YES 3.803 H-Termination proof of /home/matraf/haskell/eval_FullyBlown_Fast/empty.hs
H-Termination of the given Haskell-Program with start terms could successfully be proven:



↳ HASKELL
  ↳ CR

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

module Main where
  import qualified Prelude


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

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



↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ IFR

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

module Main where
  import qualified Prelude


If Reductions:
The following If expression
if primGEqNatS x y then Succ (primDivNatS (primMinusNatS x y) (Succ y)) else Zero

is transformed to
primDivNatS0 x y True = Succ (primDivNatS (primMinusNatS x y) (Succ y))
primDivNatS0 x y False = Zero

The following If expression
if primGEqNatS x y then primModNatS (primMinusNatS x y) (Succ y) else Succ x

is transformed to
primModNatS0 x y True = primModNatS (primMinusNatS x y) (Succ y)
primModNatS0 x y False = Succ x



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

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

module Main where
  import qualified Prelude


Replaced joker patterns by fresh variables and removed binding patterns.

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

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

module Main where
  import qualified Prelude


Cond Reductions:
The following Function with conditions
compare x y
 | x == y
 = EQ
 | x <= y
 = LT
 | otherwise
 = GT

is transformed to
compare x y = compare3 x y

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

compare0 x y True = GT

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

compare3 x y = compare2 x y (x == y)

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

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

gcd'0 x y = gcd' y (x `rem` y)

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

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

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

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

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

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

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

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

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

is transformed to
absReal x = absReal2 x

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

absReal0 x True = `negate` x

absReal2 x = absReal1 x (x >= 0)

The following Function with conditions
undefined 
 | False
 = undefined

is transformed to
undefined  = undefined1

undefined0 True = undefined

undefined1  = undefined0 False

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

is transformed to
reduce x y = reduce2 x y

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



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

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

module Main where
  import qualified Prelude


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

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

reduce2D vwv vww = gcd vwv vww

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

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

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

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

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

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



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

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

module Main where
  import qualified Prelude


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

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

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

module Main where
  import qualified Prelude


Haskell To QDPs


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

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

new_primCmpNat(Succ(vwx34000), Succ(vwx36000)) → new_primCmpNat(vwx34000, vwx36000)

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(vwx6900), Succ(vwx401000)) → new_primPlusNat(vwx6900, vwx401000)

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

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



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

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

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

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

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



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

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

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

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

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



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

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

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

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

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



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

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

new_ltEs1(Left(vwx3410), Left(vwx3610), app(ty_Maybe, bbc), baf) → new_ltEs2(vwx3410, vwx3610, bbc)
new_ltEs(@3(vwx3410, vwx3411, vwx3412), @3(vwx3610, vwx3611, vwx3612), cd, bd, app(ty_Maybe, ef)) → new_ltEs2(vwx3412, vwx3612, ef)
new_ltEs1(Left(vwx3410), Left(vwx3610), app(app(ty_Either, bba), bbb), baf) → new_ltEs1(vwx3410, vwx3610, bba, bbb)
new_ltEs1(Right(vwx3410), Right(vwx3610), bbe, app(ty_Maybe, bce)) → new_ltEs2(vwx3410, vwx3610, bce)
new_lt3(:(vwx3400, vwx3401), :(vwx3600, vwx3601), bee) → new_compare1(vwx3401, vwx3601, bee)
new_compare20(@2(vwx340, Just(vwx3410)), @2(vwx360, Just(vwx3610)), False, ff, app(ty_Maybe, app(app(ty_@2, bdb), bdc))) → new_ltEs0(vwx3410, vwx3610, bdb, bdc)
new_ltEs2(Just(vwx3410), Just(vwx3610), app(ty_[], bdg)) → new_ltEs3(vwx3410, vwx3610, bdg)
new_compare20(@2(vwx340, @2(vwx3410, vwx3411)), @2(vwx360, @2(vwx3610, vwx3611)), False, ff, app(app(ty_@2, app(app(ty_@2, gc), gd)), gb)) → new_lt0(vwx3410, vwx3610, gc, gd)
new_compare20(@2(vwx340, @3(vwx3410, vwx3411, vwx3412)), @2(vwx360, @3(vwx3610, vwx3611, vwx3612)), False, ff, app(app(app(ty_@3, app(app(app(ty_@3, ba), bb), bc)), bd), be)) → new_lt(vwx3410, vwx3610, ba, bb, bc)
new_ltEs0(@2(vwx3410, vwx3411), @2(vwx3610, vwx3611), ha, app(app(app(ty_@3, hb), hc), hd)) → new_ltEs(vwx3411, vwx3611, hb, hc, hd)
new_compare20(@2(vwx340, Just(vwx3410)), @2(vwx360, Just(vwx3610)), False, ff, app(ty_Maybe, app(ty_[], bdg))) → new_ltEs3(vwx3410, vwx3610, bdg)
new_lt0(vwx340, vwx360, fc, fd) → new_compare20(vwx340, vwx360, new_esEs5(vwx340, vwx360, fc, fd), fc, fd)
new_primCompAux(vwx3400, vwx3600, vwx96, app(app(app(ty_@3, bef), beg), beh)) → new_compare(vwx3400, vwx3600, bef, beg, beh)
new_ltEs0(@2(vwx3410, vwx3411), @2(vwx3610, vwx3611), ha, app(ty_Maybe, baa)) → new_ltEs2(vwx3411, vwx3611, baa)
new_compare20(@2(vwx340, @3(vwx3410, vwx3411, vwx3412)), @2(vwx360, @3(vwx3610, vwx3611, vwx3612)), False, ff, app(app(app(ty_@3, app(app(ty_Either, bh), ca)), bd), be)) → new_lt1(vwx3410, vwx3610, bh, ca)
new_ltEs0(@2(vwx3410, vwx3411), @2(vwx3610, vwx3611), app(ty_[], gh), gb) → new_lt3(vwx3410, vwx3610, gh)
new_ltEs2(Just(vwx3410), Just(vwx3610), app(app(ty_Either, bdd), bde)) → new_ltEs1(vwx3410, vwx3610, bdd, bde)
new_lt1(vwx340, vwx360, beb, bec) → new_compare21(vwx340, vwx360, new_esEs6(vwx340, vwx360, beb, bec), beb, bec)
new_ltEs1(Right(vwx3410), Right(vwx3610), bbe, app(app(app(ty_@3, bbf), bbg), bbh)) → new_ltEs(vwx3410, vwx3610, bbf, bbg, bbh)
new_compare1(:(vwx3400, vwx3401), :(vwx3600, vwx3601), bee) → new_compare1(vwx3401, vwx3601, bee)
new_compare20(@2(vwx340, @3(vwx3410, vwx3411, vwx3412)), @2(vwx360, @3(vwx3610, vwx3611, vwx3612)), False, ff, app(app(app(ty_@3, cd), app(ty_Maybe, de)), be)) → new_lt2(vwx3411, vwx3611, de)
new_compare1(:(vwx3400, vwx3401), :(vwx3600, vwx3601), bee) → new_primCompAux(vwx3400, vwx3600, new_compare3(vwx3401, vwx3601, bee), bee)
new_compare20(@2(vwx340, Right(vwx3410)), @2(vwx360, Right(vwx3610)), False, ff, app(app(ty_Either, bbe), app(app(app(ty_@3, bbf), bbg), bbh))) → new_ltEs(vwx3410, vwx3610, bbf, bbg, bbh)
new_compare20(@2(vwx340, Left(vwx3410)), @2(vwx360, Left(vwx3610)), False, ff, app(app(ty_Either, app(app(ty_Either, bba), bbb)), baf)) → new_ltEs1(vwx3410, vwx3610, bba, bbb)
new_ltEs(@3(vwx3410, vwx3411, vwx3412), @3(vwx3610, vwx3611, vwx3612), app(app(ty_@2, bf), bg), bd, be) → new_lt0(vwx3410, vwx3610, bf, bg)
new_ltEs(@3(vwx3410, vwx3411, vwx3412), @3(vwx3610, vwx3611, vwx3612), app(app(ty_Either, bh), ca), bd, be) → new_lt1(vwx3410, vwx3610, bh, ca)
new_compare20(@2(vwx340, Right(vwx3410)), @2(vwx360, Right(vwx3610)), False, ff, app(app(ty_Either, bbe), app(ty_[], bcf))) → new_ltEs3(vwx3410, vwx3610, bcf)
new_ltEs(@3(vwx3410, vwx3411, vwx3412), @3(vwx3610, vwx3611, vwx3612), cd, app(app(app(ty_@3, ce), cf), cg), be) → new_lt(vwx3411, vwx3611, ce, cf, cg)
new_ltEs(@3(vwx3410, vwx3411, vwx3412), @3(vwx3610, vwx3611, vwx3612), cd, bd, app(ty_[], eg)) → new_ltEs3(vwx3412, vwx3612, eg)
new_ltEs(@3(vwx3410, vwx3411, vwx3412), @3(vwx3610, vwx3611, vwx3612), cd, app(ty_[], df), be) → new_lt3(vwx3411, vwx3611, df)
new_ltEs1(Left(vwx3410), Left(vwx3610), app(ty_[], bbd), baf) → new_ltEs3(vwx3410, vwx3610, bbd)
new_compare20(@2(vwx340, vwx341), @2(vwx360, vwx361), False, app(app(app(ty_@3, eh), fa), fb), bea) → new_compare2(vwx340, vwx360, new_esEs4(vwx340, vwx360, eh, fa, fb), eh, fa, fb)
new_compare2(vwx340, vwx360, False, eh, fa, fb) → new_ltEs(vwx340, vwx360, eh, fa, fb)
new_compare(vwx340, vwx360, eh, fa, fb) → new_compare2(vwx340, vwx360, new_esEs4(vwx340, vwx360, eh, fa, fb), eh, fa, fb)
new_compare20(@2(vwx340, @2(vwx3410, vwx3411)), @2(vwx360, @2(vwx3610, vwx3611)), False, ff, app(app(ty_@2, ha), app(ty_[], bab))) → new_ltEs3(vwx3411, vwx3611, bab)
new_ltEs1(Right(vwx3410), Right(vwx3610), bbe, app(app(ty_Either, bcc), bcd)) → new_ltEs1(vwx3410, vwx3610, bcc, bcd)
new_compare20(@2(vwx340, @2(vwx3410, vwx3411)), @2(vwx360, @2(vwx3610, vwx3611)), False, ff, app(app(ty_@2, app(app(app(ty_@3, fg), fh), ga)), gb)) → new_lt(vwx3410, vwx3610, fg, fh, ga)
new_primCompAux(vwx3400, vwx3600, vwx96, app(ty_[], bff)) → new_compare1(vwx3400, vwx3600, bff)
new_ltEs0(@2(vwx3410, vwx3411), @2(vwx3610, vwx3611), app(app(app(ty_@3, fg), fh), ga), gb) → new_lt(vwx3410, vwx3610, fg, fh, ga)
new_ltEs0(@2(vwx3410, vwx3411), @2(vwx3610, vwx3611), ha, app(ty_[], bab)) → new_ltEs3(vwx3411, vwx3611, bab)
new_compare0(vwx340, vwx360, fc, fd) → new_compare20(vwx340, vwx360, new_esEs5(vwx340, vwx360, fc, fd), fc, fd)
new_ltEs(@3(vwx3410, vwx3411, vwx3412), @3(vwx3610, vwx3611, vwx3612), app(ty_[], cc), bd, be) → new_lt3(vwx3410, vwx3610, cc)
new_ltEs0(@2(vwx3410, vwx3411), @2(vwx3610, vwx3611), ha, app(app(ty_Either, hg), hh)) → new_ltEs1(vwx3411, vwx3611, hg, hh)
new_ltEs(@3(vwx3410, vwx3411, vwx3412), @3(vwx3610, vwx3611, vwx3612), cd, bd, app(app(app(ty_@3, dg), dh), ea)) → new_ltEs(vwx3412, vwx3612, dg, dh, ea)
new_compare20(@2(vwx340, vwx341), @2(vwx360, vwx361), False, app(app(ty_Either, beb), bec), bea) → new_compare21(vwx340, vwx360, new_esEs6(vwx340, vwx360, beb, bec), beb, bec)
new_compare4(vwx340, vwx360, beb, bec) → new_compare21(vwx340, vwx360, new_esEs6(vwx340, vwx360, beb, bec), beb, bec)
new_ltEs(@3(vwx3410, vwx3411, vwx3412), @3(vwx3610, vwx3611, vwx3612), cd, app(ty_Maybe, de), be) → new_lt2(vwx3411, vwx3611, de)
new_ltEs2(Just(vwx3410), Just(vwx3610), app(app(ty_@2, bdb), bdc)) → new_ltEs0(vwx3410, vwx3610, bdb, bdc)
new_compare20(@2(:(vwx3400, vwx3401), vwx341), @2(:(vwx3600, vwx3601), vwx361), False, app(ty_[], bee), bea) → new_compare1(vwx3401, vwx3601, bee)
new_compare20(@2(vwx340, @3(vwx3410, vwx3411, vwx3412)), @2(vwx360, @3(vwx3610, vwx3611, vwx3612)), False, ff, app(app(app(ty_@3, app(app(ty_@2, bf), bg)), bd), be)) → new_lt0(vwx3410, vwx3610, bf, bg)
new_ltEs1(Left(vwx3410), Left(vwx3610), app(app(ty_@2, bag), bah), baf) → new_ltEs0(vwx3410, vwx3610, bag, bah)
new_ltEs1(Right(vwx3410), Right(vwx3610), bbe, app(app(ty_@2, bca), bcb)) → new_ltEs0(vwx3410, vwx3610, bca, bcb)
new_ltEs(@3(vwx3410, vwx3411, vwx3412), @3(vwx3610, vwx3611, vwx3612), cd, bd, app(app(ty_@2, eb), ec)) → new_ltEs0(vwx3412, vwx3612, eb, ec)
new_compare20(@2(vwx340, @3(vwx3410, vwx3411, vwx3412)), @2(vwx360, @3(vwx3610, vwx3611, vwx3612)), False, ff, app(app(app(ty_@3, cd), app(app(ty_@2, da), db)), be)) → new_lt0(vwx3411, vwx3611, da, db)
new_ltEs0(@2(vwx3410, vwx3411), @2(vwx3610, vwx3611), app(app(ty_@2, gc), gd), gb) → new_lt0(vwx3410, vwx3610, gc, gd)
new_compare20(@2(vwx340, @2(vwx3410, vwx3411)), @2(vwx360, @2(vwx3610, vwx3611)), False, ff, app(app(ty_@2, app(ty_[], gh)), gb)) → new_lt3(vwx3410, vwx3610, gh)
new_compare20(@2(vwx340, @3(vwx3410, vwx3411, vwx3412)), @2(vwx360, @3(vwx3610, vwx3611, vwx3612)), False, ff, app(app(app(ty_@3, app(ty_Maybe, cb)), bd), be)) → new_lt2(vwx3410, vwx3610, cb)
new_compare20(@2(vwx340, @2(vwx3410, vwx3411)), @2(vwx360, @2(vwx3610, vwx3611)), False, ff, app(app(ty_@2, app(app(ty_Either, ge), gf)), gb)) → new_lt1(vwx3410, vwx3610, ge, gf)
new_compare20(@2(vwx340, @3(vwx3410, vwx3411, vwx3412)), @2(vwx360, @3(vwx3610, vwx3611, vwx3612)), False, ff, app(app(app(ty_@3, cd), bd), app(ty_[], eg))) → new_ltEs3(vwx3412, vwx3612, eg)
new_compare20(@2(:(vwx3400, vwx3401), vwx341), @2(:(vwx3600, vwx3601), vwx361), False, app(ty_[], bee), bea) → new_primCompAux(vwx3400, vwx3600, new_compare3(vwx3401, vwx3601, bee), bee)
new_ltEs0(@2(vwx3410, vwx3411), @2(vwx3610, vwx3611), app(app(ty_Either, ge), gf), gb) → new_lt1(vwx3410, vwx3610, ge, gf)
new_compare20(@2(vwx340, @2(vwx3410, vwx3411)), @2(vwx360, @2(vwx3610, vwx3611)), False, ff, app(app(ty_@2, ha), app(ty_Maybe, baa))) → new_ltEs2(vwx3411, vwx3611, baa)
new_compare20(@2(vwx340, @3(vwx3410, vwx3411, vwx3412)), @2(vwx360, @3(vwx3610, vwx3611, vwx3612)), False, ff, app(app(app(ty_@3, cd), bd), app(ty_Maybe, ef))) → new_ltEs2(vwx3412, vwx3612, ef)
new_compare20(@2(vwx340, Right(vwx3410)), @2(vwx360, Right(vwx3610)), False, ff, app(app(ty_Either, bbe), app(ty_Maybe, bce))) → new_ltEs2(vwx3410, vwx3610, bce)
new_compare20(@2(vwx340, @2(vwx3410, vwx3411)), @2(vwx360, @2(vwx3610, vwx3611)), False, ff, app(app(ty_@2, ha), app(app(ty_@2, he), hf))) → new_ltEs0(vwx3411, vwx3611, he, hf)
new_ltEs(@3(vwx3410, vwx3411, vwx3412), @3(vwx3610, vwx3611, vwx3612), cd, app(app(ty_@2, da), db), be) → new_lt0(vwx3411, vwx3611, da, db)
new_compare20(@2(vwx340, Left(vwx3410)), @2(vwx360, Left(vwx3610)), False, ff, app(app(ty_Either, app(ty_[], bbd)), baf)) → new_ltEs3(vwx3410, vwx3610, bbd)
new_compare20(@2(vwx340, vwx341), @2(vwx360, vwx361), False, ff, app(ty_[], bdh)) → new_compare1(vwx341, vwx361, bdh)
new_compare20(@2(vwx340, vwx341), @2(vwx360, vwx361), False, app(ty_Maybe, bed), bea) → new_compare22(vwx340, vwx360, new_esEs7(vwx340, vwx360, bed), bed)
new_compare20(@2(vwx340, Right(vwx3410)), @2(vwx360, Right(vwx3610)), False, ff, app(app(ty_Either, bbe), app(app(ty_Either, bcc), bcd))) → new_ltEs1(vwx3410, vwx3610, bcc, bcd)
new_ltEs3(vwx341, vwx361, bdh) → new_compare1(vwx341, vwx361, bdh)
new_ltEs1(Left(vwx3410), Left(vwx3610), app(app(app(ty_@3, bac), bad), bae), baf) → new_ltEs(vwx3410, vwx3610, bac, bad, bae)
new_lt3(:(vwx3400, vwx3401), :(vwx3600, vwx3601), bee) → new_primCompAux(vwx3400, vwx3600, new_compare3(vwx3401, vwx3601, bee), bee)
new_primCompAux(vwx3400, vwx3600, vwx96, app(app(ty_@2, bfa), bfb)) → new_compare0(vwx3400, vwx3600, bfa, bfb)
new_compare20(@2(vwx340, Just(vwx3410)), @2(vwx360, Just(vwx3610)), False, ff, app(ty_Maybe, app(ty_Maybe, bdf))) → new_ltEs2(vwx3410, vwx3610, bdf)
new_compare5(vwx340, vwx360, bed) → new_compare22(vwx340, vwx360, new_esEs7(vwx340, vwx360, bed), bed)
new_compare20(@2(vwx340, @2(vwx3410, vwx3411)), @2(vwx360, @2(vwx3610, vwx3611)), False, ff, app(app(ty_@2, ha), app(app(app(ty_@3, hb), hc), hd))) → new_ltEs(vwx3411, vwx3611, hb, hc, hd)
new_compare20(@2(vwx340, @3(vwx3410, vwx3411, vwx3412)), @2(vwx360, @3(vwx3610, vwx3611, vwx3612)), False, ff, app(app(app(ty_@3, cd), bd), app(app(ty_@2, eb), ec))) → new_ltEs0(vwx3412, vwx3612, eb, ec)
new_compare20(@2(vwx340, Left(vwx3410)), @2(vwx360, Left(vwx3610)), False, ff, app(app(ty_Either, app(ty_Maybe, bbc)), baf)) → new_ltEs2(vwx3410, vwx3610, bbc)
new_lt(vwx340, vwx360, eh, fa, fb) → new_compare2(vwx340, vwx360, new_esEs4(vwx340, vwx360, eh, fa, fb), eh, fa, fb)
new_compare20(@2(vwx340, @2(vwx3410, vwx3411)), @2(vwx360, @2(vwx3610, vwx3611)), False, ff, app(app(ty_@2, ha), app(app(ty_Either, hg), hh))) → new_ltEs1(vwx3411, vwx3611, hg, hh)
new_ltEs1(Right(vwx3410), Right(vwx3610), bbe, app(ty_[], bcf)) → new_ltEs3(vwx3410, vwx3610, bcf)
new_compare20(@2(vwx340, @3(vwx3410, vwx3411, vwx3412)), @2(vwx360, @3(vwx3610, vwx3611, vwx3612)), False, ff, app(app(app(ty_@3, app(ty_[], cc)), bd), be)) → new_lt3(vwx3410, vwx3610, cc)
new_compare21(vwx340, vwx360, False, beb, bec) → new_ltEs1(vwx340, vwx360, beb, bec)
new_compare20(@2(vwx340, Just(vwx3410)), @2(vwx360, Just(vwx3610)), False, ff, app(ty_Maybe, app(app(app(ty_@3, bcg), bch), bda))) → new_ltEs(vwx3410, vwx3610, bcg, bch, bda)
new_primCompAux(vwx3400, vwx3600, vwx96, app(app(ty_Either, bfc), bfd)) → new_compare4(vwx3400, vwx3600, bfc, bfd)
new_ltEs0(@2(vwx3410, vwx3411), @2(vwx3610, vwx3611), ha, app(app(ty_@2, he), hf)) → new_ltEs0(vwx3411, vwx3611, he, hf)
new_lt2(vwx340, vwx360, bed) → new_compare22(vwx340, vwx360, new_esEs7(vwx340, vwx360, bed), bed)
new_compare22(vwx340, vwx360, False, bed) → new_ltEs2(vwx340, vwx360, bed)
new_compare20(@2(vwx340, Left(vwx3410)), @2(vwx360, Left(vwx3610)), False, ff, app(app(ty_Either, app(app(ty_@2, bag), bah)), baf)) → new_ltEs0(vwx3410, vwx3610, bag, bah)
new_ltEs(@3(vwx3410, vwx3411, vwx3412), @3(vwx3610, vwx3611, vwx3612), app(app(app(ty_@3, ba), bb), bc), bd, be) → new_lt(vwx3410, vwx3610, ba, bb, bc)
new_compare20(@2(vwx340, Left(vwx3410)), @2(vwx360, Left(vwx3610)), False, ff, app(app(ty_Either, app(app(app(ty_@3, bac), bad), bae)), baf)) → new_ltEs(vwx3410, vwx3610, bac, bad, bae)
new_ltEs2(Just(vwx3410), Just(vwx3610), app(ty_Maybe, bdf)) → new_ltEs2(vwx3410, vwx3610, bdf)
new_compare20(@2(vwx340, @3(vwx3410, vwx3411, vwx3412)), @2(vwx360, @3(vwx3610, vwx3611, vwx3612)), False, ff, app(app(app(ty_@3, cd), bd), app(app(app(ty_@3, dg), dh), ea))) → new_ltEs(vwx3412, vwx3612, dg, dh, ea)
new_compare20(@2(vwx340, Just(vwx3410)), @2(vwx360, Just(vwx3610)), False, ff, app(ty_Maybe, app(app(ty_Either, bdd), bde))) → new_ltEs1(vwx3410, vwx3610, bdd, bde)
new_ltEs2(Just(vwx3410), Just(vwx3610), app(app(app(ty_@3, bcg), bch), bda)) → new_ltEs(vwx3410, vwx3610, bcg, bch, bda)
new_compare20(@2(vwx340, Right(vwx3410)), @2(vwx360, Right(vwx3610)), False, ff, app(app(ty_Either, bbe), app(app(ty_@2, bca), bcb))) → new_ltEs0(vwx3410, vwx3610, bca, bcb)
new_compare20(@2(vwx340, @3(vwx3410, vwx3411, vwx3412)), @2(vwx360, @3(vwx3610, vwx3611, vwx3612)), False, ff, app(app(app(ty_@3, cd), app(app(app(ty_@3, ce), cf), cg)), be)) → new_lt(vwx3411, vwx3611, ce, cf, cg)
new_compare20(@2(vwx340, @3(vwx3410, vwx3411, vwx3412)), @2(vwx360, @3(vwx3610, vwx3611, vwx3612)), False, ff, app(app(app(ty_@3, cd), app(ty_[], df)), be)) → new_lt3(vwx3411, vwx3611, df)
new_primCompAux(vwx3400, vwx3600, vwx96, app(ty_Maybe, bfe)) → new_compare5(vwx3400, vwx3600, bfe)
new_compare20(@2(vwx340, vwx341), @2(vwx360, vwx361), False, app(app(ty_@2, fc), fd), bea) → new_compare20(vwx340, vwx360, new_esEs5(vwx340, vwx360, fc, fd), fc, fd)
new_compare20(@2(vwx340, @3(vwx3410, vwx3411, vwx3412)), @2(vwx360, @3(vwx3610, vwx3611, vwx3612)), False, ff, app(app(app(ty_@3, cd), app(app(ty_Either, dc), dd)), be)) → new_lt1(vwx3411, vwx3611, dc, dd)
new_compare20(@2(vwx340, @2(vwx3410, vwx3411)), @2(vwx360, @2(vwx3610, vwx3611)), False, ff, app(app(ty_@2, app(ty_Maybe, gg)), gb)) → new_lt2(vwx3410, vwx3610, gg)
new_ltEs0(@2(vwx3410, vwx3411), @2(vwx3610, vwx3611), app(ty_Maybe, gg), gb) → new_lt2(vwx3410, vwx3610, gg)
new_ltEs(@3(vwx3410, vwx3411, vwx3412), @3(vwx3610, vwx3611, vwx3612), cd, bd, app(app(ty_Either, ed), ee)) → new_ltEs1(vwx3412, vwx3612, ed, ee)
new_compare20(@2(vwx340, @3(vwx3410, vwx3411, vwx3412)), @2(vwx360, @3(vwx3610, vwx3611, vwx3612)), False, ff, app(app(app(ty_@3, cd), bd), app(app(ty_Either, ed), ee))) → new_ltEs1(vwx3412, vwx3612, ed, ee)
new_ltEs(@3(vwx3410, vwx3411, vwx3412), @3(vwx3610, vwx3611, vwx3612), app(ty_Maybe, cb), bd, be) → new_lt2(vwx3410, vwx3610, cb)
new_ltEs(@3(vwx3410, vwx3411, vwx3412), @3(vwx3610, vwx3611, vwx3612), cd, app(app(ty_Either, dc), dd), be) → new_lt1(vwx3411, vwx3611, dc, dd)

The TRS R consists of the following rules:

new_esEs7(Just(vwx300), Just(vwx400), app(ty_Maybe, bhd)) → new_esEs7(vwx300, vwx400, bhd)
new_esEs20(vwx301, vwx401, app(ty_Maybe, ccg)) → new_esEs7(vwx301, vwx401, ccg)
new_ltEs19(vwx3412, vwx3612, app(ty_Ratio, ddf)) → new_ltEs11(vwx3412, vwx3612, ddf)
new_lt19(vwx3410, vwx3610, ty_Int) → new_lt18(vwx3410, vwx3610)
new_lt19(vwx3410, vwx3610, app(app(ty_Either, bh), ca)) → new_lt14(vwx3410, vwx3610, bh, ca)
new_ltEs15(True, False) → False
new_ltEs18(vwx3411, vwx3611, ty_Float) → new_ltEs8(vwx3411, vwx3611)
new_esEs28(vwx3411, vwx3611, ty_Char) → new_esEs13(vwx3411, vwx3611)
new_lt19(vwx3410, vwx3610, app(ty_[], cc)) → new_lt17(vwx3410, vwx3610, cc)
new_compare10(vwx340, vwx360, True, beb, bec) → LT
new_compare210(vwx340, vwx360, False, beb, bec) → new_compare10(vwx340, vwx360, new_ltEs6(vwx340, vwx360, beb, bec), beb, bec)
new_ltEs5(EQ, GT) → True
new_lt14(vwx340, vwx360, beb, bec) → new_esEs8(new_compare30(vwx340, vwx360, beb, bec), LT)
new_ltEs13(vwx341, vwx361) → new_not(new_esEs8(new_compare12(vwx341, vwx361), GT))
new_esEs19(vwx300, vwx400, ty_Char) → new_esEs13(vwx300, vwx400)
new_esEs27(vwx3410, vwx3610, app(ty_Maybe, cb)) → new_esEs7(vwx3410, vwx3610, cb)
new_lt19(vwx3410, vwx3610, app(app(ty_@2, bf), bg)) → new_lt10(vwx3410, vwx3610, bf, bg)
new_lt20(vwx3411, vwx3611, app(app(ty_Either, dc), dd)) → new_lt14(vwx3411, vwx3611, dc, dd)
new_esEs29(vwx340, vwx360, ty_@0) → new_esEs9(vwx340, vwx360)
new_compare28(vwx340, vwx360, False, bed) → new_compare113(vwx340, vwx360, new_ltEs12(vwx340, vwx360, bed), bed)
new_esEs26(vwx301, vwx401, ty_Float) → new_esEs17(vwx301, vwx401)
new_ltEs12(Nothing, Nothing, ceb) → True
new_lt11(vwx3410, vwx3610, app(ty_Maybe, gg)) → new_lt4(vwx3410, vwx3610, gg)
new_esEs7(Just(vwx300), Just(vwx400), app(app(ty_Either, bha), bhb)) → new_esEs6(vwx300, vwx400, bha, bhb)
new_esEs21(vwx302, vwx402, ty_Int) → new_esEs12(vwx302, vwx402)
new_primMulNat0(Zero, Zero) → Zero
new_compare19(vwx78, vwx79, vwx80, vwx81, False, bhg, bhh) → GT
new_esEs15(Double(vwx300, vwx301), Double(vwx400, vwx401)) → new_esEs12(new_sr0(vwx300, vwx400), new_sr0(vwx301, vwx401))
new_esEs6(Left(vwx300), Left(vwx400), app(ty_[], cfc), ceg) → new_esEs11(vwx300, vwx400, cfc)
new_esEs27(vwx3410, vwx3610, app(app(app(ty_@3, ba), bb), bc)) → new_esEs4(vwx3410, vwx3610, ba, bb, bc)
new_sr(Integer(vwx36000), Integer(vwx34010)) → Integer(new_primMulInt(vwx36000, vwx34010))
new_esEs25(vwx300, vwx400, app(app(ty_Either, dbf), dbg)) → new_esEs6(vwx300, vwx400, dbf, dbg)
new_lt11(vwx3410, vwx3610, ty_Bool) → new_lt8(vwx3410, vwx3610)
new_esEs28(vwx3411, vwx3611, ty_Bool) → new_esEs16(vwx3411, vwx3611)
new_esEs6(Left(vwx300), Left(vwx400), app(app(app(ty_@3, ceh), cfa), cfb), ceg) → new_esEs4(vwx300, vwx400, ceh, cfa, cfb)
new_ltEs12(Just(vwx3410), Just(vwx3610), ty_Integer) → new_ltEs13(vwx3410, vwx3610)
new_lt20(vwx3411, vwx3611, ty_Int) → new_lt18(vwx3411, vwx3611)
new_compare23(@2(vwx340, vwx341), @2(vwx360, vwx361), False, ff, bea) → new_compare112(vwx340, vwx341, vwx360, vwx361, new_lt21(vwx340, vwx360, ff), new_asAs(new_esEs29(vwx340, vwx360, ff), new_ltEs20(vwx341, vwx361, bea)), ff, bea)
new_ltEs20(vwx341, vwx361, ty_Char) → new_ltEs14(vwx341, vwx361)
new_lt21(vwx340, vwx360, ty_@0) → new_lt9(vwx340, vwx360)
new_lt11(vwx3410, vwx3610, app(ty_[], gh)) → new_lt17(vwx3410, vwx3610, gh)
new_lt8(vwx340, vwx360) → new_esEs8(new_compare16(vwx340, vwx360), LT)
new_ltEs6(Right(vwx3410), Right(vwx3610), bbe, ty_Bool) → new_ltEs15(vwx3410, vwx3610)
new_esEs29(vwx340, vwx360, app(ty_Maybe, bed)) → new_esEs7(vwx340, vwx360, bed)
new_esEs20(vwx301, vwx401, app(ty_Ratio, ccf)) → new_esEs14(vwx301, vwx401, ccf)
new_ltEs6(Right(vwx3410), Right(vwx3610), bbe, ty_Double) → new_ltEs10(vwx3410, vwx3610)
new_lt21(vwx340, vwx360, ty_Char) → new_lt16(vwx340, vwx360)
new_ltEs6(Left(vwx3410), Left(vwx3610), app(app(ty_Either, bba), bbb), baf) → new_ltEs6(vwx3410, vwx3610, bba, bbb)
new_compare26(vwx340, vwx360) → new_compare27(vwx340, vwx360, new_esEs8(vwx340, vwx360))
new_lt11(vwx3410, vwx3610, ty_Int) → new_lt18(vwx3410, vwx3610)
new_ltEs18(vwx3411, vwx3611, ty_Char) → new_ltEs14(vwx3411, vwx3611)
new_esEs11([], [], chc) → True
new_compare9(vwx340, vwx360, fc, fd) → new_compare23(vwx340, vwx360, new_esEs5(vwx340, vwx360, fc, fd), fc, fd)
new_esEs24(vwx300, vwx400, app(app(ty_@2, chd), che)) → new_esEs5(vwx300, vwx400, chd, che)
new_ltEs5(EQ, LT) → False
new_esEs6(Right(vwx300), Right(vwx400), cfh, ty_Integer) → new_esEs10(vwx300, vwx400)
new_esEs21(vwx302, vwx402, app(ty_Ratio, cdh)) → new_esEs14(vwx302, vwx402, cdh)
new_esEs25(vwx300, vwx400, ty_Double) → new_esEs15(vwx300, vwx400)
new_esEs23(vwx301, vwx401, ty_Integer) → new_esEs10(vwx301, vwx401)
new_lt20(vwx3411, vwx3611, ty_Float) → new_lt12(vwx3411, vwx3611)
new_esEs21(vwx302, vwx402, app(app(ty_Either, cdf), cdg)) → new_esEs6(vwx302, vwx402, cdf, cdg)
new_esEs26(vwx301, vwx401, ty_Char) → new_esEs13(vwx301, vwx401)
new_compare29(vwx3400, vwx3600, app(app(ty_@2, bfa), bfb)) → new_compare9(vwx3400, vwx3600, bfa, bfb)
new_esEs7(Just(vwx300), Just(vwx400), app(ty_Ratio, bhc)) → new_esEs14(vwx300, vwx400, bhc)
new_ltEs19(vwx3412, vwx3612, app(ty_Maybe, ef)) → new_ltEs12(vwx3412, vwx3612, ef)
new_ltEs6(Left(vwx3410), Left(vwx3610), ty_Double, baf) → new_ltEs10(vwx3410, vwx3610)
new_esEs18(vwx3410, vwx3610, app(app(app(ty_@3, fg), fh), ga)) → new_esEs4(vwx3410, vwx3610, fg, fh, ga)
new_esEs22(vwx300, vwx400, ty_Integer) → new_esEs10(vwx300, vwx400)
new_esEs18(vwx3410, vwx3610, ty_Integer) → new_esEs10(vwx3410, vwx3610)
new_esEs6(Left(vwx300), Left(vwx400), ty_Int, ceg) → new_esEs12(vwx300, vwx400)
new_pePe(False, vwx95) → vwx95
new_esEs24(vwx300, vwx400, app(ty_Ratio, dad)) → new_esEs14(vwx300, vwx400, dad)
new_ltEs18(vwx3411, vwx3611, app(app(app(ty_@3, hb), hc), hd)) → new_ltEs7(vwx3411, vwx3611, hb, hc, hd)
new_esEs6(Right(vwx300), Right(vwx400), cfh, app(ty_Ratio, cha)) → new_esEs14(vwx300, vwx400, cha)
new_esEs14(:%(vwx300, vwx301), :%(vwx400, vwx401), ced) → new_asAs(new_esEs22(vwx300, vwx400, ced), new_esEs23(vwx301, vwx401, ced))
new_esEs5(@2(vwx300, vwx301), @2(vwx400, vwx401), daf, dag) → new_asAs(new_esEs25(vwx300, vwx400, daf), new_esEs26(vwx301, vwx401, dag))
new_ltEs15(True, True) → True
new_lt19(vwx3410, vwx3610, app(ty_Ratio, ddd)) → new_lt7(vwx3410, vwx3610, ddd)
new_compare27(vwx340, vwx360, False) → new_compare110(vwx340, vwx360, new_ltEs5(vwx340, vwx360))
new_compare6(@0, @0) → EQ
new_esEs7(Just(vwx300), Just(vwx400), ty_Bool) → new_esEs16(vwx300, vwx400)
new_esEs27(vwx3410, vwx3610, ty_Float) → new_esEs17(vwx3410, vwx3610)
new_ltEs15(False, True) → True
new_lt21(vwx340, vwx360, app(app(app(ty_@3, eh), fa), fb)) → new_lt5(vwx340, vwx360, eh, fa, fb)
new_esEs24(vwx300, vwx400, app(ty_Maybe, dae)) → new_esEs7(vwx300, vwx400, dae)
new_compare16(vwx340, vwx360) → new_compare24(vwx340, vwx360, new_esEs16(vwx340, vwx360))
new_esEs28(vwx3411, vwx3611, app(app(app(ty_@3, ce), cf), cg)) → new_esEs4(vwx3411, vwx3611, ce, cf, cg)
new_ltEs6(Left(vwx3410), Left(vwx3610), ty_Float, baf) → new_ltEs8(vwx3410, vwx3610)
new_esEs21(vwx302, vwx402, ty_Double) → new_esEs15(vwx302, vwx402)
new_ltEs6(Left(vwx3410), Left(vwx3610), ty_Int, baf) → new_ltEs17(vwx3410, vwx3610)
new_lt11(vwx3410, vwx3610, app(ty_Ratio, bhe)) → new_lt7(vwx3410, vwx3610, bhe)
new_ltEs6(Right(vwx3410), Right(vwx3610), bbe, ty_Integer) → new_ltEs13(vwx3410, vwx3610)
new_ltEs12(Just(vwx3410), Just(vwx3610), app(ty_Ratio, cec)) → new_ltEs11(vwx3410, vwx3610, cec)
new_esEs20(vwx301, vwx401, app(app(ty_@2, cbf), cbg)) → new_esEs5(vwx301, vwx401, cbf, cbg)
new_esEs24(vwx300, vwx400, app(ty_[], daa)) → new_esEs11(vwx300, vwx400, daa)
new_ltEs15(False, False) → True
new_esEs29(vwx340, vwx360, app(ty_[], bee)) → new_esEs11(vwx340, vwx360, bee)
new_esEs4(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), caa, cab, cac) → new_asAs(new_esEs19(vwx300, vwx400, caa), new_asAs(new_esEs20(vwx301, vwx401, cab), new_esEs21(vwx302, vwx402, cac)))
new_esEs20(vwx301, vwx401, ty_Bool) → new_esEs16(vwx301, vwx401)
new_esEs18(vwx3410, vwx3610, app(app(ty_Either, ge), gf)) → new_esEs6(vwx3410, vwx3610, ge, gf)
new_esEs29(vwx340, vwx360, ty_Integer) → new_esEs10(vwx340, vwx360)
new_ltEs12(Just(vwx3410), Just(vwx3610), ty_Int) → new_ltEs17(vwx3410, vwx3610)
new_primCmpNat0(Zero, Succ(vwx36000)) → LT
new_compare113(vwx340, vwx360, True, bed) → LT
new_esEs21(vwx302, vwx402, ty_Char) → new_esEs13(vwx302, vwx402)
new_esEs25(vwx300, vwx400, ty_Bool) → new_esEs16(vwx300, vwx400)
new_ltEs18(vwx3411, vwx3611, ty_@0) → new_ltEs4(vwx3411, vwx3611)
new_esEs6(Right(vwx300), Left(vwx400), cfh, ceg) → False
new_esEs6(Left(vwx300), Right(vwx400), cfh, ceg) → False
new_esEs8(LT, LT) → True
new_ltEs20(vwx341, vwx361, ty_@0) → new_ltEs4(vwx341, vwx361)
new_compare25(vwx340, vwx360, True, eh, fa, fb) → EQ
new_esEs19(vwx300, vwx400, ty_Float) → new_esEs17(vwx300, vwx400)
new_esEs28(vwx3411, vwx3611, app(ty_[], df)) → new_esEs11(vwx3411, vwx3611, df)
new_esEs25(vwx300, vwx400, ty_Ordering) → new_esEs8(vwx300, vwx400)
new_esEs24(vwx300, vwx400, ty_Int) → new_esEs12(vwx300, vwx400)
new_esEs28(vwx3411, vwx3611, ty_Double) → new_esEs15(vwx3411, vwx3611)
new_esEs19(vwx300, vwx400, app(ty_Maybe, cbe)) → new_esEs7(vwx300, vwx400, cbe)
new_esEs28(vwx3411, vwx3611, ty_Float) → new_esEs17(vwx3411, vwx3611)
new_compare30(vwx340, vwx360, beb, bec) → new_compare210(vwx340, vwx360, new_esEs6(vwx340, vwx360, beb, bec), beb, bec)
new_ltEs12(Just(vwx3410), Just(vwx3610), ty_Double) → new_ltEs10(vwx3410, vwx3610)
new_pePe(True, vwx95) → True
new_primEqNat0(Zero, Zero) → True
new_esEs7(Just(vwx300), Just(vwx400), ty_Float) → new_esEs17(vwx300, vwx400)
new_compare29(vwx3400, vwx3600, ty_Int) → new_compare14(vwx3400, vwx3600)
new_lt20(vwx3411, vwx3611, app(app(ty_@2, da), db)) → new_lt10(vwx3411, vwx3611, da, db)
new_lt11(vwx3410, vwx3610, ty_Integer) → new_lt15(vwx3410, vwx3610)
new_compare112(vwx78, vwx79, vwx80, vwx81, True, vwx83, bhg, bhh) → new_compare19(vwx78, vwx79, vwx80, vwx81, True, bhg, bhh)
new_compare13(:%(vwx3400, vwx3401), :%(vwx3600, vwx3601), ty_Int) → new_compare14(new_sr0(vwx3400, vwx3601), new_sr0(vwx3600, vwx3401))
new_esEs6(Right(vwx300), Right(vwx400), cfh, app(app(app(ty_@3, cgc), cgd), cge)) → new_esEs4(vwx300, vwx400, cgc, cgd, cge)
new_esEs18(vwx3410, vwx3610, ty_@0) → new_esEs9(vwx3410, vwx3610)
new_esEs19(vwx300, vwx400, ty_Int) → new_esEs12(vwx300, vwx400)
new_ltEs20(vwx341, vwx361, ty_Float) → new_ltEs8(vwx341, vwx361)
new_esEs27(vwx3410, vwx3610, ty_Char) → new_esEs13(vwx3410, vwx3610)
new_esEs6(Right(vwx300), Right(vwx400), cfh, app(app(ty_Either, cgg), cgh)) → new_esEs6(vwx300, vwx400, cgg, cgh)
new_ltEs19(vwx3412, vwx3612, ty_Float) → new_ltEs8(vwx3412, vwx3612)
new_esEs6(Left(vwx300), Left(vwx400), ty_Double, ceg) → new_esEs15(vwx300, vwx400)
new_esEs19(vwx300, vwx400, ty_Double) → new_esEs15(vwx300, vwx400)
new_esEs26(vwx301, vwx401, ty_Bool) → new_esEs16(vwx301, vwx401)
new_compare29(vwx3400, vwx3600, ty_@0) → new_compare6(vwx3400, vwx3600)
new_esEs18(vwx3410, vwx3610, app(app(ty_@2, gc), gd)) → new_esEs5(vwx3410, vwx3610, gc, gd)
new_ltEs20(vwx341, vwx361, app(app(ty_@2, ha), gb)) → new_ltEs9(vwx341, vwx361, ha, gb)
new_esEs6(Left(vwx300), Left(vwx400), ty_Bool, ceg) → new_esEs16(vwx300, vwx400)
new_ltEs8(vwx341, vwx361) → new_not(new_esEs8(new_compare18(vwx341, vwx361), GT))
new_esEs28(vwx3411, vwx3611, app(app(ty_Either, dc), dd)) → new_esEs6(vwx3411, vwx3611, dc, dd)
new_compare13(:%(vwx3400, vwx3401), :%(vwx3600, vwx3601), ty_Integer) → new_compare12(new_sr(vwx3400, vwx3601), new_sr(vwx3600, vwx3401))
new_ltEs6(Left(vwx3410), Left(vwx3610), ty_@0, baf) → new_ltEs4(vwx3410, vwx3610)
new_esEs25(vwx300, vwx400, ty_@0) → new_esEs9(vwx300, vwx400)
new_esEs6(Right(vwx300), Right(vwx400), cfh, ty_Double) → new_esEs15(vwx300, vwx400)
new_esEs6(Left(vwx300), Left(vwx400), ty_Integer, ceg) → new_esEs10(vwx300, vwx400)
new_esEs26(vwx301, vwx401, ty_Ordering) → new_esEs8(vwx301, vwx401)
new_compare29(vwx3400, vwx3600, ty_Bool) → new_compare16(vwx3400, vwx3600)
new_esEs26(vwx301, vwx401, ty_Int) → new_esEs12(vwx301, vwx401)
new_esEs8(GT, GT) → True
new_ltEs20(vwx341, vwx361, app(ty_Ratio, ddg)) → new_ltEs11(vwx341, vwx361, ddg)
new_compare113(vwx340, vwx360, False, bed) → GT
new_lt18(vwx340, vwx360) → new_esEs8(new_compare14(vwx340, vwx360), LT)
new_primPlusNat0(Succ(vwx690), vwx40100) → Succ(Succ(new_primPlusNat1(vwx690, vwx40100)))
new_ltEs20(vwx341, vwx361, app(app(ty_Either, bbe), baf)) → new_ltEs6(vwx341, vwx361, bbe, baf)
new_compare18(Float(vwx3400, vwx3401), Float(vwx3600, vwx3601)) → new_compare14(new_sr0(vwx3400, vwx3600), new_sr0(vwx3401, vwx3601))
new_ltEs19(vwx3412, vwx3612, ty_Bool) → new_ltEs15(vwx3412, vwx3612)
new_esEs26(vwx301, vwx401, app(app(app(ty_@3, dcd), dce), dcf)) → new_esEs4(vwx301, vwx401, dcd, dce, dcf)
new_ltEs5(LT, LT) → True
new_ltEs19(vwx3412, vwx3612, ty_Double) → new_ltEs10(vwx3412, vwx3612)
new_esEs8(GT, LT) → False
new_esEs8(LT, GT) → False
new_esEs23(vwx301, vwx401, ty_Int) → new_esEs12(vwx301, vwx401)
new_esEs29(vwx340, vwx360, ty_Int) → new_esEs12(vwx340, vwx360)
new_lt19(vwx3410, vwx3610, ty_Bool) → new_lt8(vwx3410, vwx3610)
new_primEqInt(Neg(Succ(vwx3000)), Neg(Succ(vwx4000))) → new_primEqNat0(vwx3000, vwx4000)
new_compare29(vwx3400, vwx3600, app(app(app(ty_@3, bef), beg), beh)) → new_compare11(vwx3400, vwx3600, bef, beg, beh)
new_ltEs6(Left(vwx3410), Left(vwx3610), app(ty_Ratio, bfg), baf) → new_ltEs11(vwx3410, vwx3610, bfg)
new_ltEs6(Right(vwx3410), Right(vwx3610), bbe, ty_Ordering) → new_ltEs5(vwx3410, vwx3610)
new_esEs11(:(vwx300, vwx301), :(vwx400, vwx401), chc) → new_asAs(new_esEs24(vwx300, vwx400, chc), new_esEs11(vwx301, vwx401, chc))
new_esEs20(vwx301, vwx401, ty_Ordering) → new_esEs8(vwx301, vwx401)
new_lt21(vwx340, vwx360, app(app(ty_@2, fc), fd)) → new_lt10(vwx340, vwx360, fc, fd)
new_esEs24(vwx300, vwx400, ty_@0) → new_esEs9(vwx300, vwx400)
new_ltEs12(Just(vwx3410), Just(vwx3610), app(app(ty_Either, bdd), bde)) → new_ltEs6(vwx3410, vwx3610, bdd, bde)
new_ltEs6(Right(vwx3410), Right(vwx3610), bbe, app(ty_Maybe, bce)) → new_ltEs12(vwx3410, vwx3610, bce)
new_primPlusNat1(Zero, Succ(vwx401000)) → Succ(vwx401000)
new_primPlusNat1(Succ(vwx6900), Zero) → Succ(vwx6900)
new_ltEs6(Right(vwx3410), Right(vwx3610), bbe, app(app(ty_@2, bca), bcb)) → new_ltEs9(vwx3410, vwx3610, bca, bcb)
new_compare29(vwx3400, vwx3600, ty_Double) → new_compare15(vwx3400, vwx3600)
new_esEs16(True, False) → False
new_esEs16(False, True) → False
new_primCompAux1(vwx3400, vwx3600, vwx96, bee) → new_primCompAux0(vwx96, new_compare29(vwx3400, vwx3600, bee))
new_compare3([], :(vwx3600, vwx3601), bee) → LT
new_ltEs6(Left(vwx3410), Left(vwx3610), ty_Integer, baf) → new_ltEs13(vwx3410, vwx3610)
new_ltEs6(Right(vwx3410), Right(vwx3610), bbe, ty_Char) → new_ltEs14(vwx3410, vwx3610)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs18(vwx3410, vwx3610, ty_Float) → new_esEs17(vwx3410, vwx3610)
new_esEs27(vwx3410, vwx3610, ty_Int) → new_esEs12(vwx3410, vwx3610)
new_esEs7(Just(vwx300), Just(vwx400), ty_Ordering) → new_esEs8(vwx300, vwx400)
new_compare3(:(vwx3400, vwx3401), [], bee) → GT
new_ltEs10(vwx341, vwx361) → new_not(new_esEs8(new_compare15(vwx341, vwx361), GT))
new_lt19(vwx3410, vwx3610, ty_Integer) → new_lt15(vwx3410, vwx3610)
new_primEqInt(Neg(Succ(vwx3000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(vwx4000))) → False
new_primCompAux0(vwx105, GT) → GT
new_esEs8(EQ, EQ) → True
new_esEs6(Left(vwx300), Left(vwx400), app(ty_Ratio, cff), ceg) → new_esEs14(vwx300, vwx400, cff)
new_lt20(vwx3411, vwx3611, ty_Ordering) → new_lt13(vwx3411, vwx3611)
new_lt20(vwx3411, vwx3611, ty_Char) → new_lt16(vwx3411, vwx3611)
new_compare7(Char(vwx3400), Char(vwx3600)) → new_primCmpNat0(vwx3400, vwx3600)
new_esEs22(vwx300, vwx400, ty_Int) → new_esEs12(vwx300, vwx400)
new_esEs21(vwx302, vwx402, ty_Float) → new_esEs17(vwx302, vwx402)
new_compare19(vwx78, vwx79, vwx80, vwx81, True, bhg, bhh) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_compare14(vwx340, vwx360) → new_primCmpInt(vwx340, vwx360)
new_esEs6(Right(vwx300), Right(vwx400), cfh, ty_@0) → new_esEs9(vwx300, vwx400)
new_esEs29(vwx340, vwx360, ty_Bool) → new_esEs16(vwx340, vwx360)
new_compare29(vwx3400, vwx3600, app(ty_Ratio, ddh)) → new_compare13(vwx3400, vwx3600, ddh)
new_primCmpNat0(Succ(vwx34000), Succ(vwx36000)) → new_primCmpNat0(vwx34000, vwx36000)
new_ltEs5(EQ, EQ) → True
new_ltEs18(vwx3411, vwx3611, app(app(ty_Either, hg), hh)) → new_ltEs6(vwx3411, vwx3611, hg, hh)
new_ltEs18(vwx3411, vwx3611, ty_Integer) → new_ltEs13(vwx3411, vwx3611)
new_primEqInt(Pos(Succ(vwx3000)), Pos(Succ(vwx4000))) → new_primEqNat0(vwx3000, vwx4000)
new_compare10(vwx340, vwx360, False, beb, bec) → GT
new_ltEs19(vwx3412, vwx3612, app(app(app(ty_@3, dg), dh), ea)) → new_ltEs7(vwx3412, vwx3612, dg, dh, ea)
new_esEs26(vwx301, vwx401, ty_Integer) → new_esEs10(vwx301, vwx401)
new_esEs6(Left(vwx300), Left(vwx400), ty_Float, ceg) → new_esEs17(vwx300, vwx400)
new_ltEs6(Right(vwx3410), Right(vwx3610), bbe, ty_Int) → new_ltEs17(vwx3410, vwx3610)
new_compare29(vwx3400, vwx3600, ty_Char) → new_compare7(vwx3400, vwx3600)
new_esEs19(vwx300, vwx400, app(app(ty_Either, cbb), cbc)) → new_esEs6(vwx300, vwx400, cbb, cbc)
new_esEs7(Just(vwx300), Just(vwx400), ty_Integer) → new_esEs10(vwx300, vwx400)
new_lt12(vwx340, vwx360) → new_esEs8(new_compare18(vwx340, vwx360), LT)
new_ltEs20(vwx341, vwx361, app(app(app(ty_@3, cd), bd), be)) → new_ltEs7(vwx341, vwx361, cd, bd, be)
new_primEqNat0(Succ(vwx3000), Succ(vwx4000)) → new_primEqNat0(vwx3000, vwx4000)
new_esEs27(vwx3410, vwx3610, ty_Ordering) → new_esEs8(vwx3410, vwx3610)
new_lt11(vwx3410, vwx3610, ty_Char) → new_lt16(vwx3410, vwx3610)
new_esEs18(vwx3410, vwx3610, ty_Bool) → new_esEs16(vwx3410, vwx3610)
new_esEs6(Right(vwx300), Right(vwx400), cfh, app(app(ty_@2, cga), cgb)) → new_esEs5(vwx300, vwx400, cga, cgb)
new_esEs9(@0, @0) → True
new_compare111(vwx340, vwx360, True, eh, fa, fb) → LT
new_esEs26(vwx301, vwx401, app(ty_[], dcg)) → new_esEs11(vwx301, vwx401, dcg)
new_primCmpInt(Neg(Succ(vwx34000)), Neg(vwx3600)) → new_primCmpNat0(vwx3600, Succ(vwx34000))
new_esEs24(vwx300, vwx400, ty_Ordering) → new_esEs8(vwx300, vwx400)
new_compare29(vwx3400, vwx3600, app(ty_[], bff)) → new_compare3(vwx3400, vwx3600, bff)
new_ltEs6(Left(vwx3410), Right(vwx3610), bbe, baf) → True
new_ltEs19(vwx3412, vwx3612, ty_Int) → new_ltEs17(vwx3412, vwx3612)
new_compare25(vwx340, vwx360, False, eh, fa, fb) → new_compare111(vwx340, vwx360, new_ltEs7(vwx340, vwx360, eh, fa, fb), eh, fa, fb)
new_esEs7(Nothing, Nothing, bgb) → True
new_ltEs6(Right(vwx3410), Left(vwx3610), bbe, baf) → False
new_esEs28(vwx3411, vwx3611, ty_Ordering) → new_esEs8(vwx3411, vwx3611)
new_esEs8(EQ, LT) → False
new_esEs8(LT, EQ) → False
new_esEs18(vwx3410, vwx3610, app(ty_Maybe, gg)) → new_esEs7(vwx3410, vwx3610, gg)
new_primEqInt(Pos(Succ(vwx3000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(vwx4000))) → False
new_ltEs6(Left(vwx3410), Left(vwx3610), ty_Ordering, baf) → new_ltEs5(vwx3410, vwx3610)
new_esEs25(vwx300, vwx400, ty_Float) → new_esEs17(vwx300, vwx400)
new_ltEs20(vwx341, vwx361, app(ty_Maybe, ceb)) → new_ltEs12(vwx341, vwx361, ceb)
new_ltEs20(vwx341, vwx361, ty_Integer) → new_ltEs13(vwx341, vwx361)
new_ltEs5(GT, LT) → False
new_primCmpNat0(Zero, Zero) → EQ
new_esEs6(Right(vwx300), Right(vwx400), cfh, app(ty_Maybe, chb)) → new_esEs7(vwx300, vwx400, chb)
new_primCmpNat0(Succ(vwx34000), Zero) → GT
new_ltEs20(vwx341, vwx361, ty_Ordering) → new_ltEs5(vwx341, vwx361)
new_esEs20(vwx301, vwx401, app(app(app(ty_@3, cbh), cca), ccb)) → new_esEs4(vwx301, vwx401, cbh, cca, ccb)
new_primCmpInt(Neg(Zero), Pos(Succ(vwx36000))) → LT
new_esEs29(vwx340, vwx360, app(app(app(ty_@3, eh), fa), fb)) → new_esEs4(vwx340, vwx360, eh, fa, fb)
new_esEs6(Right(vwx300), Right(vwx400), cfh, ty_Float) → new_esEs17(vwx300, vwx400)
new_esEs7(Just(vwx300), Just(vwx400), app(app(app(ty_@3, bge), bgf), bgg)) → new_esEs4(vwx300, vwx400, bge, bgf, bgg)
new_primPlusNat1(Succ(vwx6900), Succ(vwx401000)) → Succ(Succ(new_primPlusNat1(vwx6900, vwx401000)))
new_primEqInt(Pos(Succ(vwx3000)), Neg(vwx400)) → False
new_primEqInt(Neg(Succ(vwx3000)), Pos(vwx400)) → False
new_esEs18(vwx3410, vwx3610, app(ty_Ratio, bhe)) → new_esEs14(vwx3410, vwx3610, bhe)
new_ltEs12(Just(vwx3410), Just(vwx3610), app(ty_Maybe, bdf)) → new_ltEs12(vwx3410, vwx3610, bdf)
new_esEs7(Just(vwx300), Nothing, bgb) → False
new_esEs7(Nothing, Just(vwx400), bgb) → False
new_esEs20(vwx301, vwx401, ty_Char) → new_esEs13(vwx301, vwx401)
new_compare3(:(vwx3400, vwx3401), :(vwx3600, vwx3601), bee) → new_primCompAux1(vwx3400, vwx3600, new_compare3(vwx3401, vwx3601, bee), bee)
new_ltEs11(vwx341, vwx361, ddg) → new_not(new_esEs8(new_compare13(vwx341, vwx361, ddg), GT))
new_lt19(vwx3410, vwx3610, app(app(app(ty_@3, ba), bb), bc)) → new_lt5(vwx3410, vwx3610, ba, bb, bc)
new_ltEs20(vwx341, vwx361, ty_Double) → new_ltEs10(vwx341, vwx361)
new_esEs11([], :(vwx400, vwx401), chc) → False
new_esEs11(:(vwx300, vwx301), [], chc) → False
new_esEs29(vwx340, vwx360, app(app(ty_@2, fc), fd)) → new_esEs5(vwx340, vwx360, fc, fd)
new_esEs19(vwx300, vwx400, ty_@0) → new_esEs9(vwx300, vwx400)
new_primEqInt(Pos(Zero), Neg(Succ(vwx4000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(vwx4000))) → False
new_ltEs19(vwx3412, vwx3612, app(app(ty_@2, eb), ec)) → new_ltEs9(vwx3412, vwx3612, eb, ec)
new_ltEs12(Just(vwx3410), Just(vwx3610), ty_Char) → new_ltEs14(vwx3410, vwx3610)
new_primCmpInt(Pos(Zero), Pos(Succ(vwx36000))) → new_primCmpNat0(Zero, Succ(vwx36000))
new_compare11(vwx340, vwx360, eh, fa, fb) → new_compare25(vwx340, vwx360, new_esEs4(vwx340, vwx360, eh, fa, fb), eh, fa, fb)
new_compare24(vwx340, vwx360, True) → EQ
new_ltEs18(vwx3411, vwx3611, app(ty_Ratio, bhf)) → new_ltEs11(vwx3411, vwx3611, bhf)
new_lt4(vwx340, vwx360, bed) → new_esEs8(new_compare8(vwx340, vwx360, bed), LT)
new_ltEs18(vwx3411, vwx3611, app(app(ty_@2, he), hf)) → new_ltEs9(vwx3411, vwx3611, he, hf)
new_esEs19(vwx300, vwx400, app(ty_Ratio, cbd)) → new_esEs14(vwx300, vwx400, cbd)
new_esEs27(vwx3410, vwx3610, ty_@0) → new_esEs9(vwx3410, vwx3610)
new_esEs8(GT, EQ) → False
new_esEs8(EQ, GT) → False
new_esEs19(vwx300, vwx400, ty_Integer) → new_esEs10(vwx300, vwx400)
new_esEs26(vwx301, vwx401, app(app(ty_@2, dcb), dcc)) → new_esEs5(vwx301, vwx401, dcb, dcc)
new_lt13(vwx340, vwx360) → new_esEs8(new_compare26(vwx340, vwx360), LT)
new_esEs28(vwx3411, vwx3611, app(ty_Ratio, dde)) → new_esEs14(vwx3411, vwx3611, dde)
new_esEs27(vwx3410, vwx3610, ty_Integer) → new_esEs10(vwx3410, vwx3610)
new_esEs24(vwx300, vwx400, ty_Char) → new_esEs13(vwx300, vwx400)
new_primCompAux0(vwx105, LT) → LT
new_esEs21(vwx302, vwx402, app(app(ty_@2, cch), cda)) → new_esEs5(vwx302, vwx402, cch, cda)
new_esEs6(Left(vwx300), Left(vwx400), ty_Char, ceg) → new_esEs13(vwx300, vwx400)
new_esEs28(vwx3411, vwx3611, ty_@0) → new_esEs9(vwx3411, vwx3611)
new_not(False) → True
new_esEs6(Left(vwx300), Left(vwx400), app(app(ty_Either, cfd), cfe), ceg) → new_esEs6(vwx300, vwx400, cfd, cfe)
new_lt20(vwx3411, vwx3611, ty_Bool) → new_lt8(vwx3411, vwx3611)
new_esEs21(vwx302, vwx402, ty_Bool) → new_esEs16(vwx302, vwx402)
new_compare8(vwx340, vwx360, bed) → new_compare28(vwx340, vwx360, new_esEs7(vwx340, vwx360, bed), bed)
new_primCmpInt(Pos(Succ(vwx34000)), Pos(vwx3600)) → new_primCmpNat0(Succ(vwx34000), vwx3600)
new_primPlusNat0(Zero, vwx40100) → Succ(vwx40100)
new_compare210(vwx340, vwx360, True, beb, bec) → EQ
new_esEs26(vwx301, vwx401, app(ty_Ratio, ddb)) → new_esEs14(vwx301, vwx401, ddb)
new_compare29(vwx3400, vwx3600, ty_Integer) → new_compare12(vwx3400, vwx3600)
new_esEs24(vwx300, vwx400, app(app(ty_Either, dab), dac)) → new_esEs6(vwx300, vwx400, dab, dac)
new_esEs20(vwx301, vwx401, ty_Integer) → new_esEs10(vwx301, vwx401)
new_lt11(vwx3410, vwx3610, ty_Ordering) → new_lt13(vwx3410, vwx3610)
new_ltEs6(Left(vwx3410), Left(vwx3610), ty_Bool, baf) → new_ltEs15(vwx3410, vwx3610)
new_esEs20(vwx301, vwx401, app(ty_[], ccc)) → new_esEs11(vwx301, vwx401, ccc)
new_compare17(vwx340, vwx360, True) → LT
new_esEs25(vwx300, vwx400, app(app(app(ty_@3, dbb), dbc), dbd)) → new_esEs4(vwx300, vwx400, dbb, dbc, dbd)
new_esEs25(vwx300, vwx400, ty_Integer) → new_esEs10(vwx300, vwx400)
new_esEs28(vwx3411, vwx3611, app(app(ty_@2, da), db)) → new_esEs5(vwx3411, vwx3611, da, db)
new_esEs24(vwx300, vwx400, ty_Float) → new_esEs17(vwx300, vwx400)
new_compare12(Integer(vwx3400), Integer(vwx3600)) → new_primCmpInt(vwx3400, vwx3600)
new_esEs27(vwx3410, vwx3610, app(app(ty_Either, bh), ca)) → new_esEs6(vwx3410, vwx3610, bh, ca)
new_lt20(vwx3411, vwx3611, ty_Double) → new_lt6(vwx3411, vwx3611)
new_esEs6(Right(vwx300), Right(vwx400), cfh, app(ty_[], cgf)) → new_esEs11(vwx300, vwx400, cgf)
new_ltEs12(Just(vwx3410), Just(vwx3610), ty_Ordering) → new_ltEs5(vwx3410, vwx3610)
new_esEs20(vwx301, vwx401, ty_@0) → new_esEs9(vwx301, vwx401)
new_esEs19(vwx300, vwx400, app(app(app(ty_@3, caf), cag), cah)) → new_esEs4(vwx300, vwx400, caf, cag, cah)
new_primCmpInt(Pos(Succ(vwx34000)), Neg(vwx3600)) → GT
new_ltEs16(vwx341, vwx361, bdh) → new_not(new_esEs8(new_compare3(vwx341, vwx361, bdh), GT))
new_esEs28(vwx3411, vwx3611, app(ty_Maybe, de)) → new_esEs7(vwx3411, vwx3611, de)
new_ltEs17(vwx341, vwx361) → new_not(new_esEs8(new_compare14(vwx341, vwx361), GT))
new_lt21(vwx340, vwx360, ty_Bool) → new_lt8(vwx340, vwx360)
new_esEs24(vwx300, vwx400, ty_Double) → new_esEs15(vwx300, vwx400)
new_esEs21(vwx302, vwx402, app(ty_Maybe, cea)) → new_esEs7(vwx302, vwx402, cea)
new_ltEs19(vwx3412, vwx3612, ty_@0) → new_ltEs4(vwx3412, vwx3612)
new_ltEs19(vwx3412, vwx3612, app(ty_[], eg)) → new_ltEs16(vwx3412, vwx3612, eg)
new_primMulInt(Pos(vwx3010), Pos(vwx4010)) → Pos(new_primMulNat0(vwx3010, vwx4010))
new_esEs18(vwx3410, vwx3610, ty_Double) → new_esEs15(vwx3410, vwx3610)
new_compare29(vwx3400, vwx3600, ty_Ordering) → new_compare26(vwx3400, vwx3600)
new_ltEs5(LT, GT) → True
new_esEs6(Left(vwx300), Left(vwx400), app(app(ty_@2, cee), cef), ceg) → new_esEs5(vwx300, vwx400, cee, cef)
new_esEs27(vwx3410, vwx3610, ty_Double) → new_esEs15(vwx3410, vwx3610)
new_primMulInt(Neg(vwx3010), Neg(vwx4010)) → Pos(new_primMulNat0(vwx3010, vwx4010))
new_compare110(vwx340, vwx360, True) → LT
new_esEs6(Right(vwx300), Right(vwx400), cfh, ty_Char) → new_esEs13(vwx300, vwx400)
new_primEqNat0(Zero, Succ(vwx4000)) → False
new_primEqNat0(Succ(vwx3000), Zero) → False
new_esEs7(Just(vwx300), Just(vwx400), ty_Char) → new_esEs13(vwx300, vwx400)
new_compare15(Double(vwx3400, vwx3401), Double(vwx3600, vwx3601)) → new_compare14(new_sr0(vwx3400, vwx3600), new_sr0(vwx3401, vwx3601))
new_esEs7(Just(vwx300), Just(vwx400), ty_@0) → new_esEs9(vwx300, vwx400)
new_esEs18(vwx3410, vwx3610, ty_Int) → new_esEs12(vwx3410, vwx3610)
new_lt6(vwx340, vwx360) → new_esEs8(new_compare15(vwx340, vwx360), LT)
new_compare110(vwx340, vwx360, False) → GT
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs21(vwx302, vwx402, ty_Integer) → new_esEs10(vwx302, vwx402)
new_esEs25(vwx300, vwx400, app(ty_[], dbe)) → new_esEs11(vwx300, vwx400, dbe)
new_esEs10(Integer(vwx300), Integer(vwx400)) → new_primEqInt(vwx300, vwx400)
new_compare111(vwx340, vwx360, False, eh, fa, fb) → GT
new_esEs25(vwx300, vwx400, ty_Int) → new_esEs12(vwx300, vwx400)
new_esEs27(vwx3410, vwx3610, app(app(ty_@2, bf), bg)) → new_esEs5(vwx3410, vwx3610, bf, bg)
new_esEs20(vwx301, vwx401, app(app(ty_Either, ccd), cce)) → new_esEs6(vwx301, vwx401, ccd, cce)
new_compare29(vwx3400, vwx3600, app(app(ty_Either, bfc), bfd)) → new_compare30(vwx3400, vwx3600, bfc, bfd)
new_esEs29(vwx340, vwx360, app(app(ty_Either, beb), bec)) → new_esEs6(vwx340, vwx360, beb, bec)
new_lt15(vwx340, vwx360) → new_esEs8(new_compare12(vwx340, vwx360), LT)
new_ltEs20(vwx341, vwx361, ty_Int) → new_ltEs17(vwx341, vwx361)
new_ltEs6(Right(vwx3410), Right(vwx3610), bbe, app(ty_Ratio, bfh)) → new_ltEs11(vwx3410, vwx3610, bfh)
new_esEs27(vwx3410, vwx3610, ty_Bool) → new_esEs16(vwx3410, vwx3610)
new_lt21(vwx340, vwx360, ty_Integer) → new_lt15(vwx340, vwx360)
new_lt11(vwx3410, vwx3610, app(app(ty_@2, gc), gd)) → new_lt10(vwx3410, vwx3610, gc, gd)
new_esEs16(True, True) → True
new_lt20(vwx3411, vwx3611, ty_@0) → new_lt9(vwx3411, vwx3611)
new_primCmpInt(Neg(Zero), Neg(Succ(vwx36000))) → new_primCmpNat0(Succ(vwx36000), Zero)
new_compare23(vwx34, vwx36, True, ff, bea) → EQ
new_primCmpInt(Pos(Zero), Neg(Succ(vwx36000))) → GT
new_esEs6(Left(vwx300), Left(vwx400), app(ty_Maybe, cfg), ceg) → new_esEs7(vwx300, vwx400, cfg)
new_esEs6(Left(vwx300), Left(vwx400), ty_Ordering, ceg) → new_esEs8(vwx300, vwx400)
new_esEs24(vwx300, vwx400, ty_Bool) → new_esEs16(vwx300, vwx400)
new_esEs12(vwx30, vwx40) → new_primEqInt(vwx30, vwx40)
new_esEs25(vwx300, vwx400, app(ty_Ratio, dbh)) → new_esEs14(vwx300, vwx400, dbh)
new_esEs29(vwx340, vwx360, ty_Char) → new_esEs13(vwx340, vwx360)
new_ltEs6(Right(vwx3410), Right(vwx3610), bbe, app(app(app(ty_@3, bbf), bbg), bbh)) → new_ltEs7(vwx3410, vwx3610, bbf, bbg, bbh)
new_sr0(vwx301, vwx401) → new_primMulInt(vwx301, vwx401)
new_esEs6(Left(vwx300), Left(vwx400), ty_@0, ceg) → new_esEs9(vwx300, vwx400)
new_lt7(vwx340, vwx360, bga) → new_esEs8(new_compare13(vwx340, vwx360, bga), LT)
new_esEs21(vwx302, vwx402, app(app(app(ty_@3, cdb), cdc), cdd)) → new_esEs4(vwx302, vwx402, cdb, cdc, cdd)
new_ltEs12(Just(vwx3410), Just(vwx3610), app(app(app(ty_@3, bcg), bch), bda)) → new_ltEs7(vwx3410, vwx3610, bcg, bch, bda)
new_compare29(vwx3400, vwx3600, ty_Float) → new_compare18(vwx3400, vwx3600)
new_ltEs6(Left(vwx3410), Left(vwx3610), ty_Char, baf) → new_ltEs14(vwx3410, vwx3610)
new_ltEs19(vwx3412, vwx3612, ty_Char) → new_ltEs14(vwx3412, vwx3612)
new_esEs26(vwx301, vwx401, ty_@0) → new_esEs9(vwx301, vwx401)
new_ltEs12(Just(vwx3410), Just(vwx3610), ty_Float) → new_ltEs8(vwx3410, vwx3610)
new_esEs25(vwx300, vwx400, app(ty_Maybe, dca)) → new_esEs7(vwx300, vwx400, dca)
new_ltEs20(vwx341, vwx361, app(ty_[], bdh)) → new_ltEs16(vwx341, vwx361, bdh)
new_lt10(vwx340, vwx360, fc, fd) → new_esEs8(new_compare9(vwx340, vwx360, fc, fd), LT)
new_lt19(vwx3410, vwx3610, ty_Char) → new_lt16(vwx3410, vwx3610)
new_ltEs6(Right(vwx3410), Right(vwx3610), bbe, app(app(ty_Either, bcc), bcd)) → new_ltEs6(vwx3410, vwx3610, bcc, bcd)
new_esEs18(vwx3410, vwx3610, app(ty_[], gh)) → new_esEs11(vwx3410, vwx3610, gh)
new_ltEs9(@2(vwx3410, vwx3411), @2(vwx3610, vwx3611), ha, gb) → new_pePe(new_lt11(vwx3410, vwx3610, ha), new_asAs(new_esEs18(vwx3410, vwx3610, ha), new_ltEs18(vwx3411, vwx3611, gb)))
new_lt21(vwx340, vwx360, ty_Double) → new_lt6(vwx340, vwx360)
new_esEs19(vwx300, vwx400, app(app(ty_@2, cad), cae)) → new_esEs5(vwx300, vwx400, cad, cae)
new_esEs27(vwx3410, vwx3610, app(ty_Ratio, ddd)) → new_esEs14(vwx3410, vwx3610, ddd)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_compare29(vwx3400, vwx3600, app(ty_Maybe, bfe)) → new_compare8(vwx3400, vwx3600, bfe)
new_ltEs18(vwx3411, vwx3611, ty_Double) → new_ltEs10(vwx3411, vwx3611)
new_lt19(vwx3410, vwx3610, ty_Ordering) → new_lt13(vwx3410, vwx3610)
new_ltEs7(@3(vwx3410, vwx3411, vwx3412), @3(vwx3610, vwx3611, vwx3612), cd, bd, be) → new_pePe(new_lt19(vwx3410, vwx3610, cd), new_asAs(new_esEs27(vwx3410, vwx3610, cd), new_pePe(new_lt20(vwx3411, vwx3611, bd), new_asAs(new_esEs28(vwx3411, vwx3611, bd), new_ltEs19(vwx3412, vwx3612, be)))))
new_asAs(False, vwx51) → False
new_compare3([], [], bee) → EQ
new_primMulInt(Neg(vwx3010), Pos(vwx4010)) → Neg(new_primMulNat0(vwx3010, vwx4010))
new_primMulInt(Pos(vwx3010), Neg(vwx4010)) → Neg(new_primMulNat0(vwx3010, vwx4010))
new_primMulNat0(Succ(vwx30100), Zero) → Zero
new_primMulNat0(Zero, Succ(vwx40100)) → Zero
new_lt19(vwx3410, vwx3610, ty_Float) → new_lt12(vwx3410, vwx3610)
new_ltEs18(vwx3411, vwx3611, ty_Ordering) → new_ltEs5(vwx3411, vwx3611)
new_ltEs20(vwx341, vwx361, ty_Bool) → new_ltEs15(vwx341, vwx361)
new_esEs21(vwx302, vwx402, ty_Ordering) → new_esEs8(vwx302, vwx402)
new_ltEs5(LT, EQ) → True
new_ltEs6(Left(vwx3410), Left(vwx3610), app(app(ty_@2, bag), bah), baf) → new_ltEs9(vwx3410, vwx3610, bag, bah)
new_lt21(vwx340, vwx360, ty_Ordering) → new_lt13(vwx340, vwx360)
new_esEs19(vwx300, vwx400, app(ty_[], cba)) → new_esEs11(vwx300, vwx400, cba)
new_lt21(vwx340, vwx360, app(ty_Maybe, bed)) → new_lt4(vwx340, vwx360, bed)
new_esEs26(vwx301, vwx401, app(ty_Maybe, ddc)) → new_esEs7(vwx301, vwx401, ddc)
new_ltEs6(Right(vwx3410), Right(vwx3610), bbe, ty_@0) → new_ltEs4(vwx3410, vwx3610)
new_ltEs18(vwx3411, vwx3611, app(ty_Maybe, baa)) → new_ltEs12(vwx3411, vwx3611, baa)
new_lt20(vwx3411, vwx3611, app(ty_[], df)) → new_lt17(vwx3411, vwx3611, df)
new_esEs18(vwx3410, vwx3610, ty_Ordering) → new_esEs8(vwx3410, vwx3610)
new_ltEs18(vwx3411, vwx3611, ty_Int) → new_ltEs17(vwx3411, vwx3611)
new_ltEs12(Nothing, Just(vwx3610), ceb) → True
new_esEs17(Float(vwx300, vwx301), Float(vwx400, vwx401)) → new_esEs12(new_sr0(vwx300, vwx400), new_sr0(vwx301, vwx401))
new_esEs24(vwx300, vwx400, ty_Integer) → new_esEs10(vwx300, vwx400)
new_compare27(vwx340, vwx360, True) → EQ
new_ltEs12(Just(vwx3410), Just(vwx3610), app(app(ty_@2, bdb), bdc)) → new_ltEs9(vwx3410, vwx3610, bdb, bdc)
new_esEs16(False, False) → True
new_lt21(vwx340, vwx360, app(ty_[], bee)) → new_lt17(vwx340, vwx360, bee)
new_lt11(vwx3410, vwx3610, ty_Float) → new_lt12(vwx3410, vwx3610)
new_compare24(vwx340, vwx360, False) → new_compare17(vwx340, vwx360, new_ltEs15(vwx340, vwx360))
new_esEs29(vwx340, vwx360, ty_Double) → new_esEs15(vwx340, vwx360)
new_ltEs4(vwx341, vwx361) → new_not(new_esEs8(new_compare6(vwx341, vwx361), GT))
new_esEs20(vwx301, vwx401, ty_Float) → new_esEs17(vwx301, vwx401)
new_ltEs12(Just(vwx3410), Just(vwx3610), app(ty_[], bdg)) → new_ltEs16(vwx3410, vwx3610, bdg)
new_esEs7(Just(vwx300), Just(vwx400), ty_Int) → new_esEs12(vwx300, vwx400)
new_esEs27(vwx3410, vwx3610, app(ty_[], cc)) → new_esEs11(vwx3410, vwx3610, cc)
new_lt19(vwx3410, vwx3610, app(ty_Maybe, cb)) → new_lt4(vwx3410, vwx3610, cb)
new_esEs7(Just(vwx300), Just(vwx400), app(ty_[], bgh)) → new_esEs11(vwx300, vwx400, bgh)
new_esEs25(vwx300, vwx400, app(app(ty_@2, dah), dba)) → new_esEs5(vwx300, vwx400, dah, dba)
new_esEs20(vwx301, vwx401, ty_Int) → new_esEs12(vwx301, vwx401)
new_ltEs12(Just(vwx3410), Just(vwx3610), ty_Bool) → new_ltEs15(vwx3410, vwx3610)
new_esEs21(vwx302, vwx402, ty_@0) → new_esEs9(vwx302, vwx402)
new_lt20(vwx3411, vwx3611, ty_Integer) → new_lt15(vwx3411, vwx3611)
new_esEs6(Right(vwx300), Right(vwx400), cfh, ty_Bool) → new_esEs16(vwx300, vwx400)
new_esEs13(Char(vwx300), Char(vwx400)) → new_primEqNat0(vwx300, vwx400)
new_lt21(vwx340, vwx360, app(ty_Ratio, bga)) → new_lt7(vwx340, vwx360, bga)
new_esEs6(Right(vwx300), Right(vwx400), cfh, ty_Int) → new_esEs12(vwx300, vwx400)
new_lt19(vwx3410, vwx3610, ty_Double) → new_lt6(vwx3410, vwx3610)
new_esEs21(vwx302, vwx402, app(ty_[], cde)) → new_esEs11(vwx302, vwx402, cde)
new_lt21(vwx340, vwx360, ty_Float) → new_lt12(vwx340, vwx360)
new_esEs7(Just(vwx300), Just(vwx400), app(app(ty_@2, bgc), bgd)) → new_esEs5(vwx300, vwx400, bgc, bgd)
new_lt17(vwx340, vwx360, bee) → new_esEs8(new_compare3(vwx340, vwx360, bee), LT)
new_ltEs12(Just(vwx3410), Just(vwx3610), ty_@0) → new_ltEs4(vwx3410, vwx3610)
new_lt9(vwx340, vwx360) → new_esEs8(new_compare6(vwx340, vwx360), LT)
new_lt20(vwx3411, vwx3611, app(app(app(ty_@3, ce), cf), cg)) → new_lt5(vwx3411, vwx3611, ce, cf, cg)
new_esEs28(vwx3411, vwx3611, ty_Int) → new_esEs12(vwx3411, vwx3611)
new_ltEs14(vwx341, vwx361) → new_not(new_esEs8(new_compare7(vwx341, vwx361), GT))
new_esEs26(vwx301, vwx401, app(app(ty_Either, dch), dda)) → new_esEs6(vwx301, vwx401, dch, dda)
new_ltEs19(vwx3412, vwx3612, ty_Ordering) → new_ltEs5(vwx3412, vwx3612)
new_ltEs18(vwx3411, vwx3611, ty_Bool) → new_ltEs15(vwx3411, vwx3611)
new_ltEs18(vwx3411, vwx3611, app(ty_[], bab)) → new_ltEs16(vwx3411, vwx3611, bab)
new_primPlusNat1(Zero, Zero) → Zero
new_lt21(vwx340, vwx360, app(app(ty_Either, beb), bec)) → new_lt14(vwx340, vwx360, beb, bec)
new_asAs(True, vwx51) → vwx51
new_esEs18(vwx3410, vwx3610, ty_Char) → new_esEs13(vwx3410, vwx3610)
new_esEs20(vwx301, vwx401, ty_Double) → new_esEs15(vwx301, vwx401)
new_primMulNat0(Succ(vwx30100), Succ(vwx40100)) → new_primPlusNat0(new_primMulNat0(vwx30100, Succ(vwx40100)), vwx40100)
new_ltEs5(GT, GT) → True
new_ltEs6(Left(vwx3410), Left(vwx3610), app(app(app(ty_@3, bac), bad), bae), baf) → new_ltEs7(vwx3410, vwx3610, bac, bad, bae)
new_esEs26(vwx301, vwx401, ty_Double) → new_esEs15(vwx301, vwx401)
new_ltEs12(Just(vwx3410), Nothing, ceb) → False
new_lt19(vwx3410, vwx3610, ty_@0) → new_lt9(vwx3410, vwx3610)
new_lt16(vwx340, vwx360) → new_esEs8(new_compare7(vwx340, vwx360), LT)
new_ltEs6(Left(vwx3410), Left(vwx3610), app(ty_[], bbd), baf) → new_ltEs16(vwx3410, vwx3610, bbd)
new_compare17(vwx340, vwx360, False) → GT
new_esEs7(Just(vwx300), Just(vwx400), ty_Double) → new_esEs15(vwx300, vwx400)
new_ltEs19(vwx3412, vwx3612, ty_Integer) → new_ltEs13(vwx3412, vwx3612)
new_compare28(vwx340, vwx360, True, bed) → EQ
new_esEs19(vwx300, vwx400, ty_Ordering) → new_esEs8(vwx300, vwx400)
new_ltEs6(Left(vwx3410), Left(vwx3610), app(ty_Maybe, bbc), baf) → new_ltEs12(vwx3410, vwx3610, bbc)
new_esEs29(vwx340, vwx360, ty_Float) → new_esEs17(vwx340, vwx360)
new_ltEs6(Right(vwx3410), Right(vwx3610), bbe, ty_Float) → new_ltEs8(vwx3410, vwx3610)
new_esEs29(vwx340, vwx360, app(ty_Ratio, bga)) → new_esEs14(vwx340, vwx360, bga)
new_lt11(vwx3410, vwx3610, ty_@0) → new_lt9(vwx3410, vwx3610)
new_lt11(vwx3410, vwx3610, app(app(app(ty_@3, fg), fh), ga)) → new_lt5(vwx3410, vwx3610, fg, fh, ga)
new_lt11(vwx3410, vwx3610, ty_Double) → new_lt6(vwx3410, vwx3610)
new_lt5(vwx340, vwx360, eh, fa, fb) → new_esEs8(new_compare11(vwx340, vwx360, eh, fa, fb), LT)
new_lt20(vwx3411, vwx3611, app(ty_Ratio, dde)) → new_lt7(vwx3411, vwx3611, dde)
new_esEs28(vwx3411, vwx3611, ty_Integer) → new_esEs10(vwx3411, vwx3611)
new_esEs24(vwx300, vwx400, app(app(app(ty_@3, chf), chg), chh)) → new_esEs4(vwx300, vwx400, chf, chg, chh)
new_lt21(vwx340, vwx360, ty_Int) → new_lt18(vwx340, vwx360)
new_lt11(vwx3410, vwx3610, app(app(ty_Either, ge), gf)) → new_lt14(vwx3410, vwx3610, ge, gf)
new_esEs19(vwx300, vwx400, ty_Bool) → new_esEs16(vwx300, vwx400)
new_lt20(vwx3411, vwx3611, app(ty_Maybe, de)) → new_lt4(vwx3411, vwx3611, de)
new_ltEs6(Right(vwx3410), Right(vwx3610), bbe, app(ty_[], bcf)) → new_ltEs16(vwx3410, vwx3610, bcf)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs6(Right(vwx300), Right(vwx400), cfh, ty_Ordering) → new_esEs8(vwx300, vwx400)
new_primCompAux0(vwx105, EQ) → vwx105
new_esEs29(vwx340, vwx360, ty_Ordering) → new_esEs8(vwx340, vwx360)
new_ltEs5(GT, EQ) → False
new_ltEs19(vwx3412, vwx3612, app(app(ty_Either, ed), ee)) → new_ltEs6(vwx3412, vwx3612, ed, ee)
new_compare112(vwx78, vwx79, vwx80, vwx81, False, vwx83, bhg, bhh) → new_compare19(vwx78, vwx79, vwx80, vwx81, vwx83, bhg, bhh)
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_esEs25(vwx300, vwx400, ty_Char) → new_esEs13(vwx300, vwx400)
new_primCmpInt(Neg(Succ(vwx34000)), Pos(vwx3600)) → LT
new_not(True) → False

The set Q consists of the following terms:

new_compare13(:%(x0, x1), :%(x2, x3), ty_Integer)
new_esEs24(x0, x1, ty_Integer)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_esEs29(x0, x1, ty_Int)
new_esEs19(x0, x1, ty_Int)
new_lt11(x0, x1, ty_Float)
new_compare210(x0, x1, True, x2, x3)
new_ltEs6(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs11(:(x0, x1), :(x2, x3), x4)
new_compare29(x0, x1, ty_Int)
new_lt18(x0, x1)
new_ltEs18(x0, x1, ty_Integer)
new_primPlusNat0(Succ(x0), x1)
new_esEs26(x0, x1, app(ty_[], x2))
new_esEs26(x0, x1, ty_Int)
new_ltEs6(Left(x0), Right(x1), x2, x3)
new_ltEs6(Right(x0), Left(x1), x2, x3)
new_sr(Integer(x0), Integer(x1))
new_ltEs19(x0, x1, ty_Ordering)
new_lt20(x0, x1, ty_Integer)
new_compare29(x0, x1, app(ty_[], x2))
new_lt11(x0, x1, app(ty_Maybe, x2))
new_compare29(x0, x1, ty_Char)
new_lt21(x0, x1, ty_Int)
new_lt11(x0, x1, ty_@0)
new_lt19(x0, x1, app(ty_[], x2))
new_esEs21(x0, x1, ty_Char)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs29(x0, x1, ty_Integer)
new_compare27(x0, x1, False)
new_ltEs15(True, True)
new_compare13(:%(x0, x1), :%(x2, x3), ty_Int)
new_compare3(:(x0, x1), :(x2, x3), x4)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs14(:%(x0, x1), :%(x2, x3), x4)
new_ltEs12(Nothing, Nothing, x0)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs18(x0, x1, app(app(ty_Either, x2), x3))
new_esEs7(Nothing, Nothing, x0)
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs5(GT, EQ)
new_ltEs5(EQ, GT)
new_esEs20(x0, x1, ty_Char)
new_esEs27(x0, x1, ty_Ordering)
new_esEs24(x0, x1, ty_Ordering)
new_esEs8(GT, GT)
new_esEs27(x0, x1, ty_Double)
new_ltEs15(False, False)
new_ltEs6(Right(x0), Right(x1), x2, ty_Float)
new_esEs7(Just(x0), Just(x1), ty_Integer)
new_esEs6(Right(x0), Right(x1), x2, ty_Double)
new_compare3([], :(x0, x1), x2)
new_esEs6(Left(x0), Left(x1), ty_Integer, x2)
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_ltEs18(x0, x1, ty_Int)
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs17(x0, x1)
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_ltEs6(Right(x0), Right(x1), x2, ty_Char)
new_esEs8(LT, LT)
new_lt11(x0, x1, ty_Bool)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs7(Just(x0), Just(x1), app(ty_[], x2))
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_esEs6(Left(x0), Left(x1), ty_Ordering, x2)
new_lt21(x0, x1, ty_Ordering)
new_esEs11(:(x0, x1), [], x2)
new_esEs24(x0, x1, ty_Float)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_esEs28(x0, x1, ty_Int)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs16(True, False)
new_esEs16(False, True)
new_pePe(False, x0)
new_esEs21(x0, x1, ty_Double)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, ty_Double)
new_esEs23(x0, x1, ty_Integer)
new_lt11(x0, x1, ty_Ordering)
new_esEs25(x0, x1, ty_Int)
new_esEs8(GT, LT)
new_esEs8(LT, GT)
new_primCmpNat0(Succ(x0), Succ(x1))
new_esEs13(Char(x0), Char(x1))
new_esEs16(True, True)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_pePe(True, x0)
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_primCompAux0(x0, GT)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_esEs6(Left(x0), Left(x1), ty_Int, x2)
new_compare23(@2(x0, x1), @2(x2, x3), False, x4, x5)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_compare18(Float(x0, x1), Float(x2, x3))
new_lt13(x0, x1)
new_ltEs5(LT, EQ)
new_ltEs5(EQ, LT)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_primEqNat0(Zero, Zero)
new_ltEs7(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs6(Left(x0), Left(x1), ty_Float, x2)
new_ltEs20(x0, x1, ty_Ordering)
new_esEs27(x0, x1, ty_Integer)
new_ltEs20(x0, x1, ty_Bool)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_ltEs18(x0, x1, ty_Bool)
new_esEs21(x0, x1, ty_Ordering)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_lt11(x0, x1, app(ty_Ratio, x2))
new_esEs28(x0, x1, ty_Char)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs6(Right(x0), Right(x1), x2, app(ty_[], x3))
new_lt16(x0, x1)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_ltEs12(Nothing, Just(x0), x1)
new_esEs25(x0, x1, ty_Ordering)
new_compare24(x0, x1, True)
new_primPlusNat1(Succ(x0), Zero)
new_ltEs4(x0, x1)
new_esEs28(x0, x1, ty_Integer)
new_lt19(x0, x1, ty_@0)
new_primMulNat0(Zero, Zero)
new_esEs26(x0, x1, ty_Ordering)
new_esEs21(x0, x1, ty_Float)
new_compare112(x0, x1, x2, x3, False, x4, x5, x6)
new_ltEs6(Right(x0), Right(x1), x2, ty_Bool)
new_esEs18(x0, x1, ty_Integer)
new_lt11(x0, x1, app(app(ty_Either, x2), x3))
new_lt11(x0, x1, ty_Int)
new_primCompAux1(x0, x1, x2, x3)
new_esEs6(Left(x0), Left(x1), ty_Bool, x2)
new_esEs22(x0, x1, ty_Int)
new_compare111(x0, x1, True, x2, x3, x4)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_ltEs6(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_ltEs11(x0, x1, x2)
new_lt19(x0, x1, ty_Integer)
new_esEs6(Left(x0), Left(x1), ty_Float, x2)
new_esEs7(Nothing, Just(x0), x1)
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_esEs28(x0, x1, ty_Bool)
new_ltEs12(Just(x0), Just(x1), app(ty_Maybe, x2))
new_ltEs18(x0, x1, app(ty_[], x2))
new_ltEs20(x0, x1, ty_Double)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs11([], :(x0, x1), x2)
new_ltEs6(Right(x0), Right(x1), x2, ty_Integer)
new_esEs18(x0, x1, app(app(ty_@2, x2), x3))
new_compare29(x0, x1, app(ty_Ratio, x2))
new_ltEs19(x0, x1, ty_Bool)
new_ltEs12(Just(x0), Just(x1), ty_Char)
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_compare29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs18(x0, x1, app(app(ty_Either, x2), x3))
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_esEs4(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_ltEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, ty_@0)
new_esEs26(x0, x1, ty_Integer)
new_primCompAux0(x0, LT)
new_esEs29(x0, x1, ty_Double)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs7(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_compare23(x0, x1, True, x2, x3)
new_esEs25(x0, x1, ty_Float)
new_ltEs18(x0, x1, app(ty_Maybe, x2))
new_esEs6(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs6(Left(x0), Left(x1), ty_Double, x2)
new_esEs27(x0, x1, ty_Char)
new_ltEs6(Left(x0), Left(x1), ty_Ordering, x2)
new_ltEs18(x0, x1, ty_Char)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_esEs19(x0, x1, ty_Char)
new_esEs6(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs23(x0, x1, ty_Int)
new_ltEs12(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_lt21(x0, x1, ty_Char)
new_lt8(x0, x1)
new_primCmpNat0(Succ(x0), Zero)
new_esEs19(x0, x1, ty_Ordering)
new_primMulInt(Neg(x0), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs28(x0, x1, ty_Float)
new_ltEs14(x0, x1)
new_esEs11([], [], x0)
new_esEs20(x0, x1, ty_@0)
new_esEs20(x0, x1, ty_Ordering)
new_esEs29(x0, x1, ty_Bool)
new_esEs20(x0, x1, ty_Double)
new_ltEs12(Just(x0), Just(x1), ty_Integer)
new_ltEs6(Right(x0), Right(x1), x2, ty_@0)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs19(x0, x1, ty_@0)
new_esEs20(x0, x1, ty_Int)
new_esEs24(x0, x1, ty_Int)
new_esEs22(x0, x1, ty_Integer)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_lt21(x0, x1, app(ty_Maybe, x2))
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_ltEs20(x0, x1, ty_Integer)
new_lt20(x0, x1, app(ty_[], x2))
new_esEs18(x0, x1, app(ty_Maybe, x2))
new_esEs27(x0, x1, ty_Float)
new_ltEs12(Just(x0), Just(x1), ty_Float)
new_ltEs18(x0, x1, ty_@0)
new_esEs15(Double(x0, x1), Double(x2, x3))
new_lt21(x0, x1, ty_Double)
new_lt20(x0, x1, ty_Double)
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_esEs7(Just(x0), Just(x1), app(ty_Maybe, x2))
new_ltEs19(x0, x1, ty_Float)
new_esEs20(x0, x1, ty_Bool)
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs8(x0, x1)
new_sr0(x0, x1)
new_primEqNat0(Succ(x0), Zero)
new_esEs7(Just(x0), Just(x1), ty_Char)
new_primPlusNat1(Zero, Zero)
new_lt6(x0, x1)
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_lt20(x0, x1, ty_Bool)
new_esEs28(x0, x1, app(ty_[], x2))
new_esEs19(x0, x1, app(ty_Maybe, x2))
new_esEs18(x0, x1, ty_Int)
new_esEs6(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs25(x0, x1, ty_Char)
new_compare110(x0, x1, False)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_ltEs6(Right(x0), Right(x1), x2, ty_Double)
new_esEs6(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_compare14(x0, x1)
new_esEs7(Just(x0), Nothing, x1)
new_primMulNat0(Succ(x0), Succ(x1))
new_compare3([], [], x0)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, ty_Double)
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_esEs18(x0, x1, app(ty_[], x2))
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_primMulNat0(Zero, Succ(x0))
new_esEs26(x0, x1, ty_@0)
new_esEs21(x0, x1, ty_Int)
new_esEs18(x0, x1, ty_@0)
new_lt11(x0, x1, ty_Integer)
new_esEs20(x0, x1, ty_Float)
new_esEs26(x0, x1, ty_Bool)
new_esEs19(x0, x1, app(ty_Ratio, x2))
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_asAs(False, x0)
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs19(x0, x1, ty_Integer)
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_lt7(x0, x1, x2)
new_esEs19(x0, x1, ty_Double)
new_esEs29(x0, x1, ty_Ordering)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs6(Left(x0), Left(x1), ty_Char, x2)
new_esEs7(Just(x0), Just(x1), ty_Int)
new_ltEs15(True, False)
new_ltEs15(False, True)
new_lt4(x0, x1, x2)
new_compare111(x0, x1, False, x2, x3, x4)
new_esEs6(Right(x0), Right(x1), x2, ty_@0)
new_esEs7(Just(x0), Just(x1), ty_Ordering)
new_esEs20(x0, x1, ty_Integer)
new_esEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, app(ty_[], x2))
new_ltEs6(Left(x0), Left(x1), ty_Integer, x2)
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_compare16(x0, x1)
new_compare29(x0, x1, ty_Bool)
new_compare210(x0, x1, False, x2, x3)
new_ltEs6(Left(x0), Left(x1), ty_Bool, x2)
new_lt11(x0, x1, app(ty_[], x2))
new_primPlusNat0(Zero, x0)
new_esEs29(x0, x1, ty_Float)
new_compare29(x0, x1, ty_Ordering)
new_compare19(x0, x1, x2, x3, False, x4, x5)
new_ltEs18(x0, x1, ty_Ordering)
new_compare29(x0, x1, app(ty_Maybe, x2))
new_esEs6(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs18(x0, x1, ty_Float)
new_esEs7(Just(x0), Just(x1), app(ty_Ratio, x2))
new_compare25(x0, x1, False, x2, x3, x4)
new_esEs28(x0, x1, ty_Double)
new_esEs25(x0, x1, ty_@0)
new_primMulNat0(Succ(x0), Zero)
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs6(Left(x0), Left(x1), app(ty_[], x2), x3)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs16(x0, x1, x2)
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs12(Just(x0), Just(x1), ty_Double)
new_esEs6(Right(x0), Right(x1), x2, ty_Bool)
new_esEs26(x0, x1, ty_Float)
new_ltEs19(x0, x1, app(ty_[], x2))
new_compare11(x0, x1, x2, x3, x4)
new_primEqInt(Neg(Zero), Neg(Zero))
new_ltEs12(Just(x0), Just(x1), ty_Int)
new_compare7(Char(x0), Char(x1))
new_lt20(x0, x1, ty_Float)
new_esEs19(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs6(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs6(Left(x0), Left(x1), ty_@0, x2)
new_lt21(x0, x1, ty_@0)
new_esEs6(Right(x0), Right(x1), x2, ty_Float)
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_compare29(x0, x1, ty_Integer)
new_ltEs19(x0, x1, ty_Integer)
new_esEs18(x0, x1, app(ty_Ratio, x2))
new_lt19(x0, x1, ty_Ordering)
new_esEs28(x0, x1, ty_@0)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_lt21(x0, x1, app(ty_Ratio, x2))
new_esEs6(Left(x0), Left(x1), app(ty_[], x2), x3)
new_compare24(x0, x1, False)
new_compare15(Double(x0, x1), Double(x2, x3))
new_lt19(x0, x1, ty_Float)
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs24(x0, x1, ty_Bool)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs9(@0, @0)
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_ltEs12(Just(x0), Just(x1), ty_@0)
new_ltEs12(Just(x0), Just(x1), app(ty_Ratio, x2))
new_compare6(@0, @0)
new_compare29(x0, x1, app(app(ty_@2, x2), x3))
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs6(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_lt5(x0, x1, x2, x3, x4)
new_compare28(x0, x1, False, x2)
new_lt20(x0, x1, ty_Char)
new_compare10(x0, x1, False, x2, x3)
new_primCompAux0(x0, EQ)
new_lt21(x0, x1, ty_Float)
new_ltEs5(GT, LT)
new_ltEs5(LT, GT)
new_ltEs13(x0, x1)
new_lt19(x0, x1, app(ty_Maybe, x2))
new_esEs7(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs20(x0, x1, app(ty_[], x2))
new_esEs21(x0, x1, ty_Bool)
new_compare29(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpNat0(Zero, Zero)
new_ltEs6(Left(x0), Left(x1), ty_Char, x2)
new_lt11(x0, x1, app(app(ty_@2, x2), x3))
new_compare17(x0, x1, False)
new_esEs7(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs25(x0, x1, ty_Bool)
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_esEs6(Right(x0), Right(x1), x2, ty_Ordering)
new_ltEs12(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_compare25(x0, x1, True, x2, x3, x4)
new_esEs6(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_compare12(Integer(x0), Integer(x1))
new_esEs19(x0, x1, ty_Bool)
new_compare29(x0, x1, ty_Double)
new_ltEs6(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs25(x0, x1, app(ty_[], x2))
new_compare8(x0, x1, x2)
new_esEs7(Just(x0), Just(x1), ty_@0)
new_lt21(x0, x1, ty_Integer)
new_esEs21(x0, x1, ty_@0)
new_ltEs6(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs24(x0, x1, ty_Double)
new_lt15(x0, x1)
new_lt19(x0, x1, ty_Int)
new_ltEs12(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_lt14(x0, x1, x2, x3)
new_ltEs6(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_esEs19(x0, x1, ty_Float)
new_primEqNat0(Zero, Succ(x0))
new_esEs26(x0, x1, ty_Char)
new_ltEs5(GT, GT)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt11(x0, x1, ty_Double)
new_esEs16(False, False)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs18(x0, x1, ty_Double)
new_esEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_lt21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs18(x0, x1, ty_Bool)
new_lt21(x0, x1, ty_Bool)
new_esEs26(x0, x1, ty_Double)
new_esEs18(x0, x1, ty_Ordering)
new_esEs18(x0, x1, ty_Char)
new_esEs12(x0, x1)
new_lt10(x0, x1, x2, x3)
new_ltEs18(x0, x1, app(ty_Ratio, x2))
new_compare26(x0, x1)
new_esEs17(Float(x0, x1), Float(x2, x3))
new_ltEs6(Left(x0), Left(x1), ty_Int, x2)
new_ltEs10(x0, x1)
new_primCmpNat0(Zero, Succ(x0))
new_lt11(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs27(x0, x1, ty_Bool)
new_not(True)
new_ltEs18(x0, x1, ty_Double)
new_compare110(x0, x1, True)
new_esEs6(Right(x0), Right(x1), x2, ty_Integer)
new_esEs21(x0, x1, ty_Integer)
new_ltEs12(Just(x0), Nothing, x1)
new_ltEs19(x0, x1, ty_Char)
new_lt11(x0, x1, ty_Char)
new_esEs5(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs6(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_compare9(x0, x1, x2, x3)
new_esEs29(x0, x1, app(ty_[], x2))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_not(False)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs6(Right(x0), Right(x1), x2, ty_Int)
new_ltEs12(Just(x0), Just(x1), ty_Ordering)
new_lt21(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs12(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs6(Right(x0), Right(x1), x2, ty_Ordering)
new_lt20(x0, x1, ty_Ordering)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_ltEs5(EQ, EQ)
new_ltEs6(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_ltEs18(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs9(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs19(x0, x1, app(ty_[], x2))
new_esEs25(x0, x1, ty_Integer)
new_ltEs20(x0, x1, ty_Char)
new_esEs7(Just(x0), Just(x1), ty_Float)
new_ltEs20(x0, x1, ty_Int)
new_esEs7(Just(x0), Just(x1), ty_Bool)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_ltEs20(x0, x1, ty_Float)
new_compare29(x0, x1, ty_@0)
new_esEs10(Integer(x0), Integer(x1))
new_ltEs6(Left(x0), Left(x1), ty_@0, x2)
new_esEs6(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs18(x0, x1, ty_Float)
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_compare28(x0, x1, True, x2)
new_compare30(x0, x1, x2, x3)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_compare113(x0, x1, True, x2)
new_lt20(x0, x1, ty_@0)
new_esEs29(x0, x1, ty_Char)
new_ltEs19(x0, x1, ty_@0)
new_compare27(x0, x1, True)
new_esEs27(x0, x1, ty_Int)
new_lt19(x0, x1, app(ty_Ratio, x2))
new_ltEs6(Left(x0), Left(x1), ty_Double, x2)
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs6(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs6(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_compare10(x0, x1, True, x2, x3)
new_compare3(:(x0, x1), [], x2)
new_compare113(x0, x1, False, x2)
new_esEs19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs6(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_ltEs12(Just(x0), Just(x1), ty_Bool)
new_lt21(x0, x1, app(app(ty_@2, x2), x3))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Pos(Zero), Pos(Zero))
new_ltEs20(x0, x1, app(ty_[], x2))
new_esEs24(x0, x1, ty_Char)
new_esEs7(Just(x0), Just(x1), ty_Double)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, ty_@0)
new_ltEs6(Right(x0), Right(x1), x2, ty_Int)
new_esEs27(x0, x1, app(ty_[], x2))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_esEs28(x0, x1, ty_Ordering)
new_compare17(x0, x1, True)
new_compare112(x0, x1, x2, x3, True, x4, x5, x6)
new_compare19(x0, x1, x2, x3, True, x4, x5)
new_esEs24(x0, x1, ty_@0)
new_esEs29(x0, x1, ty_@0)
new_lt12(x0, x1)
new_lt9(x0, x1)
new_ltEs19(x0, x1, ty_Int)
new_lt21(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, ty_Int)
new_primPlusNat1(Zero, Succ(x0))
new_lt17(x0, x1, x2)
new_lt19(x0, x1, ty_Char)
new_esEs6(Right(x0), Left(x1), x2, x3)
new_esEs6(Left(x0), Right(x1), x2, x3)
new_asAs(True, x0)
new_compare29(x0, x1, ty_Float)
new_ltEs5(LT, LT)
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_lt19(x0, x1, ty_Bool)
new_esEs24(x0, x1, app(ty_[], x2))
new_lt19(x0, x1, ty_Double)
new_esEs6(Right(x0), Right(x1), x2, ty_Char)

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: