YES 3.474 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 => Maybe a  ->  Maybe a  ->  Bool) :: Ord a => Maybe a  ->  Maybe 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 => Maybe a  ->  Maybe a  ->  Bool) :: Ord a => Maybe a  ->  Maybe 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 => Maybe a  ->  Maybe a  ->  Bool) :: Ord a => Maybe a  ->  Maybe 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 a => Maybe a  ->  Maybe a  ->  Bool) :: Ord a => Maybe a  ->  Maybe a  ->  Bool)

module Main where
  import qualified Prelude


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

is transformed to
compare x y = compare3 x y

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

compare0 x y True = GT

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

compare3 x y = compare2 x y (x == y)

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

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

gcd'0 x y = gcd' y (x `rem` y)

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

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

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

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

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

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

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

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

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

is transformed to
absReal x = absReal2 x

absReal0 x True = `negate` x

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

absReal2 x = absReal1 x (x >= 0)

The following Function with conditions
undefined 
 | False
 = undefined

is transformed to
undefined  = undefined1

undefined0 True = undefined

undefined1  = undefined0 False

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

is transformed to
reduce x y = reduce2 x y

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



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

mainModule Main
  (((>) :: Ord a => Maybe a  ->  Maybe a  ->  Bool) :: Ord a => Maybe a  ->  Maybe 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' x zx = gcd0Gcd'2 x zx
gcd0Gcd' x y = gcd0Gcd'0 x y

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



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

mainModule Main
  (((>) :: Ord a => Maybe a  ->  Maybe a  ->  Bool) :: Ord a => Maybe a  ->  Maybe a  ->  Bool)

module Main where
  import qualified Prelude


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

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

mainModule Main
  ((>) :: Ord a => Maybe a  ->  Maybe 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(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(vwx4400), Succ(vwx401000)) → new_primPlusNat(vwx4400, 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_esEs(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), ba, bb, app(ty_[], bh)) → new_esEs1(vwx302, vwx402, bh)
new_esEs(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), app(app(ty_Either, eb), ec), bb, cg) → new_esEs0(vwx300, vwx400, eb, ec)
new_esEs(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), ba, bb, app(app(ty_Either, bf), bg)) → new_esEs0(vwx302, vwx402, bf, bg)
new_esEs2(Just(vwx300), Just(vwx400), app(app(app(ty_@3, bag), bah), bba)) → new_esEs(vwx300, vwx400, bag, bah, bba)
new_esEs3(@2(vwx300, vwx301), @2(vwx400, vwx401), bbh, app(ty_Maybe, bcg)) → new_esEs2(vwx301, vwx401, bcg)
new_esEs(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), app(ty_Maybe, ee), bb, cg) → new_esEs2(vwx300, vwx400, ee)
new_esEs0(Right(vwx300), Right(vwx400), gc, app(app(app(ty_@3, gd), ge), gf)) → new_esEs(vwx300, vwx400, gd, ge, gf)
new_esEs(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), ba, bb, app(ty_Maybe, ca)) → new_esEs2(vwx302, vwx402, ca)
new_esEs3(@2(vwx300, vwx301), @2(vwx400, vwx401), app(app(app(ty_@3, bdb), bdc), bdd), bde) → new_esEs(vwx300, vwx400, bdb, bdc, bdd)
new_esEs(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), ba, app(ty_Maybe, dd), cg) → new_esEs2(vwx301, vwx401, dd)
new_esEs1(:(vwx300, vwx301), :(vwx400, vwx401), he) → new_esEs1(vwx301, vwx401, he)
new_esEs(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), ba, app(ty_[], dc), cg) → new_esEs1(vwx301, vwx401, dc)
new_esEs1(:(vwx300, vwx301), :(vwx400, vwx401), app(ty_[], bac)) → new_esEs1(vwx300, vwx400, bac)
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_esEs3(@2(vwx300, vwx301), @2(vwx400, vwx401), bbh, app(ty_[], bcf)) → new_esEs1(vwx301, vwx401, bcf)
new_esEs2(Just(vwx300), Just(vwx400), app(ty_[], bbd)) → new_esEs1(vwx300, vwx400, bbd)
new_esEs2(Just(vwx300), Just(vwx400), app(ty_Maybe, bbe)) → new_esEs2(vwx300, vwx400, bbe)
new_esEs0(Left(vwx300), Left(vwx400), app(app(ty_Either, fd), ff), fc) → new_esEs0(vwx300, vwx400, fd, ff)
new_esEs(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), ba, bb, app(app(ty_@2, cb), cc)) → new_esEs3(vwx302, vwx402, cb, cc)
new_esEs3(@2(vwx300, vwx301), @2(vwx400, vwx401), app(ty_[], bdh), bde) → new_esEs1(vwx300, vwx400, bdh)
new_esEs3(@2(vwx300, vwx301), @2(vwx400, vwx401), bbh, app(app(ty_Either, bcd), bce)) → new_esEs0(vwx301, vwx401, bcd, bce)
new_esEs(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), app(ty_[], ed), bb, cg) → new_esEs1(vwx300, vwx400, ed)
new_esEs3(@2(vwx300, vwx301), @2(vwx400, vwx401), bbh, app(app(app(ty_@3, bca), bcb), bcc)) → new_esEs(vwx301, vwx401, bca, bcb, bcc)
new_esEs0(Right(vwx300), Right(vwx400), gc, app(app(ty_Either, gg), gh)) → new_esEs0(vwx300, vwx400, gg, gh)
new_esEs0(Left(vwx300), Left(vwx400), app(ty_Maybe, fh), fc) → new_esEs2(vwx300, vwx400, fh)
new_esEs3(@2(vwx300, vwx301), @2(vwx400, vwx401), bbh, app(app(ty_@2, bch), bda)) → new_esEs3(vwx301, vwx401, bch, bda)
new_esEs0(Right(vwx300), Right(vwx400), gc, app(ty_Maybe, hb)) → new_esEs2(vwx300, vwx400, hb)
new_esEs(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), ba, app(app(ty_Either, da), db), cg) → new_esEs0(vwx301, vwx401, da, db)
new_esEs1(:(vwx300, vwx301), :(vwx400, vwx401), app(app(ty_@2, bae), baf)) → new_esEs3(vwx300, vwx400, bae, baf)
new_esEs3(@2(vwx300, vwx301), @2(vwx400, vwx401), app(ty_Maybe, bea), bde) → new_esEs2(vwx300, vwx400, bea)
new_esEs(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), app(app(ty_@2, ef), eg), bb, cg) → new_esEs3(vwx300, vwx400, ef, eg)
new_esEs1(:(vwx300, vwx301), :(vwx400, vwx401), app(app(ty_Either, baa), bab)) → new_esEs0(vwx300, vwx400, baa, bab)
new_esEs0(Right(vwx300), Right(vwx400), gc, app(ty_[], ha)) → new_esEs1(vwx300, vwx400, ha)
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_esEs1(:(vwx300, vwx301), :(vwx400, vwx401), app(ty_Maybe, bad)) → new_esEs2(vwx300, vwx400, bad)
new_esEs0(Left(vwx300), Left(vwx400), app(ty_[], fg), fc) → new_esEs1(vwx300, vwx400, fg)
new_esEs3(@2(vwx300, vwx301), @2(vwx400, vwx401), app(app(ty_@2, beb), bec), bde) → new_esEs3(vwx300, vwx400, beb, bec)
new_esEs0(Right(vwx300), Right(vwx400), gc, app(app(ty_@2, hc), hd)) → new_esEs3(vwx300, vwx400, hc, hd)
new_esEs1(:(vwx300, vwx301), :(vwx400, vwx401), app(app(app(ty_@3, hf), hg), hh)) → new_esEs(vwx300, vwx400, hf, hg, hh)
new_esEs2(Just(vwx300), Just(vwx400), app(app(ty_@2, bbf), bbg)) → new_esEs3(vwx300, vwx400, bbf, bbg)
new_esEs3(@2(vwx300, vwx301), @2(vwx400, vwx401), app(app(ty_Either, bdf), bdg), bde) → new_esEs0(vwx300, vwx400, bdf, bdg)
new_esEs0(Left(vwx300), Left(vwx400), app(app(app(ty_@3, eh), fa), fb), fc) → new_esEs(vwx300, vwx400, eh, fa, fb)
new_esEs2(Just(vwx300), Just(vwx400), app(app(ty_Either, bbb), bbc)) → new_esEs0(vwx300, vwx400, bbb, bbc)
new_esEs0(Left(vwx300), Left(vwx400), app(app(ty_@2, ga), gb), fc) → new_esEs3(vwx300, vwx400, ga, gb)
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)
new_esEs(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), ba, app(app(ty_@2, de), df), cg) → new_esEs3(vwx301, vwx401, de, df)

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_ltEs3(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), bca, bah, app(app(ty_Either, bdc), bdd)) → new_ltEs(vwx92, vwx102, bdc, bdd)
new_ltEs(Right(vwx90), Right(vwx100), cc, app(ty_[], cg)) → new_ltEs1(vwx90, vwx100, cg)
new_ltEs2(@2(vwx90, vwx91), @2(vwx100, vwx101), hd, app(app(ty_Either, he), hf)) → new_ltEs(vwx91, vwx101, he, hf)
new_ltEs0(Just(vwx90), Just(vwx100), app(app(app(ty_@3, ed), ee), ef)) → new_ltEs3(vwx90, vwx100, ed, ee, ef)
new_ltEs3(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), bca, app(ty_Maybe, bcd), bba) → new_lt0(vwx91, vwx101, bcd)
new_lt(vwx90, vwx100, gb, gc) → new_compare20(vwx90, vwx100, new_esEs4(vwx90, vwx100, gb, gc), gb, gc)
new_lt0(vwx90, vwx100, gd) → new_compare21(vwx90, vwx100, new_esEs5(vwx90, vwx100, gd), gd)
new_compare0(:(vwx90, vwx91), :(vwx100, vwx101), eg) → new_primCompAux(vwx90, vwx100, new_compare(vwx91, vwx101, eg), eg)
new_ltEs2(@2(vwx90, vwx91), @2(vwx100, vwx101), app(ty_Maybe, gd), gg) → new_compare21(vwx90, vwx100, new_esEs5(vwx90, vwx100, gd), gd)
new_lt3(vwx90, vwx100, ha, hb, hc) → new_compare23(vwx90, vwx100, new_esEs7(vwx90, vwx100, ha, hb, hc), ha, hb, hc)
new_ltEs(Left(vwx90), Left(vwx100), app(app(ty_Either, ba), bb), bc) → new_ltEs(vwx90, vwx100, ba, bb)
new_ltEs(Right(vwx90), Right(vwx100), cc, app(app(ty_Either, cd), ce)) → new_ltEs(vwx90, vwx100, cd, ce)
new_ltEs2(@2(vwx90, vwx91), @2(vwx100, vwx101), hd, app(app(app(ty_@3, bac), bad), bae)) → new_ltEs3(vwx91, vwx101, bac, bad, bae)
new_compare0(:(vwx90, vwx91), :(vwx100, vwx101), eg) → new_compare0(vwx91, vwx101, eg)
new_primCompAux(vwx90, vwx100, vwx65, app(app(ty_@2, fd), ff)) → new_compare3(vwx90, vwx100, fd, ff)
new_compare21(vwx90, vwx100, False, gd) → new_ltEs0(vwx90, vwx100, gd)
new_ltEs(Right(vwx90), Right(vwx100), cc, app(app(app(ty_@3, dc), dd), de)) → new_ltEs3(vwx90, vwx100, dc, dd, de)
new_ltEs0(Just(vwx90), Just(vwx100), app(ty_Maybe, dh)) → new_ltEs0(vwx90, vwx100, dh)
new_compare3(vwx90, vwx100, ge, gf) → new_compare22(vwx90, vwx100, new_esEs6(vwx90, vwx100, ge, gf), ge, gf)
new_ltEs3(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), bca, bah, app(ty_Maybe, bde)) → new_ltEs0(vwx92, vwx102, bde)
new_ltEs3(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), app(app(ty_@2, bbd), bbe), bah, bba) → new_lt2(vwx90, vwx100, bbd, bbe)
new_primCompAux(vwx90, vwx100, vwx65, app(ty_[], fc)) → new_compare0(vwx90, vwx100, fc)
new_ltEs3(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), app(app(ty_Either, baf), bag), bah, bba) → new_lt(vwx90, vwx100, baf, bag)
new_ltEs3(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), bca, app(app(ty_Either, bcb), bcc), bba) → new_lt(vwx91, vwx101, bcb, bcc)
new_primCompAux(vwx90, vwx100, vwx65, app(ty_Maybe, fb)) → new_compare2(vwx90, vwx100, fb)
new_ltEs1(:(vwx90, vwx91), :(vwx100, vwx101), eg) → new_primCompAux(vwx90, vwx100, new_compare(vwx91, vwx101, eg), eg)
new_ltEs2(@2(vwx90, vwx91), @2(vwx100, vwx101), app(ty_[], gh), gg) → new_compare0(vwx90, vwx100, gh)
new_ltEs3(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), bca, app(app(ty_@2, bcf), bcg), bba) → new_lt2(vwx91, vwx101, bcf, bcg)
new_primCompAux(vwx90, vwx100, vwx65, app(app(ty_Either, eh), fa)) → new_compare1(vwx90, vwx100, eh, fa)
new_ltEs3(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), bca, bah, app(app(ty_@2, bdg), bdh)) → new_ltEs2(vwx92, vwx102, bdg, bdh)
new_compare20(vwx90, vwx100, False, gb, gc) → new_ltEs(vwx90, vwx100, gb, gc)
new_ltEs2(@2(vwx90, vwx91), @2(vwx100, vwx101), app(app(app(ty_@3, ha), hb), hc), gg) → new_compare23(vwx90, vwx100, new_esEs7(vwx90, vwx100, ha, hb, hc), ha, hb, hc)
new_lt1(vwx90, vwx100, gh) → new_compare0(vwx90, vwx100, gh)
new_ltEs3(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), bca, bah, app(app(app(ty_@3, bea), beb), bec)) → new_ltEs3(vwx92, vwx102, bea, beb, bec)
new_ltEs2(@2(vwx90, vwx91), @2(vwx100, vwx101), hd, app(ty_Maybe, hg)) → new_ltEs0(vwx91, vwx101, hg)
new_ltEs3(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), app(ty_[], bbc), bah, bba) → new_lt1(vwx90, vwx100, bbc)
new_ltEs2(@2(vwx90, vwx91), @2(vwx100, vwx101), hd, app(app(ty_@2, baa), bab)) → new_ltEs2(vwx91, vwx101, baa, bab)
new_ltEs3(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), app(app(app(ty_@3, bbf), bbg), bbh), bah, bba) → new_lt3(vwx90, vwx100, bbf, bbg, bbh)
new_ltEs(Left(vwx90), Left(vwx100), app(ty_Maybe, bd), bc) → new_ltEs0(vwx90, vwx100, bd)
new_ltEs0(Just(vwx90), Just(vwx100), app(app(ty_@2, eb), ec)) → new_ltEs2(vwx90, vwx100, eb, ec)
new_ltEs(Left(vwx90), Left(vwx100), app(app(app(ty_@3, bh), ca), cb), bc) → new_ltEs3(vwx90, vwx100, bh, ca, cb)
new_ltEs2(@2(vwx90, vwx91), @2(vwx100, vwx101), hd, app(ty_[], hh)) → new_ltEs1(vwx91, vwx101, hh)
new_ltEs0(Just(vwx90), Just(vwx100), app(ty_[], ea)) → new_ltEs1(vwx90, vwx100, ea)
new_ltEs2(@2(vwx90, vwx91), @2(vwx100, vwx101), app(app(ty_@2, ge), gf), gg) → new_compare22(vwx90, vwx100, new_esEs6(vwx90, vwx100, ge, gf), ge, gf)
new_ltEs3(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), bca, app(app(app(ty_@3, bch), bda), bdb), bba) → new_lt3(vwx91, vwx101, bch, bda, bdb)
new_ltEs(Right(vwx90), Right(vwx100), cc, app(app(ty_@2, da), db)) → new_ltEs2(vwx90, vwx100, da, db)
new_ltEs1(:(vwx90, vwx91), :(vwx100, vwx101), eg) → new_compare0(vwx91, vwx101, eg)
new_ltEs(Left(vwx90), Left(vwx100), app(ty_[], be), bc) → new_ltEs1(vwx90, vwx100, be)
new_lt2(vwx90, vwx100, ge, gf) → new_compare22(vwx90, vwx100, new_esEs6(vwx90, vwx100, ge, gf), ge, gf)
new_compare2(vwx90, vwx100, gd) → new_compare21(vwx90, vwx100, new_esEs5(vwx90, vwx100, gd), gd)
new_ltEs3(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), bca, bah, app(ty_[], bdf)) → new_ltEs1(vwx92, vwx102, bdf)
new_compare22(vwx90, vwx100, False, ge, gf) → new_ltEs2(vwx90, vwx100, ge, gf)
new_compare4(vwx90, vwx100, ha, hb, hc) → new_compare23(vwx90, vwx100, new_esEs7(vwx90, vwx100, ha, hb, hc), ha, hb, hc)
new_ltEs(Right(vwx90), Right(vwx100), cc, app(ty_Maybe, cf)) → new_ltEs0(vwx90, vwx100, cf)
new_ltEs(Left(vwx90), Left(vwx100), app(app(ty_@2, bf), bg), bc) → new_ltEs2(vwx90, vwx100, bf, bg)
new_compare1(vwx90, vwx100, gb, gc) → new_compare20(vwx90, vwx100, new_esEs4(vwx90, vwx100, gb, gc), gb, gc)
new_ltEs2(@2(vwx90, vwx91), @2(vwx100, vwx101), app(app(ty_Either, gb), gc), gg) → new_compare20(vwx90, vwx100, new_esEs4(vwx90, vwx100, gb, gc), gb, gc)
new_compare23(vwx90, vwx100, False, ha, hb, hc) → new_ltEs3(vwx90, vwx100, ha, hb, hc)
new_primCompAux(vwx90, vwx100, vwx65, app(app(app(ty_@3, fg), fh), ga)) → new_compare4(vwx90, vwx100, fg, fh, ga)
new_ltEs0(Just(vwx90), Just(vwx100), app(app(ty_Either, df), dg)) → new_ltEs(vwx90, vwx100, df, dg)
new_ltEs3(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), bca, app(ty_[], bce), bba) → new_lt1(vwx91, vwx101, bce)
new_ltEs3(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), app(ty_Maybe, bbb), bah, bba) → new_lt0(vwx90, vwx100, bbb)

The TRS R consists of the following rules:

new_esEs28(vwx300, vwx400, app(ty_[], dbf)) → new_esEs13(vwx300, vwx400, dbf)
new_esEs4(Right(vwx300), Right(vwx400), cec, ty_Ordering) → new_esEs8(vwx300, vwx400)
new_compare5(@0, @0) → EQ
new_esEs21(vwx300, vwx400, app(app(ty_@2, cah), cba)) → new_esEs6(vwx300, vwx400, cah, cba)
new_compare32(vwx90, vwx100) → new_compare25(vwx90, vwx100, new_esEs8(vwx90, vwx100))
new_compare9(Char(vwx90), Char(vwx100)) → new_primCmpNat0(vwx90, vwx100)
new_esEs18(vwx91, vwx101, app(app(ty_@2, bcf), bcg)) → new_esEs6(vwx91, vwx101, bcf, bcg)
new_lt7(vwx91, vwx101, app(ty_Maybe, bcd)) → new_lt12(vwx91, vwx101, bcd)
new_ltEs17(LT, LT) → True
new_esEs21(vwx300, vwx400, ty_Float) → new_esEs14(vwx300, vwx400)
new_esEs5(Just(vwx300), Just(vwx400), ty_Ordering) → new_esEs8(vwx300, vwx400)
new_lt6(vwx90, vwx100, ty_Integer) → new_lt11(vwx90, vwx100)
new_lt7(vwx91, vwx101, app(ty_[], bce)) → new_lt14(vwx91, vwx101, bce)
new_compare15(vwx90, vwx100, True, gb, gc) → LT
new_esEs13([], [], cbc) → True
new_esEs28(vwx300, vwx400, ty_Float) → new_esEs14(vwx300, vwx400)
new_compare14(vwx90, vwx100, gb, gc) → new_compare24(vwx90, vwx100, new_esEs4(vwx90, vwx100, gb, gc), gb, gc)
new_compare([], :(vwx100, vwx101), eg) → LT
new_ltEs11(Just(vwx90), Just(vwx100), ty_Float) → new_ltEs18(vwx90, vwx100)
new_esEs16(Double(vwx300, vwx301), Double(vwx400, vwx401)) → new_esEs10(new_sr(vwx300, vwx400), new_sr(vwx301, vwx401))
new_ltEs11(Just(vwx90), Just(vwx100), ty_Int) → new_ltEs8(vwx90, vwx100)
new_esEs4(Right(vwx300), Right(vwx400), cec, ty_Double) → new_esEs16(vwx300, vwx400)
new_esEs22(vwx300, vwx400, ty_Char) → new_esEs12(vwx300, vwx400)
new_esEs4(Right(vwx300), Right(vwx400), cec, app(ty_Maybe, cfb)) → new_esEs5(vwx300, vwx400, cfb)
new_ltEs19(vwx91, vwx101, app(ty_Maybe, hg)) → new_ltEs11(vwx91, vwx101, hg)
new_lt6(vwx90, vwx100, app(app(ty_Either, baf), bag)) → new_lt8(vwx90, vwx100, baf, bag)
new_lt6(vwx90, vwx100, app(ty_[], bbc)) → new_lt14(vwx90, vwx100, bbc)
new_lt16(vwx90, vwx100) → new_esEs8(new_compare8(vwx90, vwx100), LT)
new_primMulNat0(Zero, Zero) → Zero
new_ltEs11(Just(vwx90), Just(vwx100), ty_Char) → new_ltEs12(vwx90, vwx100)
new_esEs20(vwx301, vwx401, app(ty_[], bhd)) → new_esEs13(vwx301, vwx401, bhd)
new_compare(:(vwx90, vwx91), [], eg) → GT
new_esEs4(Right(vwx300), Right(vwx400), cec, ty_Float) → new_esEs14(vwx300, vwx400)
new_esEs4(Left(vwx300), Left(vwx400), app(ty_Ratio, ceb), cch) → new_esEs17(vwx300, vwx400, ceb)
new_esEs5(Just(vwx300), Just(vwx400), ty_Double) → new_esEs16(vwx300, vwx400)
new_ltEs6(Right(vwx90), Right(vwx100), cc, ty_Bool) → new_ltEs14(vwx90, vwx100)
new_ltEs6(Left(vwx90), Left(vwx100), ty_Ordering, bc) → new_ltEs17(vwx90, vwx100)
new_lt20(vwx90, vwx100, app(app(app(ty_@3, ha), hb), hc)) → new_lt18(vwx90, vwx100, ha, hb, hc)
new_compare30(vwx90, vwx100, app(ty_Ratio, cga)) → new_compare6(vwx90, vwx100, cga)
new_esEs24(vwx301, vwx401, ty_Integer) → new_esEs15(vwx301, vwx401)
new_esEs19(vwx90, vwx100, ty_Int) → new_esEs10(vwx90, vwx100)
new_ltEs14(False, True) → True
new_ltEs11(Just(vwx90), Just(vwx100), ty_Bool) → new_ltEs14(vwx90, vwx100)
new_esEs4(Right(vwx300), Right(vwx400), cec, ty_Bool) → new_esEs11(vwx300, vwx400)
new_ltEs11(Just(vwx90), Just(vwx100), app(app(app(ty_@3, ed), ee), ef)) → new_ltEs4(vwx90, vwx100, ed, ee, ef)
new_esEs23(vwx90, vwx100, ty_@0) → new_esEs9(vwx90, vwx100)
new_esEs19(vwx90, vwx100, app(app(app(ty_@3, bbf), bbg), bbh)) → new_esEs7(vwx90, vwx100, bbf, bbg, bbh)
new_esEs4(Left(vwx300), Left(vwx400), ty_Float, cch) → new_esEs14(vwx300, vwx400)
new_esEs20(vwx301, vwx401, app(app(ty_Either, bhb), bhc)) → new_esEs4(vwx301, vwx401, bhb, bhc)
new_esEs4(Right(vwx300), Right(vwx400), cec, ty_Int) → new_esEs10(vwx300, vwx400)
new_esEs4(Right(vwx300), Right(vwx400), cec, app(app(app(ty_@3, ced), cee), cef)) → new_esEs7(vwx300, vwx400, ced, cee, cef)
new_ltEs11(Just(vwx90), Just(vwx100), app(ty_Ratio, ccg)) → new_ltEs7(vwx90, vwx100, ccg)
new_esEs4(Left(vwx300), Left(vwx400), app(app(ty_@2, cdh), cea), cch) → new_esEs6(vwx300, vwx400, cdh, cea)
new_ltEs6(Left(vwx90), Left(vwx100), app(app(ty_Either, ba), bb), bc) → new_ltEs6(vwx90, vwx100, ba, bb)
new_ltEs5(vwx92, vwx102, app(app(ty_Either, bdc), bdd)) → new_ltEs6(vwx92, vwx102, bdc, bdd)
new_lt6(vwx90, vwx100, ty_@0) → new_lt10(vwx90, vwx100)
new_ltEs5(vwx92, vwx102, ty_Integer) → new_ltEs10(vwx92, vwx102)
new_esEs21(vwx300, vwx400, app(app(app(ty_@3, caa), cab), cac)) → new_esEs7(vwx300, vwx400, caa, cab, cac)
new_esEs5(Just(vwx300), Just(vwx400), ty_Float) → new_esEs14(vwx300, vwx400)
new_esEs5(Just(vwx300), Just(vwx400), app(ty_Maybe, bfc)) → new_esEs5(vwx300, vwx400, bfc)
new_esEs15(Integer(vwx300), Integer(vwx400)) → new_primEqInt(vwx300, vwx400)
new_lt7(vwx91, vwx101, app(app(ty_Either, bcb), bcc)) → new_lt8(vwx91, vwx101, bcb, bcc)
new_compare30(vwx90, vwx100, ty_Float) → new_compare7(vwx90, vwx100)
new_esEs20(vwx301, vwx401, app(app(ty_@2, bhf), bhg)) → new_esEs6(vwx301, vwx401, bhf, bhg)
new_esEs6(@2(vwx300, vwx301), @2(vwx400, vwx401), bge, bgf) → new_asAs(new_esEs21(vwx300, vwx400, bge), new_esEs20(vwx301, vwx401, bgf))
new_ltEs17(EQ, LT) → False
new_esEs4(Left(vwx300), Left(vwx400), ty_Ordering, cch) → new_esEs8(vwx300, vwx400)
new_ltEs6(Left(vwx90), Left(vwx100), ty_Double, bc) → new_ltEs15(vwx90, vwx100)
new_pePe(False, vwx64) → vwx64
new_esEs23(vwx90, vwx100, ty_Float) → new_esEs14(vwx90, vwx100)
new_esEs22(vwx300, vwx400, app(app(ty_Either, cbg), cbh)) → new_esEs4(vwx300, vwx400, cbg, cbh)
new_esEs20(vwx301, vwx401, ty_Double) → new_esEs16(vwx301, vwx401)
new_compare19(vwx90, vwx100, True, ha, hb, hc) → LT
new_ltEs10(vwx9, vwx10) → new_not(new_esEs8(new_compare17(vwx9, vwx10), GT))
new_esEs26(vwx302, vwx402, ty_Char) → new_esEs12(vwx302, vwx402)
new_esEs26(vwx302, vwx402, app(ty_Ratio, chf)) → new_esEs17(vwx302, vwx402, chf)
new_lt20(vwx90, vwx100, app(app(ty_@2, ge), gf)) → new_lt17(vwx90, vwx100, ge, gf)
new_esEs19(vwx90, vwx100, ty_Float) → new_esEs14(vwx90, vwx100)
new_ltEs6(Right(vwx90), Right(vwx100), cc, app(ty_[], cg)) → new_ltEs13(vwx90, vwx100, cg)
new_esEs20(vwx301, vwx401, ty_Char) → new_esEs12(vwx301, vwx401)
new_esEs22(vwx300, vwx400, ty_Ordering) → new_esEs8(vwx300, vwx400)
new_lt20(vwx90, vwx100, ty_Float) → new_lt5(vwx90, vwx100)
new_compare29(vwx90, vwx100, ha, hb, hc) → new_compare27(vwx90, vwx100, new_esEs7(vwx90, vwx100, ha, hb, hc), ha, hb, hc)
new_esEs5(Just(vwx300), Just(vwx400), ty_Integer) → new_esEs15(vwx300, vwx400)
new_esEs20(vwx301, vwx401, app(ty_Ratio, bhh)) → new_esEs17(vwx301, vwx401, bhh)
new_esEs4(Right(vwx300), Right(vwx400), cec, ty_Integer) → new_esEs15(vwx300, vwx400)
new_ltEs6(Left(vwx90), Left(vwx100), app(ty_Maybe, bd), bc) → new_ltEs11(vwx90, vwx100, bd)
new_lt6(vwx90, vwx100, app(ty_Ratio, bfh)) → new_lt4(vwx90, vwx100, bfh)
new_ltEs19(vwx91, vwx101, ty_Int) → new_ltEs8(vwx91, vwx101)
new_esEs23(vwx90, vwx100, app(app(app(ty_@3, ha), hb), hc)) → new_esEs7(vwx90, vwx100, ha, hb, hc)
new_primCmpNat0(Zero, Succ(vwx1000)) → LT
new_lt19(vwx90, vwx100) → new_esEs8(new_compare32(vwx90, vwx100), LT)
new_esEs27(vwx301, vwx401, app(app(app(ty_@3, chg), chh), daa)) → new_esEs7(vwx301, vwx401, chg, chh, daa)
new_lt12(vwx90, vwx100, gd) → new_esEs8(new_compare31(vwx90, vwx100, gd), LT)
new_esEs26(vwx302, vwx402, ty_Bool) → new_esEs11(vwx302, vwx402)
new_esEs8(LT, LT) → True
new_lt8(vwx90, vwx100, gb, gc) → new_esEs8(new_compare14(vwx90, vwx100, gb, gc), LT)
new_esEs28(vwx300, vwx400, ty_Double) → new_esEs16(vwx300, vwx400)
new_esEs4(Left(vwx300), Left(vwx400), ty_Char, cch) → new_esEs12(vwx300, vwx400)
new_esEs20(vwx301, vwx401, ty_Bool) → new_esEs11(vwx301, vwx401)
new_ltEs19(vwx91, vwx101, app(app(app(ty_@3, bac), bad), bae)) → new_ltEs4(vwx91, vwx101, bac, bad, bae)
new_esEs18(vwx91, vwx101, app(ty_[], bce)) → new_esEs13(vwx91, vwx101, bce)
new_pePe(True, vwx64) → True
new_primEqNat0(Zero, Zero) → True
new_lt6(vwx90, vwx100, ty_Bool) → new_lt15(vwx90, vwx100)
new_ltEs6(Left(vwx90), Left(vwx100), ty_@0, bc) → new_ltEs9(vwx90, vwx100)
new_ltEs11(Nothing, Just(vwx100), ccf) → True
new_ltEs6(Right(vwx90), Right(vwx100), cc, ty_Float) → new_ltEs18(vwx90, vwx100)
new_ltEs11(Just(vwx90), Just(vwx100), app(ty_Maybe, dh)) → new_ltEs11(vwx90, vwx100, dh)
new_lt14(vwx90, vwx100, gh) → new_esEs8(new_compare(vwx90, vwx100, gh), LT)
new_esEs4(Right(vwx300), Right(vwx400), cec, app(ty_[], cfa)) → new_esEs13(vwx300, vwx400, cfa)
new_lt7(vwx91, vwx101, app(ty_Ratio, bga)) → new_lt4(vwx91, vwx101, bga)
new_lt7(vwx91, vwx101, ty_Int) → new_lt9(vwx91, vwx101)
new_lt7(vwx91, vwx101, app(app(app(ty_@3, bch), bda), bdb)) → new_lt18(vwx91, vwx101, bch, bda, bdb)
new_esEs18(vwx91, vwx101, ty_@0) → new_esEs9(vwx91, vwx101)
new_esEs27(vwx301, vwx401, ty_Char) → new_esEs12(vwx301, vwx401)
new_lt6(vwx90, vwx100, ty_Int) → new_lt9(vwx90, vwx100)
new_ltEs17(GT, LT) → False
new_sr(vwx301, vwx401) → new_primMulInt(vwx301, vwx401)
new_ltEs11(Just(vwx90), Just(vwx100), app(app(ty_Either, df), dg)) → new_ltEs6(vwx90, vwx100, df, dg)
new_ltEs5(vwx92, vwx102, app(ty_Ratio, bgb)) → new_ltEs7(vwx92, vwx102, bgb)
new_ltEs7(vwx9, vwx10, cfh) → new_not(new_esEs8(new_compare6(vwx9, vwx10, cfh), GT))
new_esEs14(Float(vwx300, vwx301), Float(vwx400, vwx401)) → new_esEs10(new_sr(vwx300, vwx400), new_sr(vwx301, vwx401))
new_esEs26(vwx302, vwx402, ty_Ordering) → new_esEs8(vwx302, vwx402)
new_esEs8(GT, GT) → True
new_esEs21(vwx300, vwx400, ty_Double) → new_esEs16(vwx300, vwx400)
new_primPlusNat0(Succ(vwx440), vwx40100) → Succ(Succ(new_primPlusNat1(vwx440, vwx40100)))
new_esEs20(vwx301, vwx401, app(app(app(ty_@3, bgg), bgh), bha)) → new_esEs7(vwx301, vwx401, bgg, bgh, bha)
new_esEs19(vwx90, vwx100, app(ty_Ratio, bfh)) → new_esEs17(vwx90, vwx100, bfh)
new_esEs8(LT, GT) → False
new_esEs8(GT, LT) → False
new_esEs4(Right(vwx300), Right(vwx400), cec, ty_Char) → new_esEs12(vwx300, vwx400)
new_esEs4(Right(vwx300), Right(vwx400), cec, app(app(ty_Either, ceg), ceh)) → new_esEs4(vwx300, vwx400, ceg, ceh)
new_compare25(vwx90, vwx100, True) → EQ
new_primEqInt(Neg(Succ(vwx3000)), Neg(Succ(vwx4000))) → new_primEqNat0(vwx3000, vwx4000)
new_esEs20(vwx301, vwx401, ty_Ordering) → new_esEs8(vwx301, vwx401)
new_lt10(vwx90, vwx100) → new_esEs8(new_compare5(vwx90, vwx100), LT)
new_esEs23(vwx90, vwx100, ty_Ordering) → new_esEs8(vwx90, vwx100)
new_esEs26(vwx302, vwx402, app(ty_[], chb)) → new_esEs13(vwx302, vwx402, chb)
new_esEs4(Left(vwx300), Left(vwx400), app(app(ty_Either, cdd), cde), cch) → new_esEs4(vwx300, vwx400, cdd, cde)
new_ltEs17(LT, GT) → True
new_lt7(vwx91, vwx101, ty_Bool) → new_lt15(vwx91, vwx101)
new_primPlusNat1(Zero, Succ(vwx401000)) → Succ(vwx401000)
new_primPlusNat1(Succ(vwx4400), Zero) → Succ(vwx4400)
new_lt7(vwx91, vwx101, ty_Ordering) → new_lt19(vwx91, vwx101)
new_esEs21(vwx300, vwx400, ty_Char) → new_esEs12(vwx300, vwx400)
new_esEs26(vwx302, vwx402, app(app(app(ty_@3, cge), cgf), cgg)) → new_esEs7(vwx302, vwx402, cge, cgf, cgg)
new_ltEs6(Right(vwx90), Right(vwx100), cc, ty_Integer) → new_ltEs10(vwx90, vwx100)
new_esEs4(Left(vwx300), Left(vwx400), ty_Int, cch) → new_esEs10(vwx300, vwx400)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_lt13(vwx90, vwx100) → new_esEs8(new_compare9(vwx90, vwx100), LT)
new_esEs5(Just(vwx300), Just(vwx400), ty_Int) → new_esEs10(vwx300, vwx400)
new_esEs5(Just(vwx300), Just(vwx400), app(ty_[], bfb)) → new_esEs13(vwx300, vwx400, bfb)
new_lt18(vwx90, vwx100, ha, hb, hc) → new_esEs8(new_compare29(vwx90, vwx100, ha, hb, hc), LT)
new_ltEs6(Left(vwx90), Left(vwx100), app(ty_[], be), bc) → new_ltEs13(vwx90, vwx100, be)
new_primEqInt(Neg(Succ(vwx3000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(vwx4000))) → False
new_ltEs19(vwx91, vwx101, ty_Char) → new_ltEs12(vwx91, vwx101)
new_lt20(vwx90, vwx100, ty_Integer) → new_lt11(vwx90, vwx100)
new_esEs8(EQ, EQ) → True
new_compare26(vwx90, vwx100, True, ge, gf) → EQ
new_compare19(vwx90, vwx100, False, ha, hb, hc) → GT
new_lt20(vwx90, vwx100, ty_@0) → new_lt10(vwx90, vwx100)
new_compare24(vwx90, vwx100, True, gb, gc) → EQ
new_esEs21(vwx300, vwx400, app(app(ty_Either, cad), cae)) → new_esEs4(vwx300, vwx400, cad, cae)
new_ltEs16(@2(vwx90, vwx91), @2(vwx100, vwx101), hd, gg) → new_pePe(new_lt20(vwx90, vwx100, hd), new_asAs(new_esEs23(vwx90, vwx100, hd), new_ltEs19(vwx91, vwx101, gg)))
new_compare30(vwx90, vwx100, app(app(ty_Either, eh), fa)) → new_compare14(vwx90, vwx100, eh, fa)
new_compare([], [], eg) → EQ
new_ltEs17(EQ, EQ) → True
new_ltEs19(vwx91, vwx101, ty_Ordering) → new_ltEs17(vwx91, vwx101)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_compare30(vwx90, vwx100, ty_Double) → new_compare8(vwx90, vwx100)
new_esEs21(vwx300, vwx400, app(ty_Ratio, cbb)) → new_esEs17(vwx300, vwx400, cbb)
new_compare27(vwx90, vwx100, False, ha, hb, hc) → new_compare19(vwx90, vwx100, new_ltEs4(vwx90, vwx100, ha, hb, hc), ha, hb, hc)
new_compare210(vwx90, vwx100, False, gd) → new_compare13(vwx90, vwx100, new_ltEs11(vwx90, vwx100, gd), gd)
new_primCmpNat0(Succ(vwx900), Succ(vwx1000)) → new_primCmpNat0(vwx900, vwx1000)
new_esEs11(False, False) → True
new_ltEs11(Just(vwx90), Just(vwx100), app(app(ty_@2, eb), ec)) → new_ltEs16(vwx90, vwx100, eb, ec)
new_lt6(vwx90, vwx100, ty_Char) → new_lt13(vwx90, vwx100)
new_primEqInt(Pos(Succ(vwx3000)), Pos(Succ(vwx4000))) → new_primEqNat0(vwx3000, vwx4000)
new_esEs18(vwx91, vwx101, ty_Int) → new_esEs10(vwx91, vwx101)
new_ltEs19(vwx91, vwx101, ty_Bool) → new_ltEs14(vwx91, vwx101)
new_lt20(vwx90, vwx100, ty_Ordering) → new_lt19(vwx90, vwx100)
new_esEs20(vwx301, vwx401, ty_Int) → new_esEs10(vwx301, vwx401)
new_esEs26(vwx302, vwx402, ty_Integer) → new_esEs15(vwx302, vwx402)
new_esEs5(Just(vwx300), Just(vwx400), ty_Bool) → new_esEs11(vwx300, vwx400)
new_primEqNat0(Succ(vwx3000), Succ(vwx4000)) → new_primEqNat0(vwx3000, vwx4000)
new_esEs27(vwx301, vwx401, ty_Ordering) → new_esEs8(vwx301, vwx401)
new_ltEs14(False, False) → True
new_lt5(vwx90, vwx100) → new_esEs8(new_compare7(vwx90, vwx100), LT)
new_esEs19(vwx90, vwx100, app(app(ty_@2, bbd), bbe)) → new_esEs6(vwx90, vwx100, bbd, bbe)
new_lt7(vwx91, vwx101, app(app(ty_@2, bcf), bcg)) → new_lt17(vwx91, vwx101, bcf, bcg)
new_ltEs4(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), bca, bah, bba) → new_pePe(new_lt6(vwx90, vwx100, bca), new_asAs(new_esEs19(vwx90, vwx100, bca), new_pePe(new_lt7(vwx91, vwx101, bah), new_asAs(new_esEs18(vwx91, vwx101, bah), new_ltEs5(vwx92, vwx102, bba)))))
new_esEs9(@0, @0) → True
new_esEs4(Left(vwx300), Left(vwx400), app(app(app(ty_@3, cda), cdb), cdc), cch) → new_esEs7(vwx300, vwx400, cda, cdb, cdc)
new_primCompAux00(vwx69, LT) → LT
new_lt6(vwx90, vwx100, ty_Double) → new_lt16(vwx90, vwx100)
new_primCmpInt(Neg(Succ(vwx900)), Neg(vwx100)) → new_primCmpNat0(vwx100, Succ(vwx900))
new_ltEs6(Left(vwx90), Right(vwx100), cc, bc) → True
new_ltEs5(vwx92, vwx102, ty_@0) → new_ltEs9(vwx92, vwx102)
new_ltEs6(Right(vwx90), Left(vwx100), cc, bc) → False
new_esEs28(vwx300, vwx400, ty_Ordering) → new_esEs8(vwx300, vwx400)
new_ltEs5(vwx92, vwx102, app(ty_Maybe, bde)) → new_ltEs11(vwx92, vwx102, bde)
new_esEs8(LT, EQ) → False
new_esEs8(EQ, LT) → False
new_ltEs5(vwx92, vwx102, ty_Int) → new_ltEs8(vwx92, vwx102)
new_primEqInt(Pos(Succ(vwx3000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(vwx4000))) → False
new_ltEs6(Left(vwx90), Left(vwx100), app(ty_Ratio, bgc), bc) → new_ltEs7(vwx90, vwx100, bgc)
new_compare13(vwx90, vwx100, True, gd) → LT
new_lt7(vwx91, vwx101, ty_Integer) → new_lt11(vwx91, vwx101)
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(vwx900), Zero) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(vwx1000))) → LT
new_compare12(vwx90, vwx100) → new_compare28(vwx90, vwx100, new_esEs11(vwx90, vwx100))
new_ltEs15(vwx9, vwx10) → new_not(new_esEs8(new_compare8(vwx9, vwx10), GT))
new_ltEs11(Just(vwx90), Just(vwx100), app(ty_[], ea)) → new_ltEs13(vwx90, vwx100, ea)
new_esEs18(vwx91, vwx101, app(app(app(ty_@3, bch), bda), bdb)) → new_esEs7(vwx91, vwx101, bch, bda, bdb)
new_esEs18(vwx91, vwx101, app(ty_Ratio, bga)) → new_esEs17(vwx91, vwx101, bga)
new_lt20(vwx90, vwx100, ty_Char) → new_lt13(vwx90, vwx100)
new_sr0(Integer(vwx1000), Integer(vwx910)) → Integer(new_primMulInt(vwx1000, vwx910))
new_compare30(vwx90, vwx100, app(ty_[], fc)) → new_compare(vwx90, vwx100, fc)
new_primPlusNat1(Succ(vwx4400), Succ(vwx401000)) → Succ(Succ(new_primPlusNat1(vwx4400, vwx401000)))
new_ltEs5(vwx92, vwx102, ty_Double) → new_ltEs15(vwx92, vwx102)
new_ltEs6(Right(vwx90), Right(vwx100), cc, ty_Int) → new_ltEs8(vwx90, vwx100)
new_lt6(vwx90, vwx100, app(app(app(ty_@3, bbf), bbg), bbh)) → new_lt18(vwx90, vwx100, bbf, bbg, bbh)
new_primEqInt(Pos(Succ(vwx3000)), Neg(vwx400)) → False
new_primEqInt(Neg(Succ(vwx3000)), Pos(vwx400)) → False
new_esEs25(vwx300, vwx400, ty_Int) → new_esEs10(vwx300, vwx400)
new_compare210(vwx90, vwx100, True, gd) → EQ
new_compare(:(vwx90, vwx91), :(vwx100, vwx101), eg) → new_primCompAux0(vwx90, vwx100, new_compare(vwx91, vwx101, eg), eg)
new_esEs27(vwx301, vwx401, app(ty_Maybe, dae)) → new_esEs5(vwx301, vwx401, dae)
new_lt11(vwx90, vwx100) → new_esEs8(new_compare17(vwx90, vwx100), LT)
new_ltEs6(Right(vwx90), Right(vwx100), cc, ty_Ordering) → new_ltEs17(vwx90, vwx100)
new_esEs19(vwx90, vwx100, ty_Bool) → new_esEs11(vwx90, vwx100)
new_esEs19(vwx90, vwx100, ty_@0) → new_esEs9(vwx90, vwx100)
new_esEs22(vwx300, vwx400, app(app(ty_@2, ccc), ccd)) → new_esEs6(vwx300, vwx400, ccc, ccd)
new_ltEs6(Right(vwx90), Right(vwx100), cc, app(app(app(ty_@3, dc), dd), de)) → new_ltEs4(vwx90, vwx100, dc, dd, de)
new_esEs22(vwx300, vwx400, ty_Float) → new_esEs14(vwx300, vwx400)
new_esEs21(vwx300, vwx400, app(ty_[], caf)) → new_esEs13(vwx300, vwx400, caf)
new_primEqInt(Pos(Zero), Neg(Succ(vwx4000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(vwx4000))) → False
new_esEs26(vwx302, vwx402, ty_Int) → new_esEs10(vwx302, vwx402)
new_esEs21(vwx300, vwx400, ty_Integer) → new_esEs15(vwx300, vwx400)
new_primCompAux00(vwx69, EQ) → vwx69
new_ltEs5(vwx92, vwx102, app(app(ty_@2, bdg), bdh)) → new_ltEs16(vwx92, vwx102, bdg, bdh)
new_primCmpInt(Pos(Zero), Pos(Succ(vwx1000))) → new_primCmpNat0(Zero, Succ(vwx1000))
new_compare30(vwx90, vwx100, app(ty_Maybe, fb)) → new_compare31(vwx90, vwx100, fb)
new_esEs23(vwx90, vwx100, ty_Bool) → new_esEs11(vwx90, vwx100)
new_esEs4(Left(vwx300), Left(vwx400), ty_Integer, cch) → new_esEs15(vwx300, vwx400)
new_ltEs13(vwx9, vwx10, eg) → new_not(new_esEs8(new_compare(vwx9, vwx10, eg), GT))
new_lt20(vwx90, vwx100, app(ty_Ratio, bfg)) → new_lt4(vwx90, vwx100, bfg)
new_esEs4(Left(vwx300), Left(vwx400), ty_Double, cch) → new_esEs16(vwx300, vwx400)
new_esEs27(vwx301, vwx401, ty_@0) → new_esEs9(vwx301, vwx401)
new_compare25(vwx90, vwx100, False) → new_compare10(vwx90, vwx100, new_ltEs17(vwx90, vwx100))
new_esEs8(EQ, GT) → False
new_esEs8(GT, EQ) → False
new_ltEs5(vwx92, vwx102, ty_Bool) → new_ltEs14(vwx92, vwx102)
new_esEs27(vwx301, vwx401, ty_Double) → new_esEs16(vwx301, vwx401)
new_lt6(vwx90, vwx100, app(app(ty_@2, bbd), bbe)) → new_lt17(vwx90, vwx100, bbd, bbe)
new_esEs12(Char(vwx300), Char(vwx400)) → new_primEqNat0(vwx300, vwx400)
new_not(False) → True
new_esEs28(vwx300, vwx400, ty_@0) → new_esEs9(vwx300, vwx400)
new_compare30(vwx90, vwx100, ty_Bool) → new_compare12(vwx90, vwx100)
new_lt20(vwx90, vwx100, ty_Bool) → new_lt15(vwx90, vwx100)
new_ltEs6(Right(vwx90), Right(vwx100), cc, app(ty_Ratio, bgd)) → new_ltEs7(vwx90, vwx100, bgd)
new_primPlusNat0(Zero, vwx40100) → Succ(vwx40100)
new_primCmpInt(Pos(Succ(vwx900)), Pos(vwx100)) → new_primCmpNat0(Succ(vwx900), vwx100)
new_esEs4(Right(vwx300), Right(vwx400), cec, app(ty_Ratio, cfe)) → new_esEs17(vwx300, vwx400, cfe)
new_esEs23(vwx90, vwx100, app(app(ty_@2, ge), gf)) → new_esEs6(vwx90, vwx100, ge, gf)
new_esEs25(vwx300, vwx400, ty_Integer) → new_esEs15(vwx300, vwx400)
new_ltEs6(Left(vwx90), Left(vwx100), ty_Float, bc) → new_ltEs18(vwx90, vwx100)
new_esEs20(vwx301, vwx401, ty_Float) → new_esEs14(vwx301, vwx401)
new_esEs18(vwx91, vwx101, ty_Char) → new_esEs12(vwx91, vwx101)
new_ltEs6(Left(vwx90), Left(vwx100), ty_Char, bc) → new_ltEs12(vwx90, vwx100)
new_compare28(vwx90, vwx100, True) → EQ
new_esEs4(Right(vwx300), Right(vwx400), cec, app(app(ty_@2, cfc), cfd)) → new_esEs6(vwx300, vwx400, cfc, cfd)
new_esEs22(vwx300, vwx400, app(ty_[], cca)) → new_esEs13(vwx300, vwx400, cca)
new_esEs5(Just(vwx300), Just(vwx400), ty_Char) → new_esEs12(vwx300, vwx400)
new_esEs18(vwx91, vwx101, app(app(ty_Either, bcb), bcc)) → new_esEs4(vwx91, vwx101, bcb, bcc)
new_esEs22(vwx300, vwx400, ty_Bool) → new_esEs11(vwx300, vwx400)
new_ltEs6(Left(vwx90), Left(vwx100), app(app(app(ty_@3, bh), ca), cb), bc) → new_ltEs4(vwx90, vwx100, bh, ca, cb)
new_esEs20(vwx301, vwx401, ty_@0) → new_esEs9(vwx301, vwx401)
new_primCmpInt(Pos(Succ(vwx900)), Neg(vwx100)) → GT
new_esEs22(vwx300, vwx400, app(app(app(ty_@3, cbd), cbe), cbf)) → new_esEs7(vwx300, vwx400, cbd, cbe, cbf)
new_ltEs11(Just(vwx90), Just(vwx100), ty_Double) → new_ltEs15(vwx90, vwx100)
new_primMulInt(Pos(vwx3010), Pos(vwx4010)) → Pos(new_primMulNat0(vwx3010, vwx4010))
new_esEs27(vwx301, vwx401, ty_Bool) → new_esEs11(vwx301, vwx401)
new_ltEs6(Left(vwx90), Left(vwx100), app(app(ty_@2, bf), bg), bc) → new_ltEs16(vwx90, vwx100, bf, bg)
new_esEs28(vwx300, vwx400, app(app(app(ty_@3, dba), dbb), dbc)) → new_esEs7(vwx300, vwx400, dba, dbb, dbc)
new_esEs23(vwx90, vwx100, app(app(ty_Either, gb), gc)) → new_esEs4(vwx90, vwx100, gb, gc)
new_esEs22(vwx300, vwx400, ty_Int) → new_esEs10(vwx300, vwx400)
new_compare26(vwx90, vwx100, False, ge, gf) → new_compare18(vwx90, vwx100, new_ltEs16(vwx90, vwx100, ge, gf), ge, gf)
new_primMulInt(Neg(vwx3010), Neg(vwx4010)) → Pos(new_primMulNat0(vwx3010, vwx4010))
new_esEs27(vwx301, vwx401, app(app(ty_@2, daf), dag)) → new_esEs6(vwx301, vwx401, daf, dag)
new_compare110(vwx90, vwx100, True) → LT
new_esEs20(vwx301, vwx401, ty_Integer) → new_esEs15(vwx301, vwx401)
new_ltEs19(vwx91, vwx101, ty_Integer) → new_ltEs10(vwx91, vwx101)
new_lt7(vwx91, vwx101, ty_Double) → new_lt16(vwx91, vwx101)
new_esEs17(:%(vwx300, vwx301), :%(vwx400, vwx401), cfg) → new_asAs(new_esEs25(vwx300, vwx400, cfg), new_esEs24(vwx301, vwx401, cfg))
new_primEqNat0(Zero, Succ(vwx4000)) → False
new_primEqNat0(Succ(vwx3000), Zero) → False
new_esEs18(vwx91, vwx101, ty_Integer) → new_esEs15(vwx91, vwx101)
new_compare110(vwx90, vwx100, False) → GT
new_ltEs14(True, True) → True
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs13(:(vwx300, vwx301), :(vwx400, vwx401), cbc) → new_asAs(new_esEs22(vwx300, vwx400, cbc), new_esEs13(vwx301, vwx401, cbc))
new_ltEs6(Left(vwx90), Left(vwx100), ty_Int, bc) → new_ltEs8(vwx90, vwx100)
new_esEs27(vwx301, vwx401, app(app(ty_Either, dab), dac)) → new_esEs4(vwx301, vwx401, dab, dac)
new_lt20(vwx90, vwx100, app(app(ty_Either, gb), gc)) → new_lt8(vwx90, vwx100, gb, gc)
new_compare31(vwx90, vwx100, gd) → new_compare210(vwx90, vwx100, new_esEs5(vwx90, vwx100, gd), gd)
new_esEs19(vwx90, vwx100, app(ty_Maybe, bbb)) → new_esEs5(vwx90, vwx100, bbb)
new_ltEs11(Just(vwx90), Just(vwx100), ty_Integer) → new_ltEs10(vwx90, vwx100)
new_lt15(vwx90, vwx100) → new_esEs8(new_compare12(vwx90, vwx100), LT)
new_esEs26(vwx302, vwx402, app(ty_Maybe, chc)) → new_esEs5(vwx302, vwx402, chc)
new_ltEs9(vwx9, vwx10) → new_not(new_esEs8(new_compare5(vwx9, vwx10), GT))
new_esEs4(Left(vwx300), Left(vwx400), app(ty_[], cdf), cch) → new_esEs13(vwx300, vwx400, cdf)
new_compare13(vwx90, vwx100, False, gd) → GT
new_esEs28(vwx300, vwx400, app(ty_Ratio, dcb)) → new_esEs17(vwx300, vwx400, dcb)
new_esEs23(vwx90, vwx100, app(ty_Ratio, bfg)) → new_esEs17(vwx90, vwx100, bfg)
new_esEs4(Right(vwx300), Right(vwx400), cec, ty_@0) → new_esEs9(vwx300, vwx400)
new_esEs18(vwx91, vwx101, ty_Double) → new_esEs16(vwx91, vwx101)
new_ltEs5(vwx92, vwx102, ty_Ordering) → new_ltEs17(vwx92, vwx102)
new_primCmpInt(Neg(Zero), Neg(Succ(vwx1000))) → new_primCmpNat0(Succ(vwx1000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(vwx1000))) → GT
new_esEs18(vwx91, vwx101, ty_Float) → new_esEs14(vwx91, vwx101)
new_esEs11(True, False) → False
new_esEs11(False, True) → False
new_lt9(vwx90, vwx100) → new_esEs8(new_compare11(vwx90, vwx100), LT)
new_compare15(vwx90, vwx100, False, gb, gc) → GT
new_esEs28(vwx300, vwx400, app(app(ty_@2, dbh), dca)) → new_esEs6(vwx300, vwx400, dbh, dca)
new_esEs26(vwx302, vwx402, ty_@0) → new_esEs9(vwx302, vwx402)
new_lt20(vwx90, vwx100, ty_Double) → new_lt16(vwx90, vwx100)
new_compare18(vwx90, vwx100, True, ge, gf) → LT
new_ltEs8(vwx9, vwx10) → new_not(new_esEs8(new_compare11(vwx9, vwx10), GT))
new_ltEs11(Just(vwx90), Just(vwx100), ty_@0) → new_ltEs9(vwx90, vwx100)
new_esEs21(vwx300, vwx400, ty_Bool) → new_esEs11(vwx300, vwx400)
new_ltEs6(Right(vwx90), Right(vwx100), cc, app(app(ty_Either, cd), ce)) → new_ltEs6(vwx90, vwx100, cd, ce)
new_ltEs6(Left(vwx90), Left(vwx100), ty_Bool, bc) → new_ltEs14(vwx90, vwx100)
new_primCompAux0(vwx90, vwx100, vwx65, eg) → new_primCompAux00(vwx65, new_compare30(vwx90, vwx100, eg))
new_ltEs6(Right(vwx90), Right(vwx100), cc, ty_Char) → new_ltEs12(vwx90, vwx100)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_ltEs18(vwx9, vwx10) → new_not(new_esEs8(new_compare7(vwx9, vwx10), GT))
new_ltEs19(vwx91, vwx101, ty_Float) → new_ltEs18(vwx91, vwx101)
new_ltEs12(vwx9, vwx10) → new_not(new_esEs8(new_compare9(vwx9, vwx10), GT))
new_esEs28(vwx300, vwx400, ty_Bool) → new_esEs11(vwx300, vwx400)
new_compare7(Float(vwx90, vwx91), Float(vwx100, vwx101)) → new_compare11(new_sr(vwx90, vwx100), new_sr(vwx91, vwx101))
new_esEs24(vwx301, vwx401, ty_Int) → new_esEs10(vwx301, vwx401)
new_esEs20(vwx301, vwx401, app(ty_Maybe, bhe)) → new_esEs5(vwx301, vwx401, bhe)
new_esEs19(vwx90, vwx100, ty_Double) → new_esEs16(vwx90, vwx100)
new_asAs(False, vwx35) → False
new_primMulInt(Pos(vwx3010), Neg(vwx4010)) → Neg(new_primMulNat0(vwx3010, vwx4010))
new_primMulInt(Neg(vwx3010), Pos(vwx4010)) → Neg(new_primMulNat0(vwx3010, vwx4010))
new_esEs13(:(vwx300, vwx301), [], cbc) → False
new_esEs13([], :(vwx400, vwx401), cbc) → False
new_primMulNat0(Succ(vwx30100), Zero) → Zero
new_primMulNat0(Zero, Succ(vwx40100)) → Zero
new_compare8(Double(vwx90, vwx91), Double(vwx100, vwx101)) → new_compare11(new_sr(vwx90, vwx100), new_sr(vwx91, vwx101))
new_compare30(vwx90, vwx100, ty_Integer) → new_compare17(vwx90, vwx100)
new_esEs21(vwx300, vwx400, ty_Ordering) → new_esEs8(vwx300, vwx400)
new_lt20(vwx90, vwx100, app(ty_[], gh)) → new_lt14(vwx90, vwx100, gh)
new_ltEs6(Left(vwx90), Left(vwx100), ty_Integer, bc) → new_ltEs10(vwx90, vwx100)
new_compare17(Integer(vwx90), Integer(vwx100)) → new_primCmpInt(vwx90, vwx100)
new_esEs5(Just(vwx300), Just(vwx400), app(app(ty_@2, bfd), bfe)) → new_esEs6(vwx300, vwx400, bfd, bfe)
new_esEs18(vwx91, vwx101, app(ty_Maybe, bcd)) → new_esEs5(vwx91, vwx101, bcd)
new_esEs28(vwx300, vwx400, ty_Integer) → new_esEs15(vwx300, vwx400)
new_esEs4(Left(vwx300), Left(vwx400), app(ty_Maybe, cdg), cch) → new_esEs5(vwx300, vwx400, cdg)
new_esEs18(vwx91, vwx101, ty_Ordering) → new_esEs8(vwx91, vwx101)
new_esEs28(vwx300, vwx400, app(app(ty_Either, dbd), dbe)) → new_esEs4(vwx300, vwx400, dbd, dbe)
new_esEs11(True, True) → True
new_compare16(vwx90, vwx100, ge, gf) → new_compare26(vwx90, vwx100, new_esEs6(vwx90, vwx100, ge, gf), ge, gf)
new_esEs23(vwx90, vwx100, ty_Char) → new_esEs12(vwx90, vwx100)
new_esEs23(vwx90, vwx100, app(ty_Maybe, gd)) → new_esEs5(vwx90, vwx100, gd)
new_ltEs5(vwx92, vwx102, ty_Char) → new_ltEs12(vwx92, vwx102)
new_lt6(vwx90, vwx100, ty_Float) → new_lt5(vwx90, vwx100)
new_compare18(vwx90, vwx100, False, ge, gf) → GT
new_esEs4(Left(vwx300), Left(vwx400), ty_@0, cch) → new_esEs9(vwx300, vwx400)
new_esEs23(vwx90, vwx100, ty_Double) → new_esEs16(vwx90, vwx100)
new_lt6(vwx90, vwx100, app(ty_Maybe, bbb)) → new_lt12(vwx90, vwx100, bbb)
new_esEs23(vwx90, vwx100, ty_Integer) → new_esEs15(vwx90, vwx100)
new_ltEs17(GT, GT) → True
new_ltEs17(GT, EQ) → False
new_esEs5(Nothing, Just(vwx400), bed) → False
new_esEs5(Just(vwx300), Nothing, bed) → False
new_ltEs6(Right(vwx90), Right(vwx100), cc, app(app(ty_@2, da), db)) → new_ltEs16(vwx90, vwx100, da, db)
new_compare11(vwx9, vwx10) → new_primCmpInt(vwx9, vwx10)
new_ltEs11(Just(vwx90), Just(vwx100), ty_Ordering) → new_ltEs17(vwx90, vwx100)
new_ltEs14(True, False) → False
new_compare30(vwx90, vwx100, ty_Int) → new_compare11(vwx90, vwx100)
new_compare24(vwx90, vwx100, False, gb, gc) → new_compare15(vwx90, vwx100, new_ltEs6(vwx90, vwx100, gb, gc), gb, gc)
new_lt7(vwx91, vwx101, ty_Char) → new_lt13(vwx91, vwx101)
new_esEs21(vwx300, vwx400, ty_@0) → new_esEs9(vwx300, vwx400)
new_ltEs6(Right(vwx90), Right(vwx100), cc, ty_Double) → new_ltEs15(vwx90, vwx100)
new_esEs5(Nothing, Nothing, bed) → True
new_esEs28(vwx300, vwx400, app(ty_Maybe, dbg)) → new_esEs5(vwx300, vwx400, dbg)
new_esEs5(Just(vwx300), Just(vwx400), app(app(app(ty_@3, bee), bef), beg)) → new_esEs7(vwx300, vwx400, bee, bef, beg)
new_compare6(:%(vwx90, vwx91), :%(vwx100, vwx101), ty_Int) → new_compare11(new_sr(vwx90, vwx101), new_sr(vwx100, vwx91))
new_esEs18(vwx91, vwx101, ty_Bool) → new_esEs11(vwx91, vwx101)
new_esEs7(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), cgb, cgc, cgd) → new_asAs(new_esEs28(vwx300, vwx400, cgb), new_asAs(new_esEs27(vwx301, vwx401, cgc), new_esEs26(vwx302, vwx402, cgd)))
new_compare6(:%(vwx90, vwx91), :%(vwx100, vwx101), ty_Integer) → new_compare17(new_sr0(vwx90, vwx101), new_sr0(vwx100, vwx91))
new_esEs5(Just(vwx300), Just(vwx400), app(ty_Ratio, bff)) → new_esEs17(vwx300, vwx400, bff)
new_ltEs5(vwx92, vwx102, ty_Float) → new_ltEs18(vwx92, vwx102)
new_lt4(vwx90, vwx100, bfg) → new_esEs8(new_compare6(vwx90, vwx100, bfg), LT)
new_ltEs6(Right(vwx90), Right(vwx100), cc, ty_@0) → new_ltEs9(vwx90, vwx100)
new_esEs28(vwx300, vwx400, ty_Int) → new_esEs10(vwx300, vwx400)
new_ltEs19(vwx91, vwx101, ty_Double) → new_ltEs15(vwx91, vwx101)
new_esEs22(vwx300, vwx400, app(ty_Ratio, cce)) → new_esEs17(vwx300, vwx400, cce)
new_compare30(vwx90, vwx100, ty_Ordering) → new_compare32(vwx90, vwx100)
new_compare28(vwx90, vwx100, False) → new_compare110(vwx90, vwx100, new_ltEs14(vwx90, vwx100))
new_esEs22(vwx300, vwx400, ty_Double) → new_esEs16(vwx300, vwx400)
new_esEs22(vwx300, vwx400, app(ty_Maybe, ccb)) → new_esEs5(vwx300, vwx400, ccb)
new_esEs21(vwx300, vwx400, app(ty_Maybe, cag)) → new_esEs5(vwx300, vwx400, cag)
new_esEs22(vwx300, vwx400, ty_Integer) → new_esEs15(vwx300, vwx400)
new_primPlusNat1(Zero, Zero) → Zero
new_ltEs19(vwx91, vwx101, app(app(ty_@2, baa), bab)) → new_ltEs16(vwx91, vwx101, baa, bab)
new_esEs4(Left(vwx300), Left(vwx400), ty_Bool, cch) → new_esEs11(vwx300, vwx400)
new_esEs19(vwx90, vwx100, ty_Integer) → new_esEs15(vwx90, vwx100)
new_ltEs5(vwx92, vwx102, app(ty_[], bdf)) → new_ltEs13(vwx92, vwx102, bdf)
new_esEs26(vwx302, vwx402, app(app(ty_Either, cgh), cha)) → new_esEs4(vwx302, vwx402, cgh, cha)
new_asAs(True, vwx35) → vwx35
new_esEs26(vwx302, vwx402, ty_Float) → new_esEs14(vwx302, vwx402)
new_esEs19(vwx90, vwx100, app(app(ty_Either, baf), bag)) → new_esEs4(vwx90, vwx100, baf, bag)
new_esEs22(vwx300, vwx400, ty_@0) → new_esEs9(vwx300, vwx400)
new_ltEs19(vwx91, vwx101, app(ty_Ratio, cff)) → new_ltEs7(vwx91, vwx101, cff)
new_primMulNat0(Succ(vwx30100), Succ(vwx40100)) → new_primPlusNat0(new_primMulNat0(vwx30100, Succ(vwx40100)), vwx40100)
new_ltEs17(LT, EQ) → True
new_lt6(vwx90, vwx100, ty_Ordering) → new_lt19(vwx90, vwx100)
new_esEs27(vwx301, vwx401, app(ty_[], dad)) → new_esEs13(vwx301, vwx401, dad)
new_ltEs11(Nothing, Nothing, ccf) → True
new_esEs4(Right(vwx300), Left(vwx400), cec, cch) → False
new_esEs4(Left(vwx300), Right(vwx400), cec, cch) → False
new_compare30(vwx90, vwx100, app(app(app(ty_@3, fg), fh), ga)) → new_compare29(vwx90, vwx100, fg, fh, ga)
new_compare30(vwx90, vwx100, app(app(ty_@2, fd), ff)) → new_compare16(vwx90, vwx100, fd, ff)
new_ltEs19(vwx91, vwx101, ty_@0) → new_ltEs9(vwx91, vwx101)
new_esEs27(vwx301, vwx401, ty_Int) → new_esEs10(vwx301, vwx401)
new_esEs23(vwx90, vwx100, ty_Int) → new_esEs10(vwx90, vwx100)
new_esEs21(vwx300, vwx400, ty_Int) → new_esEs10(vwx300, vwx400)
new_compare27(vwx90, vwx100, True, ha, hb, hc) → EQ
new_esEs26(vwx302, vwx402, app(app(ty_@2, chd), che)) → new_esEs6(vwx302, vwx402, chd, che)
new_lt20(vwx90, vwx100, ty_Int) → new_lt9(vwx90, vwx100)
new_esEs19(vwx90, vwx100, ty_Ordering) → new_esEs8(vwx90, vwx100)
new_esEs26(vwx302, vwx402, ty_Double) → new_esEs16(vwx302, vwx402)
new_esEs27(vwx301, vwx401, ty_Float) → new_esEs14(vwx301, vwx401)
new_ltEs6(Right(vwx90), Right(vwx100), cc, app(ty_Maybe, cf)) → new_ltEs11(vwx90, vwx100, cf)
new_compare30(vwx90, vwx100, ty_Char) → new_compare9(vwx90, vwx100)
new_compare30(vwx90, vwx100, ty_@0) → new_compare5(vwx90, vwx100)
new_compare10(vwx90, vwx100, True) → LT
new_esEs5(Just(vwx300), Just(vwx400), ty_@0) → new_esEs9(vwx300, vwx400)
new_lt17(vwx90, vwx100, ge, gf) → new_esEs8(new_compare16(vwx90, vwx100, ge, gf), LT)
new_esEs19(vwx90, vwx100, app(ty_[], bbc)) → new_esEs13(vwx90, vwx100, bbc)
new_esEs27(vwx301, vwx401, app(ty_Ratio, dah)) → new_esEs17(vwx301, vwx401, dah)
new_ltEs17(EQ, GT) → True
new_compare10(vwx90, vwx100, False) → GT
new_primCompAux00(vwx69, GT) → GT
new_esEs10(vwx30, vwx40) → new_primEqInt(vwx30, vwx40)
new_esEs5(Just(vwx300), Just(vwx400), app(app(ty_Either, beh), bfa)) → new_esEs4(vwx300, vwx400, beh, bfa)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_ltEs5(vwx92, vwx102, app(app(app(ty_@3, bea), beb), bec)) → new_ltEs4(vwx92, vwx102, bea, beb, bec)
new_lt7(vwx91, vwx101, ty_@0) → new_lt10(vwx91, vwx101)
new_ltEs19(vwx91, vwx101, app(app(ty_Either, he), hf)) → new_ltEs6(vwx91, vwx101, he, hf)
new_lt20(vwx90, vwx100, app(ty_Maybe, gd)) → new_lt12(vwx90, vwx100, gd)
new_ltEs19(vwx91, vwx101, app(ty_[], hh)) → new_ltEs13(vwx91, vwx101, hh)
new_esEs28(vwx300, vwx400, ty_Char) → new_esEs12(vwx300, vwx400)
new_ltEs11(Just(vwx90), Nothing, ccf) → False
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_esEs27(vwx301, vwx401, ty_Integer) → new_esEs15(vwx301, vwx401)
new_primCmpInt(Neg(Succ(vwx900)), Pos(vwx100)) → LT
new_esEs23(vwx90, vwx100, app(ty_[], gh)) → new_esEs13(vwx90, vwx100, gh)
new_esEs19(vwx90, vwx100, ty_Char) → new_esEs12(vwx90, vwx100)
new_lt7(vwx91, vwx101, ty_Float) → new_lt5(vwx91, vwx101)
new_not(True) → False

The set Q consists of the following terms:

new_compare30(x0, x1, ty_Bool)
new_esEs26(x0, x1, ty_Float)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_ltEs15(x0, x1)
new_esEs4(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs11(True, True)
new_esEs18(x0, x1, app(ty_Ratio, x2))
new_ltEs6(Left(x0), Left(x1), ty_@0, x2)
new_ltEs5(x0, x1, ty_Integer)
new_esEs4(Left(x0), Left(x1), ty_Float, x2)
new_esEs26(x0, x1, ty_Ordering)
new_esEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs11(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_ltEs6(Left(x0), Left(x1), ty_Int, x2)
new_ltEs11(Just(x0), Just(x1), ty_Float)
new_compare29(x0, x1, x2, x3, x4)
new_esEs23(x0, x1, ty_Ordering)
new_compare30(x0, x1, ty_Double)
new_ltEs6(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs4(Right(x0), Left(x1), x2, x3)
new_esEs4(Left(x0), Right(x1), x2, x3)
new_ltEs19(x0, x1, ty_Integer)
new_esEs5(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs4(Right(x0), Right(x1), x2, ty_Char)
new_ltEs18(x0, x1)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_ltEs17(EQ, GT)
new_ltEs17(GT, EQ)
new_ltEs11(Just(x0), Just(x1), app(ty_Maybe, x2))
new_lt15(x0, x1)
new_esEs4(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_compare11(x0, x1)
new_lt20(x0, x1, app(ty_[], x2))
new_lt7(x0, x1, app(ty_[], x2))
new_ltEs14(True, False)
new_ltEs14(False, True)
new_primCompAux00(x0, GT)
new_ltEs19(x0, x1, app(ty_[], x2))
new_esEs11(False, True)
new_esEs11(True, False)
new_esEs27(x0, x1, ty_@0)
new_esEs20(x0, x1, ty_Char)
new_ltEs6(Right(x0), Right(x1), x2, ty_@0)
new_esEs8(GT, GT)
new_esEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs22(x0, x1, ty_Bool)
new_lt6(x0, x1, app(app(ty_Either, x2), x3))
new_esEs18(x0, x1, app(ty_Maybe, x2))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_esEs14(Float(x0, x1), Float(x2, x3))
new_lt6(x0, x1, ty_Integer)
new_lt6(x0, x1, app(ty_[], x2))
new_ltEs10(x0, x1)
new_lt7(x0, x1, ty_Integer)
new_esEs21(x0, x1, ty_Int)
new_esEs21(x0, x1, ty_Double)
new_esEs4(Right(x0), Right(x1), x2, ty_Ordering)
new_ltEs6(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs8(LT, LT)
new_esEs18(x0, x1, app(app(ty_Either, x2), x3))
new_compare210(x0, x1, False, x2)
new_lt7(x0, x1, ty_Char)
new_compare25(x0, x1, True)
new_esEs28(x0, x1, ty_Double)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_compare10(x0, x1, True)
new_esEs28(x0, x1, ty_Bool)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs27(x0, x1, ty_Int)
new_primPlusNat1(Succ(x0), Zero)
new_esEs5(Just(x0), Just(x1), ty_Float)
new_ltEs6(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs4(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs5(x0, x1, ty_Char)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_esEs4(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs23(x0, x1, ty_Int)
new_compare30(x0, x1, ty_Integer)
new_esEs25(x0, x1, ty_Int)
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_ltEs6(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, ty_@0)
new_esEs4(Left(x0), Left(x1), app(ty_[], x2), x3)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs18(x0, x1, ty_Bool)
new_compare30(x0, x1, app(ty_Ratio, x2))
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare5(@0, @0)
new_esEs23(x0, x1, ty_Bool)
new_ltEs6(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_lt7(x0, x1, app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, ty_Char)
new_esEs18(x0, x1, ty_Char)
new_ltEs11(Nothing, Nothing, x0)
new_esEs21(x0, x1, ty_Char)
new_ltEs6(Left(x0), Right(x1), x2, x3)
new_ltEs6(Right(x0), Left(x1), x2, x3)
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, app(ty_[], x2))
new_primEqNat0(Zero, Zero)
new_esEs27(x0, x1, ty_Integer)
new_esEs19(x0, x1, app(ty_[], x2))
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare27(x0, x1, True, x2, x3, x4)
new_lt7(x0, x1, ty_Float)
new_ltEs6(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_compare27(x0, x1, False, x2, x3, x4)
new_lt6(x0, x1, ty_Ordering)
new_lt6(x0, x1, ty_Float)
new_ltEs4(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs22(x0, x1, ty_Char)
new_compare30(x0, x1, ty_Ordering)
new_compare15(x0, x1, True, x2, x3)
new_pePe(False, x0)
new_esEs27(x0, x1, ty_Char)
new_esEs19(x0, x1, ty_Integer)
new_ltEs19(x0, x1, ty_Ordering)
new_ltEs6(Right(x0), Right(x1), x2, ty_Integer)
new_esEs19(x0, x1, ty_Int)
new_lt20(x0, x1, ty_Char)
new_sr0(Integer(x0), Integer(x1))
new_lt20(x0, x1, ty_Double)
new_ltEs5(x0, x1, ty_Ordering)
new_lt10(x0, x1)
new_primMulNat0(Zero, Zero)
new_ltEs6(Left(x0), Left(x1), ty_Bool, x2)
new_asAs(False, x0)
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_esEs18(x0, x1, ty_Float)
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare25(x0, x1, False)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCompAux00(x0, EQ)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs22(x0, x1, ty_Int)
new_lt19(x0, x1)
new_lt6(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_compare15(x0, x1, False, x2, x3)
new_esEs5(Just(x0), Just(x1), ty_Double)
new_esEs4(Left(x0), Left(x1), ty_Char, x2)
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs19(x0, x1, ty_Char)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_compare([], :(x0, x1), x2)
new_compare13(x0, x1, True, x2)
new_lt5(x0, x1)
new_esEs22(x0, x1, ty_@0)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_ltEs11(Just(x0), Just(x1), app(ty_[], x2))
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs19(x0, x1, app(ty_Maybe, x2))
new_lt20(x0, x1, app(ty_Maybe, x2))
new_compare17(Integer(x0), Integer(x1))
new_compare19(x0, x1, True, x2, x3, x4)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs5(Just(x0), Just(x1), app(ty_Maybe, x2))
new_ltEs11(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, ty_@0)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_esEs19(x0, x1, app(ty_Ratio, x2))
new_esEs4(Left(x0), Left(x1), ty_Int, x2)
new_esEs28(x0, x1, ty_Int)
new_esEs6(@2(x0, x1), @2(x2, x3), x4, x5)
new_compare7(Float(x0, x1), Float(x2, x3))
new_esEs22(x0, x1, app(ty_[], x2))
new_lt6(x0, x1, ty_Char)
new_lt20(x0, x1, ty_Bool)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_compare26(x0, x1, False, x2, x3)
new_pePe(True, x0)
new_esEs16(Double(x0, x1), Double(x2, x3))
new_lt20(x0, x1, ty_Float)
new_compare([], [], x0)
new_esEs12(Char(x0), Char(x1))
new_ltEs5(x0, x1, ty_Bool)
new_esEs5(Nothing, Just(x0), x1)
new_esEs4(Right(x0), Right(x1), x2, ty_Integer)
new_esEs23(x0, x1, ty_Integer)
new_primMulInt(Neg(x0), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs11(False, False)
new_primCompAux00(x0, LT)
new_esEs21(x0, x1, ty_Float)
new_esEs20(x0, x1, ty_@0)
new_compare13(x0, x1, False, x2)
new_esEs20(x0, x1, ty_Ordering)
new_esEs20(x0, x1, ty_Double)
new_esEs5(Just(x0), Just(x1), ty_Char)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs22(x0, x1, ty_Integer)
new_esEs20(x0, x1, ty_Int)
new_compare(:(x0, x1), [], x2)
new_lt7(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_ltEs13(x0, x1, x2)
new_ltEs6(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs5(Just(x0), Nothing, x1)
new_esEs21(x0, x1, ty_@0)
new_esEs4(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_lt6(x0, x1, ty_@0)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_lt16(x0, x1)
new_esEs20(x0, x1, ty_Bool)
new_ltEs11(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs18(x0, x1, ty_Integer)
new_primEqNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, Zero)
new_esEs15(Integer(x0), Integer(x1))
new_ltEs9(x0, x1)
new_lt8(x0, x1, x2, x3)
new_esEs17(:%(x0, x1), :%(x2, x3), x4)
new_ltEs6(Right(x0), Right(x1), x2, ty_Double)
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs7(x0, x1, x2)
new_lt6(x0, x1, ty_Int)
new_esEs21(x0, x1, ty_Integer)
new_ltEs5(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs6(Left(x0), Left(x1), app(ty_[], x2), x3)
new_ltEs5(x0, x1, app(ty_Ratio, x2))
new_lt20(x0, x1, ty_Ordering)
new_esEs4(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_lt13(x0, x1)
new_esEs5(Just(x0), Just(x1), ty_Bool)
new_primCmpNat0(Succ(x0), Zero)
new_ltEs6(Left(x0), Left(x1), ty_Float, x2)
new_esEs18(x0, x1, ty_Ordering)
new_esEs28(x0, x1, ty_Char)
new_lt14(x0, x1, x2)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_compare8(Double(x0, x1), Double(x2, x3))
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs27(x0, x1, ty_Float)
new_primMulNat0(Succ(x0), Succ(x1))
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, ty_Int)
new_ltEs5(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs6(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_primMulNat0(Zero, Succ(x0))
new_compare28(x0, x1, True)
new_ltEs5(x0, x1, ty_Int)
new_esEs20(x0, x1, ty_Float)
new_ltEs6(Left(x0), Left(x1), ty_Char, x2)
new_esEs21(x0, x1, ty_Bool)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_ltEs8(x0, x1)
new_esEs26(x0, x1, ty_@0)
new_ltEs6(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs4(Right(x0), Right(x1), x2, ty_Int)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat0(Succ(x0), Succ(x1))
new_compare210(x0, x1, True, x2)
new_ltEs17(GT, GT)
new_esEs22(x0, x1, ty_Float)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_esEs5(Just(x0), Just(x1), ty_Ordering)
new_compare110(x0, x1, False)
new_esEs13(:(x0, x1), :(x2, x3), x4)
new_esEs20(x0, x1, ty_Integer)
new_esEs26(x0, x1, ty_Int)
new_lt20(x0, x1, ty_Integer)
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_lt6(x0, x1, app(app(ty_@2, x2), x3))
new_primPlusNat0(Zero, x0)
new_esEs5(Nothing, Nothing, x0)
new_lt18(x0, x1, x2, x3, x4)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_compare31(x0, x1, x2)
new_esEs21(x0, x1, ty_Ordering)
new_esEs4(Right(x0), Right(x1), x2, ty_@0)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs11(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_lt17(x0, x1, x2, x3)
new_compare24(x0, x1, True, x2, x3)
new_ltEs11(Just(x0), Nothing, x1)
new_esEs19(x0, x1, ty_Ordering)
new_compare16(x0, x1, x2, x3)
new_primEqInt(Neg(Zero), Neg(Zero))
new_compare30(x0, x1, app(app(ty_@2, x2), x3))
new_esEs22(x0, x1, ty_Double)
new_esEs4(Right(x0), Right(x1), x2, ty_Bool)
new_esEs26(x0, x1, app(ty_[], x2))
new_esEs4(Left(x0), Left(x1), ty_@0, x2)
new_esEs18(x0, x1, ty_Int)
new_ltEs11(Just(x0), Just(x1), ty_Integer)
new_esEs19(x0, x1, ty_Float)
new_esEs5(Just(x0), Just(x1), ty_Int)
new_lt7(x0, x1, app(ty_Ratio, x2))
new_compare30(x0, x1, ty_Float)
new_ltEs11(Just(x0), Just(x1), ty_@0)
new_esEs23(x0, x1, ty_Float)
new_ltEs19(x0, x1, ty_Double)
new_lt6(x0, x1, ty_Double)
new_esEs19(x0, x1, ty_Char)
new_compare12(x0, x1)
new_ltEs11(Just(x0), Just(x1), ty_Bool)
new_ltEs5(x0, x1, app(ty_[], x2))
new_ltEs12(x0, x1)
new_esEs13([], :(x0, x1), x2)
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_compare30(x0, x1, app(app(ty_Either, x2), x3))
new_esEs9(@0, @0)
new_esEs4(Right(x0), Right(x1), x2, ty_Float)
new_esEs26(x0, x1, ty_Double)
new_esEs28(x0, x1, ty_@0)
new_ltEs5(x0, x1, ty_Double)
new_esEs8(GT, EQ)
new_esEs8(EQ, GT)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs5(x0, x1, ty_@0)
new_lt7(x0, x1, ty_Int)
new_compare28(x0, x1, False)
new_esEs24(x0, x1, ty_Integer)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_primCmpNat0(Zero, Zero)
new_esEs5(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs4(Left(x0), Left(x1), ty_Integer, x2)
new_lt7(x0, x1, ty_Double)
new_ltEs6(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_lt11(x0, x1)
new_esEs23(x0, x1, ty_Double)
new_ltEs6(Right(x0), Right(x1), x2, ty_Bool)
new_compare30(x0, x1, ty_Char)
new_lt4(x0, x1, x2)
new_esEs18(x0, x1, app(ty_[], x2))
new_esEs4(Left(x0), Left(x1), ty_Bool, x2)
new_lt7(x0, x1, ty_@0)
new_esEs22(x0, x1, ty_Ordering)
new_ltEs6(Right(x0), Right(x1), x2, ty_Int)
new_ltEs19(x0, x1, ty_Bool)
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs17(LT, GT)
new_ltEs17(GT, LT)
new_esEs5(Just(x0), Just(x1), ty_Integer)
new_esEs28(x0, x1, ty_Ordering)
new_esEs28(x0, x1, ty_Integer)
new_esEs13(:(x0, x1), [], x2)
new_esEs4(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_primEqNat0(Zero, Succ(x0))
new_esEs4(Left(x0), Left(x1), ty_Double, x2)
new_esEs4(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs27(x0, x1, ty_Bool)
new_compare32(x0, x1)
new_esEs5(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_ltEs11(Just(x0), Just(x1), ty_Char)
new_ltEs14(True, True)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs11(Just(x0), Just(x1), ty_Int)
new_ltEs11(Just(x0), Just(x1), ty_Ordering)
new_lt7(x0, x1, app(app(ty_@2, x2), x3))
new_esEs10(x0, x1)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_ltEs14(False, False)
new_compare19(x0, x1, False, x2, x3, x4)
new_compare18(x0, x1, False, x2, x3)
new_esEs26(x0, x1, ty_Char)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_esEs5(Just(x0), Just(x1), ty_@0)
new_ltEs6(Left(x0), Left(x1), ty_Integer, x2)
new_ltEs5(x0, x1, app(app(ty_@2, x2), x3))
new_not(True)
new_ltEs11(Nothing, Just(x0), x1)
new_esEs5(Just(x0), Just(x1), app(ty_[], x2))
new_compare26(x0, x1, True, x2, x3)
new_compare(:(x0, x1), :(x2, x3), x4)
new_esEs28(x0, x1, ty_Float)
new_ltEs6(Right(x0), Right(x1), x2, ty_Char)
new_ltEs5(x0, x1, ty_Float)
new_compare30(x0, x1, ty_Int)
new_esEs18(x0, x1, app(app(ty_@2, x2), x3))
new_esEs21(x0, x1, app(ty_[], x2))
new_compare6(:%(x0, x1), :%(x2, x3), ty_Int)
new_esEs13([], [], x0)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_not(False)
new_esEs28(x0, x1, app(ty_[], x2))
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_ltEs6(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_primCmpNat0(Zero, Succ(x0))
new_esEs26(x0, x1, ty_Integer)
new_esEs4(Right(x0), Right(x1), x2, ty_Double)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_compare6(:%(x0, x1), :%(x2, x3), ty_Integer)
new_ltEs6(Left(x0), Left(x1), ty_Double, x2)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_compare14(x0, x1, x2, x3)
new_esEs7(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs4(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs5(x0, x1, app(ty_Maybe, x2))
new_esEs19(x0, x1, app(app(ty_Either, x2), x3))
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs19(x0, x1, ty_Double)
new_sr(x0, x1)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_esEs25(x0, x1, ty_Integer)
new_esEs4(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_lt7(x0, x1, ty_Bool)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_compare18(x0, x1, True, x2, x3)
new_ltEs6(Right(x0), Right(x1), x2, ty_Float)
new_esEs8(EQ, LT)
new_esEs8(LT, EQ)
new_compare24(x0, x1, False, x2, x3)
new_ltEs6(Right(x0), Right(x1), x2, ty_Ordering)
new_ltEs17(LT, EQ)
new_ltEs17(EQ, LT)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs23(x0, x1, app(ty_[], x2))
new_lt12(x0, x1, x2)
new_esEs27(x0, x1, ty_Double)
new_primPlusNat0(Succ(x0), x1)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_compare110(x0, x1, True)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs4(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_lt7(x0, x1, ty_Ordering)
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_esEs19(x0, x1, ty_Bool)
new_lt6(x0, x1, app(ty_Ratio, x2))
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, ty_Int)
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_lt20(x0, x1, ty_@0)
new_compare10(x0, x1, False)
new_esEs26(x0, x1, ty_Bool)
new_lt6(x0, x1, ty_Bool)
new_lt7(x0, x1, app(ty_Maybe, x2))
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare30(x0, x1, app(ty_Maybe, x2))
new_primEqInt(Pos(Zero), Pos(Zero))
new_asAs(True, x0)
new_esEs18(x0, x1, ty_@0)
new_primCompAux0(x0, x1, x2, x3)
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_lt6(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare30(x0, x1, ty_@0)
new_compare9(Char(x0), Char(x1))
new_esEs19(x0, x1, ty_@0)
new_ltEs11(Just(x0), Just(x1), ty_Double)
new_esEs5(Just(x0), Just(x1), app(ty_Ratio, x2))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_esEs18(x0, x1, ty_Double)
new_ltEs19(x0, x1, ty_Float)
new_compare30(x0, x1, app(ty_[], x2))
new_esEs24(x0, x1, ty_Int)
new_ltEs17(EQ, EQ)
new_ltEs16(@2(x0, x1), @2(x2, x3), x4, x5)
new_compare30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs17(LT, LT)
new_esEs27(x0, x1, ty_Ordering)
new_esEs4(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_primPlusNat1(Zero, Succ(x0))
new_esEs20(x0, x1, app(ty_[], x2))
new_ltEs6(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_lt9(x0, x1)

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: