YES 4.516 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 b, Ord a) => (a,b)  ->  (a,b)  ->  Bool) :: (Ord a, Ord b) => (a,b)  ->  (a,b)  ->  Bool)

module Main where
  import qualified Prelude


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

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



↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ IFR

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

module Main where
  import qualified Prelude


Replaced joker patterns by fresh variables and removed binding patterns.

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

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

compare0 x y True = GT

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

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

compare3 x y = compare2 x y (x == y)

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

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

gcd'0 x y = gcd' y (x `rem` y)

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

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

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

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

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

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

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

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

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

is transformed to
absReal x = absReal2 x

absReal0 x True = `negate` x

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

absReal2 x = absReal1 x (x >= 0)

The following Function with conditions
undefined 
 | False
 = undefined

is transformed to
undefined  = undefined1

undefined0 True = undefined

undefined1  = undefined0 False

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

is transformed to
reduce x y = reduce2 x y

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



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

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

module Main where
  import qualified Prelude


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

are unpacked to the following functions on top level
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

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

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

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

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



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

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

module Main where
  import qualified Prelude


Haskell To QDPs


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

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

new_primCmpNat(Succ(vwx220000), Succ(vwx240000)) → new_primCmpNat(vwx220000, vwx240000)

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(vwx6200), Succ(vwx400000)) → new_primPlusNat(vwx6200, 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_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_esEs1(Right(vwx300), Right(vwx400), eg, app(ty_Maybe, eh)) → new_esEs0(vwx300, vwx400, eh)
new_esEs3(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), baf, bag, app(app(app(ty_@3, bbf), bbg), bbh)) → new_esEs3(vwx302, vwx402, bbf, bbg, bbh)
new_esEs3(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), baf, bag, app(ty_[], bba)) → new_esEs(vwx302, vwx402, bba)
new_esEs2(@2(vwx300, vwx301), @2(vwx400, vwx401), gb, app(app(ty_@2, gg), gh)) → new_esEs2(vwx301, vwx401, gg, gh)
new_esEs3(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), baf, app(ty_Maybe, bca), bcb) → new_esEs0(vwx301, vwx401, bca)
new_esEs(:(vwx300, vwx301), :(vwx400, vwx401), app(app(app(ty_@3, bh), ca), cb)) → new_esEs3(vwx300, vwx400, bh, ca, cb)
new_esEs(:(vwx300, vwx301), :(vwx400, vwx401), app(app(ty_@2, bf), bg)) → new_esEs2(vwx300, vwx400, bf, bg)
new_esEs2(@2(vwx300, vwx301), @2(vwx400, vwx401), gb, app(ty_Maybe, gc)) → new_esEs0(vwx301, vwx401, gc)
new_esEs0(Just(vwx300), Just(vwx400), app(ty_Maybe, cc)) → new_esEs0(vwx300, vwx400, cc)
new_esEs2(@2(vwx300, vwx301), @2(vwx400, vwx401), app(app(ty_@2, baa), bab), he) → new_esEs2(vwx300, vwx400, baa, bab)
new_esEs3(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), baf, bag, app(ty_Maybe, bah)) → new_esEs0(vwx302, vwx402, bah)
new_esEs3(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), app(ty_[], bdd), bag, bcb) → new_esEs(vwx300, vwx400, bdd)
new_esEs0(Just(vwx300), Just(vwx400), app(ty_[], cd)) → new_esEs(vwx300, vwx400, cd)
new_esEs2(@2(vwx300, vwx301), @2(vwx400, vwx401), gb, app(app(app(ty_@3, ha), hb), hc)) → new_esEs3(vwx301, vwx401, ha, hb, hc)
new_esEs1(Left(vwx300), Left(vwx400), app(app(ty_Either, dh), ea), df) → new_esEs1(vwx300, vwx400, dh, ea)
new_esEs3(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), baf, app(ty_[], bcc), bcb) → new_esEs(vwx301, vwx401, bcc)
new_esEs1(Right(vwx300), Right(vwx400), eg, app(app(ty_Either, fb), fc)) → new_esEs1(vwx300, vwx400, fb, fc)
new_esEs3(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), app(app(ty_Either, bde), bdf), bag, bcb) → new_esEs1(vwx300, vwx400, bde, bdf)
new_esEs1(Left(vwx300), Left(vwx400), app(app(ty_@2, eb), ec), df) → new_esEs2(vwx300, vwx400, eb, ec)
new_esEs2(@2(vwx300, vwx301), @2(vwx400, vwx401), app(ty_Maybe, hd), he) → new_esEs0(vwx300, vwx400, hd)
new_esEs1(Left(vwx300), Left(vwx400), app(ty_Maybe, de), df) → new_esEs0(vwx300, vwx400, de)
new_esEs(:(vwx300, vwx301), :(vwx400, vwx401), app(ty_Maybe, bb)) → new_esEs0(vwx300, vwx400, bb)
new_esEs2(@2(vwx300, vwx301), @2(vwx400, vwx401), gb, app(app(ty_Either, ge), gf)) → new_esEs1(vwx301, vwx401, ge, gf)
new_esEs3(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), baf, app(app(ty_Either, bcd), bce), bcb) → new_esEs1(vwx301, vwx401, bcd, bce)
new_esEs3(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), baf, app(app(app(ty_@3, bch), bda), bdb), bcb) → new_esEs3(vwx301, vwx401, bch, bda, bdb)
new_esEs0(Just(vwx300), Just(vwx400), app(app(ty_@2, cg), da)) → new_esEs2(vwx300, vwx400, cg, da)
new_esEs0(Just(vwx300), Just(vwx400), app(app(app(ty_@3, db), dc), dd)) → new_esEs3(vwx300, vwx400, db, dc, dd)
new_esEs2(@2(vwx300, vwx301), @2(vwx400, vwx401), gb, app(ty_[], gd)) → new_esEs(vwx301, vwx401, gd)
new_esEs(:(vwx300, vwx301), :(vwx400, vwx401), ba) → new_esEs(vwx301, vwx401, ba)
new_esEs3(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), baf, bag, app(app(ty_@2, bbd), bbe)) → new_esEs2(vwx302, vwx402, bbd, bbe)
new_esEs0(Just(vwx300), Just(vwx400), app(app(ty_Either, ce), cf)) → new_esEs1(vwx300, vwx400, ce, cf)
new_esEs3(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), baf, app(app(ty_@2, bcf), bcg), bcb) → new_esEs2(vwx301, vwx401, bcf, bcg)
new_esEs3(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), app(app(ty_@2, bdg), bdh), bag, bcb) → new_esEs2(vwx300, vwx400, bdg, bdh)
new_esEs1(Right(vwx300), Right(vwx400), eg, app(app(app(ty_@3, fg), fh), ga)) → new_esEs3(vwx300, vwx400, fg, fh, ga)
new_esEs1(Right(vwx300), Right(vwx400), eg, app(app(ty_@2, fd), ff)) → new_esEs2(vwx300, vwx400, fd, ff)
new_esEs3(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), app(ty_Maybe, bdc), bag, bcb) → new_esEs0(vwx300, vwx400, bdc)
new_esEs2(@2(vwx300, vwx301), @2(vwx400, vwx401), app(ty_[], hf), he) → new_esEs(vwx300, vwx400, hf)
new_esEs3(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), baf, bag, app(app(ty_Either, bbb), bbc)) → new_esEs1(vwx302, vwx402, bbb, bbc)
new_esEs1(Right(vwx300), Right(vwx400), eg, app(ty_[], fa)) → new_esEs(vwx300, vwx400, fa)
new_esEs(:(vwx300, vwx301), :(vwx400, vwx401), app(app(ty_Either, bd), be)) → new_esEs1(vwx300, vwx400, bd, be)
new_esEs1(Left(vwx300), Left(vwx400), app(ty_[], dg), df) → new_esEs(vwx300, vwx400, dg)
new_esEs1(Left(vwx300), Left(vwx400), app(app(app(ty_@3, ed), ee), ef), df) → new_esEs3(vwx300, vwx400, ed, ee, ef)
new_esEs2(@2(vwx300, vwx301), @2(vwx400, vwx401), app(app(ty_Either, hg), hh), he) → new_esEs1(vwx300, vwx400, hg, hh)
new_esEs(:(vwx300, vwx301), :(vwx400, vwx401), app(ty_[], bc)) → new_esEs(vwx300, vwx400, bc)
new_esEs3(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), app(app(app(ty_@3, bea), beb), bec), bag, bcb) → new_esEs3(vwx300, vwx400, bea, beb, bec)
new_esEs2(@2(vwx300, vwx301), @2(vwx400, vwx401), app(app(app(ty_@3, bac), bad), bae), he) → new_esEs3(vwx300, vwx400, bac, bad, bae)

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

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



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

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

new_compare2(@2(vwx2200, Just(vwx22010)), @2(vwx2400, Just(vwx24010)), False, ce, app(ty_Maybe, app(app(ty_@2, ff), fg))) → new_ltEs0(vwx22010, vwx24010, ff, fg)
new_compare2(@2(vwx2200, @2(vwx22010, vwx22011)), @2(vwx2400, @2(vwx24010, vwx24011)), False, ce, app(app(ty_@2, eb), app(app(app(ty_@3, fa), fb), fc))) → new_ltEs3(vwx22011, vwx24011, fa, fb, fc)
new_lt1(vwx2200, vwx2400, bg) → new_compare20(vwx2200, vwx2400, new_esEs6(vwx2200, vwx2400, bg), bg)
new_compare2(@2(vwx2200, vwx2201), @2(vwx2400, vwx2401), False, ce, app(ty_[], cf)) → new_compare0(vwx2201, vwx2401, cf)
new_compare2(@2(vwx2200, Left(vwx22010)), @2(vwx2400, Left(vwx24010)), False, ce, app(app(ty_Either, app(ty_Maybe, hb)), gg)) → new_ltEs1(vwx22010, vwx24010, hb)
new_ltEs0(@2(vwx22010, vwx22011), @2(vwx24010, vwx24011), eb, app(ty_Maybe, ef)) → new_ltEs1(vwx22011, vwx24011, ef)
new_compare2(@2(vwx2200, @2(vwx22010, vwx22011)), @2(vwx2400, @2(vwx24010, vwx24011)), False, ce, app(app(ty_@2, eb), app(app(ty_@2, ed), ee))) → new_ltEs0(vwx22011, vwx24011, ed, ee)
new_ltEs3(@3(vwx22010, vwx22011, vwx22012), @3(vwx24010, vwx24011, vwx24012), bce, app(app(ty_Either, bdb), bdc), bbd) → new_lt2(vwx22011, vwx24011, bdb, bdc)
new_ltEs0(@2(vwx22010, vwx22011), @2(vwx24010, vwx24011), eb, app(app(app(ty_@3, fa), fb), fc)) → new_ltEs3(vwx22011, vwx24011, fa, fb, fc)
new_compare0(:(vwx22000, vwx22001), :(vwx24000, vwx24001), bc) → new_compare0(vwx22001, vwx24001, bc)
new_ltEs2(Left(vwx22010), Left(vwx24010), app(app(ty_Either, hc), hd), gg) → new_ltEs2(vwx22010, vwx24010, hc, hd)
new_compare2(@2(vwx2200, @3(vwx22010, vwx22011, vwx22012)), @2(vwx2400, @3(vwx24010, vwx24011, vwx24012)), False, ce, app(app(app(ty_@3, bce), app(app(app(ty_@3, bdd), bde), bdf)), bbd)) → new_lt3(vwx22011, vwx24011, bdd, bde, bdf)
new_compare4(vwx2200, vwx2400, cb, cc, cd) → new_compare22(vwx2200, vwx2400, new_esEs8(vwx2200, vwx2400, cb, cc, cd), cb, cc, cd)
new_ltEs3(@3(vwx22010, vwx22011, vwx22012), @3(vwx24010, vwx24011, vwx24012), bce, app(ty_[], bcf), bbd) → new_lt0(vwx22011, vwx24011, bcf)
new_compare2(@2(vwx2200, @2(vwx22010, vwx22011)), @2(vwx2400, @2(vwx24010, vwx24011)), False, ce, app(app(ty_@2, app(app(ty_@2, db), dc)), da)) → new_lt(vwx22010, vwx24010, db, dc)
new_primCompAux(vwx22000, vwx24000, vwx102, app(app(ty_@2, bfa), bfb)) → new_compare2(vwx22000, vwx24000, new_esEs9(vwx22000, vwx24000, bfa, bfb), bfa, bfb)
new_ltEs3(@3(vwx22010, vwx22011, vwx22012), @3(vwx24010, vwx24011, vwx24012), app(app(ty_@2, bbe), bbf), bbc, bbd) → new_lt(vwx22010, vwx24010, bbe, bbf)
new_compare2(@2(vwx2200, @3(vwx22010, vwx22011, vwx22012)), @2(vwx2400, @3(vwx24010, vwx24011, vwx24012)), False, ce, app(app(app(ty_@3, bce), bbc), app(ty_[], bdg))) → new_ltEs(vwx22012, vwx24012, bdg)
new_compare22(vwx2200, vwx2400, False, cb, cc, cd) → new_ltEs3(vwx2200, vwx2400, cb, cc, cd)
new_compare2(@2(vwx2200, @3(vwx22010, vwx22011, vwx22012)), @2(vwx2400, @3(vwx24010, vwx24011, vwx24012)), False, ce, app(app(app(ty_@3, bce), bbc), app(app(ty_Either, bec), bed))) → new_ltEs2(vwx22012, vwx24012, bec, bed)
new_ltEs2(Left(vwx22010), Left(vwx24010), app(app(ty_@2, gh), ha), gg) → new_ltEs0(vwx22010, vwx24010, gh, ha)
new_compare2(@2(vwx2200, @2(vwx22010, vwx22011)), @2(vwx2400, @2(vwx24010, vwx24011)), False, ce, app(app(ty_@2, eb), app(app(ty_Either, eg), eh))) → new_ltEs2(vwx22011, vwx24011, eg, eh)
new_compare20(vwx2200, vwx2400, False, bg) → new_ltEs1(vwx2200, vwx2400, bg)
new_ltEs1(Just(vwx22010), Just(vwx24010), app(app(app(ty_@3, gc), gd), ge)) → new_ltEs3(vwx22010, vwx24010, gc, gd, ge)
new_compare3(vwx2200, vwx2400, bh, ca) → new_compare21(vwx2200, vwx2400, new_esEs7(vwx2200, vwx2400, bh, ca), bh, ca)
new_ltEs3(@3(vwx22010, vwx22011, vwx22012), @3(vwx24010, vwx24011, vwx24012), bce, bbc, app(ty_Maybe, beb)) → new_ltEs1(vwx22012, vwx24012, beb)
new_compare2(@2(:(vwx22000, vwx22001), vwx2201), @2(:(vwx24000, vwx24001), vwx2401), False, app(ty_[], bc), bd) → new_compare0(vwx22001, vwx24001, bc)
new_compare2(@2(vwx2200, @3(vwx22010, vwx22011, vwx22012)), @2(vwx2400, @3(vwx24010, vwx24011, vwx24012)), False, ce, app(app(app(ty_@3, bce), app(ty_[], bcf)), bbd)) → new_lt0(vwx22011, vwx24011, bcf)
new_compare2(@2(vwx2200, vwx2201), @2(vwx2400, vwx2401), False, app(ty_Maybe, bg), bd) → new_compare20(vwx2200, vwx2400, new_esEs6(vwx2200, vwx2400, bg), bg)
new_ltEs1(Just(vwx22010), Just(vwx24010), app(ty_[], fd)) → new_ltEs(vwx22010, vwx24010, fd)
new_ltEs3(@3(vwx22010, vwx22011, vwx22012), @3(vwx24010, vwx24011, vwx24012), app(app(ty_Either, bbh), bca), bbc, bbd) → new_lt2(vwx22010, vwx24010, bbh, bca)
new_compare2(@2(:(vwx22000, vwx22001), vwx2201), @2(:(vwx24000, vwx24001), vwx2401), False, app(ty_[], bc), bd) → new_primCompAux(vwx22000, vwx24000, new_compare(vwx22001, vwx24001, bc), bc)
new_compare2(@2(vwx2200, @2(vwx22010, vwx22011)), @2(vwx2400, @2(vwx24010, vwx24011)), False, ce, app(app(ty_@2, app(ty_[], cg)), da)) → new_lt0(vwx22010, vwx24010, cg)
new_ltEs2(Left(vwx22010), Left(vwx24010), app(ty_Maybe, hb), gg) → new_ltEs1(vwx22010, vwx24010, hb)
new_lt2(vwx2200, vwx2400, bh, ca) → new_compare21(vwx2200, vwx2400, new_esEs7(vwx2200, vwx2400, bh, ca), bh, ca)
new_compare21(vwx2200, vwx2400, False, bh, ca) → new_ltEs2(vwx2200, vwx2400, bh, ca)
new_compare2(@2(vwx2200, Right(vwx22010)), @2(vwx2400, Right(vwx24010)), False, ce, app(app(ty_Either, hh), app(ty_[], baa))) → new_ltEs(vwx22010, vwx24010, baa)
new_compare2(@2(vwx2200, @2(vwx22010, vwx22011)), @2(vwx2400, @2(vwx24010, vwx24011)), False, ce, app(app(ty_@2, eb), app(ty_[], ec))) → new_ltEs(vwx22011, vwx24011, ec)
new_ltEs(vwx2201, vwx2401, cf) → new_compare0(vwx2201, vwx2401, cf)
new_compare2(@2(vwx2200, @3(vwx22010, vwx22011, vwx22012)), @2(vwx2400, @3(vwx24010, vwx24011, vwx24012)), False, ce, app(app(app(ty_@3, app(ty_[], bbb)), bbc), bbd)) → new_lt0(vwx22010, vwx24010, bbb)
new_lt3(vwx2200, vwx2400, cb, cc, cd) → new_compare22(vwx2200, vwx2400, new_esEs8(vwx2200, vwx2400, cb, cc, cd), cb, cc, cd)
new_ltEs3(@3(vwx22010, vwx22011, vwx22012), @3(vwx24010, vwx24011, vwx24012), bce, app(ty_Maybe, bda), bbd) → new_lt1(vwx22011, vwx24011, bda)
new_compare2(@2(vwx2200, @2(vwx22010, vwx22011)), @2(vwx2400, @2(vwx24010, vwx24011)), False, ce, app(app(ty_@2, app(app(app(ty_@3, dg), dh), ea)), da)) → new_lt3(vwx22010, vwx24010, dg, dh, ea)
new_ltEs3(@3(vwx22010, vwx22011, vwx22012), @3(vwx24010, vwx24011, vwx24012), app(ty_Maybe, bbg), bbc, bbd) → new_lt1(vwx22010, vwx24010, bbg)
new_primCompAux(vwx22000, vwx24000, vwx102, app(ty_Maybe, bfc)) → new_compare1(vwx22000, vwx24000, bfc)
new_primCompAux(vwx22000, vwx24000, vwx102, app(app(ty_Either, bfd), bfe)) → new_compare3(vwx22000, vwx24000, bfd, bfe)
new_compare2(@2(vwx2200, Right(vwx22010)), @2(vwx2400, Right(vwx24010)), False, ce, app(app(ty_Either, hh), app(app(app(ty_@3, bag), bah), bba))) → new_ltEs3(vwx22010, vwx24010, bag, bah, bba)
new_compare2(@2(vwx2200, @3(vwx22010, vwx22011, vwx22012)), @2(vwx2400, @3(vwx24010, vwx24011, vwx24012)), False, ce, app(app(app(ty_@3, app(app(app(ty_@3, bcb), bcc), bcd)), bbc), bbd)) → new_lt3(vwx22010, vwx24010, bcb, bcc, bcd)
new_compare2(@2(vwx2200, @3(vwx22010, vwx22011, vwx22012)), @2(vwx2400, @3(vwx24010, vwx24011, vwx24012)), False, ce, app(app(app(ty_@3, bce), bbc), app(app(ty_@2, bdh), bea))) → new_ltEs0(vwx22012, vwx24012, bdh, bea)
new_ltEs1(Just(vwx22010), Just(vwx24010), app(app(ty_Either, ga), gb)) → new_ltEs2(vwx22010, vwx24010, ga, gb)
new_ltEs3(@3(vwx22010, vwx22011, vwx22012), @3(vwx24010, vwx24011, vwx24012), bce, app(app(app(ty_@3, bdd), bde), bdf), bbd) → new_lt3(vwx22011, vwx24011, bdd, bde, bdf)
new_compare2(@2(vwx2200, @2(vwx22010, vwx22011)), @2(vwx2400, @2(vwx24010, vwx24011)), False, ce, app(app(ty_@2, app(app(ty_Either, de), df)), da)) → new_lt2(vwx22010, vwx24010, de, df)
new_compare2(@2(vwx2200, vwx2201), @2(vwx2400, vwx2401), False, app(app(app(ty_@3, cb), cc), cd), bd) → new_compare22(vwx2200, vwx2400, new_esEs8(vwx2200, vwx2400, cb, cc, cd), cb, cc, cd)
new_lt(@2(vwx30, vwx31), @2(vwx40, vwx41), bga, bgb) → new_esEs4(vwx30, vwx31, vwx40, vwx41, new_esEs10(vwx30, vwx40, bga), bga, bgb)
new_ltEs3(@3(vwx22010, vwx22011, vwx22012), @3(vwx24010, vwx24011, vwx24012), bce, bbc, app(app(ty_@2, bdh), bea)) → new_ltEs0(vwx22012, vwx24012, bdh, bea)
new_compare2(@2(vwx2200, Left(vwx22010)), @2(vwx2400, Left(vwx24010)), False, ce, app(app(ty_Either, app(app(app(ty_@3, he), hf), hg)), gg)) → new_ltEs3(vwx22010, vwx24010, he, hf, hg)
new_ltEs0(@2(vwx22010, vwx22011), @2(vwx24010, vwx24011), app(app(ty_Either, de), df), da) → new_lt2(vwx22010, vwx24010, de, df)
new_ltEs0(@2(vwx22010, vwx22011), @2(vwx24010, vwx24011), app(ty_Maybe, dd), da) → new_lt1(vwx22010, vwx24010, dd)
new_ltEs2(Right(vwx22010), Right(vwx24010), hh, app(app(app(ty_@3, bag), bah), bba)) → new_ltEs3(vwx22010, vwx24010, bag, bah, bba)
new_compare2(@2(vwx2200, Just(vwx22010)), @2(vwx2400, Just(vwx24010)), False, ce, app(ty_Maybe, app(app(app(ty_@3, gc), gd), ge))) → new_ltEs3(vwx22010, vwx24010, gc, gd, ge)
new_ltEs0(@2(vwx22010, vwx22011), @2(vwx24010, vwx24011), app(app(app(ty_@3, dg), dh), ea), da) → new_lt3(vwx22010, vwx24010, dg, dh, ea)
new_compare2(@2(vwx2200, @3(vwx22010, vwx22011, vwx22012)), @2(vwx2400, @3(vwx24010, vwx24011, vwx24012)), False, ce, app(app(app(ty_@3, app(ty_Maybe, bbg)), bbc), bbd)) → new_lt1(vwx22010, vwx24010, bbg)
new_compare0(:(vwx22000, vwx22001), :(vwx24000, vwx24001), bc) → new_primCompAux(vwx22000, vwx24000, new_compare(vwx22001, vwx24001, bc), bc)
new_compare2(@2(vwx2200, @3(vwx22010, vwx22011, vwx22012)), @2(vwx2400, @3(vwx24010, vwx24011, vwx24012)), False, ce, app(app(app(ty_@3, bce), app(app(ty_Either, bdb), bdc)), bbd)) → new_lt2(vwx22011, vwx24011, bdb, bdc)
new_ltEs2(Left(vwx22010), Left(vwx24010), app(app(app(ty_@3, he), hf), hg), gg) → new_ltEs3(vwx22010, vwx24010, he, hf, hg)
new_compare1(vwx2200, vwx2400, bg) → new_compare20(vwx2200, vwx2400, new_esEs6(vwx2200, vwx2400, bg), bg)
new_compare2(@2(vwx2200, vwx2201), @2(vwx2400, vwx2401), False, app(app(ty_Either, bh), ca), bd) → new_compare21(vwx2200, vwx2400, new_esEs7(vwx2200, vwx2400, bh, ca), bh, ca)
new_ltEs3(@3(vwx22010, vwx22011, vwx22012), @3(vwx24010, vwx24011, vwx24012), bce, bbc, app(ty_[], bdg)) → new_ltEs(vwx22012, vwx24012, bdg)
new_compare2(@2(vwx2200, vwx2201), @2(vwx2400, vwx2401), False, app(app(ty_@2, be), bf), bd) → new_lt(vwx2200, vwx2400, be, bf)
new_esEs4(vwx11, vwx12, vwx13, vwx14, True, ba, bb) → new_compare2(@2(vwx11, vwx12), @2(vwx13, vwx14), new_esEs5(vwx12, vwx14, bb), ba, bb)
new_compare2(@2(vwx2200, Right(vwx22010)), @2(vwx2400, Right(vwx24010)), False, ce, app(app(ty_Either, hh), app(app(ty_Either, bae), baf))) → new_ltEs2(vwx22010, vwx24010, bae, baf)
new_ltEs1(Just(vwx22010), Just(vwx24010), app(ty_Maybe, fh)) → new_ltEs1(vwx22010, vwx24010, fh)
new_ltEs2(Right(vwx22010), Right(vwx24010), hh, app(ty_[], baa)) → new_ltEs(vwx22010, vwx24010, baa)
new_compare2(@2(vwx2200, Just(vwx22010)), @2(vwx2400, Just(vwx24010)), False, ce, app(ty_Maybe, app(app(ty_Either, ga), gb))) → new_ltEs2(vwx22010, vwx24010, ga, gb)
new_ltEs3(@3(vwx22010, vwx22011, vwx22012), @3(vwx24010, vwx24011, vwx24012), app(ty_[], bbb), bbc, bbd) → new_lt0(vwx22010, vwx24010, bbb)
new_compare2(@2(vwx2200, @3(vwx22010, vwx22011, vwx22012)), @2(vwx2400, @3(vwx24010, vwx24011, vwx24012)), False, ce, app(app(app(ty_@3, bce), bbc), app(app(app(ty_@3, bee), bef), beg))) → new_ltEs3(vwx22012, vwx24012, bee, bef, beg)
new_compare2(@2(vwx2200, Just(vwx22010)), @2(vwx2400, Just(vwx24010)), False, ce, app(ty_Maybe, app(ty_[], fd))) → new_ltEs(vwx22010, vwx24010, fd)
new_compare2(@2(vwx2200, Left(vwx22010)), @2(vwx2400, Left(vwx24010)), False, ce, app(app(ty_Either, app(app(ty_@2, gh), ha)), gg)) → new_ltEs0(vwx22010, vwx24010, gh, ha)
new_primCompAux(vwx22000, vwx24000, vwx102, app(ty_[], beh)) → new_compare0(vwx22000, vwx24000, beh)
new_compare2(@2(vwx2200, @3(vwx22010, vwx22011, vwx22012)), @2(vwx2400, @3(vwx24010, vwx24011, vwx24012)), False, ce, app(app(app(ty_@3, bce), bbc), app(ty_Maybe, beb))) → new_ltEs1(vwx22012, vwx24012, beb)
new_compare2(@2(vwx2200, Left(vwx22010)), @2(vwx2400, Left(vwx24010)), False, ce, app(app(ty_Either, app(ty_[], gf)), gg)) → new_ltEs(vwx22010, vwx24010, gf)
new_esEs4(vwx11, vwx12, vwx13, vwx14, False, ba, bb) → new_compare2(@2(vwx11, vwx12), @2(vwx13, vwx14), False, ba, bb)
new_ltEs2(Right(vwx22010), Right(vwx24010), hh, app(app(ty_Either, bae), baf)) → new_ltEs2(vwx22010, vwx24010, bae, baf)
new_compare2(@2(vwx2200, Right(vwx22010)), @2(vwx2400, Right(vwx24010)), False, ce, app(app(ty_Either, hh), app(ty_Maybe, bad))) → new_ltEs1(vwx22010, vwx24010, bad)
new_ltEs0(@2(vwx22010, vwx22011), @2(vwx24010, vwx24011), eb, app(app(ty_@2, ed), ee)) → new_ltEs0(vwx22011, vwx24011, ed, ee)
new_ltEs0(@2(vwx22010, vwx22011), @2(vwx24010, vwx24011), eb, app(ty_[], ec)) → new_ltEs(vwx22011, vwx24011, ec)
new_ltEs3(@3(vwx22010, vwx22011, vwx22012), @3(vwx24010, vwx24011, vwx24012), bce, app(app(ty_@2, bcg), bch), bbd) → new_lt(vwx22011, vwx24011, bcg, bch)
new_ltEs3(@3(vwx22010, vwx22011, vwx22012), @3(vwx24010, vwx24011, vwx24012), bce, bbc, app(app(app(ty_@3, bee), bef), beg)) → new_ltEs3(vwx22012, vwx24012, bee, bef, beg)
new_compare2(@2(vwx2200, @3(vwx22010, vwx22011, vwx22012)), @2(vwx2400, @3(vwx24010, vwx24011, vwx24012)), False, ce, app(app(app(ty_@3, bce), app(ty_Maybe, bda)), bbd)) → new_lt1(vwx22011, vwx24011, bda)
new_ltEs1(Just(vwx22010), Just(vwx24010), app(app(ty_@2, ff), fg)) → new_ltEs0(vwx22010, vwx24010, ff, fg)
new_ltEs0(@2(vwx22010, vwx22011), @2(vwx24010, vwx24011), app(ty_[], cg), da) → new_lt0(vwx22010, vwx24010, cg)
new_ltEs0(@2(vwx22010, vwx22011), @2(vwx24010, vwx24011), eb, app(app(ty_Either, eg), eh)) → new_ltEs2(vwx22011, vwx24011, eg, eh)
new_ltEs3(@3(vwx22010, vwx22011, vwx22012), @3(vwx24010, vwx24011, vwx24012), app(app(app(ty_@3, bcb), bcc), bcd), bbc, bbd) → new_lt3(vwx22010, vwx24010, bcb, bcc, bcd)
new_compare2(@2(vwx2200, @3(vwx22010, vwx22011, vwx22012)), @2(vwx2400, @3(vwx24010, vwx24011, vwx24012)), False, ce, app(app(app(ty_@3, app(app(ty_Either, bbh), bca)), bbc), bbd)) → new_lt2(vwx22010, vwx24010, bbh, bca)
new_compare2(@2(vwx2200, Just(vwx22010)), @2(vwx2400, Just(vwx24010)), False, ce, app(ty_Maybe, app(ty_Maybe, fh))) → new_ltEs1(vwx22010, vwx24010, fh)
new_compare2(@2(vwx2200, Left(vwx22010)), @2(vwx2400, Left(vwx24010)), False, ce, app(app(ty_Either, app(app(ty_Either, hc), hd)), gg)) → new_ltEs2(vwx22010, vwx24010, hc, hd)
new_compare2(@2(vwx2200, @3(vwx22010, vwx22011, vwx22012)), @2(vwx2400, @3(vwx24010, vwx24011, vwx24012)), False, ce, app(app(app(ty_@3, bce), app(app(ty_@2, bcg), bch)), bbd)) → new_lt(vwx22011, vwx24011, bcg, bch)
new_ltEs2(Right(vwx22010), Right(vwx24010), hh, app(app(ty_@2, bab), bac)) → new_ltEs0(vwx22010, vwx24010, bab, bac)
new_compare2(@2(vwx2200, @3(vwx22010, vwx22011, vwx22012)), @2(vwx2400, @3(vwx24010, vwx24011, vwx24012)), False, ce, app(app(app(ty_@3, app(app(ty_@2, bbe), bbf)), bbc), bbd)) → new_lt(vwx22010, vwx24010, bbe, bbf)
new_lt0(:(vwx22000, vwx22001), :(vwx24000, vwx24001), bc) → new_primCompAux(vwx22000, vwx24000, new_compare(vwx22001, vwx24001, bc), bc)
new_compare2(@2(vwx2200, @2(vwx22010, vwx22011)), @2(vwx2400, @2(vwx24010, vwx24011)), False, ce, app(app(ty_@2, app(ty_Maybe, dd)), da)) → new_lt1(vwx22010, vwx24010, dd)
new_ltEs2(Left(vwx22010), Left(vwx24010), app(ty_[], gf), gg) → new_ltEs(vwx22010, vwx24010, gf)
new_ltEs3(@3(vwx22010, vwx22011, vwx22012), @3(vwx24010, vwx24011, vwx24012), bce, bbc, app(app(ty_Either, bec), bed)) → new_ltEs2(vwx22012, vwx24012, bec, bed)
new_ltEs0(@2(vwx22010, vwx22011), @2(vwx24010, vwx24011), app(app(ty_@2, db), dc), da) → new_lt(vwx22010, vwx24010, db, dc)
new_compare2(@2(vwx2200, @2(vwx22010, vwx22011)), @2(vwx2400, @2(vwx24010, vwx24011)), False, ce, app(app(ty_@2, eb), app(ty_Maybe, ef))) → new_ltEs1(vwx22011, vwx24011, ef)
new_ltEs2(Right(vwx22010), Right(vwx24010), hh, app(ty_Maybe, bad)) → new_ltEs1(vwx22010, vwx24010, bad)
new_primCompAux(vwx22000, vwx24000, vwx102, app(app(app(ty_@3, bff), bfg), bfh)) → new_compare4(vwx22000, vwx24000, bff, bfg, bfh)
new_lt0(:(vwx22000, vwx22001), :(vwx24000, vwx24001), bc) → new_compare0(vwx22001, vwx24001, bc)
new_compare2(@2(vwx2200, Right(vwx22010)), @2(vwx2400, Right(vwx24010)), False, ce, app(app(ty_Either, hh), app(app(ty_@2, bab), bac))) → new_ltEs0(vwx22010, vwx24010, bab, bac)

The TRS R consists of the following rules:

new_esEs30(vwx300, vwx400, app(ty_Maybe, chf)) → new_esEs6(vwx300, vwx400, chf)
new_esEs27(vwx301, vwx401, app(app(ty_@2, ced), cee)) → new_esEs9(vwx301, vwx401, ced, cee)
new_esEs7(Left(vwx300), Left(vwx400), app(app(ty_@2, dbd), dbe), caa) → new_esEs9(vwx300, vwx400, dbd, dbe)
new_esEs23(vwx22010, vwx24010, app(app(ty_Either, bbh), bca)) → new_esEs7(vwx22010, vwx24010, bbh, bca)
new_esEs28(vwx300, vwx400, app(ty_[], cfc)) → new_esEs19(vwx300, vwx400, cfc)
new_lt5(vwx22011, vwx24011, app(ty_Maybe, bda)) → new_lt12(vwx22011, vwx24011, bda)
new_esEs7(Left(vwx300), Left(vwx400), app(app(ty_Either, dbb), dbc), caa) → new_esEs7(vwx300, vwx400, dbb, dbc)
new_ltEs19(vwx2201, vwx2401, app(ty_Ratio, cbf)) → new_ltEs11(vwx2201, vwx2401, cbf)
new_esEs33(vwx300, vwx400, app(app(ty_Either, deh), dfa)) → new_esEs7(vwx300, vwx400, deh, dfa)
new_ltEs13(Left(vwx22010), Left(vwx24010), ty_Bool, gg) → new_ltEs5(vwx22010, vwx24010)
new_esEs18(Char(vwx300), Char(vwx400)) → new_primEqNat0(vwx300, vwx400)
new_ltEs18(vwx22012, vwx24012, ty_Float) → new_ltEs8(vwx22012, vwx24012)
new_esEs22(vwx22011, vwx24011, app(ty_[], bcf)) → new_esEs19(vwx22011, vwx24011, bcf)
new_esEs7(Right(vwx300), Right(vwx400), bhh, ty_Bool) → new_esEs15(vwx300, vwx400)
new_esEs25(vwx22010, vwx24010, ty_Bool) → new_esEs15(vwx22010, vwx24010)
new_esEs6(Just(vwx300), Just(vwx400), ty_Bool) → new_esEs15(vwx300, vwx400)
new_esEs29(vwx301, vwx401, app(app(app(ty_@3, chb), chc), chd)) → new_esEs8(vwx301, vwx401, chb, chc, chd)
new_esEs33(vwx300, vwx400, app(app(app(ty_@3, dfd), dfe), dff)) → new_esEs8(vwx300, vwx400, dfd, dfe, dff)
new_lt4(vwx22010, vwx24010, app(app(ty_Either, bbh), bca)) → new_lt15(vwx22010, vwx24010, bbh, bca)
new_ltEs14(GT, GT) → True
new_esEs29(vwx301, vwx401, app(ty_[], cge)) → new_esEs19(vwx301, vwx401, cge)
new_ltEs18(vwx22012, vwx24012, app(ty_Maybe, beb)) → new_ltEs4(vwx22012, vwx24012, beb)
new_compare([], :(vwx24000, vwx24001), bc) → LT
new_ltEs20(vwx22011, vwx24011, app(ty_[], ec)) → new_ltEs6(vwx22011, vwx24011, ec)
new_compare14(vwx2200, vwx2400) → new_compare27(vwx2200, vwx2400, new_esEs12(vwx2200, vwx2400))
new_ltEs13(Right(vwx22010), Right(vwx24010), hh, app(app(app(ty_@3, bag), bah), bba)) → new_ltEs15(vwx22010, vwx24010, bag, bah, bba)
new_ltEs13(Right(vwx22010), Right(vwx24010), hh, app(ty_Maybe, bad)) → new_ltEs4(vwx22010, vwx24010, bad)
new_esEs7(Left(vwx300), Left(vwx400), ty_Char, caa) → new_esEs18(vwx300, vwx400)
new_ltEs7(@2(vwx22010, vwx22011), @2(vwx24010, vwx24011), eb, da) → new_pePe(new_lt21(vwx22010, vwx24010, eb), new_asAs(new_esEs25(vwx22010, vwx24010, eb), new_ltEs20(vwx22011, vwx24011, da)))
new_lt13(vwx2200, vwx2400, cbe) → new_esEs12(new_compare11(vwx2200, vwx2400, cbe), LT)
new_esEs27(vwx301, vwx401, ty_Double) → new_esEs20(vwx301, vwx401)
new_ltEs13(Left(vwx22010), Left(vwx24010), app(ty_Ratio, cca), gg) → new_ltEs11(vwx22010, vwx24010, cca)
new_esEs28(vwx300, vwx400, ty_Float) → new_esEs21(vwx300, vwx400)
new_ltEs6(vwx2201, vwx2401, cf) → new_fsEs(new_compare(vwx2201, vwx2401, cf))
new_ltEs20(vwx22011, vwx24011, ty_Bool) → new_ltEs5(vwx22011, vwx24011)
new_compare112(vwx88, vwx89, vwx90, vwx91, True, cbg, cbh) → LT
new_primMulNat0(Zero, Zero) → Zero
new_ltEs4(Just(vwx22010), Just(vwx24010), app(app(ty_@2, ff), fg)) → new_ltEs7(vwx22010, vwx24010, ff, fg)
new_esEs6(Just(vwx300), Just(vwx400), app(ty_Ratio, ddc)) → new_esEs13(vwx300, vwx400, ddc)
new_compare(:(vwx22000, vwx22001), [], bc) → GT
new_compare11(:%(vwx22000, vwx22001), :%(vwx24000, vwx24001), ty_Int) → new_compare16(new_sr0(vwx22000, vwx24001), new_sr0(vwx24000, vwx22001))
new_sr(Integer(vwx240000), Integer(vwx220010)) → Integer(new_primMulInt(vwx240000, vwx220010))
new_esEs23(vwx22010, vwx24010, app(ty_Ratio, cbb)) → new_esEs13(vwx22010, vwx24010, cbb)
new_esEs11(vwx11, vwx12, vwx13, vwx14, False, ba, bb) → new_esEs12(new_compare23(@2(vwx11, vwx12), @2(vwx13, vwx14), False, ba, bb), LT)
new_compare5(vwx22000, vwx24000, app(ty_Ratio, cba)) → new_compare11(vwx22000, vwx24000, cba)
new_lt5(vwx22011, vwx24011, ty_@0) → new_lt11(vwx22011, vwx24011)
new_lt20(vwx2200, vwx2400, app(app(ty_@2, be), bf)) → new_lt8(vwx2200, vwx2400, be, bf)
new_ltEs4(Just(vwx22010), Just(vwx24010), ty_Bool) → new_ltEs5(vwx22010, vwx24010)
new_lt4(vwx22010, vwx24010, ty_Float) → new_lt9(vwx22010, vwx24010)
new_esEs6(Just(vwx300), Just(vwx400), ty_Char) → new_esEs18(vwx300, vwx400)
new_esEs7(Right(vwx300), Right(vwx400), bhh, app(app(app(ty_@3, dch), dda), ddb)) → new_esEs8(vwx300, vwx400, dch, dda, ddb)
new_lt20(vwx2200, vwx2400, ty_Int) → new_lt18(vwx2200, vwx2400)
new_esEs7(Left(vwx300), Left(vwx400), ty_Integer, caa) → new_esEs16(vwx300, vwx400)
new_fsEs(vwx94) → new_not(new_esEs12(vwx94, GT))
new_esEs24(vwx2200, vwx2400, ty_@0) → new_esEs14(vwx2200, vwx2400)
new_esEs26(vwx302, vwx402, app(ty_[], ccg)) → new_esEs19(vwx302, vwx402, ccg)
new_esEs5(vwx12, vwx14, app(ty_Maybe, bgd)) → new_esEs6(vwx12, vwx14, bgd)
new_lt5(vwx22011, vwx24011, app(app(app(ty_@3, bdd), bde), bdf)) → new_lt17(vwx22011, vwx24011, bdd, bde, bdf)
new_esEs30(vwx300, vwx400, app(app(ty_Either, chh), daa)) → new_esEs7(vwx300, vwx400, chh, daa)
new_esEs12(LT, GT) → False
new_esEs12(GT, LT) → False
new_lt4(vwx22010, vwx24010, app(app(app(ty_@3, bcb), bcc), bcd)) → new_lt17(vwx22010, vwx24010, bcb, bcc, bcd)
new_esEs23(vwx22010, vwx24010, ty_Float) → new_esEs21(vwx22010, vwx24010)
new_ltEs11(vwx2201, vwx2401, cbf) → new_fsEs(new_compare11(vwx2201, vwx2401, cbf))
new_lt17(vwx2200, vwx2400, cb, cc, cd) → new_esEs12(new_compare15(vwx2200, vwx2400, cb, cc, cd), LT)
new_esEs23(vwx22010, vwx24010, ty_Double) → new_esEs20(vwx22010, vwx24010)
new_compare7(Float(vwx22000, vwx22001), Float(vwx24000, vwx24001)) → new_compare16(new_sr0(vwx22000, vwx24000), new_sr0(vwx22001, vwx24001))
new_esEs22(vwx22011, vwx24011, app(ty_Maybe, bda)) → new_esEs6(vwx22011, vwx24011, bda)
new_esEs27(vwx301, vwx401, app(ty_Maybe, cdh)) → new_esEs6(vwx301, vwx401, cdh)
new_esEs7(Right(vwx300), Right(vwx400), bhh, app(app(ty_@2, dcf), dcg)) → new_esEs9(vwx300, vwx400, dcf, dcg)
new_esEs26(vwx302, vwx402, app(app(app(ty_@3, cdd), cde), cdf)) → new_esEs8(vwx302, vwx402, cdd, cde, cdf)
new_lt21(vwx22010, vwx24010, ty_Bool) → new_lt6(vwx22010, vwx24010)
new_ltEs19(vwx2201, vwx2401, app(ty_Maybe, cag)) → new_ltEs4(vwx2201, vwx2401, cag)
new_esEs22(vwx22011, vwx24011, ty_Double) → new_esEs20(vwx22011, vwx24011)
new_esEs33(vwx300, vwx400, ty_Float) → new_esEs21(vwx300, vwx400)
new_esEs6(Just(vwx300), Just(vwx400), app(app(app(ty_@3, deb), dec), ded)) → new_esEs8(vwx300, vwx400, deb, dec, ded)
new_ltEs4(Just(vwx22010), Just(vwx24010), ty_Double) → new_ltEs17(vwx22010, vwx24010)
new_esEs10(vwx30, vwx40, ty_Double) → new_esEs20(vwx30, vwx40)
new_esEs22(vwx22011, vwx24011, app(app(ty_Either, bdb), bdc)) → new_esEs7(vwx22011, vwx24011, bdb, bdc)
new_compare5(vwx22000, vwx24000, app(app(ty_@2, bfa), bfb)) → new_compare23(vwx22000, vwx24000, new_esEs9(vwx22000, vwx24000, bfa, bfb), bfa, bfb)
new_esEs28(vwx300, vwx400, app(app(app(ty_@3, cfh), cga), cgb)) → new_esEs8(vwx300, vwx400, cfh, cga, cgb)
new_ltEs20(vwx22011, vwx24011, app(app(ty_Either, eg), eh)) → new_ltEs13(vwx22011, vwx24011, eg, eh)
new_esEs22(vwx22011, vwx24011, ty_Ordering) → new_esEs12(vwx22011, vwx24011)
new_esEs7(Right(vwx300), Right(vwx400), bhh, app(ty_Maybe, dcb)) → new_esEs6(vwx300, vwx400, dcb)
new_pePe(False, vwx107) → vwx107
new_compare114(vwx2200, vwx2400, False) → GT
new_esEs33(vwx300, vwx400, ty_Int) → new_esEs17(vwx300, vwx400)
new_ltEs4(Just(vwx22010), Just(vwx24010), app(ty_[], fd)) → new_ltEs6(vwx22010, vwx24010, fd)
new_esEs7(Left(vwx300), Right(vwx400), bhh, caa) → False
new_esEs7(Right(vwx300), Left(vwx400), bhh, caa) → False
new_compare5(vwx22000, vwx24000, ty_Integer) → new_compare12(vwx22000, vwx24000)
new_esEs15(True, False) → False
new_esEs15(False, True) → False
new_esEs5(vwx12, vwx14, app(ty_[], bge)) → new_esEs19(vwx12, vwx14, bge)
new_esEs7(Left(vwx300), Left(vwx400), ty_Float, caa) → new_esEs21(vwx300, vwx400)
new_lt21(vwx22010, vwx24010, app(app(app(ty_@3, dg), dh), ea)) → new_lt17(vwx22010, vwx24010, dg, dh, ea)
new_esEs29(vwx301, vwx401, ty_Char) → new_esEs18(vwx301, vwx401)
new_ltEs13(Left(vwx22010), Left(vwx24010), ty_Char, gg) → new_ltEs9(vwx22010, vwx24010)
new_esEs27(vwx301, vwx401, app(app(ty_Either, ceb), cec)) → new_esEs7(vwx301, vwx401, ceb, cec)
new_compare5(vwx22000, vwx24000, ty_Float) → new_compare7(vwx22000, vwx24000)
new_compare5(vwx22000, vwx24000, app(ty_Maybe, bfc)) → new_compare10(vwx22000, vwx24000, bfc)
new_esEs5(vwx12, vwx14, ty_Ordering) → new_esEs12(vwx12, vwx14)
new_ltEs20(vwx22011, vwx24011, ty_@0) → new_ltEs10(vwx22011, vwx24011)
new_ltEs14(GT, EQ) → False
new_lt21(vwx22010, vwx24010, app(app(ty_@2, db), dc)) → new_lt8(vwx22010, vwx24010, db, dc)
new_lt5(vwx22011, vwx24011, ty_Float) → new_lt9(vwx22011, vwx24011)
new_esEs24(vwx2200, vwx2400, ty_Float) → new_esEs21(vwx2200, vwx2400)
new_esEs20(Double(vwx300, vwx301), Double(vwx400, vwx401)) → new_esEs17(new_sr0(vwx300, vwx400), new_sr0(vwx301, vwx401))
new_ltEs13(Left(vwx22010), Left(vwx24010), app(app(ty_@2, gh), ha), gg) → new_ltEs7(vwx22010, vwx24010, gh, ha)
new_lt4(vwx22010, vwx24010, ty_Ordering) → new_lt16(vwx22010, vwx24010)
new_esEs30(vwx300, vwx400, ty_Bool) → new_esEs15(vwx300, vwx400)
new_ltEs4(Nothing, Just(vwx24010), cag) → True
new_ltEs13(Left(vwx22010), Left(vwx24010), app(app(app(ty_@3, he), hf), hg), gg) → new_ltEs15(vwx22010, vwx24010, he, hf, hg)
new_lt16(vwx2200, vwx2400) → new_esEs12(new_compare14(vwx2200, vwx2400), LT)
new_esEs30(vwx300, vwx400, ty_Integer) → new_esEs16(vwx300, vwx400)
new_ltEs20(vwx22011, vwx24011, app(app(app(ty_@3, fa), fb), fc)) → new_ltEs15(vwx22011, vwx24011, fa, fb, fc)
new_ltEs13(Left(vwx22010), Left(vwx24010), ty_Int, gg) → new_ltEs16(vwx22010, vwx24010)
new_ltEs20(vwx22011, vwx24011, ty_Integer) → new_ltEs12(vwx22011, vwx24011)
new_ltEs18(vwx22012, vwx24012, ty_Int) → new_ltEs16(vwx22012, vwx24012)
new_esEs10(vwx30, vwx40, ty_Ordering) → new_esEs12(vwx30, vwx40)
new_esEs29(vwx301, vwx401, app(ty_Ratio, cgc)) → new_esEs13(vwx301, vwx401, cgc)
new_lt21(vwx22010, vwx24010, ty_Char) → new_lt10(vwx22010, vwx24010)
new_lt4(vwx22010, vwx24010, app(ty_Ratio, cbb)) → new_lt13(vwx22010, vwx24010, cbb)
new_esEs32(vwx300, vwx400, ty_Integer) → new_esEs16(vwx300, vwx400)
new_esEs24(vwx2200, vwx2400, app(ty_[], bc)) → new_esEs19(vwx2200, vwx2400, bc)
new_ltEs19(vwx2201, vwx2401, ty_Double) → new_ltEs17(vwx2201, vwx2401)
new_lt5(vwx22011, vwx24011, ty_Double) → new_lt19(vwx22011, vwx24011)
new_esEs7(Left(vwx300), Left(vwx400), app(ty_[], dba), caa) → new_esEs19(vwx300, vwx400, dba)
new_primCmpNat0(Zero, Succ(vwx240000)) → LT
new_esEs30(vwx300, vwx400, ty_Int) → new_esEs17(vwx300, vwx400)
new_ltEs20(vwx22011, vwx24011, app(app(ty_@2, ed), ee)) → new_ltEs7(vwx22011, vwx24011, ed, ee)
new_ltEs13(Left(vwx22010), Left(vwx24010), app(ty_Maybe, hb), gg) → new_ltEs4(vwx22010, vwx24010, hb)
new_esEs7(Right(vwx300), Right(vwx400), bhh, ty_Float) → new_esEs21(vwx300, vwx400)
new_esEs6(Just(vwx300), Just(vwx400), ty_Ordering) → new_esEs12(vwx300, vwx400)
new_compare25(vwx2200, vwx2400, True, cb, cc, cd) → EQ
new_esEs26(vwx302, vwx402, ty_Double) → new_esEs20(vwx302, vwx402)
new_ltEs13(Left(vwx22010), Left(vwx24010), ty_Double, gg) → new_ltEs17(vwx22010, vwx24010)
new_esEs25(vwx22010, vwx24010, ty_Double) → new_esEs20(vwx22010, vwx24010)
new_lt21(vwx22010, vwx24010, ty_Integer) → new_lt14(vwx22010, vwx24010)
new_esEs23(vwx22010, vwx24010, ty_Char) → new_esEs18(vwx22010, vwx24010)
new_esEs12(LT, LT) → True
new_esEs22(vwx22011, vwx24011, app(app(ty_@2, bcg), bch)) → new_esEs9(vwx22011, vwx24011, bcg, bch)
new_compare25(vwx2200, vwx2400, False, cb, cc, cd) → new_compare110(vwx2200, vwx2400, new_ltEs15(vwx2200, vwx2400, cb, cc, cd), cb, cc, cd)
new_esEs28(vwx300, vwx400, ty_Integer) → new_esEs16(vwx300, vwx400)
new_esEs25(vwx22010, vwx24010, app(ty_Ratio, ccc)) → new_esEs13(vwx22010, vwx24010, ccc)
new_esEs24(vwx2200, vwx2400, app(app(ty_Either, bh), ca)) → new_esEs7(vwx2200, vwx2400, bh, ca)
new_ltEs5(True, False) → False
new_pePe(True, vwx107) → True
new_primEqNat0(Zero, Zero) → True
new_ltEs18(vwx22012, vwx24012, ty_Double) → new_ltEs17(vwx22012, vwx24012)
new_esEs6(Just(vwx300), Just(vwx400), app(ty_[], dde)) → new_esEs19(vwx300, vwx400, dde)
new_esEs29(vwx301, vwx401, app(ty_Maybe, cgd)) → new_esEs6(vwx301, vwx401, cgd)
new_esEs7(Right(vwx300), Right(vwx400), bhh, ty_Ordering) → new_esEs12(vwx300, vwx400)
new_esEs26(vwx302, vwx402, app(ty_Maybe, ccf)) → new_esEs6(vwx302, vwx402, ccf)
new_esEs14(@0, @0) → True
new_lt21(vwx22010, vwx24010, ty_Double) → new_lt19(vwx22010, vwx24010)
new_compare111(vwx2200, vwx2400, False, bh, ca) → GT
new_ltEs18(vwx22012, vwx24012, ty_Char) → new_ltEs9(vwx22012, vwx24012)
new_esEs6(Just(vwx300), Just(vwx400), ty_Double) → new_esEs20(vwx300, vwx400)
new_esEs26(vwx302, vwx402, app(ty_Ratio, cce)) → new_esEs13(vwx302, vwx402, cce)
new_esEs28(vwx300, vwx400, app(app(ty_@2, cff), cfg)) → new_esEs9(vwx300, vwx400, cff, cfg)
new_ltEs20(vwx22011, vwx24011, ty_Float) → new_ltEs8(vwx22011, vwx24011)
new_esEs27(vwx301, vwx401, app(ty_Ratio, cdg)) → new_esEs13(vwx301, vwx401, cdg)
new_ltEs19(vwx2201, vwx2401, ty_Float) → new_ltEs8(vwx2201, vwx2401)
new_lt14(vwx2200, vwx2400) → new_esEs12(new_compare12(vwx2200, vwx2400), LT)
new_ltEs13(Right(vwx22010), Right(vwx24010), hh, ty_Float) → new_ltEs8(vwx22010, vwx24010)
new_ltEs5(True, True) → True
new_compare17(Double(vwx22000, vwx22001), Double(vwx24000, vwx24001)) → new_compare16(new_sr0(vwx22000, vwx24000), new_sr0(vwx22001, vwx24001))
new_esEs26(vwx302, vwx402, ty_Bool) → new_esEs15(vwx302, vwx402)
new_esEs19([], [], bhg) → True
new_ltEs9(vwx2201, vwx2401) → new_fsEs(new_compare8(vwx2201, vwx2401))
new_esEs25(vwx22010, vwx24010, app(ty_[], cg)) → new_esEs19(vwx22010, vwx24010, cg)
new_ltEs14(EQ, LT) → False
new_esEs25(vwx22010, vwx24010, ty_Int) → new_esEs17(vwx22010, vwx24010)
new_esEs23(vwx22010, vwx24010, app(app(app(ty_@3, bcb), bcc), bcd)) → new_esEs8(vwx22010, vwx24010, bcb, bcc, bcd)
new_lt20(vwx2200, vwx2400, ty_Float) → new_lt9(vwx2200, vwx2400)
new_ltEs13(Left(vwx22010), Left(vwx24010), ty_Integer, gg) → new_ltEs12(vwx22010, vwx24010)
new_ltEs10(vwx2201, vwx2401) → new_fsEs(new_compare9(vwx2201, vwx2401))
new_esEs33(vwx300, vwx400, app(ty_[], deg)) → new_esEs19(vwx300, vwx400, deg)
new_ltEs20(vwx22011, vwx24011, app(ty_Ratio, ccd)) → new_ltEs11(vwx22011, vwx24011, ccd)
new_primPlusNat0(Succ(vwx620), vwx40000) → Succ(Succ(new_primPlusNat1(vwx620, vwx40000)))
new_esEs29(vwx301, vwx401, ty_Float) → new_esEs21(vwx301, vwx401)
new_esEs7(Right(vwx300), Right(vwx400), bhh, app(app(ty_Either, dcd), dce)) → new_esEs7(vwx300, vwx400, dcd, dce)
new_esEs28(vwx300, vwx400, ty_@0) → new_esEs14(vwx300, vwx400)
new_ltEs19(vwx2201, vwx2401, app(app(app(ty_@3, bce), bbc), bbd)) → new_ltEs15(vwx2201, vwx2401, bce, bbc, bbd)
new_compare5(vwx22000, vwx24000, ty_@0) → new_compare9(vwx22000, vwx24000)
new_esEs7(Right(vwx300), Right(vwx400), bhh, ty_Char) → new_esEs18(vwx300, vwx400)
new_esEs19(:(vwx300, vwx301), [], bhg) → False
new_esEs19([], :(vwx400, vwx401), bhg) → False
new_compare27(vwx2200, vwx2400, False) → new_compare113(vwx2200, vwx2400, new_ltEs14(vwx2200, vwx2400))
new_esEs27(vwx301, vwx401, ty_Float) → new_esEs21(vwx301, vwx401)
new_esEs25(vwx22010, vwx24010, ty_Ordering) → new_esEs12(vwx22010, vwx24010)
new_ltEs20(vwx22011, vwx24011, ty_Int) → new_ltEs16(vwx22011, vwx24011)
new_ltEs13(Right(vwx22010), Right(vwx24010), hh, app(app(ty_@2, bab), bac)) → new_ltEs7(vwx22010, vwx24010, bab, bac)
new_primEqInt(Neg(Succ(vwx3000)), Neg(Succ(vwx4000))) → new_primEqNat0(vwx3000, vwx4000)
new_ltEs13(Right(vwx22010), Right(vwx24010), hh, ty_Double) → new_ltEs17(vwx22010, vwx24010)
new_lt11(vwx2200, vwx2400) → new_esEs12(new_compare9(vwx2200, vwx2400), LT)
new_esEs30(vwx300, vwx400, ty_Float) → new_esEs21(vwx300, vwx400)
new_esEs15(True, True) → True
new_ltEs20(vwx22011, vwx24011, ty_Char) → new_ltEs9(vwx22011, vwx24011)
new_ltEs5(False, False) → True
new_esEs30(vwx300, vwx400, app(ty_[], chg)) → new_esEs19(vwx300, vwx400, chg)
new_primPlusNat1(Succ(vwx6200), Zero) → Succ(vwx6200)
new_primPlusNat1(Zero, Succ(vwx400000)) → Succ(vwx400000)
new_ltEs4(Nothing, Nothing, cag) → True
new_lt6(vwx2200, vwx2400) → new_esEs12(new_compare6(vwx2200, vwx2400), LT)
new_lt5(vwx22011, vwx24011, ty_Int) → new_lt18(vwx22011, vwx24011)
new_esEs12(LT, EQ) → False
new_esEs12(EQ, LT) → False
new_lt5(vwx22011, vwx24011, ty_Integer) → new_lt14(vwx22011, vwx24011)
new_compare24(vwx2200, vwx2400, False, bg) → new_compare18(vwx2200, vwx2400, new_ltEs4(vwx2200, vwx2400, bg), bg)
new_esEs7(Right(vwx300), Right(vwx400), bhh, app(ty_Ratio, dca)) → new_esEs13(vwx300, vwx400, dca)
new_esEs25(vwx22010, vwx24010, ty_Char) → new_esEs18(vwx22010, vwx24010)
new_esEs5(vwx12, vwx14, ty_Integer) → new_esEs16(vwx12, vwx14)
new_lt21(vwx22010, vwx24010, app(ty_Ratio, ccc)) → new_lt13(vwx22010, vwx24010, ccc)
new_lt20(vwx2200, vwx2400, app(app(app(ty_@3, cb), cc), cd)) → new_lt17(vwx2200, vwx2400, cb, cc, cd)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs33(vwx300, vwx400, app(ty_Ratio, dee)) → new_esEs13(vwx300, vwx400, dee)
new_esEs7(Left(vwx300), Left(vwx400), app(ty_Ratio, dag), caa) → new_esEs13(vwx300, vwx400, dag)
new_ltEs17(vwx2201, vwx2401) → new_fsEs(new_compare17(vwx2201, vwx2401))
new_lt21(vwx22010, vwx24010, app(app(ty_Either, de), df)) → new_lt15(vwx22010, vwx24010, de, df)
new_ltEs15(@3(vwx22010, vwx22011, vwx22012), @3(vwx24010, vwx24011, vwx24012), bce, bbc, bbd) → new_pePe(new_lt4(vwx22010, vwx24010, bce), new_asAs(new_esEs23(vwx22010, vwx24010, bce), new_pePe(new_lt5(vwx22011, vwx24011, bbc), new_asAs(new_esEs22(vwx22011, vwx24011, bbc), new_ltEs18(vwx22012, vwx24012, bbd)))))
new_compare28(vwx2200, vwx2400, False) → new_compare114(vwx2200, vwx2400, new_ltEs5(vwx2200, vwx2400))
new_esEs10(vwx30, vwx40, app(ty_[], bhg)) → new_esEs19(vwx30, vwx40, bhg)
new_ltEs4(Just(vwx22010), Just(vwx24010), ty_Float) → new_ltEs8(vwx22010, vwx24010)
new_esEs29(vwx301, vwx401, ty_Int) → new_esEs17(vwx301, vwx401)
new_lt7(vwx2200, vwx2400, bc) → new_esEs12(new_compare(vwx2200, vwx2400, bc), LT)
new_primEqInt(Neg(Succ(vwx3000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(vwx4000))) → False
new_compare26(vwx2200, vwx2400, True, bh, ca) → EQ
new_esEs6(Just(vwx300), Just(vwx400), ty_@0) → new_esEs14(vwx300, vwx400)
new_esEs24(vwx2200, vwx2400, app(app(ty_@2, be), bf)) → new_esEs9(vwx2200, vwx2400, be, bf)
new_esEs23(vwx22010, vwx24010, ty_Integer) → new_esEs16(vwx22010, vwx24010)
new_lt21(vwx22010, vwx24010, ty_@0) → new_lt11(vwx22010, vwx24010)
new_lt4(vwx22010, vwx24010, app(ty_[], bbb)) → new_lt7(vwx22010, vwx24010, bbb)
new_esEs5(vwx12, vwx14, ty_@0) → new_esEs14(vwx12, vwx14)
new_compare([], [], bc) → EQ
new_esEs26(vwx302, vwx402, app(app(ty_Either, cch), cda)) → new_esEs7(vwx302, vwx402, cch, cda)
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_lt18(vwx2200, vwx2400) → new_esEs12(new_compare16(vwx2200, vwx2400), LT)
new_lt5(vwx22011, vwx24011, app(ty_[], bcf)) → new_lt7(vwx22011, vwx24011, bcf)
new_ltEs16(vwx2201, vwx2401) → new_fsEs(new_compare16(vwx2201, vwx2401))
new_esEs5(vwx12, vwx14, app(app(ty_Either, bgf), bgg)) → new_esEs7(vwx12, vwx14, bgf, bgg)
new_lt4(vwx22010, vwx24010, app(app(ty_@2, bbe), bbf)) → new_lt8(vwx22010, vwx24010, bbe, bbf)
new_primCmpNat0(Succ(vwx220000), Succ(vwx240000)) → new_primCmpNat0(vwx220000, vwx240000)
new_esEs26(vwx302, vwx402, ty_Integer) → new_esEs16(vwx302, vwx402)
new_ltEs13(Left(vwx22010), Left(vwx24010), app(ty_[], gf), gg) → new_ltEs6(vwx22010, vwx24010, gf)
new_esEs6(Nothing, Nothing, bhf) → True
new_ltEs18(vwx22012, vwx24012, app(app(ty_Either, bec), bed)) → new_ltEs13(vwx22012, vwx24012, bec, bed)
new_ltEs18(vwx22012, vwx24012, ty_Bool) → new_ltEs5(vwx22012, vwx24012)
new_primEqInt(Pos(Succ(vwx3000)), Pos(Succ(vwx4000))) → new_primEqNat0(vwx3000, vwx4000)
new_ltEs4(Just(vwx22010), Just(vwx24010), app(app(app(ty_@3, gc), gd), ge)) → new_ltEs15(vwx22010, vwx24010, gc, gd, ge)
new_esEs30(vwx300, vwx400, app(app(app(ty_@3, dad), dae), daf)) → new_esEs8(vwx300, vwx400, dad, dae, daf)
new_esEs13(:%(vwx300, vwx301), :%(vwx400, vwx401), bhe) → new_asAs(new_esEs32(vwx300, vwx400, bhe), new_esEs31(vwx301, vwx401, bhe))
new_ltEs18(vwx22012, vwx24012, ty_@0) → new_ltEs10(vwx22012, vwx24012)
new_esEs24(vwx2200, vwx2400, ty_Double) → new_esEs20(vwx2200, vwx2400)
new_ltEs18(vwx22012, vwx24012, app(app(app(ty_@3, bee), bef), beg)) → new_ltEs15(vwx22012, vwx24012, bee, bef, beg)
new_lt4(vwx22010, vwx24010, app(ty_Maybe, bbg)) → new_lt12(vwx22010, vwx24010, bbg)
new_esEs33(vwx300, vwx400, ty_@0) → new_esEs14(vwx300, vwx400)
new_esEs24(vwx2200, vwx2400, ty_Int) → new_esEs17(vwx2200, vwx2400)
new_esEs6(Nothing, Just(vwx400), bhf) → False
new_esEs6(Just(vwx300), Nothing, bhf) → False
new_primEqNat0(Succ(vwx3000), Succ(vwx4000)) → new_primEqNat0(vwx3000, vwx4000)
new_esEs27(vwx301, vwx401, app(app(app(ty_@3, cef), ceg), ceh)) → new_esEs8(vwx301, vwx401, cef, ceg, ceh)
new_esEs26(vwx302, vwx402, ty_Ordering) → new_esEs12(vwx302, vwx402)
new_ltEs19(vwx2201, vwx2401, app(app(ty_Either, hh), gg)) → new_ltEs13(vwx2201, vwx2401, hh, gg)
new_lt4(vwx22010, vwx24010, ty_Int) → new_lt18(vwx22010, vwx24010)
new_lt21(vwx22010, vwx24010, app(ty_Maybe, dd)) → new_lt12(vwx22010, vwx24010, dd)
new_lt5(vwx22011, vwx24011, ty_Bool) → new_lt6(vwx22011, vwx24011)
new_primCompAux00(vwx112, LT) → LT
new_lt4(vwx22010, vwx24010, ty_Char) → new_lt10(vwx22010, vwx24010)
new_esEs6(Just(vwx300), Just(vwx400), ty_Float) → new_esEs21(vwx300, vwx400)
new_primCmpInt(Neg(Succ(vwx220000)), Neg(vwx24000)) → new_primCmpNat0(vwx24000, Succ(vwx220000))
new_lt21(vwx22010, vwx24010, ty_Float) → new_lt9(vwx22010, vwx24010)
new_esEs23(vwx22010, vwx24010, ty_Bool) → new_esEs15(vwx22010, vwx24010)
new_lt5(vwx22011, vwx24011, app(ty_Ratio, cbc)) → new_lt13(vwx22011, vwx24011, cbc)
new_esEs12(EQ, EQ) → True
new_esEs33(vwx300, vwx400, ty_Double) → new_esEs20(vwx300, vwx400)
new_ltEs20(vwx22011, vwx24011, ty_Ordering) → new_ltEs14(vwx22011, vwx24011)
new_lt12(vwx2200, vwx2400, bg) → new_esEs12(new_compare10(vwx2200, vwx2400, bg), LT)
new_primEqInt(Pos(Succ(vwx3000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(vwx4000))) → False
new_esEs10(vwx30, vwx40, app(app(ty_Either, bhh), caa)) → new_esEs7(vwx30, vwx40, bhh, caa)
new_esEs5(vwx12, vwx14, ty_Char) → new_esEs18(vwx12, vwx14)
new_esEs5(vwx12, vwx14, app(ty_Ratio, bgc)) → new_esEs13(vwx12, vwx14, bgc)
new_esEs23(vwx22010, vwx24010, app(ty_[], bbb)) → new_esEs19(vwx22010, vwx24010, bbb)
new_primCmpNat0(Zero, Zero) → EQ
new_lt5(vwx22011, vwx24011, app(app(ty_Either, bdb), bdc)) → new_lt15(vwx22011, vwx24011, bdb, bdc)
new_primCmpNat0(Succ(vwx220000), Zero) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(vwx240000))) → LT
new_compare9(@0, @0) → EQ
new_esEs22(vwx22011, vwx24011, app(ty_Ratio, cbc)) → new_esEs13(vwx22011, vwx24011, cbc)
new_compare19(vwx88, vwx89, vwx90, vwx91, False, vwx93, cbg, cbh) → new_compare112(vwx88, vwx89, vwx90, vwx91, vwx93, cbg, cbh)
new_esEs6(Just(vwx300), Just(vwx400), app(app(ty_@2, ddh), dea)) → new_esEs9(vwx300, vwx400, ddh, dea)
new_esEs5(vwx12, vwx14, ty_Double) → new_esEs20(vwx12, vwx14)
new_primPlusNat1(Succ(vwx6200), Succ(vwx400000)) → Succ(Succ(new_primPlusNat1(vwx6200, vwx400000)))
new_ltEs4(Just(vwx22010), Just(vwx24010), ty_Integer) → new_ltEs12(vwx22010, vwx24010)
new_esEs10(vwx30, vwx40, ty_Char) → new_esEs18(vwx30, vwx40)
new_primEqInt(Pos(Succ(vwx3000)), Neg(vwx400)) → False
new_primEqInt(Neg(Succ(vwx3000)), Pos(vwx400)) → False
new_esEs24(vwx2200, vwx2400, app(ty_Ratio, cbe)) → new_esEs13(vwx2200, vwx2400, cbe)
new_esEs10(vwx30, vwx40, app(app(app(ty_@3, cad), cae), caf)) → new_esEs8(vwx30, vwx40, cad, cae, caf)
new_esEs33(vwx300, vwx400, ty_Ordering) → new_esEs12(vwx300, vwx400)
new_esEs28(vwx300, vwx400, ty_Double) → new_esEs20(vwx300, vwx400)
new_compare(:(vwx22000, vwx22001), :(vwx24000, vwx24001), bc) → new_primCompAux0(vwx22000, vwx24000, new_compare(vwx22001, vwx24001, bc), bc)
new_ltEs5(False, True) → True
new_lt4(vwx22010, vwx24010, ty_Bool) → new_lt6(vwx22010, vwx24010)
new_esEs6(Just(vwx300), Just(vwx400), ty_Integer) → new_esEs16(vwx300, vwx400)
new_esEs10(vwx30, vwx40, app(app(ty_@2, cab), cac)) → new_esEs9(vwx30, vwx40, cab, cac)
new_esEs29(vwx301, vwx401, ty_@0) → new_esEs14(vwx301, vwx401)
new_esEs26(vwx302, vwx402, ty_Int) → new_esEs17(vwx302, vwx402)
new_esEs28(vwx300, vwx400, app(ty_Maybe, cfb)) → new_esEs6(vwx300, vwx400, cfb)
new_esEs30(vwx300, vwx400, ty_Ordering) → new_esEs12(vwx300, vwx400)
new_primEqInt(Pos(Zero), Neg(Succ(vwx4000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(vwx4000))) → False
new_primCompAux00(vwx112, EQ) → vwx112
new_esEs24(vwx2200, vwx2400, ty_Ordering) → new_esEs12(vwx2200, vwx2400)
new_primCmpInt(Pos(Zero), Pos(Succ(vwx240000))) → new_primCmpNat0(Zero, Succ(vwx240000))
new_esEs31(vwx301, vwx401, ty_Integer) → new_esEs16(vwx301, vwx401)
new_esEs28(vwx300, vwx400, app(app(ty_Either, cfd), cfe)) → new_esEs7(vwx300, vwx400, cfd, cfe)
new_esEs22(vwx22011, vwx24011, ty_Float) → new_esEs21(vwx22011, vwx24011)
new_ltEs18(vwx22012, vwx24012, app(ty_Ratio, cbd)) → new_ltEs11(vwx22012, vwx24012, cbd)
new_esEs25(vwx22010, vwx24010, ty_@0) → new_esEs14(vwx22010, vwx24010)
new_esEs28(vwx300, vwx400, ty_Ordering) → new_esEs12(vwx300, vwx400)
new_compare5(vwx22000, vwx24000, ty_Int) → new_compare16(vwx22000, vwx24000)
new_esEs9(@2(vwx300, vwx301), @2(vwx400, vwx401), cab, cac) → new_asAs(new_esEs30(vwx300, vwx400, cab), new_esEs29(vwx301, vwx401, cac))
new_lt9(vwx2200, vwx2400) → new_esEs12(new_compare7(vwx2200, vwx2400), LT)
new_compare113(vwx2200, vwx2400, True) → LT
new_not(False) → True
new_esEs30(vwx300, vwx400, ty_@0) → new_esEs14(vwx300, vwx400)
new_compare26(vwx2200, vwx2400, False, bh, ca) → new_compare111(vwx2200, vwx2400, new_ltEs13(vwx2200, vwx2400, bh, ca), bh, ca)
new_ltEs13(Right(vwx22010), Right(vwx24010), hh, ty_Bool) → new_ltEs5(vwx22010, vwx24010)
new_compare24(vwx2200, vwx2400, True, bg) → EQ
new_esEs10(vwx30, vwx40, ty_@0) → new_esEs14(vwx30, vwx40)
new_esEs10(vwx30, vwx40, ty_Float) → new_esEs21(vwx30, vwx40)
new_lt5(vwx22011, vwx24011, ty_Char) → new_lt10(vwx22011, vwx24011)
new_esEs7(Left(vwx300), Left(vwx400), app(ty_Maybe, dah), caa) → new_esEs6(vwx300, vwx400, dah)
new_primPlusNat0(Zero, vwx40000) → Succ(vwx40000)
new_primCmpInt(Pos(Succ(vwx220000)), Pos(vwx24000)) → new_primCmpNat0(Succ(vwx220000), vwx24000)
new_lt8(@2(vwx30, vwx31), @2(vwx40, vwx41), bga, bgb) → new_esEs11(vwx30, vwx31, vwx40, vwx41, new_esEs10(vwx30, vwx40, bga), bga, bgb)
new_esEs12(EQ, GT) → False
new_esEs12(GT, EQ) → False
new_ltEs13(Right(vwx22010), Right(vwx24010), hh, ty_Ordering) → new_ltEs14(vwx22010, vwx24010)
new_compare10(vwx2200, vwx2400, bg) → new_compare24(vwx2200, vwx2400, new_esEs6(vwx2200, vwx2400, bg), bg)
new_compare113(vwx2200, vwx2400, False) → GT
new_ltEs18(vwx22012, vwx24012, ty_Ordering) → new_ltEs14(vwx22012, vwx24012)
new_ltEs14(LT, LT) → True
new_esEs7(Right(vwx300), Right(vwx400), bhh, ty_@0) → new_esEs14(vwx300, vwx400)
new_lt20(vwx2200, vwx2400, ty_Bool) → new_lt6(vwx2200, vwx2400)
new_compare19(vwx88, vwx89, vwx90, vwx91, True, vwx93, cbg, cbh) → new_compare112(vwx88, vwx89, vwx90, vwx91, True, cbg, cbh)
new_esEs27(vwx301, vwx401, ty_@0) → new_esEs14(vwx301, vwx401)
new_lt4(vwx22010, vwx24010, ty_Integer) → new_lt14(vwx22010, vwx24010)
new_compare12(Integer(vwx22000), Integer(vwx24000)) → new_primCmpInt(vwx22000, vwx24000)
new_compare28(vwx2200, vwx2400, True) → EQ
new_esEs10(vwx30, vwx40, ty_Bool) → new_esEs15(vwx30, vwx40)
new_compare5(vwx22000, vwx24000, ty_Double) → new_compare17(vwx22000, vwx24000)
new_esEs33(vwx300, vwx400, ty_Integer) → new_esEs16(vwx300, vwx400)
new_compare5(vwx22000, vwx24000, app(ty_[], beh)) → new_compare(vwx22000, vwx24000, beh)
new_lt4(vwx22010, vwx24010, ty_Double) → new_lt19(vwx22010, vwx24010)
new_esEs23(vwx22010, vwx24010, app(app(ty_@2, bbe), bbf)) → new_esEs9(vwx22010, vwx24010, bbe, bbf)
new_esEs22(vwx22011, vwx24011, ty_Int) → new_esEs17(vwx22011, vwx24011)
new_ltEs19(vwx2201, vwx2401, ty_Integer) → new_ltEs12(vwx2201, vwx2401)
new_primCmpInt(Pos(Succ(vwx220000)), Neg(vwx24000)) → GT
new_esEs22(vwx22011, vwx24011, ty_Char) → new_esEs18(vwx22011, vwx24011)
new_compare5(vwx22000, vwx24000, ty_Ordering) → new_compare14(vwx22000, vwx24000)
new_primMulInt(Pos(vwx3000), Pos(vwx4000)) → Pos(new_primMulNat0(vwx3000, vwx4000))
new_esEs5(vwx12, vwx14, ty_Float) → new_esEs21(vwx12, vwx14)
new_esEs24(vwx2200, vwx2400, ty_Integer) → new_esEs16(vwx2200, vwx2400)
new_ltEs4(Just(vwx22010), Just(vwx24010), app(app(ty_Either, ga), gb)) → new_ltEs13(vwx22010, vwx24010, ga, gb)
new_ltEs13(Right(vwx22010), Right(vwx24010), hh, ty_Char) → new_ltEs9(vwx22010, vwx24010)
new_esEs7(Left(vwx300), Left(vwx400), ty_@0, caa) → new_esEs14(vwx300, vwx400)
new_primMulInt(Neg(vwx3000), Neg(vwx4000)) → Pos(new_primMulNat0(vwx3000, vwx4000))
new_esEs7(Left(vwx300), Left(vwx400), app(app(app(ty_@3, dbf), dbg), dbh), caa) → new_esEs8(vwx300, vwx400, dbf, dbg, dbh)
new_esEs24(vwx2200, vwx2400, ty_Bool) → new_esEs15(vwx2200, vwx2400)
new_primEqNat0(Succ(vwx3000), Zero) → False
new_primEqNat0(Zero, Succ(vwx4000)) → False
new_esEs7(Left(vwx300), Left(vwx400), ty_Double, caa) → new_esEs20(vwx300, vwx400)
new_esEs17(vwx30, vwx40) → new_primEqInt(vwx30, vwx40)
new_esEs25(vwx22010, vwx24010, app(ty_Maybe, dd)) → new_esEs6(vwx22010, vwx24010, dd)
new_lt10(vwx2200, vwx2400) → new_esEs12(new_compare8(vwx2200, vwx2400), LT)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs7(Left(vwx300), Left(vwx400), ty_Int, caa) → new_esEs17(vwx300, vwx400)
new_esEs33(vwx300, vwx400, app(ty_Maybe, def)) → new_esEs6(vwx300, vwx400, def)
new_esEs30(vwx300, vwx400, app(app(ty_@2, dab), dac)) → new_esEs9(vwx300, vwx400, dab, dac)
new_compare112(vwx88, vwx89, vwx90, vwx91, False, cbg, cbh) → GT
new_esEs5(vwx12, vwx14, app(app(ty_@2, bgh), bha)) → new_esEs9(vwx12, vwx14, bgh, bha)
new_esEs27(vwx301, vwx401, ty_Integer) → new_esEs16(vwx301, vwx401)
new_esEs25(vwx22010, vwx24010, app(app(app(ty_@3, dg), dh), ea)) → new_esEs8(vwx22010, vwx24010, dg, dh, ea)
new_esEs27(vwx301, vwx401, ty_Int) → new_esEs17(vwx301, vwx401)
new_esEs10(vwx30, vwx40, ty_Int) → new_esEs17(vwx30, vwx40)
new_ltEs20(vwx22011, vwx24011, ty_Double) → new_ltEs17(vwx22011, vwx24011)
new_esEs23(vwx22010, vwx24010, ty_Int) → new_esEs17(vwx22010, vwx24010)
new_ltEs19(vwx2201, vwx2401, ty_Char) → new_ltEs9(vwx2201, vwx2401)
new_esEs25(vwx22010, vwx24010, ty_Integer) → new_esEs16(vwx22010, vwx24010)
new_ltEs4(Just(vwx22010), Just(vwx24010), ty_Int) → new_ltEs16(vwx22010, vwx24010)
new_primCmpInt(Neg(Zero), Neg(Succ(vwx240000))) → new_primCmpNat0(Succ(vwx240000), Zero)
new_compare23(vwx220, vwx240, True, ce, bd) → EQ
new_primCmpInt(Pos(Zero), Neg(Succ(vwx240000))) → GT
new_lt4(vwx22010, vwx24010, ty_@0) → new_lt11(vwx22010, vwx24010)
new_esEs30(vwx300, vwx400, ty_Char) → new_esEs18(vwx300, vwx400)
new_ltEs13(Right(vwx22010), Right(vwx24010), hh, ty_@0) → new_ltEs10(vwx22010, vwx24010)
new_sr0(vwx300, vwx400) → new_primMulInt(vwx300, vwx400)
new_esEs26(vwx302, vwx402, ty_@0) → new_esEs14(vwx302, vwx402)
new_ltEs19(vwx2201, vwx2401, ty_Ordering) → new_ltEs14(vwx2201, vwx2401)
new_ltEs13(Left(vwx22010), Left(vwx24010), app(app(ty_Either, hc), hd), gg) → new_ltEs13(vwx22010, vwx24010, hc, hd)
new_esEs16(Integer(vwx300), Integer(vwx400)) → new_primEqInt(vwx300, vwx400)
new_ltEs18(vwx22012, vwx24012, app(ty_[], bdg)) → new_ltEs6(vwx22012, vwx24012, bdg)
new_ltEs13(Right(vwx22010), Right(vwx24010), hh, app(app(ty_Either, bae), baf)) → new_ltEs13(vwx22010, vwx24010, bae, baf)
new_esEs31(vwx301, vwx401, ty_Int) → new_esEs17(vwx301, vwx401)
new_esEs22(vwx22011, vwx24011, app(app(app(ty_@3, bdd), bde), bdf)) → new_esEs8(vwx22011, vwx24011, bdd, bde, bdf)
new_esEs7(Right(vwx300), Right(vwx400), bhh, ty_Double) → new_esEs20(vwx300, vwx400)
new_ltEs4(Just(vwx22010), Just(vwx24010), app(ty_Maybe, fh)) → new_ltEs4(vwx22010, vwx24010, fh)
new_esEs7(Left(vwx300), Left(vwx400), ty_Ordering, caa) → new_esEs12(vwx300, vwx400)
new_ltEs13(Left(vwx22010), Left(vwx24010), ty_Float, gg) → new_ltEs8(vwx22010, vwx24010)
new_lt20(vwx2200, vwx2400, ty_Char) → new_lt10(vwx2200, vwx2400)
new_esEs23(vwx22010, vwx24010, ty_@0) → new_esEs14(vwx22010, vwx24010)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs7(Right(vwx300), Right(vwx400), bhh, app(ty_[], dcc)) → new_esEs19(vwx300, vwx400, dcc)
new_ltEs13(Left(vwx22010), Left(vwx24010), ty_Ordering, gg) → new_ltEs14(vwx22010, vwx24010)
new_esEs28(vwx300, vwx400, ty_Int) → new_esEs17(vwx300, vwx400)
new_esEs29(vwx301, vwx401, ty_Bool) → new_esEs15(vwx301, vwx401)
new_asAs(False, vwx39) → False
new_ltEs19(vwx2201, vwx2401, app(app(ty_@2, eb), da)) → new_ltEs7(vwx2201, vwx2401, eb, da)
new_ltEs13(Right(vwx22010), Right(vwx24010), hh, app(ty_[], baa)) → new_ltEs6(vwx22010, vwx24010, baa)
new_lt20(vwx2200, vwx2400, ty_Double) → new_lt19(vwx2200, vwx2400)
new_lt19(vwx2200, vwx2400) → new_esEs12(new_compare17(vwx2200, vwx2400), LT)
new_primMulInt(Pos(vwx3000), Neg(vwx4000)) → Neg(new_primMulNat0(vwx3000, vwx4000))
new_primMulInt(Neg(vwx3000), Pos(vwx4000)) → Neg(new_primMulNat0(vwx3000, vwx4000))
new_compare16(vwx2200, vwx2400) → new_primCmpInt(vwx2200, vwx2400)
new_ltEs13(Left(vwx22010), Right(vwx24010), hh, gg) → True
new_primMulNat0(Succ(vwx30000), Zero) → Zero
new_primMulNat0(Zero, Succ(vwx40000)) → Zero
new_esEs6(Just(vwx300), Just(vwx400), app(ty_Maybe, ddd)) → new_esEs6(vwx300, vwx400, ddd)
new_compare11(:%(vwx22000, vwx22001), :%(vwx24000, vwx24001), ty_Integer) → new_compare12(new_sr(vwx22000, vwx24001), new_sr(vwx24000, vwx22001))
new_esEs11(vwx11, vwx12, vwx13, vwx14, True, ba, bb) → new_esEs12(new_compare23(@2(vwx11, vwx12), @2(vwx13, vwx14), new_esEs5(vwx12, vwx14, bb), ba, bb), LT)
new_esEs26(vwx302, vwx402, app(app(ty_@2, cdb), cdc)) → new_esEs9(vwx302, vwx402, cdb, cdc)
new_ltEs18(vwx22012, vwx24012, app(app(ty_@2, bdh), bea)) → new_ltEs7(vwx22012, vwx24012, bdh, bea)
new_esEs23(vwx22010, vwx24010, ty_Ordering) → new_esEs12(vwx22010, vwx24010)
new_ltEs8(vwx2201, vwx2401) → new_fsEs(new_compare7(vwx2201, vwx2401))
new_esEs10(vwx30, vwx40, app(ty_Maybe, bhf)) → new_esEs6(vwx30, vwx40, bhf)
new_esEs10(vwx30, vwx40, app(ty_Ratio, bhe)) → new_esEs13(vwx30, vwx40, bhe)
new_ltEs19(vwx2201, vwx2401, ty_@0) → new_ltEs10(vwx2201, vwx2401)
new_esEs30(vwx300, vwx400, app(ty_Ratio, che)) → new_esEs13(vwx300, vwx400, che)
new_ltEs14(GT, LT) → False
new_compare5(vwx22000, vwx24000, app(app(ty_Either, bfd), bfe)) → new_compare13(vwx22000, vwx24000, bfd, bfe)
new_esEs8(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), cad, cae, caf) → new_asAs(new_esEs28(vwx300, vwx400, cad), new_asAs(new_esEs27(vwx301, vwx401, cae), new_esEs26(vwx302, vwx402, caf)))
new_compare110(vwx2200, vwx2400, True, cb, cc, cd) → LT
new_esEs23(vwx22010, vwx24010, app(ty_Maybe, bbg)) → new_esEs6(vwx22010, vwx24010, bbg)
new_lt21(vwx22010, vwx24010, app(ty_[], cg)) → new_lt7(vwx22010, vwx24010, cg)
new_compare18(vwx2200, vwx2400, True, bg) → LT
new_compare5(vwx22000, vwx24000, ty_Char) → new_compare8(vwx22000, vwx24000)
new_esEs33(vwx300, vwx400, app(app(ty_@2, dfb), dfc)) → new_esEs9(vwx300, vwx400, dfb, dfc)
new_lt21(vwx22010, vwx24010, ty_Ordering) → new_lt16(vwx22010, vwx24010)
new_esEs33(vwx300, vwx400, ty_Bool) → new_esEs15(vwx300, vwx400)
new_compare27(vwx2200, vwx2400, True) → EQ
new_ltEs19(vwx2201, vwx2401, ty_Int) → new_ltEs16(vwx2201, vwx2401)
new_compare18(vwx2200, vwx2400, False, bg) → GT
new_esEs25(vwx22010, vwx24010, app(app(ty_@2, db), dc)) → new_esEs9(vwx22010, vwx24010, db, dc)
new_ltEs13(Right(vwx22010), Left(vwx24010), hh, gg) → False
new_esEs22(vwx22011, vwx24011, ty_Bool) → new_esEs15(vwx22011, vwx24011)
new_ltEs19(vwx2201, vwx2401, ty_Bool) → new_ltEs5(vwx2201, vwx2401)
new_esEs28(vwx300, vwx400, ty_Bool) → new_esEs15(vwx300, vwx400)
new_compare15(vwx2200, vwx2400, cb, cc, cd) → new_compare25(vwx2200, vwx2400, new_esEs8(vwx2200, vwx2400, cb, cc, cd), cb, cc, cd)
new_lt20(vwx2200, vwx2400, ty_Ordering) → new_lt16(vwx2200, vwx2400)
new_esEs28(vwx300, vwx400, app(ty_Ratio, cfa)) → new_esEs13(vwx300, vwx400, cfa)
new_ltEs13(Right(vwx22010), Right(vwx24010), hh, app(ty_Ratio, ccb)) → new_ltEs11(vwx22010, vwx24010, ccb)
new_esEs32(vwx300, vwx400, ty_Int) → new_esEs17(vwx300, vwx400)
new_ltEs4(Just(vwx22010), Just(vwx24010), ty_Char) → new_ltEs9(vwx22010, vwx24010)
new_ltEs14(LT, GT) → True
new_esEs26(vwx302, vwx402, ty_Float) → new_esEs21(vwx302, vwx402)
new_esEs25(vwx22010, vwx24010, ty_Float) → new_esEs21(vwx22010, vwx24010)
new_ltEs14(LT, EQ) → True
new_esEs10(vwx30, vwx40, ty_Integer) → new_esEs16(vwx30, vwx40)
new_lt20(vwx2200, vwx2400, app(app(ty_Either, bh), ca)) → new_lt15(vwx2200, vwx2400, bh, ca)
new_esEs27(vwx301, vwx401, ty_Ordering) → new_esEs12(vwx301, vwx401)
new_esEs22(vwx22011, vwx24011, ty_@0) → new_esEs14(vwx22011, vwx24011)
new_compare13(vwx2200, vwx2400, bh, ca) → new_compare26(vwx2200, vwx2400, new_esEs7(vwx2200, vwx2400, bh, ca), bh, ca)
new_ltEs19(vwx2201, vwx2401, app(ty_[], cf)) → new_ltEs6(vwx2201, vwx2401, cf)
new_esEs29(vwx301, vwx401, app(app(ty_Either, cgf), cgg)) → new_esEs7(vwx301, vwx401, cgf, cgg)
new_esEs29(vwx301, vwx401, ty_Double) → new_esEs20(vwx301, vwx401)
new_esEs22(vwx22011, vwx24011, ty_Integer) → new_esEs16(vwx22011, vwx24011)
new_esEs12(GT, GT) → True
new_compare5(vwx22000, vwx24000, app(app(app(ty_@3, bff), bfg), bfh)) → new_compare15(vwx22000, vwx24000, bff, bfg, bfh)
new_esEs7(Left(vwx300), Left(vwx400), ty_Bool, caa) → new_esEs15(vwx300, vwx400)
new_esEs26(vwx302, vwx402, ty_Char) → new_esEs18(vwx302, vwx402)
new_lt5(vwx22011, vwx24011, ty_Ordering) → new_lt16(vwx22011, vwx24011)
new_ltEs4(Just(vwx22010), Just(vwx24010), app(ty_Ratio, cah)) → new_ltEs11(vwx22010, vwx24010, cah)
new_ltEs4(Just(vwx22010), Just(vwx24010), ty_@0) → new_ltEs10(vwx22010, vwx24010)
new_esEs29(vwx301, vwx401, ty_Integer) → new_esEs16(vwx301, vwx401)
new_esEs6(Just(vwx300), Just(vwx400), ty_Int) → new_esEs17(vwx300, vwx400)
new_ltEs12(vwx2201, vwx2401) → new_fsEs(new_compare12(vwx2201, vwx2401))
new_esEs5(vwx12, vwx14, ty_Int) → new_esEs17(vwx12, vwx14)
new_compare5(vwx22000, vwx24000, ty_Bool) → new_compare6(vwx22000, vwx24000)
new_lt20(vwx2200, vwx2400, ty_Integer) → new_lt14(vwx2200, vwx2400)
new_esEs27(vwx301, vwx401, app(ty_[], cea)) → new_esEs19(vwx301, vwx401, cea)
new_esEs29(vwx301, vwx401, ty_Ordering) → new_esEs12(vwx301, vwx401)
new_compare111(vwx2200, vwx2400, True, bh, ca) → LT
new_primPlusNat1(Zero, Zero) → Zero
new_asAs(True, vwx39) → vwx39
new_ltEs14(EQ, EQ) → True
new_ltEs4(Just(vwx22010), Nothing, cag) → False
new_primMulNat0(Succ(vwx30000), Succ(vwx40000)) → new_primPlusNat0(new_primMulNat0(vwx30000, Succ(vwx40000)), vwx40000)
new_esEs7(Right(vwx300), Right(vwx400), bhh, ty_Integer) → new_esEs16(vwx300, vwx400)
new_lt5(vwx22011, vwx24011, app(app(ty_@2, bcg), bch)) → new_lt8(vwx22011, vwx24011, bcg, bch)
new_lt20(vwx2200, vwx2400, app(ty_[], bc)) → new_lt7(vwx2200, vwx2400, bc)
new_esEs6(Just(vwx300), Just(vwx400), app(app(ty_Either, ddf), ddg)) → new_esEs7(vwx300, vwx400, ddf, ddg)
new_esEs30(vwx300, vwx400, ty_Double) → new_esEs20(vwx300, vwx400)
new_esEs27(vwx301, vwx401, ty_Bool) → new_esEs15(vwx301, vwx401)
new_ltEs20(vwx22011, vwx24011, app(ty_Maybe, ef)) → new_ltEs4(vwx22011, vwx24011, ef)
new_ltEs13(Right(vwx22010), Right(vwx24010), hh, ty_Int) → new_ltEs16(vwx22010, vwx24010)
new_esEs7(Right(vwx300), Right(vwx400), bhh, ty_Int) → new_esEs17(vwx300, vwx400)
new_lt20(vwx2200, vwx2400, ty_@0) → new_lt11(vwx2200, vwx2400)
new_esEs33(vwx300, vwx400, ty_Char) → new_esEs18(vwx300, vwx400)
new_primCompAux0(vwx22000, vwx24000, vwx102, bc) → new_primCompAux00(vwx102, new_compare5(vwx22000, vwx24000, bc))
new_ltEs4(Just(vwx22010), Just(vwx24010), ty_Ordering) → new_ltEs14(vwx22010, vwx24010)
new_esEs19(:(vwx300, vwx301), :(vwx400, vwx401), bhg) → new_asAs(new_esEs33(vwx300, vwx400, bhg), new_esEs19(vwx301, vwx401, bhg))
new_ltEs13(Right(vwx22010), Right(vwx24010), hh, ty_Integer) → new_ltEs12(vwx22010, vwx24010)
new_esEs27(vwx301, vwx401, ty_Char) → new_esEs18(vwx301, vwx401)
new_lt15(vwx2200, vwx2400, bh, ca) → new_esEs12(new_compare13(vwx2200, vwx2400, bh, ca), LT)
new_esEs24(vwx2200, vwx2400, app(ty_Maybe, bg)) → new_esEs6(vwx2200, vwx2400, bg)
new_esEs28(vwx300, vwx400, ty_Char) → new_esEs18(vwx300, vwx400)
new_compare114(vwx2200, vwx2400, True) → LT
new_compare110(vwx2200, vwx2400, False, cb, cc, cd) → GT
new_lt20(vwx2200, vwx2400, app(ty_Ratio, cbe)) → new_lt13(vwx2200, vwx2400, cbe)
new_lt21(vwx22010, vwx24010, ty_Int) → new_lt18(vwx22010, vwx24010)
new_ltEs13(Left(vwx22010), Left(vwx24010), ty_@0, gg) → new_ltEs10(vwx22010, vwx24010)
new_primCompAux00(vwx112, GT) → GT
new_esEs25(vwx22010, vwx24010, app(app(ty_Either, de), df)) → new_esEs7(vwx22010, vwx24010, de, df)
new_esEs29(vwx301, vwx401, app(app(ty_@2, cgh), cha)) → new_esEs9(vwx301, vwx401, cgh, cha)
new_esEs21(Float(vwx300, vwx301), Float(vwx400, vwx401)) → new_esEs17(new_sr0(vwx300, vwx400), new_sr0(vwx301, vwx401))
new_compare8(Char(vwx22000), Char(vwx24000)) → new_primCmpNat0(vwx22000, vwx24000)
new_ltEs18(vwx22012, vwx24012, ty_Integer) → new_ltEs12(vwx22012, vwx24012)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_ltEs14(EQ, GT) → True
new_compare6(vwx2200, vwx2400) → new_compare28(vwx2200, vwx2400, new_esEs15(vwx2200, vwx2400))
new_esEs24(vwx2200, vwx2400, app(app(app(ty_@3, cb), cc), cd)) → new_esEs8(vwx2200, vwx2400, cb, cc, cd)
new_esEs5(vwx12, vwx14, ty_Bool) → new_esEs15(vwx12, vwx14)
new_esEs5(vwx12, vwx14, app(app(app(ty_@3, bhb), bhc), bhd)) → new_esEs8(vwx12, vwx14, bhb, bhc, bhd)
new_lt20(vwx2200, vwx2400, app(ty_Maybe, bg)) → new_lt12(vwx2200, vwx2400, bg)
new_esEs24(vwx2200, vwx2400, ty_Char) → new_esEs18(vwx2200, vwx2400)
new_compare23(@2(vwx2200, vwx2201), @2(vwx2400, vwx2401), False, ce, bd) → new_compare19(vwx2200, vwx2201, vwx2400, vwx2401, new_lt20(vwx2200, vwx2400, ce), new_asAs(new_esEs24(vwx2200, vwx2400, ce), new_ltEs19(vwx2201, vwx2401, bd)), ce, bd)
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primCmpInt(Neg(Succ(vwx220000)), Pos(vwx24000)) → LT
new_not(True) → False
new_esEs15(False, False) → True

The set Q consists of the following terms:

new_ltEs13(Left(x0), Left(x1), ty_Char, x2)
new_esEs26(x0, x1, ty_Float)
new_esEs5(x0, x1, ty_Double)
new_ltEs4(Just(x0), Just(x1), ty_Bool)
new_lt9(x0, x1)
new_primCmpNat0(Zero, Succ(x0))
new_ltEs13(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_ltEs13(Right(x0), Right(x1), x2, ty_@0)
new_esEs25(x0, x1, ty_@0)
new_esEs7(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs24(x0, x1, ty_Float)
new_esEs10(x0, x1, app(app(ty_Either, x2), x3))
new_lt4(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, ty_Ordering)
new_lt20(x0, x1, ty_@0)
new_ltEs4(Just(x0), Just(x1), ty_@0)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, ty_Ordering)
new_esEs21(Float(x0, x1), Float(x2, x3))
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs5(x0, x1, app(ty_[], x2))
new_esEs5(x0, x1, ty_Bool)
new_esEs10(x0, x1, app(ty_Maybe, x2))
new_ltEs20(x0, x1, ty_Float)
new_compare18(x0, x1, True, x2)
new_ltEs19(x0, x1, app(ty_[], x2))
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_esEs6(Just(x0), Just(x1), ty_Bool)
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs30(x0, x1, ty_Float)
new_esEs15(True, True)
new_ltEs15(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs29(x0, x1, ty_Integer)
new_esEs7(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_compare24(x0, x1, False, x2)
new_esEs10(x0, x1, ty_Ordering)
new_compare15(x0, x1, x2, x3, x4)
new_esEs10(x0, x1, app(ty_Ratio, x2))
new_esEs22(x0, x1, app(ty_[], x2))
new_primMulInt(Neg(x0), Neg(x1))
new_ltEs13(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_ltEs4(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_ltEs8(x0, x1)
new_esEs25(x0, x1, app(ty_[], x2))
new_compare10(x0, x1, x2)
new_lt21(x0, x1, ty_@0)
new_lt5(x0, x1, app(ty_Maybe, x2))
new_esEs6(Just(x0), Just(x1), app(ty_Ratio, x2))
new_ltEs13(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs29(x0, x1, ty_Ordering)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_ltEs13(Right(x0), Right(x1), x2, ty_Int)
new_primCompAux00(x0, EQ)
new_esEs24(x0, x1, ty_Integer)
new_esEs27(x0, x1, ty_@0)
new_compare23(x0, x1, True, x2, x3)
new_esEs15(False, False)
new_esEs24(x0, x1, app(ty_[], x2))
new_esEs12(GT, EQ)
new_esEs12(EQ, GT)
new_esEs19([], :(x0, x1), x2)
new_ltEs4(Nothing, Nothing, x0)
new_lt21(x0, x1, app(ty_Ratio, x2))
new_esEs7(Left(x0), Left(x1), ty_Integer, x2)
new_ltEs19(x0, x1, ty_Double)
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_esEs30(x0, x1, ty_Double)
new_compare5(x0, x1, app(ty_[], x2))
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_sr(Integer(x0), Integer(x1))
new_lt12(x0, x1, x2)
new_esEs6(Just(x0), Nothing, x1)
new_esEs6(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs12(GT, GT)
new_esEs8(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_ltEs13(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs31(x0, x1, ty_Integer)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_compare12(Integer(x0), Integer(x1))
new_esEs28(x0, x1, ty_Double)
new_esEs18(Char(x0), Char(x1))
new_ltEs4(Just(x0), Just(x1), ty_Char)
new_compare25(x0, x1, True, x2, x3, x4)
new_esEs30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs28(x0, x1, ty_Bool)
new_lt14(x0, x1)
new_ltEs13(Left(x0), Left(x1), ty_Float, x2)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs5(False, False)
new_esEs10(x0, x1, ty_@0)
new_esEs27(x0, x1, ty_Int)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare5(x0, x1, ty_Bool)
new_lt7(x0, x1, x2)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Just(x0), Just(x1), app(ty_[], x2))
new_esEs23(x0, x1, ty_Char)
new_esEs10(x0, x1, ty_Char)
new_compare112(x0, x1, x2, x3, True, x4, x5)
new_esEs5(x0, x1, ty_Float)
new_compare114(x0, x1, True)
new_esEs22(x0, x1, ty_Integer)
new_lt6(x0, x1)
new_esEs7(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_ltEs18(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs12(x0, x1)
new_esEs19(:(x0, x1), :(x2, x3), x4)
new_compare11(:%(x0, x1), :%(x2, x3), ty_Int)
new_primCmpNat0(Succ(x0), Zero)
new_ltEs13(Left(x0), Left(x1), ty_Bool, x2)
new_esEs29(x0, x1, ty_Char)
new_lt21(x0, x1, ty_Int)
new_lt13(x0, x1, x2)
new_primCompAux0(x0, x1, x2, x3)
new_esEs5(x0, x1, app(app(ty_@2, x2), x3))
new_compare112(x0, x1, x2, x3, False, x4, x5)
new_lt4(x0, x1, app(ty_Ratio, x2))
new_compare24(x0, x1, True, x2)
new_lt20(x0, x1, ty_Char)
new_compare5(x0, x1, app(ty_Maybe, x2))
new_ltEs14(EQ, EQ)
new_primEqNat0(Zero, Zero)
new_esEs10(x0, x1, ty_Double)
new_ltEs19(x0, x1, ty_Ordering)
new_esEs27(x0, x1, ty_Integer)
new_compare8(Char(x0), Char(x1))
new_lt21(x0, x1, ty_Double)
new_esEs6(Nothing, Nothing, x0)
new_esEs16(Integer(x0), Integer(x1))
new_esEs23(x0, x1, ty_@0)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs7(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_ltEs11(x0, x1, x2)
new_ltEs20(x0, x1, app(ty_[], x2))
new_compare5(x0, x1, ty_Ordering)
new_esEs27(x0, x1, ty_Char)
new_lt20(x0, x1, ty_Double)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs7(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs29(x0, x1, ty_Bool)
new_lt18(x0, x1)
new_compare5(x0, x1, ty_Int)
new_lt4(x0, x1, ty_Bool)
new_primMulNat0(Zero, Zero)
new_compare5(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs13(Left(x0), Left(x1), ty_Double, x2)
new_lt21(x0, x1, app(ty_[], x2))
new_lt21(x0, x1, ty_Integer)
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_compare26(x0, x1, True, x2, x3)
new_esEs22(x0, x1, ty_Int)
new_esEs25(x0, x1, ty_Bool)
new_esEs5(x0, x1, ty_Char)
new_lt5(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, app(ty_Maybe, x2))
new_lt20(x0, x1, ty_Ordering)
new_esEs23(x0, x1, ty_Integer)
new_compare5(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs30(x0, x1, app(app(ty_@2, x2), x3))
new_esEs9(@2(x0, x1), @2(x2, x3), x4, x5)
new_ltEs13(Right(x0), Right(x1), x2, ty_Float)
new_esEs7(Left(x0), Left(x1), ty_Char, x2)
new_esEs25(x0, x1, ty_Integer)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_primCompAux00(x0, GT)
new_ltEs13(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt5(x0, x1, ty_Double)
new_primCmpNat0(Succ(x0), Succ(x1))
new_esEs6(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_compare19(x0, x1, x2, x3, False, x4, x5, x6)
new_esEs33(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs19(x0, x1, ty_Float)
new_esEs22(x0, x1, ty_Double)
new_esEs14(@0, @0)
new_esEs28(x0, x1, ty_Int)
new_lt20(x0, x1, ty_Integer)
new_primMulNat0(Zero, Succ(x0))
new_ltEs18(x0, x1, ty_Float)
new_esEs7(Right(x0), Right(x1), x2, ty_Double)
new_esEs23(x0, x1, ty_Double)
new_esEs28(x0, x1, app(ty_[], x2))
new_lt17(x0, x1, x2, x3, x4)
new_ltEs18(x0, x1, ty_Double)
new_ltEs13(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs23(x0, x1, ty_Int)
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs13(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs5(x0, x1, ty_@0)
new_ltEs4(Nothing, Just(x0), x1)
new_compare6(x0, x1)
new_esEs17(x0, x1)
new_esEs7(Right(x0), Right(x1), x2, ty_Char)
new_lt5(x0, x1, ty_Int)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_lt4(x0, x1, ty_Int)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_ltEs4(Just(x0), Just(x1), app(ty_[], x2))
new_esEs23(x0, x1, ty_Bool)
new_esEs22(x0, x1, ty_@0)
new_esEs6(Just(x0), Just(x1), app(ty_Maybe, x2))
new_compare113(x0, x1, True)
new_compare19(x0, x1, x2, x3, True, x4, x5, x6)
new_compare17(Double(x0, x1), Double(x2, x3))
new_esEs11(x0, x1, x2, x3, False, x4, x5)
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_primPlusNat0(Zero, x0)
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_esEs12(EQ, LT)
new_esEs12(LT, EQ)
new_esEs31(x0, x1, ty_Int)
new_esEs33(x0, x1, ty_@0)
new_ltEs4(Just(x0), Just(x1), app(ty_Maybe, x2))
new_primCompAux00(x0, LT)
new_ltEs19(x0, x1, ty_@0)
new_ltEs7(@2(x0, x1), @2(x2, x3), x4, x5)
new_primEqNat0(Succ(x0), Zero)
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_primPlusNat1(Zero, Zero)
new_esEs25(x0, x1, ty_Double)
new_esEs7(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs12(EQ, EQ)
new_ltEs18(x0, x1, ty_Bool)
new_esEs30(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs14(LT, LT)
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs7(Right(x0), Right(x1), x2, ty_Bool)
new_esEs29(x0, x1, app(ty_[], x2))
new_esEs33(x0, x1, app(ty_Ratio, x2))
new_compare(:(x0, x1), :(x2, x3), x4)
new_ltEs20(x0, x1, ty_@0)
new_esEs28(x0, x1, ty_Char)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_lt5(x0, x1, ty_@0)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_esEs27(x0, x1, ty_Float)
new_ltEs20(x0, x1, ty_Bool)
new_esEs13(:%(x0, x1), :%(x2, x3), x4)
new_esEs30(x0, x1, app(ty_Ratio, x2))
new_lt10(x0, x1)
new_esEs11(x0, x1, x2, x3, True, x4, x5)
new_ltEs18(x0, x1, app(ty_Maybe, x2))
new_esEs33(x0, x1, ty_Float)
new_esEs6(Just(x0), Just(x1), ty_Float)
new_esEs10(x0, x1, ty_Float)
new_esEs7(Left(x0), Left(x1), ty_Double, x2)
new_esEs12(GT, LT)
new_esEs12(LT, GT)
new_esEs24(x0, x1, ty_Double)
new_ltEs4(Just(x0), Just(x1), ty_Float)
new_esEs27(x0, x1, app(ty_[], x2))
new_esEs10(x0, x1, ty_Bool)
new_lt5(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs22(x0, x1, ty_Bool)
new_esEs5(x0, x1, app(ty_Maybe, x2))
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_esEs26(x0, x1, ty_@0)
new_esEs30(x0, x1, app(ty_[], x2))
new_esEs33(x0, x1, ty_Char)
new_esEs30(x0, x1, ty_Integer)
new_lt4(x0, x1, app(ty_Maybe, x2))
new_ltEs20(x0, x1, ty_Char)
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs4(Just(x0), Just(x1), ty_Ordering)
new_esEs7(Left(x0), Left(x1), ty_Float, x2)
new_compare5(x0, x1, ty_Integer)
new_compare(:(x0, x1), [], x2)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_esEs7(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs6(Just(x0), Just(x1), ty_@0)
new_esEs30(x0, x1, ty_Int)
new_esEs6(Just(x0), Just(x1), ty_Integer)
new_ltEs13(Right(x0), Right(x1), x2, ty_Integer)
new_esEs26(x0, x1, ty_Int)
new_ltEs9(x0, x1)
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_compare5(x0, x1, ty_@0)
new_ltEs14(LT, EQ)
new_ltEs14(EQ, LT)
new_compare14(x0, x1)
new_ltEs18(x0, x1, ty_@0)
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_lt21(x0, x1, ty_Ordering)
new_pePe(True, x0)
new_compare5(x0, x1, ty_Char)
new_compare7(Float(x0, x1), Float(x2, x3))
new_esEs10(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs33(x0, x1, ty_Ordering)
new_esEs33(x0, x1, app(ty_Maybe, x2))
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_lt21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(Right(x0), Right(x1), x2, ty_Integer)
new_ltEs10(x0, x1)
new_lt20(x0, x1, ty_Int)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs15(False, True)
new_esEs15(True, False)
new_lt4(x0, x1, ty_Ordering)
new_esEs6(Just(x0), Just(x1), ty_Char)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primEqInt(Neg(Zero), Neg(Zero))
new_esEs7(Right(x0), Right(x1), x2, ty_@0)
new_asAs(True, x0)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_compare113(x0, x1, False)
new_ltEs20(x0, x1, ty_Double)
new_ltEs13(Left(x0), Left(x1), ty_@0, x2)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_esEs33(x0, x1, ty_Double)
new_compare26(x0, x1, False, x2, x3)
new_lt4(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs18(x0, x1, ty_Ordering)
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_esEs19([], [], x0)
new_ltEs4(Just(x0), Just(x1), ty_Integer)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_esEs24(x0, x1, ty_@0)
new_compare111(x0, x1, True, x2, x3)
new_esEs7(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_ltEs18(x0, x1, app(app(ty_@2, x2), x3))
new_compare23(@2(x0, x1), @2(x2, x3), False, x4, x5)
new_compare114(x0, x1, False)
new_esEs5(x0, x1, ty_Integer)
new_lt21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_esEs10(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, ty_Char)
new_compare5(x0, x1, ty_Float)
new_ltEs20(x0, x1, ty_Integer)
new_ltEs13(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs33(x0, x1, ty_Int)
new_esEs33(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs7(Left(x0), Left(x1), ty_Ordering, x2)
new_lt5(x0, x1, ty_Float)
new_lt21(x0, x1, ty_Bool)
new_esEs26(x0, x1, ty_Double)
new_esEs24(x0, x1, ty_Int)
new_esEs6(Nothing, Just(x0), x1)
new_compare18(x0, x1, False, x2)
new_compare13(x0, x1, x2, x3)
new_esEs23(x0, x1, app(ty_[], x2))
new_compare([], :(x0, x1), x2)
new_esEs28(x0, x1, ty_@0)
new_ltEs13(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs7(Right(x0), Right(x1), x2, ty_Float)
new_esEs26(x0, x1, app(ty_[], x2))
new_compare25(x0, x1, False, x2, x3, x4)
new_esEs24(x0, x1, ty_Ordering)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs10(x0, x1, ty_Int)
new_esEs24(x0, x1, ty_Char)
new_lt15(x0, x1, x2, x3)
new_esEs5(x0, x1, ty_Int)
new_primPlusNat0(Succ(x0), x1)
new_ltEs13(Right(x0), Right(x1), x2, ty_Bool)
new_esEs5(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_ltEs19(x0, x1, ty_Bool)
new_asAs(False, x0)
new_ltEs16(x0, x1)
new_ltEs20(x0, x1, ty_Int)
new_ltEs14(EQ, GT)
new_ltEs14(GT, EQ)
new_esEs25(x0, x1, ty_Char)
new_ltEs4(Just(x0), Just(x1), ty_Int)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(Right(x0), Right(x1), x2, app(ty_[], x3))
new_primCmpNat0(Zero, Zero)
new_lt20(x0, x1, ty_Float)
new_esEs7(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_ltEs18(x0, x1, ty_Integer)
new_ltEs13(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_primPlusNat1(Succ(x0), Zero)
new_esEs25(x0, x1, ty_Ordering)
new_compare28(x0, x1, True)
new_esEs32(x0, x1, ty_Int)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_lt21(x0, x1, app(ty_Maybe, x2))
new_lt5(x0, x1, app(app(ty_Either, x2), x3))
new_lt20(x0, x1, ty_Bool)
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_esEs29(x0, x1, ty_@0)
new_compare5(x0, x1, app(ty_Ratio, x2))
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_lt4(x0, x1, app(app(ty_Either, x2), x3))
new_lt21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs5(x0, x1, app(ty_Ratio, x2))
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_esEs29(x0, x1, ty_Float)
new_esEs28(x0, x1, ty_Ordering)
new_esEs28(x0, x1, ty_Integer)
new_ltEs4(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Just(x0), Just(x1), ty_Int)
new_esEs25(x0, x1, ty_Int)
new_esEs30(x0, x1, app(ty_Maybe, x2))
new_esEs22(x0, x1, ty_Ordering)
new_lt11(x0, x1)
new_lt4(x0, x1, ty_Double)
new_ltEs13(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_esEs32(x0, x1, ty_Integer)
new_compare28(x0, x1, False)
new_compare111(x0, x1, False, x2, x3)
new_esEs33(x0, x1, ty_Integer)
new_esEs29(x0, x1, ty_Int)
new_primEqNat0(Zero, Succ(x0))
new_ltEs14(LT, GT)
new_ltEs14(GT, LT)
new_esEs22(x0, x1, ty_Float)
new_ltEs19(x0, x1, ty_Int)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs6(Just(x0), Just(x1), ty_Ordering)
new_esEs27(x0, x1, ty_Bool)
new_primMulNat0(Succ(x0), Zero)
new_fsEs(x0)
new_compare16(x0, x1)
new_esEs19(:(x0, x1), [], x2)
new_lt4(x0, x1, ty_Char)
new_compare9(@0, @0)
new_compare11(:%(x0, x1), :%(x2, x3), ty_Integer)
new_primMulNat0(Succ(x0), Succ(x1))
new_lt20(x0, x1, app(ty_[], x2))
new_esEs7(Left(x0), Left(x1), ty_@0, x2)
new_esEs25(x0, x1, ty_Float)
new_esEs26(x0, x1, ty_Char)
new_lt5(x0, x1, ty_Ordering)
new_ltEs5(True, True)
new_ltEs14(GT, GT)
new_ltEs18(x0, x1, app(ty_[], x2))
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_esEs30(x0, x1, ty_Ordering)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_not(True)
new_esEs30(x0, x1, ty_Bool)
new_esEs28(x0, x1, ty_Float)
new_ltEs17(x0, x1)
new_ltEs13(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_not(False)
new_ltEs18(x0, x1, ty_Char)
new_esEs10(x0, x1, ty_Integer)
new_ltEs6(x0, x1, x2)
new_ltEs13(Right(x0), Right(x1), x2, ty_Double)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs18(x0, x1, app(ty_Ratio, x2))
new_esEs24(x0, x1, ty_Bool)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_esEs30(x0, x1, ty_Char)
new_esEs23(x0, x1, ty_Float)
new_esEs30(x0, x1, ty_@0)
new_ltEs4(Just(x0), Just(x1), ty_Double)
new_esEs26(x0, x1, ty_Integer)
new_compare27(x0, x1, False)
new_ltEs13(Right(x0), Left(x1), x2, x3)
new_ltEs13(Left(x0), Right(x1), x2, x3)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_lt8(@2(x0, x1), @2(x2, x3), x4, x5)
new_lt19(x0, x1)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_lt5(x0, x1, app(ty_[], x2))
new_esEs7(Left(x0), Left(x1), ty_Int, x2)
new_primEqNat0(Succ(x0), Succ(x1))
new_primPlusNat1(Succ(x0), Succ(x1))
new_ltEs13(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs29(x0, x1, ty_Double)
new_esEs33(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs13(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_esEs7(Right(x0), Left(x1), x2, x3)
new_esEs7(Left(x0), Right(x1), x2, x3)
new_ltEs19(x0, x1, ty_Integer)
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_compare5(x0, x1, app(app(ty_@2, x2), x3))
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_compare110(x0, x1, True, x2, x3, x4)
new_ltEs13(Left(x0), Left(x1), ty_Int, x2)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs22(x0, x1, ty_Char)
new_ltEs4(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs7(Right(x0), Right(x1), x2, ty_Int)
new_pePe(False, x0)
new_ltEs4(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_compare5(x0, x1, ty_Double)
new_lt16(x0, x1)
new_esEs27(x0, x1, ty_Double)
new_lt5(x0, x1, app(ty_Ratio, x2))
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_lt5(x0, x1, ty_Char)
new_lt21(x0, x1, ty_Char)
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_esEs6(Just(x0), Just(x1), ty_Double)
new_lt4(x0, x1, ty_Float)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, ty_Bool)
new_esEs10(x0, x1, app(ty_[], x2))
new_lt21(x0, x1, ty_Float)
new_esEs7(Left(x0), Left(x1), ty_Bool, x2)
new_ltEs20(x0, x1, ty_Ordering)
new_ltEs13(Right(x0), Right(x1), x2, ty_Char)
new_primEqInt(Pos(Zero), Pos(Zero))
new_ltEs18(x0, x1, ty_Int)
new_lt5(x0, x1, ty_Integer)
new_lt4(x0, x1, ty_@0)
new_lt5(x0, x1, ty_Bool)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs33(x0, x1, app(ty_[], x2))
new_compare27(x0, x1, True)
new_esEs5(x0, x1, ty_Ordering)
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_lt4(x0, x1, ty_Integer)
new_sr0(x0, x1)
new_compare([], [], x0)
new_ltEs13(Left(x0), Left(x1), ty_Integer, x2)
new_esEs33(x0, x1, ty_Bool)
new_ltEs5(True, False)
new_primPlusNat1(Zero, Succ(x0))
new_ltEs5(False, True)
new_compare110(x0, x1, False, x2, x3, x4)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_esEs12(LT, LT)
new_esEs27(x0, x1, ty_Ordering)
new_esEs7(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs5(x0, x1, app(app(ty_Either, x2), x3))
new_lt4(x0, x1, app(ty_[], x2))
new_esEs20(Double(x0, x1), Double(x2, x3))
new_ltEs4(Just(x0), Nothing, x1)
new_ltEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))

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: