YES 3.347 H-Termination proof of /home/matraf/haskell/eval_FullyBlown_Fast/empty.hs
H-Termination of the given Haskell-Program with start terms could successfully be proven:



HASKELL
  ↳ CR

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

module Main where
  import qualified Prelude



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

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



↳ HASKELL
  ↳ CR
HASKELL
      ↳ IFR

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

module Main where
  import qualified Prelude



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

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

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

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



↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ IFR
HASKELL
          ↳ BR

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

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

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

compare0 x y True = GT

compare3 x y = compare2 x y (x == y)

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

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

gcd'0 x y = gcd' y (x `rem` y)

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

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

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

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

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

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

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

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

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

is transformed to
absReal x = absReal2 x

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

absReal0 x True = `negate` x

absReal2 x = absReal1 x (x >= 0)

The following Function with conditions
undefined 
 | False
 = undefined

is transformed to
undefined  = undefined1

undefined0 True = undefined

undefined1  = undefined0 False

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

is transformed to
reduce x y = reduce2 x y

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



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

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

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

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

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

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

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

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

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



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

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

module Main where
  import qualified Prelude



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

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

mainModule Main
  ((<=) :: (Ord a, Ord b) => Either b a  ->  Either 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_primEqNat(Succ(vwx2300), Succ(vwx2400)) → new_primEqNat(vwx2300, vwx2400)

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(vwx5300), Succ(vwx401000)) → new_primPlusNat(vwx5300, vwx401000)

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

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



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

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

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

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

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



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

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

new_esEs2(Just(vwx230), Just(vwx240), app(app(app(ty_@3, bbb), bbc), bbd)) → new_esEs1(vwx230, vwx240, bbb, bbc, bbd)
new_esEs1(@3(vwx230, vwx231, vwx232), @3(vwx240, vwx241, vwx242), gd, app(app(ty_@2, hd), he), fb) → new_esEs3(vwx231, vwx241, hd, he)
new_esEs0(Left(vwx230), Left(vwx240), app(ty_[], cc), cd) → new_esEs(vwx230, vwx240, cc)
new_esEs2(Just(vwx230), Just(vwx240), app(ty_[], bag)) → new_esEs(vwx230, vwx240, bag)
new_esEs1(@3(vwx230, vwx231, vwx232), @3(vwx240, vwx241, vwx242), gd, app(app(app(ty_@3, gh), ha), hb), fb) → new_esEs1(vwx231, vwx241, gh, ha, hb)
new_esEs3(@2(vwx230, vwx231), @2(vwx240, vwx241), bdb, app(ty_Maybe, bea)) → new_esEs2(vwx231, vwx241, bea)
new_esEs3(@2(vwx230, vwx231), @2(vwx240, vwx241), app(ty_[], bbh), bca) → new_esEs(vwx230, vwx240, bbh)
new_esEs1(@3(vwx230, vwx231, vwx232), @3(vwx240, vwx241, vwx242), gd, fa, app(app(app(ty_@3, baa), bab), bac)) → new_esEs1(vwx232, vwx242, baa, bab, bac)
new_esEs2(Just(vwx230), Just(vwx240), app(ty_Maybe, bbe)) → new_esEs2(vwx230, vwx240, bbe)
new_esEs0(Left(vwx230), Left(vwx240), app(app(ty_Either, ce), cf), cd) → new_esEs0(vwx230, vwx240, ce, cf)
new_esEs3(@2(vwx230, vwx231), @2(vwx240, vwx241), app(app(app(ty_@3, bcd), bce), bcf), bca) → new_esEs1(vwx230, vwx240, bcd, bce, bcf)
new_esEs(:(vwx230, vwx231), :(vwx240, vwx241), app(ty_Maybe, bg)) → new_esEs2(vwx230, vwx240, bg)
new_esEs3(@2(vwx230, vwx231), @2(vwx240, vwx241), bdb, app(app(ty_Either, bdd), bde)) → new_esEs0(vwx231, vwx241, bdd, bde)
new_esEs3(@2(vwx230, vwx231), @2(vwx240, vwx241), bdb, app(ty_[], bdc)) → new_esEs(vwx231, vwx241, bdc)
new_esEs0(Right(vwx230), Right(vwx240), df, app(app(ty_Either, dh), ea)) → new_esEs0(vwx230, vwx240, dh, ea)
new_esEs3(@2(vwx230, vwx231), @2(vwx240, vwx241), bdb, app(app(ty_@2, beb), bec)) → new_esEs3(vwx231, vwx241, beb, bec)
new_esEs0(Left(vwx230), Left(vwx240), app(ty_Maybe, dc), cd) → new_esEs2(vwx230, vwx240, dc)
new_esEs0(Right(vwx230), Right(vwx240), df, app(ty_Maybe, ee)) → new_esEs2(vwx230, vwx240, ee)
new_esEs1(@3(vwx230, vwx231, vwx232), @3(vwx240, vwx241, vwx242), app(app(app(ty_@3, ff), fg), fh), fa, fb) → new_esEs1(vwx230, vwx240, ff, fg, fh)
new_esEs(:(vwx230, vwx231), :(vwx240, vwx241), app(app(ty_Either, bb), bc)) → new_esEs0(vwx230, vwx240, bb, bc)
new_esEs3(@2(vwx230, vwx231), @2(vwx240, vwx241), app(ty_Maybe, bcg), bca) → new_esEs2(vwx230, vwx240, bcg)
new_esEs(:(vwx230, vwx231), :(vwx240, vwx241), cb) → new_esEs(vwx231, vwx241, cb)
new_esEs1(@3(vwx230, vwx231, vwx232), @3(vwx240, vwx241, vwx242), app(app(ty_Either, fc), fd), fa, fb) → new_esEs0(vwx230, vwx240, fc, fd)
new_esEs1(@3(vwx230, vwx231, vwx232), @3(vwx240, vwx241, vwx242), gd, app(ty_Maybe, hc), fb) → new_esEs2(vwx231, vwx241, hc)
new_esEs1(@3(vwx230, vwx231, vwx232), @3(vwx240, vwx241, vwx242), app(app(ty_@2, gb), gc), fa, fb) → new_esEs3(vwx230, vwx240, gb, gc)
new_esEs(:(vwx230, vwx231), :(vwx240, vwx241), app(app(app(ty_@3, bd), be), bf)) → new_esEs1(vwx230, vwx240, bd, be, bf)
new_esEs1(@3(vwx230, vwx231, vwx232), @3(vwx240, vwx241, vwx242), gd, app(app(ty_Either, gf), gg), fb) → new_esEs0(vwx231, vwx241, gf, gg)
new_esEs1(@3(vwx230, vwx231, vwx232), @3(vwx240, vwx241, vwx242), gd, fa, app(app(ty_Either, hg), hh)) → new_esEs0(vwx232, vwx242, hg, hh)
new_esEs1(@3(vwx230, vwx231, vwx232), @3(vwx240, vwx241, vwx242), app(ty_[], eh), fa, fb) → new_esEs(vwx230, vwx240, eh)
new_esEs1(@3(vwx230, vwx231, vwx232), @3(vwx240, vwx241, vwx242), gd, fa, app(ty_Maybe, bad)) → new_esEs2(vwx232, vwx242, bad)
new_esEs3(@2(vwx230, vwx231), @2(vwx240, vwx241), app(app(ty_@2, bch), bda), bca) → new_esEs3(vwx230, vwx240, bch, bda)
new_esEs0(Right(vwx230), Right(vwx240), df, app(app(ty_@2, ef), eg)) → new_esEs3(vwx230, vwx240, ef, eg)
new_esEs0(Right(vwx230), Right(vwx240), df, app(ty_[], dg)) → new_esEs(vwx230, vwx240, dg)
new_esEs1(@3(vwx230, vwx231, vwx232), @3(vwx240, vwx241, vwx242), app(ty_Maybe, ga), fa, fb) → new_esEs2(vwx230, vwx240, ga)
new_esEs(:(vwx230, vwx231), :(vwx240, vwx241), app(app(ty_@2, bh), ca)) → new_esEs3(vwx230, vwx240, bh, ca)
new_esEs2(Just(vwx230), Just(vwx240), app(app(ty_@2, bbf), bbg)) → new_esEs3(vwx230, vwx240, bbf, bbg)
new_esEs3(@2(vwx230, vwx231), @2(vwx240, vwx241), bdb, app(app(app(ty_@3, bdf), bdg), bdh)) → new_esEs1(vwx231, vwx241, bdf, bdg, bdh)
new_esEs1(@3(vwx230, vwx231, vwx232), @3(vwx240, vwx241, vwx242), gd, fa, app(app(ty_@2, bae), baf)) → new_esEs3(vwx232, vwx242, bae, baf)
new_esEs3(@2(vwx230, vwx231), @2(vwx240, vwx241), app(app(ty_Either, bcb), bcc), bca) → new_esEs0(vwx230, vwx240, bcb, bcc)
new_esEs2(Just(vwx230), Just(vwx240), app(app(ty_Either, bah), bba)) → new_esEs0(vwx230, vwx240, bah, bba)
new_esEs1(@3(vwx230, vwx231, vwx232), @3(vwx240, vwx241, vwx242), gd, fa, app(ty_[], hf)) → new_esEs(vwx232, vwx242, hf)
new_esEs1(@3(vwx230, vwx231, vwx232), @3(vwx240, vwx241, vwx242), gd, app(ty_[], ge), fb) → new_esEs(vwx231, vwx241, ge)
new_esEs0(Left(vwx230), Left(vwx240), app(app(ty_@2, dd), de), cd) → new_esEs3(vwx230, vwx240, dd, de)
new_esEs(:(vwx230, vwx231), :(vwx240, vwx241), app(ty_[], ba)) → new_esEs(vwx230, vwx240, ba)
new_esEs0(Left(vwx230), Left(vwx240), app(app(app(ty_@3, cg), da), db), cd) → new_esEs1(vwx230, vwx240, cg, da, db)
new_esEs0(Right(vwx230), Right(vwx240), df, app(app(app(ty_@3, eb), ec), ed)) → new_esEs1(vwx230, vwx240, eb, ec, ed)

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_primCmpNat(Succ(vwx3000), Succ(vwx4000)) → new_primCmpNat(vwx3000, vwx4000)

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

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



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

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

new_ltEs0(Left(:(vwx300, vwx301)), Left(:(vwx400, vwx401)), app(ty_[], ba), ce) → new_compare0(vwx301, vwx401, ba)
new_ltEs2(Just(vwx300), Just(vwx400), app(app(ty_@2, fg), fh)) → new_ltEs1(vwx300, vwx400, fg, fh)
new_ltEs1(@2(vwx300, vwx301), @2(vwx400, vwx401), ea, app(app(ty_@2, ee), ef)) → new_ltEs1(vwx301, vwx401, ee, ef)
new_compare0(:(vwx300, vwx301), :(vwx400, vwx401), ba) → new_primCompAux(vwx300, vwx400, new_compare(vwx301, vwx401, ba), ba)
new_ltEs0(Left(@3(vwx300, vwx301, vwx302)), Left(@3(vwx400, vwx401, vwx402)), app(app(app(ty_@3, app(app(ty_Either, gh), ha)), gf), gg), ce) → new_lt0(vwx300, vwx400, gh, ha)
new_ltEs0(Right(vwx30), Right(vwx40), bcc, app(app(app(ty_@3, bdb), bdc), bdd)) → new_ltEs3(vwx30, vwx40, bdb, bdc, bdd)
new_ltEs0(Left(@3(vwx300, vwx301, vwx302)), Left(@3(vwx400, vwx401, vwx402)), app(app(app(ty_@3, app(ty_[], ge)), gf), gg), ce) → new_lt(vwx300, vwx400, ge)
new_lt3(vwx300, vwx400, df, dg, dh) → new_compare23(vwx300, vwx400, new_esEs7(vwx300, vwx400, df, dg, dh), df, dg, dh)
new_ltEs3(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), hh, app(ty_[], baa), gg) → new_lt(vwx301, vwx401, baa)
new_ltEs0(Left(@2(vwx300, vwx301)), Left(@2(vwx400, vwx401)), app(app(ty_@2, ea), app(app(app(ty_@3, eh), fa), fb)), ce) → new_ltEs3(vwx301, vwx401, eh, fa, fb)
new_ltEs3(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), app(ty_[], ge), gf, gg) → new_lt(vwx300, vwx400, ge)
new_compare0(:(vwx300, vwx301), :(vwx400, vwx401), ba) → new_compare0(vwx301, vwx401, ba)
new_ltEs2(Just(vwx300), Just(vwx400), app(app(ty_Either, fd), ff)) → new_ltEs0(vwx300, vwx400, fd, ff)
new_ltEs3(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), hh, gf, app(ty_[], bbb)) → new_ltEs(vwx302, vwx402, bbb)
new_ltEs0(Left(Just(vwx300)), Left(Just(vwx400)), app(ty_Maybe, app(ty_Maybe, ga)), ce) → new_ltEs2(vwx300, vwx400, ga)
new_ltEs1(@2(vwx300, vwx301), @2(vwx400, vwx401), ea, app(ty_Maybe, eg)) → new_ltEs2(vwx301, vwx401, eg)
new_compare2(vwx300, vwx400, dc, dd) → new_compare21(vwx300, vwx400, new_esEs5(vwx300, vwx400, dc, dd), dc, dd)
new_ltEs1(@2(vwx300, vwx301), @2(vwx400, vwx401), app(app(ty_Either, cc), cd), db) → new_compare20(vwx300, vwx400, new_esEs4(vwx300, vwx400, cc, cd), cc, cd)
new_ltEs0(Right(vwx30), Right(vwx40), bcc, app(app(ty_@2, bcg), bch)) → new_ltEs1(vwx30, vwx40, bcg, bch)
new_ltEs1(@2(vwx300, vwx301), @2(vwx400, vwx401), app(ty_Maybe, de), db) → new_compare22(vwx300, vwx400, new_esEs6(vwx300, vwx400, de), de)
new_ltEs0(Left(vwx30), Left(vwx40), app(app(ty_Either, cf), cg), ce) → new_ltEs0(vwx30, vwx40, cf, cg)
new_ltEs0(Left(@2(vwx300, vwx301)), Left(@2(vwx400, vwx401)), app(app(ty_@2, ea), app(ty_Maybe, eg)), ce) → new_ltEs2(vwx301, vwx401, eg)
new_ltEs2(Just(vwx300), Just(vwx400), app(ty_[], fc)) → new_ltEs(vwx300, vwx400, fc)
new_ltEs0(Left(@3(vwx300, vwx301, vwx302)), Left(@3(vwx400, vwx401, vwx402)), app(app(app(ty_@3, hh), gf), app(ty_[], bbb)), ce) → new_ltEs(vwx302, vwx402, bbb)
new_ltEs3(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), app(ty_Maybe, hd), gf, gg) → new_lt2(vwx300, vwx400, hd)
new_ltEs0(Left(@3(vwx300, vwx301, vwx302)), Left(@3(vwx400, vwx401, vwx402)), app(app(app(ty_@3, hh), app(ty_[], baa)), gg), ce) → new_lt(vwx301, vwx401, baa)
new_ltEs3(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), hh, app(app(ty_@2, bad), bae), gg) → new_lt1(vwx301, vwx401, bad, bae)
new_ltEs0(Left(@3(vwx300, vwx301, vwx302)), Left(@3(vwx400, vwx401, vwx402)), app(app(app(ty_@3, hh), gf), app(app(ty_@2, bbe), bbf)), ce) → new_ltEs1(vwx302, vwx402, bbe, bbf)
new_ltEs3(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), hh, gf, app(app(ty_Either, bbc), bbd)) → new_ltEs0(vwx302, vwx402, bbc, bbd)
new_ltEs(:(vwx300, vwx301), :(vwx400, vwx401), ba) → new_primCompAux(vwx300, vwx400, new_compare(vwx301, vwx401, ba), ba)
new_ltEs0(Left(@2(vwx300, vwx301)), Left(@2(vwx400, vwx401)), app(app(ty_@2, app(app(app(ty_@3, df), dg), dh)), db), ce) → new_compare23(vwx300, vwx400, new_esEs7(vwx300, vwx400, df, dg, dh), df, dg, dh)
new_ltEs0(Left(@2(vwx300, vwx301)), Left(@2(vwx400, vwx401)), app(app(ty_@2, app(ty_Maybe, de)), db), ce) → new_compare22(vwx300, vwx400, new_esEs6(vwx300, vwx400, de), de)
new_ltEs3(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), hh, gf, app(ty_Maybe, bbg)) → new_ltEs2(vwx302, vwx402, bbg)
new_primCompAux(vwx300, vwx400, vwx35, app(ty_[], bb)) → new_compare0(vwx300, vwx400, bb)
new_ltEs0(Left(@3(vwx300, vwx301, vwx302)), Left(@3(vwx400, vwx401, vwx402)), app(app(app(ty_@3, hh), app(app(ty_Either, bab), bac)), gg), ce) → new_lt0(vwx301, vwx401, bab, bac)
new_compare20(vwx300, vwx400, False, cc, cd) → new_ltEs0(vwx300, vwx400, cc, cd)
new_compare21(vwx300, vwx400, False, dc, dd) → new_ltEs1(vwx300, vwx400, dc, dd)
new_ltEs0(Left(@2(vwx300, vwx301)), Left(@2(vwx400, vwx401)), app(app(ty_@2, app(ty_[], da)), db), ce) → new_compare0(vwx300, vwx400, da)
new_primCompAux(vwx300, vwx400, vwx35, app(app(ty_Either, bc), bd)) → new_compare1(vwx300, vwx400, bc, bd)
new_ltEs0(Left(Just(vwx300)), Left(Just(vwx400)), app(ty_Maybe, app(app(ty_@2, fg), fh)), ce) → new_ltEs1(vwx300, vwx400, fg, fh)
new_ltEs1(@2(vwx300, vwx301), @2(vwx400, vwx401), app(app(ty_@2, dc), dd), db) → new_compare21(vwx300, vwx400, new_esEs5(vwx300, vwx400, dc, dd), dc, dd)
new_lt0(vwx300, vwx400, cc, cd) → new_compare20(vwx300, vwx400, new_esEs4(vwx300, vwx400, cc, cd), cc, cd)
new_ltEs0(Left(@3(vwx300, vwx301, vwx302)), Left(@3(vwx400, vwx401, vwx402)), app(app(app(ty_@3, app(app(app(ty_@3, he), hf), hg)), gf), gg), ce) → new_lt3(vwx300, vwx400, he, hf, hg)
new_ltEs0(Left(@3(vwx300, vwx301, vwx302)), Left(@3(vwx400, vwx401, vwx402)), app(app(app(ty_@3, app(ty_Maybe, hd)), gf), gg), ce) → new_lt2(vwx300, vwx400, hd)
new_ltEs0(Left(@3(vwx300, vwx301, vwx302)), Left(@3(vwx400, vwx401, vwx402)), app(app(app(ty_@3, app(app(ty_@2, hb), hc)), gf), gg), ce) → new_lt1(vwx300, vwx400, hb, hc)
new_ltEs0(Left(@2(vwx300, vwx301)), Left(@2(vwx400, vwx401)), app(app(ty_@2, ea), app(app(ty_Either, ec), ed)), ce) → new_ltEs0(vwx301, vwx401, ec, ed)
new_ltEs2(Just(vwx300), Just(vwx400), app(app(app(ty_@3, gb), gc), gd)) → new_ltEs3(vwx300, vwx400, gb, gc, gd)
new_lt2(vwx300, vwx400, de) → new_compare22(vwx300, vwx400, new_esEs6(vwx300, vwx400, de), de)
new_ltEs0(Left(@3(vwx300, vwx301, vwx302)), Left(@3(vwx400, vwx401, vwx402)), app(app(app(ty_@3, hh), gf), app(app(ty_Either, bbc), bbd)), ce) → new_ltEs0(vwx302, vwx402, bbc, bbd)
new_ltEs3(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), app(app(ty_@2, hb), hc), gf, gg) → new_lt1(vwx300, vwx400, hb, hc)
new_ltEs0(Right(vwx30), Right(vwx40), bcc, app(ty_[], bcd)) → new_ltEs(vwx30, vwx40, bcd)
new_compare22(vwx300, vwx400, False, de) → new_ltEs2(vwx300, vwx400, de)
new_ltEs0(Right(vwx30), Right(vwx40), bcc, app(app(ty_Either, bce), bcf)) → new_ltEs0(vwx30, vwx40, bce, bcf)
new_ltEs0(Right(vwx30), Right(vwx40), bcc, app(ty_Maybe, bda)) → new_ltEs2(vwx30, vwx40, bda)
new_ltEs0(Left(Just(vwx300)), Left(Just(vwx400)), app(ty_Maybe, app(app(app(ty_@3, gb), gc), gd)), ce) → new_ltEs3(vwx300, vwx400, gb, gc, gd)
new_ltEs0(Left(@3(vwx300, vwx301, vwx302)), Left(@3(vwx400, vwx401, vwx402)), app(app(app(ty_@3, hh), gf), app(app(app(ty_@3, bbh), bca), bcb)), ce) → new_ltEs3(vwx302, vwx402, bbh, bca, bcb)
new_ltEs3(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), hh, gf, app(app(app(ty_@3, bbh), bca), bcb)) → new_ltEs3(vwx302, vwx402, bbh, bca, bcb)
new_ltEs0(Left(@2(vwx300, vwx301)), Left(@2(vwx400, vwx401)), app(app(ty_@2, ea), app(ty_[], eb)), ce) → new_ltEs(vwx301, vwx401, eb)
new_primCompAux(vwx300, vwx400, vwx35, app(app(ty_@2, be), bf)) → new_compare2(vwx300, vwx400, be, bf)
new_ltEs0(Left(@3(vwx300, vwx301, vwx302)), Left(@3(vwx400, vwx401, vwx402)), app(app(app(ty_@3, hh), app(app(ty_@2, bad), bae)), gg), ce) → new_lt1(vwx301, vwx401, bad, bae)
new_ltEs(:(vwx300, vwx301), :(vwx400, vwx401), ba) → new_compare0(vwx301, vwx401, ba)
new_ltEs3(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), hh, gf, app(app(ty_@2, bbe), bbf)) → new_ltEs1(vwx302, vwx402, bbe, bbf)
new_ltEs0(Left(@2(vwx300, vwx301)), Left(@2(vwx400, vwx401)), app(app(ty_@2, app(app(ty_@2, dc), dd)), db), ce) → new_compare21(vwx300, vwx400, new_esEs5(vwx300, vwx400, dc, dd), dc, dd)
new_ltEs2(Just(vwx300), Just(vwx400), app(ty_Maybe, ga)) → new_ltEs2(vwx300, vwx400, ga)
new_ltEs3(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), app(app(app(ty_@3, he), hf), hg), gf, gg) → new_lt3(vwx300, vwx400, he, hf, hg)
new_ltEs0(Left(Just(vwx300)), Left(Just(vwx400)), app(ty_Maybe, app(app(ty_Either, fd), ff)), ce) → new_ltEs0(vwx300, vwx400, fd, ff)
new_ltEs1(@2(vwx300, vwx301), @2(vwx400, vwx401), app(app(app(ty_@3, df), dg), dh), db) → new_compare23(vwx300, vwx400, new_esEs7(vwx300, vwx400, df, dg, dh), df, dg, dh)
new_ltEs1(@2(vwx300, vwx301), @2(vwx400, vwx401), ea, app(ty_[], eb)) → new_ltEs(vwx301, vwx401, eb)
new_ltEs1(@2(vwx300, vwx301), @2(vwx400, vwx401), app(ty_[], da), db) → new_compare0(vwx300, vwx400, da)
new_ltEs3(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), hh, app(app(app(ty_@3, bag), bah), bba), gg) → new_lt3(vwx301, vwx401, bag, bah, bba)
new_ltEs1(@2(vwx300, vwx301), @2(vwx400, vwx401), ea, app(app(ty_Either, ec), ed)) → new_ltEs0(vwx301, vwx401, ec, ed)
new_lt(vwx300, vwx400, da) → new_compare0(vwx300, vwx400, da)
new_ltEs3(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), hh, app(app(ty_Either, bab), bac), gg) → new_lt0(vwx301, vwx401, bab, bac)
new_lt1(vwx300, vwx400, dc, dd) → new_compare21(vwx300, vwx400, new_esEs5(vwx300, vwx400, dc, dd), dc, dd)
new_ltEs0(Left(@3(vwx300, vwx301, vwx302)), Left(@3(vwx400, vwx401, vwx402)), app(app(app(ty_@3, hh), app(app(app(ty_@3, bag), bah), bba)), gg), ce) → new_lt3(vwx301, vwx401, bag, bah, bba)
new_ltEs1(@2(vwx300, vwx301), @2(vwx400, vwx401), ea, app(app(app(ty_@3, eh), fa), fb)) → new_ltEs3(vwx301, vwx401, eh, fa, fb)
new_ltEs3(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), hh, app(ty_Maybe, baf), gg) → new_lt2(vwx301, vwx401, baf)
new_compare4(vwx300, vwx400, df, dg, dh) → new_compare23(vwx300, vwx400, new_esEs7(vwx300, vwx400, df, dg, dh), df, dg, dh)
new_compare1(vwx300, vwx400, cc, cd) → new_compare20(vwx300, vwx400, new_esEs4(vwx300, vwx400, cc, cd), cc, cd)
new_ltEs3(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), app(app(ty_Either, gh), ha), gf, gg) → new_lt0(vwx300, vwx400, gh, ha)
new_ltEs0(Left(Just(vwx300)), Left(Just(vwx400)), app(ty_Maybe, app(ty_[], fc)), ce) → new_ltEs(vwx300, vwx400, fc)
new_ltEs0(Left(:(vwx300, vwx301)), Left(:(vwx400, vwx401)), app(ty_[], ba), ce) → new_primCompAux(vwx300, vwx400, new_compare(vwx301, vwx401, ba), ba)
new_compare3(vwx300, vwx400, de) → new_compare22(vwx300, vwx400, new_esEs6(vwx300, vwx400, de), de)
new_primCompAux(vwx300, vwx400, vwx35, app(ty_Maybe, bg)) → new_compare3(vwx300, vwx400, bg)
new_primCompAux(vwx300, vwx400, vwx35, app(app(app(ty_@3, bh), ca), cb)) → new_compare4(vwx300, vwx400, bh, ca, cb)
new_compare23(vwx300, vwx400, False, df, dg, dh) → new_ltEs3(vwx300, vwx400, df, dg, dh)
new_ltEs0(Left(@3(vwx300, vwx301, vwx302)), Left(@3(vwx400, vwx401, vwx402)), app(app(app(ty_@3, hh), gf), app(ty_Maybe, bbg)), ce) → new_ltEs2(vwx302, vwx402, bbg)
new_ltEs0(Left(@2(vwx300, vwx301)), Left(@2(vwx400, vwx401)), app(app(ty_@2, app(app(ty_Either, cc), cd)), db), ce) → new_compare20(vwx300, vwx400, new_esEs4(vwx300, vwx400, cc, cd), cc, cd)
new_ltEs0(Left(@2(vwx300, vwx301)), Left(@2(vwx400, vwx401)), app(app(ty_@2, ea), app(app(ty_@2, ee), ef)), ce) → new_ltEs1(vwx301, vwx401, ee, ef)
new_ltEs0(Left(@3(vwx300, vwx301, vwx302)), Left(@3(vwx400, vwx401, vwx402)), app(app(app(ty_@3, hh), app(ty_Maybe, baf)), gg), ce) → new_lt2(vwx301, vwx401, baf)

The TRS R consists of the following rules:

new_compare31(vwx300, vwx400, ty_Integer) → new_compare13(vwx300, vwx400)
new_ltEs19(vwx302, vwx402, app(app(ty_@2, bbe), bbf)) → new_ltEs5(vwx302, vwx402, bbe, bbf)
new_lt8(vwx300, vwx400, app(app(ty_@2, dc), dd)) → new_lt7(vwx300, vwx400, dc, dd)
new_esEs6(Just(vwx230), Just(vwx240), app(app(ty_@2, bha), bhb)) → new_esEs5(vwx230, vwx240, bha, bhb)
new_esEs24(vwx230, vwx240, ty_Float) → new_esEs12(vwx230, vwx240)
new_ltEs15(True, False) → False
new_esEs18(Char(vwx230), Char(vwx240)) → new_primEqNat0(vwx230, vwx240)
new_esEs4(Right(vwx230), Right(vwx240), bec, app(ty_Ratio, cdc)) → new_esEs13(vwx230, vwx240, cdc)
new_ltEs18(vwx301, vwx401, ty_Int) → new_ltEs12(vwx301, vwx401)
new_ltEs18(vwx301, vwx401, ty_@0) → new_ltEs9(vwx301, vwx401)
new_ltEs18(vwx301, vwx401, ty_Integer) → new_ltEs14(vwx301, vwx401)
new_compare10(vwx300, vwx400) → new_compare25(vwx300, vwx400, new_esEs9(vwx300, vwx400))
new_compare([], :(vwx400, vwx401), ba) → LT
new_lt8(vwx300, vwx400, ty_Bool) → new_lt17(vwx300, vwx400)
new_esEs20(vwx230, vwx240, ty_Char) → new_esEs18(vwx230, vwx240)
new_lt19(vwx300, vwx400, ty_Integer) → new_lt5(vwx300, vwx400)
new_ltEs19(vwx302, vwx402, ty_Float) → new_ltEs11(vwx302, vwx402)
new_esEs27(vwx232, vwx242, ty_Ordering) → new_esEs19(vwx232, vwx242)
new_compare14(vwx300, vwx400, True, df, dg, dh) → LT
new_compare31(vwx300, vwx400, ty_Ordering) → new_compare16(vwx300, vwx400)
new_compare31(vwx300, vwx400, app(app(app(ty_@3, bh), ca), cb)) → new_compare9(vwx300, vwx400, bh, ca, cb)
new_esEs21(vwx231, vwx241, ty_Int) → new_esEs14(vwx231, vwx241)
new_lt18(vwx300, vwx400, de) → new_esEs8(new_compare32(vwx300, vwx400, de))
new_esEs6(Just(vwx230), Just(vwx240), ty_@0) → new_esEs16(vwx230, vwx240)
new_compare17(vwx300, vwx400, dc, dd) → new_compare26(vwx300, vwx400, new_esEs5(vwx300, vwx400, dc, dd), dc, dd)
new_ltEs7(Left(vwx30), Right(vwx40), bcc, ce) → True
new_primMulNat0(Zero, Zero) → Zero
new_esEs6(Just(vwx230), Just(vwx240), app(ty_Ratio, bgb)) → new_esEs13(vwx230, vwx240, bgb)
new_compare(:(vwx300, vwx301), [], ba) → GT
new_esEs27(vwx232, vwx242, ty_Bool) → new_esEs9(vwx232, vwx242)
new_esEs4(Right(vwx230), Right(vwx240), bec, app(ty_[], cdb)) → new_esEs11(vwx230, vwx240, cdb)
new_compare28(vwx300, vwx400, False, df, dg, dh) → new_compare14(vwx300, vwx400, new_ltEs17(vwx300, vwx400, df, dg, dh), df, dg, dh)
new_ltEs19(vwx302, vwx402, ty_Integer) → new_ltEs14(vwx302, vwx402)
new_esEs6(Just(vwx230), Just(vwx240), ty_Char) → new_esEs18(vwx230, vwx240)
new_lt20(vwx301, vwx401, app(app(app(ty_@3, bag), bah), bba)) → new_lt4(vwx301, vwx401, bag, bah, bba)
new_esEs24(vwx230, vwx240, ty_Integer) → new_esEs15(vwx230, vwx240)
new_lt19(vwx300, vwx400, ty_Ordering) → new_lt6(vwx300, vwx400)
new_lt14(vwx300, vwx400) → new_esEs8(new_compare7(vwx300, vwx400))
new_not(GT) → False
new_compare30(:%(vwx300, vwx301), :%(vwx400, vwx401), ty_Int) → new_compare7(new_sr(vwx300, vwx401), new_sr(vwx400, vwx301))
new_esEs20(vwx230, vwx240, app(app(ty_Either, bhf), bhg)) → new_esEs4(vwx230, vwx240, bhf, bhg)
new_esEs4(Right(vwx230), Right(vwx240), bec, app(app(app(ty_@3, cdf), cdg), cdh)) → new_esEs7(vwx230, vwx240, cdf, cdg, cdh)
new_lt19(vwx300, vwx400, ty_Bool) → new_lt17(vwx300, vwx400)
new_esEs20(vwx230, vwx240, app(ty_Ratio, bhe)) → new_esEs13(vwx230, vwx240, bhe)
new_esEs4(Left(vwx230), Left(vwx240), app(ty_Ratio, cca), bed) → new_esEs13(vwx230, vwx240, cca)
new_lt19(vwx300, vwx400, ty_Float) → new_lt13(vwx300, vwx400)
new_esEs11([], [], bea) → True
new_esEs21(vwx231, vwx241, app(app(app(ty_@3, cbb), cbc), cbd)) → new_esEs7(vwx231, vwx241, cbb, cbc, cbd)
new_esEs24(vwx230, vwx240, app(app(ty_@2, cfd), cfe)) → new_esEs5(vwx230, vwx240, cfd, cfe)
new_ltEs16(Just(vwx300), Just(vwx400), app(app(app(ty_@3, gb), gc), gd)) → new_ltEs17(vwx300, vwx400, gb, gc, gd)
new_esEs27(vwx232, vwx242, app(ty_Maybe, dba)) → new_esEs6(vwx232, vwx242, dba)
new_esEs15(Integer(vwx230), Integer(vwx240)) → new_primEqInt(vwx230, vwx240)
new_ltEs7(Right(vwx30), Right(vwx40), bcc, ty_Float) → new_ltEs11(vwx30, vwx40)
new_esEs4(Left(vwx230), Left(vwx240), app(ty_[], cbh), bed) → new_esEs11(vwx230, vwx240, cbh)
new_lt8(vwx300, vwx400, app(app(app(ty_@3, df), dg), dh)) → new_lt4(vwx300, vwx400, df, dg, dh)
new_compare15(vwx300, vwx400, False, de) → GT
new_ltEs7(Left(vwx30), Left(vwx40), ty_Char, ce) → new_ltEs4(vwx30, vwx40)
new_esEs19(GT, GT) → True
new_esEs25(vwx230, vwx240, app(app(ty_Either, cfh), cga)) → new_esEs4(vwx230, vwx240, cfh, cga)
new_ltEs15(True, True) → True
new_esEs27(vwx232, vwx242, ty_@0) → new_esEs16(vwx232, vwx242)
new_lt4(vwx300, vwx400, df, dg, dh) → new_esEs8(new_compare9(vwx300, vwx400, df, dg, dh))
new_esEs4(Right(vwx230), Right(vwx240), bec, app(ty_Maybe, cea)) → new_esEs6(vwx230, vwx240, cea)
new_ltEs4(vwx30, vwx40) → new_not(new_compare8(vwx30, vwx40))
new_ltEs7(Right(vwx30), Right(vwx40), bcc, app(ty_Ratio, bdg)) → new_ltEs13(vwx30, vwx40, bdg)
new_ltEs15(False, True) → True
new_ltEs7(Right(vwx30), Right(vwx40), bcc, ty_Bool) → new_ltEs15(vwx30, vwx40)
new_ltEs6(GT, EQ) → False
new_compare31(vwx300, vwx400, app(ty_Ratio, bhc)) → new_compare30(vwx300, vwx400, bhc)
new_esEs4(Right(vwx230), Right(vwx240), bec, ty_Integer) → new_esEs15(vwx230, vwx240)
new_esEs20(vwx230, vwx240, app(app(ty_@2, cad), cae)) → new_esEs5(vwx230, vwx240, cad, cae)
new_compare9(vwx300, vwx400, df, dg, dh) → new_compare28(vwx300, vwx400, new_esEs7(vwx300, vwx400, df, dg, dh), df, dg, dh)
new_lt6(vwx300, vwx400) → new_esEs8(new_compare16(vwx300, vwx400))
new_lt8(vwx300, vwx400, ty_Int) → new_lt14(vwx300, vwx400)
new_esEs24(vwx230, vwx240, app(ty_[], ced)) → new_esEs11(vwx230, vwx240, ced)
new_ltEs15(False, False) → True
new_lt20(vwx301, vwx401, app(app(ty_@2, bad), bae)) → new_lt7(vwx301, vwx401, bad, bae)
new_ltEs19(vwx302, vwx402, ty_Char) → new_ltEs4(vwx302, vwx402)
new_primCmpNat0(Zero, Succ(vwx4000)) → LT
new_esEs27(vwx232, vwx242, app(app(app(ty_@3, daf), dag), dah)) → new_esEs7(vwx232, vwx242, daf, dag, dah)
new_ltEs7(Left(vwx30), Left(vwx40), app(ty_Ratio, bde), ce) → new_ltEs13(vwx30, vwx40, bde)
new_esEs26(vwx231, vwx241, ty_Double) → new_esEs17(vwx231, vwx241)
new_ltEs7(Right(vwx30), Right(vwx40), bcc, ty_@0) → new_ltEs9(vwx30, vwx40)
new_compare29(vwx300, vwx400, False, de) → new_compare15(vwx300, vwx400, new_ltEs16(vwx300, vwx400, de), de)
new_esEs25(vwx230, vwx240, ty_Bool) → new_esEs9(vwx230, vwx240)
new_lt20(vwx301, vwx401, ty_Ordering) → new_lt6(vwx301, vwx401)
new_compare6(Float(vwx300, vwx301), Float(vwx400, vwx401)) → new_compare7(new_sr(vwx300, vwx400), new_sr(vwx301, vwx401))
new_esEs21(vwx231, vwx241, app(ty_Ratio, cag)) → new_esEs13(vwx231, vwx241, cag)
new_ltEs16(Nothing, Nothing, bdf) → True
new_esEs4(Right(vwx230), Right(vwx240), bec, ty_@0) → new_esEs16(vwx230, vwx240)
new_ltEs7(Right(vwx30), Right(vwx40), bcc, ty_Int) → new_ltEs12(vwx30, vwx40)
new_esEs25(vwx230, vwx240, ty_Double) → new_esEs17(vwx230, vwx240)
new_esEs10(vwx23, vwx24, app(app(ty_Either, bec), bed)) → new_esEs4(vwx23, vwx24, bec, bed)
new_esEs23(vwx231, vwx241, ty_Int) → new_esEs14(vwx231, vwx241)
new_esEs25(vwx230, vwx240, app(ty_Ratio, cfg)) → new_esEs13(vwx230, vwx240, cfg)
new_primEqNat0(Zero, Zero) → True
new_esEs6(Just(vwx230), Just(vwx240), app(app(app(ty_@3, bge), bgf), bgg)) → new_esEs7(vwx230, vwx240, bge, bgf, bgg)
new_compare24(vwx300, vwx400, False, cc, cd) → new_compare111(vwx300, vwx400, new_ltEs7(vwx300, vwx400, cc, cd), cc, cd)
new_ltEs7(Right(vwx30), Right(vwx40), bcc, ty_Char) → new_ltEs4(vwx30, vwx40)
new_esEs26(vwx231, vwx241, app(ty_Maybe, chg)) → new_esEs6(vwx231, vwx241, chg)
new_compare111(vwx300, vwx400, False, cc, cd) → GT
new_esEs7(@3(vwx230, vwx231, vwx232), @3(vwx240, vwx241, vwx242), bee, bef, beg) → new_asAs(new_esEs25(vwx230, vwx240, bee), new_asAs(new_esEs26(vwx231, vwx241, bef), new_esEs27(vwx232, vwx242, beg)))
new_esEs6(Just(vwx230), Just(vwx240), ty_Int) → new_esEs14(vwx230, vwx240)
new_esEs26(vwx231, vwx241, app(ty_Ratio, cha)) → new_esEs13(vwx231, vwx241, cha)
new_esEs26(vwx231, vwx241, ty_@0) → new_esEs16(vwx231, vwx241)
new_esEs27(vwx232, vwx242, app(ty_Ratio, dac)) → new_esEs13(vwx232, vwx242, dac)
new_ltEs11(vwx30, vwx40) → new_not(new_compare6(vwx30, vwx40))
new_compare(:(vwx300, vwx301), :(vwx400, vwx401), ba) → new_primCompAux1(vwx300, vwx400, new_compare(vwx301, vwx401, ba), ba)
new_ltEs19(vwx302, vwx402, ty_Ordering) → new_ltEs6(vwx302, vwx402)
new_sr(vwx301, vwx401) → new_primMulInt(vwx301, vwx401)
new_lt7(vwx300, vwx400, dc, dd) → new_esEs8(new_compare17(vwx300, vwx400, dc, dd))
new_compare12(vwx300, vwx400, False, dc, dd) → GT
new_compare7(vwx30, vwx40) → new_primCmpInt(vwx30, vwx40)
new_esEs26(vwx231, vwx241, ty_Ordering) → new_esEs19(vwx231, vwx241)
new_lt8(vwx300, vwx400, app(ty_[], da)) → new_lt11(vwx300, vwx400, da)
new_ltEs7(Left(vwx30), Left(vwx40), app(app(app(ty_@3, hh), gf), gg), ce) → new_ltEs17(vwx30, vwx40, hh, gf, gg)
new_esEs10(vwx23, vwx24, ty_Int) → new_esEs14(vwx23, vwx24)
new_ltEs6(EQ, GT) → True
new_primPlusNat0(Succ(vwx530), vwx40100) → Succ(Succ(new_primPlusNat1(vwx530, vwx40100)))
new_ltEs18(vwx301, vwx401, ty_Ordering) → new_ltEs6(vwx301, vwx401)
new_esEs4(Left(vwx230), Left(vwx240), app(app(ty_@2, cch), cda), bed) → new_esEs5(vwx230, vwx240, cch, cda)
new_esEs20(vwx230, vwx240, app(app(app(ty_@3, bhh), caa), cab)) → new_esEs7(vwx230, vwx240, bhh, caa, cab)
new_ltEs19(vwx302, vwx402, ty_Bool) → new_ltEs15(vwx302, vwx402)
new_esEs10(vwx23, vwx24, ty_@0) → new_esEs16(vwx23, vwx24)
new_esEs21(vwx231, vwx241, ty_Ordering) → new_esEs19(vwx231, vwx241)
new_esEs4(Left(vwx230), Left(vwx240), ty_Float, bed) → new_esEs12(vwx230, vwx240)
new_esEs26(vwx231, vwx241, ty_Bool) → new_esEs9(vwx231, vwx241)
new_esEs4(Right(vwx230), Right(vwx240), bec, app(app(ty_Either, cdd), cde)) → new_esEs4(vwx230, vwx240, cdd, cde)
new_ltEs16(Nothing, Just(vwx400), bdf) → True
new_compare25(vwx300, vwx400, True) → EQ
new_primEqInt(Neg(Succ(vwx2300)), Neg(Succ(vwx2400))) → new_primEqNat0(vwx2300, vwx2400)
new_esEs10(vwx23, vwx24, ty_Ordering) → new_esEs19(vwx23, vwx24)
new_esEs11(:(vwx230, vwx231), :(vwx240, vwx241), bea) → new_asAs(new_esEs24(vwx230, vwx240, bea), new_esEs11(vwx231, vwx241, bea))
new_esEs4(Right(vwx230), Right(vwx240), bec, ty_Bool) → new_esEs9(vwx230, vwx240)
new_esEs4(Right(vwx230), Right(vwx240), bec, ty_Ordering) → new_esEs19(vwx230, vwx240)
new_esEs4(Left(vwx230), Left(vwx240), app(app(ty_Either, ccb), ccc), bed) → new_esEs4(vwx230, vwx240, ccb, ccc)
new_ltEs18(vwx301, vwx401, app(app(ty_Either, ec), ed)) → new_ltEs7(vwx301, vwx401, ec, ed)
new_esEs19(EQ, EQ) → True
new_primPlusNat1(Zero, Succ(vwx401000)) → Succ(vwx401000)
new_primPlusNat1(Succ(vwx5300), Zero) → Succ(vwx5300)
new_esEs21(vwx231, vwx241, ty_@0) → new_esEs16(vwx231, vwx241)
new_esEs10(vwx23, vwx24, ty_Bool) → new_esEs9(vwx23, vwx24)
new_esEs26(vwx231, vwx241, app(app(app(ty_@3, chd), che), chf)) → new_esEs7(vwx231, vwx241, chd, che, chf)
new_ltEs12(vwx30, vwx40) → new_not(new_compare7(vwx30, vwx40))
new_esEs25(vwx230, vwx240, ty_Char) → new_esEs18(vwx230, vwx240)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_lt8(vwx300, vwx400, ty_Char) → new_lt12(vwx300, vwx400)
new_ltEs16(Just(vwx300), Just(vwx400), app(ty_Maybe, ga)) → new_ltEs16(vwx300, vwx400, ga)
new_lt20(vwx301, vwx401, app(ty_Maybe, baf)) → new_lt18(vwx301, vwx401, baf)
new_ltEs7(Right(vwx30), Left(vwx40), bcc, ce) → False
new_ltEs7(Left(vwx30), Left(vwx40), ty_Bool, ce) → new_ltEs15(vwx30, vwx40)
new_ltEs6(EQ, EQ) → True
new_esEs4(Left(vwx230), Left(vwx240), ty_Char, bed) → new_esEs18(vwx230, vwx240)
new_primEqInt(Neg(Zero), Neg(Succ(vwx2400))) → False
new_primEqInt(Neg(Succ(vwx2300)), Neg(Zero)) → False
new_lt8(vwx300, vwx400, ty_@0) → new_lt10(vwx300, vwx400)
new_lt19(vwx300, vwx400, ty_Char) → new_lt12(vwx300, vwx400)
new_primCompAux0(vwx39, GT) → GT
new_compare16(vwx300, vwx400) → new_compare27(vwx300, vwx400, new_esEs19(vwx300, vwx400))
new_compare26(vwx300, vwx400, True, dc, dd) → EQ
new_ltEs16(Just(vwx300), Just(vwx400), ty_Float) → new_ltEs11(vwx300, vwx400)
new_lt20(vwx301, vwx401, ty_@0) → new_lt10(vwx301, vwx401)
new_ltEs6(GT, GT) → True
new_esEs10(vwx23, vwx24, app(app(app(ty_@3, bee), bef), beg)) → new_esEs7(vwx23, vwx24, bee, bef, beg)
new_compare24(vwx300, vwx400, True, cc, cd) → EQ
new_esEs21(vwx231, vwx241, app(app(ty_Either, cah), cba)) → new_esEs4(vwx231, vwx241, cah, cba)
new_esEs6(Just(vwx230), Just(vwx240), ty_Double) → new_esEs17(vwx230, vwx240)
new_ltEs16(Just(vwx300), Just(vwx400), app(ty_Ratio, bfe)) → new_ltEs13(vwx300, vwx400, bfe)
new_compare([], [], ba) → EQ
new_compare31(vwx300, vwx400, app(ty_Maybe, bg)) → new_compare32(vwx300, vwx400, bg)
new_esEs6(Just(vwx230), Just(vwx240), app(app(ty_Either, bgc), bgd)) → new_esEs4(vwx230, vwx240, bgc, bgd)
new_ltEs19(vwx302, vwx402, app(ty_Maybe, bbg)) → new_ltEs16(vwx302, vwx402, bbg)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_compare31(vwx300, vwx400, app(app(ty_Either, bc), bd)) → new_compare5(vwx300, vwx400, bc, bd)
new_ltEs10(vwx30, vwx40, ba) → new_not(new_compare(vwx30, vwx40, ba))
new_esEs19(EQ, LT) → False
new_esEs19(LT, EQ) → False
new_primCmpNat0(Succ(vwx3000), Succ(vwx4000)) → new_primCmpNat0(vwx3000, vwx4000)
new_lt19(vwx300, vwx400, app(app(ty_Either, gh), ha)) → new_lt16(vwx300, vwx400, gh, ha)
new_esEs6(Nothing, Nothing, beh) → True
new_ltEs5(@2(vwx300, vwx301), @2(vwx400, vwx401), ea, db) → new_pePe(new_lt8(vwx300, vwx400, ea), vwx300, vwx400, new_ltEs18(vwx301, vwx401, db), ea)
new_primEqInt(Pos(Succ(vwx2300)), Pos(Succ(vwx2400))) → new_primEqNat0(vwx2300, vwx2400)
new_ltEs18(vwx301, vwx401, ty_Double) → new_ltEs8(vwx301, vwx401)
new_ltEs18(vwx301, vwx401, ty_Char) → new_ltEs4(vwx301, vwx401)
new_esEs21(vwx231, vwx241, app(ty_Maybe, cbe)) → new_esEs6(vwx231, vwx241, cbe)
new_lt19(vwx300, vwx400, app(app(app(ty_@3, he), hf), hg)) → new_lt4(vwx300, vwx400, he, hf, hg)
new_compare12(vwx300, vwx400, True, dc, dd) → LT
new_ltEs16(Just(vwx300), Just(vwx400), ty_Integer) → new_ltEs14(vwx300, vwx400)
new_esEs26(vwx231, vwx241, ty_Integer) → new_esEs15(vwx231, vwx241)
new_esEs6(Just(vwx230), Nothing, beh) → False
new_esEs6(Nothing, Just(vwx240), beh) → False
new_primEqNat0(Succ(vwx2300), Succ(vwx2400)) → new_primEqNat0(vwx2300, vwx2400)
new_esEs24(vwx230, vwx240, ty_@0) → new_esEs16(vwx230, vwx240)
new_lt13(vwx300, vwx400) → new_esEs8(new_compare6(vwx300, vwx400))
new_esEs27(vwx232, vwx242, ty_Float) → new_esEs12(vwx232, vwx242)
new_esEs4(Left(vwx230), Left(vwx240), app(app(app(ty_@3, ccd), cce), ccf), bed) → new_esEs7(vwx230, vwx240, ccd, cce, ccf)
new_esEs26(vwx231, vwx241, app(ty_[], cgh)) → new_esEs11(vwx231, vwx241, cgh)
new_esEs4(Left(vwx230), Left(vwx240), ty_Bool, bed) → new_esEs9(vwx230, vwx240)
new_ltEs19(vwx302, vwx402, app(app(ty_Either, bbc), bbd)) → new_ltEs7(vwx302, vwx402, bbc, bbd)
new_primCmpInt(Neg(Succ(vwx3000)), Neg(vwx400)) → new_primCmpNat0(vwx400, Succ(vwx3000))
new_ltEs18(vwx301, vwx401, app(app(ty_@2, ee), ef)) → new_ltEs5(vwx301, vwx401, ee, ef)
new_ltEs7(Left(vwx30), Left(vwx40), ty_Ordering, ce) → new_ltEs6(vwx30, vwx40)
new_esEs5(@2(vwx230, vwx231), @2(vwx240, vwx241), bfa, bfb) → new_asAs(new_esEs20(vwx230, vwx240, bfa), new_esEs21(vwx231, vwx241, bfb))
new_ltEs9(vwx30, vwx40) → new_not(new_compare19(vwx30, vwx40))
new_primEqInt(Pos(Zero), Pos(Succ(vwx2400))) → False
new_primEqInt(Pos(Succ(vwx2300)), Pos(Zero)) → False
new_compare19(@0, @0) → EQ
new_ltEs18(vwx301, vwx401, ty_Float) → new_ltEs11(vwx301, vwx401)
new_esEs10(vwx23, vwx24, app(ty_[], bea)) → new_esEs11(vwx23, vwx24, bea)
new_lt16(vwx300, vwx400, cc, cd) → new_esEs8(new_compare5(vwx300, vwx400, cc, cd))
new_esEs4(Left(vwx230), Left(vwx240), ty_Double, bed) → new_esEs17(vwx230, vwx240)
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(vwx3000), Zero) → GT
new_compare18(Double(vwx300, vwx301), Double(vwx400, vwx401)) → new_compare7(new_sr(vwx300, vwx400), new_sr(vwx301, vwx401))
new_ltEs19(vwx302, vwx402, app(ty_Ratio, bfh)) → new_ltEs13(vwx302, vwx402, bfh)
new_esEs8(LT) → True
new_primCmpInt(Neg(Zero), Pos(Succ(vwx4000))) → LT
new_lt8(vwx300, vwx400, ty_Double) → new_lt9(vwx300, vwx400)
new_compare14(vwx300, vwx400, False, df, dg, dh) → GT
new_sr0(Integer(vwx4000), Integer(vwx3010)) → Integer(new_primMulInt(vwx4000, vwx3010))
new_primPlusNat1(Succ(vwx5300), Succ(vwx401000)) → Succ(Succ(new_primPlusNat1(vwx5300, vwx401000)))
new_esEs21(vwx231, vwx241, ty_Double) → new_esEs17(vwx231, vwx241)
new_esEs10(vwx23, vwx24, ty_Char) → new_esEs18(vwx23, vwx24)
new_primEqInt(Neg(Succ(vwx2300)), Pos(vwx240)) → False
new_primEqInt(Pos(Succ(vwx2300)), Neg(vwx240)) → False
new_esEs24(vwx230, vwx240, app(ty_Ratio, cee)) → new_esEs13(vwx230, vwx240, cee)
new_lt11(vwx300, vwx400, da) → new_esEs8(new_compare(vwx300, vwx400, da))
new_lt19(vwx300, vwx400, app(ty_Ratio, bff)) → new_lt15(vwx300, vwx400, bff)
new_esEs20(vwx230, vwx240, ty_@0) → new_esEs16(vwx230, vwx240)
new_esEs6(Just(vwx230), Just(vwx240), ty_Bool) → new_esEs9(vwx230, vwx240)
new_esEs8(GT) → False
new_ltEs18(vwx301, vwx401, app(ty_Maybe, eg)) → new_ltEs16(vwx301, vwx401, eg)
new_esEs24(vwx230, vwx240, ty_Int) → new_esEs14(vwx230, vwx240)
new_esEs11([], :(vwx240, vwx241), bea) → False
new_esEs11(:(vwx230, vwx231), [], bea) → False
new_esEs4(Left(vwx230), Left(vwx240), ty_@0, bed) → new_esEs16(vwx230, vwx240)
new_primEqInt(Neg(Zero), Pos(Succ(vwx2400))) → False
new_primEqInt(Pos(Zero), Neg(Succ(vwx2400))) → False
new_esEs21(vwx231, vwx241, ty_Integer) → new_esEs15(vwx231, vwx241)
new_ltEs16(Just(vwx300), Just(vwx400), app(app(ty_@2, fg), fh)) → new_ltEs5(vwx300, vwx400, fg, fh)
new_esEs26(vwx231, vwx241, ty_Float) → new_esEs12(vwx231, vwx241)
new_primCmpInt(Pos(Zero), Pos(Succ(vwx4000))) → new_primCmpNat0(Zero, Succ(vwx4000))
new_esEs4(Left(vwx230), Left(vwx240), ty_Integer, bed) → new_esEs15(vwx230, vwx240)
new_ltEs7(Left(vwx30), Left(vwx40), ty_Float, ce) → new_ltEs11(vwx30, vwx40)
new_compare27(vwx300, vwx400, False) → new_compare11(vwx300, vwx400, new_ltEs6(vwx300, vwx400))
new_ltEs13(vwx30, vwx40, bde) → new_not(new_compare30(vwx30, vwx40, bde))
new_esEs21(vwx231, vwx241, ty_Char) → new_esEs18(vwx231, vwx241)
new_esEs26(vwx231, vwx241, app(app(ty_@2, chh), daa)) → new_esEs5(vwx231, vwx241, chh, daa)
new_lt12(vwx300, vwx400) → new_esEs8(new_compare8(vwx300, vwx400))
new_ltEs16(Just(vwx300), Nothing, bdf) → False
new_esEs21(vwx231, vwx241, app(app(ty_@2, cbf), cbg)) → new_esEs5(vwx231, vwx241, cbf, cbg)
new_primCompAux0(vwx39, LT) → LT
new_esEs25(vwx230, vwx240, ty_Float) → new_esEs12(vwx230, vwx240)
new_esEs4(Left(vwx230), Left(vwx240), ty_Ordering, bed) → new_esEs19(vwx230, vwx240)
new_ltEs16(Just(vwx300), Just(vwx400), ty_Ordering) → new_ltEs6(vwx300, vwx400)
new_lt19(vwx300, vwx400, app(ty_Maybe, hd)) → new_lt18(vwx300, vwx400, hd)
new_lt8(vwx300, vwx400, ty_Integer) → new_lt5(vwx300, vwx400)
new_lt17(vwx300, vwx400) → new_esEs8(new_compare10(vwx300, vwx400))
new_lt20(vwx301, vwx401, app(ty_[], baa)) → new_lt11(vwx301, vwx401, baa)
new_ltEs18(vwx301, vwx401, app(ty_Ratio, bfd)) → new_ltEs13(vwx301, vwx401, bfd)
new_primPlusNat0(Zero, vwx40100) → Succ(vwx40100)
new_primCmpInt(Pos(Succ(vwx3000)), Pos(vwx400)) → new_primCmpNat0(Succ(vwx3000), vwx400)
new_ltEs19(vwx302, vwx402, app(ty_[], bbb)) → new_ltEs10(vwx302, vwx402, bbb)
new_compare31(vwx300, vwx400, app(app(ty_@2, be), bf)) → new_compare17(vwx300, vwx400, be, bf)
new_esEs25(vwx230, vwx240, ty_Integer) → new_esEs15(vwx230, vwx240)
new_ltEs8(vwx30, vwx40) → new_not(new_compare18(vwx30, vwx40))
new_esEs20(vwx230, vwx240, app(ty_[], bhd)) → new_esEs11(vwx230, vwx240, bhd)
new_esEs24(vwx230, vwx240, ty_Ordering) → new_esEs19(vwx230, vwx240)
new_lt20(vwx301, vwx401, app(app(ty_Either, bab), bac)) → new_lt16(vwx301, vwx401, bab, bac)
new_not0True
new_esEs12(Float(vwx230, vwx231), Float(vwx240, vwx241)) → new_esEs14(new_sr(vwx230, vwx240), new_sr(vwx231, vwx241))
new_lt20(vwx301, vwx401, ty_Double) → new_lt9(vwx301, vwx401)
new_ltEs7(Right(vwx30), Right(vwx40), bcc, app(ty_[], bcd)) → new_ltEs10(vwx30, vwx40, bcd)
new_esEs19(GT, LT) → False
new_esEs19(LT, GT) → False
new_esEs9(True, True) → True
new_esEs4(Right(vwx230), Right(vwx240), bec, ty_Double) → new_esEs17(vwx230, vwx240)
new_primCmpInt(Pos(Succ(vwx3000)), Neg(vwx400)) → GT
new_ltEs7(Right(vwx30), Right(vwx40), bcc, app(ty_Maybe, bda)) → new_ltEs16(vwx30, vwx40, bda)
new_ltEs7(Right(vwx30), Right(vwx40), bcc, ty_Double) → new_ltEs8(vwx30, vwx40)
new_primMulInt(Pos(vwx3010), Pos(vwx4010)) → Pos(new_primMulNat0(vwx3010, vwx4010))
new_lt8(vwx300, vwx400, app(ty_Maybe, de)) → new_lt18(vwx300, vwx400, de)
new_ltEs7(Right(vwx30), Right(vwx40), bcc, app(app(app(ty_@3, bdb), bdc), bdd)) → new_ltEs17(vwx30, vwx40, bdb, bdc, bdd)
new_compare31(vwx300, vwx400, ty_Char) → new_compare8(vwx300, vwx400)
new_lt15(vwx300, vwx400, bfc) → new_esEs8(new_compare30(vwx300, vwx400, bfc))
new_compare32(vwx300, vwx400, de) → new_compare29(vwx300, vwx400, new_esEs6(vwx300, vwx400, de), de)
new_primMulInt(Neg(vwx3010), Neg(vwx4010)) → Pos(new_primMulNat0(vwx3010, vwx4010))
new_esEs20(vwx230, vwx240, ty_Integer) → new_esEs15(vwx230, vwx240)
new_compare110(vwx300, vwx400, True) → LT
new_esEs10(vwx23, vwx24, ty_Integer) → new_esEs15(vwx23, vwx24)
new_primEqNat0(Zero, Succ(vwx2400)) → False
new_primEqNat0(Succ(vwx2300), Zero) → False
new_esEs6(Just(vwx230), Just(vwx240), ty_Ordering) → new_esEs19(vwx230, vwx240)
new_esEs10(vwx23, vwx24, ty_Double) → new_esEs17(vwx23, vwx24)
new_ltEs19(vwx302, vwx402, ty_Int) → new_ltEs12(vwx302, vwx402)
new_compare25(vwx300, vwx400, False) → new_compare110(vwx300, vwx400, new_ltEs15(vwx300, vwx400))
new_lt20(vwx301, vwx401, app(ty_Ratio, bfg)) → new_lt15(vwx301, vwx401, bfg)
new_ltEs6(LT, LT) → True
new_ltEs6(EQ, LT) → False
new_ltEs7(Left(vwx30), Left(vwx40), app(app(ty_Either, cf), cg), ce) → new_ltEs7(vwx30, vwx40, cf, cg)
new_ltEs16(Just(vwx300), Just(vwx400), ty_Double) → new_ltEs8(vwx300, vwx400)
new_esEs25(vwx230, vwx240, app(ty_Maybe, cge)) → new_esEs6(vwx230, vwx240, cge)
new_compare110(vwx300, vwx400, False) → GT
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_ltEs18(vwx301, vwx401, app(app(app(ty_@3, eh), fa), fb)) → new_ltEs17(vwx301, vwx401, eh, fa, fb)
new_esEs24(vwx230, vwx240, app(app(ty_Either, cef), ceg)) → new_esEs4(vwx230, vwx240, cef, ceg)
new_compare31(vwx300, vwx400, ty_Double) → new_compare18(vwx300, vwx400)
new_esEs25(vwx230, vwx240, app(ty_[], cff)) → new_esEs11(vwx230, vwx240, cff)
new_lt19(vwx300, vwx400, app(ty_[], ge)) → new_lt11(vwx300, vwx400, ge)
new_esEs27(vwx232, vwx242, app(app(ty_Either, dad), dae)) → new_esEs4(vwx232, vwx242, dad, dae)
new_ltEs7(Right(vwx30), Right(vwx40), bcc, ty_Ordering) → new_ltEs6(vwx30, vwx40)
new_esEs21(vwx231, vwx241, ty_Bool) → new_esEs9(vwx231, vwx241)
new_esEs27(vwx232, vwx242, app(app(ty_@2, dbb), dbc)) → new_esEs5(vwx232, vwx242, dbb, dbc)
new_lt5(vwx300, vwx400) → new_esEs8(new_compare13(vwx300, vwx400))
new_ltEs7(Left(vwx30), Left(vwx40), app(app(ty_@2, ea), db), ce) → new_ltEs5(vwx30, vwx40, ea, db)
new_compare28(vwx300, vwx400, True, df, dg, dh) → EQ
new_ltEs7(Right(vwx30), Right(vwx40), bcc, app(app(ty_@2, bcg), bch)) → new_ltEs5(vwx30, vwx40, bcg, bch)
new_esEs10(vwx23, vwx24, app(app(ty_@2, bfa), bfb)) → new_esEs5(vwx23, vwx24, bfa, bfb)
new_esEs4(Left(vwx230), Left(vwx240), ty_Int, bed) → new_esEs14(vwx230, vwx240)
new_pePe(True, vwx23, vwx24, vwx25, bdh) → True
new_primCmpInt(Neg(Zero), Neg(Succ(vwx4000))) → new_primCmpNat0(Succ(vwx4000), Zero)
new_esEs20(vwx230, vwx240, ty_Bool) → new_esEs9(vwx230, vwx240)
new_primCmpInt(Pos(Zero), Neg(Succ(vwx4000))) → GT
new_esEs25(vwx230, vwx240, ty_Ordering) → new_esEs19(vwx230, vwx240)
new_ltEs7(Left(vwx30), Left(vwx40), ty_Integer, ce) → new_ltEs14(vwx30, vwx40)
new_compare31(vwx300, vwx400, app(ty_[], bb)) → new_compare(vwx300, vwx400, bb)
new_lt10(vwx300, vwx400) → new_esEs8(new_compare19(vwx300, vwx400))
new_ltEs19(vwx302, vwx402, ty_Double) → new_ltEs8(vwx302, vwx402)
new_esEs19(LT, LT) → True
new_esEs21(vwx231, vwx241, ty_Float) → new_esEs12(vwx231, vwx241)
new_ltEs18(vwx301, vwx401, app(ty_[], eb)) → new_ltEs10(vwx301, vwx401, eb)
new_esEs25(vwx230, vwx240, ty_Int) → new_esEs14(vwx230, vwx240)
new_ltEs7(Right(vwx30), Right(vwx40), bcc, ty_Integer) → new_ltEs14(vwx30, vwx40)
new_ltEs14(vwx30, vwx40) → new_not(new_compare13(vwx30, vwx40))
new_esEs19(GT, EQ) → False
new_esEs19(EQ, GT) → False
new_esEs9(False, True) → False
new_esEs9(True, False) → False
new_esEs6(Just(vwx230), Just(vwx240), ty_Float) → new_esEs12(vwx230, vwx240)
new_lt19(vwx300, vwx400, ty_Double) → new_lt9(vwx300, vwx400)
new_esEs27(vwx232, vwx242, ty_Int) → new_esEs14(vwx232, vwx242)
new_esEs24(vwx230, vwx240, app(app(app(ty_@3, ceh), cfa), cfb)) → new_esEs7(vwx230, vwx240, ceh, cfa, cfb)
new_compare29(vwx300, vwx400, True, de) → EQ
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCompAux1(vwx300, vwx400, vwx35, ba) → new_primCompAux0(vwx35, new_compare31(vwx300, vwx400, ba))
new_esEs10(vwx23, vwx24, ty_Float) → new_esEs12(vwx23, vwx24)
new_esEs4(Right(vwx230), Right(vwx240), bec, app(app(ty_@2, ceb), cec)) → new_esEs5(vwx230, vwx240, ceb, cec)
new_esEs20(vwx230, vwx240, app(ty_Maybe, cac)) → new_esEs6(vwx230, vwx240, cac)
new_esEs20(vwx230, vwx240, ty_Float) → new_esEs12(vwx230, vwx240)
new_esEs6(Just(vwx230), Just(vwx240), ty_Integer) → new_esEs15(vwx230, vwx240)
new_ltEs7(Right(vwx30), Right(vwx40), bcc, app(app(ty_Either, bce), bcf)) → new_ltEs7(vwx30, vwx40, bce, bcf)
new_ltEs16(Just(vwx300), Just(vwx400), app(app(ty_Either, fd), ff)) → new_ltEs7(vwx300, vwx400, fd, ff)
new_esEs26(vwx231, vwx241, ty_Int) → new_esEs14(vwx231, vwx241)
new_asAs(False, vwx34) → False
new_esEs4(Right(vwx230), Right(vwx240), bec, ty_Float) → new_esEs12(vwx230, vwx240)
new_primMulInt(Neg(vwx3010), Pos(vwx4010)) → Neg(new_primMulNat0(vwx3010, vwx4010))
new_primMulInt(Pos(vwx3010), Neg(vwx4010)) → Neg(new_primMulNat0(vwx3010, vwx4010))
new_esEs6(Just(vwx230), Just(vwx240), app(ty_[], bga)) → new_esEs11(vwx230, vwx240, bga)
new_primMulNat0(Zero, Succ(vwx40100)) → Zero
new_primMulNat0(Succ(vwx30100), Zero) → Zero
new_ltEs7(Left(vwx30), Left(vwx40), ty_Int, ce) → new_ltEs12(vwx30, vwx40)
new_ltEs16(Just(vwx300), Just(vwx400), ty_Char) → new_ltEs4(vwx300, vwx400)
new_esEs6(Just(vwx230), Just(vwx240), app(ty_Maybe, bgh)) → new_esEs6(vwx230, vwx240, bgh)
new_lt9(vwx300, vwx400) → new_esEs8(new_compare18(vwx300, vwx400))
new_esEs25(vwx230, vwx240, ty_@0) → new_esEs16(vwx230, vwx240)
new_compare5(vwx300, vwx400, cc, cd) → new_compare24(vwx300, vwx400, new_esEs4(vwx300, vwx400, cc, cd), cc, cd)
new_esEs10(vwx23, vwx24, app(ty_Maybe, beh)) → new_esEs6(vwx23, vwx24, beh)
new_esEs10(vwx23, vwx24, app(ty_Ratio, beb)) → new_esEs13(vwx23, vwx24, beb)
new_ltEs7(Left(vwx30), Left(vwx40), app(ty_Maybe, bdf), ce) → new_ltEs16(vwx30, vwx40, bdf)
new_compare26(vwx300, vwx400, False, dc, dd) → new_compare12(vwx300, vwx400, new_ltEs5(vwx300, vwx400, dc, dd), dc, dd)
new_not(EQ) → new_not0
new_lt8(vwx300, vwx400, ty_Ordering) → new_lt6(vwx300, vwx400)
new_esEs27(vwx232, vwx242, ty_Double) → new_esEs17(vwx232, vwx242)
new_esEs20(vwx230, vwx240, ty_Double) → new_esEs17(vwx230, vwx240)
new_lt20(vwx301, vwx401, ty_Float) → new_lt13(vwx301, vwx401)
new_esEs16(@0, @0) → True
new_ltEs6(LT, GT) → True
new_esEs23(vwx231, vwx241, ty_Integer) → new_esEs15(vwx231, vwx241)
new_compare27(vwx300, vwx400, True) → EQ
new_esEs9(False, False) → True
new_esEs24(vwx230, vwx240, ty_Double) → new_esEs17(vwx230, vwx240)
new_esEs4(Right(vwx230), Right(vwx240), bec, ty_Char) → new_esEs18(vwx230, vwx240)
new_esEs14(vwx23, vwx24) → new_primEqInt(vwx23, vwx24)
new_esEs25(vwx230, vwx240, app(app(app(ty_@3, cgb), cgc), cgd)) → new_esEs7(vwx230, vwx240, cgb, cgc, cgd)
new_lt8(vwx300, vwx400, ty_Float) → new_lt13(vwx300, vwx400)
new_lt20(vwx301, vwx401, ty_Integer) → new_lt5(vwx301, vwx401)
new_esEs27(vwx232, vwx242, app(ty_[], dab)) → new_esEs11(vwx232, vwx242, dab)
new_compare31(vwx300, vwx400, ty_Float) → new_compare6(vwx300, vwx400)
new_ltEs7(Left(vwx30), Left(vwx40), ty_@0, ce) → new_ltEs9(vwx30, vwx40)
new_esEs4(Right(vwx230), Right(vwx240), bec, ty_Int) → new_esEs14(vwx230, vwx240)
new_compare11(vwx300, vwx400, False) → GT
new_esEs25(vwx230, vwx240, app(app(ty_@2, cgf), cgg)) → new_esEs5(vwx230, vwx240, cgf, cgg)
new_not(LT) → new_not0
new_esEs20(vwx230, vwx240, ty_Int) → new_esEs14(vwx230, vwx240)
new_compare13(Integer(vwx300), Integer(vwx400)) → new_primCmpInt(vwx300, vwx400)
new_compare11(vwx300, vwx400, True) → LT
new_ltEs19(vwx302, vwx402, app(app(app(ty_@3, bbh), bca), bcb)) → new_ltEs17(vwx302, vwx402, bbh, bca, bcb)
new_compare31(vwx300, vwx400, ty_Bool) → new_compare10(vwx300, vwx400)
new_esEs21(vwx231, vwx241, app(ty_[], caf)) → new_esEs11(vwx231, vwx241, caf)
new_pePe(False, vwx23, vwx24, vwx25, bdh) → new_asAs(new_esEs10(vwx23, vwx24, bdh), vwx25)
new_lt20(vwx301, vwx401, ty_Char) → new_lt12(vwx301, vwx401)
new_lt19(vwx300, vwx400, app(app(ty_@2, hb), hc)) → new_lt7(vwx300, vwx400, hb, hc)
new_esEs26(vwx231, vwx241, ty_Char) → new_esEs18(vwx231, vwx241)
new_esEs22(vwx230, vwx240, ty_Int) → new_esEs14(vwx230, vwx240)
new_esEs24(vwx230, vwx240, ty_Bool) → new_esEs9(vwx230, vwx240)
new_esEs8(EQ) → False
new_lt19(vwx300, vwx400, ty_@0) → new_lt10(vwx300, vwx400)
new_esEs22(vwx230, vwx240, ty_Integer) → new_esEs15(vwx230, vwx240)
new_compare30(:%(vwx300, vwx301), :%(vwx400, vwx401), ty_Integer) → new_compare13(new_sr0(vwx300, vwx401), new_sr0(vwx400, vwx301))
new_ltEs18(vwx301, vwx401, ty_Bool) → new_ltEs15(vwx301, vwx401)
new_compare111(vwx300, vwx400, True, cc, cd) → LT
new_primPlusNat1(Zero, Zero) → Zero
new_compare15(vwx300, vwx400, True, de) → LT
new_ltEs6(LT, EQ) → True
new_ltEs6(GT, LT) → False
new_esEs26(vwx231, vwx241, app(app(ty_Either, chb), chc)) → new_esEs4(vwx231, vwx241, chb, chc)
new_asAs(True, vwx34) → vwx34
new_primMulNat0(Succ(vwx30100), Succ(vwx40100)) → new_primPlusNat0(new_primMulNat0(vwx30100, Succ(vwx40100)), vwx40100)
new_esEs4(Right(vwx230), Left(vwx240), bec, bed) → False
new_esEs4(Left(vwx230), Right(vwx240), bec, bed) → False
new_compare31(vwx300, vwx400, ty_Int) → new_compare7(vwx300, vwx400)
new_esEs17(Double(vwx230, vwx231), Double(vwx240, vwx241)) → new_esEs14(new_sr(vwx230, vwx240), new_sr(vwx231, vwx241))
new_ltEs16(Just(vwx300), Just(vwx400), app(ty_[], fc)) → new_ltEs10(vwx300, vwx400, fc)
new_ltEs19(vwx302, vwx402, ty_@0) → new_ltEs9(vwx302, vwx402)
new_esEs4(Left(vwx230), Left(vwx240), app(ty_Maybe, ccg), bed) → new_esEs6(vwx230, vwx240, ccg)
new_lt20(vwx301, vwx401, ty_Bool) → new_lt17(vwx301, vwx401)
new_ltEs7(Left(vwx30), Left(vwx40), ty_Double, ce) → new_ltEs8(vwx30, vwx40)
new_lt20(vwx301, vwx401, ty_Int) → new_lt14(vwx301, vwx401)
new_esEs20(vwx230, vwx240, ty_Ordering) → new_esEs19(vwx230, vwx240)
new_ltEs16(Just(vwx300), Just(vwx400), ty_@0) → new_ltEs9(vwx300, vwx400)
new_esEs24(vwx230, vwx240, app(ty_Maybe, cfc)) → new_esEs6(vwx230, vwx240, cfc)
new_esEs27(vwx232, vwx242, ty_Char) → new_esEs18(vwx232, vwx242)
new_ltEs17(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), hh, gf, gg) → new_pePe(new_lt19(vwx300, vwx400, hh), vwx300, vwx400, new_pePe(new_lt20(vwx301, vwx401, gf), vwx301, vwx401, new_ltEs19(vwx302, vwx402, gg), gf), hh)
new_ltEs16(Just(vwx300), Just(vwx400), ty_Int) → new_ltEs12(vwx300, vwx400)
new_compare31(vwx300, vwx400, ty_@0) → new_compare19(vwx300, vwx400)
new_compare8(Char(vwx300), Char(vwx400)) → new_primCmpNat0(vwx300, vwx400)
new_ltEs16(Just(vwx300), Just(vwx400), ty_Bool) → new_ltEs15(vwx300, vwx400)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_lt8(vwx300, vwx400, app(app(ty_Either, cc), cd)) → new_lt16(vwx300, vwx400, cc, cd)
new_primCompAux0(vwx39, EQ) → vwx39
new_lt19(vwx300, vwx400, ty_Int) → new_lt14(vwx300, vwx400)
new_ltEs7(Left(vwx30), Left(vwx40), app(ty_[], ba), ce) → new_ltEs10(vwx30, vwx40, ba)
new_lt8(vwx300, vwx400, app(ty_Ratio, bfc)) → new_lt15(vwx300, vwx400, bfc)
new_esEs24(vwx230, vwx240, ty_Char) → new_esEs18(vwx230, vwx240)
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_esEs27(vwx232, vwx242, ty_Integer) → new_esEs15(vwx232, vwx242)
new_primCmpInt(Neg(Succ(vwx3000)), Pos(vwx400)) → LT
new_esEs13(:%(vwx230, vwx231), :%(vwx240, vwx241), beb) → new_asAs(new_esEs22(vwx230, vwx240, beb), new_esEs23(vwx231, vwx241, beb))

The set Q consists of the following terms:

new_lt19(x0, x1, ty_Double)
new_esEs6(Nothing, Nothing, x0)
new_esEs24(x0, x1, ty_Float)
new_esEs4(Right(x0), Right(x1), x2, ty_Float)
new_esEs11(:(x0, x1), [], x2)
new_esEs26(x0, x1, ty_Ordering)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_esEs27(x0, x1, ty_Float)
new_esEs26(x0, x1, app(ty_[], x2))
new_esEs20(x0, x1, ty_Bool)
new_esEs25(x0, x1, ty_Int)
new_ltEs7(Right(x0), Left(x1), x2, x3)
new_ltEs7(Left(x0), Right(x1), x2, x3)
new_lt8(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs18(x0, x1, ty_Int)
new_lt20(x0, x1, app(ty_[], x2))
new_compare29(x0, x1, False, x2)
new_ltEs7(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_ltEs18(x0, x1, ty_@0)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_compare14(x0, x1, False, x2, x3, x4)
new_esEs27(x0, x1, ty_Double)
new_esEs10(x0, x1, app(app(ty_@2, x2), x3))
new_esEs6(Just(x0), Just(x1), app(ty_Ratio, x2))
new_ltEs16(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs26(x0, x1, ty_Integer)
new_ltEs7(Left(x0), Left(x1), ty_Bool, x2)
new_esEs6(Just(x0), Just(x1), ty_Integer)
new_compare8(Char(x0), Char(x1))
new_primCompAux0(x0, GT)
new_ltEs12(x0, x1)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_esEs6(Just(x0), Just(x1), ty_Float)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_lt8(x0, x1, ty_@0)
new_lt8(x0, x1, ty_Char)
new_compare31(x0, x1, app(app(ty_@2, x2), x3))
new_compare26(x0, x1, False, x2, x3)
new_ltEs16(Just(x0), Just(x1), ty_Bool)
new_ltEs7(Right(x0), Right(x1), x2, app(ty_[], x3))
new_lt20(x0, x1, ty_Float)
new_ltEs7(Left(x0), Left(x1), ty_Int, x2)
new_ltEs15(True, True)
new_primPlusNat1(Succ(x0), Succ(x1))
new_compare31(x0, x1, app(ty_[], x2))
new_esEs8(LT)
new_ltEs9(x0, x1)
new_esEs24(x0, x1, ty_Double)
new_lt8(x0, x1, ty_Integer)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_asAs(False, x0)
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, app(ty_[], x2))
new_ltEs15(False, False)
new_ltEs18(x0, x1, ty_Float)
new_ltEs17(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_ltEs19(x0, x1, app(ty_[], x2))
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_compare31(x0, x1, ty_Ordering)
new_ltEs19(x0, x1, ty_Char)
new_lt20(x0, x1, ty_Char)
new_esEs16(@0, @0)
new_esEs4(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs23(x0, x1, ty_Int)
new_compare9(x0, x1, x2, x3, x4)
new_primMulInt(Pos(x0), Pos(x1))
new_compare18(Double(x0, x1), Double(x2, x3))
new_esEs6(Just(x0), Just(x1), app(ty_[], x2))
new_lt20(x0, x1, ty_Int)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_esEs4(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs25(x0, x1, ty_Ordering)
new_esEs27(x0, x1, ty_@0)
new_esEs6(Just(x0), Just(x1), app(ty_Maybe, x2))
new_ltEs6(EQ, EQ)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs4(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs4(Left(x0), Left(x1), ty_Int, x2)
new_primCompAux0(x0, LT)
new_compare11(x0, x1, False)
new_lt14(x0, x1)
new_esEs21(x0, x1, ty_Int)
new_ltEs7(Left(x0), Left(x1), ty_Double, x2)
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs4(Left(x0), Left(x1), ty_@0, x2)
new_ltEs6(LT, EQ)
new_compare28(x0, x1, False, x2, x3, x4)
new_ltEs6(EQ, LT)
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_compare16(x0, x1)
new_primEqNat0(Zero, Zero)
new_esEs10(x0, x1, ty_Double)
new_esEs10(x0, x1, ty_Integer)
new_ltEs16(Nothing, Just(x0), x1)
new_ltEs16(Just(x0), Just(x1), ty_Char)
new_compare15(x0, x1, False, x2)
new_esEs9(True, True)
new_ltEs5(@2(x0, x1), @2(x2, x3), x4, x5)
new_ltEs19(x0, x1, ty_Int)
new_esEs26(x0, x1, ty_Bool)
new_ltEs19(x0, x1, ty_Ordering)
new_compare25(x0, x1, True)
new_esEs8(EQ)
new_esEs20(x0, x1, ty_Char)
new_lt19(x0, x1, ty_@0)
new_esEs4(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_pePe(True, x0, x1, x2, x3)
new_primMulNat0(Zero, Zero)
new_ltEs8(x0, x1)
new_compare12(x0, x1, True, x2, x3)
new_ltEs16(Nothing, Nothing, x0)
new_compare10(x0, x1)
new_ltEs7(Left(x0), Left(x1), ty_Integer, x2)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_compare29(x0, x1, True, x2)
new_esEs25(x0, x1, ty_@0)
new_esEs14(x0, x1)
new_esEs13(:%(x0, x1), :%(x2, x3), x4)
new_esEs4(Right(x0), Right(x1), x2, ty_Double)
new_lt19(x0, x1, app(ty_Maybe, x2))
new_ltEs7(Right(x0), Right(x1), x2, ty_Bool)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_compare24(x0, x1, True, x2, x3)
new_lt19(x0, x1, ty_Char)
new_esEs19(LT, LT)
new_esEs6(Nothing, Just(x0), x1)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs16(Just(x0), Nothing, x1)
new_esEs19(EQ, GT)
new_esEs19(GT, EQ)
new_esEs4(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs7(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs11([], [], x0)
new_esEs6(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs17(Double(x0, x1), Double(x2, x3))
new_esEs4(Right(x0), Right(x1), x2, ty_Integer)
new_ltEs16(Just(x0), Just(x1), ty_Float)
new_lt15(x0, x1, x2)
new_compare7(x0, x1)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_compare24(x0, x1, False, x2, x3)
new_lt16(x0, x1, x2, x3)
new_ltEs7(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs20(x0, x1, app(ty_[], x2))
new_ltEs6(GT, LT)
new_ltEs6(LT, GT)
new_ltEs18(x0, x1, ty_Integer)
new_esEs20(x0, x1, ty_Double)
new_esEs20(x0, x1, ty_Int)
new_esEs6(Just(x0), Just(x1), ty_Double)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_lt13(x0, x1)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs16(Just(x0), Just(x1), app(ty_[], x2))
new_lt8(x0, x1, app(ty_Maybe, x2))
new_lt19(x0, x1, ty_Bool)
new_lt18(x0, x1, x2)
new_esEs25(x0, x1, ty_Double)
new_compare30(:%(x0, x1), :%(x2, x3), ty_Int)
new_primMulInt(Neg(x0), Neg(x1))
new_lt8(x0, x1, ty_Float)
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_esEs24(x0, x1, ty_Bool)
new_esEs6(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_ltEs16(Just(x0), Just(x1), ty_Integer)
new_lt19(x0, x1, ty_Integer)
new_ltEs7(Right(x0), Right(x1), x2, ty_Integer)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs10(x0, x1, ty_Float)
new_ltEs19(x0, x1, ty_Bool)
new_primEqNat0(Zero, Succ(x0))
new_esEs10(x0, x1, ty_Ordering)
new_lt8(x0, x1, app(ty_Ratio, x2))
new_ltEs16(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs6(Just(x0), Just(x1), ty_@0)
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_lt10(x0, x1)
new_ltEs7(Left(x0), Left(x1), ty_Char, x2)
new_compare6(Float(x0, x1), Float(x2, x3))
new_esEs4(Right(x0), Right(x1), x2, ty_Int)
new_compare27(x0, x1, False)
new_compare31(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs11(:(x0, x1), :(x2, x3), x4)
new_esEs10(x0, x1, ty_@0)
new_ltEs11(x0, x1)
new_lt12(x0, x1)
new_primPlusNat1(Zero, Zero)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_not0
new_ltEs10(x0, x1, x2)
new_compare31(x0, x1, app(ty_Maybe, x2))
new_primEqNat0(Succ(x0), Succ(x1))
new_ltEs7(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_compare31(x0, x1, app(ty_Ratio, x2))
new_lt20(x0, x1, ty_Bool)
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_lt8(x0, x1, ty_Int)
new_esEs25(x0, x1, app(ty_[], x2))
new_ltEs16(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primMulNat0(Succ(x0), Succ(x1))
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_lt9(x0, x1)
new_esEs4(Left(x0), Left(x1), ty_Integer, x2)
new_lt19(x0, x1, ty_Ordering)
new_primMulNat0(Zero, Succ(x0))
new_esEs10(x0, x1, app(ty_[], x2))
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_compare5(x0, x1, x2, x3)
new_ltEs16(Just(x0), Just(x1), ty_Int)
new_pePe(False, x0, x1, x2, x3)
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare110(x0, x1, True)
new_esEs21(x0, x1, ty_Bool)
new_compare13(Integer(x0), Integer(x1))
new_not(GT)
new_esEs4(Right(x0), Right(x1), x2, ty_@0)
new_esEs6(Just(x0), Nothing, x1)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs15(True, False)
new_ltEs15(False, True)
new_esEs8(GT)
new_esEs4(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs6(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_ltEs18(x0, x1, ty_Ordering)
new_ltEs7(Right(x0), Right(x1), x2, ty_Int)
new_lt20(x0, x1, ty_@0)
new_esEs20(x0, x1, ty_Float)
new_primEqInt(Neg(Zero), Pos(Zero))
new_primEqInt(Pos(Zero), Neg(Zero))
new_esEs24(x0, x1, ty_@0)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_ltEs7(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_ltEs18(x0, x1, ty_Bool)
new_primPlusNat0(Zero, x0)
new_primCompAux0(x0, EQ)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_esEs10(x0, x1, ty_Int)
new_lt17(x0, x1)
new_esEs10(x0, x1, app(ty_Ratio, x2))
new_compare27(x0, x1, True)
new_primEqNat0(Succ(x0), Zero)
new_esEs4(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs26(x0, x1, ty_Char)
new_compare31(x0, x1, ty_Bool)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_esEs25(x0, x1, ty_Char)
new_ltEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_compare(:(x0, x1), [], x2)
new_lt8(x0, x1, app(ty_[], x2))
new_primMulNat0(Succ(x0), Zero)
new_esEs22(x0, x1, ty_Integer)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs25(x0, x1, ty_Bool)
new_compare(:(x0, x1), :(x2, x3), x4)
new_primPlusNat1(Succ(x0), Zero)
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_compare31(x0, x1, ty_Float)
new_compare17(x0, x1, x2, x3)
new_ltEs18(x0, x1, ty_Double)
new_primEqInt(Neg(Zero), Neg(Zero))
new_esEs27(x0, x1, ty_Integer)
new_compare32(x0, x1, x2)
new_ltEs7(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs10(x0, x1, app(ty_Maybe, x2))
new_compare31(x0, x1, ty_@0)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_esEs21(x0, x1, app(ty_[], x2))
new_esEs4(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs16(Just(x0), Just(x1), ty_Ordering)
new_esEs21(x0, x1, ty_Double)
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_compare30(:%(x0, x1), :%(x2, x3), ty_Integer)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt19(x0, x1, app(ty_Ratio, x2))
new_lt19(x0, x1, ty_Float)
new_esEs12(Float(x0, x1), Float(x2, x3))
new_compare31(x0, x1, ty_Integer)
new_compare31(x0, x1, app(app(ty_Either, x2), x3))
new_esEs6(Just(x0), Just(x1), ty_Ordering)
new_compare15(x0, x1, True, x2)
new_esEs21(x0, x1, ty_Float)
new_primCmpNat0(Zero, Succ(x0))
new_esEs10(x0, x1, ty_Bool)
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs7(Right(x0), Right(x1), x2, ty_Float)
new_ltEs7(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs19(x0, x1, ty_Integer)
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_esEs4(Right(x0), Right(x1), x2, ty_Char)
new_lt5(x0, x1)
new_esEs10(x0, x1, ty_Char)
new_compare14(x0, x1, True, x2, x3, x4)
new_compare31(x0, x1, ty_Double)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs6(GT, GT)
new_ltEs19(x0, x1, ty_Double)
new_esEs27(x0, x1, ty_Ordering)
new_ltEs7(Right(x0), Right(x1), x2, ty_Double)
new_compare11(x0, x1, True)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_lt8(x0, x1, ty_Ordering)
new_lt7(x0, x1, x2, x3)
new_ltEs16(Just(x0), Just(x1), ty_Double)
new_ltEs18(x0, x1, app(ty_Ratio, x2))
new_esEs23(x0, x1, ty_Integer)
new_esEs21(x0, x1, ty_Integer)
new_esEs24(x0, x1, ty_Ordering)
new_esEs26(x0, x1, ty_Double)
new_esEs25(x0, x1, ty_Float)
new_ltEs7(Left(x0), Left(x1), ty_Ordering, x2)
new_primCmpNat0(Zero, Zero)
new_compare31(x0, x1, ty_Char)
new_lt20(x0, x1, ty_Ordering)
new_ltEs6(LT, LT)
new_compare25(x0, x1, False)
new_esEs27(x0, x1, ty_Int)
new_ltEs7(Left(x0), Left(x1), ty_@0, x2)
new_compare26(x0, x1, True, x2, x3)
new_esEs27(x0, x1, ty_Char)
new_lt20(x0, x1, ty_Integer)
new_esEs9(False, False)
new_ltEs7(Right(x0), Right(x1), x2, ty_@0)
new_esEs4(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_ltEs14(x0, x1)
new_compare([], :(x0, x1), x2)
new_esEs24(x0, x1, ty_Integer)
new_ltEs16(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs19(GT, GT)
new_esEs6(Just(x0), Just(x1), ty_Int)
new_esEs15(Integer(x0), Integer(x1))
new_compare28(x0, x1, True, x2, x3, x4)
new_esEs11([], :(x0, x1), x2)
new_esEs4(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs19(EQ, EQ)
new_esEs4(Right(x0), Right(x1), x2, ty_Bool)
new_esEs26(x0, x1, ty_Int)
new_ltEs19(x0, x1, ty_@0)
new_esEs4(Right(x0), Right(x1), x2, ty_Ordering)
new_ltEs18(x0, x1, ty_Char)
new_esEs24(x0, x1, ty_Int)
new_lt6(x0, x1)
new_lt19(x0, x1, ty_Int)
new_primPlusNat0(Succ(x0), x1)
new_primCmpNat0(Succ(x0), Succ(x1))
new_esEs22(x0, x1, ty_Int)
new_compare31(x0, x1, ty_Int)
new_esEs19(EQ, LT)
new_esEs19(LT, EQ)
new_lt8(x0, x1, ty_Bool)
new_esEs4(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs7(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs4(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs18(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, ty_Float)
new_ltEs16(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs24(x0, x1, app(ty_[], x2))
new_esEs19(LT, GT)
new_esEs19(GT, LT)
new_esEs26(x0, x1, ty_Float)
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_not(EQ)
new_compare([], [], x0)
new_esEs21(x0, x1, ty_Char)
new_compare12(x0, x1, False, x2, x3)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCompAux1(x0, x1, x2, x3)
new_compare111(x0, x1, False, x2, x3)
new_lt8(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs18(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs4(x0, x1)
new_esEs4(Left(x0), Left(x1), ty_Float, x2)
new_esEs20(x0, x1, ty_@0)
new_ltEs13(x0, x1, x2)
new_lt19(x0, x1, app(ty_[], x2))
new_ltEs6(EQ, GT)
new_ltEs6(GT, EQ)
new_esEs10(x0, x1, app(app(ty_Either, x2), x3))
new_asAs(True, x0)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs20(x0, x1, ty_Ordering)
new_lt8(x0, x1, ty_Double)
new_sr(x0, x1)
new_esEs7(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_sr0(Integer(x0), Integer(x1))
new_ltEs7(Left(x0), Left(x1), ty_Float, x2)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_esEs27(x0, x1, ty_Bool)
new_compare19(@0, @0)
new_esEs9(True, False)
new_esEs9(False, True)
new_lt4(x0, x1, x2, x3, x4)
new_esEs26(x0, x1, ty_@0)
new_esEs6(Just(x0), Just(x1), ty_Char)
new_ltEs7(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs4(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_compare110(x0, x1, False)
new_esEs20(x0, x1, ty_Integer)
new_lt8(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt11(x0, x1, x2)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, ty_Double)
new_esEs21(x0, x1, ty_Ordering)
new_esEs4(Left(x0), Left(x1), ty_Char, x2)
new_esEs6(Just(x0), Just(x1), ty_Bool)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs7(Right(x0), Right(x1), x2, ty_Char)
new_ltEs7(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs4(Right(x0), Left(x1), x2, x3)
new_esEs4(Left(x0), Right(x1), x2, x3)
new_ltEs18(x0, x1, app(ty_[], x2))
new_primEqInt(Pos(Zero), Pos(Zero))
new_esEs4(Left(x0), Left(x1), ty_Bool, x2)
new_ltEs7(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_ltEs18(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, ty_Integer)
new_ltEs7(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs10(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare111(x0, x1, True, x2, x3)
new_esEs5(@2(x0, x1), @2(x2, x3), x4, x5)
new_primCmpNat0(Succ(x0), Zero)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs24(x0, x1, ty_Char)
new_primPlusNat1(Zero, Succ(x0))
new_not(LT)
new_ltEs16(Just(x0), Just(x1), ty_@0)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs18(Char(x0), Char(x1))
new_esEs21(x0, x1, ty_@0)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs4(Left(x0), Left(x1), ty_Double, x2)

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

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