YES 3.113 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
  ((max :: 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
  ((max :: 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
  ((max :: 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
  ((max :: 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

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

compare0 x y True = GT

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

compare3 x y = compare2 x y (x == y)

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

is transformed to
max x y = max2 x y

max1 x y True = y
max1 x y False = max0 x y otherwise

max0 x y True = x

max2 x y = max1 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
  ((max :: 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'2 x zx = gcd0Gcd'1 (zx == 0) x zx
gcd0Gcd'2 vuv vuw = gcd0Gcd'0 vuv vuw

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

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

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



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

mainModule Main
  ((max :: 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
  (max :: 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(vwx2100), Succ(vwx2200)) → new_primEqNat(vwx2100, vwx2200)

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(vwx6600), Succ(vwx401000)) → new_primPlusNat(vwx6600, 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(vwx30000), Succ(vwx40100)) → new_primMulNat(vwx30000, 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_esEs1(@3(vwx210, vwx211, vwx212), @3(vwx220, vwx221, vwx222), eg, app(app(ty_@2, hc), hd), gd) → new_esEs3(vwx211, vwx221, hc, hd)
new_esEs1(@3(vwx210, vwx211, vwx212), @3(vwx220, vwx221, vwx222), eg, app(ty_Maybe, gc), gd) → new_esEs(vwx211, vwx221, gc)
new_esEs3(@2(vwx210, vwx211), @2(vwx220, vwx221), bbh, app(ty_[], bcg)) → new_esEs2(vwx211, vwx221, bcg)
new_esEs1(@3(vwx210, vwx211, vwx212), @3(vwx220, vwx221, vwx222), eg, app(app(app(ty_@3, gg), gh), ha), gd) → new_esEs1(vwx211, vwx221, gg, gh, ha)
new_esEs1(@3(vwx210, vwx211, vwx212), @3(vwx220, vwx221, vwx222), eg, eh, app(app(app(ty_@3, fd), ff), fg)) → new_esEs1(vwx212, vwx222, fd, ff, fg)
new_esEs1(@3(vwx210, vwx211, vwx212), @3(vwx220, vwx221, vwx222), eg, eh, app(ty_[], fh)) → new_esEs2(vwx212, vwx222, fh)
new_esEs3(@2(vwx210, vwx211), @2(vwx220, vwx221), app(ty_[], bea), bdc) → new_esEs2(vwx210, vwx220, bea)
new_esEs(Just(vwx210), Just(vwx220), app(ty_Maybe, ba)) → new_esEs(vwx210, vwx220, ba)
new_esEs0(Left(vwx210), Left(vwx220), app(app(ty_Either, cd), ce), cc) → new_esEs0(vwx210, vwx220, cd, ce)
new_esEs3(@2(vwx210, vwx211), @2(vwx220, vwx221), app(app(app(ty_@3, bdf), bdg), bdh), bdc) → new_esEs1(vwx210, vwx220, bdf, bdg, bdh)
new_esEs0(Right(vwx210), Right(vwx220), de, app(ty_[], ed)) → new_esEs2(vwx210, vwx220, ed)
new_esEs3(@2(vwx210, vwx211), @2(vwx220, vwx221), bbh, app(app(ty_Either, bcb), bcc)) → new_esEs0(vwx211, vwx221, bcb, bcc)
new_esEs1(@3(vwx210, vwx211, vwx212), @3(vwx220, vwx221, vwx222), eg, app(ty_[], hb), gd) → new_esEs2(vwx211, vwx221, hb)
new_esEs1(@3(vwx210, vwx211, vwx212), @3(vwx220, vwx221, vwx222), app(ty_Maybe, he), eh, gd) → new_esEs(vwx210, vwx220, he)
new_esEs0(Right(vwx210), Right(vwx220), de, app(app(ty_Either, dg), dh)) → new_esEs0(vwx210, vwx220, dg, dh)
new_esEs3(@2(vwx210, vwx211), @2(vwx220, vwx221), bbh, app(app(ty_@2, bch), bda)) → new_esEs3(vwx211, vwx221, bch, bda)
new_esEs(Just(vwx210), Just(vwx220), app(app(ty_@2, bh), ca)) → new_esEs3(vwx210, vwx220, bh, ca)
new_esEs2(:(vwx210, vwx211), :(vwx220, vwx221), app(app(app(ty_@3, bbb), bbc), bbd)) → new_esEs1(vwx210, vwx220, bbb, bbc, bbd)
new_esEs1(@3(vwx210, vwx211, vwx212), @3(vwx220, vwx221, vwx222), app(app(app(ty_@3, hh), baa), bab), eh, gd) → new_esEs1(vwx210, vwx220, hh, baa, bab)
new_esEs(Just(vwx210), Just(vwx220), app(app(ty_Either, bb), bc)) → new_esEs0(vwx210, vwx220, bb, bc)
new_esEs2(:(vwx210, vwx211), :(vwx220, vwx221), app(app(ty_Either, bah), bba)) → new_esEs0(vwx210, vwx220, bah, bba)
new_esEs1(@3(vwx210, vwx211, vwx212), @3(vwx220, vwx221, vwx222), app(app(ty_Either, hf), hg), eh, gd) → new_esEs0(vwx210, vwx220, hf, hg)
new_esEs1(@3(vwx210, vwx211, vwx212), @3(vwx220, vwx221, vwx222), app(app(ty_@2, bad), bae), eh, gd) → new_esEs3(vwx210, vwx220, bad, bae)
new_esEs2(:(vwx210, vwx211), :(vwx220, vwx221), app(ty_Maybe, bag)) → new_esEs(vwx210, vwx220, bag)
new_esEs1(@3(vwx210, vwx211, vwx212), @3(vwx220, vwx221, vwx222), eg, app(app(ty_Either, ge), gf), gd) → new_esEs0(vwx211, vwx221, ge, gf)
new_esEs2(:(vwx210, vwx211), :(vwx220, vwx221), app(app(ty_@2, bbf), bbg)) → new_esEs3(vwx210, vwx220, bbf, bbg)
new_esEs1(@3(vwx210, vwx211, vwx212), @3(vwx220, vwx221, vwx222), eg, eh, app(app(ty_Either, fb), fc)) → new_esEs0(vwx212, vwx222, fb, fc)
new_esEs0(Right(vwx210), Right(vwx220), de, app(ty_Maybe, df)) → new_esEs(vwx210, vwx220, df)
new_esEs2(:(vwx210, vwx211), :(vwx220, vwx221), baf) → new_esEs2(vwx211, vwx221, baf)
new_esEs3(@2(vwx210, vwx211), @2(vwx220, vwx221), app(app(ty_@2, beb), bec), bdc) → new_esEs3(vwx210, vwx220, beb, bec)
new_esEs0(Right(vwx210), Right(vwx220), de, app(app(ty_@2, ee), ef)) → new_esEs3(vwx210, vwx220, ee, ef)
new_esEs0(Left(vwx210), Left(vwx220), app(ty_[], db), cc) → new_esEs2(vwx210, vwx220, db)
new_esEs3(@2(vwx210, vwx211), @2(vwx220, vwx221), bbh, app(ty_Maybe, bca)) → new_esEs(vwx211, vwx221, bca)
new_esEs2(:(vwx210, vwx211), :(vwx220, vwx221), app(ty_[], bbe)) → new_esEs2(vwx210, vwx220, bbe)
new_esEs1(@3(vwx210, vwx211, vwx212), @3(vwx220, vwx221, vwx222), app(ty_[], bac), eh, gd) → new_esEs2(vwx210, vwx220, bac)
new_esEs3(@2(vwx210, vwx211), @2(vwx220, vwx221), bbh, app(app(app(ty_@3, bcd), bce), bcf)) → new_esEs1(vwx211, vwx221, bcd, bce, bcf)
new_esEs1(@3(vwx210, vwx211, vwx212), @3(vwx220, vwx221, vwx222), eg, eh, app(app(ty_@2, ga), gb)) → new_esEs3(vwx212, vwx222, ga, gb)
new_esEs3(@2(vwx210, vwx211), @2(vwx220, vwx221), app(app(ty_Either, bdd), bde), bdc) → new_esEs0(vwx210, vwx220, bdd, bde)
new_esEs(Just(vwx210), Just(vwx220), app(ty_[], bg)) → new_esEs2(vwx210, vwx220, bg)
new_esEs(Just(vwx210), Just(vwx220), app(app(app(ty_@3, bd), be), bf)) → new_esEs1(vwx210, vwx220, bd, be, bf)
new_esEs0(Left(vwx210), Left(vwx220), app(ty_Maybe, cb), cc) → new_esEs(vwx210, vwx220, cb)
new_esEs0(Left(vwx210), Left(vwx220), app(app(ty_@2, dc), dd), cc) → new_esEs3(vwx210, vwx220, dc, dd)
new_esEs0(Left(vwx210), Left(vwx220), app(app(app(ty_@3, cf), cg), da), cc) → new_esEs1(vwx210, vwx220, cf, cg, da)
new_esEs3(@2(vwx210, vwx211), @2(vwx220, vwx221), app(ty_Maybe, bdb), bdc) → new_esEs(vwx210, vwx220, bdb)
new_esEs1(@3(vwx210, vwx211, vwx212), @3(vwx220, vwx221, vwx222), eg, eh, app(ty_Maybe, fa)) → new_esEs(vwx212, vwx222, fa)
new_esEs0(Right(vwx210), Right(vwx220), de, app(app(app(ty_@3, ea), eb), ec)) → new_esEs1(vwx210, vwx220, ea, eb, ec)

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(Left(vwx300), Left(vwx400), app(ty_[], eb), ea) → new_ltEs0(vwx300, vwx400, eb)
new_compare0(:(vwx300, vwx301), :(vwx400, vwx401), cb) → new_primCompAux(vwx300, vwx400, new_compare(vwx301, vwx401, cb), cb)
new_ltEs1(Left(vwx300), Left(vwx400), app(app(ty_Either, ec), ed), ea) → new_ltEs1(vwx300, vwx400, ec, ed)
new_ltEs0(:(vwx300, vwx301), :(vwx400, vwx401), cb) → new_primCompAux(vwx300, vwx400, new_compare(vwx301, vwx401, cb), cb)
new_ltEs2(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), ge, gf, app(app(app(ty_@3, hc), hd), he)) → new_ltEs2(vwx302, vwx402, hc, hd, he)
new_ltEs2(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), ge, gf, app(ty_[], gh)) → new_ltEs0(vwx302, vwx402, gh)
new_compare0(:(vwx300, vwx301), :(vwx400, vwx401), cb) → new_compare0(vwx301, vwx401, cb)
new_ltEs(Just(vwx300), Just(vwx400), app(ty_[], bb)) → new_ltEs0(vwx300, vwx400, bb)
new_compare2(vwx300, vwx400, df, dg) → new_compare21(vwx300, vwx400, new_esEs5(vwx300, vwx400, df, dg), df, dg)
new_ltEs2(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), ge, app(app(app(ty_@3, bae), baf), bag), baa) → new_lt2(vwx301, vwx401, bae, baf, bag)
new_ltEs2(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), ge, gf, app(app(ty_Either, ha), hb)) → new_ltEs1(vwx302, vwx402, ha, hb)
new_ltEs2(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), ge, app(app(ty_Either, bac), bad), baa) → new_lt1(vwx301, vwx401, bac, bad)
new_ltEs(Just(vwx300), Just(vwx400), app(ty_Maybe, ba)) → new_ltEs(vwx300, vwx400, ba)
new_compare3(vwx300, vwx400, bbc, bbd, bbe) → new_compare22(vwx300, vwx400, new_esEs6(vwx300, vwx400, bbc, bbd, bbe), bbc, bbd, bbe)
new_ltEs1(Left(vwx300), Left(vwx400), app(app(app(ty_@3, ee), ef), eg), ea) → new_ltEs2(vwx300, vwx400, ee, ef, eg)
new_ltEs3(@2(vwx300, vwx301), @2(vwx400, vwx401), bbh, app(ty_Maybe, bca)) → new_ltEs(vwx301, vwx401, bca)
new_ltEs3(@2(vwx300, vwx301), @2(vwx400, vwx401), app(app(ty_Either, bde), bdf), bdc) → new_lt1(vwx300, vwx400, bde, bdf)
new_lt3(vwx300, vwx400, bbf, bbg) → new_compare23(vwx300, vwx400, new_esEs7(vwx300, vwx400, bbf, bbg), bbf, bbg)
new_ltEs2(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), ge, gf, app(ty_Maybe, gg)) → new_ltEs(vwx302, vwx402, gg)
new_primCompAux(vwx300, vwx400, vwx48, app(ty_[], cd)) → new_compare0(vwx300, vwx400, cd)
new_lt(vwx300, vwx400, de) → new_compare20(vwx300, vwx400, new_esEs4(vwx300, vwx400, de), de)
new_ltEs3(@2(vwx300, vwx301), @2(vwx400, vwx401), bbh, app(app(ty_@2, bch), bda)) → new_ltEs3(vwx301, vwx401, bch, bda)
new_compare21(vwx300, vwx400, False, df, dg) → new_ltEs1(vwx300, vwx400, df, dg)
new_ltEs2(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), ge, gf, app(app(ty_@2, hf), hg)) → new_ltEs3(vwx302, vwx402, hf, hg)
new_primCompAux(vwx300, vwx400, vwx48, app(app(ty_Either, ce), cf)) → new_compare2(vwx300, vwx400, ce, cf)
new_ltEs3(@2(vwx300, vwx301), @2(vwx400, vwx401), bbh, app(app(ty_Either, bcc), bcd)) → new_ltEs1(vwx301, vwx401, bcc, bcd)
new_ltEs2(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), app(ty_[], bbb), gf, baa) → new_compare0(vwx300, vwx400, bbb)
new_ltEs2(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), app(app(app(ty_@3, bbc), bbd), bbe), gf, baa) → new_compare22(vwx300, vwx400, new_esEs6(vwx300, vwx400, bbc, bbd, bbe), bbc, bbd, bbe)
new_ltEs1(Right(vwx300), Right(vwx400), fb, app(ty_Maybe, fc)) → new_ltEs(vwx300, vwx400, fc)
new_ltEs1(Left(vwx300), Left(vwx400), app(ty_Maybe, dh), ea) → new_ltEs(vwx300, vwx400, dh)
new_ltEs1(Right(vwx300), Right(vwx400), fb, app(app(app(ty_@3, fh), ga), gb)) → new_ltEs2(vwx300, vwx400, fh, ga, gb)
new_lt2(vwx300, vwx400, bbc, bbd, bbe) → new_compare22(vwx300, vwx400, new_esEs6(vwx300, vwx400, bbc, bbd, bbe), bbc, bbd, bbe)
new_ltEs3(@2(vwx300, vwx301), @2(vwx400, vwx401), bbh, app(app(app(ty_@3, bce), bcf), bcg)) → new_ltEs2(vwx301, vwx401, bce, bcf, bcg)
new_compare23(vwx300, vwx400, False, bbf, bbg) → new_ltEs3(vwx300, vwx400, bbf, bbg)
new_ltEs3(@2(vwx300, vwx301), @2(vwx400, vwx401), app(app(ty_@2, beb), bec), bdc) → new_lt3(vwx300, vwx400, beb, bec)
new_ltEs2(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), app(app(ty_Either, df), dg), gf, baa) → new_compare21(vwx300, vwx400, new_esEs5(vwx300, vwx400, df, dg), df, dg)
new_ltEs2(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), app(app(ty_@2, bbf), bbg), gf, baa) → new_compare23(vwx300, vwx400, new_esEs7(vwx300, vwx400, bbf, bbg), bbf, bbg)
new_lt0(vwx300, vwx400, bbb) → new_compare0(vwx300, vwx400, bbb)
new_ltEs3(@2(vwx300, vwx301), @2(vwx400, vwx401), app(app(app(ty_@3, bdg), bdh), bea), bdc) → new_lt2(vwx300, vwx400, bdg, bdh, bea)
new_ltEs(Just(vwx300), Just(vwx400), app(app(app(ty_@3, be), bf), bg)) → new_ltEs2(vwx300, vwx400, be, bf, bg)
new_ltEs(Just(vwx300), Just(vwx400), app(app(ty_@2, bh), ca)) → new_ltEs3(vwx300, vwx400, bh, ca)
new_ltEs(Just(vwx300), Just(vwx400), app(app(ty_Either, bc), bd)) → new_ltEs1(vwx300, vwx400, bc, bd)
new_ltEs1(Right(vwx300), Right(vwx400), fb, app(app(ty_@2, gc), gd)) → new_ltEs3(vwx300, vwx400, gc, gd)
new_primCompAux(vwx300, vwx400, vwx48, app(ty_Maybe, cc)) → new_compare1(vwx300, vwx400, cc)
new_primCompAux(vwx300, vwx400, vwx48, app(app(app(ty_@3, cg), da), db)) → new_compare3(vwx300, vwx400, cg, da, db)
new_ltEs2(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), ge, app(ty_Maybe, hh), baa) → new_lt(vwx301, vwx401, hh)
new_primCompAux(vwx300, vwx400, vwx48, app(app(ty_@2, dc), dd)) → new_compare4(vwx300, vwx400, dc, dd)
new_ltEs1(Right(vwx300), Right(vwx400), fb, app(app(ty_Either, ff), fg)) → new_ltEs1(vwx300, vwx400, ff, fg)
new_compare1(vwx300, vwx400, de) → new_compare20(vwx300, vwx400, new_esEs4(vwx300, vwx400, de), de)
new_lt1(vwx300, vwx400, df, dg) → new_compare21(vwx300, vwx400, new_esEs5(vwx300, vwx400, df, dg), df, dg)
new_ltEs3(@2(vwx300, vwx301), @2(vwx400, vwx401), app(ty_Maybe, bdb), bdc) → new_lt(vwx300, vwx400, bdb)
new_ltEs2(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), ge, app(ty_[], bab), baa) → new_lt0(vwx301, vwx401, bab)
new_ltEs0(:(vwx300, vwx301), :(vwx400, vwx401), cb) → new_compare0(vwx301, vwx401, cb)
new_compare4(vwx300, vwx400, bbf, bbg) → new_compare23(vwx300, vwx400, new_esEs7(vwx300, vwx400, bbf, bbg), bbf, bbg)
new_ltEs3(@2(vwx300, vwx301), @2(vwx400, vwx401), bbh, app(ty_[], bcb)) → new_ltEs0(vwx301, vwx401, bcb)
new_ltEs1(Right(vwx300), Right(vwx400), fb, app(ty_[], fd)) → new_ltEs0(vwx300, vwx400, fd)
new_ltEs2(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), ge, app(app(ty_@2, bah), bba), baa) → new_lt3(vwx301, vwx401, bah, bba)
new_compare22(vwx300, vwx400, False, bbc, bbd, bbe) → new_ltEs2(vwx300, vwx400, bbc, bbd, bbe)
new_ltEs2(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), app(ty_Maybe, de), gf, baa) → new_compare20(vwx300, vwx400, new_esEs4(vwx300, vwx400, de), de)
new_compare20(vwx300, vwx400, False, de) → new_ltEs(vwx300, vwx400, de)
new_ltEs1(Left(vwx300), Left(vwx400), app(app(ty_@2, eh), fa), ea) → new_ltEs3(vwx300, vwx400, eh, fa)
new_ltEs3(@2(vwx300, vwx301), @2(vwx400, vwx401), app(ty_[], bdd), bdc) → new_lt0(vwx300, vwx400, bdd)

The TRS R consists of the following rules:

new_esEs4(Just(vwx210), Just(vwx220), app(ty_Maybe, cgd)) → new_esEs4(vwx210, vwx220, cgd)
new_esEs10(vwx211, vwx221, ty_Integer) → new_esEs20(vwx211, vwx221)
new_esEs25(vwx21, vwx22, ty_Char) → new_esEs19(vwx21, vwx22)
new_esEs21(Float(vwx210, vwx211), Float(vwx220, vwx221)) → new_esEs14(new_sr0(vwx210, vwx220), new_sr0(vwx211, vwx221))
new_esEs24(vwx210, vwx220, app(app(ty_Either, ced), cee)) → new_esEs5(vwx210, vwx220, ced, cee)
new_esEs25(vwx21, vwx22, ty_Ordering) → new_esEs17(vwx21, vwx22)
new_lt20(vwx300, vwx400, ty_Int) → new_lt16(vwx300, vwx400)
new_ltEs8(False, True) → True
new_compare210(vwx300, vwx400, False) → new_compare113(vwx300, vwx400, new_ltEs7(vwx300, vwx400))
new_esEs27(vwx210, vwx220, ty_Char) → new_esEs19(vwx210, vwx220)
new_lt17(vwx300, vwx400) → new_esEs8(new_compare13(vwx300, vwx400))
new_lt9(vwx300, vwx400, bbb) → new_esEs8(new_compare(vwx300, vwx400, bbb))
new_lt4(vwx300, vwx400, ty_Int) → new_lt16(vwx300, vwx400)
new_esEs13(True, False) → False
new_esEs13(False, True) → False
new_ltEs19(vwx302, vwx402, ty_Char) → new_ltEs15(vwx302, vwx402)
new_esEs27(vwx210, vwx220, ty_Integer) → new_esEs20(vwx210, vwx220)
new_compare110(vwx300, vwx400, True, df, dg) → LT
new_lt19(vwx301, vwx401, ty_Integer) → new_lt18(vwx301, vwx401)
new_ltEs7(LT, EQ) → True
new_compare14(vwx300, vwx400, app(ty_Maybe, cc)) → new_compare15(vwx300, vwx400, cc)
new_compare([], :(vwx400, vwx401), cb) → LT
new_esEs18(:(vwx210, vwx211), :(vwx220, vwx221), cea) → new_asAs(new_esEs24(vwx210, vwx220, cea), new_esEs18(vwx211, vwx221, cea))
new_esEs4(Just(vwx210), Nothing, cgb) → False
new_esEs4(Nothing, Just(vwx220), cgb) → False
new_esEs24(vwx210, vwx220, app(ty_Maybe, cec)) → new_esEs4(vwx210, vwx220, cec)
new_ltEs19(vwx302, vwx402, ty_Float) → new_ltEs11(vwx302, vwx402)
new_ltEs6(Nothing, Just(vwx400), cfg) → True
new_lt4(vwx300, vwx400, ty_Float) → new_lt10(vwx300, vwx400)
new_esEs5(Left(vwx210), Left(vwx220), ty_@0, cbd) → new_esEs16(vwx210, vwx220)
new_pePe(False, vwx21, vwx22, vwx38, che) → new_asAs(new_esEs25(vwx21, vwx22, che), vwx38)
new_esEs26(vwx211, vwx221, ty_Integer) → new_esEs20(vwx211, vwx221)
new_esEs11(vwx210, vwx220, app(app(ty_@2, cae), caf)) → new_esEs7(vwx210, vwx220, cae, caf)
new_lt4(vwx300, vwx400, ty_Char) → new_lt15(vwx300, vwx400)
new_ltEs13(Left(vwx300), Left(vwx400), ty_Float, ea) → new_ltEs11(vwx300, vwx400)
new_primMulNat0(Zero, Zero) → Zero
new_compare(:(vwx300, vwx301), [], cb) → GT
new_compare29(vwx300, vwx400, True) → EQ
new_sr(Integer(vwx3000), Integer(vwx4010)) → Integer(new_primMulInt(vwx3000, vwx4010))
new_esEs4(Just(vwx210), Just(vwx220), app(app(app(ty_@3, cgg), cgh), cha)) → new_esEs6(vwx210, vwx220, cgg, cgh, cha)
new_esEs5(Left(vwx210), Left(vwx220), ty_Float, cbd) → new_esEs21(vwx210, vwx220)
new_lt20(vwx300, vwx400, ty_Integer) → new_lt18(vwx300, vwx400)
new_ltEs5(vwx301, vwx401, ty_Char) → new_ltEs15(vwx301, vwx401)
new_esEs20(Integer(vwx210), Integer(vwx220)) → new_primEqInt(vwx210, vwx220)
new_lt20(vwx300, vwx400, app(app(ty_Either, df), dg)) → new_lt12(vwx300, vwx400, df, dg)
new_ltEs4(@2(vwx300, vwx301), @2(vwx400, vwx401), bbh, bdc) → new_pePe(new_lt4(vwx300, vwx400, bbh), vwx300, vwx400, new_ltEs5(vwx301, vwx401, bdc), bbh)
new_compare14(vwx300, vwx400, app(app(ty_@2, dc), dd)) → new_compare19(vwx300, vwx400, dc, dd)
new_lt19(vwx301, vwx401, ty_Ordering) → new_lt6(vwx301, vwx401)
new_not(GT) → False
new_esEs24(vwx210, vwx220, ty_Bool) → new_esEs13(vwx210, vwx220)
new_ltEs13(Right(vwx300), Right(vwx400), fb, app(ty_[], fd)) → new_ltEs10(vwx300, vwx400, fd)
new_esEs12(:%(vwx210, vwx211), :%(vwx220, vwx221), cbb) → new_asAs(new_esEs23(vwx210, vwx220, cbb), new_esEs22(vwx211, vwx221, cbb))
new_ltEs5(vwx301, vwx401, ty_@0) → new_ltEs17(vwx301, vwx401)
new_ltEs6(Just(vwx300), Just(vwx400), ty_Float) → new_ltEs11(vwx300, vwx400)
new_ltEs11(vwx30, vwx40) → new_not(new_compare8(vwx30, vwx40))
new_lt4(vwx300, vwx400, ty_Ordering) → new_lt6(vwx300, vwx400)
new_esEs25(vwx21, vwx22, ty_Double) → new_esEs15(vwx21, vwx22)
new_esEs5(Left(vwx210), Left(vwx220), app(ty_Ratio, cbc), cbd) → new_esEs12(vwx210, vwx220, cbc)
new_esEs26(vwx211, vwx221, app(ty_Maybe, daa)) → new_esEs4(vwx211, vwx221, daa)
new_esEs5(Left(vwx210), Left(vwx220), ty_Char, cbd) → new_esEs19(vwx210, vwx220)
new_compare14(vwx300, vwx400, ty_Char) → new_compare26(vwx300, vwx400)
new_compare25(vwx300, vwx400, False, bbc, bbd, bbe) → new_compare112(vwx300, vwx400, new_ltEs14(vwx300, vwx400, bbc, bbd, bbe), bbc, bbd, bbe)
new_esEs25(vwx21, vwx22, ty_Bool) → new_esEs13(vwx21, vwx22)
new_ltEs6(Just(vwx300), Just(vwx400), app(app(app(ty_@3, be), bf), bg)) → new_ltEs14(vwx300, vwx400, be, bf, bg)
new_esEs5(Right(vwx210), Right(vwx220), ccf, app(app(app(ty_@3, cdc), cdd), cde)) → new_esEs6(vwx210, vwx220, cdc, cdd, cde)
new_compare26(Char(vwx300), Char(vwx400)) → new_primCmpNat0(vwx300, vwx400)
new_esEs9(vwx212, vwx222, app(ty_[], bfh)) → new_esEs18(vwx212, vwx222, bfh)
new_compare16(vwx300, vwx400) → new_compare210(vwx300, vwx400, new_esEs17(vwx300, vwx400))
new_esEs25(vwx21, vwx22, app(app(ty_@2, chf), chg)) → new_esEs7(vwx21, vwx22, chf, chg)
new_esEs5(Right(vwx210), Right(vwx220), ccf, ty_Bool) → new_esEs13(vwx210, vwx220)
new_ltEs13(Right(vwx300), Right(vwx400), fb, app(ty_Maybe, fc)) → new_ltEs6(vwx300, vwx400, fc)
new_esEs18([], :(vwx220, vwx221), cea) → False
new_esEs18(:(vwx210, vwx211), [], cea) → False
new_esEs27(vwx210, vwx220, ty_@0) → new_esEs16(vwx210, vwx220)
new_ltEs13(Left(vwx300), Left(vwx400), app(ty_Maybe, dh), ea) → new_ltEs6(vwx300, vwx400, dh)
new_ltEs19(vwx302, vwx402, app(app(ty_@2, hf), hg)) → new_ltEs4(vwx302, vwx402, hf, hg)
new_lt20(vwx300, vwx400, ty_Float) → new_lt10(vwx300, vwx400)
new_lt19(vwx301, vwx401, app(ty_[], bab)) → new_lt9(vwx301, vwx401, bab)
new_esEs24(vwx210, vwx220, ty_Float) → new_esEs21(vwx210, vwx220)
new_compare18(:%(vwx300, vwx301), :%(vwx400, vwx401), ty_Integer) → new_compare6(new_sr(vwx300, vwx401), new_sr(vwx400, vwx301))
new_ltEs5(vwx301, vwx401, app(app(ty_@2, bch), bda)) → new_ltEs4(vwx301, vwx401, bch, bda)
new_ltEs13(Left(vwx300), Left(vwx400), ty_@0, ea) → new_ltEs17(vwx300, vwx400)
new_lt20(vwx300, vwx400, app(app(app(ty_@3, bbc), bbd), bbe)) → new_lt13(vwx300, vwx400, bbc, bbd, bbe)
new_lt20(vwx300, vwx400, app(app(ty_@2, bbf), bbg)) → new_lt14(vwx300, vwx400, bbf, bbg)
new_ltEs6(Just(vwx300), Just(vwx400), ty_Bool) → new_ltEs8(vwx300, vwx400)
new_ltEs13(Left(vwx300), Left(vwx400), ty_Int, ea) → new_ltEs16(vwx300, vwx400)
new_ltEs5(vwx301, vwx401, app(app(app(ty_@3, bce), bcf), bcg)) → new_ltEs14(vwx301, vwx401, bce, bcf, bcg)
new_ltEs7(GT, GT) → True
new_compare111(vwx300, vwx400, False) → GT
new_lt6(vwx300, vwx400) → new_esEs8(new_compare16(vwx300, vwx400))
new_compare111(vwx300, vwx400, True) → LT
new_compare10(vwx300, vwx400, True, de) → LT
new_ltEs14(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), ge, gf, baa) → new_pePe(new_lt20(vwx300, vwx400, ge), vwx300, vwx400, new_pePe(new_lt19(vwx301, vwx401, gf), vwx301, vwx401, new_ltEs19(vwx302, vwx402, baa), gf), ge)
new_esEs26(vwx211, vwx221, ty_Char) → new_esEs19(vwx211, vwx221)
new_esEs5(Left(vwx210), Left(vwx220), app(ty_Maybe, cbe), cbd) → new_esEs4(vwx210, vwx220, cbe)
new_esEs11(vwx210, vwx220, ty_Float) → new_esEs21(vwx210, vwx220)
new_compare9(vwx300, vwx400, bbc, bbd, bbe) → new_compare25(vwx300, vwx400, new_esEs6(vwx300, vwx400, bbc, bbd, bbe), bbc, bbd, bbe)
new_esEs22(vwx211, vwx221, ty_Integer) → new_esEs20(vwx211, vwx221)
new_primCmpNat0(Zero, Succ(vwx4000)) → LT
new_esEs23(vwx210, vwx220, ty_Integer) → new_esEs20(vwx210, vwx220)
new_ltEs6(Just(vwx300), Just(vwx400), app(app(ty_Either, bc), bd)) → new_ltEs13(vwx300, vwx400, bc, bd)
new_esEs17(LT, LT) → True
new_lt20(vwx300, vwx400, ty_Ordering) → new_lt6(vwx300, vwx400)
new_esEs25(vwx21, vwx22, app(app(ty_Either, ccf), cbd)) → new_esEs5(vwx21, vwx22, ccf, cbd)
new_esEs11(vwx210, vwx220, app(app(app(ty_@3, caa), cab), cac)) → new_esEs6(vwx210, vwx220, caa, cab, cac)
new_compare25(vwx300, vwx400, True, bbc, bbd, bbe) → EQ
new_ltEs5(vwx301, vwx401, ty_Ordering) → new_ltEs7(vwx301, vwx401)
new_esEs7(@2(vwx210, vwx211), @2(vwx220, vwx221), chf, chg) → new_asAs(new_esEs27(vwx210, vwx220, chf), new_esEs26(vwx211, vwx221, chg))
new_ltEs13(Right(vwx300), Right(vwx400), fb, ty_Bool) → new_ltEs8(vwx300, vwx400)
new_compare10(vwx300, vwx400, False, de) → GT
new_esEs23(vwx210, vwx220, ty_Int) → new_esEs14(vwx210, vwx220)
new_ltEs13(Right(vwx300), Right(vwx400), fb, ty_Ordering) → new_ltEs7(vwx300, vwx400)
new_primEqNat0(Zero, Zero) → True
new_ltEs19(vwx302, vwx402, ty_Integer) → new_ltEs18(vwx302, vwx402)
new_esEs10(vwx211, vwx221, ty_Bool) → new_esEs13(vwx211, vwx221)
new_ltEs5(vwx301, vwx401, ty_Bool) → new_ltEs8(vwx301, vwx401)
new_compare8(Float(vwx300, vwx301), Float(vwx400, vwx401)) → new_compare7(new_sr0(vwx300, vwx400), new_sr0(vwx301, vwx401))
new_esEs25(vwx21, vwx22, app(ty_[], cea)) → new_esEs18(vwx21, vwx22, cea)
new_primMulNat0(Succ(vwx30000), Succ(vwx40100)) → new_primPlusNat1(new_primMulNat0(vwx30000, Succ(vwx40100)), vwx40100)
new_compare12(Double(vwx300, vwx301), Double(vwx400, vwx401)) → new_compare7(new_sr0(vwx300, vwx400), new_sr0(vwx301, vwx401))
new_lt20(vwx300, vwx400, app(ty_Ratio, cff)) → new_lt8(vwx300, vwx400, cff)
new_ltEs6(Just(vwx300), Just(vwx400), ty_@0) → new_ltEs17(vwx300, vwx400)
new_lt20(vwx300, vwx400, app(ty_[], bbb)) → new_lt9(vwx300, vwx400, bbb)
new_esEs24(vwx210, vwx220, app(ty_[], cfa)) → new_esEs18(vwx210, vwx220, cfa)
new_esEs26(vwx211, vwx221, ty_@0) → new_esEs16(vwx211, vwx221)
new_lt20(vwx300, vwx400, ty_Bool) → new_lt7(vwx300, vwx400)
new_compare24(vwx300, vwx400, False, de) → new_compare10(vwx300, vwx400, new_ltEs6(vwx300, vwx400, de), de)
new_compare110(vwx300, vwx400, False, df, dg) → GT
new_compare(:(vwx300, vwx301), :(vwx400, vwx401), cb) → new_primCompAux1(vwx300, vwx400, new_compare(vwx301, vwx401, cb), cb)
new_compare7(vwx30, vwx40) → new_primCmpInt(vwx30, vwx40)
new_ltEs13(Left(vwx300), Left(vwx400), ty_Integer, ea) → new_ltEs18(vwx300, vwx400)
new_compare5(vwx300, vwx400, df, dg) → new_compare28(vwx300, vwx400, new_esEs5(vwx300, vwx400, df, dg), df, dg)
new_esEs24(vwx210, vwx220, app(app(ty_@2, cfb), cfc)) → new_esEs7(vwx210, vwx220, cfb, cfc)
new_compare14(vwx300, vwx400, ty_Bool) → new_compare17(vwx300, vwx400)
new_esEs10(vwx211, vwx221, ty_Int) → new_esEs14(vwx211, vwx221)
new_ltEs5(vwx301, vwx401, ty_Float) → new_ltEs11(vwx301, vwx401)
new_esEs24(vwx210, vwx220, ty_Char) → new_esEs19(vwx210, vwx220)
new_ltEs6(Just(vwx300), Just(vwx400), app(ty_Ratio, cfh)) → new_ltEs9(vwx300, vwx400, cfh)
new_esEs5(Right(vwx210), Right(vwx220), ccf, app(ty_[], cdf)) → new_esEs18(vwx210, vwx220, cdf)
new_esEs10(vwx211, vwx221, ty_@0) → new_esEs16(vwx211, vwx221)
new_esEs26(vwx211, vwx221, app(app(app(ty_@3, dad), dae), daf)) → new_esEs6(vwx211, vwx221, dad, dae, daf)
new_compare14(vwx300, vwx400, ty_Ordering) → new_compare16(vwx300, vwx400)
new_ltEs13(Left(vwx300), Left(vwx400), ty_Double, ea) → new_ltEs12(vwx300, vwx400)
new_esEs27(vwx210, vwx220, ty_Float) → new_esEs21(vwx210, vwx220)
new_primEqInt(Neg(Succ(vwx2100)), Neg(Succ(vwx2200))) → new_primEqNat0(vwx2100, vwx2200)
new_ltEs13(Right(vwx300), Right(vwx400), fb, ty_Double) → new_ltEs12(vwx300, vwx400)
new_compare14(vwx300, vwx400, app(app(app(ty_@3, cg), da), db)) → new_compare9(vwx300, vwx400, cg, da, db)
new_esEs27(vwx210, vwx220, ty_Bool) → new_esEs13(vwx210, vwx220)
new_lt19(vwx301, vwx401, ty_Bool) → new_lt7(vwx301, vwx401)
new_lt4(vwx300, vwx400, ty_Integer) → new_lt18(vwx300, vwx400)
new_esEs24(vwx210, vwx220, ty_Integer) → new_esEs20(vwx210, vwx220)
new_esEs10(vwx211, vwx221, app(ty_[], bhb)) → new_esEs18(vwx211, vwx221, bhb)
new_ltEs8(True, True) → True
new_ltEs19(vwx302, vwx402, app(ty_Ratio, cfd)) → new_ltEs9(vwx302, vwx402, cfd)
new_esEs9(vwx212, vwx222, ty_Float) → new_esEs21(vwx212, vwx222)
new_ltEs5(vwx301, vwx401, app(ty_Ratio, bed)) → new_ltEs9(vwx301, vwx401, bed)
new_esEs15(Double(vwx210, vwx211), Double(vwx220, vwx221)) → new_esEs14(new_sr0(vwx210, vwx220), new_sr0(vwx211, vwx221))
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs17(EQ, EQ) → True
new_esEs24(vwx210, vwx220, app(app(app(ty_@3, cef), ceg), ceh)) → new_esEs6(vwx210, vwx220, cef, ceg, ceh)
new_ltEs7(EQ, EQ) → True
new_esEs27(vwx210, vwx220, app(app(ty_Either, dbd), dbe)) → new_esEs5(vwx210, vwx220, dbd, dbe)
new_primEqInt(Neg(Succ(vwx2100)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(vwx2200))) → False
new_primCompAux0(vwx52, GT) → GT
new_primPlusNat1(Zero, vwx40100) → Succ(vwx40100)
new_lt4(vwx300, vwx400, app(app(app(ty_@3, bdg), bdh), bea)) → new_lt13(vwx300, vwx400, bdg, bdh, bea)
new_esEs5(Right(vwx210), Right(vwx220), ccf, app(ty_Ratio, ccg)) → new_esEs12(vwx210, vwx220, ccg)
new_esEs11(vwx210, vwx220, ty_Int) → new_esEs14(vwx210, vwx220)
new_esEs26(vwx211, vwx221, app(ty_[], dag)) → new_esEs18(vwx211, vwx221, dag)
new_lt20(vwx300, vwx400, app(ty_Maybe, de)) → new_lt5(vwx300, vwx400, de)
new_compare([], [], cb) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_ltEs7(GT, LT) → False
new_ltEs10(vwx30, vwx40, cb) → new_not(new_compare(vwx30, vwx40, cb))
new_primCmpNat0(Succ(vwx3000), Succ(vwx4000)) → new_primCmpNat0(vwx3000, vwx4000)
new_esEs25(vwx21, vwx22, app(ty_Maybe, cgb)) → new_esEs4(vwx21, vwx22, cgb)
new_ltEs7(GT, EQ) → False
new_primEqInt(Pos(Succ(vwx2100)), Pos(Succ(vwx2200))) → new_primEqNat0(vwx2100, vwx2200)
new_compare27(vwx300, vwx400, True, bbf, bbg) → EQ
new_esEs11(vwx210, vwx220, ty_Ordering) → new_esEs17(vwx210, vwx220)
new_esEs9(vwx212, vwx222, app(app(ty_@2, bga), bgb)) → new_esEs7(vwx212, vwx222, bga, bgb)
new_compare27(vwx300, vwx400, False, bbf, bbg) → new_compare11(vwx300, vwx400, new_ltEs4(vwx300, vwx400, bbf, bbg), bbf, bbg)
new_ltEs13(Left(vwx300), Left(vwx400), ty_Ordering, ea) → new_ltEs7(vwx300, vwx400)
new_esEs17(LT, GT) → False
new_esEs17(GT, LT) → False
new_esEs5(Right(vwx210), Right(vwx220), ccf, app(app(ty_Either, cda), cdb)) → new_esEs5(vwx210, vwx220, cda, cdb)
new_compare28(vwx300, vwx400, False, df, dg) → new_compare110(vwx300, vwx400, new_ltEs13(vwx300, vwx400, df, dg), df, dg)
new_primEqNat0(Succ(vwx2100), Succ(vwx2200)) → new_primEqNat0(vwx2100, vwx2200)
new_ltEs9(vwx30, vwx40, cga) → new_not(new_compare18(vwx30, vwx40, cga))
new_esEs24(vwx210, vwx220, ty_@0) → new_esEs16(vwx210, vwx220)
new_esEs17(EQ, GT) → False
new_esEs17(GT, EQ) → False
new_ltEs18(vwx30, vwx40) → new_not(new_compare6(vwx30, vwx40))
new_ltEs19(vwx302, vwx402, app(app(ty_Either, ha), hb)) → new_ltEs13(vwx302, vwx402, ha, hb)
new_ltEs6(Just(vwx300), Just(vwx400), ty_Int) → new_ltEs16(vwx300, vwx400)
new_esEs10(vwx211, vwx221, ty_Double) → new_esEs15(vwx211, vwx221)
new_lt4(vwx300, vwx400, ty_Double) → new_lt11(vwx300, vwx400)
new_lt13(vwx300, vwx400, bbc, bbd, bbe) → new_esEs8(new_compare9(vwx300, vwx400, bbc, bbd, bbe))
new_esEs24(vwx210, vwx220, app(ty_Ratio, ceb)) → new_esEs12(vwx210, vwx220, ceb)
new_primCmpInt(Neg(Succ(vwx3000)), Neg(vwx400)) → new_primCmpNat0(vwx400, Succ(vwx3000))
new_esEs10(vwx211, vwx221, app(app(ty_@2, bhc), bhd)) → new_esEs7(vwx211, vwx221, bhc, bhd)
new_ltEs19(vwx302, vwx402, ty_Bool) → new_ltEs8(vwx302, vwx402)
new_esEs5(Right(vwx210), Right(vwx220), ccf, ty_@0) → new_esEs16(vwx210, vwx220)
new_esEs11(vwx210, vwx220, app(ty_Maybe, bhf)) → new_esEs4(vwx210, vwx220, bhf)
new_esEs5(Left(vwx210), Left(vwx220), ty_Int, cbd) → new_esEs14(vwx210, vwx220)
new_ltEs13(Right(vwx300), Right(vwx400), fb, app(app(app(ty_@3, fh), ga), gb)) → new_ltEs14(vwx300, vwx400, fh, ga, gb)
new_esEs25(vwx21, vwx22, ty_Integer) → new_esEs20(vwx21, vwx22)
new_primEqInt(Pos(Succ(vwx2100)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(vwx2200))) → False
new_ltEs12(vwx30, vwx40) → new_not(new_compare12(vwx30, vwx40))
new_esEs11(vwx210, vwx220, app(ty_[], cad)) → new_esEs18(vwx210, vwx220, cad)
new_ltEs19(vwx302, vwx402, app(ty_Maybe, gg)) → new_ltEs6(vwx302, vwx402, gg)
new_lt4(vwx300, vwx400, app(ty_[], bdd)) → new_lt9(vwx300, vwx400, bdd)
new_primPlusNat0(Succ(vwx6600), Zero) → Succ(vwx6600)
new_primPlusNat0(Zero, Succ(vwx401000)) → Succ(vwx401000)
new_ltEs6(Just(vwx300), Nothing, cfg) → False
new_ltEs5(vwx301, vwx401, app(app(ty_Either, bcc), bcd)) → new_ltEs13(vwx301, vwx401, bcc, bcd)
new_compare14(vwx300, vwx400, app(app(ty_Either, ce), cf)) → new_compare5(vwx300, vwx400, ce, cf)
new_esEs11(vwx210, vwx220, ty_@0) → new_esEs16(vwx210, vwx220)
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(vwx3000), Zero) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(vwx4000))) → LT
new_esEs8(LT) → True
new_esEs4(Just(vwx210), Just(vwx220), app(app(ty_Either, cge), cgf)) → new_esEs5(vwx210, vwx220, cge, cgf)
new_compare11(vwx300, vwx400, True, bbf, bbg) → LT
new_compare6(Integer(vwx300), Integer(vwx400)) → new_primCmpInt(vwx300, vwx400)
new_compare28(vwx300, vwx400, True, df, dg) → EQ
new_esEs6(@3(vwx210, vwx211, vwx212), @3(vwx220, vwx221, vwx222), bef, beg, beh) → new_asAs(new_esEs11(vwx210, vwx220, bef), new_asAs(new_esEs10(vwx211, vwx221, beg), new_esEs9(vwx212, vwx222, beh)))
new_primEqInt(Pos(Succ(vwx2100)), Neg(vwx220)) → False
new_primEqInt(Neg(Succ(vwx2100)), Pos(vwx220)) → False
new_ltEs13(Left(vwx300), Left(vwx400), ty_Bool, ea) → new_ltEs8(vwx300, vwx400)
new_esEs8(GT) → False
new_esEs24(vwx210, vwx220, ty_Int) → new_esEs14(vwx210, vwx220)
new_ltEs13(Right(vwx300), Right(vwx400), fb, ty_@0) → new_ltEs17(vwx300, vwx400)
new_ltEs6(Just(vwx300), Just(vwx400), app(ty_Maybe, ba)) → new_ltEs6(vwx300, vwx400, ba)
new_esEs9(vwx212, vwx222, app(app(ty_Either, bfc), bfd)) → new_esEs5(vwx212, vwx222, bfc, bfd)
new_lt15(vwx300, vwx400) → new_esEs8(new_compare26(vwx300, vwx400))
new_ltEs7(EQ, GT) → True
new_primEqInt(Pos(Zero), Neg(Succ(vwx2200))) → False
new_primEqInt(Neg(Zero), Pos(Succ(vwx2200))) → False
new_compare14(vwx300, vwx400, ty_@0) → new_compare13(vwx300, vwx400)
new_primCmpInt(Pos(Zero), Pos(Succ(vwx4000))) → new_primCmpNat0(Zero, Succ(vwx4000))
new_esEs27(vwx210, vwx220, app(app(ty_@2, dcb), dcc)) → new_esEs7(vwx210, vwx220, dcb, dcc)
new_compare14(vwx300, vwx400, ty_Integer) → new_compare6(vwx300, vwx400)
new_esEs10(vwx211, vwx221, ty_Char) → new_esEs19(vwx211, vwx221)
new_lt16(vwx300, vwx400) → new_esEs8(new_compare7(vwx300, vwx400))
new_primCompAux0(vwx52, LT) → LT
new_ltEs13(Left(vwx300), Left(vwx400), app(ty_[], eb), ea) → new_ltEs10(vwx300, vwx400, eb)
new_ltEs8(True, False) → False
new_compare113(vwx300, vwx400, True) → LT
new_ltEs13(Right(vwx300), Right(vwx400), fb, app(ty_Ratio, cba)) → new_ltEs9(vwx300, vwx400, cba)
new_compare24(vwx300, vwx400, True, de) → EQ
new_esEs10(vwx211, vwx221, ty_Float) → new_esEs21(vwx211, vwx221)
new_primCmpInt(Pos(Succ(vwx3000)), Pos(vwx400)) → new_primCmpNat0(Succ(vwx3000), vwx400)
new_esEs9(vwx212, vwx222, ty_@0) → new_esEs16(vwx212, vwx222)
new_esEs9(vwx212, vwx222, ty_Bool) → new_esEs13(vwx212, vwx222)
new_ltEs19(vwx302, vwx402, app(ty_[], gh)) → new_ltEs10(vwx302, vwx402, gh)
new_compare14(vwx300, vwx400, ty_Double) → new_compare12(vwx300, vwx400)
new_compare113(vwx300, vwx400, False) → GT
new_compare19(vwx300, vwx400, bbf, bbg) → new_compare27(vwx300, vwx400, new_esEs7(vwx300, vwx400, bbf, bbg), bbf, bbg)
new_ltEs6(Just(vwx300), Just(vwx400), app(ty_[], bb)) → new_ltEs10(vwx300, vwx400, bb)
new_not0True
new_esEs5(Right(vwx210), Right(vwx220), ccf, ty_Int) → new_esEs14(vwx210, vwx220)
new_esEs11(vwx210, vwx220, ty_Double) → new_esEs15(vwx210, vwx220)
new_compare17(vwx300, vwx400) → new_compare29(vwx300, vwx400, new_esEs13(vwx300, vwx400))
new_esEs27(vwx210, vwx220, app(ty_[], dca)) → new_esEs18(vwx210, vwx220, dca)
new_ltEs17(vwx30, vwx40) → new_not(new_compare13(vwx30, vwx40))
new_ltEs13(Right(vwx300), Right(vwx400), fb, ty_Integer) → new_ltEs18(vwx300, vwx400)
new_esEs26(vwx211, vwx221, app(app(ty_Either, dab), dac)) → new_esEs5(vwx211, vwx221, dab, dac)
new_esEs5(Left(vwx210), Left(vwx220), ty_Integer, cbd) → new_esEs20(vwx210, vwx220)
new_esEs5(Left(vwx210), Left(vwx220), ty_Double, cbd) → new_esEs15(vwx210, vwx220)
new_compare11(vwx300, vwx400, False, bbf, bbg) → GT
new_primCmpInt(Pos(Succ(vwx3000)), Neg(vwx400)) → GT
new_esEs24(vwx210, vwx220, ty_Double) → new_esEs15(vwx210, vwx220)
new_compare14(vwx300, vwx400, app(ty_[], cd)) → new_compare(vwx300, vwx400, cd)
new_ltEs13(Left(vwx300), Left(vwx400), app(app(ty_@2, eh), fa), ea) → new_ltEs4(vwx300, vwx400, eh, fa)
new_primMulInt(Pos(vwx3000), Pos(vwx4010)) → Pos(new_primMulNat0(vwx3000, vwx4010))
new_lt19(vwx301, vwx401, app(app(ty_@2, bah), bba)) → new_lt14(vwx301, vwx401, bah, bba)
new_esEs27(vwx210, vwx220, ty_Double) → new_esEs15(vwx210, vwx220)
new_esEs5(Right(vwx210), Left(vwx220), ccf, cbd) → False
new_esEs5(Left(vwx210), Right(vwx220), ccf, cbd) → False
new_primMulInt(Neg(vwx3000), Neg(vwx4010)) → Pos(new_primMulNat0(vwx3000, vwx4010))
new_ltEs5(vwx301, vwx401, ty_Int) → new_ltEs16(vwx301, vwx401)
new_esEs11(vwx210, vwx220, ty_Integer) → new_esEs20(vwx210, vwx220)
new_ltEs6(Just(vwx300), Just(vwx400), ty_Double) → new_ltEs12(vwx300, vwx400)
new_ltEs8(False, False) → True
new_primEqNat0(Zero, Succ(vwx2200)) → False
new_primEqNat0(Succ(vwx2100), Zero) → False
new_ltEs19(vwx302, vwx402, app(app(app(ty_@3, hc), hd), he)) → new_ltEs14(vwx302, vwx402, hc, hd, he)
new_primPlusNat0(Zero, Zero) → Zero
new_esEs26(vwx211, vwx221, app(app(ty_@2, dah), dba)) → new_esEs7(vwx211, vwx221, dah, dba)
new_lt20(vwx300, vwx400, ty_@0) → new_lt17(vwx300, vwx400)
new_esEs11(vwx210, vwx220, ty_Char) → new_esEs19(vwx210, vwx220)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs4(Nothing, Nothing, cgb) → True
new_esEs5(Left(vwx210), Left(vwx220), app(ty_[], ccc), cbd) → new_esEs18(vwx210, vwx220, ccc)
new_esEs27(vwx210, vwx220, app(app(app(ty_@3, dbf), dbg), dbh)) → new_esEs6(vwx210, vwx220, dbf, dbg, dbh)
new_esEs5(Right(vwx210), Right(vwx220), ccf, ty_Float) → new_esEs21(vwx210, vwx220)
new_compare210(vwx300, vwx400, True) → EQ
new_lt10(vwx300, vwx400) → new_esEs8(new_compare8(vwx300, vwx400))
new_lt4(vwx300, vwx400, ty_Bool) → new_lt7(vwx300, vwx400)
new_esEs4(Just(vwx210), Just(vwx220), ty_Bool) → new_esEs13(vwx210, vwx220)
new_ltEs19(vwx302, vwx402, ty_@0) → new_ltEs17(vwx302, vwx402)
new_esEs27(vwx210, vwx220, app(ty_Maybe, dbc)) → new_esEs4(vwx210, vwx220, dbc)
new_pePe(True, vwx21, vwx22, vwx38, che) → True
new_primPlusNat1(Succ(vwx660), vwx40100) → Succ(Succ(new_primPlusNat0(vwx660, vwx40100)))
new_lt20(vwx300, vwx400, ty_Double) → new_lt11(vwx300, vwx400)
new_esEs5(Right(vwx210), Right(vwx220), ccf, ty_Char) → new_esEs19(vwx210, vwx220)
new_compare112(vwx300, vwx400, True, bbc, bbd, bbe) → LT
new_primCmpInt(Neg(Zero), Neg(Succ(vwx4000))) → new_primCmpNat0(Succ(vwx4000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(vwx4000))) → GT
new_sr0(vwx300, vwx401) → new_primMulInt(vwx300, vwx401)
new_esEs27(vwx210, vwx220, app(ty_Ratio, dbb)) → new_esEs12(vwx210, vwx220, dbb)
new_ltEs13(Left(vwx300), Left(vwx400), app(app(ty_Either, ec), ed), ea) → new_ltEs13(vwx300, vwx400, ec, ed)
new_esEs25(vwx21, vwx22, ty_Int) → new_esEs14(vwx21, vwx22)
new_esEs19(Char(vwx210), Char(vwx220)) → new_primEqNat0(vwx210, vwx220)
new_ltEs13(Right(vwx300), Right(vwx400), fb, app(app(ty_Either, ff), fg)) → new_ltEs13(vwx300, vwx400, ff, fg)
new_compare18(:%(vwx300, vwx301), :%(vwx400, vwx401), ty_Int) → new_compare7(new_sr0(vwx300, vwx401), new_sr0(vwx400, vwx301))
new_esEs5(Left(vwx210), Left(vwx220), app(app(ty_@2, ccd), cce), cbd) → new_esEs7(vwx210, vwx220, ccd, cce)
new_esEs27(vwx210, vwx220, ty_Int) → new_esEs14(vwx210, vwx220)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs10(vwx211, vwx221, app(app(ty_Either, bge), bgf)) → new_esEs5(vwx211, vwx221, bge, bgf)
new_esEs9(vwx212, vwx222, ty_Ordering) → new_esEs17(vwx212, vwx222)
new_compare14(vwx300, vwx400, ty_Float) → new_compare8(vwx300, vwx400)
new_esEs26(vwx211, vwx221, ty_Int) → new_esEs14(vwx211, vwx221)
new_asAs(False, vwx47) → False
new_esEs10(vwx211, vwx221, app(app(app(ty_@3, bgg), bgh), bha)) → new_esEs6(vwx211, vwx221, bgg, bgh, bha)
new_lt7(vwx300, vwx400) → new_esEs8(new_compare17(vwx300, vwx400))
new_primMulInt(Pos(vwx3000), Neg(vwx4010)) → Neg(new_primMulNat0(vwx3000, vwx4010))
new_primMulInt(Neg(vwx3000), Pos(vwx4010)) → Neg(new_primMulNat0(vwx3000, vwx4010))
new_ltEs13(Right(vwx300), Right(vwx400), fb, ty_Float) → new_ltEs11(vwx300, vwx400)
new_esEs4(Just(vwx210), Just(vwx220), app(ty_Ratio, cgc)) → new_esEs12(vwx210, vwx220, cgc)
new_esEs5(Right(vwx210), Right(vwx220), ccf, ty_Ordering) → new_esEs17(vwx210, vwx220)
new_ltEs13(Left(vwx300), Right(vwx400), fb, ea) → True
new_primMulNat0(Succ(vwx30000), Zero) → Zero
new_primMulNat0(Zero, Succ(vwx40100)) → Zero
new_lt18(vwx300, vwx400) → new_esEs8(new_compare6(vwx300, vwx400))
new_esEs18([], [], cea) → True
new_esEs25(vwx21, vwx22, ty_@0) → new_esEs16(vwx21, vwx22)
new_compare14(vwx300, vwx400, app(ty_Ratio, cag)) → new_compare18(vwx300, vwx400, cag)
new_esEs4(Just(vwx210), Just(vwx220), app(ty_[], chb)) → new_esEs18(vwx210, vwx220, chb)
new_esEs9(vwx212, vwx222, app(ty_Maybe, bfb)) → new_esEs4(vwx212, vwx222, bfb)
new_esEs5(Left(vwx210), Left(vwx220), app(app(app(ty_@3, cbh), cca), ccb), cbd) → new_esEs6(vwx210, vwx220, cbh, cca, ccb)
new_lt11(vwx300, vwx400) → new_esEs8(new_compare12(vwx300, vwx400))
new_esEs9(vwx212, vwx222, ty_Integer) → new_esEs20(vwx212, vwx222)
new_ltEs6(Just(vwx300), Just(vwx400), ty_Char) → new_ltEs15(vwx300, vwx400)
new_ltEs19(vwx302, vwx402, ty_Double) → new_ltEs12(vwx302, vwx402)
new_not(EQ) → new_not0
new_lt19(vwx301, vwx401, app(app(ty_Either, bac), bad)) → new_lt12(vwx301, vwx401, bac, bad)
new_compare13(@0, @0) → EQ
new_esEs13(False, False) → True
new_ltEs13(Left(vwx300), Left(vwx400), app(app(app(ty_@3, ee), ef), eg), ea) → new_ltEs14(vwx300, vwx400, ee, ef, eg)
new_esEs5(Right(vwx210), Right(vwx220), ccf, ty_Double) → new_esEs15(vwx210, vwx220)
new_esEs25(vwx21, vwx22, app(app(app(ty_@3, bef), beg), beh)) → new_esEs6(vwx21, vwx22, bef, beg, beh)
new_lt19(vwx301, vwx401, app(ty_Maybe, hh)) → new_lt5(vwx301, vwx401, hh)
new_esEs5(Left(vwx210), Left(vwx220), ty_Bool, cbd) → new_esEs13(vwx210, vwx220)
new_esEs16(@0, @0) → True
new_lt12(vwx300, vwx400, df, dg) → new_esEs8(new_compare5(vwx300, vwx400, df, dg))
new_compare112(vwx300, vwx400, False, bbc, bbd, bbe) → GT
new_esEs10(vwx211, vwx221, ty_Ordering) → new_esEs17(vwx211, vwx221)
new_esEs17(LT, EQ) → False
new_esEs17(EQ, LT) → False
new_ltEs19(vwx302, vwx402, ty_Int) → new_ltEs16(vwx302, vwx402)
new_ltEs13(Right(vwx300), Left(vwx400), fb, ea) → False
new_lt4(vwx300, vwx400, app(ty_Maybe, bdb)) → new_lt5(vwx300, vwx400, bdb)
new_ltEs13(Left(vwx300), Left(vwx400), ty_Char, ea) → new_ltEs15(vwx300, vwx400)
new_lt19(vwx301, vwx401, app(app(app(ty_@3, bae), baf), bag)) → new_lt13(vwx301, vwx401, bae, baf, bag)
new_esEs26(vwx211, vwx221, app(ty_Ratio, chh)) → new_esEs12(vwx211, vwx221, chh)
new_ltEs6(Just(vwx300), Just(vwx400), ty_Ordering) → new_ltEs7(vwx300, vwx400)
new_lt19(vwx301, vwx401, ty_@0) → new_lt17(vwx301, vwx401)
new_ltEs6(Nothing, Nothing, cfg) → True
new_esEs14(vwx21, vwx22) → new_primEqInt(vwx21, vwx22)
new_lt14(vwx300, vwx400, bbf, bbg) → new_esEs8(new_compare19(vwx300, vwx400, bbf, bbg))
new_ltEs5(vwx301, vwx401, app(ty_[], bcb)) → new_ltEs10(vwx301, vwx401, bcb)
new_ltEs13(Right(vwx300), Right(vwx400), fb, app(app(ty_@2, gc), gd)) → new_ltEs4(vwx300, vwx400, gc, gd)
new_primCompAux1(vwx300, vwx400, vwx48, cb) → new_primCompAux0(vwx48, new_compare14(vwx300, vwx400, cb))
new_esEs24(vwx210, vwx220, ty_Ordering) → new_esEs17(vwx210, vwx220)
new_esEs4(Just(vwx210), Just(vwx220), ty_Char) → new_esEs19(vwx210, vwx220)
new_esEs5(Right(vwx210), Right(vwx220), ccf, app(ty_Maybe, cch)) → new_esEs4(vwx210, vwx220, cch)
new_ltEs13(Left(vwx300), Left(vwx400), app(ty_Ratio, cah), ea) → new_ltEs9(vwx300, vwx400, cah)
new_esEs26(vwx211, vwx221, ty_Ordering) → new_esEs17(vwx211, vwx221)
new_esEs11(vwx210, vwx220, app(app(ty_Either, bhg), bhh)) → new_esEs5(vwx210, vwx220, bhg, bhh)
new_compare14(vwx300, vwx400, ty_Int) → new_compare7(vwx300, vwx400)
new_lt8(vwx300, vwx400, cff) → new_esEs8(new_compare18(vwx300, vwx400, cff))
new_not(LT) → new_not0
new_esEs25(vwx21, vwx22, ty_Float) → new_esEs21(vwx21, vwx22)
new_esEs26(vwx211, vwx221, ty_Float) → new_esEs21(vwx211, vwx221)
new_esEs27(vwx210, vwx220, ty_Ordering) → new_esEs17(vwx210, vwx220)
new_esEs5(Left(vwx210), Left(vwx220), app(app(ty_Either, cbf), cbg), cbd) → new_esEs5(vwx210, vwx220, cbf, cbg)
new_esEs9(vwx212, vwx222, ty_Int) → new_esEs14(vwx212, vwx222)
new_lt19(vwx301, vwx401, ty_Double) → new_lt11(vwx301, vwx401)
new_lt4(vwx300, vwx400, app(app(ty_@2, beb), bec)) → new_lt14(vwx300, vwx400, beb, bec)
new_esEs4(Just(vwx210), Just(vwx220), app(app(ty_@2, chc), chd)) → new_esEs7(vwx210, vwx220, chc, chd)
new_esEs11(vwx210, vwx220, ty_Bool) → new_esEs13(vwx210, vwx220)
new_compare29(vwx300, vwx400, False) → new_compare111(vwx300, vwx400, new_ltEs8(vwx300, vwx400))
new_ltEs7(EQ, LT) → False
new_esEs22(vwx211, vwx221, ty_Int) → new_esEs14(vwx211, vwx221)
new_ltEs7(LT, LT) → True
new_esEs8(EQ) → False
new_esEs5(Right(vwx210), Right(vwx220), ccf, app(app(ty_@2, cdg), cdh)) → new_esEs7(vwx210, vwx220, cdg, cdh)
new_primPlusNat0(Succ(vwx6600), Succ(vwx401000)) → Succ(Succ(new_primPlusNat0(vwx6600, vwx401000)))
new_esEs9(vwx212, vwx222, app(app(app(ty_@3, bfe), bff), bfg)) → new_esEs6(vwx212, vwx222, bfe, bff, bfg)
new_esEs4(Just(vwx210), Just(vwx220), ty_Integer) → new_esEs20(vwx210, vwx220)
new_esEs9(vwx212, vwx222, app(ty_Ratio, bfa)) → new_esEs12(vwx212, vwx222, bfa)
new_esEs9(vwx212, vwx222, ty_Char) → new_esEs19(vwx212, vwx222)
new_esEs9(vwx212, vwx222, ty_Double) → new_esEs15(vwx212, vwx222)
new_asAs(True, vwx47) → vwx47
new_esEs11(vwx210, vwx220, app(ty_Ratio, bhe)) → new_esEs12(vwx210, vwx220, bhe)
new_ltEs7(LT, GT) → True
new_esEs13(True, True) → True
new_esEs10(vwx211, vwx221, app(ty_Ratio, bgc)) → new_esEs12(vwx211, vwx221, bgc)
new_ltEs5(vwx301, vwx401, ty_Integer) → new_ltEs18(vwx301, vwx401)
new_ltEs5(vwx301, vwx401, app(ty_Maybe, bca)) → new_ltEs6(vwx301, vwx401, bca)
new_ltEs16(vwx30, vwx40) → new_not(new_compare7(vwx30, vwx40))
new_ltEs15(vwx30, vwx40) → new_not(new_compare26(vwx30, vwx40))
new_esEs17(GT, GT) → True
new_esEs26(vwx211, vwx221, ty_Double) → new_esEs15(vwx211, vwx221)
new_esEs4(Just(vwx210), Just(vwx220), ty_Int) → new_esEs14(vwx210, vwx220)
new_lt20(vwx300, vwx400, ty_Char) → new_lt15(vwx300, vwx400)
new_lt19(vwx301, vwx401, ty_Float) → new_lt10(vwx301, vwx401)
new_ltEs13(Right(vwx300), Right(vwx400), fb, ty_Int) → new_ltEs16(vwx300, vwx400)
new_esEs4(Just(vwx210), Just(vwx220), ty_Float) → new_esEs21(vwx210, vwx220)
new_lt19(vwx301, vwx401, ty_Int) → new_lt16(vwx301, vwx401)
new_ltEs19(vwx302, vwx402, ty_Ordering) → new_ltEs7(vwx302, vwx402)
new_ltEs13(Right(vwx300), Right(vwx400), fb, ty_Char) → new_ltEs15(vwx300, vwx400)
new_esEs4(Just(vwx210), Just(vwx220), ty_Double) → new_esEs15(vwx210, vwx220)
new_esEs4(Just(vwx210), Just(vwx220), ty_Ordering) → new_esEs17(vwx210, vwx220)
new_lt4(vwx300, vwx400, app(app(ty_Either, bde), bdf)) → new_lt12(vwx300, vwx400, bde, bdf)
new_lt19(vwx301, vwx401, app(ty_Ratio, cfe)) → new_lt8(vwx301, vwx401, cfe)
new_ltEs5(vwx301, vwx401, ty_Double) → new_ltEs12(vwx301, vwx401)
new_esEs4(Just(vwx210), Just(vwx220), ty_@0) → new_esEs16(vwx210, vwx220)
new_esEs5(Left(vwx210), Left(vwx220), ty_Ordering, cbd) → new_esEs17(vwx210, vwx220)
new_lt4(vwx300, vwx400, app(ty_Ratio, bee)) → new_lt8(vwx300, vwx400, bee)
new_esEs5(Right(vwx210), Right(vwx220), ccf, ty_Integer) → new_esEs20(vwx210, vwx220)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs26(vwx211, vwx221, ty_Bool) → new_esEs13(vwx211, vwx221)
new_primCompAux0(vwx52, EQ) → vwx52
new_ltEs6(Just(vwx300), Just(vwx400), app(app(ty_@2, bh), ca)) → new_ltEs4(vwx300, vwx400, bh, ca)
new_lt5(vwx300, vwx400, de) → new_esEs8(new_compare15(vwx300, vwx400, de))
new_lt19(vwx301, vwx401, ty_Char) → new_lt15(vwx301, vwx401)
new_compare15(vwx300, vwx400, de) → new_compare24(vwx300, vwx400, new_esEs4(vwx300, vwx400, de), de)
new_lt4(vwx300, vwx400, ty_@0) → new_lt17(vwx300, vwx400)
new_ltEs6(Just(vwx300), Just(vwx400), ty_Integer) → new_ltEs18(vwx300, vwx400)
new_esEs25(vwx21, vwx22, app(ty_Ratio, cbb)) → new_esEs12(vwx21, vwx22, cbb)
new_esEs10(vwx211, vwx221, app(ty_Maybe, bgd)) → new_esEs4(vwx211, vwx221, bgd)
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primCmpInt(Neg(Succ(vwx3000)), Pos(vwx400)) → LT

The set Q consists of the following terms:

new_esEs5(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs17(LT, GT)
new_esEs17(GT, LT)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_ltEs6(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_esEs25(x0, x1, ty_@0)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_primPlusNat1(Zero, x0)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs6(Just(x0), Just(x1), ty_Double)
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_esEs18([], [], x0)
new_primPlusNat1(Succ(x0), x1)
new_pePe(True, x0, x1, x2, x3)
new_compare18(:%(x0, x1), :%(x2, x3), ty_Integer)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_lt4(x0, x1, app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs23(x0, x1, ty_Integer)
new_esEs17(LT, LT)
new_esEs24(x0, x1, ty_@0)
new_lt20(x0, x1, ty_Double)
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_compare14(x0, x1, ty_Float)
new_lt20(x0, x1, ty_Integer)
new_lt4(x0, x1, ty_Float)
new_ltEs12(x0, x1)
new_compare14(x0, x1, app(app(ty_Either, x2), x3))
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt4(x0, x1, ty_Int)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_compare210(x0, x1, False)
new_ltEs7(EQ, EQ)
new_esEs10(x0, x1, ty_Double)
new_lt4(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs5(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs5(Right(x0), Right(x1), x2, app(ty_[], x3))
new_compare24(x0, x1, False, x2)
new_esEs5(Right(x0), Right(x1), x2, ty_@0)
new_esEs5(Right(x0), Right(x1), x2, ty_Char)
new_esEs10(x0, x1, ty_@0)
new_esEs8(LT)
new_primCompAux0(x0, GT)
new_esEs25(x0, x1, ty_Ordering)
new_esEs10(x0, x1, ty_Char)
new_lt8(x0, x1, x2)
new_esEs17(EQ, GT)
new_esEs17(GT, EQ)
new_ltEs7(EQ, LT)
new_ltEs7(LT, EQ)
new_ltEs13(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs11(x0, x1, ty_Int)
new_primEqNat0(Succ(x0), Zero)
new_esEs10(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs19(x0, x1, ty_Char)
new_ltEs8(True, True)
new_ltEs13(Right(x0), Right(x1), x2, ty_@0)
new_ltEs5(x0, x1, ty_Double)
new_lt19(x0, x1, ty_Double)
new_esEs16(@0, @0)
new_compare14(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs6(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs24(x0, x1, ty_Int)
new_compare113(x0, x1, True)
new_lt20(x0, x1, ty_Float)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs5(Left(x0), Left(x1), ty_Char, x2)
new_esEs27(x0, x1, ty_Double)
new_esEs26(x0, x1, ty_Bool)
new_asAs(True, x0)
new_ltEs7(LT, LT)
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_compare26(Char(x0), Char(x1))
new_esEs17(GT, GT)
new_compare14(x0, x1, ty_Ordering)
new_compare14(x0, x1, ty_Integer)
new_esEs4(Just(x0), Just(x1), ty_Float)
new_esEs27(x0, x1, ty_Bool)
new_esEs5(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_ltEs13(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs5(x0, x1, app(ty_Maybe, x2))
new_esEs27(x0, x1, ty_Float)
new_ltEs13(Left(x0), Left(x1), ty_Char, x2)
new_esEs5(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs6(Just(x0), Just(x1), ty_Float)
new_compare16(x0, x1)
new_esEs27(x0, x1, ty_Ordering)
new_primEqNat0(Zero, Zero)
new_lt4(x0, x1, app(ty_Ratio, x2))
new_compare111(x0, x1, False)
new_esEs10(x0, x1, ty_Float)
new_ltEs13(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs27(x0, x1, ty_Int)
new_compare10(x0, x1, False, x2)
new_esEs9(x0, x1, ty_Double)
new_esEs11(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs4(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs19(x0, x1, ty_Int)
new_esEs26(x0, x1, ty_Float)
new_compare14(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs5(x0, x1, ty_Bool)
new_ltEs19(x0, x1, ty_Ordering)
new_esEs8(EQ)
new_compare28(x0, x1, False, x2, x3)
new_lt4(x0, x1, ty_@0)
new_esEs5(Right(x0), Right(x1), x2, ty_Float)
new_primMulNat0(Zero, Zero)
new_esEs11(x0, x1, app(ty_Maybe, x2))
new_esEs13(False, False)
new_esEs4(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs24(x0, x1, ty_Integer)
new_esEs10(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs11(x0, x1, app(ty_[], x2))
new_esEs14(x0, x1)
new_compare10(x0, x1, True, x2)
new_compare14(x0, x1, app(ty_Ratio, x2))
new_esEs5(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs24(x0, x1, app(ty_[], x2))
new_ltEs13(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_lt4(x0, x1, app(ty_Maybe, x2))
new_ltEs19(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, app(ty_Maybe, x2))
new_lt12(x0, x1, x2, x3)
new_esEs27(x0, x1, app(ty_[], x2))
new_primMulInt(Pos(x0), Pos(x1))
new_esEs11(x0, x1, ty_Integer)
new_lt20(x0, x1, app(ty_[], x2))
new_esEs26(x0, x1, ty_Ordering)
new_esEs4(Just(x0), Just(x1), ty_Ordering)
new_esEs4(Just(x0), Just(x1), ty_@0)
new_lt20(x0, x1, ty_Char)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs5(x0, x1, ty_Float)
new_compare14(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs13(Right(x0), Right(x1), x2, ty_Int)
new_compare28(x0, x1, True, x2, x3)
new_esEs5(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs4(Just(x0), Just(x1), ty_Integer)
new_compare14(x0, x1, app(ty_[], x2))
new_esEs18(:(x0, x1), :(x2, x3), x4)
new_compare7(x0, x1)
new_esEs7(@2(x0, x1), @2(x2, x3), x4, x5)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs11(x0, x1, ty_Float)
new_esEs5(Right(x0), Right(x1), x2, ty_Double)
new_ltEs6(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs5(Left(x0), Left(x1), ty_Bool, x2)
new_lt20(x0, x1, ty_@0)
new_lt19(x0, x1, app(ty_Ratio, x2))
new_pePe(False, x0, x1, x2, x3)
new_lt18(x0, x1)
new_lt5(x0, x1, x2)
new_esEs15(Double(x0, x1), Double(x2, x3))
new_esEs4(Just(x0), Just(x1), ty_Char)
new_ltEs13(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs10(x0, x1, app(ty_Ratio, x2))
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs25(x0, x1, app(ty_[], x2))
new_esEs25(x0, x1, ty_Float)
new_asAs(False, x0)
new_compare(:(x0, x1), [], x2)
new_primPlusNat0(Succ(x0), Zero)
new_lt7(x0, x1)
new_esEs9(x0, x1, ty_Float)
new_esEs11(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_ltEs13(Right(x0), Right(x1), x2, ty_Char)
new_ltEs19(x0, x1, ty_Bool)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_esEs5(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_esEs22(x0, x1, ty_Int)
new_lt19(x0, x1, ty_Ordering)
new_lt10(x0, x1)
new_lt4(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs4(Just(x0), Just(x1), ty_Int)
new_esEs24(x0, x1, ty_Bool)
new_compare29(x0, x1, True)
new_ltEs11(x0, x1)
new_compare14(x0, x1, ty_Double)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs11(x0, x1, app(ty_Ratio, x2))
new_lt4(x0, x1, app(ty_[], x2))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_compare6(Integer(x0), Integer(x1))
new_not0
new_compare11(x0, x1, True, x2, x3)
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primPlusNat0(Zero, Zero)
new_esEs25(x0, x1, ty_Char)
new_compare12(Double(x0, x1), Double(x2, x3))
new_esEs9(x0, x1, ty_Bool)
new_ltEs13(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs27(x0, x1, ty_Integer)
new_ltEs13(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_ltEs13(Right(x0), Right(x1), x2, ty_Integer)
new_compare([], :(x0, x1), x2)
new_ltEs13(Right(x0), Right(x1), x2, app(ty_[], x3))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_esEs5(Right(x0), Right(x1), x2, ty_Integer)
new_ltEs18(x0, x1)
new_compare24(x0, x1, True, x2)
new_sr0(x0, x1)
new_esEs26(x0, x1, ty_Int)
new_compare25(x0, x1, True, x2, x3, x4)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_esEs5(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs23(x0, x1, ty_Int)
new_lt19(x0, x1, app(ty_[], x2))
new_primMulNat0(Zero, Succ(x0))
new_ltEs6(Just(x0), Just(x1), ty_Integer)
new_ltEs6(Just(x0), Nothing, x1)
new_ltEs5(x0, x1, app(ty_Ratio, x2))
new_esEs27(x0, x1, ty_@0)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_ltEs6(Just(x0), Just(x1), ty_Bool)
new_primPlusNat0(Zero, Succ(x0))
new_esEs11(x0, x1, ty_Char)
new_esEs24(x0, x1, ty_Ordering)
new_esEs18([], :(x0, x1), x2)
new_ltEs15(x0, x1)
new_ltEs13(Left(x0), Left(x1), ty_Double, x2)
new_not(GT)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs13(Right(x0), Right(x1), x2, ty_Double)
new_ltEs13(Left(x0), Left(x1), ty_Bool, x2)
new_ltEs8(False, False)
new_lt4(x0, x1, ty_Char)
new_esEs8(GT)
new_ltEs13(Left(x0), Left(x1), ty_@0, x2)
new_esEs9(x0, x1, app(app(ty_@2, x2), x3))
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_lt11(x0, x1)
new_esEs9(x0, x1, ty_Integer)
new_ltEs8(False, True)
new_ltEs8(True, False)
new_lt19(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, ty_Double)
new_ltEs5(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs11(x0, x1, ty_Ordering)
new_lt17(x0, x1)
new_esEs9(x0, x1, ty_Int)
new_compare13(@0, @0)
new_lt19(x0, x1, ty_Float)
new_esEs5(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_ltEs6(Just(x0), Just(x1), ty_Char)
new_esEs9(x0, x1, app(app(ty_Either, x2), x3))
new_compare14(x0, x1, ty_@0)
new_ltEs6(Just(x0), Just(x1), app(ty_[], x2))
new_compare14(x0, x1, ty_Bool)
new_ltEs5(x0, x1, app(ty_[], x2))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_lt15(x0, x1)
new_ltEs6(Nothing, Nothing, x0)
new_esEs5(Left(x0), Left(x1), ty_Float, x2)
new_esEs26(x0, x1, ty_Integer)
new_lt16(x0, x1)
new_compare11(x0, x1, False, x2, x3)
new_primEqInt(Neg(Zero), Neg(Zero))
new_esEs5(Left(x0), Right(x1), x2, x3)
new_esEs5(Right(x0), Left(x1), x2, x3)
new_ltEs13(Right(x0), Right(x1), x2, ty_Float)
new_lt19(x0, x1, ty_Bool)
new_esEs25(x0, x1, ty_Int)
new_primCompAux0(x0, LT)
new_esEs24(x0, x1, ty_Double)
new_ltEs5(x0, x1, ty_Integer)
new_esEs26(x0, x1, app(ty_[], x2))
new_esEs10(x0, x1, app(app(ty_@2, x2), x3))
new_primCompAux1(x0, x1, x2, x3)
new_ltEs13(Right(x0), Right(x1), x2, ty_Ordering)
new_compare9(x0, x1, x2, x3, x4)
new_ltEs13(Left(x0), Left(x1), ty_Int, x2)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs5(Left(x0), Left(x1), ty_@0, x2)
new_esEs24(x0, x1, ty_Char)
new_compare19(x0, x1, x2, x3)
new_compare15(x0, x1, x2)
new_compare27(x0, x1, True, x2, x3)
new_ltEs14(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs22(x0, x1, ty_Integer)
new_primCmpNat0(Zero, Succ(x0))
new_esEs4(Just(x0), Just(x1), ty_Double)
new_ltEs6(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, ty_Integer)
new_compare110(x0, x1, True, x2, x3)
new_ltEs6(Just(x0), Just(x1), ty_@0)
new_lt19(x0, x1, ty_Int)
new_esEs10(x0, x1, ty_Int)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_esEs18(:(x0, x1), [], x2)
new_lt4(x0, x1, ty_Bool)
new_lt4(x0, x1, ty_Integer)
new_lt4(x0, x1, ty_Ordering)
new_ltEs13(Left(x0), Left(x1), ty_Float, x2)
new_ltEs19(x0, x1, ty_Double)
new_esEs4(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_lt20(x0, x1, ty_Ordering)
new_compare8(Float(x0, x1), Float(x2, x3))
new_ltEs13(Left(x0), Left(x1), ty_Ordering, x2)
new_compare14(x0, x1, ty_Char)
new_esEs9(x0, x1, app(ty_[], x2))
new_ltEs5(x0, x1, app(app(ty_Either, x2), x3))
new_primMulNat0(Succ(x0), Succ(x1))
new_ltEs4(@2(x0, x1), @2(x2, x3), x4, x5)
new_ltEs13(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_ltEs5(x0, x1, app(app(ty_@2, x2), x3))
new_esEs5(Right(x0), Right(x1), x2, ty_Int)
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_esEs26(x0, x1, ty_@0)
new_lt19(x0, x1, ty_Integer)
new_primCmpNat0(Zero, Zero)
new_ltEs13(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_ltEs9(x0, x1, x2)
new_esEs4(Nothing, Just(x0), x1)
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs5(x0, x1, ty_Int)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_compare14(x0, x1, ty_Int)
new_esEs10(x0, x1, ty_Bool)
new_compare(:(x0, x1), :(x2, x3), x4)
new_esEs9(x0, x1, ty_@0)
new_compare110(x0, x1, False, x2, x3)
new_esEs25(x0, x1, ty_Integer)
new_ltEs5(x0, x1, ty_Char)
new_ltEs13(Left(x0), Right(x1), x2, x3)
new_ltEs13(Right(x0), Left(x1), x2, x3)
new_esEs24(x0, x1, ty_Float)
new_ltEs13(Right(x0), Right(x1), x2, ty_Bool)
new_compare25(x0, x1, False, x2, x3, x4)
new_esEs5(Left(x0), Left(x1), ty_Ordering, x2)
new_ltEs13(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs9(x0, x1, app(ty_Ratio, x2))
new_esEs9(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs5(Left(x0), Left(x1), ty_Integer, x2)
new_primMulNat0(Succ(x0), Zero)
new_esEs5(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_compare210(x0, x1, True)
new_ltEs19(x0, x1, ty_@0)
new_ltEs10(x0, x1, x2)
new_ltEs7(LT, GT)
new_ltEs7(GT, LT)
new_esEs13(False, True)
new_esEs13(True, False)
new_esEs4(Nothing, Nothing, x0)
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_esEs10(x0, x1, ty_Integer)
new_lt6(x0, x1)
new_primCmpNat0(Succ(x0), Succ(x1))
new_esEs5(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs13(Left(x0), Left(x1), ty_Integer, x2)
new_esEs6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_ltEs19(x0, x1, ty_Float)
new_primEqNat0(Zero, Succ(x0))
new_not(EQ)
new_ltEs16(x0, x1)
new_esEs13(True, True)
new_lt9(x0, x1, x2)
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_esEs19(Char(x0), Char(x1))
new_esEs9(x0, x1, ty_Char)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_compare112(x0, x1, True, x2, x3, x4)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_esEs4(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs10(x0, x1, app(ty_Maybe, x2))
new_ltEs5(x0, x1, ty_Ordering)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs20(Integer(x0), Integer(x1))
new_esEs11(x0, x1, ty_Double)
new_esEs25(x0, x1, ty_Bool)
new_lt14(x0, x1, x2, x3)
new_compare27(x0, x1, False, x2, x3)
new_sr(Integer(x0), Integer(x1))
new_esEs10(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs6(Just(x0), Just(x1), app(ty_Maybe, x2))
new_compare112(x0, x1, False, x2, x3, x4)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs4(Just(x0), Nothing, x1)
new_compare111(x0, x1, True)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_compare([], [], x0)
new_ltEs6(Just(x0), Just(x1), ty_Ordering)
new_lt13(x0, x1, x2, x3, x4)
new_esEs4(Just(x0), Just(x1), ty_Bool)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs26(x0, x1, ty_Char)
new_esEs11(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs6(Just(x0), Just(x1), ty_Int)
new_esEs9(x0, x1, ty_Ordering)
new_esEs4(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_compare113(x0, x1, False)
new_ltEs6(Nothing, Just(x0), x1)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs25(x0, x1, ty_Double)
new_ltEs5(x0, x1, ty_@0)
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_esEs21(Float(x0, x1), Float(x2, x3))
new_esEs5(Left(x0), Left(x1), ty_Int, x2)
new_lt19(x0, x1, ty_Char)
new_primEqInt(Pos(Zero), Pos(Zero))
new_esEs12(:%(x0, x1), :%(x2, x3), x4)
new_esEs5(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs4(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_compare18(:%(x0, x1), :%(x2, x3), ty_Int)
new_lt19(x0, x1, ty_@0)
new_esEs27(x0, x1, ty_Char)
new_esEs11(x0, x1, ty_Bool)
new_lt20(x0, x1, ty_Bool)
new_primPlusNat0(Succ(x0), Succ(x1))
new_esEs17(EQ, EQ)
new_compare29(x0, x1, False)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs10(x0, x1, ty_Ordering)
new_esEs17(EQ, LT)
new_esEs17(LT, EQ)
new_esEs11(x0, x1, ty_@0)
new_primCmpNat0(Succ(x0), Zero)
new_ltEs7(GT, EQ)
new_compare5(x0, x1, x2, x3)
new_ltEs7(EQ, GT)
new_primCompAux0(x0, EQ)
new_not(LT)
new_ltEs7(GT, GT)
new_compare17(x0, x1)
new_ltEs13(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs5(Left(x0), Left(x1), ty_Double, x2)
new_esEs5(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_lt20(x0, x1, ty_Int)
new_ltEs17(x0, x1)
new_lt4(x0, x1, ty_Double)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_esEs9(x0, x1, app(ty_Maybe, x2))

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

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