YES 3.045 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 b, Ord a) => Either a b  ->  Either a b  ->  Either a b) :: (Ord b, Ord a) => Either a b  ->  Either a b  ->  Either a b)

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, Ord b) => Either a b  ->  Either a b  ->  Either a b) :: (Ord a, Ord b) => Either a b  ->  Either a b  ->  Either a b)

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 b, Ord a) => Either b a  ->  Either b a  ->  Either b a) :: (Ord b, Ord a) => Either b a  ->  Either b a  ->  Either b 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, Ord b) => Either b a  ->  Either b a  ->  Either b a) :: (Ord a, Ord b) => Either b a  ->  Either b a  ->  Either b a)

module Main where
  import qualified Prelude


Cond Reductions:
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
compare x y
 | x == y
 = EQ
 | x <= y
 = LT
 | otherwise
 = GT

is transformed to
compare x y = compare3 x y

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

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

compare0 x y True = GT

compare3 x y = compare2 x y (x == y)

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

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

gcd'0 x y = gcd' y (x `rem` y)

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

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

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

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

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

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

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

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

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

is transformed to
absReal x = absReal2 x

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
  ((min :: (Ord b, Ord a) => Either b a  ->  Either b a  ->  Either b a) :: (Ord a, Ord b) => Either b a  ->  Either b a  ->  Either b 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
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

reduce2D vwv vww = gcd vwv vww

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

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

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

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

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



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

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

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 b, Ord a) => Either b a  ->  Either b a  ->  Either b 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(vwx3700), Succ(vwx3800)) → new_primEqNat(vwx3700, vwx3800)

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(vwx6700), Succ(vwx401000)) → new_primPlusNat(vwx6700, 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_esEs3(@3(vwx370, vwx371, vwx372), @3(vwx380, vwx381, vwx382), bca, app(app(ty_@2, bce), bcf), bah) → new_esEs1(vwx371, vwx381, bce, bcf)
new_esEs3(@3(vwx370, vwx371, vwx372), @3(vwx380, vwx381, vwx382), bca, app(ty_Maybe, bcg), bah) → new_esEs2(vwx371, vwx381, bcg)
new_esEs0(Left(vwx370), Left(vwx380), app(ty_[], cc), cd) → new_esEs(vwx370, vwx380, cc)
new_esEs2(Just(vwx370), Just(vwx380), app(ty_[], he)) → new_esEs(vwx370, vwx380, he)
new_esEs1(@2(vwx370, vwx371), @2(vwx380, vwx381), gc, app(app(app(ty_@3, hb), hc), hd)) → new_esEs3(vwx371, vwx381, hb, hc, hd)
new_esEs3(@3(vwx370, vwx371, vwx372), @3(vwx380, vwx381, vwx382), bca, bag, app(app(app(ty_@3, bea), beb), bec)) → new_esEs3(vwx372, vwx382, bea, beb, bec)
new_esEs3(@3(vwx370, vwx371, vwx372), @3(vwx380, vwx381, vwx382), bca, bag, app(ty_[], bdc)) → new_esEs(vwx372, vwx382, bdc)
new_esEs1(@2(vwx370, vwx371), @2(vwx380, vwx381), app(app(ty_Either, fb), fc), fa) → new_esEs0(vwx370, vwx380, fb, fc)
new_esEs1(@2(vwx370, vwx371), @2(vwx380, vwx381), gc, app(app(ty_Either, ge), gf)) → new_esEs0(vwx371, vwx381, ge, gf)
new_esEs3(@3(vwx370, vwx371, vwx372), @3(vwx380, vwx381, vwx382), app(app(ty_@2, bbc), bbd), bag, bah) → new_esEs1(vwx370, vwx380, bbc, bbd)
new_esEs(:(vwx370, vwx371), :(vwx380, vwx381), app(app(app(ty_@3, bg), bh), ca)) → new_esEs3(vwx370, vwx380, bg, bh, ca)
new_esEs0(Right(vwx370), Right(vwx380), df, app(app(ty_@2, eb), ec)) → new_esEs1(vwx370, vwx380, eb, ec)
new_esEs3(@3(vwx370, vwx371, vwx372), @3(vwx380, vwx381, vwx382), app(ty_[], baf), bag, bah) → new_esEs(vwx370, vwx380, baf)
new_esEs3(@3(vwx370, vwx371, vwx372), @3(vwx380, vwx381, vwx382), bca, app(ty_[], bcb), bah) → new_esEs(vwx371, vwx381, bcb)
new_esEs0(Left(vwx370), Left(vwx380), app(app(app(ty_@3, dc), dd), de), cd) → new_esEs3(vwx370, vwx380, dc, dd, de)
new_esEs2(Just(vwx370), Just(vwx380), app(ty_Maybe, bab)) → new_esEs2(vwx370, vwx380, bab)
new_esEs0(Left(vwx370), Left(vwx380), app(app(ty_Either, ce), cf), cd) → new_esEs0(vwx370, vwx380, ce, cf)
new_esEs2(Just(vwx370), Just(vwx380), app(app(ty_@2, hh), baa)) → new_esEs1(vwx370, vwx380, hh, baa)
new_esEs1(@2(vwx370, vwx371), @2(vwx380, vwx381), gc, app(ty_[], gd)) → new_esEs(vwx371, vwx381, gd)
new_esEs(:(vwx370, vwx371), :(vwx380, vwx381), app(ty_Maybe, bf)) → new_esEs2(vwx370, vwx380, bf)
new_esEs1(@2(vwx370, vwx371), @2(vwx380, vwx381), app(ty_Maybe, fg), fa) → new_esEs2(vwx370, vwx380, fg)
new_esEs0(Right(vwx370), Right(vwx380), df, app(app(app(ty_@3, ee), ef), eg)) → new_esEs3(vwx370, vwx380, ee, ef, eg)
new_esEs1(@2(vwx370, vwx371), @2(vwx380, vwx381), app(ty_[], eh), fa) → new_esEs(vwx370, vwx380, eh)
new_esEs0(Right(vwx370), Right(vwx380), df, app(app(ty_Either, dh), ea)) → new_esEs0(vwx370, vwx380, dh, ea)
new_esEs0(Left(vwx370), Left(vwx380), app(ty_Maybe, db), cd) → new_esEs2(vwx370, vwx380, db)
new_esEs0(Right(vwx370), Right(vwx380), df, app(ty_Maybe, ed)) → new_esEs2(vwx370, vwx380, ed)
new_esEs1(@2(vwx370, vwx371), @2(vwx380, vwx381), gc, app(app(ty_@2, gg), gh)) → new_esEs1(vwx371, vwx381, gg, gh)
new_esEs(:(vwx370, vwx371), :(vwx380, vwx381), app(app(ty_@2, bd), be)) → new_esEs1(vwx370, vwx380, bd, be)
new_esEs3(@3(vwx370, vwx371, vwx372), @3(vwx380, vwx381, vwx382), bca, app(app(app(ty_@3, bch), bda), bdb), bah) → new_esEs3(vwx371, vwx381, bch, bda, bdb)
new_esEs(:(vwx370, vwx371), :(vwx380, vwx381), app(app(ty_Either, bb), bc)) → new_esEs0(vwx370, vwx380, bb, bc)
new_esEs(:(vwx370, vwx371), :(vwx380, vwx381), cb) → new_esEs(vwx371, vwx381, cb)
new_esEs3(@3(vwx370, vwx371, vwx372), @3(vwx380, vwx381, vwx382), bca, bag, app(app(ty_@2, bdf), bdg)) → new_esEs1(vwx372, vwx382, bdf, bdg)
new_esEs1(@2(vwx370, vwx371), @2(vwx380, vwx381), app(app(app(ty_@3, fh), ga), gb), fa) → new_esEs3(vwx370, vwx380, fh, ga, gb)
new_esEs1(@2(vwx370, vwx371), @2(vwx380, vwx381), app(app(ty_@2, fd), ff), fa) → new_esEs1(vwx370, vwx380, fd, ff)
new_esEs3(@3(vwx370, vwx371, vwx372), @3(vwx380, vwx381, vwx382), app(ty_Maybe, bbe), bag, bah) → new_esEs2(vwx370, vwx380, bbe)
new_esEs3(@3(vwx370, vwx371, vwx372), @3(vwx380, vwx381, vwx382), bca, bag, app(ty_Maybe, bdh)) → new_esEs2(vwx372, vwx382, bdh)
new_esEs0(Right(vwx370), Right(vwx380), df, app(ty_[], dg)) → new_esEs(vwx370, vwx380, dg)
new_esEs1(@2(vwx370, vwx371), @2(vwx380, vwx381), gc, app(ty_Maybe, ha)) → new_esEs2(vwx371, vwx381, ha)
new_esEs2(Just(vwx370), Just(vwx380), app(app(ty_Either, hf), hg)) → new_esEs0(vwx370, vwx380, hf, hg)
new_esEs2(Just(vwx370), Just(vwx380), app(app(app(ty_@3, bac), bad), bae)) → new_esEs3(vwx370, vwx380, bac, bad, bae)
new_esEs3(@3(vwx370, vwx371, vwx372), @3(vwx380, vwx381, vwx382), bca, app(app(ty_Either, bcc), bcd), bah) → new_esEs0(vwx371, vwx381, bcc, bcd)
new_esEs3(@3(vwx370, vwx371, vwx372), @3(vwx380, vwx381, vwx382), bca, bag, app(app(ty_Either, bdd), bde)) → new_esEs0(vwx372, vwx382, bdd, bde)
new_esEs(:(vwx370, vwx371), :(vwx380, vwx381), app(ty_[], ba)) → new_esEs(vwx370, vwx380, ba)
new_esEs3(@3(vwx370, vwx371, vwx372), @3(vwx380, vwx381, vwx382), app(app(app(ty_@3, bbf), bbg), bbh), bag, bah) → new_esEs3(vwx370, vwx380, bbf, bbg, bbh)
new_esEs0(Left(vwx370), Left(vwx380), app(app(ty_@2, cg), da), cd) → new_esEs1(vwx370, vwx380, cg, da)
new_esEs3(@3(vwx370, vwx371, vwx372), @3(vwx380, vwx381, vwx382), app(app(ty_Either, bba), bbb), bag, bah) → new_esEs0(vwx370, vwx380, bba, bbb)

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_ltEs1(@2(vwx300, vwx301), @2(vwx400, vwx401), fb, app(app(ty_@2, fg), fh)) → new_ltEs1(vwx301, vwx401, fg, fh)
new_ltEs0(Left(vwx300), Left(vwx400), app(app(ty_@2, db), dc), cf) → new_ltEs1(vwx300, vwx400, db, dc)
new_ltEs0(Right(vwx300), Right(vwx400), dh, app(ty_Maybe, fa)) → new_ltEs3(vwx300, vwx400, fa)
new_compare0(:(vwx300, vwx301), :(vwx400, vwx401), ba) → new_primCompAux(vwx300, vwx400, new_compare(vwx301, vwx401, ba), ba)
new_ltEs0(Left(vwx300), Left(vwx400), app(app(app(ty_@3, dd), de), df), cf) → new_ltEs2(vwx300, vwx400, dd, de, df)
new_ltEs2(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), app(ty_Maybe, bdb), hf, bba) → new_lt3(vwx300, vwx400, bdb)
new_ltEs2(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), he, hf, app(app(app(ty_@3, bad), bae), baf)) → new_ltEs2(vwx302, vwx402, bad, bae, baf)
new_ltEs2(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), he, app(ty_Maybe, bca), bba) → new_lt3(vwx301, vwx401, bca)
new_ltEs2(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), app(app(ty_@2, bce), bcf), hf, bba) → new_lt1(vwx300, vwx400, bce, bcf)
new_compare23(vwx300, vwx400, False, hd) → new_ltEs3(vwx300, vwx400, hd)
new_ltEs0(Left(vwx300), Left(vwx400), app(ty_Maybe, dg), cf) → new_ltEs3(vwx300, vwx400, dg)
new_compare0(:(vwx300, vwx301), :(vwx400, vwx401), ba) → new_compare0(vwx301, vwx401, ba)
new_ltEs2(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), he, app(app(app(ty_@3, bbf), bbg), bbh), bba) → new_lt2(vwx301, vwx401, bbf, bbg, bbh)
new_compare2(vwx300, vwx400, gg, gh) → new_compare21(vwx300, vwx400, new_esEs5(vwx300, vwx400, gg, gh), gg, gh)
new_ltEs1(@2(vwx300, vwx301), @2(vwx400, vwx401), app(app(ty_Either, cc), cd), gf) → new_compare20(vwx300, vwx400, new_esEs4(vwx300, vwx400, cc, cd), cc, cd)
new_lt3(vwx300, vwx400, hd) → new_compare23(vwx300, vwx400, new_esEs7(vwx300, vwx400, hd), hd)
new_ltEs0(Right(vwx300), Right(vwx400), dh, app(app(ty_@2, ed), ee)) → new_ltEs1(vwx300, vwx400, ed, ee)
new_ltEs0(Left(vwx300), Left(vwx400), app(app(ty_Either, cg), da), cf) → new_ltEs0(vwx300, vwx400, cg, da)
new_ltEs3(Just(vwx300), Just(vwx400), app(app(ty_Either, bdd), bde)) → new_ltEs0(vwx300, vwx400, bdd, bde)
new_compare3(vwx300, vwx400, ha, hb, hc) → new_compare22(vwx300, vwx400, new_esEs6(vwx300, vwx400, ha, hb, hc), ha, hb, hc)
new_ltEs(:(vwx300, vwx301), :(vwx400, vwx401), ba) → new_primCompAux(vwx300, vwx400, new_compare(vwx301, vwx401, ba), ba)
new_ltEs1(@2(vwx300, vwx301), @2(vwx400, vwx401), fb, app(ty_Maybe, gd)) → new_ltEs3(vwx301, vwx401, gd)
new_primCompAux(vwx300, vwx400, vwx49, app(ty_[], bb)) → new_compare0(vwx300, vwx400, bb)
new_ltEs3(Just(vwx300), Just(vwx400), app(ty_[], bdc)) → new_ltEs(vwx300, vwx400, bdc)
new_ltEs0(Left(vwx300), Left(vwx400), app(ty_[], ce), cf) → new_ltEs(vwx300, vwx400, ce)
new_ltEs2(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), he, app(ty_[], bah), bba) → new_lt(vwx301, vwx401, bah)
new_ltEs3(Just(vwx300), Just(vwx400), app(app(ty_@2, bdf), bdg)) → new_ltEs1(vwx300, vwx400, bdf, bdg)
new_compare20(vwx300, vwx400, False, cc, cd) → new_ltEs0(vwx300, vwx400, cc, cd)
new_compare21(vwx300, vwx400, False, gg, gh) → new_ltEs1(vwx300, vwx400, gg, gh)
new_primCompAux(vwx300, vwx400, vwx49, app(app(ty_Either, bc), bd)) → new_compare1(vwx300, vwx400, bc, bd)
new_ltEs1(@2(vwx300, vwx301), @2(vwx400, vwx401), app(app(ty_@2, gg), gh), gf) → new_compare21(vwx300, vwx400, new_esEs5(vwx300, vwx400, gg, gh), gg, gh)
new_lt0(vwx300, vwx400, cc, cd) → new_compare20(vwx300, vwx400, new_esEs4(vwx300, vwx400, cc, cd), cc, cd)
new_ltEs1(@2(vwx300, vwx301), @2(vwx400, vwx401), app(app(app(ty_@3, ha), hb), hc), gf) → new_compare22(vwx300, vwx400, new_esEs6(vwx300, vwx400, ha, hb, hc), ha, hb, hc)
new_lt2(vwx300, vwx400, ha, hb, hc) → new_compare22(vwx300, vwx400, new_esEs6(vwx300, vwx400, ha, hb, hc), ha, hb, hc)
new_ltEs2(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), he, app(app(ty_@2, bbd), bbe), bba) → new_lt1(vwx301, vwx401, bbd, bbe)
new_ltEs2(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), he, hf, app(app(ty_@2, bab), bac)) → new_ltEs1(vwx302, vwx402, bab, bac)
new_ltEs0(Right(vwx300), Right(vwx400), dh, app(ty_[], ea)) → new_ltEs(vwx300, vwx400, ea)
new_ltEs0(Right(vwx300), Right(vwx400), dh, app(app(ty_Either, eb), ec)) → new_ltEs0(vwx300, vwx400, eb, ec)
new_ltEs0(Right(vwx300), Right(vwx400), dh, app(app(app(ty_@3, ef), eg), eh)) → new_ltEs2(vwx300, vwx400, ef, eg, eh)
new_ltEs1(@2(vwx300, vwx301), @2(vwx400, vwx401), fb, app(app(app(ty_@3, ga), gb), gc)) → new_ltEs2(vwx301, vwx401, ga, gb, gc)
new_primCompAux(vwx300, vwx400, vwx49, app(app(ty_@2, be), bf)) → new_compare2(vwx300, vwx400, be, bf)
new_ltEs2(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), app(app(ty_Either, bcc), bcd), hf, bba) → new_lt0(vwx300, vwx400, bcc, bcd)
new_ltEs(:(vwx300, vwx301), :(vwx400, vwx401), ba) → new_compare0(vwx301, vwx401, ba)
new_ltEs2(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), he, hf, app(ty_[], hg)) → new_ltEs(vwx302, vwx402, hg)
new_primCompAux(vwx300, vwx400, vwx49, app(app(app(ty_@3, bg), bh), ca)) → new_compare3(vwx300, vwx400, bg, bh, ca)
new_ltEs1(@2(vwx300, vwx301), @2(vwx400, vwx401), fb, app(ty_[], fc)) → new_ltEs(vwx301, vwx401, fc)
new_ltEs1(@2(vwx300, vwx301), @2(vwx400, vwx401), app(ty_[], ge), gf) → new_compare0(vwx300, vwx400, ge)
new_ltEs2(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), app(app(app(ty_@3, bcg), bch), bda), hf, bba) → new_lt2(vwx300, vwx400, bcg, bch, bda)
new_ltEs1(@2(vwx300, vwx301), @2(vwx400, vwx401), fb, app(app(ty_Either, fd), ff)) → new_ltEs0(vwx301, vwx401, fd, ff)
new_lt(vwx300, vwx400, ge) → new_compare0(vwx300, vwx400, ge)
new_ltEs3(Just(vwx300), Just(vwx400), app(app(app(ty_@3, bdh), bea), beb)) → new_ltEs2(vwx300, vwx400, bdh, bea, beb)
new_ltEs2(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), he, hf, app(app(ty_Either, hh), baa)) → new_ltEs0(vwx302, vwx402, hh, baa)
new_compare4(vwx300, vwx400, hd) → new_compare23(vwx300, vwx400, new_esEs7(vwx300, vwx400, hd), hd)
new_ltEs1(@2(vwx300, vwx301), @2(vwx400, vwx401), app(ty_Maybe, hd), gf) → new_compare23(vwx300, vwx400, new_esEs7(vwx300, vwx400, hd), hd)
new_primCompAux(vwx300, vwx400, vwx49, app(ty_Maybe, cb)) → new_compare4(vwx300, vwx400, cb)
new_lt1(vwx300, vwx400, gg, gh) → new_compare21(vwx300, vwx400, new_esEs5(vwx300, vwx400, gg, gh), gg, gh)
new_compare1(vwx300, vwx400, cc, cd) → new_compare20(vwx300, vwx400, new_esEs4(vwx300, vwx400, cc, cd), cc, cd)
new_ltEs2(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), he, app(app(ty_Either, bbb), bbc), bba) → new_lt0(vwx301, vwx401, bbb, bbc)
new_compare22(vwx300, vwx400, False, ha, hb, hc) → new_ltEs2(vwx300, vwx400, ha, hb, hc)
new_ltEs2(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), app(ty_[], bcb), hf, bba) → new_lt(vwx300, vwx400, bcb)
new_ltEs2(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), he, hf, app(ty_Maybe, bag)) → new_ltEs3(vwx302, vwx402, bag)
new_ltEs3(Just(vwx300), Just(vwx400), app(ty_Maybe, bec)) → new_ltEs3(vwx300, vwx400, bec)

The TRS R consists of the following rules:

new_esEs25(vwx370, vwx380, app(ty_[], cgc)) → new_esEs14(vwx370, vwx380, cgc)
new_esEs10(vwx370, vwx380, ty_Integer) → new_esEs12(vwx370, vwx380)
new_esEs7(Just(vwx370), Just(vwx380), app(ty_Maybe, bfe)) → new_esEs7(vwx370, vwx380, bfe)
new_lt12(vwx300, vwx400, app(ty_Ratio, cbb)) → new_lt17(vwx300, vwx400, cbb)
new_esEs26(vwx371, vwx381, ty_@0) → new_esEs15(vwx371, vwx381)
new_esEs16(GT, EQ) → False
new_esEs16(EQ, GT) → False
new_esEs18(Char(vwx370), Char(vwx380)) → new_primEqNat0(vwx370, vwx380)
new_ltEs17(Just(vwx300), Just(vwx400), app(ty_[], bdc)) → new_ltEs15(vwx300, vwx400, bdc)
new_esEs22(vwx371, vwx381, app(ty_Ratio, bhe)) → new_esEs9(vwx371, vwx381, bhe)
new_esEs25(vwx370, vwx380, ty_Integer) → new_esEs12(vwx370, vwx380)
new_ltEs4(EQ, GT) → True
new_compare16(vwx300, vwx400, cc, cd) → new_compare27(vwx300, vwx400, new_esEs4(vwx300, vwx400, cc, cd), cc, cd)
new_ltEs12(Right(vwx300), Right(vwx400), dh, ty_Int) → new_ltEs9(vwx300, vwx400)
new_compare15(vwx300, vwx400, True, gg, gh) → LT
new_compare5(:%(vwx300, vwx301), :%(vwx400, vwx401), ty_Int) → new_compare7(new_sr0(vwx300, vwx401), new_sr0(vwx400, vwx301))
new_ltEs18(vwx301, vwx401, app(ty_[], fc)) → new_ltEs15(vwx301, vwx401, fc)
new_compare31(vwx300, vwx400, app(ty_Maybe, cb)) → new_compare19(vwx300, vwx400, cb)
new_esEs4(Right(vwx370), Right(vwx380), ccf, app(ty_[], cch)) → new_esEs14(vwx370, vwx380, cch)
new_esEs4(Right(vwx370), Right(vwx380), ccf, ty_Integer) → new_esEs12(vwx370, vwx380)
new_compare([], :(vwx400, vwx401), ba) → LT
new_esEs4(Right(vwx370), Right(vwx380), ccf, app(app(app(ty_@3, cdf), cdg), cdh)) → new_esEs6(vwx370, vwx380, cdf, cdg, cdh)
new_ltEs16(@2(vwx300, vwx301), @2(vwx400, vwx401), fb, gf) → new_pePe(new_lt12(vwx300, vwx400, fb), vwx300, vwx400, new_ltEs18(vwx301, vwx401, gf), fb)
new_lt12(vwx300, vwx400, app(ty_[], ge)) → new_lt8(vwx300, vwx400, ge)
new_esEs27(vwx372, vwx382, app(ty_Maybe, dbd)) → new_esEs7(vwx372, vwx382, dbd)
new_ltEs19(vwx302, vwx402, ty_Double) → new_ltEs11(vwx302, vwx402)
new_esEs7(Just(vwx370), Just(vwx380), ty_Double) → new_esEs19(vwx370, vwx380)
new_esEs27(vwx372, vwx382, ty_Bool) → new_esEs17(vwx372, vwx382)
new_esEs4(Left(vwx370), Left(vwx380), ty_Double, cbd) → new_esEs19(vwx370, vwx380)
new_lt20(vwx300, vwx400, ty_@0) → new_lt6(vwx300, vwx400)
new_esEs26(vwx371, vwx381, ty_Float) → new_esEs13(vwx371, vwx381)
new_primMulNat0(Zero, Zero) → Zero
new_esEs7(Just(vwx370), Just(vwx380), ty_@0) → new_esEs15(vwx370, vwx380)
new_compare(:(vwx300, vwx301), [], ba) → GT
new_compare13(vwx300, vwx400, False, ha, hb, hc) → GT
new_lt20(vwx300, vwx400, app(ty_[], bcb)) → new_lt8(vwx300, vwx400, bcb)
new_sr(Integer(vwx4000), Integer(vwx3010)) → Integer(new_primMulInt(vwx4000, vwx3010))
new_compare19(vwx300, vwx400, hd) → new_compare28(vwx300, vwx400, new_esEs7(vwx300, vwx400, hd), hd)
new_ltEs11(vwx30, vwx40) → new_not(new_compare14(vwx30, vwx40))
new_esEs20(EQ) → False
new_esEs21(vwx370, vwx380, ty_Bool) → new_esEs17(vwx370, vwx380)
new_lt12(vwx300, vwx400, ty_@0) → new_lt6(vwx300, vwx400)
new_compare31(vwx300, vwx400, ty_Ordering) → new_compare12(vwx300, vwx400)
new_lt19(vwx301, vwx401, ty_Bool) → new_lt4(vwx301, vwx401)
new_lt6(vwx300, vwx400) → new_esEs20(new_compare8(vwx300, vwx400))
new_esEs27(vwx372, vwx382, ty_Integer) → new_esEs12(vwx372, vwx382)
new_esEs25(vwx370, vwx380, ty_Bool) → new_esEs17(vwx370, vwx380)
new_ltEs18(vwx301, vwx401, ty_Integer) → new_ltEs6(vwx301, vwx401)
new_not(GT) → False
new_ltEs6(vwx30, vwx40) → new_not(new_compare6(vwx30, vwx40))
new_esEs27(vwx372, vwx382, app(ty_Ratio, daf)) → new_esEs9(vwx372, vwx382, daf)
new_esEs17(True, True) → True
new_esEs7(Just(vwx370), Just(vwx380), ty_Bool) → new_esEs17(vwx370, vwx380)
new_ltEs18(vwx301, vwx401, ty_Char) → new_ltEs14(vwx301, vwx401)
new_esEs22(vwx371, vwx381, app(app(ty_@2, caa), cab)) → new_esEs5(vwx371, vwx381, caa, cab)
new_ltEs12(Right(vwx300), Right(vwx400), dh, ty_Double) → new_ltEs11(vwx300, vwx400)
new_esEs24(vwx37, vwx38, app(app(ty_@2, bga), bgb)) → new_esEs5(vwx37, vwx38, bga, bgb)
new_ltEs18(vwx301, vwx401, app(ty_Ratio, cba)) → new_ltEs7(vwx301, vwx401, cba)
new_compare29(vwx300, vwx400, gg, gh) → new_compare210(vwx300, vwx400, new_esEs5(vwx300, vwx400, gg, gh), gg, gh)
new_compare31(vwx300, vwx400, app(app(app(ty_@3, bg), bh), ca)) → new_compare30(vwx300, vwx400, bg, bh, ca)
new_ltEs17(Just(vwx300), Just(vwx400), app(app(app(ty_@3, bdh), bea), beb)) → new_ltEs10(vwx300, vwx400, bdh, bea, beb)
new_esEs23(vwx370, vwx380, ty_Integer) → new_esEs12(vwx370, vwx380)
new_ltEs12(Right(vwx300), Right(vwx400), dh, app(ty_Maybe, fa)) → new_ltEs17(vwx300, vwx400, fa)
new_esEs7(Just(vwx370), Just(vwx380), ty_Int) → new_esEs8(vwx370, vwx380)
new_esEs12(Integer(vwx370), Integer(vwx380)) → new_primEqInt(vwx370, vwx380)
new_ltEs12(Left(vwx300), Left(vwx400), ty_Ordering, cf) → new_ltEs4(vwx300, vwx400)
new_esEs22(vwx371, vwx381, app(ty_[], bhf)) → new_esEs14(vwx371, vwx381, bhf)
new_esEs7(Just(vwx370), Just(vwx380), app(ty_Ratio, beg)) → new_esEs9(vwx370, vwx380, beg)
new_esEs25(vwx370, vwx380, ty_Float) → new_esEs13(vwx370, vwx380)
new_compare31(vwx300, vwx400, ty_Integer) → new_compare6(vwx300, vwx400)
new_lt20(vwx300, vwx400, ty_Bool) → new_lt4(vwx300, vwx400)
new_ltEs10(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), he, hf, bba) → new_pePe(new_lt20(vwx300, vwx400, he), vwx300, vwx400, new_pePe(new_lt19(vwx301, vwx401, hf), vwx301, vwx401, new_ltEs19(vwx302, vwx402, bba), hf), he)
new_lt19(vwx301, vwx401, ty_Integer) → new_lt14(vwx301, vwx401)
new_esEs14([], [], cea) → True
new_esEs25(vwx370, vwx380, app(app(ty_Either, cgd), cge)) → new_esEs4(vwx370, vwx380, cgd, cge)
new_pePe(False, vwx37, vwx38, vwx39, cfd) → new_asAs(new_esEs24(vwx37, vwx38, cfd), vwx39)
new_esEs22(vwx371, vwx381, app(app(ty_Either, bhg), bhh)) → new_esEs4(vwx371, vwx381, bhg, bhh)
new_ltEs12(Left(vwx300), Left(vwx400), app(app(ty_@2, db), dc), cf) → new_ltEs16(vwx300, vwx400, db, dc)
new_lt20(vwx300, vwx400, ty_Float) → new_lt10(vwx300, vwx400)
new_lt19(vwx301, vwx401, app(ty_[], bah)) → new_lt8(vwx301, vwx401, bah)
new_ltEs14(vwx30, vwx40) → new_not(new_compare11(vwx30, vwx40))
new_ltEs17(Just(vwx300), Nothing, cfh) → False
new_compare31(vwx300, vwx400, app(app(ty_@2, be), bf)) → new_compare29(vwx300, vwx400, be, bf)
new_lt14(vwx300, vwx400) → new_esEs20(new_compare6(vwx300, vwx400))
new_esEs22(vwx371, vwx381, ty_@0) → new_esEs15(vwx371, vwx381)
new_esEs24(vwx37, vwx38, app(ty_Maybe, bef)) → new_esEs7(vwx37, vwx38, bef)
new_lt19(vwx301, vwx401, app(ty_Ratio, dcb)) → new_lt17(vwx301, vwx401, dcb)
new_ltEs19(vwx302, vwx402, ty_Integer) → new_ltEs6(vwx302, vwx402)
new_esEs22(vwx371, vwx381, ty_Integer) → new_esEs12(vwx371, vwx381)
new_esEs23(vwx370, vwx380, app(ty_Maybe, ceh)) → new_esEs7(vwx370, vwx380, ceh)
new_esEs27(vwx372, vwx382, ty_Ordering) → new_esEs16(vwx372, vwx382)
new_lt16(vwx300, vwx400, ha, hb, hc) → new_esEs20(new_compare30(vwx300, vwx400, ha, hb, hc))
new_lt12(vwx300, vwx400, app(ty_Maybe, hd)) → new_lt18(vwx300, vwx400, hd)
new_primCmpNat0(Zero, Succ(vwx4000)) → LT
new_ltEs17(Just(vwx300), Just(vwx400), ty_Float) → new_ltEs13(vwx300, vwx400)
new_esEs21(vwx370, vwx380, ty_Double) → new_esEs19(vwx370, vwx380)
new_ltEs12(Right(vwx300), Right(vwx400), dh, app(app(app(ty_@3, ef), eg), eh)) → new_ltEs10(vwx300, vwx400, ef, eg, eh)
new_ltEs12(Right(vwx300), Right(vwx400), dh, ty_Float) → new_ltEs13(vwx300, vwx400)
new_esEs23(vwx370, vwx380, ty_Double) → new_esEs19(vwx370, vwx380)
new_esEs23(vwx370, vwx380, ty_Char) → new_esEs18(vwx370, vwx380)
new_ltEs12(Right(vwx300), Right(vwx400), dh, ty_Bool) → new_ltEs5(vwx300, vwx400)
new_ltEs17(Just(vwx300), Just(vwx400), ty_Char) → new_ltEs14(vwx300, vwx400)
new_ltEs5(True, False) → False
new_primEqNat0(Zero, Zero) → True
new_esEs7(Just(vwx370), Just(vwx380), ty_Ordering) → new_esEs16(vwx370, vwx380)
new_primMulNat0(Succ(vwx30100), Succ(vwx40100)) → new_primPlusNat1(new_primMulNat0(vwx30100, Succ(vwx40100)), vwx40100)
new_esEs16(GT, LT) → False
new_esEs16(LT, GT) → False
new_ltEs5(True, True) → True
new_esEs17(False, False) → True
new_esEs17(True, False) → False
new_esEs17(False, True) → False
new_lt5(vwx300, vwx400) → new_esEs20(new_compare11(vwx300, vwx400))
new_ltEs18(vwx301, vwx401, app(app(app(ty_@3, ga), gb), gc)) → new_ltEs10(vwx301, vwx401, ga, gb, gc)
new_lt19(vwx301, vwx401, ty_Double) → new_lt13(vwx301, vwx401)
new_esEs24(vwx37, vwx38, ty_Bool) → new_esEs17(vwx37, vwx38)
new_esEs4(Left(vwx370), Left(vwx380), ty_Int, cbd) → new_esEs8(vwx370, vwx380)
new_compare7(vwx30, vwx40) → new_primCmpInt(vwx30, vwx40)
new_ltEs17(Just(vwx300), Just(vwx400), app(app(ty_Either, bdd), bde)) → new_ltEs12(vwx300, vwx400, bdd, bde)
new_ltEs17(Just(vwx300), Just(vwx400), ty_@0) → new_ltEs8(vwx300, vwx400)
new_esEs22(vwx371, vwx381, ty_Int) → new_esEs8(vwx371, vwx381)
new_lt8(vwx300, vwx400, ge) → new_esEs20(new_compare(vwx300, vwx400, ge))
new_esEs4(Left(vwx370), Left(vwx380), app(app(ty_@2, cbh), cca), cbd) → new_esEs5(vwx370, vwx380, cbh, cca)
new_ltEs12(Left(vwx300), Left(vwx400), ty_@0, cf) → new_ltEs8(vwx300, vwx400)
new_esEs26(vwx371, vwx381, app(app(app(ty_@3, dac), dad), dae)) → new_esEs6(vwx371, vwx381, dac, dad, dae)
new_lt12(vwx300, vwx400, ty_Float) → new_lt10(vwx300, vwx400)
new_compare31(vwx300, vwx400, ty_@0) → new_compare8(vwx300, vwx400)
new_esEs7(Just(vwx370), Just(vwx380), ty_Integer) → new_esEs12(vwx370, vwx380)
new_compare17(vwx300, vwx400, True, cc, cd) → LT
new_esEs26(vwx371, vwx381, ty_Integer) → new_esEs12(vwx371, vwx381)
new_esEs4(Right(vwx370), Right(vwx380), ccf, app(app(ty_Either, cda), cdb)) → new_esEs4(vwx370, vwx380, cda, cdb)
new_primEqInt(Neg(Succ(vwx3700)), Neg(Succ(vwx3800))) → new_primEqNat0(vwx3700, vwx3800)
new_compare25(vwx300, vwx400, True) → EQ
new_esEs22(vwx371, vwx381, app(app(app(ty_@3, cad), cae), caf)) → new_esEs6(vwx371, vwx381, cad, cae, caf)
new_ltEs5(False, False) → True
new_esEs4(Left(vwx370), Left(vwx380), app(app(ty_Either, cbf), cbg), cbd) → new_esEs4(vwx370, vwx380, cbf, cbg)
new_esEs21(vwx370, vwx380, app(ty_Ratio, bgc)) → new_esEs9(vwx370, vwx380, bgc)
new_esEs21(vwx370, vwx380, ty_@0) → new_esEs15(vwx370, vwx380)
new_esEs14([], :(vwx380, vwx381), cea) → False
new_esEs14(:(vwx370, vwx371), [], cea) → False
new_esEs25(vwx370, vwx380, ty_Char) → new_esEs18(vwx370, vwx380)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_compare26(vwx300, vwx400, False, ha, hb, hc) → new_compare13(vwx300, vwx400, new_ltEs10(vwx300, vwx400, ha, hb, hc), ha, hb, hc)
new_lt20(vwx300, vwx400, app(ty_Maybe, bdb)) → new_lt18(vwx300, vwx400, bdb)
new_esEs24(vwx37, vwx38, app(app(app(ty_@3, cfe), cff), cfg)) → new_esEs6(vwx37, vwx38, cfe, cff, cfg)
new_ltEs19(vwx302, vwx402, ty_Ordering) → new_ltEs4(vwx302, vwx402)
new_lt20(vwx300, vwx400, ty_Ordering) → new_lt7(vwx300, vwx400)
new_esEs26(vwx371, vwx381, app(ty_[], che)) → new_esEs14(vwx371, vwx381, che)
new_esEs4(Left(vwx370), Left(vwx380), ty_Char, cbd) → new_esEs18(vwx370, vwx380)
new_primEqInt(Neg(Zero), Neg(Succ(vwx3800))) → False
new_primEqInt(Neg(Succ(vwx3700)), Neg(Zero)) → False
new_esEs4(Left(vwx370), Left(vwx380), app(ty_[], cbe), cbd) → new_esEs14(vwx370, vwx380, cbe)
new_primPlusNat1(Zero, vwx40100) → Succ(vwx40100)
new_compare111(vwx300, vwx400, True, hd) → LT
new_ltEs12(Left(vwx300), Left(vwx400), app(ty_Ratio, cag), cf) → new_ltEs7(vwx300, vwx400, cag)
new_esEs22(vwx371, vwx381, ty_Float) → new_esEs13(vwx371, vwx381)
new_esEs21(vwx370, vwx380, app(app(ty_Either, bge), bgf)) → new_esEs4(vwx370, vwx380, bge, bgf)
new_ltEs12(Left(vwx300), Left(vwx400), ty_Char, cf) → new_ltEs14(vwx300, vwx400)
new_compare([], [], ba) → EQ
new_esEs21(vwx370, vwx380, ty_Ordering) → new_esEs16(vwx370, vwx380)
new_ltEs12(Right(vwx300), Right(vwx400), dh, app(ty_[], ea)) → new_ltEs15(vwx300, vwx400, ea)
new_ltEs12(Right(vwx300), Right(vwx400), dh, ty_@0) → new_ltEs8(vwx300, vwx400)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_ltEs18(vwx301, vwx401, ty_Ordering) → new_ltEs4(vwx301, vwx401)
new_ltEs4(EQ, LT) → False
new_ltEs18(vwx301, vwx401, ty_@0) → new_ltEs8(vwx301, vwx401)
new_primCmpNat0(Succ(vwx3000), Succ(vwx4000)) → new_primCmpNat0(vwx3000, vwx4000)
new_ltEs18(vwx301, vwx401, ty_Bool) → new_ltEs5(vwx301, vwx401)
new_ltEs12(Right(vwx300), Right(vwx400), dh, ty_Ordering) → new_ltEs4(vwx300, vwx400)
new_primEqInt(Pos(Succ(vwx3700)), Pos(Succ(vwx3800))) → new_primEqNat0(vwx3700, vwx3800)
new_compare27(vwx300, vwx400, True, cc, cd) → EQ
new_esEs7(Just(vwx370), Just(vwx380), ty_Char) → new_esEs18(vwx370, vwx380)
new_esEs22(vwx371, vwx381, ty_Double) → new_esEs19(vwx371, vwx381)
new_primEqNat0(Succ(vwx3700), Succ(vwx3800)) → new_primEqNat0(vwx3700, vwx3800)
new_esEs4(Left(vwx370), Left(vwx380), ty_Ordering, cbd) → new_esEs16(vwx370, vwx380)
new_esEs21(vwx370, vwx380, app(ty_[], bgd)) → new_esEs14(vwx370, vwx380, bgd)
new_compare31(vwx300, vwx400, ty_Double) → new_compare14(vwx300, vwx400)
new_ltEs12(Left(vwx300), Left(vwx400), ty_Int, cf) → new_ltEs9(vwx300, vwx400)
new_esEs11(vwx371, vwx381, ty_Int) → new_esEs8(vwx371, vwx381)
new_ltEs4(GT, EQ) → False
new_primCompAux00(vwx53, LT) → LT
new_ltEs18(vwx301, vwx401, app(ty_Maybe, gd)) → new_ltEs17(vwx301, vwx401, gd)
new_primCmpInt(Neg(Succ(vwx3000)), Neg(vwx400)) → new_primCmpNat0(vwx400, Succ(vwx3000))
new_ltEs12(Right(vwx300), Right(vwx400), dh, ty_Char) → new_ltEs14(vwx300, vwx400)
new_lt12(vwx300, vwx400, ty_Int) → new_lt9(vwx300, vwx400)
new_compare31(vwx300, vwx400, ty_Char) → new_compare11(vwx300, vwx400)
new_ltEs18(vwx301, vwx401, ty_Double) → new_ltEs11(vwx301, vwx401)
new_esEs7(Nothing, Nothing, bef) → True
new_esEs21(vwx370, vwx380, ty_Int) → new_esEs8(vwx370, vwx380)
new_primEqInt(Pos(Zero), Pos(Succ(vwx3800))) → False
new_primEqInt(Pos(Succ(vwx3700)), Pos(Zero)) → False
new_lt20(vwx300, vwx400, app(ty_Ratio, dcc)) → new_lt17(vwx300, vwx400, dcc)
new_ltEs8(vwx30, vwx40) → new_not(new_compare8(vwx30, vwx40))
new_compare5(:%(vwx300, vwx301), :%(vwx400, vwx401), ty_Integer) → new_compare6(new_sr(vwx300, vwx401), new_sr(vwx400, vwx301))
new_ltEs4(EQ, EQ) → True
new_compare210(vwx300, vwx400, False, gg, gh) → new_compare15(vwx300, vwx400, new_ltEs16(vwx300, vwx400, gg, gh), gg, gh)
new_primPlusNat0(Succ(vwx6700), Zero) → Succ(vwx6700)
new_primPlusNat0(Zero, Succ(vwx401000)) → Succ(vwx401000)
new_primCmpNat0(Zero, Zero) → EQ
new_esEs5(@2(vwx370, vwx371), @2(vwx380, vwx381), bga, bgb) → new_asAs(new_esEs21(vwx370, vwx380, bga), new_esEs22(vwx371, vwx381, bgb))
new_primCmpNat0(Succ(vwx3000), Zero) → GT
new_esEs23(vwx370, vwx380, app(app(ty_@2, cef), ceg)) → new_esEs5(vwx370, vwx380, cef, ceg)
new_lt12(vwx300, vwx400, app(app(app(ty_@3, ha), hb), hc)) → new_lt16(vwx300, vwx400, ha, hb, hc)
new_esEs24(vwx37, vwx38, ty_@0) → new_esEs15(vwx37, vwx38)
new_primCmpInt(Neg(Zero), Pos(Succ(vwx4000))) → LT
new_esEs25(vwx370, vwx380, ty_Int) → new_esEs8(vwx370, vwx380)
new_ltEs4(GT, LT) → False
new_esEs23(vwx370, vwx380, ty_Float) → new_esEs13(vwx370, vwx380)
new_compare6(Integer(vwx300), Integer(vwx400)) → new_primCmpInt(vwx300, vwx400)
new_primEqInt(Neg(Succ(vwx3700)), Pos(vwx380)) → False
new_primEqInt(Pos(Succ(vwx3700)), Neg(vwx380)) → False
new_esEs6(@3(vwx370, vwx371, vwx372), @3(vwx380, vwx381, vwx382), cfe, cff, cfg) → new_asAs(new_esEs25(vwx370, vwx380, cfe), new_asAs(new_esEs26(vwx371, vwx381, cff), new_esEs27(vwx372, vwx382, cfg)))
new_esEs7(Nothing, Just(vwx380), bef) → False
new_esEs7(Just(vwx370), Nothing, bef) → False
new_ltEs12(Left(vwx300), Right(vwx400), dh, cf) → True
new_compare(:(vwx300, vwx301), :(vwx400, vwx401), ba) → new_primCompAux0(vwx300, vwx400, new_compare(vwx301, vwx401, ba), ba)
new_ltEs5(False, True) → True
new_primEqInt(Neg(Zero), Pos(Succ(vwx3800))) → False
new_primEqInt(Pos(Zero), Neg(Succ(vwx3800))) → False
new_esEs4(Right(vwx370), Right(vwx380), ccf, app(ty_Ratio, ccg)) → new_esEs9(vwx370, vwx380, ccg)
new_primCmpInt(Pos(Zero), Pos(Succ(vwx4000))) → new_primCmpNat0(Zero, Succ(vwx4000))
new_primCompAux00(vwx53, EQ) → vwx53
new_lt13(vwx300, vwx400) → new_esEs20(new_compare14(vwx300, vwx400))
new_ltEs12(Left(vwx300), Left(vwx400), app(ty_Maybe, dg), cf) → new_ltEs17(vwx300, vwx400, dg)
new_ltEs18(vwx301, vwx401, ty_Int) → new_ltEs9(vwx301, vwx401)
new_compare24(vwx300, vwx400, True) → EQ
new_esEs4(Right(vwx370), Right(vwx380), ccf, ty_Ordering) → new_esEs16(vwx370, vwx380)
new_esEs4(Left(vwx370), Left(vwx380), ty_Integer, cbd) → new_esEs12(vwx370, vwx380)
new_esEs26(vwx371, vwx381, app(app(ty_@2, chh), daa)) → new_esEs5(vwx371, vwx381, chh, daa)
new_esEs21(vwx370, vwx380, ty_Char) → new_esEs18(vwx370, vwx380)
new_compare17(vwx300, vwx400, False, cc, cd) → GT
new_ltEs17(Just(vwx300), Just(vwx400), ty_Ordering) → new_ltEs4(vwx300, vwx400)
new_lt12(vwx300, vwx400, app(app(ty_@2, gg), gh)) → new_lt15(vwx300, vwx400, gg, gh)
new_ltEs17(Just(vwx300), Just(vwx400), ty_Int) → new_ltEs9(vwx300, vwx400)
new_esEs21(vwx370, vwx380, app(app(ty_@2, bgg), bgh)) → new_esEs5(vwx370, vwx380, bgg, bgh)
new_lt19(vwx301, vwx401, app(ty_Maybe, bca)) → new_lt18(vwx301, vwx401, bca)
new_esEs23(vwx370, vwx380, ty_Ordering) → new_esEs16(vwx370, vwx380)
new_esEs23(vwx370, vwx380, ty_@0) → new_esEs15(vwx370, vwx380)
new_compare210(vwx300, vwx400, True, gg, gh) → EQ
new_primCmpInt(Pos(Succ(vwx3000)), Pos(vwx400)) → new_primCmpNat0(Succ(vwx3000), vwx400)
new_ltEs19(vwx302, vwx402, app(app(ty_Either, hh), baa)) → new_ltEs12(vwx302, vwx402, hh, baa)
new_lt18(vwx300, vwx400, hd) → new_esEs20(new_compare19(vwx300, vwx400, hd))
new_esEs22(vwx371, vwx381, ty_Bool) → new_esEs17(vwx371, vwx381)
new_ltEs12(Right(vwx300), Right(vwx400), dh, app(app(ty_Either, eb), ec)) → new_ltEs12(vwx300, vwx400, eb, ec)
new_esEs16(EQ, LT) → False
new_esEs16(LT, EQ) → False
new_ltEs12(Right(vwx300), Left(vwx400), dh, cf) → False
new_esEs25(vwx370, vwx380, ty_@0) → new_esEs15(vwx370, vwx380)
new_esEs24(vwx37, vwx38, app(ty_[], cea)) → new_esEs14(vwx37, vwx38, cea)
new_lt12(vwx300, vwx400, ty_Ordering) → new_lt7(vwx300, vwx400)
new_esEs24(vwx37, vwx38, ty_Integer) → new_esEs12(vwx37, vwx38)
new_lt4(vwx300, vwx400) → new_esEs20(new_compare9(vwx300, vwx400))
new_not0 → True
new_lt20(vwx300, vwx400, ty_Double) → new_lt13(vwx300, vwx400)
new_esEs4(Right(vwx370), Right(vwx380), ccf, ty_Bool) → new_esEs17(vwx370, vwx380)
new_compare30(vwx300, vwx400, ha, hb, hc) → new_compare26(vwx300, vwx400, new_esEs6(vwx300, vwx400, ha, hb, hc), ha, hb, hc)
new_ltEs19(vwx302, vwx402, app(ty_[], hg)) → new_ltEs15(vwx302, vwx402, hg)
new_lt19(vwx301, vwx401, app(app(app(ty_@3, bbf), bbg), bbh)) → new_lt16(vwx301, vwx401, bbf, bbg, bbh)
new_esEs22(vwx371, vwx381, ty_Char) → new_esEs18(vwx371, vwx381)
new_primCmpInt(Pos(Succ(vwx3000)), Neg(vwx400)) → GT
new_ltEs18(vwx301, vwx401, app(app(ty_@2, fg), fh)) → new_ltEs16(vwx301, vwx401, fg, fh)
new_ltEs19(vwx302, vwx402, ty_Int) → new_ltEs9(vwx302, vwx402)
new_esEs27(vwx372, vwx382, ty_@0) → new_esEs15(vwx372, vwx382)
new_ltEs19(vwx302, vwx402, ty_Float) → new_ltEs13(vwx302, vwx402)
new_compare24(vwx300, vwx400, False) → new_compare10(vwx300, vwx400, new_ltEs5(vwx300, vwx400))
new_lt12(vwx300, vwx400, ty_Bool) → new_lt4(vwx300, vwx400)
new_esEs21(vwx370, vwx380, app(ty_Maybe, bha)) → new_esEs7(vwx370, vwx380, bha)
new_primMulInt(Pos(vwx3010), Pos(vwx4010)) → Pos(new_primMulNat0(vwx3010, vwx4010))
new_esEs24(vwx37, vwx38, ty_Int) → new_esEs8(vwx37, vwx38)
new_lt15(vwx300, vwx400, gg, gh) → new_esEs20(new_compare29(vwx300, vwx400, gg, gh))
new_esEs23(vwx370, vwx380, app(app(ty_Either, ced), cee)) → new_esEs4(vwx370, vwx380, ced, cee)
new_esEs4(Left(vwx370), Left(vwx380), app(ty_Maybe, ccb), cbd) → new_esEs7(vwx370, vwx380, ccb)
new_ltEs17(Nothing, Just(vwx400), cfh) → True
new_ltEs12(Right(vwx300), Right(vwx400), dh, ty_Integer) → new_ltEs6(vwx300, vwx400)
new_primMulInt(Neg(vwx3010), Neg(vwx4010)) → Pos(new_primMulNat0(vwx3010, vwx4010))
new_esEs16(EQ, EQ) → True
new_lt9(vwx300, vwx400) → new_esEs20(new_compare7(vwx300, vwx400))
new_compare110(vwx300, vwx400, True) → LT
new_esEs26(vwx371, vwx381, ty_Ordering) → new_esEs16(vwx371, vwx381)
new_primEqNat0(Zero, Succ(vwx3800)) → False
new_primEqNat0(Succ(vwx3700), Zero) → False
new_primPlusNat0(Zero, Zero) → Zero
new_ltEs7(vwx30, vwx40, bee) → new_not(new_compare5(vwx30, vwx40, bee))
new_ltEs15(vwx30, vwx40, ba) → new_not(new_compare(vwx30, vwx40, ba))
new_lt19(vwx301, vwx401, app(app(ty_Either, bbb), bbc)) → new_lt11(vwx301, vwx401, bbb, bbc)
new_compare110(vwx300, vwx400, False) → GT
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs24(vwx37, vwx38, app(app(ty_Either, ccf), cbd)) → new_esEs4(vwx37, vwx38, ccf, cbd)
new_esEs27(vwx372, vwx382, app(app(ty_Either, dah), dba)) → new_esEs4(vwx372, vwx382, dah, dba)
new_esEs26(vwx371, vwx381, ty_Int) → new_esEs8(vwx371, vwx381)
new_esEs27(vwx372, vwx382, app(app(app(ty_@3, dbe), dbf), dbg)) → new_esEs6(vwx372, vwx382, dbe, dbf, dbg)
new_esEs27(vwx372, vwx382, app(app(ty_@2, dbb), dbc)) → new_esEs5(vwx372, vwx382, dbb, dbc)
new_ltEs12(Left(vwx300), Left(vwx400), app(app(ty_Either, cg), da), cf) → new_ltEs12(vwx300, vwx400, cg, da)
new_ltEs17(Nothing, Nothing, cfh) → True
new_pePe(True, vwx37, vwx38, vwx39, cfd) → True
new_ltEs4(LT, GT) → True
new_primPlusNat1(Succ(vwx670), vwx40100) → Succ(Succ(new_primPlusNat0(vwx670, vwx40100)))
new_esEs24(vwx37, vwx38, ty_Double) → new_esEs19(vwx37, vwx38)
new_esEs23(vwx370, vwx380, app(ty_[], cec)) → new_esEs14(vwx370, vwx380, cec)
new_ltEs13(vwx30, vwx40) → new_not(new_compare18(vwx30, vwx40))
new_compare9(vwx300, vwx400) → new_compare24(vwx300, vwx400, new_esEs17(vwx300, vwx400))
new_lt20(vwx300, vwx400, app(app(ty_Either, bcc), bcd)) → new_lt11(vwx300, vwx400, bcc, bcd)
new_lt12(vwx300, vwx400, app(app(ty_Either, cc), cd)) → new_lt11(vwx300, vwx400, cc, cd)
new_ltEs19(vwx302, vwx402, app(ty_Maybe, bag)) → new_ltEs17(vwx302, vwx402, bag)
new_ltEs12(Left(vwx300), Left(vwx400), ty_Integer, cf) → new_ltEs6(vwx300, vwx400)
new_primCmpInt(Neg(Zero), Neg(Succ(vwx4000))) → new_primCmpNat0(Succ(vwx4000), Zero)
new_esEs23(vwx370, vwx380, ty_Bool) → new_esEs17(vwx370, vwx380)
new_primCmpInt(Pos(Zero), Neg(Succ(vwx4000))) → GT
new_lt20(vwx300, vwx400, app(app(ty_@2, bce), bcf)) → new_lt15(vwx300, vwx400, bce, bcf)
new_ltEs17(Just(vwx300), Just(vwx400), ty_Integer) → new_ltEs6(vwx300, vwx400)
new_compare31(vwx300, vwx400, app(ty_[], bb)) → new_compare(vwx300, vwx400, bb)
new_sr0(vwx301, vwx401) → new_primMulInt(vwx301, vwx401)
new_esEs14(:(vwx370, vwx371), :(vwx380, vwx381), cea) → new_asAs(new_esEs23(vwx370, vwx380, cea), new_esEs14(vwx371, vwx381, cea))
new_compare15(vwx300, vwx400, False, gg, gh) → GT
new_ltEs19(vwx302, vwx402, ty_Char) → new_ltEs14(vwx302, vwx402)
new_esEs20(GT) → False
new_esEs25(vwx370, vwx380, app(ty_Maybe, cgh)) → new_esEs7(vwx370, vwx380, cgh)
new_esEs7(Just(vwx370), Just(vwx380), app(app(app(ty_@3, bff), bfg), bfh)) → new_esEs6(vwx370, vwx380, bff, bfg, bfh)
new_compare31(vwx300, vwx400, ty_Bool) → new_compare9(vwx300, vwx400)
new_esEs25(vwx370, vwx380, ty_Ordering) → new_esEs16(vwx370, vwx380)
new_esEs21(vwx370, vwx380, ty_Float) → new_esEs13(vwx370, vwx380)
new_lt11(vwx300, vwx400, cc, cd) → new_esEs20(new_compare16(vwx300, vwx400, cc, cd))
new_lt12(vwx300, vwx400, ty_Integer) → new_lt14(vwx300, vwx400)
new_lt19(vwx301, vwx401, ty_Ordering) → new_lt7(vwx301, vwx401)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs27(vwx372, vwx382, ty_Float) → new_esEs13(vwx372, vwx382)
new_ltEs17(Just(vwx300), Just(vwx400), app(ty_Ratio, cga)) → new_ltEs7(vwx300, vwx400, cga)
new_ltEs4(LT, EQ) → True
new_esEs4(Right(vwx370), Right(vwx380), ccf, app(app(ty_@2, cdc), cdd)) → new_esEs5(vwx370, vwx380, cdc, cdd)
new_esEs10(vwx370, vwx380, ty_Int) → new_esEs8(vwx370, vwx380)
new_compare12(vwx300, vwx400) → new_compare25(vwx300, vwx400, new_esEs16(vwx300, vwx400))
new_compare28(vwx300, vwx400, False, hd) → new_compare111(vwx300, vwx400, new_ltEs17(vwx300, vwx400, hd), hd)
new_ltEs12(Left(vwx300), Left(vwx400), ty_Double, cf) → new_ltEs11(vwx300, vwx400)
new_esEs15(@0, @0) → True
new_esEs16(LT, LT) → True
new_ltEs12(Right(vwx300), Right(vwx400), dh, app(ty_Ratio, cah)) → new_ltEs7(vwx300, vwx400, cah)
new_asAs(False, vwx48) → False
new_esEs25(vwx370, vwx380, app(ty_Ratio, cgb)) → new_esEs9(vwx370, vwx380, cgb)
new_primMulInt(Pos(vwx3010), Neg(vwx4010)) → Neg(new_primMulNat0(vwx3010, vwx4010))
new_primMulInt(Neg(vwx3010), Pos(vwx4010)) → Neg(new_primMulNat0(vwx3010, vwx4010))
new_primMulNat0(Succ(vwx30100), Zero) → Zero
new_primMulNat0(Zero, Succ(vwx40100)) → Zero
new_ltEs17(Just(vwx300), Just(vwx400), ty_Bool) → new_ltEs5(vwx300, vwx400)
new_esEs23(vwx370, vwx380, app(app(app(ty_@3, cfa), cfb), cfc)) → new_esEs6(vwx370, vwx380, cfa, cfb, cfc)
new_esEs27(vwx372, vwx382, ty_Int) → new_esEs8(vwx372, vwx382)
new_compare27(vwx300, vwx400, False, cc, cd) → new_compare17(vwx300, vwx400, new_ltEs12(vwx300, vwx400, cc, cd), cc, cd)
new_esEs22(vwx371, vwx381, ty_Ordering) → new_esEs16(vwx371, vwx381)
new_esEs16(GT, GT) → True
new_lt12(vwx300, vwx400, ty_Double) → new_lt13(vwx300, vwx400)
new_lt19(vwx301, vwx401, app(app(ty_@2, bbd), bbe)) → new_lt15(vwx301, vwx401, bbd, bbe)
new_esEs26(vwx371, vwx381, app(ty_Maybe, dab)) → new_esEs7(vwx371, vwx381, dab)
new_ltEs18(vwx301, vwx401, ty_Float) → new_ltEs13(vwx301, vwx401)
new_esEs26(vwx371, vwx381, app(ty_Ratio, chd)) → new_esEs9(vwx371, vwx381, chd)
new_not(EQ) → new_not0
new_lt12(vwx300, vwx400, ty_Char) → new_lt5(vwx300, vwx400)
new_lt17(vwx300, vwx400, cbb) → new_esEs20(new_compare5(vwx300, vwx400, cbb))
new_ltEs17(Just(vwx300), Just(vwx400), app(app(ty_@2, bdf), bdg)) → new_ltEs16(vwx300, vwx400, bdf, bdg)
new_esEs4(Right(vwx370), Right(vwx380), ccf, app(ty_Maybe, cde)) → new_esEs7(vwx370, vwx380, cde)
new_esEs25(vwx370, vwx380, app(app(app(ty_@3, cha), chb), chc)) → new_esEs6(vwx370, vwx380, cha, chb, chc)
new_esEs20(LT) → True
new_ltEs12(Left(vwx300), Left(vwx400), ty_Bool, cf) → new_ltEs5(vwx300, vwx400)
new_compare111(vwx300, vwx400, False, hd) → GT
new_esEs26(vwx371, vwx381, ty_Double) → new_esEs19(vwx371, vwx381)
new_esEs7(Just(vwx370), Just(vwx380), app(app(ty_Either, bfa), bfb)) → new_esEs4(vwx370, vwx380, bfa, bfb)
new_ltEs19(vwx302, vwx402, ty_@0) → new_ltEs8(vwx302, vwx402)
new_esEs4(Right(vwx370), Right(vwx380), ccf, ty_Char) → new_esEs18(vwx370, vwx380)
new_esEs4(Left(vwx370), Left(vwx380), ty_Float, cbd) → new_esEs13(vwx370, vwx380)
new_ltEs19(vwx302, vwx402, ty_Bool) → new_ltEs5(vwx302, vwx402)
new_lt20(vwx300, vwx400, ty_Char) → new_lt5(vwx300, vwx400)
new_lt19(vwx301, vwx401, ty_Int) → new_lt9(vwx301, vwx401)
new_lt20(vwx300, vwx400, app(app(app(ty_@3, bcg), bch), bda)) → new_lt16(vwx300, vwx400, bcg, bch, bda)
new_esEs24(vwx37, vwx38, ty_Ordering) → new_esEs16(vwx37, vwx38)
new_esEs4(Right(vwx370), Right(vwx380), ccf, ty_@0) → new_esEs15(vwx370, vwx380)
new_esEs11(vwx371, vwx381, ty_Integer) → new_esEs12(vwx371, vwx381)
new_ltEs4(LT, LT) → True
new_esEs9(:%(vwx370, vwx371), :%(vwx380, vwx381), bed) → new_asAs(new_esEs10(vwx370, vwx380, bed), new_esEs11(vwx371, vwx381, bed))
new_esEs26(vwx371, vwx381, ty_Bool) → new_esEs17(vwx371, vwx381)
new_esEs25(vwx370, vwx380, app(app(ty_@2, cgf), cgg)) → new_esEs5(vwx370, vwx380, cgf, cgg)
new_ltEs12(Left(vwx300), Left(vwx400), app(ty_[], ce), cf) → new_ltEs15(vwx300, vwx400, ce)
new_not(LT) → new_not0
new_ltEs18(vwx301, vwx401, app(app(ty_Either, fd), ff)) → new_ltEs12(vwx301, vwx401, fd, ff)
new_esEs23(vwx370, vwx380, app(ty_Ratio, ceb)) → new_esEs9(vwx370, vwx380, ceb)
new_esEs7(Just(vwx370), Just(vwx380), ty_Float) → new_esEs13(vwx370, vwx380)
new_compare31(vwx300, vwx400, app(app(ty_Either, bc), bd)) → new_compare16(vwx300, vwx400, bc, bd)
new_esEs7(Just(vwx370), Just(vwx380), app(app(ty_@2, bfc), bfd)) → new_esEs5(vwx370, vwx380, bfc, bfd)
new_compare14(Double(vwx300, vwx301), Double(vwx400, vwx401)) → new_compare7(new_sr0(vwx300, vwx400), new_sr0(vwx301, vwx401))
new_esEs26(vwx371, vwx381, ty_Char) → new_esEs18(vwx371, vwx381)
new_esEs4(Right(vwx370), Right(vwx380), ccf, ty_Double) → new_esEs19(vwx370, vwx380)
new_ltEs17(Just(vwx300), Just(vwx400), app(ty_Maybe, bec)) → new_ltEs17(vwx300, vwx400, bec)
new_esEs25(vwx370, vwx380, ty_Double) → new_esEs19(vwx370, vwx380)
new_lt19(vwx301, vwx401, ty_Char) → new_lt5(vwx301, vwx401)
new_compare26(vwx300, vwx400, True, ha, hb, hc) → EQ
new_primPlusNat0(Succ(vwx6700), Succ(vwx401000)) → Succ(Succ(new_primPlusNat0(vwx6700, vwx401000)))
new_lt19(vwx301, vwx401, ty_@0) → new_lt6(vwx301, vwx401)
new_ltEs17(Just(vwx300), Just(vwx400), ty_Double) → new_ltEs11(vwx300, vwx400)
new_lt20(vwx300, vwx400, ty_Integer) → new_lt14(vwx300, vwx400)
new_esEs27(vwx372, vwx382, app(ty_[], dag)) → new_esEs14(vwx372, vwx382, dag)
new_esEs21(vwx370, vwx380, app(app(app(ty_@3, bhb), bhc), bhd)) → new_esEs6(vwx370, vwx380, bhb, bhc, bhd)
new_ltEs19(vwx302, vwx402, app(app(ty_@2, bab), bac)) → new_ltEs16(vwx302, vwx402, bab, bac)
new_ltEs12(Left(vwx300), Left(vwx400), app(app(app(ty_@3, dd), de), df), cf) → new_ltEs10(vwx300, vwx400, dd, de, df)
new_esEs26(vwx371, vwx381, app(app(ty_Either, chf), chg)) → new_esEs4(vwx371, vwx381, chf, chg)
new_esEs19(Double(vwx370, vwx371), Double(vwx380, vwx381)) → new_esEs8(new_sr0(vwx370, vwx380), new_sr0(vwx371, vwx381))
new_esEs13(Float(vwx370, vwx371), Float(vwx380, vwx381)) → new_esEs8(new_sr0(vwx370, vwx380), new_sr0(vwx371, vwx381))
new_asAs(True, vwx48) → vwx48
new_compare11(Char(vwx300), Char(vwx400)) → new_primCmpNat0(vwx300, vwx400)
new_ltEs19(vwx302, vwx402, app(ty_Ratio, dca)) → new_ltEs7(vwx302, vwx402, dca)
new_compare31(vwx300, vwx400, app(ty_Ratio, dbh)) → new_compare5(vwx300, vwx400, dbh)
new_compare31(vwx300, vwx400, ty_Int) → new_compare7(vwx300, vwx400)
new_esEs4(Right(vwx370), Left(vwx380), ccf, cbd) → False
new_esEs4(Left(vwx370), Right(vwx380), ccf, cbd) → False
new_lt10(vwx300, vwx400) → new_esEs20(new_compare18(vwx300, vwx400))
new_esEs7(Just(vwx370), Just(vwx380), app(ty_[], beh)) → new_esEs14(vwx370, vwx380, beh)
new_compare8(@0, @0) → EQ
new_esEs4(Left(vwx370), Left(vwx380), app(app(app(ty_@3, ccc), ccd), cce), cbd) → new_esEs6(vwx370, vwx380, ccc, ccd, cce)
new_lt19(vwx301, vwx401, ty_Float) → new_lt10(vwx301, vwx401)
new_esEs4(Left(vwx370), Left(vwx380), ty_@0, cbd) → new_esEs15(vwx370, vwx380)
new_compare25(vwx300, vwx400, False) → new_compare110(vwx300, vwx400, new_ltEs4(vwx300, vwx400))
new_primCompAux0(vwx300, vwx400, vwx49, ba) → new_primCompAux00(vwx49, new_compare31(vwx300, vwx400, ba))
new_esEs24(vwx37, vwx38, ty_Float) → new_esEs13(vwx37, vwx38)
new_esEs4(Right(vwx370), Right(vwx380), ccf, ty_Int) → new_esEs8(vwx370, vwx380)
new_lt7(vwx300, vwx400) → new_esEs20(new_compare12(vwx300, vwx400))
new_compare28(vwx300, vwx400, True, hd) → EQ
new_esEs4(Right(vwx370), Right(vwx380), ccf, ty_Float) → new_esEs13(vwx370, vwx380)
new_lt20(vwx300, vwx400, ty_Int) → new_lt9(vwx300, vwx400)
new_ltEs9(vwx30, vwx40) → new_not(new_compare7(vwx30, vwx40))
new_ltEs12(Right(vwx300), Right(vwx400), dh, app(app(ty_@2, ed), ee)) → new_ltEs16(vwx300, vwx400, ed, ee)
new_esEs4(Left(vwx370), Left(vwx380), app(ty_Ratio, cbc), cbd) → new_esEs9(vwx370, vwx380, cbc)
new_esEs21(vwx370, vwx380, ty_Integer) → new_esEs12(vwx370, vwx380)
new_compare10(vwx300, vwx400, True) → LT
new_ltEs19(vwx302, vwx402, app(app(app(ty_@3, bad), bae), baf)) → new_ltEs10(vwx302, vwx402, bad, bae, baf)
new_esEs27(vwx372, vwx382, ty_Char) → new_esEs18(vwx372, vwx382)
new_ltEs4(GT, GT) → True
new_compare13(vwx300, vwx400, True, ha, hb, hc) → LT
new_compare10(vwx300, vwx400, False) → GT
new_primCompAux00(vwx53, GT) → GT
new_esEs4(Left(vwx370), Left(vwx380), ty_Bool, cbd) → new_esEs17(vwx370, vwx380)
new_compare18(Float(vwx300, vwx301), Float(vwx400, vwx401)) → new_compare7(new_sr0(vwx300, vwx400), new_sr0(vwx301, vwx401))
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs24(vwx37, vwx38, app(ty_Ratio, bed)) → new_esEs9(vwx37, vwx38, bed)
new_ltEs12(Left(vwx300), Left(vwx400), ty_Float, cf) → new_ltEs13(vwx300, vwx400)
new_esEs23(vwx370, vwx380, ty_Int) → new_esEs8(vwx370, vwx380)
new_esEs24(vwx37, vwx38, ty_Char) → new_esEs18(vwx37, vwx38)
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_compare31(vwx300, vwx400, ty_Float) → new_compare18(vwx300, vwx400)
new_esEs22(vwx371, vwx381, app(ty_Maybe, cac)) → new_esEs7(vwx371, vwx381, cac)
new_esEs8(vwx37, vwx38) → new_primEqInt(vwx37, vwx38)
new_primCmpInt(Neg(Succ(vwx3000)), Pos(vwx400)) → LT
new_esEs27(vwx372, vwx382, ty_Double) → new_esEs19(vwx372, vwx382)

The set Q consists of the following terms:

new_compare27(x0, x1, False, x2, x3)
new_ltEs17(Nothing, Nothing, x0)
new_esEs26(x0, x1, ty_Int)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primPlusNat1(Zero, x0)
new_compare24(x0, x1, True)
new_esEs23(x0, x1, ty_Bool)
new_compare17(x0, x1, False, x2, x3)
new_compare12(x0, x1)
new_ltEs18(x0, x1, ty_Int)
new_compare16(x0, x1, x2, x3)
new_esEs14([], :(x0, x1), x2)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_ltEs18(x0, x1, ty_@0)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_compare17(x0, x1, True, x2, x3)
new_esEs7(Just(x0), Just(x1), app(ty_Maybe, x2))
new_ltEs12(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_esEs7(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_primPlusNat0(Succ(x0), Succ(x1))
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, app(ty_[], x2))
new_esEs4(Right(x0), Right(x1), x2, ty_@0)
new_lt20(x0, x1, ty_Double)
new_esEs27(x0, x1, ty_Float)
new_lt20(x0, x1, ty_Integer)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs4(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_ltEs12(Left(x0), Left(x1), ty_Ordering, x2)
new_lt12(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, ty_Char)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_compare31(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_compare19(x0, x1, x2)
new_esEs22(x0, x1, ty_Char)
new_ltEs12(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_ltEs12(Right(x0), Right(x1), x2, ty_Float)
new_compare29(x0, x1, x2, x3)
new_compare31(x0, x1, app(ty_[], x2))
new_esEs21(x0, x1, ty_Float)
new_lt12(x0, x1, ty_Int)
new_compare30(x0, x1, x2, x3, x4)
new_lt12(x0, x1, ty_Integer)
new_ltEs9(x0, x1)
new_esEs4(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_ltEs18(x0, x1, ty_Float)
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs4(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_lt19(x0, x1, app(ty_Maybe, x2))
new_esEs16(GT, LT)
new_esEs16(LT, GT)
new_primCompAux00(x0, EQ)
new_compare31(x0, x1, ty_Ordering)
new_ltEs19(x0, x1, ty_Char)
new_esEs23(x0, x1, ty_Float)
new_esEs27(x0, x1, ty_@0)
new_lt19(x0, x1, ty_Double)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs17(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs20(LT)
new_ltEs17(Just(x0), Nothing, x1)
new_esEs17(False, False)
new_primCompAux00(x0, LT)
new_lt20(x0, x1, ty_Float)
new_compare10(x0, x1, True)
new_esEs4(Left(x0), Left(x1), ty_Double, x2)
new_compare111(x0, x1, True, x2)
new_ltEs5(False, False)
new_esEs4(Right(x0), Right(x1), x2, ty_Integer)
new_primMulInt(Pos(x0), Pos(x1))
new_compare8(@0, @0)
new_ltEs17(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs22(x0, x1, ty_Float)
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_esEs7(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_ltEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs17(Just(x0), Just(x1), ty_Ordering)
new_lt12(x0, x1, ty_Float)
new_ltEs18(x0, x1, app(ty_[], x2))
new_esEs26(x0, x1, ty_Integer)
new_lt14(x0, x1)
new_lt12(x0, x1, app(ty_Maybe, x2))
new_ltEs17(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs21(x0, x1, ty_Bool)
new_esEs23(x0, x1, app(ty_[], x2))
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs4(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_compare15(x0, x1, True, x2, x3)
new_esEs27(x0, x1, ty_Ordering)
new_primEqNat0(Zero, Zero)
new_compare18(Float(x0, x1), Float(x2, x3))
new_esEs25(x0, x1, ty_Bool)
new_ltEs19(x0, x1, ty_Int)
new_ltEs19(x0, x1, ty_Ordering)
new_compare25(x0, x1, True)
new_esEs22(x0, x1, ty_Double)
new_esEs22(x0, x1, ty_Bool)
new_primMulNat0(Zero, Zero)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_ltEs12(Left(x0), Left(x1), ty_Integer, x2)
new_lt11(x0, x1, x2, x3)
new_ltEs8(x0, x1)
new_ltEs17(Just(x0), Just(x1), ty_Integer)
new_esEs26(x0, x1, app(ty_[], x2))
new_compare31(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs7(Just(x0), Just(x1), ty_Char)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_ltEs4(GT, GT)
new_esEs27(x0, x1, ty_Double)
new_esEs7(Just(x0), Just(x1), ty_Int)
new_lt12(x0, x1, ty_Double)
new_lt20(x0, x1, ty_Char)
new_lt19(x0, x1, app(ty_Ratio, x2))
new_esEs7(Nothing, Nothing, x0)
new_ltEs13(x0, x1)
new_esEs16(GT, GT)
new_compare28(x0, x1, False, x2)
new_esEs4(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_esEs9(:%(x0, x1), :%(x2, x3), x4)
new_esEs7(Just(x0), Just(x1), ty_@0)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs26(x0, x1, ty_Ordering)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_compare7(x0, x1)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_compare210(x0, x1, True, x2, x3)
new_lt12(x0, x1, app(app(ty_Either, x2), x3))
new_lt20(x0, x1, ty_@0)
new_esEs4(Right(x0), Right(x1), x2, ty_Float)
new_ltEs12(Right(x0), Right(x1), x2, ty_Ordering)
new_ltEs18(x0, x1, ty_Integer)
new_ltEs12(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs25(x0, x1, ty_Char)
new_esEs14([], [], x0)
new_lt13(x0, x1)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_ltEs12(Right(x0), Right(x1), x2, ty_Bool)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_lt7(x0, x1)
new_ltEs12(Right(x0), Right(x1), x2, ty_Double)
new_esEs7(Nothing, Just(x0), x1)
new_esEs4(Right(x0), Right(x1), x2, ty_Char)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_compare24(x0, x1, False)
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs4(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs24(x0, x1, ty_Bool)
new_esEs21(x0, x1, ty_Double)
new_ltEs19(x0, x1, ty_Bool)
new_lt12(x0, x1, ty_Bool)
new_esEs23(x0, x1, ty_Integer)
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs11(x0, x1, ty_Integer)
new_ltEs16(@2(x0, x1), @2(x2, x3), x4, x5)
new_lt10(x0, x1)
new_pePe(True, x0, x1, x2, x3)
new_lt19(x0, x1, ty_Ordering)
new_ltEs12(Right(x0), Right(x1), x2, ty_Integer)
new_compare111(x0, x1, False, x2)
new_ltEs17(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_ltEs11(x0, x1)
new_esEs25(x0, x1, ty_Integer)
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_sr0(x0, x1)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_compare6(Integer(x0), Integer(x1))
new_not0
new_primPlusNat0(Zero, Zero)
new_ltEs12(Right(x0), Right(x1), x2, ty_Int)
new_compare27(x0, x1, True, x2, x3)
new_esEs23(x0, x1, ty_Ordering)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_esEs5(@2(x0, x1), @2(x2, x3), x4, x5)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_lt12(x0, x1, ty_Char)
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_primMulNat0(Succ(x0), Succ(x1))
new_ltEs4(EQ, EQ)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_ltEs6(x0, x1)
new_lt9(x0, x1)
new_lt17(x0, x1, x2)
new_esEs24(x0, x1, app(ty_[], x2))
new_primEqNat0(Succ(x0), Zero)
new_primMulNat0(Zero, Succ(x0))
new_lt12(x0, x1, app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, app(ty_[], x2))
new_ltEs12(Right(x0), Right(x1), x2, ty_Char)
new_lt12(x0, x1, app(ty_[], x2))
new_ltEs18(x0, x1, app(ty_Ratio, x2))
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primPlusNat0(Zero, Succ(x0))
new_esEs11(x0, x1, ty_Int)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs4(EQ, LT)
new_ltEs4(LT, EQ)
new_compare110(x0, x1, True)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_esEs4(Right(x0), Right(x1), x2, ty_Bool)
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt18(x0, x1, x2)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_not(GT)
new_compare26(x0, x1, False, x2, x3, x4)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_esEs4(Right(x0), Left(x1), x2, x3)
new_esEs4(Left(x0), Right(x1), x2, x3)
new_primCompAux00(x0, GT)
new_ltEs12(Left(x0), Left(x1), ty_Bool, x2)
new_esEs13(Float(x0, x1), Float(x2, x3))
new_ltEs18(x0, x1, ty_Ordering)
new_primEqInt(Neg(Zero), Pos(Zero))
new_primEqInt(Pos(Zero), Neg(Zero))
new_esEs4(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_ltEs17(Just(x0), Just(x1), app(ty_Ratio, x2))
new_asAs(True, x0)
new_esEs18(Char(x0), Char(x1))
new_ltEs18(x0, x1, ty_Bool)
new_compare13(x0, x1, True, x2, x3, x4)
new_esEs7(Just(x0), Just(x1), app(ty_Ratio, x2))
new_lt19(x0, x1, ty_Float)
new_compare31(x0, x1, ty_Bool)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs25(x0, x1, ty_Int)
new_esEs4(Left(x0), Left(x1), ty_@0, x2)
new_compare(:(x0, x1), [], x2)
new_esEs24(x0, x1, ty_Int)
new_primMulNat0(Succ(x0), Zero)
new_esEs23(x0, x1, ty_@0)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs23(x0, x1, ty_Char)
new_compare210(x0, x1, False, x2, x3)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_esEs14(:(x0, x1), :(x2, x3), x4)
new_compare(:(x0, x1), :(x2, x3), x4)
new_esEs12(Integer(x0), Integer(x1))
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_compare31(x0, x1, ty_Float)
new_ltEs18(x0, x1, ty_Double)
new_primEqInt(Neg(Zero), Neg(Zero))
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_compare31(x0, x1, ty_@0)
new_lt19(x0, x1, ty_Bool)
new_ltEs12(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs27(x0, x1, ty_Int)
new_esEs16(LT, LT)
new_esEs7(Just(x0), Just(x1), ty_Ordering)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_compare31(x0, x1, ty_Integer)
new_esEs21(x0, x1, ty_Int)
new_ltEs17(Just(x0), Just(x1), ty_Bool)
new_ltEs4(LT, LT)
new_compare31(x0, x1, app(app(ty_Either, x2), x3))
new_esEs4(Left(x0), Left(x1), ty_Bool, x2)
new_esEs4(Right(x0), Right(x1), x2, ty_Double)
new_esEs4(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpNat0(Zero, Succ(x0))
new_esEs8(x0, x1)
new_esEs7(Just(x0), Just(x1), ty_Bool)
new_ltEs12(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs7(Just(x0), Just(x1), app(ty_[], x2))
new_esEs22(x0, x1, ty_Int)
new_ltEs19(x0, x1, ty_Integer)
new_ltEs12(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs10(x0, x1, ty_Int)
new_lt19(x0, x1, ty_Int)
new_ltEs18(x0, x1, app(app(ty_Either, x2), x3))
new_lt5(x0, x1)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_esEs25(x0, x1, ty_@0)
new_compare28(x0, x1, True, x2)
new_esEs22(x0, x1, app(ty_[], x2))
new_compare14(Double(x0, x1), Double(x2, x3))
new_compare5(:%(x0, x1), :%(x2, x3), ty_Int)
new_compare31(x0, x1, ty_Double)
new_compare15(x0, x1, False, x2, x3)
new_compare10(x0, x1, False)
new_esEs25(x0, x1, ty_Ordering)
new_ltEs19(x0, x1, ty_Double)
new_lt20(x0, x1, ty_Ordering)
new_esEs23(x0, x1, ty_Double)
new_ltEs12(Left(x0), Left(x1), ty_Float, x2)
new_ltEs7(x0, x1, x2)
new_lt8(x0, x1, x2)
new_esEs4(Right(x0), Right(x1), x2, ty_Int)
new_primEqNat0(Succ(x0), Succ(x1))
new_ltEs12(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_lt19(x0, x1, ty_Integer)
new_primCmpNat0(Zero, Zero)
new_esEs21(x0, x1, ty_@0)
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_compare31(x0, x1, ty_Char)
new_esEs4(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs4(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs23(x0, x1, ty_Int)
new_compare25(x0, x1, False)
new_ltEs17(Just(x0), Just(x1), app(ty_[], x2))
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs14(x0, x1)
new_esEs15(@0, @0)
new_esEs27(x0, x1, ty_Bool)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_compare([], :(x0, x1), x2)
new_esEs26(x0, x1, ty_Float)
new_ltEs12(Left(x0), Left(x1), ty_@0, x2)
new_esEs24(x0, x1, ty_Double)
new_ltEs17(Just(x0), Just(x1), ty_Float)
new_lt16(x0, x1, x2, x3, x4)
new_esEs7(Just(x0), Just(x1), ty_Double)
new_primPlusNat1(Succ(x0), x1)
new_lt12(x0, x1, app(ty_Ratio, x2))
new_ltEs17(Just(x0), Just(x1), ty_Char)
new_esEs7(Just(x0), Nothing, x1)
new_esEs4(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs24(x0, x1, ty_Char)
new_ltEs18(x0, x1, app(app(ty_@2, x2), x3))
new_esEs21(x0, x1, app(ty_[], x2))
new_ltEs12(Left(x0), Left(x1), ty_Int, x2)
new_ltEs12(Right(x0), Right(x1), x2, ty_@0)
new_ltEs19(x0, x1, ty_@0)
new_esEs20(EQ)
new_compare5(:%(x0, x1), :%(x2, x3), ty_Integer)
new_esEs4(Left(x0), Left(x1), ty_Int, x2)
new_ltEs12(Left(x0), Right(x1), x2, x3)
new_ltEs12(Right(x0), Left(x1), x2, x3)
new_ltEs18(x0, x1, ty_Char)
new_lt6(x0, x1)
new_compare13(x0, x1, False, x2, x3, x4)
new_primCmpNat0(Succ(x0), Succ(x1))
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_compare31(x0, x1, ty_Int)
new_esEs21(x0, x1, ty_Integer)
new_esEs26(x0, x1, ty_@0)
new_ltEs5(True, True)
new_compare31(x0, x1, app(ty_Maybe, x2))
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs4(GT, EQ)
new_ltEs4(EQ, GT)
new_ltEs19(x0, x1, ty_Float)
new_ltEs15(x0, x1, x2)
new_esEs7(Just(x0), Just(x1), ty_Integer)
new_ltEs12(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs27(x0, x1, ty_Integer)
new_not(EQ)
new_esEs26(x0, x1, ty_Double)
new_esEs16(LT, EQ)
new_esEs16(EQ, LT)
new_primEqNat0(Zero, Succ(x0))
new_ltEs10(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs16(EQ, EQ)
new_ltEs18(x0, x1, app(ty_Maybe, x2))
new_compare([], [], x0)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_esEs19(Double(x0, x1), Double(x2, x3))
new_lt19(x0, x1, app(ty_[], x2))
new_esEs4(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs17(Just(x0), Just(x1), ty_@0)
new_esEs20(GT)
new_esEs22(x0, x1, ty_Integer)
new_ltEs17(Just(x0), Just(x1), ty_Int)
new_esEs24(x0, x1, ty_Integer)
new_asAs(False, x0)
new_ltEs17(Just(x0), Just(x1), ty_Double)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_esEs14(:(x0, x1), [], x2)
new_esEs25(x0, x1, ty_Float)
new_sr(Integer(x0), Integer(x1))
new_primPlusNat0(Succ(x0), Zero)
new_lt4(x0, x1)
new_ltEs12(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_compare31(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_esEs10(x0, x1, ty_Integer)
new_esEs16(GT, EQ)
new_esEs16(EQ, GT)
new_ltEs12(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_lt20(x0, x1, app(ty_[], x2))
new_compare110(x0, x1, False)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_esEs25(x0, x1, app(ty_[], x2))
new_ltEs12(Left(x0), Left(x1), ty_Char, x2)
new_esEs24(x0, x1, ty_Ordering)
new_ltEs12(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(Just(x0), Just(x1), ty_Float)
new_esEs24(x0, x1, ty_@0)
new_esEs17(True, False)
new_esEs17(False, True)
new_esEs21(x0, x1, ty_Ordering)
new_esEs4(Left(x0), Left(x1), ty_Float, x2)
new_esEs6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs27(x0, x1, ty_Char)
new_ltEs12(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs24(x0, x1, ty_Float)
new_esEs26(x0, x1, ty_Char)
new_esEs26(x0, x1, ty_Bool)
new_primCompAux0(x0, x1, x2, x3)
new_lt19(x0, x1, ty_Char)
new_compare11(Char(x0), Char(x1))
new_pePe(False, x0, x1, x2, x3)
new_compare26(x0, x1, True, x2, x3, x4)
new_primEqInt(Pos(Zero), Pos(Zero))
new_esEs17(True, True)
new_esEs4(Left(x0), Left(x1), ty_Char, x2)
new_compare9(x0, x1)
new_lt12(x0, x1, ty_@0)
new_esEs4(Left(x0), Left(x1), ty_Integer, x2)
new_ltEs12(Left(x0), Left(x1), ty_Double, x2)
new_lt19(x0, x1, ty_@0)
new_esEs4(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, ty_Double)
new_lt20(x0, x1, ty_Bool)
new_ltEs17(Nothing, Just(x0), x1)
new_ltEs4(GT, LT)
new_ltEs4(LT, GT)
new_lt12(x0, x1, ty_Ordering)
new_lt15(x0, x1, x2, x3)
new_ltEs5(True, False)
new_ltEs5(False, True)
new_esEs22(x0, x1, ty_Ordering)
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpNat0(Succ(x0), Zero)
new_esEs22(x0, x1, ty_@0)
new_not(LT)
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_lt20(x0, x1, ty_Int)
new_esEs4(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_lt20(x0, x1, app(app(ty_Either, x2), x3))

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

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