YES 4.132 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
  ((min :: (Ord a, Ord b) => (a,b)  ->  (a,b)  ->  (a,b)) :: (Ord a, Ord b) => (a,b)  ->  (a,b)  ->  (a,b))

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
  ((min :: (Ord a, Ord b) => (b,a)  ->  (b,a)  ->  (b,a)) :: (Ord a, Ord b) => (b,a)  ->  (b,a)  ->  (b,a))

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
  ((min :: (Ord b, Ord a) => (a,b)  ->  (a,b)  ->  (a,b)) :: (Ord b, Ord a) => (a,b)  ->  (a,b)  ->  (a,b))

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
  ((min :: (Ord b, Ord a) => (b,a)  ->  (b,a)  ->  (b,a)) :: (Ord a, Ord b) => (b,a)  ->  (b,a)  ->  (b,a))

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

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

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

compare0 x y True = GT

compare3 x y = compare2 x y (x == y)

The following Function with conditions
min x y
 | x <= y
 = x
 | otherwise
 = y

is transformed to
min x y = min2 x y

min1 x y True = x
min1 x y False = min0 x y otherwise

min0 x y True = y

min2 x y = min1 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
  ((min :: (Ord b, Ord a) => (a,b)  ->  (a,b)  ->  (a,b)) :: (Ord b, Ord a) => (a,b)  ->  (a,b)  ->  (a,b))

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

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

reduce2D vwv vww = gcd vwv vww

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

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

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

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

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



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

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

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
  (min :: (Ord a, Ord b) => (a,b)  ->  (a,b)  ->  (a,b))

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(vwx15400), Succ(vwx400000)) → new_primPlusNat(vwx15400, 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(vwx3000), Succ(vwx4000)) → new_primCmpNat(vwx3000, vwx4000)

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

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



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

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

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

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
                                ↳ DependencyGraphProof

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

new_ltEs2(:(vwx310, vwx311), :(vwx410, vwx411), hg) → new_primCompAux(vwx310, vwx410, vwx311, vwx411, hg)
new_lt(vwx30, vwx40, ba, bb) → new_compare2(vwx30, vwx40, new_esEs4(vwx30, vwx40, ba, bb), ba, bb)
new_ltEs0(Just(vwx310), Just(vwx410), app(app(app(ty_@3, eg), eh), fa)) → new_ltEs3(vwx310, vwx410, eg, eh, fa)
new_ltEs3(@3(vwx310, vwx311, vwx312), @3(vwx410, vwx411, vwx412), bec, app(ty_Maybe, bef), bdc) → new_lt0(vwx311, vwx411, bef)
new_ltEs3(@3(vwx310, vwx311, vwx312), @3(vwx410, vwx411, vwx412), bec, app(app(ty_Either, beg), beh), bdc) → new_lt1(vwx311, vwx411, beg, beh)
new_compare2(vwx30, vwx40, False, ba, bb) → new_ltEs(vwx30, vwx40, ba, bb)
new_ltEs(@2(vwx310, vwx311), @2(vwx410, vwx411), app(ty_Maybe, bf), be) → new_lt0(vwx310, vwx410, bf)
new_ltEs1(Left(vwx310), Left(vwx410), app(app(ty_Either, fg), fh), fd) → new_ltEs1(vwx310, vwx410, fg, fh)
new_ltEs(@2(vwx310, vwx311), @2(vwx410, vwx411), app(ty_[], ca), be) → new_lt2(vwx310, vwx410, ca)
new_ltEs1(Left(vwx310), Left(vwx410), app(ty_Maybe, ff), fd) → new_ltEs0(vwx310, vwx410, ff)
new_compare1(vwx300, vwx400, baa, bab) → new_compare3(vwx300, vwx400, baa, bab)
new_compare32(vwx30, vwx40, bce, bcf, bcg) → new_compare22(vwx30, vwx40, new_esEs7(vwx30, vwx40, bce, bcf, bcg), bce, bcf, bcg)
new_ltEs1(Right(vwx310), Right(vwx410), ge, app(app(app(ty_@3, hd), he), hf)) → new_ltEs3(vwx310, vwx410, hd, he, hf)
new_ltEs3(@3(vwx310, vwx311, vwx312), @3(vwx410, vwx411, vwx412), bec, app(ty_[], bfa), bdc) → new_lt2(vwx311, vwx411, bfa)
new_compare(:(vwx310, vwx311), :(vwx410, vwx411), hg) → new_primCompAux(vwx310, vwx410, vwx311, vwx411, hg)
new_ltEs1(Left(vwx310), Left(vwx410), app(app(ty_@2, fb), fc), fd) → new_ltEs(vwx310, vwx410, fb, fc)
new_ltEs(@2(vwx310, vwx311), @2(vwx410, vwx411), app(app(app(ty_@3, cb), cc), cd), be) → new_lt3(vwx310, vwx410, cb, cc, cd)
new_ltEs3(@3(vwx310, vwx311, vwx312), @3(vwx410, vwx411, vwx412), app(app(ty_@2, bch), bda), bdb, bdc) → new_lt(vwx310, vwx410, bch, bda)
new_compare31(vwx30, vwx40, bcc, bcd) → new_compare21(vwx30, vwx40, new_esEs6(vwx30, vwx40, bcc, bcd), bcc, bcd)
new_ltEs3(@3(vwx310, vwx311, vwx312), @3(vwx410, vwx411, vwx412), app(ty_[], bdg), bdb, bdc) → new_lt2(vwx310, vwx410, bdg)
new_primCompAux(vwx300, vwx400, vwx301, vwx401, hh) → new_primCompAux0(vwx301, vwx401, new_compare0(vwx300, vwx400, hh), app(ty_[], hh))
new_ltEs1(Left(vwx310), Left(vwx410), app(ty_[], ga), fd) → new_ltEs2(vwx310, vwx410, ga)
new_ltEs0(Just(vwx310), Just(vwx410), app(ty_Maybe, ec)) → new_ltEs0(vwx310, vwx410, ec)
new_compare22(vwx30, vwx40, False, bce, bcf, bcg) → new_ltEs3(vwx30, vwx40, bce, bcf, bcg)
new_ltEs3(@3(vwx310, vwx311, vwx312), @3(vwx410, vwx411, vwx412), app(app(ty_Either, bde), bdf), bdb, bdc) → new_lt1(vwx310, vwx410, bde, bdf)
new_lt2(:(vwx300, vwx301), :(vwx400, vwx401), app(app(ty_Either, bac), bad)) → new_compare31(vwx300, vwx400, bac, bad)
new_ltEs3(@3(vwx310, vwx311, vwx312), @3(vwx410, vwx411, vwx412), bec, bdb, app(ty_Maybe, bfg)) → new_ltEs0(vwx312, vwx412, bfg)
new_primCompAux(vwx300, vwx400, vwx301, vwx401, app(app(ty_@2, baa), bab)) → new_compare3(vwx300, vwx400, baa, bab)
new_ltEs3(@3(vwx310, vwx311, vwx312), @3(vwx410, vwx411, vwx412), bec, bdb, app(ty_[], bgb)) → new_ltEs2(vwx312, vwx412, bgb)
new_ltEs(@2(vwx310, vwx311), @2(vwx410, vwx411), app(app(ty_@2, bc), bd), be) → new_lt(vwx310, vwx410, bc, bd)
new_lt3(vwx30, vwx40, bce, bcf, bcg) → new_compare22(vwx30, vwx40, new_esEs7(vwx30, vwx40, bce, bcf, bcg), bce, bcf, bcg)
new_ltEs1(Right(vwx310), Right(vwx410), ge, app(app(ty_@2, gf), gg)) → new_ltEs(vwx310, vwx410, gf, gg)
new_primCompAux0(vwx144, vwx145, EQ, app(ty_Maybe, bbd)) → new_compare4(vwx144, vwx145, bbd)
new_primCompAux0(vwx144, vwx145, EQ, app(app(ty_@2, bbb), bbc)) → new_compare1(vwx144, vwx145, bbb, bbc)
new_primCompAux0(vwx144, vwx145, EQ, app(app(app(ty_@3, bbh), bca), bcb)) → new_compare6(vwx144, vwx145, bbh, bca, bcb)
new_compare6(vwx300, vwx400, bag, bah, bba) → new_compare32(vwx300, vwx400, bag, bah, bba)
new_primCompAux(vwx300, vwx400, vwx301, vwx401, app(app(app(ty_@3, bag), bah), bba)) → new_compare32(vwx300, vwx400, bag, bah, bba)
new_compare5(vwx300, vwx400, bac, bad) → new_compare31(vwx300, vwx400, bac, bad)
new_compare21(vwx30, vwx40, False, bcc, bcd) → new_ltEs1(vwx30, vwx40, bcc, bcd)
new_ltEs1(Right(vwx310), Right(vwx410), ge, app(ty_Maybe, gh)) → new_ltEs0(vwx310, vwx410, gh)
new_compare30(vwx30, vwx40, dh) → new_compare20(vwx30, vwx40, new_esEs5(vwx30, vwx40, dh), dh)
new_compare3(vwx30, vwx40, ba, bb) → new_compare2(vwx30, vwx40, new_esEs4(vwx30, vwx40, ba, bb), ba, bb)
new_ltEs(@2(vwx310, vwx311), @2(vwx410, vwx411), app(app(ty_Either, bg), bh), be) → new_lt1(vwx310, vwx410, bg, bh)
new_ltEs(@2(vwx310, vwx311), @2(vwx410, vwx411), ce, app(app(app(ty_@3, de), df), dg)) → new_ltEs3(vwx311, vwx411, de, df, dg)
new_lt2(:(vwx300, vwx301), :(vwx400, vwx401), app(app(app(ty_@3, bag), bah), bba)) → new_compare32(vwx300, vwx400, bag, bah, bba)
new_lt1(vwx30, vwx40, bcc, bcd) → new_compare21(vwx30, vwx40, new_esEs6(vwx30, vwx40, bcc, bcd), bcc, bcd)
new_lt2(:(vwx300, vwx301), :(vwx400, vwx401), app(ty_[], bae)) → new_compare(vwx300, vwx400, bae)
new_ltEs1(Right(vwx310), Right(vwx410), ge, app(ty_[], hc)) → new_ltEs2(vwx310, vwx410, hc)
new_primCompAux(vwx300, vwx400, vwx301, vwx401, app(ty_[], bae)) → new_compare(vwx300, vwx400, bae)
new_primCompAux0(vwx144, vwx145, EQ, app(ty_[], bbg)) → new_compare(vwx144, vwx145, bbg)
new_ltEs3(@3(vwx310, vwx311, vwx312), @3(vwx410, vwx411, vwx412), bec, bdb, app(app(ty_@2, bfe), bff)) → new_ltEs(vwx312, vwx412, bfe, bff)
new_lt2(:(vwx300, vwx301), :(vwx400, vwx401), app(ty_Maybe, baf)) → new_compare30(vwx300, vwx400, baf)
new_ltEs3(@3(vwx310, vwx311, vwx312), @3(vwx410, vwx411, vwx412), bec, app(app(ty_@2, bed), bee), bdc) → new_lt(vwx311, vwx411, bed, bee)
new_ltEs3(@3(vwx310, vwx311, vwx312), @3(vwx410, vwx411, vwx412), bec, bdb, app(app(app(ty_@3, bgc), bgd), bge)) → new_ltEs3(vwx312, vwx412, bgc, bgd, bge)
new_primCompAux0(vwx144, vwx145, EQ, app(app(ty_Either, bbe), bbf)) → new_compare5(vwx144, vwx145, bbe, bbf)
new_ltEs0(Just(vwx310), Just(vwx410), app(ty_[], ef)) → new_ltEs2(vwx310, vwx410, ef)
new_ltEs3(@3(vwx310, vwx311, vwx312), @3(vwx410, vwx411, vwx412), app(app(app(ty_@3, bdh), bea), beb), bdb, bdc) → new_lt3(vwx310, vwx410, bdh, bea, beb)
new_ltEs3(@3(vwx310, vwx311, vwx312), @3(vwx410, vwx411, vwx412), bec, bdb, app(app(ty_Either, bfh), bga)) → new_ltEs1(vwx312, vwx412, bfh, bga)
new_ltEs0(Just(vwx310), Just(vwx410), app(app(ty_@2, ea), eb)) → new_ltEs(vwx310, vwx410, ea, eb)
new_ltEs0(Just(vwx310), Just(vwx410), app(app(ty_Either, ed), ee)) → new_ltEs1(vwx310, vwx410, ed, ee)
new_ltEs(@2(vwx310, vwx311), @2(vwx410, vwx411), ce, app(app(ty_@2, cf), cg)) → new_ltEs(vwx311, vwx411, cf, cg)
new_ltEs1(Right(vwx310), Right(vwx410), ge, app(app(ty_Either, ha), hb)) → new_ltEs1(vwx310, vwx410, ha, hb)
new_ltEs3(@3(vwx310, vwx311, vwx312), @3(vwx410, vwx411, vwx412), bec, app(app(app(ty_@3, bfb), bfc), bfd), bdc) → new_lt3(vwx311, vwx411, bfb, bfc, bfd)
new_ltEs(@2(vwx310, vwx311), @2(vwx410, vwx411), ce, app(ty_[], dd)) → new_ltEs2(vwx311, vwx411, dd)
new_lt2(:(vwx300, vwx301), :(vwx400, vwx401), hh) → new_primCompAux0(vwx301, vwx401, new_compare0(vwx300, vwx400, hh), app(ty_[], hh))
new_ltEs(@2(vwx310, vwx311), @2(vwx410, vwx411), ce, app(ty_Maybe, da)) → new_ltEs0(vwx311, vwx411, da)
new_primCompAux(vwx300, vwx400, vwx301, vwx401, app(app(ty_Either, bac), bad)) → new_compare31(vwx300, vwx400, bac, bad)
new_lt2(:(vwx300, vwx301), :(vwx400, vwx401), app(app(ty_@2, baa), bab)) → new_compare3(vwx300, vwx400, baa, bab)
new_compare4(vwx300, vwx400, baf) → new_compare30(vwx300, vwx400, baf)
new_primCompAux(vwx300, vwx400, vwx301, vwx401, app(ty_Maybe, baf)) → new_compare30(vwx300, vwx400, baf)
new_ltEs(@2(vwx310, vwx311), @2(vwx410, vwx411), ce, app(app(ty_Either, db), dc)) → new_ltEs1(vwx311, vwx411, db, dc)
new_compare20(vwx30, vwx40, False, dh) → new_ltEs0(vwx30, vwx40, dh)
new_ltEs1(Left(vwx310), Left(vwx410), app(app(app(ty_@3, gb), gc), gd), fd) → new_ltEs3(vwx310, vwx410, gb, gc, gd)
new_lt0(vwx30, vwx40, dh) → new_compare20(vwx30, vwx40, new_esEs5(vwx30, vwx40, dh), dh)
new_ltEs3(@3(vwx310, vwx311, vwx312), @3(vwx410, vwx411, vwx412), app(ty_Maybe, bdd), bdb, bdc) → new_lt0(vwx310, vwx410, bdd)

The TRS R consists of the following rules:

new_esEs26(vwx310, vwx410, ty_Char) → new_esEs14(vwx310, vwx410)
new_ltEs12(Right(vwx310), Right(vwx410), ge, app(ty_Ratio, cah)) → new_ltEs17(vwx310, vwx410, cah)
new_compare13(vwx300, vwx400, bac, bad) → new_compare36(vwx300, vwx400, bac, bad)
new_compare36(vwx30, vwx40, bcc, bcd) → new_compare210(vwx30, vwx40, new_esEs6(vwx30, vwx40, bcc, bcd), bcc, bcd)
new_ltEs18(EQ, GT) → True
new_compare8(Integer(vwx310), Integer(vwx410)) → new_primCmpInt(vwx310, vwx410)
new_ltEs12(Right(vwx310), Right(vwx410), ge, ty_Bool) → new_ltEs10(vwx310, vwx410)
new_ltEs10(False, True) → True
new_lt6(vwx30, vwx40, ba, bb) → new_esEs19(new_compare34(vwx30, vwx40, ba, bb), LT)
new_esEs20(vwx300, vwx400, ty_Bool) → new_esEs12(vwx300, vwx400)
new_compare110(vwx30, vwx40, True, ba, bb) → LT
new_esEs27(vwx300, vwx400, app(ty_Ratio, dad)) → new_esEs18(vwx300, vwx400, dad)
new_esEs23(vwx300, vwx400, app(app(ty_@2, cbd), cbe)) → new_esEs4(vwx300, vwx400, cbd, cbe)
new_esEs8(vwx310, vwx410, ty_Integer) → new_esEs16(vwx310, vwx410)
new_esEs9(vwx311, vwx411, ty_@0) → new_esEs13(vwx311, vwx411)
new_primCompAux00(vwx144, vwx145, EQ, app(ty_Maybe, bbd)) → new_compare39(vwx144, vwx145, bbd)
new_esEs27(vwx300, vwx400, ty_Ordering) → new_esEs19(vwx300, vwx400)
new_ltEs19(vwx311, vwx411, ty_Integer) → new_ltEs15(vwx311, vwx411)
new_esEs23(vwx300, vwx400, app(ty_[], cca)) → new_esEs17(vwx300, vwx400, cca)
new_primMulNat0(Zero, Zero) → Zero
new_lt5(vwx311, vwx411, ty_Ordering) → new_lt18(vwx311, vwx411)
new_esEs6(Left(vwx300), Left(vwx400), app(app(app(ty_@3, cga), cgb), cgc), bcd) → new_esEs7(vwx300, vwx400, cga, cgb, cgc)
new_esEs24(vwx301, vwx401, ty_@0) → new_esEs13(vwx301, vwx401)
new_lt16(:(vwx300, vwx301), :(vwx400, vwx401), hh) → new_esEs19(new_primCompAux1(vwx300, vwx400, vwx301, vwx401, hh), LT)
new_ltEs16(vwx31, vwx41, hg) → new_not(new_esEs19(new_compare19(vwx31, vwx41, hg), GT))
new_esEs25(vwx302, vwx402, app(app(ty_Either, ceb), cec)) → new_esEs6(vwx302, vwx402, ceb, cec)
new_esEs12(True, True) → True
new_esEs25(vwx302, vwx402, app(app(ty_@2, cdh), cea)) → new_esEs4(vwx302, vwx402, cdh, cea)
new_lt4(vwx310, vwx410, ty_Char) → new_lt13(vwx310, vwx410)
new_lt5(vwx311, vwx411, ty_@0) → new_lt11(vwx311, vwx411)
new_lt4(vwx310, vwx410, ty_Float) → new_lt9(vwx310, vwx410)
new_esEs23(vwx300, vwx400, ty_Bool) → new_esEs12(vwx300, vwx400)
new_lt20(vwx310, vwx410, app(app(ty_Either, bg), bh)) → new_lt12(vwx310, vwx410, bg, bh)
new_compare43(vwx300, vwx401, vwx400, vwx301, ty_Int) → new_compare15(vwx300, vwx401, vwx400, vwx301)
new_compare40(vwx31, vwx41) → new_primCmpFloat(vwx31, vwx41)
new_esEs25(vwx302, vwx402, app(ty_Ratio, ced)) → new_esEs18(vwx302, vwx402, ced)
new_esEs6(Right(vwx300), Right(vwx400), bcc, ty_Float) → new_esEs11(vwx300, vwx400)
new_ltEs12(Right(vwx310), Right(vwx410), ge, ty_Char) → new_ltEs13(vwx310, vwx410)
new_lt20(vwx310, vwx410, ty_Double) → new_lt14(vwx310, vwx410)
new_esEs20(vwx300, vwx400, ty_Float) → new_esEs11(vwx300, vwx400)
new_lt5(vwx311, vwx411, ty_Integer) → new_lt15(vwx311, vwx411)
new_esEs23(vwx300, vwx400, ty_@0) → new_esEs13(vwx300, vwx400)
new_ltEs7(Just(vwx310), Just(vwx410), ty_Ordering) → new_ltEs18(vwx310, vwx410)
new_compare23(vwx30, vwx40, False) → new_compare10(vwx30, vwx40, new_ltEs18(vwx30, vwx40))
new_compare14(vwx31, vwx41) → new_primCmpDouble(vwx31, vwx41)
new_compare34(vwx30, vwx40, ba, bb) → new_compare24(vwx30, vwx40, new_esEs4(vwx30, vwx40, ba, bb), ba, bb)
new_esEs9(vwx311, vwx411, ty_Int) → new_esEs10(vwx311, vwx411)
new_compare17(vwx30, vwx40, True, bce, bcf, bcg) → LT
new_esEs5(Just(vwx300), Just(vwx400), app(ty_Maybe, bhg)) → new_esEs5(vwx300, vwx400, bhg)
new_compare0(vwx300, vwx400, app(app(ty_@2, baa), bab)) → new_compare28(vwx300, vwx400, baa, bab)
new_compare19(:(vwx310, vwx311), [], hg) → GT
new_esEs25(vwx302, vwx402, ty_Double) → new_esEs15(vwx302, vwx402)
new_lt15(Integer(vwx300), Integer(vwx400)) → new_esEs19(new_primCmpInt(vwx300, vwx400), LT)
new_compare0(vwx300, vwx400, ty_@0) → new_compare7(vwx300, vwx400)
new_compare0(vwx300, vwx400, ty_Bool) → new_compare41(vwx300, vwx400)
new_ltEs12(Right(vwx310), Right(vwx410), ge, ty_Int) → new_ltEs8(vwx310, vwx410)
new_esEs8(vwx310, vwx410, app(app(ty_Either, bde), bdf)) → new_esEs6(vwx310, vwx410, bde, bdf)
new_lt18(vwx30, vwx40) → new_esEs19(new_compare33(vwx30, vwx40), LT)
new_ltEs10(False, False) → True
new_esEs8(vwx310, vwx410, app(app(ty_@2, bch), bda)) → new_esEs4(vwx310, vwx410, bch, bda)
new_primCompAux00(vwx144, vwx145, EQ, ty_@0) → new_compare7(vwx144, vwx145)
new_primCompAux00(vwx144, vwx145, EQ, ty_Char) → new_compare29(vwx144, vwx145)
new_esEs28(vwx301, vwx401, ty_Ordering) → new_esEs19(vwx301, vwx401)
new_lt9(vwx30, vwx40) → new_esEs19(new_primCmpFloat(vwx30, vwx40), LT)
new_compare27(vwx30, vwx40, False) → new_compare18(vwx30, vwx40, new_ltEs10(vwx30, vwx40))
new_esEs6(Left(vwx300), Left(vwx400), ty_Float, bcd) → new_esEs11(vwx300, vwx400)
new_ltEs7(Just(vwx310), Just(vwx410), ty_Double) → new_ltEs14(vwx310, vwx410)
new_pePe(False, vwx113) → vwx113
new_esEs19(GT, GT) → True
new_esEs6(Right(vwx300), Right(vwx400), bcc, ty_@0) → new_esEs13(vwx300, vwx400)
new_ltEs7(Just(vwx310), Just(vwx410), ty_Integer) → new_ltEs15(vwx310, vwx410)
new_esEs27(vwx300, vwx400, ty_Float) → new_esEs11(vwx300, vwx400)
new_esEs6(Left(vwx300), Left(vwx400), app(app(ty_@2, cfb), cfc), bcd) → new_esEs4(vwx300, vwx400, cfb, cfc)
new_compare23(vwx30, vwx40, True) → EQ
new_lt13(vwx30, vwx40) → new_esEs19(new_primCmpChar(vwx30, vwx40), LT)
new_esEs7(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), bce, bcf, bcg) → new_asAs(new_esEs23(vwx300, vwx400, bce), new_asAs(new_esEs24(vwx301, vwx401, bcf), new_esEs25(vwx302, vwx402, bcg)))
new_lt5(vwx311, vwx411, ty_Float) → new_lt9(vwx311, vwx411)
new_lt5(vwx311, vwx411, app(ty_[], bfa)) → new_lt16(vwx311, vwx411, bfa)
new_esEs28(vwx301, vwx401, ty_@0) → new_esEs13(vwx301, vwx401)
new_ltEs7(Just(vwx310), Just(vwx410), app(app(ty_@2, ea), eb)) → new_ltEs6(vwx310, vwx410, ea, eb)
new_esEs26(vwx310, vwx410, ty_@0) → new_esEs13(vwx310, vwx410)
new_esEs8(vwx310, vwx410, ty_Char) → new_esEs14(vwx310, vwx410)
new_lt16([], [], hh) → new_esEs19(EQ, LT)
new_esEs26(vwx310, vwx410, ty_Bool) → new_esEs12(vwx310, vwx410)
new_compare24(vwx30, vwx40, False, ba, bb) → new_compare110(vwx30, vwx40, new_ltEs6(vwx30, vwx40, ba, bb), ba, bb)
new_esEs5(Just(vwx300), Just(vwx400), ty_Ordering) → new_esEs19(vwx300, vwx400)
new_esEs8(vwx310, vwx410, ty_Bool) → new_esEs12(vwx310, vwx410)
new_lt5(vwx311, vwx411, ty_Bool) → new_lt10(vwx311, vwx411)
new_esEs27(vwx300, vwx400, app(ty_[], dae)) → new_esEs17(vwx300, vwx400, dae)
new_ltEs7(Just(vwx310), Just(vwx410), ty_Char) → new_ltEs13(vwx310, vwx410)
new_lt5(vwx311, vwx411, ty_Char) → new_lt13(vwx311, vwx411)
new_lt4(vwx310, vwx410, app(ty_[], bdg)) → new_lt16(vwx310, vwx410, bdg)
new_ltEs5(vwx312, vwx412, app(app(ty_@2, bfe), bff)) → new_ltEs6(vwx312, vwx412, bfe, bff)
new_ltEs19(vwx311, vwx411, ty_Int) → new_ltEs8(vwx311, vwx411)
new_esEs23(vwx300, vwx400, app(app(app(ty_@3, ccc), ccd), cce)) → new_esEs7(vwx300, vwx400, ccc, ccd, cce)
new_primCmpNat0(Zero, Succ(vwx4000)) → LT
new_esEs27(vwx300, vwx400, app(app(app(ty_@3, dag), dah), dba)) → new_esEs7(vwx300, vwx400, dag, dah, dba)
new_ltEs12(Left(vwx310), Left(vwx410), app(app(ty_@2, fb), fc), fd) → new_ltEs6(vwx310, vwx410, fb, fc)
new_esEs6(Right(vwx300), Left(vwx400), bcc, bcd) → False
new_esEs6(Left(vwx300), Right(vwx400), bcc, bcd) → False
new_compare35(vwx30, vwx40, bce, bcf, bcg) → new_compare25(vwx30, vwx40, new_esEs7(vwx30, vwx40, bce, bcf, bcg), bce, bcf, bcg)
new_esEs28(vwx301, vwx401, ty_Char) → new_esEs14(vwx301, vwx401)
new_compare25(vwx30, vwx40, True, bce, bcf, bcg) → EQ
new_esEs25(vwx302, vwx402, ty_Char) → new_esEs14(vwx302, vwx402)
new_lt4(vwx310, vwx410, app(ty_Ratio, bgf)) → new_lt17(vwx310, vwx410, bgf)
new_lt5(vwx311, vwx411, app(app(app(ty_@3, bfb), bfc), bfd)) → new_lt19(vwx311, vwx411, bfb, bfc, bfd)
new_ltEs12(Left(vwx310), Left(vwx410), ty_Integer, fd) → new_ltEs15(vwx310, vwx410)
new_ltEs9(vwx31, vwx41) → new_not(new_esEs19(new_compare40(vwx31, vwx41), GT))
new_ltEs19(vwx311, vwx411, app(app(app(ty_@3, de), df), dg)) → new_ltEs4(vwx311, vwx411, de, df, dg)
new_esEs28(vwx301, vwx401, ty_Double) → new_esEs15(vwx301, vwx401)
new_lt16([], :(vwx400, vwx401), hh) → new_esEs19(LT, LT)
new_ltEs12(Left(vwx310), Left(vwx410), ty_Ordering, fd) → new_ltEs18(vwx310, vwx410)
new_ltEs6(@2(vwx310, vwx311), @2(vwx410, vwx411), ce, be) → new_pePe(new_lt20(vwx310, vwx410, ce), new_asAs(new_esEs26(vwx310, vwx410, ce), new_ltEs19(vwx311, vwx411, be)))
new_primCompAux00(vwx144, vwx145, EQ, ty_Bool) → new_compare41(vwx144, vwx145)
new_lt12(vwx30, vwx40, bcc, bcd) → new_esEs19(new_compare36(vwx30, vwx40, bcc, bcd), LT)
new_esEs28(vwx301, vwx401, ty_Integer) → new_esEs16(vwx301, vwx401)
new_ltEs7(Just(vwx310), Just(vwx410), ty_Int) → new_ltEs8(vwx310, vwx410)
new_compare12(:%(vwx310, vwx311), :%(vwx410, vwx411), ty_Integer) → new_compare8(new_sr0(vwx310, vwx411), new_sr0(vwx410, vwx311))
new_esEs5(Just(vwx300), Just(vwx400), app(ty_[], bhf)) → new_esEs17(vwx300, vwx400, bhf)
new_esEs15(Double(vwx300, vwx301), Double(vwx400, vwx401)) → new_esEs10(new_sr(vwx300, vwx400), new_sr(vwx301, vwx401))
new_pePe(True, vwx113) → True
new_primEqNat0(Zero, Zero) → True
new_compare310(vwx30, vwx40) → new_compare27(vwx30, vwx40, new_esEs12(vwx30, vwx40))
new_esEs6(Right(vwx300), Right(vwx400), bcc, ty_Integer) → new_esEs16(vwx300, vwx400)
new_esEs23(vwx300, vwx400, app(app(ty_Either, cbf), cbg)) → new_esEs6(vwx300, vwx400, cbf, cbg)
new_esEs5(Just(vwx300), Just(vwx400), app(app(ty_@2, bha), bhb)) → new_esEs4(vwx300, vwx400, bha, bhb)
new_ltEs18(EQ, EQ) → True
new_esEs4(@2(vwx300, vwx301), @2(vwx400, vwx401), ba, bb) → new_asAs(new_esEs27(vwx300, vwx400, ba), new_esEs28(vwx301, vwx401, bb))
new_ltEs12(Right(vwx310), Right(vwx410), ge, ty_Double) → new_ltEs14(vwx310, vwx410)
new_esEs23(vwx300, vwx400, ty_Char) → new_esEs14(vwx300, vwx400)
new_primCompAux00(vwx144, vwx145, EQ, app(app(app(ty_@3, bbh), bca), bcb)) → new_compare9(vwx144, vwx145, bbh, bca, bcb)
new_esEs6(Right(vwx300), Right(vwx400), bcc, app(app(ty_Either, cgf), cgg)) → new_esEs6(vwx300, vwx400, cgf, cgg)
new_esEs6(Left(vwx300), Left(vwx400), ty_Double, bcd) → new_esEs15(vwx300, vwx400)
new_ltEs5(vwx312, vwx412, app(app(ty_Either, bfh), bga)) → new_ltEs12(vwx312, vwx412, bfh, bga)
new_compare110(vwx30, vwx40, False, ba, bb) → GT
new_ltEs14(vwx31, vwx41) → new_not(new_esEs19(new_compare14(vwx31, vwx41), GT))
new_sr(vwx300, vwx400) → new_primMulInt(vwx300, vwx400)
new_esEs26(vwx310, vwx410, ty_Ordering) → new_esEs19(vwx310, vwx410)
new_esEs28(vwx301, vwx401, app(app(ty_Either, dbd), dbe)) → new_esEs6(vwx301, vwx401, dbd, dbe)
new_lt20(vwx310, vwx410, ty_Float) → new_lt9(vwx310, vwx410)
new_esEs9(vwx311, vwx411, app(app(app(ty_@3, bfb), bfc), bfd)) → new_esEs7(vwx311, vwx411, bfb, bfc, bfd)
new_esEs6(Right(vwx300), Right(vwx400), bcc, ty_Double) → new_esEs15(vwx300, vwx400)
new_ltEs18(LT, LT) → True
new_ltEs5(vwx312, vwx412, ty_Char) → new_ltEs13(vwx312, vwx412)
new_primPlusNat0(Succ(vwx1540), vwx40000) → Succ(Succ(new_primPlusNat1(vwx1540, vwx40000)))
new_compare0(vwx300, vwx400, app(ty_[], bae)) → new_compare19(vwx300, vwx400, bae)
new_ltEs11(vwx31, vwx41) → new_not(new_esEs19(new_compare7(vwx31, vwx41), GT))
new_esEs20(vwx300, vwx400, app(app(app(ty_@3, bag), bah), bba)) → new_esEs7(vwx300, vwx400, bag, bah, bba)
new_esEs12(False, False) → True
new_esEs26(vwx310, vwx410, ty_Float) → new_esEs11(vwx310, vwx410)
new_ltEs12(Right(vwx310), Right(vwx410), ge, ty_Float) → new_ltEs9(vwx310, vwx410)
new_esEs9(vwx311, vwx411, ty_Char) → new_esEs14(vwx311, vwx411)
new_ltEs18(GT, GT) → True
new_lt4(vwx310, vwx410, app(app(app(ty_@3, bdh), bea), beb)) → new_lt19(vwx310, vwx410, bdh, bea, beb)
new_primEqInt(Neg(Succ(vwx3000)), Neg(Succ(vwx4000))) → new_primEqNat0(vwx3000, vwx4000)
new_lt4(vwx310, vwx410, ty_Double) → new_lt14(vwx310, vwx410)
new_esEs6(Right(vwx300), Right(vwx400), bcc, app(app(app(ty_@3, chc), chd), che)) → new_esEs7(vwx300, vwx400, chc, chd, che)
new_compare16(vwx30, vwx40, True, dh) → LT
new_esEs8(vwx310, vwx410, ty_Double) → new_esEs15(vwx310, vwx410)
new_compare39(vwx300, vwx400, baf) → new_compare37(vwx300, vwx400, baf)
new_esEs9(vwx311, vwx411, ty_Integer) → new_esEs16(vwx311, vwx411)
new_esEs19(EQ, EQ) → True
new_ltEs18(LT, GT) → True
new_compare25(vwx30, vwx40, False, bce, bcf, bcg) → new_compare17(vwx30, vwx40, new_ltEs4(vwx30, vwx40, bce, bcf, bcg), bce, bcf, bcg)
new_primPlusNat1(Succ(vwx15400), Zero) → Succ(vwx15400)
new_primPlusNat1(Zero, Succ(vwx400000)) → Succ(vwx400000)
new_ltEs19(vwx311, vwx411, app(ty_Ratio, chg)) → new_ltEs17(vwx311, vwx411, chg)
new_esEs26(vwx310, vwx410, app(app(app(ty_@3, cb), cc), cd)) → new_esEs7(vwx310, vwx410, cb, cc, cd)
new_ltEs18(GT, LT) → False
new_ltEs5(vwx312, vwx412, app(ty_[], bgb)) → new_ltEs16(vwx312, vwx412, bgb)
new_ltEs19(vwx311, vwx411, ty_Float) → new_ltEs9(vwx311, vwx411)
new_esEs9(vwx311, vwx411, ty_Float) → new_esEs11(vwx311, vwx411)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs5(Just(vwx300), Just(vwx400), ty_Int) → new_esEs10(vwx300, vwx400)
new_compare38(vwx300, vwx400) → new_compare33(vwx300, vwx400)
new_compare0(vwx300, vwx400, app(app(app(ty_@3, bag), bah), bba)) → new_compare9(vwx300, vwx400, bag, bah, bba)
new_compare18(vwx30, vwx40, False) → GT
new_primEqInt(Neg(Succ(vwx3000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(vwx4000))) → False
new_compare37(vwx30, vwx40, dh) → new_compare26(vwx30, vwx40, new_esEs5(vwx30, vwx40, dh), dh)
new_esEs23(vwx300, vwx400, ty_Integer) → new_esEs16(vwx300, vwx400)
new_esEs6(Right(vwx300), Right(vwx400), bcc, app(ty_[], cha)) → new_esEs17(vwx300, vwx400, cha)
new_esEs20(vwx300, vwx400, ty_Integer) → new_esEs16(vwx300, vwx400)
new_compare28(vwx300, vwx400, baa, bab) → new_compare34(vwx300, vwx400, baa, bab)
new_compare24(vwx30, vwx40, True, ba, bb) → EQ
new_lt7(vwx30, vwx40, dh) → new_esEs19(new_compare37(vwx30, vwx40, dh), LT)
new_esEs23(vwx300, vwx400, ty_Ordering) → new_esEs19(vwx300, vwx400)
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_ltEs5(vwx312, vwx412, app(ty_Ratio, bgh)) → new_ltEs17(vwx312, vwx412, bgh)
new_lt20(vwx310, vwx410, ty_Int) → new_lt8(vwx310, vwx410)
new_esEs6(Left(vwx300), Left(vwx400), app(ty_Ratio, cff), bcd) → new_esEs18(vwx300, vwx400, cff)
new_ltEs12(Right(vwx310), Right(vwx410), ge, app(ty_[], hc)) → new_ltEs16(vwx310, vwx410, hc)
new_lt4(vwx310, vwx410, ty_Int) → new_lt8(vwx310, vwx410)
new_compare29(vwx31, vwx41) → new_primCmpChar(vwx31, vwx41)
new_lt5(vwx311, vwx411, app(app(ty_@2, bed), bee)) → new_lt6(vwx311, vwx411, bed, bee)
new_primCmpNat0(Succ(vwx3000), Succ(vwx4000)) → new_primCmpNat0(vwx3000, vwx4000)
new_esEs19(LT, EQ) → False
new_esEs19(EQ, LT) → False
new_ltEs19(vwx311, vwx411, ty_@0) → new_ltEs11(vwx311, vwx411)
new_compare0(vwx300, vwx400, ty_Float) → new_compare40(vwx300, vwx400)
new_esEs26(vwx310, vwx410, ty_Integer) → new_esEs16(vwx310, vwx410)
new_ltEs12(Left(vwx310), Left(vwx410), app(ty_[], ga), fd) → new_ltEs16(vwx310, vwx410, ga)
new_primEqInt(Pos(Succ(vwx3000)), Pos(Succ(vwx4000))) → new_primEqNat0(vwx3000, vwx4000)
new_esEs25(vwx302, vwx402, app(ty_Maybe, cef)) → new_esEs5(vwx302, vwx402, cef)
new_esEs20(vwx300, vwx400, ty_Int) → new_esEs10(vwx300, vwx400)
new_esEs8(vwx310, vwx410, app(ty_Maybe, bdd)) → new_esEs5(vwx310, vwx410, bdd)
new_ltEs7(Nothing, Just(vwx410), cae) → True
new_ltEs5(vwx312, vwx412, ty_@0) → new_ltEs11(vwx312, vwx412)
new_ltEs12(Left(vwx310), Left(vwx410), ty_@0, fd) → new_ltEs11(vwx310, vwx410)
new_ltEs12(Right(vwx310), Right(vwx410), ge, app(app(ty_@2, gf), gg)) → new_ltEs6(vwx310, vwx410, gf, gg)
new_primEqNat0(Succ(vwx3000), Succ(vwx4000)) → new_primEqNat0(vwx3000, vwx4000)
new_compare7(@0, @0) → EQ
new_esEs24(vwx301, vwx401, app(ty_Ratio, cdb)) → new_esEs18(vwx301, vwx401, cdb)
new_esEs6(Left(vwx300), Left(vwx400), app(ty_[], cfg), bcd) → new_esEs17(vwx300, vwx400, cfg)
new_ltEs19(vwx311, vwx411, ty_Double) → new_ltEs14(vwx311, vwx411)
new_ltEs12(Right(vwx310), Right(vwx410), ge, app(ty_Maybe, gh)) → new_ltEs7(vwx310, vwx410, gh)
new_esEs9(vwx311, vwx411, app(app(ty_Either, beg), beh)) → new_esEs6(vwx311, vwx411, beg, beh)
new_primCmpInt(Neg(Succ(vwx3000)), Neg(vwx400)) → new_primCmpNat0(vwx400, Succ(vwx3000))
new_compare16(vwx30, vwx40, False, dh) → GT
new_esEs26(vwx310, vwx410, app(app(ty_@2, bc), bd)) → new_esEs4(vwx310, vwx410, bc, bd)
new_esEs6(Right(vwx300), Right(vwx400), bcc, app(ty_Maybe, chb)) → new_esEs5(vwx300, vwx400, chb)
new_esEs23(vwx300, vwx400, ty_Double) → new_esEs15(vwx300, vwx400)
new_compare17(vwx30, vwx40, False, bce, bcf, bcg) → GT
new_ltEs5(vwx312, vwx412, ty_Int) → new_ltEs8(vwx312, vwx412)
new_primEqInt(Pos(Succ(vwx3000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(vwx4000))) → False
new_lt20(vwx310, vwx410, app(ty_Ratio, chf)) → new_lt17(vwx310, vwx410, chf)
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(vwx3000), Zero) → GT
new_esEs6(Left(vwx300), Left(vwx400), ty_Bool, bcd) → new_esEs12(vwx300, vwx400)
new_compare18(vwx30, vwx40, True) → LT
new_primCmpInt(Neg(Zero), Pos(Succ(vwx4000))) → LT
new_compare11(vwx30, vwx40, True, bcc, bcd) → LT
new_esEs8(vwx310, vwx410, ty_Int) → new_esEs10(vwx310, vwx410)
new_lt20(vwx310, vwx410, ty_Char) → new_lt13(vwx310, vwx410)
new_sr0(Integer(vwx4000), Integer(vwx3010)) → Integer(new_primMulInt(vwx4000, vwx3010))
new_lt4(vwx310, vwx410, app(ty_Maybe, bdd)) → new_lt7(vwx310, vwx410, bdd)
new_primPlusNat1(Succ(vwx15400), Succ(vwx400000)) → Succ(Succ(new_primPlusNat1(vwx15400, vwx400000)))
new_primEqInt(Pos(Succ(vwx3000)), Neg(vwx400)) → False
new_primEqInt(Neg(Succ(vwx3000)), Pos(vwx400)) → False
new_esEs25(vwx302, vwx402, ty_Int) → new_esEs10(vwx302, vwx402)
new_esEs24(vwx301, vwx401, app(app(ty_@2, ccf), ccg)) → new_esEs4(vwx301, vwx401, ccf, ccg)
new_ltEs12(Left(vwx310), Right(vwx410), ge, fd) → True
new_esEs5(Just(vwx300), Just(vwx400), ty_Bool) → new_esEs12(vwx300, vwx400)
new_esEs25(vwx302, vwx402, ty_@0) → new_esEs13(vwx302, vwx402)
new_esEs27(vwx300, vwx400, app(ty_Maybe, daf)) → new_esEs5(vwx300, vwx400, daf)
new_primCompAux00(vwx144, vwx145, EQ, ty_Int) → new_compare42(vwx144, vwx145)
new_lt4(vwx310, vwx410, ty_Integer) → new_lt15(vwx310, vwx410)
new_esEs6(Right(vwx300), Right(vwx400), bcc, ty_Ordering) → new_esEs19(vwx300, vwx400)
new_esEs5(Just(vwx300), Just(vwx400), ty_@0) → new_esEs13(vwx300, vwx400)
new_esEs6(Left(vwx300), Left(vwx400), ty_@0, bcd) → new_esEs13(vwx300, vwx400)
new_primEqInt(Pos(Zero), Neg(Succ(vwx4000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(vwx4000))) → False
new_esEs26(vwx310, vwx410, ty_Int) → new_esEs10(vwx310, vwx410)
new_primCompAux00(vwx144, vwx145, EQ, app(ty_[], bbg)) → new_compare19(vwx144, vwx145, bbg)
new_esEs26(vwx310, vwx410, app(ty_[], ca)) → new_esEs17(vwx310, vwx410, ca)
new_esEs13(@0, @0) → True
new_lt8(vwx30, vwx40) → new_esEs19(new_primCmpInt(vwx30, vwx40), LT)
new_primCmpInt(Pos(Zero), Pos(Succ(vwx4000))) → new_primCmpNat0(Zero, Succ(vwx4000))
new_primCompAux00(vwx144, vwx145, EQ, ty_Ordering) → new_compare38(vwx144, vwx145)
new_esEs18(:%(vwx300, vwx301), :%(vwx400, vwx401), cbc) → new_asAs(new_esEs21(vwx300, vwx400, cbc), new_esEs22(vwx301, vwx401, cbc))
new_ltEs12(Left(vwx310), Left(vwx410), ty_Int, fd) → new_ltEs8(vwx310, vwx410)
new_compare26(vwx30, vwx40, True, dh) → EQ
new_compare43(Integer(vwx3000), Integer(vwx4010), vwx400, vwx301, ty_Integer) → new_compare8(Integer(new_primMulInt(vwx3000, vwx4010)), new_sr0(vwx400, vwx301))
new_ltEs18(GT, EQ) → False
new_esEs6(Left(vwx300), Left(vwx400), ty_Char, bcd) → new_esEs14(vwx300, vwx400)
new_esEs23(vwx300, vwx400, ty_Float) → new_esEs11(vwx300, vwx400)
new_not(False) → True
new_ltEs7(Just(vwx310), Just(vwx410), ty_@0) → new_ltEs11(vwx310, vwx410)
new_esEs6(Left(vwx300), Left(vwx400), app(app(ty_Either, cfd), cfe), bcd) → new_esEs6(vwx300, vwx400, cfd, cfe)
new_compare19([], [], hg) → EQ
new_compare210(vwx30, vwx40, True, bcc, bcd) → EQ
new_primCmpInt(Pos(Succ(vwx3000)), Pos(vwx400)) → new_primCmpNat0(Succ(vwx3000), vwx400)
new_primPlusNat0(Zero, vwx40000) → Succ(vwx40000)
new_esEs5(Just(vwx300), Just(vwx400), ty_Char) → new_esEs14(vwx300, vwx400)
new_esEs8(vwx310, vwx410, ty_Ordering) → new_esEs19(vwx310, vwx410)
new_ltEs19(vwx311, vwx411, app(app(ty_Either, db), dc)) → new_ltEs12(vwx311, vwx411, db, dc)
new_esEs20(vwx300, vwx400, ty_Char) → new_esEs14(vwx300, vwx400)
new_esEs24(vwx301, vwx401, app(app(ty_Either, cch), cda)) → new_esEs6(vwx301, vwx401, cch, cda)
new_ltEs12(Right(vwx310), Right(vwx410), ge, app(app(ty_Either, ha), hb)) → new_ltEs12(vwx310, vwx410, ha, hb)
new_esEs26(vwx310, vwx410, app(ty_Ratio, chf)) → new_esEs18(vwx310, vwx410, chf)
new_ltEs12(Right(vwx310), Left(vwx410), ge, fd) → False
new_esEs24(vwx301, vwx401, ty_Ordering) → new_esEs19(vwx301, vwx401)
new_compare41(vwx300, vwx400) → new_compare310(vwx300, vwx400)
new_esEs9(vwx311, vwx411, app(ty_Maybe, bef)) → new_esEs5(vwx311, vwx411, bef)
new_primCmpFloat(Float(vwx300, vwx301), Float(vwx400, vwx401)) → new_compare15(vwx300, vwx400, vwx301, vwx401)
new_ltEs18(EQ, LT) → False
new_ltEs12(Left(vwx310), Left(vwx410), app(ty_Ratio, cag), fd) → new_ltEs17(vwx310, vwx410, cag)
new_esEs6(Right(vwx300), Right(vwx400), bcc, ty_Bool) → new_esEs12(vwx300, vwx400)
new_ltEs18(LT, EQ) → True
new_esEs24(vwx301, vwx401, app(ty_[], cdc)) → new_esEs17(vwx301, vwx401, cdc)
new_lt20(vwx310, vwx410, ty_Ordering) → new_lt18(vwx310, vwx410)
new_compare0(vwx300, vwx400, app(ty_Ratio, cad)) → new_compare12(vwx300, vwx400, cad)
new_esEs27(vwx300, vwx400, app(app(ty_Either, dab), dac)) → new_esEs6(vwx300, vwx400, dab, dac)
new_esEs6(Right(vwx300), Right(vwx400), bcc, ty_Char) → new_esEs14(vwx300, vwx400)
new_esEs24(vwx301, vwx401, app(ty_Maybe, cdd)) → new_esEs5(vwx301, vwx401, cdd)
new_esEs19(LT, GT) → False
new_esEs19(GT, LT) → False
new_esEs5(Just(vwx300), Just(vwx400), ty_Float) → new_esEs11(vwx300, vwx400)
new_compare11(vwx30, vwx40, False, bcc, bcd) → GT
new_primCmpInt(Pos(Succ(vwx3000)), Neg(vwx400)) → GT
new_ltEs7(Just(vwx310), Just(vwx410), app(ty_Maybe, ec)) → new_ltEs7(vwx310, vwx410, ec)
new_esEs8(vwx310, vwx410, app(app(app(ty_@3, bdh), bea), beb)) → new_esEs7(vwx310, vwx410, bdh, bea, beb)
new_esEs21(vwx300, vwx400, ty_Integer) → new_esEs16(vwx300, vwx400)
new_primCompAux00(vwx144, vwx145, EQ, app(ty_Ratio, cbb)) → new_compare12(vwx144, vwx145, cbb)
new_esEs24(vwx301, vwx401, ty_Double) → new_esEs15(vwx301, vwx401)
new_ltEs19(vwx311, vwx411, app(ty_[], dd)) → new_ltEs16(vwx311, vwx411, dd)
new_primMulInt(Pos(vwx3000), Pos(vwx4000)) → Pos(new_primMulNat0(vwx3000, vwx4000))
new_esEs9(vwx311, vwx411, app(ty_Ratio, bgg)) → new_esEs18(vwx311, vwx411, bgg)
new_esEs24(vwx301, vwx401, ty_Integer) → new_esEs16(vwx301, vwx401)
new_esEs28(vwx301, vwx401, app(app(app(ty_@3, dca), dcb), dcc)) → new_esEs7(vwx301, vwx401, dca, dcb, dcc)
new_ltEs12(Left(vwx310), Left(vwx410), ty_Char, fd) → new_ltEs13(vwx310, vwx410)
new_ltEs12(Right(vwx310), Right(vwx410), ge, ty_Ordering) → new_ltEs18(vwx310, vwx410)
new_esEs22(vwx301, vwx401, ty_Int) → new_esEs10(vwx301, vwx401)
new_compare0(vwx300, vwx400, app(app(ty_Either, bac), bad)) → new_compare13(vwx300, vwx400, bac, bad)
new_lt10(vwx30, vwx40) → new_esEs19(new_compare310(vwx30, vwx40), LT)
new_esEs27(vwx300, vwx400, ty_Double) → new_esEs15(vwx300, vwx400)
new_ltEs12(Right(vwx310), Right(vwx410), ge, ty_Integer) → new_ltEs15(vwx310, vwx410)
new_primMulInt(Neg(vwx3000), Neg(vwx4000)) → Pos(new_primMulNat0(vwx3000, vwx4000))
new_esEs5(Just(vwx300), Just(vwx400), app(ty_Ratio, bhe)) → new_esEs18(vwx300, vwx400, bhe)
new_primEqNat0(Succ(vwx3000), Zero) → False
new_primEqNat0(Zero, Succ(vwx4000)) → False
new_esEs27(vwx300, vwx400, ty_Char) → new_esEs14(vwx300, vwx400)
new_ltEs4(@3(vwx310, vwx311, vwx312), @3(vwx410, vwx411, vwx412), bec, bdb, bdc) → new_pePe(new_lt4(vwx310, vwx410, bec), new_asAs(new_esEs8(vwx310, vwx410, bec), new_pePe(new_lt5(vwx311, vwx411, bdb), new_asAs(new_esEs9(vwx311, vwx411, bdb), new_ltEs5(vwx312, vwx412, bdc)))))
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_ltEs17(vwx31, vwx41, cac) → new_not(new_esEs19(new_compare12(vwx31, vwx41, cac), GT))
new_esEs23(vwx300, vwx400, app(ty_Ratio, cbh)) → new_esEs18(vwx300, vwx400, cbh)
new_esEs20(vwx300, vwx400, app(ty_[], bae)) → new_esEs17(vwx300, vwx400, bae)
new_esEs20(vwx300, vwx400, app(app(ty_Either, bac), bad)) → new_esEs6(vwx300, vwx400, bac, bad)
new_ltEs12(Left(vwx310), Left(vwx410), app(app(ty_Either, fg), fh), fd) → new_ltEs12(vwx310, vwx410, fg, fh)
new_lt14(vwx30, vwx40) → new_esEs19(new_primCmpDouble(vwx30, vwx40), LT)
new_compare0(vwx300, vwx400, ty_Char) → new_compare29(vwx300, vwx400)
new_ltEs7(Just(vwx310), Just(vwx410), app(app(app(ty_@3, eg), eh), fa)) → new_ltEs4(vwx310, vwx410, eg, eh, fa)
new_ltEs19(vwx311, vwx411, ty_Char) → new_ltEs13(vwx311, vwx411)
new_esEs27(vwx300, vwx400, ty_Integer) → new_esEs16(vwx300, vwx400)
new_esEs9(vwx311, vwx411, ty_Ordering) → new_esEs19(vwx311, vwx411)
new_primCompAux00(vwx144, vwx145, EQ, app(app(ty_@2, bbb), bbc)) → new_compare28(vwx144, vwx145, bbb, bbc)
new_ltEs12(Left(vwx310), Left(vwx410), ty_Bool, fd) → new_ltEs10(vwx310, vwx410)
new_ltEs7(Nothing, Nothing, cae) → True
new_compare0(vwx300, vwx400, app(ty_Maybe, baf)) → new_compare39(vwx300, vwx400, baf)
new_ltEs19(vwx311, vwx411, ty_Bool) → new_ltEs10(vwx311, vwx411)
new_esEs26(vwx310, vwx410, app(ty_Maybe, bf)) → new_esEs5(vwx310, vwx410, bf)
new_ltEs7(Just(vwx310), Just(vwx410), ty_Float) → new_ltEs9(vwx310, vwx410)
new_primCompAux00(vwx144, vwx145, EQ, ty_Float) → new_compare40(vwx144, vwx145)
new_lt5(vwx311, vwx411, ty_Double) → new_lt14(vwx311, vwx411)
new_esEs25(vwx302, vwx402, ty_Integer) → new_esEs16(vwx302, vwx402)
new_primCmpInt(Neg(Zero), Neg(Succ(vwx4000))) → new_primCmpNat0(Succ(vwx4000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(vwx4000))) → GT
new_lt4(vwx310, vwx410, ty_@0) → new_lt11(vwx310, vwx410)
new_esEs25(vwx302, vwx402, ty_Ordering) → new_esEs19(vwx302, vwx402)
new_compare19(:(vwx310, vwx311), :(vwx410, vwx411), hg) → new_primCompAux1(vwx310, vwx410, vwx311, vwx411, hg)
new_lt11(@0, @0) → new_esEs19(EQ, LT)
new_esEs6(Right(vwx300), Right(vwx400), bcc, app(app(ty_@2, cgd), cge)) → new_esEs4(vwx300, vwx400, cgd, cge)
new_lt20(vwx310, vwx410, app(app(ty_@2, bc), bd)) → new_lt6(vwx310, vwx410, bc, bd)
new_ltEs5(vwx312, vwx412, ty_Float) → new_ltEs9(vwx312, vwx412)
new_esEs20(vwx300, vwx400, app(ty_Ratio, cad)) → new_esEs18(vwx300, vwx400, cad)
new_esEs19(LT, LT) → True
new_ltEs12(Left(vwx310), Left(vwx410), app(ty_Maybe, ff), fd) → new_ltEs7(vwx310, vwx410, ff)
new_esEs16(Integer(vwx300), Integer(vwx400)) → new_primEqInt(vwx300, vwx400)
new_lt5(vwx311, vwx411, app(ty_Maybe, bef)) → new_lt7(vwx311, vwx411, bef)
new_esEs19(EQ, GT) → False
new_esEs19(GT, EQ) → False
new_compare0(vwx300, vwx400, ty_Int) → new_compare42(vwx300, vwx400)
new_lt17(:%(vwx300, vwx301), :%(vwx400, vwx401), cbc) → new_esEs19(new_compare43(vwx300, vwx401, vwx400, vwx301, cbc), LT)
new_esEs9(vwx311, vwx411, app(app(ty_@2, bed), bee)) → new_esEs4(vwx311, vwx411, bed, bee)
new_lt20(vwx310, vwx410, app(ty_[], ca)) → new_lt16(vwx310, vwx410, ca)
new_ltEs7(Just(vwx310), Just(vwx410), app(app(ty_Either, ed), ee)) → new_ltEs12(vwx310, vwx410, ed, ee)
new_ltEs12(Right(vwx310), Right(vwx410), ge, ty_@0) → new_ltEs11(vwx310, vwx410)
new_esEs6(Left(vwx300), Left(vwx400), ty_Ordering, bcd) → new_esEs19(vwx300, vwx400)
new_esEs24(vwx301, vwx401, app(app(app(ty_@3, cde), cdf), cdg)) → new_esEs7(vwx301, vwx401, cde, cdf, cdg)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs25(vwx302, vwx402, ty_Bool) → new_esEs12(vwx302, vwx402)
new_ltEs19(vwx311, vwx411, app(app(ty_@2, cf), cg)) → new_ltEs6(vwx311, vwx411, cf, cg)
new_compare12(:%(vwx310, vwx311), :%(vwx410, vwx411), ty_Int) → new_compare42(new_sr(vwx310, vwx411), new_sr(vwx410, vwx311))
new_esEs24(vwx301, vwx401, ty_Int) → new_esEs10(vwx301, vwx401)
new_esEs20(vwx300, vwx400, app(ty_Maybe, baf)) → new_esEs5(vwx300, vwx400, baf)
new_lt20(vwx310, vwx410, app(ty_Maybe, bf)) → new_lt7(vwx310, vwx410, bf)
new_lt4(vwx310, vwx410, app(app(ty_@2, bch), bda)) → new_lt6(vwx310, vwx410, bch, bda)
new_ltEs8(vwx31, vwx41) → new_not(new_esEs19(new_compare42(vwx31, vwx41), GT))
new_esEs28(vwx301, vwx401, app(app(ty_@2, dbb), dbc)) → new_esEs4(vwx301, vwx401, dbb, dbc)
new_ltEs10(True, False) → False
new_asAs(False, vwx139) → False
new_primMulInt(Pos(vwx3000), Neg(vwx4000)) → Neg(new_primMulNat0(vwx3000, vwx4000))
new_primMulInt(Neg(vwx3000), Pos(vwx4000)) → Neg(new_primMulNat0(vwx3000, vwx4000))
new_compare19([], :(vwx410, vwx411), hg) → LT
new_primMulNat0(Zero, Succ(vwx40000)) → Zero
new_primMulNat0(Succ(vwx30000), Zero) → Zero
new_compare33(vwx30, vwx40) → new_compare23(vwx30, vwx40, new_esEs19(vwx30, vwx40))
new_lt5(vwx311, vwx411, ty_Int) → new_lt8(vwx311, vwx411)
new_compare210(vwx30, vwx40, False, bcc, bcd) → new_compare11(vwx30, vwx40, new_ltEs12(vwx30, vwx40, bcc, bcd), bcc, bcd)
new_esEs6(Right(vwx300), Right(vwx400), bcc, app(ty_Ratio, cgh)) → new_esEs18(vwx300, vwx400, cgh)
new_esEs9(vwx311, vwx411, ty_Bool) → new_esEs12(vwx311, vwx411)
new_esEs24(vwx301, vwx401, ty_Float) → new_esEs11(vwx301, vwx401)
new_esEs27(vwx300, vwx400, ty_@0) → new_esEs13(vwx300, vwx400)
new_primCompAux00(vwx144, vwx145, LT, cba) → LT
new_esEs25(vwx302, vwx402, app(ty_[], cee)) → new_esEs17(vwx302, vwx402, cee)
new_primCompAux00(vwx144, vwx145, GT, cba) → GT
new_esEs23(vwx300, vwx400, app(ty_Maybe, ccb)) → new_esEs5(vwx300, vwx400, ccb)
new_esEs6(Right(vwx300), Right(vwx400), bcc, ty_Int) → new_esEs10(vwx300, vwx400)
new_esEs6(Left(vwx300), Left(vwx400), app(ty_Maybe, cfh), bcd) → new_esEs5(vwx300, vwx400, cfh)
new_esEs24(vwx301, vwx401, ty_Bool) → new_esEs12(vwx301, vwx401)
new_ltEs5(vwx312, vwx412, ty_Ordering) → new_ltEs18(vwx312, vwx412)
new_esEs8(vwx310, vwx410, app(ty_Ratio, bgf)) → new_esEs18(vwx310, vwx410, bgf)
new_esEs20(vwx300, vwx400, app(app(ty_@2, baa), bab)) → new_esEs4(vwx300, vwx400, baa, bab)
new_compare27(vwx30, vwx40, True) → EQ
new_ltEs7(Just(vwx310), Just(vwx410), ty_Bool) → new_ltEs10(vwx310, vwx410)
new_esEs12(False, True) → False
new_esEs12(True, False) → False
new_esEs5(Just(vwx300), Nothing, dh) → False
new_esEs5(Nothing, Just(vwx400), dh) → False
new_esEs14(Char(vwx300), Char(vwx400)) → new_primEqNat0(vwx300, vwx400)
new_esEs27(vwx300, vwx400, ty_Bool) → new_esEs12(vwx300, vwx400)
new_compare15(vwx300, vwx400, vwx301, vwx401) → new_primCmpInt(new_sr(vwx300, vwx400), new_sr(vwx301, vwx401))
new_esEs5(Just(vwx300), Just(vwx400), ty_Double) → new_esEs15(vwx300, vwx400)
new_esEs25(vwx302, vwx402, app(app(app(ty_@3, ceg), ceh), cfa)) → new_esEs7(vwx302, vwx402, ceg, ceh, cfa)
new_esEs28(vwx301, vwx401, app(ty_[], dbg)) → new_esEs17(vwx301, vwx401, dbg)
new_lt5(vwx311, vwx411, app(ty_Ratio, bgg)) → new_lt17(vwx311, vwx411, bgg)
new_esEs27(vwx300, vwx400, app(app(ty_@2, chh), daa)) → new_esEs4(vwx300, vwx400, chh, daa)
new_lt16(:(vwx300, vwx301), [], hh) → new_esEs19(GT, LT)
new_ltEs15(vwx31, vwx41) → new_not(new_esEs19(new_compare8(vwx31, vwx41), GT))
new_ltEs7(Just(vwx310), Nothing, cae) → False
new_primCompAux1(vwx300, vwx400, vwx301, vwx401, hh) → new_primCompAux00(vwx301, vwx401, new_compare0(vwx300, vwx400, hh), app(ty_[], hh))
new_esEs5(Just(vwx300), Just(vwx400), app(app(ty_Either, bhc), bhd)) → new_esEs6(vwx300, vwx400, bhc, bhd)
new_lt19(vwx30, vwx40, bce, bcf, bcg) → new_esEs19(new_compare35(vwx30, vwx40, bce, bcf, bcg), LT)
new_ltEs13(vwx31, vwx41) → new_not(new_esEs19(new_compare29(vwx31, vwx41), GT))
new_ltEs5(vwx312, vwx412, app(ty_Maybe, bfg)) → new_ltEs7(vwx312, vwx412, bfg)
new_lt20(vwx310, vwx410, ty_Integer) → new_lt15(vwx310, vwx410)
new_esEs5(Nothing, Nothing, dh) → True
new_ltEs19(vwx311, vwx411, app(ty_Maybe, da)) → new_ltEs7(vwx311, vwx411, da)
new_esEs28(vwx301, vwx401, app(ty_Maybe, dbh)) → new_esEs5(vwx301, vwx401, dbh)
new_lt5(vwx311, vwx411, app(app(ty_Either, beg), beh)) → new_lt12(vwx311, vwx411, beg, beh)
new_esEs5(Just(vwx300), Just(vwx400), app(app(app(ty_@3, bhh), caa), cab)) → new_esEs7(vwx300, vwx400, bhh, caa, cab)
new_ltEs7(Just(vwx310), Just(vwx410), app(ty_Ratio, caf)) → new_ltEs17(vwx310, vwx410, caf)
new_esEs5(Just(vwx300), Just(vwx400), ty_Integer) → new_esEs16(vwx300, vwx400)
new_primCompAux00(vwx144, vwx145, EQ, ty_Double) → new_compare14(vwx144, vwx145)
new_esEs28(vwx301, vwx401, ty_Float) → new_esEs11(vwx301, vwx401)
new_esEs8(vwx310, vwx410, ty_Float) → new_esEs11(vwx310, vwx410)
new_lt4(vwx310, vwx410, ty_Bool) → new_lt10(vwx310, vwx410)
new_esEs22(vwx301, vwx401, ty_Integer) → new_esEs16(vwx301, vwx401)
new_esEs28(vwx301, vwx401, ty_Int) → new_esEs10(vwx301, vwx401)
new_esEs9(vwx311, vwx411, app(ty_[], bfa)) → new_esEs17(vwx311, vwx411, bfa)
new_esEs8(vwx310, vwx410, app(ty_[], bdg)) → new_esEs17(vwx310, vwx410, bdg)
new_ltEs12(Left(vwx310), Left(vwx410), ty_Float, fd) → new_ltEs9(vwx310, vwx410)
new_compare42(vwx31, vwx41) → new_primCmpInt(vwx31, vwx41)
new_primCmpDouble(Double(vwx300, vwx301), Double(vwx400, vwx401)) → new_compare15(vwx300, vwx400, vwx301, vwx401)
new_esEs6(Left(vwx300), Left(vwx400), ty_Integer, bcd) → new_esEs16(vwx300, vwx400)
new_esEs26(vwx310, vwx410, app(app(ty_Either, bg), bh)) → new_esEs6(vwx310, vwx410, bg, bh)
new_primPlusNat1(Zero, Zero) → Zero
new_ltEs10(True, True) → True
new_esEs9(vwx311, vwx411, ty_Double) → new_esEs15(vwx311, vwx411)
new_lt20(vwx310, vwx410, app(app(app(ty_@3, cb), cc), cd)) → new_lt19(vwx310, vwx410, cb, cc, cd)
new_primCmpChar(Char(vwx300), Char(vwx400)) → new_primCmpNat0(vwx300, vwx400)
new_asAs(True, vwx139) → vwx139
new_esEs20(vwx300, vwx400, ty_Double) → new_esEs15(vwx300, vwx400)
new_primMulNat0(Succ(vwx30000), Succ(vwx40000)) → new_primPlusNat0(new_primMulNat0(vwx30000, Succ(vwx40000)), vwx40000)
new_ltEs5(vwx312, vwx412, ty_Integer) → new_ltEs15(vwx312, vwx412)
new_primCompAux00(vwx144, vwx145, EQ, app(app(ty_Either, bbe), bbf)) → new_compare13(vwx144, vwx145, bbe, bbf)
new_esEs25(vwx302, vwx402, ty_Float) → new_esEs11(vwx302, vwx402)
new_compare26(vwx30, vwx40, False, dh) → new_compare16(vwx30, vwx40, new_ltEs7(vwx30, vwx40, dh), dh)
new_esEs8(vwx310, vwx410, ty_@0) → new_esEs13(vwx310, vwx410)
new_esEs26(vwx310, vwx410, ty_Double) → new_esEs15(vwx310, vwx410)
new_esEs27(vwx300, vwx400, ty_Int) → new_esEs10(vwx300, vwx400)
new_ltEs19(vwx311, vwx411, ty_Ordering) → new_ltEs18(vwx311, vwx411)
new_ltEs12(Left(vwx310), Left(vwx410), ty_Double, fd) → new_ltEs14(vwx310, vwx410)
new_esEs28(vwx301, vwx401, app(ty_Ratio, dbf)) → new_esEs18(vwx301, vwx401, dbf)
new_esEs23(vwx300, vwx400, ty_Int) → new_esEs10(vwx300, vwx400)
new_esEs21(vwx300, vwx400, ty_Int) → new_esEs10(vwx300, vwx400)
new_ltEs12(Left(vwx310), Left(vwx410), app(app(app(ty_@3, gb), gc), gd), fd) → new_ltEs4(vwx310, vwx410, gb, gc, gd)
new_esEs17([], [], hh) → True
new_esEs17(:(vwx300, vwx301), [], hh) → False
new_esEs17([], :(vwx400, vwx401), hh) → False
new_lt20(vwx310, vwx410, ty_@0) → new_lt11(vwx310, vwx410)
new_ltEs7(Just(vwx310), Just(vwx410), app(ty_[], ef)) → new_ltEs16(vwx310, vwx410, ef)
new_esEs20(vwx300, vwx400, ty_Ordering) → new_esEs19(vwx300, vwx400)
new_compare9(vwx300, vwx400, bag, bah, bba) → new_compare35(vwx300, vwx400, bag, bah, bba)
new_esEs24(vwx301, vwx401, ty_Char) → new_esEs14(vwx301, vwx401)
new_compare0(vwx300, vwx400, ty_Integer) → new_compare8(vwx300, vwx400)
new_lt4(vwx310, vwx410, app(app(ty_Either, bde), bdf)) → new_lt12(vwx310, vwx410, bde, bdf)
new_compare10(vwx30, vwx40, True) → LT
new_esEs17(:(vwx300, vwx301), :(vwx400, vwx401), hh) → new_asAs(new_esEs20(vwx300, vwx400, hh), new_esEs17(vwx301, vwx401, hh))
new_primCompAux00(vwx144, vwx145, EQ, ty_Integer) → new_compare8(vwx144, vwx145)
new_ltEs5(vwx312, vwx412, ty_Double) → new_ltEs14(vwx312, vwx412)
new_lt4(vwx310, vwx410, ty_Ordering) → new_lt18(vwx310, vwx410)
new_compare0(vwx300, vwx400, ty_Ordering) → new_compare38(vwx300, vwx400)
new_compare10(vwx30, vwx40, False) → GT
new_esEs10(vwx30, vwx40) → new_primEqInt(vwx30, vwx40)
new_ltEs5(vwx312, vwx412, ty_Bool) → new_ltEs10(vwx312, vwx412)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_ltEs5(vwx312, vwx412, app(app(app(ty_@3, bgc), bgd), bge)) → new_ltEs4(vwx312, vwx412, bgc, bgd, bge)
new_esEs20(vwx300, vwx400, ty_@0) → new_esEs13(vwx300, vwx400)
new_ltEs12(Right(vwx310), Right(vwx410), ge, app(app(app(ty_@3, hd), he), hf)) → new_ltEs4(vwx310, vwx410, hd, he, hf)
new_esEs28(vwx301, vwx401, ty_Bool) → new_esEs12(vwx301, vwx401)
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_lt20(vwx310, vwx410, ty_Bool) → new_lt10(vwx310, vwx410)
new_compare0(vwx300, vwx400, ty_Double) → new_compare14(vwx300, vwx400)
new_esEs11(Float(vwx300, vwx301), Float(vwx400, vwx401)) → new_esEs10(new_sr(vwx300, vwx400), new_sr(vwx301, vwx401))
new_primCmpInt(Neg(Succ(vwx3000)), Pos(vwx400)) → LT
new_esEs6(Left(vwx300), Left(vwx400), ty_Int, bcd) → new_esEs10(vwx300, vwx400)
new_not(True) → False

The set Q consists of the following terms:

new_ltEs7(Just(x0), Nothing, x1)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_esEs13(@0, @0)
new_esEs26(x0, x1, ty_Double)
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_esEs20(x0, x1, ty_Bool)
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_ltEs12(Left(x0), Left(x1), ty_Integer, x2)
new_compare40(x0, x1)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_ltEs7(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs18(:%(x0, x1), :%(x2, x3), x4)
new_compare25(x0, x1, False, x2, x3, x4)
new_esEs9(x0, x1, ty_Ordering)
new_esEs9(x0, x1, ty_Integer)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs23(x0, x1, app(ty_[], x2))
new_esEs28(x0, x1, ty_Bool)
new_ltEs7(Nothing, Just(x0), x1)
new_esEs26(x0, x1, ty_Char)
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs7(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_lt5(x0, x1, app(ty_Ratio, x2))
new_lt20(x0, x1, ty_Int)
new_lt4(x0, x1, ty_Char)
new_ltEs11(x0, x1)
new_ltEs12(Left(x0), Left(x1), ty_Int, x2)
new_lt13(x0, x1)
new_esEs12(False, False)
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs12(Left(x0), Left(x1), ty_Float, x2)
new_esEs6(Left(x0), Left(x1), ty_Integer, x2)
new_ltEs12(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_ltEs19(x0, x1, ty_@0)
new_primMulInt(Neg(x0), Neg(x1))
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, ty_Int)
new_compare0(x0, x1, ty_Ordering)
new_esEs6(Left(x0), Left(x1), ty_Ordering, x2)
new_ltEs7(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, ty_Ordering)
new_esEs6(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs6(Left(x0), Left(x1), ty_@0, x2)
new_lt4(x0, x1, ty_Ordering)
new_esEs26(x0, x1, app(ty_[], x2))
new_lt5(x0, x1, ty_Bool)
new_primCompAux00(x0, x1, EQ, ty_Integer)
new_esEs6(Right(x0), Left(x1), x2, x3)
new_esEs6(Left(x0), Right(x1), x2, x3)
new_esEs26(x0, x1, ty_Int)
new_esEs23(x0, x1, ty_Ordering)
new_compare24(x0, x1, True, x2, x3)
new_esEs23(x0, x1, ty_Double)
new_esEs24(x0, x1, ty_Float)
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_lt19(x0, x1, x2, x3, x4)
new_lt20(x0, x1, ty_Char)
new_esEs20(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, ty_Int)
new_compare23(x0, x1, False)
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare19(:(x0, x1), :(x2, x3), x4)
new_compare39(x0, x1, x2)
new_esEs6(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_primCompAux00(x0, x1, EQ, app(ty_[], x2))
new_esEs26(x0, x1, ty_Ordering)
new_compare310(x0, x1)
new_esEs8(x0, x1, ty_Ordering)
new_esEs7(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs5(Just(x0), Just(x1), ty_Float)
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs12(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_compare11(x0, x1, True, x2, x3)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_primCompAux00(x0, x1, EQ, app(ty_Maybe, x2))
new_ltEs8(x0, x1)
new_sr(x0, x1)
new_esEs8(x0, x1, ty_Char)
new_ltEs12(Left(x0), Left(x1), ty_Double, x2)
new_lt16(:(x0, x1), [], x2)
new_esEs20(x0, x1, ty_Double)
new_esEs23(x0, x1, ty_Float)
new_esEs9(x0, x1, app(ty_Ratio, x2))
new_compare0(x0, x1, ty_Double)
new_ltEs18(GT, LT)
new_ltEs18(LT, GT)
new_primEqNat0(Zero, Zero)
new_primPlusNat1(Succ(x0), Zero)
new_ltEs5(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Left(x0), Left(x1), ty_Float, x2)
new_esEs26(x0, x1, ty_@0)
new_lt4(x0, x1, app(ty_Maybe, x2))
new_compare33(x0, x1)
new_esEs20(x0, x1, ty_Integer)
new_esEs5(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs16(Integer(x0), Integer(x1))
new_ltEs19(x0, x1, ty_Char)
new_primMulInt(Pos(x0), Pos(x1))
new_ltEs19(x0, x1, ty_Bool)
new_compare110(x0, x1, False, x2, x3)
new_ltEs12(Right(x0), Right(x1), x2, ty_Double)
new_primCompAux00(x0, x1, EQ, ty_Char)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_compare210(x0, x1, False, x2, x3)
new_esEs9(x0, x1, app(ty_[], x2))
new_ltEs5(x0, x1, app(ty_[], x2))
new_primCompAux00(x0, x1, EQ, app(app(app(ty_@3, x2), x3), x4))
new_lt5(x0, x1, ty_Float)
new_primMulNat0(Zero, Zero)
new_esEs25(x0, x1, ty_@0)
new_esEs24(x0, x1, ty_Ordering)
new_ltEs18(EQ, LT)
new_ltEs18(LT, EQ)
new_primCompAux00(x0, x1, EQ, ty_@0)
new_esEs5(Nothing, Nothing, x0)
new_compare27(x0, x1, True)
new_esEs25(x0, x1, ty_Double)
new_lt5(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_ltEs12(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs5(Just(x0), Just(x1), ty_Double)
new_primCompAux00(x0, x1, EQ, ty_Bool)
new_esEs25(x0, x1, ty_Ordering)
new_primCompAux00(x0, x1, EQ, ty_Float)
new_esEs27(x0, x1, ty_Bool)
new_lt5(x0, x1, ty_Char)
new_compare43(Integer(x0), Integer(x1), x2, x3, ty_Integer)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_ltEs12(Right(x0), Right(x1), x2, ty_@0)
new_esEs14(Char(x0), Char(x1))
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs20(x0, x1, ty_Char)
new_ltEs12(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_ltEs5(x0, x1, ty_Double)
new_esEs19(LT, LT)
new_ltEs12(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs19(GT, EQ)
new_esEs19(EQ, GT)
new_ltEs7(Just(x0), Just(x1), ty_Bool)
new_esEs17([], :(x0, x1), x2)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_ltEs13(x0, x1)
new_compare12(:%(x0, x1), :%(x2, x3), ty_Integer)
new_esEs22(x0, x1, ty_Integer)
new_primMulNat0(Zero, Succ(x0))
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_compare110(x0, x1, True, x2, x3)
new_lt5(x0, x1, ty_Double)
new_compare42(x0, x1)
new_ltEs12(Right(x0), Right(x1), x2, ty_Integer)
new_ltEs9(x0, x1)
new_asAs(False, x0)
new_compare41(x0, x1)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs20(x0, x1, ty_Int)
new_esEs26(x0, x1, ty_Float)
new_ltEs12(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_lt5(x0, x1, ty_Int)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_esEs5(Just(x0), Just(x1), ty_Char)
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_compare36(x0, x1, x2, x3)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs25(x0, x1, ty_Float)
new_primCompAux1(x0, x1, x2, x3, x4)
new_lt17(:%(x0, x1), :%(x2, x3), x4)
new_ltEs12(Right(x0), Right(x1), x2, ty_Char)
new_esEs27(x0, x1, ty_@0)
new_lt4(x0, x1, app(ty_Ratio, x2))
new_esEs9(x0, x1, app(app(ty_Either, x2), x3))
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs15(Double(x0, x1), Double(x2, x3))
new_esEs27(x0, x1, ty_Double)
new_primPlusNat0(Zero, x0)
new_ltEs12(Right(x0), Right(x1), x2, ty_Int)
new_esEs6(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_lt12(x0, x1, x2, x3)
new_esEs27(x0, x1, ty_Char)
new_esEs23(x0, x1, ty_Int)
new_lt14(x0, x1)
new_lt20(x0, x1, app(ty_[], x2))
new_primEqNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, Zero)
new_compare28(x0, x1, x2, x3)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_ltEs7(Just(x0), Just(x1), app(ty_[], x2))
new_esEs17([], [], x0)
new_esEs8(x0, x1, app(app(ty_@2, x2), x3))
new_esEs28(x0, x1, ty_Integer)
new_ltEs19(x0, x1, ty_Integer)
new_ltEs10(False, False)
new_esEs21(x0, x1, ty_Integer)
new_compare24(x0, x1, False, x2, x3)
new_esEs28(x0, x1, ty_Ordering)
new_esEs5(Just(x0), Just(x1), ty_Bool)
new_esEs9(x0, x1, ty_Int)
new_compare18(x0, x1, False)
new_esEs6(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_ltEs16(x0, x1, x2)
new_primCompAux00(x0, x1, LT, x2)
new_esEs9(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs12(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs28(x0, x1, ty_@0)
new_compare43(x0, x1, x2, x3, ty_Int)
new_ltEs19(x0, x1, ty_Int)
new_esEs5(Just(x0), Nothing, x1)
new_compare11(x0, x1, False, x2, x3)
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_lt4(x0, x1, ty_Bool)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_esEs24(x0, x1, ty_Char)
new_esEs12(True, True)
new_esEs27(x0, x1, ty_Float)
new_lt18(x0, x1)
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_compare0(x0, x1, app(ty_[], x2))
new_compare10(x0, x1, True)
new_lt20(x0, x1, ty_Bool)
new_compare19([], [], x0)
new_esEs5(Just(x0), Just(x1), ty_Ordering)
new_esEs6(Left(x0), Left(x1), ty_Bool, x2)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_esEs20(x0, x1, ty_Ordering)
new_esEs27(x0, x1, ty_Int)
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_compare29(x0, x1)
new_ltEs5(x0, x1, ty_Bool)
new_lt4(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs26(x0, x1, ty_Integer)
new_lt8(x0, x1)
new_lt5(x0, x1, app(ty_[], x2))
new_ltEs12(Left(x0), Left(x1), ty_Ordering, x2)
new_compare38(x0, x1)
new_esEs28(x0, x1, ty_Int)
new_lt20(x0, x1, ty_Integer)
new_esEs8(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs12(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs5(Just(x0), Just(x1), app(ty_Ratio, x2))
new_ltEs12(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_lt4(x0, x1, ty_Integer)
new_ltEs6(@2(x0, x1), @2(x2, x3), x4, x5)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs27(x0, x1, app(ty_[], x2))
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_lt4(x0, x1, ty_@0)
new_primEqInt(Neg(Zero), Neg(Zero))
new_ltEs19(x0, x1, ty_Float)
new_primCompAux00(x0, x1, EQ, ty_Double)
new_esEs24(x0, x1, ty_Double)
new_ltEs5(x0, x1, ty_@0)
new_lt5(x0, x1, ty_Ordering)
new_esEs23(x0, x1, ty_Integer)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs25(x0, x1, ty_Char)
new_compare0(x0, x1, app(ty_Ratio, x2))
new_esEs5(Just(x0), Just(x1), ty_Int)
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_ltEs18(LT, LT)
new_primPlusNat0(Succ(x0), x1)
new_lt4(x0, x1, app(ty_[], x2))
new_ltEs5(x0, x1, ty_Float)
new_compare0(x0, x1, ty_Integer)
new_lt9(x0, x1)
new_esEs5(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs5(x0, x1, app(ty_Maybe, x2))
new_compare10(x0, x1, False)
new_esEs24(x0, x1, ty_Bool)
new_ltEs12(Right(x0), Right(x1), x2, ty_Float)
new_compare7(@0, @0)
new_primCmpNat0(Zero, Succ(x0))
new_esEs6(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_compare25(x0, x1, True, x2, x3, x4)
new_esEs6(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs5(x0, x1, ty_Integer)
new_primPlusNat1(Succ(x0), Succ(x1))
new_compare37(x0, x1, x2)
new_compare0(x0, x1, ty_@0)
new_esEs6(Right(x0), Right(x1), x2, ty_Int)
new_esEs4(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs24(x0, x1, app(ty_[], x2))
new_lt16(:(x0, x1), :(x2, x3), x4)
new_ltEs15(x0, x1)
new_esEs22(x0, x1, ty_Int)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare18(x0, x1, True)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_esEs9(x0, x1, ty_Char)
new_compare35(x0, x1, x2, x3, x4)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_esEs6(Left(x0), Left(x1), ty_Double, x2)
new_lt5(x0, x1, ty_@0)
new_esEs8(x0, x1, ty_Double)
new_lt5(x0, x1, ty_Integer)
new_ltEs19(x0, x1, app(ty_[], x2))
new_lt5(x0, x1, app(app(ty_@2, x2), x3))
new_esEs24(x0, x1, ty_Integer)
new_primCompAux00(x0, x1, EQ, app(ty_Ratio, x2))
new_ltEs18(EQ, GT)
new_ltEs18(GT, EQ)
new_esEs28(x0, x1, ty_Double)
new_compare0(x0, x1, app(ty_Maybe, x2))
new_ltEs12(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_primCmpNat0(Zero, Zero)
new_ltEs12(Left(x0), Left(x1), ty_Bool, x2)
new_ltEs7(Just(x0), Just(x1), ty_Ordering)
new_lt15(Integer(x0), Integer(x1))
new_esEs8(x0, x1, app(ty_[], x2))
new_esEs6(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs7(Just(x0), Just(x1), ty_Integer)
new_ltEs5(x0, x1, ty_Int)
new_esEs17(:(x0, x1), [], x2)
new_primCompAux00(x0, x1, EQ, app(app(ty_@2, x2), x3))
new_esEs28(x0, x1, app(ty_[], x2))
new_esEs23(x0, x1, ty_Char)
new_ltEs7(Just(x0), Just(x1), ty_Int)
new_esEs8(x0, x1, ty_Bool)
new_ltEs10(True, True)
new_ltEs5(x0, x1, app(app(ty_Either, x2), x3))
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_ltEs7(Just(x0), Just(x1), ty_@0)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_esEs8(x0, x1, app(ty_Maybe, x2))
new_esEs6(Right(x0), Right(x1), x2, ty_@0)
new_esEs5(Just(x0), Just(x1), ty_Integer)
new_compare19(:(x0, x1), [], x2)
new_compare34(x0, x1, x2, x3)
new_esEs19(GT, GT)
new_ltEs12(Left(x0), Left(x1), ty_Char, x2)
new_lt4(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs12(Left(x0), Right(x1), x2, x3)
new_ltEs12(Right(x0), Left(x1), x2, x3)
new_esEs25(x0, x1, ty_Integer)
new_compare14(x0, x1)
new_ltEs5(x0, x1, app(ty_Ratio, x2))
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_primCmpDouble(Double(x0, x1), Double(x2, x3))
new_primEqNat0(Zero, Succ(x0))
new_esEs8(x0, x1, ty_@0)
new_lt5(x0, x1, app(app(ty_Either, x2), x3))
new_esEs6(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs9(x0, x1, app(app(ty_@2, x2), x3))
new_esEs12(False, True)
new_esEs12(True, False)
new_pePe(True, x0)
new_primMulNat0(Succ(x0), Zero)
new_lt6(x0, x1, x2, x3)
new_compare27(x0, x1, False)
new_esEs19(EQ, EQ)
new_esEs23(x0, x1, ty_@0)
new_primMulNat0(Succ(x0), Succ(x1))
new_esEs28(x0, x1, ty_Float)
new_lt4(x0, x1, ty_Float)
new_primCompAux00(x0, x1, EQ, ty_Ordering)
new_esEs10(x0, x1)
new_primCompAux00(x0, x1, GT, x2)
new_ltEs12(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs28(x0, x1, ty_Char)
new_primCmpNat0(Succ(x0), Succ(x1))
new_ltEs18(EQ, EQ)
new_compare0(x0, x1, ty_Bool)
new_esEs17(:(x0, x1), :(x2, x3), x4)
new_esEs23(x0, x1, ty_Bool)
new_ltEs7(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs5(Just(x0), Just(x1), ty_@0)
new_esEs19(EQ, LT)
new_esEs19(LT, EQ)
new_ltEs7(Nothing, Nothing, x0)
new_esEs27(x0, x1, ty_Integer)
new_esEs8(x0, x1, ty_Integer)
new_lt20(x0, x1, ty_Float)
new_esEs8(x0, x1, app(app(ty_Either, x2), x3))
new_compare210(x0, x1, True, x2, x3)
new_not(True)
new_compare26(x0, x1, False, x2)
new_esEs19(GT, LT)
new_esEs19(LT, GT)
new_compare9(x0, x1, x2, x3, x4)
new_ltEs5(x0, x1, ty_Ordering)
new_primCompAux00(x0, x1, EQ, ty_Int)
new_ltEs7(Just(x0), Just(x1), ty_Double)
new_esEs9(x0, x1, ty_Bool)
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, ty_Ordering)
new_esEs25(x0, x1, ty_Bool)
new_lt16([], :(x0, x1), x2)
new_lt4(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_not(False)
new_lt4(x0, x1, ty_Double)
new_lt20(x0, x1, ty_@0)
new_primCompAux00(x0, x1, EQ, app(app(ty_Either, x2), x3))
new_esEs6(Left(x0), Left(x1), ty_Char, x2)
new_compare0(x0, x1, app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, ty_Double)
new_compare0(x0, x1, app(app(ty_Either, x2), x3))
new_esEs6(Right(x0), Right(x1), x2, ty_Char)
new_ltEs12(Left(x0), Left(x1), ty_@0, x2)
new_esEs6(Right(x0), Right(x1), x2, ty_Double)
new_esEs6(Left(x0), Left(x1), ty_Int, x2)
new_ltEs4(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_ltEs7(Just(x0), Just(x1), app(ty_Maybe, x2))
new_ltEs17(x0, x1, x2)
new_esEs8(x0, x1, ty_Float)
new_esEs6(Right(x0), Right(x1), x2, ty_Float)
new_esEs5(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs9(x0, x1, ty_@0)
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs25(x0, x1, app(ty_[], x2))
new_compare17(x0, x1, True, x2, x3, x4)
new_compare0(x0, x1, ty_Char)
new_esEs24(x0, x1, ty_@0)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs7(Just(x0), Just(x1), ty_Char)
new_sr0(Integer(x0), Integer(x1))
new_ltEs12(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_lt16([], [], x0)
new_ltEs18(GT, GT)
new_ltEs12(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_compare16(x0, x1, True, x2)
new_asAs(True, x0)
new_esEs5(Just(x0), Just(x1), app(ty_[], x2))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_compare0(x0, x1, ty_Int)
new_esEs20(x0, x1, ty_Float)
new_esEs6(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs20(x0, x1, ty_@0)
new_ltEs10(False, True)
new_ltEs10(True, False)
new_primCmpFloat(Float(x0, x1), Float(x2, x3))
new_esEs8(x0, x1, ty_Int)
new_lt5(x0, x1, app(ty_Maybe, x2))
new_lt11(@0, @0)
new_compare17(x0, x1, False, x2, x3, x4)
new_ltEs7(Just(x0), Just(x1), ty_Float)
new_esEs9(x0, x1, ty_Float)
new_esEs6(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs12(Right(x0), Right(x1), x2, ty_Bool)
new_pePe(False, x0)
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_compare0(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_ltEs5(x0, x1, app(app(ty_@2, x2), x3))
new_primEqInt(Pos(Zero), Pos(Zero))
new_esEs8(x0, x1, app(ty_Ratio, x2))
new_esEs11(Float(x0, x1), Float(x2, x3))
new_ltEs14(x0, x1)
new_ltEs5(x0, x1, ty_Char)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare15(x0, x1, x2, x3)
new_lt20(x0, x1, ty_Ordering)
new_compare13(x0, x1, x2, x3)
new_lt7(x0, x1, x2)
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_lt20(x0, x1, ty_Double)
new_primCmpChar(Char(x0), Char(x1))
new_esEs24(x0, x1, ty_Int)
new_esEs26(x0, x1, ty_Bool)
new_compare12(:%(x0, x1), :%(x2, x3), ty_Int)
new_primPlusNat1(Zero, Succ(x0))
new_esEs5(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_primCmpNat0(Succ(x0), Zero)
new_compare8(Integer(x0), Integer(x1))
new_compare16(x0, x1, False, x2)
new_esEs5(Nothing, Just(x0), x1)
new_lt10(x0, x1)
new_esEs6(Right(x0), Right(x1), x2, ty_Integer)
new_compare0(x0, x1, ty_Float)
new_lt4(x0, x1, ty_Int)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs9(x0, x1, app(ty_Maybe, x2))
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_compare23(x0, x1, True)
new_compare26(x0, x1, True, x2)
new_esEs9(x0, x1, ty_Double)
new_compare19([], :(x0, x1), x2)

We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph [15,17,22] contains 1 SCC with 8 less nodes.

↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ IFR
        ↳ HASKELL
          ↳ BR
            ↳ HASKELL
              ↳ COR
                ↳ HASKELL
                  ↳ LetRed
                    ↳ HASKELL
                      ↳ NumRed
                        ↳ HASKELL
                          ↳ Narrow
                            ↳ AND
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                                ↳ DependencyGraphProof
                                  ↳ QDP
                                    ↳ UsableRulesProof

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

new_ltEs2(:(vwx310, vwx311), :(vwx410, vwx411), hg) → new_primCompAux(vwx310, vwx410, vwx311, vwx411, hg)
new_lt(vwx30, vwx40, ba, bb) → new_compare2(vwx30, vwx40, new_esEs4(vwx30, vwx40, ba, bb), ba, bb)
new_ltEs0(Just(vwx310), Just(vwx410), app(app(app(ty_@3, eg), eh), fa)) → new_ltEs3(vwx310, vwx410, eg, eh, fa)
new_ltEs3(@3(vwx310, vwx311, vwx312), @3(vwx410, vwx411, vwx412), bec, app(ty_Maybe, bef), bdc) → new_lt0(vwx311, vwx411, bef)
new_ltEs3(@3(vwx310, vwx311, vwx312), @3(vwx410, vwx411, vwx412), bec, app(app(ty_Either, beg), beh), bdc) → new_lt1(vwx311, vwx411, beg, beh)
new_compare2(vwx30, vwx40, False, ba, bb) → new_ltEs(vwx30, vwx40, ba, bb)
new_ltEs(@2(vwx310, vwx311), @2(vwx410, vwx411), app(ty_Maybe, bf), be) → new_lt0(vwx310, vwx410, bf)
new_ltEs1(Left(vwx310), Left(vwx410), app(app(ty_Either, fg), fh), fd) → new_ltEs1(vwx310, vwx410, fg, fh)
new_ltEs(@2(vwx310, vwx311), @2(vwx410, vwx411), app(ty_[], ca), be) → new_lt2(vwx310, vwx410, ca)
new_ltEs1(Left(vwx310), Left(vwx410), app(ty_Maybe, ff), fd) → new_ltEs0(vwx310, vwx410, ff)
new_compare32(vwx30, vwx40, bce, bcf, bcg) → new_compare22(vwx30, vwx40, new_esEs7(vwx30, vwx40, bce, bcf, bcg), bce, bcf, bcg)
new_ltEs1(Right(vwx310), Right(vwx410), ge, app(app(app(ty_@3, hd), he), hf)) → new_ltEs3(vwx310, vwx410, hd, he, hf)
new_ltEs3(@3(vwx310, vwx311, vwx312), @3(vwx410, vwx411, vwx412), bec, app(ty_[], bfa), bdc) → new_lt2(vwx311, vwx411, bfa)
new_ltEs1(Left(vwx310), Left(vwx410), app(app(ty_@2, fb), fc), fd) → new_ltEs(vwx310, vwx410, fb, fc)
new_compare(:(vwx310, vwx311), :(vwx410, vwx411), hg) → new_primCompAux(vwx310, vwx410, vwx311, vwx411, hg)
new_ltEs3(@3(vwx310, vwx311, vwx312), @3(vwx410, vwx411, vwx412), app(app(ty_@2, bch), bda), bdb, bdc) → new_lt(vwx310, vwx410, bch, bda)
new_ltEs(@2(vwx310, vwx311), @2(vwx410, vwx411), app(app(app(ty_@3, cb), cc), cd), be) → new_lt3(vwx310, vwx410, cb, cc, cd)
new_compare31(vwx30, vwx40, bcc, bcd) → new_compare21(vwx30, vwx40, new_esEs6(vwx30, vwx40, bcc, bcd), bcc, bcd)
new_ltEs3(@3(vwx310, vwx311, vwx312), @3(vwx410, vwx411, vwx412), app(ty_[], bdg), bdb, bdc) → new_lt2(vwx310, vwx410, bdg)
new_ltEs1(Left(vwx310), Left(vwx410), app(ty_[], ga), fd) → new_ltEs2(vwx310, vwx410, ga)
new_primCompAux(vwx300, vwx400, vwx301, vwx401, hh) → new_primCompAux0(vwx301, vwx401, new_compare0(vwx300, vwx400, hh), app(ty_[], hh))
new_ltEs0(Just(vwx310), Just(vwx410), app(ty_Maybe, ec)) → new_ltEs0(vwx310, vwx410, ec)
new_compare22(vwx30, vwx40, False, bce, bcf, bcg) → new_ltEs3(vwx30, vwx40, bce, bcf, bcg)
new_ltEs3(@3(vwx310, vwx311, vwx312), @3(vwx410, vwx411, vwx412), app(app(ty_Either, bde), bdf), bdb, bdc) → new_lt1(vwx310, vwx410, bde, bdf)
new_lt2(:(vwx300, vwx301), :(vwx400, vwx401), app(app(ty_Either, bac), bad)) → new_compare31(vwx300, vwx400, bac, bad)
new_primCompAux(vwx300, vwx400, vwx301, vwx401, app(app(ty_@2, baa), bab)) → new_compare3(vwx300, vwx400, baa, bab)
new_ltEs3(@3(vwx310, vwx311, vwx312), @3(vwx410, vwx411, vwx412), bec, bdb, app(ty_Maybe, bfg)) → new_ltEs0(vwx312, vwx412, bfg)
new_ltEs3(@3(vwx310, vwx311, vwx312), @3(vwx410, vwx411, vwx412), bec, bdb, app(ty_[], bgb)) → new_ltEs2(vwx312, vwx412, bgb)
new_ltEs(@2(vwx310, vwx311), @2(vwx410, vwx411), app(app(ty_@2, bc), bd), be) → new_lt(vwx310, vwx410, bc, bd)
new_ltEs1(Right(vwx310), Right(vwx410), ge, app(app(ty_@2, gf), gg)) → new_ltEs(vwx310, vwx410, gf, gg)
new_lt3(vwx30, vwx40, bce, bcf, bcg) → new_compare22(vwx30, vwx40, new_esEs7(vwx30, vwx40, bce, bcf, bcg), bce, bcf, bcg)
new_primCompAux(vwx300, vwx400, vwx301, vwx401, app(app(app(ty_@3, bag), bah), bba)) → new_compare32(vwx300, vwx400, bag, bah, bba)
new_compare21(vwx30, vwx40, False, bcc, bcd) → new_ltEs1(vwx30, vwx40, bcc, bcd)
new_ltEs1(Right(vwx310), Right(vwx410), ge, app(ty_Maybe, gh)) → new_ltEs0(vwx310, vwx410, gh)
new_compare3(vwx30, vwx40, ba, bb) → new_compare2(vwx30, vwx40, new_esEs4(vwx30, vwx40, ba, bb), ba, bb)
new_compare30(vwx30, vwx40, dh) → new_compare20(vwx30, vwx40, new_esEs5(vwx30, vwx40, dh), dh)
new_ltEs(@2(vwx310, vwx311), @2(vwx410, vwx411), app(app(ty_Either, bg), bh), be) → new_lt1(vwx310, vwx410, bg, bh)
new_ltEs(@2(vwx310, vwx311), @2(vwx410, vwx411), ce, app(app(app(ty_@3, de), df), dg)) → new_ltEs3(vwx311, vwx411, de, df, dg)
new_lt1(vwx30, vwx40, bcc, bcd) → new_compare21(vwx30, vwx40, new_esEs6(vwx30, vwx40, bcc, bcd), bcc, bcd)
new_lt2(:(vwx300, vwx301), :(vwx400, vwx401), app(app(app(ty_@3, bag), bah), bba)) → new_compare32(vwx300, vwx400, bag, bah, bba)
new_ltEs1(Right(vwx310), Right(vwx410), ge, app(ty_[], hc)) → new_ltEs2(vwx310, vwx410, hc)
new_lt2(:(vwx300, vwx301), :(vwx400, vwx401), app(ty_[], bae)) → new_compare(vwx300, vwx400, bae)
new_primCompAux(vwx300, vwx400, vwx301, vwx401, app(ty_[], bae)) → new_compare(vwx300, vwx400, bae)
new_primCompAux0(vwx144, vwx145, EQ, app(ty_[], bbg)) → new_compare(vwx144, vwx145, bbg)
new_ltEs3(@3(vwx310, vwx311, vwx312), @3(vwx410, vwx411, vwx412), bec, bdb, app(app(ty_@2, bfe), bff)) → new_ltEs(vwx312, vwx412, bfe, bff)
new_lt2(:(vwx300, vwx301), :(vwx400, vwx401), app(ty_Maybe, baf)) → new_compare30(vwx300, vwx400, baf)
new_ltEs3(@3(vwx310, vwx311, vwx312), @3(vwx410, vwx411, vwx412), bec, app(app(ty_@2, bed), bee), bdc) → new_lt(vwx311, vwx411, bed, bee)
new_ltEs3(@3(vwx310, vwx311, vwx312), @3(vwx410, vwx411, vwx412), bec, bdb, app(app(app(ty_@3, bgc), bgd), bge)) → new_ltEs3(vwx312, vwx412, bgc, bgd, bge)
new_ltEs0(Just(vwx310), Just(vwx410), app(ty_[], ef)) → new_ltEs2(vwx310, vwx410, ef)
new_ltEs3(@3(vwx310, vwx311, vwx312), @3(vwx410, vwx411, vwx412), app(app(app(ty_@3, bdh), bea), beb), bdb, bdc) → new_lt3(vwx310, vwx410, bdh, bea, beb)
new_ltEs3(@3(vwx310, vwx311, vwx312), @3(vwx410, vwx411, vwx412), bec, bdb, app(app(ty_Either, bfh), bga)) → new_ltEs1(vwx312, vwx412, bfh, bga)
new_ltEs0(Just(vwx310), Just(vwx410), app(app(ty_@2, ea), eb)) → new_ltEs(vwx310, vwx410, ea, eb)
new_ltEs0(Just(vwx310), Just(vwx410), app(app(ty_Either, ed), ee)) → new_ltEs1(vwx310, vwx410, ed, ee)
new_ltEs(@2(vwx310, vwx311), @2(vwx410, vwx411), ce, app(app(ty_@2, cf), cg)) → new_ltEs(vwx311, vwx411, cf, cg)
new_ltEs1(Right(vwx310), Right(vwx410), ge, app(app(ty_Either, ha), hb)) → new_ltEs1(vwx310, vwx410, ha, hb)
new_ltEs3(@3(vwx310, vwx311, vwx312), @3(vwx410, vwx411, vwx412), bec, app(app(app(ty_@3, bfb), bfc), bfd), bdc) → new_lt3(vwx311, vwx411, bfb, bfc, bfd)
new_ltEs(@2(vwx310, vwx311), @2(vwx410, vwx411), ce, app(ty_[], dd)) → new_ltEs2(vwx311, vwx411, dd)
new_lt2(:(vwx300, vwx301), :(vwx400, vwx401), hh) → new_primCompAux0(vwx301, vwx401, new_compare0(vwx300, vwx400, hh), app(ty_[], hh))
new_ltEs(@2(vwx310, vwx311), @2(vwx410, vwx411), ce, app(ty_Maybe, da)) → new_ltEs0(vwx311, vwx411, da)
new_primCompAux(vwx300, vwx400, vwx301, vwx401, app(app(ty_Either, bac), bad)) → new_compare31(vwx300, vwx400, bac, bad)
new_lt2(:(vwx300, vwx301), :(vwx400, vwx401), app(app(ty_@2, baa), bab)) → new_compare3(vwx300, vwx400, baa, bab)
new_primCompAux(vwx300, vwx400, vwx301, vwx401, app(ty_Maybe, baf)) → new_compare30(vwx300, vwx400, baf)
new_ltEs(@2(vwx310, vwx311), @2(vwx410, vwx411), ce, app(app(ty_Either, db), dc)) → new_ltEs1(vwx311, vwx411, db, dc)
new_compare20(vwx30, vwx40, False, dh) → new_ltEs0(vwx30, vwx40, dh)
new_ltEs1(Left(vwx310), Left(vwx410), app(app(app(ty_@3, gb), gc), gd), fd) → new_ltEs3(vwx310, vwx410, gb, gc, gd)
new_lt0(vwx30, vwx40, dh) → new_compare20(vwx30, vwx40, new_esEs5(vwx30, vwx40, dh), dh)
new_ltEs3(@3(vwx310, vwx311, vwx312), @3(vwx410, vwx411, vwx412), app(ty_Maybe, bdd), bdb, bdc) → new_lt0(vwx310, vwx410, bdd)

The TRS R consists of the following rules:

new_esEs26(vwx310, vwx410, ty_Char) → new_esEs14(vwx310, vwx410)
new_ltEs12(Right(vwx310), Right(vwx410), ge, app(ty_Ratio, cah)) → new_ltEs17(vwx310, vwx410, cah)
new_compare13(vwx300, vwx400, bac, bad) → new_compare36(vwx300, vwx400, bac, bad)
new_compare36(vwx30, vwx40, bcc, bcd) → new_compare210(vwx30, vwx40, new_esEs6(vwx30, vwx40, bcc, bcd), bcc, bcd)
new_ltEs18(EQ, GT) → True
new_compare8(Integer(vwx310), Integer(vwx410)) → new_primCmpInt(vwx310, vwx410)
new_ltEs12(Right(vwx310), Right(vwx410), ge, ty_Bool) → new_ltEs10(vwx310, vwx410)
new_ltEs10(False, True) → True
new_lt6(vwx30, vwx40, ba, bb) → new_esEs19(new_compare34(vwx30, vwx40, ba, bb), LT)
new_esEs20(vwx300, vwx400, ty_Bool) → new_esEs12(vwx300, vwx400)
new_compare110(vwx30, vwx40, True, ba, bb) → LT
new_esEs27(vwx300, vwx400, app(ty_Ratio, dad)) → new_esEs18(vwx300, vwx400, dad)
new_esEs23(vwx300, vwx400, app(app(ty_@2, cbd), cbe)) → new_esEs4(vwx300, vwx400, cbd, cbe)
new_esEs8(vwx310, vwx410, ty_Integer) → new_esEs16(vwx310, vwx410)
new_esEs9(vwx311, vwx411, ty_@0) → new_esEs13(vwx311, vwx411)
new_primCompAux00(vwx144, vwx145, EQ, app(ty_Maybe, bbd)) → new_compare39(vwx144, vwx145, bbd)
new_esEs27(vwx300, vwx400, ty_Ordering) → new_esEs19(vwx300, vwx400)
new_ltEs19(vwx311, vwx411, ty_Integer) → new_ltEs15(vwx311, vwx411)
new_esEs23(vwx300, vwx400, app(ty_[], cca)) → new_esEs17(vwx300, vwx400, cca)
new_primMulNat0(Zero, Zero) → Zero
new_lt5(vwx311, vwx411, ty_Ordering) → new_lt18(vwx311, vwx411)
new_esEs6(Left(vwx300), Left(vwx400), app(app(app(ty_@3, cga), cgb), cgc), bcd) → new_esEs7(vwx300, vwx400, cga, cgb, cgc)
new_esEs24(vwx301, vwx401, ty_@0) → new_esEs13(vwx301, vwx401)
new_lt16(:(vwx300, vwx301), :(vwx400, vwx401), hh) → new_esEs19(new_primCompAux1(vwx300, vwx400, vwx301, vwx401, hh), LT)
new_ltEs16(vwx31, vwx41, hg) → new_not(new_esEs19(new_compare19(vwx31, vwx41, hg), GT))
new_esEs25(vwx302, vwx402, app(app(ty_Either, ceb), cec)) → new_esEs6(vwx302, vwx402, ceb, cec)
new_esEs12(True, True) → True
new_esEs25(vwx302, vwx402, app(app(ty_@2, cdh), cea)) → new_esEs4(vwx302, vwx402, cdh, cea)
new_lt4(vwx310, vwx410, ty_Char) → new_lt13(vwx310, vwx410)
new_lt5(vwx311, vwx411, ty_@0) → new_lt11(vwx311, vwx411)
new_lt4(vwx310, vwx410, ty_Float) → new_lt9(vwx310, vwx410)
new_esEs23(vwx300, vwx400, ty_Bool) → new_esEs12(vwx300, vwx400)
new_lt20(vwx310, vwx410, app(app(ty_Either, bg), bh)) → new_lt12(vwx310, vwx410, bg, bh)
new_compare43(vwx300, vwx401, vwx400, vwx301, ty_Int) → new_compare15(vwx300, vwx401, vwx400, vwx301)
new_compare40(vwx31, vwx41) → new_primCmpFloat(vwx31, vwx41)
new_esEs25(vwx302, vwx402, app(ty_Ratio, ced)) → new_esEs18(vwx302, vwx402, ced)
new_esEs6(Right(vwx300), Right(vwx400), bcc, ty_Float) → new_esEs11(vwx300, vwx400)
new_ltEs12(Right(vwx310), Right(vwx410), ge, ty_Char) → new_ltEs13(vwx310, vwx410)
new_lt20(vwx310, vwx410, ty_Double) → new_lt14(vwx310, vwx410)
new_esEs20(vwx300, vwx400, ty_Float) → new_esEs11(vwx300, vwx400)
new_lt5(vwx311, vwx411, ty_Integer) → new_lt15(vwx311, vwx411)
new_esEs23(vwx300, vwx400, ty_@0) → new_esEs13(vwx300, vwx400)
new_ltEs7(Just(vwx310), Just(vwx410), ty_Ordering) → new_ltEs18(vwx310, vwx410)
new_compare23(vwx30, vwx40, False) → new_compare10(vwx30, vwx40, new_ltEs18(vwx30, vwx40))
new_compare14(vwx31, vwx41) → new_primCmpDouble(vwx31, vwx41)
new_compare34(vwx30, vwx40, ba, bb) → new_compare24(vwx30, vwx40, new_esEs4(vwx30, vwx40, ba, bb), ba, bb)
new_esEs9(vwx311, vwx411, ty_Int) → new_esEs10(vwx311, vwx411)
new_compare17(vwx30, vwx40, True, bce, bcf, bcg) → LT
new_esEs5(Just(vwx300), Just(vwx400), app(ty_Maybe, bhg)) → new_esEs5(vwx300, vwx400, bhg)
new_compare0(vwx300, vwx400, app(app(ty_@2, baa), bab)) → new_compare28(vwx300, vwx400, baa, bab)
new_compare19(:(vwx310, vwx311), [], hg) → GT
new_esEs25(vwx302, vwx402, ty_Double) → new_esEs15(vwx302, vwx402)
new_lt15(Integer(vwx300), Integer(vwx400)) → new_esEs19(new_primCmpInt(vwx300, vwx400), LT)
new_compare0(vwx300, vwx400, ty_@0) → new_compare7(vwx300, vwx400)
new_compare0(vwx300, vwx400, ty_Bool) → new_compare41(vwx300, vwx400)
new_ltEs12(Right(vwx310), Right(vwx410), ge, ty_Int) → new_ltEs8(vwx310, vwx410)
new_esEs8(vwx310, vwx410, app(app(ty_Either, bde), bdf)) → new_esEs6(vwx310, vwx410, bde, bdf)
new_lt18(vwx30, vwx40) → new_esEs19(new_compare33(vwx30, vwx40), LT)
new_ltEs10(False, False) → True
new_esEs8(vwx310, vwx410, app(app(ty_@2, bch), bda)) → new_esEs4(vwx310, vwx410, bch, bda)
new_primCompAux00(vwx144, vwx145, EQ, ty_@0) → new_compare7(vwx144, vwx145)
new_primCompAux00(vwx144, vwx145, EQ, ty_Char) → new_compare29(vwx144, vwx145)
new_esEs28(vwx301, vwx401, ty_Ordering) → new_esEs19(vwx301, vwx401)
new_lt9(vwx30, vwx40) → new_esEs19(new_primCmpFloat(vwx30, vwx40), LT)
new_compare27(vwx30, vwx40, False) → new_compare18(vwx30, vwx40, new_ltEs10(vwx30, vwx40))
new_esEs6(Left(vwx300), Left(vwx400), ty_Float, bcd) → new_esEs11(vwx300, vwx400)
new_ltEs7(Just(vwx310), Just(vwx410), ty_Double) → new_ltEs14(vwx310, vwx410)
new_pePe(False, vwx113) → vwx113
new_esEs19(GT, GT) → True
new_esEs6(Right(vwx300), Right(vwx400), bcc, ty_@0) → new_esEs13(vwx300, vwx400)
new_ltEs7(Just(vwx310), Just(vwx410), ty_Integer) → new_ltEs15(vwx310, vwx410)
new_esEs27(vwx300, vwx400, ty_Float) → new_esEs11(vwx300, vwx400)
new_esEs6(Left(vwx300), Left(vwx400), app(app(ty_@2, cfb), cfc), bcd) → new_esEs4(vwx300, vwx400, cfb, cfc)
new_compare23(vwx30, vwx40, True) → EQ
new_lt13(vwx30, vwx40) → new_esEs19(new_primCmpChar(vwx30, vwx40), LT)
new_esEs7(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), bce, bcf, bcg) → new_asAs(new_esEs23(vwx300, vwx400, bce), new_asAs(new_esEs24(vwx301, vwx401, bcf), new_esEs25(vwx302, vwx402, bcg)))
new_lt5(vwx311, vwx411, ty_Float) → new_lt9(vwx311, vwx411)
new_lt5(vwx311, vwx411, app(ty_[], bfa)) → new_lt16(vwx311, vwx411, bfa)
new_esEs28(vwx301, vwx401, ty_@0) → new_esEs13(vwx301, vwx401)
new_ltEs7(Just(vwx310), Just(vwx410), app(app(ty_@2, ea), eb)) → new_ltEs6(vwx310, vwx410, ea, eb)
new_esEs26(vwx310, vwx410, ty_@0) → new_esEs13(vwx310, vwx410)
new_esEs8(vwx310, vwx410, ty_Char) → new_esEs14(vwx310, vwx410)
new_lt16([], [], hh) → new_esEs19(EQ, LT)
new_esEs26(vwx310, vwx410, ty_Bool) → new_esEs12(vwx310, vwx410)
new_compare24(vwx30, vwx40, False, ba, bb) → new_compare110(vwx30, vwx40, new_ltEs6(vwx30, vwx40, ba, bb), ba, bb)
new_esEs5(Just(vwx300), Just(vwx400), ty_Ordering) → new_esEs19(vwx300, vwx400)
new_esEs8(vwx310, vwx410, ty_Bool) → new_esEs12(vwx310, vwx410)
new_lt5(vwx311, vwx411, ty_Bool) → new_lt10(vwx311, vwx411)
new_esEs27(vwx300, vwx400, app(ty_[], dae)) → new_esEs17(vwx300, vwx400, dae)
new_ltEs7(Just(vwx310), Just(vwx410), ty_Char) → new_ltEs13(vwx310, vwx410)
new_lt5(vwx311, vwx411, ty_Char) → new_lt13(vwx311, vwx411)
new_lt4(vwx310, vwx410, app(ty_[], bdg)) → new_lt16(vwx310, vwx410, bdg)
new_ltEs5(vwx312, vwx412, app(app(ty_@2, bfe), bff)) → new_ltEs6(vwx312, vwx412, bfe, bff)
new_ltEs19(vwx311, vwx411, ty_Int) → new_ltEs8(vwx311, vwx411)
new_esEs23(vwx300, vwx400, app(app(app(ty_@3, ccc), ccd), cce)) → new_esEs7(vwx300, vwx400, ccc, ccd, cce)
new_primCmpNat0(Zero, Succ(vwx4000)) → LT
new_esEs27(vwx300, vwx400, app(app(app(ty_@3, dag), dah), dba)) → new_esEs7(vwx300, vwx400, dag, dah, dba)
new_ltEs12(Left(vwx310), Left(vwx410), app(app(ty_@2, fb), fc), fd) → new_ltEs6(vwx310, vwx410, fb, fc)
new_esEs6(Right(vwx300), Left(vwx400), bcc, bcd) → False
new_esEs6(Left(vwx300), Right(vwx400), bcc, bcd) → False
new_compare35(vwx30, vwx40, bce, bcf, bcg) → new_compare25(vwx30, vwx40, new_esEs7(vwx30, vwx40, bce, bcf, bcg), bce, bcf, bcg)
new_esEs28(vwx301, vwx401, ty_Char) → new_esEs14(vwx301, vwx401)
new_compare25(vwx30, vwx40, True, bce, bcf, bcg) → EQ
new_esEs25(vwx302, vwx402, ty_Char) → new_esEs14(vwx302, vwx402)
new_lt4(vwx310, vwx410, app(ty_Ratio, bgf)) → new_lt17(vwx310, vwx410, bgf)
new_lt5(vwx311, vwx411, app(app(app(ty_@3, bfb), bfc), bfd)) → new_lt19(vwx311, vwx411, bfb, bfc, bfd)
new_ltEs12(Left(vwx310), Left(vwx410), ty_Integer, fd) → new_ltEs15(vwx310, vwx410)
new_ltEs9(vwx31, vwx41) → new_not(new_esEs19(new_compare40(vwx31, vwx41), GT))
new_ltEs19(vwx311, vwx411, app(app(app(ty_@3, de), df), dg)) → new_ltEs4(vwx311, vwx411, de, df, dg)
new_esEs28(vwx301, vwx401, ty_Double) → new_esEs15(vwx301, vwx401)
new_lt16([], :(vwx400, vwx401), hh) → new_esEs19(LT, LT)
new_ltEs12(Left(vwx310), Left(vwx410), ty_Ordering, fd) → new_ltEs18(vwx310, vwx410)
new_ltEs6(@2(vwx310, vwx311), @2(vwx410, vwx411), ce, be) → new_pePe(new_lt20(vwx310, vwx410, ce), new_asAs(new_esEs26(vwx310, vwx410, ce), new_ltEs19(vwx311, vwx411, be)))
new_primCompAux00(vwx144, vwx145, EQ, ty_Bool) → new_compare41(vwx144, vwx145)
new_lt12(vwx30, vwx40, bcc, bcd) → new_esEs19(new_compare36(vwx30, vwx40, bcc, bcd), LT)
new_esEs28(vwx301, vwx401, ty_Integer) → new_esEs16(vwx301, vwx401)
new_ltEs7(Just(vwx310), Just(vwx410), ty_Int) → new_ltEs8(vwx310, vwx410)
new_compare12(:%(vwx310, vwx311), :%(vwx410, vwx411), ty_Integer) → new_compare8(new_sr0(vwx310, vwx411), new_sr0(vwx410, vwx311))
new_esEs5(Just(vwx300), Just(vwx400), app(ty_[], bhf)) → new_esEs17(vwx300, vwx400, bhf)
new_esEs15(Double(vwx300, vwx301), Double(vwx400, vwx401)) → new_esEs10(new_sr(vwx300, vwx400), new_sr(vwx301, vwx401))
new_pePe(True, vwx113) → True
new_primEqNat0(Zero, Zero) → True
new_compare310(vwx30, vwx40) → new_compare27(vwx30, vwx40, new_esEs12(vwx30, vwx40))
new_esEs6(Right(vwx300), Right(vwx400), bcc, ty_Integer) → new_esEs16(vwx300, vwx400)
new_esEs23(vwx300, vwx400, app(app(ty_Either, cbf), cbg)) → new_esEs6(vwx300, vwx400, cbf, cbg)
new_esEs5(Just(vwx300), Just(vwx400), app(app(ty_@2, bha), bhb)) → new_esEs4(vwx300, vwx400, bha, bhb)
new_ltEs18(EQ, EQ) → True
new_esEs4(@2(vwx300, vwx301), @2(vwx400, vwx401), ba, bb) → new_asAs(new_esEs27(vwx300, vwx400, ba), new_esEs28(vwx301, vwx401, bb))
new_ltEs12(Right(vwx310), Right(vwx410), ge, ty_Double) → new_ltEs14(vwx310, vwx410)
new_esEs23(vwx300, vwx400, ty_Char) → new_esEs14(vwx300, vwx400)
new_primCompAux00(vwx144, vwx145, EQ, app(app(app(ty_@3, bbh), bca), bcb)) → new_compare9(vwx144, vwx145, bbh, bca, bcb)
new_esEs6(Right(vwx300), Right(vwx400), bcc, app(app(ty_Either, cgf), cgg)) → new_esEs6(vwx300, vwx400, cgf, cgg)
new_esEs6(Left(vwx300), Left(vwx400), ty_Double, bcd) → new_esEs15(vwx300, vwx400)
new_ltEs5(vwx312, vwx412, app(app(ty_Either, bfh), bga)) → new_ltEs12(vwx312, vwx412, bfh, bga)
new_compare110(vwx30, vwx40, False, ba, bb) → GT
new_ltEs14(vwx31, vwx41) → new_not(new_esEs19(new_compare14(vwx31, vwx41), GT))
new_sr(vwx300, vwx400) → new_primMulInt(vwx300, vwx400)
new_esEs26(vwx310, vwx410, ty_Ordering) → new_esEs19(vwx310, vwx410)
new_esEs28(vwx301, vwx401, app(app(ty_Either, dbd), dbe)) → new_esEs6(vwx301, vwx401, dbd, dbe)
new_lt20(vwx310, vwx410, ty_Float) → new_lt9(vwx310, vwx410)
new_esEs9(vwx311, vwx411, app(app(app(ty_@3, bfb), bfc), bfd)) → new_esEs7(vwx311, vwx411, bfb, bfc, bfd)
new_esEs6(Right(vwx300), Right(vwx400), bcc, ty_Double) → new_esEs15(vwx300, vwx400)
new_ltEs18(LT, LT) → True
new_ltEs5(vwx312, vwx412, ty_Char) → new_ltEs13(vwx312, vwx412)
new_primPlusNat0(Succ(vwx1540), vwx40000) → Succ(Succ(new_primPlusNat1(vwx1540, vwx40000)))
new_compare0(vwx300, vwx400, app(ty_[], bae)) → new_compare19(vwx300, vwx400, bae)
new_ltEs11(vwx31, vwx41) → new_not(new_esEs19(new_compare7(vwx31, vwx41), GT))
new_esEs20(vwx300, vwx400, app(app(app(ty_@3, bag), bah), bba)) → new_esEs7(vwx300, vwx400, bag, bah, bba)
new_esEs12(False, False) → True
new_esEs26(vwx310, vwx410, ty_Float) → new_esEs11(vwx310, vwx410)
new_ltEs12(Right(vwx310), Right(vwx410), ge, ty_Float) → new_ltEs9(vwx310, vwx410)
new_esEs9(vwx311, vwx411, ty_Char) → new_esEs14(vwx311, vwx411)
new_ltEs18(GT, GT) → True
new_lt4(vwx310, vwx410, app(app(app(ty_@3, bdh), bea), beb)) → new_lt19(vwx310, vwx410, bdh, bea, beb)
new_primEqInt(Neg(Succ(vwx3000)), Neg(Succ(vwx4000))) → new_primEqNat0(vwx3000, vwx4000)
new_lt4(vwx310, vwx410, ty_Double) → new_lt14(vwx310, vwx410)
new_esEs6(Right(vwx300), Right(vwx400), bcc, app(app(app(ty_@3, chc), chd), che)) → new_esEs7(vwx300, vwx400, chc, chd, che)
new_compare16(vwx30, vwx40, True, dh) → LT
new_esEs8(vwx310, vwx410, ty_Double) → new_esEs15(vwx310, vwx410)
new_compare39(vwx300, vwx400, baf) → new_compare37(vwx300, vwx400, baf)
new_esEs9(vwx311, vwx411, ty_Integer) → new_esEs16(vwx311, vwx411)
new_esEs19(EQ, EQ) → True
new_ltEs18(LT, GT) → True
new_compare25(vwx30, vwx40, False, bce, bcf, bcg) → new_compare17(vwx30, vwx40, new_ltEs4(vwx30, vwx40, bce, bcf, bcg), bce, bcf, bcg)
new_primPlusNat1(Succ(vwx15400), Zero) → Succ(vwx15400)
new_primPlusNat1(Zero, Succ(vwx400000)) → Succ(vwx400000)
new_ltEs19(vwx311, vwx411, app(ty_Ratio, chg)) → new_ltEs17(vwx311, vwx411, chg)
new_esEs26(vwx310, vwx410, app(app(app(ty_@3, cb), cc), cd)) → new_esEs7(vwx310, vwx410, cb, cc, cd)
new_ltEs18(GT, LT) → False
new_ltEs5(vwx312, vwx412, app(ty_[], bgb)) → new_ltEs16(vwx312, vwx412, bgb)
new_ltEs19(vwx311, vwx411, ty_Float) → new_ltEs9(vwx311, vwx411)
new_esEs9(vwx311, vwx411, ty_Float) → new_esEs11(vwx311, vwx411)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs5(Just(vwx300), Just(vwx400), ty_Int) → new_esEs10(vwx300, vwx400)
new_compare38(vwx300, vwx400) → new_compare33(vwx300, vwx400)
new_compare0(vwx300, vwx400, app(app(app(ty_@3, bag), bah), bba)) → new_compare9(vwx300, vwx400, bag, bah, bba)
new_compare18(vwx30, vwx40, False) → GT
new_primEqInt(Neg(Succ(vwx3000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(vwx4000))) → False
new_compare37(vwx30, vwx40, dh) → new_compare26(vwx30, vwx40, new_esEs5(vwx30, vwx40, dh), dh)
new_esEs23(vwx300, vwx400, ty_Integer) → new_esEs16(vwx300, vwx400)
new_esEs6(Right(vwx300), Right(vwx400), bcc, app(ty_[], cha)) → new_esEs17(vwx300, vwx400, cha)
new_esEs20(vwx300, vwx400, ty_Integer) → new_esEs16(vwx300, vwx400)
new_compare28(vwx300, vwx400, baa, bab) → new_compare34(vwx300, vwx400, baa, bab)
new_compare24(vwx30, vwx40, True, ba, bb) → EQ
new_lt7(vwx30, vwx40, dh) → new_esEs19(new_compare37(vwx30, vwx40, dh), LT)
new_esEs23(vwx300, vwx400, ty_Ordering) → new_esEs19(vwx300, vwx400)
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_ltEs5(vwx312, vwx412, app(ty_Ratio, bgh)) → new_ltEs17(vwx312, vwx412, bgh)
new_lt20(vwx310, vwx410, ty_Int) → new_lt8(vwx310, vwx410)
new_esEs6(Left(vwx300), Left(vwx400), app(ty_Ratio, cff), bcd) → new_esEs18(vwx300, vwx400, cff)
new_ltEs12(Right(vwx310), Right(vwx410), ge, app(ty_[], hc)) → new_ltEs16(vwx310, vwx410, hc)
new_lt4(vwx310, vwx410, ty_Int) → new_lt8(vwx310, vwx410)
new_compare29(vwx31, vwx41) → new_primCmpChar(vwx31, vwx41)
new_lt5(vwx311, vwx411, app(app(ty_@2, bed), bee)) → new_lt6(vwx311, vwx411, bed, bee)
new_primCmpNat0(Succ(vwx3000), Succ(vwx4000)) → new_primCmpNat0(vwx3000, vwx4000)
new_esEs19(LT, EQ) → False
new_esEs19(EQ, LT) → False
new_ltEs19(vwx311, vwx411, ty_@0) → new_ltEs11(vwx311, vwx411)
new_compare0(vwx300, vwx400, ty_Float) → new_compare40(vwx300, vwx400)
new_esEs26(vwx310, vwx410, ty_Integer) → new_esEs16(vwx310, vwx410)
new_ltEs12(Left(vwx310), Left(vwx410), app(ty_[], ga), fd) → new_ltEs16(vwx310, vwx410, ga)
new_primEqInt(Pos(Succ(vwx3000)), Pos(Succ(vwx4000))) → new_primEqNat0(vwx3000, vwx4000)
new_esEs25(vwx302, vwx402, app(ty_Maybe, cef)) → new_esEs5(vwx302, vwx402, cef)
new_esEs20(vwx300, vwx400, ty_Int) → new_esEs10(vwx300, vwx400)
new_esEs8(vwx310, vwx410, app(ty_Maybe, bdd)) → new_esEs5(vwx310, vwx410, bdd)
new_ltEs7(Nothing, Just(vwx410), cae) → True
new_ltEs5(vwx312, vwx412, ty_@0) → new_ltEs11(vwx312, vwx412)
new_ltEs12(Left(vwx310), Left(vwx410), ty_@0, fd) → new_ltEs11(vwx310, vwx410)
new_ltEs12(Right(vwx310), Right(vwx410), ge, app(app(ty_@2, gf), gg)) → new_ltEs6(vwx310, vwx410, gf, gg)
new_primEqNat0(Succ(vwx3000), Succ(vwx4000)) → new_primEqNat0(vwx3000, vwx4000)
new_compare7(@0, @0) → EQ
new_esEs24(vwx301, vwx401, app(ty_Ratio, cdb)) → new_esEs18(vwx301, vwx401, cdb)
new_esEs6(Left(vwx300), Left(vwx400), app(ty_[], cfg), bcd) → new_esEs17(vwx300, vwx400, cfg)
new_ltEs19(vwx311, vwx411, ty_Double) → new_ltEs14(vwx311, vwx411)
new_ltEs12(Right(vwx310), Right(vwx410), ge, app(ty_Maybe, gh)) → new_ltEs7(vwx310, vwx410, gh)
new_esEs9(vwx311, vwx411, app(app(ty_Either, beg), beh)) → new_esEs6(vwx311, vwx411, beg, beh)
new_primCmpInt(Neg(Succ(vwx3000)), Neg(vwx400)) → new_primCmpNat0(vwx400, Succ(vwx3000))
new_compare16(vwx30, vwx40, False, dh) → GT
new_esEs26(vwx310, vwx410, app(app(ty_@2, bc), bd)) → new_esEs4(vwx310, vwx410, bc, bd)
new_esEs6(Right(vwx300), Right(vwx400), bcc, app(ty_Maybe, chb)) → new_esEs5(vwx300, vwx400, chb)
new_esEs23(vwx300, vwx400, ty_Double) → new_esEs15(vwx300, vwx400)
new_compare17(vwx30, vwx40, False, bce, bcf, bcg) → GT
new_ltEs5(vwx312, vwx412, ty_Int) → new_ltEs8(vwx312, vwx412)
new_primEqInt(Pos(Succ(vwx3000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(vwx4000))) → False
new_lt20(vwx310, vwx410, app(ty_Ratio, chf)) → new_lt17(vwx310, vwx410, chf)
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(vwx3000), Zero) → GT
new_esEs6(Left(vwx300), Left(vwx400), ty_Bool, bcd) → new_esEs12(vwx300, vwx400)
new_compare18(vwx30, vwx40, True) → LT
new_primCmpInt(Neg(Zero), Pos(Succ(vwx4000))) → LT
new_compare11(vwx30, vwx40, True, bcc, bcd) → LT
new_esEs8(vwx310, vwx410, ty_Int) → new_esEs10(vwx310, vwx410)
new_lt20(vwx310, vwx410, ty_Char) → new_lt13(vwx310, vwx410)
new_sr0(Integer(vwx4000), Integer(vwx3010)) → Integer(new_primMulInt(vwx4000, vwx3010))
new_lt4(vwx310, vwx410, app(ty_Maybe, bdd)) → new_lt7(vwx310, vwx410, bdd)
new_primPlusNat1(Succ(vwx15400), Succ(vwx400000)) → Succ(Succ(new_primPlusNat1(vwx15400, vwx400000)))
new_primEqInt(Pos(Succ(vwx3000)), Neg(vwx400)) → False
new_primEqInt(Neg(Succ(vwx3000)), Pos(vwx400)) → False
new_esEs25(vwx302, vwx402, ty_Int) → new_esEs10(vwx302, vwx402)
new_esEs24(vwx301, vwx401, app(app(ty_@2, ccf), ccg)) → new_esEs4(vwx301, vwx401, ccf, ccg)
new_ltEs12(Left(vwx310), Right(vwx410), ge, fd) → True
new_esEs5(Just(vwx300), Just(vwx400), ty_Bool) → new_esEs12(vwx300, vwx400)
new_esEs25(vwx302, vwx402, ty_@0) → new_esEs13(vwx302, vwx402)
new_esEs27(vwx300, vwx400, app(ty_Maybe, daf)) → new_esEs5(vwx300, vwx400, daf)
new_primCompAux00(vwx144, vwx145, EQ, ty_Int) → new_compare42(vwx144, vwx145)
new_lt4(vwx310, vwx410, ty_Integer) → new_lt15(vwx310, vwx410)
new_esEs6(Right(vwx300), Right(vwx400), bcc, ty_Ordering) → new_esEs19(vwx300, vwx400)
new_esEs5(Just(vwx300), Just(vwx400), ty_@0) → new_esEs13(vwx300, vwx400)
new_esEs6(Left(vwx300), Left(vwx400), ty_@0, bcd) → new_esEs13(vwx300, vwx400)
new_primEqInt(Pos(Zero), Neg(Succ(vwx4000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(vwx4000))) → False
new_esEs26(vwx310, vwx410, ty_Int) → new_esEs10(vwx310, vwx410)
new_primCompAux00(vwx144, vwx145, EQ, app(ty_[], bbg)) → new_compare19(vwx144, vwx145, bbg)
new_esEs26(vwx310, vwx410, app(ty_[], ca)) → new_esEs17(vwx310, vwx410, ca)
new_esEs13(@0, @0) → True
new_lt8(vwx30, vwx40) → new_esEs19(new_primCmpInt(vwx30, vwx40), LT)
new_primCmpInt(Pos(Zero), Pos(Succ(vwx4000))) → new_primCmpNat0(Zero, Succ(vwx4000))
new_primCompAux00(vwx144, vwx145, EQ, ty_Ordering) → new_compare38(vwx144, vwx145)
new_esEs18(:%(vwx300, vwx301), :%(vwx400, vwx401), cbc) → new_asAs(new_esEs21(vwx300, vwx400, cbc), new_esEs22(vwx301, vwx401, cbc))
new_ltEs12(Left(vwx310), Left(vwx410), ty_Int, fd) → new_ltEs8(vwx310, vwx410)
new_compare26(vwx30, vwx40, True, dh) → EQ
new_compare43(Integer(vwx3000), Integer(vwx4010), vwx400, vwx301, ty_Integer) → new_compare8(Integer(new_primMulInt(vwx3000, vwx4010)), new_sr0(vwx400, vwx301))
new_ltEs18(GT, EQ) → False
new_esEs6(Left(vwx300), Left(vwx400), ty_Char, bcd) → new_esEs14(vwx300, vwx400)
new_esEs23(vwx300, vwx400, ty_Float) → new_esEs11(vwx300, vwx400)
new_not(False) → True
new_ltEs7(Just(vwx310), Just(vwx410), ty_@0) → new_ltEs11(vwx310, vwx410)
new_esEs6(Left(vwx300), Left(vwx400), app(app(ty_Either, cfd), cfe), bcd) → new_esEs6(vwx300, vwx400, cfd, cfe)
new_compare19([], [], hg) → EQ
new_compare210(vwx30, vwx40, True, bcc, bcd) → EQ
new_primCmpInt(Pos(Succ(vwx3000)), Pos(vwx400)) → new_primCmpNat0(Succ(vwx3000), vwx400)
new_primPlusNat0(Zero, vwx40000) → Succ(vwx40000)
new_esEs5(Just(vwx300), Just(vwx400), ty_Char) → new_esEs14(vwx300, vwx400)
new_esEs8(vwx310, vwx410, ty_Ordering) → new_esEs19(vwx310, vwx410)
new_ltEs19(vwx311, vwx411, app(app(ty_Either, db), dc)) → new_ltEs12(vwx311, vwx411, db, dc)
new_esEs20(vwx300, vwx400, ty_Char) → new_esEs14(vwx300, vwx400)
new_esEs24(vwx301, vwx401, app(app(ty_Either, cch), cda)) → new_esEs6(vwx301, vwx401, cch, cda)
new_ltEs12(Right(vwx310), Right(vwx410), ge, app(app(ty_Either, ha), hb)) → new_ltEs12(vwx310, vwx410, ha, hb)
new_esEs26(vwx310, vwx410, app(ty_Ratio, chf)) → new_esEs18(vwx310, vwx410, chf)
new_ltEs12(Right(vwx310), Left(vwx410), ge, fd) → False
new_esEs24(vwx301, vwx401, ty_Ordering) → new_esEs19(vwx301, vwx401)
new_compare41(vwx300, vwx400) → new_compare310(vwx300, vwx400)
new_esEs9(vwx311, vwx411, app(ty_Maybe, bef)) → new_esEs5(vwx311, vwx411, bef)
new_primCmpFloat(Float(vwx300, vwx301), Float(vwx400, vwx401)) → new_compare15(vwx300, vwx400, vwx301, vwx401)
new_ltEs18(EQ, LT) → False
new_ltEs12(Left(vwx310), Left(vwx410), app(ty_Ratio, cag), fd) → new_ltEs17(vwx310, vwx410, cag)
new_esEs6(Right(vwx300), Right(vwx400), bcc, ty_Bool) → new_esEs12(vwx300, vwx400)
new_ltEs18(LT, EQ) → True
new_esEs24(vwx301, vwx401, app(ty_[], cdc)) → new_esEs17(vwx301, vwx401, cdc)
new_lt20(vwx310, vwx410, ty_Ordering) → new_lt18(vwx310, vwx410)
new_compare0(vwx300, vwx400, app(ty_Ratio, cad)) → new_compare12(vwx300, vwx400, cad)
new_esEs27(vwx300, vwx400, app(app(ty_Either, dab), dac)) → new_esEs6(vwx300, vwx400, dab, dac)
new_esEs6(Right(vwx300), Right(vwx400), bcc, ty_Char) → new_esEs14(vwx300, vwx400)
new_esEs24(vwx301, vwx401, app(ty_Maybe, cdd)) → new_esEs5(vwx301, vwx401, cdd)
new_esEs19(LT, GT) → False
new_esEs19(GT, LT) → False
new_esEs5(Just(vwx300), Just(vwx400), ty_Float) → new_esEs11(vwx300, vwx400)
new_compare11(vwx30, vwx40, False, bcc, bcd) → GT
new_primCmpInt(Pos(Succ(vwx3000)), Neg(vwx400)) → GT
new_ltEs7(Just(vwx310), Just(vwx410), app(ty_Maybe, ec)) → new_ltEs7(vwx310, vwx410, ec)
new_esEs8(vwx310, vwx410, app(app(app(ty_@3, bdh), bea), beb)) → new_esEs7(vwx310, vwx410, bdh, bea, beb)
new_esEs21(vwx300, vwx400, ty_Integer) → new_esEs16(vwx300, vwx400)
new_primCompAux00(vwx144, vwx145, EQ, app(ty_Ratio, cbb)) → new_compare12(vwx144, vwx145, cbb)
new_esEs24(vwx301, vwx401, ty_Double) → new_esEs15(vwx301, vwx401)
new_ltEs19(vwx311, vwx411, app(ty_[], dd)) → new_ltEs16(vwx311, vwx411, dd)
new_primMulInt(Pos(vwx3000), Pos(vwx4000)) → Pos(new_primMulNat0(vwx3000, vwx4000))
new_esEs9(vwx311, vwx411, app(ty_Ratio, bgg)) → new_esEs18(vwx311, vwx411, bgg)
new_esEs24(vwx301, vwx401, ty_Integer) → new_esEs16(vwx301, vwx401)
new_esEs28(vwx301, vwx401, app(app(app(ty_@3, dca), dcb), dcc)) → new_esEs7(vwx301, vwx401, dca, dcb, dcc)
new_ltEs12(Left(vwx310), Left(vwx410), ty_Char, fd) → new_ltEs13(vwx310, vwx410)
new_ltEs12(Right(vwx310), Right(vwx410), ge, ty_Ordering) → new_ltEs18(vwx310, vwx410)
new_esEs22(vwx301, vwx401, ty_Int) → new_esEs10(vwx301, vwx401)
new_compare0(vwx300, vwx400, app(app(ty_Either, bac), bad)) → new_compare13(vwx300, vwx400, bac, bad)
new_lt10(vwx30, vwx40) → new_esEs19(new_compare310(vwx30, vwx40), LT)
new_esEs27(vwx300, vwx400, ty_Double) → new_esEs15(vwx300, vwx400)
new_ltEs12(Right(vwx310), Right(vwx410), ge, ty_Integer) → new_ltEs15(vwx310, vwx410)
new_primMulInt(Neg(vwx3000), Neg(vwx4000)) → Pos(new_primMulNat0(vwx3000, vwx4000))
new_esEs5(Just(vwx300), Just(vwx400), app(ty_Ratio, bhe)) → new_esEs18(vwx300, vwx400, bhe)
new_primEqNat0(Succ(vwx3000), Zero) → False
new_primEqNat0(Zero, Succ(vwx4000)) → False
new_esEs27(vwx300, vwx400, ty_Char) → new_esEs14(vwx300, vwx400)
new_ltEs4(@3(vwx310, vwx311, vwx312), @3(vwx410, vwx411, vwx412), bec, bdb, bdc) → new_pePe(new_lt4(vwx310, vwx410, bec), new_asAs(new_esEs8(vwx310, vwx410, bec), new_pePe(new_lt5(vwx311, vwx411, bdb), new_asAs(new_esEs9(vwx311, vwx411, bdb), new_ltEs5(vwx312, vwx412, bdc)))))
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_ltEs17(vwx31, vwx41, cac) → new_not(new_esEs19(new_compare12(vwx31, vwx41, cac), GT))
new_esEs23(vwx300, vwx400, app(ty_Ratio, cbh)) → new_esEs18(vwx300, vwx400, cbh)
new_esEs20(vwx300, vwx400, app(ty_[], bae)) → new_esEs17(vwx300, vwx400, bae)
new_esEs20(vwx300, vwx400, app(app(ty_Either, bac), bad)) → new_esEs6(vwx300, vwx400, bac, bad)
new_ltEs12(Left(vwx310), Left(vwx410), app(app(ty_Either, fg), fh), fd) → new_ltEs12(vwx310, vwx410, fg, fh)
new_lt14(vwx30, vwx40) → new_esEs19(new_primCmpDouble(vwx30, vwx40), LT)
new_compare0(vwx300, vwx400, ty_Char) → new_compare29(vwx300, vwx400)
new_ltEs7(Just(vwx310), Just(vwx410), app(app(app(ty_@3, eg), eh), fa)) → new_ltEs4(vwx310, vwx410, eg, eh, fa)
new_ltEs19(vwx311, vwx411, ty_Char) → new_ltEs13(vwx311, vwx411)
new_esEs27(vwx300, vwx400, ty_Integer) → new_esEs16(vwx300, vwx400)
new_esEs9(vwx311, vwx411, ty_Ordering) → new_esEs19(vwx311, vwx411)
new_primCompAux00(vwx144, vwx145, EQ, app(app(ty_@2, bbb), bbc)) → new_compare28(vwx144, vwx145, bbb, bbc)
new_ltEs12(Left(vwx310), Left(vwx410), ty_Bool, fd) → new_ltEs10(vwx310, vwx410)
new_ltEs7(Nothing, Nothing, cae) → True
new_compare0(vwx300, vwx400, app(ty_Maybe, baf)) → new_compare39(vwx300, vwx400, baf)
new_ltEs19(vwx311, vwx411, ty_Bool) → new_ltEs10(vwx311, vwx411)
new_esEs26(vwx310, vwx410, app(ty_Maybe, bf)) → new_esEs5(vwx310, vwx410, bf)
new_ltEs7(Just(vwx310), Just(vwx410), ty_Float) → new_ltEs9(vwx310, vwx410)
new_primCompAux00(vwx144, vwx145, EQ, ty_Float) → new_compare40(vwx144, vwx145)
new_lt5(vwx311, vwx411, ty_Double) → new_lt14(vwx311, vwx411)
new_esEs25(vwx302, vwx402, ty_Integer) → new_esEs16(vwx302, vwx402)
new_primCmpInt(Neg(Zero), Neg(Succ(vwx4000))) → new_primCmpNat0(Succ(vwx4000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(vwx4000))) → GT
new_lt4(vwx310, vwx410, ty_@0) → new_lt11(vwx310, vwx410)
new_esEs25(vwx302, vwx402, ty_Ordering) → new_esEs19(vwx302, vwx402)
new_compare19(:(vwx310, vwx311), :(vwx410, vwx411), hg) → new_primCompAux1(vwx310, vwx410, vwx311, vwx411, hg)
new_lt11(@0, @0) → new_esEs19(EQ, LT)
new_esEs6(Right(vwx300), Right(vwx400), bcc, app(app(ty_@2, cgd), cge)) → new_esEs4(vwx300, vwx400, cgd, cge)
new_lt20(vwx310, vwx410, app(app(ty_@2, bc), bd)) → new_lt6(vwx310, vwx410, bc, bd)
new_ltEs5(vwx312, vwx412, ty_Float) → new_ltEs9(vwx312, vwx412)
new_esEs20(vwx300, vwx400, app(ty_Ratio, cad)) → new_esEs18(vwx300, vwx400, cad)
new_esEs19(LT, LT) → True
new_ltEs12(Left(vwx310), Left(vwx410), app(ty_Maybe, ff), fd) → new_ltEs7(vwx310, vwx410, ff)
new_esEs16(Integer(vwx300), Integer(vwx400)) → new_primEqInt(vwx300, vwx400)
new_lt5(vwx311, vwx411, app(ty_Maybe, bef)) → new_lt7(vwx311, vwx411, bef)
new_esEs19(EQ, GT) → False
new_esEs19(GT, EQ) → False
new_compare0(vwx300, vwx400, ty_Int) → new_compare42(vwx300, vwx400)
new_lt17(:%(vwx300, vwx301), :%(vwx400, vwx401), cbc) → new_esEs19(new_compare43(vwx300, vwx401, vwx400, vwx301, cbc), LT)
new_esEs9(vwx311, vwx411, app(app(ty_@2, bed), bee)) → new_esEs4(vwx311, vwx411, bed, bee)
new_lt20(vwx310, vwx410, app(ty_[], ca)) → new_lt16(vwx310, vwx410, ca)
new_ltEs7(Just(vwx310), Just(vwx410), app(app(ty_Either, ed), ee)) → new_ltEs12(vwx310, vwx410, ed, ee)
new_ltEs12(Right(vwx310), Right(vwx410), ge, ty_@0) → new_ltEs11(vwx310, vwx410)
new_esEs6(Left(vwx300), Left(vwx400), ty_Ordering, bcd) → new_esEs19(vwx300, vwx400)
new_esEs24(vwx301, vwx401, app(app(app(ty_@3, cde), cdf), cdg)) → new_esEs7(vwx301, vwx401, cde, cdf, cdg)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs25(vwx302, vwx402, ty_Bool) → new_esEs12(vwx302, vwx402)
new_ltEs19(vwx311, vwx411, app(app(ty_@2, cf), cg)) → new_ltEs6(vwx311, vwx411, cf, cg)
new_compare12(:%(vwx310, vwx311), :%(vwx410, vwx411), ty_Int) → new_compare42(new_sr(vwx310, vwx411), new_sr(vwx410, vwx311))
new_esEs24(vwx301, vwx401, ty_Int) → new_esEs10(vwx301, vwx401)
new_esEs20(vwx300, vwx400, app(ty_Maybe, baf)) → new_esEs5(vwx300, vwx400, baf)
new_lt20(vwx310, vwx410, app(ty_Maybe, bf)) → new_lt7(vwx310, vwx410, bf)
new_lt4(vwx310, vwx410, app(app(ty_@2, bch), bda)) → new_lt6(vwx310, vwx410, bch, bda)
new_ltEs8(vwx31, vwx41) → new_not(new_esEs19(new_compare42(vwx31, vwx41), GT))
new_esEs28(vwx301, vwx401, app(app(ty_@2, dbb), dbc)) → new_esEs4(vwx301, vwx401, dbb, dbc)
new_ltEs10(True, False) → False
new_asAs(False, vwx139) → False
new_primMulInt(Pos(vwx3000), Neg(vwx4000)) → Neg(new_primMulNat0(vwx3000, vwx4000))
new_primMulInt(Neg(vwx3000), Pos(vwx4000)) → Neg(new_primMulNat0(vwx3000, vwx4000))
new_compare19([], :(vwx410, vwx411), hg) → LT
new_primMulNat0(Zero, Succ(vwx40000)) → Zero
new_primMulNat0(Succ(vwx30000), Zero) → Zero
new_compare33(vwx30, vwx40) → new_compare23(vwx30, vwx40, new_esEs19(vwx30, vwx40))
new_lt5(vwx311, vwx411, ty_Int) → new_lt8(vwx311, vwx411)
new_compare210(vwx30, vwx40, False, bcc, bcd) → new_compare11(vwx30, vwx40, new_ltEs12(vwx30, vwx40, bcc, bcd), bcc, bcd)
new_esEs6(Right(vwx300), Right(vwx400), bcc, app(ty_Ratio, cgh)) → new_esEs18(vwx300, vwx400, cgh)
new_esEs9(vwx311, vwx411, ty_Bool) → new_esEs12(vwx311, vwx411)
new_esEs24(vwx301, vwx401, ty_Float) → new_esEs11(vwx301, vwx401)
new_esEs27(vwx300, vwx400, ty_@0) → new_esEs13(vwx300, vwx400)
new_primCompAux00(vwx144, vwx145, LT, cba) → LT
new_esEs25(vwx302, vwx402, app(ty_[], cee)) → new_esEs17(vwx302, vwx402, cee)
new_primCompAux00(vwx144, vwx145, GT, cba) → GT
new_esEs23(vwx300, vwx400, app(ty_Maybe, ccb)) → new_esEs5(vwx300, vwx400, ccb)
new_esEs6(Right(vwx300), Right(vwx400), bcc, ty_Int) → new_esEs10(vwx300, vwx400)
new_esEs6(Left(vwx300), Left(vwx400), app(ty_Maybe, cfh), bcd) → new_esEs5(vwx300, vwx400, cfh)
new_esEs24(vwx301, vwx401, ty_Bool) → new_esEs12(vwx301, vwx401)
new_ltEs5(vwx312, vwx412, ty_Ordering) → new_ltEs18(vwx312, vwx412)
new_esEs8(vwx310, vwx410, app(ty_Ratio, bgf)) → new_esEs18(vwx310, vwx410, bgf)
new_esEs20(vwx300, vwx400, app(app(ty_@2, baa), bab)) → new_esEs4(vwx300, vwx400, baa, bab)
new_compare27(vwx30, vwx40, True) → EQ
new_ltEs7(Just(vwx310), Just(vwx410), ty_Bool) → new_ltEs10(vwx310, vwx410)
new_esEs12(False, True) → False
new_esEs12(True, False) → False
new_esEs5(Just(vwx300), Nothing, dh) → False
new_esEs5(Nothing, Just(vwx400), dh) → False
new_esEs14(Char(vwx300), Char(vwx400)) → new_primEqNat0(vwx300, vwx400)
new_esEs27(vwx300, vwx400, ty_Bool) → new_esEs12(vwx300, vwx400)
new_compare15(vwx300, vwx400, vwx301, vwx401) → new_primCmpInt(new_sr(vwx300, vwx400), new_sr(vwx301, vwx401))
new_esEs5(Just(vwx300), Just(vwx400), ty_Double) → new_esEs15(vwx300, vwx400)
new_esEs25(vwx302, vwx402, app(app(app(ty_@3, ceg), ceh), cfa)) → new_esEs7(vwx302, vwx402, ceg, ceh, cfa)
new_esEs28(vwx301, vwx401, app(ty_[], dbg)) → new_esEs17(vwx301, vwx401, dbg)
new_lt5(vwx311, vwx411, app(ty_Ratio, bgg)) → new_lt17(vwx311, vwx411, bgg)
new_esEs27(vwx300, vwx400, app(app(ty_@2, chh), daa)) → new_esEs4(vwx300, vwx400, chh, daa)
new_lt16(:(vwx300, vwx301), [], hh) → new_esEs19(GT, LT)
new_ltEs15(vwx31, vwx41) → new_not(new_esEs19(new_compare8(vwx31, vwx41), GT))
new_ltEs7(Just(vwx310), Nothing, cae) → False
new_primCompAux1(vwx300, vwx400, vwx301, vwx401, hh) → new_primCompAux00(vwx301, vwx401, new_compare0(vwx300, vwx400, hh), app(ty_[], hh))
new_esEs5(Just(vwx300), Just(vwx400), app(app(ty_Either, bhc), bhd)) → new_esEs6(vwx300, vwx400, bhc, bhd)
new_lt19(vwx30, vwx40, bce, bcf, bcg) → new_esEs19(new_compare35(vwx30, vwx40, bce, bcf, bcg), LT)
new_ltEs13(vwx31, vwx41) → new_not(new_esEs19(new_compare29(vwx31, vwx41), GT))
new_ltEs5(vwx312, vwx412, app(ty_Maybe, bfg)) → new_ltEs7(vwx312, vwx412, bfg)
new_lt20(vwx310, vwx410, ty_Integer) → new_lt15(vwx310, vwx410)
new_esEs5(Nothing, Nothing, dh) → True
new_ltEs19(vwx311, vwx411, app(ty_Maybe, da)) → new_ltEs7(vwx311, vwx411, da)
new_esEs28(vwx301, vwx401, app(ty_Maybe, dbh)) → new_esEs5(vwx301, vwx401, dbh)
new_lt5(vwx311, vwx411, app(app(ty_Either, beg), beh)) → new_lt12(vwx311, vwx411, beg, beh)
new_esEs5(Just(vwx300), Just(vwx400), app(app(app(ty_@3, bhh), caa), cab)) → new_esEs7(vwx300, vwx400, bhh, caa, cab)
new_ltEs7(Just(vwx310), Just(vwx410), app(ty_Ratio, caf)) → new_ltEs17(vwx310, vwx410, caf)
new_esEs5(Just(vwx300), Just(vwx400), ty_Integer) → new_esEs16(vwx300, vwx400)
new_primCompAux00(vwx144, vwx145, EQ, ty_Double) → new_compare14(vwx144, vwx145)
new_esEs28(vwx301, vwx401, ty_Float) → new_esEs11(vwx301, vwx401)
new_esEs8(vwx310, vwx410, ty_Float) → new_esEs11(vwx310, vwx410)
new_lt4(vwx310, vwx410, ty_Bool) → new_lt10(vwx310, vwx410)
new_esEs22(vwx301, vwx401, ty_Integer) → new_esEs16(vwx301, vwx401)
new_esEs28(vwx301, vwx401, ty_Int) → new_esEs10(vwx301, vwx401)
new_esEs9(vwx311, vwx411, app(ty_[], bfa)) → new_esEs17(vwx311, vwx411, bfa)
new_esEs8(vwx310, vwx410, app(ty_[], bdg)) → new_esEs17(vwx310, vwx410, bdg)
new_ltEs12(Left(vwx310), Left(vwx410), ty_Float, fd) → new_ltEs9(vwx310, vwx410)
new_compare42(vwx31, vwx41) → new_primCmpInt(vwx31, vwx41)
new_primCmpDouble(Double(vwx300, vwx301), Double(vwx400, vwx401)) → new_compare15(vwx300, vwx400, vwx301, vwx401)
new_esEs6(Left(vwx300), Left(vwx400), ty_Integer, bcd) → new_esEs16(vwx300, vwx400)
new_esEs26(vwx310, vwx410, app(app(ty_Either, bg), bh)) → new_esEs6(vwx310, vwx410, bg, bh)
new_primPlusNat1(Zero, Zero) → Zero
new_ltEs10(True, True) → True
new_esEs9(vwx311, vwx411, ty_Double) → new_esEs15(vwx311, vwx411)
new_lt20(vwx310, vwx410, app(app(app(ty_@3, cb), cc), cd)) → new_lt19(vwx310, vwx410, cb, cc, cd)
new_primCmpChar(Char(vwx300), Char(vwx400)) → new_primCmpNat0(vwx300, vwx400)
new_asAs(True, vwx139) → vwx139
new_esEs20(vwx300, vwx400, ty_Double) → new_esEs15(vwx300, vwx400)
new_primMulNat0(Succ(vwx30000), Succ(vwx40000)) → new_primPlusNat0(new_primMulNat0(vwx30000, Succ(vwx40000)), vwx40000)
new_ltEs5(vwx312, vwx412, ty_Integer) → new_ltEs15(vwx312, vwx412)
new_primCompAux00(vwx144, vwx145, EQ, app(app(ty_Either, bbe), bbf)) → new_compare13(vwx144, vwx145, bbe, bbf)
new_esEs25(vwx302, vwx402, ty_Float) → new_esEs11(vwx302, vwx402)
new_compare26(vwx30, vwx40, False, dh) → new_compare16(vwx30, vwx40, new_ltEs7(vwx30, vwx40, dh), dh)
new_esEs8(vwx310, vwx410, ty_@0) → new_esEs13(vwx310, vwx410)
new_esEs26(vwx310, vwx410, ty_Double) → new_esEs15(vwx310, vwx410)
new_esEs27(vwx300, vwx400, ty_Int) → new_esEs10(vwx300, vwx400)
new_ltEs19(vwx311, vwx411, ty_Ordering) → new_ltEs18(vwx311, vwx411)
new_ltEs12(Left(vwx310), Left(vwx410), ty_Double, fd) → new_ltEs14(vwx310, vwx410)
new_esEs28(vwx301, vwx401, app(ty_Ratio, dbf)) → new_esEs18(vwx301, vwx401, dbf)
new_esEs23(vwx300, vwx400, ty_Int) → new_esEs10(vwx300, vwx400)
new_esEs21(vwx300, vwx400, ty_Int) → new_esEs10(vwx300, vwx400)
new_ltEs12(Left(vwx310), Left(vwx410), app(app(app(ty_@3, gb), gc), gd), fd) → new_ltEs4(vwx310, vwx410, gb, gc, gd)
new_esEs17([], [], hh) → True
new_esEs17(:(vwx300, vwx301), [], hh) → False
new_esEs17([], :(vwx400, vwx401), hh) → False
new_lt20(vwx310, vwx410, ty_@0) → new_lt11(vwx310, vwx410)
new_ltEs7(Just(vwx310), Just(vwx410), app(ty_[], ef)) → new_ltEs16(vwx310, vwx410, ef)
new_esEs20(vwx300, vwx400, ty_Ordering) → new_esEs19(vwx300, vwx400)
new_compare9(vwx300, vwx400, bag, bah, bba) → new_compare35(vwx300, vwx400, bag, bah, bba)
new_esEs24(vwx301, vwx401, ty_Char) → new_esEs14(vwx301, vwx401)
new_compare0(vwx300, vwx400, ty_Integer) → new_compare8(vwx300, vwx400)
new_lt4(vwx310, vwx410, app(app(ty_Either, bde), bdf)) → new_lt12(vwx310, vwx410, bde, bdf)
new_compare10(vwx30, vwx40, True) → LT
new_esEs17(:(vwx300, vwx301), :(vwx400, vwx401), hh) → new_asAs(new_esEs20(vwx300, vwx400, hh), new_esEs17(vwx301, vwx401, hh))
new_primCompAux00(vwx144, vwx145, EQ, ty_Integer) → new_compare8(vwx144, vwx145)
new_ltEs5(vwx312, vwx412, ty_Double) → new_ltEs14(vwx312, vwx412)
new_lt4(vwx310, vwx410, ty_Ordering) → new_lt18(vwx310, vwx410)
new_compare0(vwx300, vwx400, ty_Ordering) → new_compare38(vwx300, vwx400)
new_compare10(vwx30, vwx40, False) → GT
new_esEs10(vwx30, vwx40) → new_primEqInt(vwx30, vwx40)
new_ltEs5(vwx312, vwx412, ty_Bool) → new_ltEs10(vwx312, vwx412)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_ltEs5(vwx312, vwx412, app(app(app(ty_@3, bgc), bgd), bge)) → new_ltEs4(vwx312, vwx412, bgc, bgd, bge)
new_esEs20(vwx300, vwx400, ty_@0) → new_esEs13(vwx300, vwx400)
new_ltEs12(Right(vwx310), Right(vwx410), ge, app(app(app(ty_@3, hd), he), hf)) → new_ltEs4(vwx310, vwx410, hd, he, hf)
new_esEs28(vwx301, vwx401, ty_Bool) → new_esEs12(vwx301, vwx401)
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_lt20(vwx310, vwx410, ty_Bool) → new_lt10(vwx310, vwx410)
new_compare0(vwx300, vwx400, ty_Double) → new_compare14(vwx300, vwx400)
new_esEs11(Float(vwx300, vwx301), Float(vwx400, vwx401)) → new_esEs10(new_sr(vwx300, vwx400), new_sr(vwx301, vwx401))
new_primCmpInt(Neg(Succ(vwx3000)), Pos(vwx400)) → LT
new_esEs6(Left(vwx300), Left(vwx400), ty_Int, bcd) → new_esEs10(vwx300, vwx400)
new_not(True) → False

The set Q consists of the following terms:

new_ltEs7(Just(x0), Nothing, x1)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_esEs13(@0, @0)
new_esEs26(x0, x1, ty_Double)
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_esEs20(x0, x1, ty_Bool)
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_ltEs12(Left(x0), Left(x1), ty_Integer, x2)
new_compare40(x0, x1)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_ltEs7(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs18(:%(x0, x1), :%(x2, x3), x4)
new_compare25(x0, x1, False, x2, x3, x4)
new_esEs9(x0, x1, ty_Ordering)
new_esEs9(x0, x1, ty_Integer)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs23(x0, x1, app(ty_[], x2))
new_esEs28(x0, x1, ty_Bool)
new_ltEs7(Nothing, Just(x0), x1)
new_esEs26(x0, x1, ty_Char)
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs7(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_lt5(x0, x1, app(ty_Ratio, x2))
new_lt20(x0, x1, ty_Int)
new_lt4(x0, x1, ty_Char)
new_ltEs11(x0, x1)
new_ltEs12(Left(x0), Left(x1), ty_Int, x2)
new_lt13(x0, x1)
new_esEs12(False, False)
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs12(Left(x0), Left(x1), ty_Float, x2)
new_esEs6(Left(x0), Left(x1), ty_Integer, x2)
new_ltEs12(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_ltEs19(x0, x1, ty_@0)
new_primMulInt(Neg(x0), Neg(x1))
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, ty_Int)
new_compare0(x0, x1, ty_Ordering)
new_esEs6(Left(x0), Left(x1), ty_Ordering, x2)
new_ltEs7(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, ty_Ordering)
new_esEs6(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs6(Left(x0), Left(x1), ty_@0, x2)
new_lt4(x0, x1, ty_Ordering)
new_esEs26(x0, x1, app(ty_[], x2))
new_lt5(x0, x1, ty_Bool)
new_primCompAux00(x0, x1, EQ, ty_Integer)
new_esEs6(Right(x0), Left(x1), x2, x3)
new_esEs6(Left(x0), Right(x1), x2, x3)
new_esEs26(x0, x1, ty_Int)
new_esEs23(x0, x1, ty_Ordering)
new_compare24(x0, x1, True, x2, x3)
new_esEs23(x0, x1, ty_Double)
new_esEs24(x0, x1, ty_Float)
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_lt19(x0, x1, x2, x3, x4)
new_lt20(x0, x1, ty_Char)
new_esEs20(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, ty_Int)
new_compare23(x0, x1, False)
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare19(:(x0, x1), :(x2, x3), x4)
new_compare39(x0, x1, x2)
new_esEs6(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_primCompAux00(x0, x1, EQ, app(ty_[], x2))
new_esEs26(x0, x1, ty_Ordering)
new_compare310(x0, x1)
new_esEs8(x0, x1, ty_Ordering)
new_esEs7(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs5(Just(x0), Just(x1), ty_Float)
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs12(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_compare11(x0, x1, True, x2, x3)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_primCompAux00(x0, x1, EQ, app(ty_Maybe, x2))
new_ltEs8(x0, x1)
new_sr(x0, x1)
new_esEs8(x0, x1, ty_Char)
new_ltEs12(Left(x0), Left(x1), ty_Double, x2)
new_lt16(:(x0, x1), [], x2)
new_esEs20(x0, x1, ty_Double)
new_esEs23(x0, x1, ty_Float)
new_esEs9(x0, x1, app(ty_Ratio, x2))
new_compare0(x0, x1, ty_Double)
new_ltEs18(GT, LT)
new_ltEs18(LT, GT)
new_primEqNat0(Zero, Zero)
new_primPlusNat1(Succ(x0), Zero)
new_ltEs5(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Left(x0), Left(x1), ty_Float, x2)
new_esEs26(x0, x1, ty_@0)
new_lt4(x0, x1, app(ty_Maybe, x2))
new_compare33(x0, x1)
new_esEs20(x0, x1, ty_Integer)
new_esEs5(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs16(Integer(x0), Integer(x1))
new_ltEs19(x0, x1, ty_Char)
new_primMulInt(Pos(x0), Pos(x1))
new_ltEs19(x0, x1, ty_Bool)
new_compare110(x0, x1, False, x2, x3)
new_ltEs12(Right(x0), Right(x1), x2, ty_Double)
new_primCompAux00(x0, x1, EQ, ty_Char)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_compare210(x0, x1, False, x2, x3)
new_esEs9(x0, x1, app(ty_[], x2))
new_ltEs5(x0, x1, app(ty_[], x2))
new_primCompAux00(x0, x1, EQ, app(app(app(ty_@3, x2), x3), x4))
new_lt5(x0, x1, ty_Float)
new_primMulNat0(Zero, Zero)
new_esEs25(x0, x1, ty_@0)
new_esEs24(x0, x1, ty_Ordering)
new_ltEs18(EQ, LT)
new_ltEs18(LT, EQ)
new_primCompAux00(x0, x1, EQ, ty_@0)
new_esEs5(Nothing, Nothing, x0)
new_compare27(x0, x1, True)
new_esEs25(x0, x1, ty_Double)
new_lt5(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_ltEs12(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs5(Just(x0), Just(x1), ty_Double)
new_primCompAux00(x0, x1, EQ, ty_Bool)
new_esEs25(x0, x1, ty_Ordering)
new_primCompAux00(x0, x1, EQ, ty_Float)
new_esEs27(x0, x1, ty_Bool)
new_lt5(x0, x1, ty_Char)
new_compare43(Integer(x0), Integer(x1), x2, x3, ty_Integer)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_ltEs12(Right(x0), Right(x1), x2, ty_@0)
new_esEs14(Char(x0), Char(x1))
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs20(x0, x1, ty_Char)
new_ltEs12(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_ltEs5(x0, x1, ty_Double)
new_esEs19(LT, LT)
new_ltEs12(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs19(GT, EQ)
new_esEs19(EQ, GT)
new_ltEs7(Just(x0), Just(x1), ty_Bool)
new_esEs17([], :(x0, x1), x2)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_ltEs13(x0, x1)
new_compare12(:%(x0, x1), :%(x2, x3), ty_Integer)
new_esEs22(x0, x1, ty_Integer)
new_primMulNat0(Zero, Succ(x0))
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_compare110(x0, x1, True, x2, x3)
new_lt5(x0, x1, ty_Double)
new_compare42(x0, x1)
new_ltEs12(Right(x0), Right(x1), x2, ty_Integer)
new_ltEs9(x0, x1)
new_asAs(False, x0)
new_compare41(x0, x1)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs20(x0, x1, ty_Int)
new_esEs26(x0, x1, ty_Float)
new_ltEs12(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_lt5(x0, x1, ty_Int)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_esEs5(Just(x0), Just(x1), ty_Char)
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_compare36(x0, x1, x2, x3)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs25(x0, x1, ty_Float)
new_primCompAux1(x0, x1, x2, x3, x4)
new_lt17(:%(x0, x1), :%(x2, x3), x4)
new_ltEs12(Right(x0), Right(x1), x2, ty_Char)
new_esEs27(x0, x1, ty_@0)
new_lt4(x0, x1, app(ty_Ratio, x2))
new_esEs9(x0, x1, app(app(ty_Either, x2), x3))
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs15(Double(x0, x1), Double(x2, x3))
new_esEs27(x0, x1, ty_Double)
new_primPlusNat0(Zero, x0)
new_ltEs12(Right(x0), Right(x1), x2, ty_Int)
new_esEs6(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_lt12(x0, x1, x2, x3)
new_esEs27(x0, x1, ty_Char)
new_esEs23(x0, x1, ty_Int)
new_lt14(x0, x1)
new_lt20(x0, x1, app(ty_[], x2))
new_primEqNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, Zero)
new_compare28(x0, x1, x2, x3)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_ltEs7(Just(x0), Just(x1), app(ty_[], x2))
new_esEs17([], [], x0)
new_esEs8(x0, x1, app(app(ty_@2, x2), x3))
new_esEs28(x0, x1, ty_Integer)
new_ltEs19(x0, x1, ty_Integer)
new_ltEs10(False, False)
new_esEs21(x0, x1, ty_Integer)
new_compare24(x0, x1, False, x2, x3)
new_esEs28(x0, x1, ty_Ordering)
new_esEs5(Just(x0), Just(x1), ty_Bool)
new_esEs9(x0, x1, ty_Int)
new_compare18(x0, x1, False)
new_esEs6(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_ltEs16(x0, x1, x2)
new_primCompAux00(x0, x1, LT, x2)
new_esEs9(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs12(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs28(x0, x1, ty_@0)
new_compare43(x0, x1, x2, x3, ty_Int)
new_ltEs19(x0, x1, ty_Int)
new_esEs5(Just(x0), Nothing, x1)
new_compare11(x0, x1, False, x2, x3)
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_lt4(x0, x1, ty_Bool)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_esEs24(x0, x1, ty_Char)
new_esEs12(True, True)
new_esEs27(x0, x1, ty_Float)
new_lt18(x0, x1)
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_compare0(x0, x1, app(ty_[], x2))
new_compare10(x0, x1, True)
new_lt20(x0, x1, ty_Bool)
new_compare19([], [], x0)
new_esEs5(Just(x0), Just(x1), ty_Ordering)
new_esEs6(Left(x0), Left(x1), ty_Bool, x2)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_esEs20(x0, x1, ty_Ordering)
new_esEs27(x0, x1, ty_Int)
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_compare29(x0, x1)
new_ltEs5(x0, x1, ty_Bool)
new_lt4(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs26(x0, x1, ty_Integer)
new_lt8(x0, x1)
new_lt5(x0, x1, app(ty_[], x2))
new_ltEs12(Left(x0), Left(x1), ty_Ordering, x2)
new_compare38(x0, x1)
new_esEs28(x0, x1, ty_Int)
new_lt20(x0, x1, ty_Integer)
new_esEs8(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs12(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs5(Just(x0), Just(x1), app(ty_Ratio, x2))
new_ltEs12(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_lt4(x0, x1, ty_Integer)
new_ltEs6(@2(x0, x1), @2(x2, x3), x4, x5)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs27(x0, x1, app(ty_[], x2))
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_lt4(x0, x1, ty_@0)
new_primEqInt(Neg(Zero), Neg(Zero))
new_ltEs19(x0, x1, ty_Float)
new_primCompAux00(x0, x1, EQ, ty_Double)
new_esEs24(x0, x1, ty_Double)
new_ltEs5(x0, x1, ty_@0)
new_lt5(x0, x1, ty_Ordering)
new_esEs23(x0, x1, ty_Integer)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs25(x0, x1, ty_Char)
new_compare0(x0, x1, app(ty_Ratio, x2))
new_esEs5(Just(x0), Just(x1), ty_Int)
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_ltEs18(LT, LT)
new_primPlusNat0(Succ(x0), x1)
new_lt4(x0, x1, app(ty_[], x2))
new_ltEs5(x0, x1, ty_Float)
new_compare0(x0, x1, ty_Integer)
new_lt9(x0, x1)
new_esEs5(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs5(x0, x1, app(ty_Maybe, x2))
new_compare10(x0, x1, False)
new_esEs24(x0, x1, ty_Bool)
new_ltEs12(Right(x0), Right(x1), x2, ty_Float)
new_compare7(@0, @0)
new_primCmpNat0(Zero, Succ(x0))
new_esEs6(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_compare25(x0, x1, True, x2, x3, x4)
new_esEs6(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs5(x0, x1, ty_Integer)
new_primPlusNat1(Succ(x0), Succ(x1))
new_compare37(x0, x1, x2)
new_compare0(x0, x1, ty_@0)
new_esEs6(Right(x0), Right(x1), x2, ty_Int)
new_esEs4(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs24(x0, x1, app(ty_[], x2))
new_lt16(:(x0, x1), :(x2, x3), x4)
new_ltEs15(x0, x1)
new_esEs22(x0, x1, ty_Int)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare18(x0, x1, True)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_esEs9(x0, x1, ty_Char)
new_compare35(x0, x1, x2, x3, x4)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_esEs6(Left(x0), Left(x1), ty_Double, x2)
new_lt5(x0, x1, ty_@0)
new_esEs8(x0, x1, ty_Double)
new_lt5(x0, x1, ty_Integer)
new_ltEs19(x0, x1, app(ty_[], x2))
new_lt5(x0, x1, app(app(ty_@2, x2), x3))
new_esEs24(x0, x1, ty_Integer)
new_primCompAux00(x0, x1, EQ, app(ty_Ratio, x2))
new_ltEs18(EQ, GT)
new_ltEs18(GT, EQ)
new_esEs28(x0, x1, ty_Double)
new_compare0(x0, x1, app(ty_Maybe, x2))
new_ltEs12(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_primCmpNat0(Zero, Zero)
new_ltEs12(Left(x0), Left(x1), ty_Bool, x2)
new_ltEs7(Just(x0), Just(x1), ty_Ordering)
new_lt15(Integer(x0), Integer(x1))
new_esEs8(x0, x1, app(ty_[], x2))
new_esEs6(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs7(Just(x0), Just(x1), ty_Integer)
new_ltEs5(x0, x1, ty_Int)
new_esEs17(:(x0, x1), [], x2)
new_primCompAux00(x0, x1, EQ, app(app(ty_@2, x2), x3))
new_esEs28(x0, x1, app(ty_[], x2))
new_esEs23(x0, x1, ty_Char)
new_ltEs7(Just(x0), Just(x1), ty_Int)
new_esEs8(x0, x1, ty_Bool)
new_ltEs10(True, True)
new_ltEs5(x0, x1, app(app(ty_Either, x2), x3))
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_ltEs7(Just(x0), Just(x1), ty_@0)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_esEs8(x0, x1, app(ty_Maybe, x2))
new_esEs6(Right(x0), Right(x1), x2, ty_@0)
new_esEs5(Just(x0), Just(x1), ty_Integer)
new_compare19(:(x0, x1), [], x2)
new_compare34(x0, x1, x2, x3)
new_esEs19(GT, GT)
new_ltEs12(Left(x0), Left(x1), ty_Char, x2)
new_lt4(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs12(Left(x0), Right(x1), x2, x3)
new_ltEs12(Right(x0), Left(x1), x2, x3)
new_esEs25(x0, x1, ty_Integer)
new_compare14(x0, x1)
new_ltEs5(x0, x1, app(ty_Ratio, x2))
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_primCmpDouble(Double(x0, x1), Double(x2, x3))
new_primEqNat0(Zero, Succ(x0))
new_esEs8(x0, x1, ty_@0)
new_lt5(x0, x1, app(app(ty_Either, x2), x3))
new_esEs6(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs9(x0, x1, app(app(ty_@2, x2), x3))
new_esEs12(False, True)
new_esEs12(True, False)
new_pePe(True, x0)
new_primMulNat0(Succ(x0), Zero)
new_lt6(x0, x1, x2, x3)
new_compare27(x0, x1, False)
new_esEs19(EQ, EQ)
new_esEs23(x0, x1, ty_@0)
new_primMulNat0(Succ(x0), Succ(x1))
new_esEs28(x0, x1, ty_Float)
new_lt4(x0, x1, ty_Float)
new_primCompAux00(x0, x1, EQ, ty_Ordering)
new_esEs10(x0, x1)
new_primCompAux00(x0, x1, GT, x2)
new_ltEs12(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs28(x0, x1, ty_Char)
new_primCmpNat0(Succ(x0), Succ(x1))
new_ltEs18(EQ, EQ)
new_compare0(x0, x1, ty_Bool)
new_esEs17(:(x0, x1), :(x2, x3), x4)
new_esEs23(x0, x1, ty_Bool)
new_ltEs7(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs5(Just(x0), Just(x1), ty_@0)
new_esEs19(EQ, LT)
new_esEs19(LT, EQ)
new_ltEs7(Nothing, Nothing, x0)
new_esEs27(x0, x1, ty_Integer)
new_esEs8(x0, x1, ty_Integer)
new_lt20(x0, x1, ty_Float)
new_esEs8(x0, x1, app(app(ty_Either, x2), x3))
new_compare210(x0, x1, True, x2, x3)
new_not(True)
new_compare26(x0, x1, False, x2)
new_esEs19(GT, LT)
new_esEs19(LT, GT)
new_compare9(x0, x1, x2, x3, x4)
new_ltEs5(x0, x1, ty_Ordering)
new_primCompAux00(x0, x1, EQ, ty_Int)
new_ltEs7(Just(x0), Just(x1), ty_Double)
new_esEs9(x0, x1, ty_Bool)
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, ty_Ordering)
new_esEs25(x0, x1, ty_Bool)
new_lt16([], :(x0, x1), x2)
new_lt4(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_not(False)
new_lt4(x0, x1, ty_Double)
new_lt20(x0, x1, ty_@0)
new_primCompAux00(x0, x1, EQ, app(app(ty_Either, x2), x3))
new_esEs6(Left(x0), Left(x1), ty_Char, x2)
new_compare0(x0, x1, app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, ty_Double)
new_compare0(x0, x1, app(app(ty_Either, x2), x3))
new_esEs6(Right(x0), Right(x1), x2, ty_Char)
new_ltEs12(Left(x0), Left(x1), ty_@0, x2)
new_esEs6(Right(x0), Right(x1), x2, ty_Double)
new_esEs6(Left(x0), Left(x1), ty_Int, x2)
new_ltEs4(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_ltEs7(Just(x0), Just(x1), app(ty_Maybe, x2))
new_ltEs17(x0, x1, x2)
new_esEs8(x0, x1, ty_Float)
new_esEs6(Right(x0), Right(x1), x2, ty_Float)
new_esEs5(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs9(x0, x1, ty_@0)
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs25(x0, x1, app(ty_[], x2))
new_compare17(x0, x1, True, x2, x3, x4)
new_compare0(x0, x1, ty_Char)
new_esEs24(x0, x1, ty_@0)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs7(Just(x0), Just(x1), ty_Char)
new_sr0(Integer(x0), Integer(x1))
new_ltEs12(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_lt16([], [], x0)
new_ltEs18(GT, GT)
new_ltEs12(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_compare16(x0, x1, True, x2)
new_asAs(True, x0)
new_esEs5(Just(x0), Just(x1), app(ty_[], x2))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_compare0(x0, x1, ty_Int)
new_esEs20(x0, x1, ty_Float)
new_esEs6(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs20(x0, x1, ty_@0)
new_ltEs10(False, True)
new_ltEs10(True, False)
new_primCmpFloat(Float(x0, x1), Float(x2, x3))
new_esEs8(x0, x1, ty_Int)
new_lt5(x0, x1, app(ty_Maybe, x2))
new_lt11(@0, @0)
new_compare17(x0, x1, False, x2, x3, x4)
new_ltEs7(Just(x0), Just(x1), ty_Float)
new_esEs9(x0, x1, ty_Float)
new_esEs6(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs12(Right(x0), Right(x1), x2, ty_Bool)
new_pePe(False, x0)
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_compare0(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_ltEs5(x0, x1, app(app(ty_@2, x2), x3))
new_primEqInt(Pos(Zero), Pos(Zero))
new_esEs8(x0, x1, app(ty_Ratio, x2))
new_esEs11(Float(x0, x1), Float(x2, x3))
new_ltEs14(x0, x1)
new_ltEs5(x0, x1, ty_Char)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare15(x0, x1, x2, x3)
new_lt20(x0, x1, ty_Ordering)
new_compare13(x0, x1, x2, x3)
new_lt7(x0, x1, x2)
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_lt20(x0, x1, ty_Double)
new_primCmpChar(Char(x0), Char(x1))
new_esEs24(x0, x1, ty_Int)
new_esEs26(x0, x1, ty_Bool)
new_compare12(:%(x0, x1), :%(x2, x3), ty_Int)
new_primPlusNat1(Zero, Succ(x0))
new_esEs5(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_primCmpNat0(Succ(x0), Zero)
new_compare8(Integer(x0), Integer(x1))
new_compare16(x0, x1, False, x2)
new_esEs5(Nothing, Just(x0), x1)
new_lt10(x0, x1)
new_esEs6(Right(x0), Right(x1), x2, ty_Integer)
new_compare0(x0, x1, ty_Float)
new_lt4(x0, x1, ty_Int)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs9(x0, x1, app(ty_Maybe, x2))
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_compare23(x0, x1, True)
new_compare26(x0, x1, True, x2)
new_esEs9(x0, x1, ty_Double)
new_compare19([], :(x0, x1), x2)

We have to consider all minimal (P,Q,R)-chains.
As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [15] we can delete all non-usable rules [17] from R.

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

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

new_ltEs2(:(vwx310, vwx311), :(vwx410, vwx411), hg) → new_primCompAux(vwx310, vwx410, vwx311, vwx411, hg)
new_lt(vwx30, vwx40, ba, bb) → new_compare2(vwx30, vwx40, new_esEs4(vwx30, vwx40, ba, bb), ba, bb)
new_ltEs0(Just(vwx310), Just(vwx410), app(app(app(ty_@3, eg), eh), fa)) → new_ltEs3(vwx310, vwx410, eg, eh, fa)
new_ltEs3(@3(vwx310, vwx311, vwx312), @3(vwx410, vwx411, vwx412), bec, app(ty_Maybe, bef), bdc) → new_lt0(vwx311, vwx411, bef)
new_ltEs3(@3(vwx310, vwx311, vwx312), @3(vwx410, vwx411, vwx412), bec, app(app(ty_Either, beg), beh), bdc) → new_lt1(vwx311, vwx411, beg, beh)
new_compare2(vwx30, vwx40, False, ba, bb) → new_ltEs(vwx30, vwx40, ba, bb)
new_ltEs(@2(vwx310, vwx311), @2(vwx410, vwx411), app(ty_Maybe, bf), be) → new_lt0(vwx310, vwx410, bf)
new_ltEs1(Left(vwx310), Left(vwx410), app(app(ty_Either, fg), fh), fd) → new_ltEs1(vwx310, vwx410, fg, fh)
new_ltEs(@2(vwx310, vwx311), @2(vwx410, vwx411), app(ty_[], ca), be) → new_lt2(vwx310, vwx410, ca)
new_ltEs1(Left(vwx310), Left(vwx410), app(ty_Maybe, ff), fd) → new_ltEs0(vwx310, vwx410, ff)
new_compare32(vwx30, vwx40, bce, bcf, bcg) → new_compare22(vwx30, vwx40, new_esEs7(vwx30, vwx40, bce, bcf, bcg), bce, bcf, bcg)
new_ltEs1(Right(vwx310), Right(vwx410), ge, app(app(app(ty_@3, hd), he), hf)) → new_ltEs3(vwx310, vwx410, hd, he, hf)
new_ltEs3(@3(vwx310, vwx311, vwx312), @3(vwx410, vwx411, vwx412), bec, app(ty_[], bfa), bdc) → new_lt2(vwx311, vwx411, bfa)
new_ltEs1(Left(vwx310), Left(vwx410), app(app(ty_@2, fb), fc), fd) → new_ltEs(vwx310, vwx410, fb, fc)
new_compare(:(vwx310, vwx311), :(vwx410, vwx411), hg) → new_primCompAux(vwx310, vwx410, vwx311, vwx411, hg)
new_ltEs3(@3(vwx310, vwx311, vwx312), @3(vwx410, vwx411, vwx412), app(app(ty_@2, bch), bda), bdb, bdc) → new_lt(vwx310, vwx410, bch, bda)
new_ltEs(@2(vwx310, vwx311), @2(vwx410, vwx411), app(app(app(ty_@3, cb), cc), cd), be) → new_lt3(vwx310, vwx410, cb, cc, cd)
new_compare31(vwx30, vwx40, bcc, bcd) → new_compare21(vwx30, vwx40, new_esEs6(vwx30, vwx40, bcc, bcd), bcc, bcd)
new_ltEs3(@3(vwx310, vwx311, vwx312), @3(vwx410, vwx411, vwx412), app(ty_[], bdg), bdb, bdc) → new_lt2(vwx310, vwx410, bdg)
new_ltEs1(Left(vwx310), Left(vwx410), app(ty_[], ga), fd) → new_ltEs2(vwx310, vwx410, ga)
new_primCompAux(vwx300, vwx400, vwx301, vwx401, hh) → new_primCompAux0(vwx301, vwx401, new_compare0(vwx300, vwx400, hh), app(ty_[], hh))
new_ltEs0(Just(vwx310), Just(vwx410), app(ty_Maybe, ec)) → new_ltEs0(vwx310, vwx410, ec)
new_compare22(vwx30, vwx40, False, bce, bcf, bcg) → new_ltEs3(vwx30, vwx40, bce, bcf, bcg)
new_ltEs3(@3(vwx310, vwx311, vwx312), @3(vwx410, vwx411, vwx412), app(app(ty_Either, bde), bdf), bdb, bdc) → new_lt1(vwx310, vwx410, bde, bdf)
new_lt2(:(vwx300, vwx301), :(vwx400, vwx401), app(app(ty_Either, bac), bad)) → new_compare31(vwx300, vwx400, bac, bad)
new_primCompAux(vwx300, vwx400, vwx301, vwx401, app(app(ty_@2, baa), bab)) → new_compare3(vwx300, vwx400, baa, bab)
new_ltEs3(@3(vwx310, vwx311, vwx312), @3(vwx410, vwx411, vwx412), bec, bdb, app(ty_Maybe, bfg)) → new_ltEs0(vwx312, vwx412, bfg)
new_ltEs3(@3(vwx310, vwx311, vwx312), @3(vwx410, vwx411, vwx412), bec, bdb, app(ty_[], bgb)) → new_ltEs2(vwx312, vwx412, bgb)
new_ltEs(@2(vwx310, vwx311), @2(vwx410, vwx411), app(app(ty_@2, bc), bd), be) → new_lt(vwx310, vwx410, bc, bd)
new_ltEs1(Right(vwx310), Right(vwx410), ge, app(app(ty_@2, gf), gg)) → new_ltEs(vwx310, vwx410, gf, gg)
new_lt3(vwx30, vwx40, bce, bcf, bcg) → new_compare22(vwx30, vwx40, new_esEs7(vwx30, vwx40, bce, bcf, bcg), bce, bcf, bcg)
new_primCompAux(vwx300, vwx400, vwx301, vwx401, app(app(app(ty_@3, bag), bah), bba)) → new_compare32(vwx300, vwx400, bag, bah, bba)
new_compare21(vwx30, vwx40, False, bcc, bcd) → new_ltEs1(vwx30, vwx40, bcc, bcd)
new_ltEs1(Right(vwx310), Right(vwx410), ge, app(ty_Maybe, gh)) → new_ltEs0(vwx310, vwx410, gh)
new_compare3(vwx30, vwx40, ba, bb) → new_compare2(vwx30, vwx40, new_esEs4(vwx30, vwx40, ba, bb), ba, bb)
new_compare30(vwx30, vwx40, dh) → new_compare20(vwx30, vwx40, new_esEs5(vwx30, vwx40, dh), dh)
new_ltEs(@2(vwx310, vwx311), @2(vwx410, vwx411), app(app(ty_Either, bg), bh), be) → new_lt1(vwx310, vwx410, bg, bh)
new_ltEs(@2(vwx310, vwx311), @2(vwx410, vwx411), ce, app(app(app(ty_@3, de), df), dg)) → new_ltEs3(vwx311, vwx411, de, df, dg)
new_lt1(vwx30, vwx40, bcc, bcd) → new_compare21(vwx30, vwx40, new_esEs6(vwx30, vwx40, bcc, bcd), bcc, bcd)
new_lt2(:(vwx300, vwx301), :(vwx400, vwx401), app(app(app(ty_@3, bag), bah), bba)) → new_compare32(vwx300, vwx400, bag, bah, bba)
new_ltEs1(Right(vwx310), Right(vwx410), ge, app(ty_[], hc)) → new_ltEs2(vwx310, vwx410, hc)
new_lt2(:(vwx300, vwx301), :(vwx400, vwx401), app(ty_[], bae)) → new_compare(vwx300, vwx400, bae)
new_primCompAux(vwx300, vwx400, vwx301, vwx401, app(ty_[], bae)) → new_compare(vwx300, vwx400, bae)
new_primCompAux0(vwx144, vwx145, EQ, app(ty_[], bbg)) → new_compare(vwx144, vwx145, bbg)
new_ltEs3(@3(vwx310, vwx311, vwx312), @3(vwx410, vwx411, vwx412), bec, bdb, app(app(ty_@2, bfe), bff)) → new_ltEs(vwx312, vwx412, bfe, bff)
new_lt2(:(vwx300, vwx301), :(vwx400, vwx401), app(ty_Maybe, baf)) → new_compare30(vwx300, vwx400, baf)
new_ltEs3(@3(vwx310, vwx311, vwx312), @3(vwx410, vwx411, vwx412), bec, app(app(ty_@2, bed), bee), bdc) → new_lt(vwx311, vwx411, bed, bee)
new_ltEs3(@3(vwx310, vwx311, vwx312), @3(vwx410, vwx411, vwx412), bec, bdb, app(app(app(ty_@3, bgc), bgd), bge)) → new_ltEs3(vwx312, vwx412, bgc, bgd, bge)
new_ltEs0(Just(vwx310), Just(vwx410), app(ty_[], ef)) → new_ltEs2(vwx310, vwx410, ef)
new_ltEs3(@3(vwx310, vwx311, vwx312), @3(vwx410, vwx411, vwx412), app(app(app(ty_@3, bdh), bea), beb), bdb, bdc) → new_lt3(vwx310, vwx410, bdh, bea, beb)
new_ltEs3(@3(vwx310, vwx311, vwx312), @3(vwx410, vwx411, vwx412), bec, bdb, app(app(ty_Either, bfh), bga)) → new_ltEs1(vwx312, vwx412, bfh, bga)
new_ltEs0(Just(vwx310), Just(vwx410), app(app(ty_@2, ea), eb)) → new_ltEs(vwx310, vwx410, ea, eb)
new_ltEs0(Just(vwx310), Just(vwx410), app(app(ty_Either, ed), ee)) → new_ltEs1(vwx310, vwx410, ed, ee)
new_ltEs(@2(vwx310, vwx311), @2(vwx410, vwx411), ce, app(app(ty_@2, cf), cg)) → new_ltEs(vwx311, vwx411, cf, cg)
new_ltEs1(Right(vwx310), Right(vwx410), ge, app(app(ty_Either, ha), hb)) → new_ltEs1(vwx310, vwx410, ha, hb)
new_ltEs3(@3(vwx310, vwx311, vwx312), @3(vwx410, vwx411, vwx412), bec, app(app(app(ty_@3, bfb), bfc), bfd), bdc) → new_lt3(vwx311, vwx411, bfb, bfc, bfd)
new_ltEs(@2(vwx310, vwx311), @2(vwx410, vwx411), ce, app(ty_[], dd)) → new_ltEs2(vwx311, vwx411, dd)
new_lt2(:(vwx300, vwx301), :(vwx400, vwx401), hh) → new_primCompAux0(vwx301, vwx401, new_compare0(vwx300, vwx400, hh), app(ty_[], hh))
new_ltEs(@2(vwx310, vwx311), @2(vwx410, vwx411), ce, app(ty_Maybe, da)) → new_ltEs0(vwx311, vwx411, da)
new_primCompAux(vwx300, vwx400, vwx301, vwx401, app(app(ty_Either, bac), bad)) → new_compare31(vwx300, vwx400, bac, bad)
new_lt2(:(vwx300, vwx301), :(vwx400, vwx401), app(app(ty_@2, baa), bab)) → new_compare3(vwx300, vwx400, baa, bab)
new_primCompAux(vwx300, vwx400, vwx301, vwx401, app(ty_Maybe, baf)) → new_compare30(vwx300, vwx400, baf)
new_ltEs(@2(vwx310, vwx311), @2(vwx410, vwx411), ce, app(app(ty_Either, db), dc)) → new_ltEs1(vwx311, vwx411, db, dc)
new_compare20(vwx30, vwx40, False, dh) → new_ltEs0(vwx30, vwx40, dh)
new_ltEs1(Left(vwx310), Left(vwx410), app(app(app(ty_@3, gb), gc), gd), fd) → new_ltEs3(vwx310, vwx410, gb, gc, gd)
new_lt0(vwx30, vwx40, dh) → new_compare20(vwx30, vwx40, new_esEs5(vwx30, vwx40, dh), dh)
new_ltEs3(@3(vwx310, vwx311, vwx312), @3(vwx410, vwx411, vwx412), app(ty_Maybe, bdd), bdb, bdc) → new_lt0(vwx310, vwx410, bdd)

The TRS R consists of the following rules:

new_esEs6(Right(vwx300), Right(vwx400), bcc, app(ty_Maybe, chb)) → new_esEs5(vwx300, vwx400, chb)
new_esEs5(Just(vwx300), Just(vwx400), app(app(ty_Either, bhc), bhd)) → new_esEs6(vwx300, vwx400, bhc, bhd)
new_esEs6(Left(vwx300), Left(vwx400), app(app(ty_Either, cfd), cfe), bcd) → new_esEs6(vwx300, vwx400, cfd, cfe)
new_esEs5(Just(vwx300), Just(vwx400), app(ty_Maybe, bhg)) → new_esEs5(vwx300, vwx400, bhg)
new_esEs6(Right(vwx300), Right(vwx400), bcc, app(app(ty_Either, cgf), cgg)) → new_esEs6(vwx300, vwx400, cgf, cgg)
new_esEs6(Left(vwx300), Left(vwx400), app(ty_Maybe, cfh), bcd) → new_esEs5(vwx300, vwx400, cfh)
new_esEs5(Just(vwx300), Just(vwx400), ty_Ordering) → new_esEs19(vwx300, vwx400)
new_esEs5(Just(vwx300), Just(vwx400), app(ty_[], bhf)) → new_esEs17(vwx300, vwx400, bhf)
new_esEs5(Just(vwx300), Just(vwx400), app(app(ty_@2, bha), bhb)) → new_esEs4(vwx300, vwx400, bha, bhb)
new_esEs5(Just(vwx300), Just(vwx400), ty_Int) → new_esEs10(vwx300, vwx400)
new_esEs5(Just(vwx300), Just(vwx400), ty_Bool) → new_esEs12(vwx300, vwx400)
new_esEs5(Just(vwx300), Just(vwx400), ty_@0) → new_esEs13(vwx300, vwx400)
new_esEs5(Just(vwx300), Just(vwx400), ty_Char) → new_esEs14(vwx300, vwx400)
new_esEs5(Just(vwx300), Just(vwx400), ty_Float) → new_esEs11(vwx300, vwx400)
new_esEs5(Just(vwx300), Just(vwx400), app(ty_Ratio, bhe)) → new_esEs18(vwx300, vwx400, bhe)
new_esEs5(Just(vwx300), Nothing, dh) → False
new_esEs5(Nothing, Just(vwx400), dh) → False
new_esEs5(Just(vwx300), Just(vwx400), ty_Double) → new_esEs15(vwx300, vwx400)
new_esEs5(Nothing, Nothing, dh) → True
new_esEs5(Just(vwx300), Just(vwx400), app(app(app(ty_@3, bhh), caa), cab)) → new_esEs7(vwx300, vwx400, bhh, caa, cab)
new_esEs5(Just(vwx300), Just(vwx400), ty_Integer) → new_esEs16(vwx300, vwx400)
new_esEs16(Integer(vwx300), Integer(vwx400)) → new_primEqInt(vwx300, vwx400)
new_primEqInt(Neg(Succ(vwx3000)), Neg(Succ(vwx4000))) → new_primEqNat0(vwx3000, vwx4000)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Succ(vwx3000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(vwx4000))) → False
new_primEqInt(Pos(Succ(vwx3000)), Pos(Succ(vwx4000))) → new_primEqNat0(vwx3000, vwx4000)
new_primEqInt(Pos(Succ(vwx3000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(vwx4000))) → False
new_primEqInt(Pos(Succ(vwx3000)), Neg(vwx400)) → False
new_primEqInt(Neg(Succ(vwx3000)), Pos(vwx400)) → False
new_primEqInt(Pos(Zero), Neg(Succ(vwx4000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(vwx4000))) → False
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqNat0(Zero, Zero) → True
new_primEqNat0(Succ(vwx3000), Succ(vwx4000)) → new_primEqNat0(vwx3000, vwx4000)
new_primEqNat0(Succ(vwx3000), Zero) → False
new_primEqNat0(Zero, Succ(vwx4000)) → False
new_esEs7(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), bce, bcf, bcg) → new_asAs(new_esEs23(vwx300, vwx400, bce), new_asAs(new_esEs24(vwx301, vwx401, bcf), new_esEs25(vwx302, vwx402, bcg)))
new_esEs23(vwx300, vwx400, app(app(ty_@2, cbd), cbe)) → new_esEs4(vwx300, vwx400, cbd, cbe)
new_esEs23(vwx300, vwx400, app(ty_[], cca)) → new_esEs17(vwx300, vwx400, cca)
new_esEs23(vwx300, vwx400, ty_Bool) → new_esEs12(vwx300, vwx400)
new_esEs23(vwx300, vwx400, ty_@0) → new_esEs13(vwx300, vwx400)
new_esEs23(vwx300, vwx400, app(app(app(ty_@3, ccc), ccd), cce)) → new_esEs7(vwx300, vwx400, ccc, ccd, cce)
new_esEs23(vwx300, vwx400, app(app(ty_Either, cbf), cbg)) → new_esEs6(vwx300, vwx400, cbf, cbg)
new_esEs23(vwx300, vwx400, ty_Char) → new_esEs14(vwx300, vwx400)
new_esEs23(vwx300, vwx400, ty_Integer) → new_esEs16(vwx300, vwx400)
new_esEs23(vwx300, vwx400, ty_Ordering) → new_esEs19(vwx300, vwx400)
new_esEs23(vwx300, vwx400, ty_Double) → new_esEs15(vwx300, vwx400)
new_esEs23(vwx300, vwx400, ty_Float) → new_esEs11(vwx300, vwx400)
new_esEs23(vwx300, vwx400, app(ty_Ratio, cbh)) → new_esEs18(vwx300, vwx400, cbh)
new_esEs23(vwx300, vwx400, app(ty_Maybe, ccb)) → new_esEs5(vwx300, vwx400, ccb)
new_esEs23(vwx300, vwx400, ty_Int) → new_esEs10(vwx300, vwx400)
new_esEs24(vwx301, vwx401, ty_@0) → new_esEs13(vwx301, vwx401)
new_esEs24(vwx301, vwx401, app(ty_Ratio, cdb)) → new_esEs18(vwx301, vwx401, cdb)
new_esEs24(vwx301, vwx401, app(app(ty_@2, ccf), ccg)) → new_esEs4(vwx301, vwx401, ccf, ccg)
new_esEs24(vwx301, vwx401, app(app(ty_Either, cch), cda)) → new_esEs6(vwx301, vwx401, cch, cda)
new_esEs24(vwx301, vwx401, ty_Ordering) → new_esEs19(vwx301, vwx401)
new_esEs24(vwx301, vwx401, app(ty_[], cdc)) → new_esEs17(vwx301, vwx401, cdc)
new_esEs24(vwx301, vwx401, app(ty_Maybe, cdd)) → new_esEs5(vwx301, vwx401, cdd)
new_esEs24(vwx301, vwx401, ty_Double) → new_esEs15(vwx301, vwx401)
new_esEs24(vwx301, vwx401, ty_Integer) → new_esEs16(vwx301, vwx401)
new_esEs24(vwx301, vwx401, app(app(app(ty_@3, cde), cdf), cdg)) → new_esEs7(vwx301, vwx401, cde, cdf, cdg)
new_esEs24(vwx301, vwx401, ty_Int) → new_esEs10(vwx301, vwx401)
new_esEs24(vwx301, vwx401, ty_Float) → new_esEs11(vwx301, vwx401)
new_esEs24(vwx301, vwx401, ty_Bool) → new_esEs12(vwx301, vwx401)
new_esEs24(vwx301, vwx401, ty_Char) → new_esEs14(vwx301, vwx401)
new_esEs25(vwx302, vwx402, app(app(ty_Either, ceb), cec)) → new_esEs6(vwx302, vwx402, ceb, cec)
new_esEs25(vwx302, vwx402, app(app(ty_@2, cdh), cea)) → new_esEs4(vwx302, vwx402, cdh, cea)
new_esEs25(vwx302, vwx402, app(ty_Ratio, ced)) → new_esEs18(vwx302, vwx402, ced)
new_esEs25(vwx302, vwx402, ty_Double) → new_esEs15(vwx302, vwx402)
new_esEs25(vwx302, vwx402, ty_Char) → new_esEs14(vwx302, vwx402)
new_esEs25(vwx302, vwx402, app(ty_Maybe, cef)) → new_esEs5(vwx302, vwx402, cef)
new_esEs25(vwx302, vwx402, ty_Int) → new_esEs10(vwx302, vwx402)
new_esEs25(vwx302, vwx402, ty_@0) → new_esEs13(vwx302, vwx402)
new_esEs25(vwx302, vwx402, ty_Integer) → new_esEs16(vwx302, vwx402)
new_esEs25(vwx302, vwx402, ty_Ordering) → new_esEs19(vwx302, vwx402)
new_esEs25(vwx302, vwx402, ty_Bool) → new_esEs12(vwx302, vwx402)
new_esEs25(vwx302, vwx402, app(ty_[], cee)) → new_esEs17(vwx302, vwx402, cee)
new_esEs25(vwx302, vwx402, app(app(app(ty_@3, ceg), ceh), cfa)) → new_esEs7(vwx302, vwx402, ceg, ceh, cfa)
new_esEs25(vwx302, vwx402, ty_Float) → new_esEs11(vwx302, vwx402)
new_asAs(False, vwx139) → False
new_asAs(True, vwx139) → vwx139
new_esEs11(Float(vwx300, vwx301), Float(vwx400, vwx401)) → new_esEs10(new_sr(vwx300, vwx400), new_sr(vwx301, vwx401))
new_sr(vwx300, vwx400) → new_primMulInt(vwx300, vwx400)
new_esEs10(vwx30, vwx40) → new_primEqInt(vwx30, vwx40)
new_primMulInt(Pos(vwx3000), Pos(vwx4000)) → Pos(new_primMulNat0(vwx3000, vwx4000))
new_primMulInt(Neg(vwx3000), Neg(vwx4000)) → Pos(new_primMulNat0(vwx3000, vwx4000))
new_primMulInt(Pos(vwx3000), Neg(vwx4000)) → Neg(new_primMulNat0(vwx3000, vwx4000))
new_primMulInt(Neg(vwx3000), Pos(vwx4000)) → Neg(new_primMulNat0(vwx3000, vwx4000))
new_primMulNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, Succ(vwx40000)) → Zero
new_primMulNat0(Succ(vwx30000), Zero) → Zero
new_primMulNat0(Succ(vwx30000), Succ(vwx40000)) → new_primPlusNat0(new_primMulNat0(vwx30000, Succ(vwx40000)), vwx40000)
new_primPlusNat0(Succ(vwx1540), vwx40000) → Succ(Succ(new_primPlusNat1(vwx1540, vwx40000)))
new_primPlusNat0(Zero, vwx40000) → Succ(vwx40000)
new_primPlusNat1(Succ(vwx15400), Zero) → Succ(vwx15400)
new_primPlusNat1(Zero, Succ(vwx400000)) → Succ(vwx400000)
new_primPlusNat1(Succ(vwx15400), Succ(vwx400000)) → Succ(Succ(new_primPlusNat1(vwx15400, vwx400000)))
new_primPlusNat1(Zero, Zero) → Zero
new_esEs17([], [], hh) → True
new_esEs17(:(vwx300, vwx301), [], hh) → False
new_esEs17([], :(vwx400, vwx401), hh) → False
new_esEs17(:(vwx300, vwx301), :(vwx400, vwx401), hh) → new_asAs(new_esEs20(vwx300, vwx400, hh), new_esEs17(vwx301, vwx401, hh))
new_esEs20(vwx300, vwx400, ty_Bool) → new_esEs12(vwx300, vwx400)
new_esEs20(vwx300, vwx400, ty_Float) → new_esEs11(vwx300, vwx400)
new_esEs20(vwx300, vwx400, app(app(app(ty_@3, bag), bah), bba)) → new_esEs7(vwx300, vwx400, bag, bah, bba)
new_esEs20(vwx300, vwx400, ty_Integer) → new_esEs16(vwx300, vwx400)
new_esEs20(vwx300, vwx400, ty_Int) → new_esEs10(vwx300, vwx400)
new_esEs20(vwx300, vwx400, ty_Char) → new_esEs14(vwx300, vwx400)
new_esEs20(vwx300, vwx400, app(ty_[], bae)) → new_esEs17(vwx300, vwx400, bae)
new_esEs20(vwx300, vwx400, app(app(ty_Either, bac), bad)) → new_esEs6(vwx300, vwx400, bac, bad)
new_esEs20(vwx300, vwx400, app(ty_Ratio, cad)) → new_esEs18(vwx300, vwx400, cad)
new_esEs20(vwx300, vwx400, app(ty_Maybe, baf)) → new_esEs5(vwx300, vwx400, baf)
new_esEs20(vwx300, vwx400, app(app(ty_@2, baa), bab)) → new_esEs4(vwx300, vwx400, baa, bab)
new_esEs20(vwx300, vwx400, ty_Double) → new_esEs15(vwx300, vwx400)
new_esEs20(vwx300, vwx400, ty_Ordering) → new_esEs19(vwx300, vwx400)
new_esEs20(vwx300, vwx400, ty_@0) → new_esEs13(vwx300, vwx400)
new_esEs13(@0, @0) → True
new_esEs19(GT, GT) → True
new_esEs19(EQ, EQ) → True
new_esEs19(LT, EQ) → False
new_esEs19(EQ, LT) → False
new_esEs19(LT, GT) → False
new_esEs19(GT, LT) → False
new_esEs19(LT, LT) → True
new_esEs19(EQ, GT) → False
new_esEs19(GT, EQ) → False
new_esEs15(Double(vwx300, vwx301), Double(vwx400, vwx401)) → new_esEs10(new_sr(vwx300, vwx400), new_sr(vwx301, vwx401))
new_esEs4(@2(vwx300, vwx301), @2(vwx400, vwx401), ba, bb) → new_asAs(new_esEs27(vwx300, vwx400, ba), new_esEs28(vwx301, vwx401, bb))
new_esEs27(vwx300, vwx400, app(ty_Ratio, dad)) → new_esEs18(vwx300, vwx400, dad)
new_esEs27(vwx300, vwx400, ty_Ordering) → new_esEs19(vwx300, vwx400)
new_esEs27(vwx300, vwx400, ty_Float) → new_esEs11(vwx300, vwx400)
new_esEs27(vwx300, vwx400, app(ty_[], dae)) → new_esEs17(vwx300, vwx400, dae)
new_esEs27(vwx300, vwx400, app(app(app(ty_@3, dag), dah), dba)) → new_esEs7(vwx300, vwx400, dag, dah, dba)
new_esEs27(vwx300, vwx400, app(ty_Maybe, daf)) → new_esEs5(vwx300, vwx400, daf)
new_esEs27(vwx300, vwx400, app(app(ty_Either, dab), dac)) → new_esEs6(vwx300, vwx400, dab, dac)
new_esEs27(vwx300, vwx400, ty_Double) → new_esEs15(vwx300, vwx400)
new_esEs27(vwx300, vwx400, ty_Char) → new_esEs14(vwx300, vwx400)
new_esEs27(vwx300, vwx400, ty_Integer) → new_esEs16(vwx300, vwx400)
new_esEs27(vwx300, vwx400, ty_@0) → new_esEs13(vwx300, vwx400)
new_esEs27(vwx300, vwx400, ty_Bool) → new_esEs12(vwx300, vwx400)
new_esEs27(vwx300, vwx400, app(app(ty_@2, chh), daa)) → new_esEs4(vwx300, vwx400, chh, daa)
new_esEs27(vwx300, vwx400, ty_Int) → new_esEs10(vwx300, vwx400)
new_esEs28(vwx301, vwx401, ty_Ordering) → new_esEs19(vwx301, vwx401)
new_esEs28(vwx301, vwx401, ty_@0) → new_esEs13(vwx301, vwx401)
new_esEs28(vwx301, vwx401, ty_Char) → new_esEs14(vwx301, vwx401)
new_esEs28(vwx301, vwx401, ty_Double) → new_esEs15(vwx301, vwx401)
new_esEs28(vwx301, vwx401, ty_Integer) → new_esEs16(vwx301, vwx401)
new_esEs28(vwx301, vwx401, app(app(ty_Either, dbd), dbe)) → new_esEs6(vwx301, vwx401, dbd, dbe)
new_esEs28(vwx301, vwx401, app(app(app(ty_@3, dca), dcb), dcc)) → new_esEs7(vwx301, vwx401, dca, dcb, dcc)
new_esEs28(vwx301, vwx401, app(app(ty_@2, dbb), dbc)) → new_esEs4(vwx301, vwx401, dbb, dbc)
new_esEs28(vwx301, vwx401, app(ty_[], dbg)) → new_esEs17(vwx301, vwx401, dbg)
new_esEs28(vwx301, vwx401, app(ty_Maybe, dbh)) → new_esEs5(vwx301, vwx401, dbh)
new_esEs28(vwx301, vwx401, ty_Float) → new_esEs11(vwx301, vwx401)
new_esEs28(vwx301, vwx401, ty_Int) → new_esEs10(vwx301, vwx401)
new_esEs28(vwx301, vwx401, app(ty_Ratio, dbf)) → new_esEs18(vwx301, vwx401, dbf)
new_esEs28(vwx301, vwx401, ty_Bool) → new_esEs12(vwx301, vwx401)
new_esEs12(True, True) → True
new_esEs12(False, False) → True
new_esEs12(False, True) → False
new_esEs12(True, False) → False
new_esEs18(:%(vwx300, vwx301), :%(vwx400, vwx401), cbc) → new_asAs(new_esEs21(vwx300, vwx400, cbc), new_esEs22(vwx301, vwx401, cbc))
new_esEs21(vwx300, vwx400, ty_Integer) → new_esEs16(vwx300, vwx400)
new_esEs21(vwx300, vwx400, ty_Int) → new_esEs10(vwx300, vwx400)
new_esEs22(vwx301, vwx401, ty_Int) → new_esEs10(vwx301, vwx401)
new_esEs22(vwx301, vwx401, ty_Integer) → new_esEs16(vwx301, vwx401)
new_esEs6(Left(vwx300), Left(vwx400), app(app(app(ty_@3, cga), cgb), cgc), bcd) → new_esEs7(vwx300, vwx400, cga, cgb, cgc)
new_esEs6(Right(vwx300), Right(vwx400), bcc, ty_Float) → new_esEs11(vwx300, vwx400)
new_esEs6(Left(vwx300), Left(vwx400), ty_Float, bcd) → new_esEs11(vwx300, vwx400)
new_esEs6(Right(vwx300), Right(vwx400), bcc, ty_@0) → new_esEs13(vwx300, vwx400)
new_esEs6(Left(vwx300), Left(vwx400), app(app(ty_@2, cfb), cfc), bcd) → new_esEs4(vwx300, vwx400, cfb, cfc)
new_esEs6(Right(vwx300), Left(vwx400), bcc, bcd) → False
new_esEs6(Left(vwx300), Right(vwx400), bcc, bcd) → False
new_esEs6(Right(vwx300), Right(vwx400), bcc, ty_Integer) → new_esEs16(vwx300, vwx400)
new_esEs6(Left(vwx300), Left(vwx400), ty_Double, bcd) → new_esEs15(vwx300, vwx400)
new_esEs6(Right(vwx300), Right(vwx400), bcc, ty_Double) → new_esEs15(vwx300, vwx400)
new_esEs6(Right(vwx300), Right(vwx400), bcc, app(app(app(ty_@3, chc), chd), che)) → new_esEs7(vwx300, vwx400, chc, chd, che)
new_esEs6(Right(vwx300), Right(vwx400), bcc, app(ty_[], cha)) → new_esEs17(vwx300, vwx400, cha)
new_esEs6(Left(vwx300), Left(vwx400), app(ty_Ratio, cff), bcd) → new_esEs18(vwx300, vwx400, cff)
new_esEs6(Left(vwx300), Left(vwx400), app(ty_[], cfg), bcd) → new_esEs17(vwx300, vwx400, cfg)
new_esEs6(Left(vwx300), Left(vwx400), ty_Bool, bcd) → new_esEs12(vwx300, vwx400)
new_esEs6(Right(vwx300), Right(vwx400), bcc, ty_Ordering) → new_esEs19(vwx300, vwx400)
new_esEs6(Left(vwx300), Left(vwx400), ty_@0, bcd) → new_esEs13(vwx300, vwx400)
new_esEs6(Left(vwx300), Left(vwx400), ty_Char, bcd) → new_esEs14(vwx300, vwx400)
new_esEs6(Right(vwx300), Right(vwx400), bcc, ty_Bool) → new_esEs12(vwx300, vwx400)
new_esEs6(Right(vwx300), Right(vwx400), bcc, ty_Char) → new_esEs14(vwx300, vwx400)
new_esEs6(Right(vwx300), Right(vwx400), bcc, app(app(ty_@2, cgd), cge)) → new_esEs4(vwx300, vwx400, cgd, cge)
new_esEs6(Left(vwx300), Left(vwx400), ty_Ordering, bcd) → new_esEs19(vwx300, vwx400)
new_esEs6(Right(vwx300), Right(vwx400), bcc, app(ty_Ratio, cgh)) → new_esEs18(vwx300, vwx400, cgh)
new_esEs6(Right(vwx300), Right(vwx400), bcc, ty_Int) → new_esEs10(vwx300, vwx400)
new_esEs6(Left(vwx300), Left(vwx400), ty_Integer, bcd) → new_esEs16(vwx300, vwx400)
new_esEs6(Left(vwx300), Left(vwx400), ty_Int, bcd) → new_esEs10(vwx300, vwx400)
new_esEs14(Char(vwx300), Char(vwx400)) → new_primEqNat0(vwx300, vwx400)
new_compare0(vwx300, vwx400, app(app(ty_@2, baa), bab)) → new_compare28(vwx300, vwx400, baa, bab)
new_compare0(vwx300, vwx400, ty_@0) → new_compare7(vwx300, vwx400)
new_compare0(vwx300, vwx400, ty_Bool) → new_compare41(vwx300, vwx400)
new_compare0(vwx300, vwx400, app(ty_[], bae)) → new_compare19(vwx300, vwx400, bae)
new_compare0(vwx300, vwx400, app(app(app(ty_@3, bag), bah), bba)) → new_compare9(vwx300, vwx400, bag, bah, bba)
new_compare0(vwx300, vwx400, ty_Float) → new_compare40(vwx300, vwx400)
new_compare0(vwx300, vwx400, app(ty_Ratio, cad)) → new_compare12(vwx300, vwx400, cad)
new_compare0(vwx300, vwx400, app(app(ty_Either, bac), bad)) → new_compare13(vwx300, vwx400, bac, bad)
new_compare0(vwx300, vwx400, ty_Char) → new_compare29(vwx300, vwx400)
new_compare0(vwx300, vwx400, app(ty_Maybe, baf)) → new_compare39(vwx300, vwx400, baf)
new_compare0(vwx300, vwx400, ty_Int) → new_compare42(vwx300, vwx400)
new_compare0(vwx300, vwx400, ty_Integer) → new_compare8(vwx300, vwx400)
new_compare0(vwx300, vwx400, ty_Ordering) → new_compare38(vwx300, vwx400)
new_compare0(vwx300, vwx400, ty_Double) → new_compare14(vwx300, vwx400)
new_compare14(vwx31, vwx41) → new_primCmpDouble(vwx31, vwx41)
new_primCmpDouble(Double(vwx300, vwx301), Double(vwx400, vwx401)) → new_compare15(vwx300, vwx400, vwx301, vwx401)
new_compare15(vwx300, vwx400, vwx301, vwx401) → new_primCmpInt(new_sr(vwx300, vwx400), new_sr(vwx301, vwx401))
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(vwx3000)), Neg(vwx400)) → new_primCmpNat0(vwx400, Succ(vwx3000))
new_primCmpInt(Neg(Zero), Pos(Succ(vwx4000))) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(vwx4000))) → new_primCmpNat0(Zero, Succ(vwx4000))
new_primCmpInt(Pos(Succ(vwx3000)), Pos(vwx400)) → new_primCmpNat0(Succ(vwx3000), vwx400)
new_primCmpInt(Pos(Succ(vwx3000)), Neg(vwx400)) → GT
new_primCmpInt(Neg(Zero), Neg(Succ(vwx4000))) → new_primCmpNat0(Succ(vwx4000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(vwx4000))) → GT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(vwx3000)), Pos(vwx400)) → LT
new_primCmpNat0(Succ(vwx3000), Zero) → GT
new_primCmpNat0(Succ(vwx3000), Succ(vwx4000)) → new_primCmpNat0(vwx3000, vwx4000)
new_primCmpNat0(Zero, Succ(vwx4000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_compare38(vwx300, vwx400) → new_compare33(vwx300, vwx400)
new_compare33(vwx30, vwx40) → new_compare23(vwx30, vwx40, new_esEs19(vwx30, vwx40))
new_compare23(vwx30, vwx40, False) → new_compare10(vwx30, vwx40, new_ltEs18(vwx30, vwx40))
new_compare23(vwx30, vwx40, True) → EQ
new_ltEs18(EQ, GT) → True
new_ltEs18(EQ, EQ) → True
new_ltEs18(LT, LT) → True
new_ltEs18(GT, GT) → True
new_ltEs18(LT, GT) → True
new_ltEs18(GT, LT) → False
new_ltEs18(GT, EQ) → False
new_ltEs18(EQ, LT) → False
new_ltEs18(LT, EQ) → True
new_compare10(vwx30, vwx40, True) → LT
new_compare10(vwx30, vwx40, False) → GT
new_compare8(Integer(vwx310), Integer(vwx410)) → new_primCmpInt(vwx310, vwx410)
new_compare42(vwx31, vwx41) → new_primCmpInt(vwx31, vwx41)
new_compare39(vwx300, vwx400, baf) → new_compare37(vwx300, vwx400, baf)
new_compare37(vwx30, vwx40, dh) → new_compare26(vwx30, vwx40, new_esEs5(vwx30, vwx40, dh), dh)
new_compare26(vwx30, vwx40, True, dh) → EQ
new_compare26(vwx30, vwx40, False, dh) → new_compare16(vwx30, vwx40, new_ltEs7(vwx30, vwx40, dh), dh)
new_ltEs7(Just(vwx310), Just(vwx410), ty_Ordering) → new_ltEs18(vwx310, vwx410)
new_ltEs7(Just(vwx310), Just(vwx410), ty_Double) → new_ltEs14(vwx310, vwx410)
new_ltEs7(Just(vwx310), Just(vwx410), ty_Integer) → new_ltEs15(vwx310, vwx410)
new_ltEs7(Just(vwx310), Just(vwx410), app(app(ty_@2, ea), eb)) → new_ltEs6(vwx310, vwx410, ea, eb)
new_ltEs7(Just(vwx310), Just(vwx410), ty_Char) → new_ltEs13(vwx310, vwx410)
new_ltEs7(Just(vwx310), Just(vwx410), ty_Int) → new_ltEs8(vwx310, vwx410)
new_ltEs7(Nothing, Just(vwx410), cae) → True
new_ltEs7(Just(vwx310), Just(vwx410), ty_@0) → new_ltEs11(vwx310, vwx410)
new_ltEs7(Just(vwx310), Just(vwx410), app(app(app(ty_@3, eg), eh), fa)) → new_ltEs4(vwx310, vwx410, eg, eh, fa)
new_ltEs7(Nothing, Nothing, cae) → True
new_ltEs7(Just(vwx310), Just(vwx410), ty_Float) → new_ltEs9(vwx310, vwx410)
new_ltEs7(Just(vwx310), Just(vwx410), ty_Bool) → new_ltEs10(vwx310, vwx410)
new_ltEs7(Just(vwx310), Nothing, cae) → False
new_ltEs7(Just(vwx310), Just(vwx410), app(ty_Ratio, caf)) → new_ltEs17(vwx310, vwx410, caf)
new_ltEs7(Just(vwx310), Just(vwx410), app(ty_[], ef)) → new_ltEs16(vwx310, vwx410, ef)
new_compare16(vwx30, vwx40, True, dh) → LT
new_compare16(vwx30, vwx40, False, dh) → GT
new_ltEs12(Left(vwx310), Left(vwx410), app(app(ty_Either, fg), fh), fd) → new_ltEs12(vwx310, vwx410, fg, fh)
new_ltEs12(Left(vwx310), Left(vwx410), app(ty_Maybe, ff), fd) → new_ltEs7(vwx310, vwx410, ff)
new_ltEs7(Just(vwx310), Just(vwx410), app(ty_Maybe, ec)) → new_ltEs7(vwx310, vwx410, ec)
new_ltEs12(Right(vwx310), Right(vwx410), ge, app(app(ty_Either, ha), hb)) → new_ltEs12(vwx310, vwx410, ha, hb)
new_ltEs7(Just(vwx310), Just(vwx410), app(app(ty_Either, ed), ee)) → new_ltEs12(vwx310, vwx410, ed, ee)
new_ltEs12(Right(vwx310), Right(vwx410), ge, app(ty_Maybe, gh)) → new_ltEs7(vwx310, vwx410, gh)
new_ltEs12(Right(vwx310), Right(vwx410), ge, app(ty_Ratio, cah)) → new_ltEs17(vwx310, vwx410, cah)
new_ltEs12(Right(vwx310), Right(vwx410), ge, ty_Bool) → new_ltEs10(vwx310, vwx410)
new_ltEs12(Right(vwx310), Right(vwx410), ge, ty_Char) → new_ltEs13(vwx310, vwx410)
new_ltEs12(Right(vwx310), Right(vwx410), ge, ty_Int) → new_ltEs8(vwx310, vwx410)
new_ltEs12(Left(vwx310), Left(vwx410), app(app(ty_@2, fb), fc), fd) → new_ltEs6(vwx310, vwx410, fb, fc)
new_ltEs12(Left(vwx310), Left(vwx410), ty_Integer, fd) → new_ltEs15(vwx310, vwx410)
new_ltEs12(Left(vwx310), Left(vwx410), ty_Ordering, fd) → new_ltEs18(vwx310, vwx410)
new_ltEs12(Right(vwx310), Right(vwx410), ge, ty_Double) → new_ltEs14(vwx310, vwx410)
new_ltEs12(Right(vwx310), Right(vwx410), ge, ty_Float) → new_ltEs9(vwx310, vwx410)
new_ltEs12(Right(vwx310), Right(vwx410), ge, app(ty_[], hc)) → new_ltEs16(vwx310, vwx410, hc)
new_ltEs12(Left(vwx310), Left(vwx410), app(ty_[], ga), fd) → new_ltEs16(vwx310, vwx410, ga)
new_ltEs12(Left(vwx310), Left(vwx410), ty_@0, fd) → new_ltEs11(vwx310, vwx410)
new_ltEs12(Right(vwx310), Right(vwx410), ge, app(app(ty_@2, gf), gg)) → new_ltEs6(vwx310, vwx410, gf, gg)
new_ltEs12(Left(vwx310), Right(vwx410), ge, fd) → True
new_ltEs12(Left(vwx310), Left(vwx410), ty_Int, fd) → new_ltEs8(vwx310, vwx410)
new_ltEs12(Right(vwx310), Left(vwx410), ge, fd) → False
new_ltEs12(Left(vwx310), Left(vwx410), app(ty_Ratio, cag), fd) → new_ltEs17(vwx310, vwx410, cag)
new_ltEs12(Left(vwx310), Left(vwx410), ty_Char, fd) → new_ltEs13(vwx310, vwx410)
new_ltEs12(Right(vwx310), Right(vwx410), ge, ty_Ordering) → new_ltEs18(vwx310, vwx410)
new_ltEs12(Right(vwx310), Right(vwx410), ge, ty_Integer) → new_ltEs15(vwx310, vwx410)
new_ltEs12(Left(vwx310), Left(vwx410), ty_Bool, fd) → new_ltEs10(vwx310, vwx410)
new_ltEs12(Right(vwx310), Right(vwx410), ge, ty_@0) → new_ltEs11(vwx310, vwx410)
new_ltEs12(Left(vwx310), Left(vwx410), ty_Float, fd) → new_ltEs9(vwx310, vwx410)
new_ltEs12(Left(vwx310), Left(vwx410), ty_Double, fd) → new_ltEs14(vwx310, vwx410)
new_ltEs12(Left(vwx310), Left(vwx410), app(app(app(ty_@3, gb), gc), gd), fd) → new_ltEs4(vwx310, vwx410, gb, gc, gd)
new_ltEs12(Right(vwx310), Right(vwx410), ge, app(app(app(ty_@3, hd), he), hf)) → new_ltEs4(vwx310, vwx410, hd, he, hf)
new_ltEs4(@3(vwx310, vwx311, vwx312), @3(vwx410, vwx411, vwx412), bec, bdb, bdc) → new_pePe(new_lt4(vwx310, vwx410, bec), new_asAs(new_esEs8(vwx310, vwx410, bec), new_pePe(new_lt5(vwx311, vwx411, bdb), new_asAs(new_esEs9(vwx311, vwx411, bdb), new_ltEs5(vwx312, vwx412, bdc)))))
new_lt4(vwx310, vwx410, ty_Char) → new_lt13(vwx310, vwx410)
new_lt4(vwx310, vwx410, ty_Float) → new_lt9(vwx310, vwx410)
new_lt4(vwx310, vwx410, app(ty_[], bdg)) → new_lt16(vwx310, vwx410, bdg)
new_lt4(vwx310, vwx410, app(ty_Ratio, bgf)) → new_lt17(vwx310, vwx410, bgf)
new_lt4(vwx310, vwx410, app(app(app(ty_@3, bdh), bea), beb)) → new_lt19(vwx310, vwx410, bdh, bea, beb)
new_lt4(vwx310, vwx410, ty_Double) → new_lt14(vwx310, vwx410)
new_lt4(vwx310, vwx410, ty_Int) → new_lt8(vwx310, vwx410)
new_lt4(vwx310, vwx410, app(ty_Maybe, bdd)) → new_lt7(vwx310, vwx410, bdd)
new_lt4(vwx310, vwx410, ty_Integer) → new_lt15(vwx310, vwx410)
new_lt4(vwx310, vwx410, ty_@0) → new_lt11(vwx310, vwx410)
new_lt4(vwx310, vwx410, app(app(ty_@2, bch), bda)) → new_lt6(vwx310, vwx410, bch, bda)
new_lt4(vwx310, vwx410, ty_Bool) → new_lt10(vwx310, vwx410)
new_lt4(vwx310, vwx410, app(app(ty_Either, bde), bdf)) → new_lt12(vwx310, vwx410, bde, bdf)
new_lt4(vwx310, vwx410, ty_Ordering) → new_lt18(vwx310, vwx410)
new_esEs8(vwx310, vwx410, ty_Integer) → new_esEs16(vwx310, vwx410)
new_esEs8(vwx310, vwx410, app(app(ty_Either, bde), bdf)) → new_esEs6(vwx310, vwx410, bde, bdf)
new_esEs8(vwx310, vwx410, app(app(ty_@2, bch), bda)) → new_esEs4(vwx310, vwx410, bch, bda)
new_esEs8(vwx310, vwx410, ty_Char) → new_esEs14(vwx310, vwx410)
new_esEs8(vwx310, vwx410, ty_Bool) → new_esEs12(vwx310, vwx410)
new_esEs8(vwx310, vwx410, ty_Double) → new_esEs15(vwx310, vwx410)
new_esEs8(vwx310, vwx410, app(ty_Maybe, bdd)) → new_esEs5(vwx310, vwx410, bdd)
new_esEs8(vwx310, vwx410, ty_Int) → new_esEs10(vwx310, vwx410)
new_esEs8(vwx310, vwx410, ty_Ordering) → new_esEs19(vwx310, vwx410)
new_esEs8(vwx310, vwx410, app(app(app(ty_@3, bdh), bea), beb)) → new_esEs7(vwx310, vwx410, bdh, bea, beb)
new_esEs8(vwx310, vwx410, app(ty_Ratio, bgf)) → new_esEs18(vwx310, vwx410, bgf)
new_esEs8(vwx310, vwx410, ty_Float) → new_esEs11(vwx310, vwx410)
new_esEs8(vwx310, vwx410, app(ty_[], bdg)) → new_esEs17(vwx310, vwx410, bdg)
new_esEs8(vwx310, vwx410, ty_@0) → new_esEs13(vwx310, vwx410)
new_lt5(vwx311, vwx411, ty_Ordering) → new_lt18(vwx311, vwx411)
new_lt5(vwx311, vwx411, ty_@0) → new_lt11(vwx311, vwx411)
new_lt5(vwx311, vwx411, ty_Integer) → new_lt15(vwx311, vwx411)
new_lt5(vwx311, vwx411, ty_Float) → new_lt9(vwx311, vwx411)
new_lt5(vwx311, vwx411, app(ty_[], bfa)) → new_lt16(vwx311, vwx411, bfa)
new_lt5(vwx311, vwx411, ty_Bool) → new_lt10(vwx311, vwx411)
new_lt5(vwx311, vwx411, ty_Char) → new_lt13(vwx311, vwx411)
new_lt5(vwx311, vwx411, app(app(app(ty_@3, bfb), bfc), bfd)) → new_lt19(vwx311, vwx411, bfb, bfc, bfd)
new_lt5(vwx311, vwx411, app(app(ty_@2, bed), bee)) → new_lt6(vwx311, vwx411, bed, bee)
new_lt5(vwx311, vwx411, ty_Double) → new_lt14(vwx311, vwx411)
new_lt5(vwx311, vwx411, app(ty_Maybe, bef)) → new_lt7(vwx311, vwx411, bef)
new_lt5(vwx311, vwx411, ty_Int) → new_lt8(vwx311, vwx411)
new_lt5(vwx311, vwx411, app(ty_Ratio, bgg)) → new_lt17(vwx311, vwx411, bgg)
new_lt5(vwx311, vwx411, app(app(ty_Either, beg), beh)) → new_lt12(vwx311, vwx411, beg, beh)
new_esEs9(vwx311, vwx411, ty_@0) → new_esEs13(vwx311, vwx411)
new_esEs9(vwx311, vwx411, ty_Int) → new_esEs10(vwx311, vwx411)
new_esEs9(vwx311, vwx411, app(app(app(ty_@3, bfb), bfc), bfd)) → new_esEs7(vwx311, vwx411, bfb, bfc, bfd)
new_esEs9(vwx311, vwx411, ty_Char) → new_esEs14(vwx311, vwx411)
new_esEs9(vwx311, vwx411, ty_Integer) → new_esEs16(vwx311, vwx411)
new_esEs9(vwx311, vwx411, ty_Float) → new_esEs11(vwx311, vwx411)
new_esEs9(vwx311, vwx411, app(app(ty_Either, beg), beh)) → new_esEs6(vwx311, vwx411, beg, beh)
new_esEs9(vwx311, vwx411, app(ty_Maybe, bef)) → new_esEs5(vwx311, vwx411, bef)
new_esEs9(vwx311, vwx411, app(ty_Ratio, bgg)) → new_esEs18(vwx311, vwx411, bgg)
new_esEs9(vwx311, vwx411, ty_Ordering) → new_esEs19(vwx311, vwx411)
new_esEs9(vwx311, vwx411, app(app(ty_@2, bed), bee)) → new_esEs4(vwx311, vwx411, bed, bee)
new_esEs9(vwx311, vwx411, ty_Bool) → new_esEs12(vwx311, vwx411)
new_esEs9(vwx311, vwx411, app(ty_[], bfa)) → new_esEs17(vwx311, vwx411, bfa)
new_esEs9(vwx311, vwx411, ty_Double) → new_esEs15(vwx311, vwx411)
new_ltEs5(vwx312, vwx412, app(app(ty_@2, bfe), bff)) → new_ltEs6(vwx312, vwx412, bfe, bff)
new_ltEs5(vwx312, vwx412, app(app(ty_Either, bfh), bga)) → new_ltEs12(vwx312, vwx412, bfh, bga)
new_ltEs5(vwx312, vwx412, ty_Char) → new_ltEs13(vwx312, vwx412)
new_ltEs5(vwx312, vwx412, app(ty_[], bgb)) → new_ltEs16(vwx312, vwx412, bgb)
new_ltEs5(vwx312, vwx412, app(ty_Ratio, bgh)) → new_ltEs17(vwx312, vwx412, bgh)
new_ltEs5(vwx312, vwx412, ty_@0) → new_ltEs11(vwx312, vwx412)
new_ltEs5(vwx312, vwx412, ty_Int) → new_ltEs8(vwx312, vwx412)
new_ltEs5(vwx312, vwx412, ty_Float) → new_ltEs9(vwx312, vwx412)
new_ltEs5(vwx312, vwx412, ty_Ordering) → new_ltEs18(vwx312, vwx412)
new_ltEs5(vwx312, vwx412, app(ty_Maybe, bfg)) → new_ltEs7(vwx312, vwx412, bfg)
new_ltEs5(vwx312, vwx412, ty_Integer) → new_ltEs15(vwx312, vwx412)
new_ltEs5(vwx312, vwx412, ty_Double) → new_ltEs14(vwx312, vwx412)
new_ltEs5(vwx312, vwx412, ty_Bool) → new_ltEs10(vwx312, vwx412)
new_ltEs5(vwx312, vwx412, app(app(app(ty_@3, bgc), bgd), bge)) → new_ltEs4(vwx312, vwx412, bgc, bgd, bge)
new_pePe(False, vwx113) → vwx113
new_pePe(True, vwx113) → True
new_ltEs10(False, True) → True
new_ltEs10(False, False) → True
new_ltEs10(True, False) → False
new_ltEs10(True, True) → True
new_ltEs14(vwx31, vwx41) → new_not(new_esEs19(new_compare14(vwx31, vwx41), GT))
new_not(False) → True
new_not(True) → False
new_ltEs15(vwx31, vwx41) → new_not(new_esEs19(new_compare8(vwx31, vwx41), GT))
new_ltEs9(vwx31, vwx41) → new_not(new_esEs19(new_compare40(vwx31, vwx41), GT))
new_compare40(vwx31, vwx41) → new_primCmpFloat(vwx31, vwx41)
new_primCmpFloat(Float(vwx300, vwx301), Float(vwx400, vwx401)) → new_compare15(vwx300, vwx400, vwx301, vwx401)
new_ltEs8(vwx31, vwx41) → new_not(new_esEs19(new_compare42(vwx31, vwx41), GT))
new_ltEs11(vwx31, vwx41) → new_not(new_esEs19(new_compare7(vwx31, vwx41), GT))
new_compare7(@0, @0) → EQ
new_ltEs17(vwx31, vwx41, cac) → new_not(new_esEs19(new_compare12(vwx31, vwx41, cac), GT))
new_compare12(:%(vwx310, vwx311), :%(vwx410, vwx411), ty_Integer) → new_compare8(new_sr0(vwx310, vwx411), new_sr0(vwx410, vwx311))
new_compare12(:%(vwx310, vwx311), :%(vwx410, vwx411), ty_Int) → new_compare42(new_sr(vwx310, vwx411), new_sr(vwx410, vwx311))
new_sr0(Integer(vwx4000), Integer(vwx3010)) → Integer(new_primMulInt(vwx4000, vwx3010))
new_ltEs16(vwx31, vwx41, hg) → new_not(new_esEs19(new_compare19(vwx31, vwx41, hg), GT))
new_compare19(:(vwx310, vwx311), [], hg) → GT
new_compare19([], [], hg) → EQ
new_compare19(:(vwx310, vwx311), :(vwx410, vwx411), hg) → new_primCompAux1(vwx310, vwx410, vwx311, vwx411, hg)
new_primCompAux00(vwx144, vwx145, EQ, app(ty_[], bbg)) → new_compare19(vwx144, vwx145, bbg)
new_primCompAux1(vwx300, vwx400, vwx301, vwx401, hh) → new_primCompAux00(vwx301, vwx401, new_compare0(vwx300, vwx400, hh), app(ty_[], hh))
new_compare19([], :(vwx410, vwx411), hg) → LT
new_primCompAux00(vwx144, vwx145, LT, cba) → LT
new_primCompAux00(vwx144, vwx145, GT, cba) → GT
new_ltEs13(vwx31, vwx41) → new_not(new_esEs19(new_compare29(vwx31, vwx41), GT))
new_compare29(vwx31, vwx41) → new_primCmpChar(vwx31, vwx41)
new_primCmpChar(Char(vwx300), Char(vwx400)) → new_primCmpNat0(vwx300, vwx400)
new_ltEs6(@2(vwx310, vwx311), @2(vwx410, vwx411), ce, be) → new_pePe(new_lt20(vwx310, vwx410, ce), new_asAs(new_esEs26(vwx310, vwx410, ce), new_ltEs19(vwx311, vwx411, be)))
new_lt20(vwx310, vwx410, app(app(ty_Either, bg), bh)) → new_lt12(vwx310, vwx410, bg, bh)
new_lt20(vwx310, vwx410, ty_Double) → new_lt14(vwx310, vwx410)
new_lt20(vwx310, vwx410, ty_Float) → new_lt9(vwx310, vwx410)
new_lt20(vwx310, vwx410, ty_Int) → new_lt8(vwx310, vwx410)
new_lt20(vwx310, vwx410, app(ty_Ratio, chf)) → new_lt17(vwx310, vwx410, chf)
new_lt20(vwx310, vwx410, ty_Char) → new_lt13(vwx310, vwx410)
new_lt20(vwx310, vwx410, ty_Ordering) → new_lt18(vwx310, vwx410)
new_lt20(vwx310, vwx410, app(app(ty_@2, bc), bd)) → new_lt6(vwx310, vwx410, bc, bd)
new_lt20(vwx310, vwx410, app(ty_[], ca)) → new_lt16(vwx310, vwx410, ca)
new_lt20(vwx310, vwx410, app(ty_Maybe, bf)) → new_lt7(vwx310, vwx410, bf)
new_lt20(vwx310, vwx410, ty_Integer) → new_lt15(vwx310, vwx410)
new_lt20(vwx310, vwx410, app(app(app(ty_@3, cb), cc), cd)) → new_lt19(vwx310, vwx410, cb, cc, cd)
new_lt20(vwx310, vwx410, ty_@0) → new_lt11(vwx310, vwx410)
new_lt20(vwx310, vwx410, ty_Bool) → new_lt10(vwx310, vwx410)
new_esEs26(vwx310, vwx410, ty_Char) → new_esEs14(vwx310, vwx410)
new_esEs26(vwx310, vwx410, ty_@0) → new_esEs13(vwx310, vwx410)
new_esEs26(vwx310, vwx410, ty_Bool) → new_esEs12(vwx310, vwx410)
new_esEs26(vwx310, vwx410, ty_Ordering) → new_esEs19(vwx310, vwx410)
new_esEs26(vwx310, vwx410, ty_Float) → new_esEs11(vwx310, vwx410)
new_esEs26(vwx310, vwx410, app(app(app(ty_@3, cb), cc), cd)) → new_esEs7(vwx310, vwx410, cb, cc, cd)
new_esEs26(vwx310, vwx410, ty_Integer) → new_esEs16(vwx310, vwx410)
new_esEs26(vwx310, vwx410, app(app(ty_@2, bc), bd)) → new_esEs4(vwx310, vwx410, bc, bd)
new_esEs26(vwx310, vwx410, ty_Int) → new_esEs10(vwx310, vwx410)
new_esEs26(vwx310, vwx410, app(ty_[], ca)) → new_esEs17(vwx310, vwx410, ca)
new_esEs26(vwx310, vwx410, app(ty_Ratio, chf)) → new_esEs18(vwx310, vwx410, chf)
new_esEs26(vwx310, vwx410, app(ty_Maybe, bf)) → new_esEs5(vwx310, vwx410, bf)
new_esEs26(vwx310, vwx410, app(app(ty_Either, bg), bh)) → new_esEs6(vwx310, vwx410, bg, bh)
new_esEs26(vwx310, vwx410, ty_Double) → new_esEs15(vwx310, vwx410)
new_ltEs19(vwx311, vwx411, ty_Integer) → new_ltEs15(vwx311, vwx411)
new_ltEs19(vwx311, vwx411, ty_Int) → new_ltEs8(vwx311, vwx411)
new_ltEs19(vwx311, vwx411, app(app(app(ty_@3, de), df), dg)) → new_ltEs4(vwx311, vwx411, de, df, dg)
new_ltEs19(vwx311, vwx411, app(ty_Ratio, chg)) → new_ltEs17(vwx311, vwx411, chg)
new_ltEs19(vwx311, vwx411, ty_Float) → new_ltEs9(vwx311, vwx411)
new_ltEs19(vwx311, vwx411, ty_@0) → new_ltEs11(vwx311, vwx411)
new_ltEs19(vwx311, vwx411, ty_Double) → new_ltEs14(vwx311, vwx411)
new_ltEs19(vwx311, vwx411, app(app(ty_Either, db), dc)) → new_ltEs12(vwx311, vwx411, db, dc)
new_ltEs19(vwx311, vwx411, app(ty_[], dd)) → new_ltEs16(vwx311, vwx411, dd)
new_ltEs19(vwx311, vwx411, ty_Char) → new_ltEs13(vwx311, vwx411)
new_ltEs19(vwx311, vwx411, ty_Bool) → new_ltEs10(vwx311, vwx411)
new_ltEs19(vwx311, vwx411, app(app(ty_@2, cf), cg)) → new_ltEs6(vwx311, vwx411, cf, cg)
new_ltEs19(vwx311, vwx411, app(ty_Maybe, da)) → new_ltEs7(vwx311, vwx411, da)
new_ltEs19(vwx311, vwx411, ty_Ordering) → new_ltEs18(vwx311, vwx411)
new_lt10(vwx30, vwx40) → new_esEs19(new_compare310(vwx30, vwx40), LT)
new_compare310(vwx30, vwx40) → new_compare27(vwx30, vwx40, new_esEs12(vwx30, vwx40))
new_compare27(vwx30, vwx40, False) → new_compare18(vwx30, vwx40, new_ltEs10(vwx30, vwx40))
new_compare27(vwx30, vwx40, True) → EQ
new_compare18(vwx30, vwx40, False) → GT
new_compare18(vwx30, vwx40, True) → LT
new_lt11(@0, @0) → new_esEs19(EQ, LT)
new_lt19(vwx30, vwx40, bce, bcf, bcg) → new_esEs19(new_compare35(vwx30, vwx40, bce, bcf, bcg), LT)
new_compare35(vwx30, vwx40, bce, bcf, bcg) → new_compare25(vwx30, vwx40, new_esEs7(vwx30, vwx40, bce, bcf, bcg), bce, bcf, bcg)
new_compare25(vwx30, vwx40, True, bce, bcf, bcg) → EQ
new_compare25(vwx30, vwx40, False, bce, bcf, bcg) → new_compare17(vwx30, vwx40, new_ltEs4(vwx30, vwx40, bce, bcf, bcg), bce, bcf, bcg)
new_compare17(vwx30, vwx40, True, bce, bcf, bcg) → LT
new_compare17(vwx30, vwx40, False, bce, bcf, bcg) → GT
new_lt15(Integer(vwx300), Integer(vwx400)) → new_esEs19(new_primCmpInt(vwx300, vwx400), LT)
new_lt7(vwx30, vwx40, dh) → new_esEs19(new_compare37(vwx30, vwx40, dh), LT)
new_lt16(:(vwx300, vwx301), :(vwx400, vwx401), hh) → new_esEs19(new_primCompAux1(vwx300, vwx400, vwx301, vwx401, hh), LT)
new_lt16([], [], hh) → new_esEs19(EQ, LT)
new_lt16([], :(vwx400, vwx401), hh) → new_esEs19(LT, LT)
new_lt16(:(vwx300, vwx301), [], hh) → new_esEs19(GT, LT)
new_lt6(vwx30, vwx40, ba, bb) → new_esEs19(new_compare34(vwx30, vwx40, ba, bb), LT)
new_compare34(vwx30, vwx40, ba, bb) → new_compare24(vwx30, vwx40, new_esEs4(vwx30, vwx40, ba, bb), ba, bb)
new_compare24(vwx30, vwx40, False, ba, bb) → new_compare110(vwx30, vwx40, new_ltEs6(vwx30, vwx40, ba, bb), ba, bb)
new_compare24(vwx30, vwx40, True, ba, bb) → EQ
new_compare110(vwx30, vwx40, True, ba, bb) → LT
new_compare110(vwx30, vwx40, False, ba, bb) → GT
new_lt18(vwx30, vwx40) → new_esEs19(new_compare33(vwx30, vwx40), LT)
new_lt13(vwx30, vwx40) → new_esEs19(new_primCmpChar(vwx30, vwx40), LT)
new_lt17(:%(vwx300, vwx301), :%(vwx400, vwx401), cbc) → new_esEs19(new_compare43(vwx300, vwx401, vwx400, vwx301, cbc), LT)
new_compare43(vwx300, vwx401, vwx400, vwx301, ty_Int) → new_compare15(vwx300, vwx401, vwx400, vwx301)
new_compare43(Integer(vwx3000), Integer(vwx4010), vwx400, vwx301, ty_Integer) → new_compare8(Integer(new_primMulInt(vwx3000, vwx4010)), new_sr0(vwx400, vwx301))
new_lt8(vwx30, vwx40) → new_esEs19(new_primCmpInt(vwx30, vwx40), LT)
new_lt9(vwx30, vwx40) → new_esEs19(new_primCmpFloat(vwx30, vwx40), LT)
new_lt14(vwx30, vwx40) → new_esEs19(new_primCmpDouble(vwx30, vwx40), LT)
new_lt12(vwx30, vwx40, bcc, bcd) → new_esEs19(new_compare36(vwx30, vwx40, bcc, bcd), LT)
new_compare36(vwx30, vwx40, bcc, bcd) → new_compare210(vwx30, vwx40, new_esEs6(vwx30, vwx40, bcc, bcd), bcc, bcd)
new_compare210(vwx30, vwx40, True, bcc, bcd) → EQ
new_compare210(vwx30, vwx40, False, bcc, bcd) → new_compare11(vwx30, vwx40, new_ltEs12(vwx30, vwx40, bcc, bcd), bcc, bcd)
new_compare11(vwx30, vwx40, True, bcc, bcd) → LT
new_compare11(vwx30, vwx40, False, bcc, bcd) → GT
new_compare13(vwx300, vwx400, bac, bad) → new_compare36(vwx300, vwx400, bac, bad)
new_compare9(vwx300, vwx400, bag, bah, bba) → new_compare35(vwx300, vwx400, bag, bah, bba)
new_compare41(vwx300, vwx400) → new_compare310(vwx300, vwx400)
new_compare28(vwx300, vwx400, baa, bab) → new_compare34(vwx300, vwx400, baa, bab)

The set Q consists of the following terms:

new_ltEs7(Just(x0), Nothing, x1)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_esEs13(@0, @0)
new_esEs26(x0, x1, ty_Double)
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_esEs20(x0, x1, ty_Bool)
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_ltEs12(Left(x0), Left(x1), ty_Integer, x2)
new_compare40(x0, x1)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_ltEs7(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs18(:%(x0, x1), :%(x2, x3), x4)
new_compare25(x0, x1, False, x2, x3, x4)
new_esEs9(x0, x1, ty_Ordering)
new_esEs9(x0, x1, ty_Integer)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs23(x0, x1, app(ty_[], x2))
new_esEs28(x0, x1, ty_Bool)
new_ltEs7(Nothing, Just(x0), x1)
new_esEs26(x0, x1, ty_Char)
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs7(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_lt5(x0, x1, app(ty_Ratio, x2))
new_lt20(x0, x1, ty_Int)
new_lt4(x0, x1, ty_Char)
new_ltEs11(x0, x1)
new_ltEs12(Left(x0), Left(x1), ty_Int, x2)
new_lt13(x0, x1)
new_esEs12(False, False)
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs12(Left(x0), Left(x1), ty_Float, x2)
new_esEs6(Left(x0), Left(x1), ty_Integer, x2)
new_ltEs12(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_ltEs19(x0, x1, ty_@0)
new_primMulInt(Neg(x0), Neg(x1))
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, ty_Int)
new_compare0(x0, x1, ty_Ordering)
new_esEs6(Left(x0), Left(x1), ty_Ordering, x2)
new_ltEs7(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, ty_Ordering)
new_esEs6(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs6(Left(x0), Left(x1), ty_@0, x2)
new_lt4(x0, x1, ty_Ordering)
new_esEs26(x0, x1, app(ty_[], x2))
new_lt5(x0, x1, ty_Bool)
new_primCompAux00(x0, x1, EQ, ty_Integer)
new_esEs6(Right(x0), Left(x1), x2, x3)
new_esEs6(Left(x0), Right(x1), x2, x3)
new_esEs26(x0, x1, ty_Int)
new_esEs23(x0, x1, ty_Ordering)
new_compare24(x0, x1, True, x2, x3)
new_esEs23(x0, x1, ty_Double)
new_esEs24(x0, x1, ty_Float)
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_lt19(x0, x1, x2, x3, x4)
new_lt20(x0, x1, ty_Char)
new_esEs20(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, ty_Int)
new_compare23(x0, x1, False)
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare19(:(x0, x1), :(x2, x3), x4)
new_compare39(x0, x1, x2)
new_esEs6(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_primCompAux00(x0, x1, EQ, app(ty_[], x2))
new_esEs26(x0, x1, ty_Ordering)
new_compare310(x0, x1)
new_esEs8(x0, x1, ty_Ordering)
new_esEs7(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs5(Just(x0), Just(x1), ty_Float)
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs12(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_compare11(x0, x1, True, x2, x3)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_primCompAux00(x0, x1, EQ, app(ty_Maybe, x2))
new_ltEs8(x0, x1)
new_sr(x0, x1)
new_esEs8(x0, x1, ty_Char)
new_ltEs12(Left(x0), Left(x1), ty_Double, x2)
new_lt16(:(x0, x1), [], x2)
new_esEs20(x0, x1, ty_Double)
new_esEs23(x0, x1, ty_Float)
new_esEs9(x0, x1, app(ty_Ratio, x2))
new_compare0(x0, x1, ty_Double)
new_ltEs18(GT, LT)
new_ltEs18(LT, GT)
new_primEqNat0(Zero, Zero)
new_primPlusNat1(Succ(x0), Zero)
new_ltEs5(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Left(x0), Left(x1), ty_Float, x2)
new_esEs26(x0, x1, ty_@0)
new_lt4(x0, x1, app(ty_Maybe, x2))
new_compare33(x0, x1)
new_esEs20(x0, x1, ty_Integer)
new_esEs5(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs16(Integer(x0), Integer(x1))
new_ltEs19(x0, x1, ty_Char)
new_primMulInt(Pos(x0), Pos(x1))
new_ltEs19(x0, x1, ty_Bool)
new_compare110(x0, x1, False, x2, x3)
new_ltEs12(Right(x0), Right(x1), x2, ty_Double)
new_primCompAux00(x0, x1, EQ, ty_Char)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_compare210(x0, x1, False, x2, x3)
new_esEs9(x0, x1, app(ty_[], x2))
new_ltEs5(x0, x1, app(ty_[], x2))
new_primCompAux00(x0, x1, EQ, app(app(app(ty_@3, x2), x3), x4))
new_lt5(x0, x1, ty_Float)
new_primMulNat0(Zero, Zero)
new_esEs25(x0, x1, ty_@0)
new_esEs24(x0, x1, ty_Ordering)
new_ltEs18(EQ, LT)
new_ltEs18(LT, EQ)
new_primCompAux00(x0, x1, EQ, ty_@0)
new_esEs5(Nothing, Nothing, x0)
new_compare27(x0, x1, True)
new_esEs25(x0, x1, ty_Double)
new_lt5(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_ltEs12(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs5(Just(x0), Just(x1), ty_Double)
new_primCompAux00(x0, x1, EQ, ty_Bool)
new_esEs25(x0, x1, ty_Ordering)
new_primCompAux00(x0, x1, EQ, ty_Float)
new_esEs27(x0, x1, ty_Bool)
new_lt5(x0, x1, ty_Char)
new_compare43(Integer(x0), Integer(x1), x2, x3, ty_Integer)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_ltEs12(Right(x0), Right(x1), x2, ty_@0)
new_esEs14(Char(x0), Char(x1))
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs20(x0, x1, ty_Char)
new_ltEs12(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_ltEs5(x0, x1, ty_Double)
new_esEs19(LT, LT)
new_ltEs12(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs19(GT, EQ)
new_esEs19(EQ, GT)
new_ltEs7(Just(x0), Just(x1), ty_Bool)
new_esEs17([], :(x0, x1), x2)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_ltEs13(x0, x1)
new_compare12(:%(x0, x1), :%(x2, x3), ty_Integer)
new_esEs22(x0, x1, ty_Integer)
new_primMulNat0(Zero, Succ(x0))
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_compare110(x0, x1, True, x2, x3)
new_lt5(x0, x1, ty_Double)
new_compare42(x0, x1)
new_ltEs12(Right(x0), Right(x1), x2, ty_Integer)
new_ltEs9(x0, x1)
new_asAs(False, x0)
new_compare41(x0, x1)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs20(x0, x1, ty_Int)
new_esEs26(x0, x1, ty_Float)
new_ltEs12(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_lt5(x0, x1, ty_Int)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_esEs5(Just(x0), Just(x1), ty_Char)
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_compare36(x0, x1, x2, x3)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs25(x0, x1, ty_Float)
new_primCompAux1(x0, x1, x2, x3, x4)
new_lt17(:%(x0, x1), :%(x2, x3), x4)
new_ltEs12(Right(x0), Right(x1), x2, ty_Char)
new_esEs27(x0, x1, ty_@0)
new_lt4(x0, x1, app(ty_Ratio, x2))
new_esEs9(x0, x1, app(app(ty_Either, x2), x3))
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs15(Double(x0, x1), Double(x2, x3))
new_esEs27(x0, x1, ty_Double)
new_primPlusNat0(Zero, x0)
new_ltEs12(Right(x0), Right(x1), x2, ty_Int)
new_esEs6(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_lt12(x0, x1, x2, x3)
new_esEs27(x0, x1, ty_Char)
new_esEs23(x0, x1, ty_Int)
new_lt14(x0, x1)
new_lt20(x0, x1, app(ty_[], x2))
new_primEqNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, Zero)
new_compare28(x0, x1, x2, x3)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_ltEs7(Just(x0), Just(x1), app(ty_[], x2))
new_esEs17([], [], x0)
new_esEs8(x0, x1, app(app(ty_@2, x2), x3))
new_esEs28(x0, x1, ty_Integer)
new_ltEs19(x0, x1, ty_Integer)
new_ltEs10(False, False)
new_esEs21(x0, x1, ty_Integer)
new_compare24(x0, x1, False, x2, x3)
new_esEs28(x0, x1, ty_Ordering)
new_esEs5(Just(x0), Just(x1), ty_Bool)
new_esEs9(x0, x1, ty_Int)
new_compare18(x0, x1, False)
new_esEs6(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_ltEs16(x0, x1, x2)
new_primCompAux00(x0, x1, LT, x2)
new_esEs9(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs12(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs28(x0, x1, ty_@0)
new_compare43(x0, x1, x2, x3, ty_Int)
new_ltEs19(x0, x1, ty_Int)
new_esEs5(Just(x0), Nothing, x1)
new_compare11(x0, x1, False, x2, x3)
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_lt4(x0, x1, ty_Bool)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_esEs24(x0, x1, ty_Char)
new_esEs12(True, True)
new_esEs27(x0, x1, ty_Float)
new_lt18(x0, x1)
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_compare0(x0, x1, app(ty_[], x2))
new_compare10(x0, x1, True)
new_lt20(x0, x1, ty_Bool)
new_compare19([], [], x0)
new_esEs5(Just(x0), Just(x1), ty_Ordering)
new_esEs6(Left(x0), Left(x1), ty_Bool, x2)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_esEs20(x0, x1, ty_Ordering)
new_esEs27(x0, x1, ty_Int)
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_compare29(x0, x1)
new_ltEs5(x0, x1, ty_Bool)
new_lt4(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs26(x0, x1, ty_Integer)
new_lt8(x0, x1)
new_lt5(x0, x1, app(ty_[], x2))
new_ltEs12(Left(x0), Left(x1), ty_Ordering, x2)
new_compare38(x0, x1)
new_esEs28(x0, x1, ty_Int)
new_lt20(x0, x1, ty_Integer)
new_esEs8(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs12(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs5(Just(x0), Just(x1), app(ty_Ratio, x2))
new_ltEs12(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_lt4(x0, x1, ty_Integer)
new_ltEs6(@2(x0, x1), @2(x2, x3), x4, x5)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs27(x0, x1, app(ty_[], x2))
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_lt4(x0, x1, ty_@0)
new_primEqInt(Neg(Zero), Neg(Zero))
new_ltEs19(x0, x1, ty_Float)
new_primCompAux00(x0, x1, EQ, ty_Double)
new_esEs24(x0, x1, ty_Double)
new_ltEs5(x0, x1, ty_@0)
new_lt5(x0, x1, ty_Ordering)
new_esEs23(x0, x1, ty_Integer)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs25(x0, x1, ty_Char)
new_compare0(x0, x1, app(ty_Ratio, x2))
new_esEs5(Just(x0), Just(x1), ty_Int)
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_ltEs18(LT, LT)
new_primPlusNat0(Succ(x0), x1)
new_lt4(x0, x1, app(ty_[], x2))
new_ltEs5(x0, x1, ty_Float)
new_compare0(x0, x1, ty_Integer)
new_lt9(x0, x1)
new_esEs5(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs5(x0, x1, app(ty_Maybe, x2))
new_compare10(x0, x1, False)
new_esEs24(x0, x1, ty_Bool)
new_ltEs12(Right(x0), Right(x1), x2, ty_Float)
new_compare7(@0, @0)
new_primCmpNat0(Zero, Succ(x0))
new_esEs6(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_compare25(x0, x1, True, x2, x3, x4)
new_esEs6(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs5(x0, x1, ty_Integer)
new_primPlusNat1(Succ(x0), Succ(x1))
new_compare37(x0, x1, x2)
new_compare0(x0, x1, ty_@0)
new_esEs6(Right(x0), Right(x1), x2, ty_Int)
new_esEs4(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs24(x0, x1, app(ty_[], x2))
new_lt16(:(x0, x1), :(x2, x3), x4)
new_ltEs15(x0, x1)
new_esEs22(x0, x1, ty_Int)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare18(x0, x1, True)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_esEs9(x0, x1, ty_Char)
new_compare35(x0, x1, x2, x3, x4)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_esEs6(Left(x0), Left(x1), ty_Double, x2)
new_lt5(x0, x1, ty_@0)
new_esEs8(x0, x1, ty_Double)
new_lt5(x0, x1, ty_Integer)
new_ltEs19(x0, x1, app(ty_[], x2))
new_lt5(x0, x1, app(app(ty_@2, x2), x3))
new_esEs24(x0, x1, ty_Integer)
new_primCompAux00(x0, x1, EQ, app(ty_Ratio, x2))
new_ltEs18(EQ, GT)
new_ltEs18(GT, EQ)
new_esEs28(x0, x1, ty_Double)
new_compare0(x0, x1, app(ty_Maybe, x2))
new_ltEs12(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_primCmpNat0(Zero, Zero)
new_ltEs12(Left(x0), Left(x1), ty_Bool, x2)
new_ltEs7(Just(x0), Just(x1), ty_Ordering)
new_lt15(Integer(x0), Integer(x1))
new_esEs8(x0, x1, app(ty_[], x2))
new_esEs6(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs7(Just(x0), Just(x1), ty_Integer)
new_ltEs5(x0, x1, ty_Int)
new_esEs17(:(x0, x1), [], x2)
new_primCompAux00(x0, x1, EQ, app(app(ty_@2, x2), x3))
new_esEs28(x0, x1, app(ty_[], x2))
new_esEs23(x0, x1, ty_Char)
new_ltEs7(Just(x0), Just(x1), ty_Int)
new_esEs8(x0, x1, ty_Bool)
new_ltEs10(True, True)
new_ltEs5(x0, x1, app(app(ty_Either, x2), x3))
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_ltEs7(Just(x0), Just(x1), ty_@0)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_esEs8(x0, x1, app(ty_Maybe, x2))
new_esEs6(Right(x0), Right(x1), x2, ty_@0)
new_esEs5(Just(x0), Just(x1), ty_Integer)
new_compare19(:(x0, x1), [], x2)
new_compare34(x0, x1, x2, x3)
new_esEs19(GT, GT)
new_ltEs12(Left(x0), Left(x1), ty_Char, x2)
new_lt4(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs12(Left(x0), Right(x1), x2, x3)
new_ltEs12(Right(x0), Left(x1), x2, x3)
new_esEs25(x0, x1, ty_Integer)
new_compare14(x0, x1)
new_ltEs5(x0, x1, app(ty_Ratio, x2))
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_primCmpDouble(Double(x0, x1), Double(x2, x3))
new_primEqNat0(Zero, Succ(x0))
new_esEs8(x0, x1, ty_@0)
new_lt5(x0, x1, app(app(ty_Either, x2), x3))
new_esEs6(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs9(x0, x1, app(app(ty_@2, x2), x3))
new_esEs12(False, True)
new_esEs12(True, False)
new_pePe(True, x0)
new_primMulNat0(Succ(x0), Zero)
new_lt6(x0, x1, x2, x3)
new_compare27(x0, x1, False)
new_esEs19(EQ, EQ)
new_esEs23(x0, x1, ty_@0)
new_primMulNat0(Succ(x0), Succ(x1))
new_esEs28(x0, x1, ty_Float)
new_lt4(x0, x1, ty_Float)
new_primCompAux00(x0, x1, EQ, ty_Ordering)
new_esEs10(x0, x1)
new_primCompAux00(x0, x1, GT, x2)
new_ltEs12(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs28(x0, x1, ty_Char)
new_primCmpNat0(Succ(x0), Succ(x1))
new_ltEs18(EQ, EQ)
new_compare0(x0, x1, ty_Bool)
new_esEs17(:(x0, x1), :(x2, x3), x4)
new_esEs23(x0, x1, ty_Bool)
new_ltEs7(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs5(Just(x0), Just(x1), ty_@0)
new_esEs19(EQ, LT)
new_esEs19(LT, EQ)
new_ltEs7(Nothing, Nothing, x0)
new_esEs27(x0, x1, ty_Integer)
new_esEs8(x0, x1, ty_Integer)
new_lt20(x0, x1, ty_Float)
new_esEs8(x0, x1, app(app(ty_Either, x2), x3))
new_compare210(x0, x1, True, x2, x3)
new_not(True)
new_compare26(x0, x1, False, x2)
new_esEs19(GT, LT)
new_esEs19(LT, GT)
new_compare9(x0, x1, x2, x3, x4)
new_ltEs5(x0, x1, ty_Ordering)
new_primCompAux00(x0, x1, EQ, ty_Int)
new_ltEs7(Just(x0), Just(x1), ty_Double)
new_esEs9(x0, x1, ty_Bool)
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, ty_Ordering)
new_esEs25(x0, x1, ty_Bool)
new_lt16([], :(x0, x1), x2)
new_lt4(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_not(False)
new_lt4(x0, x1, ty_Double)
new_lt20(x0, x1, ty_@0)
new_primCompAux00(x0, x1, EQ, app(app(ty_Either, x2), x3))
new_esEs6(Left(x0), Left(x1), ty_Char, x2)
new_compare0(x0, x1, app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, ty_Double)
new_compare0(x0, x1, app(app(ty_Either, x2), x3))
new_esEs6(Right(x0), Right(x1), x2, ty_Char)
new_ltEs12(Left(x0), Left(x1), ty_@0, x2)
new_esEs6(Right(x0), Right(x1), x2, ty_Double)
new_esEs6(Left(x0), Left(x1), ty_Int, x2)
new_ltEs4(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_ltEs7(Just(x0), Just(x1), app(ty_Maybe, x2))
new_ltEs17(x0, x1, x2)
new_esEs8(x0, x1, ty_Float)
new_esEs6(Right(x0), Right(x1), x2, ty_Float)
new_esEs5(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs9(x0, x1, ty_@0)
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs25(x0, x1, app(ty_[], x2))
new_compare17(x0, x1, True, x2, x3, x4)
new_compare0(x0, x1, ty_Char)
new_esEs24(x0, x1, ty_@0)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs7(Just(x0), Just(x1), ty_Char)
new_sr0(Integer(x0), Integer(x1))
new_ltEs12(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_lt16([], [], x0)
new_ltEs18(GT, GT)
new_ltEs12(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_compare16(x0, x1, True, x2)
new_asAs(True, x0)
new_esEs5(Just(x0), Just(x1), app(ty_[], x2))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_compare0(x0, x1, ty_Int)
new_esEs20(x0, x1, ty_Float)
new_esEs6(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs20(x0, x1, ty_@0)
new_ltEs10(False, True)
new_ltEs10(True, False)
new_primCmpFloat(Float(x0, x1), Float(x2, x3))
new_esEs8(x0, x1, ty_Int)
new_lt5(x0, x1, app(ty_Maybe, x2))
new_lt11(@0, @0)
new_compare17(x0, x1, False, x2, x3, x4)
new_ltEs7(Just(x0), Just(x1), ty_Float)
new_esEs9(x0, x1, ty_Float)
new_esEs6(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs12(Right(x0), Right(x1), x2, ty_Bool)
new_pePe(False, x0)
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_compare0(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_ltEs5(x0, x1, app(app(ty_@2, x2), x3))
new_primEqInt(Pos(Zero), Pos(Zero))
new_esEs8(x0, x1, app(ty_Ratio, x2))
new_esEs11(Float(x0, x1), Float(x2, x3))
new_ltEs14(x0, x1)
new_ltEs5(x0, x1, ty_Char)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare15(x0, x1, x2, x3)
new_lt20(x0, x1, ty_Ordering)
new_compare13(x0, x1, x2, x3)
new_lt7(x0, x1, x2)
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_lt20(x0, x1, ty_Double)
new_primCmpChar(Char(x0), Char(x1))
new_esEs24(x0, x1, ty_Int)
new_esEs26(x0, x1, ty_Bool)
new_compare12(:%(x0, x1), :%(x2, x3), ty_Int)
new_primPlusNat1(Zero, Succ(x0))
new_esEs5(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_primCmpNat0(Succ(x0), Zero)
new_compare8(Integer(x0), Integer(x1))
new_compare16(x0, x1, False, x2)
new_esEs5(Nothing, Just(x0), x1)
new_lt10(x0, x1)
new_esEs6(Right(x0), Right(x1), x2, ty_Integer)
new_compare0(x0, x1, ty_Float)
new_lt4(x0, x1, ty_Int)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs9(x0, x1, app(ty_Maybe, x2))
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_compare23(x0, x1, True)
new_compare26(x0, x1, True, x2)
new_esEs9(x0, x1, ty_Double)
new_compare19([], :(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: