YES 3.97 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
  ((compare :: (Ord a, Ord b) => Either b a  ->  Either b a  ->  Ordering) :: (Ord a, Ord b) => Either b a  ->  Either b a  ->  Ordering)

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
  ((compare :: (Ord b, Ord a) => Either b a  ->  Either b a  ->  Ordering) :: (Ord b, Ord a) => Either b a  ->  Either b a  ->  Ordering)

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
  ((compare :: (Ord b, Ord a) => Either a b  ->  Either a b  ->  Ordering) :: (Ord b, Ord a) => Either a b  ->  Either a b  ->  Ordering)

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
  ((compare :: (Ord a, Ord b) => Either a b  ->  Either a b  ->  Ordering) :: (Ord b, Ord a) => Either a b  ->  Either a b  ->  Ordering)

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

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

compare0 x y True = GT

compare3 x y = compare2 x y (x == y)

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

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

gcd'0 x y = gcd' y (x `rem` y)

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

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

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

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

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

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

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

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

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

is transformed to
absReal x = absReal2 x

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

absReal0 x True = `negate` x

absReal2 x = absReal1 x (x >= 0)

The following Function with conditions
undefined 
 | False
 = undefined

is transformed to
undefined  = undefined1

undefined0 True = undefined

undefined1  = undefined0 False

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

is transformed to
reduce x y = reduce2 x y

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



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

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

module Main where
  import qualified Prelude


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

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

reduce2D vwv vww = gcd vwv vww

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

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

are unpacked to the following functions on top level
gcd0Gcd' x zx = gcd0Gcd'2 x zx
gcd0Gcd' x y = gcd0Gcd'0 x y

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

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

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



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

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

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
  (compare :: (Ord b, Ord a) => Either b a  ->  Either b a  ->  Ordering)

module Main where
  import qualified Prelude


Haskell To QDPs


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

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

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

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

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



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

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

new_primPlusNat(Succ(vwx5500), Succ(vwx400000)) → new_primPlusNat(vwx5500, vwx400000)

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

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



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

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

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

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

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



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

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

new_primCmpNat(Succ(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_esEs3(Just(vwx300), Just(vwx400), app(app(ty_@2, bde), bdf)) → new_esEs0(vwx300, vwx400, bde, bdf)
new_esEs2(:(vwx300, vwx301), :(vwx400, vwx401), app(app(ty_@2, bcc), bcd)) → new_esEs0(vwx300, vwx400, bcc, bcd)
new_esEs2(:(vwx300, vwx301), :(vwx400, vwx401), app(ty_Maybe, bda)) → new_esEs3(vwx300, vwx400, bda)
new_esEs1(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), hf, app(app(app(ty_@3, bac), bad), bae), gf) → new_esEs1(vwx301, vwx401, bac, bad, bae)
new_esEs3(Just(vwx300), Just(vwx400), app(ty_[], beb)) → new_esEs2(vwx300, vwx400, beb)
new_esEs(Right(vwx300), Right(vwx400), cc, app(ty_Maybe, de)) → new_esEs3(vwx300, vwx400, de)
new_esEs1(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), hf, app(ty_Maybe, bag), gf) → new_esEs3(vwx301, vwx401, bag)
new_esEs0(@2(vwx300, vwx301), @2(vwx400, vwx401), eh, app(app(app(ty_@3, ff), fg), fh)) → new_esEs1(vwx301, vwx401, ff, fg, fh)
new_esEs(Left(vwx300), Left(vwx400), app(ty_[], ca), bc) → new_esEs2(vwx300, vwx400, ca)
new_esEs1(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), hf, ge, app(app(app(ty_@3, bbd), bbe), bbf)) → new_esEs1(vwx302, vwx402, bbd, bbe, bbf)
new_esEs1(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), hf, ge, app(ty_[], bbg)) → new_esEs2(vwx302, vwx402, bbg)
new_esEs(Right(vwx300), Right(vwx400), cc, app(app(ty_@2, cf), cg)) → new_esEs0(vwx300, vwx400, cf, cg)
new_esEs1(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), hf, ge, app(app(ty_@2, bbb), bbc)) → new_esEs0(vwx302, vwx402, bbb, bbc)
new_esEs0(@2(vwx300, vwx301), @2(vwx400, vwx401), app(app(ty_Either, df), dg), dh) → new_esEs(vwx300, vwx400, df, dg)
new_esEs1(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), app(app(ty_@2, gg), gh), ge, gf) → new_esEs0(vwx300, vwx400, gg, gh)
new_esEs0(@2(vwx300, vwx301), @2(vwx400, vwx401), eh, app(app(ty_Either, fa), fb)) → new_esEs(vwx301, vwx401, fa, fb)
new_esEs1(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), hf, app(ty_[], baf), gf) → new_esEs2(vwx301, vwx401, baf)
new_esEs3(Just(vwx300), Just(vwx400), app(app(app(ty_@3, bdg), bdh), bea)) → new_esEs1(vwx300, vwx400, bdg, bdh, bea)
new_esEs2(:(vwx300, vwx301), :(vwx400, vwx401), app(app(app(ty_@3, bce), bcf), bcg)) → new_esEs1(vwx300, vwx400, bce, bcf, bcg)
new_esEs2(:(vwx300, vwx301), :(vwx400, vwx401), app(app(ty_Either, bca), bcb)) → new_esEs(vwx300, vwx400, bca, bcb)
new_esEs1(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), app(app(app(ty_@3, ha), hb), hc), ge, gf) → new_esEs1(vwx300, vwx400, ha, hb, hc)
new_esEs(Right(vwx300), Right(vwx400), cc, app(ty_[], dd)) → new_esEs2(vwx300, vwx400, dd)
new_esEs(Right(vwx300), Right(vwx400), cc, app(app(app(ty_@3, da), db), dc)) → new_esEs1(vwx300, vwx400, da, db, dc)
new_esEs(Right(vwx300), Right(vwx400), cc, app(app(ty_Either, cd), ce)) → new_esEs(vwx300, vwx400, cd, ce)
new_esEs1(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), hf, ge, app(ty_Maybe, bbh)) → new_esEs3(vwx302, vwx402, bbh)
new_esEs0(@2(vwx300, vwx301), @2(vwx400, vwx401), eh, app(ty_Maybe, gb)) → new_esEs3(vwx301, vwx401, gb)
new_esEs(Left(vwx300), Left(vwx400), app(app(ty_@2, bd), be), bc) → new_esEs0(vwx300, vwx400, bd, be)
new_esEs1(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), hf, ge, app(app(ty_Either, bah), bba)) → new_esEs(vwx302, vwx402, bah, bba)
new_esEs1(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), app(ty_Maybe, he), ge, gf) → new_esEs3(vwx300, vwx400, he)
new_esEs0(@2(vwx300, vwx301), @2(vwx400, vwx401), app(ty_Maybe, eg), dh) → new_esEs3(vwx300, vwx400, eg)
new_esEs2(:(vwx300, vwx301), :(vwx400, vwx401), bdb) → new_esEs2(vwx301, vwx401, bdb)
new_esEs3(Just(vwx300), Just(vwx400), app(ty_Maybe, bec)) → new_esEs3(vwx300, vwx400, bec)
new_esEs1(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), hf, app(app(ty_Either, hg), hh), gf) → new_esEs(vwx301, vwx401, hg, hh)
new_esEs(Left(vwx300), Left(vwx400), app(ty_Maybe, cb), bc) → new_esEs3(vwx300, vwx400, cb)
new_esEs3(Just(vwx300), Just(vwx400), app(app(ty_Either, bdc), bdd)) → new_esEs(vwx300, vwx400, bdc, bdd)
new_esEs1(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), app(app(ty_Either, gc), gd), ge, gf) → new_esEs(vwx300, vwx400, gc, gd)
new_esEs0(@2(vwx300, vwx301), @2(vwx400, vwx401), app(ty_[], ef), dh) → new_esEs2(vwx300, vwx400, ef)
new_esEs0(@2(vwx300, vwx301), @2(vwx400, vwx401), app(app(ty_@2, ea), eb), dh) → new_esEs0(vwx300, vwx400, ea, eb)
new_esEs2(:(vwx300, vwx301), :(vwx400, vwx401), app(ty_[], bch)) → new_esEs2(vwx300, vwx400, bch)
new_esEs1(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), app(ty_[], hd), ge, gf) → new_esEs2(vwx300, vwx400, hd)
new_esEs(Left(vwx300), Left(vwx400), app(app(app(ty_@3, bf), bg), bh), bc) → new_esEs1(vwx300, vwx400, bf, bg, bh)
new_esEs0(@2(vwx300, vwx301), @2(vwx400, vwx401), app(app(app(ty_@3, ec), ed), ee), dh) → new_esEs1(vwx300, vwx400, ec, ed, ee)
new_esEs1(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), hf, app(app(ty_@2, baa), bab), gf) → new_esEs0(vwx301, vwx401, baa, bab)
new_esEs0(@2(vwx300, vwx301), @2(vwx400, vwx401), eh, app(app(ty_@2, fc), fd)) → new_esEs0(vwx301, vwx401, fc, fd)
new_esEs(Left(vwx300), Left(vwx400), app(app(ty_Either, ba), bb), bc) → new_esEs(vwx300, vwx400, ba, bb)
new_esEs0(@2(vwx300, vwx301), @2(vwx400, vwx401), eh, app(ty_[], ga)) → new_esEs2(vwx301, vwx401, ga)

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

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



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

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

new_ltEs0(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), app(ty_[], bc), bd, be) → new_compare0(vwx90, vwx100, bc)
new_compare2(Right(vwx90), Right(vwx100), False, app(app(ty_Either, hf), app(app(ty_@2, baf), bag)), bb) → new_ltEs3(vwx90, vwx100, baf, bag)
new_compare2(@2(vwx90, vwx91), @2(vwx100, vwx101), False, app(app(ty_@2, bcb), app(app(app(ty_@3, bcd), bce), bcf)), bb) → new_ltEs0(vwx91, vwx101, bcd, bce, bcf)
new_ltEs0(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), app(app(app(ty_@3, bf), bg), bh), bd, be) → new_compare20(vwx90, vwx100, new_esEs4(vwx90, vwx100, bf, bg, bh), bf, bg, bh)
new_ltEs3(@2(vwx90, vwx91), @2(vwx100, vwx101), app(app(ty_Either, bbf), bbg), bba) → new_lt2(vwx90, vwx100, bbf, bbg)
new_ltEs3(@2(vwx90, vwx91), @2(vwx100, vwx101), app(ty_[], bah), bba) → new_lt(vwx90, vwx100, bah)
new_compare0(:(vwx90, vwx91), :(vwx100, vwx101), ba) → new_compare0(vwx91, vwx101, ba)
new_ltEs2(Left(vwx90), Left(vwx100), app(app(ty_Either, hb), hc), ge) → new_ltEs2(vwx90, vwx100, hb, hc)
new_compare2(Right(vwx90), Right(vwx100), False, app(app(ty_Either, hf), app(ty_[], hg)), bb) → new_ltEs(vwx90, vwx100, hg)
new_compare2(Just(vwx90), Just(vwx100), False, app(ty_Maybe, app(ty_Maybe, fg)), bb) → new_ltEs1(vwx90, vwx100, fg)
new_compare2(Right(vwx90), Right(vwx100), False, app(app(ty_Either, hf), app(ty_Maybe, bac)), bb) → new_ltEs1(vwx90, vwx100, bac)
new_compare2(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), False, app(app(app(ty_@3, cf), bd), app(ty_[], ea)), bb) → new_ltEs(vwx92, vwx102, ea)
new_compare3(vwx90, vwx100, bf, bg, bh) → new_compare20(vwx90, vwx100, new_esEs4(vwx90, vwx100, bf, bg, bh), bf, bg, bh)
new_compare2(@2(vwx90, vwx91), @2(vwx100, vwx101), False, app(app(ty_@2, app(ty_Maybe, bbe)), bba), bb) → new_lt1(vwx90, vwx100, bbe)
new_lt3(vwx90, vwx100, cd, ce) → new_compare22(vwx90, vwx100, new_esEs6(vwx90, vwx100, cd, ce), cd, ce)
new_ltEs0(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), cf, bd, app(app(ty_@2, eh), fa)) → new_ltEs3(vwx92, vwx102, eh, fa)
new_lt1(vwx90, vwx100, ca) → new_compare21(vwx90, vwx100, new_esEs5(vwx90, vwx100, ca), ca)
new_compare2(Just(vwx90), Just(vwx100), False, app(ty_Maybe, app(ty_[], fb)), bb) → new_ltEs(vwx90, vwx100, fb)
new_ltEs0(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), app(ty_Maybe, ca), bd, be) → new_compare21(vwx90, vwx100, new_esEs5(vwx90, vwx100, ca), ca)
new_ltEs3(@2(vwx90, vwx91), @2(vwx100, vwx101), app(ty_Maybe, bbe), bba) → new_lt1(vwx90, vwx100, bbe)
new_ltEs0(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), cf, bd, app(ty_Maybe, ee)) → new_ltEs1(vwx92, vwx102, ee)
new_compare2(@2(vwx90, vwx91), @2(vwx100, vwx101), False, app(app(ty_@2, bcb), app(app(ty_Either, bch), bda)), bb) → new_ltEs2(vwx91, vwx101, bch, bda)
new_compare2(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), False, app(app(app(ty_@3, cf), bd), app(app(ty_Either, ef), eg)), bb) → new_ltEs2(vwx92, vwx102, ef, eg)
new_ltEs1(Just(vwx90), Just(vwx100), app(ty_[], fb)) → new_ltEs(vwx90, vwx100, fb)
new_ltEs3(@2(vwx90, vwx91), @2(vwx100, vwx101), bcb, app(app(app(ty_@3, bcd), bce), bcf)) → new_ltEs0(vwx91, vwx101, bcd, bce, bcf)
new_ltEs3(@2(vwx90, vwx91), @2(vwx100, vwx101), bcb, app(app(ty_@2, bdb), bdc)) → new_ltEs3(vwx91, vwx101, bdb, bdc)
new_ltEs2(Right(vwx90), Right(vwx100), hf, app(app(ty_@2, baf), bag)) → new_ltEs3(vwx90, vwx100, baf, bag)
new_ltEs2(Left(vwx90), Left(vwx100), app(ty_Maybe, ha), ge) → new_ltEs1(vwx90, vwx100, ha)
new_compare2(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), False, app(app(app(ty_@3, cf), app(app(ty_Either, de), df)), be), bb) → new_lt2(vwx91, vwx101, de, df)
new_compare23(vwx16, vwx17, False, beg, app(app(app(ty_@3, bfa), bfb), bfc)) → new_ltEs0(vwx16, vwx17, bfa, bfb, bfc)
new_ltEs0(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), cf, bd, app(app(app(ty_@3, eb), ec), ed)) → new_ltEs0(vwx92, vwx102, eb, ec, ed)
new_ltEs3(@2(vwx90, vwx91), @2(vwx100, vwx101), app(app(ty_@2, bbh), bca), bba) → new_lt3(vwx90, vwx100, bbh, bca)
new_compare2(:(vwx90, vwx91), :(vwx100, vwx101), False, app(ty_[], ba), bb) → new_compare0(vwx91, vwx101, ba)
new_compare2(@2(vwx90, vwx91), @2(vwx100, vwx101), False, app(app(ty_@2, app(ty_[], bah)), bba), bb) → new_lt(vwx90, vwx100, bah)
new_primCompAux(vwx90, vwx100, vwx54, app(app(app(ty_@3, bde), bdf), bdg)) → new_compare3(vwx90, vwx100, bde, bdf, bdg)
new_ltEs1(Just(vwx90), Just(vwx100), app(app(ty_Either, fh), ga)) → new_ltEs2(vwx90, vwx100, fh, ga)
new_compare2(Right(vwx90), Right(vwx100), False, app(app(ty_Either, hf), app(app(ty_Either, bad), bae)), bb) → new_ltEs2(vwx90, vwx100, bad, bae)
new_ltEs0(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), app(app(ty_Either, cb), cc), bd, be) → new_compare1(vwx90, vwx100, cb, cc)
new_compare2(@2(vwx90, vwx91), @2(vwx100, vwx101), False, app(app(ty_@2, app(app(ty_@2, bbh), bca)), bba), bb) → new_lt3(vwx90, vwx100, bbh, bca)
new_ltEs3(@2(vwx90, vwx91), @2(vwx100, vwx101), bcb, app(app(ty_Either, bch), bda)) → new_ltEs2(vwx91, vwx101, bch, bda)
new_compare23(vwx16, vwx17, False, beg, app(app(ty_@2, bfg), bfh)) → new_ltEs3(vwx16, vwx17, bfg, bfh)
new_compare2(Just(vwx90), Just(vwx100), False, app(ty_Maybe, app(app(ty_@2, gb), gc)), bb) → new_ltEs3(vwx90, vwx100, gb, gc)
new_compare20(vwx90, vwx100, False, bf, bg, bh) → new_ltEs0(vwx90, vwx100, bf, bg, bh)
new_ltEs2(Left(vwx90), Left(vwx100), app(app(app(ty_@3, gf), gg), gh), ge) → new_ltEs0(vwx90, vwx100, gf, gg, gh)
new_compare5(vwx90, vwx100, cd, ce) → new_compare22(vwx90, vwx100, new_esEs6(vwx90, vwx100, cd, ce), cd, ce)
new_compare2(Just(vwx90), Just(vwx100), False, app(ty_Maybe, app(app(app(ty_@3, fc), fd), ff)), bb) → new_ltEs0(vwx90, vwx100, fc, fd, ff)
new_compare2(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), False, app(app(app(ty_@3, cf), app(ty_[], cg)), be), bb) → new_lt(vwx91, vwx101, cg)
new_compare2(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), False, app(app(app(ty_@3, app(ty_Maybe, ca)), bd), be), bb) → new_compare21(vwx90, vwx100, new_esEs5(vwx90, vwx100, ca), ca)
new_compare4(vwx90, vwx100, ca) → new_compare21(vwx90, vwx100, new_esEs5(vwx90, vwx100, ca), ca)
new_primCompAux(vwx90, vwx100, vwx54, app(app(ty_@2, bec), bed)) → new_compare5(vwx90, vwx100, bec, bed)
new_compare2(@2(vwx90, vwx91), @2(vwx100, vwx101), False, app(app(ty_@2, bcb), app(ty_Maybe, bcg)), bb) → new_ltEs1(vwx91, vwx101, bcg)
new_compare1(Left(vwx30), Left(vwx40), bee, bef) → new_compare2(vwx30, vwx40, new_esEs7(vwx30, vwx40, bee), bee, bef)
new_compare22(vwx90, vwx100, False, cd, ce) → new_ltEs3(vwx90, vwx100, cd, ce)
new_compare0(:(vwx90, vwx91), :(vwx100, vwx101), ba) → new_primCompAux(vwx90, vwx100, new_compare(vwx91, vwx101, ba), ba)
new_compare2(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), False, app(app(app(ty_@3, cf), app(app(ty_@2, dg), dh)), be), bb) → new_lt3(vwx91, vwx101, dg, dh)
new_compare23(vwx16, vwx17, False, beg, app(ty_Maybe, bfd)) → new_ltEs1(vwx16, vwx17, bfd)
new_compare2(@2(vwx90, vwx91), @2(vwx100, vwx101), False, app(app(ty_@2, app(app(ty_Either, bbf), bbg)), bba), bb) → new_lt2(vwx90, vwx100, bbf, bbg)
new_lt0(vwx90, vwx100, bf, bg, bh) → new_compare20(vwx90, vwx100, new_esEs4(vwx90, vwx100, bf, bg, bh), bf, bg, bh)
new_compare2(@2(vwx90, vwx91), @2(vwx100, vwx101), False, app(app(ty_@2, bcb), app(ty_[], bcc)), bb) → new_ltEs(vwx91, vwx101, bcc)
new_compare23(vwx16, vwx17, False, beg, app(ty_[], beh)) → new_ltEs(vwx16, vwx17, beh)
new_ltEs0(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), cf, app(app(ty_@2, dg), dh), be) → new_lt3(vwx91, vwx101, dg, dh)
new_compare2(Left(vwx90), Left(vwx100), False, app(app(ty_Either, app(ty_[], gd)), ge), bb) → new_ltEs(vwx90, vwx100, gd)
new_ltEs1(Just(vwx90), Just(vwx100), app(ty_Maybe, fg)) → new_ltEs1(vwx90, vwx100, fg)
new_ltEs2(Right(vwx90), Right(vwx100), hf, app(ty_[], hg)) → new_ltEs(vwx90, vwx100, hg)
new_compare2(Right(vwx90), Right(vwx100), False, app(app(ty_Either, hf), app(app(app(ty_@3, hh), baa), bab)), bb) → new_ltEs0(vwx90, vwx100, hh, baa, bab)
new_ltEs0(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), cf, app(app(ty_Either, de), df), be) → new_lt2(vwx91, vwx101, de, df)
new_compare2(Left(vwx90), Left(vwx100), False, app(app(ty_Either, app(app(ty_Either, hb), hc)), ge), bb) → new_ltEs2(vwx90, vwx100, hb, hc)
new_ltEs1(Just(vwx90), Just(vwx100), app(app(app(ty_@3, fc), fd), ff)) → new_ltEs0(vwx90, vwx100, fc, fd, ff)
new_ltEs2(Right(vwx90), Right(vwx100), hf, app(app(app(ty_@3, hh), baa), bab)) → new_ltEs0(vwx90, vwx100, hh, baa, bab)
new_ltEs2(Left(vwx90), Left(vwx100), app(app(ty_@2, hd), he), ge) → new_ltEs3(vwx90, vwx100, hd, he)
new_ltEs(:(vwx90, vwx91), :(vwx100, vwx101), ba) → new_primCompAux(vwx90, vwx100, new_compare(vwx91, vwx101, ba), ba)
new_ltEs0(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), cf, app(ty_[], cg), be) → new_lt(vwx91, vwx101, cg)
new_primCompAux(vwx90, vwx100, vwx54, app(ty_[], bdd)) → new_compare0(vwx90, vwx100, bdd)
new_compare2(Left(vwx90), Left(vwx100), False, app(app(ty_Either, app(app(ty_@2, hd), he)), ge), bb) → new_ltEs3(vwx90, vwx100, hd, he)
new_ltEs0(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), cf, app(app(app(ty_@3, da), db), dc), be) → new_lt0(vwx91, vwx101, da, db, dc)
new_compare23(vwx16, vwx17, False, beg, app(app(ty_Either, bfe), bff)) → new_ltEs2(vwx16, vwx17, bfe, bff)
new_compare2(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), False, app(app(app(ty_@3, cf), app(ty_Maybe, dd)), be), bb) → new_lt1(vwx91, vwx101, dd)
new_compare2(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), False, app(app(app(ty_@3, app(app(ty_Either, cb), cc)), bd), be), bb) → new_compare1(vwx90, vwx100, cb, cc)
new_compare2(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), False, app(app(app(ty_@3, cf), app(app(app(ty_@3, da), db), dc)), be), bb) → new_lt0(vwx91, vwx101, da, db, dc)
new_ltEs0(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), cf, bd, app(ty_[], ea)) → new_ltEs(vwx92, vwx102, ea)
new_compare2(Left(vwx90), Left(vwx100), False, app(app(ty_Either, app(app(app(ty_@3, gf), gg), gh)), ge), bb) → new_ltEs0(vwx90, vwx100, gf, gg, gh)
new_lt2(vwx90, vwx100, cb, cc) → new_compare1(vwx90, vwx100, cb, cc)
new_primCompAux(vwx90, vwx100, vwx54, app(app(ty_Either, bea), beb)) → new_compare1(vwx90, vwx100, bea, beb)
new_compare2(:(vwx90, vwx91), :(vwx100, vwx101), False, app(ty_[], ba), bb) → new_primCompAux(vwx90, vwx100, new_compare(vwx91, vwx101, ba), ba)
new_ltEs2(Right(vwx90), Right(vwx100), hf, app(app(ty_Either, bad), bae)) → new_ltEs2(vwx90, vwx100, bad, bae)
new_compare2(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), False, app(app(app(ty_@3, app(app(ty_@2, cd), ce)), bd), be), bb) → new_compare22(vwx90, vwx100, new_esEs6(vwx90, vwx100, cd, ce), cd, ce)
new_ltEs0(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), cf, bd, app(app(ty_Either, ef), eg)) → new_ltEs2(vwx92, vwx102, ef, eg)
new_compare2(Just(vwx90), Just(vwx100), False, app(ty_Maybe, app(app(ty_Either, fh), ga)), bb) → new_ltEs2(vwx90, vwx100, fh, ga)
new_compare2(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), False, app(app(app(ty_@3, cf), bd), app(ty_Maybe, ee)), bb) → new_ltEs1(vwx92, vwx102, ee)
new_compare2(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), False, app(app(app(ty_@3, app(app(app(ty_@3, bf), bg), bh)), bd), be), bb) → new_compare20(vwx90, vwx100, new_esEs4(vwx90, vwx100, bf, bg, bh), bf, bg, bh)
new_ltEs(:(vwx90, vwx91), :(vwx100, vwx101), ba) → new_compare0(vwx91, vwx101, ba)
new_compare2(@2(vwx90, vwx91), @2(vwx100, vwx101), False, app(app(ty_@2, bcb), app(app(ty_@2, bdb), bdc)), bb) → new_ltEs3(vwx91, vwx101, bdb, bdc)
new_compare2(@2(vwx90, vwx91), @2(vwx100, vwx101), False, app(app(ty_@2, app(app(app(ty_@3, bbb), bbc), bbd)), bba), bb) → new_lt0(vwx90, vwx100, bbb, bbc, bbd)
new_compare2(Left(vwx90), Left(vwx100), False, app(app(ty_Either, app(ty_Maybe, ha)), ge), bb) → new_ltEs1(vwx90, vwx100, ha)
new_compare1(Right(vwx30), Right(vwx40), bee, bef) → new_compare23(vwx30, vwx40, new_esEs8(vwx30, vwx40, bef), bee, bef)
new_ltEs3(@2(vwx90, vwx91), @2(vwx100, vwx101), bcb, app(ty_Maybe, bcg)) → new_ltEs1(vwx91, vwx101, bcg)
new_lt(vwx90, vwx100, bc) → new_compare0(vwx90, vwx100, bc)
new_primCompAux(vwx90, vwx100, vwx54, app(ty_Maybe, bdh)) → new_compare4(vwx90, vwx100, bdh)
new_ltEs3(@2(vwx90, vwx91), @2(vwx100, vwx101), bcb, app(ty_[], bcc)) → new_ltEs(vwx91, vwx101, bcc)
new_ltEs2(Left(vwx90), Left(vwx100), app(ty_[], gd), ge) → new_ltEs(vwx90, vwx100, gd)
new_ltEs0(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), cf, app(ty_Maybe, dd), be) → new_lt1(vwx91, vwx101, dd)
new_ltEs1(Just(vwx90), Just(vwx100), app(app(ty_@2, gb), gc)) → new_ltEs3(vwx90, vwx100, gb, gc)
new_compare2(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), False, app(app(app(ty_@3, cf), bd), app(app(ty_@2, eh), fa)), bb) → new_ltEs3(vwx92, vwx102, eh, fa)
new_compare2(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), False, app(app(app(ty_@3, cf), bd), app(app(app(ty_@3, eb), ec), ed)), bb) → new_ltEs0(vwx92, vwx102, eb, ec, ed)
new_ltEs3(@2(vwx90, vwx91), @2(vwx100, vwx101), app(app(app(ty_@3, bbb), bbc), bbd), bba) → new_lt0(vwx90, vwx100, bbb, bbc, bbd)
new_compare2(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), False, app(app(app(ty_@3, app(ty_[], bc)), bd), be), bb) → new_compare0(vwx90, vwx100, bc)
new_compare21(vwx90, vwx100, False, ca) → new_ltEs1(vwx90, vwx100, ca)
new_ltEs2(Right(vwx90), Right(vwx100), hf, app(ty_Maybe, bac)) → new_ltEs1(vwx90, vwx100, bac)
new_ltEs0(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), app(app(ty_@2, cd), ce), bd, be) → new_compare22(vwx90, vwx100, new_esEs6(vwx90, vwx100, cd, ce), cd, ce)

The TRS R consists of the following rules:

new_ltEs7(Left(vwx90), Left(vwx100), app(ty_Maybe, ha), ge) → new_ltEs13(vwx90, vwx100, ha)
new_esEs26(vwx302, vwx402, ty_@0) → new_esEs15(vwx302, vwx402)
new_ltEs19(vwx16, vwx17, app(ty_[], beh)) → new_ltEs8(vwx16, vwx17, beh)
new_esEs29(vwx301, vwx401, ty_Int) → new_esEs16(vwx301, vwx401)
new_ltEs16(@2(vwx90, vwx91), @2(vwx100, vwx101), bcb, bba) → new_pePe(new_lt20(vwx90, vwx100, bcb), new_asAs(new_esEs30(vwx90, vwx100, bcb), new_ltEs21(vwx91, vwx101, bba)))
new_esEs21(vwx91, vwx101, app(app(ty_@2, dg), dh)) → new_esEs6(vwx91, vwx101, dg, dh)
new_ltEs7(Left(vwx90), Left(vwx100), ty_Ordering, ge) → new_ltEs14(vwx90, vwx100)
new_esEs10(Right(vwx300), Right(vwx400), bhf, app(ty_[], cag)) → new_esEs12(vwx300, vwx400, cag)
new_ltEs13(Just(vwx90), Just(vwx100), ty_Bool) → new_ltEs9(vwx90, vwx100)
new_lt7(vwx90, vwx100, ty_Char) → new_lt4(vwx90, vwx100)
new_esEs20(vwx90, vwx100, ty_Double) → new_esEs19(vwx90, vwx100)
new_esEs9(GT, LT) → False
new_esEs9(LT, GT) → False
new_compare27(vwx90, vwx100, False, bf, bg, bh) → new_compare15(vwx90, vwx100, new_ltEs11(vwx90, vwx100, bf, bg, bh), bf, bg, bh)
new_ltEs7(Left(vwx90), Left(vwx100), ty_@0, ge) → new_ltEs10(vwx90, vwx100)
new_ltEs14(GT, GT) → True
new_ltEs18(vwx92, vwx102, ty_Float) → new_ltEs15(vwx92, vwx102)
new_compare([], :(vwx100, vwx101), ba) → LT
new_ltEs20(vwx9, vwx10, ty_Int) → new_ltEs4(vwx9, vwx10)
new_ltEs21(vwx91, vwx101, ty_Bool) → new_ltEs9(vwx91, vwx101)
new_esEs19(Double(vwx300, vwx301), Double(vwx400, vwx401)) → new_esEs16(new_sr(vwx300, vwx400), new_sr(vwx301, vwx401))
new_compare211(vwx90, vwx100, False, ca) → new_compare11(vwx90, vwx100, new_ltEs13(vwx90, vwx100, ca), ca)
new_esEs22(vwx300, vwx400, ty_Ordering) → new_esEs9(vwx300, vwx400)
new_esEs27(vwx300, vwx400, ty_Bool) → new_esEs17(vwx300, vwx400)
new_primMulNat0(Zero, Zero) → Zero
new_ltEs7(Left(vwx90), Right(vwx100), hf, ge) → True
new_esEs10(Left(vwx300), Left(vwx400), ty_Double, bgc) → new_esEs19(vwx300, vwx400)
new_esEs7(vwx30, vwx40, ty_Integer) → new_esEs14(vwx30, vwx40)
new_compare32(Left(vwx30), Right(vwx40), bee, bef) → LT
new_compare(:(vwx90, vwx91), [], ba) → GT
new_esEs27(vwx300, vwx400, app(app(app(ty_@3, dcb), dcc), dcd)) → new_esEs4(vwx300, vwx400, dcb, dcc, dcd)
new_esEs10(Left(vwx300), Left(vwx400), ty_Bool, bgc) → new_esEs17(vwx300, vwx400)
new_compare210(vwx9, vwx10, False, dcg, bb) → new_compare18(vwx9, vwx10, new_ltEs20(vwx9, vwx10, dcg), dcg, bb)
new_compare33(vwx90, vwx100, ty_Float) → new_compare16(vwx90, vwx100)
new_ltEs21(vwx91, vwx101, app(ty_Maybe, bcg)) → new_ltEs13(vwx91, vwx101, bcg)
new_ltEs13(Nothing, Just(vwx100), dag) → True
new_compare9(Double(vwx90, vwx91), Double(vwx100, vwx101)) → new_compare6(new_sr(vwx90, vwx100), new_sr(vwx91, vwx101))
new_esEs21(vwx91, vwx101, ty_Bool) → new_esEs17(vwx91, vwx101)
new_lt20(vwx90, vwx100, app(ty_Maybe, bbe)) → new_lt13(vwx90, vwx100, bbe)
new_compare32(Right(vwx30), Left(vwx40), bee, bef) → GT
new_ltEs20(vwx9, vwx10, app(ty_Maybe, dag)) → new_ltEs13(vwx9, vwx10, dag)
new_esEs25(vwx301, vwx401, ty_Bool) → new_esEs17(vwx301, vwx401)
new_esEs30(vwx90, vwx100, app(ty_Ratio, ded)) → new_esEs11(vwx90, vwx100, ded)
new_ltEs9(True, False) → False
new_lt7(vwx90, vwx100, app(app(app(ty_@3, bf), bg), bh)) → new_lt11(vwx90, vwx100, bf, bg, bh)
new_ltEs21(vwx91, vwx101, app(app(ty_@2, bdb), bdc)) → new_ltEs16(vwx91, vwx101, bdb, bdc)
new_ltEs19(vwx16, vwx17, ty_Double) → new_ltEs6(vwx16, vwx17)
new_lt5(vwx90, vwx100) → new_esEs9(new_compare8(vwx90, vwx100), LT)
new_compare28(vwx90, vwx100, False) → new_compare13(vwx90, vwx100, new_ltEs14(vwx90, vwx100))
new_ltEs20(vwx9, vwx10, app(app(app(ty_@3, cf), bd), be)) → new_ltEs11(vwx9, vwx10, cf, bd, be)
new_esEs17(True, True) → True
new_esEs12([], [], dbd) → True
new_ltEs18(vwx92, vwx102, app(ty_[], ea)) → new_ltEs8(vwx92, vwx102, ea)
new_lt7(vwx90, vwx100, ty_Int) → new_lt14(vwx90, vwx100)
new_ltEs10(vwx9, vwx10) → new_not(new_esEs9(new_compare14(vwx9, vwx10), GT))
new_esEs5(Just(vwx300), Just(vwx400), app(ty_Maybe, dfh)) → new_esEs5(vwx300, vwx400, dfh)
new_esEs8(vwx30, vwx40, app(app(app(ty_@3, ddg), ddh), dea)) → new_esEs4(vwx30, vwx40, ddg, ddh, dea)
new_esEs26(vwx302, vwx402, ty_Float) → new_esEs18(vwx302, vwx402)
new_lt18(vwx90, vwx100, cd, ce) → new_esEs9(new_compare17(vwx90, vwx100, cd, ce), LT)
new_esEs10(Left(vwx300), Left(vwx400), app(ty_Ratio, bgh), bgc) → new_esEs11(vwx300, vwx400, bgh)
new_ltEs18(vwx92, vwx102, ty_Int) → new_ltEs4(vwx92, vwx102)
new_lt11(vwx90, vwx100, bf, bg, bh) → new_esEs9(new_compare29(vwx90, vwx100, bf, bg, bh), LT)
new_esEs26(vwx302, vwx402, ty_Char) → new_esEs13(vwx302, vwx402)
new_esEs26(vwx302, vwx402, ty_Integer) → new_esEs14(vwx302, vwx402)
new_esEs20(vwx90, vwx100, app(app(ty_@2, cd), ce)) → new_esEs6(vwx90, vwx100, cd, ce)
new_lt20(vwx90, vwx100, ty_Ordering) → new_lt15(vwx90, vwx100)
new_ltEs19(vwx16, vwx17, ty_Bool) → new_ltEs9(vwx16, vwx17)
new_compare33(vwx90, vwx100, ty_Double) → new_compare9(vwx90, vwx100)
new_esEs24(vwx300, vwx400, app(ty_[], cga)) → new_esEs12(vwx300, vwx400, cga)
new_esEs10(Left(vwx300), Right(vwx400), bhf, bgc) → False
new_esEs10(Right(vwx300), Left(vwx400), bhf, bgc) → False
new_lt20(vwx90, vwx100, ty_Char) → new_lt4(vwx90, vwx100)
new_pePe(False, vwx53) → vwx53
new_esEs12([], :(vwx400, vwx401), dbd) → False
new_esEs12(:(vwx300, vwx301), [], dbd) → False
new_esEs7(vwx30, vwx40, app(app(ty_@2, cbh), cca)) → new_esEs6(vwx30, vwx40, cbh, cca)
new_esEs10(Left(vwx300), Left(vwx400), app(ty_[], bhd), bgc) → new_esEs12(vwx300, vwx400, bhd)
new_compare33(vwx90, vwx100, ty_Char) → new_compare7(vwx90, vwx100)
new_esEs10(Left(vwx300), Left(vwx400), ty_Int, bgc) → new_esEs16(vwx300, vwx400)
new_esEs20(vwx90, vwx100, ty_Int) → new_esEs16(vwx90, vwx100)
new_ltEs20(vwx9, vwx10, ty_@0) → new_ltEs10(vwx9, vwx10)
new_ltEs14(GT, EQ) → False
new_esEs27(vwx300, vwx400, ty_Ordering) → new_esEs9(vwx300, vwx400)
new_esEs22(vwx300, vwx400, app(app(ty_Either, ccb), ccc)) → new_esEs10(vwx300, vwx400, ccb, ccc)
new_esEs22(vwx300, vwx400, ty_@0) → new_esEs15(vwx300, vwx400)
new_compare14(@0, @0) → EQ
new_compare33(vwx90, vwx100, ty_@0) → new_compare14(vwx90, vwx100)
new_esEs25(vwx301, vwx401, app(app(ty_Either, cgc), cgd)) → new_esEs10(vwx301, vwx401, cgc, cgd)
new_ltEs7(Right(vwx90), Right(vwx100), hf, app(ty_Ratio, cbb)) → new_ltEs17(vwx90, vwx100, cbb)
new_ltEs20(vwx9, vwx10, ty_Integer) → new_ltEs12(vwx9, vwx10)
new_esEs9(GT, EQ) → False
new_esEs9(EQ, GT) → False
new_ltEs7(Right(vwx90), Right(vwx100), hf, ty_Char) → new_ltEs5(vwx90, vwx100)
new_esEs5(Just(vwx300), Just(vwx400), app(ty_[], dfg)) → new_esEs12(vwx300, vwx400, dfg)
new_lt8(vwx91, vwx101, ty_Integer) → new_lt12(vwx91, vwx101)
new_esEs14(Integer(vwx300), Integer(vwx400)) → new_primEqInt(vwx300, vwx400)
new_lt8(vwx91, vwx101, ty_Int) → new_lt14(vwx91, vwx101)
new_compare19(:%(vwx90, vwx91), :%(vwx100, vwx101), ty_Int) → new_compare6(new_sr(vwx90, vwx101), new_sr(vwx100, vwx91))
new_compare15(vwx90, vwx100, False, bf, bg, bh) → GT
new_compare24(vwx16, vwx17, False, beg, cbf) → new_compare12(vwx16, vwx17, new_ltEs19(vwx16, vwx17, cbf), beg, cbf)
new_primCmpNat0(Zero, Succ(vwx1000)) → LT
new_ltEs13(Nothing, Nothing, dag) → True
new_esEs21(vwx91, vwx101, ty_Char) → new_esEs13(vwx91, vwx101)
new_ltEs19(vwx16, vwx17, ty_Float) → new_ltEs15(vwx16, vwx17)
new_esEs10(Right(vwx300), Right(vwx400), bhf, app(ty_Maybe, cah)) → new_esEs5(vwx300, vwx400, cah)
new_esEs21(vwx91, vwx101, ty_Double) → new_esEs19(vwx91, vwx101)
new_esEs25(vwx301, vwx401, app(app(ty_@2, cge), cgf)) → new_esEs6(vwx301, vwx401, cge, cgf)
new_esEs30(vwx90, vwx100, ty_Float) → new_esEs18(vwx90, vwx100)
new_ltEs13(Just(vwx90), Just(vwx100), ty_@0) → new_ltEs10(vwx90, vwx100)
new_esEs10(Right(vwx300), Right(vwx400), bhf, app(app(ty_@2, caa), cab)) → new_esEs6(vwx300, vwx400, caa, cab)
new_esEs23(vwx301, vwx401, ty_Double) → new_esEs19(vwx301, vwx401)
new_esEs10(Right(vwx300), Right(vwx400), bhf, ty_Char) → new_esEs13(vwx300, vwx400)
new_ltEs7(Left(vwx90), Left(vwx100), ty_Double, ge) → new_ltEs6(vwx90, vwx100)
new_ltEs21(vwx91, vwx101, ty_Ordering) → new_ltEs14(vwx91, vwx101)
new_esEs10(Right(vwx300), Right(vwx400), bhf, ty_Float) → new_esEs18(vwx300, vwx400)
new_esEs8(vwx30, vwx40, app(app(ty_@2, ddd), dde)) → new_esEs6(vwx30, vwx40, ddd, dde)
new_pePe(True, vwx53) → True
new_esEs24(vwx300, vwx400, app(app(ty_@2, cfc), cfd)) → new_esEs6(vwx300, vwx400, cfc, cfd)
new_primEqNat0(Zero, Zero) → True
new_esEs24(vwx300, vwx400, ty_Int) → new_esEs16(vwx300, vwx400)
new_lt19(vwx90, vwx100, cbc) → new_esEs9(new_compare19(vwx90, vwx100, cbc), LT)
new_esEs4(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), cef, ceg, ceh) → new_asAs(new_esEs24(vwx300, vwx400, cef), new_asAs(new_esEs25(vwx301, vwx401, ceg), new_esEs26(vwx302, vwx402, ceh)))
new_ltEs21(vwx91, vwx101, ty_@0) → new_ltEs10(vwx91, vwx101)
new_esEs8(vwx30, vwx40, ty_Integer) → new_esEs14(vwx30, vwx40)
new_ltEs7(Right(vwx90), Right(vwx100), hf, app(ty_[], hg)) → new_ltEs8(vwx90, vwx100, hg)
new_compare11(vwx90, vwx100, True, ca) → LT
new_lt12(vwx90, vwx100) → new_esEs9(new_compare10(vwx90, vwx100), LT)
new_compare111(vwx90, vwx100, False, cd, ce) → GT
new_ltEs21(vwx91, vwx101, app(app(app(ty_@3, bcd), bce), bcf)) → new_ltEs11(vwx91, vwx101, bcd, bce, bcf)
new_ltEs12(vwx9, vwx10) → new_not(new_esEs9(new_compare10(vwx9, vwx10), GT))
new_ltEs5(vwx9, vwx10) → new_not(new_esEs9(new_compare7(vwx9, vwx10), GT))
new_lt20(vwx90, vwx100, app(ty_[], bah)) → new_lt9(vwx90, vwx100, bah)
new_lt8(vwx91, vwx101, app(ty_[], cg)) → new_lt9(vwx91, vwx101, cg)
new_esEs27(vwx300, vwx400, ty_Char) → new_esEs13(vwx300, vwx400)
new_esEs17(False, False) → True
new_esEs17(True, False) → False
new_esEs17(False, True) → False
new_esEs7(vwx30, vwx40, ty_Ordering) → new_esEs9(vwx30, vwx40)
new_compare(:(vwx90, vwx91), :(vwx100, vwx101), ba) → new_primCompAux1(vwx90, vwx100, new_compare(vwx91, vwx101, ba), ba)
new_ltEs14(EQ, LT) → False
new_sr(vwx300, vwx400) → new_primMulInt(vwx300, vwx400)
new_esEs24(vwx300, vwx400, ty_Bool) → new_esEs17(vwx300, vwx400)
new_esEs5(Just(vwx300), Just(vwx400), ty_Integer) → new_esEs14(vwx300, vwx400)
new_compare12(vwx30, vwx31, False, bga, bgb) → GT
new_esEs30(vwx90, vwx100, ty_Bool) → new_esEs17(vwx90, vwx100)
new_esEs10(Right(vwx300), Right(vwx400), bhf, ty_Ordering) → new_esEs9(vwx300, vwx400)
new_ltEs8(vwx9, vwx10, ba) → new_not(new_esEs9(new_compare(vwx9, vwx10, ba), GT))
new_esEs30(vwx90, vwx100, app(app(app(ty_@3, bbb), bbc), bbd)) → new_esEs4(vwx90, vwx100, bbb, bbc, bbd)
new_esEs11(:%(vwx300, vwx301), :%(vwx400, vwx401), dch) → new_asAs(new_esEs28(vwx300, vwx400, dch), new_esEs29(vwx301, vwx401, dch))
new_primPlusNat0(Succ(vwx550), vwx40000) → Succ(Succ(new_primPlusNat1(vwx550, vwx40000)))
new_esEs30(vwx90, vwx100, ty_Char) → new_esEs13(vwx90, vwx100)
new_esEs20(vwx90, vwx100, ty_Bool) → new_esEs17(vwx90, vwx100)
new_esEs26(vwx302, vwx402, app(app(app(ty_@3, dab), dac), dad)) → new_esEs4(vwx302, vwx402, dab, dac, dad)
new_esEs21(vwx91, vwx101, ty_Ordering) → new_esEs9(vwx91, vwx101)
new_lt20(vwx90, vwx100, app(app(ty_Either, bbf), bbg)) → new_lt17(vwx90, vwx100, bbf, bbg)
new_esEs8(vwx30, vwx40, ty_Bool) → new_esEs17(vwx30, vwx40)
new_ltEs7(Right(vwx90), Right(vwx100), hf, ty_Double) → new_ltEs6(vwx90, vwx100)
new_esEs9(EQ, EQ) → True
new_ltEs7(Right(vwx90), Right(vwx100), hf, app(app(ty_@2, baf), bag)) → new_ltEs16(vwx90, vwx100, baf, bag)
new_esEs25(vwx301, vwx401, app(ty_[], chc)) → new_esEs12(vwx301, vwx401, chc)
new_lt20(vwx90, vwx100, app(app(ty_@2, bbh), bca)) → new_lt18(vwx90, vwx100, bbh, bca)
new_compare211(vwx90, vwx100, True, ca) → EQ
new_primEqInt(Neg(Succ(vwx3000)), Neg(Succ(vwx4000))) → new_primEqNat0(vwx3000, vwx4000)
new_compare25(vwx90, vwx100, True) → EQ
new_esEs24(vwx300, vwx400, app(ty_Ratio, cfe)) → new_esEs11(vwx300, vwx400, cfe)
new_esEs8(vwx30, vwx40, ty_Float) → new_esEs18(vwx30, vwx40)
new_ltEs18(vwx92, vwx102, app(app(ty_Either, ef), eg)) → new_ltEs7(vwx92, vwx102, ef, eg)
new_ltEs7(Left(vwx90), Left(vwx100), app(app(ty_@2, hd), he), ge) → new_ltEs16(vwx90, vwx100, hd, he)
new_esEs20(vwx90, vwx100, ty_Float) → new_esEs18(vwx90, vwx100)
new_lt8(vwx91, vwx101, ty_Char) → new_lt4(vwx91, vwx101)
new_primPlusNat1(Succ(vwx5500), Zero) → Succ(vwx5500)
new_primPlusNat1(Zero, Succ(vwx400000)) → Succ(vwx400000)
new_compare33(vwx90, vwx100, ty_Int) → new_compare6(vwx90, vwx100)
new_ltEs19(vwx16, vwx17, app(ty_Ratio, cbg)) → new_ltEs17(vwx16, vwx17, cbg)
new_esEs5(Just(vwx300), Just(vwx400), ty_@0) → new_esEs15(vwx300, vwx400)
new_compare13(vwx90, vwx100, False) → GT
new_esEs8(vwx30, vwx40, ty_@0) → new_esEs15(vwx30, vwx40)
new_lt8(vwx91, vwx101, app(app(app(ty_@3, da), db), dc)) → new_lt11(vwx91, vwx101, da, db, dc)
new_esEs16(vwx30, vwx40) → new_primEqInt(vwx30, vwx40)
new_esEs21(vwx91, vwx101, ty_@0) → new_esEs15(vwx91, vwx101)
new_lt8(vwx91, vwx101, ty_Float) → new_lt16(vwx91, vwx101)
new_ltEs7(Left(vwx90), Left(vwx100), ty_Char, ge) → new_ltEs5(vwx90, vwx100)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_ltEs7(Right(vwx90), Left(vwx100), hf, ge) → False
new_ltEs21(vwx91, vwx101, app(app(ty_Either, bch), bda)) → new_ltEs7(vwx91, vwx101, bch, bda)
new_lt8(vwx91, vwx101, app(app(ty_@2, dg), dh)) → new_lt18(vwx91, vwx101, dg, dh)
new_ltEs20(vwx9, vwx10, app(ty_Ratio, dbc)) → new_ltEs17(vwx9, vwx10, dbc)
new_compare29(vwx90, vwx100, bf, bg, bh) → new_compare27(vwx90, vwx100, new_esEs4(vwx90, vwx100, bf, bg, bh), bf, bg, bh)
new_esEs28(vwx300, vwx400, ty_Int) → new_esEs16(vwx300, vwx400)
new_primEqInt(Neg(Succ(vwx3000)), Neg(Zero)) → False
new_compare8(vwx90, vwx100) → new_compare25(vwx90, vwx100, new_esEs17(vwx90, vwx100))
new_lt7(vwx90, vwx100, ty_Double) → new_lt6(vwx90, vwx100)
new_compare10(Integer(vwx90), Integer(vwx100)) → new_primCmpInt(vwx90, vwx100)
new_lt8(vwx91, vwx101, ty_@0) → new_lt10(vwx91, vwx101)
new_primEqInt(Neg(Zero), Neg(Succ(vwx4000))) → False
new_primCompAux0(vwx59, GT) → GT
new_lt8(vwx91, vwx101, ty_Bool) → new_lt5(vwx91, vwx101)
new_esEs25(vwx301, vwx401, ty_Ordering) → new_esEs9(vwx301, vwx401)
new_compare26(vwx90, vwx100, True, cd, ce) → EQ
new_lt20(vwx90, vwx100, ty_@0) → new_lt10(vwx90, vwx100)
new_esEs23(vwx301, vwx401, app(app(app(ty_@3, cea), ceb), cec)) → new_esEs4(vwx301, vwx401, cea, ceb, cec)
new_compare24(vwx16, vwx17, True, beg, cbf) → EQ
new_compare7(Char(vwx90), Char(vwx100)) → new_primCmpNat0(vwx90, vwx100)
new_esEs7(vwx30, vwx40, app(app(app(ty_@3, cef), ceg), ceh)) → new_esEs4(vwx30, vwx40, cef, ceg, ceh)
new_compare([], [], ba) → EQ
new_ltEs20(vwx9, vwx10, app(ty_[], ba)) → new_ltEs8(vwx9, vwx10, ba)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_esEs23(vwx301, vwx401, ty_Integer) → new_esEs14(vwx301, vwx401)
new_compare6(vwx9, vwx10) → new_primCmpInt(vwx9, vwx10)
new_ltEs7(Right(vwx90), Right(vwx100), hf, ty_@0) → new_ltEs10(vwx90, vwx100)
new_esEs23(vwx301, vwx401, app(app(ty_Either, cdd), cde)) → new_esEs10(vwx301, vwx401, cdd, cde)
new_primCmpNat0(Succ(vwx900), Succ(vwx1000)) → new_primCmpNat0(vwx900, vwx1000)
new_esEs30(vwx90, vwx100, ty_@0) → new_esEs15(vwx90, vwx100)
new_ltEs7(Left(vwx90), Left(vwx100), app(app(app(ty_@3, gf), gg), gh), ge) → new_ltEs11(vwx90, vwx100, gf, gg, gh)
new_compare11(vwx90, vwx100, False, ca) → GT
new_esEs5(Just(vwx300), Just(vwx400), app(app(app(ty_@3, dfd), dfe), dff)) → new_esEs4(vwx300, vwx400, dfd, dfe, dff)
new_primEqInt(Pos(Succ(vwx3000)), Pos(Succ(vwx4000))) → new_primEqNat0(vwx3000, vwx4000)
new_ltEs7(Right(vwx90), Right(vwx100), hf, ty_Int) → new_ltEs4(vwx90, vwx100)
new_esEs25(vwx301, vwx401, app(ty_Maybe, chd)) → new_esEs5(vwx301, vwx401, chd)
new_ltEs18(vwx92, vwx102, ty_@0) → new_ltEs10(vwx92, vwx102)
new_compare12(vwx30, vwx31, True, bga, bgb) → LT
new_ltEs18(vwx92, vwx102, app(app(app(ty_@3, eb), ec), ed)) → new_ltEs11(vwx92, vwx102, eb, ec, ed)
new_esEs23(vwx301, vwx401, app(ty_[], ced)) → new_esEs12(vwx301, vwx401, ced)
new_esEs8(vwx30, vwx40, app(ty_Maybe, dec)) → new_esEs5(vwx30, vwx40, dec)
new_esEs30(vwx90, vwx100, ty_Int) → new_esEs16(vwx90, vwx100)
new_esEs22(vwx300, vwx400, ty_Double) → new_esEs19(vwx300, vwx400)
new_primEqNat0(Succ(vwx3000), Succ(vwx4000)) → new_primEqNat0(vwx3000, vwx4000)
new_primCompAux1(vwx90, vwx100, vwx54, ba) → new_primCompAux0(vwx54, new_compare33(vwx90, vwx100, ba))
new_ltEs7(Left(vwx90), Left(vwx100), ty_Bool, ge) → new_ltEs9(vwx90, vwx100)
new_compare32(Left(vwx30), Left(vwx40), bee, bef) → new_compare210(vwx30, vwx40, new_esEs7(vwx30, vwx40, bee), bee, bef)
new_ltEs17(vwx9, vwx10, dbc) → new_not(new_esEs9(new_compare19(vwx9, vwx10, dbc), GT))
new_ltEs20(vwx9, vwx10, ty_Char) → new_ltEs5(vwx9, vwx10)
new_ltEs7(Right(vwx90), Right(vwx100), hf, ty_Bool) → new_ltEs9(vwx90, vwx100)
new_esEs30(vwx90, vwx100, app(app(ty_Either, bbf), bbg)) → new_esEs10(vwx90, vwx100, bbf, bbg)
new_lt7(vwx90, vwx100, ty_Float) → new_lt16(vwx90, vwx100)
new_ltEs13(Just(vwx90), Just(vwx100), ty_Integer) → new_ltEs12(vwx90, vwx100)
new_compare33(vwx90, vwx100, app(ty_[], bdd)) → new_compare(vwx90, vwx100, bdd)
new_ltEs19(vwx16, vwx17, app(app(ty_Either, bfe), bff)) → new_ltEs7(vwx16, vwx17, bfe, bff)
new_ltEs21(vwx91, vwx101, ty_Int) → new_ltEs4(vwx91, vwx101)
new_primCmpInt(Neg(Succ(vwx900)), Neg(vwx100)) → new_primCmpNat0(vwx100, Succ(vwx900))
new_lt8(vwx91, vwx101, app(ty_Ratio, cbd)) → new_lt19(vwx91, vwx101, cbd)
new_esEs10(Left(vwx300), Left(vwx400), app(ty_Maybe, bhe), bgc) → new_esEs5(vwx300, vwx400, bhe)
new_ltEs20(vwx9, vwx10, ty_Ordering) → new_ltEs14(vwx9, vwx10)
new_lt14(vwx90, vwx100) → new_esEs9(new_compare6(vwx90, vwx100), LT)
new_compare33(vwx90, vwx100, app(app(app(ty_@3, bde), bdf), bdg)) → new_compare29(vwx90, vwx100, bde, bdf, bdg)
new_primEqInt(Pos(Zero), Pos(Succ(vwx4000))) → False
new_primEqInt(Pos(Succ(vwx3000)), Pos(Zero)) → False
new_ltEs18(vwx92, vwx102, ty_Double) → new_ltEs6(vwx92, vwx102)
new_esEs10(Right(vwx300), Right(vwx400), bhf, ty_Bool) → new_esEs17(vwx300, vwx400)
new_esEs23(vwx301, vwx401, ty_Char) → new_esEs13(vwx301, vwx401)
new_ltEs7(Left(vwx90), Left(vwx100), ty_Float, ge) → new_ltEs15(vwx90, vwx100)
new_lt17(vwx90, vwx100, cb, cc) → new_esEs9(new_compare32(vwx90, vwx100, cb, cc), LT)
new_primCmpNat0(Zero, Zero) → EQ
new_esEs24(vwx300, vwx400, app(app(ty_Either, cfa), cfb)) → new_esEs10(vwx300, vwx400, cfa, cfb)
new_primCmpNat0(Succ(vwx900), Zero) → GT
new_lt20(vwx90, vwx100, ty_Bool) → new_lt5(vwx90, vwx100)
new_ltEs21(vwx91, vwx101, app(ty_Ratio, dee)) → new_ltEs17(vwx91, vwx101, dee)
new_compare30(vwx90, vwx100) → new_compare28(vwx90, vwx100, new_esEs9(vwx90, vwx100))
new_esEs24(vwx300, vwx400, ty_@0) → new_esEs15(vwx300, vwx400)
new_esEs22(vwx300, vwx400, ty_Integer) → new_esEs14(vwx300, vwx400)
new_esEs20(vwx90, vwx100, app(app(app(ty_@3, bf), bg), bh)) → new_esEs4(vwx90, vwx100, bf, bg, bh)
new_ltEs7(Right(vwx90), Right(vwx100), hf, app(app(app(ty_@3, hh), baa), bab)) → new_ltEs11(vwx90, vwx100, hh, baa, bab)
new_primCmpInt(Neg(Zero), Pos(Succ(vwx1000))) → LT
new_ltEs13(Just(vwx90), Just(vwx100), app(ty_[], fb)) → new_ltEs8(vwx90, vwx100, fb)
new_ltEs15(vwx9, vwx10) → new_not(new_esEs9(new_compare16(vwx9, vwx10), GT))
new_sr0(Integer(vwx1000), Integer(vwx910)) → Integer(new_primMulInt(vwx1000, vwx910))
new_compare13(vwx90, vwx100, True) → LT
new_primPlusNat1(Succ(vwx5500), Succ(vwx400000)) → Succ(Succ(new_primPlusNat1(vwx5500, vwx400000)))
new_primEqInt(Neg(Succ(vwx3000)), Pos(vwx400)) → False
new_primEqInt(Pos(Succ(vwx3000)), Neg(vwx400)) → False
new_esEs7(vwx30, vwx40, ty_Float) → new_esEs18(vwx30, vwx40)
new_esEs10(Left(vwx300), Left(vwx400), app(app(app(ty_@3, bha), bhb), bhc), bgc) → new_esEs4(vwx300, vwx400, bha, bhb, bhc)
new_esEs10(Left(vwx300), Left(vwx400), app(app(ty_@2, bgf), bgg), bgc) → new_esEs6(vwx300, vwx400, bgf, bgg)
new_esEs25(vwx301, vwx401, app(ty_Ratio, cgg)) → new_esEs11(vwx301, vwx401, cgg)
new_esEs20(vwx90, vwx100, ty_Char) → new_esEs13(vwx90, vwx100)
new_esEs27(vwx300, vwx400, app(ty_Maybe, dcf)) → new_esEs5(vwx300, vwx400, dcf)
new_esEs27(vwx300, vwx400, app(app(ty_Either, dbe), dbf)) → new_esEs10(vwx300, vwx400, dbe, dbf)
new_lt15(vwx90, vwx100) → new_esEs9(new_compare30(vwx90, vwx100), LT)
new_ltEs20(vwx9, vwx10, ty_Float) → new_ltEs15(vwx9, vwx10)
new_esEs22(vwx300, vwx400, app(app(ty_@2, ccd), cce)) → new_esEs6(vwx300, vwx400, ccd, cce)
new_esEs27(vwx300, vwx400, app(ty_Ratio, dca)) → new_esEs11(vwx300, vwx400, dca)
new_primEqInt(Neg(Zero), Pos(Succ(vwx4000))) → False
new_primEqInt(Pos(Zero), Neg(Succ(vwx4000))) → False
new_esEs20(vwx90, vwx100, app(ty_[], bc)) → new_esEs12(vwx90, vwx100, bc)
new_primCmpInt(Pos(Zero), Pos(Succ(vwx1000))) → new_primCmpNat0(Zero, Succ(vwx1000))
new_esEs10(Left(vwx300), Left(vwx400), ty_Ordering, bgc) → new_esEs9(vwx300, vwx400)
new_compare33(vwx90, vwx100, app(app(ty_Either, bea), beb)) → new_compare32(vwx90, vwx100, bea, beb)
new_esEs7(vwx30, vwx40, ty_Double) → new_esEs19(vwx30, vwx40)
new_lt7(vwx90, vwx100, app(app(ty_@2, cd), ce)) → new_lt18(vwx90, vwx100, cd, ce)
new_esEs24(vwx300, vwx400, ty_Char) → new_esEs13(vwx300, vwx400)
new_esEs22(vwx300, vwx400, ty_Float) → new_esEs18(vwx300, vwx400)
new_primCompAux0(vwx59, LT) → LT
new_esEs21(vwx91, vwx101, ty_Integer) → new_esEs14(vwx91, vwx101)
new_not(False) → True
new_esEs5(Just(vwx300), Just(vwx400), ty_Ordering) → new_esEs9(vwx300, vwx400)
new_esEs10(Left(vwx300), Left(vwx400), ty_@0, bgc) → new_esEs15(vwx300, vwx400)
new_compare210(vwx9, vwx10, True, dcg, bb) → EQ
new_esEs23(vwx301, vwx401, ty_@0) → new_esEs15(vwx301, vwx401)
new_primPlusNat0(Zero, vwx40000) → Succ(vwx40000)
new_primCmpInt(Pos(Succ(vwx900)), Pos(vwx100)) → new_primCmpNat0(Succ(vwx900), vwx100)
new_esEs23(vwx301, vwx401, app(app(ty_@2, cdf), cdg)) → new_esEs6(vwx301, vwx401, cdf, cdg)
new_esEs22(vwx300, vwx400, ty_Bool) → new_esEs17(vwx300, vwx400)
new_esEs9(GT, GT) → True
new_esEs23(vwx301, vwx401, ty_Float) → new_esEs18(vwx301, vwx401)
new_ltEs18(vwx92, vwx102, ty_Ordering) → new_ltEs14(vwx92, vwx102)
new_ltEs14(LT, LT) → True
new_esEs25(vwx301, vwx401, ty_@0) → new_esEs15(vwx301, vwx401)
new_esEs25(vwx301, vwx401, ty_Float) → new_esEs18(vwx301, vwx401)
new_esEs25(vwx301, vwx401, app(app(app(ty_@3, cgh), cha), chb)) → new_esEs4(vwx301, vwx401, cgh, cha, chb)
new_ltEs7(Right(vwx90), Right(vwx100), hf, app(ty_Maybe, bac)) → new_ltEs13(vwx90, vwx100, bac)
new_ltEs7(Right(vwx90), Right(vwx100), hf, ty_Integer) → new_ltEs12(vwx90, vwx100)
new_esEs23(vwx301, vwx401, app(ty_Ratio, cdh)) → new_esEs11(vwx301, vwx401, cdh)
new_compare33(vwx90, vwx100, app(app(ty_@2, bec), bed)) → new_compare17(vwx90, vwx100, bec, bed)
new_lt8(vwx91, vwx101, ty_Ordering) → new_lt15(vwx91, vwx101)
new_compare28(vwx90, vwx100, True) → EQ
new_esEs22(vwx300, vwx400, app(app(app(ty_@3, ccg), cch), cda)) → new_esEs4(vwx300, vwx400, ccg, cch, cda)
new_esEs24(vwx300, vwx400, app(ty_Maybe, cgb)) → new_esEs5(vwx300, vwx400, cgb)
new_esEs7(vwx30, vwx40, ty_Bool) → new_esEs17(vwx30, vwx40)
new_lt20(vwx90, vwx100, ty_Double) → new_lt6(vwx90, vwx100)
new_ltEs13(Just(vwx90), Just(vwx100), ty_Float) → new_ltEs15(vwx90, vwx100)
new_esEs20(vwx90, vwx100, app(ty_Ratio, cbc)) → new_esEs11(vwx90, vwx100, cbc)
new_ltEs19(vwx16, vwx17, ty_Integer) → new_ltEs12(vwx16, vwx17)
new_primCmpInt(Pos(Succ(vwx900)), Neg(vwx100)) → GT
new_ltEs18(vwx92, vwx102, app(app(ty_@2, eh), fa)) → new_ltEs16(vwx92, vwx102, eh, fa)
new_esEs27(vwx300, vwx400, ty_@0) → new_esEs15(vwx300, vwx400)
new_esEs24(vwx300, vwx400, ty_Float) → new_esEs18(vwx300, vwx400)
new_esEs30(vwx90, vwx100, app(ty_[], bah)) → new_esEs12(vwx90, vwx100, bah)
new_esEs10(Right(vwx300), Right(vwx400), bhf, ty_Integer) → new_esEs14(vwx300, vwx400)
new_esEs10(Right(vwx300), Right(vwx400), bhf, app(app(ty_Either, bhg), bhh)) → new_esEs10(vwx300, vwx400, bhg, bhh)
new_esEs10(Right(vwx300), Right(vwx400), bhf, app(ty_Ratio, cac)) → new_esEs11(vwx300, vwx400, cac)
new_primMulInt(Pos(vwx3000), Pos(vwx4000)) → Pos(new_primMulNat0(vwx3000, vwx4000))
new_esEs29(vwx301, vwx401, ty_Integer) → new_esEs14(vwx301, vwx401)
new_esEs5(Just(vwx300), Just(vwx400), ty_Bool) → new_esEs17(vwx300, vwx400)
new_esEs10(Left(vwx300), Left(vwx400), ty_Float, bgc) → new_esEs18(vwx300, vwx400)
new_ltEs7(Right(vwx90), Right(vwx100), hf, ty_Ordering) → new_ltEs14(vwx90, vwx100)
new_ltEs20(vwx9, vwx10, ty_Bool) → new_ltEs9(vwx9, vwx10)
new_esEs7(vwx30, vwx40, ty_Char) → new_esEs13(vwx30, vwx40)
new_ltEs9(True, True) → True
new_esEs23(vwx301, vwx401, ty_Ordering) → new_esEs9(vwx301, vwx401)
new_esEs27(vwx300, vwx400, app(app(ty_@2, dbg), dbh)) → new_esEs6(vwx300, vwx400, dbg, dbh)
new_primMulInt(Neg(vwx3000), Neg(vwx4000)) → Pos(new_primMulNat0(vwx3000, vwx4000))
new_compare110(vwx90, vwx100, True) → LT
new_lt20(vwx90, vwx100, app(app(app(ty_@3, bbb), bbc), bbd)) → new_lt11(vwx90, vwx100, bbb, bbc, bbd)
new_primEqNat0(Zero, Succ(vwx4000)) → False
new_primEqNat0(Succ(vwx3000), Zero) → False
new_esEs8(vwx30, vwx40, app(ty_[], deb)) → new_esEs12(vwx30, vwx40, deb)
new_lt7(vwx90, vwx100, ty_Integer) → new_lt12(vwx90, vwx100)
new_esEs21(vwx91, vwx101, app(ty_[], cg)) → new_esEs12(vwx91, vwx101, cg)
new_ltEs7(Left(vwx90), Left(vwx100), app(app(ty_Either, hb), hc), ge) → new_ltEs7(vwx90, vwx100, hb, hc)
new_compare32(Right(vwx30), Right(vwx40), bee, bef) → new_compare24(vwx30, vwx40, new_esEs8(vwx30, vwx40, bef), bee, bef)
new_esEs7(vwx30, vwx40, ty_@0) → new_esEs15(vwx30, vwx40)
new_compare110(vwx90, vwx100, False) → GT
new_esEs20(vwx90, vwx100, ty_@0) → new_esEs15(vwx90, vwx100)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_ltEs9(False, False) → True
new_compare17(vwx90, vwx100, cd, ce) → new_compare26(vwx90, vwx100, new_esEs6(vwx90, vwx100, cd, ce), cd, ce)
new_ltEs13(Just(vwx90), Just(vwx100), app(app(ty_Either, fh), ga)) → new_ltEs7(vwx90, vwx100, fh, ga)
new_ltEs7(Left(vwx90), Left(vwx100), ty_Integer, ge) → new_ltEs12(vwx90, vwx100)
new_compare33(vwx90, vwx100, app(ty_Maybe, bdh)) → new_compare31(vwx90, vwx100, bdh)
new_lt7(vwx90, vwx100, app(ty_[], bc)) → new_lt9(vwx90, vwx100, bc)
new_ltEs18(vwx92, vwx102, ty_Bool) → new_ltEs9(vwx92, vwx102)
new_esEs6(@2(vwx300, vwx301), @2(vwx400, vwx401), cbh, cca) → new_asAs(new_esEs22(vwx300, vwx400, cbh), new_esEs23(vwx301, vwx401, cca))
new_esEs26(vwx302, vwx402, ty_Int) → new_esEs16(vwx302, vwx402)
new_ltEs21(vwx91, vwx101, ty_Char) → new_ltEs5(vwx91, vwx101)
new_lt16(vwx90, vwx100) → new_esEs9(new_compare16(vwx90, vwx100), LT)
new_esEs26(vwx302, vwx402, app(ty_Maybe, daf)) → new_esEs5(vwx302, vwx402, daf)
new_esEs24(vwx300, vwx400, ty_Double) → new_esEs19(vwx300, vwx400)
new_esEs5(Just(vwx300), Just(vwx400), ty_Double) → new_esEs19(vwx300, vwx400)
new_lt4(vwx90, vwx100) → new_esEs9(new_compare7(vwx90, vwx100), LT)
new_lt13(vwx90, vwx100, ca) → new_esEs9(new_compare31(vwx90, vwx100, ca), LT)
new_esEs8(vwx30, vwx40, app(app(ty_Either, ddb), ddc)) → new_esEs10(vwx30, vwx40, ddb, ddc)
new_esEs18(Float(vwx300, vwx301), Float(vwx400, vwx401)) → new_esEs16(new_sr(vwx300, vwx400), new_sr(vwx301, vwx401))
new_primCmpInt(Neg(Zero), Neg(Succ(vwx1000))) → new_primCmpNat0(Succ(vwx1000), Zero)
new_esEs25(vwx301, vwx401, ty_Int) → new_esEs16(vwx301, vwx401)
new_esEs23(vwx301, vwx401, ty_Bool) → new_esEs17(vwx301, vwx401)
new_primCmpInt(Pos(Zero), Neg(Succ(vwx1000))) → GT
new_ltEs13(Just(vwx90), Just(vwx100), ty_Int) → new_ltEs4(vwx90, vwx100)
new_lt7(vwx90, vwx100, ty_Ordering) → new_lt15(vwx90, vwx100)
new_lt20(vwx90, vwx100, ty_Float) → new_lt16(vwx90, vwx100)
new_esEs25(vwx301, vwx401, ty_Integer) → new_esEs14(vwx301, vwx401)
new_compare26(vwx90, vwx100, False, cd, ce) → new_compare111(vwx90, vwx100, new_ltEs16(vwx90, vwx100, cd, ce), cd, ce)
new_lt7(vwx90, vwx100, ty_Bool) → new_lt5(vwx90, vwx100)
new_esEs21(vwx91, vwx101, app(app(app(ty_@3, da), db), dc)) → new_esEs4(vwx91, vwx101, da, db, dc)
new_lt7(vwx90, vwx100, app(ty_Ratio, cbc)) → new_lt19(vwx90, vwx100, cbc)
new_lt8(vwx91, vwx101, app(app(ty_Either, de), df)) → new_lt17(vwx91, vwx101, de, df)
new_lt20(vwx90, vwx100, app(ty_Ratio, ded)) → new_lt19(vwx90, vwx100, ded)
new_ltEs19(vwx16, vwx17, ty_Ordering) → new_ltEs14(vwx16, vwx17)
new_esEs21(vwx91, vwx101, ty_Float) → new_esEs18(vwx91, vwx101)
new_esEs8(vwx30, vwx40, ty_Ordering) → new_esEs9(vwx30, vwx40)
new_esEs30(vwx90, vwx100, ty_Ordering) → new_esEs9(vwx90, vwx100)
new_esEs5(Just(vwx300), Just(vwx400), ty_Int) → new_esEs16(vwx300, vwx400)
new_ltEs21(vwx91, vwx101, ty_Integer) → new_ltEs12(vwx91, vwx101)
new_compare18(vwx23, vwx24, True, dba, dbb) → LT
new_ltEs13(Just(vwx90), Just(vwx100), app(ty_Maybe, fg)) → new_ltEs13(vwx90, vwx100, fg)
new_esEs26(vwx302, vwx402, app(app(ty_Either, che), chf)) → new_esEs10(vwx302, vwx402, che, chf)
new_ltEs13(Just(vwx90), Nothing, dag) → False
new_ltEs7(Left(vwx90), Left(vwx100), app(ty_[], gd), ge) → new_ltEs8(vwx90, vwx100, gd)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_lt6(vwx90, vwx100) → new_esEs9(new_compare9(vwx90, vwx100), LT)
new_lt8(vwx91, vwx101, ty_Double) → new_lt6(vwx91, vwx101)
new_esEs8(vwx30, vwx40, ty_Char) → new_esEs13(vwx30, vwx40)
new_esEs20(vwx90, vwx100, app(app(ty_Either, cb), cc)) → new_esEs10(vwx90, vwx100, cb, cc)
new_compare15(vwx90, vwx100, True, bf, bg, bh) → LT
new_esEs27(vwx300, vwx400, ty_Float) → new_esEs18(vwx300, vwx400)
new_esEs20(vwx90, vwx100, app(ty_Maybe, ca)) → new_esEs5(vwx90, vwx100, ca)
new_compare33(vwx90, vwx100, ty_Ordering) → new_compare30(vwx90, vwx100)
new_esEs15(@0, @0) → True
new_ltEs7(Right(vwx90), Right(vwx100), hf, app(app(ty_Either, bad), bae)) → new_ltEs7(vwx90, vwx100, bad, bae)
new_compare33(vwx90, vwx100, app(ty_Ratio, def)) → new_compare19(vwx90, vwx100, def)
new_asAs(False, vwx45) → False
new_primMulInt(Neg(vwx3000), Pos(vwx4000)) → Neg(new_primMulNat0(vwx3000, vwx4000))
new_primMulInt(Pos(vwx3000), Neg(vwx4000)) → Neg(new_primMulNat0(vwx3000, vwx4000))
new_primMulNat0(Zero, Succ(vwx40000)) → Zero
new_primMulNat0(Succ(vwx30000), Zero) → Zero
new_ltEs13(Just(vwx90), Just(vwx100), app(app(ty_@2, gb), gc)) → new_ltEs16(vwx90, vwx100, gb, gc)
new_lt7(vwx90, vwx100, app(app(ty_Either, cb), cc)) → new_lt17(vwx90, vwx100, cb, cc)
new_esEs26(vwx302, vwx402, app(ty_[], dae)) → new_esEs12(vwx302, vwx402, dae)
new_esEs21(vwx91, vwx101, ty_Int) → new_esEs16(vwx91, vwx101)
new_esEs10(Left(vwx300), Left(vwx400), ty_Integer, bgc) → new_esEs14(vwx300, vwx400)
new_esEs10(Left(vwx300), Left(vwx400), app(app(ty_Either, bgd), bge), bgc) → new_esEs10(vwx300, vwx400, bgd, bge)
new_esEs10(Right(vwx300), Right(vwx400), bhf, ty_@0) → new_esEs15(vwx300, vwx400)
new_ltEs19(vwx16, vwx17, ty_@0) → new_ltEs10(vwx16, vwx17)
new_compare33(vwx90, vwx100, ty_Bool) → new_compare8(vwx90, vwx100)
new_ltEs14(GT, LT) → False
new_esEs10(Left(vwx300), Left(vwx400), ty_Char, bgc) → new_esEs13(vwx300, vwx400)
new_esEs5(Just(vwx300), Just(vwx400), app(app(ty_@2, dfa), dfb)) → new_esEs6(vwx300, vwx400, dfa, dfb)
new_esEs23(vwx301, vwx401, app(ty_Maybe, cee)) → new_esEs5(vwx301, vwx401, cee)
new_ltEs18(vwx92, vwx102, app(ty_Ratio, cbe)) → new_ltEs17(vwx92, vwx102, cbe)
new_esEs8(vwx30, vwx40, app(ty_Ratio, ddf)) → new_esEs11(vwx30, vwx40, ddf)
new_ltEs18(vwx92, vwx102, ty_Char) → new_ltEs5(vwx92, vwx102)
new_compare18(vwx23, vwx24, False, dba, dbb) → GT
new_ltEs9(False, True) → True
new_ltEs18(vwx92, vwx102, app(ty_Maybe, ee)) → new_ltEs13(vwx92, vwx102, ee)
new_esEs7(vwx30, vwx40, app(app(ty_Either, bhf), bgc)) → new_esEs10(vwx30, vwx40, bhf, bgc)
new_esEs8(vwx30, vwx40, ty_Int) → new_esEs16(vwx30, vwx40)
new_lt8(vwx91, vwx101, app(ty_Maybe, dd)) → new_lt13(vwx91, vwx101, dd)
new_esEs23(vwx301, vwx401, ty_Int) → new_esEs16(vwx301, vwx401)
new_esEs26(vwx302, vwx402, ty_Double) → new_esEs19(vwx302, vwx402)
new_esEs20(vwx90, vwx100, ty_Integer) → new_esEs14(vwx90, vwx100)
new_esEs20(vwx90, vwx100, ty_Ordering) → new_esEs9(vwx90, vwx100)
new_esEs22(vwx300, vwx400, app(ty_[], cdb)) → new_esEs12(vwx300, vwx400, cdb)
new_esEs5(Nothing, Just(vwx400), dda) → False
new_esEs5(Just(vwx300), Nothing, dda) → False
new_esEs27(vwx300, vwx400, ty_Int) → new_esEs16(vwx300, vwx400)
new_esEs24(vwx300, vwx400, ty_Integer) → new_esEs14(vwx300, vwx400)
new_compare25(vwx90, vwx100, False) → new_compare110(vwx90, vwx100, new_ltEs9(vwx90, vwx100))
new_esEs7(vwx30, vwx40, ty_Int) → new_esEs16(vwx30, vwx40)
new_ltEs20(vwx9, vwx10, app(app(ty_Either, hf), ge)) → new_ltEs7(vwx9, vwx10, hf, ge)
new_esEs10(Right(vwx300), Right(vwx400), bhf, app(app(app(ty_@3, cad), cae), caf)) → new_esEs4(vwx300, vwx400, cad, cae, caf)
new_esEs7(vwx30, vwx40, app(ty_Maybe, dda)) → new_esEs5(vwx30, vwx40, dda)
new_ltEs19(vwx16, vwx17, app(ty_Maybe, bfd)) → new_ltEs13(vwx16, vwx17, bfd)
new_ltEs19(vwx16, vwx17, app(app(app(ty_@3, bfa), bfb), bfc)) → new_ltEs11(vwx16, vwx17, bfa, bfb, bfc)
new_esEs5(Just(vwx300), Just(vwx400), app(ty_Ratio, dfc)) → new_esEs11(vwx300, vwx400, dfc)
new_esEs30(vwx90, vwx100, app(app(ty_@2, bbh), bca)) → new_esEs6(vwx90, vwx100, bbh, bca)
new_esEs22(vwx300, vwx400, ty_Char) → new_esEs13(vwx300, vwx400)
new_ltEs14(LT, GT) → True
new_esEs26(vwx302, vwx402, ty_Bool) → new_esEs17(vwx302, vwx402)
new_lt20(vwx90, vwx100, ty_Integer) → new_lt12(vwx90, vwx100)
new_esEs9(EQ, LT) → False
new_esEs9(LT, EQ) → False
new_ltEs14(LT, EQ) → True
new_esEs10(Right(vwx300), Right(vwx400), bhf, ty_Int) → new_esEs16(vwx300, vwx400)
new_ltEs4(vwx9, vwx10) → new_not(new_esEs9(new_compare6(vwx9, vwx10), GT))
new_esEs5(Nothing, Nothing, dda) → True
new_compare33(vwx90, vwx100, ty_Integer) → new_compare10(vwx90, vwx100)
new_esEs13(Char(vwx300), Char(vwx400)) → new_primEqNat0(vwx300, vwx400)
new_esEs5(Just(vwx300), Just(vwx400), ty_Float) → new_esEs18(vwx300, vwx400)
new_ltEs13(Just(vwx90), Just(vwx100), ty_Char) → new_ltEs5(vwx90, vwx100)
new_esEs30(vwx90, vwx100, ty_Double) → new_esEs19(vwx90, vwx100)
new_esEs5(Just(vwx300), Just(vwx400), app(app(ty_Either, deg), deh)) → new_esEs10(vwx300, vwx400, deg, deh)
new_esEs26(vwx302, vwx402, app(ty_Ratio, daa)) → new_esEs11(vwx302, vwx402, daa)
new_esEs24(vwx300, vwx400, ty_Ordering) → new_esEs9(vwx300, vwx400)
new_esEs25(vwx301, vwx401, ty_Double) → new_esEs19(vwx301, vwx401)
new_esEs22(vwx300, vwx400, app(ty_Maybe, cdc)) → new_esEs5(vwx300, vwx400, cdc)
new_esEs21(vwx91, vwx101, app(ty_Maybe, dd)) → new_esEs5(vwx91, vwx101, dd)
new_esEs12(:(vwx300, vwx301), :(vwx400, vwx401), dbd) → new_asAs(new_esEs27(vwx300, vwx400, dbd), new_esEs12(vwx301, vwx401, dbd))
new_primPlusNat1(Zero, Zero) → Zero
new_compare111(vwx90, vwx100, True, cd, ce) → LT
new_ltEs6(vwx9, vwx10) → new_not(new_esEs9(new_compare9(vwx9, vwx10), GT))
new_esEs26(vwx302, vwx402, ty_Ordering) → new_esEs9(vwx302, vwx402)
new_ltEs7(Left(vwx90), Left(vwx100), ty_Int, ge) → new_ltEs4(vwx90, vwx100)
new_ltEs19(vwx16, vwx17, app(app(ty_@2, bfg), bfh)) → new_ltEs16(vwx16, vwx17, bfg, bfh)
new_esEs27(vwx300, vwx400, ty_Integer) → new_esEs14(vwx300, vwx400)
new_asAs(True, vwx45) → vwx45
new_ltEs14(EQ, EQ) → True
new_lt10(vwx90, vwx100) → new_esEs9(new_compare14(vwx90, vwx100), LT)
new_ltEs13(Just(vwx90), Just(vwx100), app(ty_Ratio, dah)) → new_ltEs17(vwx90, vwx100, dah)
new_ltEs21(vwx91, vwx101, app(ty_[], bcc)) → new_ltEs8(vwx91, vwx101, bcc)
new_esEs27(vwx300, vwx400, app(ty_[], dce)) → new_esEs12(vwx300, vwx400, dce)
new_primMulNat0(Succ(vwx30000), Succ(vwx40000)) → new_primPlusNat0(new_primMulNat0(vwx30000, Succ(vwx40000)), vwx40000)
new_esEs21(vwx91, vwx101, app(app(ty_Either, de), df)) → new_esEs10(vwx91, vwx101, de, df)
new_esEs10(Right(vwx300), Right(vwx400), bhf, ty_Double) → new_esEs19(vwx300, vwx400)
new_esEs30(vwx90, vwx100, app(ty_Maybe, bbe)) → new_esEs5(vwx90, vwx100, bbe)
new_ltEs21(vwx91, vwx101, ty_Float) → new_ltEs15(vwx91, vwx101)
new_ltEs13(Just(vwx90), Just(vwx100), ty_Double) → new_ltEs6(vwx90, vwx100)
new_compare27(vwx90, vwx100, True, bf, bg, bh) → EQ
new_ltEs13(Just(vwx90), Just(vwx100), app(app(app(ty_@3, fc), fd), ff)) → new_ltEs11(vwx90, vwx100, fc, fd, ff)
new_ltEs19(vwx16, vwx17, ty_Char) → new_ltEs5(vwx16, vwx17)
new_ltEs20(vwx9, vwx10, ty_Double) → new_ltEs6(vwx9, vwx10)
new_ltEs7(Right(vwx90), Right(vwx100), hf, ty_Float) → new_ltEs15(vwx90, vwx100)
new_esEs26(vwx302, vwx402, app(app(ty_@2, chg), chh)) → new_esEs6(vwx302, vwx402, chg, chh)
new_lt20(vwx90, vwx100, ty_Int) → new_lt14(vwx90, vwx100)
new_compare19(:%(vwx90, vwx91), :%(vwx100, vwx101), ty_Integer) → new_compare10(new_sr0(vwx90, vwx101), new_sr0(vwx100, vwx91))
new_lt7(vwx90, vwx100, app(ty_Maybe, ca)) → new_lt13(vwx90, vwx100, ca)
new_esEs5(Just(vwx300), Just(vwx400), ty_Char) → new_esEs13(vwx300, vwx400)
new_esEs7(vwx30, vwx40, app(ty_Ratio, dch)) → new_esEs11(vwx30, vwx40, dch)
new_ltEs13(Just(vwx90), Just(vwx100), ty_Ordering) → new_ltEs14(vwx90, vwx100)
new_esEs30(vwx90, vwx100, ty_Integer) → new_esEs14(vwx90, vwx100)
new_esEs7(vwx30, vwx40, app(ty_[], dbd)) → new_esEs12(vwx30, vwx40, dbd)
new_esEs24(vwx300, vwx400, app(app(app(ty_@3, cff), cfg), cfh)) → new_esEs4(vwx300, vwx400, cff, cfg, cfh)
new_ltEs7(Left(vwx90), Left(vwx100), app(ty_Ratio, cba), ge) → new_ltEs17(vwx90, vwx100, cba)
new_esEs9(LT, LT) → True
new_esEs8(vwx30, vwx40, ty_Double) → new_esEs19(vwx30, vwx40)
new_compare31(vwx90, vwx100, ca) → new_compare211(vwx90, vwx100, new_esEs5(vwx90, vwx100, ca), ca)
new_ltEs20(vwx9, vwx10, app(app(ty_@2, bcb), bba)) → new_ltEs16(vwx9, vwx10, bcb, bba)
new_esEs28(vwx300, vwx400, ty_Integer) → new_esEs14(vwx300, vwx400)
new_lt9(vwx90, vwx100, bc) → new_esEs9(new_compare(vwx90, vwx100, bc), LT)
new_ltEs19(vwx16, vwx17, ty_Int) → new_ltEs4(vwx16, vwx17)
new_esEs21(vwx91, vwx101, app(ty_Ratio, cbd)) → new_esEs11(vwx91, vwx101, cbd)
new_ltEs18(vwx92, vwx102, ty_Integer) → new_ltEs12(vwx92, vwx102)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_ltEs14(EQ, GT) → True
new_primCompAux0(vwx59, EQ) → vwx59
new_lt7(vwx90, vwx100, ty_@0) → new_lt10(vwx90, vwx100)
new_ltEs11(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), cf, bd, be) → new_pePe(new_lt7(vwx90, vwx100, cf), new_asAs(new_esEs20(vwx90, vwx100, cf), new_pePe(new_lt8(vwx91, vwx101, bd), new_asAs(new_esEs21(vwx91, vwx101, bd), new_ltEs18(vwx92, vwx102, be)))))
new_ltEs21(vwx91, vwx101, ty_Double) → new_ltEs6(vwx91, vwx101)
new_esEs22(vwx300, vwx400, app(ty_Ratio, ccf)) → new_esEs11(vwx300, vwx400, ccf)
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_esEs25(vwx301, vwx401, ty_Char) → new_esEs13(vwx301, vwx401)
new_primCmpInt(Neg(Succ(vwx900)), Pos(vwx100)) → LT
new_esEs22(vwx300, vwx400, ty_Int) → new_esEs16(vwx300, vwx400)
new_not(True) → False
new_esEs27(vwx300, vwx400, ty_Double) → new_esEs19(vwx300, vwx400)
new_compare16(Float(vwx90, vwx91), Float(vwx100, vwx101)) → new_compare6(new_sr(vwx90, vwx100), new_sr(vwx91, vwx101))

The set Q consists of the following terms:

new_esEs25(x0, x1, ty_Double)
new_ltEs7(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_ltEs19(x0, x1, ty_Integer)
new_esEs24(x0, x1, ty_Integer)
new_compare33(x0, x1, ty_Bool)
new_esEs30(x0, x1, app(app(ty_Either, x2), x3))
new_esEs26(x0, x1, ty_Float)
new_ltEs15(x0, x1)
new_lt7(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare33(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt6(x0, x1)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, app(ty_[], x2))
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, ty_@0)
new_esEs8(x0, x1, app(app(ty_Either, x2), x3))
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_esEs20(x0, x1, ty_@0)
new_ltEs7(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs7(x0, x1, ty_Integer)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs12([], :(x0, x1), x2)
new_ltEs7(Left(x0), Left(x1), ty_Double, x2)
new_compare29(x0, x1, x2, x3, x4)
new_ltEs7(Right(x0), Right(x1), x2, ty_Integer)
new_lt20(x0, x1, app(ty_[], x2))
new_ltEs21(x0, x1, ty_Ordering)
new_lt9(x0, x1, x2)
new_esEs26(x0, x1, ty_Ordering)
new_esEs6(@2(x0, x1), @2(x2, x3), x4, x5)
new_compare33(x0, x1, ty_Double)
new_esEs5(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_lt8(x0, x1, ty_Bool)
new_esEs7(x0, x1, app(ty_Maybe, x2))
new_ltEs13(Nothing, Just(x0), x1)
new_ltEs7(Left(x0), Left(x1), ty_@0, x2)
new_esEs7(x0, x1, app(ty_[], x2))
new_esEs7(x0, x1, app(ty_Ratio, x2))
new_ltEs13(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_asAs(False, x0)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs10(Right(x0), Right(x1), x2, ty_Float)
new_esEs29(x0, x1, ty_Integer)
new_ltEs4(x0, x1)
new_lt15(x0, x1)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_primCompAux0(x0, EQ)
new_esEs16(x0, x1)
new_primMulInt(Neg(x0), Neg(x1))
new_ltEs18(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs21(x0, x1, ty_Float)
new_esEs10(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs20(x0, x1, ty_Double)
new_ltEs18(x0, x1, ty_Float)
new_ltEs20(x0, x1, ty_Char)
new_compare26(x0, x1, True, x2, x3)
new_primPlusNat1(Succ(x0), Zero)
new_lt7(x0, x1, ty_Ordering)
new_ltEs7(Right(x0), Right(x1), x2, ty_Float)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_ltEs21(x0, x1, ty_Char)
new_ltEs20(x0, x1, ty_Float)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs24(x0, x1, ty_Ordering)
new_ltEs7(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_ltEs7(Right(x0), Right(x1), x2, ty_Double)
new_esEs10(Right(x0), Right(x1), x2, ty_Ordering)
new_lt7(x0, x1, ty_Int)
new_esEs22(x0, x1, ty_Bool)
new_ltEs7(Left(x0), Left(x1), ty_Int, x2)
new_esEs5(Just(x0), Just(x1), app(ty_Ratio, x2))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_esEs9(GT, LT)
new_esEs9(LT, GT)
new_ltEs10(x0, x1)
new_esEs10(Left(x0), Left(x1), ty_Char, x2)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_compare211(x0, x1, True, x2)
new_esEs10(Right(x0), Right(x1), x2, ty_Integer)
new_compare25(x0, x1, True)
new_esEs17(False, False)
new_esEs9(EQ, GT)
new_esEs9(GT, EQ)
new_esEs10(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs24(x0, x1, ty_Float)
new_ltEs18(x0, x1, ty_@0)
new_esEs10(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_esEs5(Just(x0), Just(x1), ty_Float)
new_esEs10(Right(x0), Right(x1), x2, ty_Bool)
new_esEs10(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs7(Left(x0), Left(x1), ty_Ordering, x2)
new_lt18(x0, x1, x2, x3)
new_compare210(x0, x1, True, x2, x3)
new_compare33(x0, x1, app(app(ty_@2, x2), x3))
new_esEs30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs5(Nothing, Just(x0), x1)
new_lt8(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare33(x0, x1, app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, ty_Integer)
new_lt8(x0, x1, ty_Float)
new_compare11(x0, x1, True, x2)
new_esEs13(Char(x0), Char(x1))
new_ltEs6(x0, x1)
new_lt8(x0, x1, ty_Int)
new_esEs7(x0, x1, ty_Int)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_sr(x0, x1)
new_lt8(x0, x1, app(ty_Maybe, x2))
new_esEs8(x0, x1, ty_Int)
new_ltEs20(x0, x1, ty_Int)
new_esEs8(x0, x1, app(ty_Maybe, x2))
new_ltEs13(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs23(x0, x1, app(ty_[], x2))
new_ltEs21(x0, x1, app(ty_[], x2))
new_ltEs19(x0, x1, ty_Double)
new_esEs10(Left(x0), Left(x1), ty_Int, x2)
new_ltEs7(Left(x0), Left(x1), ty_Char, x2)
new_lt14(x0, x1)
new_lt7(x0, x1, app(ty_Maybe, x2))
new_esEs8(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs14(EQ, EQ)
new_esEs30(x0, x1, ty_Ordering)
new_compare32(Right(x0), Left(x1), x2, x3)
new_compare32(Left(x0), Right(x1), x2, x3)
new_primEqNat0(Zero, Zero)
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs8(x0, x1, ty_@0)
new_ltEs21(x0, x1, app(ty_Maybe, x2))
new_esEs24(x0, x1, app(ty_[], x2))
new_ltEs21(x0, x1, ty_Bool)
new_ltEs13(Nothing, Nothing, x0)
new_esEs25(x0, x1, ty_Float)
new_esEs23(x0, x1, ty_Char)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs22(x0, x1, ty_Char)
new_esEs10(Right(x0), Right(x1), x2, ty_@0)
new_compare33(x0, x1, ty_Int)
new_ltEs13(Just(x0), Just(x1), ty_Bool)
new_compare211(x0, x1, False, x2)
new_primCompAux1(x0, x1, x2, x3)
new_pePe(False, x0)
new_esEs25(x0, x1, ty_Integer)
new_ltEs9(False, False)
new_compare111(x0, x1, True, x2, x3)
new_lt20(x0, x1, ty_Char)
new_sr0(Integer(x0), Integer(x1))
new_ltEs19(x0, x1, ty_Ordering)
new_lt20(x0, x1, ty_Double)
new_compare17(x0, x1, x2, x3)
new_lt10(x0, x1)
new_primMulNat0(Zero, Zero)
new_esEs25(x0, x1, app(ty_[], x2))
new_esEs30(x0, x1, ty_@0)
new_ltEs7(Right(x0), Right(x1), x2, ty_@0)
new_esEs21(x0, x1, ty_Char)
new_ltEs7(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_lt8(x0, x1, ty_Integer)
new_compare6(x0, x1)
new_compare25(x0, x1, False)
new_esEs21(x0, x1, ty_Double)
new_esEs10(Left(x0), Left(x1), ty_@0, x2)
new_ltEs13(Just(x0), Just(x1), ty_Int)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_pePe(True, x0)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs22(x0, x1, ty_Int)
new_lt8(x0, x1, ty_@0)
new_esEs21(x0, x1, ty_Integer)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_lt7(x0, x1, ty_Integer)
new_esEs5(Just(x0), Just(x1), ty_Double)
new_ltEs7(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs11(:%(x0, x1), :%(x2, x3), x4)
new_lt8(x0, x1, app(ty_[], x2))
new_esEs27(x0, x1, ty_Bool)
new_ltEs20(x0, x1, ty_Integer)
new_esEs14(Integer(x0), Integer(x1))
new_esEs10(Right(x0), Right(x1), x2, app(ty_[], x3))
new_compare24(x0, x1, False, x2, x3)
new_lt5(x0, x1)
new_esEs22(x0, x1, ty_@0)
new_esEs10(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_compare8(x0, x1)
new_compare32(Right(x0), Right(x1), x2, x3)
new_primPlusNat1(Succ(x0), Succ(x1))
new_ltEs19(x0, x1, ty_Bool)
new_compare27(x0, x1, False, x2, x3, x4)
new_compare11(x0, x1, False, x2)
new_compare33(x0, x1, app(ty_[], x2))
new_esEs8(x0, x1, ty_Bool)
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_esEs20(x0, x1, ty_Bool)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_esEs28(x0, x1, ty_Int)
new_esEs9(EQ, LT)
new_esEs9(LT, EQ)
new_primMulNat0(Zero, Succ(x0))
new_ltEs13(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs21(x0, x1, ty_Int)
new_lt20(x0, x1, ty_Bool)
new_ltEs18(x0, x1, app(ty_Ratio, x2))
new_esEs20(x0, x1, ty_Int)
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_ltEs13(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, ty_Int)
new_esEs8(x0, x1, ty_Float)
new_lt20(x0, x1, ty_Float)
new_ltEs18(x0, x1, ty_Bool)
new_esEs5(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs12(:(x0, x1), :(x2, x3), x4)
new_esEs8(x0, x1, ty_Integer)
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_compare([], :(x0, x1), x2)
new_compare210(x0, x1, False, x2, x3)
new_compare19(:%(x0, x1), :%(x2, x3), ty_Integer)
new_compare33(x0, x1, app(ty_Maybe, x2))
new_esEs5(Just(x0), Just(x1), ty_Char)
new_esEs7(x0, x1, ty_Double)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs24(x0, x1, ty_Int)
new_esEs22(x0, x1, ty_Integer)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs10(Right(x0), Right(x1), x2, ty_Char)
new_esEs27(x0, x1, ty_@0)
new_esEs27(x0, x1, ty_Double)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs18(x0, x1, ty_Char)
new_lt12(x0, x1)
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs13(Just(x0), Just(x1), ty_Integer)
new_esEs7(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primPlusNat0(Zero, x0)
new_esEs30(x0, x1, ty_Float)
new_esEs10(Left(x0), Left(x1), ty_Double, x2)
new_lt16(x0, x1)
new_lt8(x0, x1, ty_Double)
new_ltEs5(x0, x1)
new_ltEs19(x0, x1, ty_Float)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, ty_Char)
new_primEqNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, Zero)
new_esEs10(Right(x0), Right(x1), x2, ty_Int)
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs18(x0, x1, ty_Double)
new_ltEs18(x0, x1, ty_Ordering)
new_esEs10(Left(x0), Left(x1), ty_Integer, x2)
new_esEs10(Left(x0), Left(x1), ty_Float, x2)
new_ltEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs14(LT, LT)
new_lt20(x0, x1, ty_Ordering)
new_ltEs7(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs23(x0, x1, ty_Bool)
new_primCmpNat0(Succ(x0), Zero)
new_esEs5(Just(x0), Just(x1), ty_Bool)
new_esEs21(x0, x1, ty_Float)
new_esEs25(x0, x1, ty_Bool)
new_esEs12([], [], x0)
new_compare32(Left(x0), Left(x1), x2, x3)
new_esEs23(x0, x1, ty_Double)
new_ltEs18(x0, x1, app(ty_[], x2))
new_ltEs20(x0, x1, ty_Ordering)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_compare12(x0, x1, True, x2, x3)
new_ltEs19(x0, x1, app(ty_[], x2))
new_esEs20(x0, x1, ty_Integer)
new_compare27(x0, x1, True, x2, x3, x4)
new_ltEs13(Just(x0), Just(x1), ty_@0)
new_esEs12(:(x0, x1), [], x2)
new_lt19(x0, x1, x2)
new_lt20(x0, x1, ty_Int)
new_lt7(x0, x1, app(app(ty_@2, x2), x3))
new_compare33(x0, x1, app(ty_Ratio, x2))
new_ltEs13(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs7(x0, x1, ty_@0)
new_compare28(x0, x1, True)
new_esEs26(x0, x1, app(ty_[], x2))
new_ltEs7(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs9(False, True)
new_ltEs9(True, False)
new_esEs30(x0, x1, ty_Int)
new_esEs8(x0, x1, app(ty_Ratio, x2))
new_esEs23(x0, x1, ty_Ordering)
new_ltEs21(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs16(@2(x0, x1), @2(x2, x3), x4, x5)
new_ltEs9(True, True)
new_ltEs21(x0, x1, ty_@0)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_esEs30(x0, x1, app(ty_Maybe, x2))
new_esEs22(x0, x1, app(ty_[], x2))
new_esEs26(x0, x1, ty_@0)
new_compare18(x0, x1, False, x2, x3)
new_esEs27(x0, x1, ty_Float)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_esEs9(GT, GT)
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_ltEs13(Just(x0), Just(x1), ty_Ordering)
new_primCmpNat0(Succ(x0), Succ(x1))
new_esEs8(x0, x1, app(app(ty_@2, x2), x3))
new_esEs22(x0, x1, ty_Float)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_ltEs21(x0, x1, ty_Int)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_esEs5(Just(x0), Just(x1), ty_Ordering)
new_esEs5(Just(x0), Just(x1), app(ty_[], x2))
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_compare110(x0, x1, False)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, ty_Int)
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_esEs26(x0, x1, ty_Int)
new_lt20(x0, x1, ty_Integer)
new_primEqInt(Neg(Zero), Pos(Zero))
new_primEqInt(Pos(Zero), Neg(Zero))
new_ltEs8(x0, x1, x2)
new_ltEs14(LT, EQ)
new_ltEs14(EQ, LT)
new_ltEs19(x0, x1, ty_Char)
new_esEs21(x0, x1, app(ty_[], x2))
new_esEs21(x0, x1, ty_@0)
new_ltEs18(x0, x1, ty_Integer)
new_ltEs7(Left(x0), Left(x1), app(ty_[], x2), x3)
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_ltEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_lt7(x0, x1, app(ty_Ratio, x2))
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt11(x0, x1, x2, x3, x4)
new_esEs9(EQ, EQ)
new_lt8(x0, x1, app(ty_Ratio, x2))
new_esEs5(Nothing, Nothing, x0)
new_ltEs7(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs7(x0, x1, ty_Ordering)
new_primEqInt(Neg(Zero), Neg(Zero))
new_esEs22(x0, x1, ty_Double)
new_compare14(@0, @0)
new_ltEs18(x0, x1, app(ty_Maybe, x2))
new_ltEs20(x0, x1, ty_Double)
new_esEs10(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs5(Just(x0), Just(x1), ty_Int)
new_ltEs20(x0, x1, app(ty_[], x2))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, ty_Float)
new_esEs25(x0, x1, ty_Char)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs12(x0, x1)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_ltEs7(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_esEs24(x0, x1, ty_Bool)
new_compare15(x0, x1, False, x2, x3, x4)
new_lt8(x0, x1, ty_Ordering)
new_compare16(Float(x0, x1), Float(x2, x3))
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs26(x0, x1, ty_Double)
new_esEs7(x0, x1, ty_Char)
new_ltEs20(x0, x1, ty_@0)
new_lt7(x0, x1, ty_@0)
new_ltEs21(x0, x1, ty_Double)
new_ltEs19(x0, x1, ty_@0)
new_ltEs7(Left(x0), Left(x1), ty_Float, x2)
new_compare28(x0, x1, False)
new_asAs(True, x0)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs25(x0, x1, ty_Ordering)
new_primCompAux0(x0, LT)
new_ltEs14(EQ, GT)
new_ltEs14(GT, EQ)
new_compare15(x0, x1, True, x2, x3, x4)
new_esEs20(x0, x1, ty_Float)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_lt13(x0, x1, x2)
new_primCmpNat0(Zero, Zero)
new_esEs10(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs30(x0, x1, ty_Bool)
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs5(Just(x0), Nothing, x1)
new_lt4(x0, x1)
new_compare12(x0, x1, False, x2, x3)
new_lt7(x0, x1, ty_Char)
new_compare9(Double(x0, x1), Double(x2, x3))
new_esEs22(x0, x1, ty_Ordering)
new_esEs15(@0, @0)
new_primCompAux0(x0, GT)
new_ltEs7(Right(x0), Right(x1), x2, ty_Int)
new_esEs20(x0, x1, ty_Ordering)
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_esEs4(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs7(x0, x1, ty_Bool)
new_esEs5(Just(x0), Just(x1), ty_Integer)
new_esEs28(x0, x1, ty_Integer)
new_esEs30(x0, x1, ty_Integer)
new_esEs24(x0, x1, ty_Double)
new_ltEs18(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs7(Right(x0), Right(x1), x2, ty_Char)
new_esEs20(x0, x1, app(ty_[], x2))
new_esEs29(x0, x1, ty_Int)
new_lt7(x0, x1, ty_Bool)
new_primEqNat0(Zero, Succ(x0))
new_ltEs14(LT, GT)
new_ltEs14(GT, LT)
new_primMulNat0(Succ(x0), Zero)
new_lt8(x0, x1, ty_Char)
new_compare7(Char(x0), Char(x1))
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_primMulNat0(Succ(x0), Succ(x1))
new_esEs10(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare(:(x0, x1), :(x2, x3), x4)
new_esEs7(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs7(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, ty_Char)
new_esEs5(Just(x0), Just(x1), ty_@0)
new_esEs27(x0, x1, ty_Integer)
new_compare33(x0, x1, ty_Ordering)
new_ltEs13(Just(x0), Nothing, x1)
new_ltEs17(x0, x1, x2)
new_esEs30(x0, x1, ty_Char)
new_ltEs14(GT, GT)
new_esEs25(x0, x1, ty_@0)
new_esEs5(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_not(True)
new_compare111(x0, x1, False, x2, x3)
new_ltEs13(Just(x0), Just(x1), app(ty_[], x2))
new_esEs30(x0, x1, app(app(ty_@2, x2), x3))
new_compare18(x0, x1, True, x2, x3)
new_esEs30(x0, x1, app(ty_Ratio, x2))
new_esEs10(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs27(x0, x1, ty_Ordering)
new_ltEs18(x0, x1, ty_Int)
new_compare([], [], x0)
new_ltEs7(Left(x0), Left(x1), ty_Bool, x2)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_not(False)
new_ltEs11(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_ltEs7(Left(x0), Left(x1), ty_Integer, x2)
new_ltEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs21(x0, x1, ty_Ordering)
new_primCmpNat0(Zero, Succ(x0))
new_esEs26(x0, x1, ty_Integer)
new_lt7(x0, x1, app(app(ty_Either, x2), x3))
new_esEs30(x0, x1, ty_Double)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs8(x0, x1, ty_Double)
new_esEs10(Left(x0), Left(x1), ty_Bool, x2)
new_primPlusNat0(Succ(x0), x1)
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_esEs8(x0, x1, app(ty_[], x2))
new_esEs21(x0, x1, ty_Bool)
new_lt17(x0, x1, x2, x3)
new_esEs5(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_compare13(x0, x1, False)
new_lt8(x0, x1, app(app(ty_@2, x2), x3))
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_ltEs19(x0, x1, ty_Int)
new_ltEs13(Just(x0), Just(x1), ty_Char)
new_esEs7(x0, x1, app(app(ty_Either, x2), x3))
new_lt7(x0, x1, ty_Float)
new_compare30(x0, x1)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs7(Right(x0), Right(x1), x2, app(ty_[], x3))
new_compare24(x0, x1, True, x2, x3)
new_esEs19(Double(x0, x1), Double(x2, x3))
new_compare33(x0, x1, ty_Char)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_compare110(x0, x1, True)
new_esEs17(True, False)
new_esEs17(False, True)
new_esEs20(x0, x1, ty_Char)
new_lt7(x0, x1, ty_Double)
new_ltEs13(Just(x0), Just(x1), ty_Double)
new_compare33(x0, x1, ty_Float)
new_lt20(x0, x1, ty_@0)
new_esEs30(x0, x1, app(ty_[], x2))
new_esEs26(x0, x1, ty_Bool)
new_ltEs21(x0, x1, app(ty_Ratio, x2))
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_esEs18(Float(x0, x1), Float(x2, x3))
new_compare26(x0, x1, False, x2, x3)
new_compare13(x0, x1, True)
new_primEqInt(Pos(Zero), Pos(Zero))
new_esEs17(True, True)
new_esEs10(Right(x0), Left(x1), x2, x3)
new_esEs10(Left(x0), Right(x1), x2, x3)
new_esEs24(x0, x1, ty_Char)
new_esEs8(x0, x1, ty_Char)
new_compare10(Integer(x0), Integer(x1))
new_ltEs13(Just(x0), Just(x1), ty_Float)
new_compare31(x0, x1, x2)
new_esEs10(Left(x0), Left(x1), ty_Ordering, x2)
new_ltEs7(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs10(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_ltEs7(Right(x0), Left(x1), x2, x3)
new_ltEs7(Left(x0), Right(x1), x2, x3)
new_compare19(:%(x0, x1), :%(x2, x3), ty_Int)
new_esEs10(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_lt8(x0, x1, app(app(ty_Either, x2), x3))
new_primPlusNat1(Zero, Succ(x0))
new_compare33(x0, x1, ty_@0)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_esEs24(x0, x1, ty_@0)
new_esEs7(x0, x1, ty_Float)
new_ltEs7(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs25(x0, x1, ty_Int)
new_compare33(x0, x1, ty_Integer)
new_esEs9(LT, LT)
new_ltEs21(x0, x1, ty_Integer)
new_lt7(x0, x1, app(ty_[], x2))
new_ltEs20(x0, x1, ty_Bool)
new_esEs10(Right(x0), Right(x1), x2, ty_Double)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs8(x0, x1, ty_Ordering)
new_compare(:(x0, x1), [], x2)

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: