YES 3.727 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
  ((compare :: Ord a => Maybe a  ->  Maybe a  ->  Ordering) :: Ord a => Maybe a  ->  Maybe a  ->  Ordering)

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
  ((compare :: Ord a => Maybe a  ->  Maybe a  ->  Ordering) :: Ord a => Maybe a  ->  Maybe a  ->  Ordering)

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
  ((compare :: Ord a => Maybe a  ->  Maybe a  ->  Ordering) :: Ord a => Maybe a  ->  Maybe a  ->  Ordering)

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
  ((compare :: Ord a => Maybe a  ->  Maybe a  ->  Ordering) :: Ord a => Maybe a  ->  Maybe a  ->  Ordering)

module Main where
  import qualified Prelude


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

is transformed to
compare x y = compare3 x y

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

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

compare0 x y True = GT

compare3 x y = compare2 x y (x == y)

The following Function with conditions
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
  ((compare :: Ord a => Maybe a  ->  Maybe a  ->  Ordering) :: Ord a => Maybe a  ->  Maybe a  ->  Ordering)

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'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
  ((compare :: Ord a => Maybe a  ->  Maybe a  ->  Ordering) :: Ord a => Maybe a  ->  Maybe a  ->  Ordering)

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
  (compare :: Ord a => Maybe a  ->  Maybe a  ->  Ordering)

module Main where
  import qualified Prelude


Haskell To QDPs


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

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

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

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

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



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

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

new_primPlusNat(Succ(vwx4600), Succ(vwx401000)) → new_primPlusNat(vwx4600, 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_primCmpNat(Succ(vwx900), Succ(vwx1000)) → new_primCmpNat(vwx900, vwx1000)

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

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



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

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

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

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(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), False, app(app(app(ty_@3, app(app(ty_@2, bcc), bcd)), hf), bba)) → new_lt0(vwx90, vwx100, bcc, bcd)
new_compare2(:(vwx90, vwx91), :(vwx100, vwx101), False, app(ty_[], ba)) → new_compare0(vwx91, vwx101, ba)
new_compare2(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), False, app(app(app(ty_@3, he), app(app(app(ty_@3, bbg), bbh), bca)), bba)) → new_lt3(vwx91, vwx101, bbg, bbh, bca)
new_ltEs3(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), he, app(ty_[], bah), bba) → new_lt(vwx91, vwx101, bah)
new_ltEs0(@2(vwx90, vwx91), @2(vwx100, vwx101), bb, app(ty_Maybe, bf)) → new_ltEs1(vwx91, vwx101, bf)
new_ltEs3(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), he, app(app(ty_Either, bbe), bbf), bba) → new_lt2(vwx91, vwx101, bbe, bbf)
new_ltEs0(@2(vwx90, vwx91), @2(vwx100, vwx101), bb, app(app(app(ty_@3, ca), cb), cc)) → new_ltEs3(vwx91, vwx101, ca, cb, cc)
new_compare2(@2(vwx90, vwx91), @2(vwx100, vwx101), False, app(app(ty_@2, app(app(ty_Either, db), dc)), ce)) → new_compare21(vwx90, vwx100, new_esEs5(vwx90, vwx100, db, dc), db, dc)
new_compare0(:(vwx90, vwx91), :(vwx100, vwx101), ba) → new_compare0(vwx91, vwx101, ba)
new_lt3(vwx90, vwx100, dd, de, df) → new_compare22(vwx90, vwx100, new_esEs6(vwx90, vwx100, dd, de, df), dd, de, df)
new_ltEs2(Left(vwx90), Left(vwx100), app(app(ty_Either, ff), fg), fa) → new_ltEs2(vwx90, vwx100, ff, fg)
new_ltEs0(@2(vwx90, vwx91), @2(vwx100, vwx101), app(ty_Maybe, da), ce) → new_compare1(vwx90, vwx100, da)
new_ltEs0(@2(vwx90, vwx91), @2(vwx100, vwx101), app(app(app(ty_@3, dd), de), df), ce) → new_compare22(vwx90, vwx100, new_esEs6(vwx90, vwx100, dd, de, df), dd, de, df)
new_compare22(vwx90, vwx100, False, dd, de, df) → new_ltEs3(vwx90, vwx100, dd, de, df)
new_ltEs2(Left(vwx90), Left(vwx100), app(app(ty_@2, fb), fc), fa) → new_ltEs0(vwx90, vwx100, fb, fc)
new_compare2(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), False, app(app(app(ty_@3, he), app(ty_Maybe, bbd)), bba)) → new_lt1(vwx91, vwx101, bbd)
new_lt1(vwx90, vwx100, da) → new_compare1(vwx90, vwx100, da)
new_ltEs1(Just(vwx90), Just(vwx100), app(app(app(ty_@3, ee), ef), eg)) → new_ltEs3(vwx90, vwx100, ee, ef, eg)
new_ltEs3(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), app(app(ty_@2, bcc), bcd), hf, bba) → new_lt0(vwx90, vwx100, bcc, bcd)
new_ltEs3(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), he, hf, app(ty_Maybe, bab)) → new_ltEs1(vwx92, vwx102, bab)
new_compare2(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), False, app(app(app(ty_@3, he), app(ty_[], bah)), bba)) → new_lt(vwx91, vwx101, bah)
new_ltEs0(@2(vwx90, vwx91), @2(vwx100, vwx101), app(app(ty_@2, cf), cg), ce) → new_compare20(vwx90, vwx100, new_esEs4(vwx90, vwx100, cf, cg), cf, cg)
new_ltEs1(Just(vwx90), Just(vwx100), app(ty_[], dg)) → new_ltEs(vwx90, vwx100, dg)
new_ltEs3(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), app(app(ty_Either, bcf), bcg), hf, bba) → new_lt2(vwx90, vwx100, bcf, bcg)
new_ltEs2(Left(vwx90), Left(vwx100), app(ty_Maybe, fd), fa) → new_ltEs1(vwx90, vwx100, fd)
new_compare2(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), False, app(app(app(ty_@3, app(app(ty_Either, bcf), bcg)), hf), bba)) → new_lt2(vwx90, vwx100, bcf, bcg)
new_lt0(vwx90, vwx100, cf, cg) → new_compare20(vwx90, vwx100, new_esEs4(vwx90, vwx100, cf, cg), cf, cg)
new_compare2(@2(vwx90, vwx91), @2(vwx100, vwx101), False, app(app(ty_@2, app(ty_[], cd)), ce)) → new_compare0(vwx90, vwx100, cd)
new_lt2(vwx90, vwx100, db, dc) → new_compare21(vwx90, vwx100, new_esEs5(vwx90, vwx100, db, dc), db, dc)
new_compare21(vwx90, vwx100, False, db, dc) → new_ltEs2(vwx90, vwx100, db, dc)
new_compare2(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), False, app(app(app(ty_@3, he), hf), app(app(app(ty_@3, bae), baf), bag))) → new_ltEs3(vwx92, vwx102, bae, baf, bag)
new_compare2(Left(vwx90), Left(vwx100), False, app(app(ty_Either, app(app(app(ty_@3, fh), ga), gb)), fa)) → new_ltEs3(vwx90, vwx100, fh, ga, gb)
new_compare2(@2(vwx90, vwx91), @2(vwx100, vwx101), False, app(app(ty_@2, bb), app(app(ty_@2, bd), be))) → new_ltEs0(vwx91, vwx101, bd, be)
new_compare2(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), False, app(app(app(ty_@3, he), app(app(ty_Either, bbe), bbf)), bba)) → new_lt2(vwx91, vwx101, bbe, bbf)
new_ltEs3(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), he, app(ty_Maybe, bbd), bba) → new_lt1(vwx91, vwx101, bbd)
new_primCompAux(vwx90, vwx100, vwx45, app(app(app(ty_@3, bea), beb), bec)) → new_compare5(vwx90, vwx100, bea, beb, bec)
new_compare2(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), False, app(app(app(ty_@3, app(ty_[], bcb)), hf), bba)) → new_lt(vwx90, vwx100, bcb)
new_compare2(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), False, app(app(app(ty_@3, app(app(app(ty_@3, bch), bda), bdb)), hf), bba)) → new_lt3(vwx90, vwx100, bch, bda, bdb)
new_compare2(@2(vwx90, vwx91), @2(vwx100, vwx101), False, app(app(ty_@2, bb), app(ty_[], bc))) → new_ltEs(vwx91, vwx101, bc)
new_ltEs3(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), app(ty_Maybe, bce), hf, bba) → new_lt1(vwx90, vwx100, bce)
new_compare2(:(vwx90, vwx91), :(vwx100, vwx101), False, app(ty_[], ba)) → new_primCompAux(vwx90, vwx100, new_compare(vwx91, vwx101, ba), ba)
new_primCompAux(vwx90, vwx100, vwx45, app(ty_Maybe, bdf)) → new_compare1(vwx90, vwx100, bdf)
new_compare2(Just(vwx90), Just(vwx100), False, app(ty_Maybe, app(ty_Maybe, eb))) → new_ltEs1(vwx90, vwx100, eb)
new_compare2(Right(vwx90), Right(vwx100), False, app(app(ty_Either, gc), app(app(ty_@2, ge), gf))) → new_ltEs0(vwx90, vwx100, ge, gf)
new_ltEs1(Just(vwx90), Just(vwx100), app(app(ty_Either, ec), ed)) → new_ltEs2(vwx90, vwx100, ec, ed)
new_compare2(Right(vwx90), Right(vwx100), False, app(app(ty_Either, gc), app(app(ty_Either, gh), ha))) → new_ltEs2(vwx90, vwx100, gh, ha)
new_ltEs3(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), he, app(app(app(ty_@3, bbg), bbh), bca), bba) → new_lt3(vwx91, vwx101, bbg, bbh, bca)
new_compare2(Left(vwx90), Left(vwx100), False, app(app(ty_Either, app(app(ty_Either, ff), fg)), fa)) → new_ltEs2(vwx90, vwx100, ff, fg)
new_compare2(Right(vwx90), Right(vwx100), False, app(app(ty_Either, gc), app(ty_Maybe, gg))) → new_ltEs1(vwx90, vwx100, gg)
new_ltEs3(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), he, hf, app(app(ty_@2, hh), baa)) → new_ltEs0(vwx92, vwx102, hh, baa)
new_compare2(Just(vwx90), Just(vwx100), False, app(ty_Maybe, app(app(ty_@2, dh), ea))) → new_ltEs0(vwx90, vwx100, dh, ea)
new_ltEs2(Right(vwx90), Right(vwx100), gc, app(app(app(ty_@3, hb), hc), hd)) → new_ltEs3(vwx90, vwx100, hb, hc, hd)
new_compare2(Right(vwx90), Right(vwx100), False, app(app(ty_Either, gc), app(ty_[], gd))) → new_ltEs(vwx90, vwx100, gd)
new_compare2(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), False, app(app(app(ty_@3, he), hf), app(app(ty_Either, bac), bad))) → new_ltEs2(vwx92, vwx102, bac, bad)
new_compare2(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), False, app(app(app(ty_@3, he), hf), app(ty_Maybe, bab))) → new_ltEs1(vwx92, vwx102, bab)
new_ltEs0(@2(vwx90, vwx91), @2(vwx100, vwx101), app(ty_[], cd), ce) → new_compare0(vwx90, vwx100, cd)
new_compare0(:(vwx90, vwx91), :(vwx100, vwx101), ba) → new_primCompAux(vwx90, vwx100, new_compare(vwx91, vwx101, ba), ba)
new_ltEs2(Left(vwx90), Left(vwx100), app(app(app(ty_@3, fh), ga), gb), fa) → new_ltEs3(vwx90, vwx100, fh, ga, gb)
new_compare2(@2(vwx90, vwx91), @2(vwx100, vwx101), False, app(app(ty_@2, app(ty_Maybe, da)), ce)) → new_compare1(vwx90, vwx100, da)
new_ltEs3(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), app(ty_[], bcb), hf, bba) → new_lt(vwx90, vwx100, bcb)
new_primCompAux(vwx90, vwx100, vwx45, app(app(ty_@2, bdd), bde)) → new_compare3(vwx90, vwx100, bdd, bde)
new_compare2(Left(vwx90), Left(vwx100), False, app(app(ty_Either, app(app(ty_@2, fb), fc)), fa)) → new_ltEs0(vwx90, vwx100, fb, fc)
new_ltEs3(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), he, hf, app(ty_[], hg)) → new_ltEs(vwx92, vwx102, hg)
new_ltEs1(Just(vwx90), Just(vwx100), app(ty_Maybe, eb)) → new_ltEs1(vwx90, vwx100, eb)
new_compare2(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), False, app(app(app(ty_@3, he), hf), app(app(ty_@2, hh), baa))) → new_ltEs0(vwx92, vwx102, hh, baa)
new_compare2(@2(vwx90, vwx91), @2(vwx100, vwx101), False, app(app(ty_@2, bb), app(app(app(ty_@3, ca), cb), cc))) → new_ltEs3(vwx91, vwx101, ca, cb, cc)
new_ltEs2(Right(vwx90), Right(vwx100), gc, app(ty_[], gd)) → new_ltEs(vwx90, vwx100, gd)
new_compare2(Just(vwx90), Just(vwx100), False, app(ty_Maybe, app(app(ty_Either, ec), ed))) → new_ltEs2(vwx90, vwx100, ec, ed)
new_ltEs(:(vwx90, vwx91), :(vwx100, vwx101), ba) → new_primCompAux(vwx90, vwx100, new_compare(vwx91, vwx101, ba), ba)
new_primCompAux(vwx90, vwx100, vwx45, app(ty_[], bdc)) → new_compare0(vwx90, vwx100, bdc)
new_ltEs3(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), he, app(app(ty_@2, bbb), bbc), bba) → new_lt0(vwx91, vwx101, bbb, bbc)
new_compare1(Just(vwx30), Just(vwx40), bed) → new_compare2(vwx30, vwx40, new_esEs7(vwx30, vwx40, bed), bed)
new_compare20(vwx90, vwx100, False, cf, cg) → new_ltEs0(vwx90, vwx100, cf, cg)
new_compare2(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), False, app(app(app(ty_@3, he), hf), app(ty_[], hg))) → new_ltEs(vwx92, vwx102, hg)
new_compare5(vwx90, vwx100, dd, de, df) → new_compare22(vwx90, vwx100, new_esEs6(vwx90, vwx100, dd, de, df), dd, de, df)
new_compare2(Just(vwx90), Just(vwx100), False, app(ty_Maybe, app(ty_[], dg))) → new_ltEs(vwx90, vwx100, dg)
new_compare2(@2(vwx90, vwx91), @2(vwx100, vwx101), False, app(app(ty_@2, app(app(ty_@2, cf), cg)), ce)) → new_compare20(vwx90, vwx100, new_esEs4(vwx90, vwx100, cf, cg), cf, cg)
new_primCompAux(vwx90, vwx100, vwx45, app(app(ty_Either, bdg), bdh)) → new_compare4(vwx90, vwx100, bdg, bdh)
new_compare2(Left(vwx90), Left(vwx100), False, app(app(ty_Either, app(ty_[], eh)), fa)) → new_ltEs(vwx90, vwx100, eh)
new_ltEs2(Right(vwx90), Right(vwx100), gc, app(app(ty_Either, gh), ha)) → new_ltEs2(vwx90, vwx100, gh, ha)
new_ltEs0(@2(vwx90, vwx91), @2(vwx100, vwx101), bb, app(app(ty_@2, bd), be)) → new_ltEs0(vwx91, vwx101, bd, be)
new_ltEs0(@2(vwx90, vwx91), @2(vwx100, vwx101), bb, app(ty_[], bc)) → new_ltEs(vwx91, vwx101, bc)
new_compare2(Just(vwx90), Just(vwx100), False, app(ty_Maybe, app(app(app(ty_@3, ee), ef), eg))) → new_ltEs3(vwx90, vwx100, ee, ef, eg)
new_compare2(@2(vwx90, vwx91), @2(vwx100, vwx101), False, app(app(ty_@2, bb), app(ty_Maybe, bf))) → new_ltEs1(vwx91, vwx101, bf)
new_ltEs3(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), he, hf, app(app(app(ty_@3, bae), baf), bag)) → new_ltEs3(vwx92, vwx102, bae, baf, bag)
new_ltEs1(Just(vwx90), Just(vwx100), app(app(ty_@2, dh), ea)) → new_ltEs0(vwx90, vwx100, dh, ea)
new_compare3(vwx90, vwx100, cf, cg) → new_compare20(vwx90, vwx100, new_esEs4(vwx90, vwx100, cf, cg), cf, cg)
new_ltEs(:(vwx90, vwx91), :(vwx100, vwx101), ba) → new_compare0(vwx91, vwx101, ba)
new_ltEs0(@2(vwx90, vwx91), @2(vwx100, vwx101), bb, app(app(ty_Either, bg), bh)) → new_ltEs2(vwx91, vwx101, bg, bh)
new_ltEs3(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), app(app(app(ty_@3, bch), bda), bdb), hf, bba) → new_lt3(vwx90, vwx100, bch, bda, bdb)
new_compare2(Left(vwx90), Left(vwx100), False, app(app(ty_Either, app(ty_Maybe, fd)), fa)) → new_ltEs1(vwx90, vwx100, fd)
new_compare2(Right(vwx90), Right(vwx100), False, app(app(ty_Either, gc), app(app(app(ty_@3, hb), hc), hd))) → new_ltEs3(vwx90, vwx100, hb, hc, hd)
new_ltEs2(Right(vwx90), Right(vwx100), gc, app(app(ty_@2, ge), gf)) → new_ltEs0(vwx90, vwx100, ge, gf)
new_lt(vwx90, vwx100, cd) → new_compare0(vwx90, vwx100, cd)
new_compare2(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), False, app(app(app(ty_@3, app(ty_Maybe, bce)), hf), bba)) → new_lt1(vwx90, vwx100, bce)
new_compare2(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), False, app(app(app(ty_@3, he), app(app(ty_@2, bbb), bbc)), bba)) → new_lt0(vwx91, vwx101, bbb, bbc)
new_ltEs3(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), he, hf, app(app(ty_Either, bac), bad)) → new_ltEs2(vwx92, vwx102, bac, bad)
new_ltEs2(Left(vwx90), Left(vwx100), app(ty_[], eh), fa) → new_ltEs(vwx90, vwx100, eh)
new_compare4(vwx90, vwx100, db, dc) → new_compare21(vwx90, vwx100, new_esEs5(vwx90, vwx100, db, dc), db, dc)
new_compare2(@2(vwx90, vwx91), @2(vwx100, vwx101), False, app(app(ty_@2, app(app(app(ty_@3, dd), de), df)), ce)) → new_compare22(vwx90, vwx100, new_esEs6(vwx90, vwx100, dd, de, df), dd, de, df)
new_ltEs2(Right(vwx90), Right(vwx100), gc, app(ty_Maybe, gg)) → new_ltEs1(vwx90, vwx100, gg)
new_ltEs0(@2(vwx90, vwx91), @2(vwx100, vwx101), app(app(ty_Either, db), dc), ce) → new_compare21(vwx90, vwx100, new_esEs5(vwx90, vwx100, db, dc), db, dc)
new_compare2(@2(vwx90, vwx91), @2(vwx100, vwx101), False, app(app(ty_@2, bb), app(app(ty_Either, bg), bh))) → new_ltEs2(vwx91, vwx101, bg, bh)

The TRS R consists of the following rules:

new_ltEs7(Left(vwx90), Left(vwx100), app(ty_Maybe, fd), fa) → new_ltEs13(vwx90, vwx100, fd)
new_esEs23(vwx91, vwx101, ty_Integer) → new_esEs13(vwx91, vwx101)
new_esEs24(vwx90, vwx100, app(app(ty_Either, bcf), bcg)) → new_esEs5(vwx90, vwx100, bcf, bcg)
new_esEs24(vwx90, vwx100, ty_Float) → new_esEs12(vwx90, vwx100)
new_ltEs14(vwx9, vwx10) → new_not(new_esEs8(new_compare13(vwx9, vwx10), GT))
new_ltEs19(vwx92, vwx102, app(ty_Ratio, cee)) → new_ltEs11(vwx92, vwx102, cee)
new_lt19(vwx91, vwx101, app(ty_Ratio, cef)) → new_lt10(vwx91, vwx101, cef)
new_ltEs17(LT, LT) → True
new_esEs24(vwx90, vwx100, ty_Char) → new_esEs15(vwx90, vwx100)
new_compare110(vwx90, vwx100, True, cf, cg) → LT
new_esEs29(vwx300, vwx400, ty_Integer) → new_esEs13(vwx300, vwx400)
new_esEs23(vwx91, vwx101, app(app(ty_Either, bbe), bbf)) → new_esEs5(vwx91, vwx101, bbe, bbf)
new_esEs23(vwx91, vwx101, app(app(ty_@2, bbb), bbc)) → new_esEs4(vwx91, vwx101, bbb, bbc)
new_esEs20(vwx301, vwx401, ty_Integer) → new_esEs13(vwx301, vwx401)
new_compare([], :(vwx100, vwx101), ba) → LT
new_esEs29(vwx300, vwx400, ty_Double) → new_esEs14(vwx300, vwx400)
new_compare10(vwx90, vwx100, True, db, dc) → LT
new_ltEs20(vwx9, vwx10, ty_Int) → new_ltEs4(vwx9, vwx10)
new_lt19(vwx91, vwx101, ty_Integer) → new_lt5(vwx91, vwx101)
new_esEs29(vwx300, vwx400, ty_Int) → new_esEs9(vwx300, vwx400)
new_esEs20(vwx301, vwx401, ty_Int) → new_esEs9(vwx301, vwx401)
new_compare14(vwx90, vwx100, True, dd, de, df) → LT
new_esEs7(vwx30, vwx40, ty_Ordering) → new_esEs8(vwx30, vwx40)
new_esEs5(Right(vwx300), Right(vwx400), bga, ty_Char) → new_esEs15(vwx300, vwx400)
new_ltEs6(True, False) → False
new_lt20(vwx90, vwx100, ty_@0) → new_lt6(vwx90, vwx100)
new_esEs21(vwx300, vwx400, ty_@0) → new_esEs17(vwx300, vwx400)
new_ltEs7(Left(vwx90), Right(vwx100), gc, fa) → True
new_primMulNat0(Zero, Zero) → Zero
new_esEs24(vwx90, vwx100, ty_Integer) → new_esEs13(vwx90, vwx100)
new_compare(:(vwx90, vwx91), [], ba) → GT
new_esEs16(Nothing, Nothing, ceb) → True
new_compare29(vwx90, vwx100, ty_Float) → new_compare16(vwx90, vwx100)
new_ltEs10(vwx91, vwx101, app(ty_[], bc)) → new_ltEs12(vwx91, vwx101, bc)
new_ltEs13(Nothing, Just(vwx100), cfb) → True
new_compare9(Double(vwx90, vwx91), Double(vwx100, vwx101)) → new_compare6(new_sr(vwx90, vwx100), new_sr(vwx91, vwx101))
new_lt8(vwx90, vwx100, ty_Int) → new_lt9(vwx90, vwx100)
new_ltEs13(Just(vwx90), Just(vwx100), ty_Integer) → new_ltEs14(vwx90, vwx100)
new_esEs23(vwx91, vwx101, ty_Float) → new_esEs12(vwx91, vwx101)
new_ltEs19(vwx92, vwx102, ty_Integer) → new_ltEs14(vwx92, vwx102)
new_compare27(vwx90, vwx100, cf, cg) → new_compare28(vwx90, vwx100, new_esEs4(vwx90, vwx100, cf, cg), cf, cg)
new_lt20(vwx90, vwx100, app(ty_Maybe, bce)) → new_lt13(vwx90, vwx100, bce)
new_lt20(vwx90, vwx100, app(app(app(ty_@3, bch), bda), bdb)) → new_lt18(vwx90, vwx100, bch, bda, bdb)
new_esEs22(vwx90, vwx100, ty_@0) → new_esEs17(vwx90, vwx100)
new_ltEs20(vwx9, vwx10, app(ty_Maybe, cfb)) → new_ltEs13(vwx9, vwx10, cfb)
new_esEs21(vwx300, vwx400, ty_Integer) → new_esEs13(vwx300, vwx400)
new_lt19(vwx91, vwx101, ty_Ordering) → new_lt17(vwx91, vwx101)
new_esEs23(vwx91, vwx101, ty_Char) → new_esEs15(vwx91, vwx101)
new_esEs27(vwx301, vwx401, ty_Char) → new_esEs15(vwx301, vwx401)
new_compare29(vwx90, vwx100, app(ty_Maybe, bdf)) → new_compare18(vwx90, vwx100, bdf)
new_esEs19(vwx302, vwx402, ty_Int) → new_esEs9(vwx302, vwx402)
new_esEs22(vwx90, vwx100, ty_Bool) → new_esEs10(vwx90, vwx100)
new_compare29(vwx90, vwx100, app(app(app(ty_@3, bea), beb), bec)) → new_compare31(vwx90, vwx100, bea, beb, bec)
new_compare210(vwx90, vwx100, False, dd, de, df) → new_compare14(vwx90, vwx100, new_ltEs18(vwx90, vwx100, dd, de, df), dd, de, df)
new_lt5(vwx90, vwx100) → new_esEs8(new_compare13(vwx90, vwx100), LT)
new_esEs16(Just(vwx300), Just(vwx400), ty_Double) → new_esEs14(vwx300, vwx400)
new_esEs27(vwx301, vwx401, ty_Bool) → new_esEs10(vwx301, vwx401)
new_ltEs13(Just(vwx90), Just(vwx100), ty_@0) → new_ltEs16(vwx90, vwx100)
new_esEs27(vwx301, vwx401, ty_Integer) → new_esEs13(vwx301, vwx401)
new_compare26(vwx9, vwx10, False, ceh) → new_compare11(vwx9, vwx10, new_ltEs20(vwx9, vwx10, ceh), ceh)
new_esEs24(vwx90, vwx100, ty_@0) → new_esEs17(vwx90, vwx100)
new_esEs28(vwx300, vwx400, ty_Double) → new_esEs14(vwx300, vwx400)
new_esEs5(Right(vwx300), Right(vwx400), bga, ty_@0) → new_esEs17(vwx300, vwx400)
new_ltEs7(Right(vwx90), Right(vwx100), gc, app(app(ty_@2, ge), gf)) → new_ltEs9(vwx90, vwx100, ge, gf)
new_compare29(vwx90, vwx100, ty_Integer) → new_compare13(vwx90, vwx100)
new_compare15(vwx90, vwx100, False) → GT
new_ltEs13(Just(vwx90), Just(vwx100), app(app(ty_@2, dh), ea)) → new_ltEs9(vwx90, vwx100, dh, ea)
new_esEs27(vwx301, vwx401, ty_Double) → new_esEs14(vwx301, vwx401)
new_compare29(vwx90, vwx100, ty_Int) → new_compare6(vwx90, vwx100)
new_esEs11(:%(vwx300, vwx301), :%(vwx400, vwx401), cdg) → new_asAs(new_esEs26(vwx300, vwx400, cdg), new_esEs25(vwx301, vwx401, cdg))
new_esEs19(vwx302, vwx402, app(app(ty_Either, cag), cah)) → new_esEs5(vwx302, vwx402, cag, cah)
new_ltEs17(EQ, LT) → False
new_esEs5(Right(vwx300), Right(vwx400), bga, app(app(app(ty_@3, bgb), bgc), bgd)) → new_esEs6(vwx300, vwx400, bgb, bgc, bgd)
new_esEs17(@0, @0) → True
new_esEs7(vwx30, vwx40, app(ty_Maybe, ceb)) → new_esEs16(vwx30, vwx40, ceb)
new_pePe(False, vwx44) → vwx44
new_esEs7(vwx30, vwx40, ty_Char) → new_esEs15(vwx30, vwx40)
new_esEs18(:(vwx300, vwx301), [], cec) → False
new_esEs18([], :(vwx400, vwx401), cec) → False
new_esEs14(Double(vwx300, vwx301), Double(vwx400, vwx401)) → new_esEs9(new_sr(vwx300, vwx400), new_sr(vwx301, vwx401))
new_esEs18(:(vwx300, vwx301), :(vwx400, vwx401), cec) → new_asAs(new_esEs29(vwx300, vwx400, cec), new_esEs18(vwx301, vwx401, cec))
new_esEs29(vwx300, vwx400, ty_@0) → new_esEs17(vwx300, vwx400)
new_lt6(vwx90, vwx100) → new_esEs8(new_compare8(vwx90, vwx100), LT)
new_esEs27(vwx301, vwx401, app(ty_Maybe, cga)) → new_esEs16(vwx301, vwx401, cga)
new_esEs22(vwx90, vwx100, app(app(ty_@2, cf), cg)) → new_esEs4(vwx90, vwx100, cf, cg)
new_compare15(vwx90, vwx100, True) → LT
new_esEs12(Float(vwx300, vwx301), Float(vwx400, vwx401)) → new_esEs9(new_sr(vwx300, vwx400), new_sr(vwx301, vwx401))
new_lt20(vwx90, vwx100, ty_Ordering) → new_lt17(vwx90, vwx100)
new_compare18(Nothing, Just(vwx40), bed) → LT
new_esEs22(vwx90, vwx100, ty_Ordering) → new_esEs8(vwx90, vwx100)
new_ltEs7(Right(vwx90), Right(vwx100), gc, ty_Char) → new_ltEs5(vwx90, vwx100)
new_esEs20(vwx301, vwx401, app(ty_[], cbh)) → new_esEs18(vwx301, vwx401, cbh)
new_compare31(vwx90, vwx100, dd, de, df) → new_compare210(vwx90, vwx100, new_esEs6(vwx90, vwx100, dd, de, df), dd, de, df)
new_compare111(vwx90, vwx100, False) → GT
new_compare111(vwx90, vwx100, True) → LT
new_ltEs20(vwx9, vwx10, app(ty_[], ba)) → new_ltEs12(vwx9, vwx10, ba)
new_esEs29(vwx300, vwx400, app(app(ty_@2, dbg), dbh)) → new_esEs4(vwx300, vwx400, dbg, dbh)
new_compare19(:%(vwx90, vwx91), :%(vwx100, vwx101), ty_Int) → new_compare6(new_sr(vwx90, vwx101), new_sr(vwx100, vwx91))
new_esEs5(Right(vwx300), Right(vwx400), bga, app(app(ty_@2, bgf), bgg)) → new_esEs4(vwx300, vwx400, bgf, bgg)
new_esEs5(Left(vwx300), Left(vwx400), ty_Ordering, bfa) → new_esEs8(vwx300, vwx400)
new_esEs23(vwx91, vwx101, ty_Double) → new_esEs14(vwx91, vwx101)
new_primCmpNat0(Zero, Succ(vwx1000)) → LT
new_primCompAux0(vwx90, vwx100, vwx45, ba) → new_primCompAux00(vwx45, new_compare29(vwx90, vwx100, ba))
new_esEs5(Right(vwx300), Right(vwx400), bga, app(ty_Maybe, bgh)) → new_esEs16(vwx300, vwx400, bgh)
new_compare18(Just(vwx30), Nothing, bed) → GT
new_esEs19(vwx302, vwx402, app(ty_Maybe, cae)) → new_esEs16(vwx302, vwx402, cae)
new_ltEs13(Nothing, Nothing, cfb) → True
new_compare29(vwx90, vwx100, app(ty_Ratio, ced)) → new_compare19(vwx90, vwx100, ced)
new_ltEs19(vwx92, vwx102, ty_Float) → new_ltEs15(vwx92, vwx102)
new_ltEs19(vwx92, vwx102, ty_Bool) → new_ltEs6(vwx92, vwx102)
new_ltEs10(vwx91, vwx101, ty_Int) → new_ltEs4(vwx91, vwx101)
new_ltEs7(Left(vwx90), Left(vwx100), app(ty_Ratio, chg), fa) → new_ltEs11(vwx90, vwx100, chg)
new_ltEs7(Left(vwx90), Left(vwx100), app(app(ty_@2, fb), fc), fa) → new_ltEs9(vwx90, vwx100, fb, fc)
new_ltEs7(Left(vwx90), Left(vwx100), app(app(app(ty_@3, fh), ga), gb), fa) → new_ltEs18(vwx90, vwx100, fh, ga, gb)
new_esEs8(LT, LT) → True
new_compare17(vwx90, vwx100) → new_compare25(vwx90, vwx100, new_esEs10(vwx90, vwx100))
new_lt8(vwx90, vwx100, ty_Bool) → new_lt15(vwx90, vwx100)
new_compare29(vwx90, vwx100, ty_Double) → new_compare9(vwx90, vwx100)
new_esEs16(Just(vwx300), Just(vwx400), ty_Integer) → new_esEs13(vwx300, vwx400)
new_esEs20(vwx301, vwx401, app(app(app(ty_@3, cba), cbb), cbc)) → new_esEs6(vwx301, vwx401, cba, cbb, cbc)
new_esEs7(vwx30, vwx40, ty_Integer) → new_esEs13(vwx30, vwx40)
new_pePe(True, vwx44) → True
new_primEqNat0(Zero, Zero) → True
new_esEs16(Just(vwx300), Just(vwx400), ty_Ordering) → new_esEs8(vwx300, vwx400)
new_esEs19(vwx302, vwx402, ty_Integer) → new_esEs13(vwx302, vwx402)
new_esEs19(vwx302, vwx402, ty_Bool) → new_esEs10(vwx302, vwx402)
new_ltEs7(Right(vwx90), Right(vwx100), gc, ty_@0) → new_ltEs16(vwx90, vwx100)
new_compare11(vwx16, vwx17, True, bee) → LT
new_primMulNat0(Succ(vwx30100), Succ(vwx40100)) → new_primPlusNat1(new_primMulNat0(vwx30100, Succ(vwx40100)), vwx40100)
new_esEs5(Left(vwx300), Left(vwx400), ty_Int, bfa) → new_esEs9(vwx300, vwx400)
new_ltEs20(vwx9, vwx10, ty_Integer) → new_ltEs14(vwx9, vwx10)
new_esEs16(Just(vwx300), Just(vwx400), ty_@0) → new_esEs17(vwx300, vwx400)
new_esEs4(@2(vwx300, vwx301), @2(vwx400, vwx401), cdh, cea) → new_asAs(new_esEs28(vwx300, vwx400, cdh), new_esEs27(vwx301, vwx401, cea))
new_ltEs11(vwx9, vwx10, cfa) → new_not(new_esEs8(new_compare19(vwx9, vwx10, cfa), GT))
new_esEs24(vwx90, vwx100, app(ty_[], bcb)) → new_esEs18(vwx90, vwx100, bcb)
new_esEs16(Just(vwx300), Just(vwx400), ty_Bool) → new_esEs10(vwx300, vwx400)
new_ltEs13(Just(vwx90), Just(vwx100), ty_Bool) → new_ltEs6(vwx90, vwx100)
new_esEs24(vwx90, vwx100, app(ty_Maybe, bce)) → new_esEs16(vwx90, vwx100, bce)
new_ltEs17(GT, LT) → False
new_compare110(vwx90, vwx100, False, cf, cg) → GT
new_ltEs20(vwx9, vwx10, app(app(ty_@2, bb), ce)) → new_ltEs9(vwx9, vwx10, bb, ce)
new_esEs15(Char(vwx300), Char(vwx400)) → new_primEqNat0(vwx300, vwx400)
new_sr(vwx301, vwx401) → new_primMulInt(vwx301, vwx401)
new_esEs20(vwx301, vwx401, ty_Char) → new_esEs15(vwx301, vwx401)
new_lt8(vwx90, vwx100, app(ty_[], cd)) → new_lt11(vwx90, vwx100, cd)
new_esEs8(GT, GT) → True
new_lt18(vwx90, vwx100, dd, de, df) → new_esEs8(new_compare31(vwx90, vwx100, dd, de, df), LT)
new_ltEs20(vwx9, vwx10, app(ty_Ratio, cfa)) → new_ltEs11(vwx9, vwx10, cfa)
new_esEs7(vwx30, vwx40, ty_@0) → new_esEs17(vwx30, vwx40)
new_esEs5(Right(vwx300), Right(vwx400), bga, app(ty_[], bha)) → new_esEs18(vwx300, vwx400, bha)
new_esEs8(GT, LT) → False
new_esEs8(LT, GT) → False
new_esEs22(vwx90, vwx100, app(ty_[], cd)) → new_esEs18(vwx90, vwx100, cd)
new_lt8(vwx90, vwx100, ty_@0) → new_lt6(vwx90, vwx100)
new_esEs13(Integer(vwx300), Integer(vwx400)) → new_primEqInt(vwx300, vwx400)
new_lt17(vwx90, vwx100) → new_esEs8(new_compare12(vwx90, vwx100), LT)
new_primEqInt(Neg(Succ(vwx3000)), Neg(Succ(vwx4000))) → new_primEqNat0(vwx3000, vwx4000)
new_compare25(vwx90, vwx100, True) → EQ
new_esEs24(vwx90, vwx100, app(ty_Ratio, ceg)) → new_esEs11(vwx90, vwx100, ceg)
new_ltEs5(vwx9, vwx10) → new_not(new_esEs8(new_compare7(vwx9, vwx10), GT))
new_compare12(vwx90, vwx100) → new_compare24(vwx90, vwx100, new_esEs8(vwx90, vwx100))
new_esEs20(vwx301, vwx401, ty_Ordering) → new_esEs8(vwx301, vwx401)
new_esEs22(vwx90, vwx100, app(app(app(ty_@3, dd), de), df)) → new_esEs6(vwx90, vwx100, dd, de, df)
new_esEs23(vwx91, vwx101, ty_Ordering) → new_esEs8(vwx91, vwx101)
new_esEs28(vwx300, vwx400, ty_Char) → new_esEs15(vwx300, vwx400)
new_ltEs17(LT, GT) → True
new_esEs23(vwx91, vwx101, app(ty_Maybe, bbd)) → new_esEs16(vwx91, vwx101, bbd)
new_lt8(vwx90, vwx100, app(app(app(ty_@3, dd), de), df)) → new_lt18(vwx90, vwx100, dd, de, df)
new_esEs28(vwx300, vwx400, ty_@0) → new_esEs17(vwx300, vwx400)
new_esEs29(vwx300, vwx400, app(app(ty_Either, dcc), dcd)) → new_esEs5(vwx300, vwx400, dcc, dcd)
new_esEs21(vwx300, vwx400, ty_Char) → new_esEs15(vwx300, vwx400)
new_lt19(vwx91, vwx101, ty_Char) → new_lt14(vwx91, vwx101)
new_esEs19(vwx302, vwx402, app(ty_Ratio, cab)) → new_esEs11(vwx302, vwx402, cab)
new_ltEs7(Left(vwx90), Left(vwx100), ty_Char, fa) → new_ltEs5(vwx90, vwx100)
new_esEs19(vwx302, vwx402, app(ty_[], caf)) → new_esEs18(vwx302, vwx402, caf)
new_esEs21(vwx300, vwx400, ty_Double) → new_esEs14(vwx300, vwx400)
new_esEs21(vwx300, vwx400, app(ty_[], cdb)) → new_esEs18(vwx300, vwx400, cdb)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs24(vwx90, vwx100, ty_Bool) → new_esEs10(vwx90, vwx100)
new_ltEs7(Right(vwx90), Left(vwx100), gc, fa) → False
new_esEs24(vwx90, vwx100, app(app(app(ty_@3, bch), bda), bdb)) → new_esEs6(vwx90, vwx100, bch, bda, bdb)
new_esEs7(vwx30, vwx40, ty_Int) → new_esEs9(vwx30, vwx40)
new_esEs27(vwx301, vwx401, app(app(ty_Either, cgc), cgd)) → new_esEs5(vwx301, vwx401, cgc, cgd)
new_primEqInt(Neg(Zero), Neg(Succ(vwx4000))) → False
new_primEqInt(Neg(Succ(vwx3000)), Neg(Zero)) → False
new_esEs8(EQ, EQ) → True
new_esEs5(Left(vwx300), Left(vwx400), ty_Double, bfa) → new_esEs14(vwx300, vwx400)
new_primPlusNat1(Zero, vwx40100) → Succ(vwx40100)
new_ltEs7(Left(vwx90), Left(vwx100), ty_@0, fa) → new_ltEs16(vwx90, vwx100)
new_ltEs7(Right(vwx90), Right(vwx100), gc, app(ty_Ratio, chh)) → new_ltEs11(vwx90, vwx100, chh)
new_compare7(Char(vwx90), Char(vwx100)) → new_primCmpNat0(vwx90, vwx100)
new_esEs10(False, False) → True
new_ltEs10(vwx91, vwx101, ty_Float) → new_ltEs15(vwx91, vwx101)
new_esEs20(vwx301, vwx401, ty_@0) → new_esEs17(vwx301, vwx401)
new_esEs5(Right(vwx300), Right(vwx400), bga, ty_Int) → new_esEs9(vwx300, vwx400)
new_compare([], [], ba) → EQ
new_ltEs17(EQ, EQ) → True
new_ltEs19(vwx92, vwx102, ty_Ordering) → new_ltEs17(vwx92, vwx102)
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_esEs5(Right(vwx300), Right(vwx400), bga, ty_Bool) → new_esEs10(vwx300, vwx400)
new_compare6(vwx9, vwx10) → new_primCmpInt(vwx9, vwx10)
new_esEs7(vwx30, vwx40, app(app(ty_Either, bga), bfa)) → new_esEs5(vwx30, vwx40, bga, bfa)
new_primCmpNat0(Succ(vwx900), Succ(vwx1000)) → new_primCmpNat0(vwx900, vwx1000)
new_lt19(vwx91, vwx101, app(app(ty_Either, bbe), bbf)) → new_lt16(vwx91, vwx101, bbe, bbf)
new_compare11(vwx16, vwx17, False, bee) → GT
new_primEqInt(Pos(Succ(vwx3000)), Pos(Succ(vwx4000))) → new_primEqNat0(vwx3000, vwx4000)
new_compare10(vwx90, vwx100, False, db, dc) → GT
new_ltEs7(Right(vwx90), Right(vwx100), gc, ty_Int) → new_ltEs4(vwx90, vwx100)
new_lt19(vwx91, vwx101, ty_Double) → new_lt4(vwx91, vwx101)
new_lt19(vwx91, vwx101, app(app(ty_@2, bbb), bbc)) → new_lt12(vwx91, vwx101, bbb, bbc)
new_compare29(vwx90, vwx100, ty_Char) → new_compare7(vwx90, vwx100)
new_ltEs6(False, True) → True
new_compare29(vwx90, vwx100, app(app(ty_@2, bdd), bde)) → new_compare27(vwx90, vwx100, bdd, bde)
new_esEs25(vwx301, vwx401, ty_Int) → new_esEs9(vwx301, vwx401)
new_ltEs10(vwx91, vwx101, ty_Integer) → new_ltEs14(vwx91, vwx101)
new_ltEs20(vwx9, vwx10, ty_@0) → new_ltEs16(vwx9, vwx10)
new_esEs5(Right(vwx300), Right(vwx400), bga, app(app(ty_Either, bhb), bhc)) → new_esEs5(vwx300, vwx400, bhb, bhc)
new_primEqNat0(Succ(vwx3000), Succ(vwx4000)) → new_primEqNat0(vwx3000, vwx4000)
new_esEs27(vwx301, vwx401, ty_Ordering) → new_esEs8(vwx301, vwx401)
new_ltEs6(True, True) → True
new_esEs5(Left(vwx300), Left(vwx400), ty_Char, bfa) → new_esEs15(vwx300, vwx400)
new_lt8(vwx90, vwx100, app(ty_Ratio, cdf)) → new_lt10(vwx90, vwx100, cdf)
new_esEs19(vwx302, vwx402, app(app(app(ty_@3, bhg), bhh), caa)) → new_esEs6(vwx302, vwx402, bhg, bhh, caa)
new_ltEs20(vwx9, vwx10, ty_Char) → new_ltEs5(vwx9, vwx10)
new_esEs27(vwx301, vwx401, ty_Float) → new_esEs12(vwx301, vwx401)
new_esEs20(vwx301, vwx401, ty_Double) → new_esEs14(vwx301, vwx401)
new_primCompAux00(vwx50, LT) → LT
new_primCmpInt(Neg(Succ(vwx900)), Neg(vwx100)) → new_primCmpNat0(vwx100, Succ(vwx900))
new_ltEs19(vwx92, vwx102, app(app(app(ty_@3, bae), baf), bag)) → new_ltEs18(vwx92, vwx102, bae, baf, bag)
new_ltEs19(vwx92, vwx102, app(app(ty_Either, bac), bad)) → new_ltEs7(vwx92, vwx102, bac, bad)
new_esEs24(vwx90, vwx100, ty_Ordering) → new_esEs8(vwx90, vwx100)
new_esEs22(vwx90, vwx100, ty_Char) → new_esEs15(vwx90, vwx100)
new_compare29(vwx90, vwx100, ty_Bool) → new_compare17(vwx90, vwx100)
new_esEs28(vwx300, vwx400, ty_Ordering) → new_esEs8(vwx300, vwx400)
new_esEs8(EQ, LT) → False
new_esEs8(LT, EQ) → False
new_primEqInt(Pos(Zero), Pos(Succ(vwx4000))) → False
new_primEqInt(Pos(Succ(vwx3000)), Pos(Zero)) → False
new_esEs16(Just(vwx300), Just(vwx400), app(app(app(ty_@3, daa), dab), dac)) → new_esEs6(vwx300, vwx400, daa, dab, dac)
new_ltEs10(vwx91, vwx101, app(app(ty_@2, bd), be)) → new_ltEs9(vwx91, vwx101, bd, be)
new_ltEs16(vwx9, vwx10) → new_not(new_esEs8(new_compare8(vwx9, vwx10), GT))
new_esEs22(vwx90, vwx100, ty_Integer) → new_esEs13(vwx90, vwx100)
new_esEs7(vwx30, vwx40, app(app(app(ty_@3, bhd), bhe), bhf)) → new_esEs6(vwx30, vwx40, bhd, bhe, bhf)
new_primPlusNat0(Succ(vwx4600), Zero) → Succ(vwx4600)
new_primPlusNat0(Zero, Succ(vwx401000)) → Succ(vwx401000)
new_compare18(Just(vwx30), Just(vwx40), bed) → new_compare26(vwx30, vwx40, new_esEs7(vwx30, vwx40, bed), bed)
new_lt7(vwx90, vwx100) → new_esEs8(new_compare16(vwx90, vwx100), LT)
new_ltEs7(Left(vwx90), Left(vwx100), ty_Float, fa) → new_ltEs15(vwx90, vwx100)
new_esEs23(vwx91, vwx101, ty_@0) → new_esEs17(vwx91, vwx101)
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(vwx900), Zero) → GT
new_ltEs10(vwx91, vwx101, ty_Double) → new_ltEs8(vwx91, vwx101)
new_compare29(vwx90, vwx100, app(ty_[], bdc)) → new_compare(vwx90, vwx100, bdc)
new_primCmpInt(Neg(Zero), Pos(Succ(vwx1000))) → LT
new_ltEs18(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), he, hf, bba) → new_pePe(new_lt20(vwx90, vwx100, he), new_asAs(new_esEs24(vwx90, vwx100, he), new_pePe(new_lt19(vwx91, vwx101, hf), new_asAs(new_esEs23(vwx91, vwx101, hf), new_ltEs19(vwx92, vwx102, bba)))))
new_esEs16(Just(vwx300), Just(vwx400), app(app(ty_Either, dba), dbb)) → new_esEs5(vwx300, vwx400, dba, dbb)
new_esEs20(vwx301, vwx401, app(app(ty_Either, cca), ccb)) → new_esEs5(vwx301, vwx401, cca, ccb)
new_compare210(vwx90, vwx100, True, dd, de, df) → EQ
new_compare14(vwx90, vwx100, False, dd, de, df) → GT
new_sr0(Integer(vwx900), Integer(vwx1010)) → Integer(new_primMulInt(vwx900, vwx1010))
new_esEs5(Left(vwx300), Left(vwx400), app(ty_Ratio, bfb), bfa) → new_esEs11(vwx300, vwx400, bfb)
new_lt8(vwx90, vwx100, ty_Char) → new_lt14(vwx90, vwx100)
new_compare28(vwx90, vwx100, True, cf, cg) → EQ
new_primEqInt(Neg(Succ(vwx3000)), Pos(vwx400)) → False
new_primEqInt(Pos(Succ(vwx3000)), Neg(vwx400)) → False
new_esEs21(vwx300, vwx400, app(ty_Maybe, cda)) → new_esEs16(vwx300, vwx400, cda)
new_esEs28(vwx300, vwx400, app(app(ty_Either, che), chf)) → new_esEs5(vwx300, vwx400, che, chf)
new_esEs24(vwx90, vwx100, app(app(ty_@2, bcc), bcd)) → new_esEs4(vwx90, vwx100, bcc, bcd)
new_compare(:(vwx90, vwx91), :(vwx100, vwx101), ba) → new_primCompAux0(vwx90, vwx100, new_compare(vwx91, vwx101, ba), ba)
new_compare25(vwx90, vwx100, False) → new_compare15(vwx90, vwx100, new_ltEs6(vwx90, vwx100))
new_ltEs20(vwx9, vwx10, ty_Float) → new_ltEs15(vwx9, vwx10)
new_esEs27(vwx301, vwx401, app(ty_Ratio, cff)) → new_esEs11(vwx301, vwx401, cff)
new_esEs26(vwx300, vwx400, ty_Int) → new_esEs9(vwx300, vwx400)
new_esEs16(Just(vwx300), Just(vwx400), app(ty_[], dah)) → new_esEs18(vwx300, vwx400, dah)
new_primEqInt(Neg(Zero), Pos(Succ(vwx4000))) → False
new_primEqInt(Pos(Zero), Neg(Succ(vwx4000))) → False
new_ltEs19(vwx92, vwx102, app(app(ty_@2, hh), baa)) → new_ltEs9(vwx92, vwx102, hh, baa)
new_esEs5(Left(vwx300), Left(vwx400), app(app(ty_@2, bfc), bfd), bfa) → new_esEs4(vwx300, vwx400, bfc, bfd)
new_primCmpInt(Pos(Zero), Pos(Succ(vwx1000))) → new_primCmpNat0(Zero, Succ(vwx1000))
new_primCompAux00(vwx50, EQ) → vwx50
new_compare24(vwx90, vwx100, True) → EQ
new_lt8(vwx90, vwx100, ty_Ordering) → new_lt17(vwx90, vwx100)
new_ltEs10(vwx91, vwx101, app(app(ty_Either, bg), bh)) → new_ltEs7(vwx91, vwx101, bg, bh)
new_esEs20(vwx301, vwx401, ty_Bool) → new_esEs10(vwx301, vwx401)
new_esEs8(GT, EQ) → False
new_esEs8(EQ, GT) → False
new_esEs28(vwx300, vwx400, ty_Float) → new_esEs12(vwx300, vwx400)
new_compare26(vwx9, vwx10, True, ceh) → EQ
new_esEs6(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), bhd, bhe, bhf) → new_asAs(new_esEs21(vwx300, vwx400, bhd), new_asAs(new_esEs20(vwx301, vwx401, bhe), new_esEs19(vwx302, vwx402, bhf)))
new_ltEs13(Just(vwx90), Just(vwx100), app(app(app(ty_@3, ee), ef), eg)) → new_ltEs18(vwx90, vwx100, ee, ef, eg)
new_not(False) → True
new_lt8(vwx90, vwx100, ty_Integer) → new_lt5(vwx90, vwx100)
new_lt20(vwx90, vwx100, app(ty_[], bcb)) → new_lt11(vwx90, vwx100, bcb)
new_lt20(vwx90, vwx100, ty_Bool) → new_lt15(vwx90, vwx100)
new_primCmpInt(Pos(Succ(vwx900)), Pos(vwx100)) → new_primCmpNat0(Succ(vwx900), vwx100)
new_esEs29(vwx300, vwx400, app(ty_Maybe, dca)) → new_esEs16(vwx300, vwx400, dca)
new_ltEs10(vwx91, vwx101, app(ty_Maybe, bf)) → new_ltEs13(vwx91, vwx101, bf)
new_ltEs19(vwx92, vwx102, app(ty_[], hg)) → new_ltEs12(vwx92, vwx102, hg)
new_ltEs7(Right(vwx90), Right(vwx100), gc, app(app(app(ty_@3, hb), hc), hd)) → new_ltEs18(vwx90, vwx100, hb, hc, hd)
new_compare23(vwx90, vwx100, False, db, dc) → new_compare10(vwx90, vwx100, new_ltEs7(vwx90, vwx100, db, dc), db, dc)
new_esEs20(vwx301, vwx401, app(ty_Maybe, cbg)) → new_esEs16(vwx301, vwx401, cbg)
new_lt19(vwx91, vwx101, ty_Float) → new_lt7(vwx91, vwx101)
new_lt20(vwx90, vwx100, app(app(ty_Either, bcf), bcg)) → new_lt16(vwx90, vwx100, bcf, bcg)
new_ltEs7(Right(vwx90), Right(vwx100), gc, app(ty_[], gd)) → new_ltEs12(vwx90, vwx100, gd)
new_ltEs7(Right(vwx90), Right(vwx100), gc, app(ty_Maybe, gg)) → new_ltEs13(vwx90, vwx100, gg)
new_esEs23(vwx91, vwx101, app(ty_Ratio, cef)) → new_esEs11(vwx91, vwx101, cef)
new_ltEs9(@2(vwx90, vwx91), @2(vwx100, vwx101), bb, ce) → new_pePe(new_lt8(vwx90, vwx100, bb), new_asAs(new_esEs22(vwx90, vwx100, bb), new_ltEs10(vwx91, vwx101, ce)))
new_esEs27(vwx301, vwx401, app(ty_[], cgb)) → new_esEs18(vwx301, vwx401, cgb)
new_ltEs8(vwx9, vwx10) → new_not(new_esEs8(new_compare9(vwx9, vwx10), GT))
new_esEs16(Just(vwx300), Just(vwx400), app(ty_Maybe, dag)) → new_esEs16(vwx300, vwx400, dag)
new_ltEs13(Just(vwx90), Just(vwx100), ty_Float) → new_ltEs15(vwx90, vwx100)
new_esEs19(vwx302, vwx402, ty_Float) → new_esEs12(vwx302, vwx402)
new_esEs20(vwx301, vwx401, app(ty_Ratio, cbd)) → new_esEs11(vwx301, vwx401, cbd)
new_primCmpInt(Pos(Succ(vwx900)), Neg(vwx100)) → GT
new_ltEs7(Right(vwx90), Right(vwx100), gc, ty_Double) → new_ltEs8(vwx90, vwx100)
new_esEs5(Right(vwx300), Right(vwx400), bga, app(ty_Ratio, bge)) → new_esEs11(vwx300, vwx400, bge)
new_primMulInt(Pos(vwx3010), Pos(vwx4010)) → Pos(new_primMulNat0(vwx3010, vwx4010))
new_esEs21(vwx300, vwx400, app(app(ty_@2, ccg), cch)) → new_esEs4(vwx300, vwx400, ccg, cch)
new_ltEs10(vwx91, vwx101, app(app(app(ty_@3, ca), cb), cc)) → new_ltEs18(vwx91, vwx101, ca, cb, cc)
new_esEs5(Left(vwx300), Left(vwx400), ty_@0, bfa) → new_esEs17(vwx300, vwx400)
new_esEs10(True, True) → True
new_compare28(vwx90, vwx100, False, cf, cg) → new_compare110(vwx90, vwx100, new_ltEs9(vwx90, vwx100, cf, cg), cf, cg)
new_esEs5(Left(vwx300), Left(vwx400), app(ty_Maybe, bfe), bfa) → new_esEs16(vwx300, vwx400, bfe)
new_esEs5(Right(vwx300), Left(vwx400), bga, bfa) → False
new_esEs5(Left(vwx300), Right(vwx400), bga, bfa) → False
new_primMulInt(Neg(vwx3010), Neg(vwx4010)) → Pos(new_primMulNat0(vwx3010, vwx4010))
new_lt8(vwx90, vwx100, app(app(ty_@2, cf), cg)) → new_lt12(vwx90, vwx100, cf, cg)
new_esEs5(Right(vwx300), Right(vwx400), bga, ty_Ordering) → new_esEs8(vwx300, vwx400)
new_esEs29(vwx300, vwx400, ty_Char) → new_esEs15(vwx300, vwx400)
new_primEqNat0(Succ(vwx3000), Zero) → False
new_primEqNat0(Zero, Succ(vwx4000)) → False
new_esEs21(vwx300, vwx400, ty_Int) → new_esEs9(vwx300, vwx400)
new_ltEs12(vwx9, vwx10, ba) → new_not(new_esEs8(new_compare(vwx9, vwx10, ba), GT))
new_lt20(vwx90, vwx100, app(app(ty_@2, bcc), bcd)) → new_lt12(vwx90, vwx100, bcc, bcd)
new_primPlusNat0(Zero, Zero) → Zero
new_ltEs7(Left(vwx90), Left(vwx100), app(app(ty_Either, ff), fg), fa) → new_ltEs7(vwx90, vwx100, ff, fg)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs22(vwx90, vwx100, ty_Double) → new_esEs14(vwx90, vwx100)
new_esEs28(vwx300, vwx400, app(app(app(ty_@3, cge), cgf), cgg)) → new_esEs6(vwx300, vwx400, cge, cgf, cgg)
new_lt19(vwx91, vwx101, app(ty_[], bah)) → new_lt11(vwx91, vwx101, bah)
new_esEs5(Left(vwx300), Left(vwx400), app(ty_[], bff), bfa) → new_esEs18(vwx300, vwx400, bff)
new_esEs27(vwx301, vwx401, app(app(app(ty_@3, cfc), cfd), cfe)) → new_esEs6(vwx301, vwx401, cfc, cfd, cfe)
new_ltEs7(Left(vwx90), Left(vwx100), ty_Bool, fa) → new_ltEs6(vwx90, vwx100)
new_ltEs13(Just(vwx90), Just(vwx100), app(app(ty_Either, ec), ed)) → new_ltEs7(vwx90, vwx100, ec, ed)
new_lt11(vwx90, vwx100, cd) → new_esEs8(new_compare(vwx90, vwx100, cd), LT)
new_esEs22(vwx90, vwx100, ty_Int) → new_esEs9(vwx90, vwx100)
new_lt4(vwx90, vwx100) → new_esEs8(new_compare9(vwx90, vwx100), LT)
new_compare29(vwx90, vwx100, app(app(ty_Either, bdg), bdh)) → new_compare30(vwx90, vwx100, bdg, bdh)
new_lt20(vwx90, vwx100, ty_Char) → new_lt14(vwx90, vwx100)
new_primPlusNat1(Succ(vwx460), vwx40100) → Succ(Succ(new_primPlusNat0(vwx460, vwx40100)))
new_compare18(Nothing, Nothing, bed) → EQ
new_esEs24(vwx90, vwx100, ty_Int) → new_esEs9(vwx90, vwx100)
new_primCmpInt(Neg(Zero), Neg(Succ(vwx1000))) → new_primCmpNat0(Succ(vwx1000), Zero)
new_compare23(vwx90, vwx100, True, db, dc) → EQ
new_primCmpInt(Pos(Zero), Neg(Succ(vwx1000))) → GT
new_ltEs10(vwx91, vwx101, ty_Char) → new_ltEs5(vwx91, vwx101)
new_ltEs13(Just(vwx90), Just(vwx100), ty_Int) → new_ltEs4(vwx90, vwx100)
new_esEs5(Left(vwx300), Left(vwx400), ty_Integer, bfa) → new_esEs13(vwx300, vwx400)
new_ltEs7(Left(vwx90), Left(vwx100), ty_Integer, fa) → new_ltEs14(vwx90, vwx100)
new_esEs5(Right(vwx300), Right(vwx400), bga, ty_Double) → new_esEs14(vwx300, vwx400)
new_esEs27(vwx301, vwx401, ty_@0) → new_esEs17(vwx301, vwx401)
new_esEs27(vwx301, vwx401, ty_Int) → new_esEs9(vwx301, vwx401)
new_ltEs19(vwx92, vwx102, ty_Double) → new_ltEs8(vwx92, vwx102)
new_esEs19(vwx302, vwx402, ty_Double) → new_esEs14(vwx302, vwx402)
new_esEs21(vwx300, vwx400, ty_Float) → new_esEs12(vwx300, vwx400)
new_lt20(vwx90, vwx100, ty_Float) → new_lt7(vwx90, vwx100)
new_ltEs7(Right(vwx90), Right(vwx100), gc, ty_Integer) → new_ltEs14(vwx90, vwx100)
new_ltEs20(vwx9, vwx10, ty_Ordering) → new_ltEs17(vwx9, vwx10)
new_ltEs13(Just(vwx90), Just(vwx100), app(ty_Maybe, eb)) → new_ltEs13(vwx90, vwx100, eb)
new_compare30(vwx90, vwx100, db, dc) → new_compare23(vwx90, vwx100, new_esEs5(vwx90, vwx100, db, dc), db, dc)
new_ltEs13(Just(vwx90), Just(vwx100), ty_Double) → new_ltEs8(vwx90, vwx100)
new_esEs28(vwx300, vwx400, app(ty_[], chd)) → new_esEs18(vwx300, vwx400, chd)
new_esEs29(vwx300, vwx400, ty_Bool) → new_esEs10(vwx300, vwx400)
new_ltEs13(Just(vwx90), Nothing, cfb) → False
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_ltEs7(Left(vwx90), Left(vwx100), ty_Ordering, fa) → new_ltEs17(vwx90, vwx100)
new_esEs5(Left(vwx300), Left(vwx400), ty_Bool, bfa) → new_esEs10(vwx300, vwx400)
new_esEs20(vwx301, vwx401, ty_Float) → new_esEs12(vwx301, vwx401)
new_ltEs7(Right(vwx90), Right(vwx100), gc, app(app(ty_Either, gh), ha)) → new_ltEs7(vwx90, vwx100, gh, ha)
new_esEs28(vwx300, vwx400, app(app(ty_@2, cha), chb)) → new_esEs4(vwx300, vwx400, cha, chb)
new_ltEs13(Just(vwx90), Just(vwx100), app(ty_Ratio, dce)) → new_ltEs11(vwx90, vwx100, dce)
new_lt12(vwx90, vwx100, cf, cg) → new_esEs8(new_compare27(vwx90, vwx100, cf, cg), LT)
new_asAs(False, vwx37) → False
new_esEs5(Left(vwx300), Left(vwx400), ty_Float, bfa) → new_esEs12(vwx300, vwx400)
new_primMulInt(Pos(vwx3010), Neg(vwx4010)) → Neg(new_primMulNat0(vwx3010, vwx4010))
new_primMulInt(Neg(vwx3010), Pos(vwx4010)) → Neg(new_primMulNat0(vwx3010, vwx4010))
new_esEs22(vwx90, vwx100, ty_Float) → new_esEs12(vwx90, vwx100)
new_primMulNat0(Succ(vwx30100), Zero) → Zero
new_primMulNat0(Zero, Succ(vwx40100)) → Zero
new_esEs21(vwx300, vwx400, app(app(ty_Either, cdc), cdd)) → new_esEs5(vwx300, vwx400, cdc, cdd)
new_esEs18([], [], cec) → True
new_esEs26(vwx300, vwx400, ty_Integer) → new_esEs13(vwx300, vwx400)
new_esEs23(vwx91, vwx101, app(app(app(ty_@3, bbg), bbh), bca)) → new_esEs6(vwx91, vwx101, bbg, bbh, bca)
new_esEs28(vwx300, vwx400, app(ty_Maybe, chc)) → new_esEs16(vwx300, vwx400, chc)
new_esEs21(vwx300, vwx400, ty_Ordering) → new_esEs8(vwx300, vwx400)
new_esEs5(Left(vwx300), Left(vwx400), app(app(app(ty_@3, bef), beg), beh), bfa) → new_esEs6(vwx300, vwx400, bef, beg, beh)
new_compare19(:%(vwx90, vwx91), :%(vwx100, vwx101), ty_Integer) → new_compare13(new_sr0(vwx90, vwx101), new_sr0(vwx100, vwx91))
new_ltEs20(vwx9, vwx10, ty_Bool) → new_ltEs6(vwx9, vwx10)
new_esEs23(vwx91, vwx101, ty_Int) → new_esEs9(vwx91, vwx101)
new_lt19(vwx91, vwx101, app(app(app(ty_@3, bbg), bbh), bca)) → new_lt18(vwx91, vwx101, bbg, bbh, bca)
new_esEs5(Right(vwx300), Right(vwx400), bga, ty_Integer) → new_esEs13(vwx300, vwx400)
new_lt15(vwx90, vwx100) → new_esEs8(new_compare17(vwx90, vwx100), LT)
new_compare24(vwx90, vwx100, False) → new_compare111(vwx90, vwx100, new_ltEs17(vwx90, vwx100))
new_esEs25(vwx301, vwx401, ty_Integer) → new_esEs13(vwx301, vwx401)
new_esEs16(Just(vwx300), Just(vwx400), app(app(ty_@2, dae), daf)) → new_esEs4(vwx300, vwx400, dae, daf)
new_ltEs13(Just(vwx90), Just(vwx100), app(ty_[], dg)) → new_ltEs12(vwx90, vwx100, dg)
new_ltEs20(vwx9, vwx10, app(app(app(ty_@3, he), hf), bba)) → new_ltEs18(vwx9, vwx10, he, hf, bba)
new_lt8(vwx90, vwx100, ty_Double) → new_lt4(vwx90, vwx100)
new_esEs7(vwx30, vwx40, ty_Bool) → new_esEs10(vwx30, vwx40)
new_esEs28(vwx300, vwx400, ty_Integer) → new_esEs13(vwx300, vwx400)
new_esEs20(vwx301, vwx401, app(app(ty_@2, cbe), cbf)) → new_esEs4(vwx301, vwx401, cbe, cbf)
new_esEs7(vwx30, vwx40, ty_Double) → new_esEs14(vwx30, vwx40)
new_lt8(vwx90, vwx100, app(ty_Maybe, da)) → new_lt13(vwx90, vwx100, da)
new_esEs23(vwx91, vwx101, ty_Bool) → new_esEs10(vwx91, vwx101)
new_ltEs17(GT, GT) → True
new_esEs7(vwx30, vwx40, app(app(ty_@2, cdh), cea)) → new_esEs4(vwx30, vwx40, cdh, cea)
new_ltEs13(Just(vwx90), Just(vwx100), ty_Ordering) → new_ltEs17(vwx90, vwx100)
new_lt19(vwx91, vwx101, ty_Bool) → new_lt15(vwx91, vwx101)
new_ltEs7(Right(vwx90), Right(vwx100), gc, ty_Ordering) → new_ltEs17(vwx90, vwx100)
new_ltEs17(GT, EQ) → False
new_ltEs4(vwx9, vwx10) → new_not(new_esEs8(new_compare6(vwx9, vwx10), GT))
new_lt19(vwx91, vwx101, ty_Int) → new_lt9(vwx91, vwx101)
new_ltEs20(vwx9, vwx10, app(app(ty_Either, gc), fa)) → new_ltEs7(vwx9, vwx10, gc, fa)
new_esEs27(vwx301, vwx401, app(app(ty_@2, cfg), cfh)) → new_esEs4(vwx301, vwx401, cfg, cfh)
new_ltEs7(Left(vwx90), Left(vwx100), app(ty_[], eh), fa) → new_ltEs12(vwx90, vwx100, eh)
new_lt20(vwx90, vwx100, ty_Integer) → new_lt5(vwx90, vwx100)
new_ltEs19(vwx92, vwx102, app(ty_Maybe, bab)) → new_ltEs13(vwx92, vwx102, bab)
new_esEs19(vwx302, vwx402, ty_Char) → new_esEs15(vwx302, vwx402)
new_ltEs20(vwx9, vwx10, ty_Double) → new_ltEs8(vwx9, vwx10)
new_compare13(Integer(vwx90), Integer(vwx100)) → new_primCmpInt(vwx90, vwx100)
new_lt8(vwx90, vwx100, ty_Float) → new_lt7(vwx90, vwx100)
new_lt10(vwx90, vwx100, cdf) → new_esEs8(new_compare19(vwx90, vwx100, cdf), LT)
new_esEs5(Left(vwx300), Left(vwx400), app(app(ty_Either, bfg), bfh), bfa) → new_esEs5(vwx300, vwx400, bfg, bfh)
new_ltEs10(vwx91, vwx101, app(ty_Ratio, cde)) → new_ltEs11(vwx91, vwx101, cde)
new_esEs29(vwx300, vwx400, app(app(app(ty_@3, dbc), dbd), dbe)) → new_esEs6(vwx300, vwx400, dbc, dbd, dbe)
new_ltEs10(vwx91, vwx101, ty_Bool) → new_ltEs6(vwx91, vwx101)
new_ltEs13(Just(vwx90), Just(vwx100), ty_Char) → new_ltEs5(vwx90, vwx100)
new_esEs28(vwx300, vwx400, ty_Int) → new_esEs9(vwx300, vwx400)
new_esEs16(Nothing, Just(vwx400), ceb) → False
new_esEs16(Just(vwx300), Nothing, ceb) → False
new_esEs28(vwx300, vwx400, ty_Bool) → new_esEs10(vwx300, vwx400)
new_esEs28(vwx300, vwx400, app(ty_Ratio, cgh)) → new_esEs11(vwx300, vwx400, cgh)
new_lt9(vwx90, vwx100) → new_esEs8(new_compare6(vwx90, vwx100), LT)
new_lt19(vwx91, vwx101, ty_@0) → new_lt6(vwx91, vwx101)
new_primPlusNat0(Succ(vwx4600), Succ(vwx401000)) → Succ(Succ(new_primPlusNat0(vwx4600, vwx401000)))
new_ltEs10(vwx91, vwx101, ty_@0) → new_ltEs16(vwx91, vwx101)
new_ltEs10(vwx91, vwx101, ty_Ordering) → new_ltEs17(vwx91, vwx101)
new_esEs29(vwx300, vwx400, app(ty_[], dcb)) → new_esEs18(vwx300, vwx400, dcb)
new_esEs19(vwx302, vwx402, ty_@0) → new_esEs17(vwx302, vwx402)
new_esEs21(vwx300, vwx400, app(app(app(ty_@3, ccc), ccd), cce)) → new_esEs6(vwx300, vwx400, ccc, ccd, cce)
new_ltEs7(Left(vwx90), Left(vwx100), ty_Int, fa) → new_ltEs4(vwx90, vwx100)
new_lt13(vwx90, vwx100, da) → new_esEs8(new_compare18(vwx90, vwx100, da), LT)
new_asAs(True, vwx37) → vwx37
new_lt19(vwx91, vwx101, app(ty_Maybe, bbd)) → new_lt13(vwx91, vwx101, bbd)
new_esEs16(Just(vwx300), Just(vwx400), app(ty_Ratio, dad)) → new_esEs11(vwx300, vwx400, dad)
new_esEs22(vwx90, vwx100, app(ty_Maybe, da)) → new_esEs16(vwx90, vwx100, da)
new_ltEs17(LT, EQ) → True
new_ltEs15(vwx9, vwx10) → new_not(new_esEs8(new_compare16(vwx9, vwx10), GT))
new_esEs10(False, True) → False
new_esEs10(True, False) → False
new_lt20(vwx90, vwx100, app(ty_Ratio, ceg)) → new_lt10(vwx90, vwx100, ceg)
new_esEs16(Just(vwx300), Just(vwx400), ty_Char) → new_esEs15(vwx300, vwx400)
new_esEs29(vwx300, vwx400, ty_Float) → new_esEs12(vwx300, vwx400)
new_esEs29(vwx300, vwx400, app(ty_Ratio, dbf)) → new_esEs11(vwx300, vwx400, dbf)
new_compare8(@0, @0) → EQ
new_compare29(vwx90, vwx100, ty_@0) → new_compare8(vwx90, vwx100)
new_ltEs19(vwx92, vwx102, ty_Char) → new_ltEs5(vwx92, vwx102)
new_ltEs7(Left(vwx90), Left(vwx100), ty_Double, fa) → new_ltEs8(vwx90, vwx100)
new_ltEs7(Right(vwx90), Right(vwx100), gc, ty_Float) → new_ltEs15(vwx90, vwx100)
new_lt20(vwx90, vwx100, ty_Int) → new_lt9(vwx90, vwx100)
new_esEs19(vwx302, vwx402, ty_Ordering) → new_esEs8(vwx302, vwx402)
new_ltEs6(False, False) → True
new_esEs9(vwx30, vwx40) → new_primEqInt(vwx30, vwx40)
new_esEs7(vwx30, vwx40, app(ty_Ratio, cdg)) → new_esEs11(vwx30, vwx40, cdg)
new_lt20(vwx90, vwx100, ty_Double) → new_lt4(vwx90, vwx100)
new_esEs21(vwx300, vwx400, ty_Bool) → new_esEs10(vwx300, vwx400)
new_lt16(vwx90, vwx100, db, dc) → new_esEs8(new_compare30(vwx90, vwx100, db, dc), LT)
new_ltEs17(EQ, GT) → True
new_esEs23(vwx91, vwx101, app(ty_[], bah)) → new_esEs18(vwx91, vwx101, bah)
new_esEs5(Right(vwx300), Right(vwx400), bga, ty_Float) → new_esEs12(vwx300, vwx400)
new_lt14(vwx90, vwx100) → new_esEs8(new_compare7(vwx90, vwx100), LT)
new_esEs22(vwx90, vwx100, app(app(ty_Either, db), dc)) → new_esEs5(vwx90, vwx100, db, dc)
new_primCompAux00(vwx50, GT) → GT
new_compare29(vwx90, vwx100, ty_Ordering) → new_compare12(vwx90, vwx100)
new_ltEs19(vwx92, vwx102, ty_Int) → new_ltEs4(vwx92, vwx102)
new_esEs21(vwx300, vwx400, app(ty_Ratio, ccf)) → new_esEs11(vwx300, vwx400, ccf)
new_esEs7(vwx30, vwx40, app(ty_[], cec)) → new_esEs18(vwx30, vwx40, cec)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_lt8(vwx90, vwx100, app(app(ty_Either, db), dc)) → new_lt16(vwx90, vwx100, db, dc)
new_esEs29(vwx300, vwx400, ty_Ordering) → new_esEs8(vwx300, vwx400)
new_esEs19(vwx302, vwx402, app(app(ty_@2, cac), cad)) → new_esEs4(vwx302, vwx402, cac, cad)
new_ltEs19(vwx92, vwx102, ty_@0) → new_ltEs16(vwx92, vwx102)
new_esEs16(Just(vwx300), Just(vwx400), ty_Float) → new_esEs12(vwx300, vwx400)
new_esEs22(vwx90, vwx100, app(ty_Ratio, cdf)) → new_esEs11(vwx90, vwx100, cdf)
new_ltEs7(Right(vwx90), Right(vwx100), gc, ty_Bool) → new_ltEs6(vwx90, vwx100)
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primCmpInt(Neg(Succ(vwx900)), Pos(vwx100)) → LT
new_esEs16(Just(vwx300), Just(vwx400), ty_Int) → new_esEs9(vwx300, vwx400)
new_esEs7(vwx30, vwx40, ty_Float) → new_esEs12(vwx30, vwx40)
new_esEs24(vwx90, vwx100, ty_Double) → new_esEs14(vwx90, vwx100)
new_not(True) → False
new_compare16(Float(vwx90, vwx91), Float(vwx100, vwx101)) → new_compare6(new_sr(vwx90, vwx100), new_sr(vwx91, vwx101))

The set Q consists of the following terms:

new_esEs23(x0, x1, app(ty_Maybe, x2))
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_esEs5(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs7(x0, x1, app(ty_[], x2))
new_ltEs15(x0, x1)
new_esEs24(x0, x1, ty_Double)
new_primPlusNat1(Zero, x0)
new_lt6(x0, x1)
new_esEs7(x0, x1, ty_Integer)
new_ltEs19(x0, x1, ty_Integer)
new_ltEs7(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs5(Left(x0), Left(x1), ty_Bool, x2)
new_lt20(x0, x1, app(ty_[], x2))
new_ltEs7(Right(x0), Right(x1), x2, ty_Float)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs18([], [], x0)
new_ltEs17(EQ, GT)
new_ltEs4(x0, x1)
new_ltEs17(GT, EQ)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt15(x0, x1)
new_esEs5(Right(x0), Right(x1), x2, ty_Float)
new_compare10(x0, x1, False, x2, x3)
new_compare13(Integer(x0), Integer(x1))
new_compare26(x0, x1, True, x2)
new_ltEs20(x0, x1, ty_Char)
new_lt8(x0, x1, app(app(ty_Either, x2), x3))
new_esEs5(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs5(Right(x0), Right(x1), x2, ty_Int)
new_ltEs10(x0, x1, ty_Float)
new_ltEs18(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_ltEs20(x0, x1, ty_Float)
new_esEs19(x0, x1, ty_Float)
new_esEs27(x0, x1, ty_@0)
new_esEs20(x0, x1, ty_Char)
new_esEs5(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs5(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs8(GT, GT)
new_lt12(x0, x1, x2, x3)
new_esEs5(Left(x0), Left(x1), ty_Int, x2)
new_esEs19(x0, x1, app(ty_Ratio, x2))
new_esEs29(x0, x1, ty_Double)
new_esEs4(@2(x0, x1), @2(x2, x3), x4, x5)
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs10(x0, x1, ty_Bool)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_esEs21(x0, x1, ty_Double)
new_esEs21(x0, x1, ty_Int)
new_esEs6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_compare28(x0, x1, True, x2, x3)
new_esEs8(LT, LT)
new_ltEs10(x0, x1, ty_Int)
new_compare25(x0, x1, True)
new_esEs28(x0, x1, ty_Double)
new_lt8(x0, x1, ty_@0)
new_ltEs19(x0, x1, ty_Bool)
new_compare23(x0, x1, True, x2, x3)
new_esEs18(:(x0, x1), [], x2)
new_esEs14(Double(x0, x1), Double(x2, x3))
new_ltEs6(True, True)
new_esEs29(x0, x1, ty_Float)
new_esEs28(x0, x1, ty_Bool)
new_esEs23(x0, x1, ty_Float)
new_compare26(x0, x1, False, x2)
new_primMulInt(Pos(x0), Pos(x1))
new_compare8(@0, @0)
new_esEs27(x0, x1, ty_Int)
new_esEs16(Just(x0), Nothing, x1)
new_ltEs10(x0, x1, app(ty_[], x2))
new_compare31(x0, x1, x2, x3, x4)
new_compare24(x0, x1, True)
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, ty_Integer)
new_ltEs7(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs29(x0, x1, ty_Int)
new_esEs8(GT, LT)
new_esEs8(LT, GT)
new_esEs16(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs7(x0, x1, ty_Int)
new_compare111(x0, x1, False)
new_esEs16(Nothing, Just(x0), x1)
new_ltEs20(x0, x1, ty_Int)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_esEs5(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs24(x0, x1, ty_Ordering)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt16(x0, x1, x2, x3)
new_lt14(x0, x1)
new_esEs21(x0, x1, ty_Char)
new_esEs19(x0, x1, app(app(ty_Either, x2), x3))
new_compare210(x0, x1, False, x2, x3, x4)
new_primEqNat0(Zero, Zero)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_esEs27(x0, x1, ty_Integer)
new_esEs22(x0, x1, ty_@0)
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs22(x0, x1, ty_Char)
new_compare18(Just(x0), Just(x1), x2)
new_ltEs7(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_ltEs11(x0, x1, x2)
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_compare110(x0, x1, True, x2, x3)
new_ltEs13(Just(x0), Just(x1), ty_Bool)
new_esEs27(x0, x1, ty_Char)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs25(x0, x1, ty_Integer)
new_ltEs7(Left(x0), Left(x1), ty_Double, x2)
new_esEs26(x0, x1, ty_Integer)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_esEs5(Left(x0), Left(x1), ty_Char, x2)
new_sr0(Integer(x0), Integer(x1))
new_lt20(x0, x1, ty_Char)
new_compare23(x0, x1, False, x2, x3)
new_lt20(x0, x1, ty_Double)
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_esEs16(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_compare27(x0, x1, x2, x3)
new_primMulNat0(Zero, Zero)
new_esEs16(Just(x0), Just(x1), ty_Ordering)
new_esEs24(x0, x1, ty_Float)
new_esEs16(Just(x0), Just(x1), ty_Char)
new_ltEs13(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs10(False, True)
new_esEs10(True, False)
new_compare6(x0, x1)
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_compare25(x0, x1, False)
new_ltEs13(Just(x0), Just(x1), ty_Int)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs5(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs16(Nothing, Nothing, x0)
new_esEs16(Just(x0), Just(x1), ty_Int)
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_lt7(x0, x1)
new_compare29(x0, x1, ty_Int)
new_compare29(x0, x1, ty_Bool)
new_ltEs20(x0, x1, ty_Integer)
new_lt5(x0, x1)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs16(Just(x0), Just(x1), ty_Float)
new_esEs24(x0, x1, ty_Integer)
new_esEs15(Char(x0), Char(x1))
new_ltEs7(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs29(x0, x1, ty_Ordering)
new_lt8(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs19(x0, x1, ty_Double)
new_lt8(x0, x1, ty_Int)
new_esEs5(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs29(x0, x1, ty_Integer)
new_ltEs10(x0, x1, app(app(ty_@2, x2), x3))
new_esEs28(x0, x1, ty_Int)
new_lt20(x0, x1, ty_Bool)
new_esEs16(Just(x0), Just(x1), app(ty_[], x2))
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_lt8(x0, x1, app(ty_Maybe, x2))
new_compare11(x0, x1, False, x2)
new_esEs23(x0, x1, ty_Double)
new_compare111(x0, x1, True)
new_lt20(x0, x1, ty_Float)
new_esEs23(x0, x1, ty_@0)
new_primCompAux0(x0, x1, x2, x3)
new_ltEs10(x0, x1, app(ty_Ratio, x2))
new_primMulInt(Neg(x0), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_compare([], :(x0, x1), x2)
new_esEs27(x0, x1, app(ty_[], x2))
new_lt19(x0, x1, ty_Bool)
new_compare19(:%(x0, x1), :%(x2, x3), ty_Integer)
new_esEs21(x0, x1, ty_Float)
new_esEs20(x0, x1, ty_@0)
new_esEs20(x0, x1, ty_Ordering)
new_ltEs9(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs20(x0, x1, ty_Double)
new_ltEs7(Right(x0), Right(x1), x2, ty_Double)
new_esEs7(x0, x1, ty_Double)
new_compare29(x0, x1, app(app(ty_Either, x2), x3))
new_compare30(x0, x1, x2, x3)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs20(x0, x1, ty_Int)
new_ltEs7(Left(x0), Left(x1), ty_Float, x2)
new_ltEs7(Left(x0), Left(x1), ty_Integer, x2)
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_ltEs10(x0, x1, ty_@0)
new_esEs19(x0, x1, ty_Bool)
new_primPlusNat0(Succ(x0), Succ(x1))
new_esEs21(x0, x1, ty_@0)
new_ltEs13(Just(x0), Just(x1), ty_Integer)
new_esEs20(x0, x1, app(ty_[], x2))
new_ltEs5(x0, x1)
new_esEs20(x0, x1, ty_Bool)
new_ltEs10(x0, x1, ty_Char)
new_primEqNat0(Succ(x0), Zero)
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_compare18(Nothing, Nothing, x0)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_primPlusNat0(Zero, Zero)
new_esEs16(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs16(Just(x0), Just(x1), ty_Bool)
new_esEs10(True, True)
new_esEs21(x0, x1, ty_Integer)
new_esEs28(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, ty_Ordering)
new_primCmpNat0(Succ(x0), Zero)
new_ltEs20(x0, x1, ty_Ordering)
new_esEs28(x0, x1, ty_Char)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_compare17(x0, x1)
new_lt8(x0, x1, app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, ty_Float)
new_esEs5(Left(x0), Right(x1), x2, x3)
new_esEs5(Right(x0), Left(x1), x2, x3)
new_primMulNat0(Succ(x0), Succ(x1))
new_ltEs13(Just(x0), Just(x1), ty_@0)
new_lt20(x0, x1, ty_Int)
new_ltEs7(Right(x0), Right(x1), x2, ty_Char)
new_esEs17(@0, @0)
new_esEs22(x0, x1, ty_Ordering)
new_esEs7(x0, x1, ty_@0)
new_esEs19(x0, x1, ty_Ordering)
new_ltEs6(True, False)
new_ltEs6(False, True)
new_primMulNat0(Zero, Succ(x0))
new_lt10(x0, x1, x2)
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_lt8(x0, x1, ty_Bool)
new_compare28(x0, x1, False, x2, x3)
new_primPlusNat0(Zero, Succ(x0))
new_esEs20(x0, x1, ty_Float)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs10(x0, x1, ty_Integer)
new_primCompAux00(x0, EQ)
new_esEs21(x0, x1, ty_Bool)
new_esEs22(x0, x1, ty_Float)
new_esEs11(:%(x0, x1), :%(x2, x3), x4)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_ltEs8(x0, x1)
new_asAs(False, x0)
new_lt19(x0, x1, ty_Double)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_ltEs13(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_ltEs13(Just(x0), Just(x1), ty_Ordering)
new_primCmpNat0(Succ(x0), Succ(x1))
new_lt11(x0, x1, x2)
new_ltEs17(GT, GT)
new_ltEs7(Left(x0), Left(x1), ty_Ordering, x2)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_compare11(x0, x1, True, x2)
new_compare29(x0, x1, ty_Ordering)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_esEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt8(x0, x1, app(ty_Ratio, x2))
new_esEs20(x0, x1, ty_Integer)
new_compare29(x0, x1, ty_@0)
new_compare24(x0, x1, False)
new_lt20(x0, x1, ty_Integer)
new_compare29(x0, x1, app(ty_Maybe, x2))
new_primCompAux00(x0, LT)
new_primEqInt(Neg(Zero), Pos(Zero))
new_primEqInt(Pos(Zero), Neg(Zero))
new_ltEs7(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_primPlusNat0(Succ(x0), Zero)
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_pePe(True, x0)
new_esEs21(x0, x1, ty_Ordering)
new_compare29(x0, x1, ty_Float)
new_compare18(Nothing, Just(x0), x1)
new_ltEs7(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_primMulNat0(Succ(x0), Zero)
new_ltEs13(Just(x0), Nothing, x1)
new_esEs12(Float(x0, x1), Float(x2, x3))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_ltEs6(False, False)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_compare29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs16(x0, x1)
new_ltEs7(Left(x0), Left(x1), ty_Bool, x2)
new_ltEs19(x0, x1, ty_Float)
new_esEs5(Right(x0), Right(x1), x2, ty_Bool)
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_esEs7(x0, x1, ty_Ordering)
new_primEqInt(Neg(Zero), Neg(Zero))
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs10(x0, x1, app(ty_Maybe, x2))
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_ltEs7(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs5(Left(x0), Left(x1), ty_@0, x2)
new_ltEs13(Just(x0), Just(x1), app(ty_[], x2))
new_compare29(x0, x1, ty_Integer)
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_primPlusNat1(Succ(x0), x1)
new_esEs23(x0, x1, app(ty_[], x2))
new_ltEs20(x0, x1, ty_Double)
new_compare210(x0, x1, True, x2, x3, x4)
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_lt19(x0, x1, ty_@0)
new_ltEs20(x0, x1, app(ty_[], x2))
new_lt19(x0, x1, ty_Ordering)
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs22(x0, x1, ty_Int)
new_compare29(x0, x1, app(app(ty_@2, x2), x3))
new_esEs16(Just(x0), Just(x1), app(ty_Maybe, x2))
new_ltEs7(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_compare12(x0, x1)
new_esEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs21(x0, x1, app(ty_[], x2))
new_ltEs19(x0, x1, app(ty_[], x2))
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_lt13(x0, x1, x2)
new_lt19(x0, x1, ty_Integer)
new_compare16(Float(x0, x1), Float(x2, x3))
new_esEs24(x0, x1, app(ty_[], x2))
new_esEs7(x0, x1, ty_Char)
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs19(x0, x1, app(ty_[], x2))
new_ltEs10(x0, x1, ty_Ordering)
new_ltEs13(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs28(x0, x1, ty_@0)
new_esEs19(x0, x1, ty_Integer)
new_ltEs20(x0, x1, ty_@0)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_esEs9(x0, x1)
new_ltEs7(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs5(Right(x0), Right(x1), x2, ty_Char)
new_lt8(x0, x1, ty_Integer)
new_ltEs19(x0, x1, ty_@0)
new_asAs(True, x0)
new_ltEs7(Right(x0), Right(x1), x2, ty_Int)
new_esEs5(Left(x0), Left(x1), ty_Double, x2)
new_lt19(x0, x1, ty_Int)
new_esEs16(Just(x0), Just(x1), ty_Integer)
new_primCmpNat0(Zero, Zero)
new_esEs5(Left(x0), Left(x1), ty_Float, x2)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_esEs10(False, False)
new_lt4(x0, x1)
new_compare29(x0, x1, ty_Char)
new_ltEs7(Right(x0), Right(x1), x2, ty_Integer)
new_compare9(Double(x0, x1), Double(x2, x3))
new_ltEs7(Left(x0), Left(x1), ty_@0, x2)
new_ltEs12(x0, x1, x2)
new_esEs7(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs17(LT, GT)
new_ltEs17(GT, LT)
new_esEs16(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_lt17(x0, x1)
new_esEs7(x0, x1, ty_Bool)
new_esEs5(Right(x0), Right(x1), x2, ty_@0)
new_esEs28(x0, x1, ty_Ordering)
new_esEs28(x0, x1, ty_Integer)
new_esEs23(x0, x1, ty_Ordering)
new_lt19(x0, x1, ty_Char)
new_esEs5(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs23(x0, x1, ty_Int)
new_lt18(x0, x1, x2, x3, x4)
new_esEs22(x0, x1, app(ty_[], x2))
new_primEqNat0(Zero, Succ(x0))
new_ltEs7(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs24(x0, x1, ty_Char)
new_esEs29(x0, x1, app(ty_[], x2))
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs27(x0, x1, ty_Bool)
new_compare7(Char(x0), Char(x1))
new_esEs23(x0, x1, ty_Bool)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_lt19(x0, x1, app(ty_Maybe, x2))
new_ltEs13(Nothing, Nothing, x0)
new_esEs16(Just(x0), Just(x1), ty_Double)
new_compare(:(x0, x1), :(x2, x3), x4)
new_compare14(x0, x1, True, x2, x3, x4)
new_ltEs10(x0, x1, ty_Double)
new_esEs19(x0, x1, ty_Int)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_lt19(x0, x1, app(ty_[], x2))
new_ltEs13(Nothing, Just(x0), x1)
new_esEs5(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs18([], :(x0, x1), x2)
new_not(True)
new_ltEs10(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs7(x0, x1, app(app(ty_@2, x2), x3))
new_esEs19(x0, x1, ty_Char)
new_lt8(x0, x1, ty_Float)
new_esEs28(x0, x1, ty_Float)
new_esEs18(:(x0, x1), :(x2, x3), x4)
new_compare29(x0, x1, ty_Double)
new_ltEs7(Left(x0), Left(x1), ty_Char, x2)
new_compare([], [], x0)
new_ltEs7(Right(x0), Right(x1), x2, ty_@0)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_not(False)
new_esEs7(x0, x1, app(ty_Maybe, x2))
new_esEs19(x0, x1, app(ty_Maybe, x2))
new_compare14(x0, x1, False, x2, x3, x4)
new_esEs5(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs13(Integer(x0), Integer(x1))
new_esEs26(x0, x1, ty_Int)
new_ltEs7(Left(x0), Left(x1), app(ty_[], x2), x3)
new_ltEs19(x0, x1, ty_Char)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_ltEs19(x0, x1, ty_Int)
new_primCmpNat0(Zero, Succ(x0))
new_esEs5(Right(x0), Right(x1), x2, ty_Double)
new_esEs5(Right(x0), Right(x1), x2, ty_Integer)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_ltEs7(Right(x0), Right(x1), x2, ty_Ordering)
new_compare29(x0, x1, app(ty_[], x2))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_lt19(x0, x1, app(ty_Ratio, x2))
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs7(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, ty_Double)
new_esEs22(x0, x1, ty_Bool)
new_sr(x0, x1)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_ltEs7(Right(x0), Left(x1), x2, x3)
new_ltEs7(Left(x0), Right(x1), x2, x3)
new_ltEs19(x0, x1, ty_Ordering)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_compare15(x0, x1, False)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_pePe(False, x0)
new_ltEs17(LT, EQ)
new_ltEs17(EQ, LT)
new_ltEs7(Left(x0), Left(x1), ty_Int, x2)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_ltEs13(Just(x0), Just(x1), ty_Char)
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_compare29(x0, x1, app(ty_Ratio, x2))
new_esEs27(x0, x1, ty_Double)
new_ltEs7(Right(x0), Right(x1), x2, ty_Bool)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_esEs16(Just(x0), Just(x1), ty_@0)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_esEs29(x0, x1, ty_Bool)
new_esEs24(x0, x1, ty_Int)
new_lt8(x0, x1, ty_Double)
new_esEs7(x0, x1, app(ty_Ratio, x2))
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs13(Just(x0), Just(x1), ty_Double)
new_ltEs14(x0, x1)
new_lt8(x0, x1, ty_Ordering)
new_esEs5(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_lt20(x0, x1, ty_@0)
new_esEs5(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs19(x0, x1, ty_@0)
new_lt8(x0, x1, app(ty_[], x2))
new_esEs5(Left(x0), Left(x1), ty_Integer, x2)
new_primEqInt(Pos(Zero), Pos(Zero))
new_ltEs7(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_lt8(x0, x1, ty_Char)
new_ltEs13(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_ltEs13(Just(x0), Just(x1), ty_Float)
new_esEs24(x0, x1, ty_Bool)
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_esEs22(x0, x1, ty_Double)
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_esEs5(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_compare19(:%(x0, x1), :%(x2, x3), ty_Int)
new_esEs23(x0, x1, ty_Char)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs5(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_ltEs13(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_esEs29(x0, x1, ty_Char)
new_esEs24(x0, x1, ty_@0)
new_ltEs17(EQ, EQ)
new_esEs7(x0, x1, ty_Float)
new_ltEs17(LT, LT)
new_esEs25(x0, x1, ty_Int)
new_esEs27(x0, x1, ty_Ordering)
new_compare110(x0, x1, False, x2, x3)
new_esEs22(x0, x1, ty_Integer)
new_compare18(Just(x0), Nothing, x1)
new_compare15(x0, x1, True)
new_primCompAux00(x0, GT)
new_ltEs20(x0, x1, ty_Bool)
new_lt9(x0, x1)
new_compare10(x0, x1, True, x2, x3)
new_compare(:(x0, x1), [], x2)
new_lt19(x0, x1, ty_Float)
new_esEs29(x0, x1, ty_@0)
new_ltEs10(x0, x1, app(app(ty_Either, x2), x3))

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: