YES 3.863 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) => (a,b)  ->  (a,b)  ->  Bool) :: (Ord a, Ord b) => (a,b)  ->  (a,b)  ->  Bool)

module Main where
  import qualified Prelude


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

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



↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ IFR

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

module Main where
  import qualified Prelude


Replaced joker patterns by fresh variables and removed binding patterns.

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

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

absReal0 x True = `negate` x

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

absReal2 x = absReal1 x (x >= 0)

The following Function with conditions
undefined 
 | False
 = undefined

is transformed to
undefined  = undefined1

undefined0 True = undefined

undefined1  = undefined0 False

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

is transformed to
reduce x y = reduce2 x y

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



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

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

module Main where
  import qualified Prelude


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

are unpacked to the following functions on top level
reduce2Reduce1 vwv vww x y True = error []
reduce2Reduce1 vwv vww x y False = reduce2Reduce0 vwv vww x y otherwise

reduce2D vwv vww = gcd vwv vww

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

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

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

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

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

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



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

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

module Main where
  import qualified Prelude


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

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

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

module Main where
  import qualified Prelude


Haskell To QDPs


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

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

new_primPlusNat(Succ(vwx6300), Succ(vwx400000)) → new_primPlusNat(vwx6300, vwx400000)

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

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



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

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

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

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

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



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

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

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

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

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



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

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

new_primCmpNat(Succ(vwx22000), Succ(vwx24000)) → new_primCmpNat(vwx22000, vwx24000)

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

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



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

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

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

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

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



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

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

new_compare2(@2(vwx220, @2(vwx2210, vwx2211)), @2(vwx240, @2(vwx2410, vwx2411)), False, cc, app(app(ty_@2, app(ty_Maybe, eb)), ea)) → new_lt0(vwx2210, vwx2410, eb)
new_compare2(@2(vwx220, @3(vwx2210, vwx2211, vwx2212)), @2(vwx240, @3(vwx2410, vwx2411, vwx2412)), False, cc, app(app(app(ty_@3, bag), bah), app(app(ty_Either, bbd), bbe))) → new_ltEs1(vwx2212, vwx2412, bbd, bbe)
new_ltEs(@2(vwx2210, vwx2211), @2(vwx2410, vwx2411), app(ty_Maybe, eb), ea) → new_lt0(vwx2210, vwx2410, eb)
new_ltEs1(Left(vwx2210), Left(vwx2410), app(app(ty_Either, gg), gh), ge) → new_ltEs1(vwx2210, vwx2410, gg, gh)
new_ltEs1(Left(vwx2210), Left(vwx2410), app(ty_Maybe, gf), ge) → new_ltEs0(vwx2210, vwx2410, gf)
new_lt3(:(vwx2200, vwx2201), :(vwx2400, vwx2401), cb) → new_compare1(vwx2201, vwx2401, cb)
new_compare2(@2(vwx220, Left(vwx2210)), @2(vwx240, Left(vwx2410)), False, cc, app(app(ty_Either, app(app(ty_@2, gc), gd)), ge)) → new_ltEs(vwx2210, vwx2410, gc, gd)
new_compare3(vwx220, vwx240, bd) → new_compare20(vwx220, vwx240, new_esEs5(vwx220, vwx240, bd), bd)
new_ltEs2(@3(vwx2210, vwx2211, vwx2212), @3(vwx2410, vwx2411, vwx2412), app(app(ty_Either, bdg), bdh), bah, bcd) → new_lt1(vwx2210, vwx2410, bdg, bdh)
new_compare2(@2(vwx220, Right(vwx2210)), @2(vwx240, Right(vwx2410)), False, cc, app(app(ty_Either, he), app(app(ty_@2, hf), hg))) → new_ltEs(vwx2210, vwx2410, hf, hg)
new_ltEs2(@3(vwx2210, vwx2211, vwx2212), @3(vwx2410, vwx2411, vwx2412), bag, app(ty_[], bdc), bcd) → new_lt3(vwx2211, vwx2411, bdc)
new_ltEs2(@3(vwx2210, vwx2211, vwx2212), @3(vwx2410, vwx2411, vwx2412), bag, app(app(app(ty_@3, bch), bda), bdb), bcd) → new_lt2(vwx2211, vwx2411, bch, bda, bdb)
new_compare2(@2(vwx220, @2(vwx2210, vwx2211)), @2(vwx240, @2(vwx2410, vwx2411)), False, cc, app(app(ty_@2, app(app(ty_@2, dg), dh)), ea)) → new_lt(vwx2210, vwx2410, dg, dh)
new_compare2(@2(vwx220, Left(vwx2210)), @2(vwx240, Left(vwx2410)), False, cc, app(app(ty_Either, app(app(ty_Either, gg), gh)), ge)) → new_ltEs1(vwx2210, vwx2410, gg, gh)
new_ltEs(@2(vwx2210, vwx2211), @2(vwx2410, vwx2411), app(app(app(ty_@3, ee), ef), eg), ea) → new_lt2(vwx2210, vwx2410, ee, ef, eg)
new_compare(vwx220, vwx240, ba, bb) → new_compare2(vwx220, vwx240, new_esEs4(vwx220, vwx240, ba, bb), ba, bb)
new_compare2(@2(vwx220, vwx221), @2(vwx240, vwx241), False, cc, app(ty_[], bee)) → new_compare1(vwx221, vwx241, bee)
new_ltEs0(Just(vwx2210), Just(vwx2410), app(ty_Maybe, fc)) → new_ltEs0(vwx2210, vwx2410, fc)
new_compare1(:(vwx2200, vwx2201), :(vwx2400, vwx2401), cb) → new_primCompAux(vwx2200, vwx2400, new_compare0(vwx2201, vwx2401, cb), cb)
new_compare2(@2(vwx220, @3(vwx2210, vwx2211, vwx2212)), @2(vwx240, @3(vwx2410, vwx2411, vwx2412)), False, cc, app(app(app(ty_@3, app(ty_[], bed)), bah), bcd)) → new_lt3(vwx2210, vwx2410, bed)
new_compare2(@2(vwx220, @2(vwx2210, vwx2211)), @2(vwx240, @2(vwx2410, vwx2411)), False, cc, app(app(ty_@2, cd), app(app(ty_@2, ce), cf))) → new_ltEs(vwx2211, vwx2411, ce, cf)
new_compare2(@2(vwx220, Right(vwx2210)), @2(vwx240, Right(vwx2410)), False, cc, app(app(ty_Either, he), app(ty_Maybe, hh))) → new_ltEs0(vwx2210, vwx2410, hh)
new_ltEs1(Right(vwx2210), Right(vwx2410), he, app(app(ty_@2, hf), hg)) → new_ltEs(vwx2210, vwx2410, hf, hg)
new_compare2(@2(vwx220, @3(vwx2210, vwx2211, vwx2212)), @2(vwx240, @3(vwx2410, vwx2411, vwx2412)), False, cc, app(app(app(ty_@3, bag), app(ty_Maybe, bce)), bcd)) → new_lt0(vwx2211, vwx2411, bce)
new_compare2(@2(vwx220, Just(vwx2210)), @2(vwx240, Just(vwx2410)), False, cc, app(ty_Maybe, app(ty_[], gb))) → new_ltEs3(vwx2210, vwx2410, gb)
new_compare2(@2(vwx220, @2(vwx2210, vwx2211)), @2(vwx240, @2(vwx2410, vwx2411)), False, cc, app(app(ty_@2, app(ty_[], eh)), ea)) → new_lt3(vwx2210, vwx2410, eh)
new_compare2(@2(vwx220, Just(vwx2210)), @2(vwx240, Just(vwx2410)), False, cc, app(ty_Maybe, app(app(ty_Either, fd), ff))) → new_ltEs1(vwx2210, vwx2410, fd, ff)
new_primCompAux(vwx2200, vwx2400, vwx86, app(app(ty_@2, bef), beg)) → new_compare(vwx2200, vwx2400, bef, beg)
new_ltEs2(@3(vwx2210, vwx2211, vwx2212), @3(vwx2410, vwx2411, vwx2412), app(ty_Maybe, bdf), bah, bcd) → new_lt0(vwx2210, vwx2410, bdf)
new_ltEs1(Right(vwx2210), Right(vwx2410), he, app(ty_Maybe, hh)) → new_ltEs0(vwx2210, vwx2410, hh)
new_ltEs0(Just(vwx2210), Just(vwx2410), app(ty_[], gb)) → new_ltEs3(vwx2210, vwx2410, gb)
new_compare2(@2(vwx220, @3(vwx2210, vwx2211, vwx2212)), @2(vwx240, @3(vwx2410, vwx2411, vwx2412)), False, cc, app(app(app(ty_@3, bag), bah), app(app(ty_@2, bba), bbb))) → new_ltEs(vwx2212, vwx2412, bba, bbb)
new_ltEs2(@3(vwx2210, vwx2211, vwx2212), @3(vwx2410, vwx2411, vwx2412), bag, bah, app(ty_[], bca)) → new_ltEs3(vwx2212, vwx2412, bca)
new_lt1(vwx220, vwx240, be, bf) → new_compare21(vwx220, vwx240, new_esEs6(vwx220, vwx240, be, bf), be, bf)
new_compare1(:(vwx2200, vwx2201), :(vwx2400, vwx2401), cb) → new_compare1(vwx2201, vwx2401, cb)
new_compare2(@2(vwx220, vwx221), @2(vwx240, vwx241), False, app(ty_Maybe, bd), bc) → new_compare20(vwx220, vwx240, new_esEs5(vwx220, vwx240, bd), bd)
new_ltEs1(Right(vwx2210), Right(vwx2410), he, app(app(app(ty_@3, bac), bad), bae)) → new_ltEs2(vwx2210, vwx2410, bac, bad, bae)
new_compare2(@2(vwx220, @3(vwx2210, vwx2211, vwx2212)), @2(vwx240, @3(vwx2410, vwx2411, vwx2412)), False, cc, app(app(app(ty_@3, bag), app(ty_[], bdc)), bcd)) → new_lt3(vwx2211, vwx2411, bdc)
new_compare2(@2(vwx220, @3(vwx2210, vwx2211, vwx2212)), @2(vwx240, @3(vwx2410, vwx2411, vwx2412)), False, cc, app(app(app(ty_@3, bag), bah), app(app(app(ty_@3, bbf), bbg), bbh))) → new_ltEs2(vwx2212, vwx2412, bbf, bbg, bbh)
new_compare2(@2(:(vwx2200, vwx2201), vwx221), @2(:(vwx2400, vwx2401), vwx241), False, app(ty_[], cb), bc) → new_primCompAux(vwx2200, vwx2400, new_compare0(vwx2201, vwx2401, cb), cb)
new_primCompAux(vwx2200, vwx2400, vwx86, app(app(app(ty_@3, bfc), bfd), bfe)) → new_compare5(vwx2200, vwx2400, bfc, bfd, bfe)
new_compare2(@2(vwx220, Just(vwx2210)), @2(vwx240, Just(vwx2410)), False, cc, app(ty_Maybe, app(ty_Maybe, fc))) → new_ltEs0(vwx2210, vwx2410, fc)
new_ltEs1(Left(vwx2210), Left(vwx2410), app(ty_[], hd), ge) → new_ltEs3(vwx2210, vwx2410, hd)
new_ltEs(@2(vwx2210, vwx2211), @2(vwx2410, vwx2411), app(ty_[], eh), ea) → new_lt3(vwx2210, vwx2410, eh)
new_ltEs(@2(vwx2210, vwx2211), @2(vwx2410, vwx2411), cd, app(app(ty_@2, ce), cf)) → new_ltEs(vwx2211, vwx2411, ce, cf)
new_ltEs1(Right(vwx2210), Right(vwx2410), he, app(app(ty_Either, baa), bab)) → new_ltEs1(vwx2210, vwx2410, baa, bab)
new_primCompAux(vwx2200, vwx2400, vwx86, app(ty_[], bff)) → new_compare1(vwx2200, vwx2400, bff)
new_ltEs2(@3(vwx2210, vwx2211, vwx2212), @3(vwx2410, vwx2411, vwx2412), bag, app(ty_Maybe, bce), bcd) → new_lt0(vwx2211, vwx2411, bce)
new_ltEs(@2(vwx2210, vwx2211), @2(vwx2410, vwx2411), cd, app(ty_Maybe, cg)) → new_ltEs0(vwx2211, vwx2411, cg)
new_compare2(@2(vwx220, Just(vwx2210)), @2(vwx240, Just(vwx2410)), False, cc, app(ty_Maybe, app(app(app(ty_@3, fg), fh), ga))) → new_ltEs2(vwx2210, vwx2410, fg, fh, ga)
new_compare2(@2(vwx220, @3(vwx2210, vwx2211, vwx2212)), @2(vwx240, @3(vwx2410, vwx2411, vwx2412)), False, cc, app(app(app(ty_@3, bag), bah), app(ty_Maybe, bbc))) → new_ltEs0(vwx2212, vwx2412, bbc)
new_compare2(@2(vwx220, Right(vwx2210)), @2(vwx240, Right(vwx2410)), False, cc, app(app(ty_Either, he), app(app(ty_Either, baa), bab))) → new_ltEs1(vwx2210, vwx2410, baa, bab)
new_compare2(@2(vwx220, Left(vwx2210)), @2(vwx240, Left(vwx2410)), False, cc, app(app(ty_Either, app(app(app(ty_@3, ha), hb), hc)), ge)) → new_ltEs2(vwx2210, vwx2410, ha, hb, hc)
new_compare4(vwx220, vwx240, be, bf) → new_compare21(vwx220, vwx240, new_esEs6(vwx220, vwx240, be, bf), be, bf)
new_compare2(@2(vwx220, @3(vwx2210, vwx2211, vwx2212)), @2(vwx240, @3(vwx2410, vwx2411, vwx2412)), False, cc, app(app(app(ty_@3, bag), app(app(app(ty_@3, bch), bda), bdb)), bcd)) → new_lt2(vwx2211, vwx2411, bch, bda, bdb)
new_compare22(vwx220, vwx240, False, bg, bh, ca) → new_ltEs2(vwx220, vwx240, bg, bh, ca)
new_compare2(@2(vwx220, @3(vwx2210, vwx2211, vwx2212)), @2(vwx240, @3(vwx2410, vwx2411, vwx2412)), False, cc, app(app(app(ty_@3, app(ty_Maybe, bdf)), bah), bcd)) → new_lt0(vwx2210, vwx2410, bdf)
new_lt(vwx220, vwx240, ba, bb) → new_compare2(vwx220, vwx240, new_esEs4(vwx220, vwx240, ba, bb), ba, bb)
new_compare2(@2(vwx220, @3(vwx2210, vwx2211, vwx2212)), @2(vwx240, @3(vwx2410, vwx2411, vwx2412)), False, cc, app(app(app(ty_@3, app(app(app(ty_@3, bea), beb), bec)), bah), bcd)) → new_lt2(vwx2210, vwx2410, bea, beb, bec)
new_ltEs2(@3(vwx2210, vwx2211, vwx2212), @3(vwx2410, vwx2411, vwx2412), bag, bah, app(app(app(ty_@3, bbf), bbg), bbh)) → new_ltEs2(vwx2212, vwx2412, bbf, bbg, bbh)
new_compare5(vwx220, vwx240, bg, bh, ca) → new_compare22(vwx220, vwx240, new_esEs7(vwx220, vwx240, bg, bh, ca), bg, bh, ca)
new_compare2(@2(vwx220, @2(vwx2210, vwx2211)), @2(vwx240, @2(vwx2410, vwx2411)), False, cc, app(app(ty_@2, cd), app(app(app(ty_@3, dc), dd), de))) → new_ltEs2(vwx2211, vwx2411, dc, dd, de)
new_ltEs2(@3(vwx2210, vwx2211, vwx2212), @3(vwx2410, vwx2411, vwx2412), app(ty_[], bed), bah, bcd) → new_lt3(vwx2210, vwx2410, bed)
new_ltEs1(Left(vwx2210), Left(vwx2410), app(app(ty_@2, gc), gd), ge) → new_ltEs(vwx2210, vwx2410, gc, gd)
new_compare2(@2(vwx220, Left(vwx2210)), @2(vwx240, Left(vwx2410)), False, cc, app(app(ty_Either, app(ty_[], hd)), ge)) → new_ltEs3(vwx2210, vwx2410, hd)
new_ltEs3(vwx221, vwx241, bee) → new_compare1(vwx221, vwx241, bee)
new_ltEs2(@3(vwx2210, vwx2211, vwx2212), @3(vwx2410, vwx2411, vwx2412), bag, bah, app(app(ty_Either, bbd), bbe)) → new_ltEs1(vwx2212, vwx2412, bbd, bbe)
new_compare2(@2(vwx220, @2(vwx2210, vwx2211)), @2(vwx240, @2(vwx2410, vwx2411)), False, cc, app(app(ty_@2, cd), app(ty_[], df))) → new_ltEs3(vwx2211, vwx2411, df)
new_compare2(@2(vwx220, Left(vwx2210)), @2(vwx240, Left(vwx2410)), False, cc, app(app(ty_Either, app(ty_Maybe, gf)), ge)) → new_ltEs0(vwx2210, vwx2410, gf)
new_ltEs0(Just(vwx2210), Just(vwx2410), app(app(app(ty_@3, fg), fh), ga)) → new_ltEs2(vwx2210, vwx2410, fg, fh, ga)
new_compare2(@2(vwx220, Right(vwx2210)), @2(vwx240, Right(vwx2410)), False, cc, app(app(ty_Either, he), app(app(app(ty_@3, bac), bad), bae))) → new_ltEs2(vwx2210, vwx2410, bac, bad, bae)
new_compare2(@2(vwx220, Right(vwx2210)), @2(vwx240, Right(vwx2410)), False, cc, app(app(ty_Either, he), app(ty_[], baf))) → new_ltEs3(vwx2210, vwx2410, baf)
new_compare2(@2(vwx220, @3(vwx2210, vwx2211, vwx2212)), @2(vwx240, @3(vwx2410, vwx2411, vwx2412)), False, cc, app(app(app(ty_@3, app(app(ty_Either, bdg), bdh)), bah), bcd)) → new_lt1(vwx2210, vwx2410, bdg, bdh)
new_compare2(@2(vwx220, Just(vwx2210)), @2(vwx240, Just(vwx2410)), False, cc, app(ty_Maybe, app(app(ty_@2, fa), fb))) → new_ltEs(vwx2210, vwx2410, fa, fb)
new_ltEs(@2(vwx2210, vwx2211), @2(vwx2410, vwx2411), cd, app(ty_[], df)) → new_ltEs3(vwx2211, vwx2411, df)
new_ltEs2(@3(vwx2210, vwx2211, vwx2212), @3(vwx2410, vwx2411, vwx2412), bag, app(app(ty_Either, bcf), bcg), bcd) → new_lt1(vwx2211, vwx2411, bcf, bcg)
new_ltEs(@2(vwx2210, vwx2211), @2(vwx2410, vwx2411), app(app(ty_@2, dg), dh), ea) → new_lt(vwx2210, vwx2410, dg, dh)
new_ltEs1(Left(vwx2210), Left(vwx2410), app(app(app(ty_@3, ha), hb), hc), ge) → new_ltEs2(vwx2210, vwx2410, ha, hb, hc)
new_ltEs(@2(vwx2210, vwx2211), @2(vwx2410, vwx2411), cd, app(app(app(ty_@3, dc), dd), de)) → new_ltEs2(vwx2211, vwx2411, dc, dd, de)
new_compare2(@2(vwx220, @2(vwx2210, vwx2211)), @2(vwx240, @2(vwx2410, vwx2411)), False, cc, app(app(ty_@2, cd), app(ty_Maybe, cg))) → new_ltEs0(vwx2211, vwx2411, cg)
new_compare2(@2(vwx220, vwx221), @2(vwx240, vwx241), False, app(app(ty_@2, ba), bb), bc) → new_compare2(vwx220, vwx240, new_esEs4(vwx220, vwx240, ba, bb), ba, bb)
new_compare2(@2(vwx220, @3(vwx2210, vwx2211, vwx2212)), @2(vwx240, @3(vwx2410, vwx2411, vwx2412)), False, cc, app(app(app(ty_@3, bag), app(app(ty_Either, bcf), bcg)), bcd)) → new_lt1(vwx2211, vwx2411, bcf, bcg)
new_ltEs1(Right(vwx2210), Right(vwx2410), he, app(ty_[], baf)) → new_ltEs3(vwx2210, vwx2410, baf)
new_compare2(@2(:(vwx2200, vwx2201), vwx221), @2(:(vwx2400, vwx2401), vwx241), False, app(ty_[], cb), bc) → new_compare1(vwx2201, vwx2401, cb)
new_compare21(vwx220, vwx240, False, be, bf) → new_ltEs1(vwx220, vwx240, be, bf)
new_primCompAux(vwx2200, vwx2400, vwx86, app(app(ty_Either, bfa), bfb)) → new_compare4(vwx2200, vwx2400, bfa, bfb)
new_ltEs(@2(vwx2210, vwx2211), @2(vwx2410, vwx2411), app(app(ty_Either, ec), ed), ea) → new_lt1(vwx2210, vwx2410, ec, ed)
new_compare2(@2(vwx220, vwx221), @2(vwx240, vwx241), False, app(app(ty_Either, be), bf), bc) → new_compare21(vwx220, vwx240, new_esEs6(vwx220, vwx240, be, bf), be, bf)
new_compare2(@2(vwx220, @3(vwx2210, vwx2211, vwx2212)), @2(vwx240, @3(vwx2410, vwx2411, vwx2412)), False, cc, app(app(app(ty_@3, bag), bah), app(ty_[], bca))) → new_ltEs3(vwx2212, vwx2412, bca)
new_ltEs2(@3(vwx2210, vwx2211, vwx2212), @3(vwx2410, vwx2411, vwx2412), bag, bah, app(app(ty_@2, bba), bbb)) → new_ltEs(vwx2212, vwx2412, bba, bbb)
new_ltEs2(@3(vwx2210, vwx2211, vwx2212), @3(vwx2410, vwx2411, vwx2412), app(app(ty_@2, bdd), bde), bah, bcd) → new_lt(vwx2210, vwx2410, bdd, bde)
new_ltEs2(@3(vwx2210, vwx2211, vwx2212), @3(vwx2410, vwx2411, vwx2412), bag, bah, app(ty_Maybe, bbc)) → new_ltEs0(vwx2212, vwx2412, bbc)
new_compare2(@2(vwx220, @2(vwx2210, vwx2211)), @2(vwx240, @2(vwx2410, vwx2411)), False, cc, app(app(ty_@2, app(app(ty_Either, ec), ed)), ea)) → new_lt1(vwx2210, vwx2410, ec, ed)
new_ltEs2(@3(vwx2210, vwx2211, vwx2212), @3(vwx2410, vwx2411, vwx2412), bag, app(app(ty_@2, bcb), bcc), bcd) → new_lt(vwx2211, vwx2411, bcb, bcc)
new_ltEs0(Just(vwx2210), Just(vwx2410), app(app(ty_@2, fa), fb)) → new_ltEs(vwx2210, vwx2410, fa, fb)
new_ltEs0(Just(vwx2210), Just(vwx2410), app(app(ty_Either, fd), ff)) → new_ltEs1(vwx2210, vwx2410, fd, ff)
new_compare2(@2(vwx220, @2(vwx2210, vwx2211)), @2(vwx240, @2(vwx2410, vwx2411)), False, cc, app(app(ty_@2, app(app(app(ty_@3, ee), ef), eg)), ea)) → new_lt2(vwx2210, vwx2410, ee, ef, eg)
new_ltEs2(@3(vwx2210, vwx2211, vwx2212), @3(vwx2410, vwx2411, vwx2412), app(app(app(ty_@3, bea), beb), bec), bah, bcd) → new_lt2(vwx2210, vwx2410, bea, beb, bec)
new_compare2(@2(vwx220, @3(vwx2210, vwx2211, vwx2212)), @2(vwx240, @3(vwx2410, vwx2411, vwx2412)), False, cc, app(app(app(ty_@3, bag), app(app(ty_@2, bcb), bcc)), bcd)) → new_lt(vwx2211, vwx2411, bcb, bcc)
new_compare2(@2(vwx220, @3(vwx2210, vwx2211, vwx2212)), @2(vwx240, @3(vwx2410, vwx2411, vwx2412)), False, cc, app(app(app(ty_@3, app(app(ty_@2, bdd), bde)), bah), bcd)) → new_lt(vwx2210, vwx2410, bdd, bde)
new_compare2(@2(vwx220, vwx221), @2(vwx240, vwx241), False, app(app(app(ty_@3, bg), bh), ca), bc) → new_compare22(vwx220, vwx240, new_esEs7(vwx220, vwx240, bg, bh, ca), bg, bh, ca)
new_lt2(vwx220, vwx240, bg, bh, ca) → new_compare22(vwx220, vwx240, new_esEs7(vwx220, vwx240, bg, bh, ca), bg, bh, ca)
new_ltEs(@2(vwx2210, vwx2211), @2(vwx2410, vwx2411), cd, app(app(ty_Either, da), db)) → new_ltEs1(vwx2211, vwx2411, da, db)
new_compare20(vwx220, vwx240, False, bd) → new_ltEs0(vwx220, vwx240, bd)
new_compare2(@2(vwx220, @2(vwx2210, vwx2211)), @2(vwx240, @2(vwx2410, vwx2411)), False, cc, app(app(ty_@2, cd), app(app(ty_Either, da), db))) → new_ltEs1(vwx2211, vwx2411, da, db)
new_primCompAux(vwx2200, vwx2400, vwx86, app(ty_Maybe, beh)) → new_compare3(vwx2200, vwx2400, beh)
new_lt3(:(vwx2200, vwx2201), :(vwx2400, vwx2401), cb) → new_primCompAux(vwx2200, vwx2400, new_compare0(vwx2201, vwx2401, cb), cb)
new_lt0(vwx220, vwx240, bd) → new_compare20(vwx220, vwx240, new_esEs5(vwx220, vwx240, bd), bd)

The TRS R consists of the following rules:

new_lt5(vwx2210, vwx2410, ty_Double) → new_lt18(vwx2210, vwx2410)
new_esEs8(vwx2210, vwx2410, ty_Ordering) → new_esEs13(vwx2210, vwx2410)
new_ltEs14(Right(vwx2210), Right(vwx2410), he, ty_Bool) → new_ltEs7(vwx2210, vwx2410)
new_ltEs11(Just(vwx2210), Just(vwx2410), app(app(ty_Either, fd), ff)) → new_ltEs14(vwx2210, vwx2410, fd, ff)
new_lt16(vwx220, vwx240, bg, bh, ca) → new_esEs13(new_compare24(vwx220, vwx240, bg, bh, ca), LT)
new_ltEs4(@3(vwx2210, vwx2211, vwx2212), @3(vwx2410, vwx2411, vwx2412), bag, bah, bcd) → new_pePe(new_lt5(vwx2210, vwx2410, bag), new_asAs(new_esEs8(vwx2210, vwx2410, bag), new_pePe(new_lt4(vwx2211, vwx2411, bah), new_asAs(new_esEs9(vwx2211, vwx2411, bah), new_ltEs5(vwx2212, vwx2412, bcd)))))
new_esEs6(Left(vwx300), Left(vwx400), ty_Ordering, bgb) → new_esEs13(vwx300, vwx400)
new_ltEs14(Right(vwx2210), Right(vwx2410), he, ty_Ordering) → new_ltEs10(vwx2210, vwx2410)
new_compare19(:%(vwx2200, vwx2201), :%(vwx2400, vwx2401), ty_Int) → new_compare17(new_sr(vwx2200, vwx2401), new_sr(vwx2400, vwx2201))
new_esEs23(vwx300, vwx400, app(app(ty_@2, cdg), cdh)) → new_esEs4(vwx300, vwx400, cdg, cdh)
new_esEs28(vwx302, vwx402, ty_Float) → new_esEs14(vwx302, vwx402)
new_ltEs20(vwx221, vwx241, ty_Ordering) → new_ltEs10(vwx221, vwx241)
new_ltEs5(vwx2212, vwx2412, ty_Char) → new_ltEs9(vwx2212, vwx2412)
new_ltEs11(Just(vwx2210), Just(vwx2410), ty_Bool) → new_ltEs7(vwx2210, vwx2410)
new_lt20(vwx2210, vwx2410, app(app(ty_Either, ec), ed)) → new_lt14(vwx2210, vwx2410, ec, ed)
new_ltEs14(Right(vwx2210), Right(vwx2410), he, ty_Double) → new_ltEs17(vwx2210, vwx2410)
new_lt10(vwx220, vwx240) → new_esEs13(new_compare14(vwx220, vwx240), LT)
new_ltEs19(vwx2211, vwx2411, app(ty_Maybe, cg)) → new_ltEs11(vwx2211, vwx2411, cg)
new_esEs23(vwx300, vwx400, app(ty_[], cde)) → new_esEs17(vwx300, vwx400, cde)
new_lt21(vwx220, vwx240, ty_Ordering) → new_lt10(vwx220, vwx240)
new_lt12(vwx220, vwx240) → new_esEs13(new_compare16(vwx220, vwx240), LT)
new_ltEs20(vwx221, vwx241, app(ty_Ratio, chg)) → new_ltEs15(vwx221, vwx241, chg)
new_primMulNat0(Zero, Zero) → Zero
new_lt20(vwx2210, vwx2410, ty_Int) → new_lt13(vwx2210, vwx2410)
new_esEs5(Just(vwx300), Just(vwx400), app(ty_Ratio, cbg)) → new_esEs16(vwx300, vwx400, cbg)
new_esEs6(Left(vwx300), Left(vwx400), app(app(app(ty_@3, bgc), bgd), bge), bgb) → new_esEs7(vwx300, vwx400, bgc, bgd, bge)
new_ltEs20(vwx221, vwx241, ty_Float) → new_ltEs12(vwx221, vwx241)
new_esEs25(vwx300, vwx400, app(app(ty_Either, chc), chd)) → new_esEs6(vwx300, vwx400, chc, chd)
new_esEs20(vwx2210, vwx2410, app(ty_Ratio, cba)) → new_esEs16(vwx2210, vwx2410, cba)
new_esEs25(vwx300, vwx400, app(app(ty_@2, cha), chb)) → new_esEs4(vwx300, vwx400, cha, chb)
new_esEs6(Left(vwx300), Left(vwx400), app(ty_Ratio, bgf), bgb) → new_esEs16(vwx300, vwx400, bgf)
new_lt4(vwx2211, vwx2411, ty_Float) → new_lt12(vwx2211, vwx2411)
new_esEs26(vwx300, vwx400, ty_@0) → new_esEs19(vwx300, vwx400)
new_esEs4(@2(vwx300, vwx301), @2(vwx400, vwx401), ccg, cch) → new_asAs(new_esEs23(vwx300, vwx400, ccg), new_esEs24(vwx301, vwx401, cch))
new_lt20(vwx2210, vwx2410, app(app(ty_@2, dg), dh)) → new_lt8(vwx2210, vwx2410, dg, dh)
new_esEs28(vwx302, vwx402, ty_Int) → new_esEs15(vwx302, vwx402)
new_ltEs11(Just(vwx2210), Just(vwx2410), app(app(app(ty_@3, fg), fh), ga)) → new_ltEs4(vwx2210, vwx2410, fg, fh, ga)
new_esEs13(EQ, EQ) → True
new_ltEs14(Left(vwx2210), Left(vwx2410), app(ty_[], hd), ge) → new_ltEs16(vwx2210, vwx2410, hd)
new_ltEs7(True, True) → True
new_ltEs11(Just(vwx2210), Just(vwx2410), ty_Int) → new_ltEs13(vwx2210, vwx2410)
new_esEs6(Left(vwx300), Left(vwx400), ty_Bool, bgb) → new_esEs11(vwx300, vwx400)
new_ltEs14(Right(vwx2210), Right(vwx2410), he, ty_Int) → new_ltEs13(vwx2210, vwx2410)
new_lt5(vwx2210, vwx2410, app(ty_Ratio, bfg)) → new_lt15(vwx2210, vwx2410, bfg)
new_lt21(vwx220, vwx240, app(ty_Maybe, bd)) → new_lt11(vwx220, vwx240, bd)
new_lt11(vwx220, vwx240, bd) → new_esEs13(new_compare15(vwx220, vwx240, bd), LT)
new_esEs21(vwx300, vwx400, ty_Int) → new_esEs15(vwx300, vwx400)
new_esEs5(Just(vwx300), Just(vwx400), ty_Integer) → new_esEs10(vwx300, vwx400)
new_ltEs5(vwx2212, vwx2412, ty_Int) → new_ltEs13(vwx2212, vwx2412)
new_ltEs19(vwx2211, vwx2411, ty_Ordering) → new_ltEs10(vwx2211, vwx2411)
new_compare0(:(vwx2200, vwx2201), :(vwx2400, vwx2401), cb) → new_primCompAux0(vwx2200, vwx2400, new_compare0(vwx2201, vwx2401, cb), cb)
new_esEs8(vwx2210, vwx2410, ty_Bool) → new_esEs11(vwx2210, vwx2410)
new_esEs5(Just(vwx300), Just(vwx400), ty_Float) → new_esEs14(vwx300, vwx400)
new_esEs5(Just(vwx300), Just(vwx400), app(ty_Maybe, cca)) → new_esEs5(vwx300, vwx400, cca)
new_esEs6(Right(vwx300), Right(vwx400), bhe, ty_Integer) → new_esEs10(vwx300, vwx400)
new_esEs23(vwx300, vwx400, ty_Integer) → new_esEs10(vwx300, vwx400)
new_ltEs10(EQ, GT) → True
new_esEs6(Left(vwx300), Left(vwx400), ty_Float, bgb) → new_esEs14(vwx300, vwx400)
new_lt20(vwx2210, vwx2410, ty_Float) → new_lt12(vwx2210, vwx2410)
new_esEs29(vwx220, vwx240, app(app(app(ty_@3, bg), bh), ca)) → new_esEs7(vwx220, vwx240, bg, bh, ca)
new_ltEs20(vwx221, vwx241, app(ty_Maybe, cfh)) → new_ltEs11(vwx221, vwx241, cfh)
new_esEs8(vwx2210, vwx2410, app(app(ty_Either, bdg), bdh)) → new_esEs6(vwx2210, vwx2410, bdg, bdh)
new_compare24(vwx220, vwx240, bg, bh, ca) → new_compare28(vwx220, vwx240, new_esEs7(vwx220, vwx240, bg, bh, ca), bg, bh, ca)
new_ltEs5(vwx2212, vwx2412, app(app(ty_@2, bba), bbb)) → new_ltEs8(vwx2212, vwx2412, bba, bbb)
new_esEs8(vwx2210, vwx2410, app(app(ty_@2, bdd), bde)) → new_esEs4(vwx2210, vwx2410, bdd, bde)
new_esEs22(vwx301, vwx401, ty_Integer) → new_esEs10(vwx301, vwx401)
new_ltEs5(vwx2212, vwx2412, ty_@0) → new_ltEs18(vwx2212, vwx2412)
new_ltEs19(vwx2211, vwx2411, app(app(ty_@2, ce), cf)) → new_ltEs8(vwx2211, vwx2411, ce, cf)
new_ltEs7(True, False) → False
new_pePe(False, vwx91) → vwx91
new_esEs23(vwx300, vwx400, ty_@0) → new_esEs19(vwx300, vwx400)
new_esEs13(LT, EQ) → False
new_esEs13(EQ, LT) → False
new_esEs6(Left(vwx300), Left(vwx400), app(app(ty_@2, bha), bhb), bgb) → new_esEs4(vwx300, vwx400, bha, bhb)
new_ltEs7(False, True) → True
new_compare6(@0, @0) → EQ
new_compare9(vwx2200, vwx2400, app(app(ty_@2, bef), beg)) → new_compare8(vwx2200, vwx2400, bef, beg)
new_esEs23(vwx300, vwx400, ty_Float) → new_esEs14(vwx300, vwx400)
new_lt17(vwx220, vwx240, cb) → new_esEs13(new_compare0(vwx220, vwx240, cb), LT)
new_esEs15(vwx30, vwx40) → new_primEqInt(vwx30, vwx40)
new_compare23(vwx220, vwx240, True) → EQ
new_compare9(vwx2200, vwx2400, ty_Float) → new_compare16(vwx2200, vwx2400)
new_ltEs20(vwx221, vwx241, app(app(ty_@2, cd), ea)) → new_ltEs8(vwx221, vwx241, cd, ea)
new_compare14(vwx220, vwx240) → new_compare27(vwx220, vwx240, new_esEs13(vwx220, vwx240))
new_lt21(vwx220, vwx240, app(app(ty_@2, ba), bb)) → new_lt8(vwx220, vwx240, ba, bb)
new_esEs26(vwx300, vwx400, ty_Char) → new_esEs12(vwx300, vwx400)
new_esEs24(vwx301, vwx401, ty_Float) → new_esEs14(vwx301, vwx401)
new_ltEs19(vwx2211, vwx2411, ty_Integer) → new_ltEs6(vwx2211, vwx2411)
new_ltEs14(Left(vwx2210), Left(vwx2410), app(app(app(ty_@3, ha), hb), hc), ge) → new_ltEs4(vwx2210, vwx2410, ha, hb, hc)
new_compare11(vwx220, vwx240, False, bg, bh, ca) → GT
new_esEs20(vwx2210, vwx2410, ty_Char) → new_esEs12(vwx2210, vwx2410)
new_esEs27(vwx301, vwx401, app(ty_[], dca)) → new_esEs17(vwx301, vwx401, dca)
new_esEs9(vwx2211, vwx2411, app(ty_Ratio, bfh)) → new_esEs16(vwx2211, vwx2411, bfh)
new_esEs9(vwx2211, vwx2411, ty_Double) → new_esEs18(vwx2211, vwx2411)
new_esEs28(vwx302, vwx402, app(ty_Ratio, ddb)) → new_esEs16(vwx302, vwx402, ddb)
new_ltEs19(vwx2211, vwx2411, ty_Double) → new_ltEs17(vwx2211, vwx2411)
new_esEs29(vwx220, vwx240, app(app(ty_@2, ba), bb)) → new_esEs4(vwx220, vwx240, ba, bb)
new_esEs29(vwx220, vwx240, ty_Integer) → new_esEs10(vwx220, vwx240)
new_ltEs14(Left(vwx2210), Left(vwx2410), ty_Integer, ge) → new_ltEs6(vwx2210, vwx2410)
new_esEs23(vwx300, vwx400, app(app(app(ty_@3, cda), cdb), cdc)) → new_esEs7(vwx300, vwx400, cda, cdb, cdc)
new_lt5(vwx2210, vwx2410, ty_Float) → new_lt12(vwx2210, vwx2410)
new_primCmpNat0(Zero, Succ(vwx24000)) → LT
new_ltEs19(vwx2211, vwx2411, app(ty_Ratio, cbb)) → new_ltEs15(vwx2211, vwx2411, cbb)
new_esEs27(vwx301, vwx401, app(app(app(ty_@3, dbe), dbf), dbg)) → new_esEs7(vwx301, vwx401, dbe, dbf, dbg)
new_lt4(vwx2211, vwx2411, ty_@0) → new_lt19(vwx2211, vwx2411)
new_esEs26(vwx300, vwx400, ty_Bool) → new_esEs11(vwx300, vwx400)
new_esEs6(Left(vwx300), Right(vwx400), bhe, bgb) → False
new_esEs6(Right(vwx300), Left(vwx400), bhe, bgb) → False
new_ltEs12(vwx221, vwx241) → new_fsEs(new_compare16(vwx221, vwx241))
new_lt21(vwx220, vwx240, ty_@0) → new_lt19(vwx220, vwx240)
new_esEs20(vwx2210, vwx2410, ty_Bool) → new_esEs11(vwx2210, vwx2410)
new_ltEs19(vwx2211, vwx2411, app(app(app(ty_@3, dc), dd), de)) → new_ltEs4(vwx2211, vwx2411, dc, dd, de)
new_ltEs15(vwx221, vwx241, chg) → new_fsEs(new_compare19(vwx221, vwx241, chg))
new_compare16(Float(vwx2200, vwx2201), Float(vwx2400, vwx2401)) → new_compare17(new_sr(vwx2200, vwx2400), new_sr(vwx2201, vwx2401))
new_esEs27(vwx301, vwx401, ty_Ordering) → new_esEs13(vwx301, vwx401)
new_lt5(vwx2210, vwx2410, ty_@0) → new_lt19(vwx2210, vwx2410)
new_esEs5(Just(vwx300), Just(vwx400), app(ty_[], cbh)) → new_esEs17(vwx300, vwx400, cbh)
new_pePe(True, vwx91) → True
new_compare0([], [], cb) → EQ
new_primEqNat0(Zero, Zero) → True
new_ltEs19(vwx2211, vwx2411, ty_Int) → new_ltEs13(vwx2211, vwx2411)
new_ltEs11(Nothing, Just(vwx2410), cfh) → True
new_ltEs11(Just(vwx2210), Just(vwx2410), app(ty_Maybe, fc)) → new_ltEs11(vwx2210, vwx2410, fc)
new_compare29(vwx220, vwx240, True, be, bf) → EQ
new_esEs23(vwx300, vwx400, app(app(ty_Either, cea), ceb)) → new_esEs6(vwx300, vwx400, cea, ceb)
new_compare9(vwx2200, vwx2400, ty_Double) → new_compare25(vwx2200, vwx2400)
new_esEs5(Just(vwx300), Just(vwx400), app(app(ty_@2, ccb), ccc)) → new_esEs4(vwx300, vwx400, ccb, ccc)
new_esEs29(vwx220, vwx240, ty_Ordering) → new_esEs13(vwx220, vwx240)
new_esEs13(LT, GT) → False
new_esEs13(GT, LT) → False
new_ltEs14(Right(vwx2210), Right(vwx2410), he, app(app(ty_@2, hf), hg)) → new_ltEs8(vwx2210, vwx2410, hf, hg)
new_lt5(vwx2210, vwx2410, app(app(app(ty_@3, bea), beb), bec)) → new_lt16(vwx2210, vwx2410, bea, beb, bec)
new_esEs27(vwx301, vwx401, ty_Char) → new_esEs12(vwx301, vwx401)
new_esEs6(Right(vwx300), Right(vwx400), bhe, app(app(ty_Either, caf), cag)) → new_esEs6(vwx300, vwx400, caf, cag)
new_lt20(vwx2210, vwx2410, ty_Bool) → new_lt7(vwx2210, vwx2410)
new_esEs29(vwx220, vwx240, ty_@0) → new_esEs19(vwx220, vwx240)
new_esEs25(vwx300, vwx400, ty_Int) → new_esEs15(vwx300, vwx400)
new_lt21(vwx220, vwx240, ty_Bool) → new_lt7(vwx220, vwx240)
new_compare9(vwx2200, vwx2400, app(app(ty_Either, bfa), bfb)) → new_compare18(vwx2200, vwx2400, bfa, bfb)
new_sr(vwx300, vwx400) → new_primMulInt(vwx300, vwx400)
new_esEs28(vwx302, vwx402, app(app(ty_Either, ddg), ddh)) → new_esEs6(vwx302, vwx402, ddg, ddh)
new_esEs24(vwx301, vwx401, ty_Ordering) → new_esEs13(vwx301, vwx401)
new_esEs9(vwx2211, vwx2411, app(app(app(ty_@3, bch), bda), bdb)) → new_esEs7(vwx2211, vwx2411, bch, bda, bdb)
new_ltEs14(Right(vwx2210), Right(vwx2410), he, ty_Char) → new_ltEs9(vwx2210, vwx2410)
new_esEs24(vwx301, vwx401, ty_Char) → new_esEs12(vwx301, vwx401)
new_esEs6(Left(vwx300), Left(vwx400), ty_Integer, bgb) → new_esEs10(vwx300, vwx400)
new_esEs6(Left(vwx300), Left(vwx400), ty_Char, bgb) → new_esEs12(vwx300, vwx400)
new_lt20(vwx2210, vwx2410, app(ty_Maybe, eb)) → new_lt11(vwx2210, vwx2410, eb)
new_primPlusNat0(Succ(vwx630), vwx40000) → Succ(Succ(new_primPlusNat1(vwx630, vwx40000)))
new_ltEs11(Just(vwx2210), Just(vwx2410), ty_Float) → new_ltEs12(vwx2210, vwx2410)
new_esEs20(vwx2210, vwx2410, app(app(app(ty_@3, ee), ef), eg)) → new_esEs7(vwx2210, vwx2410, ee, ef, eg)
new_lt21(vwx220, vwx240, ty_Double) → new_lt18(vwx220, vwx240)
new_compare9(vwx2200, vwx2400, ty_Char) → new_compare13(vwx2200, vwx2400)
new_ltEs5(vwx2212, vwx2412, ty_Integer) → new_ltEs6(vwx2212, vwx2412)
new_esEs29(vwx220, vwx240, ty_Bool) → new_esEs11(vwx220, vwx240)
new_ltEs8(@2(vwx2210, vwx2211), @2(vwx2410, vwx2411), cd, ea) → new_pePe(new_lt20(vwx2210, vwx2410, cd), new_asAs(new_esEs20(vwx2210, vwx2410, cd), new_ltEs19(vwx2211, vwx2411, ea)))
new_ltEs14(Left(vwx2210), Left(vwx2410), ty_Double, ge) → new_ltEs17(vwx2210, vwx2410)
new_esEs8(vwx2210, vwx2410, ty_@0) → new_esEs19(vwx2210, vwx2410)
new_esEs6(Left(vwx300), Left(vwx400), ty_Int, bgb) → new_esEs15(vwx300, vwx400)
new_esEs8(vwx2210, vwx2410, ty_Char) → new_esEs12(vwx2210, vwx2410)
new_primEqInt(Neg(Succ(vwx3000)), Neg(Succ(vwx4000))) → new_primEqNat0(vwx3000, vwx4000)
new_ltEs20(vwx221, vwx241, app(app(app(ty_@3, bag), bah), bcd)) → new_ltEs4(vwx221, vwx241, bag, bah, bcd)
new_esEs25(vwx300, vwx400, ty_Bool) → new_esEs11(vwx300, vwx400)
new_ltEs20(vwx221, vwx241, ty_Char) → new_ltEs9(vwx221, vwx241)
new_esEs23(vwx300, vwx400, ty_Int) → new_esEs15(vwx300, vwx400)
new_esEs6(Right(vwx300), Right(vwx400), bhe, app(app(app(ty_@3, bhf), bhg), bhh)) → new_esEs7(vwx300, vwx400, bhf, bhg, bhh)
new_lt7(vwx220, vwx240) → new_esEs13(new_compare12(vwx220, vwx240), LT)
new_primPlusNat1(Succ(vwx6300), Zero) → Succ(vwx6300)
new_primPlusNat1(Zero, Succ(vwx400000)) → Succ(vwx400000)
new_ltEs14(Left(vwx2210), Left(vwx2410), ty_Bool, ge) → new_ltEs7(vwx2210, vwx2410)
new_esEs22(vwx301, vwx401, ty_Int) → new_esEs15(vwx301, vwx401)
new_esEs26(vwx300, vwx400, app(app(app(ty_@3, dac), dad), dae)) → new_esEs7(vwx300, vwx400, dac, dad, dae)
new_ltEs14(Right(vwx2210), Right(vwx2410), he, app(ty_Maybe, hh)) → new_ltEs11(vwx2210, vwx2410, hh)
new_ltEs14(Right(vwx2210), Left(vwx2410), he, ge) → False
new_ltEs9(vwx221, vwx241) → new_fsEs(new_compare13(vwx221, vwx241))
new_esEs20(vwx2210, vwx2410, ty_Int) → new_esEs15(vwx2210, vwx2410)
new_lt4(vwx2211, vwx2411, app(ty_[], bdc)) → new_lt17(vwx2211, vwx2411, bdc)
new_compare111(vwx72, vwx73, vwx74, vwx75, True, cfe, cff) → LT
new_ltEs5(vwx2212, vwx2412, app(ty_[], bca)) → new_ltEs16(vwx2212, vwx2412, bca)
new_ltEs11(Just(vwx2210), Just(vwx2410), app(app(ty_@2, fa), fb)) → new_ltEs8(vwx2210, vwx2410, fa, fb)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_compare11(vwx220, vwx240, True, bg, bh, ca) → LT
new_esEs8(vwx2210, vwx2410, ty_Double) → new_esEs18(vwx2210, vwx2410)
new_compare112(vwx220, vwx240, False, be, bf) → GT
new_primEqInt(Neg(Zero), Neg(Succ(vwx4000))) → False
new_primEqInt(Neg(Succ(vwx3000)), Neg(Zero)) → False
new_compare26(vwx22, vwx24, True, cc, bc) → EQ
new_compare9(vwx2200, vwx2400, app(ty_Maybe, beh)) → new_compare15(vwx2200, vwx2400, beh)
new_lt5(vwx2210, vwx2410, app(ty_[], bed)) → new_lt17(vwx2210, vwx2410, bed)
new_esEs6(Right(vwx300), Right(vwx400), bhe, app(ty_[], cab)) → new_esEs17(vwx300, vwx400, cab)
new_esEs6(Right(vwx300), Right(vwx400), bhe, ty_@0) → new_esEs19(vwx300, vwx400)
new_esEs20(vwx2210, vwx2410, ty_@0) → new_esEs19(vwx2210, vwx2410)
new_ltEs13(vwx221, vwx241) → new_fsEs(new_compare17(vwx221, vwx241))
new_esEs19(@0, @0) → True
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_compare12(vwx220, vwx240) → new_compare23(vwx220, vwx240, new_esEs11(vwx220, vwx240))
new_ltEs14(Right(vwx2210), Right(vwx2410), he, ty_@0) → new_ltEs18(vwx2210, vwx2410)
new_lt4(vwx2211, vwx2411, app(app(ty_@2, bcb), bcc)) → new_lt8(vwx2211, vwx2411, bcb, bcc)
new_lt6(vwx220, vwx240) → new_esEs13(new_compare7(vwx220, vwx240), LT)
new_primCmpNat0(Succ(vwx22000), Succ(vwx24000)) → new_primCmpNat0(vwx22000, vwx24000)
new_esEs13(LT, LT) → True
new_esEs11(False, False) → True
new_primEqInt(Pos(Succ(vwx3000)), Pos(Succ(vwx4000))) → new_primEqNat0(vwx3000, vwx4000)
new_ltEs14(Right(vwx2210), Right(vwx2410), he, app(app(app(ty_@3, bac), bad), bae)) → new_ltEs4(vwx2210, vwx2410, bac, bad, bae)
new_esEs26(vwx300, vwx400, ty_Integer) → new_esEs10(vwx300, vwx400)
new_esEs25(vwx300, vwx400, app(ty_Maybe, cgh)) → new_esEs5(vwx300, vwx400, cgh)
new_esEs24(vwx301, vwx401, app(ty_Ratio, cef)) → new_esEs16(vwx301, vwx401, cef)
new_esEs29(vwx220, vwx240, app(ty_Maybe, bd)) → new_esEs5(vwx220, vwx240, bd)
new_compare9(vwx2200, vwx2400, app(ty_[], bff)) → new_compare0(vwx2200, vwx2400, bff)
new_esEs8(vwx2210, vwx2410, app(ty_Maybe, bdf)) → new_esEs5(vwx2210, vwx2410, bdf)
new_esEs5(Just(vwx300), Just(vwx400), ty_Bool) → new_esEs11(vwx300, vwx400)
new_ltEs10(GT, EQ) → False
new_ltEs14(Right(vwx2210), Right(vwx2410), he, ty_Integer) → new_ltEs6(vwx2210, vwx2410)
new_primEqNat0(Succ(vwx3000), Succ(vwx4000)) → new_primEqNat0(vwx3000, vwx4000)
new_esEs17(:(vwx300, vwx301), :(vwx400, vwx401), cgb) → new_asAs(new_esEs25(vwx300, vwx400, cgb), new_esEs17(vwx301, vwx401, cgb))
new_esEs6(Left(vwx300), Left(vwx400), app(ty_[], bgg), bgb) → new_esEs17(vwx300, vwx400, bgg)
new_primCompAux00(vwx100, LT) → LT
new_ltEs11(Just(vwx2210), Just(vwx2410), ty_Char) → new_ltEs9(vwx2210, vwx2410)
new_ltEs14(Left(vwx2210), Left(vwx2410), app(ty_Ratio, che), ge) → new_ltEs15(vwx2210, vwx2410, che)
new_esEs25(vwx300, vwx400, ty_@0) → new_esEs19(vwx300, vwx400)
new_esEs9(vwx2211, vwx2411, app(app(ty_Either, bcf), bcg)) → new_esEs6(vwx2211, vwx2411, bcf, bcg)
new_lt4(vwx2211, vwx2411, app(ty_Maybe, bce)) → new_lt11(vwx2211, vwx2411, bce)
new_primCmpInt(Neg(Succ(vwx22000)), Neg(vwx2400)) → new_primCmpNat0(vwx2400, Succ(vwx22000))
new_esEs26(vwx300, vwx400, app(app(ty_@2, dba), dbb)) → new_esEs4(vwx300, vwx400, dba, dbb)
new_ltEs14(Left(vwx2210), Left(vwx2410), ty_Ordering, ge) → new_ltEs10(vwx2210, vwx2410)
new_esEs6(Right(vwx300), Right(vwx400), bhe, app(ty_Maybe, cac)) → new_esEs5(vwx300, vwx400, cac)
new_esEs6(Right(vwx300), Right(vwx400), bhe, ty_Char) → new_esEs12(vwx300, vwx400)
new_ltEs5(vwx2212, vwx2412, app(ty_Maybe, bbc)) → new_ltEs11(vwx2212, vwx2412, bbc)
new_lt9(vwx220, vwx240) → new_esEs13(new_compare13(vwx220, vwx240), LT)
new_compare29(vwx220, vwx240, False, be, bf) → new_compare112(vwx220, vwx240, new_ltEs14(vwx220, vwx240, be, bf), be, bf)
new_primEqInt(Pos(Zero), Pos(Succ(vwx4000))) → False
new_primEqInt(Pos(Succ(vwx3000)), Pos(Zero)) → False
new_esEs27(vwx301, vwx401, ty_@0) → new_esEs19(vwx301, vwx401)
new_primCmpNat0(Zero, Zero) → EQ
new_esEs23(vwx300, vwx400, ty_Ordering) → new_esEs13(vwx300, vwx400)
new_esEs5(Just(vwx300), Just(vwx400), ty_@0) → new_esEs19(vwx300, vwx400)
new_compare23(vwx220, vwx240, False) → new_compare10(vwx220, vwx240, new_ltEs7(vwx220, vwx240))
new_primCmpNat0(Succ(vwx22000), Zero) → GT
new_esEs29(vwx220, vwx240, ty_Double) → new_esEs18(vwx220, vwx240)
new_ltEs10(LT, EQ) → True
new_primCmpInt(Neg(Zero), Pos(Succ(vwx24000))) → LT
new_esEs24(vwx301, vwx401, ty_Double) → new_esEs18(vwx301, vwx401)
new_lt4(vwx2211, vwx2411, ty_Integer) → new_lt6(vwx2211, vwx2411)
new_sr0(Integer(vwx24000), Integer(vwx22010)) → Integer(new_primMulInt(vwx24000, vwx22010))
new_primPlusNat1(Succ(vwx6300), Succ(vwx400000)) → Succ(Succ(new_primPlusNat1(vwx6300, vwx400000)))
new_ltEs20(vwx221, vwx241, ty_Integer) → new_ltEs6(vwx221, vwx241)
new_primEqInt(Neg(Succ(vwx3000)), Pos(vwx400)) → False
new_primEqInt(Pos(Succ(vwx3000)), Neg(vwx400)) → False
new_compare25(Double(vwx2200, vwx2201), Double(vwx2400, vwx2401)) → new_compare17(new_sr(vwx2200, vwx2400), new_sr(vwx2201, vwx2401))
new_esEs24(vwx301, vwx401, app(app(ty_@2, cfa), cfb)) → new_esEs4(vwx301, vwx401, cfa, cfb)
new_compare210(vwx220, vwx240, True, bd) → EQ
new_ltEs14(Right(vwx2210), Right(vwx2410), he, app(ty_[], baf)) → new_ltEs16(vwx2210, vwx2410, baf)
new_esEs27(vwx301, vwx401, app(ty_Maybe, dcb)) → new_esEs5(vwx301, vwx401, dcb)
new_esEs26(vwx300, vwx400, ty_Double) → new_esEs18(vwx300, vwx400)
new_ltEs5(vwx2212, vwx2412, ty_Bool) → new_ltEs7(vwx2212, vwx2412)
new_ltEs10(GT, GT) → True
new_esEs26(vwx300, vwx400, app(ty_Ratio, daf)) → new_esEs16(vwx300, vwx400, daf)
new_esEs25(vwx300, vwx400, ty_Char) → new_esEs12(vwx300, vwx400)
new_ltEs14(Left(vwx2210), Left(vwx2410), ty_Float, ge) → new_ltEs12(vwx2210, vwx2410)
new_primEqInt(Neg(Zero), Pos(Succ(vwx4000))) → False
new_primEqInt(Pos(Zero), Neg(Succ(vwx4000))) → False
new_esEs26(vwx300, vwx400, app(ty_[], dag)) → new_esEs17(vwx300, vwx400, dag)
new_primCompAux00(vwx100, EQ) → vwx100
new_primCmpInt(Pos(Zero), Pos(Succ(vwx24000))) → new_primCmpNat0(Zero, Succ(vwx24000))
new_lt21(vwx220, vwx240, app(app(app(ty_@3, bg), bh), ca)) → new_lt16(vwx220, vwx240, bg, bh, ca)
new_esEs6(Right(vwx300), Right(vwx400), bhe, ty_Double) → new_esEs18(vwx300, vwx400)
new_ltEs20(vwx221, vwx241, ty_Int) → new_ltEs13(vwx221, vwx241)
new_esEs9(vwx2211, vwx2411, ty_Bool) → new_esEs11(vwx2211, vwx2411)
new_esEs23(vwx300, vwx400, ty_Bool) → new_esEs11(vwx300, vwx400)
new_lt20(vwx2210, vwx2410, ty_Integer) → new_lt6(vwx2210, vwx2410)
new_ltEs5(vwx2212, vwx2412, ty_Double) → new_ltEs17(vwx2212, vwx2412)
new_ltEs5(vwx2212, vwx2412, app(app(ty_Either, bbd), bbe)) → new_ltEs14(vwx2212, vwx2412, bbd, bbe)
new_esEs27(vwx301, vwx401, app(ty_Ratio, dbh)) → new_esEs16(vwx301, vwx401, dbh)
new_esEs8(vwx2210, vwx2410, ty_Int) → new_esEs15(vwx2210, vwx2410)
new_esEs27(vwx301, vwx401, ty_Integer) → new_esEs10(vwx301, vwx401)
new_lt5(vwx2210, vwx2410, ty_Char) → new_lt9(vwx2210, vwx2410)
new_esEs9(vwx2211, vwx2411, ty_Float) → new_esEs14(vwx2211, vwx2411)
new_esEs12(Char(vwx300), Char(vwx400)) → new_primEqNat0(vwx300, vwx400)
new_not(False) → True
new_lt20(vwx2210, vwx2410, ty_Char) → new_lt9(vwx2210, vwx2410)
new_esEs6(Left(vwx300), Left(vwx400), app(app(ty_Either, bhc), bhd), bgb) → new_esEs6(vwx300, vwx400, bhc, bhd)
new_primCompAux0(vwx2200, vwx2400, vwx86, cb) → new_primCompAux00(vwx86, new_compare9(vwx2200, vwx2400, cb))
new_primPlusNat0(Zero, vwx40000) → Succ(vwx40000)
new_primCmpInt(Pos(Succ(vwx22000)), Pos(vwx2400)) → new_primCmpNat0(Succ(vwx22000), vwx2400)
new_esEs29(vwx220, vwx240, app(ty_[], cb)) → new_esEs17(vwx220, vwx240, cb)
new_esEs24(vwx301, vwx401, app(app(ty_Either, cfc), cfd)) → new_esEs6(vwx301, vwx401, cfc, cfd)
new_compare113(vwx72, vwx73, vwx74, vwx75, True, vwx77, cfe, cff) → new_compare111(vwx72, vwx73, vwx74, vwx75, True, cfe, cff)
new_esEs24(vwx301, vwx401, ty_@0) → new_esEs19(vwx301, vwx401)
new_esEs20(vwx2210, vwx2410, ty_Integer) → new_esEs10(vwx2210, vwx2410)
new_esEs20(vwx2210, vwx2410, ty_Float) → new_esEs14(vwx2210, vwx2410)
new_lt4(vwx2211, vwx2411, app(app(ty_Either, bcf), bcg)) → new_lt14(vwx2211, vwx2411, bcf, bcg)
new_esEs25(vwx300, vwx400, app(ty_Ratio, cgf)) → new_esEs16(vwx300, vwx400, cgf)
new_lt5(vwx2210, vwx2410, ty_Bool) → new_lt7(vwx2210, vwx2410)
new_esEs9(vwx2211, vwx2411, app(ty_Maybe, bce)) → new_esEs5(vwx2211, vwx2411, bce)
new_esEs25(vwx300, vwx400, ty_Integer) → new_esEs10(vwx300, vwx400)
new_lt18(vwx220, vwx240) → new_esEs13(new_compare25(vwx220, vwx240), LT)
new_ltEs19(vwx2211, vwx2411, ty_@0) → new_ltEs18(vwx2211, vwx2411)
new_compare0(:(vwx2200, vwx2201), [], cb) → GT
new_esEs24(vwx301, vwx401, app(ty_[], ceg)) → new_esEs17(vwx301, vwx401, ceg)
new_lt4(vwx2211, vwx2411, ty_Char) → new_lt9(vwx2211, vwx2411)
new_ltEs5(vwx2212, vwx2412, ty_Float) → new_ltEs12(vwx2212, vwx2412)
new_esEs29(vwx220, vwx240, ty_Int) → new_esEs15(vwx220, vwx240)
new_esEs27(vwx301, vwx401, app(app(ty_Either, dce), dcf)) → new_esEs6(vwx301, vwx401, dce, dcf)
new_esEs24(vwx301, vwx401, app(ty_Maybe, ceh)) → new_esEs5(vwx301, vwx401, ceh)
new_esEs5(Just(vwx300), Just(vwx400), ty_Char) → new_esEs12(vwx300, vwx400)
new_lt14(vwx220, vwx240, be, bf) → new_esEs13(new_compare18(vwx220, vwx240, be, bf), LT)
new_esEs24(vwx301, vwx401, ty_Int) → new_esEs15(vwx301, vwx401)
new_compare9(vwx2200, vwx2400, ty_Integer) → new_compare7(vwx2200, vwx2400)
new_esEs8(vwx2210, vwx2410, app(app(app(ty_@3, bea), beb), bec)) → new_esEs7(vwx2210, vwx2410, bea, beb, bec)
new_esEs6(Right(vwx300), Right(vwx400), bhe, ty_Bool) → new_esEs11(vwx300, vwx400)
new_primCmpInt(Pos(Succ(vwx22000)), Neg(vwx2400)) → GT
new_esEs6(Left(vwx300), Left(vwx400), ty_Double, bgb) → new_esEs18(vwx300, vwx400)
new_esEs9(vwx2211, vwx2411, ty_Char) → new_esEs12(vwx2211, vwx2411)
new_compare9(vwx2200, vwx2400, ty_Ordering) → new_compare14(vwx2200, vwx2400)
new_ltEs19(vwx2211, vwx2411, app(ty_[], df)) → new_ltEs16(vwx2211, vwx2411, df)
new_esEs5(Just(vwx300), Just(vwx400), ty_Int) → new_esEs15(vwx300, vwx400)
new_ltEs14(Left(vwx2210), Left(vwx2410), ty_Char, ge) → new_ltEs9(vwx2210, vwx2410)
new_primMulInt(Pos(vwx3000), Pos(vwx4000)) → Pos(new_primMulNat0(vwx3000, vwx4000))
new_esEs27(vwx301, vwx401, ty_Bool) → new_esEs11(vwx301, vwx401)
new_lt4(vwx2211, vwx2411, ty_Double) → new_lt18(vwx2211, vwx2411)
new_esEs28(vwx302, vwx402, app(app(app(ty_@3, dcg), dch), dda)) → new_esEs7(vwx302, vwx402, dcg, dch, dda)
new_lt13(vwx220, vwx240) → new_esEs13(new_compare17(vwx220, vwx240), LT)
new_esEs5(Just(vwx300), Just(vwx400), ty_Double) → new_esEs18(vwx300, vwx400)
new_primMulInt(Neg(vwx3000), Neg(vwx4000)) → Pos(new_primMulNat0(vwx3000, vwx4000))
new_esEs13(GT, GT) → True
new_compare110(vwx220, vwx240, True) → LT
new_ltEs11(Just(vwx2210), Just(vwx2410), app(ty_[], gb)) → new_ltEs16(vwx2210, vwx2410, gb)
new_primEqNat0(Succ(vwx3000), Zero) → False
new_primEqNat0(Zero, Succ(vwx4000)) → False
new_ltEs11(Just(vwx2210), Just(vwx2410), app(ty_Ratio, cga)) → new_ltEs15(vwx2210, vwx2410, cga)
new_lt20(vwx2210, vwx2410, app(ty_Ratio, cba)) → new_lt15(vwx2210, vwx2410, cba)
new_compare110(vwx220, vwx240, False) → GT
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs21(vwx300, vwx400, ty_Integer) → new_esEs10(vwx300, vwx400)
new_esEs10(Integer(vwx300), Integer(vwx400)) → new_primEqInt(vwx300, vwx400)
new_esEs6(Right(vwx300), Right(vwx400), bhe, ty_Float) → new_esEs14(vwx300, vwx400)
new_esEs20(vwx2210, vwx2410, ty_Ordering) → new_esEs13(vwx2210, vwx2410)
new_lt4(vwx2211, vwx2411, app(app(app(ty_@3, bch), bda), bdb)) → new_lt16(vwx2211, vwx2411, bch, bda, bdb)
new_esEs20(vwx2210, vwx2410, app(ty_[], eh)) → new_esEs17(vwx2210, vwx2410, eh)
new_esEs20(vwx2210, vwx2410, app(app(ty_Either, ec), ed)) → new_esEs6(vwx2210, vwx2410, ec, ed)
new_compare28(vwx220, vwx240, True, bg, bh, ca) → EQ
new_esEs5(Just(vwx300), Just(vwx400), ty_Ordering) → new_esEs13(vwx300, vwx400)
new_lt4(vwx2211, vwx2411, ty_Bool) → new_lt7(vwx2211, vwx2411)
new_lt21(vwx220, vwx240, ty_Integer) → new_lt6(vwx220, vwx240)
new_esEs29(vwx220, vwx240, app(app(ty_Either, be), bf)) → new_esEs6(vwx220, vwx240, be, bf)
new_ltEs14(Left(vwx2210), Left(vwx2410), app(app(ty_@2, gc), gd), ge) → new_ltEs8(vwx2210, vwx2410, gc, gd)
new_ltEs20(vwx221, vwx241, ty_Double) → new_ltEs17(vwx221, vwx241)
new_esEs26(vwx300, vwx400, app(ty_Maybe, dah)) → new_esEs5(vwx300, vwx400, dah)
new_esEs23(vwx300, vwx400, ty_Double) → new_esEs18(vwx300, vwx400)
new_ltEs19(vwx2211, vwx2411, ty_Char) → new_ltEs9(vwx2211, vwx2411)
new_ltEs19(vwx2211, vwx2411, ty_Bool) → new_ltEs7(vwx2211, vwx2411)
new_compare27(vwx220, vwx240, False) → new_compare110(vwx220, vwx240, new_ltEs10(vwx220, vwx240))
new_primCmpInt(Neg(Zero), Neg(Succ(vwx24000))) → new_primCmpNat0(Succ(vwx24000), Zero)
new_esEs8(vwx2210, vwx2410, ty_Integer) → new_esEs10(vwx2210, vwx2410)
new_primCmpInt(Pos(Zero), Neg(Succ(vwx24000))) → GT
new_compare13(Char(vwx2200), Char(vwx2400)) → new_primCmpNat0(vwx2200, vwx2400)
new_esEs11(True, False) → False
new_esEs11(False, True) → False
new_lt5(vwx2210, vwx2410, app(app(ty_Either, bdg), bdh)) → new_lt14(vwx2210, vwx2410, bdg, bdh)
new_lt20(vwx2210, vwx2410, ty_Double) → new_lt18(vwx2210, vwx2410)
new_esEs6(Right(vwx300), Right(vwx400), bhe, app(app(ty_@2, cad), cae)) → new_esEs4(vwx300, vwx400, cad, cae)
new_esEs6(Left(vwx300), Left(vwx400), ty_@0, bgb) → new_esEs19(vwx300, vwx400)
new_compare114(vwx220, vwx240, True, bd) → LT
new_ltEs20(vwx221, vwx241, app(ty_[], bee)) → new_ltEs16(vwx221, vwx241, bee)
new_compare210(vwx220, vwx240, False, bd) → new_compare114(vwx220, vwx240, new_ltEs11(vwx220, vwx240, bd), bd)
new_esEs23(vwx300, vwx400, app(ty_Ratio, cdd)) → new_esEs16(vwx300, vwx400, cdd)
new_ltEs18(vwx221, vwx241) → new_fsEs(new_compare6(vwx221, vwx241))
new_compare28(vwx220, vwx240, False, bg, bh, ca) → new_compare11(vwx220, vwx240, new_ltEs4(vwx220, vwx240, bg, bh, ca), bg, bh, ca)
new_esEs9(vwx2211, vwx2411, app(app(ty_@2, bcb), bcc)) → new_esEs4(vwx2211, vwx2411, bcb, bcc)
new_esEs16(:%(vwx300, vwx301), :%(vwx400, vwx401), ccf) → new_asAs(new_esEs21(vwx300, vwx400, ccf), new_esEs22(vwx301, vwx401, ccf))
new_esEs27(vwx301, vwx401, ty_Double) → new_esEs18(vwx301, vwx401)
new_ltEs14(Right(vwx2210), Right(vwx2410), he, app(ty_Ratio, chf)) → new_ltEs15(vwx2210, vwx2410, chf)
new_ltEs5(vwx2212, vwx2412, ty_Ordering) → new_ltEs10(vwx2212, vwx2412)
new_ltEs17(vwx221, vwx241) → new_fsEs(new_compare25(vwx221, vwx241))
new_esEs24(vwx301, vwx401, app(app(app(ty_@3, cec), ced), cee)) → new_esEs7(vwx301, vwx401, cec, ced, cee)
new_lt4(vwx2211, vwx2411, ty_Int) → new_lt13(vwx2211, vwx2411)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs28(vwx302, vwx402, ty_Bool) → new_esEs11(vwx302, vwx402)
new_ltEs14(Left(vwx2210), Right(vwx2410), he, ge) → True
new_ltEs20(vwx221, vwx241, ty_@0) → new_ltEs18(vwx221, vwx241)
new_compare8(vwx220, vwx240, ba, bb) → new_compare26(vwx220, vwx240, new_esEs4(vwx220, vwx240, ba, bb), ba, bb)
new_ltEs20(vwx221, vwx241, ty_Bool) → new_ltEs7(vwx221, vwx241)
new_esEs20(vwx2210, vwx2410, app(ty_Maybe, eb)) → new_esEs5(vwx2210, vwx2410, eb)
new_esEs7(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), chh, daa, dab) → new_asAs(new_esEs26(vwx300, vwx400, chh), new_asAs(new_esEs27(vwx301, vwx401, daa), new_esEs28(vwx302, vwx402, dab)))
new_esEs28(vwx302, vwx402, app(app(ty_@2, dde), ddf)) → new_esEs4(vwx302, vwx402, dde, ddf)
new_ltEs20(vwx221, vwx241, app(app(ty_Either, he), ge)) → new_ltEs14(vwx221, vwx241, he, ge)
new_asAs(False, vwx45) → False
new_ltEs19(vwx2211, vwx2411, app(app(ty_Either, da), db)) → new_ltEs14(vwx2211, vwx2411, da, db)
new_primMulInt(Pos(vwx3000), Neg(vwx4000)) → Neg(new_primMulNat0(vwx3000, vwx4000))
new_primMulInt(Neg(vwx3000), Pos(vwx4000)) → Neg(new_primMulNat0(vwx3000, vwx4000))
new_ltEs10(LT, GT) → True
new_lt20(vwx2210, vwx2410, ty_@0) → new_lt19(vwx2210, vwx2410)
new_primMulNat0(Zero, Succ(vwx40000)) → Zero
new_primMulNat0(Succ(vwx30000), Zero) → Zero
new_lt21(vwx220, vwx240, ty_Char) → new_lt9(vwx220, vwx240)
new_esEs29(vwx220, vwx240, ty_Char) → new_esEs12(vwx220, vwx240)
new_fsEs(vwx78) → new_not(new_esEs13(vwx78, GT))
new_esEs13(EQ, GT) → False
new_esEs13(GT, EQ) → False
new_ltEs11(Just(vwx2210), Just(vwx2410), ty_Double) → new_ltEs17(vwx2210, vwx2410)
new_esEs9(vwx2211, vwx2411, ty_Integer) → new_esEs10(vwx2211, vwx2411)
new_ltEs14(Right(vwx2210), Right(vwx2410), he, ty_Float) → new_ltEs12(vwx2210, vwx2410)
new_esEs6(Right(vwx300), Right(vwx400), bhe, app(ty_Ratio, caa)) → new_esEs16(vwx300, vwx400, caa)
new_lt19(vwx220, vwx240) → new_esEs13(new_compare6(vwx220, vwx240), LT)
new_compare18(vwx220, vwx240, be, bf) → new_compare29(vwx220, vwx240, new_esEs6(vwx220, vwx240, be, bf), be, bf)
new_compare17(vwx220, vwx240) → new_primCmpInt(vwx220, vwx240)
new_esEs28(vwx302, vwx402, ty_Double) → new_esEs18(vwx302, vwx402)
new_lt20(vwx2210, vwx2410, app(ty_[], eh)) → new_lt17(vwx2210, vwx2410, eh)
new_ltEs14(Right(vwx2210), Right(vwx2410), he, app(app(ty_Either, baa), bab)) → new_ltEs14(vwx2210, vwx2410, baa, bab)
new_ltEs11(Just(vwx2210), Just(vwx2410), ty_@0) → new_ltEs18(vwx2210, vwx2410)
new_lt5(vwx2210, vwx2410, ty_Integer) → new_lt6(vwx2210, vwx2410)
new_ltEs11(Just(vwx2210), Just(vwx2410), ty_Integer) → new_ltEs6(vwx2210, vwx2410)
new_esEs29(vwx220, vwx240, app(ty_Ratio, cfg)) → new_esEs16(vwx220, vwx240, cfg)
new_ltEs14(Left(vwx2210), Left(vwx2410), ty_Int, ge) → new_ltEs13(vwx2210, vwx2410)
new_esEs25(vwx300, vwx400, app(ty_[], cgg)) → new_esEs17(vwx300, vwx400, cgg)
new_esEs11(True, True) → True
new_esEs18(Double(vwx300, vwx301), Double(vwx400, vwx401)) → new_esEs15(new_sr(vwx300, vwx400), new_sr(vwx301, vwx401))
new_esEs28(vwx302, vwx402, ty_@0) → new_esEs19(vwx302, vwx402)
new_esEs23(vwx300, vwx400, ty_Char) → new_esEs12(vwx300, vwx400)
new_esEs23(vwx300, vwx400, app(ty_Maybe, cdf)) → new_esEs5(vwx300, vwx400, cdf)
new_esEs29(vwx220, vwx240, ty_Float) → new_esEs14(vwx220, vwx240)
new_esEs6(Left(vwx300), Left(vwx400), app(ty_Maybe, bgh), bgb) → new_esEs5(vwx300, vwx400, bgh)
new_compare111(vwx72, vwx73, vwx74, vwx75, False, cfe, cff) → GT
new_ltEs10(EQ, EQ) → True
new_lt4(vwx2211, vwx2411, app(ty_Ratio, bfh)) → new_lt15(vwx2211, vwx2411, bfh)
new_esEs20(vwx2210, vwx2410, app(app(ty_@2, dg), dh)) → new_esEs4(vwx2210, vwx2410, dg, dh)
new_esEs24(vwx301, vwx401, ty_Integer) → new_esEs10(vwx301, vwx401)
new_compare27(vwx220, vwx240, True) → EQ
new_ltEs10(LT, LT) → True
new_compare113(vwx72, vwx73, vwx74, vwx75, False, vwx77, cfe, cff) → new_compare111(vwx72, vwx73, vwx74, vwx75, vwx77, cfe, cff)
new_esEs8(vwx2210, vwx2410, app(ty_Ratio, bfg)) → new_esEs16(vwx2210, vwx2410, bfg)
new_esEs5(Just(vwx300), Nothing, cbc) → False
new_esEs5(Nothing, Just(vwx400), cbc) → False
new_lt21(vwx220, vwx240, app(ty_[], cb)) → new_lt17(vwx220, vwx240, cb)
new_lt5(vwx2210, vwx2410, ty_Int) → new_lt13(vwx2210, vwx2410)
new_lt21(vwx220, vwx240, ty_Int) → new_lt13(vwx220, vwx240)
new_ltEs14(Left(vwx2210), Left(vwx2410), app(app(ty_Either, gg), gh), ge) → new_ltEs14(vwx2210, vwx2410, gg, gh)
new_esEs28(vwx302, vwx402, app(ty_[], ddc)) → new_esEs17(vwx302, vwx402, ddc)
new_esEs25(vwx300, vwx400, app(app(app(ty_@3, cgc), cgd), cge)) → new_esEs7(vwx300, vwx400, cgc, cgd, cge)
new_lt20(vwx2210, vwx2410, app(app(app(ty_@3, ee), ef), eg)) → new_lt16(vwx2210, vwx2410, ee, ef, eg)
new_esEs27(vwx301, vwx401, app(app(ty_@2, dcc), dcd)) → new_esEs4(vwx301, vwx401, dcc, dcd)
new_esEs27(vwx301, vwx401, ty_Int) → new_esEs15(vwx301, vwx401)
new_lt5(vwx2210, vwx2410, ty_Ordering) → new_lt10(vwx2210, vwx2410)
new_esEs5(Just(vwx300), Just(vwx400), app(app(ty_Either, ccd), cce)) → new_esEs6(vwx300, vwx400, ccd, cce)
new_ltEs5(vwx2212, vwx2412, app(ty_Ratio, bga)) → new_ltEs15(vwx2212, vwx2412, bga)
new_ltEs11(Just(vwx2210), Just(vwx2410), ty_Ordering) → new_ltEs10(vwx2210, vwx2410)
new_compare7(Integer(vwx2200), Integer(vwx2400)) → new_primCmpInt(vwx2200, vwx2400)
new_compare9(vwx2200, vwx2400, app(app(app(ty_@3, bfc), bfd), bfe)) → new_compare24(vwx2200, vwx2400, bfc, bfd, bfe)
new_esEs6(Right(vwx300), Right(vwx400), bhe, ty_Ordering) → new_esEs13(vwx300, vwx400)
new_esEs25(vwx300, vwx400, ty_Double) → new_esEs18(vwx300, vwx400)
new_ltEs14(Left(vwx2210), Left(vwx2410), ty_@0, ge) → new_ltEs18(vwx2210, vwx2410)
new_esEs5(Nothing, Nothing, cbc) → True
new_esEs9(vwx2211, vwx2411, ty_@0) → new_esEs19(vwx2211, vwx2411)
new_esEs28(vwx302, vwx402, app(ty_Maybe, ddd)) → new_esEs5(vwx302, vwx402, ddd)
new_esEs8(vwx2210, vwx2410, ty_Float) → new_esEs14(vwx2210, vwx2410)
new_esEs5(Just(vwx300), Just(vwx400), app(app(app(ty_@3, cbd), cbe), cbf)) → new_esEs7(vwx300, vwx400, cbd, cbe, cbf)
new_compare19(:%(vwx2200, vwx2201), :%(vwx2400, vwx2401), ty_Integer) → new_compare7(new_sr0(vwx2200, vwx2401), new_sr0(vwx2400, vwx2201))
new_ltEs7(False, False) → True
new_lt21(vwx220, vwx240, ty_Float) → new_lt12(vwx220, vwx240)
new_ltEs10(EQ, LT) → False
new_esEs9(vwx2211, vwx2411, app(ty_[], bdc)) → new_esEs17(vwx2211, vwx2411, bdc)
new_compare114(vwx220, vwx240, False, bd) → GT
new_esEs8(vwx2210, vwx2410, app(ty_[], bed)) → new_esEs17(vwx2210, vwx2410, bed)
new_compare15(vwx220, vwx240, bd) → new_compare210(vwx220, vwx240, new_esEs5(vwx220, vwx240, bd), bd)
new_ltEs10(GT, LT) → False
new_compare9(vwx2200, vwx2400, app(ty_Ratio, cah)) → new_compare19(vwx2200, vwx2400, cah)
new_esEs26(vwx300, vwx400, app(app(ty_Either, dbc), dbd)) → new_esEs6(vwx300, vwx400, dbc, dbd)
new_lt20(vwx2210, vwx2410, ty_Ordering) → new_lt10(vwx2210, vwx2410)
new_primPlusNat1(Zero, Zero) → Zero
new_compare0([], :(vwx2400, vwx2401), cb) → LT
new_esEs14(Float(vwx300, vwx301), Float(vwx400, vwx401)) → new_esEs15(new_sr(vwx300, vwx400), new_sr(vwx301, vwx401))
new_lt21(vwx220, vwx240, app(app(ty_Either, be), bf)) → new_lt14(vwx220, vwx240, be, bf)
new_esEs9(vwx2211, vwx2411, ty_Ordering) → new_esEs13(vwx2211, vwx2411)
new_asAs(True, vwx45) → vwx45
new_esEs26(vwx300, vwx400, ty_Float) → new_esEs14(vwx300, vwx400)
new_esEs28(vwx302, vwx402, ty_Ordering) → new_esEs13(vwx302, vwx402)
new_compare112(vwx220, vwx240, True, be, bf) → LT
new_primMulNat0(Succ(vwx30000), Succ(vwx40000)) → new_primPlusNat0(new_primMulNat0(vwx30000, Succ(vwx40000)), vwx40000)
new_ltEs11(Nothing, Nothing, cfh) → True
new_lt5(vwx2210, vwx2410, app(app(ty_@2, bdd), bde)) → new_lt8(vwx2210, vwx2410, bdd, bde)
new_ltEs19(vwx2211, vwx2411, ty_Float) → new_ltEs12(vwx2211, vwx2411)
new_compare9(vwx2200, vwx2400, ty_@0) → new_compare6(vwx2200, vwx2400)
new_esEs17([], [], cgb) → True
new_esEs17([], :(vwx400, vwx401), cgb) → False
new_esEs17(:(vwx300, vwx301), [], cgb) → False
new_esEs25(vwx300, vwx400, ty_Ordering) → new_esEs13(vwx300, vwx400)
new_ltEs6(vwx221, vwx241) → new_fsEs(new_compare7(vwx221, vwx241))
new_esEs27(vwx301, vwx401, ty_Float) → new_esEs14(vwx301, vwx401)
new_esEs9(vwx2211, vwx2411, ty_Int) → new_esEs15(vwx2211, vwx2411)
new_compare9(vwx2200, vwx2400, ty_Bool) → new_compare12(vwx2200, vwx2400)
new_lt21(vwx220, vwx240, app(ty_Ratio, cfg)) → new_lt15(vwx220, vwx240, cfg)
new_compare10(vwx220, vwx240, True) → LT
new_lt5(vwx2210, vwx2410, app(ty_Maybe, bdf)) → new_lt11(vwx2210, vwx2410, bdf)
new_esEs28(vwx302, vwx402, ty_Integer) → new_esEs10(vwx302, vwx402)
new_esEs26(vwx300, vwx400, ty_Int) → new_esEs15(vwx300, vwx400)
new_compare10(vwx220, vwx240, False) → GT
new_primCompAux00(vwx100, GT) → GT
new_esEs24(vwx301, vwx401, ty_Bool) → new_esEs11(vwx301, vwx401)
new_esEs25(vwx300, vwx400, ty_Float) → new_esEs14(vwx300, vwx400)
new_compare26(@2(vwx220, vwx221), @2(vwx240, vwx241), False, cc, bc) → new_compare113(vwx220, vwx221, vwx240, vwx241, new_lt21(vwx220, vwx240, cc), new_asAs(new_esEs29(vwx220, vwx240, cc), new_ltEs20(vwx221, vwx241, bc)), cc, bc)
new_compare9(vwx2200, vwx2400, ty_Int) → new_compare17(vwx2200, vwx2400)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_ltEs14(Left(vwx2210), Left(vwx2410), app(ty_Maybe, gf), ge) → new_ltEs11(vwx2210, vwx2410, gf)
new_lt15(vwx220, vwx240, cfg) → new_esEs13(new_compare19(vwx220, vwx240, cfg), LT)
new_ltEs5(vwx2212, vwx2412, app(app(app(ty_@3, bbf), bbg), bbh)) → new_ltEs4(vwx2212, vwx2412, bbf, bbg, bbh)
new_esEs26(vwx300, vwx400, ty_Ordering) → new_esEs13(vwx300, vwx400)
new_ltEs16(vwx221, vwx241, bee) → new_fsEs(new_compare0(vwx221, vwx241, bee))
new_esEs28(vwx302, vwx402, ty_Char) → new_esEs12(vwx302, vwx402)
new_ltEs11(Just(vwx2210), Nothing, cfh) → False
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_esEs6(Right(vwx300), Right(vwx400), bhe, ty_Int) → new_esEs15(vwx300, vwx400)
new_primCmpInt(Neg(Succ(vwx22000)), Pos(vwx2400)) → LT
new_lt4(vwx2211, vwx2411, ty_Ordering) → new_lt10(vwx2211, vwx2411)
new_lt8(vwx220, vwx240, ba, bb) → new_esEs13(new_compare8(vwx220, vwx240, ba, bb), LT)
new_esEs20(vwx2210, vwx2410, ty_Double) → new_esEs18(vwx2210, vwx2410)
new_not(True) → False

The set Q consists of the following terms:

new_esEs23(x0, x1, app(ty_Ratio, x2))
new_compare111(x0, x1, x2, x3, True, x4, x5)
new_primCompAux00(x0, GT)
new_lt21(x0, x1, app(ty_[], x2))
new_esEs29(x0, x1, ty_Ordering)
new_compare27(x0, x1, True)
new_esEs6(Left(x0), Left(x1), ty_Int, x2)
new_ltEs14(Right(x0), Right(x1), x2, ty_Double)
new_ltEs11(Just(x0), Just(x1), app(ty_[], x2))
new_compare19(:%(x0, x1), :%(x2, x3), ty_Integer)
new_esEs11(True, True)
new_lt21(x0, x1, ty_Ordering)
new_esEs28(x0, x1, app(ty_[], x2))
new_ltEs5(x0, x1, ty_@0)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_lt4(x0, x1, app(ty_Maybe, x2))
new_ltEs11(Just(x0), Just(x1), ty_Integer)
new_ltEs14(Right(x0), Left(x1), x2, x3)
new_ltEs14(Left(x0), Right(x1), x2, x3)
new_ltEs8(@2(x0, x1), @2(x2, x3), x4, x5)
new_ltEs14(Right(x0), Right(x1), x2, ty_Float)
new_lt5(x0, x1, ty_@0)
new_compare23(x0, x1, False)
new_compare17(x0, x1)
new_lt20(x0, x1, ty_Bool)
new_ltEs19(x0, x1, ty_Double)
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_lt21(x0, x1, app(ty_Maybe, x2))
new_esEs6(Left(x0), Left(x1), ty_Float, x2)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_ltEs5(x0, x1, ty_Integer)
new_ltEs5(x0, x1, ty_Int)
new_esEs28(x0, x1, ty_Integer)
new_esEs28(x0, x1, ty_Double)
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs20(x0, x1, ty_Int)
new_esEs13(GT, GT)
new_asAs(False, x0)
new_esEs8(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs5(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs8(x0, x1, ty_Integer)
new_ltEs10(LT, LT)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_lt18(x0, x1)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs26(x0, x1, app(ty_[], x2))
new_esEs9(x0, x1, app(ty_Maybe, x2))
new_esEs29(x0, x1, ty_Bool)
new_esEs9(x0, x1, app(ty_[], x2))
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_esEs8(x0, x1, ty_Double)
new_esEs7(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_lt16(x0, x1, x2, x3, x4)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs5(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs29(x0, x1, ty_Double)
new_esEs11(False, True)
new_esEs11(True, False)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_esEs17([], [], x0)
new_esEs27(x0, x1, ty_@0)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_ltEs9(x0, x1)
new_pePe(True, x0)
new_esEs23(x0, x1, ty_Ordering)
new_compare14(x0, x1)
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, ty_Double)
new_lt17(x0, x1, x2)
new_primCompAux0(x0, x1, x2, x3)
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs24(x0, x1, ty_Float)
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_ltEs16(x0, x1, x2)
new_esEs14(Float(x0, x1), Float(x2, x3))
new_lt4(x0, x1, app(app(ty_Either, x2), x3))
new_esEs21(x0, x1, ty_Int)
new_ltEs11(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs20(x0, x1, ty_Double)
new_ltEs20(x0, x1, ty_Bool)
new_ltEs14(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs11(Nothing, Just(x0), x1)
new_ltEs7(True, True)
new_primPlusNat0(Succ(x0), x1)
new_compare26(x0, x1, True, x2, x3)
new_ltEs19(x0, x1, ty_Int)
new_esEs6(Right(x0), Right(x1), x2, ty_Char)
new_esEs6(Right(x0), Right(x1), x2, ty_Ordering)
new_lt20(x0, x1, ty_Int)
new_esEs27(x0, x1, ty_Int)
new_esEs5(Just(x0), Just(x1), ty_Float)
new_compare8(x0, x1, x2, x3)
new_ltEs11(Just(x0), Just(x1), ty_Double)
new_lt14(x0, x1, x2, x3)
new_esEs25(x0, x1, ty_Int)
new_lt21(x0, x1, ty_Char)
new_ltEs7(True, False)
new_ltEs7(False, True)
new_ltEs14(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_compare18(x0, x1, x2, x3)
new_esEs9(x0, x1, app(app(ty_Either, x2), x3))
new_compare9(x0, x1, ty_Bool)
new_lt21(x0, x1, app(app(ty_@2, x2), x3))
new_sr(x0, x1)
new_esEs13(LT, GT)
new_esEs13(GT, LT)
new_esEs9(x0, x1, ty_Integer)
new_esEs9(x0, x1, app(ty_Ratio, x2))
new_ltEs14(Right(x0), Right(x1), x2, ty_Integer)
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, ty_Float)
new_compare23(x0, x1, True)
new_lt7(x0, x1)
new_esEs9(x0, x1, ty_Double)
new_compare0([], [], x0)
new_primEqNat0(Zero, Zero)
new_lt5(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs27(x0, x1, ty_Integer)
new_compare9(x0, x1, app(ty_[], x2))
new_esEs9(x0, x1, ty_Int)
new_esEs8(x0, x1, ty_Bool)
new_primMulInt(Pos(x0), Pos(x1))
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_esEs25(x0, x1, ty_Ordering)
new_esEs13(EQ, GT)
new_esEs13(GT, EQ)
new_esEs27(x0, x1, ty_Char)
new_lt5(x0, x1, app(ty_Ratio, x2))
new_esEs26(x0, x1, ty_Integer)
new_esEs18(Double(x0, x1), Double(x2, x3))
new_lt13(x0, x1)
new_primMulNat0(Zero, Zero)
new_esEs24(x0, x1, ty_Ordering)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_esEs28(x0, x1, ty_Ordering)
new_ltEs11(Just(x0), Just(x1), ty_Ordering)
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_esEs24(x0, x1, app(ty_[], x2))
new_ltEs10(EQ, LT)
new_ltEs10(LT, EQ)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs11(Just(x0), Nothing, x1)
new_esEs6(Left(x0), Left(x1), ty_Integer, x2)
new_esEs5(Just(x0), Just(x1), ty_Double)
new_esEs4(@2(x0, x1), @2(x2, x3), x4, x5)
new_lt15(x0, x1, x2)
new_esEs6(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_esEs5(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs5(x0, x1, app(ty_[], x2))
new_ltEs19(x0, x1, ty_@0)
new_compare114(x0, x1, True, x2)
new_ltEs14(Left(x0), Left(x1), app(ty_[], x2), x3)
new_ltEs5(x0, x1, app(app(ty_@2, x2), x3))
new_esEs29(x0, x1, ty_Float)
new_primPlusNat1(Succ(x0), Zero)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_lt4(x0, x1, ty_Char)
new_lt20(x0, x1, ty_Char)
new_ltEs14(Left(x0), Left(x1), ty_Bool, x2)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_compare114(x0, x1, False, x2)
new_esEs6(Left(x0), Left(x1), ty_Double, x2)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt4(x0, x1, app(ty_Ratio, x2))
new_esEs13(EQ, EQ)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs25(x0, x1, ty_Float)
new_esEs9(x0, x1, app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare19(:%(x0, x1), :%(x2, x3), ty_Int)
new_esEs22(x0, x1, ty_Integer)
new_fsEs(x0)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Right(x0), Right(x1), x2, ty_Bool)
new_primMulNat0(Zero, Succ(x0))
new_ltEs5(x0, x1, app(ty_Maybe, x2))
new_esEs8(x0, x1, app(ty_Ratio, x2))
new_ltEs14(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_lt21(x0, x1, ty_@0)
new_primCmpNat0(Succ(x0), Succ(x1))
new_lt4(x0, x1, app(app(ty_@2, x2), x3))
new_compare0(:(x0, x1), [], x2)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_lt21(x0, x1, app(ty_Ratio, x2))
new_ltEs14(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs12(Char(x0), Char(x1))
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs17(:(x0, x1), :(x2, x3), x4)
new_lt4(x0, x1, ty_Integer)
new_compare9(x0, x1, ty_Ordering)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_lt4(x0, x1, app(ty_[], x2))
new_ltEs20(x0, x1, ty_Char)
new_esEs11(False, False)
new_lt19(x0, x1)
new_esEs5(Just(x0), Just(x1), ty_Char)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_ltEs19(x0, x1, ty_Integer)
new_lt5(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpNat0(Zero, Succ(x0))
new_esEs28(x0, x1, ty_Float)
new_esEs17(:(x0, x1), [], x2)
new_esEs20(x0, x1, ty_Bool)
new_lt4(x0, x1, ty_@0)
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare26(@2(x0, x1), @2(x2, x3), False, x4, x5)
new_primPlusNat0(Zero, x0)
new_ltEs14(Right(x0), Right(x1), x2, ty_Char)
new_esEs6(Left(x0), Left(x1), ty_@0, x2)
new_esEs23(x0, x1, ty_Int)
new_compare13(Char(x0), Char(x1))
new_primEqNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, Zero)
new_lt21(x0, x1, ty_Double)
new_lt4(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs11(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs21(x0, x1, ty_Integer)
new_esEs5(Nothing, Just(x0), x1)
new_esEs8(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, ty_Char)
new_esEs9(x0, x1, ty_Float)
new_esEs5(Just(x0), Just(x1), ty_Bool)
new_lt6(x0, x1)
new_ltEs20(x0, x1, ty_Float)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_compare111(x0, x1, x2, x3, False, x4, x5)
new_esEs29(x0, x1, ty_Integer)
new_esEs27(x0, x1, ty_Float)
new_ltEs14(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_compare11(x0, x1, False, x2, x3, x4)
new_ltEs20(x0, x1, app(ty_[], x2))
new_ltEs11(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs25(x0, x1, ty_Double)
new_lt5(x0, x1, ty_Integer)
new_lt4(x0, x1, ty_Int)
new_esEs8(x0, x1, app(app(ty_Either, x2), x3))
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs5(x0, x1, app(ty_Ratio, x2))
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_ltEs10(GT, LT)
new_ltEs10(LT, GT)
new_esEs20(x0, x1, ty_@0)
new_esEs29(x0, x1, ty_Char)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_esEs24(x0, x1, ty_Char)
new_lt8(x0, x1, x2, x3)
new_primCompAux00(x0, EQ)
new_lt21(x0, x1, ty_Integer)
new_lt5(x0, x1, ty_Char)
new_lt21(x0, x1, ty_Int)
new_compare16(Float(x0, x1), Float(x2, x3))
new_esEs8(x0, x1, app(ty_[], x2))
new_esEs5(Just(x0), Just(x1), app(ty_Maybe, x2))
new_lt4(x0, x1, ty_Bool)
new_esEs8(x0, x1, ty_Int)
new_compare9(x0, x1, ty_Integer)
new_compare0([], :(x0, x1), x2)
new_compare113(x0, x1, x2, x3, False, x4, x5, x6)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs5(Just(x0), Just(x1), ty_Ordering)
new_esEs6(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs26(x0, x1, ty_@0)
new_primEqInt(Neg(Zero), Pos(Zero))
new_primEqInt(Pos(Zero), Neg(Zero))
new_compare9(x0, x1, ty_Double)
new_ltEs15(x0, x1, x2)
new_compare210(x0, x1, True, x2)
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs5(x0, x1, ty_Ordering)
new_compare9(x0, x1, ty_Int)
new_esEs6(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs6(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs25(x0, x1, ty_@0)
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_esEs6(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_compare210(x0, x1, False, x2)
new_ltEs5(x0, x1, ty_Bool)
new_primEqInt(Neg(Zero), Neg(Zero))
new_compare110(x0, x1, False)
new_esEs6(Right(x0), Right(x1), x2, ty_Double)
new_ltEs6(x0, x1)
new_esEs24(x0, x1, ty_Double)
new_lt21(x0, x1, ty_Bool)
new_esEs23(x0, x1, ty_Integer)
new_ltEs4(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_ltEs20(x0, x1, ty_@0)
new_compare9(x0, x1, app(app(ty_@2, x2), x3))
new_esEs5(Just(x0), Just(x1), ty_Int)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_ltEs14(Left(x0), Left(x1), ty_Integer, x2)
new_esEs6(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_lt21(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs20(x0, x1, ty_Ordering)
new_compare27(x0, x1, False)
new_esEs24(x0, x1, ty_Bool)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_esEs6(Right(x0), Right(x1), x2, ty_@0)
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs5(x0, x1, app(app(ty_Either, x2), x3))
new_compare10(x0, x1, True)
new_compare28(x0, x1, True, x2, x3, x4)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_lt5(x0, x1, ty_Double)
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, ty_Float)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare11(x0, x1, True, x2, x3, x4)
new_esEs29(x0, x1, ty_Int)
new_lt20(x0, x1, ty_Ordering)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_compare113(x0, x1, x2, x3, True, x4, x5, x6)
new_esEs22(x0, x1, ty_Int)
new_pePe(False, x0)
new_compare9(x0, x1, ty_Float)
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs28(x0, x1, ty_Bool)
new_compare6(@0, @0)
new_ltEs11(Just(x0), Just(x1), app(ty_Maybe, x2))
new_ltEs5(x0, x1, ty_Char)
new_esEs6(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_lt4(x0, x1, ty_Double)
new_esEs9(x0, x1, ty_Ordering)
new_ltEs11(Just(x0), Just(x1), ty_Char)
new_compare25(Double(x0, x1), Double(x2, x3))
new_esEs24(x0, x1, ty_Integer)
new_asAs(True, x0)
new_compare9(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs29(x0, x1, ty_@0)
new_esEs9(x0, x1, ty_@0)
new_ltEs14(Left(x0), Left(x1), ty_Char, x2)
new_lt5(x0, x1, app(ty_[], x2))
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs14(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_primCmpNat0(Zero, Zero)
new_ltEs19(x0, x1, ty_Char)
new_ltEs18(x0, x1)
new_compare9(x0, x1, app(ty_Maybe, x2))
new_compare28(x0, x1, False, x2, x3, x4)
new_ltEs17(x0, x1)
new_lt5(x0, x1, ty_Float)
new_esEs25(x0, x1, ty_Bool)
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs20(x0, x1, ty_Char)
new_esEs26(x0, x1, ty_Char)
new_sr0(Integer(x0), Integer(x1))
new_ltEs14(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_ltEs5(x0, x1, ty_Double)
new_esEs23(x0, x1, ty_Char)
new_compare112(x0, x1, False, x2, x3)
new_compare10(x0, x1, False)
new_ltEs14(Right(x0), Right(x1), x2, ty_Bool)
new_esEs5(Just(x0), Just(x1), ty_Integer)
new_lt20(x0, x1, ty_@0)
new_esEs9(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs23(x0, x1, app(ty_[], x2))
new_esEs6(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs26(x0, x1, ty_Float)
new_esEs13(LT, LT)
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_primEqNat0(Zero, Succ(x0))
new_esEs6(Right(x0), Right(x1), x2, ty_Float)
new_esEs9(x0, x1, ty_Char)
new_primMulNat0(Succ(x0), Zero)
new_esEs27(x0, x1, ty_Bool)
new_ltEs14(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs10(GT, GT)
new_esEs23(x0, x1, ty_@0)
new_compare15(x0, x1, x2)
new_ltEs14(Right(x0), Right(x1), x2, ty_Ordering)
new_primMulNat0(Succ(x0), Succ(x1))
new_esEs29(x0, x1, app(ty_[], x2))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_esEs20(x0, x1, app(ty_[], x2))
new_esEs26(x0, x1, ty_Ordering)
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs11(Just(x0), Just(x1), ty_Bool)
new_compare0(:(x0, x1), :(x2, x3), x4)
new_compare12(x0, x1)
new_esEs23(x0, x1, ty_Bool)
new_esEs5(Just(x0), Just(x1), ty_@0)
new_esEs6(Right(x0), Right(x1), x2, ty_Int)
new_ltEs19(x0, x1, ty_Float)
new_esEs6(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs6(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_not(True)
new_ltEs11(Just(x0), Just(x1), app(ty_Ratio, x2))
new_lt5(x0, x1, app(app(ty_@2, x2), x3))
new_lt5(x0, x1, ty_Ordering)
new_ltEs14(Right(x0), Right(x1), x2, ty_Int)
new_compare24(x0, x1, x2, x3, x4)
new_esEs13(EQ, LT)
new_esEs13(LT, EQ)
new_compare7(Integer(x0), Integer(x1))
new_esEs28(x0, x1, ty_Char)
new_compare9(x0, x1, app(app(ty_Either, x2), x3))
new_lt10(x0, x1)
new_primCmpNat0(Succ(x0), Zero)
new_esEs26(x0, x1, ty_Bool)
new_ltEs19(x0, x1, ty_Bool)
new_lt9(x0, x1)
new_ltEs14(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs5(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_esEs8(x0, x1, app(app(ty_@2, x2), x3))
new_not(False)
new_compare29(x0, x1, True, x2, x3)
new_esEs26(x0, x1, ty_Int)
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs20(x0, x1, ty_Float)
new_ltEs13(x0, x1)
new_esEs25(x0, x1, app(ty_[], x2))
new_ltEs14(Right(x0), Right(x1), x2, ty_@0)
new_esEs8(x0, x1, ty_@0)
new_ltEs14(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_ltEs10(EQ, GT)
new_esEs27(x0, x1, app(ty_[], x2))
new_ltEs10(GT, EQ)
new_ltEs14(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_esEs8(x0, x1, ty_Float)
new_ltEs14(Left(x0), Left(x1), ty_Int, x2)
new_ltEs14(Left(x0), Left(x1), ty_@0, x2)
new_esEs28(x0, x1, ty_@0)
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_esEs28(x0, x1, ty_Int)
new_primEqNat0(Succ(x0), Succ(x1))
new_lt20(x0, x1, app(ty_[], x2))
new_esEs5(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_lt20(x0, x1, ty_Integer)
new_esEs24(x0, x1, ty_@0)
new_lt5(x0, x1, ty_Bool)
new_esEs25(x0, x1, ty_Integer)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs20(x0, x1, ty_Integer)
new_ltEs11(Just(x0), Just(x1), ty_Float)
new_esEs5(Nothing, Nothing, x0)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_lt4(x0, x1, ty_Float)
new_compare9(x0, x1, app(ty_Ratio, x2))
new_esEs10(Integer(x0), Integer(x1))
new_esEs17([], :(x0, x1), x2)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_lt20(x0, x1, app(ty_Ratio, x2))
new_esEs20(x0, x1, ty_Ordering)
new_lt21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_ltEs14(Left(x0), Left(x1), ty_Ordering, x2)
new_lt5(x0, x1, app(ty_Maybe, x2))
new_compare9(x0, x1, ty_@0)
new_ltEs20(x0, x1, ty_Double)
new_compare29(x0, x1, False, x2, x3)
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_esEs6(Left(x0), Left(x1), ty_Char, x2)
new_esEs6(Right(x0), Right(x1), x2, ty_Integer)
new_lt5(x0, x1, ty_Int)
new_esEs27(x0, x1, ty_Double)
new_ltEs19(x0, x1, app(ty_[], x2))
new_esEs6(Left(x0), Right(x1), x2, x3)
new_esEs6(Right(x0), Left(x1), x2, x3)
new_lt12(x0, x1)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_esEs15(x0, x1)
new_ltEs11(Just(x0), Just(x1), ty_Int)
new_compare9(x0, x1, ty_Char)
new_esEs8(x0, x1, ty_Char)
new_ltEs11(Just(x0), Just(x1), ty_@0)
new_ltEs12(x0, x1)
new_primCompAux00(x0, LT)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_primEqInt(Pos(Zero), Pos(Zero))
new_lt11(x0, x1, x2)
new_ltEs19(x0, x1, ty_Ordering)
new_esEs5(Just(x0), Just(x1), app(ty_[], x2))
new_compare112(x0, x1, True, x2, x3)
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_esEs9(x0, x1, ty_Bool)
new_esEs8(x0, x1, ty_Ordering)
new_ltEs5(x0, x1, ty_Float)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs19(@0, @0)
new_esEs24(x0, x1, ty_Int)
new_esEs26(x0, x1, ty_Double)
new_esEs20(x0, x1, ty_Integer)
new_primPlusNat1(Zero, Succ(x0))
new_ltEs14(Left(x0), Left(x1), ty_Double, x2)
new_esEs6(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs20(x0, x1, ty_Int)
new_esEs5(Just(x0), Nothing, x1)
new_esEs27(x0, x1, ty_Ordering)
new_lt20(x0, x1, ty_Double)
new_esEs16(:%(x0, x1), :%(x2, x3), x4)
new_ltEs14(Left(x0), Left(x1), ty_Float, x2)
new_compare110(x0, x1, True)
new_lt4(x0, x1, ty_Ordering)
new_ltEs11(Nothing, Nothing, x0)
new_esEs6(Left(x0), Left(x1), ty_Bool, x2)
new_lt21(x0, x1, ty_Float)
new_ltEs7(False, False)
new_ltEs10(EQ, EQ)

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: