YES 3.025 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
  ((min :: Ord a => Maybe a  ->  Maybe a  ->  Maybe a) :: Ord a => Maybe a  ->  Maybe a  ->  Maybe a)

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
  ((min :: Ord a => Maybe a  ->  Maybe a  ->  Maybe a) :: Ord a => Maybe a  ->  Maybe a  ->  Maybe a)

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
  ((min :: Ord a => Maybe a  ->  Maybe a  ->  Maybe a) :: Ord a => Maybe a  ->  Maybe a  ->  Maybe a)

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
  ((min :: Ord a => Maybe a  ->  Maybe a  ->  Maybe a) :: Ord a => Maybe a  ->  Maybe a  ->  Maybe a)

module Main where
  import qualified Prelude


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

is transformed to
compare x y = compare3 x y

compare0 x y True = GT

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

compare3 x y = compare2 x y (x == y)

The following Function with conditions
min x y
 | x <= y
 = x
 | otherwise
 = y

is transformed to
min x y = min2 x y

min0 x y True = y

min1 x y True = x
min1 x y False = min0 x y otherwise

min2 x y = min1 x y (x <= y)

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

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

gcd'0 x y = gcd' y (x `rem` y)

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

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

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

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

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

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

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

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

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

is transformed to
absReal x = absReal2 x

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

absReal0 x True = `negate` x

absReal2 x = absReal1 x (x >= 0)

The following Function with conditions
undefined 
 | False
 = undefined

is transformed to
undefined  = undefined1

undefined0 True = undefined

undefined1  = undefined0 False

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

is transformed to
reduce x y = reduce2 x y

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



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

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

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'0 x y = gcd0Gcd' y (x `rem` y)

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

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

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



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

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

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
  (min :: Ord a => Maybe a  ->  Maybe a  ->  Maybe a)

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(vwx3100)) → new_primEqNat(vwx3000, vwx3100)

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(vwx6000), Succ(vwx301000)) → new_primPlusNat(vwx6000, vwx301000)

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(vwx40000), Succ(vwx30100)) → new_primMulNat(vwx40000, Succ(vwx30100))

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_esEs(Right(vwx300), Right(vwx310), cc, app(app(app(ty_@3, dc), dd), de)) → new_esEs3(vwx300, vwx310, dc, dd, de)
new_esEs3(@3(vwx300, vwx301, vwx302), @3(vwx310, vwx311, vwx312), bca, app(ty_Maybe, bcg), bba) → new_esEs2(vwx301, vwx311, bcg)
new_esEs3(@3(vwx300, vwx301, vwx302), @3(vwx310, vwx311, vwx312), app(app(ty_Either, baf), bag), bah, bba) → new_esEs(vwx300, vwx310, baf, bag)
new_esEs3(@3(vwx300, vwx301, vwx302), @3(vwx310, vwx311, vwx312), bca, bah, app(app(app(ty_@3, bea), beb), bec)) → new_esEs3(vwx302, vwx312, bea, beb, bec)
new_esEs2(Just(vwx300), Just(vwx310), app(app(ty_Either, he), hf)) → new_esEs(vwx300, vwx310, he, hf)
new_esEs3(@3(vwx300, vwx301, vwx302), @3(vwx310, vwx311, vwx312), app(app(ty_@2, bbb), bbc), bah, bba) → new_esEs0(vwx300, vwx310, bbb, bbc)
new_esEs(Right(vwx300), Right(vwx310), cc, app(ty_[], da)) → new_esEs1(vwx300, vwx310, da)
new_esEs3(@3(vwx300, vwx301, vwx302), @3(vwx310, vwx311, vwx312), bca, bah, app(ty_[], bdg)) → new_esEs1(vwx302, vwx312, bdg)
new_esEs1(:(vwx300, vwx301), :(vwx310, vwx311), hd) → new_esEs1(vwx301, vwx311, hd)
new_esEs0(@2(vwx300, vwx301), @2(vwx310, vwx311), app(ty_[], ec), dh) → new_esEs1(vwx300, vwx310, ec)
new_esEs3(@3(vwx300, vwx301, vwx302), @3(vwx310, vwx311, vwx312), bca, bah, app(app(ty_Either, bdc), bdd)) → new_esEs(vwx302, vwx312, bdc, bdd)
new_esEs1(:(vwx300, vwx301), :(vwx310, vwx311), app(ty_[], gg)) → new_esEs1(vwx300, vwx310, gg)
new_esEs3(@3(vwx300, vwx301, vwx302), @3(vwx310, vwx311, vwx312), bca, app(ty_[], bcf), bba) → new_esEs1(vwx301, vwx311, bcf)
new_esEs2(Just(vwx300), Just(vwx310), app(ty_[], baa)) → new_esEs1(vwx300, vwx310, baa)
new_esEs(Right(vwx300), Right(vwx310), cc, app(app(ty_@2, cf), cg)) → new_esEs0(vwx300, vwx310, cf, cg)
new_esEs2(Just(vwx300), Just(vwx310), app(ty_Maybe, bab)) → new_esEs2(vwx300, vwx310, bab)
new_esEs0(@2(vwx300, vwx301), @2(vwx310, vwx311), app(app(ty_Either, df), dg), dh) → new_esEs(vwx300, vwx310, df, dg)
new_esEs3(@3(vwx300, vwx301, vwx302), @3(vwx310, vwx311, vwx312), bca, app(app(ty_@2, bcd), bce), bba) → new_esEs0(vwx301, vwx311, bcd, bce)
new_esEs(Left(vwx300), Left(vwx310), app(ty_Maybe, bg), bc) → new_esEs2(vwx300, vwx310, bg)
new_esEs0(@2(vwx300, vwx301), @2(vwx310, vwx311), eh, app(app(ty_Either, fa), fb)) → new_esEs(vwx301, vwx311, fa, fb)
new_esEs(Left(vwx300), Left(vwx310), app(app(app(ty_@3, bh), ca), cb), bc) → new_esEs3(vwx300, vwx310, bh, ca, cb)
new_esEs3(@3(vwx300, vwx301, vwx302), @3(vwx310, vwx311, vwx312), bca, app(app(app(ty_@3, bch), bda), bdb), bba) → new_esEs3(vwx301, vwx311, bch, bda, bdb)
new_esEs0(@2(vwx300, vwx301), @2(vwx310, vwx311), eh, app(ty_Maybe, fg)) → new_esEs2(vwx301, vwx311, fg)
new_esEs(Right(vwx300), Right(vwx310), cc, app(app(ty_Either, cd), ce)) → new_esEs(vwx300, vwx310, cd, ce)
new_esEs0(@2(vwx300, vwx301), @2(vwx310, vwx311), app(app(app(ty_@3, ee), ef), eg), dh) → new_esEs3(vwx300, vwx310, ee, ef, eg)
new_esEs(Left(vwx300), Left(vwx310), app(app(ty_@2, bd), be), bc) → new_esEs0(vwx300, vwx310, bd, be)
new_esEs1(:(vwx300, vwx301), :(vwx310, vwx311), app(ty_Maybe, gh)) → new_esEs2(vwx300, vwx310, gh)
new_esEs0(@2(vwx300, vwx301), @2(vwx310, vwx311), app(ty_Maybe, ed), dh) → new_esEs2(vwx300, vwx310, ed)
new_esEs3(@3(vwx300, vwx301, vwx302), @3(vwx310, vwx311, vwx312), bca, app(app(ty_Either, bcb), bcc), bba) → new_esEs(vwx301, vwx311, bcb, bcc)
new_esEs1(:(vwx300, vwx301), :(vwx310, vwx311), app(app(app(ty_@3, ha), hb), hc)) → new_esEs3(vwx300, vwx310, ha, hb, hc)
new_esEs3(@3(vwx300, vwx301, vwx302), @3(vwx310, vwx311, vwx312), app(ty_Maybe, bbe), bah, bba) → new_esEs2(vwx300, vwx310, bbe)
new_esEs3(@3(vwx300, vwx301, vwx302), @3(vwx310, vwx311, vwx312), bca, bah, app(ty_Maybe, bdh)) → new_esEs2(vwx302, vwx312, bdh)
new_esEs(Right(vwx300), Right(vwx310), cc, app(ty_Maybe, db)) → new_esEs2(vwx300, vwx310, db)
new_esEs0(@2(vwx300, vwx301), @2(vwx310, vwx311), app(app(ty_@2, ea), eb), dh) → new_esEs0(vwx300, vwx310, ea, eb)
new_esEs(Left(vwx300), Left(vwx310), app(ty_[], bf), bc) → new_esEs1(vwx300, vwx310, bf)
new_esEs3(@3(vwx300, vwx301, vwx302), @3(vwx310, vwx311, vwx312), app(ty_[], bbd), bah, bba) → new_esEs1(vwx300, vwx310, bbd)
new_esEs0(@2(vwx300, vwx301), @2(vwx310, vwx311), eh, app(ty_[], ff)) → new_esEs1(vwx301, vwx311, ff)
new_esEs2(Just(vwx300), Just(vwx310), app(app(app(ty_@3, bac), bad), bae)) → new_esEs3(vwx300, vwx310, bac, bad, bae)
new_esEs0(@2(vwx300, vwx301), @2(vwx310, vwx311), eh, app(app(ty_@2, fc), fd)) → new_esEs0(vwx301, vwx311, fc, fd)
new_esEs1(:(vwx300, vwx301), :(vwx310, vwx311), app(app(ty_Either, gc), gd)) → new_esEs(vwx300, vwx310, gc, gd)
new_esEs3(@3(vwx300, vwx301, vwx302), @3(vwx310, vwx311, vwx312), bca, bah, app(app(ty_@2, bde), bdf)) → new_esEs0(vwx302, vwx312, bde, bdf)
new_esEs0(@2(vwx300, vwx301), @2(vwx310, vwx311), eh, app(app(app(ty_@3, fh), ga), gb)) → new_esEs3(vwx301, vwx311, fh, ga, gb)
new_esEs1(:(vwx300, vwx301), :(vwx310, vwx311), app(app(ty_@2, ge), gf)) → new_esEs0(vwx300, vwx310, ge, gf)
new_esEs(Left(vwx300), Left(vwx310), app(app(ty_Either, ba), bb), bc) → new_esEs(vwx300, vwx310, ba, bb)
new_esEs3(@3(vwx300, vwx301, vwx302), @3(vwx310, vwx311, vwx312), app(app(app(ty_@3, bbf), bbg), bbh), bah, bba) → new_esEs3(vwx300, vwx310, bbf, bbg, bbh)
new_esEs2(Just(vwx300), Just(vwx310), app(app(ty_@2, hg), hh)) → new_esEs0(vwx300, vwx310, hg, hh)

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

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



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

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

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

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

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



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

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

new_compare(:(vwx300, vwx301), :(vwx400, vwx401), baf) → new_primCompAux(vwx300, vwx400, new_compare4(vwx301, vwx401, baf), baf)
new_compare0(vwx300, vwx400, cb) → new_compare2(vwx300, vwx400, new_esEs4(vwx300, vwx400, cb), cb)
new_ltEs3(Left(vwx300), Left(vwx400), app(app(ty_Either, bch), bda), bca) → new_ltEs3(vwx300, vwx400, bch, bda)
new_ltEs1(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), gc, app(app(app(ty_@3, gg), gh), ha), fa) → new_lt1(vwx301, vwx401, gg, gh, ha)
new_ltEs1(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), gc, app(ty_[], hb), fa) → new_lt2(vwx301, vwx401, hb)
new_compare22(vwx300, vwx400, False, dc, dd) → new_ltEs3(vwx300, vwx400, dc, dd)
new_ltEs0(@2(vwx300, vwx301), @2(vwx400, vwx401), app(ty_Maybe, cb), cc) → new_compare2(vwx300, vwx400, new_esEs4(vwx300, vwx400, cb), cb)
new_ltEs3(Right(vwx300), Right(vwx400), bdb, app(ty_[], bea)) → new_ltEs2(vwx300, vwx400, bea)
new_ltEs(Just(vwx300), Just(vwx400), app(ty_[], bg)) → new_ltEs2(vwx300, vwx400, bg)
new_ltEs3(Right(vwx300), Right(vwx400), bdb, app(app(app(ty_@3, bdf), bdg), bdh)) → new_ltEs1(vwx300, vwx400, bdf, bdg, bdh)
new_ltEs0(@2(vwx300, vwx301), @2(vwx400, vwx401), de, app(app(app(ty_@3, ea), eb), ec)) → new_ltEs1(vwx301, vwx401, ea, eb, ec)
new_ltEs1(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), app(app(ty_Either, ga), gb), eh, fa) → new_lt3(vwx300, vwx400, ga, gb)
new_ltEs1(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), app(ty_[], fh), eh, fa) → new_lt2(vwx300, vwx400, fh)
new_ltEs0(@2(vwx300, vwx301), @2(vwx400, vwx401), de, app(ty_Maybe, df)) → new_ltEs(vwx301, vwx401, df)
new_compare21(vwx300, vwx400, False, cf, cg, da) → new_ltEs1(vwx300, vwx400, cf, cg, da)
new_ltEs0(@2(vwx300, vwx301), @2(vwx400, vwx401), app(app(app(ty_@3, cf), cg), da), cc) → new_compare21(vwx300, vwx400, new_esEs6(vwx300, vwx400, cf, cg, da), cf, cg, da)
new_ltEs1(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), app(ty_Maybe, eg), eh, fa) → new_lt(vwx300, vwx400, eg)
new_ltEs3(Left(vwx300), Left(vwx400), app(ty_Maybe, bbh), bca) → new_ltEs(vwx300, vwx400, bbh)
new_ltEs1(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), app(app(ty_@2, fb), fc), eh, fa) → new_lt0(vwx300, vwx400, fb, fc)
new_ltEs(Just(vwx300), Just(vwx400), app(app(ty_@2, bb), bc)) → new_ltEs0(vwx300, vwx400, bb, bc)
new_ltEs0(@2(vwx300, vwx301), @2(vwx400, vwx401), app(app(ty_@2, cd), ce), cc) → new_compare20(vwx300, vwx400, new_esEs5(vwx300, vwx400, cd, ce), cd, ce)
new_ltEs(Just(vwx300), Just(vwx400), app(app(app(ty_@3, bd), be), bf)) → new_ltEs1(vwx300, vwx400, bd, be, bf)
new_lt3(vwx300, vwx400, dc, dd) → new_compare22(vwx300, vwx400, new_esEs7(vwx300, vwx400, dc, dd), dc, dd)
new_ltEs(Just(vwx300), Just(vwx400), app(app(ty_Either, bh), ca)) → new_ltEs3(vwx300, vwx400, bh, ca)
new_lt(vwx300, vwx400, cb) → new_compare2(vwx300, vwx400, new_esEs4(vwx300, vwx400, cb), cb)
new_ltEs(Just(vwx300), Just(vwx400), app(ty_Maybe, ba)) → new_ltEs(vwx300, vwx400, ba)
new_primCompAux(vwx300, vwx400, vwx42, app(ty_[], bbe)) → new_compare(vwx300, vwx400, bbe)
new_ltEs0(@2(vwx300, vwx301), @2(vwx400, vwx401), app(ty_[], db), cc) → new_compare(vwx300, vwx400, db)
new_ltEs3(Left(vwx300), Left(vwx400), app(ty_[], bcg), bca) → new_ltEs2(vwx300, vwx400, bcg)
new_lt0(vwx300, vwx400, cd, ce) → new_compare20(vwx300, vwx400, new_esEs5(vwx300, vwx400, cd, ce), cd, ce)
new_primCompAux(vwx300, vwx400, vwx42, app(app(ty_Either, bbf), bbg)) → new_compare5(vwx300, vwx400, bbf, bbg)
new_ltEs1(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), gc, eh, app(app(ty_Either, bad), bae)) → new_ltEs3(vwx302, vwx402, bad, bae)
new_ltEs1(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), gc, eh, app(app(ty_@2, hf), hg)) → new_ltEs0(vwx302, vwx402, hf, hg)
new_compare20(vwx300, vwx400, False, cd, ce) → new_ltEs0(vwx300, vwx400, cd, ce)
new_ltEs3(Right(vwx300), Right(vwx400), bdb, app(app(ty_Either, beb), bec)) → new_ltEs3(vwx300, vwx400, beb, bec)
new_ltEs3(Left(vwx300), Left(vwx400), app(app(app(ty_@3, bcd), bce), bcf), bca) → new_ltEs1(vwx300, vwx400, bcd, bce, bcf)
new_ltEs0(@2(vwx300, vwx301), @2(vwx400, vwx401), de, app(app(ty_@2, dg), dh)) → new_ltEs0(vwx301, vwx401, dg, dh)
new_ltEs3(Left(vwx300), Left(vwx400), app(app(ty_@2, bcb), bcc), bca) → new_ltEs0(vwx300, vwx400, bcb, bcc)
new_compare3(vwx300, vwx400, cf, cg, da) → new_compare21(vwx300, vwx400, new_esEs6(vwx300, vwx400, cf, cg, da), cf, cg, da)
new_ltEs0(@2(vwx300, vwx301), @2(vwx400, vwx401), app(app(ty_Either, dc), dd), cc) → new_compare22(vwx300, vwx400, new_esEs7(vwx300, vwx400, dc, dd), dc, dd)
new_ltEs1(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), gc, app(ty_Maybe, gd), fa) → new_lt(vwx301, vwx401, gd)
new_compare2(vwx300, vwx400, False, cb) → new_ltEs(vwx300, vwx400, cb)
new_ltEs2(:(vwx300, vwx301), :(vwx400, vwx401), baf) → new_compare(vwx301, vwx401, baf)
new_ltEs1(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), gc, eh, app(ty_[], bac)) → new_ltEs2(vwx302, vwx402, bac)
new_ltEs2(:(vwx300, vwx301), :(vwx400, vwx401), baf) → new_primCompAux(vwx300, vwx400, new_compare4(vwx301, vwx401, baf), baf)
new_ltEs1(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), gc, app(app(ty_Either, hc), hd), fa) → new_lt3(vwx301, vwx401, hc, hd)
new_compare(:(vwx300, vwx301), :(vwx400, vwx401), baf) → new_compare(vwx301, vwx401, baf)
new_primCompAux(vwx300, vwx400, vwx42, app(app(app(ty_@3, bbb), bbc), bbd)) → new_compare3(vwx300, vwx400, bbb, bbc, bbd)
new_compare5(vwx300, vwx400, dc, dd) → new_compare22(vwx300, vwx400, new_esEs7(vwx300, vwx400, dc, dd), dc, dd)
new_ltEs1(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), gc, eh, app(ty_Maybe, he)) → new_ltEs(vwx302, vwx402, he)
new_ltEs1(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), gc, eh, app(app(app(ty_@3, hh), baa), bab)) → new_ltEs1(vwx302, vwx402, hh, baa, bab)
new_lt2(vwx300, vwx400, db) → new_compare(vwx300, vwx400, db)
new_ltEs1(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), gc, app(app(ty_@2, ge), gf), fa) → new_lt0(vwx301, vwx401, ge, gf)
new_ltEs3(Right(vwx300), Right(vwx400), bdb, app(ty_Maybe, bdc)) → new_ltEs(vwx300, vwx400, bdc)
new_lt1(vwx300, vwx400, cf, cg, da) → new_compare21(vwx300, vwx400, new_esEs6(vwx300, vwx400, cf, cg, da), cf, cg, da)
new_ltEs0(@2(vwx300, vwx301), @2(vwx400, vwx401), de, app(ty_[], ed)) → new_ltEs2(vwx301, vwx401, ed)
new_compare1(vwx300, vwx400, cd, ce) → new_compare20(vwx300, vwx400, new_esEs5(vwx300, vwx400, cd, ce), cd, ce)
new_ltEs3(Right(vwx300), Right(vwx400), bdb, app(app(ty_@2, bdd), bde)) → new_ltEs0(vwx300, vwx400, bdd, bde)
new_primCompAux(vwx300, vwx400, vwx42, app(app(ty_@2, bah), bba)) → new_compare1(vwx300, vwx400, bah, bba)
new_primCompAux(vwx300, vwx400, vwx42, app(ty_Maybe, bag)) → new_compare0(vwx300, vwx400, bag)
new_ltEs1(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), app(app(app(ty_@3, fd), ff), fg), eh, fa) → new_lt1(vwx300, vwx400, fd, ff, fg)
new_ltEs0(@2(vwx300, vwx301), @2(vwx400, vwx401), de, app(app(ty_Either, ee), ef)) → new_ltEs3(vwx301, vwx401, ee, ef)

The TRS R consists of the following rules:

new_esEs4(Just(vwx300), Just(vwx310), app(ty_Maybe, ccg)) → new_esEs4(vwx300, vwx310, ccg)
new_esEs23(vwx300, vwx310, ty_Integer) → new_esEs13(vwx300, vwx310)
new_esEs23(vwx300, vwx310, app(app(ty_Either, ced), cee)) → new_esEs7(vwx300, vwx310, ced, cee)
new_ltEs17(Left(vwx300), Left(vwx400), ty_Bool, bca) → new_ltEs15(vwx300, vwx400)
new_ltEs19(vwx302, vwx402, app(ty_[], bac)) → new_ltEs8(vwx302, vwx402, bac)
new_esEs25(vwx302, vwx312, ty_Ordering) → new_esEs17(vwx302, vwx312)
new_esEs24(vwx301, vwx311, ty_Float) → new_esEs12(vwx301, vwx311)
new_esEs7(Left(vwx300), Left(vwx310), app(app(ty_Either, bhd), bhe), bhc) → new_esEs7(vwx300, vwx310, bhd, bhe)
new_ltEs17(Right(vwx300), Right(vwx400), bdb, ty_Double) → new_ltEs5(vwx300, vwx400)
new_ltEs15(True, False) → False
new_lt19(vwx300, vwx400, ty_Int) → new_lt18(vwx300, vwx400)
new_lt19(vwx300, vwx400, app(ty_Ratio, cdf)) → new_lt10(vwx300, vwx400, cdf)
new_esEs18(Char(vwx300), Char(vwx310)) → new_primEqNat0(vwx300, vwx310)
new_esEs27(vwx30, vwx31, app(ty_[], dab)) → new_esEs16(vwx30, vwx31, dab)
new_lt19(vwx300, vwx400, ty_Double) → new_lt7(vwx300, vwx400)
new_ltEs17(Left(vwx300), Left(vwx400), app(ty_[], bcg), bca) → new_ltEs8(vwx300, vwx400, bcg)
new_esEs25(vwx302, vwx312, app(ty_[], chd)) → new_esEs16(vwx302, vwx312, chd)
new_lt19(vwx300, vwx400, app(app(app(ty_@3, fd), ff), fg)) → new_lt8(vwx300, vwx400, fd, ff, fg)
new_compare17(:%(vwx300, vwx301), :%(vwx400, vwx401), ty_Int) → new_compare15(new_sr(vwx300, vwx401), new_sr(vwx400, vwx301))
new_esEs7(Left(vwx300), Left(vwx310), app(ty_Maybe, caa), bhc) → new_esEs4(vwx300, vwx310, caa)
new_compare110(vwx300, vwx400, True, dc, dd) → LT
new_lt9(vwx300, vwx400, db) → new_esEs8(new_compare4(vwx300, vwx400, db))
new_ltEs12(vwx301, vwx401, app(app(ty_Either, ee), ef)) → new_ltEs17(vwx301, vwx401, ee, ef)
new_ltEs12(vwx301, vwx401, ty_Bool) → new_ltEs15(vwx301, vwx401)
new_lt13(vwx300, vwx400, app(app(app(ty_@3, cf), cg), da)) → new_lt8(vwx300, vwx400, cf, cg, da)
new_ltEs17(Left(vwx300), Left(vwx400), ty_Integer, bca) → new_ltEs7(vwx300, vwx400)
new_esEs24(vwx301, vwx311, app(ty_Maybe, cgc)) → new_esEs4(vwx301, vwx311, cgc)
new_esEs4(Nothing, Just(vwx310), cca) → False
new_esEs4(Just(vwx300), Nothing, cca) → False
new_lt20(vwx301, vwx401, app(app(app(ty_@3, gg), gh), ha)) → new_lt8(vwx301, vwx401, gg, gh, ha)
new_esEs7(Left(vwx300), Left(vwx310), ty_Char, bhc) → new_esEs18(vwx300, vwx310)
new_esEs23(vwx300, vwx310, ty_Bool) → new_esEs14(vwx300, vwx310)
new_esEs27(vwx30, vwx31, ty_Double) → new_esEs20(vwx30, vwx31)
new_ltEs19(vwx302, vwx402, ty_Float) → new_ltEs4(vwx302, vwx402)
new_esEs4(Just(vwx300), Just(vwx310), app(ty_Ratio, cdc)) → new_esEs19(vwx300, vwx310, cdc)
new_lt13(vwx300, vwx400, ty_Float) → new_lt11(vwx300, vwx400)
new_ltEs17(Left(vwx300), Left(vwx400), ty_Double, bca) → new_ltEs5(vwx300, vwx400)
new_ltEs18(vwx30, vwx40) → new_not(new_compare15(vwx30, vwx40))
new_primMulNat0(Zero, Zero) → Zero
new_esEs27(vwx30, vwx31, app(ty_Ratio, cde)) → new_esEs19(vwx30, vwx31, cde)
new_esEs24(vwx301, vwx311, ty_Integer) → new_esEs13(vwx301, vwx311)
new_lt13(vwx300, vwx400, ty_Int) → new_lt18(vwx300, vwx400)
new_esEs26(vwx300, vwx310, app(ty_[], dag)) → new_esEs16(vwx300, vwx310, dag)
new_lt18(vwx300, vwx400) → new_esEs8(new_compare15(vwx300, vwx400))
new_esEs4(Just(vwx300), Just(vwx310), app(app(app(ty_@3, cch), cda), cdb)) → new_esEs6(vwx300, vwx310, cch, cda, cdb)
new_esEs9(vwx300, vwx310, ty_Float) → new_esEs12(vwx300, vwx310)
new_ltEs13(Nothing, Just(vwx400), dcb) → True
new_esEs7(Left(vwx300), Left(vwx310), app(ty_Ratio, cae), bhc) → new_esEs19(vwx300, vwx310, cae)
new_esEs23(vwx300, vwx310, ty_Float) → new_esEs12(vwx300, vwx310)
new_ltEs19(vwx302, vwx402, app(app(ty_@2, hf), hg)) → new_ltEs11(vwx302, vwx402, hf, hg)
new_esEs7(Left(vwx300), Left(vwx310), ty_Bool, bhc) → new_esEs14(vwx300, vwx310)
new_ltEs12(vwx301, vwx401, app(ty_Maybe, df)) → new_ltEs13(vwx301, vwx401, df)
new_lt20(vwx301, vwx401, ty_Int) → new_lt18(vwx301, vwx401)
new_ltEs17(Right(vwx300), Right(vwx400), bdb, app(app(ty_@2, bdd), bde)) → new_ltEs11(vwx300, vwx400, bdd, bde)
new_esEs21(vwx300, vwx310, ty_Integer) → new_esEs13(vwx300, vwx310)
new_esEs6(@3(vwx300, vwx301, vwx302), @3(vwx310, vwx311, vwx312), cea, ceb, cec) → new_asAs(new_esEs23(vwx300, vwx310, cea), new_asAs(new_esEs24(vwx301, vwx311, ceb), new_esEs25(vwx302, vwx312, cec)))
new_not(GT) → False
new_esEs23(vwx300, vwx310, app(ty_Maybe, cfa)) → new_esEs4(vwx300, vwx310, cfa)
new_esEs7(Left(vwx300), Left(vwx310), ty_Int, bhc) → new_esEs15(vwx300, vwx310)
new_esEs21(vwx300, vwx310, ty_Int) → new_esEs15(vwx300, vwx310)
new_esEs23(vwx300, vwx310, ty_Double) → new_esEs20(vwx300, vwx310)
new_ltEs13(Just(vwx300), Just(vwx400), app(ty_Ratio, dcc)) → new_ltEs14(vwx300, vwx400, dcc)
new_esEs24(vwx301, vwx311, app(app(ty_@2, cfh), cga)) → new_esEs5(vwx301, vwx311, cfh, cga)
new_compare15(vwx30, vwx40) → new_primCmpInt(vwx30, vwx40)
new_ltEs13(Just(vwx300), Just(vwx400), ty_@0) → new_ltEs16(vwx300, vwx400)
new_esEs27(vwx30, vwx31, ty_Integer) → new_esEs13(vwx30, vwx31)
new_compare29(vwx300, vwx400, cd, ce) → new_compare210(vwx300, vwx400, new_esEs5(vwx300, vwx400, cd, ce), cd, ce)
new_esEs9(vwx300, vwx310, ty_Integer) → new_esEs13(vwx300, vwx310)
new_esEs26(vwx300, vwx310, app(ty_Maybe, dah)) → new_esEs4(vwx300, vwx310, dah)
new_esEs10(vwx301, vwx311, ty_Double) → new_esEs20(vwx301, vwx311)
new_ltEs17(Left(vwx300), Left(vwx400), ty_@0, bca) → new_ltEs16(vwx300, vwx400)
new_ltEs17(Right(vwx300), Right(vwx400), bdb, app(ty_Maybe, bdc)) → new_ltEs13(vwx300, vwx400, bdc)
new_lt20(vwx301, vwx401, ty_Double) → new_lt7(vwx301, vwx401)
new_ltEs12(vwx301, vwx401, app(ty_[], ed)) → new_ltEs8(vwx301, vwx401, ed)
new_esEs7(Left(vwx300), Right(vwx310), caf, bhc) → False
new_esEs7(Right(vwx300), Left(vwx310), caf, bhc) → False
new_ltEs15(True, True) → True
new_esEs25(vwx302, vwx312, ty_Bool) → new_esEs14(vwx302, vwx312)
new_esEs15(vwx30, vwx31) → new_primEqInt(vwx30, vwx31)
new_esEs27(vwx30, vwx31, app(app(ty_Either, caf), bhc)) → new_esEs7(vwx30, vwx31, caf, bhc)
new_esEs10(vwx301, vwx311, ty_Bool) → new_esEs14(vwx301, vwx311)
new_compare19(vwx300, vwx400, True, cf, cg, da) → LT
new_lt19(vwx300, vwx400, app(ty_[], fh)) → new_lt9(vwx300, vwx400, fh)
new_ltEs15(False, True) → True
new_compare31(vwx300, vwx400, app(app(ty_@2, bah), bba)) → new_compare29(vwx300, vwx400, bah, bba)
new_esEs24(vwx301, vwx311, ty_@0) → new_esEs11(vwx301, vwx311)
new_lt19(vwx300, vwx400, app(ty_Maybe, eg)) → new_lt14(vwx300, vwx400, eg)
new_compare31(vwx300, vwx400, app(app(app(ty_@3, bbb), bbc), bbd)) → new_compare13(vwx300, vwx400, bbb, bbc, bbd)
new_compare23(vwx300, vwx400, True, cf, cg, da) → EQ
new_ltEs6(GT, EQ) → False
new_ltEs17(Left(vwx300), Left(vwx400), app(app(app(ty_@3, bcd), bce), bcf), bca) → new_ltEs9(vwx300, vwx400, bcd, bce, bcf)
new_ltEs13(Just(vwx300), Just(vwx400), ty_Integer) → new_ltEs7(vwx300, vwx400)
new_esEs10(vwx301, vwx311, ty_@0) → new_esEs11(vwx301, vwx311)
new_compare10(vwx300, vwx400, True, cb) → LT
new_ltEs15(False, False) → True
new_compare31(vwx300, vwx400, ty_@0) → new_compare26(vwx300, vwx400)
new_esEs7(Right(vwx300), Right(vwx310), caf, app(app(ty_@2, cba), cbb)) → new_esEs5(vwx300, vwx310, cba, cbb)
new_primCmpNat0(Zero, Succ(vwx4000)) → LT
new_ltEs13(Nothing, Nothing, dcb) → True
new_esEs17(LT, LT) → True
new_compare14(vwx300, vwx400, False) → GT
new_esEs7(Right(vwx300), Right(vwx310), caf, ty_Bool) → new_esEs14(vwx300, vwx310)
new_compare31(vwx300, vwx400, ty_Integer) → new_compare16(vwx300, vwx400)
new_esEs26(vwx300, vwx310, ty_Double) → new_esEs20(vwx300, vwx310)
new_esEs25(vwx302, vwx312, ty_Double) → new_esEs20(vwx302, vwx312)
new_ltEs13(Just(vwx300), Just(vwx400), app(app(ty_@2, bb), bc)) → new_ltEs11(vwx300, vwx400, bb, bc)
new_esEs23(vwx300, vwx310, ty_Char) → new_esEs18(vwx300, vwx310)
new_compare10(vwx300, vwx400, False, cb) → GT
new_compare31(vwx300, vwx400, app(ty_Maybe, bag)) → new_compare30(vwx300, vwx400, bag)
new_esEs24(vwx301, vwx311, app(app(ty_Either, cff), cfg)) → new_esEs7(vwx301, vwx311, cff, cfg)
new_esEs10(vwx301, vwx311, app(ty_Ratio, bhb)) → new_esEs19(vwx301, vwx311, bhb)
new_primEqNat0(Zero, Zero) → True
new_lt20(vwx301, vwx401, app(app(ty_Either, hc), hd)) → new_lt5(vwx301, vwx401, hc, hd)
new_esEs23(vwx300, vwx310, ty_@0) → new_esEs11(vwx300, vwx310)
new_ltEs13(Just(vwx300), Just(vwx400), ty_Int) → new_ltEs18(vwx300, vwx400)
new_esEs7(Left(vwx300), Left(vwx310), app(app(ty_@2, bhf), bhg), bhc) → new_esEs5(vwx300, vwx310, bhf, bhg)
new_esEs7(Right(vwx300), Right(vwx310), caf, ty_Int) → new_esEs15(vwx300, vwx310)
new_compare14(vwx300, vwx400, True) → LT
new_lt20(vwx301, vwx401, app(ty_[], hb)) → new_lt9(vwx301, vwx401, hb)
new_lt13(vwx300, vwx400, app(ty_Ratio, bed)) → new_lt10(vwx300, vwx400, bed)
new_esEs25(vwx302, vwx312, ty_Int) → new_esEs15(vwx302, vwx312)
new_ltEs17(Right(vwx300), Left(vwx400), bdb, bca) → False
new_lt14(vwx300, vwx400, cb) → new_esEs8(new_compare30(vwx300, vwx400, cb))
new_esEs7(Right(vwx300), Right(vwx310), caf, ty_Ordering) → new_esEs17(vwx300, vwx310)
new_compare110(vwx300, vwx400, False, dc, dd) → GT
new_lt6(vwx300, vwx400) → new_esEs8(new_compare9(vwx300, vwx400))
new_ltEs17(Right(vwx300), Right(vwx400), bdb, ty_Ordering) → new_ltEs6(vwx300, vwx400)
new_ltEs19(vwx302, vwx402, ty_Ordering) → new_ltEs6(vwx302, vwx402)
new_esEs7(Right(vwx300), Right(vwx310), caf, app(app(app(ty_@3, cbe), cbf), cbg)) → new_esEs6(vwx300, vwx310, cbe, cbf, cbg)
new_ltEs12(vwx301, vwx401, app(app(ty_@2, dg), dh)) → new_ltEs11(vwx301, vwx401, dg, dh)
new_sr(vwx400, vwx301) → new_primMulInt(vwx400, vwx301)
new_esEs4(Just(vwx300), Just(vwx310), ty_Double) → new_esEs20(vwx300, vwx310)
new_lt4(vwx300, vwx400) → new_esEs8(new_compare7(vwx300, vwx400))
new_esEs9(vwx300, vwx310, ty_@0) → new_esEs11(vwx300, vwx310)
new_ltEs17(Right(vwx300), Right(vwx400), bdb, app(app(app(ty_@3, bdf), bdg), bdh)) → new_ltEs9(vwx300, vwx400, bdf, bdg, bdh)
new_esEs9(vwx300, vwx310, app(ty_[], bfc)) → new_esEs16(vwx300, vwx310, bfc)
new_esEs23(vwx300, vwx310, app(ty_Ratio, cfe)) → new_esEs19(vwx300, vwx310, cfe)
new_ltEs19(vwx302, vwx402, ty_Char) → new_ltEs10(vwx302, vwx402)
new_ltEs6(EQ, GT) → True
new_primPlusNat0(Succ(vwx600), vwx30100) → Succ(Succ(new_primPlusNat1(vwx600, vwx30100)))
new_compare4([], [], baf) → EQ
new_lt13(vwx300, vwx400, ty_Ordering) → new_lt4(vwx300, vwx400)
new_esEs7(Right(vwx300), Right(vwx310), caf, app(app(ty_Either, cag), cah)) → new_esEs7(vwx300, vwx310, cag, cah)
new_ltEs19(vwx302, vwx402, ty_Bool) → new_ltEs15(vwx302, vwx402)
new_esEs26(vwx300, vwx310, app(app(app(ty_@3, dba), dbb), dbc)) → new_esEs6(vwx300, vwx310, dba, dbb, dbc)
new_ltEs19(vwx302, vwx402, app(ty_Ratio, cdh)) → new_ltEs14(vwx302, vwx402, cdh)
new_lt20(vwx301, vwx401, ty_Char) → new_lt17(vwx301, vwx401)
new_compare30(vwx300, vwx400, cb) → new_compare27(vwx300, vwx400, new_esEs4(vwx300, vwx400, cb), cb)
new_esEs7(Right(vwx300), Right(vwx310), caf, ty_Char) → new_esEs18(vwx300, vwx310)
new_esEs13(Integer(vwx300), Integer(vwx310)) → new_primEqInt(vwx300, vwx310)
new_ltEs4(vwx30, vwx40) → new_not(new_compare6(vwx30, vwx40))
new_esEs7(Right(vwx300), Right(vwx310), caf, ty_@0) → new_esEs11(vwx300, vwx310)
new_primEqInt(Neg(Succ(vwx3000)), Neg(Succ(vwx3100))) → new_primEqNat0(vwx3000, vwx3100)
new_lt15(vwx300, vwx400, cd, ce) → new_esEs8(new_compare29(vwx300, vwx400, cd, ce))
new_esEs23(vwx300, vwx310, ty_Int) → new_esEs15(vwx300, vwx310)
new_ltEs19(vwx302, vwx402, ty_Double) → new_ltEs5(vwx302, vwx402)
new_ltEs19(vwx302, vwx402, app(app(app(ty_@3, hh), baa), bab)) → new_ltEs9(vwx302, vwx402, hh, baa, bab)
new_esEs7(Left(vwx300), Left(vwx310), ty_Integer, bhc) → new_esEs13(vwx300, vwx310)
new_esEs24(vwx301, vwx311, ty_Bool) → new_esEs14(vwx301, vwx311)
new_primPlusNat1(Succ(vwx6000), Zero) → Succ(vwx6000)
new_primPlusNat1(Zero, Succ(vwx301000)) → Succ(vwx301000)
new_esEs22(vwx301, vwx311, ty_Int) → new_esEs15(vwx301, vwx311)
new_compare23(vwx300, vwx400, False, cf, cg, da) → new_compare19(vwx300, vwx400, new_ltEs9(vwx300, vwx400, cf, cg, da), cf, cg, da)
new_esEs25(vwx302, vwx312, ty_Char) → new_esEs18(vwx302, vwx312)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs17(EQ, EQ) → True
new_esEs24(vwx301, vwx311, app(app(app(ty_@3, cgd), cge), cgf)) → new_esEs6(vwx301, vwx311, cgd, cge, cgf)
new_ltEs6(EQ, EQ) → True
new_esEs7(Left(vwx300), Left(vwx310), ty_Ordering, bhc) → new_esEs17(vwx300, vwx310)
new_lt19(vwx300, vwx400, ty_Integer) → new_lt12(vwx300, vwx400)
new_esEs9(vwx300, vwx310, app(ty_Ratio, bfh)) → new_esEs19(vwx300, vwx310, bfh)
new_compare18(vwx300, vwx400, False) → GT
new_primEqInt(Neg(Zero), Neg(Succ(vwx3100))) → False
new_primEqInt(Neg(Succ(vwx3000)), Neg(Zero)) → False
new_esEs10(vwx301, vwx311, ty_Integer) → new_esEs13(vwx301, vwx311)
new_primCompAux0(vwx46, GT) → GT
new_compare31(vwx300, vwx400, ty_Ordering) → new_compare7(vwx300, vwx400)
new_compare19(vwx300, vwx400, False, cf, cg, da) → GT
new_ltEs6(GT, GT) → True
new_ltEs14(vwx30, vwx40, dbe) → new_not(new_compare17(vwx30, vwx40, dbe))
new_esEs25(vwx302, vwx312, app(ty_Ratio, daa)) → new_esEs19(vwx302, vwx312, daa)
new_lt19(vwx300, vwx400, ty_Float) → new_lt11(vwx300, vwx400)
new_esEs26(vwx300, vwx310, app(app(ty_Either, dac), dad)) → new_esEs7(vwx300, vwx310, dac, dad)
new_esEs26(vwx300, vwx310, ty_@0) → new_esEs11(vwx300, vwx310)
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_compare17(:%(vwx300, vwx301), :%(vwx400, vwx401), ty_Integer) → new_compare16(new_sr0(vwx300, vwx401), new_sr0(vwx400, vwx301))
new_primCmpNat0(Succ(vwx3000), Succ(vwx4000)) → new_primCmpNat0(vwx3000, vwx4000)
new_ltEs8(vwx30, vwx40, baf) → new_not(new_compare4(vwx30, vwx40, baf))
new_esEs4(Just(vwx300), Just(vwx310), app(app(ty_Either, ccb), ccc)) → new_esEs7(vwx300, vwx310, ccb, ccc)
new_esEs25(vwx302, vwx312, app(ty_Maybe, che)) → new_esEs4(vwx302, vwx312, che)
new_primEqInt(Pos(Succ(vwx3000)), Pos(Succ(vwx3100))) → new_primEqNat0(vwx3000, vwx3100)
new_esEs4(Just(vwx300), Just(vwx310), app(app(ty_@2, ccd), cce)) → new_esEs5(vwx300, vwx310, ccd, cce)
new_ltEs17(Left(vwx300), Left(vwx400), ty_Ordering, bca) → new_ltEs6(vwx300, vwx400)
new_esEs24(vwx301, vwx311, ty_Double) → new_esEs20(vwx301, vwx311)
new_esEs14(True, False) → False
new_esEs14(False, True) → False
new_lt7(vwx300, vwx400) → new_esEs8(new_compare12(vwx300, vwx400))
new_esEs17(GT, LT) → False
new_esEs17(LT, GT) → False
new_ltEs13(Just(vwx300), Just(vwx400), ty_Float) → new_ltEs4(vwx300, vwx400)
new_primEqNat0(Succ(vwx3000), Succ(vwx3100)) → new_primEqNat0(vwx3000, vwx3100)
new_esEs17(GT, EQ) → False
new_esEs17(EQ, GT) → False
new_esEs7(Right(vwx300), Right(vwx310), caf, app(ty_[], cbc)) → new_esEs16(vwx300, vwx310, cbc)
new_esEs27(vwx30, vwx31, ty_Float) → new_esEs12(vwx30, vwx31)
new_ltEs11(@2(vwx300, vwx301), @2(vwx400, vwx401), de, cc) → new_pePe(new_lt13(vwx300, vwx400, de), vwx300, vwx400, new_ltEs12(vwx301, vwx401, cc), de)
new_compare8(vwx300, vwx400, dc, dd) → new_compare25(vwx300, vwx400, new_esEs7(vwx300, vwx400, dc, dd), dc, dd)
new_esEs20(Double(vwx300, vwx301), Double(vwx310, vwx311)) → new_esEs15(new_sr(vwx300, vwx310), new_sr(vwx301, vwx311))
new_primCmpInt(Neg(Succ(vwx3000)), Neg(vwx400)) → new_primCmpNat0(vwx400, Succ(vwx3000))
new_compare31(vwx300, vwx400, ty_Char) → new_compare24(vwx300, vwx400)
new_ltEs17(Left(vwx300), Left(vwx400), app(ty_Maybe, bbh), bca) → new_ltEs13(vwx300, vwx400, bbh)
new_primEqInt(Pos(Zero), Pos(Succ(vwx3100))) → False
new_primEqInt(Pos(Succ(vwx3000)), Pos(Zero)) → False
new_esEs10(vwx301, vwx311, app(app(ty_Either, bga), bgb)) → new_esEs7(vwx301, vwx311, bga, bgb)
new_ltEs10(vwx30, vwx40) → new_not(new_compare24(vwx30, vwx40))
new_esEs22(vwx301, vwx311, ty_Integer) → new_esEs13(vwx301, vwx311)
new_ltEs17(Left(vwx300), Left(vwx400), ty_Char, bca) → new_ltEs10(vwx300, vwx400)
new_ltEs19(vwx302, vwx402, app(app(ty_Either, bad), bae)) → new_ltEs17(vwx302, vwx402, bad, bae)
new_primCmpNat0(Zero, Zero) → EQ
new_esEs24(vwx301, vwx311, app(ty_Ratio, cgg)) → new_esEs19(vwx301, vwx311, cgg)
new_primCmpNat0(Succ(vwx3000), Zero) → GT
new_compare18(vwx300, vwx400, True) → LT
new_esEs23(vwx300, vwx310, app(app(ty_@2, cef), ceg)) → new_esEs5(vwx300, vwx310, cef, ceg)
new_primCmpInt(Neg(Zero), Pos(Succ(vwx4000))) → LT
new_esEs8(LT) → True
new_compare11(vwx300, vwx400, True, cd, ce) → LT
new_compare24(Char(vwx300), Char(vwx400)) → new_primCmpNat0(vwx300, vwx400)
new_esEs10(vwx301, vwx311, ty_Int) → new_esEs15(vwx301, vwx311)
new_ltEs13(Just(vwx300), Just(vwx400), app(ty_[], bg)) → new_ltEs8(vwx300, vwx400, bg)
new_sr0(Integer(vwx4000), Integer(vwx3010)) → Integer(new_primMulInt(vwx4000, vwx3010))
new_primPlusNat1(Succ(vwx6000), Succ(vwx301000)) → Succ(Succ(new_primPlusNat1(vwx6000, vwx301000)))
new_esEs4(Just(vwx300), Just(vwx310), ty_Float) → new_esEs12(vwx300, vwx310)
new_primEqInt(Neg(Succ(vwx3000)), Pos(vwx310)) → False
new_primEqInt(Pos(Succ(vwx3000)), Neg(vwx310)) → False
new_esEs10(vwx301, vwx311, ty_Char) → new_esEs18(vwx301, vwx311)
new_esEs8(GT) → False
new_primEqInt(Neg(Zero), Pos(Succ(vwx3100))) → False
new_primEqInt(Pos(Zero), Neg(Succ(vwx3100))) → False
new_esEs26(vwx300, vwx310, ty_Float) → new_esEs12(vwx300, vwx310)
new_primCmpInt(Pos(Zero), Pos(Succ(vwx4000))) → new_primCmpNat0(Zero, Succ(vwx4000))
new_esEs7(Right(vwx300), Right(vwx310), caf, ty_Float) → new_esEs12(vwx300, vwx310)
new_esEs7(Right(vwx300), Right(vwx310), caf, app(ty_Maybe, cbd)) → new_esEs4(vwx300, vwx310, cbd)
new_pePe(False, vwx30, vwx31, vwx32, dbf) → new_asAs(new_esEs27(vwx30, vwx31, dbf), vwx32)
new_lt20(vwx301, vwx401, ty_Ordering) → new_lt4(vwx301, vwx401)
new_ltEs17(Right(vwx300), Right(vwx400), bdb, app(ty_[], bea)) → new_ltEs8(vwx300, vwx400, bea)
new_ltEs17(Left(vwx300), Left(vwx400), ty_Int, bca) → new_ltEs18(vwx300, vwx400)
new_ltEs13(Just(vwx300), Just(vwx400), ty_Double) → new_ltEs5(vwx300, vwx400)
new_lt13(vwx300, vwx400, app(ty_[], db)) → new_lt9(vwx300, vwx400, db)
new_esEs10(vwx301, vwx311, app(ty_[], bge)) → new_esEs16(vwx301, vwx311, bge)
new_lt13(vwx300, vwx400, app(ty_Maybe, cb)) → new_lt14(vwx300, vwx400, cb)
new_esEs26(vwx300, vwx310, app(app(ty_@2, dae), daf)) → new_esEs5(vwx300, vwx310, dae, daf)
new_ltEs12(vwx301, vwx401, ty_Int) → new_ltEs18(vwx301, vwx401)
new_lt20(vwx301, vwx401, ty_@0) → new_lt16(vwx301, vwx401)
new_esEs5(@2(vwx300, vwx301), @2(vwx310, vwx311), bee, bef) → new_asAs(new_esEs9(vwx300, vwx310, bee), new_esEs10(vwx301, vwx311, bef))
new_primCompAux0(vwx46, LT) → LT
new_esEs25(vwx302, vwx312, ty_Float) → new_esEs12(vwx302, vwx312)
new_esEs7(Right(vwx300), Right(vwx310), caf, app(ty_Ratio, cbh)) → new_esEs19(vwx300, vwx310, cbh)
new_ltEs12(vwx301, vwx401, ty_@0) → new_ltEs16(vwx301, vwx401)
new_ltEs13(Just(vwx300), Just(vwx400), ty_Ordering) → new_ltEs6(vwx300, vwx400)
new_esEs4(Just(vwx300), Just(vwx310), ty_@0) → new_esEs11(vwx300, vwx310)
new_compare16(Integer(vwx300), Integer(vwx400)) → new_primCmpInt(vwx300, vwx400)
new_compare210(vwx300, vwx400, True, cd, ce) → EQ
new_primCmpInt(Pos(Succ(vwx3000)), Pos(vwx400)) → new_primCmpNat0(Succ(vwx3000), vwx400)
new_primPlusNat0(Zero, vwx30100) → Succ(vwx30100)
new_lt13(vwx300, vwx400, ty_Integer) → new_lt12(vwx300, vwx400)
new_lt11(vwx300, vwx400) → new_esEs8(new_compare6(vwx300, vwx400))
new_compare12(Double(vwx300, vwx301), Double(vwx400, vwx401)) → new_compare15(new_sr(vwx300, vwx400), new_sr(vwx301, vwx401))
new_compare31(vwx300, vwx400, app(app(ty_Either, bbf), bbg)) → new_compare8(vwx300, vwx400, bbf, bbg)
new_ltEs12(vwx301, vwx401, ty_Ordering) → new_ltEs6(vwx301, vwx401)
new_ltEs19(vwx302, vwx402, ty_Int) → new_ltEs18(vwx302, vwx402)
new_ltEs12(vwx301, vwx401, ty_Double) → new_ltEs5(vwx301, vwx401)
new_ltEs17(Right(vwx300), Right(vwx400), bdb, app(app(ty_Either, beb), bec)) → new_ltEs17(vwx300, vwx400, beb, bec)
new_esEs26(vwx300, vwx310, ty_Bool) → new_esEs14(vwx300, vwx310)
new_lt20(vwx301, vwx401, ty_Bool) → new_lt6(vwx301, vwx401)
new_not0 → True
new_compare28(vwx300, vwx400, True) → EQ
new_esEs4(Just(vwx300), Just(vwx310), ty_Char) → new_esEs18(vwx300, vwx310)
new_esEs4(Just(vwx300), Just(vwx310), ty_Int) → new_esEs15(vwx300, vwx310)
new_esEs24(vwx301, vwx311, ty_Int) → new_esEs15(vwx301, vwx311)
new_compare11(vwx300, vwx400, False, cd, ce) → GT
new_primCmpInt(Pos(Succ(vwx3000)), Neg(vwx400)) → GT
new_lt19(vwx300, vwx400, ty_Char) → new_lt17(vwx300, vwx400)
new_primMulInt(Pos(vwx4000), Pos(vwx3010)) → Pos(new_primMulNat0(vwx4000, vwx3010))
new_ltEs17(Left(vwx300), Left(vwx400), app(app(ty_Either, bch), bda), bca) → new_ltEs17(vwx300, vwx400, bch, bda)
new_ltEs17(Left(vwx300), Left(vwx400), app(ty_Ratio, dbg), bca) → new_ltEs14(vwx300, vwx400, dbg)
new_primMulInt(Neg(vwx4000), Neg(vwx3010)) → Pos(new_primMulNat0(vwx4000, vwx3010))
new_compare27(vwx300, vwx400, False, cb) → new_compare10(vwx300, vwx400, new_ltEs13(vwx300, vwx400, cb), cb)
new_primEqNat0(Zero, Succ(vwx3100)) → False
new_primEqNat0(Succ(vwx3000), Zero) → False
new_esEs7(Left(vwx300), Left(vwx310), app(ty_[], bhh), bhc) → new_esEs16(vwx300, vwx310, bhh)
new_esEs7(Left(vwx300), Left(vwx310), ty_Double, bhc) → new_esEs20(vwx300, vwx310)
new_ltEs17(Right(vwx300), Right(vwx400), bdb, ty_Int) → new_ltEs18(vwx300, vwx400)
new_esEs27(vwx30, vwx31, ty_@0) → new_esEs11(vwx30, vwx31)
new_ltEs6(LT, LT) → True
new_compare25(vwx300, vwx400, True, dc, dd) → EQ
new_ltEs6(EQ, LT) → False
new_compare211(vwx300, vwx400, False) → new_compare18(vwx300, vwx400, new_ltEs15(vwx300, vwx400))
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs4(Nothing, Nothing, cca) → True
new_ltEs17(Right(vwx300), Right(vwx400), bdb, ty_Integer) → new_ltEs7(vwx300, vwx400)
new_esEs27(vwx30, vwx31, app(app(app(ty_@3, cea), ceb), cec)) → new_esEs6(vwx30, vwx31, cea, ceb, cec)
new_compare4(:(vwx300, vwx301), [], baf) → GT
new_ltEs7(vwx30, vwx40) → new_not(new_compare16(vwx30, vwx40))
new_esEs11(@0, @0) → True
new_esEs27(vwx30, vwx31, app(app(ty_@2, bee), bef)) → new_esEs5(vwx30, vwx31, bee, bef)
new_esEs25(vwx302, vwx312, ty_@0) → new_esEs11(vwx302, vwx312)
new_esEs16([], :(vwx310, vwx311), dab) → False
new_esEs16(:(vwx300, vwx301), [], dab) → False
new_ltEs12(vwx301, vwx401, app(ty_Ratio, cdd)) → new_ltEs14(vwx301, vwx401, cdd)
new_esEs10(vwx301, vwx311, app(app(ty_@2, bgc), bgd)) → new_esEs5(vwx301, vwx311, bgc, bgd)
new_esEs9(vwx300, vwx310, ty_Bool) → new_esEs14(vwx300, vwx310)
new_esEs27(vwx30, vwx31, app(ty_Maybe, cca)) → new_esEs4(vwx30, vwx31, cca)
new_pePe(True, vwx30, vwx31, vwx32, dbf) → True
new_lt10(vwx300, vwx400, bed) → new_esEs8(new_compare17(vwx300, vwx400, bed))
new_primCmpInt(Neg(Zero), Neg(Succ(vwx4000))) → new_primCmpNat0(Succ(vwx4000), Zero)
new_lt20(vwx301, vwx401, app(app(ty_@2, ge), gf)) → new_lt15(vwx301, vwx401, ge, gf)
new_primCmpInt(Pos(Zero), Neg(Succ(vwx4000))) → GT
new_ltEs17(Right(vwx300), Right(vwx400), bdb, ty_Bool) → new_ltEs15(vwx300, vwx400)
new_compare4([], :(vwx400, vwx401), baf) → LT
new_esEs4(Just(vwx300), Just(vwx310), app(ty_[], ccf)) → new_esEs16(vwx300, vwx310, ccf)
new_esEs9(vwx300, vwx310, ty_Double) → new_esEs20(vwx300, vwx310)
new_lt16(vwx300, vwx400) → new_esEs8(new_compare26(vwx300, vwx400))
new_ltEs17(Right(vwx300), Right(vwx400), bdb, ty_Char) → new_ltEs10(vwx300, vwx400)
new_ltEs17(Left(vwx300), Right(vwx400), bdb, bca) → True
new_ltEs13(Just(vwx300), Just(vwx400), ty_Bool) → new_ltEs15(vwx300, vwx400)
new_compare28(vwx300, vwx400, False) → new_compare14(vwx300, vwx400, new_ltEs6(vwx300, vwx400))
new_compare31(vwx300, vwx400, ty_Bool) → new_compare9(vwx300, vwx400)
new_lt13(vwx300, vwx400, app(app(ty_Either, dc), dd)) → new_lt5(vwx300, vwx400, dc, dd)
new_esEs23(vwx300, vwx310, ty_Ordering) → new_esEs17(vwx300, vwx310)
new_ltEs13(Just(vwx300), Just(vwx400), app(ty_Maybe, ba)) → new_ltEs13(vwx300, vwx400, ba)
new_esEs7(Right(vwx300), Right(vwx310), caf, ty_Double) → new_esEs20(vwx300, vwx310)
new_esEs9(vwx300, vwx310, app(app(ty_@2, bfa), bfb)) → new_esEs5(vwx300, vwx310, bfa, bfb)
new_ltEs13(Just(vwx300), Nothing, dcb) → False
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_compare31(vwx300, vwx400, app(ty_[], bbe)) → new_compare4(vwx300, vwx400, bbe)
new_lt19(vwx300, vwx400, ty_Ordering) → new_lt4(vwx300, vwx400)
new_primCompAux1(vwx300, vwx400, vwx42, baf) → new_primCompAux0(vwx42, new_compare31(vwx300, vwx400, baf))
new_esEs10(vwx301, vwx311, ty_Float) → new_esEs12(vwx301, vwx311)
new_esEs9(vwx300, vwx310, ty_Ordering) → new_esEs17(vwx300, vwx310)
new_esEs4(Just(vwx300), Just(vwx310), ty_Bool) → new_esEs14(vwx300, vwx310)
new_ltEs17(Left(vwx300), Left(vwx400), app(app(ty_@2, bcb), bcc), bca) → new_ltEs11(vwx300, vwx400, bcb, bcc)
new_compare210(vwx300, vwx400, False, cd, ce) → new_compare11(vwx300, vwx400, new_ltEs11(vwx300, vwx400, cd, ce), cd, ce)
new_asAs(False, vwx41) → False
new_esEs10(vwx301, vwx311, app(app(app(ty_@3, bgg), bgh), bha)) → new_esEs6(vwx301, vwx311, bgg, bgh, bha)
new_primMulInt(Pos(vwx4000), Neg(vwx3010)) → Neg(new_primMulNat0(vwx4000, vwx3010))
new_primMulInt(Neg(vwx4000), Pos(vwx3010)) → Neg(new_primMulNat0(vwx4000, vwx3010))
new_primMulNat0(Zero, Succ(vwx30100)) → Zero
new_primMulNat0(Succ(vwx40000), Zero) → Zero
new_lt13(vwx300, vwx400, ty_Char) → new_lt17(vwx300, vwx400)
new_esEs26(vwx300, vwx310, ty_Integer) → new_esEs13(vwx300, vwx310)
new_esEs23(vwx300, vwx310, app(app(app(ty_@3, cfb), cfc), cfd)) → new_esEs6(vwx300, vwx310, cfb, cfc, cfd)
new_compare13(vwx300, vwx400, cf, cg, da) → new_compare23(vwx300, vwx400, new_esEs6(vwx300, vwx400, cf, cg, da), cf, cg, da)
new_esEs9(vwx300, vwx310, app(ty_Maybe, bfd)) → new_esEs4(vwx300, vwx310, bfd)
new_ltEs12(vwx301, vwx401, ty_Char) → new_ltEs10(vwx301, vwx401)
new_compare31(vwx300, vwx400, ty_Double) → new_compare12(vwx300, vwx400)
new_lt19(vwx300, vwx400, app(app(ty_@2, fb), fc)) → new_lt15(vwx300, vwx400, fb, fc)
new_esEs24(vwx301, vwx311, app(ty_[], cgb)) → new_esEs16(vwx301, vwx311, cgb)
new_esEs7(Left(vwx300), Left(vwx310), ty_@0, bhc) → new_esEs11(vwx300, vwx310)
new_ltEs17(Right(vwx300), Right(vwx400), bdb, ty_@0) → new_ltEs16(vwx300, vwx400)
new_esEs19(:%(vwx300, vwx301), :%(vwx310, vwx311), cde) → new_asAs(new_esEs21(vwx300, vwx310, cde), new_esEs22(vwx301, vwx311, cde))
new_not(EQ) → new_not0
new_lt19(vwx300, vwx400, app(app(ty_Either, ga), gb)) → new_lt5(vwx300, vwx400, ga, gb)
new_esEs25(vwx302, vwx312, ty_Integer) → new_esEs13(vwx302, vwx312)
new_lt20(vwx301, vwx401, app(ty_Maybe, gd)) → new_lt14(vwx301, vwx401, gd)
new_esEs25(vwx302, vwx312, app(app(app(ty_@3, chf), chg), chh)) → new_esEs6(vwx302, vwx312, chf, chg, chh)
new_lt13(vwx300, vwx400, ty_Double) → new_lt7(vwx300, vwx400)
new_lt12(vwx300, vwx400) → new_esEs8(new_compare16(vwx300, vwx400))
new_ltEs17(Left(vwx300), Left(vwx400), ty_Float, bca) → new_ltEs4(vwx300, vwx400)
new_ltEs6(LT, GT) → True
new_esEs10(vwx301, vwx311, ty_Ordering) → new_esEs17(vwx301, vwx311)
new_lt19(vwx300, vwx400, ty_@0) → new_lt16(vwx300, vwx400)
new_esEs17(EQ, LT) → False
new_esEs17(LT, EQ) → False
new_esEs14(True, True) → True
new_esEs7(Left(vwx300), Left(vwx310), app(app(app(ty_@3, cab), cac), cad), bhc) → new_esEs6(vwx300, vwx310, cab, cac, cad)
new_esEs27(vwx30, vwx31, ty_Bool) → new_esEs14(vwx30, vwx31)
new_compare9(vwx300, vwx400) → new_compare211(vwx300, vwx400, new_esEs14(vwx300, vwx400))
new_lt8(vwx300, vwx400, cf, cg, da) → new_esEs8(new_compare13(vwx300, vwx400, cf, cg, da))
new_ltEs13(Just(vwx300), Just(vwx400), app(app(ty_Either, bh), ca)) → new_ltEs17(vwx300, vwx400, bh, ca)
new_ltEs17(Right(vwx300), Right(vwx400), bdb, app(ty_Ratio, dbh)) → new_ltEs14(vwx300, vwx400, dbh)
new_compare6(Float(vwx300, vwx301), Float(vwx400, vwx401)) → new_compare15(new_sr(vwx300, vwx400), new_sr(vwx301, vwx401))
new_compare26(@0, @0) → EQ
new_esEs24(vwx301, vwx311, ty_Ordering) → new_esEs17(vwx301, vwx311)
new_ltEs19(vwx302, vwx402, app(ty_Maybe, he)) → new_ltEs13(vwx302, vwx402, he)
new_esEs27(vwx30, vwx31, ty_Int) → new_esEs15(vwx30, vwx31)
new_compare31(vwx300, vwx400, ty_Float) → new_compare6(vwx300, vwx400)
new_esEs16([], [], dab) → True
new_ltEs16(vwx30, vwx40) → new_not(new_compare26(vwx30, vwx40))
new_esEs12(Float(vwx300, vwx301), Float(vwx310, vwx311)) → new_esEs15(new_sr(vwx300, vwx310), new_sr(vwx301, vwx311))
new_esEs26(vwx300, vwx310, ty_Ordering) → new_esEs17(vwx300, vwx310)
new_esEs25(vwx302, vwx312, app(app(ty_@2, chb), chc)) → new_esEs5(vwx302, vwx312, chb, chc)
new_lt20(vwx301, vwx401, ty_Float) → new_lt11(vwx301, vwx401)
new_lt20(vwx301, vwx401, ty_Integer) → new_lt12(vwx301, vwx401)
new_not(LT) → new_not0
new_compare4(:(vwx300, vwx301), :(vwx400, vwx401), baf) → new_primCompAux1(vwx300, vwx400, new_compare4(vwx301, vwx401, baf), baf)
new_lt17(vwx300, vwx400) → new_esEs8(new_compare24(vwx300, vwx400))
new_esEs27(vwx30, vwx31, ty_Ordering) → new_esEs17(vwx30, vwx31)
new_esEs14(False, False) → True
new_compare27(vwx300, vwx400, True, cb) → EQ
new_esEs26(vwx300, vwx310, ty_Char) → new_esEs18(vwx300, vwx310)
new_ltEs19(vwx302, vwx402, ty_Integer) → new_ltEs7(vwx302, vwx402)
new_esEs8(EQ) → False
new_esEs23(vwx300, vwx310, app(ty_[], ceh)) → new_esEs16(vwx300, vwx310, ceh)
new_esEs9(vwx300, vwx310, app(app(app(ty_@3, bfe), bff), bfg)) → new_esEs6(vwx300, vwx310, bfe, bff, bfg)
new_primPlusNat1(Zero, Zero) → Zero
new_ltEs6(LT, EQ) → True
new_esEs7(Right(vwx300), Right(vwx310), caf, ty_Integer) → new_esEs13(vwx300, vwx310)
new_ltEs6(GT, LT) → False
new_asAs(True, vwx41) → vwx41
new_primMulNat0(Succ(vwx40000), Succ(vwx30100)) → new_primPlusNat0(new_primMulNat0(vwx40000, Succ(vwx30100)), vwx30100)
new_compare25(vwx300, vwx400, False, dc, dd) → new_compare110(vwx300, vwx400, new_ltEs17(vwx300, vwx400, dc, dd), dc, dd)
new_ltEs12(vwx301, vwx401, ty_Integer) → new_ltEs7(vwx301, vwx401)
new_ltEs17(Right(vwx300), Right(vwx400), bdb, ty_Float) → new_ltEs4(vwx300, vwx400)
new_esEs17(GT, GT) → True
new_lt13(vwx300, vwx400, ty_Bool) → new_lt6(vwx300, vwx400)
new_lt20(vwx301, vwx401, app(ty_Ratio, cdg)) → new_lt10(vwx301, vwx401, cdg)
new_compare31(vwx300, vwx400, app(ty_Ratio, dca)) → new_compare17(vwx300, vwx400, dca)
new_esEs9(vwx300, vwx310, app(app(ty_Either, beg), beh)) → new_esEs7(vwx300, vwx310, beg, beh)
new_ltEs12(vwx301, vwx401, ty_Float) → new_ltEs4(vwx301, vwx401)
new_lt13(vwx300, vwx400, ty_@0) → new_lt16(vwx300, vwx400)
new_compare211(vwx300, vwx400, True) → EQ
new_compare7(vwx300, vwx400) → new_compare28(vwx300, vwx400, new_esEs17(vwx300, vwx400))
new_esEs9(vwx300, vwx310, ty_Int) → new_esEs15(vwx300, vwx310)
new_esEs9(vwx300, vwx310, ty_Char) → new_esEs18(vwx300, vwx310)
new_esEs4(Just(vwx300), Just(vwx310), ty_Integer) → new_esEs13(vwx300, vwx310)
new_esEs4(Just(vwx300), Just(vwx310), ty_Ordering) → new_esEs17(vwx300, vwx310)
new_ltEs13(Just(vwx300), Just(vwx400), ty_Char) → new_ltEs10(vwx300, vwx400)
new_esEs16(:(vwx300, vwx301), :(vwx310, vwx311), dab) → new_asAs(new_esEs26(vwx300, vwx310, dab), new_esEs16(vwx301, vwx311, dab))
new_esEs27(vwx30, vwx31, ty_Char) → new_esEs18(vwx30, vwx31)
new_esEs26(vwx300, vwx310, app(ty_Ratio, dbd)) → new_esEs19(vwx300, vwx310, dbd)
new_esEs26(vwx300, vwx310, ty_Int) → new_esEs15(vwx300, vwx310)
new_lt13(vwx300, vwx400, app(app(ty_@2, cd), ce)) → new_lt15(vwx300, vwx400, cd, ce)
new_ltEs12(vwx301, vwx401, app(app(app(ty_@3, ea), eb), ec)) → new_ltEs9(vwx301, vwx401, ea, eb, ec)
new_esEs7(Left(vwx300), Left(vwx310), ty_Float, bhc) → new_esEs12(vwx300, vwx310)
new_ltEs13(Just(vwx300), Just(vwx400), app(app(app(ty_@3, bd), be), bf)) → new_ltEs9(vwx300, vwx400, bd, be, bf)
new_esEs25(vwx302, vwx312, app(app(ty_Either, cgh), cha)) → new_esEs7(vwx302, vwx312, cgh, cha)
new_compare31(vwx300, vwx400, ty_Int) → new_compare15(vwx300, vwx400)
new_lt5(vwx300, vwx400, dc, dd) → new_esEs8(new_compare8(vwx300, vwx400, dc, dd))
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCompAux0(vwx46, EQ) → vwx46
new_esEs24(vwx301, vwx311, ty_Char) → new_esEs18(vwx301, vwx311)
new_ltEs19(vwx302, vwx402, ty_@0) → new_ltEs16(vwx302, vwx402)
new_lt19(vwx300, vwx400, ty_Bool) → new_lt6(vwx300, vwx400)
new_ltEs5(vwx30, vwx40) → new_not(new_compare12(vwx30, vwx40))
new_esEs10(vwx301, vwx311, app(ty_Maybe, bgf)) → new_esEs4(vwx301, vwx311, bgf)
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primCmpInt(Neg(Succ(vwx3000)), Pos(vwx400)) → LT
new_ltEs9(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), gc, eh, fa) → new_pePe(new_lt19(vwx300, vwx400, gc), vwx300, vwx400, new_pePe(new_lt20(vwx301, vwx401, eh), vwx301, vwx401, new_ltEs19(vwx302, vwx402, fa), eh), gc)

The set Q consists of the following terms:

new_lt19(x0, x1, ty_Double)
new_compare110(x0, x1, True, x2, x3)
new_esEs17(LT, GT)
new_esEs17(GT, LT)
new_lt15(x0, x1, x2, x3)
new_esEs4(Just(x0), Just(x1), ty_Char)
new_compare31(x0, x1, app(ty_[], x2))
new_esEs10(x0, x1, ty_Double)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, ty_Int)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_compare23(x0, x1, True, x2, x3, x4)
new_ltEs17(Left(x0), Left(x1), ty_Bool, x2)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs4(Just(x0), Just(x1), ty_Double)
new_esEs7(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs4(Nothing, Just(x0), x1)
new_esEs17(LT, LT)
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs17(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs27(x0, x1, ty_Ordering)
new_esEs4(Nothing, Nothing, x0)
new_esEs7(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs13(Just(x0), Just(x1), ty_Double)
new_esEs9(x0, x1, app(ty_[], x2))
new_compare13(x0, x1, x2, x3, x4)
new_esEs25(x0, x1, ty_Char)
new_esEs24(x0, x1, ty_Integer)
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_ltEs17(Right(x0), Right(x1), x2, ty_@0)
new_esEs7(Right(x0), Right(x1), x2, ty_Int)
new_esEs16([], [], x0)
new_lt13(x0, x1, ty_Char)
new_lt20(x0, x1, ty_Float)
new_compare16(Integer(x0), Integer(x1))
new_ltEs15(True, True)
new_esEs10(x0, x1, ty_@0)
new_asAs(False, x0)
new_pePe(False, x0, x1, x2, x3)
new_lt5(x0, x1, x2, x3)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_ltEs11(@2(x0, x1), @2(x2, x3), x4, x5)
new_lt13(x0, x1, ty_Double)
new_esEs7(Left(x0), Left(x1), ty_Integer, x2)
new_esEs25(x0, x1, ty_Int)
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs8(LT)
new_esEs11(@0, @0)
new_ltEs17(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs17(EQ, GT)
new_esEs17(GT, EQ)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_primEqNat0(Succ(x0), Succ(x1))
new_ltEs17(Right(x0), Right(x1), x2, ty_Integer)
new_ltEs17(Left(x0), Left(x1), ty_Float, x2)
new_ltEs15(False, False)
new_ltEs13(Just(x0), Just(x1), app(ty_Maybe, x2))
new_primPlusNat1(Succ(x0), Succ(x1))
new_lt13(x0, x1, app(app(ty_@2, x2), x3))
new_compare31(x0, x1, ty_Ordering)
new_esEs27(x0, x1, app(ty_[], x2))
new_esEs7(Right(x0), Right(x1), x2, ty_@0)
new_esEs5(@2(x0, x1), @2(x2, x3), x4, x5)
new_ltEs19(x0, x1, ty_Char)
new_ltEs13(Just(x0), Just(x1), ty_@0)
new_lt20(x0, x1, ty_Char)
new_ltEs17(Left(x0), Left(x1), app(ty_[], x2), x3)
new_primCompAux0(x0, EQ)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, ty_@0)
new_esEs10(x0, x1, app(app(ty_@2, x2), x3))
new_lt13(x0, x1, ty_Ordering)
new_esEs7(Left(x0), Left(x1), ty_Bool, x2)
new_compare11(x0, x1, False, x2, x3)
new_ltEs17(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_esEs4(Just(x0), Just(x1), ty_Ordering)
new_ltEs13(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs10(x0, x1, ty_Int)
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_lt20(x0, x1, ty_Int)
new_compare17(:%(x0, x1), :%(x2, x3), ty_Int)
new_esEs17(GT, GT)
new_ltEs6(EQ, EQ)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_lt13(x0, x1, app(ty_[], x2))
new_esEs7(Right(x0), Right(x1), x2, ty_Double)
new_compare19(x0, x1, False, x2, x3, x4)
new_esEs7(Left(x0), Left(x1), ty_Double, x2)
new_esEs7(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs27(x0, x1, ty_Double)
new_esEs27(x0, x1, ty_Integer)
new_esEs14(True, True)
new_ltEs6(LT, EQ)
new_ltEs6(EQ, LT)
new_primPlusNat1(Zero, Succ(x0))
new_esEs23(x0, x1, ty_Float)
new_esEs25(x0, x1, ty_Bool)
new_ltEs17(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_esEs9(x0, x1, ty_Float)
new_primEqNat0(Zero, Zero)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_compare14(x0, x1, True)
new_esEs9(x0, x1, ty_@0)
new_esEs10(x0, x1, ty_Bool)
new_esEs22(x0, x1, ty_Int)
new_esEs10(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs13(Just(x0), Nothing, x1)
new_ltEs17(Left(x0), Left(x1), ty_Char, x2)
new_ltEs19(x0, x1, ty_Int)
new_primEqNat0(Zero, Succ(x0))
new_esEs9(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, ty_Ordering)
new_esEs8(EQ)
new_ltEs13(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_lt19(x0, x1, ty_@0)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primMulNat0(Zero, Zero)
new_compare31(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs17(Left(x0), Left(x1), ty_Integer, x2)
new_compare24(Char(x0), Char(x1))
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_ltEs10(x0, x1)
new_ltEs13(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs4(Just(x0), Just(x1), app(ty_[], x2))
new_lt9(x0, x1, x2)
new_ltEs12(x0, x1, ty_Bool)
new_ltEs17(Right(x0), Right(x1), x2, ty_Bool)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs26(x0, x1, ty_Ordering)
new_esEs24(x0, x1, ty_Int)
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, ty_Bool)
new_esEs10(x0, x1, ty_Integer)
new_lt10(x0, x1, x2)
new_esEs27(x0, x1, ty_Float)
new_lt19(x0, x1, ty_Char)
new_ltEs14(x0, x1, x2)
new_ltEs17(Right(x0), Right(x1), x2, ty_Int)
new_esEs4(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_compare110(x0, x1, False, x2, x3)
new_lt13(x0, x1, app(ty_Ratio, x2))
new_ltEs13(Just(x0), Just(x1), ty_Float)
new_ltEs13(Just(x0), Just(x1), app(ty_[], x2))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs23(x0, x1, app(ty_[], x2))
new_compare7(x0, x1)
new_primPlusNat1(Succ(x0), Zero)
new_primMulNat0(Succ(x0), Zero)
new_esEs19(:%(x0, x1), :%(x2, x3), x4)
new_compare18(x0, x1, True)
new_lt13(x0, x1, app(ty_Maybe, x2))
new_lt18(x0, x1)
new_ltEs6(GT, LT)
new_compare210(x0, x1, True, x2, x3)
new_ltEs6(LT, GT)
new_compare31(x0, x1, app(ty_Ratio, x2))
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt19(x0, x1, ty_Bool)
new_esEs9(x0, x1, app(app(ty_Either, x2), x3))
new_esEs4(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_lt7(x0, x1)
new_esEs25(x0, x1, ty_Ordering)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs7(Left(x0), Left(x1), app(ty_[], x2), x3)
new_lt19(x0, x1, ty_Integer)
new_esEs20(Double(x0, x1), Double(x2, x3))
new_compare29(x0, x1, x2, x3)
new_ltEs19(x0, x1, ty_Bool)
new_ltEs17(Right(x0), Left(x1), x2, x3)
new_esEs9(x0, x1, ty_Bool)
new_ltEs17(Left(x0), Right(x1), x2, x3)
new_compare25(x0, x1, False, x2, x3)
new_compare211(x0, x1, False)
new_esEs9(x0, x1, app(app(ty_@2, x2), x3))
new_compare211(x0, x1, True)
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs12(x0, x1, ty_Char)
new_compare6(Float(x0, x1), Float(x2, x3))
new_esEs23(x0, x1, ty_Bool)
new_esEs9(x0, x1, app(ty_Ratio, x2))
new_esEs25(x0, x1, ty_@0)
new_pePe(True, x0, x1, x2, x3)
new_esEs15(x0, x1)
new_esEs25(x0, x1, app(ty_[], x2))
new_lt12(x0, x1)
new_primEqNat0(Succ(x0), Zero)
new_esEs7(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_compare28(x0, x1, True)
new_primPlusNat1(Zero, Zero)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_not0
new_sr(x0, x1)
new_compare12(Double(x0, x1), Double(x2, x3))
new_ltEs13(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs7(Right(x0), Right(x1), x2, app(ty_[], x3))
new_compare10(x0, x1, False, x2)
new_esEs23(x0, x1, ty_Integer)
new_lt20(x0, x1, ty_Bool)
new_esEs10(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_lt13(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs17(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs4(Just(x0), Just(x1), ty_@0)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs18(x0, x1)
new_esEs24(x0, x1, ty_Char)
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, ty_Int)
new_compare4([], [], x0)
new_esEs7(Right(x0), Right(x1), x2, ty_Float)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_lt19(x0, x1, ty_Ordering)
new_primCompAux0(x0, LT)
new_esEs7(Right(x0), Left(x1), x2, x3)
new_esEs7(Left(x0), Right(x1), x2, x3)
new_ltEs12(x0, x1, ty_@0)
new_lt20(x0, x1, app(ty_[], x2))
new_esEs4(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs4(Just(x0), Just(x1), ty_Bool)
new_compare23(x0, x1, False, x2, x3, x4)
new_ltEs12(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs17(Left(x0), Left(x1), ty_@0, x2)
new_esEs7(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs21(x0, x1, ty_Integer)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_compare31(x0, x1, app(ty_Maybe, x2))
new_not(GT)
new_ltEs15(True, False)
new_ltEs15(False, True)
new_esEs8(GT)
new_esEs24(x0, x1, ty_Bool)
new_esEs7(Left(x0), Left(x1), ty_Float, x2)
new_esEs9(x0, x1, ty_Ordering)
new_esEs23(x0, x1, ty_Ordering)
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs25(x0, x1, ty_Double)
new_esEs10(x0, x1, app(ty_Maybe, x2))
new_ltEs17(Left(x0), Left(x1), ty_Ordering, x2)
new_lt20(x0, x1, ty_@0)
new_primEqInt(Neg(Zero), Pos(Zero))
new_primEqInt(Pos(Zero), Neg(Zero))
new_lt11(x0, x1)
new_lt14(x0, x1, x2)
new_esEs9(x0, x1, app(ty_Maybe, x2))
new_ltEs7(x0, x1)
new_ltEs17(Right(x0), Right(x1), x2, ty_Double)
new_lt17(x0, x1)
new_ltEs17(Left(x0), Left(x1), ty_Int, x2)
new_lt13(x0, x1, ty_Int)
new_compare31(x0, x1, ty_Bool)
new_primCompAux0(x0, GT)
new_esEs12(Float(x0, x1), Float(x2, x3))
new_primMulNat0(Zero, Succ(x0))
new_ltEs13(Nothing, Just(x0), x1)
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_esEs27(x0, x1, ty_@0)
new_ltEs13(Just(x0), Just(x1), ty_Bool)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs21(x0, x1, ty_Int)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_ltEs12(x0, x1, app(ty_[], x2))
new_lt16(x0, x1)
new_compare31(x0, x1, ty_Float)
new_primEqInt(Neg(Zero), Neg(Zero))
new_esEs13(Integer(x0), Integer(x1))
new_compare31(x0, x1, ty_@0)
new_esEs7(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs4(Just(x0), Just(x1), app(ty_Ratio, x2))
new_compare25(x0, x1, True, x2, x3)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_esEs24(x0, x1, ty_Double)
new_esEs14(False, True)
new_esEs14(True, False)
new_lt19(x0, x1, ty_Float)
new_compare31(x0, x1, ty_Integer)
new_ltEs17(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs23(x0, x1, ty_Double)
new_ltEs12(x0, x1, ty_Float)
new_ltEs12(x0, x1, ty_Int)
new_ltEs9(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_primCmpNat0(Zero, Succ(x0))
new_compare15(x0, x1)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_compare30(x0, x1, x2)
new_ltEs19(x0, x1, ty_Integer)
new_esEs10(x0, x1, app(ty_[], x2))
new_esEs9(x0, x1, ty_Integer)
new_esEs7(Right(x0), Right(x1), x2, ty_Bool)
new_esEs10(x0, x1, app(app(ty_Either, x2), x3))
new_esEs7(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_compare31(x0, x1, ty_Double)
new_ltEs6(GT, GT)
new_ltEs19(x0, x1, ty_Double)
new_esEs24(x0, x1, app(ty_[], x2))
new_ltEs13(Just(x0), Just(x1), ty_Integer)
new_esEs7(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_primPlusNat0(Zero, x0)
new_ltEs17(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs16(:(x0, x1), [], x2)
new_esEs9(x0, x1, ty_Char)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_compare27(x0, x1, False, x2)
new_esEs26(x0, x1, ty_Float)
new_esEs26(x0, x1, ty_Integer)
new_esEs4(Just(x0), Nothing, x1)
new_compare31(x0, x1, app(app(ty_Either, x2), x3))
new_primCompAux1(x0, x1, x2, x3)
new_esEs9(x0, x1, ty_Int)
new_primMulNat0(Succ(x0), Succ(x1))
new_lt13(x0, x1, app(app(ty_Either, x2), x3))
new_lt13(x0, x1, ty_Bool)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpNat0(Zero, Zero)
new_esEs7(Left(x0), Left(x1), ty_@0, x2)
new_compare31(x0, x1, ty_Char)
new_lt20(x0, x1, ty_Ordering)
new_esEs26(x0, x1, ty_Char)
new_ltEs6(LT, LT)
new_ltEs12(x0, x1, ty_Ordering)
new_ltEs17(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_lt20(x0, x1, ty_Integer)
new_ltEs13(Nothing, Nothing, x0)
new_compare11(x0, x1, True, x2, x3)
new_esEs4(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_ltEs12(x0, x1, ty_Integer)
new_primPlusNat0(Succ(x0), x1)
new_compare27(x0, x1, True, x2)
new_esEs16(:(x0, x1), :(x2, x3), x4)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs19(x0, x1, app(ty_[], x2))
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_esEs18(Char(x0), Char(x1))
new_lt8(x0, x1, x2, x3, x4)
new_esEs23(x0, x1, ty_Int)
new_ltEs8(x0, x1, x2)
new_compare8(x0, x1, x2, x3)
new_esEs22(x0, x1, ty_Integer)
new_ltEs19(x0, x1, ty_@0)
new_compare4(:(x0, x1), :(x2, x3), x4)
new_ltEs17(Right(x0), Right(x1), x2, ty_Float)
new_compare17(:%(x0, x1), :%(x2, x3), ty_Integer)
new_lt6(x0, x1)
new_lt19(x0, x1, ty_Int)
new_primCmpNat0(Succ(x0), Succ(x1))
new_compare210(x0, x1, False, x2, x3)
new_ltEs17(Left(x0), Left(x1), ty_Double, x2)
new_compare19(x0, x1, True, x2, x3, x4)
new_compare31(x0, x1, ty_Int)
new_esEs26(x0, x1, app(ty_[], x2))
new_esEs25(x0, x1, ty_Float)
new_ltEs19(x0, x1, ty_Float)
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_compare14(x0, x1, False)
new_not(EQ)
new_esEs4(Just(x0), Just(x1), ty_Int)
new_esEs23(x0, x1, ty_Char)
new_ltEs16(x0, x1)
new_ltEs17(Right(x0), Right(x1), x2, ty_Char)
new_ltEs12(x0, x1, app(ty_Ratio, x2))
new_ltEs17(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_ltEs5(x0, x1)
new_ltEs13(Just(x0), Just(x1), ty_Char)
new_esEs7(Left(x0), Left(x1), ty_Int, x2)
new_esEs26(x0, x1, ty_@0)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_ltEs17(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_asAs(True, x0)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_ltEs4(x0, x1)
new_esEs10(x0, x1, ty_Char)
new_esEs25(x0, x1, ty_Integer)
new_compare10(x0, x1, True, x2)
new_ltEs6(EQ, GT)
new_ltEs6(GT, EQ)
new_esEs4(Just(x0), Just(x1), ty_Integer)
new_esEs10(x0, x1, ty_Float)
new_esEs4(Just(x0), Just(x1), ty_Float)
new_ltEs13(Just(x0), Just(x1), ty_Int)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare4(:(x0, x1), [], x2)
new_esEs27(x0, x1, ty_Bool)
new_lt4(x0, x1)
new_ltEs12(x0, x1, app(ty_Maybe, x2))
new_sr0(Integer(x0), Integer(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs24(x0, x1, ty_Float)
new_lt13(x0, x1, ty_Integer)
new_compare18(x0, x1, False)
new_ltEs13(Just(x0), Just(x1), ty_Ordering)
new_esEs26(x0, x1, ty_Double)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_compare31(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs10(x0, x1, ty_Ordering)
new_esEs7(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs24(x0, x1, ty_Ordering)
new_esEs24(x0, x1, ty_@0)
new_ltEs12(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs7(Right(x0), Right(x1), x2, ty_Integer)
new_lt20(x0, x1, ty_Double)
new_esEs27(x0, x1, ty_Char)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_compare4([], :(x0, x1), x2)
new_primMulInt(Neg(x0), Neg(x1))
new_lt19(x0, x1, app(ty_Ratio, x2))
new_esEs16([], :(x0, x1), x2)
new_lt19(x0, x1, app(ty_Maybe, x2))
new_ltEs17(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_compare28(x0, x1, False)
new_compare26(@0, @0)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_ltEs17(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_ltEs12(x0, x1, ty_Double)
new_esEs14(False, False)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primEqInt(Pos(Zero), Pos(Zero))
new_esEs9(x0, x1, ty_Double)
new_compare9(x0, x1)
new_esEs7(Right(x0), Right(x1), x2, ty_Char)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_lt13(x0, x1, ty_Float)
new_esEs7(Left(x0), Left(x1), ty_Char, x2)
new_esEs17(EQ, EQ)
new_esEs17(LT, EQ)
new_esEs17(EQ, LT)
new_primCmpNat0(Succ(x0), Zero)
new_lt13(x0, x1, ty_@0)
new_not(LT)
new_lt19(x0, x1, app(ty_[], x2))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs12(x0, x1, app(app(ty_@2, 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: