltEs20(x0, x1, ty_Integer)
new_ltEs21(x0, x1, ty_@0)
new_ltEs9(GT, LT)
new_esEs28(x0, x1, ty_Char)
new_ltEs9(LT, GT)
new_esEs5(Nothing, Nothing, x0)
new_ltEs4(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs11(x0, x1, app(app(ty_@2, x2), x3))
new_esEs5(Just(x0), Just(x1), ty_@0)
new_ltEs4(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs21(True, True)
new_lt5(x0, x1, ty_Integer)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_not(True)
new_esEs13(x0, x1, ty_Float)
new_ltEs4(Right(x0), Right(x1), x2, ty_Float)
new_esEs33(x0, x1, ty_Bool)
new_esEs11(x0, x1, ty_Double)
new_esEs8(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_ltEs19(x0, x1, ty_Integer)
new_compare9(:%(x0, x1), :%(x2, x3), ty_Integer)
new_ltEs8(Nothing, Just(x0), x1)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_esEs11(x0, x1, ty_Float)
new_esEs9(x0, x1, ty_@0)
new_not(False)
new_ltEs4(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_compare27(x0, x1, False, x2, x3, x4)
new_ltEs6(x0, x1, ty_Char)
new_esEs9(x0, x1, ty_Integer)
new_pePe(True, x0)
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_lt20(x0, x1, app(ty_Maybe, x2))
new_lt5(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpNat0(Zero, Succ(x0))
new_esEs16([], :(x0, x1), x2)
new_esEs13(x0, x1, app(app(ty_@2, x2), x3))
new_esEs21(False, True)
new_esEs21(True, False)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_esEs13(x0, x1, app(ty_Ratio, x2))
new_esEs9(x0, x1, ty_Bool)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs4(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs32(x0, x1, ty_Float)
new_lt5(x0, x1, ty_Char)
new_esEs8(Left(x0), Left(x1), ty_@0, x2)
new_primEqNat0(Succ(x0), Succ(x1))
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare31(x0, x1, app(ty_[], x2))
new_esEs24(x0, x1, ty_@0)
new_esEs13(x0, x1, app(ty_[], x2))
new_sr(x0, x1)
new_esEs25(x0, x1, ty_Integer)
new_esEs8(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs8(Right(x0), Left(x1), x2, x3)
new_esEs8(Left(x0), Right(x1), x2, x3)
new_ltEs19(x0, x1, ty_Ordering)
new_compare31(x0, x1, ty_@0)
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_compare15(x0, x1, False)
new_esEs26(x0, x1, False, x2, x3)
new_esEs32(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs34(x0, x1, ty_Int)
new_esEs8(Right(x0), Right(x1), x2, ty_@0)
new_primPlusNat0(Succ(x0), Zero)
new_esEs13(x0, x1, ty_Integer)
new_esEs31(x0, x1, ty_Int)
new_lt15(x0, x1, x2, x3)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_compare23(x0, x1, False, x2, x3)
new_compare30(x0, x1)
new_ltEs9(GT, GT)
new_esEs9(x0, x1, ty_Double)
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_compare10(x0, x1, True, x2, x3)
new_esEs29(x0, x1, ty_Bool)
new_esEs32(x0, x1, ty_Double)
new_esEs11(x0, x1, ty_Integer)
new_ltEs14(x0, x1)
new_compare31(x0, x1, ty_Float)
new_esEs33(x0, x1, app(ty_Maybe, x2))
new_lt5(x0, x1, ty_Float)
new_lt20(x0, x1, ty_@0)
new_lt5(x0, x1, app(app(ty_Either, x2), x3))
new_esEs8(Right(x0), Right(x1), x2, ty_Float)
new_ltEs8(Nothing, Nothing, x0)
new_esEs21(False, False)
new_primEqInt(Pos(Zero), Pos(Zero))
new_compare31(x0, x1, ty_Int)
new_compare26(x0, x1, False)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs5(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_ltEs4(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs32(x0, x1, app(app(ty_Either, x2), x3))
new_esEs17(Char(x0), Char(x1))
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs8(Just(x0), Just(x1), ty_Integer)
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_esEs13(x0, x1, ty_Ordering)
new_esEs24(x0, x1, ty_Int)
new_compare14(x0, x1, False)
new_esEs29(x0, x1, ty_Char)
new_esEs12(LT, LT)
new_ltEs16(False, False)
new_compare15(x0, x1, True)
new_compare31(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs4(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs28(x0, x1, app(ty_[], x2))
new_ltEs19(x0, x1, ty_Char)
new_esEs20(Double(x0, x1), Double(x2, x3))
new_primPlusNat1(Succ(x0), x1)
new_lt9(x0, x1)
new_lt19(x0, x1, ty_Float)
new_esEs29(x0, x1, ty_@0)
new_ltEs6(x0, x1, ty_Double)

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: