YES 9.700000000000001 H-Termination proof of /home/matraf/haskell/eval_FullyBlown_Fast/List.hs
H-Termination of the given Haskell-Program with start terms could successfully be proven:



↳ HASKELL
  ↳ CR

mainModule List
  ((insert :: (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 List where
  import qualified Maybe
import qualified Prelude
  insert :: Ord a => a  ->  [a]  ->  [a]
insert e ls = insertBy compare e ls

  insertBy :: (a  ->  a  ->  Ordering)  ->  a  ->  [a]  ->  [a]
insertBy _ x [] = x : []
insertBy cmp x ys@(y : ys') = 
case cmp x y of
  GT-> y : insertBy cmp x ys'
  _-> x : ys


module Maybe where
  import qualified List
import qualified Prelude


Case Reductions:
The following Case expression
case cmp x y of
 GT → y : insertBy cmp x ys'
 _ → x : ys

is transformed to
insertBy0 y cmp x ys' ys GT = y : insertBy cmp x ys'
insertBy0 y cmp x ys' ys _ = x : ys

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 List
  ((insert :: (Ord a, Ord b) => Either b a  ->  [Either b a]  ->  [Either b a]) :: (Ord b, Ord a) => Either b a  ->  [Either b a]  ->  [Either b a])

module List where
  import qualified Maybe
import qualified Prelude
  insert :: Ord a => a  ->  [a]  ->  [a]
insert e ls = insertBy compare e ls

  insertBy :: (a  ->  a  ->  Ordering)  ->  a  ->  [a]  ->  [a]
insertBy _ x [] = x : []
insertBy cmp x ys@(y : ys') = insertBy0 y cmp x ys' ys (cmp x y)

  
insertBy0 y cmp x ys' ys GT = y : insertBy cmp x ys'
insertBy0 y cmp x ys' ys _ = x : ys


module Maybe where
  import qualified List
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 List
  ((insert :: (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 List where
  import qualified Maybe
import qualified Prelude
  insert :: Ord a => a  ->  [a]  ->  [a]
insert e ls = insertBy compare e ls

  insertBy :: (a  ->  a  ->  Ordering)  ->  a  ->  [a]  ->  [a]
insertBy _ x [] = x : []
insertBy cmp x ys@(y : ys') = insertBy0 y cmp x ys' ys (cmp x y)

  
insertBy0 y cmp x ys' ys GT = y : insertBy cmp x ys'
insertBy0 y cmp x ys' ys _ = x : ys


module Maybe where
  import qualified List
import qualified Prelude


Replaced joker patterns by fresh variables and removed binding patterns.
Binding Reductions:
The bind variable of the following binding Pattern
ys@(vy : vz)

is replaced by the following term
vy : vz



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

mainModule List
  ((insert :: (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 List where
  import qualified Maybe
import qualified Prelude
  insert :: Ord a => a  ->  [a]  ->  [a]
insert e ls = insertBy compare e ls

  insertBy :: (a  ->  a  ->  Ordering)  ->  a  ->  [a]  ->  [a]
insertBy vx x [] = x : []
insertBy cmp x (vy : vz) = insertBy0 vy cmp x vz (vy : vz) (cmp x vy)

  
insertBy0 y cmp x ys' ys GT = y : insertBy cmp x ys'
insertBy0 y cmp x ys' ys vw = x : ys


module Maybe where
  import qualified List
import qualified Prelude


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

is transformed to
compare x y = compare3 x y

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

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

compare0 x y True = GT

compare3 x y = compare2 x y (x == y)

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

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

gcd'0 x y = gcd' y (x `rem` y)

gcd'1 True x vuw = x
gcd'1 vux vuy vuz = gcd'0 vuy vuz

gcd'2 x vuw = gcd'1 (vuw == 0) x vuw
gcd'2 vvu vvv = gcd'0 vvu vvv

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 vvw vvx = gcd3 vvw vvx
gcd x y = gcd0 x y

gcd0 x y = 
gcd' (abs x) (abs y)
where 
gcd' x vuw = gcd'2 x vuw
gcd' x y = gcd'0 x y
gcd'0 x y = gcd' y (x `rem` y)
gcd'1 True x vuw = x
gcd'1 vux vuy vuz = gcd'0 vuy vuz
gcd'2 x vuw = gcd'1 (vuw == 0) x vuw
gcd'2 vvu vvv = gcd'0 vvu vvv

gcd1 True vvw vvx = error []
gcd1 vvy vvz vwu = gcd0 vvz vwu

gcd2 True vvw vvx = gcd1 (vvx == 0) vvw vvx
gcd2 vwv vww vwx = gcd0 vww vwx

gcd3 vvw vvx = gcd2 (vvw == 0) vvw vvx
gcd3 vwy vwz = gcd0 vwy vwz

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 List
  ((insert :: (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 List where
  import qualified Maybe
import qualified Prelude
  insert :: Ord a => a  ->  [a]  ->  [a]
insert e ls = insertBy compare e ls

  insertBy :: (a  ->  a  ->  Ordering)  ->  a  ->  [a]  ->  [a]
insertBy vx x [] = x : []
insertBy cmp x (vy : vz) = insertBy0 vy cmp x vz (vy : vz) (cmp x vy)

  
insertBy0 y cmp x ys' ys GT = y : insertBy cmp x ys'
insertBy0 y cmp x ys' ys vw = x : ys


module Maybe where
  import qualified List
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 vxu vxv x y True = x `quot` reduce2D vxu vxv :% (y `quot` reduce2D vxu vxv)

reduce2Reduce1 vxu vxv x y True = error []
reduce2Reduce1 vxu vxv x y False = reduce2Reduce0 vxu vxv x y otherwise

reduce2D vxu vxv = gcd vxu vxv

The bindings of the following Let/Where expression
gcd' (abs x) (abs y)
where 
gcd' x vuw = gcd'2 x vuw
gcd' x y = gcd'0 x y
gcd'0 x y = gcd' y (x `rem` y)
gcd'1 True x vuw = x
gcd'1 vux vuy vuz = gcd'0 vuy vuz
gcd'2 x vuw = gcd'1 (vuw == 0) x vuw
gcd'2 vvu vvv = gcd'0 vvu vvv

are unpacked to the following functions on top level
gcd0Gcd'1 True x vuw = x
gcd0Gcd'1 vux vuy vuz = gcd0Gcd'0 vuy vuz

gcd0Gcd'2 x vuw = gcd0Gcd'1 (vuw == 0) x vuw
gcd0Gcd'2 vvu vvv = gcd0Gcd'0 vvu vvv

gcd0Gcd' x vuw = gcd0Gcd'2 x vuw
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 List
  ((insert :: (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 List where
  import qualified Maybe
import qualified Prelude
  insert :: Ord a => a  ->  [a]  ->  [a]
insert e ls = insertBy compare e ls

  insertBy :: (a  ->  a  ->  Ordering)  ->  a  ->  [a]  ->  [a]
insertBy vx x [] = x : []
insertBy cmp x (vy : vz) = insertBy0 vy cmp x vz (vy : vz) (cmp x vy)

  
insertBy0 y cmp x ys' ys GT = y : insertBy cmp x ys'
insertBy0 y cmp x ys' ys vw = x : ys


module Maybe where
  import qualified List
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 List
  (insert :: (Ord b, Ord a) => Either b a  ->  [Either b a]  ->  [Either b a])

module List where
  import qualified Maybe
import qualified Prelude
  insert :: Ord a => a  ->  [a]  ->  [a]
insert e ls = insertBy compare e ls

  insertBy :: (a  ->  a  ->  Ordering)  ->  a  ->  [a]  ->  [a]
insertBy vx x [] = x : []
insertBy cmp x (vy : vz) = insertBy0 vy cmp x vz (vy : vz) (cmp x vy)

  
insertBy0 y cmp x ys' ys GT = y : insertBy cmp x ys'
insertBy0 y cmp x ys' ys vw = x : ys


module Maybe where
  import qualified List
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
                              ↳ QDP

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

new_primEqNat(Succ(vxw3000), Succ(vxw40000)) → new_primEqNat(vxw3000, vxw40000)

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
                              ↳ QDP

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

new_primPlusNat(Succ(vxw6200), Succ(vxw4000000)) → new_primPlusNat(vxw6200, vxw4000000)

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
                              ↳ QDP

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

new_primMulNat(Succ(vxw30000), Succ(vxw400000)) → new_primMulNat(vxw30000, Succ(vxw400000))

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
                              ↳ QDP

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

new_primCmpNat(Succ(vxw1100), Succ(vxw1000)) → new_primCmpNat(vxw1100, vxw1000)

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
                              ↳ QDP

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

new_esEs(@2(vxw300, vxw301), @2(vxw4000, vxw4001), app(app(ty_@2, cc), cd), ce) → new_esEs(vxw300, vxw4000, cc, cd)
new_esEs(@2(vxw300, vxw301), @2(vxw4000, vxw4001), ba, app(app(app(ty_@3, bd), be), bf)) → new_esEs0(vxw301, vxw4001, bd, be, bf)
new_esEs1(:(vxw300, vxw301), :(vxw4000, vxw4001), app(app(ty_@2, hf), hg)) → new_esEs(vxw300, vxw4000, hf, hg)
new_esEs0(@3(vxw300, vxw301, vxw302), @3(vxw4000, vxw4001, vxw4002), app(ty_[], ha), dg, fc) → new_esEs1(vxw300, vxw4000, ha)
new_esEs(@2(vxw300, vxw301), @2(vxw4000, vxw4001), ba, app(ty_Maybe, bh)) → new_esEs2(vxw301, vxw4001, bh)
new_esEs0(@3(vxw300, vxw301, vxw302), @3(vxw4000, vxw4001, vxw4002), df, dg, app(app(ty_@2, dh), ea)) → new_esEs(vxw302, vxw4002, dh, ea)
new_esEs0(@3(vxw300, vxw301, vxw302), @3(vxw4000, vxw4001, vxw4002), df, dg, app(app(ty_Either, eg), eh)) → new_esEs3(vxw302, vxw4002, eg, eh)
new_esEs0(@3(vxw300, vxw301, vxw302), @3(vxw4000, vxw4001, vxw4002), app(ty_Maybe, hb), dg, fc) → new_esEs2(vxw300, vxw4000, hb)
new_esEs0(@3(vxw300, vxw301, vxw302), @3(vxw4000, vxw4001, vxw4002), df, dg, app(ty_Maybe, ef)) → new_esEs2(vxw302, vxw4002, ef)
new_esEs(@2(vxw300, vxw301), @2(vxw4000, vxw4001), app(ty_[], db), ce) → new_esEs1(vxw300, vxw4000, db)
new_esEs0(@3(vxw300, vxw301, vxw302), @3(vxw4000, vxw4001, vxw4002), df, app(ty_[], fh), fc) → new_esEs1(vxw301, vxw4001, fh)
new_esEs3(Right(vxw300), Right(vxw4000), bdb, app(app(ty_Either, beb), bec)) → new_esEs3(vxw300, vxw4000, beb, bec)
new_esEs1(:(vxw300, vxw301), :(vxw4000, vxw4001), he) → new_esEs1(vxw301, vxw4001, he)
new_esEs0(@3(vxw300, vxw301, vxw302), @3(vxw4000, vxw4001, vxw4002), df, app(app(ty_@2, fa), fb), fc) → new_esEs(vxw301, vxw4001, fa, fb)
new_esEs1(:(vxw300, vxw301), :(vxw4000, vxw4001), app(ty_[], bac)) → new_esEs1(vxw300, vxw4000, bac)
new_esEs2(Just(vxw300), Just(vxw4000), app(ty_[], bbd)) → new_esEs1(vxw300, vxw4000, bbd)
new_esEs2(Just(vxw300), Just(vxw4000), app(ty_Maybe, bbe)) → new_esEs2(vxw300, vxw4000, bbe)
new_esEs0(@3(vxw300, vxw301, vxw302), @3(vxw4000, vxw4001, vxw4002), df, app(app(app(ty_@3, fd), ff), fg), fc) → new_esEs0(vxw301, vxw4001, fd, ff, fg)
new_esEs3(Right(vxw300), Right(vxw4000), bdb, app(app(app(ty_@3, bde), bdf), bdg)) → new_esEs0(vxw300, vxw4000, bde, bdf, bdg)
new_esEs3(Left(vxw300), Left(vxw4000), app(app(ty_Either, bch), bda), bcb) → new_esEs3(vxw300, vxw4000, bch, bda)
new_esEs0(@3(vxw300, vxw301, vxw302), @3(vxw4000, vxw4001, vxw4002), app(app(ty_@2, gd), ge), dg, fc) → new_esEs(vxw300, vxw4000, gd, ge)
new_esEs3(Left(vxw300), Left(vxw4000), app(app(ty_@2, bbh), bca), bcb) → new_esEs(vxw300, vxw4000, bbh, bca)
new_esEs0(@3(vxw300, vxw301, vxw302), @3(vxw4000, vxw4001, vxw4002), df, dg, app(ty_[], ee)) → new_esEs1(vxw302, vxw4002, ee)
new_esEs1(:(vxw300, vxw301), :(vxw4000, vxw4001), app(app(ty_Either, bae), baf)) → new_esEs3(vxw300, vxw4000, bae, baf)
new_esEs2(Just(vxw300), Just(vxw4000), app(app(app(ty_@3, bba), bbb), bbc)) → new_esEs0(vxw300, vxw4000, bba, bbb, bbc)
new_esEs3(Left(vxw300), Left(vxw4000), app(app(app(ty_@3, bcc), bcd), bce), bcb) → new_esEs0(vxw300, vxw4000, bcc, bcd, bce)
new_esEs(@2(vxw300, vxw301), @2(vxw4000, vxw4001), app(app(ty_Either, dd), de), ce) → new_esEs3(vxw300, vxw4000, dd, de)
new_esEs3(Left(vxw300), Left(vxw4000), app(ty_Maybe, bcg), bcb) → new_esEs2(vxw300, vxw4000, bcg)
new_esEs(@2(vxw300, vxw301), @2(vxw4000, vxw4001), ba, app(ty_[], bg)) → new_esEs1(vxw301, vxw4001, bg)
new_esEs2(Just(vxw300), Just(vxw4000), app(app(ty_@2, bag), bah)) → new_esEs(vxw300, vxw4000, bag, bah)
new_esEs0(@3(vxw300, vxw301, vxw302), @3(vxw4000, vxw4001, vxw4002), df, dg, app(app(app(ty_@3, eb), ec), ed)) → new_esEs0(vxw302, vxw4002, eb, ec, ed)
new_esEs(@2(vxw300, vxw301), @2(vxw4000, vxw4001), ba, app(app(ty_Either, ca), cb)) → new_esEs3(vxw301, vxw4001, ca, cb)
new_esEs3(Right(vxw300), Right(vxw4000), bdb, app(ty_[], bdh)) → new_esEs1(vxw300, vxw4000, bdh)
new_esEs1(:(vxw300, vxw301), :(vxw4000, vxw4001), app(ty_Maybe, bad)) → new_esEs2(vxw300, vxw4000, bad)
new_esEs0(@3(vxw300, vxw301, vxw302), @3(vxw4000, vxw4001, vxw4002), app(app(ty_Either, hc), hd), dg, fc) → new_esEs3(vxw300, vxw4000, hc, hd)
new_esEs(@2(vxw300, vxw301), @2(vxw4000, vxw4001), app(ty_Maybe, dc), ce) → new_esEs2(vxw300, vxw4000, dc)
new_esEs(@2(vxw300, vxw301), @2(vxw4000, vxw4001), ba, app(app(ty_@2, bb), bc)) → new_esEs(vxw301, vxw4001, bb, bc)
new_esEs1(:(vxw300, vxw301), :(vxw4000, vxw4001), app(app(app(ty_@3, hh), baa), bab)) → new_esEs0(vxw300, vxw4000, hh, baa, bab)
new_esEs3(Right(vxw300), Right(vxw4000), bdb, app(ty_Maybe, bea)) → new_esEs2(vxw300, vxw4000, bea)
new_esEs2(Just(vxw300), Just(vxw4000), app(app(ty_Either, bbf), bbg)) → new_esEs3(vxw300, vxw4000, bbf, bbg)
new_esEs0(@3(vxw300, vxw301, vxw302), @3(vxw4000, vxw4001, vxw4002), df, app(ty_Maybe, ga), fc) → new_esEs2(vxw301, vxw4001, ga)
new_esEs3(Left(vxw300), Left(vxw4000), app(ty_[], bcf), bcb) → new_esEs1(vxw300, vxw4000, bcf)
new_esEs(@2(vxw300, vxw301), @2(vxw4000, vxw4001), app(app(app(ty_@3, cf), cg), da), ce) → new_esEs0(vxw300, vxw4000, cf, cg, da)
new_esEs0(@3(vxw300, vxw301, vxw302), @3(vxw4000, vxw4001, vxw4002), df, app(app(ty_Either, gb), gc), fc) → new_esEs3(vxw301, vxw4001, gb, gc)
new_esEs0(@3(vxw300, vxw301, vxw302), @3(vxw4000, vxw4001, vxw4002), app(app(app(ty_@3, gf), gg), gh), dg, fc) → new_esEs0(vxw300, vxw4000, gf, gg, gh)
new_esEs3(Right(vxw300), Right(vxw4000), bdb, app(app(ty_@2, bdc), bdd)) → new_esEs(vxw300, vxw4000, bdc, bdd)

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
                              ↳ QDP

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

new_ltEs1(:(vxw110, vxw111), :(vxw100, vxw101), eg) → new_compare(vxw111, vxw101, eg)
new_ltEs3(Left(vxw110), Left(vxw100), app(app(ty_Either, bch), bda), bca) → new_ltEs3(vxw110, vxw100, bch, bda)
new_compare22(vxw110, vxw100, False, ee, ef) → new_ltEs3(vxw110, vxw100, ee, ef)
new_ltEs3(Right(vxw110), Right(vxw100), bdb, app(app(app(ty_@3, bdg), bdh), bea)) → new_ltEs2(vxw110, vxw100, bdg, bdh, bea)
new_ltEs0(@2(vxw110, vxw111), @2(vxw100, vxw101), app(ty_Maybe, de), df) → new_compare2(vxw110, vxw100, new_esEs4(vxw110, vxw100, de), de)
new_compare1(vxw110, vxw100, de) → new_compare2(vxw110, vxw100, new_esEs4(vxw110, vxw100, de), de)
new_ltEs2(@3(vxw110, vxw111, vxw112), @3(vxw100, vxw101, vxw102), gb, gc, app(app(app(ty_@3, gh), ha), hb)) → new_ltEs2(vxw112, vxw102, gh, ha, hb)
new_primCompAux(vxw110, vxw100, vxw61, app(app(ty_@2, fa), fb)) → new_compare3(vxw110, vxw100, fa, fb)
new_ltEs2(@3(vxw110, vxw111, vxw112), @3(vxw100, vxw101, vxw102), gb, gc, app(app(ty_Either, hc), hd)) → new_ltEs3(vxw112, vxw102, hc, hd)
new_ltEs0(@2(vxw110, vxw111), @2(vxw100, vxw101), cb, app(ty_Maybe, cc)) → new_ltEs(vxw111, vxw101, cc)
new_ltEs0(@2(vxw110, vxw111), @2(vxw100, vxw101), app(app(app(ty_@3, eb), ec), ed), df) → new_compare21(vxw110, vxw100, new_esEs6(vxw110, vxw100, eb, ec, ed), eb, ec, ed)
new_ltEs2(@3(vxw110, vxw111, vxw112), @3(vxw100, vxw101, vxw102), gb, app(app(app(ty_@3, bab), bac), bad), hf) → new_lt2(vxw111, vxw101, bab, bac, bad)
new_ltEs3(Left(vxw110), Left(vxw100), app(ty_Maybe, bbh), bca) → new_ltEs(vxw110, vxw100, bbh)
new_compare3(vxw110, vxw100, dg, dh) → new_compare20(vxw110, vxw100, new_esEs5(vxw110, vxw100, dg, dh), dg, dh)
new_ltEs(Just(vxw110), Just(vxw100), app(app(ty_@2, bb), bc)) → new_ltEs0(vxw110, vxw100, bb, bc)
new_ltEs0(@2(vxw110, vxw111), @2(vxw100, vxw101), app(app(ty_@2, dg), dh), df) → new_compare20(vxw110, vxw100, new_esEs5(vxw110, vxw100, dg, dh), dg, dh)
new_ltEs2(@3(vxw110, vxw111, vxw112), @3(vxw100, vxw101, vxw102), app(app(ty_Either, bbf), bbg), gc, hf) → new_lt3(vxw110, vxw100, bbf, bbg)
new_lt3(vxw110, vxw100, ee, ef) → new_compare22(vxw110, vxw100, new_esEs7(vxw110, vxw100, ee, ef), ee, ef)
new_ltEs(Just(vxw110), Just(vxw100), app(app(ty_Either, bh), ca)) → new_ltEs3(vxw110, vxw100, bh, ca)
new_ltEs(Just(vxw110), Just(vxw100), app(ty_Maybe, ba)) → new_ltEs(vxw110, vxw100, ba)
new_primCompAux(vxw110, vxw100, vxw61, app(ty_[], fc)) → new_compare(vxw110, vxw100, fc)
new_lt(vxw110, vxw100, de) → new_compare2(vxw110, vxw100, new_esEs4(vxw110, vxw100, de), de)
new_ltEs0(@2(vxw110, vxw111), @2(vxw100, vxw101), app(ty_[], ea), df) → new_compare(vxw110, vxw100, ea)
new_ltEs2(@3(vxw110, vxw111, vxw112), @3(vxw100, vxw101, vxw102), gb, gc, app(ty_Maybe, gd)) → new_ltEs(vxw112, vxw102, gd)
new_lt0(vxw110, vxw100, dg, dh) → new_compare20(vxw110, vxw100, new_esEs5(vxw110, vxw100, dg, dh), dg, dh)
new_primCompAux(vxw110, vxw100, vxw61, app(app(ty_Either, fh), ga)) → new_compare5(vxw110, vxw100, fh, ga)
new_ltEs2(@3(vxw110, vxw111, vxw112), @3(vxw100, vxw101, vxw102), app(ty_[], bbb), gc, hf) → new_lt1(vxw110, vxw100, bbb)
new_compare4(vxw110, vxw100, eb, ec, ed) → new_compare21(vxw110, vxw100, new_esEs6(vxw110, vxw100, eb, ec, ed), eb, ec, ed)
new_ltEs2(@3(vxw110, vxw111, vxw112), @3(vxw100, vxw101, vxw102), gb, app(app(ty_@2, hg), hh), hf) → new_lt0(vxw111, vxw101, hg, hh)
new_compare20(vxw110, vxw100, False, dg, dh) → new_ltEs0(vxw110, vxw100, dg, dh)
new_ltEs0(@2(vxw110, vxw111), @2(vxw100, vxw101), cb, app(app(app(ty_@3, cg), da), db)) → new_ltEs2(vxw111, vxw101, cg, da, db)
new_ltEs3(Right(vxw110), Right(vxw100), bdb, app(app(ty_Either, beb), bec)) → new_ltEs3(vxw110, vxw100, beb, bec)
new_ltEs2(@3(vxw110, vxw111, vxw112), @3(vxw100, vxw101, vxw102), gb, gc, app(ty_[], gg)) → new_ltEs1(vxw112, vxw102, gg)
new_lt2(vxw110, vxw100, eb, ec, ed) → new_compare21(vxw110, vxw100, new_esEs6(vxw110, vxw100, eb, ec, ed), eb, ec, ed)
new_ltEs0(@2(vxw110, vxw111), @2(vxw100, vxw101), cb, app(app(ty_@2, cd), ce)) → new_ltEs0(vxw111, vxw101, cd, ce)
new_ltEs0(@2(vxw110, vxw111), @2(vxw100, vxw101), cb, app(ty_[], cf)) → new_ltEs1(vxw111, vxw101, cf)
new_ltEs3(Right(vxw110), Right(vxw100), bdb, app(ty_[], bdf)) → new_ltEs1(vxw110, vxw100, bdf)
new_ltEs3(Left(vxw110), Left(vxw100), app(app(ty_@2, bcb), bcc), bca) → new_ltEs0(vxw110, vxw100, bcb, bcc)
new_ltEs0(@2(vxw110, vxw111), @2(vxw100, vxw101), app(app(ty_Either, ee), ef), df) → new_compare22(vxw110, vxw100, new_esEs7(vxw110, vxw100, ee, ef), ee, ef)
new_lt1(vxw110, vxw100, ea) → new_compare(vxw110, vxw100, ea)
new_compare2(vxw110, vxw100, False, de) → new_ltEs(vxw110, vxw100, de)
new_ltEs(Just(vxw110), Just(vxw100), app(app(app(ty_@3, be), bf), bg)) → new_ltEs2(vxw110, vxw100, be, bf, bg)
new_compare(:(vxw110, vxw111), :(vxw100, vxw101), eg) → new_compare(vxw111, vxw101, eg)
new_primCompAux(vxw110, vxw100, vxw61, app(ty_Maybe, eh)) → new_compare1(vxw110, vxw100, eh)
new_ltEs(Just(vxw110), Just(vxw100), app(ty_[], bd)) → new_ltEs1(vxw110, vxw100, bd)
new_ltEs2(@3(vxw110, vxw111, vxw112), @3(vxw100, vxw101, vxw102), app(ty_Maybe, bag), gc, hf) → new_lt(vxw110, vxw100, bag)
new_compare5(vxw110, vxw100, ee, ef) → new_compare22(vxw110, vxw100, new_esEs7(vxw110, vxw100, ee, ef), ee, ef)
new_compare(:(vxw110, vxw111), :(vxw100, vxw101), eg) → new_primCompAux(vxw110, vxw100, new_compare0(vxw111, vxw101, eg), eg)
new_ltEs2(@3(vxw110, vxw111, vxw112), @3(vxw100, vxw101, vxw102), gb, app(ty_Maybe, he), hf) → new_lt(vxw111, vxw101, he)
new_ltEs2(@3(vxw110, vxw111, vxw112), @3(vxw100, vxw101, vxw102), app(app(app(ty_@3, bbc), bbd), bbe), gc, hf) → new_lt2(vxw110, vxw100, bbc, bbd, bbe)
new_ltEs3(Left(vxw110), Left(vxw100), app(ty_[], bcd), bca) → new_ltEs1(vxw110, vxw100, bcd)
new_ltEs3(Left(vxw110), Left(vxw100), app(app(app(ty_@3, bce), bcf), bcg), bca) → new_ltEs2(vxw110, vxw100, bce, bcf, bcg)
new_ltEs2(@3(vxw110, vxw111, vxw112), @3(vxw100, vxw101, vxw102), gb, gc, app(app(ty_@2, ge), gf)) → new_ltEs0(vxw112, vxw102, ge, gf)
new_ltEs3(Right(vxw110), Right(vxw100), bdb, app(ty_Maybe, bdc)) → new_ltEs(vxw110, vxw100, bdc)
new_ltEs2(@3(vxw110, vxw111, vxw112), @3(vxw100, vxw101, vxw102), gb, app(app(ty_Either, bae), baf), hf) → new_lt3(vxw111, vxw101, bae, baf)
new_ltEs1(:(vxw110, vxw111), :(vxw100, vxw101), eg) → new_primCompAux(vxw110, vxw100, new_compare0(vxw111, vxw101, eg), eg)
new_ltEs3(Right(vxw110), Right(vxw100), bdb, app(app(ty_@2, bdd), bde)) → new_ltEs0(vxw110, vxw100, bdd, bde)
new_ltEs2(@3(vxw110, vxw111, vxw112), @3(vxw100, vxw101, vxw102), app(app(ty_@2, bah), bba), gc, hf) → new_lt0(vxw110, vxw100, bah, bba)
new_ltEs2(@3(vxw110, vxw111, vxw112), @3(vxw100, vxw101, vxw102), gb, app(ty_[], baa), hf) → new_lt1(vxw111, vxw101, baa)
new_compare21(vxw110, vxw100, False, eb, ec, ed) → new_ltEs2(vxw110, vxw100, eb, ec, ed)
new_primCompAux(vxw110, vxw100, vxw61, app(app(app(ty_@3, fd), ff), fg)) → new_compare4(vxw110, vxw100, fd, ff, fg)
new_ltEs0(@2(vxw110, vxw111), @2(vxw100, vxw101), cb, app(app(ty_Either, dc), dd)) → new_ltEs3(vxw111, vxw101, dc, dd)

The TRS R consists of the following rules:

new_esEs25(vxw111, vxw101, app(ty_[], baa)) → new_esEs14(vxw111, vxw101, baa)
new_esEs4(Just(vxw300), Just(vxw4000), app(ty_Maybe, cfd)) → new_esEs4(vxw300, vxw4000, cfd)
new_esEs26(vxw110, vxw100, ty_@0) → new_esEs15(vxw110, vxw100)
new_esEs23(vxw110, vxw100, app(app(ty_Either, ee), ef)) → new_esEs7(vxw110, vxw100, ee, ef)
new_compare112(vxw110, vxw100, True, de) → LT
new_esEs4(Just(vxw300), Just(vxw4000), ty_Ordering) → new_esEs8(vxw300, vxw4000)
new_esEs7(Left(vxw300), Left(vxw4000), app(app(ty_Either, bfe), bff), bef) → new_esEs7(vxw300, vxw4000, bfe, bff)
new_ltEs19(vxw112, vxw102, app(ty_Ratio, chb)) → new_ltEs11(vxw112, vxw102, chb)
new_compare210(vxw110, vxw100, False, de) → new_compare112(vxw110, vxw100, new_ltEs7(vxw110, vxw100, de), de)
new_esEs7(Left(vxw300), Left(vxw4000), app(ty_Maybe, bfd), bef) → new_esEs4(vxw300, vxw4000, bfd)
new_ltEs18(vxw111, vxw101, ty_Float) → new_ltEs15(vxw111, vxw101)
new_compare10(vxw110, vxw100, True, dg, dh) → LT
new_esEs26(vxw110, vxw100, ty_Float) → new_esEs10(vxw110, vxw100)
new_esEs24(vxw300, vxw4000, app(ty_Maybe, cgg)) → new_esEs4(vxw300, vxw4000, cgg)
new_esEs4(Just(vxw300), Nothing, ced) → False
new_esEs4(Nothing, Just(vxw4000), ced) → False
new_esEs11(Integer(vxw300), Integer(vxw4000)) → new_primEqInt(vxw300, vxw4000)
new_lt19(vxw111, vxw101, app(app(ty_Either, bae), baf)) → new_lt18(vxw111, vxw101, bae, baf)
new_esEs28(vxw300, vxw4000, ty_Integer) → new_esEs11(vxw300, vxw4000)
new_esEs26(vxw110, vxw100, ty_Integer) → new_esEs11(vxw110, vxw100)
new_ltEs17(Right(vxw110), Right(vxw100), bdb, app(ty_Ratio, cea)) → new_ltEs11(vxw110, vxw100, cea)
new_lt19(vxw111, vxw101, ty_@0) → new_lt8(vxw111, vxw101)
new_esEs22(vxw300, vxw4000, ty_Char) → new_esEs12(vxw300, vxw4000)
new_ltEs17(Left(vxw110), Left(vxw100), app(ty_Ratio, cdh), bca) → new_ltEs11(vxw110, vxw100, cdh)
new_esEs4(Just(vxw300), Just(vxw4000), ty_Char) → new_esEs12(vxw300, vxw4000)
new_esEs27(vxw301, vxw4001, ty_Bool) → new_esEs17(vxw301, vxw4001)
new_lt12(vxw110, vxw100) → new_esEs8(new_compare14(vxw110, vxw100), LT)
new_primMulNat0(Zero, Zero) → Zero
new_esEs23(vxw110, vxw100, app(ty_Ratio, cec)) → new_esEs13(vxw110, vxw100, cec)
new_esEs4(Just(vxw300), Just(vxw4000), app(app(app(ty_@3, ceg), ceh), cfa)) → new_esEs6(vxw300, vxw4000, ceg, ceh, cfa)
new_ltEs19(vxw112, vxw102, ty_Double) → new_ltEs9(vxw112, vxw102)
new_esEs20(vxw302, vxw4002, app(ty_Maybe, cba)) → new_esEs4(vxw302, vxw4002, cba)
new_lt20(vxw110, vxw100, ty_Integer) → new_lt4(vxw110, vxw100)
new_lt20(vxw110, vxw100, ty_@0) → new_lt8(vxw110, vxw100)
new_esEs21(vxw301, vxw4001, ty_Bool) → new_esEs17(vxw301, vxw4001)
new_esEs23(vxw110, vxw100, ty_Double) → new_esEs9(vxw110, vxw100)
new_esEs7(Right(vxw300), Right(vxw4000), bfg, ty_Ordering) → new_esEs8(vxw300, vxw4000)
new_lt19(vxw111, vxw101, ty_Ordering) → new_lt6(vxw111, vxw101)
new_esEs25(vxw111, vxw101, ty_Bool) → new_esEs17(vxw111, vxw101)
new_ltEs17(Left(vxw110), Left(vxw100), ty_Integer, bca) → new_ltEs13(vxw110, vxw100)
new_compare13(vxw110, vxw100, dg, dh) → new_compare23(vxw110, vxw100, new_esEs5(vxw110, vxw100, dg, dh), dg, dh)
new_compare9(vxw110, vxw100, ty_Double) → new_compare15(vxw110, vxw100)
new_lt20(vxw110, vxw100, app(app(ty_@2, bah), bba)) → new_lt11(vxw110, vxw100, bah, bba)
new_esEs23(vxw110, vxw100, app(ty_Maybe, de)) → new_esEs4(vxw110, vxw100, de)
new_compare9(vxw110, vxw100, ty_Integer) → new_compare6(vxw110, vxw100)
new_ltEs7(Just(vxw110), Just(vxw100), ty_Bool) → new_ltEs5(vxw110, vxw100)
new_esEs17(True, True) → True
new_esEs20(vxw302, vxw4002, app(ty_Ratio, cag)) → new_esEs13(vxw302, vxw4002, cag)
new_ltEs19(vxw112, vxw102, ty_Ordering) → new_ltEs10(vxw112, vxw102)
new_ltEs7(Just(vxw110), Just(vxw100), app(app(app(ty_@3, be), bf), bg)) → new_ltEs6(vxw110, vxw100, be, bf, bg)
new_compare0(:(vxw110, vxw111), :(vxw100, vxw101), eg) → new_primCompAux0(vxw110, vxw100, new_compare0(vxw111, vxw101, eg), eg)
new_esEs22(vxw300, vxw4000, app(app(ty_@2, ccf), ccg)) → new_esEs5(vxw300, vxw4000, ccf, ccg)
new_lt15(vxw110, vxw100, ea) → new_esEs8(new_compare0(vxw110, vxw100, ea), LT)
new_esEs24(vxw300, vxw4000, app(app(ty_@2, cfh), cga)) → new_esEs5(vxw300, vxw4000, cfh, cga)
new_esEs4(Just(vxw300), Just(vxw4000), ty_Float) → new_esEs10(vxw300, vxw4000)
new_ltEs18(vxw111, vxw101, ty_Char) → new_ltEs8(vxw111, vxw101)
new_ltEs17(Right(vxw110), Right(vxw100), bdb, ty_Integer) → new_ltEs13(vxw110, vxw100)
new_ltEs10(EQ, GT) → True
new_compare29(vxw110, vxw100, False, ee, ef) → new_compare111(vxw110, vxw100, new_ltEs17(vxw110, vxw100, ee, ef), ee, ef)
new_compare9(vxw110, vxw100, ty_Int) → new_compare27(vxw110, vxw100)
new_esEs26(vxw110, vxw100, app(ty_Maybe, bag)) → new_esEs4(vxw110, vxw100, bag)
new_esEs22(vxw300, vxw4000, app(ty_[], cdd)) → new_esEs14(vxw300, vxw4000, cdd)
new_lt20(vxw110, vxw100, ty_Float) → new_lt17(vxw110, vxw100)
new_esEs22(vxw300, vxw4000, app(app(ty_Either, cdf), cdg)) → new_esEs7(vxw300, vxw4000, cdf, cdg)
new_ltEs7(Just(vxw110), Just(vxw100), app(app(ty_Either, bh), ca)) → new_ltEs17(vxw110, vxw100, bh, ca)
new_ltEs7(Just(vxw110), Just(vxw100), app(app(ty_@2, bb), bc)) → new_ltEs4(vxw110, vxw100, bb, bc)
new_esEs25(vxw111, vxw101, ty_Double) → new_esEs9(vxw111, vxw101)
new_pePe(False, vxw60) → vxw60
new_esEs14([], [], cfg) → True
new_ltEs7(Just(vxw110), Just(vxw100), ty_Ordering) → new_ltEs10(vxw110, vxw100)
new_ltEs17(Left(vxw110), Left(vxw100), ty_Bool, bca) → new_ltEs5(vxw110, vxw100)
new_esEs7(Left(vxw300), Right(vxw4000), bfg, bef) → False
new_esEs7(Right(vxw300), Left(vxw4000), bfg, bef) → False
new_esEs4(Just(vxw300), Just(vxw4000), ty_Integer) → new_esEs11(vxw300, vxw4000)
new_ltEs19(vxw112, vxw102, app(app(ty_@2, ge), gf)) → new_ltEs4(vxw112, vxw102, ge, gf)
new_ltEs7(Just(vxw110), Just(vxw100), ty_Integer) → new_ltEs13(vxw110, vxw100)
new_esEs27(vxw301, vxw4001, app(app(ty_Either, dag), dah)) → new_esEs7(vxw301, vxw4001, dag, dah)
new_esEs20(vxw302, vxw4002, ty_Int) → new_esEs16(vxw302, vxw4002)
new_esEs26(vxw110, vxw100, ty_Char) → new_esEs12(vxw110, vxw100)
new_esEs22(vxw300, vxw4000, ty_@0) → new_esEs15(vxw300, vxw4000)
new_lt9(vxw110, vxw100) → new_esEs8(new_compare18(vxw110, vxw100), LT)
new_esEs28(vxw300, vxw4000, ty_@0) → new_esEs15(vxw300, vxw4000)
new_esEs20(vxw302, vxw4002, ty_Char) → new_esEs12(vxw302, vxw4002)
new_ltEs17(Left(vxw110), Left(vxw100), app(ty_Maybe, bbh), bca) → new_ltEs7(vxw110, vxw100, bbh)
new_ltEs18(vxw111, vxw101, ty_Int) → new_ltEs16(vxw111, vxw101)
new_esEs22(vxw300, vxw4000, ty_Ordering) → new_esEs8(vxw300, vxw4000)
new_esEs7(Left(vxw300), Left(vxw4000), ty_Double, bef) → new_esEs9(vxw300, vxw4000)
new_esEs20(vxw302, vxw4002, app(app(ty_@2, cab), cac)) → new_esEs5(vxw302, vxw4002, cab, cac)
new_esEs7(Right(vxw300), Right(vxw4000), bfg, ty_Double) → new_esEs9(vxw300, vxw4000)
new_esEs7(Right(vxw300), Right(vxw4000), bfg, app(app(ty_@2, bfh), bga)) → new_esEs5(vxw300, vxw4000, bfh, bga)
new_primCmpNat0(Zero, Succ(vxw1000)) → LT
new_lt10(vxw110, vxw100, ty_Double) → new_lt13(vxw110, vxw100)
new_ltEs19(vxw112, vxw102, ty_Float) → new_ltEs15(vxw112, vxw102)
new_lt10(vxw110, vxw100, ty_Bool) → new_lt9(vxw110, vxw100)
new_lt20(vxw110, vxw100, ty_Ordering) → new_lt6(vxw110, vxw100)
new_esEs8(LT, LT) → True
new_lt19(vxw111, vxw101, ty_Bool) → new_lt9(vxw111, vxw101)
new_compare25(vxw110, vxw100, True, eb, ec, ed) → EQ
new_ltEs15(vxw11, vxw10) → new_not(new_esEs8(new_compare26(vxw11, vxw10), GT))
new_esEs21(vxw301, vxw4001, app(ty_Ratio, cca)) → new_esEs13(vxw301, vxw4001, cca)
new_lt5(vxw110, vxw100, de) → new_esEs8(new_compare8(vxw110, vxw100, de), LT)
new_esEs7(Left(vxw300), Left(vxw4000), ty_Integer, bef) → new_esEs11(vxw300, vxw4000)
new_esEs25(vxw111, vxw101, ty_Ordering) → new_esEs8(vxw111, vxw101)
new_esEs20(vxw302, vxw4002, ty_Integer) → new_esEs11(vxw302, vxw4002)
new_esEs25(vxw111, vxw101, app(ty_Ratio, chc)) → new_esEs13(vxw111, vxw101, chc)
new_esEs24(vxw300, vxw4000, app(app(ty_Either, cgh), cha)) → new_esEs7(vxw300, vxw4000, cgh, cha)
new_compare9(vxw110, vxw100, app(app(app(ty_@3, fd), ff), fg)) → new_compare19(vxw110, vxw100, fd, ff, fg)
new_esEs20(vxw302, vxw4002, app(app(app(ty_@3, cad), cae), caf)) → new_esEs6(vxw302, vxw4002, cad, cae, caf)
new_esEs28(vxw300, vxw4000, ty_Float) → new_esEs10(vxw300, vxw4000)
new_ltEs5(True, False) → False
new_lt19(vxw111, vxw101, app(app(ty_@2, hg), hh)) → new_lt11(vxw111, vxw101, hg, hh)
new_esEs18(vxw301, vxw4001, ty_Integer) → new_esEs11(vxw301, vxw4001)
new_compare0([], [], eg) → EQ
new_pePe(True, vxw60) → True
new_esEs24(vxw300, vxw4000, ty_Int) → new_esEs16(vxw300, vxw4000)
new_primEqNat0(Zero, Zero) → True
new_esEs7(Left(vxw300), Left(vxw4000), app(app(ty_@2, bed), bee), bef) → new_esEs5(vxw300, vxw4000, bed, bee)
new_ltEs17(Left(vxw110), Left(vxw100), ty_Double, bca) → new_ltEs9(vxw110, vxw100)
new_compare29(vxw110, vxw100, True, ee, ef) → EQ
new_compare111(vxw110, vxw100, False, ee, ef) → GT
new_esEs26(vxw110, vxw100, app(ty_Ratio, chd)) → new_esEs13(vxw110, vxw100, chd)
new_esEs27(vxw301, vxw4001, app(ty_Ratio, dad)) → new_esEs13(vxw301, vxw4001, dad)
new_esEs27(vxw301, vxw4001, ty_Char) → new_esEs12(vxw301, vxw4001)
new_lt18(vxw110, vxw100, ee, ef) → new_esEs8(new_compare28(vxw110, vxw100, ee, ef), LT)
new_ltEs5(True, True) → True
new_ltEs17(Left(vxw110), Left(vxw100), ty_Ordering, bca) → new_ltEs10(vxw110, vxw100)
new_esEs17(False, False) → True
new_ltEs17(Right(vxw110), Left(vxw100), bdb, bca) → False
new_esEs17(False, True) → False
new_esEs17(True, False) → False
new_esEs7(Left(vxw300), Left(vxw4000), ty_Ordering, bef) → new_esEs8(vxw300, vxw4000)
new_compare17(:%(vxw110, vxw111), :%(vxw100, vxw101), ty_Int) → new_compare27(new_sr(vxw110, vxw101), new_sr(vxw100, vxw111))
new_lt19(vxw111, vxw101, ty_Double) → new_lt13(vxw111, vxw101)
new_ltEs18(vxw111, vxw101, app(app(ty_Either, dc), dd)) → new_ltEs17(vxw111, vxw101, dc, dd)
new_esEs7(Right(vxw300), Right(vxw4000), bfg, app(app(app(ty_@3, bgb), bgc), bgd)) → new_esEs6(vxw300, vxw4000, bgb, bgc, bgd)
new_sr(vxw300, vxw4000) → new_primMulInt(vxw300, vxw4000)
new_esEs24(vxw300, vxw4000, ty_Bool) → new_esEs17(vxw300, vxw4000)
new_compare12(vxw110, vxw100, True, eb, ec, ed) → LT
new_esEs24(vxw300, vxw4000, ty_Char) → new_esEs12(vxw300, vxw4000)
new_esEs22(vxw300, vxw4000, ty_Double) → new_esEs9(vxw300, vxw4000)
new_esEs26(vxw110, vxw100, ty_Ordering) → new_esEs8(vxw110, vxw100)
new_esEs4(Just(vxw300), Just(vxw4000), ty_Bool) → new_esEs17(vxw300, vxw4000)
new_esEs8(GT, GT) → True
new_primPlusNat0(Succ(vxw620), vxw400000) → Succ(Succ(new_primPlusNat1(vxw620, vxw400000)))
new_ltEs9(vxw11, vxw10) → new_not(new_esEs8(new_compare15(vxw11, vxw10), GT))
new_esEs7(Right(vxw300), Right(vxw4000), bfg, app(app(ty_Either, bgh), bha)) → new_esEs7(vxw300, vxw4000, bgh, bha)
new_lt10(vxw110, vxw100, app(app(ty_@2, dg), dh)) → new_lt11(vxw110, vxw100, dg, dh)
new_esEs26(vxw110, vxw100, app(app(app(ty_@3, bbc), bbd), bbe)) → new_esEs6(vxw110, vxw100, bbc, bbd, bbe)
new_esEs20(vxw302, vxw4002, ty_Bool) → new_esEs17(vxw302, vxw4002)
new_ltEs17(Right(vxw110), Right(vxw100), bdb, ty_Ordering) → new_ltEs10(vxw110, vxw100)
new_esEs8(LT, GT) → False
new_esEs8(GT, LT) → False
new_lt20(vxw110, vxw100, ty_Bool) → new_lt9(vxw110, vxw100)
new_esEs7(Right(vxw300), Right(vxw4000), bfg, ty_Char) → new_esEs12(vxw300, vxw4000)
new_ltEs7(Just(vxw110), Just(vxw100), ty_Int) → new_ltEs16(vxw110, vxw100)
new_primEqInt(Neg(Succ(vxw3000)), Neg(Succ(vxw40000))) → new_primEqNat0(vxw3000, vxw40000)
new_esEs7(Right(vxw300), Right(vxw4000), bfg, ty_@0) → new_esEs15(vxw300, vxw4000)
new_lt10(vxw110, vxw100, ty_Char) → new_lt12(vxw110, vxw100)
new_esEs20(vxw302, vxw4002, ty_Ordering) → new_esEs8(vxw302, vxw4002)
new_lt10(vxw110, vxw100, app(app(ty_Either, ee), ef)) → new_lt18(vxw110, vxw100, ee, ef)
new_esEs22(vxw300, vxw4000, app(app(app(ty_@3, cch), cda), cdb)) → new_esEs6(vxw300, vxw4000, cch, cda, cdb)
new_esEs23(vxw110, vxw100, ty_Ordering) → new_esEs8(vxw110, vxw100)
new_ltEs5(False, False) → True
new_primPlusNat1(Zero, Succ(vxw4000000)) → Succ(vxw4000000)
new_primPlusNat1(Succ(vxw6200), Zero) → Succ(vxw6200)
new_lt19(vxw111, vxw101, ty_Float) → new_lt17(vxw111, vxw101)
new_esEs6(@3(vxw300, vxw301, vxw302), @3(vxw4000, vxw4001, vxw4002), bhg, bhh, caa) → new_asAs(new_esEs22(vxw300, vxw4000, bhg), new_asAs(new_esEs21(vxw301, vxw4001, bhh), new_esEs20(vxw302, vxw4002, caa)))
new_esEs21(vxw301, vxw4001, ty_Char) → new_esEs12(vxw301, vxw4001)
new_esEs16(vxw30, vxw400) → new_primEqInt(vxw30, vxw400)
new_esEs28(vxw300, vxw4000, app(ty_Maybe, dbh)) → new_esEs4(vxw300, vxw4000, dbh)
new_esEs21(vxw301, vxw4001, ty_@0) → new_esEs15(vxw301, vxw4001)
new_esEs14([], :(vxw4000, vxw4001), cfg) → False
new_esEs14(:(vxw300, vxw301), [], cfg) → False
new_esEs7(Right(vxw300), Right(vxw4000), bfg, app(ty_Ratio, bge)) → new_esEs13(vxw300, vxw4000, bge)
new_lt6(vxw110, vxw100) → new_esEs8(new_compare16(vxw110, vxw100), LT)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs7(Left(vxw300), Left(vxw4000), app(ty_Ratio, bfb), bef) → new_esEs13(vxw300, vxw4000, bfb)
new_esEs24(vxw300, vxw4000, app(app(app(ty_@3, cgb), cgc), cgd)) → new_esEs6(vxw300, vxw4000, cgb, cgc, cgd)
new_ltEs17(Right(vxw110), Right(vxw100), bdb, ty_Int) → new_ltEs16(vxw110, vxw100)
new_esEs21(vxw301, vxw4001, ty_Integer) → new_esEs11(vxw301, vxw4001)
new_esEs26(vxw110, vxw100, app(ty_[], bbb)) → new_esEs14(vxw110, vxw100, bbb)
new_ltEs18(vxw111, vxw101, ty_@0) → new_ltEs14(vxw111, vxw101)
new_esEs28(vxw300, vxw4000, ty_Int) → new_esEs16(vxw300, vxw4000)
new_lt19(vxw111, vxw101, ty_Char) → new_lt12(vxw111, vxw101)
new_primEqInt(Neg(Succ(vxw3000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(vxw40000))) → False
new_esEs8(EQ, EQ) → True
new_compare27(vxw11, vxw10) → new_primCmpInt(vxw11, vxw10)
new_esEs5(@2(vxw300, vxw301), @2(vxw4000, vxw4001), che, chf) → new_asAs(new_esEs28(vxw300, vxw4000, che), new_esEs27(vxw301, vxw4001, chf))
new_esEs28(vxw300, vxw4000, app(ty_[], dbg)) → new_esEs14(vxw300, vxw4000, dbg)
new_lt20(vxw110, vxw100, app(ty_Maybe, bag)) → new_lt5(vxw110, vxw100, bag)
new_esEs26(vxw110, vxw100, app(app(ty_Either, bbf), bbg)) → new_esEs7(vxw110, vxw100, bbf, bbg)
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_compare14(Char(vxw110), Char(vxw100)) → new_primCmpNat0(vxw110, vxw100)
new_esEs21(vxw301, vxw4001, ty_Float) → new_esEs10(vxw301, vxw4001)
new_esEs4(Just(vxw300), Just(vxw4000), app(app(ty_Either, cfe), cff)) → new_esEs7(vxw300, vxw4000, cfe, cff)
new_esEs7(Left(vxw300), Left(vxw4000), ty_@0, bef) → new_esEs15(vxw300, vxw4000)
new_primCmpNat0(Succ(vxw1100), Succ(vxw1000)) → new_primCmpNat0(vxw1100, vxw1000)
new_esEs23(vxw110, vxw100, ty_Float) → new_esEs10(vxw110, vxw100)
new_esEs22(vxw300, vxw4000, app(ty_Maybe, cde)) → new_esEs4(vxw300, vxw4000, cde)
new_esEs25(vxw111, vxw101, app(ty_Maybe, he)) → new_esEs4(vxw111, vxw101, he)
new_compare19(vxw110, vxw100, eb, ec, ed) → new_compare25(vxw110, vxw100, new_esEs6(vxw110, vxw100, eb, ec, ed), eb, ec, ed)
new_lt14(vxw110, vxw100, cec) → new_esEs8(new_compare17(vxw110, vxw100, cec), LT)
new_ltEs18(vxw111, vxw101, ty_Integer) → new_ltEs13(vxw111, vxw101)
new_ltEs6(@3(vxw110, vxw111, vxw112), @3(vxw100, vxw101, vxw102), gb, gc, hf) → new_pePe(new_lt20(vxw110, vxw100, gb), new_asAs(new_esEs26(vxw110, vxw100, gb), new_pePe(new_lt19(vxw111, vxw101, gc), new_asAs(new_esEs25(vxw111, vxw101, gc), new_ltEs19(vxw112, vxw102, hf)))))
new_ltEs18(vxw111, vxw101, ty_Bool) → new_ltEs5(vxw111, vxw101)
new_ltEs17(Left(vxw110), Left(vxw100), app(app(ty_@2, bcb), bcc), bca) → new_ltEs4(vxw110, vxw100, bcb, bcc)
new_primEqInt(Pos(Succ(vxw3000)), Pos(Succ(vxw40000))) → new_primEqNat0(vxw3000, vxw40000)
new_compare10(vxw110, vxw100, False, dg, dh) → GT
new_compare9(vxw110, vxw100, app(ty_Maybe, eh)) → new_compare8(vxw110, vxw100, eh)
new_esEs18(vxw301, vxw4001, ty_Int) → new_esEs16(vxw301, vxw4001)
new_esEs4(Just(vxw300), Just(vxw4000), app(app(ty_@2, cee), cef)) → new_esEs5(vxw300, vxw4000, cee, cef)
new_lt20(vxw110, vxw100, ty_Int) → new_lt7(vxw110, vxw100)
new_compare9(vxw110, vxw100, app(ty_[], fc)) → new_compare0(vxw110, vxw100, fc)
new_ltEs7(Nothing, Just(vxw100), bhd) → True
new_esEs4(Just(vxw300), Just(vxw4000), ty_Int) → new_esEs16(vxw300, vxw4000)
new_ltEs10(GT, EQ) → False
new_primEqNat0(Succ(vxw3000), Succ(vxw40000)) → new_primEqNat0(vxw3000, vxw40000)
new_esEs23(vxw110, vxw100, ty_Integer) → new_esEs11(vxw110, vxw100)
new_esEs27(vxw301, vxw4001, ty_Ordering) → new_esEs8(vxw301, vxw4001)
new_compare7(@0, @0) → EQ
new_esEs21(vxw301, vxw4001, app(ty_[], ccb)) → new_esEs14(vxw301, vxw4001, ccb)
new_esEs9(Double(vxw300, vxw301), Double(vxw4000, vxw4001)) → new_esEs16(new_sr(vxw300, vxw4000), new_sr(vxw301, vxw4001))
new_esEs7(Right(vxw300), Right(vxw4000), bfg, ty_Float) → new_esEs10(vxw300, vxw4000)
new_esEs20(vxw302, vxw4002, ty_Float) → new_esEs10(vxw302, vxw4002)
new_primCompAux00(vxw72, LT) → LT
new_lt10(vxw110, vxw100, app(app(app(ty_@3, eb), ec), ed)) → new_lt16(vxw110, vxw100, eb, ec, ed)
new_primCmpInt(Neg(Succ(vxw1100)), Neg(vxw100)) → new_primCmpNat0(vxw100, Succ(vxw1100))
new_esEs4(Just(vxw300), Just(vxw4000), ty_@0) → new_esEs15(vxw300, vxw4000)
new_esEs24(vxw300, vxw4000, ty_Ordering) → new_esEs8(vxw300, vxw4000)
new_lt10(vxw110, vxw100, ty_Float) → new_lt17(vxw110, vxw100)
new_esEs28(vxw300, vxw4000, ty_Ordering) → new_esEs8(vxw300, vxw4000)
new_esEs7(Left(vxw300), Left(vxw4000), ty_Int, bef) → new_esEs16(vxw300, vxw4000)
new_esEs8(LT, EQ) → False
new_esEs8(EQ, LT) → False
new_primEqInt(Pos(Zero), Pos(Succ(vxw40000))) → False
new_primEqInt(Pos(Succ(vxw3000)), Pos(Zero)) → False
new_lt4(vxw110, vxw100) → new_esEs8(new_compare6(vxw110, vxw100), LT)
new_ltEs19(vxw112, vxw102, app(app(ty_Either, hc), hd)) → new_ltEs17(vxw112, vxw102, hc, hd)
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(vxw1100), Zero) → GT
new_esEs23(vxw110, vxw100, app(app(ty_@2, dg), dh)) → new_esEs5(vxw110, vxw100, dg, dh)
new_esEs24(vxw300, vxw4000, ty_@0) → new_esEs15(vxw300, vxw4000)
new_ltEs17(Right(vxw110), Right(vxw100), bdb, app(ty_Maybe, bdc)) → new_ltEs7(vxw110, vxw100, bdc)
new_ltEs10(LT, EQ) → True
new_primCmpInt(Neg(Zero), Pos(Succ(vxw1000))) → LT
new_lt10(vxw110, vxw100, app(ty_Ratio, cec)) → new_lt14(vxw110, vxw100, cec)
new_compare9(vxw110, vxw100, ty_Bool) → new_compare18(vxw110, vxw100)
new_esEs27(vxw301, vxw4001, ty_Double) → new_esEs9(vxw301, vxw4001)
new_ltEs17(Left(vxw110), Left(vxw100), app(app(app(ty_@3, bce), bcf), bcg), bca) → new_ltEs6(vxw110, vxw100, bce, bcf, bcg)
new_esEs22(vxw300, vxw4000, app(ty_Ratio, cdc)) → new_esEs13(vxw300, vxw4000, cdc)
new_esEs19(vxw300, vxw4000, ty_Integer) → new_esEs11(vxw300, vxw4000)
new_sr0(Integer(vxw1100), Integer(vxw1010)) → Integer(new_primMulInt(vxw1100, vxw1010))
new_primPlusNat1(Succ(vxw6200), Succ(vxw4000000)) → Succ(Succ(new_primPlusNat1(vxw6200, vxw4000000)))
new_compare6(Integer(vxw110), Integer(vxw100)) → new_primCmpInt(vxw110, vxw100)
new_primEqInt(Neg(Succ(vxw3000)), Pos(vxw4000)) → False
new_primEqInt(Pos(Succ(vxw3000)), Neg(vxw4000)) → False
new_ltEs17(Left(vxw110), Left(vxw100), app(ty_[], bcd), bca) → new_ltEs12(vxw110, vxw100, bcd)
new_esEs24(vxw300, vxw4000, app(ty_Ratio, cge)) → new_esEs13(vxw300, vxw4000, cge)
new_compare210(vxw110, vxw100, True, de) → EQ
new_ltEs4(@2(vxw110, vxw111), @2(vxw100, vxw101), cb, df) → new_pePe(new_lt10(vxw110, vxw100, cb), new_asAs(new_esEs23(vxw110, vxw100, cb), new_ltEs18(vxw111, vxw101, df)))
new_ltEs5(False, True) → True
new_ltEs10(GT, GT) → True
new_esEs25(vxw111, vxw101, ty_Char) → new_esEs12(vxw111, vxw101)
new_lt19(vxw111, vxw101, ty_Int) → new_lt7(vxw111, vxw101)
new_primEqInt(Pos(Zero), Neg(Succ(vxw40000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(vxw40000))) → False
new_primCmpInt(Pos(Zero), Pos(Succ(vxw1000))) → new_primCmpNat0(Zero, Succ(vxw1000))
new_primCompAux00(vxw72, EQ) → vxw72
new_esEs28(vxw300, vxw4000, app(app(ty_Either, dca), dcb)) → new_esEs7(vxw300, vxw4000, dca, dcb)
new_ltEs18(vxw111, vxw101, app(ty_Ratio, ceb)) → new_ltEs11(vxw111, vxw101, ceb)
new_compare24(vxw110, vxw100, True) → EQ
new_esEs7(Right(vxw300), Right(vxw4000), bfg, app(ty_Maybe, bgg)) → new_esEs4(vxw300, vxw4000, bgg)
new_compare17(:%(vxw110, vxw111), :%(vxw100, vxw101), ty_Integer) → new_compare6(new_sr0(vxw110, vxw101), new_sr0(vxw100, vxw111))
new_esEs27(vxw301, vxw4001, ty_Float) → new_esEs10(vxw301, vxw4001)
new_esEs8(EQ, GT) → False
new_esEs8(GT, EQ) → False
new_lt10(vxw110, vxw100, app(ty_Maybe, de)) → new_lt5(vxw110, vxw100, de)
new_ltEs7(Just(vxw110), Just(vxw100), ty_Float) → new_ltEs15(vxw110, vxw100)
new_esEs26(vxw110, vxw100, app(app(ty_@2, bah), bba)) → new_esEs5(vxw110, vxw100, bah, bba)
new_compare18(vxw110, vxw100) → new_compare24(vxw110, vxw100, new_esEs17(vxw110, vxw100))
new_esEs21(vxw301, vxw4001, app(app(ty_@2, cbd), cbe)) → new_esEs5(vxw301, vxw4001, cbd, cbe)
new_ltEs19(vxw112, vxw102, ty_Char) → new_ltEs8(vxw112, vxw102)
new_lt8(vxw110, vxw100) → new_esEs8(new_compare7(vxw110, vxw100), LT)
new_ltEs7(Just(vxw110), Just(vxw100), ty_Double) → new_ltEs9(vxw110, vxw100)
new_esEs12(Char(vxw300), Char(vxw4000)) → new_primEqNat0(vxw300, vxw4000)
new_not(False) → True
new_esEs7(Right(vxw300), Right(vxw4000), bfg, ty_Integer) → new_esEs11(vxw300, vxw4000)
new_esEs24(vxw300, vxw4000, ty_Double) → new_esEs9(vxw300, vxw4000)
new_primCompAux0(vxw110, vxw100, vxw61, eg) → new_primCompAux00(vxw61, new_compare9(vxw110, vxw100, eg))
new_primPlusNat0(Zero, vxw400000) → Succ(vxw400000)
new_primCmpInt(Pos(Succ(vxw1100)), Pos(vxw100)) → new_primCmpNat0(Succ(vxw1100), vxw100)
new_esEs23(vxw110, vxw100, ty_@0) → new_esEs15(vxw110, vxw100)
new_compare9(vxw110, vxw100, ty_Float) → new_compare26(vxw110, vxw100)
new_compare12(vxw110, vxw100, False, eb, ec, ed) → GT
new_esEs7(Right(vxw300), Right(vxw4000), bfg, ty_Bool) → new_esEs17(vxw300, vxw4000)
new_esEs22(vxw300, vxw4000, ty_Bool) → new_esEs17(vxw300, vxw4000)
new_ltEs18(vxw111, vxw101, app(app(app(ty_@3, cg), da), db)) → new_ltEs6(vxw111, vxw101, cg, da, db)
new_compare9(vxw110, vxw100, ty_@0) → new_compare7(vxw110, vxw100)
new_ltEs19(vxw112, vxw102, app(ty_[], gg)) → new_ltEs12(vxw112, vxw102, gg)
new_ltEs17(Right(vxw110), Right(vxw100), bdb, app(app(ty_Either, beb), bec)) → new_ltEs17(vxw110, vxw100, beb, bec)
new_esEs25(vxw111, vxw101, ty_Float) → new_esEs10(vxw111, vxw101)
new_compare16(vxw110, vxw100) → new_compare211(vxw110, vxw100, new_esEs8(vxw110, vxw100))
new_esEs25(vxw111, vxw101, ty_@0) → new_esEs15(vxw111, vxw101)
new_esEs24(vxw300, vxw4000, app(ty_[], cgf)) → new_esEs14(vxw300, vxw4000, cgf)
new_lt20(vxw110, vxw100, ty_Double) → new_lt13(vxw110, vxw100)
new_lt20(vxw110, vxw100, app(ty_Ratio, chd)) → new_lt14(vxw110, vxw100, chd)
new_esEs28(vxw300, vxw4000, app(app(ty_@2, dba), dbb)) → new_esEs5(vxw300, vxw4000, dba, dbb)
new_compare0(:(vxw110, vxw111), [], eg) → GT
new_esEs22(vxw300, vxw4000, ty_Integer) → new_esEs11(vxw300, vxw4000)
new_ltEs19(vxw112, vxw102, app(app(app(ty_@3, gh), ha), hb)) → new_ltEs6(vxw112, vxw102, gh, ha, hb)
new_ltEs18(vxw111, vxw101, app(ty_Maybe, cc)) → new_ltEs7(vxw111, vxw101, cc)
new_compare9(vxw110, vxw100, app(app(ty_@2, fa), fb)) → new_compare13(vxw110, vxw100, fa, fb)
new_lt19(vxw111, vxw101, ty_Integer) → new_lt4(vxw111, vxw101)
new_esEs14(:(vxw300, vxw301), :(vxw4000, vxw4001), cfg) → new_asAs(new_esEs24(vxw300, vxw4000, cfg), new_esEs14(vxw301, vxw4001, cfg))
new_compare8(vxw110, vxw100, de) → new_compare210(vxw110, vxw100, new_esEs4(vxw110, vxw100, de), de)
new_lt19(vxw111, vxw101, app(app(app(ty_@3, bab), bac), bad)) → new_lt16(vxw111, vxw101, bab, bac, bad)
new_esEs25(vxw111, vxw101, ty_Integer) → new_esEs11(vxw111, vxw101)
new_primCmpInt(Pos(Succ(vxw1100)), Neg(vxw100)) → GT
new_ltEs7(Just(vxw110), Just(vxw100), app(ty_Maybe, ba)) → new_ltEs7(vxw110, vxw100, ba)
new_esEs10(Float(vxw300, vxw301), Float(vxw4000, vxw4001)) → new_esEs16(new_sr(vxw300, vxw4000), new_sr(vxw301, vxw4001))
new_esEs27(vxw301, vxw4001, ty_@0) → new_esEs15(vxw301, vxw4001)
new_esEs28(vxw300, vxw4000, ty_Double) → new_esEs9(vxw300, vxw4000)
new_lt19(vxw111, vxw101, app(ty_[], baa)) → new_lt15(vxw111, vxw101, baa)
new_primMulInt(Pos(vxw3000), Pos(vxw40000)) → Pos(new_primMulNat0(vxw3000, vxw40000))
new_esEs24(vxw300, vxw4000, ty_Integer) → new_esEs11(vxw300, vxw4000)
new_esEs7(Left(vxw300), Left(vxw4000), ty_Char, bef) → new_esEs12(vxw300, vxw4000)
new_ltEs17(Left(vxw110), Left(vxw100), app(app(ty_Either, bch), bda), bca) → new_ltEs17(vxw110, vxw100, bch, bda)
new_primMulInt(Neg(vxw3000), Neg(vxw40000)) → Pos(new_primMulNat0(vxw3000, vxw40000))
new_ltEs17(Left(vxw110), Left(vxw100), ty_Float, bca) → new_ltEs15(vxw110, vxw100)
new_compare9(vxw110, vxw100, ty_Ordering) → new_compare16(vxw110, vxw100)
new_compare110(vxw110, vxw100, True) → LT
new_primEqNat0(Succ(vxw3000), Zero) → False
new_primEqNat0(Zero, Succ(vxw40000)) → False
new_lt20(vxw110, vxw100, app(app(ty_Either, bbf), bbg)) → new_lt18(vxw110, vxw100, bbf, bbg)
new_compare110(vxw110, vxw100, False) → GT
new_esEs20(vxw302, vxw4002, ty_@0) → new_esEs15(vxw302, vxw4002)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_compare23(vxw110, vxw100, False, dg, dh) → new_compare10(vxw110, vxw100, new_ltEs4(vxw110, vxw100, dg, dh), dg, dh)
new_esEs28(vxw300, vxw4000, app(app(app(ty_@3, dbc), dbd), dbe)) → new_esEs6(vxw300, vxw4000, dbc, dbd, dbe)
new_esEs4(Nothing, Nothing, ced) → True
new_esEs4(Just(vxw300), Just(vxw4000), app(ty_Ratio, cfb)) → new_esEs13(vxw300, vxw4000, cfb)
new_esEs27(vxw301, vxw4001, app(app(app(ty_@3, daa), dab), dac)) → new_esEs6(vxw301, vxw4001, daa, dab, dac)
new_lt10(vxw110, vxw100, app(ty_[], ea)) → new_lt15(vxw110, vxw100, ea)
new_esEs27(vxw301, vxw4001, app(app(ty_@2, chg), chh)) → new_esEs5(vxw301, vxw4001, chg, chh)
new_esEs26(vxw110, vxw100, ty_Int) → new_esEs16(vxw110, vxw100)
new_ltEs7(Nothing, Nothing, bhd) → True
new_esEs27(vxw301, vxw4001, app(ty_Maybe, daf)) → new_esEs4(vxw301, vxw4001, daf)
new_esEs21(vxw301, vxw4001, app(app(ty_Either, ccd), cce)) → new_esEs7(vxw301, vxw4001, ccd, cce)
new_esEs23(vxw110, vxw100, app(ty_[], ea)) → new_esEs14(vxw110, vxw100, ea)
new_ltEs17(Left(vxw110), Left(vxw100), ty_Char, bca) → new_ltEs8(vxw110, vxw100)
new_ltEs17(Right(vxw110), Right(vxw100), bdb, ty_@0) → new_ltEs14(vxw110, vxw100)
new_lt10(vxw110, vxw100, ty_@0) → new_lt8(vxw110, vxw100)
new_lt10(vxw110, vxw100, ty_Int) → new_lt7(vxw110, vxw100)
new_esEs7(Right(vxw300), Right(vxw4000), bfg, app(ty_[], bgf)) → new_esEs14(vxw300, vxw4000, bgf)
new_ltEs12(vxw11, vxw10, eg) → new_not(new_esEs8(new_compare0(vxw11, vxw10, eg), GT))
new_primCmpInt(Neg(Zero), Neg(Succ(vxw1000))) → new_primCmpNat0(Succ(vxw1000), Zero)
new_compare23(vxw110, vxw100, True, dg, dh) → EQ
new_esEs25(vxw111, vxw101, ty_Int) → new_esEs16(vxw111, vxw101)
new_primCmpInt(Pos(Zero), Neg(Succ(vxw1000))) → GT
new_esEs23(vxw110, vxw100, ty_Bool) → new_esEs17(vxw110, vxw100)
new_ltEs17(Left(vxw110), Left(vxw100), ty_@0, bca) → new_ltEs14(vxw110, vxw100)
new_esEs4(Just(vxw300), Just(vxw4000), app(ty_[], cfc)) → new_esEs14(vxw300, vxw4000, cfc)
new_ltEs17(Right(vxw110), Right(vxw100), bdb, ty_Float) → new_ltEs15(vxw110, vxw100)
new_ltEs17(Left(vxw110), Right(vxw100), bdb, bca) → True
new_esEs21(vxw301, vxw4001, app(ty_Maybe, ccc)) → new_esEs4(vxw301, vxw4001, ccc)
new_esEs20(vxw302, vxw4002, app(app(ty_Either, cbb), cbc)) → new_esEs7(vxw302, vxw4002, cbb, cbc)
new_esEs21(vxw301, vxw4001, ty_Double) → new_esEs9(vxw301, vxw4001)
new_lt7(vxw110, vxw100) → new_esEs8(new_compare27(vxw110, vxw100), LT)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_lt20(vxw110, vxw100, app(ty_[], bbb)) → new_lt15(vxw110, vxw100, bbb)
new_ltEs7(Just(vxw110), Just(vxw100), app(ty_[], bd)) → new_ltEs12(vxw110, vxw100, bd)
new_ltEs17(Right(vxw110), Right(vxw100), bdb, app(ty_[], bdf)) → new_ltEs12(vxw110, vxw100, bdf)
new_esEs15(@0, @0) → True
new_lt17(vxw110, vxw100) → new_esEs8(new_compare26(vxw110, vxw100), LT)
new_compare15(Double(vxw110, vxw111), Double(vxw100, vxw101)) → new_compare27(new_sr(vxw110, vxw100), new_sr(vxw111, vxw101))
new_asAs(False, vxw53) → False
new_ltEs17(Right(vxw110), Right(vxw100), bdb, ty_Double) → new_ltEs9(vxw110, vxw100)
new_compare24(vxw110, vxw100, False) → new_compare11(vxw110, vxw100, new_ltEs5(vxw110, vxw100))
new_primMulInt(Neg(vxw3000), Pos(vxw40000)) → Neg(new_primMulNat0(vxw3000, vxw40000))
new_primMulInt(Pos(vxw3000), Neg(vxw40000)) → Neg(new_primMulNat0(vxw3000, vxw40000))
new_esEs26(vxw110, vxw100, ty_Double) → new_esEs9(vxw110, vxw100)
new_compare28(vxw110, vxw100, ee, ef) → new_compare29(vxw110, vxw100, new_esEs7(vxw110, vxw100, ee, ef), ee, ef)
new_ltEs10(LT, GT) → True
new_primMulNat0(Zero, Succ(vxw400000)) → Zero
new_primMulNat0(Succ(vxw30000), Zero) → Zero
new_esEs7(Left(vxw300), Left(vxw4000), ty_Float, bef) → new_esEs10(vxw300, vxw4000)
new_compare25(vxw110, vxw100, False, eb, ec, ed) → new_compare12(vxw110, vxw100, new_ltEs6(vxw110, vxw100, eb, ec, ed), eb, ec, ed)
new_esEs23(vxw110, vxw100, app(app(app(ty_@3, eb), ec), ed)) → new_esEs6(vxw110, vxw100, eb, ec, ed)
new_ltEs7(Just(vxw110), Just(vxw100), ty_Char) → new_ltEs8(vxw110, vxw100)
new_esEs21(vxw301, vxw4001, ty_Ordering) → new_esEs8(vxw301, vxw4001)
new_esEs21(vxw301, vxw4001, ty_Int) → new_esEs16(vxw301, vxw4001)
new_esEs24(vxw300, vxw4000, ty_Float) → new_esEs10(vxw300, vxw4000)
new_esEs19(vxw300, vxw4000, ty_Int) → new_esEs16(vxw300, vxw4000)
new_ltEs13(vxw11, vxw10) → new_not(new_esEs8(new_compare6(vxw11, vxw10), GT))
new_ltEs16(vxw11, vxw10) → new_not(new_esEs8(new_compare27(vxw11, vxw10), GT))
new_lt10(vxw110, vxw100, ty_Integer) → new_lt4(vxw110, vxw100)
new_esEs23(vxw110, vxw100, ty_Char) → new_esEs12(vxw110, vxw100)
new_esEs25(vxw111, vxw101, app(app(app(ty_@3, bab), bac), bad)) → new_esEs6(vxw111, vxw101, bab, bac, bad)
new_lt19(vxw111, vxw101, app(ty_Maybe, he)) → new_lt5(vxw111, vxw101, he)
new_lt13(vxw110, vxw100) → new_esEs8(new_compare15(vxw110, vxw100), LT)
new_ltEs10(EQ, EQ) → True
new_esEs13(:%(vxw300, vxw301), :%(vxw4000, vxw4001), bhc) → new_asAs(new_esEs19(vxw300, vxw4000, bhc), new_esEs18(vxw301, vxw4001, bhc))
new_compare9(vxw110, vxw100, app(app(ty_Either, fh), ga)) → new_compare28(vxw110, vxw100, fh, ga)
new_esEs23(vxw110, vxw100, ty_Int) → new_esEs16(vxw110, vxw100)
new_ltEs10(LT, LT) → True
new_ltEs19(vxw112, vxw102, ty_Int) → new_ltEs16(vxw112, vxw102)
new_ltEs19(vxw112, vxw102, ty_@0) → new_ltEs14(vxw112, vxw102)
new_compare211(vxw110, vxw100, False) → new_compare110(vxw110, vxw100, new_ltEs10(vxw110, vxw100))
new_esEs7(Left(vxw300), Left(vxw4000), app(app(app(ty_@3, beg), beh), bfa), bef) → new_esEs6(vxw300, vxw4000, beg, beh, bfa)
new_lt10(vxw110, vxw100, ty_Ordering) → new_lt6(vxw110, vxw100)
new_esEs27(vxw301, vxw4001, ty_Int) → new_esEs16(vxw301, vxw4001)
new_ltEs7(Just(vxw110), Just(vxw100), ty_@0) → new_ltEs14(vxw110, vxw100)
new_ltEs17(Right(vxw110), Right(vxw100), bdb, ty_Char) → new_ltEs8(vxw110, vxw100)
new_ltEs19(vxw112, vxw102, ty_Bool) → new_ltEs5(vxw112, vxw102)
new_ltEs8(vxw11, vxw10) → new_not(new_esEs8(new_compare14(vxw11, vxw10), GT))
new_lt20(vxw110, vxw100, app(app(app(ty_@3, bbc), bbd), bbe)) → new_lt16(vxw110, vxw100, bbc, bbd, bbe)
new_esEs7(Right(vxw300), Right(vxw4000), bfg, ty_Int) → new_esEs16(vxw300, vxw4000)
new_ltEs7(Just(vxw110), Nothing, bhd) → False
new_esEs28(vxw300, vxw4000, ty_Bool) → new_esEs17(vxw300, vxw4000)
new_esEs28(vxw300, vxw4000, app(ty_Ratio, dbf)) → new_esEs13(vxw300, vxw4000, dbf)
new_ltEs17(Left(vxw110), Left(vxw100), ty_Int, bca) → new_ltEs16(vxw110, vxw100)
new_compare11(vxw110, vxw100, False) → GT
new_lt16(vxw110, vxw100, eb, ec, ed) → new_esEs8(new_compare19(vxw110, vxw100, eb, ec, ed), LT)
new_esEs26(vxw110, vxw100, ty_Bool) → new_esEs17(vxw110, vxw100)
new_esEs25(vxw111, vxw101, app(app(ty_@2, hg), hh)) → new_esEs5(vxw111, vxw101, hg, hh)
new_compare11(vxw110, vxw100, True) → LT
new_ltEs19(vxw112, vxw102, app(ty_Maybe, gd)) → new_ltEs7(vxw112, vxw102, gd)
new_esEs7(Left(vxw300), Left(vxw4000), ty_Bool, bef) → new_esEs17(vxw300, vxw4000)
new_ltEs10(EQ, LT) → False
new_compare112(vxw110, vxw100, False, de) → GT
new_compare9(vxw110, vxw100, ty_Char) → new_compare14(vxw110, vxw100)
new_lt20(vxw110, vxw100, ty_Char) → new_lt12(vxw110, vxw100)
new_esEs22(vxw300, vxw4000, ty_Float) → new_esEs10(vxw300, vxw4000)
new_ltEs10(GT, LT) → False
new_ltEs14(vxw11, vxw10) → new_not(new_esEs8(new_compare7(vxw11, vxw10), GT))
new_primPlusNat1(Zero, Zero) → Zero
new_compare0([], :(vxw100, vxw101), eg) → LT
new_compare111(vxw110, vxw100, True, ee, ef) → LT
new_esEs21(vxw301, vxw4001, app(app(app(ty_@3, cbf), cbg), cbh)) → new_esEs6(vxw301, vxw4001, cbf, cbg, cbh)
new_esEs27(vxw301, vxw4001, app(ty_[], dae)) → new_esEs14(vxw301, vxw4001, dae)
new_asAs(True, vxw53) → vxw53
new_primMulNat0(Succ(vxw30000), Succ(vxw400000)) → new_primPlusNat0(new_primMulNat0(vxw30000, Succ(vxw400000)), vxw400000)
new_compare9(vxw110, vxw100, app(ty_Ratio, bhb)) → new_compare17(vxw110, vxw100, bhb)
new_esEs20(vxw302, vxw4002, ty_Double) → new_esEs9(vxw302, vxw4002)
new_esEs27(vxw301, vxw4001, ty_Integer) → new_esEs11(vxw301, vxw4001)
new_ltEs17(Right(vxw110), Right(vxw100), bdb, app(app(app(ty_@3, bdg), bdh), bea)) → new_ltEs6(vxw110, vxw100, bdg, bdh, bea)
new_compare211(vxw110, vxw100, True) → EQ
new_ltEs17(Right(vxw110), Right(vxw100), bdb, app(app(ty_@2, bdd), bde)) → new_ltEs4(vxw110, vxw100, bdd, bde)
new_ltEs19(vxw112, vxw102, ty_Integer) → new_ltEs13(vxw112, vxw102)
new_ltEs18(vxw111, vxw101, app(ty_[], cf)) → new_ltEs12(vxw111, vxw101, cf)
new_esEs20(vxw302, vxw4002, app(ty_[], cah)) → new_esEs14(vxw302, vxw4002, cah)
new_esEs4(Just(vxw300), Just(vxw4000), ty_Double) → new_esEs9(vxw300, vxw4000)
new_ltEs18(vxw111, vxw101, app(app(ty_@2, cd), ce)) → new_ltEs4(vxw111, vxw101, cd, ce)
new_ltEs7(Just(vxw110), Just(vxw100), app(ty_Ratio, bhe)) → new_ltEs11(vxw110, vxw100, bhe)
new_primCompAux00(vxw72, GT) → GT
new_ltEs17(Right(vxw110), Right(vxw100), bdb, ty_Bool) → new_ltEs5(vxw110, vxw100)
new_esEs25(vxw111, vxw101, app(app(ty_Either, bae), baf)) → new_esEs7(vxw111, vxw101, bae, baf)
new_ltEs18(vxw111, vxw101, ty_Double) → new_ltEs9(vxw111, vxw101)
new_ltEs11(vxw11, vxw10, bhf) → new_not(new_esEs8(new_compare17(vxw11, vxw10, bhf), GT))
new_lt11(vxw110, vxw100, dg, dh) → new_esEs8(new_compare13(vxw110, vxw100, dg, dh), LT)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_compare26(Float(vxw110, vxw111), Float(vxw100, vxw101)) → new_compare27(new_sr(vxw110, vxw100), new_sr(vxw111, vxw101))
new_lt19(vxw111, vxw101, app(ty_Ratio, chc)) → new_lt14(vxw111, vxw101, chc)
new_ltEs18(vxw111, vxw101, ty_Ordering) → new_ltEs10(vxw111, vxw101)
new_esEs7(Left(vxw300), Left(vxw4000), app(ty_[], bfc), bef) → new_esEs14(vxw300, vxw4000, bfc)
new_esEs28(vxw300, vxw4000, ty_Char) → new_esEs12(vxw300, vxw4000)
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primCmpInt(Neg(Succ(vxw1100)), Pos(vxw100)) → LT
new_esEs22(vxw300, vxw4000, ty_Int) → new_esEs16(vxw300, vxw4000)
new_not(True) → False

The set Q consists of the following terms:

new_esEs11(Integer(x0), Integer(x1))
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_esEs4(Just(x0), Just(x1), ty_Int)
new_lt16(x0, x1, x2, x3, x4)
new_ltEs13(x0, x1)
new_esEs7(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_asAs(True, x0)
new_esEs21(x0, x1, ty_Ordering)
new_primMulNat0(Zero, Succ(x0))
new_lt10(x0, x1, ty_Int)
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_lt20(x0, x1, app(ty_Ratio, x2))
new_esEs4(Nothing, Nothing, x0)
new_compare11(x0, x1, True)
new_primCmpNat0(Succ(x0), Zero)
new_ltEs7(Nothing, Nothing, x0)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare13(x0, x1, x2, x3)
new_compare23(x0, x1, False, x2, x3)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, ty_Integer)
new_ltEs19(x0, x1, ty_@0)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs17(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_lt19(x0, x1, ty_Int)
new_compare111(x0, x1, True, x2, x3)
new_esEs7(Right(x0), Right(x1), x2, ty_Char)
new_compare9(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_esEs4(Nothing, Just(x0), x1)
new_esEs23(x0, x1, ty_Float)
new_ltEs18(x0, x1, ty_Float)
new_compare9(x0, x1, ty_Bool)
new_esEs25(x0, x1, ty_Bool)
new_compare9(x0, x1, ty_Float)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs14(:(x0, x1), :(x2, x3), x4)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_ltEs10(LT, LT)
new_lt10(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs23(x0, x1, ty_Ordering)
new_lt4(x0, x1)
new_esEs14(:(x0, x1), [], x2)
new_esEs14([], [], x0)
new_esEs9(Double(x0, x1), Double(x2, x3))
new_lt20(x0, x1, ty_Double)
new_esEs27(x0, x1, ty_@0)
new_ltEs6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_compare0([], :(x0, x1), x2)
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs18(x0, x1, ty_Double)
new_esEs23(x0, x1, ty_Char)
new_esEs8(GT, GT)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs7(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs7(Left(x0), Left(x1), ty_Float, x2)
new_esEs22(x0, x1, ty_Ordering)
new_ltEs17(Right(x0), Right(x1), x2, ty_Float)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs24(x0, x1, ty_Char)
new_compare12(x0, x1, False, x2, x3, x4)
new_ltEs17(Left(x0), Left(x1), ty_Int, x2)
new_esEs7(Right(x0), Right(x1), x2, ty_Ordering)
new_compare6(Integer(x0), Integer(x1))
new_esEs8(LT, LT)
new_primMulNat0(Succ(x0), Succ(x1))
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs7(Just(x0), Just(x1), ty_Integer)
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, ty_Double)
new_esEs21(x0, x1, ty_Integer)
new_esEs17(False, False)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_ltEs17(Left(x0), Left(x1), ty_Double, x2)
new_primEqNat0(Succ(x0), Zero)
new_esEs26(x0, x1, ty_Bool)
new_ltEs5(False, False)
new_esEs22(x0, x1, ty_Bool)
new_esEs7(Right(x0), Right(x1), x2, ty_Float)
new_esEs7(Left(x0), Left(x1), ty_@0, x2)
new_ltEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs20(x0, x1, ty_Float)
new_esEs27(x0, x1, app(ty_[], x2))
new_esEs27(x0, x1, ty_Ordering)
new_compare9(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs17(Right(x0), Right(x1), x2, ty_Bool)
new_esEs24(x0, x1, ty_@0)
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_compare29(x0, x1, False, x2, x3)
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_lt20(x0, x1, app(ty_Maybe, x2))
new_ltEs17(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_ltEs17(Right(x0), Right(x1), x2, ty_Integer)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_lt7(x0, x1)
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_compare211(x0, x1, True)
new_primEqNat0(Zero, Zero)
new_esEs7(Left(x0), Left(x1), ty_Integer, x2)
new_compare9(x0, x1, ty_Integer)
new_esEs21(x0, x1, ty_Bool)
new_lt19(x0, x1, app(ty_Ratio, x2))
new_lt10(x0, x1, ty_Integer)
new_esEs21(x0, x1, ty_Char)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_esEs4(Just(x0), Just(x1), ty_Bool)
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_ltEs7(Just(x0), Just(x1), ty_Double)
new_esEs22(x0, x1, ty_Int)
new_lt20(x0, x1, ty_Float)
new_esEs7(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_esEs4(Just(x0), Just(x1), ty_Ordering)
new_esEs25(x0, x1, ty_Float)
new_compare25(x0, x1, False, x2, x3, x4)
new_primMulNat0(Zero, Zero)
new_ltEs18(x0, x1, ty_Int)
new_esEs21(x0, x1, ty_Float)
new_lt10(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_ltEs10(EQ, LT)
new_ltEs10(LT, EQ)
new_esEs22(x0, x1, app(ty_[], x2))
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs18(x0, x1, ty_Integer)
new_primCompAux00(x0, EQ)
new_pePe(True, x0)
new_esEs20(x0, x1, ty_Ordering)
new_esEs28(x0, x1, ty_Int)
new_lt20(x0, x1, ty_Ordering)
new_esEs12(Char(x0), Char(x1))
new_lt19(x0, x1, ty_Char)
new_compare110(x0, x1, False)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_esEs4(Just(x0), Just(x1), ty_@0)
new_lt10(x0, x1, ty_Ordering)
new_esEs22(x0, x1, ty_Char)
new_esEs26(x0, x1, ty_@0)
new_esEs24(x0, x1, ty_Integer)
new_esEs7(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs25(x0, x1, ty_Ordering)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_primCompAux00(x0, LT)
new_compare112(x0, x1, False, x2)
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs7(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs7(Left(x0), Left(x1), ty_Int, x2)
new_ltEs19(x0, x1, ty_Integer)
new_esEs7(Left(x0), Left(x1), ty_Char, x2)
new_ltEs19(x0, x1, ty_Int)
new_ltEs17(Right(x0), Right(x1), x2, ty_@0)
new_esEs25(x0, x1, ty_Double)
new_lt20(x0, x1, app(ty_[], x2))
new_ltEs17(Right(x0), Right(x1), x2, ty_Char)
new_esEs27(x0, x1, ty_Double)
new_esEs26(x0, x1, ty_Integer)
new_esEs19(x0, x1, ty_Integer)
new_esEs23(x0, x1, ty_Integer)
new_lt6(x0, x1)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs23(x0, x1, app(ty_[], x2))
new_ltEs19(x0, x1, app(ty_[], x2))
new_compare9(x0, x1, ty_@0)
new_ltEs17(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs4(Just(x0), Just(x1), ty_Double)
new_compare29(x0, x1, True, x2, x3)
new_ltEs19(x0, x1, ty_Bool)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_esEs28(x0, x1, ty_@0)
new_lt20(x0, x1, ty_Bool)
new_ltEs15(x0, x1)
new_ltEs17(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_compare9(x0, x1, app(ty_[], x2))
new_primCompAux0(x0, x1, x2, x3)
new_esEs13(:%(x0, x1), :%(x2, x3), x4)
new_compare11(x0, x1, False)
new_ltEs17(Left(x0), Left(x1), ty_Ordering, x2)
new_lt10(x0, x1, ty_Double)
new_lt19(x0, x1, ty_@0)
new_ltEs18(x0, x1, ty_Char)
new_compare27(x0, x1)
new_ltEs7(Nothing, Just(x0), x1)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_primPlusNat1(Zero, Zero)
new_compare19(x0, x1, x2, x3, x4)
new_ltEs18(x0, x1, app(ty_Maybe, x2))
new_sr(x0, x1)
new_lt5(x0, x1, x2)
new_esEs20(x0, x1, ty_@0)
new_esEs28(x0, x1, app(ty_[], x2))
new_ltEs7(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs4(Just(x0), Nothing, x1)
new_esEs16(x0, x1)
new_esEs24(x0, x1, ty_Float)
new_compare9(x0, x1, ty_Ordering)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_ltEs7(Just(x0), Just(x1), ty_Int)
new_esEs28(x0, x1, ty_Float)
new_lt18(x0, x1, x2, x3)
new_esEs23(x0, x1, ty_@0)
new_ltEs17(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_ltEs18(x0, x1, ty_Ordering)
new_esEs23(x0, x1, ty_Int)
new_esEs7(Left(x0), Left(x1), ty_Double, x2)
new_esEs26(x0, x1, ty_Double)
new_ltEs17(Left(x0), Left(x1), ty_Bool, x2)
new_ltEs11(x0, x1, x2)
new_esEs24(x0, x1, ty_Bool)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_primMulInt(Pos(x0), Pos(x1))
new_ltEs7(Just(x0), Just(x1), ty_Char)
new_esEs14([], :(x0, x1), x2)
new_esEs4(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_primPlusNat0(Succ(x0), x1)
new_ltEs10(GT, LT)
new_ltEs10(LT, GT)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_sr0(Integer(x0), Integer(x1))
new_esEs23(x0, x1, ty_Double)
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_esEs4(Just(x0), Just(x1), app(ty_[], x2))
new_esEs25(x0, x1, ty_Integer)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_esEs20(x0, x1, ty_Char)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primEqNat0(Zero, Succ(x0))
new_esEs7(Right(x0), Right(x1), x2, ty_@0)
new_ltEs17(Left(x0), Left(x1), ty_Integer, x2)
new_esEs27(x0, x1, ty_Bool)
new_esEs25(x0, x1, app(ty_[], x2))
new_compare17(:%(x0, x1), :%(x2, x3), ty_Int)
new_lt9(x0, x1)
new_esEs7(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs7(Just(x0), Nothing, x1)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_primMulInt(Neg(x0), Neg(x1))
new_ltEs17(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_ltEs17(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs27(x0, x1, ty_Char)
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_compare211(x0, x1, False)
new_ltEs9(x0, x1)
new_ltEs7(Just(x0), Just(x1), app(ty_Ratio, x2))
new_lt10(x0, x1, ty_@0)
new_ltEs18(x0, x1, ty_Integer)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_esEs27(x0, x1, ty_Float)
new_ltEs19(x0, x1, ty_Double)
new_esEs4(Just(x0), Just(x1), app(ty_Maybe, x2))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primEqInt(Neg(Zero), Neg(Zero))
new_esEs7(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs19(x0, x1, ty_Ordering)
new_compare23(x0, x1, True, x2, x3)
new_lt15(x0, x1, x2)
new_ltEs14(x0, x1)
new_compare9(x0, x1, app(app(ty_@2, x2), x3))
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs24(x0, x1, ty_Ordering)
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_compare7(@0, @0)
new_esEs18(x0, x1, ty_Int)
new_ltEs17(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCompAux00(x0, GT)
new_ltEs17(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_lt19(x0, x1, ty_Double)
new_esEs26(x0, x1, ty_Float)
new_ltEs7(Just(x0), Just(x1), ty_Ordering)
new_ltEs16(x0, x1)
new_esEs21(x0, x1, ty_@0)
new_compare18(x0, x1)
new_lt19(x0, x1, ty_Ordering)
new_ltEs17(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs7(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_asAs(False, x0)
new_lt10(x0, x1, ty_Char)
new_esEs20(x0, x1, ty_Int)
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat1(Succ(x0), Zero)
new_esEs8(GT, EQ)
new_esEs8(EQ, GT)
new_esEs22(x0, x1, ty_Integer)
new_ltEs18(x0, x1, app(app(ty_@2, x2), x3))
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_compare17(:%(x0, x1), :%(x2, x3), ty_Integer)
new_compare112(x0, x1, True, x2)
new_ltEs7(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_primPlusNat0(Zero, x0)
new_esEs20(x0, x1, ty_Integer)
new_esEs5(@2(x0, x1), @2(x2, x3), x4, x5)
new_compare26(Float(x0, x1), Float(x2, x3))
new_primCmpNat0(Zero, Zero)
new_lt10(x0, x1, ty_Bool)
new_compare9(x0, x1, app(ty_Ratio, x2))
new_lt10(x0, x1, app(ty_Maybe, x2))
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs15(@0, @0)
new_compare16(x0, x1)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_compare25(x0, x1, True, x2, x3, x4)
new_compare210(x0, x1, True, x2)
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_compare10(x0, x1, False, x2, x3)
new_lt11(x0, x1, x2, x3)
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs23(x0, x1, ty_Bool)
new_compare0([], [], x0)
new_primCmpNat0(Zero, Succ(x0))
new_esEs27(x0, x1, ty_Integer)
new_esEs21(x0, x1, ty_Int)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs24(x0, x1, ty_Double)
new_ltEs7(Just(x0), Just(x1), app(ty_[], x2))
new_esEs20(x0, x1, ty_Bool)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_lt19(x0, x1, ty_Integer)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_ltEs10(GT, GT)
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_lt14(x0, x1, x2)
new_ltEs17(Left(x0), Left(x1), ty_Float, x2)
new_compare0(:(x0, x1), :(x2, x3), x4)
new_ltEs7(Just(x0), Just(x1), ty_Float)
new_lt17(x0, x1)
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_compare15(Double(x0, x1), Double(x2, x3))
new_esEs22(x0, x1, ty_Float)
new_lt13(x0, x1)
new_ltEs17(Right(x0), Right(x1), x2, app(ty_[], x3))
new_compare28(x0, x1, x2, x3)
new_esEs7(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_compare9(x0, x1, ty_Char)
new_ltEs5(True, True)
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare14(Char(x0), Char(x1))
new_esEs7(Right(x0), Left(x1), x2, x3)
new_esEs7(Left(x0), Right(x1), x2, x3)
new_ltEs17(Right(x0), Right(x1), x2, ty_Double)
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_not(True)
new_ltEs7(Just(x0), Just(x1), ty_@0)
new_ltEs17(Right(x0), Right(x1), x2, ty_Ordering)
new_lt10(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs18(x0, x1, app(app(ty_Either, x2), x3))
new_esEs7(Right(x0), Right(x1), x2, ty_Double)
new_lt19(x0, x1, app(ty_[], x2))
new_compare210(x0, x1, False, x2)
new_esEs28(x0, x1, ty_Double)
new_esEs26(x0, x1, ty_Ordering)
new_ltEs12(x0, x1, x2)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, ty_Int)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_not(False)
new_esEs4(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs4(Just(x0), Just(x1), ty_Integer)
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs21(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, ty_Char)
new_lt19(x0, x1, ty_Bool)
new_primCmpNat0(Succ(x0), Succ(x1))
new_esEs20(x0, x1, app(ty_[], x2))
new_esEs7(Left(x0), Left(x1), ty_Bool, x2)
new_ltEs10(EQ, GT)
new_ltEs10(GT, EQ)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs18(x0, x1, app(ty_[], x2))
new_esEs22(x0, x1, ty_Double)
new_esEs7(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs10(Float(x0, x1), Float(x2, x3))
new_esEs7(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs26(x0, x1, ty_Int)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_esEs4(Just(x0), Just(x1), ty_Float)
new_ltEs4(@2(x0, x1), @2(x2, x3), x4, x5)
new_compare24(x0, x1, True)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_compare111(x0, x1, False, x2, x3)
new_esEs25(x0, x1, ty_@0)
new_esEs7(Right(x0), Right(x1), x2, ty_Int)
new_compare9(x0, x1, ty_Int)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_ltEs17(Left(x0), Left(x1), ty_Char, x2)
new_primMulNat0(Succ(x0), Zero)
new_esEs28(x0, x1, ty_Bool)
new_lt19(x0, x1, ty_Float)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs8(EQ, LT)
new_esEs8(LT, EQ)
new_esEs24(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, ty_@0)
new_ltEs17(Left(x0), Left(x1), ty_@0, x2)
new_esEs4(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs7(Right(x0), Right(x1), x2, ty_Integer)
new_ltEs17(Left(x0), Left(x1), app(ty_[], x2), x3)
new_lt8(x0, x1)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, ty_Int)
new_compare12(x0, x1, True, x2, x3, x4)
new_esEs6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_ltEs7(Just(x0), Just(x1), ty_Bool)
new_esEs17(False, True)
new_esEs17(True, False)
new_esEs7(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_compare110(x0, x1, True)
new_esEs7(Left(x0), Left(x1), ty_Ordering, x2)
new_lt19(x0, x1, app(ty_Maybe, x2))
new_ltEs18(x0, x1, app(ty_Ratio, x2))
new_ltEs8(x0, x1)
new_esEs26(x0, x1, app(ty_[], x2))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_compare24(x0, x1, False)
new_esEs28(x0, x1, ty_Char)
new_compare9(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs26(x0, x1, ty_Char)
new_compare9(x0, x1, ty_Double)
new_primEqInt(Pos(Zero), Pos(Zero))
new_lt10(x0, x1, app(ty_[], x2))
new_esEs17(True, True)
new_lt12(x0, x1)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_ltEs18(x0, x1, ty_@0)
new_ltEs17(Right(x0), Right(x1), x2, ty_Int)
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_esEs20(x0, x1, ty_Double)
new_lt10(x0, x1, app(app(ty_@2, x2), x3))
new_lt10(x0, x1, ty_Float)
new_esEs25(x0, x1, ty_Char)
new_ltEs19(x0, x1, ty_Char)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_compare8(x0, x1, x2)
new_esEs7(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs28(x0, x1, ty_Ordering)
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_compare10(x0, x1, True, x2, x3)
new_ltEs5(True, False)
new_ltEs5(False, True)
new_esEs19(x0, x1, ty_Int)
new_esEs24(x0, x1, ty_Int)
new_ltEs18(x0, x1, ty_Bool)
new_compare0(:(x0, x1), [], x2)
new_esEs4(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs4(Just(x0), Just(x1), ty_Char)
new_lt20(x0, x1, ty_Int)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_pePe(False, x0)
new_esEs22(x0, x1, ty_@0)
new_ltEs19(x0, x1, ty_Float)
new_ltEs17(Right(x0), Left(x1), x2, x3)
new_esEs28(x0, x1, ty_Integer)
new_ltEs17(Left(x0), Right(x1), x2, x3)
new_ltEs10(EQ, EQ)
new_esEs24(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: 



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

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

new_insertBy02(vxw37, vxw38, vxw39, False, ca, cb) → new_insertBy(Right(vxw38), vxw39, ca, cb)
new_insertBy0(vxw10, vxw11, vxw12, False, ba, bb) → new_insertBy00(vxw10, vxw11, vxw12, new_ltEs20(vxw11, vxw10, ba), ba, bb)
new_insertBy(Right(vxw30), :(Right(vxw400), vxw41), be, bf) → new_insertBy01(vxw400, vxw30, vxw41, new_esEs30(vxw30, vxw400, bf), be, bf)
new_insertBy01(vxw19, vxw20, vxw21, False, bg, bh) → new_insertBy02(vxw19, vxw20, vxw21, new_ltEs21(vxw20, vxw19, bh), bg, bh)
new_insertBy(Left(vxw30), :(Left(vxw400), vxw41), be, bf) → new_insertBy0(vxw400, vxw30, vxw41, new_esEs29(vxw30, vxw400, be), be, bf)
new_insertBy00(vxw28, vxw29, vxw30, False, bc, bd) → new_insertBy(Left(vxw29), vxw30, bc, bd)
new_insertBy(Right(vxw30), :(Left(vxw400), vxw41), be, bf) → new_insertBy(Right(vxw30), vxw41, be, bf)

The TRS R consists of the following rules:

new_esEs4(Just(vxw300), Just(vxw4000), app(ty_Maybe, ceh)) → new_esEs4(vxw300, vxw4000, ceh)
new_esEs25(vxw111, vxw101, app(ty_[], dac)) → new_esEs14(vxw111, vxw101, dac)
new_esEs26(vxw110, vxw100, ty_@0) → new_esEs15(vxw110, vxw100)
new_esEs23(vxw110, vxw100, app(app(ty_Either, cdg), cdh)) → new_esEs7(vxw110, vxw100, cdg, cdh)
new_esEs29(vxw30, vxw400, ty_Int) → new_esEs16(vxw30, vxw400)
new_compare112(vxw110, vxw100, True, cd) → LT
new_esEs4(Just(vxw300), Just(vxw4000), ty_Ordering) → new_esEs8(vxw300, vxw4000)
new_esEs7(Left(vxw300), Left(vxw4000), app(app(ty_Either, fc), fd), ed) → new_esEs7(vxw300, vxw4000, fc, fd)
new_ltEs19(vxw112, vxw102, app(ty_Ratio, cgh)) → new_ltEs11(vxw112, vxw102, cgh)
new_ltEs21(vxw20, vxw19, app(ty_[], dfc)) → new_ltEs12(vxw20, vxw19, dfc)
new_compare210(vxw110, vxw100, False, cd) → new_compare112(vxw110, vxw100, new_ltEs7(vxw110, vxw100, cd), cd)
new_esEs7(Left(vxw300), Left(vxw4000), app(ty_Maybe, fb), ed) → new_esEs4(vxw300, vxw4000, fb)
new_ltEs18(vxw111, vxw101, ty_Float) → new_ltEs15(vxw111, vxw101)
new_ltEs20(vxw11, vxw10, ty_Ordering) → new_ltEs10(vxw11, vxw10)
new_compare10(vxw110, vxw100, True, dh, ea) → LT
new_esEs26(vxw110, vxw100, ty_Float) → new_esEs10(vxw110, vxw100)
new_esEs24(vxw300, vxw4000, app(ty_Maybe, cgb)) → new_esEs4(vxw300, vxw4000, cgb)
new_esEs4(Just(vxw300), Nothing, bbe) → False
new_esEs4(Nothing, Just(vxw4000), bbe) → False
new_esEs11(Integer(vxw300), Integer(vxw4000)) → new_primEqInt(vxw300, vxw4000)
new_lt19(vxw111, vxw101, app(app(ty_Either, dag), dah)) → new_lt18(vxw111, vxw101, dag, dah)
new_esEs28(vxw300, vxw4000, ty_Integer) → new_esEs11(vxw300, vxw4000)
new_esEs26(vxw110, vxw100, ty_Integer) → new_esEs11(vxw110, vxw100)
new_ltEs17(Right(vxw110), Right(vxw100), bdg, app(ty_Ratio, cbd)) → new_ltEs11(vxw110, vxw100, cbd)
new_lt19(vxw111, vxw101, ty_@0) → new_lt8(vxw111, vxw101)
new_esEs22(vxw300, vxw4000, ty_Char) → new_esEs12(vxw300, vxw4000)
new_ltEs17(Left(vxw110), Left(vxw100), app(ty_Ratio, cab), bdh) → new_ltEs11(vxw110, vxw100, cab)
new_esEs30(vxw30, vxw400, app(ty_[], dd)) → new_esEs14(vxw30, vxw400, dd)
new_ltEs20(vxw11, vxw10, ty_Bool) → new_ltEs5(vxw11, vxw10)
new_esEs4(Just(vxw300), Just(vxw4000), ty_Char) → new_esEs12(vxw300, vxw4000)
new_esEs27(vxw301, vxw4001, ty_Bool) → new_esEs17(vxw301, vxw4001)
new_lt12(vxw110, vxw100) → new_esEs8(new_compare14(vxw110, vxw100), LT)
new_primMulNat0(Zero, Zero) → Zero
new_ltEs21(vxw20, vxw19, ty_Int) → new_ltEs16(vxw20, vxw19)
new_esEs23(vxw110, vxw100, app(ty_Ratio, cde)) → new_esEs13(vxw110, vxw100, cde)
new_esEs4(Just(vxw300), Just(vxw4000), app(app(app(ty_@3, cec), ced), cee)) → new_esEs6(vxw300, vxw4000, cec, ced, cee)
new_ltEs19(vxw112, vxw102, ty_Double) → new_ltEs9(vxw112, vxw102)
new_esEs20(vxw302, vxw4002, app(ty_Maybe, beh)) → new_esEs4(vxw302, vxw4002, beh)
new_lt20(vxw110, vxw100, ty_Integer) → new_lt4(vxw110, vxw100)
new_lt20(vxw110, vxw100, ty_@0) → new_lt8(vxw110, vxw100)
new_esEs21(vxw301, vxw4001, ty_Bool) → new_esEs17(vxw301, vxw4001)
new_esEs23(vxw110, vxw100, ty_Double) → new_esEs9(vxw110, vxw100)
new_esEs7(Right(vxw300), Right(vxw4000), ff, ty_Ordering) → new_esEs8(vxw300, vxw4000)
new_lt19(vxw111, vxw101, ty_Ordering) → new_lt6(vxw111, vxw101)
new_ltEs17(Left(vxw110), Left(vxw100), ty_Integer, bdh) → new_ltEs13(vxw110, vxw100)
new_esEs25(vxw111, vxw101, ty_Bool) → new_esEs17(vxw111, vxw101)
new_compare13(vxw110, vxw100, dh, ea) → new_compare23(vxw110, vxw100, new_esEs5(vxw110, vxw100, dh, ea), dh, ea)
new_compare9(vxw110, vxw100, ty_Double) → new_compare15(vxw110, vxw100)
new_lt20(vxw110, vxw100, app(app(ty_@2, dbb), dbc)) → new_lt11(vxw110, vxw100, dbb, dbc)
new_esEs23(vxw110, vxw100, app(ty_Maybe, cd)) → new_esEs4(vxw110, vxw100, cd)
new_compare9(vxw110, vxw100, ty_Integer) → new_compare6(vxw110, vxw100)
new_esEs30(vxw30, vxw400, app(app(ty_Either, df), dg)) → new_esEs7(vxw30, vxw400, df, dg)
new_ltEs7(Just(vxw110), Just(vxw100), ty_Bool) → new_ltEs5(vxw110, vxw100)
new_esEs17(True, True) → True
new_esEs20(vxw302, vxw4002, app(ty_Ratio, bef)) → new_esEs13(vxw302, vxw4002, bef)
new_ltEs19(vxw112, vxw102, ty_Ordering) → new_ltEs10(vxw112, vxw102)
new_compare0(:(vxw110, vxw111), :(vxw100, vxw101), cc) → new_primCompAux0(vxw110, vxw100, new_compare0(vxw111, vxw101, cc), cc)
new_ltEs7(Just(vxw110), Just(vxw100), app(app(app(ty_@3, bcd), bce), bcf)) → new_ltEs6(vxw110, vxw100, bcd, bce, bcf)
new_esEs22(vxw300, vxw4000, app(app(ty_@2, bge), bgf)) → new_esEs5(vxw300, vxw4000, bge, bgf)
new_lt15(vxw110, vxw100, cdf) → new_esEs8(new_compare0(vxw110, vxw100, cdf), LT)
new_esEs24(vxw300, vxw4000, app(app(ty_@2, cfc), cfd)) → new_esEs5(vxw300, vxw4000, cfc, cfd)
new_esEs4(Just(vxw300), Just(vxw4000), ty_Float) → new_esEs10(vxw300, vxw4000)
new_ltEs18(vxw111, vxw101, ty_Char) → new_ltEs8(vxw111, vxw101)
new_ltEs17(Right(vxw110), Right(vxw100), bdg, ty_Integer) → new_ltEs13(vxw110, vxw100)
new_ltEs10(EQ, GT) → True
new_compare29(vxw110, vxw100, False, cdg, cdh) → new_compare111(vxw110, vxw100, new_ltEs17(vxw110, vxw100, cdg, cdh), cdg, cdh)
new_ltEs21(vxw20, vxw19, app(app(ty_@2, deh), dfa)) → new_ltEs4(vxw20, vxw19, deh, dfa)
new_ltEs20(vxw11, vxw10, ty_Double) → new_ltEs9(vxw11, vxw10)
new_compare9(vxw110, vxw100, ty_Int) → new_compare27(vxw110, vxw100)
new_esEs26(vxw110, vxw100, app(ty_Maybe, dba)) → new_esEs4(vxw110, vxw100, dba)
new_esEs22(vxw300, vxw4000, app(ty_[], bhc)) → new_esEs14(vxw300, vxw4000, bhc)
new_lt20(vxw110, vxw100, ty_Float) → new_lt17(vxw110, vxw100)
new_esEs22(vxw300, vxw4000, app(app(ty_Either, bhe), bhf)) → new_esEs7(vxw300, vxw4000, bhe, bhf)
new_ltEs7(Just(vxw110), Just(vxw100), app(app(ty_Either, bcg), bch)) → new_ltEs17(vxw110, vxw100, bcg, bch)
new_ltEs7(Just(vxw110), Just(vxw100), app(app(ty_@2, bbh), bca)) → new_ltEs4(vxw110, vxw100, bbh, bca)
new_esEs25(vxw111, vxw101, ty_Double) → new_esEs9(vxw111, vxw101)
new_pePe(False, vxw60) → vxw60
new_esEs14([], [], bbd) → True
new_ltEs7(Just(vxw110), Just(vxw100), ty_Ordering) → new_ltEs10(vxw110, vxw100)
new_ltEs17(Left(vxw110), Left(vxw100), ty_Bool, bdh) → new_ltEs5(vxw110, vxw100)
new_esEs7(Left(vxw300), Right(vxw4000), ff, ed) → False
new_esEs7(Right(vxw300), Left(vxw4000), ff, ed) → False
new_esEs4(Just(vxw300), Just(vxw4000), ty_Integer) → new_esEs11(vxw300, vxw4000)
new_ltEs19(vxw112, vxw102, app(app(ty_@2, cgf), cgg)) → new_ltEs4(vxw112, vxw102, cgf, cgg)
new_esEs29(vxw30, vxw400, app(ty_[], bbd)) → new_esEs14(vxw30, vxw400, bbd)
new_ltEs7(Just(vxw110), Just(vxw100), ty_Integer) → new_ltEs13(vxw110, vxw100)
new_esEs27(vxw301, vxw4001, app(app(ty_Either, ddc), ddd)) → new_esEs7(vxw301, vxw4001, ddc, ddd)
new_esEs20(vxw302, vxw4002, ty_Int) → new_esEs16(vxw302, vxw4002)
new_esEs26(vxw110, vxw100, ty_Char) → new_esEs12(vxw110, vxw100)
new_esEs22(vxw300, vxw4000, ty_@0) → new_esEs15(vxw300, vxw4000)
new_lt9(vxw110, vxw100) → new_esEs8(new_compare18(vxw110, vxw100), LT)
new_esEs28(vxw300, vxw4000, ty_@0) → new_esEs15(vxw300, vxw4000)
new_esEs20(vxw302, vxw4002, ty_Char) → new_esEs12(vxw302, vxw4002)
new_ltEs17(Left(vxw110), Left(vxw100), app(ty_Maybe, bhg), bdh) → new_ltEs7(vxw110, vxw100, bhg)
new_ltEs18(vxw111, vxw101, ty_Int) → new_ltEs16(vxw111, vxw101)
new_esEs22(vxw300, vxw4000, ty_Ordering) → new_esEs8(vxw300, vxw4000)
new_esEs7(Left(vxw300), Left(vxw4000), ty_Double, ed) → new_esEs9(vxw300, vxw4000)
new_esEs29(vxw30, vxw400, app(ty_Ratio, bbc)) → new_esEs13(vxw30, vxw400, bbc)
new_esEs20(vxw302, vxw4002, app(app(ty_@2, bea), beb)) → new_esEs5(vxw302, vxw4002, bea, beb)
new_esEs7(Right(vxw300), Right(vxw4000), ff, ty_Double) → new_esEs9(vxw300, vxw4000)
new_ltEs20(vxw11, vxw10, app(ty_[], cc)) → new_ltEs12(vxw11, vxw10, cc)
new_ltEs21(vxw20, vxw19, ty_@0) → new_ltEs14(vxw20, vxw19)
new_esEs7(Right(vxw300), Right(vxw4000), ff, app(app(ty_@2, fg), fh)) → new_esEs5(vxw300, vxw4000, fg, fh)
new_ltEs20(vxw11, vxw10, app(app(ty_@2, bdb), bdc)) → new_ltEs4(vxw11, vxw10, bdb, bdc)
new_primCmpNat0(Zero, Succ(vxw1000)) → LT
new_lt10(vxw110, vxw100, ty_Double) → new_lt13(vxw110, vxw100)
new_ltEs19(vxw112, vxw102, ty_Float) → new_ltEs15(vxw112, vxw102)
new_lt10(vxw110, vxw100, ty_Bool) → new_lt9(vxw110, vxw100)
new_lt20(vxw110, vxw100, ty_Ordering) → new_lt6(vxw110, vxw100)
new_esEs8(LT, LT) → True
new_lt19(vxw111, vxw101, ty_Bool) → new_lt9(vxw111, vxw101)
new_compare25(vxw110, vxw100, True, ha, hb, hc) → EQ
new_ltEs15(vxw11, vxw10) → new_not(new_esEs8(new_compare26(vxw11, vxw10), GT))
new_esEs21(vxw301, vxw4001, app(ty_Ratio, bfh)) → new_esEs13(vxw301, vxw4001, bfh)
new_lt5(vxw110, vxw100, cd) → new_esEs8(new_compare8(vxw110, vxw100, cd), LT)
new_esEs7(Left(vxw300), Left(vxw4000), ty_Integer, ed) → new_esEs11(vxw300, vxw4000)
new_esEs25(vxw111, vxw101, ty_Ordering) → new_esEs8(vxw111, vxw101)
new_esEs20(vxw302, vxw4002, ty_Integer) → new_esEs11(vxw302, vxw4002)
new_esEs24(vxw300, vxw4000, app(app(ty_Either, cgc), cgd)) → new_esEs7(vxw300, vxw4000, cgc, cgd)
new_compare9(vxw110, vxw100, app(app(app(ty_@3, baa), bab), bac)) → new_compare19(vxw110, vxw100, baa, bab, bac)
new_esEs20(vxw302, vxw4002, app(app(app(ty_@3, bec), bed), bee)) → new_esEs6(vxw302, vxw4002, bec, bed, bee)
new_esEs25(vxw111, vxw101, app(ty_Ratio, dab)) → new_esEs13(vxw111, vxw101, dab)
new_esEs30(vxw30, vxw400, ty_Float) → new_esEs10(vxw30, vxw400)
new_esEs28(vxw300, vxw4000, ty_Float) → new_esEs10(vxw300, vxw4000)
new_ltEs5(True, False) → False
new_lt19(vxw111, vxw101, app(app(ty_@2, chh), daa)) → new_lt11(vxw111, vxw101, chh, daa)
new_esEs18(vxw301, vxw4001, ty_Integer) → new_esEs11(vxw301, vxw4001)
new_compare0([], [], cc) → EQ
new_pePe(True, vxw60) → True
new_esEs24(vxw300, vxw4000, ty_Int) → new_esEs16(vxw300, vxw4000)
new_primEqNat0(Zero, Zero) → True
new_ltEs21(vxw20, vxw19, ty_Bool) → new_ltEs5(vxw20, vxw19)
new_ltEs17(Left(vxw110), Left(vxw100), ty_Double, bdh) → new_ltEs9(vxw110, vxw100)
new_esEs7(Left(vxw300), Left(vxw4000), app(app(ty_@2, eb), ec), ed) → new_esEs5(vxw300, vxw4000, eb, ec)
new_compare29(vxw110, vxw100, True, cdg, cdh) → EQ
new_compare111(vxw110, vxw100, False, cdg, cdh) → GT
new_esEs26(vxw110, vxw100, app(ty_Ratio, dbd)) → new_esEs13(vxw110, vxw100, dbd)
new_ltEs21(vxw20, vxw19, app(ty_Ratio, dfb)) → new_ltEs11(vxw20, vxw19, dfb)
new_esEs27(vxw301, vxw4001, app(ty_Ratio, dch)) → new_esEs13(vxw301, vxw4001, dch)
new_esEs27(vxw301, vxw4001, ty_Char) → new_esEs12(vxw301, vxw4001)
new_lt18(vxw110, vxw100, cdg, cdh) → new_esEs8(new_compare28(vxw110, vxw100, cdg, cdh), LT)
new_ltEs5(True, True) → True
new_ltEs17(Left(vxw110), Left(vxw100), ty_Ordering, bdh) → new_ltEs10(vxw110, vxw100)
new_esEs17(False, False) → True
new_ltEs17(Right(vxw110), Left(vxw100), bdg, bdh) → False
new_esEs17(False, True) → False
new_esEs17(True, False) → False
new_esEs7(Left(vxw300), Left(vxw4000), ty_Ordering, ed) → new_esEs8(vxw300, vxw4000)
new_compare17(:%(vxw110, vxw111), :%(vxw100, vxw101), ty_Int) → new_compare27(new_sr(vxw110, vxw101), new_sr(vxw100, vxw111))
new_lt19(vxw111, vxw101, ty_Double) → new_lt13(vxw111, vxw101)
new_ltEs18(vxw111, vxw101, app(app(ty_Either, cdc), cdd)) → new_ltEs17(vxw111, vxw101, cdc, cdd)
new_esEs7(Right(vxw300), Right(vxw4000), ff, app(app(app(ty_@3, ga), gb), gc)) → new_esEs6(vxw300, vxw4000, ga, gb, gc)
new_sr(vxw300, vxw4000) → new_primMulInt(vxw300, vxw4000)
new_esEs24(vxw300, vxw4000, ty_Bool) → new_esEs17(vxw300, vxw4000)
new_compare12(vxw110, vxw100, True, ha, hb, hc) → LT
new_esEs30(vxw30, vxw400, ty_Char) → new_esEs12(vxw30, vxw400)
new_esEs30(vxw30, vxw400, ty_Bool) → new_esEs17(vxw30, vxw400)
new_esEs24(vxw300, vxw4000, ty_Char) → new_esEs12(vxw300, vxw4000)
new_esEs22(vxw300, vxw4000, ty_Double) → new_esEs9(vxw300, vxw4000)
new_esEs4(Just(vxw300), Just(vxw4000), ty_Bool) → new_esEs17(vxw300, vxw4000)
new_esEs26(vxw110, vxw100, ty_Ordering) → new_esEs8(vxw110, vxw100)
new_esEs8(GT, GT) → True
new_ltEs20(vxw11, vxw10, app(ty_Ratio, bda)) → new_ltEs11(vxw11, vxw10, bda)
new_primPlusNat0(Succ(vxw620), vxw400000) → Succ(Succ(new_primPlusNat1(vxw620, vxw400000)))
new_ltEs9(vxw11, vxw10) → new_not(new_esEs8(new_compare15(vxw11, vxw10), GT))
new_esEs7(Right(vxw300), Right(vxw4000), ff, app(app(ty_Either, gg), gh)) → new_esEs7(vxw300, vxw4000, gg, gh)
new_lt10(vxw110, vxw100, app(app(ty_@2, dh), ea)) → new_lt11(vxw110, vxw100, dh, ea)
new_esEs20(vxw302, vxw4002, ty_Bool) → new_esEs17(vxw302, vxw4002)
new_esEs26(vxw110, vxw100, app(app(app(ty_@3, dbf), dbg), dbh)) → new_esEs6(vxw110, vxw100, dbf, dbg, dbh)
new_ltEs17(Right(vxw110), Right(vxw100), bdg, ty_Ordering) → new_ltEs10(vxw110, vxw100)
new_esEs8(LT, GT) → False
new_esEs8(GT, LT) → False
new_lt20(vxw110, vxw100, ty_Bool) → new_lt9(vxw110, vxw100)
new_esEs7(Right(vxw300), Right(vxw4000), ff, ty_Char) → new_esEs12(vxw300, vxw4000)
new_ltEs7(Just(vxw110), Just(vxw100), ty_Int) → new_ltEs16(vxw110, vxw100)
new_ltEs20(vxw11, vxw10, ty_Int) → new_ltEs16(vxw11, vxw10)
new_esEs7(Right(vxw300), Right(vxw4000), ff, ty_@0) → new_esEs15(vxw300, vxw4000)
new_primEqInt(Neg(Succ(vxw3000)), Neg(Succ(vxw40000))) → new_primEqNat0(vxw3000, vxw40000)
new_lt10(vxw110, vxw100, ty_Char) → new_lt12(vxw110, vxw100)
new_esEs20(vxw302, vxw4002, ty_Ordering) → new_esEs8(vxw302, vxw4002)
new_lt10(vxw110, vxw100, app(app(ty_Either, cdg), cdh)) → new_lt18(vxw110, vxw100, cdg, cdh)
new_esEs22(vxw300, vxw4000, app(app(app(ty_@3, bgg), bgh), bha)) → new_esEs6(vxw300, vxw4000, bgg, bgh, bha)
new_esEs23(vxw110, vxw100, ty_Ordering) → new_esEs8(vxw110, vxw100)
new_ltEs5(False, False) → True
new_primPlusNat1(Zero, Succ(vxw4000000)) → Succ(vxw4000000)
new_primPlusNat1(Succ(vxw6200), Zero) → Succ(vxw6200)
new_esEs30(vxw30, vxw400, app(ty_Maybe, de)) → new_esEs4(vxw30, vxw400, de)
new_lt19(vxw111, vxw101, ty_Float) → new_lt17(vxw111, vxw101)
new_esEs6(@3(vxw300, vxw301, vxw302), @3(vxw4000, vxw4001, vxw4002), bah, bba, bbb) → new_asAs(new_esEs22(vxw300, vxw4000, bah), new_asAs(new_esEs21(vxw301, vxw4001, bba), new_esEs20(vxw302, vxw4002, bbb)))
new_esEs21(vxw301, vxw4001, ty_Char) → new_esEs12(vxw301, vxw4001)
new_esEs16(vxw30, vxw400) → new_primEqInt(vxw30, vxw400)
new_esEs28(vxw300, vxw4000, app(ty_Maybe, ded)) → new_esEs4(vxw300, vxw4000, ded)
new_esEs21(vxw301, vxw4001, ty_@0) → new_esEs15(vxw301, vxw4001)
new_esEs14([], :(vxw4000, vxw4001), bbd) → False
new_esEs14(:(vxw300, vxw301), [], bbd) → False
new_esEs7(Right(vxw300), Right(vxw4000), ff, app(ty_Ratio, gd)) → new_esEs13(vxw300, vxw4000, gd)
new_ltEs21(vxw20, vxw19, ty_Integer) → new_ltEs13(vxw20, vxw19)
new_lt6(vxw110, vxw100) → new_esEs8(new_compare16(vxw110, vxw100), LT)
new_esEs30(vxw30, vxw400, ty_Integer) → new_esEs11(vxw30, vxw400)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs7(Left(vxw300), Left(vxw4000), app(ty_Ratio, eh), ed) → new_esEs13(vxw300, vxw4000, eh)
new_esEs24(vxw300, vxw4000, app(app(app(ty_@3, cfe), cff), cfg)) → new_esEs6(vxw300, vxw4000, cfe, cff, cfg)
new_ltEs17(Right(vxw110), Right(vxw100), bdg, ty_Int) → new_ltEs16(vxw110, vxw100)
new_esEs21(vxw301, vxw4001, ty_Integer) → new_esEs11(vxw301, vxw4001)
new_esEs26(vxw110, vxw100, app(ty_[], dbe)) → new_esEs14(vxw110, vxw100, dbe)
new_ltEs18(vxw111, vxw101, ty_@0) → new_ltEs14(vxw111, vxw101)
new_esEs28(vxw300, vxw4000, ty_Int) → new_esEs16(vxw300, vxw4000)
new_primEqInt(Neg(Succ(vxw3000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(vxw40000))) → False
new_lt19(vxw111, vxw101, ty_Char) → new_lt12(vxw111, vxw101)
new_esEs8(EQ, EQ) → True
new_compare27(vxw11, vxw10) → new_primCmpInt(vxw11, vxw10)
new_esEs5(@2(vxw300, vxw301), @2(vxw4000, vxw4001), baf, bag) → new_asAs(new_esEs28(vxw300, vxw4000, baf), new_esEs27(vxw301, vxw4001, bag))
new_esEs28(vxw300, vxw4000, app(ty_[], dec)) → new_esEs14(vxw300, vxw4000, dec)
new_lt20(vxw110, vxw100, app(ty_Maybe, dba)) → new_lt5(vxw110, vxw100, dba)
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_esEs26(vxw110, vxw100, app(app(ty_Either, dca), dcb)) → new_esEs7(vxw110, vxw100, dca, dcb)
new_compare14(Char(vxw110), Char(vxw100)) → new_primCmpNat0(vxw110, vxw100)
new_esEs21(vxw301, vxw4001, ty_Float) → new_esEs10(vxw301, vxw4001)
new_esEs4(Just(vxw300), Just(vxw4000), app(app(ty_Either, cfa), cfb)) → new_esEs7(vxw300, vxw4000, cfa, cfb)
new_esEs7(Left(vxw300), Left(vxw4000), ty_@0, ed) → new_esEs15(vxw300, vxw4000)
new_primCmpNat0(Succ(vxw1100), Succ(vxw1000)) → new_primCmpNat0(vxw1100, vxw1000)
new_esEs23(vxw110, vxw100, ty_Float) → new_esEs10(vxw110, vxw100)
new_esEs22(vxw300, vxw4000, app(ty_Maybe, bhd)) → new_esEs4(vxw300, vxw4000, bhd)
new_esEs30(vxw30, vxw400, ty_@0) → new_esEs15(vxw30, vxw400)
new_esEs25(vxw111, vxw101, app(ty_Maybe, chg)) → new_esEs4(vxw111, vxw101, chg)
new_compare19(vxw110, vxw100, ha, hb, hc) → new_compare25(vxw110, vxw100, new_esEs6(vxw110, vxw100, ha, hb, hc), ha, hb, hc)
new_lt14(vxw110, vxw100, cde) → new_esEs8(new_compare17(vxw110, vxw100, cde), LT)
new_ltEs18(vxw111, vxw101, ty_Integer) → new_ltEs13(vxw111, vxw101)
new_ltEs6(@3(vxw110, vxw111, vxw112), @3(vxw100, vxw101, vxw102), bdd, bde, bdf) → new_pePe(new_lt20(vxw110, vxw100, bdd), new_asAs(new_esEs26(vxw110, vxw100, bdd), new_pePe(new_lt19(vxw111, vxw101, bde), new_asAs(new_esEs25(vxw111, vxw101, bde), new_ltEs19(vxw112, vxw102, bdf)))))
new_ltEs18(vxw111, vxw101, ty_Bool) → new_ltEs5(vxw111, vxw101)
new_ltEs17(Left(vxw110), Left(vxw100), app(app(ty_@2, bhh), caa), bdh) → new_ltEs4(vxw110, vxw100, bhh, caa)
new_primEqInt(Pos(Succ(vxw3000)), Pos(Succ(vxw40000))) → new_primEqNat0(vxw3000, vxw40000)
new_compare10(vxw110, vxw100, False, dh, ea) → GT
new_compare9(vxw110, vxw100, app(ty_Maybe, hd)) → new_compare8(vxw110, vxw100, hd)
new_esEs18(vxw301, vxw4001, ty_Int) → new_esEs16(vxw301, vxw4001)
new_esEs4(Just(vxw300), Just(vxw4000), app(app(ty_@2, cea), ceb)) → new_esEs5(vxw300, vxw4000, cea, ceb)
new_lt20(vxw110, vxw100, ty_Int) → new_lt7(vxw110, vxw100)
new_compare9(vxw110, vxw100, app(ty_[], hh)) → new_compare0(vxw110, vxw100, hh)
new_esEs30(vxw30, vxw400, ty_Int) → new_esEs16(vxw30, vxw400)
new_ltEs7(Nothing, Just(vxw100), bbf) → True
new_esEs4(Just(vxw300), Just(vxw4000), ty_Int) → new_esEs16(vxw300, vxw4000)
new_ltEs10(GT, EQ) → False
new_primEqNat0(Succ(vxw3000), Succ(vxw40000)) → new_primEqNat0(vxw3000, vxw40000)
new_esEs23(vxw110, vxw100, ty_Integer) → new_esEs11(vxw110, vxw100)
new_esEs27(vxw301, vxw4001, ty_Ordering) → new_esEs8(vxw301, vxw4001)
new_compare7(@0, @0) → EQ
new_esEs21(vxw301, vxw4001, app(ty_[], bga)) → new_esEs14(vxw301, vxw4001, bga)
new_esEs29(vxw30, vxw400, ty_Double) → new_esEs9(vxw30, vxw400)
new_esEs9(Double(vxw300, vxw301), Double(vxw4000, vxw4001)) → new_esEs16(new_sr(vxw300, vxw4000), new_sr(vxw301, vxw4001))
new_esEs7(Right(vxw300), Right(vxw4000), ff, ty_Float) → new_esEs10(vxw300, vxw4000)
new_esEs20(vxw302, vxw4002, ty_Float) → new_esEs10(vxw302, vxw4002)
new_primCompAux00(vxw72, LT) → LT
new_lt10(vxw110, vxw100, app(app(app(ty_@3, ha), hb), hc)) → new_lt16(vxw110, vxw100, ha, hb, hc)
new_primCmpInt(Neg(Succ(vxw1100)), Neg(vxw100)) → new_primCmpNat0(vxw100, Succ(vxw1100))
new_esEs4(Just(vxw300), Just(vxw4000), ty_@0) → new_esEs15(vxw300, vxw4000)
new_esEs24(vxw300, vxw4000, ty_Ordering) → new_esEs8(vxw300, vxw4000)
new_lt10(vxw110, vxw100, ty_Float) → new_lt17(vxw110, vxw100)
new_esEs28(vxw300, vxw4000, ty_Ordering) → new_esEs8(vxw300, vxw4000)
new_esEs7(Left(vxw300), Left(vxw4000), ty_Int, ed) → new_esEs16(vxw300, vxw4000)
new_esEs8(LT, EQ) → False
new_esEs8(EQ, LT) → False
new_primEqInt(Pos(Succ(vxw3000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(vxw40000))) → False
new_lt4(vxw110, vxw100) → new_esEs8(new_compare6(vxw110, vxw100), LT)
new_ltEs20(vxw11, vxw10, ty_Integer) → new_ltEs13(vxw11, vxw10)
new_ltEs19(vxw112, vxw102, app(app(ty_Either, che), chf)) → new_ltEs17(vxw112, vxw102, che, chf)
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(vxw1100), Zero) → GT
new_esEs23(vxw110, vxw100, app(app(ty_@2, dh), ea)) → new_esEs5(vxw110, vxw100, dh, ea)
new_esEs24(vxw300, vxw4000, ty_@0) → new_esEs15(vxw300, vxw4000)
new_ltEs17(Right(vxw110), Right(vxw100), bdg, app(ty_Maybe, cba)) → new_ltEs7(vxw110, vxw100, cba)
new_ltEs10(LT, EQ) → True
new_primCmpInt(Neg(Zero), Pos(Succ(vxw1000))) → LT
new_ltEs20(vxw11, vxw10, ty_@0) → new_ltEs14(vxw11, vxw10)
new_ltEs21(vxw20, vxw19, app(app(app(ty_@3, dfd), dfe), dff)) → new_ltEs6(vxw20, vxw19, dfd, dfe, dff)
new_lt10(vxw110, vxw100, app(ty_Ratio, cde)) → new_lt14(vxw110, vxw100, cde)
new_compare9(vxw110, vxw100, ty_Bool) → new_compare18(vxw110, vxw100)
new_esEs27(vxw301, vxw4001, ty_Double) → new_esEs9(vxw301, vxw4001)
new_ltEs17(Left(vxw110), Left(vxw100), app(app(app(ty_@3, cad), cae), caf), bdh) → new_ltEs6(vxw110, vxw100, cad, cae, caf)
new_esEs22(vxw300, vxw4000, app(ty_Ratio, bhb)) → new_esEs13(vxw300, vxw4000, bhb)
new_esEs19(vxw300, vxw4000, ty_Integer) → new_esEs11(vxw300, vxw4000)
new_sr0(Integer(vxw1100), Integer(vxw1010)) → Integer(new_primMulInt(vxw1100, vxw1010))
new_primPlusNat1(Succ(vxw6200), Succ(vxw4000000)) → Succ(Succ(new_primPlusNat1(vxw6200, vxw4000000)))
new_compare6(Integer(vxw110), Integer(vxw100)) → new_primCmpInt(vxw110, vxw100)
new_primEqInt(Pos(Succ(vxw3000)), Neg(vxw4000)) → False
new_primEqInt(Neg(Succ(vxw3000)), Pos(vxw4000)) → False
new_ltEs17(Left(vxw110), Left(vxw100), app(ty_[], cac), bdh) → new_ltEs12(vxw110, vxw100, cac)
new_esEs24(vxw300, vxw4000, app(ty_Ratio, cfh)) → new_esEs13(vxw300, vxw4000, cfh)
new_compare210(vxw110, vxw100, True, cd) → EQ
new_ltEs4(@2(vxw110, vxw111), @2(vxw100, vxw101), bdb, bdc) → new_pePe(new_lt10(vxw110, vxw100, bdb), new_asAs(new_esEs23(vxw110, vxw100, bdb), new_ltEs18(vxw111, vxw101, bdc)))
new_ltEs5(False, True) → True
new_ltEs10(GT, GT) → True
new_esEs29(vxw30, vxw400, app(app(ty_@2, baf), bag)) → new_esEs5(vxw30, vxw400, baf, bag)
new_ltEs20(vxw11, vxw10, ty_Float) → new_ltEs15(vxw11, vxw10)
new_esEs25(vxw111, vxw101, ty_Char) → new_esEs12(vxw111, vxw101)
new_lt19(vxw111, vxw101, ty_Int) → new_lt7(vxw111, vxw101)
new_esEs29(vxw30, vxw400, ty_Integer) → new_esEs11(vxw30, vxw400)
new_primEqInt(Pos(Zero), Neg(Succ(vxw40000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(vxw40000))) → False
new_primCmpInt(Pos(Zero), Pos(Succ(vxw1000))) → new_primCmpNat0(Zero, Succ(vxw1000))
new_primCompAux00(vxw72, EQ) → vxw72
new_esEs28(vxw300, vxw4000, app(app(ty_Either, dee), def)) → new_esEs7(vxw300, vxw4000, dee, def)
new_ltEs18(vxw111, vxw101, app(ty_Ratio, ccf)) → new_ltEs11(vxw111, vxw101, ccf)
new_esEs7(Right(vxw300), Right(vxw4000), ff, app(ty_Maybe, gf)) → new_esEs4(vxw300, vxw4000, gf)
new_compare24(vxw110, vxw100, True) → EQ
new_compare17(:%(vxw110, vxw111), :%(vxw100, vxw101), ty_Integer) → new_compare6(new_sr0(vxw110, vxw101), new_sr0(vxw100, vxw111))
new_esEs27(vxw301, vxw4001, ty_Float) → new_esEs10(vxw301, vxw4001)
new_esEs8(EQ, GT) → False
new_esEs8(GT, EQ) → False
new_lt10(vxw110, vxw100, app(ty_Maybe, cd)) → new_lt5(vxw110, vxw100, cd)
new_ltEs7(Just(vxw110), Just(vxw100), ty_Float) → new_ltEs15(vxw110, vxw100)
new_esEs26(vxw110, vxw100, app(app(ty_@2, dbb), dbc)) → new_esEs5(vxw110, vxw100, dbb, dbc)
new_compare18(vxw110, vxw100) → new_compare24(vxw110, vxw100, new_esEs17(vxw110, vxw100))
new_esEs21(vxw301, vxw4001, app(app(ty_@2, bfc), bfd)) → new_esEs5(vxw301, vxw4001, bfc, bfd)
new_ltEs19(vxw112, vxw102, ty_Char) → new_ltEs8(vxw112, vxw102)
new_lt8(vxw110, vxw100) → new_esEs8(new_compare7(vxw110, vxw100), LT)
new_ltEs7(Just(vxw110), Just(vxw100), ty_Double) → new_ltEs9(vxw110, vxw100)
new_esEs12(Char(vxw300), Char(vxw4000)) → new_primEqNat0(vxw300, vxw4000)
new_ltEs20(vxw11, vxw10, app(app(app(ty_@3, bdd), bde), bdf)) → new_ltEs6(vxw11, vxw10, bdd, bde, bdf)
new_not(False) → True
new_esEs7(Right(vxw300), Right(vxw4000), ff, ty_Integer) → new_esEs11(vxw300, vxw4000)
new_esEs24(vxw300, vxw4000, ty_Double) → new_esEs9(vxw300, vxw4000)
new_primCompAux0(vxw110, vxw100, vxw61, cc) → new_primCompAux00(vxw61, new_compare9(vxw110, vxw100, cc))
new_primPlusNat0(Zero, vxw400000) → Succ(vxw400000)
new_primCmpInt(Pos(Succ(vxw1100)), Pos(vxw100)) → new_primCmpNat0(Succ(vxw1100), vxw100)
new_esEs23(vxw110, vxw100, ty_@0) → new_esEs15(vxw110, vxw100)
new_compare9(vxw110, vxw100, ty_Float) → new_compare26(vxw110, vxw100)
new_compare12(vxw110, vxw100, False, ha, hb, hc) → GT
new_esEs7(Right(vxw300), Right(vxw4000), ff, ty_Bool) → new_esEs17(vxw300, vxw4000)
new_esEs22(vxw300, vxw4000, ty_Bool) → new_esEs17(vxw300, vxw4000)
new_ltEs18(vxw111, vxw101, app(app(app(ty_@3, cch), cda), cdb)) → new_ltEs6(vxw111, vxw101, cch, cda, cdb)
new_compare9(vxw110, vxw100, ty_@0) → new_compare7(vxw110, vxw100)
new_ltEs19(vxw112, vxw102, app(ty_[], cha)) → new_ltEs12(vxw112, vxw102, cha)
new_ltEs17(Right(vxw110), Right(vxw100), bdg, app(app(ty_Either, cca), ccb)) → new_ltEs17(vxw110, vxw100, cca, ccb)
new_esEs25(vxw111, vxw101, ty_Float) → new_esEs10(vxw111, vxw101)
new_compare16(vxw110, vxw100) → new_compare211(vxw110, vxw100, new_esEs8(vxw110, vxw100))
new_esEs24(vxw300, vxw4000, app(ty_[], cga)) → new_esEs14(vxw300, vxw4000, cga)
new_esEs25(vxw111, vxw101, ty_@0) → new_esEs15(vxw111, vxw101)
new_lt20(vxw110, vxw100, ty_Double) → new_lt13(vxw110, vxw100)
new_lt20(vxw110, vxw100, app(ty_Ratio, dbd)) → new_lt14(vxw110, vxw100, dbd)
new_esEs28(vxw300, vxw4000, app(app(ty_@2, dde), ddf)) → new_esEs5(vxw300, vxw4000, dde, ddf)
new_compare0(:(vxw110, vxw111), [], cc) → GT
new_esEs22(vxw300, vxw4000, ty_Integer) → new_esEs11(vxw300, vxw4000)
new_ltEs19(vxw112, vxw102, app(app(app(ty_@3, chb), chc), chd)) → new_ltEs6(vxw112, vxw102, chb, chc, chd)
new_ltEs18(vxw111, vxw101, app(ty_Maybe, ccc)) → new_ltEs7(vxw111, vxw101, ccc)
new_compare9(vxw110, vxw100, app(app(ty_@2, he), hf)) → new_compare13(vxw110, vxw100, he, hf)
new_lt19(vxw111, vxw101, ty_Integer) → new_lt4(vxw111, vxw101)
new_esEs14(:(vxw300, vxw301), :(vxw4000, vxw4001), bbd) → new_asAs(new_esEs24(vxw300, vxw4000, bbd), new_esEs14(vxw301, vxw4001, bbd))
new_compare8(vxw110, vxw100, cd) → new_compare210(vxw110, vxw100, new_esEs4(vxw110, vxw100, cd), cd)
new_lt19(vxw111, vxw101, app(app(app(ty_@3, dad), dae), daf)) → new_lt16(vxw111, vxw101, dad, dae, daf)
new_esEs25(vxw111, vxw101, ty_Integer) → new_esEs11(vxw111, vxw101)
new_primCmpInt(Pos(Succ(vxw1100)), Neg(vxw100)) → GT
new_ltEs7(Just(vxw110), Just(vxw100), app(ty_Maybe, bbg)) → new_ltEs7(vxw110, vxw100, bbg)
new_esEs10(Float(vxw300, vxw301), Float(vxw4000, vxw4001)) → new_esEs16(new_sr(vxw300, vxw4000), new_sr(vxw301, vxw4001))
new_ltEs21(vxw20, vxw19, app(app(ty_Either, dfg), dfh)) → new_ltEs17(vxw20, vxw19, dfg, dfh)
new_esEs27(vxw301, vxw4001, ty_@0) → new_esEs15(vxw301, vxw4001)
new_esEs28(vxw300, vxw4000, ty_Double) → new_esEs9(vxw300, vxw4000)
new_lt19(vxw111, vxw101, app(ty_[], dac)) → new_lt15(vxw111, vxw101, dac)
new_ltEs20(vxw11, vxw10, app(app(ty_Either, bdg), bdh)) → new_ltEs17(vxw11, vxw10, bdg, bdh)
new_primMulInt(Pos(vxw3000), Pos(vxw40000)) → Pos(new_primMulNat0(vxw3000, vxw40000))
new_esEs30(vxw30, vxw400, app(app(ty_@2, ce), cf)) → new_esEs5(vxw30, vxw400, ce, cf)
new_esEs24(vxw300, vxw4000, ty_Integer) → new_esEs11(vxw300, vxw4000)
new_ltEs17(Left(vxw110), Left(vxw100), app(app(ty_Either, cag), cah), bdh) → new_ltEs17(vxw110, vxw100, cag, cah)
new_esEs7(Left(vxw300), Left(vxw4000), ty_Char, ed) → new_esEs12(vxw300, vxw4000)
new_primMulInt(Neg(vxw3000), Neg(vxw40000)) → Pos(new_primMulNat0(vxw3000, vxw40000))
new_ltEs17(Left(vxw110), Left(vxw100), ty_Float, bdh) → new_ltEs15(vxw110, vxw100)
new_compare9(vxw110, vxw100, ty_Ordering) → new_compare16(vxw110, vxw100)
new_compare110(vxw110, vxw100, True) → LT
new_primEqNat0(Succ(vxw3000), Zero) → False
new_primEqNat0(Zero, Succ(vxw40000)) → False
new_lt20(vxw110, vxw100, app(app(ty_Either, dca), dcb)) → new_lt18(vxw110, vxw100, dca, dcb)
new_compare110(vxw110, vxw100, False) → GT
new_esEs20(vxw302, vxw4002, ty_@0) → new_esEs15(vxw302, vxw4002)
new_compare23(vxw110, vxw100, False, dh, ea) → new_compare10(vxw110, vxw100, new_ltEs4(vxw110, vxw100, dh, ea), dh, ea)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs28(vxw300, vxw4000, app(app(app(ty_@3, ddg), ddh), dea)) → new_esEs6(vxw300, vxw4000, ddg, ddh, dea)
new_esEs4(Nothing, Nothing, bbe) → True
new_esEs4(Just(vxw300), Just(vxw4000), app(ty_Ratio, cef)) → new_esEs13(vxw300, vxw4000, cef)
new_esEs27(vxw301, vxw4001, app(app(app(ty_@3, dce), dcf), dcg)) → new_esEs6(vxw301, vxw4001, dce, dcf, dcg)
new_lt10(vxw110, vxw100, app(ty_[], cdf)) → new_lt15(vxw110, vxw100, cdf)
new_esEs27(vxw301, vxw4001, app(app(ty_@2, dcc), dcd)) → new_esEs5(vxw301, vxw4001, dcc, dcd)
new_esEs26(vxw110, vxw100, ty_Int) → new_esEs16(vxw110, vxw100)
new_ltEs7(Nothing, Nothing, bbf) → True
new_esEs27(vxw301, vxw4001, app(ty_Maybe, ddb)) → new_esEs4(vxw301, vxw4001, ddb)
new_esEs21(vxw301, vxw4001, app(app(ty_Either, bgc), bgd)) → new_esEs7(vxw301, vxw4001, bgc, bgd)
new_esEs23(vxw110, vxw100, app(ty_[], cdf)) → new_esEs14(vxw110, vxw100, cdf)
new_ltEs17(Right(vxw110), Right(vxw100), bdg, ty_@0) → new_ltEs14(vxw110, vxw100)
new_ltEs17(Left(vxw110), Left(vxw100), ty_Char, bdh) → new_ltEs8(vxw110, vxw100)
new_lt10(vxw110, vxw100, ty_@0) → new_lt8(vxw110, vxw100)
new_lt10(vxw110, vxw100, ty_Int) → new_lt7(vxw110, vxw100)
new_esEs7(Right(vxw300), Right(vxw4000), ff, app(ty_[], ge)) → new_esEs14(vxw300, vxw4000, ge)
new_ltEs12(vxw11, vxw10, cc) → new_not(new_esEs8(new_compare0(vxw11, vxw10, cc), GT))
new_primCmpInt(Neg(Zero), Neg(Succ(vxw1000))) → new_primCmpNat0(Succ(vxw1000), Zero)
new_compare23(vxw110, vxw100, True, dh, ea) → EQ
new_primCmpInt(Pos(Zero), Neg(Succ(vxw1000))) → GT
new_esEs23(vxw110, vxw100, ty_Bool) → new_esEs17(vxw110, vxw100)
new_esEs25(vxw111, vxw101, ty_Int) → new_esEs16(vxw111, vxw101)
new_ltEs20(vxw11, vxw10, ty_Char) → new_ltEs8(vxw11, vxw10)
new_ltEs17(Left(vxw110), Left(vxw100), ty_@0, bdh) → new_ltEs14(vxw110, vxw100)
new_esEs29(vxw30, vxw400, ty_@0) → new_esEs15(vxw30, vxw400)
new_esEs4(Just(vxw300), Just(vxw4000), app(ty_[], ceg)) → new_esEs14(vxw300, vxw4000, ceg)
new_ltEs17(Right(vxw110), Right(vxw100), bdg, ty_Float) → new_ltEs15(vxw110, vxw100)
new_ltEs17(Left(vxw110), Right(vxw100), bdg, bdh) → True
new_esEs21(vxw301, vxw4001, app(ty_Maybe, bgb)) → new_esEs4(vxw301, vxw4001, bgb)
new_esEs20(vxw302, vxw4002, app(app(ty_Either, bfa), bfb)) → new_esEs7(vxw302, vxw4002, bfa, bfb)
new_esEs21(vxw301, vxw4001, ty_Double) → new_esEs9(vxw301, vxw4001)
new_lt7(vxw110, vxw100) → new_esEs8(new_compare27(vxw110, vxw100), LT)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_lt20(vxw110, vxw100, app(ty_[], dbe)) → new_lt15(vxw110, vxw100, dbe)
new_ltEs21(vxw20, vxw19, ty_Ordering) → new_ltEs10(vxw20, vxw19)
new_ltEs21(vxw20, vxw19, ty_Char) → new_ltEs8(vxw20, vxw19)
new_ltEs17(Right(vxw110), Right(vxw100), bdg, app(ty_[], cbe)) → new_ltEs12(vxw110, vxw100, cbe)
new_ltEs7(Just(vxw110), Just(vxw100), app(ty_[], bcc)) → new_ltEs12(vxw110, vxw100, bcc)
new_esEs29(vxw30, vxw400, ty_Bool) → new_esEs17(vxw30, vxw400)
new_esEs15(@0, @0) → True
new_lt17(vxw110, vxw100) → new_esEs8(new_compare26(vxw110, vxw100), LT)
new_compare15(Double(vxw110, vxw111), Double(vxw100, vxw101)) → new_compare27(new_sr(vxw110, vxw100), new_sr(vxw111, vxw101))
new_asAs(False, vxw53) → False
new_ltEs17(Right(vxw110), Right(vxw100), bdg, ty_Double) → new_ltEs9(vxw110, vxw100)
new_compare24(vxw110, vxw100, False) → new_compare11(vxw110, vxw100, new_ltEs5(vxw110, vxw100))
new_primMulInt(Neg(vxw3000), Pos(vxw40000)) → Neg(new_primMulNat0(vxw3000, vxw40000))
new_primMulInt(Pos(vxw3000), Neg(vxw40000)) → Neg(new_primMulNat0(vxw3000, vxw40000))
new_esEs26(vxw110, vxw100, ty_Double) → new_esEs9(vxw110, vxw100)
new_compare28(vxw110, vxw100, cdg, cdh) → new_compare29(vxw110, vxw100, new_esEs7(vxw110, vxw100, cdg, cdh), cdg, cdh)
new_ltEs10(LT, GT) → True
new_primMulNat0(Zero, Succ(vxw400000)) → Zero
new_primMulNat0(Succ(vxw30000), Zero) → Zero
new_esEs29(vxw30, vxw400, ty_Char) → new_esEs12(vxw30, vxw400)
new_compare25(vxw110, vxw100, False, ha, hb, hc) → new_compare12(vxw110, vxw100, new_ltEs6(vxw110, vxw100, ha, hb, hc), ha, hb, hc)
new_esEs7(Left(vxw300), Left(vxw4000), ty_Float, ed) → new_esEs10(vxw300, vxw4000)
new_esEs23(vxw110, vxw100, app(app(app(ty_@3, ha), hb), hc)) → new_esEs6(vxw110, vxw100, ha, hb, hc)
new_ltEs7(Just(vxw110), Just(vxw100), ty_Char) → new_ltEs8(vxw110, vxw100)
new_esEs21(vxw301, vxw4001, ty_Ordering) → new_esEs8(vxw301, vxw4001)
new_esEs21(vxw301, vxw4001, ty_Int) → new_esEs16(vxw301, vxw4001)
new_esEs24(vxw300, vxw4000, ty_Float) → new_esEs10(vxw300, vxw4000)
new_esEs19(vxw300, vxw4000, ty_Int) → new_esEs16(vxw300, vxw4000)
new_esEs30(vxw30, vxw400, app(ty_Ratio, dc)) → new_esEs13(vxw30, vxw400, dc)
new_ltEs13(vxw11, vxw10) → new_not(new_esEs8(new_compare6(vxw11, vxw10), GT))
new_ltEs16(vxw11, vxw10) → new_not(new_esEs8(new_compare27(vxw11, vxw10), GT))
new_lt10(vxw110, vxw100, ty_Integer) → new_lt4(vxw110, vxw100)
new_esEs29(vxw30, vxw400, ty_Float) → new_esEs10(vxw30, vxw400)
new_esEs23(vxw110, vxw100, ty_Char) → new_esEs12(vxw110, vxw100)
new_esEs25(vxw111, vxw101, app(app(app(ty_@3, dad), dae), daf)) → new_esEs6(vxw111, vxw101, dad, dae, daf)
new_lt13(vxw110, vxw100) → new_esEs8(new_compare15(vxw110, vxw100), LT)
new_lt19(vxw111, vxw101, app(ty_Maybe, chg)) → new_lt5(vxw111, vxw101, chg)
new_ltEs10(EQ, EQ) → True
new_esEs13(:%(vxw300, vxw301), :%(vxw4000, vxw4001), bbc) → new_asAs(new_esEs19(vxw300, vxw4000, bbc), new_esEs18(vxw301, vxw4001, bbc))
new_compare9(vxw110, vxw100, app(app(ty_Either, bad), bae)) → new_compare28(vxw110, vxw100, bad, bae)
new_esEs23(vxw110, vxw100, ty_Int) → new_esEs16(vxw110, vxw100)
new_ltEs10(LT, LT) → True
new_ltEs19(vxw112, vxw102, ty_Int) → new_ltEs16(vxw112, vxw102)
new_ltEs19(vxw112, vxw102, ty_@0) → new_ltEs14(vxw112, vxw102)
new_compare211(vxw110, vxw100, False) → new_compare110(vxw110, vxw100, new_ltEs10(vxw110, vxw100))
new_esEs7(Left(vxw300), Left(vxw4000), app(app(app(ty_@3, ee), ef), eg), ed) → new_esEs6(vxw300, vxw4000, ee, ef, eg)
new_lt10(vxw110, vxw100, ty_Ordering) → new_lt6(vxw110, vxw100)
new_esEs27(vxw301, vxw4001, ty_Int) → new_esEs16(vxw301, vxw4001)
new_ltEs17(Right(vxw110), Right(vxw100), bdg, ty_Char) → new_ltEs8(vxw110, vxw100)
new_ltEs7(Just(vxw110), Just(vxw100), ty_@0) → new_ltEs14(vxw110, vxw100)
new_ltEs19(vxw112, vxw102, ty_Bool) → new_ltEs5(vxw112, vxw102)
new_ltEs8(vxw11, vxw10) → new_not(new_esEs8(new_compare14(vxw11, vxw10), GT))
new_lt20(vxw110, vxw100, app(app(app(ty_@3, dbf), dbg), dbh)) → new_lt16(vxw110, vxw100, dbf, dbg, dbh)
new_esEs7(Right(vxw300), Right(vxw4000), ff, ty_Int) → new_esEs16(vxw300, vxw4000)
new_ltEs7(Just(vxw110), Nothing, bbf) → False
new_esEs28(vxw300, vxw4000, ty_Bool) → new_esEs17(vxw300, vxw4000)
new_esEs28(vxw300, vxw4000, app(ty_Ratio, deb)) → new_esEs13(vxw300, vxw4000, deb)
new_ltEs17(Left(vxw110), Left(vxw100), ty_Int, bdh) → new_ltEs16(vxw110, vxw100)
new_compare11(vxw110, vxw100, False) → GT
new_lt16(vxw110, vxw100, ha, hb, hc) → new_esEs8(new_compare19(vxw110, vxw100, ha, hb, hc), LT)
new_esEs25(vxw111, vxw101, app(app(ty_@2, chh), daa)) → new_esEs5(vxw111, vxw101, chh, daa)
new_esEs26(vxw110, vxw100, ty_Bool) → new_esEs17(vxw110, vxw100)
new_compare11(vxw110, vxw100, True) → LT
new_ltEs19(vxw112, vxw102, app(ty_Maybe, cge)) → new_ltEs7(vxw112, vxw102, cge)
new_ltEs21(vxw20, vxw19, app(ty_Maybe, deg)) → new_ltEs7(vxw20, vxw19, deg)
new_esEs29(vxw30, vxw400, app(app(app(ty_@3, bah), bba), bbb)) → new_esEs6(vxw30, vxw400, bah, bba, bbb)
new_esEs29(vxw30, vxw400, app(app(ty_Either, ff), ed)) → new_esEs7(vxw30, vxw400, ff, ed)
new_esEs7(Left(vxw300), Left(vxw4000), ty_Bool, ed) → new_esEs17(vxw300, vxw4000)
new_ltEs10(EQ, LT) → False
new_compare112(vxw110, vxw100, False, cd) → GT
new_compare9(vxw110, vxw100, ty_Char) → new_compare14(vxw110, vxw100)
new_lt20(vxw110, vxw100, ty_Char) → new_lt12(vxw110, vxw100)
new_esEs22(vxw300, vxw4000, ty_Float) → new_esEs10(vxw300, vxw4000)
new_esEs30(vxw30, vxw400, ty_Ordering) → new_esEs8(vxw30, vxw400)
new_ltEs10(GT, LT) → False
new_esEs30(vxw30, vxw400, ty_Double) → new_esEs9(vxw30, vxw400)
new_ltEs14(vxw11, vxw10) → new_not(new_esEs8(new_compare7(vxw11, vxw10), GT))
new_primPlusNat1(Zero, Zero) → Zero
new_compare0([], :(vxw100, vxw101), cc) → LT
new_compare111(vxw110, vxw100, True, cdg, cdh) → LT
new_esEs21(vxw301, vxw4001, app(app(app(ty_@3, bfe), bff), bfg)) → new_esEs6(vxw301, vxw4001, bfe, bff, bfg)
new_esEs27(vxw301, vxw4001, app(ty_[], dda)) → new_esEs14(vxw301, vxw4001, dda)
new_asAs(True, vxw53) → vxw53
new_primMulNat0(Succ(vxw30000), Succ(vxw400000)) → new_primPlusNat0(new_primMulNat0(vxw30000, Succ(vxw400000)), vxw400000)
new_compare9(vxw110, vxw100, app(ty_Ratio, hg)) → new_compare17(vxw110, vxw100, hg)
new_esEs20(vxw302, vxw4002, ty_Double) → new_esEs9(vxw302, vxw4002)
new_esEs27(vxw301, vxw4001, ty_Integer) → new_esEs11(vxw301, vxw4001)
new_ltEs21(vxw20, vxw19, ty_Float) → new_ltEs15(vxw20, vxw19)
new_ltEs17(Right(vxw110), Right(vxw100), bdg, app(app(app(ty_@3, cbf), cbg), cbh)) → new_ltEs6(vxw110, vxw100, cbf, cbg, cbh)
new_compare211(vxw110, vxw100, True) → EQ
new_ltEs17(Right(vxw110), Right(vxw100), bdg, app(app(ty_@2, cbb), cbc)) → new_ltEs4(vxw110, vxw100, cbb, cbc)
new_ltEs19(vxw112, vxw102, ty_Integer) → new_ltEs13(vxw112, vxw102)
new_ltEs18(vxw111, vxw101, app(ty_[], ccg)) → new_ltEs12(vxw111, vxw101, ccg)
new_esEs20(vxw302, vxw4002, app(ty_[], beg)) → new_esEs14(vxw302, vxw4002, beg)
new_esEs4(Just(vxw300), Just(vxw4000), ty_Double) → new_esEs9(vxw300, vxw4000)
new_ltEs18(vxw111, vxw101, app(app(ty_@2, ccd), cce)) → new_ltEs4(vxw111, vxw101, ccd, cce)
new_esEs29(vxw30, vxw400, app(ty_Maybe, bbe)) → new_esEs4(vxw30, vxw400, bbe)
new_ltEs7(Just(vxw110), Just(vxw100), app(ty_Ratio, bcb)) → new_ltEs11(vxw110, vxw100, bcb)
new_ltEs20(vxw11, vxw10, app(ty_Maybe, bbf)) → new_ltEs7(vxw11, vxw10, bbf)
new_ltEs17(Right(vxw110), Right(vxw100), bdg, ty_Bool) → new_ltEs5(vxw110, vxw100)
new_primCompAux00(vxw72, GT) → GT
new_esEs30(vxw30, vxw400, app(app(app(ty_@3, cg), da), db)) → new_esEs6(vxw30, vxw400, cg, da, db)
new_esEs25(vxw111, vxw101, app(app(ty_Either, dag), dah)) → new_esEs7(vxw111, vxw101, dag, dah)
new_ltEs18(vxw111, vxw101, ty_Double) → new_ltEs9(vxw111, vxw101)
new_ltEs11(vxw11, vxw10, bda) → new_not(new_esEs8(new_compare17(vxw11, vxw10, bda), GT))
new_lt11(vxw110, vxw100, dh, ea) → new_esEs8(new_compare13(vxw110, vxw100, dh, ea), LT)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_compare26(Float(vxw110, vxw111), Float(vxw100, vxw101)) → new_compare27(new_sr(vxw110, vxw100), new_sr(vxw111, vxw101))
new_esEs29(vxw30, vxw400, ty_Ordering) → new_esEs8(vxw30, vxw400)
new_lt19(vxw111, vxw101, app(ty_Ratio, dab)) → new_lt14(vxw111, vxw101, dab)
new_ltEs18(vxw111, vxw101, ty_Ordering) → new_ltEs10(vxw111, vxw101)
new_esEs7(Left(vxw300), Left(vxw4000), app(ty_[], fa), ed) → new_esEs14(vxw300, vxw4000, fa)
new_esEs28(vxw300, vxw4000, ty_Char) → new_esEs12(vxw300, vxw4000)
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_ltEs21(vxw20, vxw19, ty_Double) → new_ltEs9(vxw20, vxw19)
new_primCmpInt(Neg(Succ(vxw1100)), Pos(vxw100)) → LT
new_esEs22(vxw300, vxw4000, ty_Int) → new_esEs16(vxw300, vxw4000)
new_not(True) → False

The set Q consists of the following terms:

new_esEs11(Integer(x0), Integer(x1))
new_compare12(x0, x1, True, x2, x3, x4)
new_esEs4(Just(x0), Just(x1), ty_Int)
new_ltEs17(Left(x0), Left(x1), ty_@0, x2)
new_ltEs13(x0, x1)
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs20(x0, x1, ty_Char)
new_esEs7(Left(x0), Left(x1), ty_Int, x2)
new_asAs(True, x0)
new_lt5(x0, x1, x2)
new_ltEs17(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs21(x0, x1, ty_Ordering)
new_primMulNat0(Zero, Succ(x0))
new_esEs7(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_ltEs17(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_ltEs17(Left(x0), Left(x1), ty_Int, x2)
new_lt10(x0, x1, ty_Int)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_compare11(x0, x1, True)
new_ltEs21(x0, x1, ty_Bool)
new_primCmpNat0(Succ(x0), Zero)
new_lt18(x0, x1, x2, x3)
new_esEs7(Left(x0), Left(x1), ty_Integer, x2)
new_lt20(x0, x1, ty_Integer)
new_ltEs19(x0, x1, ty_@0)
new_ltEs21(x0, x1, app(ty_Maybe, x2))
new_esEs30(x0, x1, app(ty_Maybe, x2))
new_lt19(x0, x1, ty_Int)
new_esEs29(x0, x1, ty_Bool)
new_esEs23(x0, x1, ty_Float)
new_ltEs18(x0, x1, ty_Float)
new_ltEs17(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_compare9(x0, x1, ty_Bool)
new_esEs25(x0, x1, ty_Bool)
new_compare9(x0, x1, ty_Float)
new_esEs7(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs7(Right(x0), Right(x1), x2, ty_Char)
new_esEs29(x0, x1, ty_Double)
new_ltEs10(LT, LT)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_esEs14(:(x0, x1), :(x2, x3), x4)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs17(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs23(x0, x1, ty_Ordering)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt10(x0, x1, app(app(ty_Either, x2), x3))
new_lt4(x0, x1)
new_esEs9(Double(x0, x1), Double(x2, x3))
new_esEs5(@2(x0, x1), @2(x2, x3), x4, x5)
new_lt20(x0, x1, ty_Double)
new_esEs27(x0, x1, ty_@0)
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs30(x0, x1, ty_Integer)
new_ltEs18(x0, x1, ty_Double)
new_ltEs6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs23(x0, x1, ty_Char)
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs18(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_esEs8(GT, GT)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_ltEs18(x0, x1, app(ty_[], x2))
new_ltEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs17(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs22(x0, x1, ty_Ordering)
new_compare25(x0, x1, True, x2, x3, x4)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs24(x0, x1, ty_Char)
new_ltEs7(Just(x0), Just(x1), app(ty_[], x2))
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_esEs22(x0, x1, app(ty_[], x2))
new_compare6(Integer(x0), Integer(x1))
new_esEs29(x0, x1, ty_@0)
new_esEs8(LT, LT)
new_primMulNat0(Succ(x0), Succ(x1))
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs7(Just(x0), Just(x1), ty_Integer)
new_ltEs12(x0, x1, x2)
new_ltEs20(x0, x1, ty_Double)
new_esEs21(x0, x1, ty_Double)
new_esEs17(False, False)
new_esEs21(x0, x1, ty_Integer)
new_primEqNat0(Succ(x0), Zero)
new_esEs26(x0, x1, ty_Bool)
new_ltEs5(False, False)
new_ltEs11(x0, x1, x2)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_esEs22(x0, x1, ty_Bool)
new_lt11(x0, x1, x2, x3)
new_esEs30(x0, x1, ty_Double)
new_esEs7(Right(x0), Right(x1), x2, ty_Integer)
new_esEs7(Left(x0), Left(x1), ty_Double, x2)
new_esEs7(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs20(x0, x1, ty_Float)
new_compare0(:(x0, x1), [], x2)
new_ltEs21(x0, x1, app(ty_Ratio, x2))
new_esEs27(x0, x1, ty_Ordering)
new_esEs24(x0, x1, ty_@0)
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_esEs7(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_compare9(x0, x1, app(ty_Maybe, x2))
new_esEs7(Left(x0), Left(x1), ty_@0, x2)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs7(Right(x0), Right(x1), x2, ty_Ordering)
new_lt7(x0, x1)
new_ltEs18(x0, x1, app(ty_Ratio, x2))
new_lt10(x0, x1, app(ty_[], x2))
new_compare211(x0, x1, True)
new_compare8(x0, x1, x2)
new_esEs7(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_primEqNat0(Zero, Zero)
new_compare9(x0, x1, ty_Integer)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_esEs21(x0, x1, ty_Bool)
new_lt10(x0, x1, ty_Integer)
new_esEs21(x0, x1, ty_Char)
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_esEs4(Just(x0), Just(x1), ty_Bool)
new_compare210(x0, x1, False, x2)
new_esEs14([], :(x0, x1), x2)
new_ltEs7(Just(x0), Just(x1), ty_Double)
new_esEs22(x0, x1, ty_Int)
new_lt20(x0, x1, ty_Float)
new_ltEs7(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_esEs7(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs4(Just(x0), Just(x1), ty_Ordering)
new_esEs25(x0, x1, ty_Float)
new_compare23(x0, x1, False, x2, x3)
new_esEs7(Left(x0), Left(x1), ty_Bool, x2)
new_primMulNat0(Zero, Zero)
new_ltEs18(x0, x1, ty_Int)
new_esEs21(x0, x1, ty_Float)
new_esEs7(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs20(x0, x1, ty_Ordering)
new_ltEs17(Left(x0), Left(x1), ty_Ordering, x2)
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_ltEs10(EQ, LT)
new_ltEs10(LT, EQ)
new_compare23(x0, x1, True, x2, x3)
new_ltEs21(x0, x1, ty_@0)
new_esEs21(x0, x1, app(ty_[], x2))
new_ltEs20(x0, x1, ty_@0)
new_ltEs17(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_esEs18(x0, x1, ty_Integer)
new_lt14(x0, x1, x2)
new_primCompAux00(x0, EQ)
new_compare10(x0, x1, True, x2, x3)
new_esEs13(:%(x0, x1), :%(x2, x3), x4)
new_compare210(x0, x1, True, x2)
new_pePe(True, x0)
new_esEs20(x0, x1, ty_Ordering)
new_ltEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, ty_Ordering)
new_esEs28(x0, x1, ty_Int)
new_esEs12(Char(x0), Char(x1))
new_lt19(x0, x1, ty_Char)
new_compare110(x0, x1, False)
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs4(Just(x0), Just(x1), ty_@0)
new_lt10(x0, x1, ty_Ordering)
new_esEs22(x0, x1, ty_Char)
new_esEs30(x0, x1, ty_Bool)
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs26(x0, x1, ty_@0)
new_esEs24(x0, x1, ty_Integer)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs25(x0, x1, ty_Ordering)
new_esEs4(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, app(ty_[], x2))
new_primCompAux00(x0, LT)
new_ltEs21(x0, x1, ty_Ordering)
new_ltEs19(x0, x1, ty_Integer)
new_ltEs17(Left(x0), Left(x1), ty_Bool, x2)
new_ltEs17(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs17(Left(x0), Left(x1), ty_Float, x2)
new_ltEs19(x0, x1, ty_Int)
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs25(x0, x1, ty_Double)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs7(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_ltEs20(x0, x1, ty_Bool)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_esEs27(x0, x1, ty_Double)
new_esEs26(x0, x1, ty_Integer)
new_esEs19(x0, x1, ty_Integer)
new_ltEs20(x0, x1, app(ty_[], x2))
new_esEs23(x0, x1, ty_Integer)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_compare13(x0, x1, x2, x3)
new_lt6(x0, x1)
new_compare0([], [], x0)
new_esEs4(Just(x0), Just(x1), app(ty_Maybe, x2))
new_compare9(x0, x1, ty_@0)
new_esEs4(Just(x0), Just(x1), ty_Double)
new_ltEs17(Right(x0), Right(x1), x2, ty_Float)
new_lt10(x0, x1, app(ty_Maybe, x2))
new_ltEs19(x0, x1, ty_Bool)
new_esEs28(x0, x1, ty_@0)
new_lt20(x0, x1, ty_Bool)
new_ltEs15(x0, x1)
new_lt10(x0, x1, app(app(ty_@2, x2), x3))
new_compare11(x0, x1, False)
new_lt10(x0, x1, ty_Double)
new_compare111(x0, x1, True, x2, x3)
new_lt19(x0, x1, ty_@0)
new_esEs30(x0, x1, app(ty_Ratio, x2))
new_ltEs18(x0, x1, ty_Char)
new_esEs4(Just(x0), Nothing, x1)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_compare25(x0, x1, False, x2, x3, x4)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_compare27(x0, x1)
new_primPlusNat1(Zero, Zero)
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_compare0(:(x0, x1), :(x2, x3), x4)
new_sr(x0, x1)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_esEs20(x0, x1, ty_@0)
new_esEs7(Left(x0), Left(x1), ty_Float, x2)
new_ltEs18(x0, x1, app(app(ty_Either, x2), x3))
new_esEs16(x0, x1)
new_esEs25(x0, x1, app(ty_[], x2))
new_esEs24(x0, x1, ty_Float)
new_esEs4(Nothing, Just(x0), x1)
new_compare9(x0, x1, ty_Ordering)
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare28(x0, x1, x2, x3)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_ltEs7(Just(x0), Just(x1), ty_Int)
new_esEs28(x0, x1, ty_Float)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, ty_@0)
new_ltEs18(x0, x1, ty_Ordering)
new_esEs23(x0, x1, ty_Int)
new_esEs7(Right(x0), Right(x1), x2, ty_Double)
new_compare10(x0, x1, False, x2, x3)
new_esEs26(x0, x1, ty_Double)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs24(x0, x1, ty_Bool)
new_esEs23(x0, x1, app(ty_[], x2))
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs21(x0, x1, ty_Float)
new_primMulInt(Pos(x0), Pos(x1))
new_ltEs7(Just(x0), Just(x1), ty_Char)
new_compare112(x0, x1, True, x2)
new_compare9(x0, x1, app(app(ty_Either, x2), x3))
new_primPlusNat0(Succ(x0), x1)
new_ltEs10(GT, LT)
new_ltEs10(LT, GT)
new_ltEs17(Right(x0), Right(x1), x2, ty_@0)
new_ltEs7(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_sr0(Integer(x0), Integer(x1))
new_esEs23(x0, x1, ty_Double)
new_compare9(x0, x1, app(ty_[], x2))
new_esEs25(x0, x1, ty_Integer)
new_esEs20(x0, x1, ty_Char)
new_ltEs7(Nothing, Just(x0), x1)
new_primEqNat0(Zero, Succ(x0))
new_esEs27(x0, x1, ty_Bool)
new_esEs30(x0, x1, ty_Int)
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare17(:%(x0, x1), :%(x2, x3), ty_Int)
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_lt9(x0, x1)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_ltEs20(x0, x1, ty_Integer)
new_primMulInt(Neg(x0), Neg(x1))
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_esEs4(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, ty_Char)
new_ltEs20(x0, x1, ty_Int)
new_compare211(x0, x1, False)
new_ltEs17(Left(x0), Left(x1), ty_Double, x2)
new_compare29(x0, x1, False, x2, x3)
new_ltEs9(x0, x1)
new_esEs7(Right(x0), Right(x1), x2, ty_Float)
new_ltEs17(Right(x0), Right(x1), x2, ty_Ordering)
new_lt10(x0, x1, ty_@0)
new_esEs30(x0, x1, ty_Ordering)
new_ltEs7(Just(x0), Nothing, x1)
new_esEs4(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_compare112(x0, x1, False, x2)
new_esEs29(x0, x1, ty_Char)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs18(x0, x1, ty_Integer)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_esEs27(x0, x1, ty_Float)
new_ltEs19(x0, x1, ty_Double)
new_ltEs21(x0, x1, ty_Double)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Neg(Zero), Neg(Zero))
new_ltEs19(x0, x1, ty_Ordering)
new_ltEs21(x0, x1, ty_Integer)
new_ltEs14(x0, x1)
new_ltEs17(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_ltEs7(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_compare29(x0, x1, True, x2, x3)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs24(x0, x1, ty_Ordering)
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs26(x0, x1, app(ty_[], x2))
new_ltEs17(Right(x0), Right(x1), x2, ty_Bool)
new_esEs29(x0, x1, ty_Ordering)
new_compare9(x0, x1, app(ty_Ratio, x2))
new_esEs30(x0, x1, ty_@0)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_compare7(@0, @0)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_esEs18(x0, x1, ty_Int)
new_ltEs17(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_lt19(x0, x1, app(ty_Maybe, x2))
new_primCompAux00(x0, GT)
new_ltEs21(x0, x1, ty_Int)
new_lt19(x0, x1, ty_Double)
new_esEs26(x0, x1, ty_Float)
new_esEs30(x0, x1, app(ty_[], x2))
new_ltEs7(Just(x0), Just(x1), ty_Ordering)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_esEs4(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs16(x0, x1)
new_esEs21(x0, x1, ty_@0)
new_compare18(x0, x1)
new_lt19(x0, x1, ty_Ordering)
new_esEs4(Nothing, Nothing, x0)
new_esEs30(x0, x1, ty_Char)
new_esEs7(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_ltEs21(x0, x1, app(app(ty_@2, x2), x3))
new_asAs(False, x0)
new_lt10(x0, x1, ty_Char)
new_esEs20(x0, x1, ty_Int)
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat1(Succ(x0), Zero)
new_esEs8(GT, EQ)
new_esEs8(EQ, GT)
new_esEs22(x0, x1, ty_Integer)
new_lt15(x0, x1, x2)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_compare17(:%(x0, x1), :%(x2, x3), ty_Integer)
new_esEs29(x0, x1, app(ty_[], x2))
new_ltEs20(x0, x1, ty_Float)
new_primPlusNat0(Zero, x0)
new_esEs20(x0, x1, ty_Integer)
new_compare26(Float(x0, x1), Float(x2, x3))
new_ltEs17(Left(x0), Left(x1), ty_Char, x2)
new_primCmpNat0(Zero, Zero)
new_lt10(x0, x1, ty_Bool)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_ltEs17(Left(x0), Left(x1), ty_Integer, x2)
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_compare111(x0, x1, False, x2, x3)
new_ltEs7(Nothing, Nothing, x0)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs15(@0, @0)
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_compare16(x0, x1)
new_compare9(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare9(x0, x1, app(app(ty_@2, x2), x3))
new_lt16(x0, x1, x2, x3, x4)
new_esEs23(x0, x1, ty_Bool)
new_primEqNat0(Succ(x0), Succ(x1))
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_esEs7(Left(x0), Left(x1), ty_Char, x2)
new_primCmpNat0(Zero, Succ(x0))
new_esEs27(x0, x1, ty_Integer)
new_esEs21(x0, x1, ty_Int)
new_esEs24(x0, x1, ty_Double)
new_esEs24(x0, x1, app(ty_[], x2))
new_esEs20(x0, x1, ty_Bool)
new_lt10(x0, x1, app(ty_Ratio, x2))
new_lt19(x0, x1, ty_Integer)
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_ltEs10(GT, GT)
new_esEs27(x0, x1, app(ty_[], x2))
new_ltEs7(Just(x0), Just(x1), ty_Float)
new_lt17(x0, x1)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_compare15(Double(x0, x1), Double(x2, x3))
new_esEs22(x0, x1, ty_Float)
new_lt13(x0, x1)
new_ltEs17(Right(x0), Right(x1), x2, ty_Double)
new_esEs30(x0, x1, app(app(ty_Either, x2), x3))
new_primCompAux0(x0, x1, x2, x3)
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_compare9(x0, x1, ty_Char)
new_ltEs5(True, True)
new_esEs7(Right(x0), Right(x1), x2, ty_@0)
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_compare14(Char(x0), Char(x1))
new_lt19(x0, x1, app(ty_Ratio, x2))
new_ltEs17(Right(x0), Right(x1), x2, ty_Integer)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_not(True)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_ltEs7(Just(x0), Just(x1), ty_@0)
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs28(x0, x1, ty_Double)
new_esEs26(x0, x1, ty_Ordering)
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs17(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs27(x0, x1, ty_Int)
new_esEs6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_lt10(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_not(False)
new_esEs4(Just(x0), Just(x1), ty_Integer)
new_ltEs17(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_lt20(x0, x1, ty_Char)
new_lt19(x0, x1, ty_Bool)
new_primCmpNat0(Succ(x0), Succ(x1))
new_ltEs10(EQ, GT)
new_ltEs10(GT, EQ)
new_esEs22(x0, x1, ty_Double)
new_esEs10(Float(x0, x1), Float(x2, x3))
new_esEs26(x0, x1, ty_Int)
new_esEs4(Just(x0), Just(x1), ty_Float)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_compare24(x0, x1, True)
new_ltEs17(Right(x0), Right(x1), x2, ty_Int)
new_esEs25(x0, x1, ty_@0)
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_compare9(x0, x1, ty_Int)
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs21(x0, x1, app(ty_[], x2))
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primMulNat0(Succ(x0), Zero)
new_esEs28(x0, x1, ty_Bool)
new_lt19(x0, x1, ty_Float)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs8(EQ, LT)
new_esEs8(LT, EQ)
new_lt20(x0, x1, ty_@0)
new_compare0([], :(x0, x1), x2)
new_lt19(x0, x1, app(ty_[], x2))
new_esEs7(Right(x0), Right(x1), x2, ty_Int)
new_esEs7(Left(x0), Left(x1), ty_Ordering, x2)
new_compare19(x0, x1, x2, x3, x4)
new_ltEs4(@2(x0, x1), @2(x2, x3), x4, x5)
new_lt8(x0, x1)
new_esEs25(x0, x1, ty_Int)
new_esEs4(Just(x0), Just(x1), app(ty_Ratio, x2))
new_ltEs7(Just(x0), Just(x1), ty_Bool)
new_compare12(x0, x1, False, x2, x3, x4)
new_esEs17(False, True)
new_esEs17(True, False)
new_ltEs17(Right(x0), Right(x1), x2, ty_Char)
new_esEs28(x0, x1, app(ty_[], x2))
new_compare110(x0, x1, True)
new_ltEs7(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs30(x0, x1, ty_Float)
new_ltEs8(x0, x1)
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_compare24(x0, x1, False)
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_esEs28(x0, x1, ty_Char)
new_esEs26(x0, x1, ty_Char)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare9(x0, x1, ty_Double)
new_ltEs17(Left(x0), Right(x1), x2, x3)
new_ltEs17(Right(x0), Left(x1), x2, x3)
new_esEs14([], [], x0)
new_primEqInt(Pos(Zero), Pos(Zero))
new_esEs17(True, True)
new_ltEs21(x0, x1, app(app(ty_Either, x2), x3))
new_lt12(x0, x1)
new_esEs29(x0, x1, ty_Integer)
new_ltEs18(x0, x1, app(ty_Maybe, x2))
new_ltEs21(x0, x1, ty_Char)
new_ltEs18(x0, x1, ty_@0)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs20(x0, x1, ty_Double)
new_lt10(x0, x1, ty_Float)
new_esEs25(x0, x1, ty_Char)
new_ltEs19(x0, x1, ty_Char)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs28(x0, x1, ty_Ordering)
new_esEs29(x0, x1, ty_Int)
new_ltEs17(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_ltEs5(True, False)
new_ltEs5(False, True)
new_ltEs19(x0, x1, app(ty_[], x2))
new_esEs19(x0, x1, ty_Int)
new_esEs24(x0, x1, ty_Int)
new_ltEs18(x0, x1, ty_Bool)
new_esEs4(Just(x0), Just(x1), ty_Char)
new_ltEs7(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs7(Right(x0), Left(x1), x2, x3)
new_esEs7(Left(x0), Right(x1), x2, x3)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, ty_Int)
new_pePe(False, x0)
new_esEs30(x0, x1, app(app(ty_@2, x2), x3))
new_esEs22(x0, x1, ty_@0)
new_esEs29(x0, x1, ty_Float)
new_ltEs19(x0, x1, ty_Float)
new_esEs14(:(x0, x1), [], x2)
new_esEs28(x0, x1, ty_Integer)
new_ltEs10(EQ, EQ)
new_esEs20(x0, x1, app(ty_[], x2))

We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph [15,17,22] contains 2 SCCs.

↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ IFR
        ↳ HASKELL
          ↳ BR
            ↳ HASKELL
              ↳ COR
                ↳ HASKELL
                  ↳ LetRed
                    ↳ HASKELL
                      ↳ NumRed
                        ↳ HASKELL
                          ↳ Narrow
                            ↳ AND
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                                ↳ DependencyGraphProof
                                  ↳ AND
                                    ↳ QDP
                                      ↳ UsableRulesProof
                                    ↳ QDP

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

new_insertBy0(vxw10, vxw11, vxw12, False, ba, bb) → new_insertBy00(vxw10, vxw11, vxw12, new_ltEs20(vxw11, vxw10, ba), ba, bb)
new_insertBy(Left(vxw30), :(Left(vxw400), vxw41), be, bf) → new_insertBy0(vxw400, vxw30, vxw41, new_esEs29(vxw30, vxw400, be), be, bf)
new_insertBy00(vxw28, vxw29, vxw30, False, bc, bd) → new_insertBy(Left(vxw29), vxw30, bc, bd)

The TRS R consists of the following rules:

new_esEs4(Just(vxw300), Just(vxw4000), app(ty_Maybe, ceh)) → new_esEs4(vxw300, vxw4000, ceh)
new_esEs25(vxw111, vxw101, app(ty_[], dac)) → new_esEs14(vxw111, vxw101, dac)
new_esEs26(vxw110, vxw100, ty_@0) → new_esEs15(vxw110, vxw100)
new_esEs23(vxw110, vxw100, app(app(ty_Either, cdg), cdh)) → new_esEs7(vxw110, vxw100, cdg, cdh)
new_esEs29(vxw30, vxw400, ty_Int) → new_esEs16(vxw30, vxw400)
new_compare112(vxw110, vxw100, True, cd) → LT
new_esEs4(Just(vxw300), Just(vxw4000), ty_Ordering) → new_esEs8(vxw300, vxw4000)
new_esEs7(Left(vxw300), Left(vxw4000), app(app(ty_Either, fc), fd), ed) → new_esEs7(vxw300, vxw4000, fc, fd)
new_ltEs19(vxw112, vxw102, app(ty_Ratio, cgh)) → new_ltEs11(vxw112, vxw102, cgh)
new_ltEs21(vxw20, vxw19, app(ty_[], dfc)) → new_ltEs12(vxw20, vxw19, dfc)
new_compare210(vxw110, vxw100, False, cd) → new_compare112(vxw110, vxw100, new_ltEs7(vxw110, vxw100, cd), cd)
new_esEs7(Left(vxw300), Left(vxw4000), app(ty_Maybe, fb), ed) → new_esEs4(vxw300, vxw4000, fb)
new_ltEs18(vxw111, vxw101, ty_Float) → new_ltEs15(vxw111, vxw101)
new_ltEs20(vxw11, vxw10, ty_Ordering) → new_ltEs10(vxw11, vxw10)
new_compare10(vxw110, vxw100, True, dh, ea) → LT
new_esEs26(vxw110, vxw100, ty_Float) → new_esEs10(vxw110, vxw100)
new_esEs24(vxw300, vxw4000, app(ty_Maybe, cgb)) → new_esEs4(vxw300, vxw4000, cgb)
new_esEs4(Just(vxw300), Nothing, bbe) → False
new_esEs4(Nothing, Just(vxw4000), bbe) → False
new_esEs11(Integer(vxw300), Integer(vxw4000)) → new_primEqInt(vxw300, vxw4000)
new_lt19(vxw111, vxw101, app(app(ty_Either, dag), dah)) → new_lt18(vxw111, vxw101, dag, dah)
new_esEs28(vxw300, vxw4000, ty_Integer) → new_esEs11(vxw300, vxw4000)
new_esEs26(vxw110, vxw100, ty_Integer) → new_esEs11(vxw110, vxw100)
new_ltEs17(Right(vxw110), Right(vxw100), bdg, app(ty_Ratio, cbd)) → new_ltEs11(vxw110, vxw100, cbd)
new_lt19(vxw111, vxw101, ty_@0) → new_lt8(vxw111, vxw101)
new_esEs22(vxw300, vxw4000, ty_Char) → new_esEs12(vxw300, vxw4000)
new_ltEs17(Left(vxw110), Left(vxw100), app(ty_Ratio, cab), bdh) → new_ltEs11(vxw110, vxw100, cab)
new_esEs30(vxw30, vxw400, app(ty_[], dd)) → new_esEs14(vxw30, vxw400, dd)
new_ltEs20(vxw11, vxw10, ty_Bool) → new_ltEs5(vxw11, vxw10)
new_esEs4(Just(vxw300), Just(vxw4000), ty_Char) → new_esEs12(vxw300, vxw4000)
new_esEs27(vxw301, vxw4001, ty_Bool) → new_esEs17(vxw301, vxw4001)
new_lt12(vxw110, vxw100) → new_esEs8(new_compare14(vxw110, vxw100), LT)
new_primMulNat0(Zero, Zero) → Zero
new_ltEs21(vxw20, vxw19, ty_Int) → new_ltEs16(vxw20, vxw19)
new_esEs23(vxw110, vxw100, app(ty_Ratio, cde)) → new_esEs13(vxw110, vxw100, cde)
new_esEs4(Just(vxw300), Just(vxw4000), app(app(app(ty_@3, cec), ced), cee)) → new_esEs6(vxw300, vxw4000, cec, ced, cee)
new_ltEs19(vxw112, vxw102, ty_Double) → new_ltEs9(vxw112, vxw102)
new_esEs20(vxw302, vxw4002, app(ty_Maybe, beh)) → new_esEs4(vxw302, vxw4002, beh)
new_lt20(vxw110, vxw100, ty_Integer) → new_lt4(vxw110, vxw100)
new_lt20(vxw110, vxw100, ty_@0) → new_lt8(vxw110, vxw100)
new_esEs21(vxw301, vxw4001, ty_Bool) → new_esEs17(vxw301, vxw4001)
new_esEs23(vxw110, vxw100, ty_Double) → new_esEs9(vxw110, vxw100)
new_esEs7(Right(vxw300), Right(vxw4000), ff, ty_Ordering) → new_esEs8(vxw300, vxw4000)
new_lt19(vxw111, vxw101, ty_Ordering) → new_lt6(vxw111, vxw101)
new_ltEs17(Left(vxw110), Left(vxw100), ty_Integer, bdh) → new_ltEs13(vxw110, vxw100)
new_esEs25(vxw111, vxw101, ty_Bool) → new_esEs17(vxw111, vxw101)
new_compare13(vxw110, vxw100, dh, ea) → new_compare23(vxw110, vxw100, new_esEs5(vxw110, vxw100, dh, ea), dh, ea)
new_compare9(vxw110, vxw100, ty_Double) → new_compare15(vxw110, vxw100)
new_lt20(vxw110, vxw100, app(app(ty_@2, dbb), dbc)) → new_lt11(vxw110, vxw100, dbb, dbc)
new_esEs23(vxw110, vxw100, app(ty_Maybe, cd)) → new_esEs4(vxw110, vxw100, cd)
new_compare9(vxw110, vxw100, ty_Integer) → new_compare6(vxw110, vxw100)
new_esEs30(vxw30, vxw400, app(app(ty_Either, df), dg)) → new_esEs7(vxw30, vxw400, df, dg)
new_ltEs7(Just(vxw110), Just(vxw100), ty_Bool) → new_ltEs5(vxw110, vxw100)
new_esEs17(True, True) → True
new_esEs20(vxw302, vxw4002, app(ty_Ratio, bef)) → new_esEs13(vxw302, vxw4002, bef)
new_ltEs19(vxw112, vxw102, ty_Ordering) → new_ltEs10(vxw112, vxw102)
new_compare0(:(vxw110, vxw111), :(vxw100, vxw101), cc) → new_primCompAux0(vxw110, vxw100, new_compare0(vxw111, vxw101, cc), cc)
new_ltEs7(Just(vxw110), Just(vxw100), app(app(app(ty_@3, bcd), bce), bcf)) → new_ltEs6(vxw110, vxw100, bcd, bce, bcf)
new_esEs22(vxw300, vxw4000, app(app(ty_@2, bge), bgf)) → new_esEs5(vxw300, vxw4000, bge, bgf)
new_lt15(vxw110, vxw100, cdf) → new_esEs8(new_compare0(vxw110, vxw100, cdf), LT)
new_esEs24(vxw300, vxw4000, app(app(ty_@2, cfc), cfd)) → new_esEs5(vxw300, vxw4000, cfc, cfd)
new_esEs4(Just(vxw300), Just(vxw4000), ty_Float) → new_esEs10(vxw300, vxw4000)
new_ltEs18(vxw111, vxw101, ty_Char) → new_ltEs8(vxw111, vxw101)
new_ltEs17(Right(vxw110), Right(vxw100), bdg, ty_Integer) → new_ltEs13(vxw110, vxw100)
new_ltEs10(EQ, GT) → True
new_compare29(vxw110, vxw100, False, cdg, cdh) → new_compare111(vxw110, vxw100, new_ltEs17(vxw110, vxw100, cdg, cdh), cdg, cdh)
new_ltEs21(vxw20, vxw19, app(app(ty_@2, deh), dfa)) → new_ltEs4(vxw20, vxw19, deh, dfa)
new_ltEs20(vxw11, vxw10, ty_Double) → new_ltEs9(vxw11, vxw10)
new_compare9(vxw110, vxw100, ty_Int) → new_compare27(vxw110, vxw100)
new_esEs26(vxw110, vxw100, app(ty_Maybe, dba)) → new_esEs4(vxw110, vxw100, dba)
new_esEs22(vxw300, vxw4000, app(ty_[], bhc)) → new_esEs14(vxw300, vxw4000, bhc)
new_lt20(vxw110, vxw100, ty_Float) → new_lt17(vxw110, vxw100)
new_esEs22(vxw300, vxw4000, app(app(ty_Either, bhe), bhf)) → new_esEs7(vxw300, vxw4000, bhe, bhf)
new_ltEs7(Just(vxw110), Just(vxw100), app(app(ty_Either, bcg), bch)) → new_ltEs17(vxw110, vxw100, bcg, bch)
new_ltEs7(Just(vxw110), Just(vxw100), app(app(ty_@2, bbh), bca)) → new_ltEs4(vxw110, vxw100, bbh, bca)
new_esEs25(vxw111, vxw101, ty_Double) → new_esEs9(vxw111, vxw101)
new_pePe(False, vxw60) → vxw60
new_esEs14([], [], bbd) → True
new_ltEs7(Just(vxw110), Just(vxw100), ty_Ordering) → new_ltEs10(vxw110, vxw100)
new_ltEs17(Left(vxw110), Left(vxw100), ty_Bool, bdh) → new_ltEs5(vxw110, vxw100)
new_esEs7(Left(vxw300), Right(vxw4000), ff, ed) → False
new_esEs7(Right(vxw300), Left(vxw4000), ff, ed) → False
new_esEs4(Just(vxw300), Just(vxw4000), ty_Integer) → new_esEs11(vxw300, vxw4000)
new_ltEs19(vxw112, vxw102, app(app(ty_@2, cgf), cgg)) → new_ltEs4(vxw112, vxw102, cgf, cgg)
new_esEs29(vxw30, vxw400, app(ty_[], bbd)) → new_esEs14(vxw30, vxw400, bbd)
new_ltEs7(Just(vxw110), Just(vxw100), ty_Integer) → new_ltEs13(vxw110, vxw100)
new_esEs27(vxw301, vxw4001, app(app(ty_Either, ddc), ddd)) → new_esEs7(vxw301, vxw4001, ddc, ddd)
new_esEs20(vxw302, vxw4002, ty_Int) → new_esEs16(vxw302, vxw4002)
new_esEs26(vxw110, vxw100, ty_Char) → new_esEs12(vxw110, vxw100)
new_esEs22(vxw300, vxw4000, ty_@0) → new_esEs15(vxw300, vxw4000)
new_lt9(vxw110, vxw100) → new_esEs8(new_compare18(vxw110, vxw100), LT)
new_esEs28(vxw300, vxw4000, ty_@0) → new_esEs15(vxw300, vxw4000)
new_esEs20(vxw302, vxw4002, ty_Char) → new_esEs12(vxw302, vxw4002)
new_ltEs17(Left(vxw110), Left(vxw100), app(ty_Maybe, bhg), bdh) → new_ltEs7(vxw110, vxw100, bhg)
new_ltEs18(vxw111, vxw101, ty_Int) → new_ltEs16(vxw111, vxw101)
new_esEs22(vxw300, vxw4000, ty_Ordering) → new_esEs8(vxw300, vxw4000)
new_esEs7(Left(vxw300), Left(vxw4000), ty_Double, ed) → new_esEs9(vxw300, vxw4000)
new_esEs29(vxw30, vxw400, app(ty_Ratio, bbc)) → new_esEs13(vxw30, vxw400, bbc)
new_esEs20(vxw302, vxw4002, app(app(ty_@2, bea), beb)) → new_esEs5(vxw302, vxw4002, bea, beb)
new_esEs7(Right(vxw300), Right(vxw4000), ff, ty_Double) → new_esEs9(vxw300, vxw4000)
new_ltEs20(vxw11, vxw10, app(ty_[], cc)) → new_ltEs12(vxw11, vxw10, cc)
new_ltEs21(vxw20, vxw19, ty_@0) → new_ltEs14(vxw20, vxw19)
new_esEs7(Right(vxw300), Right(vxw4000), ff, app(app(ty_@2, fg), fh)) → new_esEs5(vxw300, vxw4000, fg, fh)
new_ltEs20(vxw11, vxw10, app(app(ty_@2, bdb), bdc)) → new_ltEs4(vxw11, vxw10, bdb, bdc)
new_primCmpNat0(Zero, Succ(vxw1000)) → LT
new_lt10(vxw110, vxw100, ty_Double) → new_lt13(vxw110, vxw100)
new_ltEs19(vxw112, vxw102, ty_Float) → new_ltEs15(vxw112, vxw102)
new_lt10(vxw110, vxw100, ty_Bool) → new_lt9(vxw110, vxw100)
new_lt20(vxw110, vxw100, ty_Ordering) → new_lt6(vxw110, vxw100)
new_esEs8(LT, LT) → True
new_lt19(vxw111, vxw101, ty_Bool) → new_lt9(vxw111, vxw101)
new_compare25(vxw110, vxw100, True, ha, hb, hc) → EQ
new_ltEs15(vxw11, vxw10) → new_not(new_esEs8(new_compare26(vxw11, vxw10), GT))
new_esEs21(vxw301, vxw4001, app(ty_Ratio, bfh)) → new_esEs13(vxw301, vxw4001, bfh)
new_lt5(vxw110, vxw100, cd) → new_esEs8(new_compare8(vxw110, vxw100, cd), LT)
new_esEs7(Left(vxw300), Left(vxw4000), ty_Integer, ed) → new_esEs11(vxw300, vxw4000)
new_esEs25(vxw111, vxw101, ty_Ordering) → new_esEs8(vxw111, vxw101)
new_esEs20(vxw302, vxw4002, ty_Integer) → new_esEs11(vxw302, vxw4002)
new_esEs24(vxw300, vxw4000, app(app(ty_Either, cgc), cgd)) → new_esEs7(vxw300, vxw4000, cgc, cgd)
new_compare9(vxw110, vxw100, app(app(app(ty_@3, baa), bab), bac)) → new_compare19(vxw110, vxw100, baa, bab, bac)
new_esEs20(vxw302, vxw4002, app(app(app(ty_@3, bec), bed), bee)) → new_esEs6(vxw302, vxw4002, bec, bed, bee)
new_esEs25(vxw111, vxw101, app(ty_Ratio, dab)) → new_esEs13(vxw111, vxw101, dab)
new_esEs30(vxw30, vxw400, ty_Float) → new_esEs10(vxw30, vxw400)
new_esEs28(vxw300, vxw4000, ty_Float) → new_esEs10(vxw300, vxw4000)
new_ltEs5(True, False) → False
new_lt19(vxw111, vxw101, app(app(ty_@2, chh), daa)) → new_lt11(vxw111, vxw101, chh, daa)
new_esEs18(vxw301, vxw4001, ty_Integer) → new_esEs11(vxw301, vxw4001)
new_compare0([], [], cc) → EQ
new_pePe(True, vxw60) → True
new_esEs24(vxw300, vxw4000, ty_Int) → new_esEs16(vxw300, vxw4000)
new_primEqNat0(Zero, Zero) → True
new_ltEs21(vxw20, vxw19, ty_Bool) → new_ltEs5(vxw20, vxw19)
new_ltEs17(Left(vxw110), Left(vxw100), ty_Double, bdh) → new_ltEs9(vxw110, vxw100)
new_esEs7(Left(vxw300), Left(vxw4000), app(app(ty_@2, eb), ec), ed) → new_esEs5(vxw300, vxw4000, eb, ec)
new_compare29(vxw110, vxw100, True, cdg, cdh) → EQ
new_compare111(vxw110, vxw100, False, cdg, cdh) → GT
new_esEs26(vxw110, vxw100, app(ty_Ratio, dbd)) → new_esEs13(vxw110, vxw100, dbd)
new_ltEs21(vxw20, vxw19, app(ty_Ratio, dfb)) → new_ltEs11(vxw20, vxw19, dfb)
new_esEs27(vxw301, vxw4001, app(ty_Ratio, dch)) → new_esEs13(vxw301, vxw4001, dch)
new_esEs27(vxw301, vxw4001, ty_Char) → new_esEs12(vxw301, vxw4001)
new_lt18(vxw110, vxw100, cdg, cdh) → new_esEs8(new_compare28(vxw110, vxw100, cdg, cdh), LT)
new_ltEs5(True, True) → True
new_ltEs17(Left(vxw110), Left(vxw100), ty_Ordering, bdh) → new_ltEs10(vxw110, vxw100)
new_esEs17(False, False) → True
new_ltEs17(Right(vxw110), Left(vxw100), bdg, bdh) → False
new_esEs17(False, True) → False
new_esEs17(True, False) → False
new_esEs7(Left(vxw300), Left(vxw4000), ty_Ordering, ed) → new_esEs8(vxw300, vxw4000)
new_compare17(:%(vxw110, vxw111), :%(vxw100, vxw101), ty_Int) → new_compare27(new_sr(vxw110, vxw101), new_sr(vxw100, vxw111))
new_lt19(vxw111, vxw101, ty_Double) → new_lt13(vxw111, vxw101)
new_ltEs18(vxw111, vxw101, app(app(ty_Either, cdc), cdd)) → new_ltEs17(vxw111, vxw101, cdc, cdd)
new_esEs7(Right(vxw300), Right(vxw4000), ff, app(app(app(ty_@3, ga), gb), gc)) → new_esEs6(vxw300, vxw4000, ga, gb, gc)
new_sr(vxw300, vxw4000) → new_primMulInt(vxw300, vxw4000)
new_esEs24(vxw300, vxw4000, ty_Bool) → new_esEs17(vxw300, vxw4000)
new_compare12(vxw110, vxw100, True, ha, hb, hc) → LT
new_esEs30(vxw30, vxw400, ty_Char) → new_esEs12(vxw30, vxw400)
new_esEs30(vxw30, vxw400, ty_Bool) → new_esEs17(vxw30, vxw400)
new_esEs24(vxw300, vxw4000, ty_Char) → new_esEs12(vxw300, vxw4000)
new_esEs22(vxw300, vxw4000, ty_Double) → new_esEs9(vxw300, vxw4000)
new_esEs4(Just(vxw300), Just(vxw4000), ty_Bool) → new_esEs17(vxw300, vxw4000)
new_esEs26(vxw110, vxw100, ty_Ordering) → new_esEs8(vxw110, vxw100)
new_esEs8(GT, GT) → True
new_ltEs20(vxw11, vxw10, app(ty_Ratio, bda)) → new_ltEs11(vxw11, vxw10, bda)
new_primPlusNat0(Succ(vxw620), vxw400000) → Succ(Succ(new_primPlusNat1(vxw620, vxw400000)))
new_ltEs9(vxw11, vxw10) → new_not(new_esEs8(new_compare15(vxw11, vxw10), GT))
new_esEs7(Right(vxw300), Right(vxw4000), ff, app(app(ty_Either, gg), gh)) → new_esEs7(vxw300, vxw4000, gg, gh)
new_lt10(vxw110, vxw100, app(app(ty_@2, dh), ea)) → new_lt11(vxw110, vxw100, dh, ea)
new_esEs20(vxw302, vxw4002, ty_Bool) → new_esEs17(vxw302, vxw4002)
new_esEs26(vxw110, vxw100, app(app(app(ty_@3, dbf), dbg), dbh)) → new_esEs6(vxw110, vxw100, dbf, dbg, dbh)
new_ltEs17(Right(vxw110), Right(vxw100), bdg, ty_Ordering) → new_ltEs10(vxw110, vxw100)
new_esEs8(LT, GT) → False
new_esEs8(GT, LT) → False
new_lt20(vxw110, vxw100, ty_Bool) → new_lt9(vxw110, vxw100)
new_esEs7(Right(vxw300), Right(vxw4000), ff, ty_Char) → new_esEs12(vxw300, vxw4000)
new_ltEs7(Just(vxw110), Just(vxw100), ty_Int) → new_ltEs16(vxw110, vxw100)
new_ltEs20(vxw11, vxw10, ty_Int) → new_ltEs16(vxw11, vxw10)
new_esEs7(Right(vxw300), Right(vxw4000), ff, ty_@0) → new_esEs15(vxw300, vxw4000)
new_primEqInt(Neg(Succ(vxw3000)), Neg(Succ(vxw40000))) → new_primEqNat0(vxw3000, vxw40000)
new_lt10(vxw110, vxw100, ty_Char) → new_lt12(vxw110, vxw100)
new_esEs20(vxw302, vxw4002, ty_Ordering) → new_esEs8(vxw302, vxw4002)
new_lt10(vxw110, vxw100, app(app(ty_Either, cdg), cdh)) → new_lt18(vxw110, vxw100, cdg, cdh)
new_esEs22(vxw300, vxw4000, app(app(app(ty_@3, bgg), bgh), bha)) → new_esEs6(vxw300, vxw4000, bgg, bgh, bha)
new_esEs23(vxw110, vxw100, ty_Ordering) → new_esEs8(vxw110, vxw100)
new_ltEs5(False, False) → True
new_primPlusNat1(Zero, Succ(vxw4000000)) → Succ(vxw4000000)
new_primPlusNat1(Succ(vxw6200), Zero) → Succ(vxw6200)
new_esEs30(vxw30, vxw400, app(ty_Maybe, de)) → new_esEs4(vxw30, vxw400, de)
new_lt19(vxw111, vxw101, ty_Float) → new_lt17(vxw111, vxw101)
new_esEs6(@3(vxw300, vxw301, vxw302), @3(vxw4000, vxw4001, vxw4002), bah, bba, bbb) → new_asAs(new_esEs22(vxw300, vxw4000, bah), new_asAs(new_esEs21(vxw301, vxw4001, bba), new_esEs20(vxw302, vxw4002, bbb)))
new_esEs21(vxw301, vxw4001, ty_Char) → new_esEs12(vxw301, vxw4001)
new_esEs16(vxw30, vxw400) → new_primEqInt(vxw30, vxw400)
new_esEs28(vxw300, vxw4000, app(ty_Maybe, ded)) → new_esEs4(vxw300, vxw4000, ded)
new_esEs21(vxw301, vxw4001, ty_@0) → new_esEs15(vxw301, vxw4001)
new_esEs14([], :(vxw4000, vxw4001), bbd) → False
new_esEs14(:(vxw300, vxw301), [], bbd) → False
new_esEs7(Right(vxw300), Right(vxw4000), ff, app(ty_Ratio, gd)) → new_esEs13(vxw300, vxw4000, gd)
new_ltEs21(vxw20, vxw19, ty_Integer) → new_ltEs13(vxw20, vxw19)
new_lt6(vxw110, vxw100) → new_esEs8(new_compare16(vxw110, vxw100), LT)
new_esEs30(vxw30, vxw400, ty_Integer) → new_esEs11(vxw30, vxw400)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs7(Left(vxw300), Left(vxw4000), app(ty_Ratio, eh), ed) → new_esEs13(vxw300, vxw4000, eh)
new_esEs24(vxw300, vxw4000, app(app(app(ty_@3, cfe), cff), cfg)) → new_esEs6(vxw300, vxw4000, cfe, cff, cfg)
new_ltEs17(Right(vxw110), Right(vxw100), bdg, ty_Int) → new_ltEs16(vxw110, vxw100)
new_esEs21(vxw301, vxw4001, ty_Integer) → new_esEs11(vxw301, vxw4001)
new_esEs26(vxw110, vxw100, app(ty_[], dbe)) → new_esEs14(vxw110, vxw100, dbe)
new_ltEs18(vxw111, vxw101, ty_@0) → new_ltEs14(vxw111, vxw101)
new_esEs28(vxw300, vxw4000, ty_Int) → new_esEs16(vxw300, vxw4000)
new_primEqInt(Neg(Succ(vxw3000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(vxw40000))) → False
new_lt19(vxw111, vxw101, ty_Char) → new_lt12(vxw111, vxw101)
new_esEs8(EQ, EQ) → True
new_compare27(vxw11, vxw10) → new_primCmpInt(vxw11, vxw10)
new_esEs5(@2(vxw300, vxw301), @2(vxw4000, vxw4001), baf, bag) → new_asAs(new_esEs28(vxw300, vxw4000, baf), new_esEs27(vxw301, vxw4001, bag))
new_esEs28(vxw300, vxw4000, app(ty_[], dec)) → new_esEs14(vxw300, vxw4000, dec)
new_lt20(vxw110, vxw100, app(ty_Maybe, dba)) → new_lt5(vxw110, vxw100, dba)
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_esEs26(vxw110, vxw100, app(app(ty_Either, dca), dcb)) → new_esEs7(vxw110, vxw100, dca, dcb)
new_compare14(Char(vxw110), Char(vxw100)) → new_primCmpNat0(vxw110, vxw100)
new_esEs21(vxw301, vxw4001, ty_Float) → new_esEs10(vxw301, vxw4001)
new_esEs4(Just(vxw300), Just(vxw4000), app(app(ty_Either, cfa), cfb)) → new_esEs7(vxw300, vxw4000, cfa, cfb)
new_esEs7(Left(vxw300), Left(vxw4000), ty_@0, ed) → new_esEs15(vxw300, vxw4000)
new_primCmpNat0(Succ(vxw1100), Succ(vxw1000)) → new_primCmpNat0(vxw1100, vxw1000)
new_esEs23(vxw110, vxw100, ty_Float) → new_esEs10(vxw110, vxw100)
new_esEs22(vxw300, vxw4000, app(ty_Maybe, bhd)) → new_esEs4(vxw300, vxw4000, bhd)
new_esEs30(vxw30, vxw400, ty_@0) → new_esEs15(vxw30, vxw400)
new_esEs25(vxw111, vxw101, app(ty_Maybe, chg)) → new_esEs4(vxw111, vxw101, chg)
new_compare19(vxw110, vxw100, ha, hb, hc) → new_compare25(vxw110, vxw100, new_esEs6(vxw110, vxw100, ha, hb, hc), ha, hb, hc)
new_lt14(vxw110, vxw100, cde) → new_esEs8(new_compare17(vxw110, vxw100, cde), LT)
new_ltEs18(vxw111, vxw101, ty_Integer) → new_ltEs13(vxw111, vxw101)
new_ltEs6(@3(vxw110, vxw111, vxw112), @3(vxw100, vxw101, vxw102), bdd, bde, bdf) → new_pePe(new_lt20(vxw110, vxw100, bdd), new_asAs(new_esEs26(vxw110, vxw100, bdd), new_pePe(new_lt19(vxw111, vxw101, bde), new_asAs(new_esEs25(vxw111, vxw101, bde), new_ltEs19(vxw112, vxw102, bdf)))))
new_ltEs18(vxw111, vxw101, ty_Bool) → new_ltEs5(vxw111, vxw101)
new_ltEs17(Left(vxw110), Left(vxw100), app(app(ty_@2, bhh), caa), bdh) → new_ltEs4(vxw110, vxw100, bhh, caa)
new_primEqInt(Pos(Succ(vxw3000)), Pos(Succ(vxw40000))) → new_primEqNat0(vxw3000, vxw40000)
new_compare10(vxw110, vxw100, False, dh, ea) → GT
new_compare9(vxw110, vxw100, app(ty_Maybe, hd)) → new_compare8(vxw110, vxw100, hd)
new_esEs18(vxw301, vxw4001, ty_Int) → new_esEs16(vxw301, vxw4001)
new_esEs4(Just(vxw300), Just(vxw4000), app(app(ty_@2, cea), ceb)) → new_esEs5(vxw300, vxw4000, cea, ceb)
new_lt20(vxw110, vxw100, ty_Int) → new_lt7(vxw110, vxw100)
new_compare9(vxw110, vxw100, app(ty_[], hh)) → new_compare0(vxw110, vxw100, hh)
new_esEs30(vxw30, vxw400, ty_Int) → new_esEs16(vxw30, vxw400)
new_ltEs7(Nothing, Just(vxw100), bbf) → True
new_esEs4(Just(vxw300), Just(vxw4000), ty_Int) → new_esEs16(vxw300, vxw4000)
new_ltEs10(GT, EQ) → False
new_primEqNat0(Succ(vxw3000), Succ(vxw40000)) → new_primEqNat0(vxw3000, vxw40000)
new_esEs23(vxw110, vxw100, ty_Integer) → new_esEs11(vxw110, vxw100)
new_esEs27(vxw301, vxw4001, ty_Ordering) → new_esEs8(vxw301, vxw4001)
new_compare7(@0, @0) → EQ
new_esEs21(vxw301, vxw4001, app(ty_[], bga)) → new_esEs14(vxw301, vxw4001, bga)
new_esEs29(vxw30, vxw400, ty_Double) → new_esEs9(vxw30, vxw400)
new_esEs9(Double(vxw300, vxw301), Double(vxw4000, vxw4001)) → new_esEs16(new_sr(vxw300, vxw4000), new_sr(vxw301, vxw4001))
new_esEs7(Right(vxw300), Right(vxw4000), ff, ty_Float) → new_esEs10(vxw300, vxw4000)
new_esEs20(vxw302, vxw4002, ty_Float) → new_esEs10(vxw302, vxw4002)
new_primCompAux00(vxw72, LT) → LT
new_lt10(vxw110, vxw100, app(app(app(ty_@3, ha), hb), hc)) → new_lt16(vxw110, vxw100, ha, hb, hc)
new_primCmpInt(Neg(Succ(vxw1100)), Neg(vxw100)) → new_primCmpNat0(vxw100, Succ(vxw1100))
new_esEs4(Just(vxw300), Just(vxw4000), ty_@0) → new_esEs15(vxw300, vxw4000)
new_esEs24(vxw300, vxw4000, ty_Ordering) → new_esEs8(vxw300, vxw4000)
new_lt10(vxw110, vxw100, ty_Float) → new_lt17(vxw110, vxw100)
new_esEs28(vxw300, vxw4000, ty_Ordering) → new_esEs8(vxw300, vxw4000)
new_esEs7(Left(vxw300), Left(vxw4000), ty_Int, ed) → new_esEs16(vxw300, vxw4000)
new_esEs8(LT, EQ) → False
new_esEs8(EQ, LT) → False
new_primEqInt(Pos(Succ(vxw3000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(vxw40000))) → False
new_lt4(vxw110, vxw100) → new_esEs8(new_compare6(vxw110, vxw100), LT)
new_ltEs20(vxw11, vxw10, ty_Integer) → new_ltEs13(vxw11, vxw10)
new_ltEs19(vxw112, vxw102, app(app(ty_Either, che), chf)) → new_ltEs17(vxw112, vxw102, che, chf)
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(vxw1100), Zero) → GT
new_esEs23(vxw110, vxw100, app(app(ty_@2, dh), ea)) → new_esEs5(vxw110, vxw100, dh, ea)
new_esEs24(vxw300, vxw4000, ty_@0) → new_esEs15(vxw300, vxw4000)
new_ltEs17(Right(vxw110), Right(vxw100), bdg, app(ty_Maybe, cba)) → new_ltEs7(vxw110, vxw100, cba)
new_ltEs10(LT, EQ) → True
new_primCmpInt(Neg(Zero), Pos(Succ(vxw1000))) → LT
new_ltEs20(vxw11, vxw10, ty_@0) → new_ltEs14(vxw11, vxw10)
new_ltEs21(vxw20, vxw19, app(app(app(ty_@3, dfd), dfe), dff)) → new_ltEs6(vxw20, vxw19, dfd, dfe, dff)
new_lt10(vxw110, vxw100, app(ty_Ratio, cde)) → new_lt14(vxw110, vxw100, cde)
new_compare9(vxw110, vxw100, ty_Bool) → new_compare18(vxw110, vxw100)
new_esEs27(vxw301, vxw4001, ty_Double) → new_esEs9(vxw301, vxw4001)
new_ltEs17(Left(vxw110), Left(vxw100), app(app(app(ty_@3, cad), cae), caf), bdh) → new_ltEs6(vxw110, vxw100, cad, cae, caf)
new_esEs22(vxw300, vxw4000, app(ty_Ratio, bhb)) → new_esEs13(vxw300, vxw4000, bhb)
new_esEs19(vxw300, vxw4000, ty_Integer) → new_esEs11(vxw300, vxw4000)
new_sr0(Integer(vxw1100), Integer(vxw1010)) → Integer(new_primMulInt(vxw1100, vxw1010))
new_primPlusNat1(Succ(vxw6200), Succ(vxw4000000)) → Succ(Succ(new_primPlusNat1(vxw6200, vxw4000000)))
new_compare6(Integer(vxw110), Integer(vxw100)) → new_primCmpInt(vxw110, vxw100)
new_primEqInt(Pos(Succ(vxw3000)), Neg(vxw4000)) → False
new_primEqInt(Neg(Succ(vxw3000)), Pos(vxw4000)) → False
new_ltEs17(Left(vxw110), Left(vxw100), app(ty_[], cac), bdh) → new_ltEs12(vxw110, vxw100, cac)
new_esEs24(vxw300, vxw4000, app(ty_Ratio, cfh)) → new_esEs13(vxw300, vxw4000, cfh)
new_compare210(vxw110, vxw100, True, cd) → EQ
new_ltEs4(@2(vxw110, vxw111), @2(vxw100, vxw101), bdb, bdc) → new_pePe(new_lt10(vxw110, vxw100, bdb), new_asAs(new_esEs23(vxw110, vxw100, bdb), new_ltEs18(vxw111, vxw101, bdc)))
new_ltEs5(False, True) → True
new_ltEs10(GT, GT) → True
new_esEs29(vxw30, vxw400, app(app(ty_@2, baf), bag)) → new_esEs5(vxw30, vxw400, baf, bag)
new_ltEs20(vxw11, vxw10, ty_Float) → new_ltEs15(vxw11, vxw10)
new_esEs25(vxw111, vxw101, ty_Char) → new_esEs12(vxw111, vxw101)
new_lt19(vxw111, vxw101, ty_Int) → new_lt7(vxw111, vxw101)
new_esEs29(vxw30, vxw400, ty_Integer) → new_esEs11(vxw30, vxw400)
new_primEqInt(Pos(Zero), Neg(Succ(vxw40000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(vxw40000))) → False
new_primCmpInt(Pos(Zero), Pos(Succ(vxw1000))) → new_primCmpNat0(Zero, Succ(vxw1000))
new_primCompAux00(vxw72, EQ) → vxw72
new_esEs28(vxw300, vxw4000, app(app(ty_Either, dee), def)) → new_esEs7(vxw300, vxw4000, dee, def)
new_ltEs18(vxw111, vxw101, app(ty_Ratio, ccf)) → new_ltEs11(vxw111, vxw101, ccf)
new_esEs7(Right(vxw300), Right(vxw4000), ff, app(ty_Maybe, gf)) → new_esEs4(vxw300, vxw4000, gf)
new_compare24(vxw110, vxw100, True) → EQ
new_compare17(:%(vxw110, vxw111), :%(vxw100, vxw101), ty_Integer) → new_compare6(new_sr0(vxw110, vxw101), new_sr0(vxw100, vxw111))
new_esEs27(vxw301, vxw4001, ty_Float) → new_esEs10(vxw301, vxw4001)
new_esEs8(EQ, GT) → False
new_esEs8(GT, EQ) → False
new_lt10(vxw110, vxw100, app(ty_Maybe, cd)) → new_lt5(vxw110, vxw100, cd)
new_ltEs7(Just(vxw110), Just(vxw100), ty_Float) → new_ltEs15(vxw110, vxw100)
new_esEs26(vxw110, vxw100, app(app(ty_@2, dbb), dbc)) → new_esEs5(vxw110, vxw100, dbb, dbc)
new_compare18(vxw110, vxw100) → new_compare24(vxw110, vxw100, new_esEs17(vxw110, vxw100))
new_esEs21(vxw301, vxw4001, app(app(ty_@2, bfc), bfd)) → new_esEs5(vxw301, vxw4001, bfc, bfd)
new_ltEs19(vxw112, vxw102, ty_Char) → new_ltEs8(vxw112, vxw102)
new_lt8(vxw110, vxw100) → new_esEs8(new_compare7(vxw110, vxw100), LT)
new_ltEs7(Just(vxw110), Just(vxw100), ty_Double) → new_ltEs9(vxw110, vxw100)
new_esEs12(Char(vxw300), Char(vxw4000)) → new_primEqNat0(vxw300, vxw4000)
new_ltEs20(vxw11, vxw10, app(app(app(ty_@3, bdd), bde), bdf)) → new_ltEs6(vxw11, vxw10, bdd, bde, bdf)
new_not(False) → True
new_esEs7(Right(vxw300), Right(vxw4000), ff, ty_Integer) → new_esEs11(vxw300, vxw4000)
new_esEs24(vxw300, vxw4000, ty_Double) → new_esEs9(vxw300, vxw4000)
new_primCompAux0(vxw110, vxw100, vxw61, cc) → new_primCompAux00(vxw61, new_compare9(vxw110, vxw100, cc))
new_primPlusNat0(Zero, vxw400000) → Succ(vxw400000)
new_primCmpInt(Pos(Succ(vxw1100)), Pos(vxw100)) → new_primCmpNat0(Succ(vxw1100), vxw100)
new_esEs23(vxw110, vxw100, ty_@0) → new_esEs15(vxw110, vxw100)
new_compare9(vxw110, vxw100, ty_Float) → new_compare26(vxw110, vxw100)
new_compare12(vxw110, vxw100, False, ha, hb, hc) → GT
new_esEs7(Right(vxw300), Right(vxw4000), ff, ty_Bool) → new_esEs17(vxw300, vxw4000)
new_esEs22(vxw300, vxw4000, ty_Bool) → new_esEs17(vxw300, vxw4000)
new_ltEs18(vxw111, vxw101, app(app(app(ty_@3, cch), cda), cdb)) → new_ltEs6(vxw111, vxw101, cch, cda, cdb)
new_compare9(vxw110, vxw100, ty_@0) → new_compare7(vxw110, vxw100)
new_ltEs19(vxw112, vxw102, app(ty_[], cha)) → new_ltEs12(vxw112, vxw102, cha)
new_ltEs17(Right(vxw110), Right(vxw100), bdg, app(app(ty_Either, cca), ccb)) → new_ltEs17(vxw110, vxw100, cca, ccb)
new_esEs25(vxw111, vxw101, ty_Float) → new_esEs10(vxw111, vxw101)
new_compare16(vxw110, vxw100) → new_compare211(vxw110, vxw100, new_esEs8(vxw110, vxw100))
new_esEs24(vxw300, vxw4000, app(ty_[], cga)) → new_esEs14(vxw300, vxw4000, cga)
new_esEs25(vxw111, vxw101, ty_@0) → new_esEs15(vxw111, vxw101)
new_lt20(vxw110, vxw100, ty_Double) → new_lt13(vxw110, vxw100)
new_lt20(vxw110, vxw100, app(ty_Ratio, dbd)) → new_lt14(vxw110, vxw100, dbd)
new_esEs28(vxw300, vxw4000, app(app(ty_@2, dde), ddf)) → new_esEs5(vxw300, vxw4000, dde, ddf)
new_compare0(:(vxw110, vxw111), [], cc) → GT
new_esEs22(vxw300, vxw4000, ty_Integer) → new_esEs11(vxw300, vxw4000)
new_ltEs19(vxw112, vxw102, app(app(app(ty_@3, chb), chc), chd)) → new_ltEs6(vxw112, vxw102, chb, chc, chd)
new_ltEs18(vxw111, vxw101, app(ty_Maybe, ccc)) → new_ltEs7(vxw111, vxw101, ccc)
new_compare9(vxw110, vxw100, app(app(ty_@2, he), hf)) → new_compare13(vxw110, vxw100, he, hf)
new_lt19(vxw111, vxw101, ty_Integer) → new_lt4(vxw111, vxw101)
new_esEs14(:(vxw300, vxw301), :(vxw4000, vxw4001), bbd) → new_asAs(new_esEs24(vxw300, vxw4000, bbd), new_esEs14(vxw301, vxw4001, bbd))
new_compare8(vxw110, vxw100, cd) → new_compare210(vxw110, vxw100, new_esEs4(vxw110, vxw100, cd), cd)
new_lt19(vxw111, vxw101, app(app(app(ty_@3, dad), dae), daf)) → new_lt16(vxw111, vxw101, dad, dae, daf)
new_esEs25(vxw111, vxw101, ty_Integer) → new_esEs11(vxw111, vxw101)
new_primCmpInt(Pos(Succ(vxw1100)), Neg(vxw100)) → GT
new_ltEs7(Just(vxw110), Just(vxw100), app(ty_Maybe, bbg)) → new_ltEs7(vxw110, vxw100, bbg)
new_esEs10(Float(vxw300, vxw301), Float(vxw4000, vxw4001)) → new_esEs16(new_sr(vxw300, vxw4000), new_sr(vxw301, vxw4001))
new_ltEs21(vxw20, vxw19, app(app(ty_Either, dfg), dfh)) → new_ltEs17(vxw20, vxw19, dfg, dfh)
new_esEs27(vxw301, vxw4001, ty_@0) → new_esEs15(vxw301, vxw4001)
new_esEs28(vxw300, vxw4000, ty_Double) → new_esEs9(vxw300, vxw4000)
new_lt19(vxw111, vxw101, app(ty_[], dac)) → new_lt15(vxw111, vxw101, dac)
new_ltEs20(vxw11, vxw10, app(app(ty_Either, bdg), bdh)) → new_ltEs17(vxw11, vxw10, bdg, bdh)
new_primMulInt(Pos(vxw3000), Pos(vxw40000)) → Pos(new_primMulNat0(vxw3000, vxw40000))
new_esEs30(vxw30, vxw400, app(app(ty_@2, ce), cf)) → new_esEs5(vxw30, vxw400, ce, cf)
new_esEs24(vxw300, vxw4000, ty_Integer) → new_esEs11(vxw300, vxw4000)
new_ltEs17(Left(vxw110), Left(vxw100), app(app(ty_Either, cag), cah), bdh) → new_ltEs17(vxw110, vxw100, cag, cah)
new_esEs7(Left(vxw300), Left(vxw4000), ty_Char, ed) → new_esEs12(vxw300, vxw4000)
new_primMulInt(Neg(vxw3000), Neg(vxw40000)) → Pos(new_primMulNat0(vxw3000, vxw40000))
new_ltEs17(Left(vxw110), Left(vxw100), ty_Float, bdh) → new_ltEs15(vxw110, vxw100)
new_compare9(vxw110, vxw100, ty_Ordering) → new_compare16(vxw110, vxw100)
new_compare110(vxw110, vxw100, True) → LT
new_primEqNat0(Succ(vxw3000), Zero) → False
new_primEqNat0(Zero, Succ(vxw40000)) → False
new_lt20(vxw110, vxw100, app(app(ty_Either, dca), dcb)) → new_lt18(vxw110, vxw100, dca, dcb)
new_compare110(vxw110, vxw100, False) → GT
new_esEs20(vxw302, vxw4002, ty_@0) → new_esEs15(vxw302, vxw4002)
new_compare23(vxw110, vxw100, False, dh, ea) → new_compare10(vxw110, vxw100, new_ltEs4(vxw110, vxw100, dh, ea), dh, ea)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs28(vxw300, vxw4000, app(app(app(ty_@3, ddg), ddh), dea)) → new_esEs6(vxw300, vxw4000, ddg, ddh, dea)
new_esEs4(Nothing, Nothing, bbe) → True
new_esEs4(Just(vxw300), Just(vxw4000), app(ty_Ratio, cef)) → new_esEs13(vxw300, vxw4000, cef)
new_esEs27(vxw301, vxw4001, app(app(app(ty_@3, dce), dcf), dcg)) → new_esEs6(vxw301, vxw4001, dce, dcf, dcg)
new_lt10(vxw110, vxw100, app(ty_[], cdf)) → new_lt15(vxw110, vxw100, cdf)
new_esEs27(vxw301, vxw4001, app(app(ty_@2, dcc), dcd)) → new_esEs5(vxw301, vxw4001, dcc, dcd)
new_esEs26(vxw110, vxw100, ty_Int) → new_esEs16(vxw110, vxw100)
new_ltEs7(Nothing, Nothing, bbf) → True
new_esEs27(vxw301, vxw4001, app(ty_Maybe, ddb)) → new_esEs4(vxw301, vxw4001, ddb)
new_esEs21(vxw301, vxw4001, app(app(ty_Either, bgc), bgd)) → new_esEs7(vxw301, vxw4001, bgc, bgd)
new_esEs23(vxw110, vxw100, app(ty_[], cdf)) → new_esEs14(vxw110, vxw100, cdf)
new_ltEs17(Right(vxw110), Right(vxw100), bdg, ty_@0) → new_ltEs14(vxw110, vxw100)
new_ltEs17(Left(vxw110), Left(vxw100), ty_Char, bdh) → new_ltEs8(vxw110, vxw100)
new_lt10(vxw110, vxw100, ty_@0) → new_lt8(vxw110, vxw100)
new_lt10(vxw110, vxw100, ty_Int) → new_lt7(vxw110, vxw100)
new_esEs7(Right(vxw300), Right(vxw4000), ff, app(ty_[], ge)) → new_esEs14(vxw300, vxw4000, ge)
new_ltEs12(vxw11, vxw10, cc) → new_not(new_esEs8(new_compare0(vxw11, vxw10, cc), GT))
new_primCmpInt(Neg(Zero), Neg(Succ(vxw1000))) → new_primCmpNat0(Succ(vxw1000), Zero)
new_compare23(vxw110, vxw100, True, dh, ea) → EQ
new_primCmpInt(Pos(Zero), Neg(Succ(vxw1000))) → GT
new_esEs23(vxw110, vxw100, ty_Bool) → new_esEs17(vxw110, vxw100)
new_esEs25(vxw111, vxw101, ty_Int) → new_esEs16(vxw111, vxw101)
new_ltEs20(vxw11, vxw10, ty_Char) → new_ltEs8(vxw11, vxw10)
new_ltEs17(Left(vxw110), Left(vxw100), ty_@0, bdh) → new_ltEs14(vxw110, vxw100)
new_esEs29(vxw30, vxw400, ty_@0) → new_esEs15(vxw30, vxw400)
new_esEs4(Just(vxw300), Just(vxw4000), app(ty_[], ceg)) → new_esEs14(vxw300, vxw4000, ceg)
new_ltEs17(Right(vxw110), Right(vxw100), bdg, ty_Float) → new_ltEs15(vxw110, vxw100)
new_ltEs17(Left(vxw110), Right(vxw100), bdg, bdh) → True
new_esEs21(vxw301, vxw4001, app(ty_Maybe, bgb)) → new_esEs4(vxw301, vxw4001, bgb)
new_esEs20(vxw302, vxw4002, app(app(ty_Either, bfa), bfb)) → new_esEs7(vxw302, vxw4002, bfa, bfb)
new_esEs21(vxw301, vxw4001, ty_Double) → new_esEs9(vxw301, vxw4001)
new_lt7(vxw110, vxw100) → new_esEs8(new_compare27(vxw110, vxw100), LT)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_lt20(vxw110, vxw100, app(ty_[], dbe)) → new_lt15(vxw110, vxw100, dbe)
new_ltEs21(vxw20, vxw19, ty_Ordering) → new_ltEs10(vxw20, vxw19)
new_ltEs21(vxw20, vxw19, ty_Char) → new_ltEs8(vxw20, vxw19)
new_ltEs17(Right(vxw110), Right(vxw100), bdg, app(ty_[], cbe)) → new_ltEs12(vxw110, vxw100, cbe)
new_ltEs7(Just(vxw110), Just(vxw100), app(ty_[], bcc)) → new_ltEs12(vxw110, vxw100, bcc)
new_esEs29(vxw30, vxw400, ty_Bool) → new_esEs17(vxw30, vxw400)
new_esEs15(@0, @0) → True
new_lt17(vxw110, vxw100) → new_esEs8(new_compare26(vxw110, vxw100), LT)
new_compare15(Double(vxw110, vxw111), Double(vxw100, vxw101)) → new_compare27(new_sr(vxw110, vxw100), new_sr(vxw111, vxw101))
new_asAs(False, vxw53) → False
new_ltEs17(Right(vxw110), Right(vxw100), bdg, ty_Double) → new_ltEs9(vxw110, vxw100)
new_compare24(vxw110, vxw100, False) → new_compare11(vxw110, vxw100, new_ltEs5(vxw110, vxw100))
new_primMulInt(Neg(vxw3000), Pos(vxw40000)) → Neg(new_primMulNat0(vxw3000, vxw40000))
new_primMulInt(Pos(vxw3000), Neg(vxw40000)) → Neg(new_primMulNat0(vxw3000, vxw40000))
new_esEs26(vxw110, vxw100, ty_Double) → new_esEs9(vxw110, vxw100)
new_compare28(vxw110, vxw100, cdg, cdh) → new_compare29(vxw110, vxw100, new_esEs7(vxw110, vxw100, cdg, cdh), cdg, cdh)
new_ltEs10(LT, GT) → True
new_primMulNat0(Zero, Succ(vxw400000)) → Zero
new_primMulNat0(Succ(vxw30000), Zero) → Zero
new_esEs29(vxw30, vxw400, ty_Char) → new_esEs12(vxw30, vxw400)
new_compare25(vxw110, vxw100, False, ha, hb, hc) → new_compare12(vxw110, vxw100, new_ltEs6(vxw110, vxw100, ha, hb, hc), ha, hb, hc)
new_esEs7(Left(vxw300), Left(vxw4000), ty_Float, ed) → new_esEs10(vxw300, vxw4000)
new_esEs23(vxw110, vxw100, app(app(app(ty_@3, ha), hb), hc)) → new_esEs6(vxw110, vxw100, ha, hb, hc)
new_ltEs7(Just(vxw110), Just(vxw100), ty_Char) → new_ltEs8(vxw110, vxw100)
new_esEs21(vxw301, vxw4001, ty_Ordering) → new_esEs8(vxw301, vxw4001)
new_esEs21(vxw301, vxw4001, ty_Int) → new_esEs16(vxw301, vxw4001)
new_esEs24(vxw300, vxw4000, ty_Float) → new_esEs10(vxw300, vxw4000)
new_esEs19(vxw300, vxw4000, ty_Int) → new_esEs16(vxw300, vxw4000)
new_esEs30(vxw30, vxw400, app(ty_Ratio, dc)) → new_esEs13(vxw30, vxw400, dc)
new_ltEs13(vxw11, vxw10) → new_not(new_esEs8(new_compare6(vxw11, vxw10), GT))
new_ltEs16(vxw11, vxw10) → new_not(new_esEs8(new_compare27(vxw11, vxw10), GT))
new_lt10(vxw110, vxw100, ty_Integer) → new_lt4(vxw110, vxw100)
new_esEs29(vxw30, vxw400, ty_Float) → new_esEs10(vxw30, vxw400)
new_esEs23(vxw110, vxw100, ty_Char) → new_esEs12(vxw110, vxw100)
new_esEs25(vxw111, vxw101, app(app(app(ty_@3, dad), dae), daf)) → new_esEs6(vxw111, vxw101, dad, dae, daf)
new_lt13(vxw110, vxw100) → new_esEs8(new_compare15(vxw110, vxw100), LT)
new_lt19(vxw111, vxw101, app(ty_Maybe, chg)) → new_lt5(vxw111, vxw101, chg)
new_ltEs10(EQ, EQ) → True
new_esEs13(:%(vxw300, vxw301), :%(vxw4000, vxw4001), bbc) → new_asAs(new_esEs19(vxw300, vxw4000, bbc), new_esEs18(vxw301, vxw4001, bbc))
new_compare9(vxw110, vxw100, app(app(ty_Either, bad), bae)) → new_compare28(vxw110, vxw100, bad, bae)
new_esEs23(vxw110, vxw100, ty_Int) → new_esEs16(vxw110, vxw100)
new_ltEs10(LT, LT) → True
new_ltEs19(vxw112, vxw102, ty_Int) → new_ltEs16(vxw112, vxw102)
new_ltEs19(vxw112, vxw102, ty_@0) → new_ltEs14(vxw112, vxw102)
new_compare211(vxw110, vxw100, False) → new_compare110(vxw110, vxw100, new_ltEs10(vxw110, vxw100))
new_esEs7(Left(vxw300), Left(vxw4000), app(app(app(ty_@3, ee), ef), eg), ed) → new_esEs6(vxw300, vxw4000, ee, ef, eg)
new_lt10(vxw110, vxw100, ty_Ordering) → new_lt6(vxw110, vxw100)
new_esEs27(vxw301, vxw4001, ty_Int) → new_esEs16(vxw301, vxw4001)
new_ltEs17(Right(vxw110), Right(vxw100), bdg, ty_Char) → new_ltEs8(vxw110, vxw100)
new_ltEs7(Just(vxw110), Just(vxw100), ty_@0) → new_ltEs14(vxw110, vxw100)
new_ltEs19(vxw112, vxw102, ty_Bool) → new_ltEs5(vxw112, vxw102)
new_ltEs8(vxw11, vxw10) → new_not(new_esEs8(new_compare14(vxw11, vxw10), GT))
new_lt20(vxw110, vxw100, app(app(app(ty_@3, dbf), dbg), dbh)) → new_lt16(vxw110, vxw100, dbf, dbg, dbh)
new_esEs7(Right(vxw300), Right(vxw4000), ff, ty_Int) → new_esEs16(vxw300, vxw4000)
new_ltEs7(Just(vxw110), Nothing, bbf) → False
new_esEs28(vxw300, vxw4000, ty_Bool) → new_esEs17(vxw300, vxw4000)
new_esEs28(vxw300, vxw4000, app(ty_Ratio, deb)) → new_esEs13(vxw300, vxw4000, deb)
new_ltEs17(Left(vxw110), Left(vxw100), ty_Int, bdh) → new_ltEs16(vxw110, vxw100)
new_compare11(vxw110, vxw100, False) → GT
new_lt16(vxw110, vxw100, ha, hb, hc) → new_esEs8(new_compare19(vxw110, vxw100, ha, hb, hc), LT)
new_esEs25(vxw111, vxw101, app(app(ty_@2, chh), daa)) → new_esEs5(vxw111, vxw101, chh, daa)
new_esEs26(vxw110, vxw100, ty_Bool) → new_esEs17(vxw110, vxw100)
new_compare11(vxw110, vxw100, True) → LT
new_ltEs19(vxw112, vxw102, app(ty_Maybe, cge)) → new_ltEs7(vxw112, vxw102, cge)
new_ltEs21(vxw20, vxw19, app(ty_Maybe, deg)) → new_ltEs7(vxw20, vxw19, deg)
new_esEs29(vxw30, vxw400, app(app(app(ty_@3, bah), bba), bbb)) → new_esEs6(vxw30, vxw400, bah, bba, bbb)
new_esEs29(vxw30, vxw400, app(app(ty_Either, ff), ed)) → new_esEs7(vxw30, vxw400, ff, ed)
new_esEs7(Left(vxw300), Left(vxw4000), ty_Bool, ed) → new_esEs17(vxw300, vxw4000)
new_ltEs10(EQ, LT) → False
new_compare112(vxw110, vxw100, False, cd) → GT
new_compare9(vxw110, vxw100, ty_Char) → new_compare14(vxw110, vxw100)
new_lt20(vxw110, vxw100, ty_Char) → new_lt12(vxw110, vxw100)
new_esEs22(vxw300, vxw4000, ty_Float) → new_esEs10(vxw300, vxw4000)
new_esEs30(vxw30, vxw400, ty_Ordering) → new_esEs8(vxw30, vxw400)
new_ltEs10(GT, LT) → False
new_esEs30(vxw30, vxw400, ty_Double) → new_esEs9(vxw30, vxw400)
new_ltEs14(vxw11, vxw10) → new_not(new_esEs8(new_compare7(vxw11, vxw10), GT))
new_primPlusNat1(Zero, Zero) → Zero
new_compare0([], :(vxw100, vxw101), cc) → LT
new_compare111(vxw110, vxw100, True, cdg, cdh) → LT
new_esEs21(vxw301, vxw4001, app(app(app(ty_@3, bfe), bff), bfg)) → new_esEs6(vxw301, vxw4001, bfe, bff, bfg)
new_esEs27(vxw301, vxw4001, app(ty_[], dda)) → new_esEs14(vxw301, vxw4001, dda)
new_asAs(True, vxw53) → vxw53
new_primMulNat0(Succ(vxw30000), Succ(vxw400000)) → new_primPlusNat0(new_primMulNat0(vxw30000, Succ(vxw400000)), vxw400000)
new_compare9(vxw110, vxw100, app(ty_Ratio, hg)) → new_compare17(vxw110, vxw100, hg)
new_esEs20(vxw302, vxw4002, ty_Double) → new_esEs9(vxw302, vxw4002)
new_esEs27(vxw301, vxw4001, ty_Integer) → new_esEs11(vxw301, vxw4001)
new_ltEs21(vxw20, vxw19, ty_Float) → new_ltEs15(vxw20, vxw19)
new_ltEs17(Right(vxw110), Right(vxw100), bdg, app(app(app(ty_@3, cbf), cbg), cbh)) → new_ltEs6(vxw110, vxw100, cbf, cbg, cbh)
new_compare211(vxw110, vxw100, True) → EQ
new_ltEs17(Right(vxw110), Right(vxw100), bdg, app(app(ty_@2, cbb), cbc)) → new_ltEs4(vxw110, vxw100, cbb, cbc)
new_ltEs19(vxw112, vxw102, ty_Integer) → new_ltEs13(vxw112, vxw102)
new_ltEs18(vxw111, vxw101, app(ty_[], ccg)) → new_ltEs12(vxw111, vxw101, ccg)
new_esEs20(vxw302, vxw4002, app(ty_[], beg)) → new_esEs14(vxw302, vxw4002, beg)
new_esEs4(Just(vxw300), Just(vxw4000), ty_Double) → new_esEs9(vxw300, vxw4000)
new_ltEs18(vxw111, vxw101, app(app(ty_@2, ccd), cce)) → new_ltEs4(vxw111, vxw101, ccd, cce)
new_esEs29(vxw30, vxw400, app(ty_Maybe, bbe)) → new_esEs4(vxw30, vxw400, bbe)
new_ltEs7(Just(vxw110), Just(vxw100), app(ty_Ratio, bcb)) → new_ltEs11(vxw110, vxw100, bcb)
new_ltEs20(vxw11, vxw10, app(ty_Maybe, bbf)) → new_ltEs7(vxw11, vxw10, bbf)
new_ltEs17(Right(vxw110), Right(vxw100), bdg, ty_Bool) → new_ltEs5(vxw110, vxw100)
new_primCompAux00(vxw72, GT) → GT
new_esEs30(vxw30, vxw400, app(app(app(ty_@3, cg), da), db)) → new_esEs6(vxw30, vxw400, cg, da, db)
new_esEs25(vxw111, vxw101, app(app(ty_Either, dag), dah)) → new_esEs7(vxw111, vxw101, dag, dah)
new_ltEs18(vxw111, vxw101, ty_Double) → new_ltEs9(vxw111, vxw101)
new_ltEs11(vxw11, vxw10, bda) → new_not(new_esEs8(new_compare17(vxw11, vxw10, bda), GT))
new_lt11(vxw110, vxw100, dh, ea) → new_esEs8(new_compare13(vxw110, vxw100, dh, ea), LT)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_compare26(Float(vxw110, vxw111), Float(vxw100, vxw101)) → new_compare27(new_sr(vxw110, vxw100), new_sr(vxw111, vxw101))
new_esEs29(vxw30, vxw400, ty_Ordering) → new_esEs8(vxw30, vxw400)
new_lt19(vxw111, vxw101, app(ty_Ratio, dab)) → new_lt14(vxw111, vxw101, dab)
new_ltEs18(vxw111, vxw101, ty_Ordering) → new_ltEs10(vxw111, vxw101)
new_esEs7(Left(vxw300), Left(vxw4000), app(ty_[], fa), ed) → new_esEs14(vxw300, vxw4000, fa)
new_esEs28(vxw300, vxw4000, ty_Char) → new_esEs12(vxw300, vxw4000)
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_ltEs21(vxw20, vxw19, ty_Double) → new_ltEs9(vxw20, vxw19)
new_primCmpInt(Neg(Succ(vxw1100)), Pos(vxw100)) → LT
new_esEs22(vxw300, vxw4000, ty_Int) → new_esEs16(vxw300, vxw4000)
new_not(True) → False

The set Q consists of the following terms:

new_esEs11(Integer(x0), Integer(x1))
new_compare12(x0, x1, True, x2, x3, x4)
new_esEs4(Just(x0), Just(x1), ty_Int)
new_ltEs17(Left(x0), Left(x1), ty_@0, x2)
new_ltEs13(x0, x1)
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs20(x0, x1, ty_Char)
new_esEs7(Left(x0), Left(x1), ty_Int, x2)
new_asAs(True, x0)
new_lt5(x0, x1, x2)
new_ltEs17(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs21(x0, x1, ty_Ordering)
new_primMulNat0(Zero, Succ(x0))
new_esEs7(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_ltEs17(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_ltEs17(Left(x0), Left(x1), ty_Int, x2)
new_lt10(x0, x1, ty_Int)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_compare11(x0, x1, True)
new_ltEs21(x0, x1, ty_Bool)
new_primCmpNat0(Succ(x0), Zero)
new_lt18(x0, x1, x2, x3)
new_esEs7(Left(x0), Left(x1), ty_Integer, x2)
new_lt20(x0, x1, ty_Integer)
new_ltEs19(x0, x1, ty_@0)
new_ltEs21(x0, x1, app(ty_Maybe, x2))
new_esEs30(x0, x1, app(ty_Maybe, x2))
new_lt19(x0, x1, ty_Int)
new_esEs29(x0, x1, ty_Bool)
new_esEs23(x0, x1, ty_Float)
new_ltEs18(x0, x1, ty_Float)
new_ltEs17(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_compare9(x0, x1, ty_Bool)
new_esEs25(x0, x1, ty_Bool)
new_compare9(x0, x1, ty_Float)
new_esEs7(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs7(Right(x0), Right(x1), x2, ty_Char)
new_esEs29(x0, x1, ty_Double)
new_ltEs10(LT, LT)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_esEs14(:(x0, x1), :(x2, x3), x4)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs17(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs23(x0, x1, ty_Ordering)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt10(x0, x1, app(app(ty_Either, x2), x3))
new_lt4(x0, x1)
new_esEs9(Double(x0, x1), Double(x2, x3))
new_esEs5(@2(x0, x1), @2(x2, x3), x4, x5)
new_lt20(x0, x1, ty_Double)
new_esEs27(x0, x1, ty_@0)
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs30(x0, x1, ty_Integer)
new_ltEs18(x0, x1, ty_Double)
new_ltEs6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs23(x0, x1, ty_Char)
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs18(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_esEs8(GT, GT)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_ltEs18(x0, x1, app(ty_[], x2))
new_ltEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs17(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs22(x0, x1, ty_Ordering)
new_compare25(x0, x1, True, x2, x3, x4)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs24(x0, x1, ty_Char)
new_ltEs7(Just(x0), Just(x1), app(ty_[], x2))
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_esEs22(x0, x1, app(ty_[], x2))
new_compare6(Integer(x0), Integer(x1))
new_esEs29(x0, x1, ty_@0)
new_esEs8(LT, LT)
new_primMulNat0(Succ(x0), Succ(x1))
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs7(Just(x0), Just(x1), ty_Integer)
new_ltEs12(x0, x1, x2)
new_ltEs20(x0, x1, ty_Double)
new_esEs21(x0, x1, ty_Double)
new_esEs17(False, False)
new_esEs21(x0, x1, ty_Integer)
new_primEqNat0(Succ(x0), Zero)
new_esEs26(x0, x1, ty_Bool)
new_ltEs5(False, False)
new_ltEs11(x0, x1, x2)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_esEs22(x0, x1, ty_Bool)
new_lt11(x0, x1, x2, x3)
new_esEs30(x0, x1, ty_Double)
new_esEs7(Right(x0), Right(x1), x2, ty_Integer)
new_esEs7(Left(x0), Left(x1), ty_Double, x2)
new_esEs7(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs20(x0, x1, ty_Float)
new_compare0(:(x0, x1), [], x2)
new_ltEs21(x0, x1, app(ty_Ratio, x2))
new_esEs27(x0, x1, ty_Ordering)
new_esEs24(x0, x1, ty_@0)
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_esEs7(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_compare9(x0, x1, app(ty_Maybe, x2))
new_esEs7(Left(x0), Left(x1), ty_@0, x2)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs7(Right(x0), Right(x1), x2, ty_Ordering)
new_lt7(x0, x1)
new_ltEs18(x0, x1, app(ty_Ratio, x2))
new_lt10(x0, x1, app(ty_[], x2))
new_compare211(x0, x1, True)
new_compare8(x0, x1, x2)
new_esEs7(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_primEqNat0(Zero, Zero)
new_compare9(x0, x1, ty_Integer)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_esEs21(x0, x1, ty_Bool)
new_lt10(x0, x1, ty_Integer)
new_esEs21(x0, x1, ty_Char)
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_esEs4(Just(x0), Just(x1), ty_Bool)
new_compare210(x0, x1, False, x2)
new_esEs14([], :(x0, x1), x2)
new_ltEs7(Just(x0), Just(x1), ty_Double)
new_esEs22(x0, x1, ty_Int)
new_lt20(x0, x1, ty_Float)
new_ltEs7(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_esEs7(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs4(Just(x0), Just(x1), ty_Ordering)
new_esEs25(x0, x1, ty_Float)
new_compare23(x0, x1, False, x2, x3)
new_esEs7(Left(x0), Left(x1), ty_Bool, x2)
new_primMulNat0(Zero, Zero)
new_ltEs18(x0, x1, ty_Int)
new_esEs21(x0, x1, ty_Float)
new_esEs7(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs20(x0, x1, ty_Ordering)
new_ltEs17(Left(x0), Left(x1), ty_Ordering, x2)
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_ltEs10(EQ, LT)
new_ltEs10(LT, EQ)
new_compare23(x0, x1, True, x2, x3)
new_ltEs21(x0, x1, ty_@0)
new_esEs21(x0, x1, app(ty_[], x2))
new_ltEs20(x0, x1, ty_@0)
new_ltEs17(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_esEs18(x0, x1, ty_Integer)
new_lt14(x0, x1, x2)
new_primCompAux00(x0, EQ)
new_compare10(x0, x1, True, x2, x3)
new_esEs13(:%(x0, x1), :%(x2, x3), x4)
new_compare210(x0, x1, True, x2)
new_pePe(True, x0)
new_esEs20(x0, x1, ty_Ordering)
new_ltEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, ty_Ordering)
new_esEs28(x0, x1, ty_Int)
new_esEs12(Char(x0), Char(x1))
new_lt19(x0, x1, ty_Char)
new_compare110(x0, x1, False)
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs4(Just(x0), Just(x1), ty_@0)
new_lt10(x0, x1, ty_Ordering)
new_esEs22(x0, x1, ty_Char)
new_esEs30(x0, x1, ty_Bool)
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs26(x0, x1, ty_@0)
new_esEs24(x0, x1, ty_Integer)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs25(x0, x1, ty_Ordering)
new_esEs4(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, app(ty_[], x2))
new_primCompAux00(x0, LT)
new_ltEs21(x0, x1, ty_Ordering)
new_ltEs19(x0, x1, ty_Integer)
new_ltEs17(Left(x0), Left(x1), ty_Bool, x2)
new_ltEs17(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs17(Left(x0), Left(x1), ty_Float, x2)
new_ltEs19(x0, x1, ty_Int)
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs25(x0, x1, ty_Double)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs7(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_ltEs20(x0, x1, ty_Bool)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_esEs27(x0, x1, ty_Double)
new_esEs26(x0, x1, ty_Integer)
new_esEs19(x0, x1, ty_Integer)
new_ltEs20(x0, x1, app(ty_[], x2))
new_esEs23(x0, x1, ty_Integer)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_compare13(x0, x1, x2, x3)
new_lt6(x0, x1)
new_compare0([], [], x0)
new_esEs4(Just(x0), Just(x1), app(ty_Maybe, x2))
new_compare9(x0, x1, ty_@0)
new_esEs4(Just(x0), Just(x1), ty_Double)
new_ltEs17(Right(x0), Right(x1), x2, ty_Float)
new_lt10(x0, x1, app(ty_Maybe, x2))
new_ltEs19(x0, x1, ty_Bool)
new_esEs28(x0, x1, ty_@0)
new_lt20(x0, x1, ty_Bool)
new_ltEs15(x0, x1)
new_lt10(x0, x1, app(app(ty_@2, x2), x3))
new_compare11(x0, x1, False)
new_lt10(x0, x1, ty_Double)
new_compare111(x0, x1, True, x2, x3)
new_lt19(x0, x1, ty_@0)
new_esEs30(x0, x1, app(ty_Ratio, x2))
new_ltEs18(x0, x1, ty_Char)
new_esEs4(Just(x0), Nothing, x1)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_compare25(x0, x1, False, x2, x3, x4)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_compare27(x0, x1)
new_primPlusNat1(Zero, Zero)
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_compare0(:(x0, x1), :(x2, x3), x4)
new_sr(x0, x1)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_esEs20(x0, x1, ty_@0)
new_esEs7(Left(x0), Left(x1), ty_Float, x2)
new_ltEs18(x0, x1, app(app(ty_Either, x2), x3))
new_esEs16(x0, x1)
new_esEs25(x0, x1, app(ty_[], x2))
new_esEs24(x0, x1, ty_Float)
new_esEs4(Nothing, Just(x0), x1)
new_compare9(x0, x1, ty_Ordering)
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare28(x0, x1, x2, x3)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_ltEs7(Just(x0), Just(x1), ty_Int)
new_esEs28(x0, x1, ty_Float)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, ty_@0)
new_ltEs18(x0, x1, ty_Ordering)
new_esEs23(x0, x1, ty_Int)
new_esEs7(Right(x0), Right(x1), x2, ty_Double)
new_compare10(x0, x1, False, x2, x3)
new_esEs26(x0, x1, ty_Double)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs24(x0, x1, ty_Bool)
new_esEs23(x0, x1, app(ty_[], x2))
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs21(x0, x1, ty_Float)
new_primMulInt(Pos(x0), Pos(x1))
new_ltEs7(Just(x0), Just(x1), ty_Char)
new_compare112(x0, x1, True, x2)
new_compare9(x0, x1, app(app(ty_Either, x2), x3))
new_primPlusNat0(Succ(x0), x1)
new_ltEs10(GT, LT)
new_ltEs10(LT, GT)
new_ltEs17(Right(x0), Right(x1), x2, ty_@0)
new_ltEs7(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_sr0(Integer(x0), Integer(x1))
new_esEs23(x0, x1, ty_Double)
new_compare9(x0, x1, app(ty_[], x2))
new_esEs25(x0, x1, ty_Integer)
new_esEs20(x0, x1, ty_Char)
new_ltEs7(Nothing, Just(x0), x1)
new_primEqNat0(Zero, Succ(x0))
new_esEs27(x0, x1, ty_Bool)
new_esEs30(x0, x1, ty_Int)
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare17(:%(x0, x1), :%(x2, x3), ty_Int)
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_lt9(x0, x1)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_ltEs20(x0, x1, ty_Integer)
new_primMulInt(Neg(x0), Neg(x1))
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_esEs4(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, ty_Char)
new_ltEs20(x0, x1, ty_Int)
new_compare211(x0, x1, False)
new_ltEs17(Left(x0), Left(x1), ty_Double, x2)
new_compare29(x0, x1, False, x2, x3)
new_ltEs9(x0, x1)
new_esEs7(Right(x0), Right(x1), x2, ty_Float)
new_ltEs17(Right(x0), Right(x1), x2, ty_Ordering)
new_lt10(x0, x1, ty_@0)
new_esEs30(x0, x1, ty_Ordering)
new_ltEs7(Just(x0), Nothing, x1)
new_esEs4(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_compare112(x0, x1, False, x2)
new_esEs29(x0, x1, ty_Char)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs18(x0, x1, ty_Integer)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_esEs27(x0, x1, ty_Float)
new_ltEs19(x0, x1, ty_Double)
new_ltEs21(x0, x1, ty_Double)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Neg(Zero), Neg(Zero))
new_ltEs19(x0, x1, ty_Ordering)
new_ltEs21(x0, x1, ty_Integer)
new_ltEs14(x0, x1)
new_ltEs17(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_ltEs7(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_compare29(x0, x1, True, x2, x3)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs24(x0, x1, ty_Ordering)
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs26(x0, x1, app(ty_[], x2))
new_ltEs17(Right(x0), Right(x1), x2, ty_Bool)
new_esEs29(x0, x1, ty_Ordering)
new_compare9(x0, x1, app(ty_Ratio, x2))
new_esEs30(x0, x1, ty_@0)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_compare7(@0, @0)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_esEs18(x0, x1, ty_Int)
new_ltEs17(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_lt19(x0, x1, app(ty_Maybe, x2))
new_primCompAux00(x0, GT)
new_ltEs21(x0, x1, ty_Int)
new_lt19(x0, x1, ty_Double)
new_esEs26(x0, x1, ty_Float)
new_esEs30(x0, x1, app(ty_[], x2))
new_ltEs7(Just(x0), Just(x1), ty_Ordering)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_esEs4(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs16(x0, x1)
new_esEs21(x0, x1, ty_@0)
new_compare18(x0, x1)
new_lt19(x0, x1, ty_Ordering)
new_esEs4(Nothing, Nothing, x0)
new_esEs30(x0, x1, ty_Char)
new_esEs7(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_ltEs21(x0, x1, app(app(ty_@2, x2), x3))
new_asAs(False, x0)
new_lt10(x0, x1, ty_Char)
new_esEs20(x0, x1, ty_Int)
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat1(Succ(x0), Zero)
new_esEs8(GT, EQ)
new_esEs8(EQ, GT)
new_esEs22(x0, x1, ty_Integer)
new_lt15(x0, x1, x2)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_compare17(:%(x0, x1), :%(x2, x3), ty_Integer)
new_esEs29(x0, x1, app(ty_[], x2))
new_ltEs20(x0, x1, ty_Float)
new_primPlusNat0(Zero, x0)
new_esEs20(x0, x1, ty_Integer)
new_compare26(Float(x0, x1), Float(x2, x3))
new_ltEs17(Left(x0), Left(x1), ty_Char, x2)
new_primCmpNat0(Zero, Zero)
new_lt10(x0, x1, ty_Bool)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_ltEs17(Left(x0), Left(x1), ty_Integer, x2)
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_compare111(x0, x1, False, x2, x3)
new_ltEs7(Nothing, Nothing, x0)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs15(@0, @0)
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_compare16(x0, x1)
new_compare9(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare9(x0, x1, app(app(ty_@2, x2), x3))
new_lt16(x0, x1, x2, x3, x4)
new_esEs23(x0, x1, ty_Bool)
new_primEqNat0(Succ(x0), Succ(x1))
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_esEs7(Left(x0), Left(x1), ty_Char, x2)
new_primCmpNat0(Zero, Succ(x0))
new_esEs27(x0, x1, ty_Integer)
new_esEs21(x0, x1, ty_Int)
new_esEs24(x0, x1, ty_Double)
new_esEs24(x0, x1, app(ty_[], x2))
new_esEs20(x0, x1, ty_Bool)
new_lt10(x0, x1, app(ty_Ratio, x2))
new_lt19(x0, x1, ty_Integer)
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_ltEs10(GT, GT)
new_esEs27(x0, x1, app(ty_[], x2))
new_ltEs7(Just(x0), Just(x1), ty_Float)
new_lt17(x0, x1)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_compare15(Double(x0, x1), Double(x2, x3))
new_esEs22(x0, x1, ty_Float)
new_lt13(x0, x1)
new_ltEs17(Right(x0), Right(x1), x2, ty_Double)
new_esEs30(x0, x1, app(app(ty_Either, x2), x3))
new_primCompAux0(x0, x1, x2, x3)
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_compare9(x0, x1, ty_Char)
new_ltEs5(True, True)
new_esEs7(Right(x0), Right(x1), x2, ty_@0)
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_compare14(Char(x0), Char(x1))
new_lt19(x0, x1, app(ty_Ratio, x2))
new_ltEs17(Right(x0), Right(x1), x2, ty_Integer)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_not(True)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_ltEs7(Just(x0), Just(x1), ty_@0)
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs28(x0, x1, ty_Double)
new_esEs26(x0, x1, ty_Ordering)
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs17(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs27(x0, x1, ty_Int)
new_esEs6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_lt10(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_not(False)
new_esEs4(Just(x0), Just(x1), ty_Integer)
new_ltEs17(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_lt20(x0, x1, ty_Char)
new_lt19(x0, x1, ty_Bool)
new_primCmpNat0(Succ(x0), Succ(x1))
new_ltEs10(EQ, GT)
new_ltEs10(GT, EQ)
new_esEs22(x0, x1, ty_Double)
new_esEs10(Float(x0, x1), Float(x2, x3))
new_esEs26(x0, x1, ty_Int)
new_esEs4(Just(x0), Just(x1), ty_Float)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_compare24(x0, x1, True)
new_ltEs17(Right(x0), Right(x1), x2, ty_Int)
new_esEs25(x0, x1, ty_@0)
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_compare9(x0, x1, ty_Int)
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs21(x0, x1, app(ty_[], x2))
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primMulNat0(Succ(x0), Zero)
new_esEs28(x0, x1, ty_Bool)
new_lt19(x0, x1, ty_Float)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs8(EQ, LT)
new_esEs8(LT, EQ)
new_lt20(x0, x1, ty_@0)
new_compare0([], :(x0, x1), x2)
new_lt19(x0, x1, app(ty_[], x2))
new_esEs7(Right(x0), Right(x1), x2, ty_Int)
new_esEs7(Left(x0), Left(x1), ty_Ordering, x2)
new_compare19(x0, x1, x2, x3, x4)
new_ltEs4(@2(x0, x1), @2(x2, x3), x4, x5)
new_lt8(x0, x1)
new_esEs25(x0, x1, ty_Int)
new_esEs4(Just(x0), Just(x1), app(ty_Ratio, x2))
new_ltEs7(Just(x0), Just(x1), ty_Bool)
new_compare12(x0, x1, False, x2, x3, x4)
new_esEs17(False, True)
new_esEs17(True, False)
new_ltEs17(Right(x0), Right(x1), x2, ty_Char)
new_esEs28(x0, x1, app(ty_[], x2))
new_compare110(x0, x1, True)
new_ltEs7(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs30(x0, x1, ty_Float)
new_ltEs8(x0, x1)
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_compare24(x0, x1, False)
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_esEs28(x0, x1, ty_Char)
new_esEs26(x0, x1, ty_Char)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare9(x0, x1, ty_Double)
new_ltEs17(Left(x0), Right(x1), x2, x3)
new_ltEs17(Right(x0), Left(x1), x2, x3)
new_esEs14([], [], x0)
new_primEqInt(Pos(Zero), Pos(Zero))
new_esEs17(True, True)
new_ltEs21(x0, x1, app(app(ty_Either, x2), x3))
new_lt12(x0, x1)
new_esEs29(x0, x1, ty_Integer)
new_ltEs18(x0, x1, app(ty_Maybe, x2))
new_ltEs21(x0, x1, ty_Char)
new_ltEs18(x0, x1, ty_@0)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs20(x0, x1, ty_Double)
new_lt10(x0, x1, ty_Float)
new_esEs25(x0, x1, ty_Char)
new_ltEs19(x0, x1, ty_Char)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs28(x0, x1, ty_Ordering)
new_esEs29(x0, x1, ty_Int)
new_ltEs17(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_ltEs5(True, False)
new_ltEs5(False, True)
new_ltEs19(x0, x1, app(ty_[], x2))
new_esEs19(x0, x1, ty_Int)
new_esEs24(x0, x1, ty_Int)
new_ltEs18(x0, x1, ty_Bool)
new_esEs4(Just(x0), Just(x1), ty_Char)
new_ltEs7(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs7(Right(x0), Left(x1), x2, x3)
new_esEs7(Left(x0), Right(x1), x2, x3)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, ty_Int)
new_pePe(False, x0)
new_esEs30(x0, x1, app(app(ty_@2, x2), x3))
new_esEs22(x0, x1, ty_@0)
new_esEs29(x0, x1, ty_Float)
new_ltEs19(x0, x1, ty_Float)
new_esEs14(:(x0, x1), [], x2)
new_esEs28(x0, x1, ty_Integer)
new_ltEs10(EQ, EQ)
new_esEs20(x0, x1, app(ty_[], x2))

We have to consider all minimal (P,Q,R)-chains.
As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [15] we can delete all non-usable rules [17] from R.

↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ IFR
        ↳ HASKELL
          ↳ BR
            ↳ HASKELL
              ↳ COR
                ↳ HASKELL
                  ↳ LetRed
                    ↳ HASKELL
                      ↳ NumRed
                        ↳ HASKELL
                          ↳ Narrow
                            ↳ AND
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                                ↳ DependencyGraphProof
                                  ↳ AND
                                    ↳ QDP
                                      ↳ UsableRulesProof
                                        ↳ QDP
                                          ↳ QReductionProof
                                    ↳ QDP

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

new_insertBy0(vxw10, vxw11, vxw12, False, ba, bb) → new_insertBy00(vxw10, vxw11, vxw12, new_ltEs20(vxw11, vxw10, ba), ba, bb)
new_insertBy(Left(vxw30), :(Left(vxw400), vxw41), be, bf) → new_insertBy0(vxw400, vxw30, vxw41, new_esEs29(vxw30, vxw400, be), be, bf)
new_insertBy00(vxw28, vxw29, vxw30, False, bc, bd) → new_insertBy(Left(vxw29), vxw30, bc, bd)

The TRS R consists of the following rules:

new_esEs29(vxw30, vxw400, ty_Int) → new_esEs16(vxw30, vxw400)
new_esEs29(vxw30, vxw400, app(ty_[], bbd)) → new_esEs14(vxw30, vxw400, bbd)
new_esEs29(vxw30, vxw400, app(ty_Ratio, bbc)) → new_esEs13(vxw30, vxw400, bbc)
new_esEs29(vxw30, vxw400, ty_Double) → new_esEs9(vxw30, vxw400)
new_esEs29(vxw30, vxw400, app(app(ty_@2, baf), bag)) → new_esEs5(vxw30, vxw400, baf, bag)
new_esEs29(vxw30, vxw400, ty_Integer) → new_esEs11(vxw30, vxw400)
new_esEs29(vxw30, vxw400, ty_@0) → new_esEs15(vxw30, vxw400)
new_esEs29(vxw30, vxw400, ty_Bool) → new_esEs17(vxw30, vxw400)
new_esEs29(vxw30, vxw400, ty_Char) → new_esEs12(vxw30, vxw400)
new_esEs29(vxw30, vxw400, ty_Float) → new_esEs10(vxw30, vxw400)
new_esEs29(vxw30, vxw400, app(app(app(ty_@3, bah), bba), bbb)) → new_esEs6(vxw30, vxw400, bah, bba, bbb)
new_esEs29(vxw30, vxw400, app(app(ty_Either, ff), ed)) → new_esEs7(vxw30, vxw400, ff, ed)
new_esEs29(vxw30, vxw400, app(ty_Maybe, bbe)) → new_esEs4(vxw30, vxw400, bbe)
new_esEs29(vxw30, vxw400, ty_Ordering) → new_esEs8(vxw30, vxw400)
new_esEs8(LT, LT) → True
new_esEs8(GT, GT) → True
new_esEs8(LT, GT) → False
new_esEs8(GT, LT) → False
new_esEs8(EQ, EQ) → True
new_esEs8(LT, EQ) → False
new_esEs8(EQ, LT) → False
new_esEs8(EQ, GT) → False
new_esEs8(GT, EQ) → False
new_esEs4(Just(vxw300), Just(vxw4000), ty_Ordering) → new_esEs8(vxw300, vxw4000)
new_esEs4(Just(vxw300), Nothing, bbe) → False
new_esEs4(Nothing, Just(vxw4000), bbe) → False
new_esEs4(Just(vxw300), Just(vxw4000), ty_Char) → new_esEs12(vxw300, vxw4000)
new_esEs4(Just(vxw300), Just(vxw4000), app(app(app(ty_@3, cec), ced), cee)) → new_esEs6(vxw300, vxw4000, cec, ced, cee)
new_esEs4(Just(vxw300), Just(vxw4000), ty_Float) → new_esEs10(vxw300, vxw4000)
new_esEs4(Just(vxw300), Just(vxw4000), ty_Integer) → new_esEs11(vxw300, vxw4000)
new_esEs4(Just(vxw300), Just(vxw4000), ty_Bool) → new_esEs17(vxw300, vxw4000)
new_esEs7(Left(vxw300), Left(vxw4000), app(app(ty_Either, fc), fd), ed) → new_esEs7(vxw300, vxw4000, fc, fd)
new_esEs4(Just(vxw300), Just(vxw4000), app(app(ty_Either, cfa), cfb)) → new_esEs7(vxw300, vxw4000, cfa, cfb)
new_esEs4(Just(vxw300), Just(vxw4000), app(ty_Maybe, ceh)) → new_esEs4(vxw300, vxw4000, ceh)
new_esEs7(Right(vxw300), Right(vxw4000), ff, app(app(ty_Either, gg), gh)) → new_esEs7(vxw300, vxw4000, gg, gh)
new_esEs7(Left(vxw300), Left(vxw4000), app(ty_Maybe, fb), ed) → new_esEs4(vxw300, vxw4000, fb)
new_esEs7(Right(vxw300), Right(vxw4000), ff, app(ty_Maybe, gf)) → new_esEs4(vxw300, vxw4000, gf)
new_esEs4(Just(vxw300), Just(vxw4000), app(app(ty_@2, cea), ceb)) → new_esEs5(vxw300, vxw4000, cea, ceb)
new_esEs4(Just(vxw300), Just(vxw4000), ty_Int) → new_esEs16(vxw300, vxw4000)
new_esEs4(Just(vxw300), Just(vxw4000), ty_@0) → new_esEs15(vxw300, vxw4000)
new_esEs4(Nothing, Nothing, bbe) → True
new_esEs4(Just(vxw300), Just(vxw4000), app(ty_Ratio, cef)) → new_esEs13(vxw300, vxw4000, cef)
new_esEs4(Just(vxw300), Just(vxw4000), app(ty_[], ceg)) → new_esEs14(vxw300, vxw4000, ceg)
new_esEs4(Just(vxw300), Just(vxw4000), ty_Double) → new_esEs9(vxw300, vxw4000)
new_esEs9(Double(vxw300, vxw301), Double(vxw4000, vxw4001)) → new_esEs16(new_sr(vxw300, vxw4000), new_sr(vxw301, vxw4001))
new_sr(vxw300, vxw4000) → new_primMulInt(vxw300, vxw4000)
new_esEs16(vxw30, vxw400) → new_primEqInt(vxw30, vxw400)
new_primEqInt(Neg(Succ(vxw3000)), Neg(Succ(vxw40000))) → new_primEqNat0(vxw3000, vxw40000)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Succ(vxw3000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(vxw40000))) → False
new_primEqInt(Pos(Succ(vxw3000)), Pos(Succ(vxw40000))) → new_primEqNat0(vxw3000, vxw40000)
new_primEqInt(Pos(Succ(vxw3000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(vxw40000))) → False
new_primEqInt(Pos(Succ(vxw3000)), Neg(vxw4000)) → False
new_primEqInt(Neg(Succ(vxw3000)), Pos(vxw4000)) → False
new_primEqInt(Pos(Zero), Neg(Succ(vxw40000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(vxw40000))) → False
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqNat0(Zero, Zero) → True
new_primEqNat0(Succ(vxw3000), Succ(vxw40000)) → new_primEqNat0(vxw3000, vxw40000)
new_primEqNat0(Succ(vxw3000), Zero) → False
new_primEqNat0(Zero, Succ(vxw40000)) → False
new_primMulInt(Pos(vxw3000), Pos(vxw40000)) → Pos(new_primMulNat0(vxw3000, vxw40000))
new_primMulInt(Neg(vxw3000), Neg(vxw40000)) → Pos(new_primMulNat0(vxw3000, vxw40000))
new_primMulInt(Neg(vxw3000), Pos(vxw40000)) → Neg(new_primMulNat0(vxw3000, vxw40000))
new_primMulInt(Pos(vxw3000), Neg(vxw40000)) → Neg(new_primMulNat0(vxw3000, vxw40000))
new_primMulNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, Succ(vxw400000)) → Zero
new_primMulNat0(Succ(vxw30000), Zero) → Zero
new_primMulNat0(Succ(vxw30000), Succ(vxw400000)) → new_primPlusNat0(new_primMulNat0(vxw30000, Succ(vxw400000)), vxw400000)
new_primPlusNat0(Succ(vxw620), vxw400000) → Succ(Succ(new_primPlusNat1(vxw620, vxw400000)))
new_primPlusNat0(Zero, vxw400000) → Succ(vxw400000)
new_primPlusNat1(Zero, Succ(vxw4000000)) → Succ(vxw4000000)
new_primPlusNat1(Succ(vxw6200), Zero) → Succ(vxw6200)
new_primPlusNat1(Succ(vxw6200), Succ(vxw4000000)) → Succ(Succ(new_primPlusNat1(vxw6200, vxw4000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_esEs14([], [], bbd) → True
new_esEs14([], :(vxw4000, vxw4001), bbd) → False
new_esEs14(:(vxw300, vxw301), [], bbd) → False
new_esEs14(:(vxw300, vxw301), :(vxw4000, vxw4001), bbd) → new_asAs(new_esEs24(vxw300, vxw4000, bbd), new_esEs14(vxw301, vxw4001, bbd))
new_esEs24(vxw300, vxw4000, app(ty_Maybe, cgb)) → new_esEs4(vxw300, vxw4000, cgb)
new_esEs24(vxw300, vxw4000, app(app(ty_@2, cfc), cfd)) → new_esEs5(vxw300, vxw4000, cfc, cfd)
new_esEs24(vxw300, vxw4000, app(app(ty_Either, cgc), cgd)) → new_esEs7(vxw300, vxw4000, cgc, cgd)
new_esEs24(vxw300, vxw4000, ty_Int) → new_esEs16(vxw300, vxw4000)
new_esEs24(vxw300, vxw4000, ty_Bool) → new_esEs17(vxw300, vxw4000)
new_esEs24(vxw300, vxw4000, ty_Char) → new_esEs12(vxw300, vxw4000)
new_esEs24(vxw300, vxw4000, app(app(app(ty_@3, cfe), cff), cfg)) → new_esEs6(vxw300, vxw4000, cfe, cff, cfg)
new_esEs24(vxw300, vxw4000, ty_Ordering) → new_esEs8(vxw300, vxw4000)
new_esEs24(vxw300, vxw4000, ty_@0) → new_esEs15(vxw300, vxw4000)
new_esEs24(vxw300, vxw4000, app(ty_Ratio, cfh)) → new_esEs13(vxw300, vxw4000, cfh)
new_esEs24(vxw300, vxw4000, ty_Double) → new_esEs9(vxw300, vxw4000)
new_esEs24(vxw300, vxw4000, app(ty_[], cga)) → new_esEs14(vxw300, vxw4000, cga)
new_esEs24(vxw300, vxw4000, ty_Integer) → new_esEs11(vxw300, vxw4000)
new_esEs24(vxw300, vxw4000, ty_Float) → new_esEs10(vxw300, vxw4000)
new_asAs(False, vxw53) → False
new_asAs(True, vxw53) → vxw53
new_esEs10(Float(vxw300, vxw301), Float(vxw4000, vxw4001)) → new_esEs16(new_sr(vxw300, vxw4000), new_sr(vxw301, vxw4001))
new_esEs11(Integer(vxw300), Integer(vxw4000)) → new_primEqInt(vxw300, vxw4000)
new_esEs13(:%(vxw300, vxw301), :%(vxw4000, vxw4001), bbc) → new_asAs(new_esEs19(vxw300, vxw4000, bbc), new_esEs18(vxw301, vxw4001, bbc))
new_esEs19(vxw300, vxw4000, ty_Integer) → new_esEs11(vxw300, vxw4000)
new_esEs19(vxw300, vxw4000, ty_Int) → new_esEs16(vxw300, vxw4000)
new_esEs18(vxw301, vxw4001, ty_Integer) → new_esEs11(vxw301, vxw4001)
new_esEs18(vxw301, vxw4001, ty_Int) → new_esEs16(vxw301, vxw4001)
new_esEs15(@0, @0) → True
new_esEs6(@3(vxw300, vxw301, vxw302), @3(vxw4000, vxw4001, vxw4002), bah, bba, bbb) → new_asAs(new_esEs22(vxw300, vxw4000, bah), new_asAs(new_esEs21(vxw301, vxw4001, bba), new_esEs20(vxw302, vxw4002, bbb)))
new_esEs22(vxw300, vxw4000, ty_Char) → new_esEs12(vxw300, vxw4000)
new_esEs22(vxw300, vxw4000, app(app(ty_@2, bge), bgf)) → new_esEs5(vxw300, vxw4000, bge, bgf)
new_esEs22(vxw300, vxw4000, app(ty_[], bhc)) → new_esEs14(vxw300, vxw4000, bhc)
new_esEs22(vxw300, vxw4000, app(app(ty_Either, bhe), bhf)) → new_esEs7(vxw300, vxw4000, bhe, bhf)
new_esEs22(vxw300, vxw4000, ty_@0) → new_esEs15(vxw300, vxw4000)
new_esEs22(vxw300, vxw4000, ty_Ordering) → new_esEs8(vxw300, vxw4000)
new_esEs22(vxw300, vxw4000, ty_Double) → new_esEs9(vxw300, vxw4000)
new_esEs22(vxw300, vxw4000, app(app(app(ty_@3, bgg), bgh), bha)) → new_esEs6(vxw300, vxw4000, bgg, bgh, bha)
new_esEs22(vxw300, vxw4000, app(ty_Maybe, bhd)) → new_esEs4(vxw300, vxw4000, bhd)
new_esEs22(vxw300, vxw4000, app(ty_Ratio, bhb)) → new_esEs13(vxw300, vxw4000, bhb)
new_esEs22(vxw300, vxw4000, ty_Bool) → new_esEs17(vxw300, vxw4000)
new_esEs22(vxw300, vxw4000, ty_Integer) → new_esEs11(vxw300, vxw4000)
new_esEs22(vxw300, vxw4000, ty_Float) → new_esEs10(vxw300, vxw4000)
new_esEs22(vxw300, vxw4000, ty_Int) → new_esEs16(vxw300, vxw4000)
new_esEs21(vxw301, vxw4001, ty_Bool) → new_esEs17(vxw301, vxw4001)
new_esEs21(vxw301, vxw4001, app(ty_Ratio, bfh)) → new_esEs13(vxw301, vxw4001, bfh)
new_esEs21(vxw301, vxw4001, ty_Char) → new_esEs12(vxw301, vxw4001)
new_esEs21(vxw301, vxw4001, ty_@0) → new_esEs15(vxw301, vxw4001)
new_esEs21(vxw301, vxw4001, ty_Integer) → new_esEs11(vxw301, vxw4001)
new_esEs21(vxw301, vxw4001, ty_Float) → new_esEs10(vxw301, vxw4001)
new_esEs21(vxw301, vxw4001, app(ty_[], bga)) → new_esEs14(vxw301, vxw4001, bga)
new_esEs21(vxw301, vxw4001, app(app(ty_@2, bfc), bfd)) → new_esEs5(vxw301, vxw4001, bfc, bfd)
new_esEs21(vxw301, vxw4001, app(app(ty_Either, bgc), bgd)) → new_esEs7(vxw301, vxw4001, bgc, bgd)
new_esEs21(vxw301, vxw4001, app(ty_Maybe, bgb)) → new_esEs4(vxw301, vxw4001, bgb)
new_esEs21(vxw301, vxw4001, ty_Double) → new_esEs9(vxw301, vxw4001)
new_esEs21(vxw301, vxw4001, ty_Ordering) → new_esEs8(vxw301, vxw4001)
new_esEs21(vxw301, vxw4001, ty_Int) → new_esEs16(vxw301, vxw4001)
new_esEs21(vxw301, vxw4001, app(app(app(ty_@3, bfe), bff), bfg)) → new_esEs6(vxw301, vxw4001, bfe, bff, bfg)
new_esEs20(vxw302, vxw4002, app(ty_Maybe, beh)) → new_esEs4(vxw302, vxw4002, beh)
new_esEs20(vxw302, vxw4002, app(ty_Ratio, bef)) → new_esEs13(vxw302, vxw4002, bef)
new_esEs20(vxw302, vxw4002, ty_Int) → new_esEs16(vxw302, vxw4002)
new_esEs20(vxw302, vxw4002, ty_Char) → new_esEs12(vxw302, vxw4002)
new_esEs20(vxw302, vxw4002, app(app(ty_@2, bea), beb)) → new_esEs5(vxw302, vxw4002, bea, beb)
new_esEs20(vxw302, vxw4002, ty_Integer) → new_esEs11(vxw302, vxw4002)
new_esEs20(vxw302, vxw4002, app(app(app(ty_@3, bec), bed), bee)) → new_esEs6(vxw302, vxw4002, bec, bed, bee)
new_esEs20(vxw302, vxw4002, ty_Bool) → new_esEs17(vxw302, vxw4002)
new_esEs20(vxw302, vxw4002, ty_Ordering) → new_esEs8(vxw302, vxw4002)
new_esEs20(vxw302, vxw4002, ty_Float) → new_esEs10(vxw302, vxw4002)
new_esEs20(vxw302, vxw4002, ty_@0) → new_esEs15(vxw302, vxw4002)
new_esEs20(vxw302, vxw4002, app(app(ty_Either, bfa), bfb)) → new_esEs7(vxw302, vxw4002, bfa, bfb)
new_esEs20(vxw302, vxw4002, ty_Double) → new_esEs9(vxw302, vxw4002)
new_esEs20(vxw302, vxw4002, app(ty_[], beg)) → new_esEs14(vxw302, vxw4002, beg)
new_esEs7(Right(vxw300), Right(vxw4000), ff, ty_Ordering) → new_esEs8(vxw300, vxw4000)
new_esEs7(Left(vxw300), Right(vxw4000), ff, ed) → False
new_esEs7(Right(vxw300), Left(vxw4000), ff, ed) → False
new_esEs7(Left(vxw300), Left(vxw4000), ty_Double, ed) → new_esEs9(vxw300, vxw4000)
new_esEs7(Right(vxw300), Right(vxw4000), ff, ty_Double) → new_esEs9(vxw300, vxw4000)
new_esEs7(Right(vxw300), Right(vxw4000), ff, app(app(ty_@2, fg), fh)) → new_esEs5(vxw300, vxw4000, fg, fh)
new_esEs7(Left(vxw300), Left(vxw4000), ty_Integer, ed) → new_esEs11(vxw300, vxw4000)
new_esEs7(Left(vxw300), Left(vxw4000), app(app(ty_@2, eb), ec), ed) → new_esEs5(vxw300, vxw4000, eb, ec)
new_esEs7(Left(vxw300), Left(vxw4000), ty_Ordering, ed) → new_esEs8(vxw300, vxw4000)
new_esEs7(Right(vxw300), Right(vxw4000), ff, app(app(app(ty_@3, ga), gb), gc)) → new_esEs6(vxw300, vxw4000, ga, gb, gc)
new_esEs7(Right(vxw300), Right(vxw4000), ff, ty_Char) → new_esEs12(vxw300, vxw4000)
new_esEs7(Right(vxw300), Right(vxw4000), ff, ty_@0) → new_esEs15(vxw300, vxw4000)
new_esEs7(Right(vxw300), Right(vxw4000), ff, app(ty_Ratio, gd)) → new_esEs13(vxw300, vxw4000, gd)
new_esEs7(Left(vxw300), Left(vxw4000), app(ty_Ratio, eh), ed) → new_esEs13(vxw300, vxw4000, eh)
new_esEs7(Left(vxw300), Left(vxw4000), ty_@0, ed) → new_esEs15(vxw300, vxw4000)
new_esEs7(Right(vxw300), Right(vxw4000), ff, ty_Float) → new_esEs10(vxw300, vxw4000)
new_esEs7(Left(vxw300), Left(vxw4000), ty_Int, ed) → new_esEs16(vxw300, vxw4000)
new_esEs7(Right(vxw300), Right(vxw4000), ff, ty_Integer) → new_esEs11(vxw300, vxw4000)
new_esEs7(Right(vxw300), Right(vxw4000), ff, ty_Bool) → new_esEs17(vxw300, vxw4000)
new_esEs7(Left(vxw300), Left(vxw4000), ty_Char, ed) → new_esEs12(vxw300, vxw4000)
new_esEs7(Right(vxw300), Right(vxw4000), ff, app(ty_[], ge)) → new_esEs14(vxw300, vxw4000, ge)
new_esEs7(Left(vxw300), Left(vxw4000), ty_Float, ed) → new_esEs10(vxw300, vxw4000)
new_esEs7(Left(vxw300), Left(vxw4000), app(app(app(ty_@3, ee), ef), eg), ed) → new_esEs6(vxw300, vxw4000, ee, ef, eg)
new_esEs7(Right(vxw300), Right(vxw4000), ff, ty_Int) → new_esEs16(vxw300, vxw4000)
new_esEs7(Left(vxw300), Left(vxw4000), ty_Bool, ed) → new_esEs17(vxw300, vxw4000)
new_esEs7(Left(vxw300), Left(vxw4000), app(ty_[], fa), ed) → new_esEs14(vxw300, vxw4000, fa)
new_esEs17(True, True) → True
new_esEs17(False, False) → True
new_esEs17(False, True) → False
new_esEs17(True, False) → False
new_esEs12(Char(vxw300), Char(vxw4000)) → new_primEqNat0(vxw300, vxw4000)
new_esEs5(@2(vxw300, vxw301), @2(vxw4000, vxw4001), baf, bag) → new_asAs(new_esEs28(vxw300, vxw4000, baf), new_esEs27(vxw301, vxw4001, bag))
new_esEs28(vxw300, vxw4000, ty_Integer) → new_esEs11(vxw300, vxw4000)
new_esEs28(vxw300, vxw4000, ty_@0) → new_esEs15(vxw300, vxw4000)
new_esEs28(vxw300, vxw4000, ty_Float) → new_esEs10(vxw300, vxw4000)
new_esEs28(vxw300, vxw4000, app(ty_Maybe, ded)) → new_esEs4(vxw300, vxw4000, ded)
new_esEs28(vxw300, vxw4000, ty_Int) → new_esEs16(vxw300, vxw4000)
new_esEs28(vxw300, vxw4000, app(ty_[], dec)) → new_esEs14(vxw300, vxw4000, dec)
new_esEs28(vxw300, vxw4000, ty_Ordering) → new_esEs8(vxw300, vxw4000)
new_esEs28(vxw300, vxw4000, app(app(ty_Either, dee), def)) → new_esEs7(vxw300, vxw4000, dee, def)
new_esEs28(vxw300, vxw4000, app(app(ty_@2, dde), ddf)) → new_esEs5(vxw300, vxw4000, dde, ddf)
new_esEs28(vxw300, vxw4000, ty_Double) → new_esEs9(vxw300, vxw4000)
new_esEs28(vxw300, vxw4000, app(app(app(ty_@3, ddg), ddh), dea)) → new_esEs6(vxw300, vxw4000, ddg, ddh, dea)
new_esEs28(vxw300, vxw4000, ty_Bool) → new_esEs17(vxw300, vxw4000)
new_esEs28(vxw300, vxw4000, app(ty_Ratio, deb)) → new_esEs13(vxw300, vxw4000, deb)
new_esEs28(vxw300, vxw4000, ty_Char) → new_esEs12(vxw300, vxw4000)
new_esEs27(vxw301, vxw4001, ty_Bool) → new_esEs17(vxw301, vxw4001)
new_esEs27(vxw301, vxw4001, app(app(ty_Either, ddc), ddd)) → new_esEs7(vxw301, vxw4001, ddc, ddd)
new_esEs27(vxw301, vxw4001, app(ty_Ratio, dch)) → new_esEs13(vxw301, vxw4001, dch)
new_esEs27(vxw301, vxw4001, ty_Char) → new_esEs12(vxw301, vxw4001)
new_esEs27(vxw301, vxw4001, ty_Ordering) → new_esEs8(vxw301, vxw4001)
new_esEs27(vxw301, vxw4001, ty_Double) → new_esEs9(vxw301, vxw4001)
new_esEs27(vxw301, vxw4001, ty_Float) → new_esEs10(vxw301, vxw4001)
new_esEs27(vxw301, vxw4001, ty_@0) → new_esEs15(vxw301, vxw4001)
new_esEs27(vxw301, vxw4001, app(app(app(ty_@3, dce), dcf), dcg)) → new_esEs6(vxw301, vxw4001, dce, dcf, dcg)
new_esEs27(vxw301, vxw4001, app(app(ty_@2, dcc), dcd)) → new_esEs5(vxw301, vxw4001, dcc, dcd)
new_esEs27(vxw301, vxw4001, app(ty_Maybe, ddb)) → new_esEs4(vxw301, vxw4001, ddb)
new_esEs27(vxw301, vxw4001, ty_Int) → new_esEs16(vxw301, vxw4001)
new_esEs27(vxw301, vxw4001, app(ty_[], dda)) → new_esEs14(vxw301, vxw4001, dda)
new_esEs27(vxw301, vxw4001, ty_Integer) → new_esEs11(vxw301, vxw4001)
new_ltEs20(vxw11, vxw10, ty_Ordering) → new_ltEs10(vxw11, vxw10)
new_ltEs20(vxw11, vxw10, ty_Bool) → new_ltEs5(vxw11, vxw10)
new_ltEs20(vxw11, vxw10, ty_Double) → new_ltEs9(vxw11, vxw10)
new_ltEs20(vxw11, vxw10, app(ty_[], cc)) → new_ltEs12(vxw11, vxw10, cc)
new_ltEs20(vxw11, vxw10, app(app(ty_@2, bdb), bdc)) → new_ltEs4(vxw11, vxw10, bdb, bdc)
new_ltEs20(vxw11, vxw10, app(ty_Ratio, bda)) → new_ltEs11(vxw11, vxw10, bda)
new_ltEs20(vxw11, vxw10, ty_Int) → new_ltEs16(vxw11, vxw10)
new_ltEs20(vxw11, vxw10, ty_Integer) → new_ltEs13(vxw11, vxw10)
new_ltEs20(vxw11, vxw10, ty_@0) → new_ltEs14(vxw11, vxw10)
new_ltEs20(vxw11, vxw10, ty_Float) → new_ltEs15(vxw11, vxw10)
new_ltEs20(vxw11, vxw10, app(app(app(ty_@3, bdd), bde), bdf)) → new_ltEs6(vxw11, vxw10, bdd, bde, bdf)
new_ltEs20(vxw11, vxw10, app(app(ty_Either, bdg), bdh)) → new_ltEs17(vxw11, vxw10, bdg, bdh)
new_ltEs20(vxw11, vxw10, ty_Char) → new_ltEs8(vxw11, vxw10)
new_ltEs20(vxw11, vxw10, app(ty_Maybe, bbf)) → new_ltEs7(vxw11, vxw10, bbf)
new_ltEs7(Just(vxw110), Just(vxw100), ty_Bool) → new_ltEs5(vxw110, vxw100)
new_ltEs7(Just(vxw110), Just(vxw100), app(app(app(ty_@3, bcd), bce), bcf)) → new_ltEs6(vxw110, vxw100, bcd, bce, bcf)
new_ltEs7(Just(vxw110), Just(vxw100), app(app(ty_@2, bbh), bca)) → new_ltEs4(vxw110, vxw100, bbh, bca)
new_ltEs7(Just(vxw110), Just(vxw100), ty_Ordering) → new_ltEs10(vxw110, vxw100)
new_ltEs7(Just(vxw110), Just(vxw100), ty_Integer) → new_ltEs13(vxw110, vxw100)
new_ltEs7(Just(vxw110), Just(vxw100), ty_Int) → new_ltEs16(vxw110, vxw100)
new_ltEs7(Nothing, Just(vxw100), bbf) → True
new_ltEs7(Just(vxw110), Just(vxw100), ty_Float) → new_ltEs15(vxw110, vxw100)
new_ltEs7(Just(vxw110), Just(vxw100), ty_Double) → new_ltEs9(vxw110, vxw100)
new_ltEs7(Nothing, Nothing, bbf) → True
new_ltEs7(Just(vxw110), Just(vxw100), app(ty_[], bcc)) → new_ltEs12(vxw110, vxw100, bcc)
new_ltEs7(Just(vxw110), Just(vxw100), ty_Char) → new_ltEs8(vxw110, vxw100)
new_ltEs7(Just(vxw110), Just(vxw100), ty_@0) → new_ltEs14(vxw110, vxw100)
new_ltEs7(Just(vxw110), Nothing, bbf) → False
new_ltEs7(Just(vxw110), Just(vxw100), app(ty_Ratio, bcb)) → new_ltEs11(vxw110, vxw100, bcb)
new_ltEs17(Left(vxw110), Left(vxw100), app(app(ty_Either, cag), cah), bdh) → new_ltEs17(vxw110, vxw100, cag, cah)
new_ltEs17(Right(vxw110), Right(vxw100), bdg, app(app(ty_Either, cca), ccb)) → new_ltEs17(vxw110, vxw100, cca, ccb)
new_ltEs7(Just(vxw110), Just(vxw100), app(ty_Maybe, bbg)) → new_ltEs7(vxw110, vxw100, bbg)
new_ltEs7(Just(vxw110), Just(vxw100), app(app(ty_Either, bcg), bch)) → new_ltEs17(vxw110, vxw100, bcg, bch)
new_ltEs17(Right(vxw110), Right(vxw100), bdg, app(ty_Maybe, cba)) → new_ltEs7(vxw110, vxw100, cba)
new_ltEs17(Left(vxw110), Left(vxw100), app(ty_Maybe, bhg), bdh) → new_ltEs7(vxw110, vxw100, bhg)
new_ltEs17(Right(vxw110), Right(vxw100), bdg, app(ty_Ratio, cbd)) → new_ltEs11(vxw110, vxw100, cbd)
new_ltEs17(Left(vxw110), Left(vxw100), app(ty_Ratio, cab), bdh) → new_ltEs11(vxw110, vxw100, cab)
new_ltEs17(Left(vxw110), Left(vxw100), ty_Integer, bdh) → new_ltEs13(vxw110, vxw100)
new_ltEs17(Right(vxw110), Right(vxw100), bdg, ty_Integer) → new_ltEs13(vxw110, vxw100)
new_ltEs17(Left(vxw110), Left(vxw100), ty_Bool, bdh) → new_ltEs5(vxw110, vxw100)
new_ltEs17(Left(vxw110), Left(vxw100), ty_Double, bdh) → new_ltEs9(vxw110, vxw100)
new_ltEs17(Left(vxw110), Left(vxw100), ty_Ordering, bdh) → new_ltEs10(vxw110, vxw100)
new_ltEs17(Right(vxw110), Left(vxw100), bdg, bdh) → False
new_ltEs17(Right(vxw110), Right(vxw100), bdg, ty_Ordering) → new_ltEs10(vxw110, vxw100)
new_ltEs17(Right(vxw110), Right(vxw100), bdg, ty_Int) → new_ltEs16(vxw110, vxw100)
new_ltEs17(Left(vxw110), Left(vxw100), app(app(ty_@2, bhh), caa), bdh) → new_ltEs4(vxw110, vxw100, bhh, caa)
new_ltEs17(Left(vxw110), Left(vxw100), app(app(app(ty_@3, cad), cae), caf), bdh) → new_ltEs6(vxw110, vxw100, cad, cae, caf)
new_ltEs17(Left(vxw110), Left(vxw100), app(ty_[], cac), bdh) → new_ltEs12(vxw110, vxw100, cac)
new_ltEs17(Left(vxw110), Left(vxw100), ty_Float, bdh) → new_ltEs15(vxw110, vxw100)
new_ltEs17(Right(vxw110), Right(vxw100), bdg, ty_@0) → new_ltEs14(vxw110, vxw100)
new_ltEs17(Left(vxw110), Left(vxw100), ty_Char, bdh) → new_ltEs8(vxw110, vxw100)
new_ltEs17(Left(vxw110), Left(vxw100), ty_@0, bdh) → new_ltEs14(vxw110, vxw100)
new_ltEs17(Right(vxw110), Right(vxw100), bdg, ty_Float) → new_ltEs15(vxw110, vxw100)
new_ltEs17(Left(vxw110), Right(vxw100), bdg, bdh) → True
new_ltEs17(Right(vxw110), Right(vxw100), bdg, app(ty_[], cbe)) → new_ltEs12(vxw110, vxw100, cbe)
new_ltEs17(Right(vxw110), Right(vxw100), bdg, ty_Double) → new_ltEs9(vxw110, vxw100)
new_ltEs17(Right(vxw110), Right(vxw100), bdg, ty_Char) → new_ltEs8(vxw110, vxw100)
new_ltEs17(Left(vxw110), Left(vxw100), ty_Int, bdh) → new_ltEs16(vxw110, vxw100)
new_ltEs17(Right(vxw110), Right(vxw100), bdg, app(app(app(ty_@3, cbf), cbg), cbh)) → new_ltEs6(vxw110, vxw100, cbf, cbg, cbh)
new_ltEs17(Right(vxw110), Right(vxw100), bdg, app(app(ty_@2, cbb), cbc)) → new_ltEs4(vxw110, vxw100, cbb, cbc)
new_ltEs17(Right(vxw110), Right(vxw100), bdg, ty_Bool) → new_ltEs5(vxw110, vxw100)
new_ltEs5(True, False) → False
new_ltEs5(True, True) → True
new_ltEs5(False, False) → True
new_ltEs5(False, True) → True
new_ltEs4(@2(vxw110, vxw111), @2(vxw100, vxw101), bdb, bdc) → new_pePe(new_lt10(vxw110, vxw100, bdb), new_asAs(new_esEs23(vxw110, vxw100, bdb), new_ltEs18(vxw111, vxw101, bdc)))
new_lt10(vxw110, vxw100, ty_Double) → new_lt13(vxw110, vxw100)
new_lt10(vxw110, vxw100, ty_Bool) → new_lt9(vxw110, vxw100)
new_lt10(vxw110, vxw100, app(app(ty_@2, dh), ea)) → new_lt11(vxw110, vxw100, dh, ea)
new_lt10(vxw110, vxw100, ty_Char) → new_lt12(vxw110, vxw100)
new_lt10(vxw110, vxw100, app(app(ty_Either, cdg), cdh)) → new_lt18(vxw110, vxw100, cdg, cdh)
new_lt10(vxw110, vxw100, app(app(app(ty_@3, ha), hb), hc)) → new_lt16(vxw110, vxw100, ha, hb, hc)
new_lt10(vxw110, vxw100, ty_Float) → new_lt17(vxw110, vxw100)
new_lt10(vxw110, vxw100, app(ty_Ratio, cde)) → new_lt14(vxw110, vxw100, cde)
new_lt10(vxw110, vxw100, app(ty_Maybe, cd)) → new_lt5(vxw110, vxw100, cd)
new_lt10(vxw110, vxw100, app(ty_[], cdf)) → new_lt15(vxw110, vxw100, cdf)
new_lt10(vxw110, vxw100, ty_@0) → new_lt8(vxw110, vxw100)
new_lt10(vxw110, vxw100, ty_Int) → new_lt7(vxw110, vxw100)
new_lt10(vxw110, vxw100, ty_Integer) → new_lt4(vxw110, vxw100)
new_lt10(vxw110, vxw100, ty_Ordering) → new_lt6(vxw110, vxw100)
new_esEs23(vxw110, vxw100, app(app(ty_Either, cdg), cdh)) → new_esEs7(vxw110, vxw100, cdg, cdh)
new_esEs23(vxw110, vxw100, app(ty_Ratio, cde)) → new_esEs13(vxw110, vxw100, cde)
new_esEs23(vxw110, vxw100, ty_Double) → new_esEs9(vxw110, vxw100)
new_esEs23(vxw110, vxw100, app(ty_Maybe, cd)) → new_esEs4(vxw110, vxw100, cd)
new_esEs23(vxw110, vxw100, ty_Ordering) → new_esEs8(vxw110, vxw100)
new_esEs23(vxw110, vxw100, ty_Float) → new_esEs10(vxw110, vxw100)
new_esEs23(vxw110, vxw100, ty_Integer) → new_esEs11(vxw110, vxw100)
new_esEs23(vxw110, vxw100, app(app(ty_@2, dh), ea)) → new_esEs5(vxw110, vxw100, dh, ea)
new_esEs23(vxw110, vxw100, ty_@0) → new_esEs15(vxw110, vxw100)
new_esEs23(vxw110, vxw100, app(ty_[], cdf)) → new_esEs14(vxw110, vxw100, cdf)
new_esEs23(vxw110, vxw100, ty_Bool) → new_esEs17(vxw110, vxw100)
new_esEs23(vxw110, vxw100, app(app(app(ty_@3, ha), hb), hc)) → new_esEs6(vxw110, vxw100, ha, hb, hc)
new_esEs23(vxw110, vxw100, ty_Char) → new_esEs12(vxw110, vxw100)
new_esEs23(vxw110, vxw100, ty_Int) → new_esEs16(vxw110, vxw100)
new_ltEs18(vxw111, vxw101, ty_Float) → new_ltEs15(vxw111, vxw101)
new_ltEs18(vxw111, vxw101, ty_Char) → new_ltEs8(vxw111, vxw101)
new_ltEs18(vxw111, vxw101, ty_Int) → new_ltEs16(vxw111, vxw101)
new_ltEs18(vxw111, vxw101, app(app(ty_Either, cdc), cdd)) → new_ltEs17(vxw111, vxw101, cdc, cdd)
new_ltEs18(vxw111, vxw101, ty_@0) → new_ltEs14(vxw111, vxw101)
new_ltEs18(vxw111, vxw101, ty_Integer) → new_ltEs13(vxw111, vxw101)
new_ltEs18(vxw111, vxw101, ty_Bool) → new_ltEs5(vxw111, vxw101)
new_ltEs18(vxw111, vxw101, app(ty_Ratio, ccf)) → new_ltEs11(vxw111, vxw101, ccf)
new_ltEs18(vxw111, vxw101, app(app(app(ty_@3, cch), cda), cdb)) → new_ltEs6(vxw111, vxw101, cch, cda, cdb)
new_ltEs18(vxw111, vxw101, app(ty_Maybe, ccc)) → new_ltEs7(vxw111, vxw101, ccc)
new_ltEs18(vxw111, vxw101, app(ty_[], ccg)) → new_ltEs12(vxw111, vxw101, ccg)
new_ltEs18(vxw111, vxw101, app(app(ty_@2, ccd), cce)) → new_ltEs4(vxw111, vxw101, ccd, cce)
new_ltEs18(vxw111, vxw101, ty_Double) → new_ltEs9(vxw111, vxw101)
new_ltEs18(vxw111, vxw101, ty_Ordering) → new_ltEs10(vxw111, vxw101)
new_pePe(False, vxw60) → vxw60
new_pePe(True, vxw60) → True
new_ltEs10(EQ, GT) → True
new_ltEs10(GT, EQ) → False
new_ltEs10(LT, EQ) → True
new_ltEs10(GT, GT) → True
new_ltEs10(LT, GT) → True
new_ltEs10(EQ, EQ) → True
new_ltEs10(LT, LT) → True
new_ltEs10(EQ, LT) → False
new_ltEs10(GT, LT) → False
new_ltEs9(vxw11, vxw10) → new_not(new_esEs8(new_compare15(vxw11, vxw10), GT))
new_compare15(Double(vxw110, vxw111), Double(vxw100, vxw101)) → new_compare27(new_sr(vxw110, vxw100), new_sr(vxw111, vxw101))
new_not(False) → True
new_not(True) → False
new_compare27(vxw11, vxw10) → new_primCmpInt(vxw11, vxw10)
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(vxw1100)), Neg(vxw100)) → new_primCmpNat0(vxw100, Succ(vxw1100))
new_primCmpInt(Neg(Zero), Pos(Succ(vxw1000))) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(vxw1000))) → new_primCmpNat0(Zero, Succ(vxw1000))
new_primCmpInt(Pos(Succ(vxw1100)), Pos(vxw100)) → new_primCmpNat0(Succ(vxw1100), vxw100)
new_primCmpInt(Pos(Succ(vxw1100)), Neg(vxw100)) → GT
new_primCmpInt(Neg(Zero), Neg(Succ(vxw1000))) → new_primCmpNat0(Succ(vxw1000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(vxw1000))) → GT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(vxw1100)), Pos(vxw100)) → LT
new_primCmpNat0(Succ(vxw1100), Zero) → GT
new_primCmpNat0(Succ(vxw1100), Succ(vxw1000)) → new_primCmpNat0(vxw1100, vxw1000)
new_primCmpNat0(Zero, Succ(vxw1000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_ltEs12(vxw11, vxw10, cc) → new_not(new_esEs8(new_compare0(vxw11, vxw10, cc), GT))
new_compare0(:(vxw110, vxw111), :(vxw100, vxw101), cc) → new_primCompAux0(vxw110, vxw100, new_compare0(vxw111, vxw101, cc), cc)
new_compare0([], [], cc) → EQ
new_compare0(:(vxw110, vxw111), [], cc) → GT
new_compare0([], :(vxw100, vxw101), cc) → LT
new_primCompAux0(vxw110, vxw100, vxw61, cc) → new_primCompAux00(vxw61, new_compare9(vxw110, vxw100, cc))
new_compare9(vxw110, vxw100, ty_Double) → new_compare15(vxw110, vxw100)
new_compare9(vxw110, vxw100, ty_Integer) → new_compare6(vxw110, vxw100)
new_compare9(vxw110, vxw100, ty_Int) → new_compare27(vxw110, vxw100)
new_compare9(vxw110, vxw100, app(app(app(ty_@3, baa), bab), bac)) → new_compare19(vxw110, vxw100, baa, bab, bac)
new_compare9(vxw110, vxw100, app(ty_Maybe, hd)) → new_compare8(vxw110, vxw100, hd)
new_compare9(vxw110, vxw100, app(ty_[], hh)) → new_compare0(vxw110, vxw100, hh)
new_compare9(vxw110, vxw100, ty_Bool) → new_compare18(vxw110, vxw100)
new_compare9(vxw110, vxw100, ty_Float) → new_compare26(vxw110, vxw100)
new_compare9(vxw110, vxw100, ty_@0) → new_compare7(vxw110, vxw100)
new_compare9(vxw110, vxw100, app(app(ty_@2, he), hf)) → new_compare13(vxw110, vxw100, he, hf)
new_compare9(vxw110, vxw100, ty_Ordering) → new_compare16(vxw110, vxw100)
new_compare9(vxw110, vxw100, app(app(ty_Either, bad), bae)) → new_compare28(vxw110, vxw100, bad, bae)
new_compare9(vxw110, vxw100, ty_Char) → new_compare14(vxw110, vxw100)
new_compare9(vxw110, vxw100, app(ty_Ratio, hg)) → new_compare17(vxw110, vxw100, hg)
new_primCompAux00(vxw72, LT) → LT
new_primCompAux00(vxw72, EQ) → vxw72
new_primCompAux00(vxw72, GT) → GT
new_compare17(:%(vxw110, vxw111), :%(vxw100, vxw101), ty_Int) → new_compare27(new_sr(vxw110, vxw101), new_sr(vxw100, vxw111))
new_compare17(:%(vxw110, vxw111), :%(vxw100, vxw101), ty_Integer) → new_compare6(new_sr0(vxw110, vxw101), new_sr0(vxw100, vxw111))
new_sr0(Integer(vxw1100), Integer(vxw1010)) → Integer(new_primMulInt(vxw1100, vxw1010))
new_compare6(Integer(vxw110), Integer(vxw100)) → new_primCmpInt(vxw110, vxw100)
new_compare14(Char(vxw110), Char(vxw100)) → new_primCmpNat0(vxw110, vxw100)
new_compare28(vxw110, vxw100, cdg, cdh) → new_compare29(vxw110, vxw100, new_esEs7(vxw110, vxw100, cdg, cdh), cdg, cdh)
new_compare29(vxw110, vxw100, False, cdg, cdh) → new_compare111(vxw110, vxw100, new_ltEs17(vxw110, vxw100, cdg, cdh), cdg, cdh)
new_compare29(vxw110, vxw100, True, cdg, cdh) → EQ
new_compare111(vxw110, vxw100, False, cdg, cdh) → GT
new_compare111(vxw110, vxw100, True, cdg, cdh) → LT
new_compare16(vxw110, vxw100) → new_compare211(vxw110, vxw100, new_esEs8(vxw110, vxw100))
new_compare211(vxw110, vxw100, False) → new_compare110(vxw110, vxw100, new_ltEs10(vxw110, vxw100))
new_compare211(vxw110, vxw100, True) → EQ
new_compare110(vxw110, vxw100, True) → LT
new_compare110(vxw110, vxw100, False) → GT
new_compare13(vxw110, vxw100, dh, ea) → new_compare23(vxw110, vxw100, new_esEs5(vxw110, vxw100, dh, ea), dh, ea)
new_compare23(vxw110, vxw100, False, dh, ea) → new_compare10(vxw110, vxw100, new_ltEs4(vxw110, vxw100, dh, ea), dh, ea)
new_compare23(vxw110, vxw100, True, dh, ea) → EQ
new_compare10(vxw110, vxw100, True, dh, ea) → LT
new_compare10(vxw110, vxw100, False, dh, ea) → GT
new_compare7(@0, @0) → EQ
new_compare26(Float(vxw110, vxw111), Float(vxw100, vxw101)) → new_compare27(new_sr(vxw110, vxw100), new_sr(vxw111, vxw101))
new_compare18(vxw110, vxw100) → new_compare24(vxw110, vxw100, new_esEs17(vxw110, vxw100))
new_compare24(vxw110, vxw100, True) → EQ
new_compare24(vxw110, vxw100, False) → new_compare11(vxw110, vxw100, new_ltEs5(vxw110, vxw100))
new_compare11(vxw110, vxw100, False) → GT
new_compare11(vxw110, vxw100, True) → LT
new_compare8(vxw110, vxw100, cd) → new_compare210(vxw110, vxw100, new_esEs4(vxw110, vxw100, cd), cd)
new_compare210(vxw110, vxw100, False, cd) → new_compare112(vxw110, vxw100, new_ltEs7(vxw110, vxw100, cd), cd)
new_compare210(vxw110, vxw100, True, cd) → EQ
new_compare112(vxw110, vxw100, True, cd) → LT
new_compare112(vxw110, vxw100, False, cd) → GT
new_compare19(vxw110, vxw100, ha, hb, hc) → new_compare25(vxw110, vxw100, new_esEs6(vxw110, vxw100, ha, hb, hc), ha, hb, hc)
new_compare25(vxw110, vxw100, True, ha, hb, hc) → EQ
new_compare25(vxw110, vxw100, False, ha, hb, hc) → new_compare12(vxw110, vxw100, new_ltEs6(vxw110, vxw100, ha, hb, hc), ha, hb, hc)
new_ltEs6(@3(vxw110, vxw111, vxw112), @3(vxw100, vxw101, vxw102), bdd, bde, bdf) → new_pePe(new_lt20(vxw110, vxw100, bdd), new_asAs(new_esEs26(vxw110, vxw100, bdd), new_pePe(new_lt19(vxw111, vxw101, bde), new_asAs(new_esEs25(vxw111, vxw101, bde), new_ltEs19(vxw112, vxw102, bdf)))))
new_compare12(vxw110, vxw100, True, ha, hb, hc) → LT
new_compare12(vxw110, vxw100, False, ha, hb, hc) → GT
new_lt20(vxw110, vxw100, ty_Integer) → new_lt4(vxw110, vxw100)
new_lt20(vxw110, vxw100, ty_@0) → new_lt8(vxw110, vxw100)
new_lt20(vxw110, vxw100, app(app(ty_@2, dbb), dbc)) → new_lt11(vxw110, vxw100, dbb, dbc)
new_lt20(vxw110, vxw100, ty_Float) → new_lt17(vxw110, vxw100)
new_lt20(vxw110, vxw100, ty_Ordering) → new_lt6(vxw110, vxw100)
new_lt20(vxw110, vxw100, ty_Bool) → new_lt9(vxw110, vxw100)
new_lt20(vxw110, vxw100, app(ty_Maybe, dba)) → new_lt5(vxw110, vxw100, dba)
new_lt20(vxw110, vxw100, ty_Int) → new_lt7(vxw110, vxw100)
new_lt20(vxw110, vxw100, ty_Double) → new_lt13(vxw110, vxw100)
new_lt20(vxw110, vxw100, app(ty_Ratio, dbd)) → new_lt14(vxw110, vxw100, dbd)
new_lt20(vxw110, vxw100, app(app(ty_Either, dca), dcb)) → new_lt18(vxw110, vxw100, dca, dcb)
new_lt20(vxw110, vxw100, app(ty_[], dbe)) → new_lt15(vxw110, vxw100, dbe)
new_lt20(vxw110, vxw100, app(app(app(ty_@3, dbf), dbg), dbh)) → new_lt16(vxw110, vxw100, dbf, dbg, dbh)
new_lt20(vxw110, vxw100, ty_Char) → new_lt12(vxw110, vxw100)
new_esEs26(vxw110, vxw100, ty_@0) → new_esEs15(vxw110, vxw100)
new_esEs26(vxw110, vxw100, ty_Float) → new_esEs10(vxw110, vxw100)
new_esEs26(vxw110, vxw100, ty_Integer) → new_esEs11(vxw110, vxw100)
new_esEs26(vxw110, vxw100, app(ty_Maybe, dba)) → new_esEs4(vxw110, vxw100, dba)
new_esEs26(vxw110, vxw100, ty_Char) → new_esEs12(vxw110, vxw100)
new_esEs26(vxw110, vxw100, app(ty_Ratio, dbd)) → new_esEs13(vxw110, vxw100, dbd)
new_esEs26(vxw110, vxw100, ty_Ordering) → new_esEs8(vxw110, vxw100)
new_esEs26(vxw110, vxw100, app(app(app(ty_@3, dbf), dbg), dbh)) → new_esEs6(vxw110, vxw100, dbf, dbg, dbh)
new_esEs26(vxw110, vxw100, app(ty_[], dbe)) → new_esEs14(vxw110, vxw100, dbe)
new_esEs26(vxw110, vxw100, app(app(ty_Either, dca), dcb)) → new_esEs7(vxw110, vxw100, dca, dcb)
new_esEs26(vxw110, vxw100, app(app(ty_@2, dbb), dbc)) → new_esEs5(vxw110, vxw100, dbb, dbc)
new_esEs26(vxw110, vxw100, ty_Int) → new_esEs16(vxw110, vxw100)
new_esEs26(vxw110, vxw100, ty_Double) → new_esEs9(vxw110, vxw100)
new_esEs26(vxw110, vxw100, ty_Bool) → new_esEs17(vxw110, vxw100)
new_lt19(vxw111, vxw101, app(app(ty_Either, dag), dah)) → new_lt18(vxw111, vxw101, dag, dah)
new_lt19(vxw111, vxw101, ty_@0) → new_lt8(vxw111, vxw101)
new_lt19(vxw111, vxw101, ty_Ordering) → new_lt6(vxw111, vxw101)
new_lt19(vxw111, vxw101, ty_Bool) → new_lt9(vxw111, vxw101)
new_lt19(vxw111, vxw101, app(app(ty_@2, chh), daa)) → new_lt11(vxw111, vxw101, chh, daa)
new_lt19(vxw111, vxw101, ty_Double) → new_lt13(vxw111, vxw101)
new_lt19(vxw111, vxw101, ty_Float) → new_lt17(vxw111, vxw101)
new_lt19(vxw111, vxw101, ty_Char) → new_lt12(vxw111, vxw101)
new_lt19(vxw111, vxw101, ty_Int) → new_lt7(vxw111, vxw101)
new_lt19(vxw111, vxw101, ty_Integer) → new_lt4(vxw111, vxw101)
new_lt19(vxw111, vxw101, app(app(app(ty_@3, dad), dae), daf)) → new_lt16(vxw111, vxw101, dad, dae, daf)
new_lt19(vxw111, vxw101, app(ty_[], dac)) → new_lt15(vxw111, vxw101, dac)
new_lt19(vxw111, vxw101, app(ty_Maybe, chg)) → new_lt5(vxw111, vxw101, chg)
new_lt19(vxw111, vxw101, app(ty_Ratio, dab)) → new_lt14(vxw111, vxw101, dab)
new_esEs25(vxw111, vxw101, app(ty_[], dac)) → new_esEs14(vxw111, vxw101, dac)
new_esEs25(vxw111, vxw101, ty_Bool) → new_esEs17(vxw111, vxw101)
new_esEs25(vxw111, vxw101, ty_Double) → new_esEs9(vxw111, vxw101)
new_esEs25(vxw111, vxw101, ty_Ordering) → new_esEs8(vxw111, vxw101)
new_esEs25(vxw111, vxw101, app(ty_Ratio, dab)) → new_esEs13(vxw111, vxw101, dab)
new_esEs25(vxw111, vxw101, app(ty_Maybe, chg)) → new_esEs4(vxw111, vxw101, chg)
new_esEs25(vxw111, vxw101, ty_Char) → new_esEs12(vxw111, vxw101)
new_esEs25(vxw111, vxw101, ty_Float) → new_esEs10(vxw111, vxw101)
new_esEs25(vxw111, vxw101, ty_@0) → new_esEs15(vxw111, vxw101)
new_esEs25(vxw111, vxw101, ty_Integer) → new_esEs11(vxw111, vxw101)
new_esEs25(vxw111, vxw101, ty_Int) → new_esEs16(vxw111, vxw101)
new_esEs25(vxw111, vxw101, app(app(app(ty_@3, dad), dae), daf)) → new_esEs6(vxw111, vxw101, dad, dae, daf)
new_esEs25(vxw111, vxw101, app(app(ty_@2, chh), daa)) → new_esEs5(vxw111, vxw101, chh, daa)
new_esEs25(vxw111, vxw101, app(app(ty_Either, dag), dah)) → new_esEs7(vxw111, vxw101, dag, dah)
new_ltEs19(vxw112, vxw102, app(ty_Ratio, cgh)) → new_ltEs11(vxw112, vxw102, cgh)
new_ltEs19(vxw112, vxw102, ty_Double) → new_ltEs9(vxw112, vxw102)
new_ltEs19(vxw112, vxw102, ty_Ordering) → new_ltEs10(vxw112, vxw102)
new_ltEs19(vxw112, vxw102, app(app(ty_@2, cgf), cgg)) → new_ltEs4(vxw112, vxw102, cgf, cgg)
new_ltEs19(vxw112, vxw102, ty_Float) → new_ltEs15(vxw112, vxw102)
new_ltEs19(vxw112, vxw102, app(app(ty_Either, che), chf)) → new_ltEs17(vxw112, vxw102, che, chf)
new_ltEs19(vxw112, vxw102, ty_Char) → new_ltEs8(vxw112, vxw102)
new_ltEs19(vxw112, vxw102, app(ty_[], cha)) → new_ltEs12(vxw112, vxw102, cha)
new_ltEs19(vxw112, vxw102, app(app(app(ty_@3, chb), chc), chd)) → new_ltEs6(vxw112, vxw102, chb, chc, chd)
new_ltEs19(vxw112, vxw102, ty_Int) → new_ltEs16(vxw112, vxw102)
new_ltEs19(vxw112, vxw102, ty_@0) → new_ltEs14(vxw112, vxw102)
new_ltEs19(vxw112, vxw102, ty_Bool) → new_ltEs5(vxw112, vxw102)
new_ltEs19(vxw112, vxw102, app(ty_Maybe, cge)) → new_ltEs7(vxw112, vxw102, cge)
new_ltEs19(vxw112, vxw102, ty_Integer) → new_ltEs13(vxw112, vxw102)
new_ltEs13(vxw11, vxw10) → new_not(new_esEs8(new_compare6(vxw11, vxw10), GT))
new_ltEs14(vxw11, vxw10) → new_not(new_esEs8(new_compare7(vxw11, vxw10), GT))
new_ltEs16(vxw11, vxw10) → new_not(new_esEs8(new_compare27(vxw11, vxw10), GT))
new_ltEs8(vxw11, vxw10) → new_not(new_esEs8(new_compare14(vxw11, vxw10), GT))
new_ltEs15(vxw11, vxw10) → new_not(new_esEs8(new_compare26(vxw11, vxw10), GT))
new_ltEs11(vxw11, vxw10, bda) → new_not(new_esEs8(new_compare17(vxw11, vxw10, bda), GT))
new_lt14(vxw110, vxw100, cde) → new_esEs8(new_compare17(vxw110, vxw100, cde), LT)
new_lt5(vxw110, vxw100, cd) → new_esEs8(new_compare8(vxw110, vxw100, cd), LT)
new_lt15(vxw110, vxw100, cdf) → new_esEs8(new_compare0(vxw110, vxw100, cdf), LT)
new_lt16(vxw110, vxw100, ha, hb, hc) → new_esEs8(new_compare19(vxw110, vxw100, ha, hb, hc), LT)
new_lt4(vxw110, vxw100) → new_esEs8(new_compare6(vxw110, vxw100), LT)
new_lt7(vxw110, vxw100) → new_esEs8(new_compare27(vxw110, vxw100), LT)
new_lt12(vxw110, vxw100) → new_esEs8(new_compare14(vxw110, vxw100), LT)
new_lt17(vxw110, vxw100) → new_esEs8(new_compare26(vxw110, vxw100), LT)
new_lt13(vxw110, vxw100) → new_esEs8(new_compare15(vxw110, vxw100), LT)
new_lt11(vxw110, vxw100, dh, ea) → new_esEs8(new_compare13(vxw110, vxw100, dh, ea), LT)
new_lt9(vxw110, vxw100) → new_esEs8(new_compare18(vxw110, vxw100), LT)
new_lt6(vxw110, vxw100) → new_esEs8(new_compare16(vxw110, vxw100), LT)
new_lt8(vxw110, vxw100) → new_esEs8(new_compare7(vxw110, vxw100), LT)
new_lt18(vxw110, vxw100, cdg, cdh) → new_esEs8(new_compare28(vxw110, vxw100, cdg, cdh), LT)

The set Q consists of the following terms:

new_esEs11(Integer(x0), Integer(x1))
new_compare12(x0, x1, True, x2, x3, x4)
new_esEs4(Just(x0), Just(x1), ty_Int)
new_ltEs17(Left(x0), Left(x1), ty_@0, x2)
new_ltEs13(x0, x1)
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs20(x0, x1, ty_Char)
new_esEs7(Left(x0), Left(x1), ty_Int, x2)
new_asAs(True, x0)
new_lt5(x0, x1, x2)
new_ltEs17(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs21(x0, x1, ty_Ordering)
new_primMulNat0(Zero, Succ(x0))
new_esEs7(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_ltEs17(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_ltEs17(Left(x0), Left(x1), ty_Int, x2)
new_lt10(x0, x1, ty_Int)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_compare11(x0, x1, True)
new_ltEs21(x0, x1, ty_Bool)
new_primCmpNat0(Succ(x0), Zero)
new_lt18(x0, x1, x2, x3)
new_esEs7(Left(x0), Left(x1), ty_Integer, x2)
new_lt20(x0, x1, ty_Integer)
new_ltEs19(x0, x1, ty_@0)
new_ltEs21(x0, x1, app(ty_Maybe, x2))
new_esEs30(x0, x1, app(ty_Maybe, x2))
new_lt19(x0, x1, ty_Int)
new_esEs29(x0, x1, ty_Bool)
new_esEs23(x0, x1, ty_Float)
new_ltEs18(x0, x1, ty_Float)
new_ltEs17(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_compare9(x0, x1, ty_Bool)
new_esEs25(x0, x1, ty_Bool)
new_compare9(x0, x1, ty_Float)
new_esEs7(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs7(Right(x0), Right(x1), x2, ty_Char)
new_esEs29(x0, x1, ty_Double)
new_ltEs10(LT, LT)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_esEs14(:(x0, x1), :(x2, x3), x4)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs17(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs23(x0, x1, ty_Ordering)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt10(x0, x1, app(app(ty_Either, x2), x3))
new_lt4(x0, x1)
new_esEs9(Double(x0, x1), Double(x2, x3))
new_esEs5(@2(x0, x1), @2(x2, x3), x4, x5)
new_lt20(x0, x1, ty_Double)
new_esEs27(x0, x1, ty_@0)
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs30(x0, x1, ty_Integer)
new_ltEs18(x0, x1, ty_Double)
new_ltEs6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs23(x0, x1, ty_Char)
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs18(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_esEs8(GT, GT)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_ltEs18(x0, x1, app(ty_[], x2))
new_ltEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs17(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs22(x0, x1, ty_Ordering)
new_compare25(x0, x1, True, x2, x3, x4)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs24(x0, x1, ty_Char)
new_ltEs7(Just(x0), Just(x1), app(ty_[], x2))
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_esEs22(x0, x1, app(ty_[], x2))
new_compare6(Integer(x0), Integer(x1))
new_esEs29(x0, x1, ty_@0)
new_esEs8(LT, LT)
new_primMulNat0(Succ(x0), Succ(x1))
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs7(Just(x0), Just(x1), ty_Integer)
new_ltEs12(x0, x1, x2)
new_ltEs20(x0, x1, ty_Double)
new_esEs21(x0, x1, ty_Double)
new_esEs17(False, False)
new_esEs21(x0, x1, ty_Integer)
new_primEqNat0(Succ(x0), Zero)
new_esEs26(x0, x1, ty_Bool)
new_ltEs5(False, False)
new_ltEs11(x0, x1, x2)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_esEs22(x0, x1, ty_Bool)
new_lt11(x0, x1, x2, x3)
new_esEs30(x0, x1, ty_Double)
new_esEs7(Right(x0), Right(x1), x2, ty_Integer)
new_esEs7(Left(x0), Left(x1), ty_Double, x2)
new_esEs7(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs20(x0, x1, ty_Float)
new_compare0(:(x0, x1), [], x2)
new_ltEs21(x0, x1, app(ty_Ratio, x2))
new_esEs27(x0, x1, ty_Ordering)
new_esEs24(x0, x1, ty_@0)
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_esEs7(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_compare9(x0, x1, app(ty_Maybe, x2))
new_esEs7(Left(x0), Left(x1), ty_@0, x2)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs7(Right(x0), Right(x1), x2, ty_Ordering)
new_lt7(x0, x1)
new_ltEs18(x0, x1, app(ty_Ratio, x2))
new_lt10(x0, x1, app(ty_[], x2))
new_compare211(x0, x1, True)
new_compare8(x0, x1, x2)
new_esEs7(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_primEqNat0(Zero, Zero)
new_compare9(x0, x1, ty_Integer)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_esEs21(x0, x1, ty_Bool)
new_lt10(x0, x1, ty_Integer)
new_esEs21(x0, x1, ty_Char)
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_esEs4(Just(x0), Just(x1), ty_Bool)
new_compare210(x0, x1, False, x2)
new_esEs14([], :(x0, x1), x2)
new_ltEs7(Just(x0), Just(x1), ty_Double)
new_esEs22(x0, x1, ty_Int)
new_lt20(x0, x1, ty_Float)
new_ltEs7(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_esEs7(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs4(Just(x0), Just(x1), ty_Ordering)
new_esEs25(x0, x1, ty_Float)
new_compare23(x0, x1, False, x2, x3)
new_esEs7(Left(x0), Left(x1), ty_Bool, x2)
new_primMulNat0(Zero, Zero)
new_ltEs18(x0, x1, ty_Int)
new_esEs21(x0, x1, ty_Float)
new_esEs7(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs20(x0, x1, ty_Ordering)
new_ltEs17(Left(x0), Left(x1), ty_Ordering, x2)
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_ltEs10(EQ, LT)
new_ltEs10(LT, EQ)
new_compare23(x0, x1, True, x2, x3)
new_ltEs21(x0, x1, ty_@0)
new_esEs21(x0, x1, app(ty_[], x2))
new_ltEs20(x0, x1, ty_@0)
new_ltEs17(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_esEs18(x0, x1, ty_Integer)
new_lt14(x0, x1, x2)
new_primCompAux00(x0, EQ)
new_compare10(x0, x1, True, x2, x3)
new_esEs13(:%(x0, x1), :%(x2, x3), x4)
new_compare210(x0, x1, True, x2)
new_pePe(True, x0)
new_esEs20(x0, x1, ty_Ordering)
new_ltEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, ty_Ordering)
new_esEs28(x0, x1, ty_Int)
new_esEs12(Char(x0), Char(x1))
new_lt19(x0, x1, ty_Char)
new_compare110(x0, x1, False)
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs4(Just(x0), Just(x1), ty_@0)
new_lt10(x0, x1, ty_Ordering)
new_esEs22(x0, x1, ty_Char)
new_esEs30(x0, x1, ty_Bool)
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs26(x0, x1, ty_@0)
new_esEs24(x0, x1, ty_Integer)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs25(x0, x1, ty_Ordering)
new_esEs4(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, app(ty_[], x2))
new_primCompAux00(x0, LT)
new_ltEs21(x0, x1, ty_Ordering)
new_ltEs19(x0, x1, ty_Integer)
new_ltEs17(Left(x0), Left(x1), ty_Bool, x2)
new_ltEs17(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs17(Left(x0), Left(x1), ty_Float, x2)
new_ltEs19(x0, x1, ty_Int)
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs25(x0, x1, ty_Double)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs7(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_ltEs20(x0, x1, ty_Bool)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_esEs27(x0, x1, ty_Double)
new_esEs26(x0, x1, ty_Integer)
new_esEs19(x0, x1, ty_Integer)
new_ltEs20(x0, x1, app(ty_[], x2))
new_esEs23(x0, x1, ty_Integer)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_compare13(x0, x1, x2, x3)
new_lt6(x0, x1)
new_compare0([], [], x0)
new_esEs4(Just(x0), Just(x1), app(ty_Maybe, x2))
new_compare9(x0, x1, ty_@0)
new_esEs4(Just(x0), Just(x1), ty_Double)
new_ltEs17(Right(x0), Right(x1), x2, ty_Float)
new_lt10(x0, x1, app(ty_Maybe, x2))
new_ltEs19(x0, x1, ty_Bool)
new_esEs28(x0, x1, ty_@0)
new_lt20(x0, x1, ty_Bool)
new_ltEs15(x0, x1)
new_lt10(x0, x1, app(app(ty_@2, x2), x3))
new_compare11(x0, x1, False)
new_lt10(x0, x1, ty_Double)
new_compare111(x0, x1, True, x2, x3)
new_lt19(x0, x1, ty_@0)
new_esEs30(x0, x1, app(ty_Ratio, x2))
new_ltEs18(x0, x1, ty_Char)
new_esEs4(Just(x0), Nothing, x1)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_compare25(x0, x1, False, x2, x3, x4)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_compare27(x0, x1)
new_primPlusNat1(Zero, Zero)
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_compare0(:(x0, x1), :(x2, x3), x4)
new_sr(x0, x1)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_esEs20(x0, x1, ty_@0)
new_esEs7(Left(x0), Left(x1), ty_Float, x2)
new_ltEs18(x0, x1, app(app(ty_Either, x2), x3))
new_esEs16(x0, x1)
new_esEs25(x0, x1, app(ty_[], x2))
new_esEs24(x0, x1, ty_Float)
new_esEs4(Nothing, Just(x0), x1)
new_compare9(x0, x1, ty_Ordering)
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare28(x0, x1, x2, x3)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_ltEs7(Just(x0), Just(x1), ty_Int)
new_esEs28(x0, x1, ty_Float)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, ty_@0)
new_ltEs18(x0, x1, ty_Ordering)
new_esEs23(x0, x1, ty_Int)
new_esEs7(Right(x0), Right(x1), x2, ty_Double)
new_compare10(x0, x1, False, x2, x3)
new_esEs26(x0, x1, ty_Double)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs24(x0, x1, ty_Bool)
new_esEs23(x0, x1, app(ty_[], x2))
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs21(x0, x1, ty_Float)
new_primMulInt(Pos(x0), Pos(x1))
new_ltEs7(Just(x0), Just(x1), ty_Char)
new_compare112(x0, x1, True, x2)
new_compare9(x0, x1, app(app(ty_Either, x2), x3))
new_primPlusNat0(Succ(x0), x1)
new_ltEs10(GT, LT)
new_ltEs10(LT, GT)
new_ltEs17(Right(x0), Right(x1), x2, ty_@0)
new_ltEs7(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_sr0(Integer(x0), Integer(x1))
new_esEs23(x0, x1, ty_Double)
new_compare9(x0, x1, app(ty_[], x2))
new_esEs25(x0, x1, ty_Integer)
new_esEs20(x0, x1, ty_Char)
new_ltEs7(Nothing, Just(x0), x1)
new_primEqNat0(Zero, Succ(x0))
new_esEs27(x0, x1, ty_Bool)
new_esEs30(x0, x1, ty_Int)
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare17(:%(x0, x1), :%(x2, x3), ty_Int)
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_lt9(x0, x1)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_ltEs20(x0, x1, ty_Integer)
new_primMulInt(Neg(x0), Neg(x1))
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_esEs4(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, ty_Char)
new_ltEs20(x0, x1, ty_Int)
new_compare211(x0, x1, False)
new_ltEs17(Left(x0), Left(x1), ty_Double, x2)
new_compare29(x0, x1, False, x2, x3)
new_ltEs9(x0, x1)
new_esEs7(Right(x0), Right(x1), x2, ty_Float)
new_ltEs17(Right(x0), Right(x1), x2, ty_Ordering)
new_lt10(x0, x1, ty_@0)
new_esEs30(x0, x1, ty_Ordering)
new_ltEs7(Just(x0), Nothing, x1)
new_esEs4(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_compare112(x0, x1, False, x2)
new_esEs29(x0, x1, ty_Char)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs18(x0, x1, ty_Integer)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_esEs27(x0, x1, ty_Float)
new_ltEs19(x0, x1, ty_Double)
new_ltEs21(x0, x1, ty_Double)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Neg(Zero), Neg(Zero))
new_ltEs19(x0, x1, ty_Ordering)
new_ltEs21(x0, x1, ty_Integer)
new_ltEs14(x0, x1)
new_ltEs17(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_ltEs7(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_compare29(x0, x1, True, x2, x3)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs24(x0, x1, ty_Ordering)
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs26(x0, x1, app(ty_[], x2))
new_ltEs17(Right(x0), Right(x1), x2, ty_Bool)
new_esEs29(x0, x1, ty_Ordering)
new_compare9(x0, x1, app(ty_Ratio, x2))
new_esEs30(x0, x1, ty_@0)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_compare7(@0, @0)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_esEs18(x0, x1, ty_Int)
new_ltEs17(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_lt19(x0, x1, app(ty_Maybe, x2))
new_primCompAux00(x0, GT)
new_ltEs21(x0, x1, ty_Int)
new_lt19(x0, x1, ty_Double)
new_esEs26(x0, x1, ty_Float)
new_esEs30(x0, x1, app(ty_[], x2))
new_ltEs7(Just(x0), Just(x1), ty_Ordering)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_esEs4(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs16(x0, x1)
new_esEs21(x0, x1, ty_@0)
new_compare18(x0, x1)
new_lt19(x0, x1, ty_Ordering)
new_esEs4(Nothing, Nothing, x0)
new_esEs30(x0, x1, ty_Char)
new_esEs7(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_ltEs21(x0, x1, app(app(ty_@2, x2), x3))
new_asAs(False, x0)
new_lt10(x0, x1, ty_Char)
new_esEs20(x0, x1, ty_Int)
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat1(Succ(x0), Zero)
new_esEs8(GT, EQ)
new_esEs8(EQ, GT)
new_esEs22(x0, x1, ty_Integer)
new_lt15(x0, x1, x2)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_compare17(:%(x0, x1), :%(x2, x3), ty_Integer)
new_esEs29(x0, x1, app(ty_[], x2))
new_ltEs20(x0, x1, ty_Float)
new_primPlusNat0(Zero, x0)
new_esEs20(x0, x1, ty_Integer)
new_compare26(Float(x0, x1), Float(x2, x3))
new_ltEs17(Left(x0), Left(x1), ty_Char, x2)
new_primCmpNat0(Zero, Zero)
new_lt10(x0, x1, ty_Bool)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_ltEs17(Left(x0), Left(x1), ty_Integer, x2)
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_compare111(x0, x1, False, x2, x3)
new_ltEs7(Nothing, Nothing, x0)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs15(@0, @0)
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_compare16(x0, x1)
new_compare9(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare9(x0, x1, app(app(ty_@2, x2), x3))
new_lt16(x0, x1, x2, x3, x4)
new_esEs23(x0, x1, ty_Bool)
new_primEqNat0(Succ(x0), Succ(x1))
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_esEs7(Left(x0), Left(x1), ty_Char, x2)
new_primCmpNat0(Zero, Succ(x0))
new_esEs27(x0, x1, ty_Integer)
new_esEs21(x0, x1, ty_Int)
new_esEs24(x0, x1, ty_Double)
new_esEs24(x0, x1, app(ty_[], x2))
new_esEs20(x0, x1, ty_Bool)
new_lt10(x0, x1, app(ty_Ratio, x2))
new_lt19(x0, x1, ty_Integer)
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_ltEs10(GT, GT)
new_esEs27(x0, x1, app(ty_[], x2))
new_ltEs7(Just(x0), Just(x1), ty_Float)
new_lt17(x0, x1)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_compare15(Double(x0, x1), Double(x2, x3))
new_esEs22(x0, x1, ty_Float)
new_lt13(x0, x1)
new_ltEs17(Right(x0), Right(x1), x2, ty_Double)
new_esEs30(x0, x1, app(app(ty_Either, x2), x3))
new_primCompAux0(x0, x1, x2, x3)
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_compare9(x0, x1, ty_Char)
new_ltEs5(True, True)
new_esEs7(Right(x0), Right(x1), x2, ty_@0)
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_compare14(Char(x0), Char(x1))
new_lt19(x0, x1, app(ty_Ratio, x2))
new_ltEs17(Right(x0), Right(x1), x2, ty_Integer)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_not(True)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_ltEs7(Just(x0), Just(x1), ty_@0)
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs28(x0, x1, ty_Double)
new_esEs26(x0, x1, ty_Ordering)
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs17(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs27(x0, x1, ty_Int)
new_esEs6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_lt10(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_not(False)
new_esEs4(Just(x0), Just(x1), ty_Integer)
new_ltEs17(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_lt20(x0, x1, ty_Char)
new_lt19(x0, x1, ty_Bool)
new_primCmpNat0(Succ(x0), Succ(x1))
new_ltEs10(EQ, GT)
new_ltEs10(GT, EQ)
new_esEs22(x0, x1, ty_Double)
new_esEs10(Float(x0, x1), Float(x2, x3))
new_esEs26(x0, x1, ty_Int)
new_esEs4(Just(x0), Just(x1), ty_Float)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_compare24(x0, x1, True)
new_ltEs17(Right(x0), Right(x1), x2, ty_Int)
new_esEs25(x0, x1, ty_@0)
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_compare9(x0, x1, ty_Int)
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs21(x0, x1, app(ty_[], x2))
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primMulNat0(Succ(x0), Zero)
new_esEs28(x0, x1, ty_Bool)
new_lt19(x0, x1, ty_Float)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs8(EQ, LT)
new_esEs8(LT, EQ)
new_lt20(x0, x1, ty_@0)
new_compare0([], :(x0, x1), x2)
new_lt19(x0, x1, app(ty_[], x2))
new_esEs7(Right(x0), Right(x1), x2, ty_Int)
new_esEs7(Left(x0), Left(x1), ty_Ordering, x2)
new_compare19(x0, x1, x2, x3, x4)
new_ltEs4(@2(x0, x1), @2(x2, x3), x4, x5)
new_lt8(x0, x1)
new_esEs25(x0, x1, ty_Int)
new_esEs4(Just(x0), Just(x1), app(ty_Ratio, x2))
new_ltEs7(Just(x0), Just(x1), ty_Bool)
new_compare12(x0, x1, False, x2, x3, x4)
new_esEs17(False, True)
new_esEs17(True, False)
new_ltEs17(Right(x0), Right(x1), x2, ty_Char)
new_esEs28(x0, x1, app(ty_[], x2))
new_compare110(x0, x1, True)
new_ltEs7(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs30(x0, x1, ty_Float)
new_ltEs8(x0, x1)
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_compare24(x0, x1, False)
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_esEs28(x0, x1, ty_Char)
new_esEs26(x0, x1, ty_Char)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare9(x0, x1, ty_Double)
new_ltEs17(Left(x0), Right(x1), x2, x3)
new_ltEs17(Right(x0), Left(x1), x2, x3)
new_esEs14([], [], x0)
new_primEqInt(Pos(Zero), Pos(Zero))
new_esEs17(True, True)
new_ltEs21(x0, x1, app(app(ty_Either, x2), x3))
new_lt12(x0, x1)
new_esEs29(x0, x1, ty_Integer)
new_ltEs18(x0, x1, app(ty_Maybe, x2))
new_ltEs21(x0, x1, ty_Char)
new_ltEs18(x0, x1, ty_@0)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs20(x0, x1, ty_Double)
new_lt10(x0, x1, ty_Float)
new_esEs25(x0, x1, ty_Char)
new_ltEs19(x0, x1, ty_Char)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs28(x0, x1, ty_Ordering)
new_esEs29(x0, x1, ty_Int)
new_ltEs17(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_ltEs5(True, False)
new_ltEs5(False, True)
new_ltEs19(x0, x1, app(ty_[], x2))
new_esEs19(x0, x1, ty_Int)
new_esEs24(x0, x1, ty_Int)
new_ltEs18(x0, x1, ty_Bool)
new_esEs4(Just(x0), Just(x1), ty_Char)
new_ltEs7(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs7(Right(x0), Left(x1), x2, x3)
new_esEs7(Left(x0), Right(x1), x2, x3)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, ty_Int)
new_pePe(False, x0)
new_esEs30(x0, x1, app(app(ty_@2, x2), x3))
new_esEs22(x0, x1, ty_@0)
new_esEs29(x0, x1, ty_Float)
new_ltEs19(x0, x1, ty_Float)
new_esEs14(:(x0, x1), [], x2)
new_esEs28(x0, x1, ty_Integer)
new_ltEs10(EQ, EQ)
new_esEs20(x0, x1, app(ty_[], x2))

We have to consider all minimal (P,Q,R)-chains.
We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.

new_ltEs21(x0, x1, ty_Bool)
new_ltEs21(x0, x1, app(ty_Maybe, x2))
new_esEs30(x0, x1, app(ty_Maybe, x2))
new_esEs30(x0, x1, ty_Integer)
new_ltEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs30(x0, x1, ty_Double)
new_ltEs21(x0, x1, app(ty_Ratio, x2))
new_ltEs21(x0, x1, ty_@0)
new_esEs30(x0, x1, ty_Bool)
new_esEs30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs21(x0, x1, ty_Ordering)
new_esEs30(x0, x1, app(ty_Ratio, x2))
new_ltEs21(x0, x1, ty_Float)
new_esEs30(x0, x1, ty_Int)
new_esEs30(x0, x1, ty_Ordering)
new_ltEs21(x0, x1, ty_Double)
new_ltEs21(x0, x1, ty_Integer)
new_esEs30(x0, x1, ty_@0)
new_ltEs21(x0, x1, ty_Int)
new_esEs30(x0, x1, app(ty_[], x2))
new_esEs30(x0, x1, ty_Char)
new_ltEs21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs30(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs21(x0, x1, app(ty_[], x2))
new_esEs30(x0, x1, ty_Float)
new_ltEs21(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs21(x0, x1, ty_Char)
new_esEs30(x0, x1, app(app(ty_@2, x2), x3))



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

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

new_insertBy0(vxw10, vxw11, vxw12, False, ba, bb) → new_insertBy00(vxw10, vxw11, vxw12, new_ltEs20(vxw11, vxw10, ba), ba, bb)
new_insertBy(Left(vxw30), :(Left(vxw400), vxw41), be, bf) → new_insertBy0(vxw400, vxw30, vxw41, new_esEs29(vxw30, vxw400, be), be, bf)
new_insertBy00(vxw28, vxw29, vxw30, False, bc, bd) → new_insertBy(Left(vxw29), vxw30, bc, bd)

The TRS R consists of the following rules:

new_esEs29(vxw30, vxw400, ty_Int) → new_esEs16(vxw30, vxw400)
new_esEs29(vxw30, vxw400, app(ty_[], bbd)) → new_esEs14(vxw30, vxw400, bbd)
new_esEs29(vxw30, vxw400, app(ty_Ratio, bbc)) → new_esEs13(vxw30, vxw400, bbc)
new_esEs29(vxw30, vxw400, ty_Double) → new_esEs9(vxw30, vxw400)
new_esEs29(vxw30, vxw400, app(app(ty_@2, baf), bag)) → new_esEs5(vxw30, vxw400, baf, bag)
new_esEs29(vxw30, vxw400, ty_Integer) → new_esEs11(vxw30, vxw400)
new_esEs29(vxw30, vxw400, ty_@0) → new_esEs15(vxw30, vxw400)
new_esEs29(vxw30, vxw400, ty_Bool) → new_esEs17(vxw30, vxw400)
new_esEs29(vxw30, vxw400, ty_Char) → new_esEs12(vxw30, vxw400)
new_esEs29(vxw30, vxw400, ty_Float) → new_esEs10(vxw30, vxw400)
new_esEs29(vxw30, vxw400, app(app(app(ty_@3, bah), bba), bbb)) → new_esEs6(vxw30, vxw400, bah, bba, bbb)
new_esEs29(vxw30, vxw400, app(app(ty_Either, ff), ed)) → new_esEs7(vxw30, vxw400, ff, ed)
new_esEs29(vxw30, vxw400, app(ty_Maybe, bbe)) → new_esEs4(vxw30, vxw400, bbe)
new_esEs29(vxw30, vxw400, ty_Ordering) → new_esEs8(vxw30, vxw400)
new_esEs8(LT, LT) → True
new_esEs8(GT, GT) → True
new_esEs8(LT, GT) → False
new_esEs8(GT, LT) → False
new_esEs8(EQ, EQ) → True
new_esEs8(LT, EQ) → False
new_esEs8(EQ, LT) → False
new_esEs8(EQ, GT) → False
new_esEs8(GT, EQ) → False
new_esEs4(Just(vxw300), Just(vxw4000), ty_Ordering) → new_esEs8(vxw300, vxw4000)
new_esEs4(Just(vxw300), Nothing, bbe) → False
new_esEs4(Nothing, Just(vxw4000), bbe) → False
new_esEs4(Just(vxw300), Just(vxw4000), ty_Char) → new_esEs12(vxw300, vxw4000)
new_esEs4(Just(vxw300), Just(vxw4000), app(app(app(ty_@3, cec), ced), cee)) → new_esEs6(vxw300, vxw4000, cec, ced, cee)
new_esEs4(Just(vxw300), Just(vxw4000), ty_Float) → new_esEs10(vxw300, vxw4000)
new_esEs4(Just(vxw300), Just(vxw4000), ty_Integer) → new_esEs11(vxw300, vxw4000)
new_esEs4(Just(vxw300), Just(vxw4000), ty_Bool) → new_esEs17(vxw300, vxw4000)
new_esEs7(Left(vxw300), Left(vxw4000), app(app(ty_Either, fc), fd), ed) → new_esEs7(vxw300, vxw4000, fc, fd)
new_esEs4(Just(vxw300), Just(vxw4000), app(app(ty_Either, cfa), cfb)) → new_esEs7(vxw300, vxw4000, cfa, cfb)
new_esEs4(Just(vxw300), Just(vxw4000), app(ty_Maybe, ceh)) → new_esEs4(vxw300, vxw4000, ceh)
new_esEs7(Right(vxw300), Right(vxw4000), ff, app(app(ty_Either, gg), gh)) → new_esEs7(vxw300, vxw4000, gg, gh)
new_esEs7(Left(vxw300), Left(vxw4000), app(ty_Maybe, fb), ed) → new_esEs4(vxw300, vxw4000, fb)
new_esEs7(Right(vxw300), Right(vxw4000), ff, app(ty_Maybe, gf)) → new_esEs4(vxw300, vxw4000, gf)
new_esEs4(Just(vxw300), Just(vxw4000), app(app(ty_@2, cea), ceb)) → new_esEs5(vxw300, vxw4000, cea, ceb)
new_esEs4(Just(vxw300), Just(vxw4000), ty_Int) → new_esEs16(vxw300, vxw4000)
new_esEs4(Just(vxw300), Just(vxw4000), ty_@0) → new_esEs15(vxw300, vxw4000)
new_esEs4(Nothing, Nothing, bbe) → True
new_esEs4(Just(vxw300), Just(vxw4000), app(ty_Ratio, cef)) → new_esEs13(vxw300, vxw4000, cef)
new_esEs4(Just(vxw300), Just(vxw4000), app(ty_[], ceg)) → new_esEs14(vxw300, vxw4000, ceg)
new_esEs4(Just(vxw300), Just(vxw4000), ty_Double) → new_esEs9(vxw300, vxw4000)
new_esEs9(Double(vxw300, vxw301), Double(vxw4000, vxw4001)) → new_esEs16(new_sr(vxw300, vxw4000), new_sr(vxw301, vxw4001))
new_sr(vxw300, vxw4000) → new_primMulInt(vxw300, vxw4000)
new_esEs16(vxw30, vxw400) → new_primEqInt(vxw30, vxw400)
new_primEqInt(Neg(Succ(vxw3000)), Neg(Succ(vxw40000))) → new_primEqNat0(vxw3000, vxw40000)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Succ(vxw3000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(vxw40000))) → False
new_primEqInt(Pos(Succ(vxw3000)), Pos(Succ(vxw40000))) → new_primEqNat0(vxw3000, vxw40000)
new_primEqInt(Pos(Succ(vxw3000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(vxw40000))) → False
new_primEqInt(Pos(Succ(vxw3000)), Neg(vxw4000)) → False
new_primEqInt(Neg(Succ(vxw3000)), Pos(vxw4000)) → False
new_primEqInt(Pos(Zero), Neg(Succ(vxw40000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(vxw40000))) → False
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqNat0(Zero, Zero) → True
new_primEqNat0(Succ(vxw3000), Succ(vxw40000)) → new_primEqNat0(vxw3000, vxw40000)
new_primEqNat0(Succ(vxw3000), Zero) → False
new_primEqNat0(Zero, Succ(vxw40000)) → False
new_primMulInt(Pos(vxw3000), Pos(vxw40000)) → Pos(new_primMulNat0(vxw3000, vxw40000))
new_primMulInt(Neg(vxw3000), Neg(vxw40000)) → Pos(new_primMulNat0(vxw3000, vxw40000))
new_primMulInt(Neg(vxw3000), Pos(vxw40000)) → Neg(new_primMulNat0(vxw3000, vxw40000))
new_primMulInt(Pos(vxw3000), Neg(vxw40000)) → Neg(new_primMulNat0(vxw3000, vxw40000))
new_primMulNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, Succ(vxw400000)) → Zero
new_primMulNat0(Succ(vxw30000), Zero) → Zero
new_primMulNat0(Succ(vxw30000), Succ(vxw400000)) → new_primPlusNat0(new_primMulNat0(vxw30000, Succ(vxw400000)), vxw400000)
new_primPlusNat0(Succ(vxw620), vxw400000) → Succ(Succ(new_primPlusNat1(vxw620, vxw400000)))
new_primPlusNat0(Zero, vxw400000) → Succ(vxw400000)
new_primPlusNat1(Zero, Succ(vxw4000000)) → Succ(vxw4000000)
new_primPlusNat1(Succ(vxw6200), Zero) → Succ(vxw6200)
new_primPlusNat1(Succ(vxw6200), Succ(vxw4000000)) → Succ(Succ(new_primPlusNat1(vxw6200, vxw4000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_esEs14([], [], bbd) → True
new_esEs14([], :(vxw4000, vxw4001), bbd) → False
new_esEs14(:(vxw300, vxw301), [], bbd) → False
new_esEs14(:(vxw300, vxw301), :(vxw4000, vxw4001), bbd) → new_asAs(new_esEs24(vxw300, vxw4000, bbd), new_esEs14(vxw301, vxw4001, bbd))
new_esEs24(vxw300, vxw4000, app(ty_Maybe, cgb)) → new_esEs4(vxw300, vxw4000, cgb)
new_esEs24(vxw300, vxw4000, app(app(ty_@2, cfc), cfd)) → new_esEs5(vxw300, vxw4000, cfc, cfd)
new_esEs24(vxw300, vxw4000, app(app(ty_Either, cgc), cgd)) → new_esEs7(vxw300, vxw4000, cgc, cgd)
new_esEs24(vxw300, vxw4000, ty_Int) → new_esEs16(vxw300, vxw4000)
new_esEs24(vxw300, vxw4000, ty_Bool) → new_esEs17(vxw300, vxw4000)
new_esEs24(vxw300, vxw4000, ty_Char) → new_esEs12(vxw300, vxw4000)
new_esEs24(vxw300, vxw4000, app(app(app(ty_@3, cfe), cff), cfg)) → new_esEs6(vxw300, vxw4000, cfe, cff, cfg)
new_esEs24(vxw300, vxw4000, ty_Ordering) → new_esEs8(vxw300, vxw4000)
new_esEs24(vxw300, vxw4000, ty_@0) → new_esEs15(vxw300, vxw4000)
new_esEs24(vxw300, vxw4000, app(ty_Ratio, cfh)) → new_esEs13(vxw300, vxw4000, cfh)
new_esEs24(vxw300, vxw4000, ty_Double) → new_esEs9(vxw300, vxw4000)
new_esEs24(vxw300, vxw4000, app(ty_[], cga)) → new_esEs14(vxw300, vxw4000, cga)
new_esEs24(vxw300, vxw4000, ty_Integer) → new_esEs11(vxw300, vxw4000)
new_esEs24(vxw300, vxw4000, ty_Float) → new_esEs10(vxw300, vxw4000)
new_asAs(False, vxw53) → False
new_asAs(True, vxw53) → vxw53
new_esEs10(Float(vxw300, vxw301), Float(vxw4000, vxw4001)) → new_esEs16(new_sr(vxw300, vxw4000), new_sr(vxw301, vxw4001))
new_esEs11(Integer(vxw300), Integer(vxw4000)) → new_primEqInt(vxw300, vxw4000)
new_esEs13(:%(vxw300, vxw301), :%(vxw4000, vxw4001), bbc) → new_asAs(new_esEs19(vxw300, vxw4000, bbc), new_esEs18(vxw301, vxw4001, bbc))
new_esEs19(vxw300, vxw4000, ty_Integer) → new_esEs11(vxw300, vxw4000)
new_esEs19(vxw300, vxw4000, ty_Int) → new_esEs16(vxw300, vxw4000)
new_esEs18(vxw301, vxw4001, ty_Integer) → new_esEs11(vxw301, vxw4001)
new_esEs18(vxw301, vxw4001, ty_Int) → new_esEs16(vxw301, vxw4001)
new_esEs15(@0, @0) → True
new_esEs6(@3(vxw300, vxw301, vxw302), @3(vxw4000, vxw4001, vxw4002), bah, bba, bbb) → new_asAs(new_esEs22(vxw300, vxw4000, bah), new_asAs(new_esEs21(vxw301, vxw4001, bba), new_esEs20(vxw302, vxw4002, bbb)))
new_esEs22(vxw300, vxw4000, ty_Char) → new_esEs12(vxw300, vxw4000)
new_esEs22(vxw300, vxw4000, app(app(ty_@2, bge), bgf)) → new_esEs5(vxw300, vxw4000, bge, bgf)
new_esEs22(vxw300, vxw4000, app(ty_[], bhc)) → new_esEs14(vxw300, vxw4000, bhc)
new_esEs22(vxw300, vxw4000, app(app(ty_Either, bhe), bhf)) → new_esEs7(vxw300, vxw4000, bhe, bhf)
new_esEs22(vxw300, vxw4000, ty_@0) → new_esEs15(vxw300, vxw4000)
new_esEs22(vxw300, vxw4000, ty_Ordering) → new_esEs8(vxw300, vxw4000)
new_esEs22(vxw300, vxw4000, ty_Double) → new_esEs9(vxw300, vxw4000)
new_esEs22(vxw300, vxw4000, app(app(app(ty_@3, bgg), bgh), bha)) → new_esEs6(vxw300, vxw4000, bgg, bgh, bha)
new_esEs22(vxw300, vxw4000, app(ty_Maybe, bhd)) → new_esEs4(vxw300, vxw4000, bhd)
new_esEs22(vxw300, vxw4000, app(ty_Ratio, bhb)) → new_esEs13(vxw300, vxw4000, bhb)
new_esEs22(vxw300, vxw4000, ty_Bool) → new_esEs17(vxw300, vxw4000)
new_esEs22(vxw300, vxw4000, ty_Integer) → new_esEs11(vxw300, vxw4000)
new_esEs22(vxw300, vxw4000, ty_Float) → new_esEs10(vxw300, vxw4000)
new_esEs22(vxw300, vxw4000, ty_Int) → new_esEs16(vxw300, vxw4000)
new_esEs21(vxw301, vxw4001, ty_Bool) → new_esEs17(vxw301, vxw4001)
new_esEs21(vxw301, vxw4001, app(ty_Ratio, bfh)) → new_esEs13(vxw301, vxw4001, bfh)
new_esEs21(vxw301, vxw4001, ty_Char) → new_esEs12(vxw301, vxw4001)
new_esEs21(vxw301, vxw4001, ty_@0) → new_esEs15(vxw301, vxw4001)
new_esEs21(vxw301, vxw4001, ty_Integer) → new_esEs11(vxw301, vxw4001)
new_esEs21(vxw301, vxw4001, ty_Float) → new_esEs10(vxw301, vxw4001)
new_esEs21(vxw301, vxw4001, app(ty_[], bga)) → new_esEs14(vxw301, vxw4001, bga)
new_esEs21(vxw301, vxw4001, app(app(ty_@2, bfc), bfd)) → new_esEs5(vxw301, vxw4001, bfc, bfd)
new_esEs21(vxw301, vxw4001, app(app(ty_Either, bgc), bgd)) → new_esEs7(vxw301, vxw4001, bgc, bgd)
new_esEs21(vxw301, vxw4001, app(ty_Maybe, bgb)) → new_esEs4(vxw301, vxw4001, bgb)
new_esEs21(vxw301, vxw4001, ty_Double) → new_esEs9(vxw301, vxw4001)
new_esEs21(vxw301, vxw4001, ty_Ordering) → new_esEs8(vxw301, vxw4001)
new_esEs21(vxw301, vxw4001, ty_Int) → new_esEs16(vxw301, vxw4001)
new_esEs21(vxw301, vxw4001, app(app(app(ty_@3, bfe), bff), bfg)) → new_esEs6(vxw301, vxw4001, bfe, bff, bfg)
new_esEs20(vxw302, vxw4002, app(ty_Maybe, beh)) → new_esEs4(vxw302, vxw4002, beh)
new_esEs20(vxw302, vxw4002, app(ty_Ratio, bef)) → new_esEs13(vxw302, vxw4002, bef)
new_esEs20(vxw302, vxw4002, ty_Int) → new_esEs16(vxw302, vxw4002)
new_esEs20(vxw302, vxw4002, ty_Char) → new_esEs12(vxw302, vxw4002)
new_esEs20(vxw302, vxw4002, app(app(ty_@2, bea), beb)) → new_esEs5(vxw302, vxw4002, bea, beb)
new_esEs20(vxw302, vxw4002, ty_Integer) → new_esEs11(vxw302, vxw4002)
new_esEs20(vxw302, vxw4002, app(app(app(ty_@3, bec), bed), bee)) → new_esEs6(vxw302, vxw4002, bec, bed, bee)
new_esEs20(vxw302, vxw4002, ty_Bool) → new_esEs17(vxw302, vxw4002)
new_esEs20(vxw302, vxw4002, ty_Ordering) → new_esEs8(vxw302, vxw4002)
new_esEs20(vxw302, vxw4002, ty_Float) → new_esEs10(vxw302, vxw4002)
new_esEs20(vxw302, vxw4002, ty_@0) → new_esEs15(vxw302, vxw4002)
new_esEs20(vxw302, vxw4002, app(app(ty_Either, bfa), bfb)) → new_esEs7(vxw302, vxw4002, bfa, bfb)
new_esEs20(vxw302, vxw4002, ty_Double) → new_esEs9(vxw302, vxw4002)
new_esEs20(vxw302, vxw4002, app(ty_[], beg)) → new_esEs14(vxw302, vxw4002, beg)
new_esEs7(Right(vxw300), Right(vxw4000), ff, ty_Ordering) → new_esEs8(vxw300, vxw4000)
new_esEs7(Left(vxw300), Right(vxw4000), ff, ed) → False
new_esEs7(Right(vxw300), Left(vxw4000), ff, ed) → False
new_esEs7(Left(vxw300), Left(vxw4000), ty_Double, ed) → new_esEs9(vxw300, vxw4000)
new_esEs7(Right(vxw300), Right(vxw4000), ff, ty_Double) → new_esEs9(vxw300, vxw4000)
new_esEs7(Right(vxw300), Right(vxw4000), ff, app(app(ty_@2, fg), fh)) → new_esEs5(vxw300, vxw4000, fg, fh)
new_esEs7(Left(vxw300), Left(vxw4000), ty_Integer, ed) → new_esEs11(vxw300, vxw4000)
new_esEs7(Left(vxw300), Left(vxw4000), app(app(ty_@2, eb), ec), ed) → new_esEs5(vxw300, vxw4000, eb, ec)
new_esEs7(Left(vxw300), Left(vxw4000), ty_Ordering, ed) → new_esEs8(vxw300, vxw4000)
new_esEs7(Right(vxw300), Right(vxw4000), ff, app(app(app(ty_@3, ga), gb), gc)) → new_esEs6(vxw300, vxw4000, ga, gb, gc)
new_esEs7(Right(vxw300), Right(vxw4000), ff, ty_Char) → new_esEs12(vxw300, vxw4000)
new_esEs7(Right(vxw300), Right(vxw4000), ff, ty_@0) → new_esEs15(vxw300, vxw4000)
new_esEs7(Right(vxw300), Right(vxw4000), ff, app(ty_Ratio, gd)) → new_esEs13(vxw300, vxw4000, gd)
new_esEs7(Left(vxw300), Left(vxw4000), app(ty_Ratio, eh), ed) → new_esEs13(vxw300, vxw4000, eh)
new_esEs7(Left(vxw300), Left(vxw4000), ty_@0, ed) → new_esEs15(vxw300, vxw4000)
new_esEs7(Right(vxw300), Right(vxw4000), ff, ty_Float) → new_esEs10(vxw300, vxw4000)
new_esEs7(Left(vxw300), Left(vxw4000), ty_Int, ed) → new_esEs16(vxw300, vxw4000)
new_esEs7(Right(vxw300), Right(vxw4000), ff, ty_Integer) → new_esEs11(vxw300, vxw4000)
new_esEs7(Right(vxw300), Right(vxw4000), ff, ty_Bool) → new_esEs17(vxw300, vxw4000)
new_esEs7(Left(vxw300), Left(vxw4000), ty_Char, ed) → new_esEs12(vxw300, vxw4000)
new_esEs7(Right(vxw300), Right(vxw4000), ff, app(ty_[], ge)) → new_esEs14(vxw300, vxw4000, ge)
new_esEs7(Left(vxw300), Left(vxw4000), ty_Float, ed) → new_esEs10(vxw300, vxw4000)
new_esEs7(Left(vxw300), Left(vxw4000), app(app(app(ty_@3, ee), ef), eg), ed) → new_esEs6(vxw300, vxw4000, ee, ef, eg)
new_esEs7(Right(vxw300), Right(vxw4000), ff, ty_Int) → new_esEs16(vxw300, vxw4000)
new_esEs7(Left(vxw300), Left(vxw4000), ty_Bool, ed) → new_esEs17(vxw300, vxw4000)
new_esEs7(Left(vxw300), Left(vxw4000), app(ty_[], fa), ed) → new_esEs14(vxw300, vxw4000, fa)
new_esEs17(True, True) → True
new_esEs17(False, False) → True
new_esEs17(False, True) → False
new_esEs17(True, False) → False
new_esEs12(Char(vxw300), Char(vxw4000)) → new_primEqNat0(vxw300, vxw4000)
new_esEs5(@2(vxw300, vxw301), @2(vxw4000, vxw4001), baf, bag) → new_asAs(new_esEs28(vxw300, vxw4000, baf), new_esEs27(vxw301, vxw4001, bag))
new_esEs28(vxw300, vxw4000, ty_Integer) → new_esEs11(vxw300, vxw4000)
new_esEs28(vxw300, vxw4000, ty_@0) → new_esEs15(vxw300, vxw4000)
new_esEs28(vxw300, vxw4000, ty_Float) → new_esEs10(vxw300, vxw4000)
new_esEs28(vxw300, vxw4000, app(ty_Maybe, ded)) → new_esEs4(vxw300, vxw4000, ded)
new_esEs28(vxw300, vxw4000, ty_Int) → new_esEs16(vxw300, vxw4000)
new_esEs28(vxw300, vxw4000, app(ty_[], dec)) → new_esEs14(vxw300, vxw4000, dec)
new_esEs28(vxw300, vxw4000, ty_Ordering) → new_esEs8(vxw300, vxw4000)
new_esEs28(vxw300, vxw4000, app(app(ty_Either, dee), def)) → new_esEs7(vxw300, vxw4000, dee, def)
new_esEs28(vxw300, vxw4000, app(app(ty_@2, dde), ddf)) → new_esEs5(vxw300, vxw4000, dde, ddf)
new_esEs28(vxw300, vxw4000, ty_Double) → new_esEs9(vxw300, vxw4000)
new_esEs28(vxw300, vxw4000, app(app(app(ty_@3, ddg), ddh), dea)) → new_esEs6(vxw300, vxw4000, ddg, ddh, dea)
new_esEs28(vxw300, vxw4000, ty_Bool) → new_esEs17(vxw300, vxw4000)
new_esEs28(vxw300, vxw4000, app(ty_Ratio, deb)) → new_esEs13(vxw300, vxw4000, deb)
new_esEs28(vxw300, vxw4000, ty_Char) → new_esEs12(vxw300, vxw4000)
new_esEs27(vxw301, vxw4001, ty_Bool) → new_esEs17(vxw301, vxw4001)
new_esEs27(vxw301, vxw4001, app(app(ty_Either, ddc), ddd)) → new_esEs7(vxw301, vxw4001, ddc, ddd)
new_esEs27(vxw301, vxw4001, app(ty_Ratio, dch)) → new_esEs13(vxw301, vxw4001, dch)
new_esEs27(vxw301, vxw4001, ty_Char) → new_esEs12(vxw301, vxw4001)
new_esEs27(vxw301, vxw4001, ty_Ordering) → new_esEs8(vxw301, vxw4001)
new_esEs27(vxw301, vxw4001, ty_Double) → new_esEs9(vxw301, vxw4001)
new_esEs27(vxw301, vxw4001, ty_Float) → new_esEs10(vxw301, vxw4001)
new_esEs27(vxw301, vxw4001, ty_@0) → new_esEs15(vxw301, vxw4001)
new_esEs27(vxw301, vxw4001, app(app(app(ty_@3, dce), dcf), dcg)) → new_esEs6(vxw301, vxw4001, dce, dcf, dcg)
new_esEs27(vxw301, vxw4001, app(app(ty_@2, dcc), dcd)) → new_esEs5(vxw301, vxw4001, dcc, dcd)
new_esEs27(vxw301, vxw4001, app(ty_Maybe, ddb)) → new_esEs4(vxw301, vxw4001, ddb)
new_esEs27(vxw301, vxw4001, ty_Int) → new_esEs16(vxw301, vxw4001)
new_esEs27(vxw301, vxw4001, app(ty_[], dda)) → new_esEs14(vxw301, vxw4001, dda)
new_esEs27(vxw301, vxw4001, ty_Integer) → new_esEs11(vxw301, vxw4001)
new_ltEs20(vxw11, vxw10, ty_Ordering) → new_ltEs10(vxw11, vxw10)
new_ltEs20(vxw11, vxw10, ty_Bool) → new_ltEs5(vxw11, vxw10)
new_ltEs20(vxw11, vxw10, ty_Double) → new_ltEs9(vxw11, vxw10)
new_ltEs20(vxw11, vxw10, app(ty_[], cc)) → new_ltEs12(vxw11, vxw10, cc)
new_ltEs20(vxw11, vxw10, app(app(ty_@2, bdb), bdc)) → new_ltEs4(vxw11, vxw10, bdb, bdc)
new_ltEs20(vxw11, vxw10, app(ty_Ratio, bda)) → new_ltEs11(vxw11, vxw10, bda)
new_ltEs20(vxw11, vxw10, ty_Int) → new_ltEs16(vxw11, vxw10)
new_ltEs20(vxw11, vxw10, ty_Integer) → new_ltEs13(vxw11, vxw10)
new_ltEs20(vxw11, vxw10, ty_@0) → new_ltEs14(vxw11, vxw10)
new_ltEs20(vxw11, vxw10, ty_Float) → new_ltEs15(vxw11, vxw10)
new_ltEs20(vxw11, vxw10, app(app(app(ty_@3, bdd), bde), bdf)) → new_ltEs6(vxw11, vxw10, bdd, bde, bdf)
new_ltEs20(vxw11, vxw10, app(app(ty_Either, bdg), bdh)) → new_ltEs17(vxw11, vxw10, bdg, bdh)
new_ltEs20(vxw11, vxw10, ty_Char) → new_ltEs8(vxw11, vxw10)
new_ltEs20(vxw11, vxw10, app(ty_Maybe, bbf)) → new_ltEs7(vxw11, vxw10, bbf)
new_ltEs7(Just(vxw110), Just(vxw100), ty_Bool) → new_ltEs5(vxw110, vxw100)
new_ltEs7(Just(vxw110), Just(vxw100), app(app(app(ty_@3, bcd), bce), bcf)) → new_ltEs6(vxw110, vxw100, bcd, bce, bcf)
new_ltEs7(Just(vxw110), Just(vxw100), app(app(ty_@2, bbh), bca)) → new_ltEs4(vxw110, vxw100, bbh, bca)
new_ltEs7(Just(vxw110), Just(vxw100), ty_Ordering) → new_ltEs10(vxw110, vxw100)
new_ltEs7(Just(vxw110), Just(vxw100), ty_Integer) → new_ltEs13(vxw110, vxw100)
new_ltEs7(Just(vxw110), Just(vxw100), ty_Int) → new_ltEs16(vxw110, vxw100)
new_ltEs7(Nothing, Just(vxw100), bbf) → True
new_ltEs7(Just(vxw110), Just(vxw100), ty_Float) → new_ltEs15(vxw110, vxw100)
new_ltEs7(Just(vxw110), Just(vxw100), ty_Double) → new_ltEs9(vxw110, vxw100)
new_ltEs7(Nothing, Nothing, bbf) → True
new_ltEs7(Just(vxw110), Just(vxw100), app(ty_[], bcc)) → new_ltEs12(vxw110, vxw100, bcc)
new_ltEs7(Just(vxw110), Just(vxw100), ty_Char) → new_ltEs8(vxw110, vxw100)
new_ltEs7(Just(vxw110), Just(vxw100), ty_@0) → new_ltEs14(vxw110, vxw100)
new_ltEs7(Just(vxw110), Nothing, bbf) → False
new_ltEs7(Just(vxw110), Just(vxw100), app(ty_Ratio, bcb)) → new_ltEs11(vxw110, vxw100, bcb)
new_ltEs17(Left(vxw110), Left(vxw100), app(app(ty_Either, cag), cah), bdh) → new_ltEs17(vxw110, vxw100, cag, cah)
new_ltEs17(Right(vxw110), Right(vxw100), bdg, app(app(ty_Either, cca), ccb)) → new_ltEs17(vxw110, vxw100, cca, ccb)
new_ltEs7(Just(vxw110), Just(vxw100), app(ty_Maybe, bbg)) → new_ltEs7(vxw110, vxw100, bbg)
new_ltEs7(Just(vxw110), Just(vxw100), app(app(ty_Either, bcg), bch)) → new_ltEs17(vxw110, vxw100, bcg, bch)
new_ltEs17(Right(vxw110), Right(vxw100), bdg, app(ty_Maybe, cba)) → new_ltEs7(vxw110, vxw100, cba)
new_ltEs17(Left(vxw110), Left(vxw100), app(ty_Maybe, bhg), bdh) → new_ltEs7(vxw110, vxw100, bhg)
new_ltEs17(Right(vxw110), Right(vxw100), bdg, app(ty_Ratio, cbd)) → new_ltEs11(vxw110, vxw100, cbd)
new_ltEs17(Left(vxw110), Left(vxw100), app(ty_Ratio, cab), bdh) → new_ltEs11(vxw110, vxw100, cab)
new_ltEs17(Left(vxw110), Left(vxw100), ty_Integer, bdh) → new_ltEs13(vxw110, vxw100)
new_ltEs17(Right(vxw110), Right(vxw100), bdg, ty_Integer) → new_ltEs13(vxw110, vxw100)
new_ltEs17(Left(vxw110), Left(vxw100), ty_Bool, bdh) → new_ltEs5(vxw110, vxw100)
new_ltEs17(Left(vxw110), Left(vxw100), ty_Double, bdh) → new_ltEs9(vxw110, vxw100)
new_ltEs17(Left(vxw110), Left(vxw100), ty_Ordering, bdh) → new_ltEs10(vxw110, vxw100)
new_ltEs17(Right(vxw110), Left(vxw100), bdg, bdh) → False
new_ltEs17(Right(vxw110), Right(vxw100), bdg, ty_Ordering) → new_ltEs10(vxw110, vxw100)
new_ltEs17(Right(vxw110), Right(vxw100), bdg, ty_Int) → new_ltEs16(vxw110, vxw100)
new_ltEs17(Left(vxw110), Left(vxw100), app(app(ty_@2, bhh), caa), bdh) → new_ltEs4(vxw110, vxw100, bhh, caa)
new_ltEs17(Left(vxw110), Left(vxw100), app(app(app(ty_@3, cad), cae), caf), bdh) → new_ltEs6(vxw110, vxw100, cad, cae, caf)
new_ltEs17(Left(vxw110), Left(vxw100), app(ty_[], cac), bdh) → new_ltEs12(vxw110, vxw100, cac)
new_ltEs17(Left(vxw110), Left(vxw100), ty_Float, bdh) → new_ltEs15(vxw110, vxw100)
new_ltEs17(Right(vxw110), Right(vxw100), bdg, ty_@0) → new_ltEs14(vxw110, vxw100)
new_ltEs17(Left(vxw110), Left(vxw100), ty_Char, bdh) → new_ltEs8(vxw110, vxw100)
new_ltEs17(Left(vxw110), Left(vxw100), ty_@0, bdh) → new_ltEs14(vxw110, vxw100)
new_ltEs17(Right(vxw110), Right(vxw100), bdg, ty_Float) → new_ltEs15(vxw110, vxw100)
new_ltEs17(Left(vxw110), Right(vxw100), bdg, bdh) → True
new_ltEs17(Right(vxw110), Right(vxw100), bdg, app(ty_[], cbe)) → new_ltEs12(vxw110, vxw100, cbe)
new_ltEs17(Right(vxw110), Right(vxw100), bdg, ty_Double) → new_ltEs9(vxw110, vxw100)
new_ltEs17(Right(vxw110), Right(vxw100), bdg, ty_Char) → new_ltEs8(vxw110, vxw100)
new_ltEs17(Left(vxw110), Left(vxw100), ty_Int, bdh) → new_ltEs16(vxw110, vxw100)
new_ltEs17(Right(vxw110), Right(vxw100), bdg, app(app(app(ty_@3, cbf), cbg), cbh)) → new_ltEs6(vxw110, vxw100, cbf, cbg, cbh)
new_ltEs17(Right(vxw110), Right(vxw100), bdg, app(app(ty_@2, cbb), cbc)) → new_ltEs4(vxw110, vxw100, cbb, cbc)
new_ltEs17(Right(vxw110), Right(vxw100), bdg, ty_Bool) → new_ltEs5(vxw110, vxw100)
new_ltEs5(True, False) → False
new_ltEs5(True, True) → True
new_ltEs5(False, False) → True
new_ltEs5(False, True) → True
new_ltEs4(@2(vxw110, vxw111), @2(vxw100, vxw101), bdb, bdc) → new_pePe(new_lt10(vxw110, vxw100, bdb), new_asAs(new_esEs23(vxw110, vxw100, bdb), new_ltEs18(vxw111, vxw101, bdc)))
new_lt10(vxw110, vxw100, ty_Double) → new_lt13(vxw110, vxw100)
new_lt10(vxw110, vxw100, ty_Bool) → new_lt9(vxw110, vxw100)
new_lt10(vxw110, vxw100, app(app(ty_@2, dh), ea)) → new_lt11(vxw110, vxw100, dh, ea)
new_lt10(vxw110, vxw100, ty_Char) → new_lt12(vxw110, vxw100)
new_lt10(vxw110, vxw100, app(app(ty_Either, cdg), cdh)) → new_lt18(vxw110, vxw100, cdg, cdh)
new_lt10(vxw110, vxw100, app(app(app(ty_@3, ha), hb), hc)) → new_lt16(vxw110, vxw100, ha, hb, hc)
new_lt10(vxw110, vxw100, ty_Float) → new_lt17(vxw110, vxw100)
new_lt10(vxw110, vxw100, app(ty_Ratio, cde)) → new_lt14(vxw110, vxw100, cde)
new_lt10(vxw110, vxw100, app(ty_Maybe, cd)) → new_lt5(vxw110, vxw100, cd)
new_lt10(vxw110, vxw100, app(ty_[], cdf)) → new_lt15(vxw110, vxw100, cdf)
new_lt10(vxw110, vxw100, ty_@0) → new_lt8(vxw110, vxw100)
new_lt10(vxw110, vxw100, ty_Int) → new_lt7(vxw110, vxw100)
new_lt10(vxw110, vxw100, ty_Integer) → new_lt4(vxw110, vxw100)
new_lt10(vxw110, vxw100, ty_Ordering) → new_lt6(vxw110, vxw100)
new_esEs23(vxw110, vxw100, app(app(ty_Either, cdg), cdh)) → new_esEs7(vxw110, vxw100, cdg, cdh)
new_esEs23(vxw110, vxw100, app(ty_Ratio, cde)) → new_esEs13(vxw110, vxw100, cde)
new_esEs23(vxw110, vxw100, ty_Double) → new_esEs9(vxw110, vxw100)
new_esEs23(vxw110, vxw100, app(ty_Maybe, cd)) → new_esEs4(vxw110, vxw100, cd)
new_esEs23(vxw110, vxw100, ty_Ordering) → new_esEs8(vxw110, vxw100)
new_esEs23(vxw110, vxw100, ty_Float) → new_esEs10(vxw110, vxw100)
new_esEs23(vxw110, vxw100, ty_Integer) → new_esEs11(vxw110, vxw100)
new_esEs23(vxw110, vxw100, app(app(ty_@2, dh), ea)) → new_esEs5(vxw110, vxw100, dh, ea)
new_esEs23(vxw110, vxw100, ty_@0) → new_esEs15(vxw110, vxw100)
new_esEs23(vxw110, vxw100, app(ty_[], cdf)) → new_esEs14(vxw110, vxw100, cdf)
new_esEs23(vxw110, vxw100, ty_Bool) → new_esEs17(vxw110, vxw100)
new_esEs23(vxw110, vxw100, app(app(app(ty_@3, ha), hb), hc)) → new_esEs6(vxw110, vxw100, ha, hb, hc)
new_esEs23(vxw110, vxw100, ty_Char) → new_esEs12(vxw110, vxw100)
new_esEs23(vxw110, vxw100, ty_Int) → new_esEs16(vxw110, vxw100)
new_ltEs18(vxw111, vxw101, ty_Float) → new_ltEs15(vxw111, vxw101)
new_ltEs18(vxw111, vxw101, ty_Char) → new_ltEs8(vxw111, vxw101)
new_ltEs18(vxw111, vxw101, ty_Int) → new_ltEs16(vxw111, vxw101)
new_ltEs18(vxw111, vxw101, app(app(ty_Either, cdc), cdd)) → new_ltEs17(vxw111, vxw101, cdc, cdd)
new_ltEs18(vxw111, vxw101, ty_@0) → new_ltEs14(vxw111, vxw101)
new_ltEs18(vxw111, vxw101, ty_Integer) → new_ltEs13(vxw111, vxw101)
new_ltEs18(vxw111, vxw101, ty_Bool) → new_ltEs5(vxw111, vxw101)
new_ltEs18(vxw111, vxw101, app(ty_Ratio, ccf)) → new_ltEs11(vxw111, vxw101, ccf)
new_ltEs18(vxw111, vxw101, app(app(app(ty_@3, cch), cda), cdb)) → new_ltEs6(vxw111, vxw101, cch, cda, cdb)
new_ltEs18(vxw111, vxw101, app(ty_Maybe, ccc)) → new_ltEs7(vxw111, vxw101, ccc)
new_ltEs18(vxw111, vxw101, app(ty_[], ccg)) → new_ltEs12(vxw111, vxw101, ccg)
new_ltEs18(vxw111, vxw101, app(app(ty_@2, ccd), cce)) → new_ltEs4(vxw111, vxw101, ccd, cce)
new_ltEs18(vxw111, vxw101, ty_Double) → new_ltEs9(vxw111, vxw101)
new_ltEs18(vxw111, vxw101, ty_Ordering) → new_ltEs10(vxw111, vxw101)
new_pePe(False, vxw60) → vxw60
new_pePe(True, vxw60) → True
new_ltEs10(EQ, GT) → True
new_ltEs10(GT, EQ) → False
new_ltEs10(LT, EQ) → True
new_ltEs10(GT, GT) → True
new_ltEs10(LT, GT) → True
new_ltEs10(EQ, EQ) → True
new_ltEs10(LT, LT) → True
new_ltEs10(EQ, LT) → False
new_ltEs10(GT, LT) → False
new_ltEs9(vxw11, vxw10) → new_not(new_esEs8(new_compare15(vxw11, vxw10), GT))
new_compare15(Double(vxw110, vxw111), Double(vxw100, vxw101)) → new_compare27(new_sr(vxw110, vxw100), new_sr(vxw111, vxw101))
new_not(False) → True
new_not(True) → False
new_compare27(vxw11, vxw10) → new_primCmpInt(vxw11, vxw10)
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(vxw1100)), Neg(vxw100)) → new_primCmpNat0(vxw100, Succ(vxw1100))
new_primCmpInt(Neg(Zero), Pos(Succ(vxw1000))) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(vxw1000))) → new_primCmpNat0(Zero, Succ(vxw1000))
new_primCmpInt(Pos(Succ(vxw1100)), Pos(vxw100)) → new_primCmpNat0(Succ(vxw1100), vxw100)
new_primCmpInt(Pos(Succ(vxw1100)), Neg(vxw100)) → GT
new_primCmpInt(Neg(Zero), Neg(Succ(vxw1000))) → new_primCmpNat0(Succ(vxw1000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(vxw1000))) → GT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(vxw1100)), Pos(vxw100)) → LT
new_primCmpNat0(Succ(vxw1100), Zero) → GT
new_primCmpNat0(Succ(vxw1100), Succ(vxw1000)) → new_primCmpNat0(vxw1100, vxw1000)
new_primCmpNat0(Zero, Succ(vxw1000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_ltEs12(vxw11, vxw10, cc) → new_not(new_esEs8(new_compare0(vxw11, vxw10, cc), GT))
new_compare0(:(vxw110, vxw111), :(vxw100, vxw101), cc) → new_primCompAux0(vxw110, vxw100, new_compare0(vxw111, vxw101, cc), cc)
new_compare0([], [], cc) → EQ
new_compare0(:(vxw110, vxw111), [], cc) → GT
new_compare0([], :(vxw100, vxw101), cc) → LT
new_primCompAux0(vxw110, vxw100, vxw61, cc) → new_primCompAux00(vxw61, new_compare9(vxw110, vxw100, cc))
new_compare9(vxw110, vxw100, ty_Double) → new_compare15(vxw110, vxw100)
new_compare9(vxw110, vxw100, ty_Integer) → new_compare6(vxw110, vxw100)
new_compare9(vxw110, vxw100, ty_Int) → new_compare27(vxw110, vxw100)
new_compare9(vxw110, vxw100, app(app(app(ty_@3, baa), bab), bac)) → new_compare19(vxw110, vxw100, baa, bab, bac)
new_compare9(vxw110, vxw100, app(ty_Maybe, hd)) → new_compare8(vxw110, vxw100, hd)
new_compare9(vxw110, vxw100, app(ty_[], hh)) → new_compare0(vxw110, vxw100, hh)
new_compare9(vxw110, vxw100, ty_Bool) → new_compare18(vxw110, vxw100)
new_compare9(vxw110, vxw100, ty_Float) → new_compare26(vxw110, vxw100)
new_compare9(vxw110, vxw100, ty_@0) → new_compare7(vxw110, vxw100)
new_compare9(vxw110, vxw100, app(app(ty_@2, he), hf)) → new_compare13(vxw110, vxw100, he, hf)
new_compare9(vxw110, vxw100, ty_Ordering) → new_compare16(vxw110, vxw100)
new_compare9(vxw110, vxw100, app(app(ty_Either, bad), bae)) → new_compare28(vxw110, vxw100, bad, bae)
new_compare9(vxw110, vxw100, ty_Char) → new_compare14(vxw110, vxw100)
new_compare9(vxw110, vxw100, app(ty_Ratio, hg)) → new_compare17(vxw110, vxw100, hg)
new_primCompAux00(vxw72, LT) → LT
new_primCompAux00(vxw72, EQ) → vxw72
new_primCompAux00(vxw72, GT) → GT
new_compare17(:%(vxw110, vxw111), :%(vxw100, vxw101), ty_Int) → new_compare27(new_sr(vxw110, vxw101), new_sr(vxw100, vxw111))
new_compare17(:%(vxw110, vxw111), :%(vxw100, vxw101), ty_Integer) → new_compare6(new_sr0(vxw110, vxw101), new_sr0(vxw100, vxw111))
new_sr0(Integer(vxw1100), Integer(vxw1010)) → Integer(new_primMulInt(vxw1100, vxw1010))
new_compare6(Integer(vxw110), Integer(vxw100)) → new_primCmpInt(vxw110, vxw100)
new_compare14(Char(vxw110), Char(vxw100)) → new_primCmpNat0(vxw110, vxw100)
new_compare28(vxw110, vxw100, cdg, cdh) → new_compare29(vxw110, vxw100, new_esEs7(vxw110, vxw100, cdg, cdh), cdg, cdh)
new_compare29(vxw110, vxw100, False, cdg, cdh) → new_compare111(vxw110, vxw100, new_ltEs17(vxw110, vxw100, cdg, cdh), cdg, cdh)
new_compare29(vxw110, vxw100, True, cdg, cdh) → EQ
new_compare111(vxw110, vxw100, False, cdg, cdh) → GT
new_compare111(vxw110, vxw100, True, cdg, cdh) → LT
new_compare16(vxw110, vxw100) → new_compare211(vxw110, vxw100, new_esEs8(vxw110, vxw100))
new_compare211(vxw110, vxw100, False) → new_compare110(vxw110, vxw100, new_ltEs10(vxw110, vxw100))
new_compare211(vxw110, vxw100, True) → EQ
new_compare110(vxw110, vxw100, True) → LT
new_compare110(vxw110, vxw100, False) → GT
new_compare13(vxw110, vxw100, dh, ea) → new_compare23(vxw110, vxw100, new_esEs5(vxw110, vxw100, dh, ea), dh, ea)
new_compare23(vxw110, vxw100, False, dh, ea) → new_compare10(vxw110, vxw100, new_ltEs4(vxw110, vxw100, dh, ea), dh, ea)
new_compare23(vxw110, vxw100, True, dh, ea) → EQ
new_compare10(vxw110, vxw100, True, dh, ea) → LT
new_compare10(vxw110, vxw100, False, dh, ea) → GT
new_compare7(@0, @0) → EQ
new_compare26(Float(vxw110, vxw111), Float(vxw100, vxw101)) → new_compare27(new_sr(vxw110, vxw100), new_sr(vxw111, vxw101))
new_compare18(vxw110, vxw100) → new_compare24(vxw110, vxw100, new_esEs17(vxw110, vxw100))
new_compare24(vxw110, vxw100, True) → EQ
new_compare24(vxw110, vxw100, False) → new_compare11(vxw110, vxw100, new_ltEs5(vxw110, vxw100))
new_compare11(vxw110, vxw100, False) → GT
new_compare11(vxw110, vxw100, True) → LT
new_compare8(vxw110, vxw100, cd) → new_compare210(vxw110, vxw100, new_esEs4(vxw110, vxw100, cd), cd)
new_compare210(vxw110, vxw100, False, cd) → new_compare112(vxw110, vxw100, new_ltEs7(vxw110, vxw100, cd), cd)
new_compare210(vxw110, vxw100, True, cd) → EQ
new_compare112(vxw110, vxw100, True, cd) → LT
new_compare112(vxw110, vxw100, False, cd) → GT
new_compare19(vxw110, vxw100, ha, hb, hc) → new_compare25(vxw110, vxw100, new_esEs6(vxw110, vxw100, ha, hb, hc), ha, hb, hc)
new_compare25(vxw110, vxw100, True, ha, hb, hc) → EQ
new_compare25(vxw110, vxw100, False, ha, hb, hc) → new_compare12(vxw110, vxw100, new_ltEs6(vxw110, vxw100, ha, hb, hc), ha, hb, hc)
new_ltEs6(@3(vxw110, vxw111, vxw112), @3(vxw100, vxw101, vxw102), bdd, bde, bdf) → new_pePe(new_lt20(vxw110, vxw100, bdd), new_asAs(new_esEs26(vxw110, vxw100, bdd), new_pePe(new_lt19(vxw111, vxw101, bde), new_asAs(new_esEs25(vxw111, vxw101, bde), new_ltEs19(vxw112, vxw102, bdf)))))
new_compare12(vxw110, vxw100, True, ha, hb, hc) → LT
new_compare12(vxw110, vxw100, False, ha, hb, hc) → GT
new_lt20(vxw110, vxw100, ty_Integer) → new_lt4(vxw110, vxw100)
new_lt20(vxw110, vxw100, ty_@0) → new_lt8(vxw110, vxw100)
new_lt20(vxw110, vxw100, app(app(ty_@2, dbb), dbc)) → new_lt11(vxw110, vxw100, dbb, dbc)
new_lt20(vxw110, vxw100, ty_Float) → new_lt17(vxw110, vxw100)
new_lt20(vxw110, vxw100, ty_Ordering) → new_lt6(vxw110, vxw100)
new_lt20(vxw110, vxw100, ty_Bool) → new_lt9(vxw110, vxw100)
new_lt20(vxw110, vxw100, app(ty_Maybe, dba)) → new_lt5(vxw110, vxw100, dba)
new_lt20(vxw110, vxw100, ty_Int) → new_lt7(vxw110, vxw100)
new_lt20(vxw110, vxw100, ty_Double) → new_lt13(vxw110, vxw100)
new_lt20(vxw110, vxw100, app(ty_Ratio, dbd)) → new_lt14(vxw110, vxw100, dbd)
new_lt20(vxw110, vxw100, app(app(ty_Either, dca), dcb)) → new_lt18(vxw110, vxw100, dca, dcb)
new_lt20(vxw110, vxw100, app(ty_[], dbe)) → new_lt15(vxw110, vxw100, dbe)
new_lt20(vxw110, vxw100, app(app(app(ty_@3, dbf), dbg), dbh)) → new_lt16(vxw110, vxw100, dbf, dbg, dbh)
new_lt20(vxw110, vxw100, ty_Char) → new_lt12(vxw110, vxw100)
new_esEs26(vxw110, vxw100, ty_@0) → new_esEs15(vxw110, vxw100)
new_esEs26(vxw110, vxw100, ty_Float) → new_esEs10(vxw110, vxw100)
new_esEs26(vxw110, vxw100, ty_Integer) → new_esEs11(vxw110, vxw100)
new_esEs26(vxw110, vxw100, app(ty_Maybe, dba)) → new_esEs4(vxw110, vxw100, dba)
new_esEs26(vxw110, vxw100, ty_Char) → new_esEs12(vxw110, vxw100)
new_esEs26(vxw110, vxw100, app(ty_Ratio, dbd)) → new_esEs13(vxw110, vxw100, dbd)
new_esEs26(vxw110, vxw100, ty_Ordering) → new_esEs8(vxw110, vxw100)
new_esEs26(vxw110, vxw100, app(app(app(ty_@3, dbf), dbg), dbh)) → new_esEs6(vxw110, vxw100, dbf, dbg, dbh)
new_esEs26(vxw110, vxw100, app(ty_[], dbe)) → new_esEs14(vxw110, vxw100, dbe)
new_esEs26(vxw110, vxw100, app(app(ty_Either, dca), dcb)) → new_esEs7(vxw110, vxw100, dca, dcb)
new_esEs26(vxw110, vxw100, app(app(ty_@2, dbb), dbc)) → new_esEs5(vxw110, vxw100, dbb, dbc)
new_esEs26(vxw110, vxw100, ty_Int) → new_esEs16(vxw110, vxw100)
new_esEs26(vxw110, vxw100, ty_Double) → new_esEs9(vxw110, vxw100)
new_esEs26(vxw110, vxw100, ty_Bool) → new_esEs17(vxw110, vxw100)
new_lt19(vxw111, vxw101, app(app(ty_Either, dag), dah)) → new_lt18(vxw111, vxw101, dag, dah)
new_lt19(vxw111, vxw101, ty_@0) → new_lt8(vxw111, vxw101)
new_lt19(vxw111, vxw101, ty_Ordering) → new_lt6(vxw111, vxw101)
new_lt19(vxw111, vxw101, ty_Bool) → new_lt9(vxw111, vxw101)
new_lt19(vxw111, vxw101, app(app(ty_@2, chh), daa)) → new_lt11(vxw111, vxw101, chh, daa)
new_lt19(vxw111, vxw101, ty_Double) → new_lt13(vxw111, vxw101)
new_lt19(vxw111, vxw101, ty_Float) → new_lt17(vxw111, vxw101)
new_lt19(vxw111, vxw101, ty_Char) → new_lt12(vxw111, vxw101)
new_lt19(vxw111, vxw101, ty_Int) → new_lt7(vxw111, vxw101)
new_lt19(vxw111, vxw101, ty_Integer) → new_lt4(vxw111, vxw101)
new_lt19(vxw111, vxw101, app(app(app(ty_@3, dad), dae), daf)) → new_lt16(vxw111, vxw101, dad, dae, daf)
new_lt19(vxw111, vxw101, app(ty_[], dac)) → new_lt15(vxw111, vxw101, dac)
new_lt19(vxw111, vxw101, app(ty_Maybe, chg)) → new_lt5(vxw111, vxw101, chg)
new_lt19(vxw111, vxw101, app(ty_Ratio, dab)) → new_lt14(vxw111, vxw101, dab)
new_esEs25(vxw111, vxw101, app(ty_[], dac)) → new_esEs14(vxw111, vxw101, dac)
new_esEs25(vxw111, vxw101, ty_Bool) → new_esEs17(vxw111, vxw101)
new_esEs25(vxw111, vxw101, ty_Double) → new_esEs9(vxw111, vxw101)
new_esEs25(vxw111, vxw101, ty_Ordering) → new_esEs8(vxw111, vxw101)
new_esEs25(vxw111, vxw101, app(ty_Ratio, dab)) → new_esEs13(vxw111, vxw101, dab)
new_esEs25(vxw111, vxw101, app(ty_Maybe, chg)) → new_esEs4(vxw111, vxw101, chg)
new_esEs25(vxw111, vxw101, ty_Char) → new_esEs12(vxw111, vxw101)
new_esEs25(vxw111, vxw101, ty_Float) → new_esEs10(vxw111, vxw101)
new_esEs25(vxw111, vxw101, ty_@0) → new_esEs15(vxw111, vxw101)
new_esEs25(vxw111, vxw101, ty_Integer) → new_esEs11(vxw111, vxw101)
new_esEs25(vxw111, vxw101, ty_Int) → new_esEs16(vxw111, vxw101)
new_esEs25(vxw111, vxw101, app(app(app(ty_@3, dad), dae), daf)) → new_esEs6(vxw111, vxw101, dad, dae, daf)
new_esEs25(vxw111, vxw101, app(app(ty_@2, chh), daa)) → new_esEs5(vxw111, vxw101, chh, daa)
new_esEs25(vxw111, vxw101, app(app(ty_Either, dag), dah)) → new_esEs7(vxw111, vxw101, dag, dah)
new_ltEs19(vxw112, vxw102, app(ty_Ratio, cgh)) → new_ltEs11(vxw112, vxw102, cgh)
new_ltEs19(vxw112, vxw102, ty_Double) → new_ltEs9(vxw112, vxw102)
new_ltEs19(vxw112, vxw102, ty_Ordering) → new_ltEs10(vxw112, vxw102)
new_ltEs19(vxw112, vxw102, app(app(ty_@2, cgf), cgg)) → new_ltEs4(vxw112, vxw102, cgf, cgg)
new_ltEs19(vxw112, vxw102, ty_Float) → new_ltEs15(vxw112, vxw102)
new_ltEs19(vxw112, vxw102, app(app(ty_Either, che), chf)) → new_ltEs17(vxw112, vxw102, che, chf)
new_ltEs19(vxw112, vxw102, ty_Char) → new_ltEs8(vxw112, vxw102)
new_ltEs19(vxw112, vxw102, app(ty_[], cha)) → new_ltEs12(vxw112, vxw102, cha)
new_ltEs19(vxw112, vxw102, app(app(app(ty_@3, chb), chc), chd)) → new_ltEs6(vxw112, vxw102, chb, chc, chd)
new_ltEs19(vxw112, vxw102, ty_Int) → new_ltEs16(vxw112, vxw102)
new_ltEs19(vxw112, vxw102, ty_@0) → new_ltEs14(vxw112, vxw102)
new_ltEs19(vxw112, vxw102, ty_Bool) → new_ltEs5(vxw112, vxw102)
new_ltEs19(vxw112, vxw102, app(ty_Maybe, cge)) → new_ltEs7(vxw112, vxw102, cge)
new_ltEs19(vxw112, vxw102, ty_Integer) → new_ltEs13(vxw112, vxw102)
new_ltEs13(vxw11, vxw10) → new_not(new_esEs8(new_compare6(vxw11, vxw10), GT))
new_ltEs14(vxw11, vxw10) → new_not(new_esEs8(new_compare7(vxw11, vxw10), GT))
new_ltEs16(vxw11, vxw10) → new_not(new_esEs8(new_compare27(vxw11, vxw10), GT))
new_ltEs8(vxw11, vxw10) → new_not(new_esEs8(new_compare14(vxw11, vxw10), GT))
new_ltEs15(vxw11, vxw10) → new_not(new_esEs8(new_compare26(vxw11, vxw10), GT))
new_ltEs11(vxw11, vxw10, bda) → new_not(new_esEs8(new_compare17(vxw11, vxw10, bda), GT))
new_lt14(vxw110, vxw100, cde) → new_esEs8(new_compare17(vxw110, vxw100, cde), LT)
new_lt5(vxw110, vxw100, cd) → new_esEs8(new_compare8(vxw110, vxw100, cd), LT)
new_lt15(vxw110, vxw100, cdf) → new_esEs8(new_compare0(vxw110, vxw100, cdf), LT)
new_lt16(vxw110, vxw100, ha, hb, hc) → new_esEs8(new_compare19(vxw110, vxw100, ha, hb, hc), LT)
new_lt4(vxw110, vxw100) → new_esEs8(new_compare6(vxw110, vxw100), LT)
new_lt7(vxw110, vxw100) → new_esEs8(new_compare27(vxw110, vxw100), LT)
new_lt12(vxw110, vxw100) → new_esEs8(new_compare14(vxw110, vxw100), LT)
new_lt17(vxw110, vxw100) → new_esEs8(new_compare26(vxw110, vxw100), LT)
new_lt13(vxw110, vxw100) → new_esEs8(new_compare15(vxw110, vxw100), LT)
new_lt11(vxw110, vxw100, dh, ea) → new_esEs8(new_compare13(vxw110, vxw100, dh, ea), LT)
new_lt9(vxw110, vxw100) → new_esEs8(new_compare18(vxw110, vxw100), LT)
new_lt6(vxw110, vxw100) → new_esEs8(new_compare16(vxw110, vxw100), LT)
new_lt8(vxw110, vxw100) → new_esEs8(new_compare7(vxw110, vxw100), LT)
new_lt18(vxw110, vxw100, cdg, cdh) → new_esEs8(new_compare28(vxw110, vxw100, cdg, cdh), LT)

The set Q consists of the following terms:

new_esEs11(Integer(x0), Integer(x1))
new_compare12(x0, x1, True, x2, x3, x4)
new_esEs4(Just(x0), Just(x1), ty_Int)
new_ltEs17(Left(x0), Left(x1), ty_@0, x2)
new_ltEs13(x0, x1)
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs20(x0, x1, ty_Char)
new_esEs7(Left(x0), Left(x1), ty_Int, x2)
new_asAs(True, x0)
new_lt5(x0, x1, x2)
new_ltEs17(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs21(x0, x1, ty_Ordering)
new_primMulNat0(Zero, Succ(x0))
new_esEs7(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_ltEs17(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_ltEs17(Left(x0), Left(x1), ty_Int, x2)
new_lt10(x0, x1, ty_Int)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_compare11(x0, x1, True)
new_primCmpNat0(Succ(x0), Zero)
new_lt18(x0, x1, x2, x3)
new_esEs7(Left(x0), Left(x1), ty_Integer, x2)
new_lt20(x0, x1, ty_Integer)
new_ltEs19(x0, x1, ty_@0)
new_lt19(x0, x1, ty_Int)
new_esEs29(x0, x1, ty_Bool)
new_esEs23(x0, x1, ty_Float)
new_ltEs18(x0, x1, ty_Float)
new_ltEs17(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_compare9(x0, x1, ty_Bool)
new_esEs25(x0, x1, ty_Bool)
new_compare9(x0, x1, ty_Float)
new_esEs7(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs7(Right(x0), Right(x1), x2, ty_Char)
new_esEs29(x0, x1, ty_Double)
new_ltEs10(LT, LT)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_esEs14(:(x0, x1), :(x2, x3), x4)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs17(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs23(x0, x1, ty_Ordering)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt10(x0, x1, app(app(ty_Either, x2), x3))
new_lt4(x0, x1)
new_esEs9(Double(x0, x1), Double(x2, x3))
new_esEs5(@2(x0, x1), @2(x2, x3), x4, x5)
new_lt20(x0, x1, ty_Double)
new_esEs27(x0, x1, ty_@0)
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs18(x0, x1, ty_Double)
new_ltEs6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs23(x0, x1, ty_Char)
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs18(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_esEs8(GT, GT)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_ltEs18(x0, x1, app(ty_[], x2))
new_ltEs17(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs22(x0, x1, ty_Ordering)
new_compare25(x0, x1, True, x2, x3, x4)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs24(x0, x1, ty_Char)
new_ltEs7(Just(x0), Just(x1), app(ty_[], x2))
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_esEs22(x0, x1, app(ty_[], x2))
new_compare6(Integer(x0), Integer(x1))
new_esEs29(x0, x1, ty_@0)
new_esEs8(LT, LT)
new_primMulNat0(Succ(x0), Succ(x1))
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs7(Just(x0), Just(x1), ty_Integer)
new_ltEs12(x0, x1, x2)
new_ltEs20(x0, x1, ty_Double)
new_esEs21(x0, x1, ty_Double)
new_esEs17(False, False)
new_esEs21(x0, x1, ty_Integer)
new_primEqNat0(Succ(x0), Zero)
new_esEs26(x0, x1, ty_Bool)
new_ltEs5(False, False)
new_ltEs11(x0, x1, x2)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_esEs22(x0, x1, ty_Bool)
new_lt11(x0, x1, x2, x3)
new_esEs7(Right(x0), Right(x1), x2, ty_Integer)
new_esEs7(Left(x0), Left(x1), ty_Double, x2)
new_esEs7(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs20(x0, x1, ty_Float)
new_compare0(:(x0, x1), [], x2)
new_esEs27(x0, x1, ty_Ordering)
new_esEs24(x0, x1, ty_@0)
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_esEs7(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_compare9(x0, x1, app(ty_Maybe, x2))
new_esEs7(Left(x0), Left(x1), ty_@0, x2)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs7(Right(x0), Right(x1), x2, ty_Ordering)
new_lt7(x0, x1)
new_ltEs18(x0, x1, app(ty_Ratio, x2))
new_lt10(x0, x1, app(ty_[], x2))
new_compare211(x0, x1, True)
new_compare8(x0, x1, x2)
new_esEs7(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_primEqNat0(Zero, Zero)
new_compare9(x0, x1, ty_Integer)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_esEs21(x0, x1, ty_Bool)
new_lt10(x0, x1, ty_Integer)
new_esEs21(x0, x1, ty_Char)
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_esEs4(Just(x0), Just(x1), ty_Bool)
new_compare210(x0, x1, False, x2)
new_esEs14([], :(x0, x1), x2)
new_ltEs7(Just(x0), Just(x1), ty_Double)
new_esEs22(x0, x1, ty_Int)
new_lt20(x0, x1, ty_Float)
new_ltEs7(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_esEs7(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs4(Just(x0), Just(x1), ty_Ordering)
new_esEs25(x0, x1, ty_Float)
new_compare23(x0, x1, False, x2, x3)
new_esEs7(Left(x0), Left(x1), ty_Bool, x2)
new_primMulNat0(Zero, Zero)
new_ltEs18(x0, x1, ty_Int)
new_esEs21(x0, x1, ty_Float)
new_esEs7(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs20(x0, x1, ty_Ordering)
new_ltEs17(Left(x0), Left(x1), ty_Ordering, x2)
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_ltEs10(EQ, LT)
new_ltEs10(LT, EQ)
new_compare23(x0, x1, True, x2, x3)
new_esEs21(x0, x1, app(ty_[], x2))
new_ltEs20(x0, x1, ty_@0)
new_ltEs17(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_esEs18(x0, x1, ty_Integer)
new_lt14(x0, x1, x2)
new_primCompAux00(x0, EQ)
new_compare10(x0, x1, True, x2, x3)
new_esEs13(:%(x0, x1), :%(x2, x3), x4)
new_compare210(x0, x1, True, x2)
new_pePe(True, x0)
new_esEs20(x0, x1, ty_Ordering)
new_ltEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, ty_Ordering)
new_esEs28(x0, x1, ty_Int)
new_esEs12(Char(x0), Char(x1))
new_lt19(x0, x1, ty_Char)
new_compare110(x0, x1, False)
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs4(Just(x0), Just(x1), ty_@0)
new_lt10(x0, x1, ty_Ordering)
new_esEs22(x0, x1, ty_Char)
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs26(x0, x1, ty_@0)
new_esEs24(x0, x1, ty_Integer)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs25(x0, x1, ty_Ordering)
new_esEs4(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, app(ty_[], x2))
new_primCompAux00(x0, LT)
new_ltEs19(x0, x1, ty_Integer)
new_ltEs17(Left(x0), Left(x1), ty_Bool, x2)
new_ltEs17(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs17(Left(x0), Left(x1), ty_Float, x2)
new_ltEs19(x0, x1, ty_Int)
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs25(x0, x1, ty_Double)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs7(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_ltEs20(x0, x1, ty_Bool)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_esEs27(x0, x1, ty_Double)
new_esEs26(x0, x1, ty_Integer)
new_esEs19(x0, x1, ty_Integer)
new_ltEs20(x0, x1, app(ty_[], x2))
new_esEs23(x0, x1, ty_Integer)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_compare13(x0, x1, x2, x3)
new_lt6(x0, x1)
new_compare0([], [], x0)
new_esEs4(Just(x0), Just(x1), app(ty_Maybe, x2))
new_compare9(x0, x1, ty_@0)
new_esEs4(Just(x0), Just(x1), ty_Double)
new_ltEs17(Right(x0), Right(x1), x2, ty_Float)
new_lt10(x0, x1, app(ty_Maybe, x2))
new_ltEs19(x0, x1, ty_Bool)
new_esEs28(x0, x1, ty_@0)
new_lt20(x0, x1, ty_Bool)
new_ltEs15(x0, x1)
new_lt10(x0, x1, app(app(ty_@2, x2), x3))
new_compare11(x0, x1, False)
new_lt10(x0, x1, ty_Double)
new_compare111(x0, x1, True, x2, x3)
new_lt19(x0, x1, ty_@0)
new_ltEs18(x0, x1, ty_Char)
new_esEs4(Just(x0), Nothing, x1)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_compare25(x0, x1, False, x2, x3, x4)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_compare27(x0, x1)
new_primPlusNat1(Zero, Zero)
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_compare0(:(x0, x1), :(x2, x3), x4)
new_sr(x0, x1)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_esEs20(x0, x1, ty_@0)
new_esEs7(Left(x0), Left(x1), ty_Float, x2)
new_ltEs18(x0, x1, app(app(ty_Either, x2), x3))
new_esEs16(x0, x1)
new_esEs25(x0, x1, app(ty_[], x2))
new_esEs24(x0, x1, ty_Float)
new_esEs4(Nothing, Just(x0), x1)
new_compare9(x0, x1, ty_Ordering)
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare28(x0, x1, x2, x3)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_ltEs7(Just(x0), Just(x1), ty_Int)
new_esEs28(x0, x1, ty_Float)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, ty_@0)
new_ltEs18(x0, x1, ty_Ordering)
new_esEs23(x0, x1, ty_Int)
new_esEs7(Right(x0), Right(x1), x2, ty_Double)
new_compare10(x0, x1, False, x2, x3)
new_esEs26(x0, x1, ty_Double)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs24(x0, x1, ty_Bool)
new_esEs23(x0, x1, app(ty_[], x2))
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_primMulInt(Pos(x0), Pos(x1))
new_ltEs7(Just(x0), Just(x1), ty_Char)
new_compare112(x0, x1, True, x2)
new_compare9(x0, x1, app(app(ty_Either, x2), x3))
new_primPlusNat0(Succ(x0), x1)
new_ltEs10(GT, LT)
new_ltEs10(LT, GT)
new_ltEs17(Right(x0), Right(x1), x2, ty_@0)
new_ltEs7(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_sr0(Integer(x0), Integer(x1))
new_esEs23(x0, x1, ty_Double)
new_compare9(x0, x1, app(ty_[], x2))
new_esEs25(x0, x1, ty_Integer)
new_esEs20(x0, x1, ty_Char)
new_ltEs7(Nothing, Just(x0), x1)
new_primEqNat0(Zero, Succ(x0))
new_esEs27(x0, x1, ty_Bool)
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare17(:%(x0, x1), :%(x2, x3), ty_Int)
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_lt9(x0, x1)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_ltEs20(x0, x1, ty_Integer)
new_primMulInt(Neg(x0), Neg(x1))
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_esEs4(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, ty_Char)
new_ltEs20(x0, x1, ty_Int)
new_compare211(x0, x1, False)
new_ltEs17(Left(x0), Left(x1), ty_Double, x2)
new_compare29(x0, x1, False, x2, x3)
new_ltEs9(x0, x1)
new_esEs7(Right(x0), Right(x1), x2, ty_Float)
new_ltEs17(Right(x0), Right(x1), x2, ty_Ordering)
new_lt10(x0, x1, ty_@0)
new_ltEs7(Just(x0), Nothing, x1)
new_esEs4(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_compare112(x0, x1, False, x2)
new_esEs29(x0, x1, ty_Char)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs18(x0, x1, ty_Integer)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_esEs27(x0, x1, ty_Float)
new_ltEs19(x0, x1, ty_Double)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Neg(Zero), Neg(Zero))
new_ltEs19(x0, x1, ty_Ordering)
new_ltEs14(x0, x1)
new_ltEs17(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_ltEs7(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_compare29(x0, x1, True, x2, x3)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs24(x0, x1, ty_Ordering)
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs26(x0, x1, app(ty_[], x2))
new_ltEs17(Right(x0), Right(x1), x2, ty_Bool)
new_esEs29(x0, x1, ty_Ordering)
new_compare9(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_compare7(@0, @0)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_esEs18(x0, x1, ty_Int)
new_ltEs17(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_lt19(x0, x1, app(ty_Maybe, x2))
new_primCompAux00(x0, GT)
new_lt19(x0, x1, ty_Double)
new_esEs26(x0, x1, ty_Float)
new_ltEs7(Just(x0), Just(x1), ty_Ordering)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_esEs4(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs16(x0, x1)
new_esEs21(x0, x1, ty_@0)
new_compare18(x0, x1)
new_lt19(x0, x1, ty_Ordering)
new_esEs4(Nothing, Nothing, x0)
new_esEs7(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_asAs(False, x0)
new_lt10(x0, x1, ty_Char)
new_esEs20(x0, x1, ty_Int)
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat1(Succ(x0), Zero)
new_esEs8(GT, EQ)
new_esEs8(EQ, GT)
new_esEs22(x0, x1, ty_Integer)
new_lt15(x0, x1, x2)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_compare17(:%(x0, x1), :%(x2, x3), ty_Integer)
new_esEs29(x0, x1, app(ty_[], x2))
new_ltEs20(x0, x1, ty_Float)
new_primPlusNat0(Zero, x0)
new_esEs20(x0, x1, ty_Integer)
new_compare26(Float(x0, x1), Float(x2, x3))
new_ltEs17(Left(x0), Left(x1), ty_Char, x2)
new_primCmpNat0(Zero, Zero)
new_lt10(x0, x1, ty_Bool)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_ltEs17(Left(x0), Left(x1), ty_Integer, x2)
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_compare111(x0, x1, False, x2, x3)
new_ltEs7(Nothing, Nothing, x0)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs15(@0, @0)
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_compare16(x0, x1)
new_compare9(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare9(x0, x1, app(app(ty_@2, x2), x3))
new_lt16(x0, x1, x2, x3, x4)
new_esEs23(x0, x1, ty_Bool)
new_primEqNat0(Succ(x0), Succ(x1))
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_esEs7(Left(x0), Left(x1), ty_Char, x2)
new_primCmpNat0(Zero, Succ(x0))
new_esEs27(x0, x1, ty_Integer)
new_esEs21(x0, x1, ty_Int)
new_esEs24(x0, x1, ty_Double)
new_esEs24(x0, x1, app(ty_[], x2))
new_esEs20(x0, x1, ty_Bool)
new_lt10(x0, x1, app(ty_Ratio, x2))
new_lt19(x0, x1, ty_Integer)
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_ltEs10(GT, GT)
new_esEs27(x0, x1, app(ty_[], x2))
new_ltEs7(Just(x0), Just(x1), ty_Float)
new_lt17(x0, x1)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_compare15(Double(x0, x1), Double(x2, x3))
new_esEs22(x0, x1, ty_Float)
new_lt13(x0, x1)
new_ltEs17(Right(x0), Right(x1), x2, ty_Double)
new_primCompAux0(x0, x1, x2, x3)
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_compare9(x0, x1, ty_Char)
new_ltEs5(True, True)
new_esEs7(Right(x0), Right(x1), x2, ty_@0)
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_compare14(Char(x0), Char(x1))
new_lt19(x0, x1, app(ty_Ratio, x2))
new_ltEs17(Right(x0), Right(x1), x2, ty_Integer)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_not(True)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_ltEs7(Just(x0), Just(x1), ty_@0)
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs28(x0, x1, ty_Double)
new_esEs26(x0, x1, ty_Ordering)
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs17(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs27(x0, x1, ty_Int)
new_esEs6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_lt10(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_not(False)
new_esEs4(Just(x0), Just(x1), ty_Integer)
new_ltEs17(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_lt20(x0, x1, ty_Char)
new_lt19(x0, x1, ty_Bool)
new_primCmpNat0(Succ(x0), Succ(x1))
new_ltEs10(EQ, GT)
new_ltEs10(GT, EQ)
new_esEs22(x0, x1, ty_Double)
new_esEs10(Float(x0, x1), Float(x2, x3))
new_esEs26(x0, x1, ty_Int)
new_esEs4(Just(x0), Just(x1), ty_Float)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_compare24(x0, x1, True)
new_ltEs17(Right(x0), Right(x1), x2, ty_Int)
new_esEs25(x0, x1, ty_@0)
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_compare9(x0, x1, ty_Int)
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primMulNat0(Succ(x0), Zero)
new_esEs28(x0, x1, ty_Bool)
new_lt19(x0, x1, ty_Float)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs8(EQ, LT)
new_esEs8(LT, EQ)
new_lt20(x0, x1, ty_@0)
new_compare0([], :(x0, x1), x2)
new_lt19(x0, x1, app(ty_[], x2))
new_esEs7(Right(x0), Right(x1), x2, ty_Int)
new_esEs7(Left(x0), Left(x1), ty_Ordering, x2)
new_compare19(x0, x1, x2, x3, x4)
new_ltEs4(@2(x0, x1), @2(x2, x3), x4, x5)
new_lt8(x0, x1)
new_esEs25(x0, x1, ty_Int)
new_esEs4(Just(x0), Just(x1), app(ty_Ratio, x2))
new_ltEs7(Just(x0), Just(x1), ty_Bool)
new_compare12(x0, x1, False, x2, x3, x4)
new_esEs17(False, True)
new_esEs17(True, False)
new_ltEs17(Right(x0), Right(x1), x2, ty_Char)
new_esEs28(x0, x1, app(ty_[], x2))
new_compare110(x0, x1, True)
new_ltEs7(Just(x0), Just(x1), app(ty_Maybe, x2))
new_ltEs8(x0, x1)
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_compare24(x0, x1, False)
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_esEs28(x0, x1, ty_Char)
new_esEs26(x0, x1, ty_Char)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare9(x0, x1, ty_Double)
new_ltEs17(Left(x0), Right(x1), x2, x3)
new_ltEs17(Right(x0), Left(x1), x2, x3)
new_esEs14([], [], x0)
new_primEqInt(Pos(Zero), Pos(Zero))
new_esEs17(True, True)
new_lt12(x0, x1)
new_esEs29(x0, x1, ty_Integer)
new_ltEs18(x0, x1, app(ty_Maybe, x2))
new_ltEs18(x0, x1, ty_@0)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs20(x0, x1, ty_Double)
new_lt10(x0, x1, ty_Float)
new_esEs25(x0, x1, ty_Char)
new_ltEs19(x0, x1, ty_Char)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs28(x0, x1, ty_Ordering)
new_esEs29(x0, x1, ty_Int)
new_ltEs17(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_ltEs5(True, False)
new_ltEs5(False, True)
new_ltEs19(x0, x1, app(ty_[], x2))
new_esEs19(x0, x1, ty_Int)
new_esEs24(x0, x1, ty_Int)
new_ltEs18(x0, x1, ty_Bool)
new_esEs4(Just(x0), Just(x1), ty_Char)
new_ltEs7(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs7(Right(x0), Left(x1), x2, x3)
new_esEs7(Left(x0), Right(x1), x2, x3)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, ty_Int)
new_pePe(False, x0)
new_esEs22(x0, x1, ty_@0)
new_esEs29(x0, x1, ty_Float)
new_ltEs19(x0, x1, ty_Float)
new_esEs14(:(x0, x1), [], x2)
new_esEs28(x0, x1, ty_Integer)
new_ltEs10(EQ, EQ)
new_esEs20(x0, x1, app(ty_[], 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: 



↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ IFR
        ↳ HASKELL
          ↳ BR
            ↳ HASKELL
              ↳ COR
                ↳ HASKELL
                  ↳ LetRed
                    ↳ HASKELL
                      ↳ NumRed
                        ↳ HASKELL
                          ↳ Narrow
                            ↳ AND
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                                ↳ DependencyGraphProof
                                  ↳ AND
                                    ↳ QDP
                                    ↳ QDP
                                      ↳ UsableRulesProof

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

new_insertBy02(vxw37, vxw38, vxw39, False, ca, cb) → new_insertBy(Right(vxw38), vxw39, ca, cb)
new_insertBy01(vxw19, vxw20, vxw21, False, bg, bh) → new_insertBy02(vxw19, vxw20, vxw21, new_ltEs21(vxw20, vxw19, bh), bg, bh)
new_insertBy(Right(vxw30), :(Right(vxw400), vxw41), be, bf) → new_insertBy01(vxw400, vxw30, vxw41, new_esEs30(vxw30, vxw400, bf), be, bf)
new_insertBy(Right(vxw30), :(Left(vxw400), vxw41), be, bf) → new_insertBy(Right(vxw30), vxw41, be, bf)

The TRS R consists of the following rules:

new_esEs4(Just(vxw300), Just(vxw4000), app(ty_Maybe, ceh)) → new_esEs4(vxw300, vxw4000, ceh)
new_esEs25(vxw111, vxw101, app(ty_[], dac)) → new_esEs14(vxw111, vxw101, dac)
new_esEs26(vxw110, vxw100, ty_@0) → new_esEs15(vxw110, vxw100)
new_esEs23(vxw110, vxw100, app(app(ty_Either, cdg), cdh)) → new_esEs7(vxw110, vxw100, cdg, cdh)
new_esEs29(vxw30, vxw400, ty_Int) → new_esEs16(vxw30, vxw400)
new_compare112(vxw110, vxw100, True, cd) → LT
new_esEs4(Just(vxw300), Just(vxw4000), ty_Ordering) → new_esEs8(vxw300, vxw4000)
new_esEs7(Left(vxw300), Left(vxw4000), app(app(ty_Either, fc), fd), ed) → new_esEs7(vxw300, vxw4000, fc, fd)
new_ltEs19(vxw112, vxw102, app(ty_Ratio, cgh)) → new_ltEs11(vxw112, vxw102, cgh)
new_ltEs21(vxw20, vxw19, app(ty_[], dfc)) → new_ltEs12(vxw20, vxw19, dfc)
new_compare210(vxw110, vxw100, False, cd) → new_compare112(vxw110, vxw100, new_ltEs7(vxw110, vxw100, cd), cd)
new_esEs7(Left(vxw300), Left(vxw4000), app(ty_Maybe, fb), ed) → new_esEs4(vxw300, vxw4000, fb)
new_ltEs18(vxw111, vxw101, ty_Float) → new_ltEs15(vxw111, vxw101)
new_ltEs20(vxw11, vxw10, ty_Ordering) → new_ltEs10(vxw11, vxw10)
new_compare10(vxw110, vxw100, True, dh, ea) → LT
new_esEs26(vxw110, vxw100, ty_Float) → new_esEs10(vxw110, vxw100)
new_esEs24(vxw300, vxw4000, app(ty_Maybe, cgb)) → new_esEs4(vxw300, vxw4000, cgb)
new_esEs4(Just(vxw300), Nothing, bbe) → False
new_esEs4(Nothing, Just(vxw4000), bbe) → False
new_esEs11(Integer(vxw300), Integer(vxw4000)) → new_primEqInt(vxw300, vxw4000)
new_lt19(vxw111, vxw101, app(app(ty_Either, dag), dah)) → new_lt18(vxw111, vxw101, dag, dah)
new_esEs28(vxw300, vxw4000, ty_Integer) → new_esEs11(vxw300, vxw4000)
new_esEs26(vxw110, vxw100, ty_Integer) → new_esEs11(vxw110, vxw100)
new_ltEs17(Right(vxw110), Right(vxw100), bdg, app(ty_Ratio, cbd)) → new_ltEs11(vxw110, vxw100, cbd)
new_lt19(vxw111, vxw101, ty_@0) → new_lt8(vxw111, vxw101)
new_esEs22(vxw300, vxw4000, ty_Char) → new_esEs12(vxw300, vxw4000)
new_ltEs17(Left(vxw110), Left(vxw100), app(ty_Ratio, cab), bdh) → new_ltEs11(vxw110, vxw100, cab)
new_esEs30(vxw30, vxw400, app(ty_[], dd)) → new_esEs14(vxw30, vxw400, dd)
new_ltEs20(vxw11, vxw10, ty_Bool) → new_ltEs5(vxw11, vxw10)
new_esEs4(Just(vxw300), Just(vxw4000), ty_Char) → new_esEs12(vxw300, vxw4000)
new_esEs27(vxw301, vxw4001, ty_Bool) → new_esEs17(vxw301, vxw4001)
new_lt12(vxw110, vxw100) → new_esEs8(new_compare14(vxw110, vxw100), LT)
new_primMulNat0(Zero, Zero) → Zero
new_ltEs21(vxw20, vxw19, ty_Int) → new_ltEs16(vxw20, vxw19)
new_esEs23(vxw110, vxw100, app(ty_Ratio, cde)) → new_esEs13(vxw110, vxw100, cde)
new_esEs4(Just(vxw300), Just(vxw4000), app(app(app(ty_@3, cec), ced), cee)) → new_esEs6(vxw300, vxw4000, cec, ced, cee)
new_ltEs19(vxw112, vxw102, ty_Double) → new_ltEs9(vxw112, vxw102)
new_esEs20(vxw302, vxw4002, app(ty_Maybe, beh)) → new_esEs4(vxw302, vxw4002, beh)
new_lt20(vxw110, vxw100, ty_Integer) → new_lt4(vxw110, vxw100)
new_lt20(vxw110, vxw100, ty_@0) → new_lt8(vxw110, vxw100)
new_esEs21(vxw301, vxw4001, ty_Bool) → new_esEs17(vxw301, vxw4001)
new_esEs23(vxw110, vxw100, ty_Double) → new_esEs9(vxw110, vxw100)
new_esEs7(Right(vxw300), Right(vxw4000), ff, ty_Ordering) → new_esEs8(vxw300, vxw4000)
new_lt19(vxw111, vxw101, ty_Ordering) → new_lt6(vxw111, vxw101)
new_ltEs17(Left(vxw110), Left(vxw100), ty_Integer, bdh) → new_ltEs13(vxw110, vxw100)
new_esEs25(vxw111, vxw101, ty_Bool) → new_esEs17(vxw111, vxw101)
new_compare13(vxw110, vxw100, dh, ea) → new_compare23(vxw110, vxw100, new_esEs5(vxw110, vxw100, dh, ea), dh, ea)
new_compare9(vxw110, vxw100, ty_Double) → new_compare15(vxw110, vxw100)
new_lt20(vxw110, vxw100, app(app(ty_@2, dbb), dbc)) → new_lt11(vxw110, vxw100, dbb, dbc)
new_esEs23(vxw110, vxw100, app(ty_Maybe, cd)) → new_esEs4(vxw110, vxw100, cd)
new_compare9(vxw110, vxw100, ty_Integer) → new_compare6(vxw110, vxw100)
new_esEs30(vxw30, vxw400, app(app(ty_Either, df), dg)) → new_esEs7(vxw30, vxw400, df, dg)
new_ltEs7(Just(vxw110), Just(vxw100), ty_Bool) → new_ltEs5(vxw110, vxw100)
new_esEs17(True, True) → True
new_esEs20(vxw302, vxw4002, app(ty_Ratio, bef)) → new_esEs13(vxw302, vxw4002, bef)
new_ltEs19(vxw112, vxw102, ty_Ordering) → new_ltEs10(vxw112, vxw102)
new_compare0(:(vxw110, vxw111), :(vxw100, vxw101), cc) → new_primCompAux0(vxw110, vxw100, new_compare0(vxw111, vxw101, cc), cc)
new_ltEs7(Just(vxw110), Just(vxw100), app(app(app(ty_@3, bcd), bce), bcf)) → new_ltEs6(vxw110, vxw100, bcd, bce, bcf)
new_esEs22(vxw300, vxw4000, app(app(ty_@2, bge), bgf)) → new_esEs5(vxw300, vxw4000, bge, bgf)
new_lt15(vxw110, vxw100, cdf) → new_esEs8(new_compare0(vxw110, vxw100, cdf), LT)
new_esEs24(vxw300, vxw4000, app(app(ty_@2, cfc), cfd)) → new_esEs5(vxw300, vxw4000, cfc, cfd)
new_esEs4(Just(vxw300), Just(vxw4000), ty_Float) → new_esEs10(vxw300, vxw4000)
new_ltEs18(vxw111, vxw101, ty_Char) → new_ltEs8(vxw111, vxw101)
new_ltEs17(Right(vxw110), Right(vxw100), bdg, ty_Integer) → new_ltEs13(vxw110, vxw100)
new_ltEs10(EQ, GT) → True
new_compare29(vxw110, vxw100, False, cdg, cdh) → new_compare111(vxw110, vxw100, new_ltEs17(vxw110, vxw100, cdg, cdh), cdg, cdh)
new_ltEs21(vxw20, vxw19, app(app(ty_@2, deh), dfa)) → new_ltEs4(vxw20, vxw19, deh, dfa)
new_ltEs20(vxw11, vxw10, ty_Double) → new_ltEs9(vxw11, vxw10)
new_compare9(vxw110, vxw100, ty_Int) → new_compare27(vxw110, vxw100)
new_esEs26(vxw110, vxw100, app(ty_Maybe, dba)) → new_esEs4(vxw110, vxw100, dba)
new_esEs22(vxw300, vxw4000, app(ty_[], bhc)) → new_esEs14(vxw300, vxw4000, bhc)
new_lt20(vxw110, vxw100, ty_Float) → new_lt17(vxw110, vxw100)
new_esEs22(vxw300, vxw4000, app(app(ty_Either, bhe), bhf)) → new_esEs7(vxw300, vxw4000, bhe, bhf)
new_ltEs7(Just(vxw110), Just(vxw100), app(app(ty_Either, bcg), bch)) → new_ltEs17(vxw110, vxw100, bcg, bch)
new_ltEs7(Just(vxw110), Just(vxw100), app(app(ty_@2, bbh), bca)) → new_ltEs4(vxw110, vxw100, bbh, bca)
new_esEs25(vxw111, vxw101, ty_Double) → new_esEs9(vxw111, vxw101)
new_pePe(False, vxw60) → vxw60
new_esEs14([], [], bbd) → True
new_ltEs7(Just(vxw110), Just(vxw100), ty_Ordering) → new_ltEs10(vxw110, vxw100)
new_ltEs17(Left(vxw110), Left(vxw100), ty_Bool, bdh) → new_ltEs5(vxw110, vxw100)
new_esEs7(Left(vxw300), Right(vxw4000), ff, ed) → False
new_esEs7(Right(vxw300), Left(vxw4000), ff, ed) → False
new_esEs4(Just(vxw300), Just(vxw4000), ty_Integer) → new_esEs11(vxw300, vxw4000)
new_ltEs19(vxw112, vxw102, app(app(ty_@2, cgf), cgg)) → new_ltEs4(vxw112, vxw102, cgf, cgg)
new_esEs29(vxw30, vxw400, app(ty_[], bbd)) → new_esEs14(vxw30, vxw400, bbd)
new_ltEs7(Just(vxw110), Just(vxw100), ty_Integer) → new_ltEs13(vxw110, vxw100)
new_esEs27(vxw301, vxw4001, app(app(ty_Either, ddc), ddd)) → new_esEs7(vxw301, vxw4001, ddc, ddd)
new_esEs20(vxw302, vxw4002, ty_Int) → new_esEs16(vxw302, vxw4002)
new_esEs26(vxw110, vxw100, ty_Char) → new_esEs12(vxw110, vxw100)
new_esEs22(vxw300, vxw4000, ty_@0) → new_esEs15(vxw300, vxw4000)
new_lt9(vxw110, vxw100) → new_esEs8(new_compare18(vxw110, vxw100), LT)
new_esEs28(vxw300, vxw4000, ty_@0) → new_esEs15(vxw300, vxw4000)
new_esEs20(vxw302, vxw4002, ty_Char) → new_esEs12(vxw302, vxw4002)
new_ltEs17(Left(vxw110), Left(vxw100), app(ty_Maybe, bhg), bdh) → new_ltEs7(vxw110, vxw100, bhg)
new_ltEs18(vxw111, vxw101, ty_Int) → new_ltEs16(vxw111, vxw101)
new_esEs22(vxw300, vxw4000, ty_Ordering) → new_esEs8(vxw300, vxw4000)
new_esEs7(Left(vxw300), Left(vxw4000), ty_Double, ed) → new_esEs9(vxw300, vxw4000)
new_esEs29(vxw30, vxw400, app(ty_Ratio, bbc)) → new_esEs13(vxw30, vxw400, bbc)
new_esEs20(vxw302, vxw4002, app(app(ty_@2, bea), beb)) → new_esEs5(vxw302, vxw4002, bea, beb)
new_esEs7(Right(vxw300), Right(vxw4000), ff, ty_Double) → new_esEs9(vxw300, vxw4000)
new_ltEs20(vxw11, vxw10, app(ty_[], cc)) → new_ltEs12(vxw11, vxw10, cc)
new_ltEs21(vxw20, vxw19, ty_@0) → new_ltEs14(vxw20, vxw19)
new_esEs7(Right(vxw300), Right(vxw4000), ff, app(app(ty_@2, fg), fh)) → new_esEs5(vxw300, vxw4000, fg, fh)
new_ltEs20(vxw11, vxw10, app(app(ty_@2, bdb), bdc)) → new_ltEs4(vxw11, vxw10, bdb, bdc)
new_primCmpNat0(Zero, Succ(vxw1000)) → LT
new_lt10(vxw110, vxw100, ty_Double) → new_lt13(vxw110, vxw100)
new_ltEs19(vxw112, vxw102, ty_Float) → new_ltEs15(vxw112, vxw102)
new_lt10(vxw110, vxw100, ty_Bool) → new_lt9(vxw110, vxw100)
new_lt20(vxw110, vxw100, ty_Ordering) → new_lt6(vxw110, vxw100)
new_esEs8(LT, LT) → True
new_lt19(vxw111, vxw101, ty_Bool) → new_lt9(vxw111, vxw101)
new_compare25(vxw110, vxw100, True, ha, hb, hc) → EQ
new_ltEs15(vxw11, vxw10) → new_not(new_esEs8(new_compare26(vxw11, vxw10), GT))
new_esEs21(vxw301, vxw4001, app(ty_Ratio, bfh)) → new_esEs13(vxw301, vxw4001, bfh)
new_lt5(vxw110, vxw100, cd) → new_esEs8(new_compare8(vxw110, vxw100, cd), LT)
new_esEs7(Left(vxw300), Left(vxw4000), ty_Integer, ed) → new_esEs11(vxw300, vxw4000)
new_esEs25(vxw111, vxw101, ty_Ordering) → new_esEs8(vxw111, vxw101)
new_esEs20(vxw302, vxw4002, ty_Integer) → new_esEs11(vxw302, vxw4002)
new_esEs24(vxw300, vxw4000, app(app(ty_Either, cgc), cgd)) → new_esEs7(vxw300, vxw4000, cgc, cgd)
new_compare9(vxw110, vxw100, app(app(app(ty_@3, baa), bab), bac)) → new_compare19(vxw110, vxw100, baa, bab, bac)
new_esEs20(vxw302, vxw4002, app(app(app(ty_@3, bec), bed), bee)) → new_esEs6(vxw302, vxw4002, bec, bed, bee)
new_esEs25(vxw111, vxw101, app(ty_Ratio, dab)) → new_esEs13(vxw111, vxw101, dab)
new_esEs30(vxw30, vxw400, ty_Float) → new_esEs10(vxw30, vxw400)
new_esEs28(vxw300, vxw4000, ty_Float) → new_esEs10(vxw300, vxw4000)
new_ltEs5(True, False) → False
new_lt19(vxw111, vxw101, app(app(ty_@2, chh), daa)) → new_lt11(vxw111, vxw101, chh, daa)
new_esEs18(vxw301, vxw4001, ty_Integer) → new_esEs11(vxw301, vxw4001)
new_compare0([], [], cc) → EQ
new_pePe(True, vxw60) → True
new_esEs24(vxw300, vxw4000, ty_Int) → new_esEs16(vxw300, vxw4000)
new_primEqNat0(Zero, Zero) → True
new_ltEs21(vxw20, vxw19, ty_Bool) → new_ltEs5(vxw20, vxw19)
new_ltEs17(Left(vxw110), Left(vxw100), ty_Double, bdh) → new_ltEs9(vxw110, vxw100)
new_esEs7(Left(vxw300), Left(vxw4000), app(app(ty_@2, eb), ec), ed) → new_esEs5(vxw300, vxw4000, eb, ec)
new_compare29(vxw110, vxw100, True, cdg, cdh) → EQ
new_compare111(vxw110, vxw100, False, cdg, cdh) → GT
new_esEs26(vxw110, vxw100, app(ty_Ratio, dbd)) → new_esEs13(vxw110, vxw100, dbd)
new_ltEs21(vxw20, vxw19, app(ty_Ratio, dfb)) → new_ltEs11(vxw20, vxw19, dfb)
new_esEs27(vxw301, vxw4001, app(ty_Ratio, dch)) → new_esEs13(vxw301, vxw4001, dch)
new_esEs27(vxw301, vxw4001, ty_Char) → new_esEs12(vxw301, vxw4001)
new_lt18(vxw110, vxw100, cdg, cdh) → new_esEs8(new_compare28(vxw110, vxw100, cdg, cdh), LT)
new_ltEs5(True, True) → True
new_ltEs17(Left(vxw110), Left(vxw100), ty_Ordering, bdh) → new_ltEs10(vxw110, vxw100)
new_esEs17(False, False) → True
new_ltEs17(Right(vxw110), Left(vxw100), bdg, bdh) → False
new_esEs17(False, True) → False
new_esEs17(True, False) → False
new_esEs7(Left(vxw300), Left(vxw4000), ty_Ordering, ed) → new_esEs8(vxw300, vxw4000)
new_compare17(:%(vxw110, vxw111), :%(vxw100, vxw101), ty_Int) → new_compare27(new_sr(vxw110, vxw101), new_sr(vxw100, vxw111))
new_lt19(vxw111, vxw101, ty_Double) → new_lt13(vxw111, vxw101)
new_ltEs18(vxw111, vxw101, app(app(ty_Either, cdc), cdd)) → new_ltEs17(vxw111, vxw101, cdc, cdd)
new_esEs7(Right(vxw300), Right(vxw4000), ff, app(app(app(ty_@3, ga), gb), gc)) → new_esEs6(vxw300, vxw4000, ga, gb, gc)
new_sr(vxw300, vxw4000) → new_primMulInt(vxw300, vxw4000)
new_esEs24(vxw300, vxw4000, ty_Bool) → new_esEs17(vxw300, vxw4000)
new_compare12(vxw110, vxw100, True, ha, hb, hc) → LT
new_esEs30(vxw30, vxw400, ty_Char) → new_esEs12(vxw30, vxw400)
new_esEs30(vxw30, vxw400, ty_Bool) → new_esEs17(vxw30, vxw400)
new_esEs24(vxw300, vxw4000, ty_Char) → new_esEs12(vxw300, vxw4000)
new_esEs22(vxw300, vxw4000, ty_Double) → new_esEs9(vxw300, vxw4000)
new_esEs4(Just(vxw300), Just(vxw4000), ty_Bool) → new_esEs17(vxw300, vxw4000)
new_esEs26(vxw110, vxw100, ty_Ordering) → new_esEs8(vxw110, vxw100)
new_esEs8(GT, GT) → True
new_ltEs20(vxw11, vxw10, app(ty_Ratio, bda)) → new_ltEs11(vxw11, vxw10, bda)
new_primPlusNat0(Succ(vxw620), vxw400000) → Succ(Succ(new_primPlusNat1(vxw620, vxw400000)))
new_ltEs9(vxw11, vxw10) → new_not(new_esEs8(new_compare15(vxw11, vxw10), GT))
new_esEs7(Right(vxw300), Right(vxw4000), ff, app(app(ty_Either, gg), gh)) → new_esEs7(vxw300, vxw4000, gg, gh)
new_lt10(vxw110, vxw100, app(app(ty_@2, dh), ea)) → new_lt11(vxw110, vxw100, dh, ea)
new_esEs20(vxw302, vxw4002, ty_Bool) → new_esEs17(vxw302, vxw4002)
new_esEs26(vxw110, vxw100, app(app(app(ty_@3, dbf), dbg), dbh)) → new_esEs6(vxw110, vxw100, dbf, dbg, dbh)
new_ltEs17(Right(vxw110), Right(vxw100), bdg, ty_Ordering) → new_ltEs10(vxw110, vxw100)
new_esEs8(LT, GT) → False
new_esEs8(GT, LT) → False
new_lt20(vxw110, vxw100, ty_Bool) → new_lt9(vxw110, vxw100)
new_esEs7(Right(vxw300), Right(vxw4000), ff, ty_Char) → new_esEs12(vxw300, vxw4000)
new_ltEs7(Just(vxw110), Just(vxw100), ty_Int) → new_ltEs16(vxw110, vxw100)
new_ltEs20(vxw11, vxw10, ty_Int) → new_ltEs16(vxw11, vxw10)
new_esEs7(Right(vxw300), Right(vxw4000), ff, ty_@0) → new_esEs15(vxw300, vxw4000)
new_primEqInt(Neg(Succ(vxw3000)), Neg(Succ(vxw40000))) → new_primEqNat0(vxw3000, vxw40000)
new_lt10(vxw110, vxw100, ty_Char) → new_lt12(vxw110, vxw100)
new_esEs20(vxw302, vxw4002, ty_Ordering) → new_esEs8(vxw302, vxw4002)
new_lt10(vxw110, vxw100, app(app(ty_Either, cdg), cdh)) → new_lt18(vxw110, vxw100, cdg, cdh)
new_esEs22(vxw300, vxw4000, app(app(app(ty_@3, bgg), bgh), bha)) → new_esEs6(vxw300, vxw4000, bgg, bgh, bha)
new_esEs23(vxw110, vxw100, ty_Ordering) → new_esEs8(vxw110, vxw100)
new_ltEs5(False, False) → True
new_primPlusNat1(Zero, Succ(vxw4000000)) → Succ(vxw4000000)
new_primPlusNat1(Succ(vxw6200), Zero) → Succ(vxw6200)
new_esEs30(vxw30, vxw400, app(ty_Maybe, de)) → new_esEs4(vxw30, vxw400, de)
new_lt19(vxw111, vxw101, ty_Float) → new_lt17(vxw111, vxw101)
new_esEs6(@3(vxw300, vxw301, vxw302), @3(vxw4000, vxw4001, vxw4002), bah, bba, bbb) → new_asAs(new_esEs22(vxw300, vxw4000, bah), new_asAs(new_esEs21(vxw301, vxw4001, bba), new_esEs20(vxw302, vxw4002, bbb)))
new_esEs21(vxw301, vxw4001, ty_Char) → new_esEs12(vxw301, vxw4001)
new_esEs16(vxw30, vxw400) → new_primEqInt(vxw30, vxw400)
new_esEs28(vxw300, vxw4000, app(ty_Maybe, ded)) → new_esEs4(vxw300, vxw4000, ded)
new_esEs21(vxw301, vxw4001, ty_@0) → new_esEs15(vxw301, vxw4001)
new_esEs14([], :(vxw4000, vxw4001), bbd) → False
new_esEs14(:(vxw300, vxw301), [], bbd) → False
new_esEs7(Right(vxw300), Right(vxw4000), ff, app(ty_Ratio, gd)) → new_esEs13(vxw300, vxw4000, gd)
new_ltEs21(vxw20, vxw19, ty_Integer) → new_ltEs13(vxw20, vxw19)
new_lt6(vxw110, vxw100) → new_esEs8(new_compare16(vxw110, vxw100), LT)
new_esEs30(vxw30, vxw400, ty_Integer) → new_esEs11(vxw30, vxw400)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs7(Left(vxw300), Left(vxw4000), app(ty_Ratio, eh), ed) → new_esEs13(vxw300, vxw4000, eh)
new_esEs24(vxw300, vxw4000, app(app(app(ty_@3, cfe), cff), cfg)) → new_esEs6(vxw300, vxw4000, cfe, cff, cfg)
new_ltEs17(Right(vxw110), Right(vxw100), bdg, ty_Int) → new_ltEs16(vxw110, vxw100)
new_esEs21(vxw301, vxw4001, ty_Integer) → new_esEs11(vxw301, vxw4001)
new_esEs26(vxw110, vxw100, app(ty_[], dbe)) → new_esEs14(vxw110, vxw100, dbe)
new_ltEs18(vxw111, vxw101, ty_@0) → new_ltEs14(vxw111, vxw101)
new_esEs28(vxw300, vxw4000, ty_Int) → new_esEs16(vxw300, vxw4000)
new_primEqInt(Neg(Succ(vxw3000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(vxw40000))) → False
new_lt19(vxw111, vxw101, ty_Char) → new_lt12(vxw111, vxw101)
new_esEs8(EQ, EQ) → True
new_compare27(vxw11, vxw10) → new_primCmpInt(vxw11, vxw10)
new_esEs5(@2(vxw300, vxw301), @2(vxw4000, vxw4001), baf, bag) → new_asAs(new_esEs28(vxw300, vxw4000, baf), new_esEs27(vxw301, vxw4001, bag))
new_esEs28(vxw300, vxw4000, app(ty_[], dec)) → new_esEs14(vxw300, vxw4000, dec)
new_lt20(vxw110, vxw100, app(ty_Maybe, dba)) → new_lt5(vxw110, vxw100, dba)
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_esEs26(vxw110, vxw100, app(app(ty_Either, dca), dcb)) → new_esEs7(vxw110, vxw100, dca, dcb)
new_compare14(Char(vxw110), Char(vxw100)) → new_primCmpNat0(vxw110, vxw100)
new_esEs21(vxw301, vxw4001, ty_Float) → new_esEs10(vxw301, vxw4001)
new_esEs4(Just(vxw300), Just(vxw4000), app(app(ty_Either, cfa), cfb)) → new_esEs7(vxw300, vxw4000, cfa, cfb)
new_esEs7(Left(vxw300), Left(vxw4000), ty_@0, ed) → new_esEs15(vxw300, vxw4000)
new_primCmpNat0(Succ(vxw1100), Succ(vxw1000)) → new_primCmpNat0(vxw1100, vxw1000)
new_esEs23(vxw110, vxw100, ty_Float) → new_esEs10(vxw110, vxw100)
new_esEs22(vxw300, vxw4000, app(ty_Maybe, bhd)) → new_esEs4(vxw300, vxw4000, bhd)
new_esEs30(vxw30, vxw400, ty_@0) → new_esEs15(vxw30, vxw400)
new_esEs25(vxw111, vxw101, app(ty_Maybe, chg)) → new_esEs4(vxw111, vxw101, chg)
new_compare19(vxw110, vxw100, ha, hb, hc) → new_compare25(vxw110, vxw100, new_esEs6(vxw110, vxw100, ha, hb, hc), ha, hb, hc)
new_lt14(vxw110, vxw100, cde) → new_esEs8(new_compare17(vxw110, vxw100, cde), LT)
new_ltEs18(vxw111, vxw101, ty_Integer) → new_ltEs13(vxw111, vxw101)
new_ltEs6(@3(vxw110, vxw111, vxw112), @3(vxw100, vxw101, vxw102), bdd, bde, bdf) → new_pePe(new_lt20(vxw110, vxw100, bdd), new_asAs(new_esEs26(vxw110, vxw100, bdd), new_pePe(new_lt19(vxw111, vxw101, bde), new_asAs(new_esEs25(vxw111, vxw101, bde), new_ltEs19(vxw112, vxw102, bdf)))))
new_ltEs18(vxw111, vxw101, ty_Bool) → new_ltEs5(vxw111, vxw101)
new_ltEs17(Left(vxw110), Left(vxw100), app(app(ty_@2, bhh), caa), bdh) → new_ltEs4(vxw110, vxw100, bhh, caa)
new_primEqInt(Pos(Succ(vxw3000)), Pos(Succ(vxw40000))) → new_primEqNat0(vxw3000, vxw40000)
new_compare10(vxw110, vxw100, False, dh, ea) → GT
new_compare9(vxw110, vxw100, app(ty_Maybe, hd)) → new_compare8(vxw110, vxw100, hd)
new_esEs18(vxw301, vxw4001, ty_Int) → new_esEs16(vxw301, vxw4001)
new_esEs4(Just(vxw300), Just(vxw4000), app(app(ty_@2, cea), ceb)) → new_esEs5(vxw300, vxw4000, cea, ceb)
new_lt20(vxw110, vxw100, ty_Int) → new_lt7(vxw110, vxw100)
new_compare9(vxw110, vxw100, app(ty_[], hh)) → new_compare0(vxw110, vxw100, hh)
new_esEs30(vxw30, vxw400, ty_Int) → new_esEs16(vxw30, vxw400)
new_ltEs7(Nothing, Just(vxw100), bbf) → True
new_esEs4(Just(vxw300), Just(vxw4000), ty_Int) → new_esEs16(vxw300, vxw4000)
new_ltEs10(GT, EQ) → False
new_primEqNat0(Succ(vxw3000), Succ(vxw40000)) → new_primEqNat0(vxw3000, vxw40000)
new_esEs23(vxw110, vxw100, ty_Integer) → new_esEs11(vxw110, vxw100)
new_esEs27(vxw301, vxw4001, ty_Ordering) → new_esEs8(vxw301, vxw4001)
new_compare7(@0, @0) → EQ
new_esEs21(vxw301, vxw4001, app(ty_[], bga)) → new_esEs14(vxw301, vxw4001, bga)
new_esEs29(vxw30, vxw400, ty_Double) → new_esEs9(vxw30, vxw400)
new_esEs9(Double(vxw300, vxw301), Double(vxw4000, vxw4001)) → new_esEs16(new_sr(vxw300, vxw4000), new_sr(vxw301, vxw4001))
new_esEs7(Right(vxw300), Right(vxw4000), ff, ty_Float) → new_esEs10(vxw300, vxw4000)
new_esEs20(vxw302, vxw4002, ty_Float) → new_esEs10(vxw302, vxw4002)
new_primCompAux00(vxw72, LT) → LT
new_lt10(vxw110, vxw100, app(app(app(ty_@3, ha), hb), hc)) → new_lt16(vxw110, vxw100, ha, hb, hc)
new_primCmpInt(Neg(Succ(vxw1100)), Neg(vxw100)) → new_primCmpNat0(vxw100, Succ(vxw1100))
new_esEs4(Just(vxw300), Just(vxw4000), ty_@0) → new_esEs15(vxw300, vxw4000)
new_esEs24(vxw300, vxw4000, ty_Ordering) → new_esEs8(vxw300, vxw4000)
new_lt10(vxw110, vxw100, ty_Float) → new_lt17(vxw110, vxw100)
new_esEs28(vxw300, vxw4000, ty_Ordering) → new_esEs8(vxw300, vxw4000)
new_esEs7(Left(vxw300), Left(vxw4000), ty_Int, ed) → new_esEs16(vxw300, vxw4000)
new_esEs8(LT, EQ) → False
new_esEs8(EQ, LT) → False
new_primEqInt(Pos(Succ(vxw3000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(vxw40000))) → False
new_lt4(vxw110, vxw100) → new_esEs8(new_compare6(vxw110, vxw100), LT)
new_ltEs20(vxw11, vxw10, ty_Integer) → new_ltEs13(vxw11, vxw10)
new_ltEs19(vxw112, vxw102, app(app(ty_Either, che), chf)) → new_ltEs17(vxw112, vxw102, che, chf)
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(vxw1100), Zero) → GT
new_esEs23(vxw110, vxw100, app(app(ty_@2, dh), ea)) → new_esEs5(vxw110, vxw100, dh, ea)
new_esEs24(vxw300, vxw4000, ty_@0) → new_esEs15(vxw300, vxw4000)
new_ltEs17(Right(vxw110), Right(vxw100), bdg, app(ty_Maybe, cba)) → new_ltEs7(vxw110, vxw100, cba)
new_ltEs10(LT, EQ) → True
new_primCmpInt(Neg(Zero), Pos(Succ(vxw1000))) → LT
new_ltEs20(vxw11, vxw10, ty_@0) → new_ltEs14(vxw11, vxw10)
new_ltEs21(vxw20, vxw19, app(app(app(ty_@3, dfd), dfe), dff)) → new_ltEs6(vxw20, vxw19, dfd, dfe, dff)
new_lt10(vxw110, vxw100, app(ty_Ratio, cde)) → new_lt14(vxw110, vxw100, cde)
new_compare9(vxw110, vxw100, ty_Bool) → new_compare18(vxw110, vxw100)
new_esEs27(vxw301, vxw4001, ty_Double) → new_esEs9(vxw301, vxw4001)
new_ltEs17(Left(vxw110), Left(vxw100), app(app(app(ty_@3, cad), cae), caf), bdh) → new_ltEs6(vxw110, vxw100, cad, cae, caf)
new_esEs22(vxw300, vxw4000, app(ty_Ratio, bhb)) → new_esEs13(vxw300, vxw4000, bhb)
new_esEs19(vxw300, vxw4000, ty_Integer) → new_esEs11(vxw300, vxw4000)
new_sr0(Integer(vxw1100), Integer(vxw1010)) → Integer(new_primMulInt(vxw1100, vxw1010))
new_primPlusNat1(Succ(vxw6200), Succ(vxw4000000)) → Succ(Succ(new_primPlusNat1(vxw6200, vxw4000000)))
new_compare6(Integer(vxw110), Integer(vxw100)) → new_primCmpInt(vxw110, vxw100)
new_primEqInt(Pos(Succ(vxw3000)), Neg(vxw4000)) → False
new_primEqInt(Neg(Succ(vxw3000)), Pos(vxw4000)) → False
new_ltEs17(Left(vxw110), Left(vxw100), app(ty_[], cac), bdh) → new_ltEs12(vxw110, vxw100, cac)
new_esEs24(vxw300, vxw4000, app(ty_Ratio, cfh)) → new_esEs13(vxw300, vxw4000, cfh)
new_compare210(vxw110, vxw100, True, cd) → EQ
new_ltEs4(@2(vxw110, vxw111), @2(vxw100, vxw101), bdb, bdc) → new_pePe(new_lt10(vxw110, vxw100, bdb), new_asAs(new_esEs23(vxw110, vxw100, bdb), new_ltEs18(vxw111, vxw101, bdc)))
new_ltEs5(False, True) → True
new_ltEs10(GT, GT) → True
new_esEs29(vxw30, vxw400, app(app(ty_@2, baf), bag)) → new_esEs5(vxw30, vxw400, baf, bag)
new_ltEs20(vxw11, vxw10, ty_Float) → new_ltEs15(vxw11, vxw10)
new_esEs25(vxw111, vxw101, ty_Char) → new_esEs12(vxw111, vxw101)
new_lt19(vxw111, vxw101, ty_Int) → new_lt7(vxw111, vxw101)
new_esEs29(vxw30, vxw400, ty_Integer) → new_esEs11(vxw30, vxw400)
new_primEqInt(Pos(Zero), Neg(Succ(vxw40000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(vxw40000))) → False
new_primCmpInt(Pos(Zero), Pos(Succ(vxw1000))) → new_primCmpNat0(Zero, Succ(vxw1000))
new_primCompAux00(vxw72, EQ) → vxw72
new_esEs28(vxw300, vxw4000, app(app(ty_Either, dee), def)) → new_esEs7(vxw300, vxw4000, dee, def)
new_ltEs18(vxw111, vxw101, app(ty_Ratio, ccf)) → new_ltEs11(vxw111, vxw101, ccf)
new_esEs7(Right(vxw300), Right(vxw4000), ff, app(ty_Maybe, gf)) → new_esEs4(vxw300, vxw4000, gf)
new_compare24(vxw110, vxw100, True) → EQ
new_compare17(:%(vxw110, vxw111), :%(vxw100, vxw101), ty_Integer) → new_compare6(new_sr0(vxw110, vxw101), new_sr0(vxw100, vxw111))
new_esEs27(vxw301, vxw4001, ty_Float) → new_esEs10(vxw301, vxw4001)
new_esEs8(EQ, GT) → False
new_esEs8(GT, EQ) → False
new_lt10(vxw110, vxw100, app(ty_Maybe, cd)) → new_lt5(vxw110, vxw100, cd)
new_ltEs7(Just(vxw110), Just(vxw100), ty_Float) → new_ltEs15(vxw110, vxw100)
new_esEs26(vxw110, vxw100, app(app(ty_@2, dbb), dbc)) → new_esEs5(vxw110, vxw100, dbb, dbc)
new_compare18(vxw110, vxw100) → new_compare24(vxw110, vxw100, new_esEs17(vxw110, vxw100))
new_esEs21(vxw301, vxw4001, app(app(ty_@2, bfc), bfd)) → new_esEs5(vxw301, vxw4001, bfc, bfd)
new_ltEs19(vxw112, vxw102, ty_Char) → new_ltEs8(vxw112, vxw102)
new_lt8(vxw110, vxw100) → new_esEs8(new_compare7(vxw110, vxw100), LT)
new_ltEs7(Just(vxw110), Just(vxw100), ty_Double) → new_ltEs9(vxw110, vxw100)
new_esEs12(Char(vxw300), Char(vxw4000)) → new_primEqNat0(vxw300, vxw4000)
new_ltEs20(vxw11, vxw10, app(app(app(ty_@3, bdd), bde), bdf)) → new_ltEs6(vxw11, vxw10, bdd, bde, bdf)
new_not(False) → True
new_esEs7(Right(vxw300), Right(vxw4000), ff, ty_Integer) → new_esEs11(vxw300, vxw4000)
new_esEs24(vxw300, vxw4000, ty_Double) → new_esEs9(vxw300, vxw4000)
new_primCompAux0(vxw110, vxw100, vxw61, cc) → new_primCompAux00(vxw61, new_compare9(vxw110, vxw100, cc))
new_primPlusNat0(Zero, vxw400000) → Succ(vxw400000)
new_primCmpInt(Pos(Succ(vxw1100)), Pos(vxw100)) → new_primCmpNat0(Succ(vxw1100), vxw100)
new_esEs23(vxw110, vxw100, ty_@0) → new_esEs15(vxw110, vxw100)
new_compare9(vxw110, vxw100, ty_Float) → new_compare26(vxw110, vxw100)
new_compare12(vxw110, vxw100, False, ha, hb, hc) → GT
new_esEs7(Right(vxw300), Right(vxw4000), ff, ty_Bool) → new_esEs17(vxw300, vxw4000)
new_esEs22(vxw300, vxw4000, ty_Bool) → new_esEs17(vxw300, vxw4000)
new_ltEs18(vxw111, vxw101, app(app(app(ty_@3, cch), cda), cdb)) → new_ltEs6(vxw111, vxw101, cch, cda, cdb)
new_compare9(vxw110, vxw100, ty_@0) → new_compare7(vxw110, vxw100)
new_ltEs19(vxw112, vxw102, app(ty_[], cha)) → new_ltEs12(vxw112, vxw102, cha)
new_ltEs17(Right(vxw110), Right(vxw100), bdg, app(app(ty_Either, cca), ccb)) → new_ltEs17(vxw110, vxw100, cca, ccb)
new_esEs25(vxw111, vxw101, ty_Float) → new_esEs10(vxw111, vxw101)
new_compare16(vxw110, vxw100) → new_compare211(vxw110, vxw100, new_esEs8(vxw110, vxw100))
new_esEs24(vxw300, vxw4000, app(ty_[], cga)) → new_esEs14(vxw300, vxw4000, cga)
new_esEs25(vxw111, vxw101, ty_@0) → new_esEs15(vxw111, vxw101)
new_lt20(vxw110, vxw100, ty_Double) → new_lt13(vxw110, vxw100)
new_lt20(vxw110, vxw100, app(ty_Ratio, dbd)) → new_lt14(vxw110, vxw100, dbd)
new_esEs28(vxw300, vxw4000, app(app(ty_@2, dde), ddf)) → new_esEs5(vxw300, vxw4000, dde, ddf)
new_compare0(:(vxw110, vxw111), [], cc) → GT
new_esEs22(vxw300, vxw4000, ty_Integer) → new_esEs11(vxw300, vxw4000)
new_ltEs19(vxw112, vxw102, app(app(app(ty_@3, chb), chc), chd)) → new_ltEs6(vxw112, vxw102, chb, chc, chd)
new_ltEs18(vxw111, vxw101, app(ty_Maybe, ccc)) → new_ltEs7(vxw111, vxw101, ccc)
new_compare9(vxw110, vxw100, app(app(ty_@2, he), hf)) → new_compare13(vxw110, vxw100, he, hf)
new_lt19(vxw111, vxw101, ty_Integer) → new_lt4(vxw111, vxw101)
new_esEs14(:(vxw300, vxw301), :(vxw4000, vxw4001), bbd) → new_asAs(new_esEs24(vxw300, vxw4000, bbd), new_esEs14(vxw301, vxw4001, bbd))
new_compare8(vxw110, vxw100, cd) → new_compare210(vxw110, vxw100, new_esEs4(vxw110, vxw100, cd), cd)
new_lt19(vxw111, vxw101, app(app(app(ty_@3, dad), dae), daf)) → new_lt16(vxw111, vxw101, dad, dae, daf)
new_esEs25(vxw111, vxw101, ty_Integer) → new_esEs11(vxw111, vxw101)
new_primCmpInt(Pos(Succ(vxw1100)), Neg(vxw100)) → GT
new_ltEs7(Just(vxw110), Just(vxw100), app(ty_Maybe, bbg)) → new_ltEs7(vxw110, vxw100, bbg)
new_esEs10(Float(vxw300, vxw301), Float(vxw4000, vxw4001)) → new_esEs16(new_sr(vxw300, vxw4000), new_sr(vxw301, vxw4001))
new_ltEs21(vxw20, vxw19, app(app(ty_Either, dfg), dfh)) → new_ltEs17(vxw20, vxw19, dfg, dfh)
new_esEs27(vxw301, vxw4001, ty_@0) → new_esEs15(vxw301, vxw4001)
new_esEs28(vxw300, vxw4000, ty_Double) → new_esEs9(vxw300, vxw4000)
new_lt19(vxw111, vxw101, app(ty_[], dac)) → new_lt15(vxw111, vxw101, dac)
new_ltEs20(vxw11, vxw10, app(app(ty_Either, bdg), bdh)) → new_ltEs17(vxw11, vxw10, bdg, bdh)
new_primMulInt(Pos(vxw3000), Pos(vxw40000)) → Pos(new_primMulNat0(vxw3000, vxw40000))
new_esEs30(vxw30, vxw400, app(app(ty_@2, ce), cf)) → new_esEs5(vxw30, vxw400, ce, cf)
new_esEs24(vxw300, vxw4000, ty_Integer) → new_esEs11(vxw300, vxw4000)
new_ltEs17(Left(vxw110), Left(vxw100), app(app(ty_Either, cag), cah), bdh) → new_ltEs17(vxw110, vxw100, cag, cah)
new_esEs7(Left(vxw300), Left(vxw4000), ty_Char, ed) → new_esEs12(vxw300, vxw4000)
new_primMulInt(Neg(vxw3000), Neg(vxw40000)) → Pos(new_primMulNat0(vxw3000, vxw40000))
new_ltEs17(Left(vxw110), Left(vxw100), ty_Float, bdh) → new_ltEs15(vxw110, vxw100)
new_compare9(vxw110, vxw100, ty_Ordering) → new_compare16(vxw110, vxw100)
new_compare110(vxw110, vxw100, True) → LT
new_primEqNat0(Succ(vxw3000), Zero) → False
new_primEqNat0(Zero, Succ(vxw40000)) → False
new_lt20(vxw110, vxw100, app(app(ty_Either, dca), dcb)) → new_lt18(vxw110, vxw100, dca, dcb)
new_compare110(vxw110, vxw100, False) → GT
new_esEs20(vxw302, vxw4002, ty_@0) → new_esEs15(vxw302, vxw4002)
new_compare23(vxw110, vxw100, False, dh, ea) → new_compare10(vxw110, vxw100, new_ltEs4(vxw110, vxw100, dh, ea), dh, ea)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs28(vxw300, vxw4000, app(app(app(ty_@3, ddg), ddh), dea)) → new_esEs6(vxw300, vxw4000, ddg, ddh, dea)
new_esEs4(Nothing, Nothing, bbe) → True
new_esEs4(Just(vxw300), Just(vxw4000), app(ty_Ratio, cef)) → new_esEs13(vxw300, vxw4000, cef)
new_esEs27(vxw301, vxw4001, app(app(app(ty_@3, dce), dcf), dcg)) → new_esEs6(vxw301, vxw4001, dce, dcf, dcg)
new_lt10(vxw110, vxw100, app(ty_[], cdf)) → new_lt15(vxw110, vxw100, cdf)
new_esEs27(vxw301, vxw4001, app(app(ty_@2, dcc), dcd)) → new_esEs5(vxw301, vxw4001, dcc, dcd)
new_esEs26(vxw110, vxw100, ty_Int) → new_esEs16(vxw110, vxw100)
new_ltEs7(Nothing, Nothing, bbf) → True
new_esEs27(vxw301, vxw4001, app(ty_Maybe, ddb)) → new_esEs4(vxw301, vxw4001, ddb)
new_esEs21(vxw301, vxw4001, app(app(ty_Either, bgc), bgd)) → new_esEs7(vxw301, vxw4001, bgc, bgd)
new_esEs23(vxw110, vxw100, app(ty_[], cdf)) → new_esEs14(vxw110, vxw100, cdf)
new_ltEs17(Right(vxw110), Right(vxw100), bdg, ty_@0) → new_ltEs14(vxw110, vxw100)
new_ltEs17(Left(vxw110), Left(vxw100), ty_Char, bdh) → new_ltEs8(vxw110, vxw100)
new_lt10(vxw110, vxw100, ty_@0) → new_lt8(vxw110, vxw100)
new_lt10(vxw110, vxw100, ty_Int) → new_lt7(vxw110, vxw100)
new_esEs7(Right(vxw300), Right(vxw4000), ff, app(ty_[], ge)) → new_esEs14(vxw300, vxw4000, ge)
new_ltEs12(vxw11, vxw10, cc) → new_not(new_esEs8(new_compare0(vxw11, vxw10, cc), GT))
new_primCmpInt(Neg(Zero), Neg(Succ(vxw1000))) → new_primCmpNat0(Succ(vxw1000), Zero)
new_compare23(vxw110, vxw100, True, dh, ea) → EQ
new_primCmpInt(Pos(Zero), Neg(Succ(vxw1000))) → GT
new_esEs23(vxw110, vxw100, ty_Bool) → new_esEs17(vxw110, vxw100)
new_esEs25(vxw111, vxw101, ty_Int) → new_esEs16(vxw111, vxw101)
new_ltEs20(vxw11, vxw10, ty_Char) → new_ltEs8(vxw11, vxw10)
new_ltEs17(Left(vxw110), Left(vxw100), ty_@0, bdh) → new_ltEs14(vxw110, vxw100)
new_esEs29(vxw30, vxw400, ty_@0) → new_esEs15(vxw30, vxw400)
new_esEs4(Just(vxw300), Just(vxw4000), app(ty_[], ceg)) → new_esEs14(vxw300, vxw4000, ceg)
new_ltEs17(Right(vxw110), Right(vxw100), bdg, ty_Float) → new_ltEs15(vxw110, vxw100)
new_ltEs17(Left(vxw110), Right(vxw100), bdg, bdh) → True
new_esEs21(vxw301, vxw4001, app(ty_Maybe, bgb)) → new_esEs4(vxw301, vxw4001, bgb)
new_esEs20(vxw302, vxw4002, app(app(ty_Either, bfa), bfb)) → new_esEs7(vxw302, vxw4002, bfa, bfb)
new_esEs21(vxw301, vxw4001, ty_Double) → new_esEs9(vxw301, vxw4001)
new_lt7(vxw110, vxw100) → new_esEs8(new_compare27(vxw110, vxw100), LT)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_lt20(vxw110, vxw100, app(ty_[], dbe)) → new_lt15(vxw110, vxw100, dbe)
new_ltEs21(vxw20, vxw19, ty_Ordering) → new_ltEs10(vxw20, vxw19)
new_ltEs21(vxw20, vxw19, ty_Char) → new_ltEs8(vxw20, vxw19)
new_ltEs17(Right(vxw110), Right(vxw100), bdg, app(ty_[], cbe)) → new_ltEs12(vxw110, vxw100, cbe)
new_ltEs7(Just(vxw110), Just(vxw100), app(ty_[], bcc)) → new_ltEs12(vxw110, vxw100, bcc)
new_esEs29(vxw30, vxw400, ty_Bool) → new_esEs17(vxw30, vxw400)
new_esEs15(@0, @0) → True
new_lt17(vxw110, vxw100) → new_esEs8(new_compare26(vxw110, vxw100), LT)
new_compare15(Double(vxw110, vxw111), Double(vxw100, vxw101)) → new_compare27(new_sr(vxw110, vxw100), new_sr(vxw111, vxw101))
new_asAs(False, vxw53) → False
new_ltEs17(Right(vxw110), Right(vxw100), bdg, ty_Double) → new_ltEs9(vxw110, vxw100)
new_compare24(vxw110, vxw100, False) → new_compare11(vxw110, vxw100, new_ltEs5(vxw110, vxw100))
new_primMulInt(Neg(vxw3000), Pos(vxw40000)) → Neg(new_primMulNat0(vxw3000, vxw40000))
new_primMulInt(Pos(vxw3000), Neg(vxw40000)) → Neg(new_primMulNat0(vxw3000, vxw40000))
new_esEs26(vxw110, vxw100, ty_Double) → new_esEs9(vxw110, vxw100)
new_compare28(vxw110, vxw100, cdg, cdh) → new_compare29(vxw110, vxw100, new_esEs7(vxw110, vxw100, cdg, cdh), cdg, cdh)
new_ltEs10(LT, GT) → True
new_primMulNat0(Zero, Succ(vxw400000)) → Zero
new_primMulNat0(Succ(vxw30000), Zero) → Zero
new_esEs29(vxw30, vxw400, ty_Char) → new_esEs12(vxw30, vxw400)
new_compare25(vxw110, vxw100, False, ha, hb, hc) → new_compare12(vxw110, vxw100, new_ltEs6(vxw110, vxw100, ha, hb, hc), ha, hb, hc)
new_esEs7(Left(vxw300), Left(vxw4000), ty_Float, ed) → new_esEs10(vxw300, vxw4000)
new_esEs23(vxw110, vxw100, app(app(app(ty_@3, ha), hb), hc)) → new_esEs6(vxw110, vxw100, ha, hb, hc)
new_ltEs7(Just(vxw110), Just(vxw100), ty_Char) → new_ltEs8(vxw110, vxw100)
new_esEs21(vxw301, vxw4001, ty_Ordering) → new_esEs8(vxw301, vxw4001)
new_esEs21(vxw301, vxw4001, ty_Int) → new_esEs16(vxw301, vxw4001)
new_esEs24(vxw300, vxw4000, ty_Float) → new_esEs10(vxw300, vxw4000)
new_esEs19(vxw300, vxw4000, ty_Int) → new_esEs16(vxw300, vxw4000)
new_esEs30(vxw30, vxw400, app(ty_Ratio, dc)) → new_esEs13(vxw30, vxw400, dc)
new_ltEs13(vxw11, vxw10) → new_not(new_esEs8(new_compare6(vxw11, vxw10), GT))
new_ltEs16(vxw11, vxw10) → new_not(new_esEs8(new_compare27(vxw11, vxw10), GT))
new_lt10(vxw110, vxw100, ty_Integer) → new_lt4(vxw110, vxw100)
new_esEs29(vxw30, vxw400, ty_Float) → new_esEs10(vxw30, vxw400)
new_esEs23(vxw110, vxw100, ty_Char) → new_esEs12(vxw110, vxw100)
new_esEs25(vxw111, vxw101, app(app(app(ty_@3, dad), dae), daf)) → new_esEs6(vxw111, vxw101, dad, dae, daf)
new_lt13(vxw110, vxw100) → new_esEs8(new_compare15(vxw110, vxw100), LT)
new_lt19(vxw111, vxw101, app(ty_Maybe, chg)) → new_lt5(vxw111, vxw101, chg)
new_ltEs10(EQ, EQ) → True
new_esEs13(:%(vxw300, vxw301), :%(vxw4000, vxw4001), bbc) → new_asAs(new_esEs19(vxw300, vxw4000, bbc), new_esEs18(vxw301, vxw4001, bbc))
new_compare9(vxw110, vxw100, app(app(ty_Either, bad), bae)) → new_compare28(vxw110, vxw100, bad, bae)
new_esEs23(vxw110, vxw100, ty_Int) → new_esEs16(vxw110, vxw100)
new_ltEs10(LT, LT) → True
new_ltEs19(vxw112, vxw102, ty_Int) → new_ltEs16(vxw112, vxw102)
new_ltEs19(vxw112, vxw102, ty_@0) → new_ltEs14(vxw112, vxw102)
new_compare211(vxw110, vxw100, False) → new_compare110(vxw110, vxw100, new_ltEs10(vxw110, vxw100))
new_esEs7(Left(vxw300), Left(vxw4000), app(app(app(ty_@3, ee), ef), eg), ed) → new_esEs6(vxw300, vxw4000, ee, ef, eg)
new_lt10(vxw110, vxw100, ty_Ordering) → new_lt6(vxw110, vxw100)
new_esEs27(vxw301, vxw4001, ty_Int) → new_esEs16(vxw301, vxw4001)
new_ltEs17(Right(vxw110), Right(vxw100), bdg, ty_Char) → new_ltEs8(vxw110, vxw100)
new_ltEs7(Just(vxw110), Just(vxw100), ty_@0) → new_ltEs14(vxw110, vxw100)
new_ltEs19(vxw112, vxw102, ty_Bool) → new_ltEs5(vxw112, vxw102)
new_ltEs8(vxw11, vxw10) → new_not(new_esEs8(new_compare14(vxw11, vxw10), GT))
new_lt20(vxw110, vxw100, app(app(app(ty_@3, dbf), dbg), dbh)) → new_lt16(vxw110, vxw100, dbf, dbg, dbh)
new_esEs7(Right(vxw300), Right(vxw4000), ff, ty_Int) → new_esEs16(vxw300, vxw4000)
new_ltEs7(Just(vxw110), Nothing, bbf) → False
new_esEs28(vxw300, vxw4000, ty_Bool) → new_esEs17(vxw300, vxw4000)
new_esEs28(vxw300, vxw4000, app(ty_Ratio, deb)) → new_esEs13(vxw300, vxw4000, deb)
new_ltEs17(Left(vxw110), Left(vxw100), ty_Int, bdh) → new_ltEs16(vxw110, vxw100)
new_compare11(vxw110, vxw100, False) → GT
new_lt16(vxw110, vxw100, ha, hb, hc) → new_esEs8(new_compare19(vxw110, vxw100, ha, hb, hc), LT)
new_esEs25(vxw111, vxw101, app(app(ty_@2, chh), daa)) → new_esEs5(vxw111, vxw101, chh, daa)
new_esEs26(vxw110, vxw100, ty_Bool) → new_esEs17(vxw110, vxw100)
new_compare11(vxw110, vxw100, True) → LT
new_ltEs19(vxw112, vxw102, app(ty_Maybe, cge)) → new_ltEs7(vxw112, vxw102, cge)
new_ltEs21(vxw20, vxw19, app(ty_Maybe, deg)) → new_ltEs7(vxw20, vxw19, deg)
new_esEs29(vxw30, vxw400, app(app(app(ty_@3, bah), bba), bbb)) → new_esEs6(vxw30, vxw400, bah, bba, bbb)
new_esEs29(vxw30, vxw400, app(app(ty_Either, ff), ed)) → new_esEs7(vxw30, vxw400, ff, ed)
new_esEs7(Left(vxw300), Left(vxw4000), ty_Bool, ed) → new_esEs17(vxw300, vxw4000)
new_ltEs10(EQ, LT) → False
new_compare112(vxw110, vxw100, False, cd) → GT
new_compare9(vxw110, vxw100, ty_Char) → new_compare14(vxw110, vxw100)
new_lt20(vxw110, vxw100, ty_Char) → new_lt12(vxw110, vxw100)
new_esEs22(vxw300, vxw4000, ty_Float) → new_esEs10(vxw300, vxw4000)
new_esEs30(vxw30, vxw400, ty_Ordering) → new_esEs8(vxw30, vxw400)
new_ltEs10(GT, LT) → False
new_esEs30(vxw30, vxw400, ty_Double) → new_esEs9(vxw30, vxw400)
new_ltEs14(vxw11, vxw10) → new_not(new_esEs8(new_compare7(vxw11, vxw10), GT))
new_primPlusNat1(Zero, Zero) → Zero
new_compare0([], :(vxw100, vxw101), cc) → LT
new_compare111(vxw110, vxw100, True, cdg, cdh) → LT
new_esEs21(vxw301, vxw4001, app(app(app(ty_@3, bfe), bff), bfg)) → new_esEs6(vxw301, vxw4001, bfe, bff, bfg)
new_esEs27(vxw301, vxw4001, app(ty_[], dda)) → new_esEs14(vxw301, vxw4001, dda)
new_asAs(True, vxw53) → vxw53
new_primMulNat0(Succ(vxw30000), Succ(vxw400000)) → new_primPlusNat0(new_primMulNat0(vxw30000, Succ(vxw400000)), vxw400000)
new_compare9(vxw110, vxw100, app(ty_Ratio, hg)) → new_compare17(vxw110, vxw100, hg)
new_esEs20(vxw302, vxw4002, ty_Double) → new_esEs9(vxw302, vxw4002)
new_esEs27(vxw301, vxw4001, ty_Integer) → new_esEs11(vxw301, vxw4001)
new_ltEs21(vxw20, vxw19, ty_Float) → new_ltEs15(vxw20, vxw19)
new_ltEs17(Right(vxw110), Right(vxw100), bdg, app(app(app(ty_@3, cbf), cbg), cbh)) → new_ltEs6(vxw110, vxw100, cbf, cbg, cbh)
new_compare211(vxw110, vxw100, True) → EQ
new_ltEs17(Right(vxw110), Right(vxw100), bdg, app(app(ty_@2, cbb), cbc)) → new_ltEs4(vxw110, vxw100, cbb, cbc)
new_ltEs19(vxw112, vxw102, ty_Integer) → new_ltEs13(vxw112, vxw102)
new_ltEs18(vxw111, vxw101, app(ty_[], ccg)) → new_ltEs12(vxw111, vxw101, ccg)
new_esEs20(vxw302, vxw4002, app(ty_[], beg)) → new_esEs14(vxw302, vxw4002, beg)
new_esEs4(Just(vxw300), Just(vxw4000), ty_Double) → new_esEs9(vxw300, vxw4000)
new_ltEs18(vxw111, vxw101, app(app(ty_@2, ccd), cce)) → new_ltEs4(vxw111, vxw101, ccd, cce)
new_esEs29(vxw30, vxw400, app(ty_Maybe, bbe)) → new_esEs4(vxw30, vxw400, bbe)
new_ltEs7(Just(vxw110), Just(vxw100), app(ty_Ratio, bcb)) → new_ltEs11(vxw110, vxw100, bcb)
new_ltEs20(vxw11, vxw10, app(ty_Maybe, bbf)) → new_ltEs7(vxw11, vxw10, bbf)
new_ltEs17(Right(vxw110), Right(vxw100), bdg, ty_Bool) → new_ltEs5(vxw110, vxw100)
new_primCompAux00(vxw72, GT) → GT
new_esEs30(vxw30, vxw400, app(app(app(ty_@3, cg), da), db)) → new_esEs6(vxw30, vxw400, cg, da, db)
new_esEs25(vxw111, vxw101, app(app(ty_Either, dag), dah)) → new_esEs7(vxw111, vxw101, dag, dah)
new_ltEs18(vxw111, vxw101, ty_Double) → new_ltEs9(vxw111, vxw101)
new_ltEs11(vxw11, vxw10, bda) → new_not(new_esEs8(new_compare17(vxw11, vxw10, bda), GT))
new_lt11(vxw110, vxw100, dh, ea) → new_esEs8(new_compare13(vxw110, vxw100, dh, ea), LT)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_compare26(Float(vxw110, vxw111), Float(vxw100, vxw101)) → new_compare27(new_sr(vxw110, vxw100), new_sr(vxw111, vxw101))
new_esEs29(vxw30, vxw400, ty_Ordering) → new_esEs8(vxw30, vxw400)
new_lt19(vxw111, vxw101, app(ty_Ratio, dab)) → new_lt14(vxw111, vxw101, dab)
new_ltEs18(vxw111, vxw101, ty_Ordering) → new_ltEs10(vxw111, vxw101)
new_esEs7(Left(vxw300), Left(vxw4000), app(ty_[], fa), ed) → new_esEs14(vxw300, vxw4000, fa)
new_esEs28(vxw300, vxw4000, ty_Char) → new_esEs12(vxw300, vxw4000)
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_ltEs21(vxw20, vxw19, ty_Double) → new_ltEs9(vxw20, vxw19)
new_primCmpInt(Neg(Succ(vxw1100)), Pos(vxw100)) → LT
new_esEs22(vxw300, vxw4000, ty_Int) → new_esEs16(vxw300, vxw4000)
new_not(True) → False

The set Q consists of the following terms:

new_esEs11(Integer(x0), Integer(x1))
new_compare12(x0, x1, True, x2, x3, x4)
new_esEs4(Just(x0), Just(x1), ty_Int)
new_ltEs17(Left(x0), Left(x1), ty_@0, x2)
new_ltEs13(x0, x1)
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs20(x0, x1, ty_Char)
new_esEs7(Left(x0), Left(x1), ty_Int, x2)
new_asAs(True, x0)
new_lt5(x0, x1, x2)
new_ltEs17(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs21(x0, x1, ty_Ordering)
new_primMulNat0(Zero, Succ(x0))
new_esEs7(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_ltEs17(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_ltEs17(Left(x0), Left(x1), ty_Int, x2)
new_lt10(x0, x1, ty_Int)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_compare11(x0, x1, True)
new_ltEs21(x0, x1, ty_Bool)
new_primCmpNat0(Succ(x0), Zero)
new_lt18(x0, x1, x2, x3)
new_esEs7(Left(x0), Left(x1), ty_Integer, x2)
new_lt20(x0, x1, ty_Integer)
new_ltEs19(x0, x1, ty_@0)
new_ltEs21(x0, x1, app(ty_Maybe, x2))
new_esEs30(x0, x1, app(ty_Maybe, x2))
new_lt19(x0, x1, ty_Int)
new_esEs29(x0, x1, ty_Bool)
new_esEs23(x0, x1, ty_Float)
new_ltEs18(x0, x1, ty_Float)
new_ltEs17(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_compare9(x0, x1, ty_Bool)
new_esEs25(x0, x1, ty_Bool)
new_compare9(x0, x1, ty_Float)
new_esEs7(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs7(Right(x0), Right(x1), x2, ty_Char)
new_esEs29(x0, x1, ty_Double)
new_ltEs10(LT, LT)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_esEs14(:(x0, x1), :(x2, x3), x4)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs17(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs23(x0, x1, ty_Ordering)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt10(x0, x1, app(app(ty_Either, x2), x3))
new_lt4(x0, x1)
new_esEs9(Double(x0, x1), Double(x2, x3))
new_esEs5(@2(x0, x1), @2(x2, x3), x4, x5)
new_lt20(x0, x1, ty_Double)
new_esEs27(x0, x1, ty_@0)
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs30(x0, x1, ty_Integer)
new_ltEs18(x0, x1, ty_Double)
new_ltEs6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs23(x0, x1, ty_Char)
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs18(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_esEs8(GT, GT)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_ltEs18(x0, x1, app(ty_[], x2))
new_ltEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs17(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs22(x0, x1, ty_Ordering)
new_compare25(x0, x1, True, x2, x3, x4)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs24(x0, x1, ty_Char)
new_ltEs7(Just(x0), Just(x1), app(ty_[], x2))
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_esEs22(x0, x1, app(ty_[], x2))
new_compare6(Integer(x0), Integer(x1))
new_esEs29(x0, x1, ty_@0)
new_esEs8(LT, LT)
new_primMulNat0(Succ(x0), Succ(x1))
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs7(Just(x0), Just(x1), ty_Integer)
new_ltEs12(x0, x1, x2)
new_ltEs20(x0, x1, ty_Double)
new_esEs21(x0, x1, ty_Double)
new_esEs17(False, False)
new_esEs21(x0, x1, ty_Integer)
new_primEqNat0(Succ(x0), Zero)
new_esEs26(x0, x1, ty_Bool)
new_ltEs5(False, False)
new_ltEs11(x0, x1, x2)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_esEs22(x0, x1, ty_Bool)
new_lt11(x0, x1, x2, x3)
new_esEs30(x0, x1, ty_Double)
new_esEs7(Right(x0), Right(x1), x2, ty_Integer)
new_esEs7(Left(x0), Left(x1), ty_Double, x2)
new_esEs7(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs20(x0, x1, ty_Float)
new_compare0(:(x0, x1), [], x2)
new_ltEs21(x0, x1, app(ty_Ratio, x2))
new_esEs27(x0, x1, ty_Ordering)
new_esEs24(x0, x1, ty_@0)
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_esEs7(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_compare9(x0, x1, app(ty_Maybe, x2))
new_esEs7(Left(x0), Left(x1), ty_@0, x2)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs7(Right(x0), Right(x1), x2, ty_Ordering)
new_lt7(x0, x1)
new_ltEs18(x0, x1, app(ty_Ratio, x2))
new_lt10(x0, x1, app(ty_[], x2))
new_compare211(x0, x1, True)
new_compare8(x0, x1, x2)
new_esEs7(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_primEqNat0(Zero, Zero)
new_compare9(x0, x1, ty_Integer)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_esEs21(x0, x1, ty_Bool)
new_lt10(x0, x1, ty_Integer)
new_esEs21(x0, x1, ty_Char)
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_esEs4(Just(x0), Just(x1), ty_Bool)
new_compare210(x0, x1, False, x2)
new_esEs14([], :(x0, x1), x2)
new_ltEs7(Just(x0), Just(x1), ty_Double)
new_esEs22(x0, x1, ty_Int)
new_lt20(x0, x1, ty_Float)
new_ltEs7(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_esEs7(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs4(Just(x0), Just(x1), ty_Ordering)
new_esEs25(x0, x1, ty_Float)
new_compare23(x0, x1, False, x2, x3)
new_esEs7(Left(x0), Left(x1), ty_Bool, x2)
new_primMulNat0(Zero, Zero)
new_ltEs18(x0, x1, ty_Int)
new_esEs21(x0, x1, ty_Float)
new_esEs7(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs20(x0, x1, ty_Ordering)
new_ltEs17(Left(x0), Left(x1), ty_Ordering, x2)
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_ltEs10(EQ, LT)
new_ltEs10(LT, EQ)
new_compare23(x0, x1, True, x2, x3)
new_ltEs21(x0, x1, ty_@0)
new_esEs21(x0, x1, app(ty_[], x2))
new_ltEs20(x0, x1, ty_@0)
new_ltEs17(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_esEs18(x0, x1, ty_Integer)
new_lt14(x0, x1, x2)
new_primCompAux00(x0, EQ)
new_compare10(x0, x1, True, x2, x3)
new_esEs13(:%(x0, x1), :%(x2, x3), x4)
new_compare210(x0, x1, True, x2)
new_pePe(True, x0)
new_esEs20(x0, x1, ty_Ordering)
new_ltEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, ty_Ordering)
new_esEs28(x0, x1, ty_Int)
new_esEs12(Char(x0), Char(x1))
new_lt19(x0, x1, ty_Char)
new_compare110(x0, x1, False)
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs4(Just(x0), Just(x1), ty_@0)
new_lt10(x0, x1, ty_Ordering)
new_esEs22(x0, x1, ty_Char)
new_esEs30(x0, x1, ty_Bool)
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs26(x0, x1, ty_@0)
new_esEs24(x0, x1, ty_Integer)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs25(x0, x1, ty_Ordering)
new_esEs4(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, app(ty_[], x2))
new_primCompAux00(x0, LT)
new_ltEs21(x0, x1, ty_Ordering)
new_ltEs19(x0, x1, ty_Integer)
new_ltEs17(Left(x0), Left(x1), ty_Bool, x2)
new_ltEs17(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs17(Left(x0), Left(x1), ty_Float, x2)
new_ltEs19(x0, x1, ty_Int)
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs25(x0, x1, ty_Double)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs7(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_ltEs20(x0, x1, ty_Bool)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_esEs27(x0, x1, ty_Double)
new_esEs26(x0, x1, ty_Integer)
new_esEs19(x0, x1, ty_Integer)
new_ltEs20(x0, x1, app(ty_[], x2))
new_esEs23(x0, x1, ty_Integer)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_compare13(x0, x1, x2, x3)
new_lt6(x0, x1)
new_compare0([], [], x0)
new_esEs4(Just(x0), Just(x1), app(ty_Maybe, x2))
new_compare9(x0, x1, ty_@0)
new_esEs4(Just(x0), Just(x1), ty_Double)
new_ltEs17(Right(x0), Right(x1), x2, ty_Float)
new_lt10(x0, x1, app(ty_Maybe, x2))
new_ltEs19(x0, x1, ty_Bool)
new_esEs28(x0, x1, ty_@0)
new_lt20(x0, x1, ty_Bool)
new_ltEs15(x0, x1)
new_lt10(x0, x1, app(app(ty_@2, x2), x3))
new_compare11(x0, x1, False)
new_lt10(x0, x1, ty_Double)
new_compare111(x0, x1, True, x2, x3)
new_lt19(x0, x1, ty_@0)
new_esEs30(x0, x1, app(ty_Ratio, x2))
new_ltEs18(x0, x1, ty_Char)
new_esEs4(Just(x0), Nothing, x1)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_compare25(x0, x1, False, x2, x3, x4)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_compare27(x0, x1)
new_primPlusNat1(Zero, Zero)
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_compare0(:(x0, x1), :(x2, x3), x4)
new_sr(x0, x1)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_esEs20(x0, x1, ty_@0)
new_esEs7(Left(x0), Left(x1), ty_Float, x2)
new_ltEs18(x0, x1, app(app(ty_Either, x2), x3))
new_esEs16(x0, x1)
new_esEs25(x0, x1, app(ty_[], x2))
new_esEs24(x0, x1, ty_Float)
new_esEs4(Nothing, Just(x0), x1)
new_compare9(x0, x1, ty_Ordering)
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare28(x0, x1, x2, x3)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_ltEs7(Just(x0), Just(x1), ty_Int)
new_esEs28(x0, x1, ty_Float)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, ty_@0)
new_ltEs18(x0, x1, ty_Ordering)
new_esEs23(x0, x1, ty_Int)
new_esEs7(Right(x0), Right(x1), x2, ty_Double)
new_compare10(x0, x1, False, x2, x3)
new_esEs26(x0, x1, ty_Double)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs24(x0, x1, ty_Bool)
new_esEs23(x0, x1, app(ty_[], x2))
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs21(x0, x1, ty_Float)
new_primMulInt(Pos(x0), Pos(x1))
new_ltEs7(Just(x0), Just(x1), ty_Char)
new_compare112(x0, x1, True, x2)
new_compare9(x0, x1, app(app(ty_Either, x2), x3))
new_primPlusNat0(Succ(x0), x1)
new_ltEs10(GT, LT)
new_ltEs10(LT, GT)
new_ltEs17(Right(x0), Right(x1), x2, ty_@0)
new_ltEs7(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_sr0(Integer(x0), Integer(x1))
new_esEs23(x0, x1, ty_Double)
new_compare9(x0, x1, app(ty_[], x2))
new_esEs25(x0, x1, ty_Integer)
new_esEs20(x0, x1, ty_Char)
new_ltEs7(Nothing, Just(x0), x1)
new_primEqNat0(Zero, Succ(x0))
new_esEs27(x0, x1, ty_Bool)
new_esEs30(x0, x1, ty_Int)
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare17(:%(x0, x1), :%(x2, x3), ty_Int)
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_lt9(x0, x1)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_ltEs20(x0, x1, ty_Integer)
new_primMulInt(Neg(x0), Neg(x1))
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_esEs4(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, ty_Char)
new_ltEs20(x0, x1, ty_Int)
new_compare211(x0, x1, False)
new_ltEs17(Left(x0), Left(x1), ty_Double, x2)
new_compare29(x0, x1, False, x2, x3)
new_ltEs9(x0, x1)
new_esEs7(Right(x0), Right(x1), x2, ty_Float)
new_ltEs17(Right(x0), Right(x1), x2, ty_Ordering)
new_lt10(x0, x1, ty_@0)
new_esEs30(x0, x1, ty_Ordering)
new_ltEs7(Just(x0), Nothing, x1)
new_esEs4(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_compare112(x0, x1, False, x2)
new_esEs29(x0, x1, ty_Char)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs18(x0, x1, ty_Integer)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_esEs27(x0, x1, ty_Float)
new_ltEs19(x0, x1, ty_Double)
new_ltEs21(x0, x1, ty_Double)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Neg(Zero), Neg(Zero))
new_ltEs19(x0, x1, ty_Ordering)
new_ltEs21(x0, x1, ty_Integer)
new_ltEs14(x0, x1)
new_ltEs17(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_ltEs7(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_compare29(x0, x1, True, x2, x3)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs24(x0, x1, ty_Ordering)
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs26(x0, x1, app(ty_[], x2))
new_ltEs17(Right(x0), Right(x1), x2, ty_Bool)
new_esEs29(x0, x1, ty_Ordering)
new_compare9(x0, x1, app(ty_Ratio, x2))
new_esEs30(x0, x1, ty_@0)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_compare7(@0, @0)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_esEs18(x0, x1, ty_Int)
new_ltEs17(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_lt19(x0, x1, app(ty_Maybe, x2))
new_primCompAux00(x0, GT)
new_ltEs21(x0, x1, ty_Int)
new_lt19(x0, x1, ty_Double)
new_esEs26(x0, x1, ty_Float)
new_esEs30(x0, x1, app(ty_[], x2))
new_ltEs7(Just(x0), Just(x1), ty_Ordering)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_esEs4(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs16(x0, x1)
new_esEs21(x0, x1, ty_@0)
new_compare18(x0, x1)
new_lt19(x0, x1, ty_Ordering)
new_esEs4(Nothing, Nothing, x0)
new_esEs30(x0, x1, ty_Char)
new_esEs7(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_ltEs21(x0, x1, app(app(ty_@2, x2), x3))
new_asAs(False, x0)
new_lt10(x0, x1, ty_Char)
new_esEs20(x0, x1, ty_Int)
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat1(Succ(x0), Zero)
new_esEs8(GT, EQ)
new_esEs8(EQ, GT)
new_esEs22(x0, x1, ty_Integer)
new_lt15(x0, x1, x2)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_compare17(:%(x0, x1), :%(x2, x3), ty_Integer)
new_esEs29(x0, x1, app(ty_[], x2))
new_ltEs20(x0, x1, ty_Float)
new_primPlusNat0(Zero, x0)
new_esEs20(x0, x1, ty_Integer)
new_compare26(Float(x0, x1), Float(x2, x3))
new_ltEs17(Left(x0), Left(x1), ty_Char, x2)
new_primCmpNat0(Zero, Zero)
new_lt10(x0, x1, ty_Bool)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_ltEs17(Left(x0), Left(x1), ty_Integer, x2)
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_compare111(x0, x1, False, x2, x3)
new_ltEs7(Nothing, Nothing, x0)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs15(@0, @0)
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_compare16(x0, x1)
new_compare9(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare9(x0, x1, app(app(ty_@2, x2), x3))
new_lt16(x0, x1, x2, x3, x4)
new_esEs23(x0, x1, ty_Bool)
new_primEqNat0(Succ(x0), Succ(x1))
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_esEs7(Left(x0), Left(x1), ty_Char, x2)
new_primCmpNat0(Zero, Succ(x0))
new_esEs27(x0, x1, ty_Integer)
new_esEs21(x0, x1, ty_Int)
new_esEs24(x0, x1, ty_Double)
new_esEs24(x0, x1, app(ty_[], x2))
new_esEs20(x0, x1, ty_Bool)
new_lt10(x0, x1, app(ty_Ratio, x2))
new_lt19(x0, x1, ty_Integer)
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_ltEs10(GT, GT)
new_esEs27(x0, x1, app(ty_[], x2))
new_ltEs7(Just(x0), Just(x1), ty_Float)
new_lt17(x0, x1)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_compare15(Double(x0, x1), Double(x2, x3))
new_esEs22(x0, x1, ty_Float)
new_lt13(x0, x1)
new_ltEs17(Right(x0), Right(x1), x2, ty_Double)
new_esEs30(x0, x1, app(app(ty_Either, x2), x3))
new_primCompAux0(x0, x1, x2, x3)
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_compare9(x0, x1, ty_Char)
new_ltEs5(True, True)
new_esEs7(Right(x0), Right(x1), x2, ty_@0)
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_compare14(Char(x0), Char(x1))
new_lt19(x0, x1, app(ty_Ratio, x2))
new_ltEs17(Right(x0), Right(x1), x2, ty_Integer)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_not(True)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_ltEs7(Just(x0), Just(x1), ty_@0)
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs28(x0, x1, ty_Double)
new_esEs26(x0, x1, ty_Ordering)
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs17(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs27(x0, x1, ty_Int)
new_esEs6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_lt10(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_not(False)
new_esEs4(Just(x0), Just(x1), ty_Integer)
new_ltEs17(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_lt20(x0, x1, ty_Char)
new_lt19(x0, x1, ty_Bool)
new_primCmpNat0(Succ(x0), Succ(x1))
new_ltEs10(EQ, GT)
new_ltEs10(GT, EQ)
new_esEs22(x0, x1, ty_Double)
new_esEs10(Float(x0, x1), Float(x2, x3))
new_esEs26(x0, x1, ty_Int)
new_esEs4(Just(x0), Just(x1), ty_Float)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_compare24(x0, x1, True)
new_ltEs17(Right(x0), Right(x1), x2, ty_Int)
new_esEs25(x0, x1, ty_@0)
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_compare9(x0, x1, ty_Int)
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs21(x0, x1, app(ty_[], x2))
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primMulNat0(Succ(x0), Zero)
new_esEs28(x0, x1, ty_Bool)
new_lt19(x0, x1, ty_Float)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs8(EQ, LT)
new_esEs8(LT, EQ)
new_lt20(x0, x1, ty_@0)
new_compare0([], :(x0, x1), x2)
new_lt19(x0, x1, app(ty_[], x2))
new_esEs7(Right(x0), Right(x1), x2, ty_Int)
new_esEs7(Left(x0), Left(x1), ty_Ordering, x2)
new_compare19(x0, x1, x2, x3, x4)
new_ltEs4(@2(x0, x1), @2(x2, x3), x4, x5)
new_lt8(x0, x1)
new_esEs25(x0, x1, ty_Int)
new_esEs4(Just(x0), Just(x1), app(ty_Ratio, x2))
new_ltEs7(Just(x0), Just(x1), ty_Bool)
new_compare12(x0, x1, False, x2, x3, x4)
new_esEs17(False, True)
new_esEs17(True, False)
new_ltEs17(Right(x0), Right(x1), x2, ty_Char)
new_esEs28(x0, x1, app(ty_[], x2))
new_compare110(x0, x1, True)
new_ltEs7(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs30(x0, x1, ty_Float)
new_ltEs8(x0, x1)
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_compare24(x0, x1, False)
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_esEs28(x0, x1, ty_Char)
new_esEs26(x0, x1, ty_Char)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare9(x0, x1, ty_Double)
new_ltEs17(Left(x0), Right(x1), x2, x3)
new_ltEs17(Right(x0), Left(x1), x2, x3)
new_esEs14([], [], x0)
new_primEqInt(Pos(Zero), Pos(Zero))
new_esEs17(True, True)
new_ltEs21(x0, x1, app(app(ty_Either, x2), x3))
new_lt12(x0, x1)
new_esEs29(x0, x1, ty_Integer)
new_ltEs18(x0, x1, app(ty_Maybe, x2))
new_ltEs21(x0, x1, ty_Char)
new_ltEs18(x0, x1, ty_@0)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs20(x0, x1, ty_Double)
new_lt10(x0, x1, ty_Float)
new_esEs25(x0, x1, ty_Char)
new_ltEs19(x0, x1, ty_Char)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs28(x0, x1, ty_Ordering)
new_esEs29(x0, x1, ty_Int)
new_ltEs17(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_ltEs5(True, False)
new_ltEs5(False, True)
new_ltEs19(x0, x1, app(ty_[], x2))
new_esEs19(x0, x1, ty_Int)
new_esEs24(x0, x1, ty_Int)
new_ltEs18(x0, x1, ty_Bool)
new_esEs4(Just(x0), Just(x1), ty_Char)
new_ltEs7(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs7(Right(x0), Left(x1), x2, x3)
new_esEs7(Left(x0), Right(x1), x2, x3)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, ty_Int)
new_pePe(False, x0)
new_esEs30(x0, x1, app(app(ty_@2, x2), x3))
new_esEs22(x0, x1, ty_@0)
new_esEs29(x0, x1, ty_Float)
new_ltEs19(x0, x1, ty_Float)
new_esEs14(:(x0, x1), [], x2)
new_esEs28(x0, x1, ty_Integer)
new_ltEs10(EQ, EQ)
new_esEs20(x0, x1, app(ty_[], x2))

We have to consider all minimal (P,Q,R)-chains.
As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [15] we can delete all non-usable rules [17] from R.

↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ IFR
        ↳ HASKELL
          ↳ BR
            ↳ HASKELL
              ↳ COR
                ↳ HASKELL
                  ↳ LetRed
                    ↳ HASKELL
                      ↳ NumRed
                        ↳ HASKELL
                          ↳ Narrow
                            ↳ AND
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                                ↳ DependencyGraphProof
                                  ↳ AND
                                    ↳ QDP
                                    ↳ QDP
                                      ↳ UsableRulesProof
                                        ↳ QDP
                                          ↳ QReductionProof

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

new_insertBy02(vxw37, vxw38, vxw39, False, ca, cb) → new_insertBy(Right(vxw38), vxw39, ca, cb)
new_insertBy01(vxw19, vxw20, vxw21, False, bg, bh) → new_insertBy02(vxw19, vxw20, vxw21, new_ltEs21(vxw20, vxw19, bh), bg, bh)
new_insertBy(Right(vxw30), :(Right(vxw400), vxw41), be, bf) → new_insertBy01(vxw400, vxw30, vxw41, new_esEs30(vxw30, vxw400, bf), be, bf)
new_insertBy(Right(vxw30), :(Left(vxw400), vxw41), be, bf) → new_insertBy(Right(vxw30), vxw41, be, bf)

The TRS R consists of the following rules:

new_ltEs21(vxw20, vxw19, app(ty_[], dfc)) → new_ltEs12(vxw20, vxw19, dfc)
new_ltEs21(vxw20, vxw19, ty_Int) → new_ltEs16(vxw20, vxw19)
new_ltEs21(vxw20, vxw19, app(app(ty_@2, deh), dfa)) → new_ltEs4(vxw20, vxw19, deh, dfa)
new_ltEs21(vxw20, vxw19, ty_@0) → new_ltEs14(vxw20, vxw19)
new_ltEs21(vxw20, vxw19, ty_Bool) → new_ltEs5(vxw20, vxw19)
new_ltEs21(vxw20, vxw19, app(ty_Ratio, dfb)) → new_ltEs11(vxw20, vxw19, dfb)
new_ltEs21(vxw20, vxw19, ty_Integer) → new_ltEs13(vxw20, vxw19)
new_ltEs21(vxw20, vxw19, app(app(app(ty_@3, dfd), dfe), dff)) → new_ltEs6(vxw20, vxw19, dfd, dfe, dff)
new_ltEs21(vxw20, vxw19, app(app(ty_Either, dfg), dfh)) → new_ltEs17(vxw20, vxw19, dfg, dfh)
new_ltEs21(vxw20, vxw19, ty_Ordering) → new_ltEs10(vxw20, vxw19)
new_ltEs21(vxw20, vxw19, ty_Char) → new_ltEs8(vxw20, vxw19)
new_ltEs21(vxw20, vxw19, app(ty_Maybe, deg)) → new_ltEs7(vxw20, vxw19, deg)
new_ltEs21(vxw20, vxw19, ty_Float) → new_ltEs15(vxw20, vxw19)
new_ltEs21(vxw20, vxw19, ty_Double) → new_ltEs9(vxw20, vxw19)
new_ltEs9(vxw11, vxw10) → new_not(new_esEs8(new_compare15(vxw11, vxw10), GT))
new_compare15(Double(vxw110, vxw111), Double(vxw100, vxw101)) → new_compare27(new_sr(vxw110, vxw100), new_sr(vxw111, vxw101))
new_esEs8(GT, GT) → True
new_esEs8(LT, GT) → False
new_esEs8(EQ, GT) → False
new_not(False) → True
new_not(True) → False
new_sr(vxw300, vxw4000) → new_primMulInt(vxw300, vxw4000)
new_compare27(vxw11, vxw10) → new_primCmpInt(vxw11, vxw10)
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(vxw1100)), Neg(vxw100)) → new_primCmpNat0(vxw100, Succ(vxw1100))
new_primCmpInt(Neg(Zero), Pos(Succ(vxw1000))) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(vxw1000))) → new_primCmpNat0(Zero, Succ(vxw1000))
new_primCmpInt(Pos(Succ(vxw1100)), Pos(vxw100)) → new_primCmpNat0(Succ(vxw1100), vxw100)
new_primCmpInt(Pos(Succ(vxw1100)), Neg(vxw100)) → GT
new_primCmpInt(Neg(Zero), Neg(Succ(vxw1000))) → new_primCmpNat0(Succ(vxw1000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(vxw1000))) → GT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(vxw1100)), Pos(vxw100)) → LT
new_primCmpNat0(Succ(vxw1100), Zero) → GT
new_primCmpNat0(Succ(vxw1100), Succ(vxw1000)) → new_primCmpNat0(vxw1100, vxw1000)
new_primCmpNat0(Zero, Succ(vxw1000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primMulInt(Pos(vxw3000), Pos(vxw40000)) → Pos(new_primMulNat0(vxw3000, vxw40000))
new_primMulInt(Neg(vxw3000), Neg(vxw40000)) → Pos(new_primMulNat0(vxw3000, vxw40000))
new_primMulInt(Neg(vxw3000), Pos(vxw40000)) → Neg(new_primMulNat0(vxw3000, vxw40000))
new_primMulInt(Pos(vxw3000), Neg(vxw40000)) → Neg(new_primMulNat0(vxw3000, vxw40000))
new_primMulNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, Succ(vxw400000)) → Zero
new_primMulNat0(Succ(vxw30000), Zero) → Zero
new_primMulNat0(Succ(vxw30000), Succ(vxw400000)) → new_primPlusNat0(new_primMulNat0(vxw30000, Succ(vxw400000)), vxw400000)
new_primPlusNat0(Succ(vxw620), vxw400000) → Succ(Succ(new_primPlusNat1(vxw620, vxw400000)))
new_primPlusNat0(Zero, vxw400000) → Succ(vxw400000)
new_primPlusNat1(Zero, Succ(vxw4000000)) → Succ(vxw4000000)
new_primPlusNat1(Succ(vxw6200), Zero) → Succ(vxw6200)
new_primPlusNat1(Succ(vxw6200), Succ(vxw4000000)) → Succ(Succ(new_primPlusNat1(vxw6200, vxw4000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_ltEs15(vxw11, vxw10) → new_not(new_esEs8(new_compare26(vxw11, vxw10), GT))
new_compare26(Float(vxw110, vxw111), Float(vxw100, vxw101)) → new_compare27(new_sr(vxw110, vxw100), new_sr(vxw111, vxw101))
new_ltEs7(Just(vxw110), Just(vxw100), ty_Bool) → new_ltEs5(vxw110, vxw100)
new_ltEs7(Just(vxw110), Just(vxw100), app(app(app(ty_@3, bcd), bce), bcf)) → new_ltEs6(vxw110, vxw100, bcd, bce, bcf)
new_ltEs7(Just(vxw110), Just(vxw100), app(app(ty_@2, bbh), bca)) → new_ltEs4(vxw110, vxw100, bbh, bca)
new_ltEs7(Just(vxw110), Just(vxw100), ty_Ordering) → new_ltEs10(vxw110, vxw100)
new_ltEs7(Just(vxw110), Just(vxw100), ty_Integer) → new_ltEs13(vxw110, vxw100)
new_ltEs7(Just(vxw110), Just(vxw100), ty_Int) → new_ltEs16(vxw110, vxw100)
new_ltEs7(Nothing, Just(vxw100), bbf) → True
new_ltEs7(Just(vxw110), Just(vxw100), ty_Float) → new_ltEs15(vxw110, vxw100)
new_ltEs7(Just(vxw110), Just(vxw100), ty_Double) → new_ltEs9(vxw110, vxw100)
new_ltEs7(Nothing, Nothing, bbf) → True
new_ltEs7(Just(vxw110), Just(vxw100), app(ty_[], bcc)) → new_ltEs12(vxw110, vxw100, bcc)
new_ltEs7(Just(vxw110), Just(vxw100), ty_Char) → new_ltEs8(vxw110, vxw100)
new_ltEs7(Just(vxw110), Just(vxw100), ty_@0) → new_ltEs14(vxw110, vxw100)
new_ltEs7(Just(vxw110), Nothing, bbf) → False
new_ltEs7(Just(vxw110), Just(vxw100), app(ty_Ratio, bcb)) → new_ltEs11(vxw110, vxw100, bcb)
new_ltEs17(Left(vxw110), Left(vxw100), app(app(ty_Either, cag), cah), bdh) → new_ltEs17(vxw110, vxw100, cag, cah)
new_ltEs17(Right(vxw110), Right(vxw100), bdg, app(app(ty_Either, cca), ccb)) → new_ltEs17(vxw110, vxw100, cca, ccb)
new_ltEs7(Just(vxw110), Just(vxw100), app(ty_Maybe, bbg)) → new_ltEs7(vxw110, vxw100, bbg)
new_ltEs7(Just(vxw110), Just(vxw100), app(app(ty_Either, bcg), bch)) → new_ltEs17(vxw110, vxw100, bcg, bch)
new_ltEs17(Right(vxw110), Right(vxw100), bdg, app(ty_Maybe, cba)) → new_ltEs7(vxw110, vxw100, cba)
new_ltEs17(Left(vxw110), Left(vxw100), app(ty_Maybe, bhg), bdh) → new_ltEs7(vxw110, vxw100, bhg)
new_ltEs17(Right(vxw110), Right(vxw100), bdg, app(ty_Ratio, cbd)) → new_ltEs11(vxw110, vxw100, cbd)
new_ltEs17(Left(vxw110), Left(vxw100), app(ty_Ratio, cab), bdh) → new_ltEs11(vxw110, vxw100, cab)
new_ltEs17(Left(vxw110), Left(vxw100), ty_Integer, bdh) → new_ltEs13(vxw110, vxw100)
new_ltEs17(Right(vxw110), Right(vxw100), bdg, ty_Integer) → new_ltEs13(vxw110, vxw100)
new_ltEs17(Left(vxw110), Left(vxw100), ty_Bool, bdh) → new_ltEs5(vxw110, vxw100)
new_ltEs17(Left(vxw110), Left(vxw100), ty_Double, bdh) → new_ltEs9(vxw110, vxw100)
new_ltEs17(Left(vxw110), Left(vxw100), ty_Ordering, bdh) → new_ltEs10(vxw110, vxw100)
new_ltEs17(Right(vxw110), Left(vxw100), bdg, bdh) → False
new_ltEs17(Right(vxw110), Right(vxw100), bdg, ty_Ordering) → new_ltEs10(vxw110, vxw100)
new_ltEs17(Right(vxw110), Right(vxw100), bdg, ty_Int) → new_ltEs16(vxw110, vxw100)
new_ltEs17(Left(vxw110), Left(vxw100), app(app(ty_@2, bhh), caa), bdh) → new_ltEs4(vxw110, vxw100, bhh, caa)
new_ltEs17(Left(vxw110), Left(vxw100), app(app(app(ty_@3, cad), cae), caf), bdh) → new_ltEs6(vxw110, vxw100, cad, cae, caf)
new_ltEs17(Left(vxw110), Left(vxw100), app(ty_[], cac), bdh) → new_ltEs12(vxw110, vxw100, cac)
new_ltEs17(Left(vxw110), Left(vxw100), ty_Float, bdh) → new_ltEs15(vxw110, vxw100)
new_ltEs17(Right(vxw110), Right(vxw100), bdg, ty_@0) → new_ltEs14(vxw110, vxw100)
new_ltEs17(Left(vxw110), Left(vxw100), ty_Char, bdh) → new_ltEs8(vxw110, vxw100)
new_ltEs17(Left(vxw110), Left(vxw100), ty_@0, bdh) → new_ltEs14(vxw110, vxw100)
new_ltEs17(Right(vxw110), Right(vxw100), bdg, ty_Float) → new_ltEs15(vxw110, vxw100)
new_ltEs17(Left(vxw110), Right(vxw100), bdg, bdh) → True
new_ltEs17(Right(vxw110), Right(vxw100), bdg, app(ty_[], cbe)) → new_ltEs12(vxw110, vxw100, cbe)
new_ltEs17(Right(vxw110), Right(vxw100), bdg, ty_Double) → new_ltEs9(vxw110, vxw100)
new_ltEs17(Right(vxw110), Right(vxw100), bdg, ty_Char) → new_ltEs8(vxw110, vxw100)
new_ltEs17(Left(vxw110), Left(vxw100), ty_Int, bdh) → new_ltEs16(vxw110, vxw100)
new_ltEs17(Right(vxw110), Right(vxw100), bdg, app(app(app(ty_@3, cbf), cbg), cbh)) → new_ltEs6(vxw110, vxw100, cbf, cbg, cbh)
new_ltEs17(Right(vxw110), Right(vxw100), bdg, app(app(ty_@2, cbb), cbc)) → new_ltEs4(vxw110, vxw100, cbb, cbc)
new_ltEs17(Right(vxw110), Right(vxw100), bdg, ty_Bool) → new_ltEs5(vxw110, vxw100)
new_ltEs5(True, False) → False
new_ltEs5(True, True) → True
new_ltEs5(False, False) → True
new_ltEs5(False, True) → True
new_ltEs4(@2(vxw110, vxw111), @2(vxw100, vxw101), bdb, bdc) → new_pePe(new_lt10(vxw110, vxw100, bdb), new_asAs(new_esEs23(vxw110, vxw100, bdb), new_ltEs18(vxw111, vxw101, bdc)))
new_lt10(vxw110, vxw100, ty_Double) → new_lt13(vxw110, vxw100)
new_lt10(vxw110, vxw100, ty_Bool) → new_lt9(vxw110, vxw100)
new_lt10(vxw110, vxw100, app(app(ty_@2, dh), ea)) → new_lt11(vxw110, vxw100, dh, ea)
new_lt10(vxw110, vxw100, ty_Char) → new_lt12(vxw110, vxw100)
new_lt10(vxw110, vxw100, app(app(ty_Either, cdg), cdh)) → new_lt18(vxw110, vxw100, cdg, cdh)
new_lt10(vxw110, vxw100, app(app(app(ty_@3, ha), hb), hc)) → new_lt16(vxw110, vxw100, ha, hb, hc)
new_lt10(vxw110, vxw100, ty_Float) → new_lt17(vxw110, vxw100)
new_lt10(vxw110, vxw100, app(ty_Ratio, cde)) → new_lt14(vxw110, vxw100, cde)
new_lt10(vxw110, vxw100, app(ty_Maybe, cd)) → new_lt5(vxw110, vxw100, cd)
new_lt10(vxw110, vxw100, app(ty_[], cdf)) → new_lt15(vxw110, vxw100, cdf)
new_lt10(vxw110, vxw100, ty_@0) → new_lt8(vxw110, vxw100)
new_lt10(vxw110, vxw100, ty_Int) → new_lt7(vxw110, vxw100)
new_lt10(vxw110, vxw100, ty_Integer) → new_lt4(vxw110, vxw100)
new_lt10(vxw110, vxw100, ty_Ordering) → new_lt6(vxw110, vxw100)
new_esEs23(vxw110, vxw100, app(app(ty_Either, cdg), cdh)) → new_esEs7(vxw110, vxw100, cdg, cdh)
new_esEs23(vxw110, vxw100, app(ty_Ratio, cde)) → new_esEs13(vxw110, vxw100, cde)
new_esEs23(vxw110, vxw100, ty_Double) → new_esEs9(vxw110, vxw100)
new_esEs23(vxw110, vxw100, app(ty_Maybe, cd)) → new_esEs4(vxw110, vxw100, cd)
new_esEs23(vxw110, vxw100, ty_Ordering) → new_esEs8(vxw110, vxw100)
new_esEs23(vxw110, vxw100, ty_Float) → new_esEs10(vxw110, vxw100)
new_esEs23(vxw110, vxw100, ty_Integer) → new_esEs11(vxw110, vxw100)
new_esEs23(vxw110, vxw100, app(app(ty_@2, dh), ea)) → new_esEs5(vxw110, vxw100, dh, ea)
new_esEs23(vxw110, vxw100, ty_@0) → new_esEs15(vxw110, vxw100)
new_esEs23(vxw110, vxw100, app(ty_[], cdf)) → new_esEs14(vxw110, vxw100, cdf)
new_esEs23(vxw110, vxw100, ty_Bool) → new_esEs17(vxw110, vxw100)
new_esEs23(vxw110, vxw100, app(app(app(ty_@3, ha), hb), hc)) → new_esEs6(vxw110, vxw100, ha, hb, hc)
new_esEs23(vxw110, vxw100, ty_Char) → new_esEs12(vxw110, vxw100)
new_esEs23(vxw110, vxw100, ty_Int) → new_esEs16(vxw110, vxw100)
new_ltEs18(vxw111, vxw101, ty_Float) → new_ltEs15(vxw111, vxw101)
new_ltEs18(vxw111, vxw101, ty_Char) → new_ltEs8(vxw111, vxw101)
new_ltEs18(vxw111, vxw101, ty_Int) → new_ltEs16(vxw111, vxw101)
new_ltEs18(vxw111, vxw101, app(app(ty_Either, cdc), cdd)) → new_ltEs17(vxw111, vxw101, cdc, cdd)
new_ltEs18(vxw111, vxw101, ty_@0) → new_ltEs14(vxw111, vxw101)
new_ltEs18(vxw111, vxw101, ty_Integer) → new_ltEs13(vxw111, vxw101)
new_ltEs18(vxw111, vxw101, ty_Bool) → new_ltEs5(vxw111, vxw101)
new_ltEs18(vxw111, vxw101, app(ty_Ratio, ccf)) → new_ltEs11(vxw111, vxw101, ccf)
new_ltEs18(vxw111, vxw101, app(app(app(ty_@3, cch), cda), cdb)) → new_ltEs6(vxw111, vxw101, cch, cda, cdb)
new_ltEs18(vxw111, vxw101, app(ty_Maybe, ccc)) → new_ltEs7(vxw111, vxw101, ccc)
new_ltEs18(vxw111, vxw101, app(ty_[], ccg)) → new_ltEs12(vxw111, vxw101, ccg)
new_ltEs18(vxw111, vxw101, app(app(ty_@2, ccd), cce)) → new_ltEs4(vxw111, vxw101, ccd, cce)
new_ltEs18(vxw111, vxw101, ty_Double) → new_ltEs9(vxw111, vxw101)
new_ltEs18(vxw111, vxw101, ty_Ordering) → new_ltEs10(vxw111, vxw101)
new_asAs(False, vxw53) → False
new_asAs(True, vxw53) → vxw53
new_pePe(False, vxw60) → vxw60
new_pePe(True, vxw60) → True
new_ltEs10(EQ, GT) → True
new_ltEs10(GT, EQ) → False
new_ltEs10(LT, EQ) → True
new_ltEs10(GT, GT) → True
new_ltEs10(LT, GT) → True
new_ltEs10(EQ, EQ) → True
new_ltEs10(LT, LT) → True
new_ltEs10(EQ, LT) → False
new_ltEs10(GT, LT) → False
new_ltEs12(vxw11, vxw10, cc) → new_not(new_esEs8(new_compare0(vxw11, vxw10, cc), GT))
new_compare0(:(vxw110, vxw111), :(vxw100, vxw101), cc) → new_primCompAux0(vxw110, vxw100, new_compare0(vxw111, vxw101, cc), cc)
new_compare0([], [], cc) → EQ
new_compare0(:(vxw110, vxw111), [], cc) → GT
new_compare0([], :(vxw100, vxw101), cc) → LT
new_primCompAux0(vxw110, vxw100, vxw61, cc) → new_primCompAux00(vxw61, new_compare9(vxw110, vxw100, cc))
new_compare9(vxw110, vxw100, ty_Double) → new_compare15(vxw110, vxw100)
new_compare9(vxw110, vxw100, ty_Integer) → new_compare6(vxw110, vxw100)
new_compare9(vxw110, vxw100, ty_Int) → new_compare27(vxw110, vxw100)
new_compare9(vxw110, vxw100, app(app(app(ty_@3, baa), bab), bac)) → new_compare19(vxw110, vxw100, baa, bab, bac)
new_compare9(vxw110, vxw100, app(ty_Maybe, hd)) → new_compare8(vxw110, vxw100, hd)
new_compare9(vxw110, vxw100, app(ty_[], hh)) → new_compare0(vxw110, vxw100, hh)
new_compare9(vxw110, vxw100, ty_Bool) → new_compare18(vxw110, vxw100)
new_compare9(vxw110, vxw100, ty_Float) → new_compare26(vxw110, vxw100)
new_compare9(vxw110, vxw100, ty_@0) → new_compare7(vxw110, vxw100)
new_compare9(vxw110, vxw100, app(app(ty_@2, he), hf)) → new_compare13(vxw110, vxw100, he, hf)
new_compare9(vxw110, vxw100, ty_Ordering) → new_compare16(vxw110, vxw100)
new_compare9(vxw110, vxw100, app(app(ty_Either, bad), bae)) → new_compare28(vxw110, vxw100, bad, bae)
new_compare9(vxw110, vxw100, ty_Char) → new_compare14(vxw110, vxw100)
new_compare9(vxw110, vxw100, app(ty_Ratio, hg)) → new_compare17(vxw110, vxw100, hg)
new_primCompAux00(vxw72, LT) → LT
new_primCompAux00(vxw72, EQ) → vxw72
new_primCompAux00(vxw72, GT) → GT
new_compare17(:%(vxw110, vxw111), :%(vxw100, vxw101), ty_Int) → new_compare27(new_sr(vxw110, vxw101), new_sr(vxw100, vxw111))
new_compare17(:%(vxw110, vxw111), :%(vxw100, vxw101), ty_Integer) → new_compare6(new_sr0(vxw110, vxw101), new_sr0(vxw100, vxw111))
new_sr0(Integer(vxw1100), Integer(vxw1010)) → Integer(new_primMulInt(vxw1100, vxw1010))
new_compare6(Integer(vxw110), Integer(vxw100)) → new_primCmpInt(vxw110, vxw100)
new_compare14(Char(vxw110), Char(vxw100)) → new_primCmpNat0(vxw110, vxw100)
new_compare28(vxw110, vxw100, cdg, cdh) → new_compare29(vxw110, vxw100, new_esEs7(vxw110, vxw100, cdg, cdh), cdg, cdh)
new_esEs7(Right(vxw300), Right(vxw4000), ff, ty_Ordering) → new_esEs8(vxw300, vxw4000)
new_esEs7(Left(vxw300), Right(vxw4000), ff, ed) → False
new_esEs7(Right(vxw300), Left(vxw4000), ff, ed) → False
new_esEs7(Left(vxw300), Left(vxw4000), ty_Double, ed) → new_esEs9(vxw300, vxw4000)
new_esEs7(Right(vxw300), Right(vxw4000), ff, ty_Double) → new_esEs9(vxw300, vxw4000)
new_esEs7(Right(vxw300), Right(vxw4000), ff, app(app(ty_@2, fg), fh)) → new_esEs5(vxw300, vxw4000, fg, fh)
new_esEs7(Left(vxw300), Left(vxw4000), ty_Integer, ed) → new_esEs11(vxw300, vxw4000)
new_esEs7(Left(vxw300), Left(vxw4000), app(app(ty_@2, eb), ec), ed) → new_esEs5(vxw300, vxw4000, eb, ec)
new_esEs7(Left(vxw300), Left(vxw4000), ty_Ordering, ed) → new_esEs8(vxw300, vxw4000)
new_esEs7(Right(vxw300), Right(vxw4000), ff, app(app(app(ty_@3, ga), gb), gc)) → new_esEs6(vxw300, vxw4000, ga, gb, gc)
new_esEs7(Right(vxw300), Right(vxw4000), ff, ty_Char) → new_esEs12(vxw300, vxw4000)
new_esEs7(Right(vxw300), Right(vxw4000), ff, ty_@0) → new_esEs15(vxw300, vxw4000)
new_esEs7(Right(vxw300), Right(vxw4000), ff, app(ty_Ratio, gd)) → new_esEs13(vxw300, vxw4000, gd)
new_esEs7(Left(vxw300), Left(vxw4000), app(ty_Ratio, eh), ed) → new_esEs13(vxw300, vxw4000, eh)
new_esEs7(Left(vxw300), Left(vxw4000), ty_@0, ed) → new_esEs15(vxw300, vxw4000)
new_esEs7(Right(vxw300), Right(vxw4000), ff, ty_Float) → new_esEs10(vxw300, vxw4000)
new_esEs7(Left(vxw300), Left(vxw4000), ty_Int, ed) → new_esEs16(vxw300, vxw4000)
new_esEs7(Right(vxw300), Right(vxw4000), ff, ty_Integer) → new_esEs11(vxw300, vxw4000)
new_esEs7(Right(vxw300), Right(vxw4000), ff, ty_Bool) → new_esEs17(vxw300, vxw4000)
new_esEs7(Left(vxw300), Left(vxw4000), ty_Char, ed) → new_esEs12(vxw300, vxw4000)
new_esEs7(Right(vxw300), Right(vxw4000), ff, app(ty_[], ge)) → new_esEs14(vxw300, vxw4000, ge)
new_esEs7(Left(vxw300), Left(vxw4000), ty_Float, ed) → new_esEs10(vxw300, vxw4000)
new_esEs7(Left(vxw300), Left(vxw4000), app(app(app(ty_@3, ee), ef), eg), ed) → new_esEs6(vxw300, vxw4000, ee, ef, eg)
new_esEs7(Right(vxw300), Right(vxw4000), ff, ty_Int) → new_esEs16(vxw300, vxw4000)
new_esEs7(Left(vxw300), Left(vxw4000), ty_Bool, ed) → new_esEs17(vxw300, vxw4000)
new_esEs7(Left(vxw300), Left(vxw4000), app(ty_[], fa), ed) → new_esEs14(vxw300, vxw4000, fa)
new_compare29(vxw110, vxw100, False, cdg, cdh) → new_compare111(vxw110, vxw100, new_ltEs17(vxw110, vxw100, cdg, cdh), cdg, cdh)
new_compare29(vxw110, vxw100, True, cdg, cdh) → EQ
new_esEs7(Left(vxw300), Left(vxw4000), app(app(ty_Either, fc), fd), ed) → new_esEs7(vxw300, vxw4000, fc, fd)
new_esEs4(Just(vxw300), Just(vxw4000), app(app(ty_Either, cfa), cfb)) → new_esEs7(vxw300, vxw4000, cfa, cfb)
new_esEs4(Just(vxw300), Just(vxw4000), app(ty_Maybe, ceh)) → new_esEs4(vxw300, vxw4000, ceh)
new_esEs7(Right(vxw300), Right(vxw4000), ff, app(app(ty_Either, gg), gh)) → new_esEs7(vxw300, vxw4000, gg, gh)
new_esEs7(Left(vxw300), Left(vxw4000), app(ty_Maybe, fb), ed) → new_esEs4(vxw300, vxw4000, fb)
new_esEs7(Right(vxw300), Right(vxw4000), ff, app(ty_Maybe, gf)) → new_esEs4(vxw300, vxw4000, gf)
new_esEs4(Just(vxw300), Just(vxw4000), ty_Ordering) → new_esEs8(vxw300, vxw4000)
new_esEs4(Just(vxw300), Nothing, bbe) → False
new_esEs4(Nothing, Just(vxw4000), bbe) → False
new_esEs4(Just(vxw300), Just(vxw4000), ty_Char) → new_esEs12(vxw300, vxw4000)
new_esEs4(Just(vxw300), Just(vxw4000), app(app(app(ty_@3, cec), ced), cee)) → new_esEs6(vxw300, vxw4000, cec, ced, cee)
new_esEs4(Just(vxw300), Just(vxw4000), ty_Float) → new_esEs10(vxw300, vxw4000)
new_esEs4(Just(vxw300), Just(vxw4000), ty_Integer) → new_esEs11(vxw300, vxw4000)
new_esEs4(Just(vxw300), Just(vxw4000), ty_Bool) → new_esEs17(vxw300, vxw4000)
new_esEs4(Just(vxw300), Just(vxw4000), app(app(ty_@2, cea), ceb)) → new_esEs5(vxw300, vxw4000, cea, ceb)
new_esEs4(Just(vxw300), Just(vxw4000), ty_Int) → new_esEs16(vxw300, vxw4000)
new_esEs4(Just(vxw300), Just(vxw4000), ty_@0) → new_esEs15(vxw300, vxw4000)
new_esEs4(Nothing, Nothing, bbe) → True
new_esEs4(Just(vxw300), Just(vxw4000), app(ty_Ratio, cef)) → new_esEs13(vxw300, vxw4000, cef)
new_esEs4(Just(vxw300), Just(vxw4000), app(ty_[], ceg)) → new_esEs14(vxw300, vxw4000, ceg)
new_esEs4(Just(vxw300), Just(vxw4000), ty_Double) → new_esEs9(vxw300, vxw4000)
new_esEs9(Double(vxw300, vxw301), Double(vxw4000, vxw4001)) → new_esEs16(new_sr(vxw300, vxw4000), new_sr(vxw301, vxw4001))
new_esEs16(vxw30, vxw400) → new_primEqInt(vxw30, vxw400)
new_primEqInt(Neg(Succ(vxw3000)), Neg(Succ(vxw40000))) → new_primEqNat0(vxw3000, vxw40000)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Succ(vxw3000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(vxw40000))) → False
new_primEqInt(Pos(Succ(vxw3000)), Pos(Succ(vxw40000))) → new_primEqNat0(vxw3000, vxw40000)
new_primEqInt(Pos(Succ(vxw3000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(vxw40000))) → False
new_primEqInt(Pos(Succ(vxw3000)), Neg(vxw4000)) → False
new_primEqInt(Neg(Succ(vxw3000)), Pos(vxw4000)) → False
new_primEqInt(Pos(Zero), Neg(Succ(vxw40000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(vxw40000))) → False
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqNat0(Zero, Zero) → True
new_primEqNat0(Succ(vxw3000), Succ(vxw40000)) → new_primEqNat0(vxw3000, vxw40000)
new_primEqNat0(Succ(vxw3000), Zero) → False
new_primEqNat0(Zero, Succ(vxw40000)) → False
new_esEs14([], [], bbd) → True
new_esEs14([], :(vxw4000, vxw4001), bbd) → False
new_esEs14(:(vxw300, vxw301), [], bbd) → False
new_esEs14(:(vxw300, vxw301), :(vxw4000, vxw4001), bbd) → new_asAs(new_esEs24(vxw300, vxw4000, bbd), new_esEs14(vxw301, vxw4001, bbd))
new_esEs24(vxw300, vxw4000, app(ty_Maybe, cgb)) → new_esEs4(vxw300, vxw4000, cgb)
new_esEs24(vxw300, vxw4000, app(app(ty_@2, cfc), cfd)) → new_esEs5(vxw300, vxw4000, cfc, cfd)
new_esEs24(vxw300, vxw4000, app(app(ty_Either, cgc), cgd)) → new_esEs7(vxw300, vxw4000, cgc, cgd)
new_esEs24(vxw300, vxw4000, ty_Int) → new_esEs16(vxw300, vxw4000)
new_esEs24(vxw300, vxw4000, ty_Bool) → new_esEs17(vxw300, vxw4000)
new_esEs24(vxw300, vxw4000, ty_Char) → new_esEs12(vxw300, vxw4000)
new_esEs24(vxw300, vxw4000, app(app(app(ty_@3, cfe), cff), cfg)) → new_esEs6(vxw300, vxw4000, cfe, cff, cfg)
new_esEs24(vxw300, vxw4000, ty_Ordering) → new_esEs8(vxw300, vxw4000)
new_esEs24(vxw300, vxw4000, ty_@0) → new_esEs15(vxw300, vxw4000)
new_esEs24(vxw300, vxw4000, app(ty_Ratio, cfh)) → new_esEs13(vxw300, vxw4000, cfh)
new_esEs24(vxw300, vxw4000, ty_Double) → new_esEs9(vxw300, vxw4000)
new_esEs24(vxw300, vxw4000, app(ty_[], cga)) → new_esEs14(vxw300, vxw4000, cga)
new_esEs24(vxw300, vxw4000, ty_Integer) → new_esEs11(vxw300, vxw4000)
new_esEs24(vxw300, vxw4000, ty_Float) → new_esEs10(vxw300, vxw4000)
new_esEs10(Float(vxw300, vxw301), Float(vxw4000, vxw4001)) → new_esEs16(new_sr(vxw300, vxw4000), new_sr(vxw301, vxw4001))
new_esEs11(Integer(vxw300), Integer(vxw4000)) → new_primEqInt(vxw300, vxw4000)
new_esEs13(:%(vxw300, vxw301), :%(vxw4000, vxw4001), bbc) → new_asAs(new_esEs19(vxw300, vxw4000, bbc), new_esEs18(vxw301, vxw4001, bbc))
new_esEs19(vxw300, vxw4000, ty_Integer) → new_esEs11(vxw300, vxw4000)
new_esEs19(vxw300, vxw4000, ty_Int) → new_esEs16(vxw300, vxw4000)
new_esEs18(vxw301, vxw4001, ty_Integer) → new_esEs11(vxw301, vxw4001)
new_esEs18(vxw301, vxw4001, ty_Int) → new_esEs16(vxw301, vxw4001)
new_esEs15(@0, @0) → True
new_esEs8(LT, LT) → True
new_esEs8(GT, LT) → False
new_esEs8(EQ, EQ) → True
new_esEs8(LT, EQ) → False
new_esEs8(EQ, LT) → False
new_esEs8(GT, EQ) → False
new_esEs6(@3(vxw300, vxw301, vxw302), @3(vxw4000, vxw4001, vxw4002), bah, bba, bbb) → new_asAs(new_esEs22(vxw300, vxw4000, bah), new_asAs(new_esEs21(vxw301, vxw4001, bba), new_esEs20(vxw302, vxw4002, bbb)))
new_esEs22(vxw300, vxw4000, ty_Char) → new_esEs12(vxw300, vxw4000)
new_esEs22(vxw300, vxw4000, app(app(ty_@2, bge), bgf)) → new_esEs5(vxw300, vxw4000, bge, bgf)
new_esEs22(vxw300, vxw4000, app(ty_[], bhc)) → new_esEs14(vxw300, vxw4000, bhc)
new_esEs22(vxw300, vxw4000, app(app(ty_Either, bhe), bhf)) → new_esEs7(vxw300, vxw4000, bhe, bhf)
new_esEs22(vxw300, vxw4000, ty_@0) → new_esEs15(vxw300, vxw4000)
new_esEs22(vxw300, vxw4000, ty_Ordering) → new_esEs8(vxw300, vxw4000)
new_esEs22(vxw300, vxw4000, ty_Double) → new_esEs9(vxw300, vxw4000)
new_esEs22(vxw300, vxw4000, app(app(app(ty_@3, bgg), bgh), bha)) → new_esEs6(vxw300, vxw4000, bgg, bgh, bha)
new_esEs22(vxw300, vxw4000, app(ty_Maybe, bhd)) → new_esEs4(vxw300, vxw4000, bhd)
new_esEs22(vxw300, vxw4000, app(ty_Ratio, bhb)) → new_esEs13(vxw300, vxw4000, bhb)
new_esEs22(vxw300, vxw4000, ty_Bool) → new_esEs17(vxw300, vxw4000)
new_esEs22(vxw300, vxw4000, ty_Integer) → new_esEs11(vxw300, vxw4000)
new_esEs22(vxw300, vxw4000, ty_Float) → new_esEs10(vxw300, vxw4000)
new_esEs22(vxw300, vxw4000, ty_Int) → new_esEs16(vxw300, vxw4000)
new_esEs21(vxw301, vxw4001, ty_Bool) → new_esEs17(vxw301, vxw4001)
new_esEs21(vxw301, vxw4001, app(ty_Ratio, bfh)) → new_esEs13(vxw301, vxw4001, bfh)
new_esEs21(vxw301, vxw4001, ty_Char) → new_esEs12(vxw301, vxw4001)
new_esEs21(vxw301, vxw4001, ty_@0) → new_esEs15(vxw301, vxw4001)
new_esEs21(vxw301, vxw4001, ty_Integer) → new_esEs11(vxw301, vxw4001)
new_esEs21(vxw301, vxw4001, ty_Float) → new_esEs10(vxw301, vxw4001)
new_esEs21(vxw301, vxw4001, app(ty_[], bga)) → new_esEs14(vxw301, vxw4001, bga)
new_esEs21(vxw301, vxw4001, app(app(ty_@2, bfc), bfd)) → new_esEs5(vxw301, vxw4001, bfc, bfd)
new_esEs21(vxw301, vxw4001, app(app(ty_Either, bgc), bgd)) → new_esEs7(vxw301, vxw4001, bgc, bgd)
new_esEs21(vxw301, vxw4001, app(ty_Maybe, bgb)) → new_esEs4(vxw301, vxw4001, bgb)
new_esEs21(vxw301, vxw4001, ty_Double) → new_esEs9(vxw301, vxw4001)
new_esEs21(vxw301, vxw4001, ty_Ordering) → new_esEs8(vxw301, vxw4001)
new_esEs21(vxw301, vxw4001, ty_Int) → new_esEs16(vxw301, vxw4001)
new_esEs21(vxw301, vxw4001, app(app(app(ty_@3, bfe), bff), bfg)) → new_esEs6(vxw301, vxw4001, bfe, bff, bfg)
new_esEs20(vxw302, vxw4002, app(ty_Maybe, beh)) → new_esEs4(vxw302, vxw4002, beh)
new_esEs20(vxw302, vxw4002, app(ty_Ratio, bef)) → new_esEs13(vxw302, vxw4002, bef)
new_esEs20(vxw302, vxw4002, ty_Int) → new_esEs16(vxw302, vxw4002)
new_esEs20(vxw302, vxw4002, ty_Char) → new_esEs12(vxw302, vxw4002)
new_esEs20(vxw302, vxw4002, app(app(ty_@2, bea), beb)) → new_esEs5(vxw302, vxw4002, bea, beb)
new_esEs20(vxw302, vxw4002, ty_Integer) → new_esEs11(vxw302, vxw4002)
new_esEs20(vxw302, vxw4002, app(app(app(ty_@3, bec), bed), bee)) → new_esEs6(vxw302, vxw4002, bec, bed, bee)
new_esEs20(vxw302, vxw4002, ty_Bool) → new_esEs17(vxw302, vxw4002)
new_esEs20(vxw302, vxw4002, ty_Ordering) → new_esEs8(vxw302, vxw4002)
new_esEs20(vxw302, vxw4002, ty_Float) → new_esEs10(vxw302, vxw4002)
new_esEs20(vxw302, vxw4002, ty_@0) → new_esEs15(vxw302, vxw4002)
new_esEs20(vxw302, vxw4002, app(app(ty_Either, bfa), bfb)) → new_esEs7(vxw302, vxw4002, bfa, bfb)
new_esEs20(vxw302, vxw4002, ty_Double) → new_esEs9(vxw302, vxw4002)
new_esEs20(vxw302, vxw4002, app(ty_[], beg)) → new_esEs14(vxw302, vxw4002, beg)
new_esEs17(True, True) → True
new_esEs17(False, False) → True
new_esEs17(False, True) → False
new_esEs17(True, False) → False
new_esEs5(@2(vxw300, vxw301), @2(vxw4000, vxw4001), baf, bag) → new_asAs(new_esEs28(vxw300, vxw4000, baf), new_esEs27(vxw301, vxw4001, bag))
new_esEs28(vxw300, vxw4000, ty_Integer) → new_esEs11(vxw300, vxw4000)
new_esEs28(vxw300, vxw4000, ty_@0) → new_esEs15(vxw300, vxw4000)
new_esEs28(vxw300, vxw4000, ty_Float) → new_esEs10(vxw300, vxw4000)
new_esEs28(vxw300, vxw4000, app(ty_Maybe, ded)) → new_esEs4(vxw300, vxw4000, ded)
new_esEs28(vxw300, vxw4000, ty_Int) → new_esEs16(vxw300, vxw4000)
new_esEs28(vxw300, vxw4000, app(ty_[], dec)) → new_esEs14(vxw300, vxw4000, dec)
new_esEs28(vxw300, vxw4000, ty_Ordering) → new_esEs8(vxw300, vxw4000)
new_esEs28(vxw300, vxw4000, app(app(ty_Either, dee), def)) → new_esEs7(vxw300, vxw4000, dee, def)
new_esEs28(vxw300, vxw4000, app(app(ty_@2, dde), ddf)) → new_esEs5(vxw300, vxw4000, dde, ddf)
new_esEs28(vxw300, vxw4000, ty_Double) → new_esEs9(vxw300, vxw4000)
new_esEs28(vxw300, vxw4000, app(app(app(ty_@3, ddg), ddh), dea)) → new_esEs6(vxw300, vxw4000, ddg, ddh, dea)
new_esEs28(vxw300, vxw4000, ty_Bool) → new_esEs17(vxw300, vxw4000)
new_esEs28(vxw300, vxw4000, app(ty_Ratio, deb)) → new_esEs13(vxw300, vxw4000, deb)
new_esEs28(vxw300, vxw4000, ty_Char) → new_esEs12(vxw300, vxw4000)
new_esEs27(vxw301, vxw4001, ty_Bool) → new_esEs17(vxw301, vxw4001)
new_esEs27(vxw301, vxw4001, app(app(ty_Either, ddc), ddd)) → new_esEs7(vxw301, vxw4001, ddc, ddd)
new_esEs27(vxw301, vxw4001, app(ty_Ratio, dch)) → new_esEs13(vxw301, vxw4001, dch)
new_esEs27(vxw301, vxw4001, ty_Char) → new_esEs12(vxw301, vxw4001)
new_esEs27(vxw301, vxw4001, ty_Ordering) → new_esEs8(vxw301, vxw4001)
new_esEs27(vxw301, vxw4001, ty_Double) → new_esEs9(vxw301, vxw4001)
new_esEs27(vxw301, vxw4001, ty_Float) → new_esEs10(vxw301, vxw4001)
new_esEs27(vxw301, vxw4001, ty_@0) → new_esEs15(vxw301, vxw4001)
new_esEs27(vxw301, vxw4001, app(app(app(ty_@3, dce), dcf), dcg)) → new_esEs6(vxw301, vxw4001, dce, dcf, dcg)
new_esEs27(vxw301, vxw4001, app(app(ty_@2, dcc), dcd)) → new_esEs5(vxw301, vxw4001, dcc, dcd)
new_esEs27(vxw301, vxw4001, app(ty_Maybe, ddb)) → new_esEs4(vxw301, vxw4001, ddb)
new_esEs27(vxw301, vxw4001, ty_Int) → new_esEs16(vxw301, vxw4001)
new_esEs27(vxw301, vxw4001, app(ty_[], dda)) → new_esEs14(vxw301, vxw4001, dda)
new_esEs27(vxw301, vxw4001, ty_Integer) → new_esEs11(vxw301, vxw4001)
new_esEs12(Char(vxw300), Char(vxw4000)) → new_primEqNat0(vxw300, vxw4000)
new_compare111(vxw110, vxw100, False, cdg, cdh) → GT
new_compare111(vxw110, vxw100, True, cdg, cdh) → LT
new_compare16(vxw110, vxw100) → new_compare211(vxw110, vxw100, new_esEs8(vxw110, vxw100))
new_compare211(vxw110, vxw100, False) → new_compare110(vxw110, vxw100, new_ltEs10(vxw110, vxw100))
new_compare211(vxw110, vxw100, True) → EQ
new_compare110(vxw110, vxw100, True) → LT
new_compare110(vxw110, vxw100, False) → GT
new_compare13(vxw110, vxw100, dh, ea) → new_compare23(vxw110, vxw100, new_esEs5(vxw110, vxw100, dh, ea), dh, ea)
new_compare23(vxw110, vxw100, False, dh, ea) → new_compare10(vxw110, vxw100, new_ltEs4(vxw110, vxw100, dh, ea), dh, ea)
new_compare23(vxw110, vxw100, True, dh, ea) → EQ
new_compare10(vxw110, vxw100, True, dh, ea) → LT
new_compare10(vxw110, vxw100, False, dh, ea) → GT
new_compare7(@0, @0) → EQ
new_compare18(vxw110, vxw100) → new_compare24(vxw110, vxw100, new_esEs17(vxw110, vxw100))
new_compare24(vxw110, vxw100, True) → EQ
new_compare24(vxw110, vxw100, False) → new_compare11(vxw110, vxw100, new_ltEs5(vxw110, vxw100))
new_compare11(vxw110, vxw100, False) → GT
new_compare11(vxw110, vxw100, True) → LT
new_compare8(vxw110, vxw100, cd) → new_compare210(vxw110, vxw100, new_esEs4(vxw110, vxw100, cd), cd)
new_compare210(vxw110, vxw100, False, cd) → new_compare112(vxw110, vxw100, new_ltEs7(vxw110, vxw100, cd), cd)
new_compare210(vxw110, vxw100, True, cd) → EQ
new_compare112(vxw110, vxw100, True, cd) → LT
new_compare112(vxw110, vxw100, False, cd) → GT
new_compare19(vxw110, vxw100, ha, hb, hc) → new_compare25(vxw110, vxw100, new_esEs6(vxw110, vxw100, ha, hb, hc), ha, hb, hc)
new_compare25(vxw110, vxw100, True, ha, hb, hc) → EQ
new_compare25(vxw110, vxw100, False, ha, hb, hc) → new_compare12(vxw110, vxw100, new_ltEs6(vxw110, vxw100, ha, hb, hc), ha, hb, hc)
new_ltEs6(@3(vxw110, vxw111, vxw112), @3(vxw100, vxw101, vxw102), bdd, bde, bdf) → new_pePe(new_lt20(vxw110, vxw100, bdd), new_asAs(new_esEs26(vxw110, vxw100, bdd), new_pePe(new_lt19(vxw111, vxw101, bde), new_asAs(new_esEs25(vxw111, vxw101, bde), new_ltEs19(vxw112, vxw102, bdf)))))
new_compare12(vxw110, vxw100, True, ha, hb, hc) → LT
new_compare12(vxw110, vxw100, False, ha, hb, hc) → GT
new_lt20(vxw110, vxw100, ty_Integer) → new_lt4(vxw110, vxw100)
new_lt20(vxw110, vxw100, ty_@0) → new_lt8(vxw110, vxw100)
new_lt20(vxw110, vxw100, app(app(ty_@2, dbb), dbc)) → new_lt11(vxw110, vxw100, dbb, dbc)
new_lt20(vxw110, vxw100, ty_Float) → new_lt17(vxw110, vxw100)
new_lt20(vxw110, vxw100, ty_Ordering) → new_lt6(vxw110, vxw100)
new_lt20(vxw110, vxw100, ty_Bool) → new_lt9(vxw110, vxw100)
new_lt20(vxw110, vxw100, app(ty_Maybe, dba)) → new_lt5(vxw110, vxw100, dba)
new_lt20(vxw110, vxw100, ty_Int) → new_lt7(vxw110, vxw100)
new_lt20(vxw110, vxw100, ty_Double) → new_lt13(vxw110, vxw100)
new_lt20(vxw110, vxw100, app(ty_Ratio, dbd)) → new_lt14(vxw110, vxw100, dbd)
new_lt20(vxw110, vxw100, app(app(ty_Either, dca), dcb)) → new_lt18(vxw110, vxw100, dca, dcb)
new_lt20(vxw110, vxw100, app(ty_[], dbe)) → new_lt15(vxw110, vxw100, dbe)
new_lt20(vxw110, vxw100, app(app(app(ty_@3, dbf), dbg), dbh)) → new_lt16(vxw110, vxw100, dbf, dbg, dbh)
new_lt20(vxw110, vxw100, ty_Char) → new_lt12(vxw110, vxw100)
new_esEs26(vxw110, vxw100, ty_@0) → new_esEs15(vxw110, vxw100)
new_esEs26(vxw110, vxw100, ty_Float) → new_esEs10(vxw110, vxw100)
new_esEs26(vxw110, vxw100, ty_Integer) → new_esEs11(vxw110, vxw100)
new_esEs26(vxw110, vxw100, app(ty_Maybe, dba)) → new_esEs4(vxw110, vxw100, dba)
new_esEs26(vxw110, vxw100, ty_Char) → new_esEs12(vxw110, vxw100)
new_esEs26(vxw110, vxw100, app(ty_Ratio, dbd)) → new_esEs13(vxw110, vxw100, dbd)
new_esEs26(vxw110, vxw100, ty_Ordering) → new_esEs8(vxw110, vxw100)
new_esEs26(vxw110, vxw100, app(app(app(ty_@3, dbf), dbg), dbh)) → new_esEs6(vxw110, vxw100, dbf, dbg, dbh)
new_esEs26(vxw110, vxw100, app(ty_[], dbe)) → new_esEs14(vxw110, vxw100, dbe)
new_esEs26(vxw110, vxw100, app(app(ty_Either, dca), dcb)) → new_esEs7(vxw110, vxw100, dca, dcb)
new_esEs26(vxw110, vxw100, app(app(ty_@2, dbb), dbc)) → new_esEs5(vxw110, vxw100, dbb, dbc)
new_esEs26(vxw110, vxw100, ty_Int) → new_esEs16(vxw110, vxw100)
new_esEs26(vxw110, vxw100, ty_Double) → new_esEs9(vxw110, vxw100)
new_esEs26(vxw110, vxw100, ty_Bool) → new_esEs17(vxw110, vxw100)
new_lt19(vxw111, vxw101, app(app(ty_Either, dag), dah)) → new_lt18(vxw111, vxw101, dag, dah)
new_lt19(vxw111, vxw101, ty_@0) → new_lt8(vxw111, vxw101)
new_lt19(vxw111, vxw101, ty_Ordering) → new_lt6(vxw111, vxw101)
new_lt19(vxw111, vxw101, ty_Bool) → new_lt9(vxw111, vxw101)
new_lt19(vxw111, vxw101, app(app(ty_@2, chh), daa)) → new_lt11(vxw111, vxw101, chh, daa)
new_lt19(vxw111, vxw101, ty_Double) → new_lt13(vxw111, vxw101)
new_lt19(vxw111, vxw101, ty_Float) → new_lt17(vxw111, vxw101)
new_lt19(vxw111, vxw101, ty_Char) → new_lt12(vxw111, vxw101)
new_lt19(vxw111, vxw101, ty_Int) → new_lt7(vxw111, vxw101)
new_lt19(vxw111, vxw101, ty_Integer) → new_lt4(vxw111, vxw101)
new_lt19(vxw111, vxw101, app(app(app(ty_@3, dad), dae), daf)) → new_lt16(vxw111, vxw101, dad, dae, daf)
new_lt19(vxw111, vxw101, app(ty_[], dac)) → new_lt15(vxw111, vxw101, dac)
new_lt19(vxw111, vxw101, app(ty_Maybe, chg)) → new_lt5(vxw111, vxw101, chg)
new_lt19(vxw111, vxw101, app(ty_Ratio, dab)) → new_lt14(vxw111, vxw101, dab)
new_esEs25(vxw111, vxw101, app(ty_[], dac)) → new_esEs14(vxw111, vxw101, dac)
new_esEs25(vxw111, vxw101, ty_Bool) → new_esEs17(vxw111, vxw101)
new_esEs25(vxw111, vxw101, ty_Double) → new_esEs9(vxw111, vxw101)
new_esEs25(vxw111, vxw101, ty_Ordering) → new_esEs8(vxw111, vxw101)
new_esEs25(vxw111, vxw101, app(ty_Ratio, dab)) → new_esEs13(vxw111, vxw101, dab)
new_esEs25(vxw111, vxw101, app(ty_Maybe, chg)) → new_esEs4(vxw111, vxw101, chg)
new_esEs25(vxw111, vxw101, ty_Char) → new_esEs12(vxw111, vxw101)
new_esEs25(vxw111, vxw101, ty_Float) → new_esEs10(vxw111, vxw101)
new_esEs25(vxw111, vxw101, ty_@0) → new_esEs15(vxw111, vxw101)
new_esEs25(vxw111, vxw101, ty_Integer) → new_esEs11(vxw111, vxw101)
new_esEs25(vxw111, vxw101, ty_Int) → new_esEs16(vxw111, vxw101)
new_esEs25(vxw111, vxw101, app(app(app(ty_@3, dad), dae), daf)) → new_esEs6(vxw111, vxw101, dad, dae, daf)
new_esEs25(vxw111, vxw101, app(app(ty_@2, chh), daa)) → new_esEs5(vxw111, vxw101, chh, daa)
new_esEs25(vxw111, vxw101, app(app(ty_Either, dag), dah)) → new_esEs7(vxw111, vxw101, dag, dah)
new_ltEs19(vxw112, vxw102, app(ty_Ratio, cgh)) → new_ltEs11(vxw112, vxw102, cgh)
new_ltEs19(vxw112, vxw102, ty_Double) → new_ltEs9(vxw112, vxw102)
new_ltEs19(vxw112, vxw102, ty_Ordering) → new_ltEs10(vxw112, vxw102)
new_ltEs19(vxw112, vxw102, app(app(ty_@2, cgf), cgg)) → new_ltEs4(vxw112, vxw102, cgf, cgg)
new_ltEs19(vxw112, vxw102, ty_Float) → new_ltEs15(vxw112, vxw102)
new_ltEs19(vxw112, vxw102, app(app(ty_Either, che), chf)) → new_ltEs17(vxw112, vxw102, che, chf)
new_ltEs19(vxw112, vxw102, ty_Char) → new_ltEs8(vxw112, vxw102)
new_ltEs19(vxw112, vxw102, app(ty_[], cha)) → new_ltEs12(vxw112, vxw102, cha)
new_ltEs19(vxw112, vxw102, app(app(app(ty_@3, chb), chc), chd)) → new_ltEs6(vxw112, vxw102, chb, chc, chd)
new_ltEs19(vxw112, vxw102, ty_Int) → new_ltEs16(vxw112, vxw102)
new_ltEs19(vxw112, vxw102, ty_@0) → new_ltEs14(vxw112, vxw102)
new_ltEs19(vxw112, vxw102, ty_Bool) → new_ltEs5(vxw112, vxw102)
new_ltEs19(vxw112, vxw102, app(ty_Maybe, cge)) → new_ltEs7(vxw112, vxw102, cge)
new_ltEs19(vxw112, vxw102, ty_Integer) → new_ltEs13(vxw112, vxw102)
new_ltEs13(vxw11, vxw10) → new_not(new_esEs8(new_compare6(vxw11, vxw10), GT))
new_ltEs14(vxw11, vxw10) → new_not(new_esEs8(new_compare7(vxw11, vxw10), GT))
new_ltEs16(vxw11, vxw10) → new_not(new_esEs8(new_compare27(vxw11, vxw10), GT))
new_ltEs8(vxw11, vxw10) → new_not(new_esEs8(new_compare14(vxw11, vxw10), GT))
new_ltEs11(vxw11, vxw10, bda) → new_not(new_esEs8(new_compare17(vxw11, vxw10, bda), GT))
new_lt14(vxw110, vxw100, cde) → new_esEs8(new_compare17(vxw110, vxw100, cde), LT)
new_lt5(vxw110, vxw100, cd) → new_esEs8(new_compare8(vxw110, vxw100, cd), LT)
new_lt15(vxw110, vxw100, cdf) → new_esEs8(new_compare0(vxw110, vxw100, cdf), LT)
new_lt16(vxw110, vxw100, ha, hb, hc) → new_esEs8(new_compare19(vxw110, vxw100, ha, hb, hc), LT)
new_lt4(vxw110, vxw100) → new_esEs8(new_compare6(vxw110, vxw100), LT)
new_lt7(vxw110, vxw100) → new_esEs8(new_compare27(vxw110, vxw100), LT)
new_lt12(vxw110, vxw100) → new_esEs8(new_compare14(vxw110, vxw100), LT)
new_lt17(vxw110, vxw100) → new_esEs8(new_compare26(vxw110, vxw100), LT)
new_lt13(vxw110, vxw100) → new_esEs8(new_compare15(vxw110, vxw100), LT)
new_lt11(vxw110, vxw100, dh, ea) → new_esEs8(new_compare13(vxw110, vxw100, dh, ea), LT)
new_lt9(vxw110, vxw100) → new_esEs8(new_compare18(vxw110, vxw100), LT)
new_lt6(vxw110, vxw100) → new_esEs8(new_compare16(vxw110, vxw100), LT)
new_lt8(vxw110, vxw100) → new_esEs8(new_compare7(vxw110, vxw100), LT)
new_lt18(vxw110, vxw100, cdg, cdh) → new_esEs8(new_compare28(vxw110, vxw100, cdg, cdh), LT)
new_esEs30(vxw30, vxw400, app(ty_[], dd)) → new_esEs14(vxw30, vxw400, dd)
new_esEs30(vxw30, vxw400, app(app(ty_Either, df), dg)) → new_esEs7(vxw30, vxw400, df, dg)
new_esEs30(vxw30, vxw400, ty_Float) → new_esEs10(vxw30, vxw400)
new_esEs30(vxw30, vxw400, ty_Char) → new_esEs12(vxw30, vxw400)
new_esEs30(vxw30, vxw400, ty_Bool) → new_esEs17(vxw30, vxw400)
new_esEs30(vxw30, vxw400, app(ty_Maybe, de)) → new_esEs4(vxw30, vxw400, de)
new_esEs30(vxw30, vxw400, ty_Integer) → new_esEs11(vxw30, vxw400)
new_esEs30(vxw30, vxw400, ty_@0) → new_esEs15(vxw30, vxw400)
new_esEs30(vxw30, vxw400, ty_Int) → new_esEs16(vxw30, vxw400)
new_esEs30(vxw30, vxw400, app(app(ty_@2, ce), cf)) → new_esEs5(vxw30, vxw400, ce, cf)
new_esEs30(vxw30, vxw400, app(ty_Ratio, dc)) → new_esEs13(vxw30, vxw400, dc)
new_esEs30(vxw30, vxw400, ty_Ordering) → new_esEs8(vxw30, vxw400)
new_esEs30(vxw30, vxw400, ty_Double) → new_esEs9(vxw30, vxw400)
new_esEs30(vxw30, vxw400, app(app(app(ty_@3, cg), da), db)) → new_esEs6(vxw30, vxw400, cg, da, db)

The set Q consists of the following terms:

new_esEs11(Integer(x0), Integer(x1))
new_compare12(x0, x1, True, x2, x3, x4)
new_esEs4(Just(x0), Just(x1), ty_Int)
new_ltEs17(Left(x0), Left(x1), ty_@0, x2)
new_ltEs13(x0, x1)
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs20(x0, x1, ty_Char)
new_esEs7(Left(x0), Left(x1), ty_Int, x2)
new_asAs(True, x0)
new_lt5(x0, x1, x2)
new_ltEs17(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs21(x0, x1, ty_Ordering)
new_primMulNat0(Zero, Succ(x0))
new_esEs7(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_ltEs17(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_ltEs17(Left(x0), Left(x1), ty_Int, x2)
new_lt10(x0, x1, ty_Int)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_compare11(x0, x1, True)
new_ltEs21(x0, x1, ty_Bool)
new_primCmpNat0(Succ(x0), Zero)
new_lt18(x0, x1, x2, x3)
new_esEs7(Left(x0), Left(x1), ty_Integer, x2)
new_lt20(x0, x1, ty_Integer)
new_ltEs19(x0, x1, ty_@0)
new_ltEs21(x0, x1, app(ty_Maybe, x2))
new_esEs30(x0, x1, app(ty_Maybe, x2))
new_lt19(x0, x1, ty_Int)
new_esEs29(x0, x1, ty_Bool)
new_esEs23(x0, x1, ty_Float)
new_ltEs18(x0, x1, ty_Float)
new_ltEs17(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_compare9(x0, x1, ty_Bool)
new_esEs25(x0, x1, ty_Bool)
new_compare9(x0, x1, ty_Float)
new_esEs7(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs7(Right(x0), Right(x1), x2, ty_Char)
new_esEs29(x0, x1, ty_Double)
new_ltEs10(LT, LT)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_esEs14(:(x0, x1), :(x2, x3), x4)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs17(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs23(x0, x1, ty_Ordering)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt10(x0, x1, app(app(ty_Either, x2), x3))
new_lt4(x0, x1)
new_esEs9(Double(x0, x1), Double(x2, x3))
new_esEs5(@2(x0, x1), @2(x2, x3), x4, x5)
new_lt20(x0, x1, ty_Double)
new_esEs27(x0, x1, ty_@0)
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs30(x0, x1, ty_Integer)
new_ltEs18(x0, x1, ty_Double)
new_ltEs6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs23(x0, x1, ty_Char)
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs18(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_esEs8(GT, GT)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_ltEs18(x0, x1, app(ty_[], x2))
new_ltEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs17(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs22(x0, x1, ty_Ordering)
new_compare25(x0, x1, True, x2, x3, x4)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs24(x0, x1, ty_Char)
new_ltEs7(Just(x0), Just(x1), app(ty_[], x2))
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_esEs22(x0, x1, app(ty_[], x2))
new_compare6(Integer(x0), Integer(x1))
new_esEs29(x0, x1, ty_@0)
new_esEs8(LT, LT)
new_primMulNat0(Succ(x0), Succ(x1))
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs7(Just(x0), Just(x1), ty_Integer)
new_ltEs12(x0, x1, x2)
new_ltEs20(x0, x1, ty_Double)
new_esEs21(x0, x1, ty_Double)
new_esEs17(False, False)
new_esEs21(x0, x1, ty_Integer)
new_primEqNat0(Succ(x0), Zero)
new_esEs26(x0, x1, ty_Bool)
new_ltEs5(False, False)
new_ltEs11(x0, x1, x2)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_esEs22(x0, x1, ty_Bool)
new_lt11(x0, x1, x2, x3)
new_esEs30(x0, x1, ty_Double)
new_esEs7(Right(x0), Right(x1), x2, ty_Integer)
new_esEs7(Left(x0), Left(x1), ty_Double, x2)
new_esEs7(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs20(x0, x1, ty_Float)
new_compare0(:(x0, x1), [], x2)
new_ltEs21(x0, x1, app(ty_Ratio, x2))
new_esEs27(x0, x1, ty_Ordering)
new_esEs24(x0, x1, ty_@0)
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_esEs7(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_compare9(x0, x1, app(ty_Maybe, x2))
new_esEs7(Left(x0), Left(x1), ty_@0, x2)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs7(Right(x0), Right(x1), x2, ty_Ordering)
new_lt7(x0, x1)
new_ltEs18(x0, x1, app(ty_Ratio, x2))
new_lt10(x0, x1, app(ty_[], x2))
new_compare211(x0, x1, True)
new_compare8(x0, x1, x2)
new_esEs7(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_primEqNat0(Zero, Zero)
new_compare9(x0, x1, ty_Integer)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_esEs21(x0, x1, ty_Bool)
new_lt10(x0, x1, ty_Integer)
new_esEs21(x0, x1, ty_Char)
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_esEs4(Just(x0), Just(x1), ty_Bool)
new_compare210(x0, x1, False, x2)
new_esEs14([], :(x0, x1), x2)
new_ltEs7(Just(x0), Just(x1), ty_Double)
new_esEs22(x0, x1, ty_Int)
new_lt20(x0, x1, ty_Float)
new_ltEs7(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_esEs7(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs4(Just(x0), Just(x1), ty_Ordering)
new_esEs25(x0, x1, ty_Float)
new_compare23(x0, x1, False, x2, x3)
new_esEs7(Left(x0), Left(x1), ty_Bool, x2)
new_primMulNat0(Zero, Zero)
new_ltEs18(x0, x1, ty_Int)
new_esEs21(x0, x1, ty_Float)
new_esEs7(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs20(x0, x1, ty_Ordering)
new_ltEs17(Left(x0), Left(x1), ty_Ordering, x2)
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_ltEs10(EQ, LT)
new_ltEs10(LT, EQ)
new_compare23(x0, x1, True, x2, x3)
new_ltEs21(x0, x1, ty_@0)
new_esEs21(x0, x1, app(ty_[], x2))
new_ltEs20(x0, x1, ty_@0)
new_ltEs17(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_esEs18(x0, x1, ty_Integer)
new_lt14(x0, x1, x2)
new_primCompAux00(x0, EQ)
new_compare10(x0, x1, True, x2, x3)
new_esEs13(:%(x0, x1), :%(x2, x3), x4)
new_compare210(x0, x1, True, x2)
new_pePe(True, x0)
new_esEs20(x0, x1, ty_Ordering)
new_ltEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, ty_Ordering)
new_esEs28(x0, x1, ty_Int)
new_esEs12(Char(x0), Char(x1))
new_lt19(x0, x1, ty_Char)
new_compare110(x0, x1, False)
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs4(Just(x0), Just(x1), ty_@0)
new_lt10(x0, x1, ty_Ordering)
new_esEs22(x0, x1, ty_Char)
new_esEs30(x0, x1, ty_Bool)
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs26(x0, x1, ty_@0)
new_esEs24(x0, x1, ty_Integer)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs25(x0, x1, ty_Ordering)
new_esEs4(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, app(ty_[], x2))
new_primCompAux00(x0, LT)
new_ltEs21(x0, x1, ty_Ordering)
new_ltEs19(x0, x1, ty_Integer)
new_ltEs17(Left(x0), Left(x1), ty_Bool, x2)
new_ltEs17(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs17(Left(x0), Left(x1), ty_Float, x2)
new_ltEs19(x0, x1, ty_Int)
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs25(x0, x1, ty_Double)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs7(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_ltEs20(x0, x1, ty_Bool)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_esEs27(x0, x1, ty_Double)
new_esEs26(x0, x1, ty_Integer)
new_esEs19(x0, x1, ty_Integer)
new_ltEs20(x0, x1, app(ty_[], x2))
new_esEs23(x0, x1, ty_Integer)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_compare13(x0, x1, x2, x3)
new_lt6(x0, x1)
new_compare0([], [], x0)
new_esEs4(Just(x0), Just(x1), app(ty_Maybe, x2))
new_compare9(x0, x1, ty_@0)
new_esEs4(Just(x0), Just(x1), ty_Double)
new_ltEs17(Right(x0), Right(x1), x2, ty_Float)
new_lt10(x0, x1, app(ty_Maybe, x2))
new_ltEs19(x0, x1, ty_Bool)
new_esEs28(x0, x1, ty_@0)
new_lt20(x0, x1, ty_Bool)
new_ltEs15(x0, x1)
new_lt10(x0, x1, app(app(ty_@2, x2), x3))
new_compare11(x0, x1, False)
new_lt10(x0, x1, ty_Double)
new_compare111(x0, x1, True, x2, x3)
new_lt19(x0, x1, ty_@0)
new_esEs30(x0, x1, app(ty_Ratio, x2))
new_ltEs18(x0, x1, ty_Char)
new_esEs4(Just(x0), Nothing, x1)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_compare25(x0, x1, False, x2, x3, x4)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_compare27(x0, x1)
new_primPlusNat1(Zero, Zero)
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_compare0(:(x0, x1), :(x2, x3), x4)
new_sr(x0, x1)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_esEs20(x0, x1, ty_@0)
new_esEs7(Left(x0), Left(x1), ty_Float, x2)
new_ltEs18(x0, x1, app(app(ty_Either, x2), x3))
new_esEs16(x0, x1)
new_esEs25(x0, x1, app(ty_[], x2))
new_esEs24(x0, x1, ty_Float)
new_esEs4(Nothing, Just(x0), x1)
new_compare9(x0, x1, ty_Ordering)
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare28(x0, x1, x2, x3)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_ltEs7(Just(x0), Just(x1), ty_Int)
new_esEs28(x0, x1, ty_Float)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, ty_@0)
new_ltEs18(x0, x1, ty_Ordering)
new_esEs23(x0, x1, ty_Int)
new_esEs7(Right(x0), Right(x1), x2, ty_Double)
new_compare10(x0, x1, False, x2, x3)
new_esEs26(x0, x1, ty_Double)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs24(x0, x1, ty_Bool)
new_esEs23(x0, x1, app(ty_[], x2))
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs21(x0, x1, ty_Float)
new_primMulInt(Pos(x0), Pos(x1))
new_ltEs7(Just(x0), Just(x1), ty_Char)
new_compare112(x0, x1, True, x2)
new_compare9(x0, x1, app(app(ty_Either, x2), x3))
new_primPlusNat0(Succ(x0), x1)
new_ltEs10(GT, LT)
new_ltEs10(LT, GT)
new_ltEs17(Right(x0), Right(x1), x2, ty_@0)
new_ltEs7(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_sr0(Integer(x0), Integer(x1))
new_esEs23(x0, x1, ty_Double)
new_compare9(x0, x1, app(ty_[], x2))
new_esEs25(x0, x1, ty_Integer)
new_esEs20(x0, x1, ty_Char)
new_ltEs7(Nothing, Just(x0), x1)
new_primEqNat0(Zero, Succ(x0))
new_esEs27(x0, x1, ty_Bool)
new_esEs30(x0, x1, ty_Int)
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare17(:%(x0, x1), :%(x2, x3), ty_Int)
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_lt9(x0, x1)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_ltEs20(x0, x1, ty_Integer)
new_primMulInt(Neg(x0), Neg(x1))
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_esEs4(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, ty_Char)
new_ltEs20(x0, x1, ty_Int)
new_compare211(x0, x1, False)
new_ltEs17(Left(x0), Left(x1), ty_Double, x2)
new_compare29(x0, x1, False, x2, x3)
new_ltEs9(x0, x1)
new_esEs7(Right(x0), Right(x1), x2, ty_Float)
new_ltEs17(Right(x0), Right(x1), x2, ty_Ordering)
new_lt10(x0, x1, ty_@0)
new_esEs30(x0, x1, ty_Ordering)
new_ltEs7(Just(x0), Nothing, x1)
new_esEs4(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_compare112(x0, x1, False, x2)
new_esEs29(x0, x1, ty_Char)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs18(x0, x1, ty_Integer)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_esEs27(x0, x1, ty_Float)
new_ltEs19(x0, x1, ty_Double)
new_ltEs21(x0, x1, ty_Double)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Neg(Zero), Neg(Zero))
new_ltEs19(x0, x1, ty_Ordering)
new_ltEs21(x0, x1, ty_Integer)
new_ltEs14(x0, x1)
new_ltEs17(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_ltEs7(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_compare29(x0, x1, True, x2, x3)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs24(x0, x1, ty_Ordering)
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs26(x0, x1, app(ty_[], x2))
new_ltEs17(Right(x0), Right(x1), x2, ty_Bool)
new_esEs29(x0, x1, ty_Ordering)
new_compare9(x0, x1, app(ty_Ratio, x2))
new_esEs30(x0, x1, ty_@0)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_compare7(@0, @0)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_esEs18(x0, x1, ty_Int)
new_ltEs17(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_lt19(x0, x1, app(ty_Maybe, x2))
new_primCompAux00(x0, GT)
new_ltEs21(x0, x1, ty_Int)
new_lt19(x0, x1, ty_Double)
new_esEs26(x0, x1, ty_Float)
new_esEs30(x0, x1, app(ty_[], x2))
new_ltEs7(Just(x0), Just(x1), ty_Ordering)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_esEs4(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs16(x0, x1)
new_esEs21(x0, x1, ty_@0)
new_compare18(x0, x1)
new_lt19(x0, x1, ty_Ordering)
new_esEs4(Nothing, Nothing, x0)
new_esEs30(x0, x1, ty_Char)
new_esEs7(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_ltEs21(x0, x1, app(app(ty_@2, x2), x3))
new_asAs(False, x0)
new_lt10(x0, x1, ty_Char)
new_esEs20(x0, x1, ty_Int)
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat1(Succ(x0), Zero)
new_esEs8(GT, EQ)
new_esEs8(EQ, GT)
new_esEs22(x0, x1, ty_Integer)
new_lt15(x0, x1, x2)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_compare17(:%(x0, x1), :%(x2, x3), ty_Integer)
new_esEs29(x0, x1, app(ty_[], x2))
new_ltEs20(x0, x1, ty_Float)
new_primPlusNat0(Zero, x0)
new_esEs20(x0, x1, ty_Integer)
new_compare26(Float(x0, x1), Float(x2, x3))
new_ltEs17(Left(x0), Left(x1), ty_Char, x2)
new_primCmpNat0(Zero, Zero)
new_lt10(x0, x1, ty_Bool)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_ltEs17(Left(x0), Left(x1), ty_Integer, x2)
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_compare111(x0, x1, False, x2, x3)
new_ltEs7(Nothing, Nothing, x0)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs15(@0, @0)
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_compare16(x0, x1)
new_compare9(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare9(x0, x1, app(app(ty_@2, x2), x3))
new_lt16(x0, x1, x2, x3, x4)
new_esEs23(x0, x1, ty_Bool)
new_primEqNat0(Succ(x0), Succ(x1))
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_esEs7(Left(x0), Left(x1), ty_Char, x2)
new_primCmpNat0(Zero, Succ(x0))
new_esEs27(x0, x1, ty_Integer)
new_esEs21(x0, x1, ty_Int)
new_esEs24(x0, x1, ty_Double)
new_esEs24(x0, x1, app(ty_[], x2))
new_esEs20(x0, x1, ty_Bool)
new_lt10(x0, x1, app(ty_Ratio, x2))
new_lt19(x0, x1, ty_Integer)
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_ltEs10(GT, GT)
new_esEs27(x0, x1, app(ty_[], x2))
new_ltEs7(Just(x0), Just(x1), ty_Float)
new_lt17(x0, x1)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_compare15(Double(x0, x1), Double(x2, x3))
new_esEs22(x0, x1, ty_Float)
new_lt13(x0, x1)
new_ltEs17(Right(x0), Right(x1), x2, ty_Double)
new_esEs30(x0, x1, app(app(ty_Either, x2), x3))
new_primCompAux0(x0, x1, x2, x3)
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_compare9(x0, x1, ty_Char)
new_ltEs5(True, True)
new_esEs7(Right(x0), Right(x1), x2, ty_@0)
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_compare14(Char(x0), Char(x1))
new_lt19(x0, x1, app(ty_Ratio, x2))
new_ltEs17(Right(x0), Right(x1), x2, ty_Integer)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_not(True)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_ltEs7(Just(x0), Just(x1), ty_@0)
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs28(x0, x1, ty_Double)
new_esEs26(x0, x1, ty_Ordering)
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs17(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs27(x0, x1, ty_Int)
new_esEs6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_lt10(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_not(False)
new_esEs4(Just(x0), Just(x1), ty_Integer)
new_ltEs17(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_lt20(x0, x1, ty_Char)
new_lt19(x0, x1, ty_Bool)
new_primCmpNat0(Succ(x0), Succ(x1))
new_ltEs10(EQ, GT)
new_ltEs10(GT, EQ)
new_esEs22(x0, x1, ty_Double)
new_esEs10(Float(x0, x1), Float(x2, x3))
new_esEs26(x0, x1, ty_Int)
new_esEs4(Just(x0), Just(x1), ty_Float)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_compare24(x0, x1, True)
new_ltEs17(Right(x0), Right(x1), x2, ty_Int)
new_esEs25(x0, x1, ty_@0)
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_compare9(x0, x1, ty_Int)
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs21(x0, x1, app(ty_[], x2))
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primMulNat0(Succ(x0), Zero)
new_esEs28(x0, x1, ty_Bool)
new_lt19(x0, x1, ty_Float)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs8(EQ, LT)
new_esEs8(LT, EQ)
new_lt20(x0, x1, ty_@0)
new_compare0([], :(x0, x1), x2)
new_lt19(x0, x1, app(ty_[], x2))
new_esEs7(Right(x0), Right(x1), x2, ty_Int)
new_esEs7(Left(x0), Left(x1), ty_Ordering, x2)
new_compare19(x0, x1, x2, x3, x4)
new_ltEs4(@2(x0, x1), @2(x2, x3), x4, x5)
new_lt8(x0, x1)
new_esEs25(x0, x1, ty_Int)
new_esEs4(Just(x0), Just(x1), app(ty_Ratio, x2))
new_ltEs7(Just(x0), Just(x1), ty_Bool)
new_compare12(x0, x1, False, x2, x3, x4)
new_esEs17(False, True)
new_esEs17(True, False)
new_ltEs17(Right(x0), Right(x1), x2, ty_Char)
new_esEs28(x0, x1, app(ty_[], x2))
new_compare110(x0, x1, True)
new_ltEs7(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs30(x0, x1, ty_Float)
new_ltEs8(x0, x1)
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_compare24(x0, x1, False)
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_esEs28(x0, x1, ty_Char)
new_esEs26(x0, x1, ty_Char)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare9(x0, x1, ty_Double)
new_ltEs17(Left(x0), Right(x1), x2, x3)
new_ltEs17(Right(x0), Left(x1), x2, x3)
new_esEs14([], [], x0)
new_primEqInt(Pos(Zero), Pos(Zero))
new_esEs17(True, True)
new_ltEs21(x0, x1, app(app(ty_Either, x2), x3))
new_lt12(x0, x1)
new_esEs29(x0, x1, ty_Integer)
new_ltEs18(x0, x1, app(ty_Maybe, x2))
new_ltEs21(x0, x1, ty_Char)
new_ltEs18(x0, x1, ty_@0)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs20(x0, x1, ty_Double)
new_lt10(x0, x1, ty_Float)
new_esEs25(x0, x1, ty_Char)
new_ltEs19(x0, x1, ty_Char)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs28(x0, x1, ty_Ordering)
new_esEs29(x0, x1, ty_Int)
new_ltEs17(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_ltEs5(True, False)
new_ltEs5(False, True)
new_ltEs19(x0, x1, app(ty_[], x2))
new_esEs19(x0, x1, ty_Int)
new_esEs24(x0, x1, ty_Int)
new_ltEs18(x0, x1, ty_Bool)
new_esEs4(Just(x0), Just(x1), ty_Char)
new_ltEs7(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs7(Right(x0), Left(x1), x2, x3)
new_esEs7(Left(x0), Right(x1), x2, x3)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, ty_Int)
new_pePe(False, x0)
new_esEs30(x0, x1, app(app(ty_@2, x2), x3))
new_esEs22(x0, x1, ty_@0)
new_esEs29(x0, x1, ty_Float)
new_ltEs19(x0, x1, ty_Float)
new_esEs14(:(x0, x1), [], x2)
new_esEs28(x0, x1, ty_Integer)
new_ltEs10(EQ, EQ)
new_esEs20(x0, x1, app(ty_[], x2))

We have to consider all minimal (P,Q,R)-chains.
We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.

new_ltEs20(x0, x1, ty_Char)
new_esEs29(x0, x1, ty_Bool)
new_esEs29(x0, x1, ty_Double)
new_esEs29(x0, x1, ty_@0)
new_ltEs20(x0, x1, ty_Double)
new_ltEs20(x0, x1, ty_Ordering)
new_ltEs20(x0, x1, ty_@0)
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, ty_Bool)
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_ltEs20(x0, x1, app(ty_[], x2))
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs20(x0, x1, ty_Integer)
new_ltEs20(x0, x1, ty_Int)
new_esEs29(x0, x1, ty_Char)
new_esEs29(x0, x1, ty_Ordering)
new_esEs29(x0, x1, app(ty_[], x2))
new_ltEs20(x0, x1, ty_Float)
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs29(x0, x1, ty_Integer)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs29(x0, x1, ty_Int)
new_esEs29(x0, x1, ty_Float)



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

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

new_insertBy02(vxw37, vxw38, vxw39, False, ca, cb) → new_insertBy(Right(vxw38), vxw39, ca, cb)
new_insertBy(Right(vxw30), :(Right(vxw400), vxw41), be, bf) → new_insertBy01(vxw400, vxw30, vxw41, new_esEs30(vxw30, vxw400, bf), be, bf)
new_insertBy01(vxw19, vxw20, vxw21, False, bg, bh) → new_insertBy02(vxw19, vxw20, vxw21, new_ltEs21(vxw20, vxw19, bh), bg, bh)
new_insertBy(Right(vxw30), :(Left(vxw400), vxw41), be, bf) → new_insertBy(Right(vxw30), vxw41, be, bf)

The TRS R consists of the following rules:

new_ltEs21(vxw20, vxw19, app(ty_[], dfc)) → new_ltEs12(vxw20, vxw19, dfc)
new_ltEs21(vxw20, vxw19, ty_Int) → new_ltEs16(vxw20, vxw19)
new_ltEs21(vxw20, vxw19, app(app(ty_@2, deh), dfa)) → new_ltEs4(vxw20, vxw19, deh, dfa)
new_ltEs21(vxw20, vxw19, ty_@0) → new_ltEs14(vxw20, vxw19)
new_ltEs21(vxw20, vxw19, ty_Bool) → new_ltEs5(vxw20, vxw19)
new_ltEs21(vxw20, vxw19, app(ty_Ratio, dfb)) → new_ltEs11(vxw20, vxw19, dfb)
new_ltEs21(vxw20, vxw19, ty_Integer) → new_ltEs13(vxw20, vxw19)
new_ltEs21(vxw20, vxw19, app(app(app(ty_@3, dfd), dfe), dff)) → new_ltEs6(vxw20, vxw19, dfd, dfe, dff)
new_ltEs21(vxw20, vxw19, app(app(ty_Either, dfg), dfh)) → new_ltEs17(vxw20, vxw19, dfg, dfh)
new_ltEs21(vxw20, vxw19, ty_Ordering) → new_ltEs10(vxw20, vxw19)
new_ltEs21(vxw20, vxw19, ty_Char) → new_ltEs8(vxw20, vxw19)
new_ltEs21(vxw20, vxw19, app(ty_Maybe, deg)) → new_ltEs7(vxw20, vxw19, deg)
new_ltEs21(vxw20, vxw19, ty_Float) → new_ltEs15(vxw20, vxw19)
new_ltEs21(vxw20, vxw19, ty_Double) → new_ltEs9(vxw20, vxw19)
new_ltEs9(vxw11, vxw10) → new_not(new_esEs8(new_compare15(vxw11, vxw10), GT))
new_compare15(Double(vxw110, vxw111), Double(vxw100, vxw101)) → new_compare27(new_sr(vxw110, vxw100), new_sr(vxw111, vxw101))
new_esEs8(GT, GT) → True
new_esEs8(LT, GT) → False
new_esEs8(EQ, GT) → False
new_not(False) → True
new_not(True) → False
new_sr(vxw300, vxw4000) → new_primMulInt(vxw300, vxw4000)
new_compare27(vxw11, vxw10) → new_primCmpInt(vxw11, vxw10)
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(vxw1100)), Neg(vxw100)) → new_primCmpNat0(vxw100, Succ(vxw1100))
new_primCmpInt(Neg(Zero), Pos(Succ(vxw1000))) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(vxw1000))) → new_primCmpNat0(Zero, Succ(vxw1000))
new_primCmpInt(Pos(Succ(vxw1100)), Pos(vxw100)) → new_primCmpNat0(Succ(vxw1100), vxw100)
new_primCmpInt(Pos(Succ(vxw1100)), Neg(vxw100)) → GT
new_primCmpInt(Neg(Zero), Neg(Succ(vxw1000))) → new_primCmpNat0(Succ(vxw1000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(vxw1000))) → GT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(vxw1100)), Pos(vxw100)) → LT
new_primCmpNat0(Succ(vxw1100), Zero) → GT
new_primCmpNat0(Succ(vxw1100), Succ(vxw1000)) → new_primCmpNat0(vxw1100, vxw1000)
new_primCmpNat0(Zero, Succ(vxw1000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primMulInt(Pos(vxw3000), Pos(vxw40000)) → Pos(new_primMulNat0(vxw3000, vxw40000))
new_primMulInt(Neg(vxw3000), Neg(vxw40000)) → Pos(new_primMulNat0(vxw3000, vxw40000))
new_primMulInt(Neg(vxw3000), Pos(vxw40000)) → Neg(new_primMulNat0(vxw3000, vxw40000))
new_primMulInt(Pos(vxw3000), Neg(vxw40000)) → Neg(new_primMulNat0(vxw3000, vxw40000))
new_primMulNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, Succ(vxw400000)) → Zero
new_primMulNat0(Succ(vxw30000), Zero) → Zero
new_primMulNat0(Succ(vxw30000), Succ(vxw400000)) → new_primPlusNat0(new_primMulNat0(vxw30000, Succ(vxw400000)), vxw400000)
new_primPlusNat0(Succ(vxw620), vxw400000) → Succ(Succ(new_primPlusNat1(vxw620, vxw400000)))
new_primPlusNat0(Zero, vxw400000) → Succ(vxw400000)
new_primPlusNat1(Zero, Succ(vxw4000000)) → Succ(vxw4000000)
new_primPlusNat1(Succ(vxw6200), Zero) → Succ(vxw6200)
new_primPlusNat1(Succ(vxw6200), Succ(vxw4000000)) → Succ(Succ(new_primPlusNat1(vxw6200, vxw4000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_ltEs15(vxw11, vxw10) → new_not(new_esEs8(new_compare26(vxw11, vxw10), GT))
new_compare26(Float(vxw110, vxw111), Float(vxw100, vxw101)) → new_compare27(new_sr(vxw110, vxw100), new_sr(vxw111, vxw101))
new_ltEs7(Just(vxw110), Just(vxw100), ty_Bool) → new_ltEs5(vxw110, vxw100)
new_ltEs7(Just(vxw110), Just(vxw100), app(app(app(ty_@3, bcd), bce), bcf)) → new_ltEs6(vxw110, vxw100, bcd, bce, bcf)
new_ltEs7(Just(vxw110), Just(vxw100), app(app(ty_@2, bbh), bca)) → new_ltEs4(vxw110, vxw100, bbh, bca)
new_ltEs7(Just(vxw110), Just(vxw100), ty_Ordering) → new_ltEs10(vxw110, vxw100)
new_ltEs7(Just(vxw110), Just(vxw100), ty_Integer) → new_ltEs13(vxw110, vxw100)
new_ltEs7(Just(vxw110), Just(vxw100), ty_Int) → new_ltEs16(vxw110, vxw100)
new_ltEs7(Nothing, Just(vxw100), bbf) → True
new_ltEs7(Just(vxw110), Just(vxw100), ty_Float) → new_ltEs15(vxw110, vxw100)
new_ltEs7(Just(vxw110), Just(vxw100), ty_Double) → new_ltEs9(vxw110, vxw100)
new_ltEs7(Nothing, Nothing, bbf) → True
new_ltEs7(Just(vxw110), Just(vxw100), app(ty_[], bcc)) → new_ltEs12(vxw110, vxw100, bcc)
new_ltEs7(Just(vxw110), Just(vxw100), ty_Char) → new_ltEs8(vxw110, vxw100)
new_ltEs7(Just(vxw110), Just(vxw100), ty_@0) → new_ltEs14(vxw110, vxw100)
new_ltEs7(Just(vxw110), Nothing, bbf) → False
new_ltEs7(Just(vxw110), Just(vxw100), app(ty_Ratio, bcb)) → new_ltEs11(vxw110, vxw100, bcb)
new_ltEs17(Left(vxw110), Left(vxw100), app(app(ty_Either, cag), cah), bdh) → new_ltEs17(vxw110, vxw100, cag, cah)
new_ltEs17(Right(vxw110), Right(vxw100), bdg, app(app(ty_Either, cca), ccb)) → new_ltEs17(vxw110, vxw100, cca, ccb)
new_ltEs7(Just(vxw110), Just(vxw100), app(ty_Maybe, bbg)) → new_ltEs7(vxw110, vxw100, bbg)
new_ltEs7(Just(vxw110), Just(vxw100), app(app(ty_Either, bcg), bch)) → new_ltEs17(vxw110, vxw100, bcg, bch)
new_ltEs17(Right(vxw110), Right(vxw100), bdg, app(ty_Maybe, cba)) → new_ltEs7(vxw110, vxw100, cba)
new_ltEs17(Left(vxw110), Left(vxw100), app(ty_Maybe, bhg), bdh) → new_ltEs7(vxw110, vxw100, bhg)
new_ltEs17(Right(vxw110), Right(vxw100), bdg, app(ty_Ratio, cbd)) → new_ltEs11(vxw110, vxw100, cbd)
new_ltEs17(Left(vxw110), Left(vxw100), app(ty_Ratio, cab), bdh) → new_ltEs11(vxw110, vxw100, cab)
new_ltEs17(Left(vxw110), Left(vxw100), ty_Integer, bdh) → new_ltEs13(vxw110, vxw100)
new_ltEs17(Right(vxw110), Right(vxw100), bdg, ty_Integer) → new_ltEs13(vxw110, vxw100)
new_ltEs17(Left(vxw110), Left(vxw100), ty_Bool, bdh) → new_ltEs5(vxw110, vxw100)
new_ltEs17(Left(vxw110), Left(vxw100), ty_Double, bdh) → new_ltEs9(vxw110, vxw100)
new_ltEs17(Left(vxw110), Left(vxw100), ty_Ordering, bdh) → new_ltEs10(vxw110, vxw100)
new_ltEs17(Right(vxw110), Left(vxw100), bdg, bdh) → False
new_ltEs17(Right(vxw110), Right(vxw100), bdg, ty_Ordering) → new_ltEs10(vxw110, vxw100)
new_ltEs17(Right(vxw110), Right(vxw100), bdg, ty_Int) → new_ltEs16(vxw110, vxw100)
new_ltEs17(Left(vxw110), Left(vxw100), app(app(ty_@2, bhh), caa), bdh) → new_ltEs4(vxw110, vxw100, bhh, caa)
new_ltEs17(Left(vxw110), Left(vxw100), app(app(app(ty_@3, cad), cae), caf), bdh) → new_ltEs6(vxw110, vxw100, cad, cae, caf)
new_ltEs17(Left(vxw110), Left(vxw100), app(ty_[], cac), bdh) → new_ltEs12(vxw110, vxw100, cac)
new_ltEs17(Left(vxw110), Left(vxw100), ty_Float, bdh) → new_ltEs15(vxw110, vxw100)
new_ltEs17(Right(vxw110), Right(vxw100), bdg, ty_@0) → new_ltEs14(vxw110, vxw100)
new_ltEs17(Left(vxw110), Left(vxw100), ty_Char, bdh) → new_ltEs8(vxw110, vxw100)
new_ltEs17(Left(vxw110), Left(vxw100), ty_@0, bdh) → new_ltEs14(vxw110, vxw100)
new_ltEs17(Right(vxw110), Right(vxw100), bdg, ty_Float) → new_ltEs15(vxw110, vxw100)
new_ltEs17(Left(vxw110), Right(vxw100), bdg, bdh) → True
new_ltEs17(Right(vxw110), Right(vxw100), bdg, app(ty_[], cbe)) → new_ltEs12(vxw110, vxw100, cbe)
new_ltEs17(Right(vxw110), Right(vxw100), bdg, ty_Double) → new_ltEs9(vxw110, vxw100)
new_ltEs17(Right(vxw110), Right(vxw100), bdg, ty_Char) → new_ltEs8(vxw110, vxw100)
new_ltEs17(Left(vxw110), Left(vxw100), ty_Int, bdh) → new_ltEs16(vxw110, vxw100)
new_ltEs17(Right(vxw110), Right(vxw100), bdg, app(app(app(ty_@3, cbf), cbg), cbh)) → new_ltEs6(vxw110, vxw100, cbf, cbg, cbh)
new_ltEs17(Right(vxw110), Right(vxw100), bdg, app(app(ty_@2, cbb), cbc)) → new_ltEs4(vxw110, vxw100, cbb, cbc)
new_ltEs17(Right(vxw110), Right(vxw100), bdg, ty_Bool) → new_ltEs5(vxw110, vxw100)
new_ltEs5(True, False) → False
new_ltEs5(True, True) → True
new_ltEs5(False, False) → True
new_ltEs5(False, True) → True
new_ltEs4(@2(vxw110, vxw111), @2(vxw100, vxw101), bdb, bdc) → new_pePe(new_lt10(vxw110, vxw100, bdb), new_asAs(new_esEs23(vxw110, vxw100, bdb), new_ltEs18(vxw111, vxw101, bdc)))
new_lt10(vxw110, vxw100, ty_Double) → new_lt13(vxw110, vxw100)
new_lt10(vxw110, vxw100, ty_Bool) → new_lt9(vxw110, vxw100)
new_lt10(vxw110, vxw100, app(app(ty_@2, dh), ea)) → new_lt11(vxw110, vxw100, dh, ea)
new_lt10(vxw110, vxw100, ty_Char) → new_lt12(vxw110, vxw100)
new_lt10(vxw110, vxw100, app(app(ty_Either, cdg), cdh)) → new_lt18(vxw110, vxw100, cdg, cdh)
new_lt10(vxw110, vxw100, app(app(app(ty_@3, ha), hb), hc)) → new_lt16(vxw110, vxw100, ha, hb, hc)
new_lt10(vxw110, vxw100, ty_Float) → new_lt17(vxw110, vxw100)
new_lt10(vxw110, vxw100, app(ty_Ratio, cde)) → new_lt14(vxw110, vxw100, cde)
new_lt10(vxw110, vxw100, app(ty_Maybe, cd)) → new_lt5(vxw110, vxw100, cd)
new_lt10(vxw110, vxw100, app(ty_[], cdf)) → new_lt15(vxw110, vxw100, cdf)
new_lt10(vxw110, vxw100, ty_@0) → new_lt8(vxw110, vxw100)
new_lt10(vxw110, vxw100, ty_Int) → new_lt7(vxw110, vxw100)
new_lt10(vxw110, vxw100, ty_Integer) → new_lt4(vxw110, vxw100)
new_lt10(vxw110, vxw100, ty_Ordering) → new_lt6(vxw110, vxw100)
new_esEs23(vxw110, vxw100, app(app(ty_Either, cdg), cdh)) → new_esEs7(vxw110, vxw100, cdg, cdh)
new_esEs23(vxw110, vxw100, app(ty_Ratio, cde)) → new_esEs13(vxw110, vxw100, cde)
new_esEs23(vxw110, vxw100, ty_Double) → new_esEs9(vxw110, vxw100)
new_esEs23(vxw110, vxw100, app(ty_Maybe, cd)) → new_esEs4(vxw110, vxw100, cd)
new_esEs23(vxw110, vxw100, ty_Ordering) → new_esEs8(vxw110, vxw100)
new_esEs23(vxw110, vxw100, ty_Float) → new_esEs10(vxw110, vxw100)
new_esEs23(vxw110, vxw100, ty_Integer) → new_esEs11(vxw110, vxw100)
new_esEs23(vxw110, vxw100, app(app(ty_@2, dh), ea)) → new_esEs5(vxw110, vxw100, dh, ea)
new_esEs23(vxw110, vxw100, ty_@0) → new_esEs15(vxw110, vxw100)
new_esEs23(vxw110, vxw100, app(ty_[], cdf)) → new_esEs14(vxw110, vxw100, cdf)
new_esEs23(vxw110, vxw100, ty_Bool) → new_esEs17(vxw110, vxw100)
new_esEs23(vxw110, vxw100, app(app(app(ty_@3, ha), hb), hc)) → new_esEs6(vxw110, vxw100, ha, hb, hc)
new_esEs23(vxw110, vxw100, ty_Char) → new_esEs12(vxw110, vxw100)
new_esEs23(vxw110, vxw100, ty_Int) → new_esEs16(vxw110, vxw100)
new_ltEs18(vxw111, vxw101, ty_Float) → new_ltEs15(vxw111, vxw101)
new_ltEs18(vxw111, vxw101, ty_Char) → new_ltEs8(vxw111, vxw101)
new_ltEs18(vxw111, vxw101, ty_Int) → new_ltEs16(vxw111, vxw101)
new_ltEs18(vxw111, vxw101, app(app(ty_Either, cdc), cdd)) → new_ltEs17(vxw111, vxw101, cdc, cdd)
new_ltEs18(vxw111, vxw101, ty_@0) → new_ltEs14(vxw111, vxw101)
new_ltEs18(vxw111, vxw101, ty_Integer) → new_ltEs13(vxw111, vxw101)
new_ltEs18(vxw111, vxw101, ty_Bool) → new_ltEs5(vxw111, vxw101)
new_ltEs18(vxw111, vxw101, app(ty_Ratio, ccf)) → new_ltEs11(vxw111, vxw101, ccf)
new_ltEs18(vxw111, vxw101, app(app(app(ty_@3, cch), cda), cdb)) → new_ltEs6(vxw111, vxw101, cch, cda, cdb)
new_ltEs18(vxw111, vxw101, app(ty_Maybe, ccc)) → new_ltEs7(vxw111, vxw101, ccc)
new_ltEs18(vxw111, vxw101, app(ty_[], ccg)) → new_ltEs12(vxw111, vxw101, ccg)
new_ltEs18(vxw111, vxw101, app(app(ty_@2, ccd), cce)) → new_ltEs4(vxw111, vxw101, ccd, cce)
new_ltEs18(vxw111, vxw101, ty_Double) → new_ltEs9(vxw111, vxw101)
new_ltEs18(vxw111, vxw101, ty_Ordering) → new_ltEs10(vxw111, vxw101)
new_asAs(False, vxw53) → False
new_asAs(True, vxw53) → vxw53
new_pePe(False, vxw60) → vxw60
new_pePe(True, vxw60) → True
new_ltEs10(EQ, GT) → True
new_ltEs10(GT, EQ) → False
new_ltEs10(LT, EQ) → True
new_ltEs10(GT, GT) → True
new_ltEs10(LT, GT) → True
new_ltEs10(EQ, EQ) → True
new_ltEs10(LT, LT) → True
new_ltEs10(EQ, LT) → False
new_ltEs10(GT, LT) → False
new_ltEs12(vxw11, vxw10, cc) → new_not(new_esEs8(new_compare0(vxw11, vxw10, cc), GT))
new_compare0(:(vxw110, vxw111), :(vxw100, vxw101), cc) → new_primCompAux0(vxw110, vxw100, new_compare0(vxw111, vxw101, cc), cc)
new_compare0([], [], cc) → EQ
new_compare0(:(vxw110, vxw111), [], cc) → GT
new_compare0([], :(vxw100, vxw101), cc) → LT
new_primCompAux0(vxw110, vxw100, vxw61, cc) → new_primCompAux00(vxw61, new_compare9(vxw110, vxw100, cc))
new_compare9(vxw110, vxw100, ty_Double) → new_compare15(vxw110, vxw100)
new_compare9(vxw110, vxw100, ty_Integer) → new_compare6(vxw110, vxw100)
new_compare9(vxw110, vxw100, ty_Int) → new_compare27(vxw110, vxw100)
new_compare9(vxw110, vxw100, app(app(app(ty_@3, baa), bab), bac)) → new_compare19(vxw110, vxw100, baa, bab, bac)
new_compare9(vxw110, vxw100, app(ty_Maybe, hd)) → new_compare8(vxw110, vxw100, hd)
new_compare9(vxw110, vxw100, app(ty_[], hh)) → new_compare0(vxw110, vxw100, hh)
new_compare9(vxw110, vxw100, ty_Bool) → new_compare18(vxw110, vxw100)
new_compare9(vxw110, vxw100, ty_Float) → new_compare26(vxw110, vxw100)
new_compare9(vxw110, vxw100, ty_@0) → new_compare7(vxw110, vxw100)
new_compare9(vxw110, vxw100, app(app(ty_@2, he), hf)) → new_compare13(vxw110, vxw100, he, hf)
new_compare9(vxw110, vxw100, ty_Ordering) → new_compare16(vxw110, vxw100)
new_compare9(vxw110, vxw100, app(app(ty_Either, bad), bae)) → new_compare28(vxw110, vxw100, bad, bae)
new_compare9(vxw110, vxw100, ty_Char) → new_compare14(vxw110, vxw100)
new_compare9(vxw110, vxw100, app(ty_Ratio, hg)) → new_compare17(vxw110, vxw100, hg)
new_primCompAux00(vxw72, LT) → LT
new_primCompAux00(vxw72, EQ) → vxw72
new_primCompAux00(vxw72, GT) → GT
new_compare17(:%(vxw110, vxw111), :%(vxw100, vxw101), ty_Int) → new_compare27(new_sr(vxw110, vxw101), new_sr(vxw100, vxw111))
new_compare17(:%(vxw110, vxw111), :%(vxw100, vxw101), ty_Integer) → new_compare6(new_sr0(vxw110, vxw101), new_sr0(vxw100, vxw111))
new_sr0(Integer(vxw1100), Integer(vxw1010)) → Integer(new_primMulInt(vxw1100, vxw1010))
new_compare6(Integer(vxw110), Integer(vxw100)) → new_primCmpInt(vxw110, vxw100)
new_compare14(Char(vxw110), Char(vxw100)) → new_primCmpNat0(vxw110, vxw100)
new_compare28(vxw110, vxw100, cdg, cdh) → new_compare29(vxw110, vxw100, new_esEs7(vxw110, vxw100, cdg, cdh), cdg, cdh)
new_esEs7(Right(vxw300), Right(vxw4000), ff, ty_Ordering) → new_esEs8(vxw300, vxw4000)
new_esEs7(Left(vxw300), Right(vxw4000), ff, ed) → False
new_esEs7(Right(vxw300), Left(vxw4000), ff, ed) → False
new_esEs7(Left(vxw300), Left(vxw4000), ty_Double, ed) → new_esEs9(vxw300, vxw4000)
new_esEs7(Right(vxw300), Right(vxw4000), ff, ty_Double) → new_esEs9(vxw300, vxw4000)
new_esEs7(Right(vxw300), Right(vxw4000), ff, app(app(ty_@2, fg), fh)) → new_esEs5(vxw300, vxw4000, fg, fh)
new_esEs7(Left(vxw300), Left(vxw4000), ty_Integer, ed) → new_esEs11(vxw300, vxw4000)
new_esEs7(Left(vxw300), Left(vxw4000), app(app(ty_@2, eb), ec), ed) → new_esEs5(vxw300, vxw4000, eb, ec)
new_esEs7(Left(vxw300), Left(vxw4000), ty_Ordering, ed) → new_esEs8(vxw300, vxw4000)
new_esEs7(Right(vxw300), Right(vxw4000), ff, app(app(app(ty_@3, ga), gb), gc)) → new_esEs6(vxw300, vxw4000, ga, gb, gc)
new_esEs7(Right(vxw300), Right(vxw4000), ff, ty_Char) → new_esEs12(vxw300, vxw4000)
new_esEs7(Right(vxw300), Right(vxw4000), ff, ty_@0) → new_esEs15(vxw300, vxw4000)
new_esEs7(Right(vxw300), Right(vxw4000), ff, app(ty_Ratio, gd)) → new_esEs13(vxw300, vxw4000, gd)
new_esEs7(Left(vxw300), Left(vxw4000), app(ty_Ratio, eh), ed) → new_esEs13(vxw300, vxw4000, eh)
new_esEs7(Left(vxw300), Left(vxw4000), ty_@0, ed) → new_esEs15(vxw300, vxw4000)
new_esEs7(Right(vxw300), Right(vxw4000), ff, ty_Float) → new_esEs10(vxw300, vxw4000)
new_esEs7(Left(vxw300), Left(vxw4000), ty_Int, ed) → new_esEs16(vxw300, vxw4000)
new_esEs7(Right(vxw300), Right(vxw4000), ff, ty_Integer) → new_esEs11(vxw300, vxw4000)
new_esEs7(Right(vxw300), Right(vxw4000), ff, ty_Bool) → new_esEs17(vxw300, vxw4000)
new_esEs7(Left(vxw300), Left(vxw4000), ty_Char, ed) → new_esEs12(vxw300, vxw4000)
new_esEs7(Right(vxw300), Right(vxw4000), ff, app(ty_[], ge)) → new_esEs14(vxw300, vxw4000, ge)
new_esEs7(Left(vxw300), Left(vxw4000), ty_Float, ed) → new_esEs10(vxw300, vxw4000)
new_esEs7(Left(vxw300), Left(vxw4000), app(app(app(ty_@3, ee), ef), eg), ed) → new_esEs6(vxw300, vxw4000, ee, ef, eg)
new_esEs7(Right(vxw300), Right(vxw4000), ff, ty_Int) → new_esEs16(vxw300, vxw4000)
new_esEs7(Left(vxw300), Left(vxw4000), ty_Bool, ed) → new_esEs17(vxw300, vxw4000)
new_esEs7(Left(vxw300), Left(vxw4000), app(ty_[], fa), ed) → new_esEs14(vxw300, vxw4000, fa)
new_compare29(vxw110, vxw100, False, cdg, cdh) → new_compare111(vxw110, vxw100, new_ltEs17(vxw110, vxw100, cdg, cdh), cdg, cdh)
new_compare29(vxw110, vxw100, True, cdg, cdh) → EQ
new_esEs7(Left(vxw300), Left(vxw4000), app(app(ty_Either, fc), fd), ed) → new_esEs7(vxw300, vxw4000, fc, fd)
new_esEs4(Just(vxw300), Just(vxw4000), app(app(ty_Either, cfa), cfb)) → new_esEs7(vxw300, vxw4000, cfa, cfb)
new_esEs4(Just(vxw300), Just(vxw4000), app(ty_Maybe, ceh)) → new_esEs4(vxw300, vxw4000, ceh)
new_esEs7(Right(vxw300), Right(vxw4000), ff, app(app(ty_Either, gg), gh)) → new_esEs7(vxw300, vxw4000, gg, gh)
new_esEs7(Left(vxw300), Left(vxw4000), app(ty_Maybe, fb), ed) → new_esEs4(vxw300, vxw4000, fb)
new_esEs7(Right(vxw300), Right(vxw4000), ff, app(ty_Maybe, gf)) → new_esEs4(vxw300, vxw4000, gf)
new_esEs4(Just(vxw300), Just(vxw4000), ty_Ordering) → new_esEs8(vxw300, vxw4000)
new_esEs4(Just(vxw300), Nothing, bbe) → False
new_esEs4(Nothing, Just(vxw4000), bbe) → False
new_esEs4(Just(vxw300), Just(vxw4000), ty_Char) → new_esEs12(vxw300, vxw4000)
new_esEs4(Just(vxw300), Just(vxw4000), app(app(app(ty_@3, cec), ced), cee)) → new_esEs6(vxw300, vxw4000, cec, ced, cee)
new_esEs4(Just(vxw300), Just(vxw4000), ty_Float) → new_esEs10(vxw300, vxw4000)
new_esEs4(Just(vxw300), Just(vxw4000), ty_Integer) → new_esEs11(vxw300, vxw4000)
new_esEs4(Just(vxw300), Just(vxw4000), ty_Bool) → new_esEs17(vxw300, vxw4000)
new_esEs4(Just(vxw300), Just(vxw4000), app(app(ty_@2, cea), ceb)) → new_esEs5(vxw300, vxw4000, cea, ceb)
new_esEs4(Just(vxw300), Just(vxw4000), ty_Int) → new_esEs16(vxw300, vxw4000)
new_esEs4(Just(vxw300), Just(vxw4000), ty_@0) → new_esEs15(vxw300, vxw4000)
new_esEs4(Nothing, Nothing, bbe) → True
new_esEs4(Just(vxw300), Just(vxw4000), app(ty_Ratio, cef)) → new_esEs13(vxw300, vxw4000, cef)
new_esEs4(Just(vxw300), Just(vxw4000), app(ty_[], ceg)) → new_esEs14(vxw300, vxw4000, ceg)
new_esEs4(Just(vxw300), Just(vxw4000), ty_Double) → new_esEs9(vxw300, vxw4000)
new_esEs9(Double(vxw300, vxw301), Double(vxw4000, vxw4001)) → new_esEs16(new_sr(vxw300, vxw4000), new_sr(vxw301, vxw4001))
new_esEs16(vxw30, vxw400) → new_primEqInt(vxw30, vxw400)
new_primEqInt(Neg(Succ(vxw3000)), Neg(Succ(vxw40000))) → new_primEqNat0(vxw3000, vxw40000)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Succ(vxw3000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(vxw40000))) → False
new_primEqInt(Pos(Succ(vxw3000)), Pos(Succ(vxw40000))) → new_primEqNat0(vxw3000, vxw40000)
new_primEqInt(Pos(Succ(vxw3000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(vxw40000))) → False
new_primEqInt(Pos(Succ(vxw3000)), Neg(vxw4000)) → False
new_primEqInt(Neg(Succ(vxw3000)), Pos(vxw4000)) → False
new_primEqInt(Pos(Zero), Neg(Succ(vxw40000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(vxw40000))) → False
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqNat0(Zero, Zero) → True
new_primEqNat0(Succ(vxw3000), Succ(vxw40000)) → new_primEqNat0(vxw3000, vxw40000)
new_primEqNat0(Succ(vxw3000), Zero) → False
new_primEqNat0(Zero, Succ(vxw40000)) → False
new_esEs14([], [], bbd) → True
new_esEs14([], :(vxw4000, vxw4001), bbd) → False
new_esEs14(:(vxw300, vxw301), [], bbd) → False
new_esEs14(:(vxw300, vxw301), :(vxw4000, vxw4001), bbd) → new_asAs(new_esEs24(vxw300, vxw4000, bbd), new_esEs14(vxw301, vxw4001, bbd))
new_esEs24(vxw300, vxw4000, app(ty_Maybe, cgb)) → new_esEs4(vxw300, vxw4000, cgb)
new_esEs24(vxw300, vxw4000, app(app(ty_@2, cfc), cfd)) → new_esEs5(vxw300, vxw4000, cfc, cfd)
new_esEs24(vxw300, vxw4000, app(app(ty_Either, cgc), cgd)) → new_esEs7(vxw300, vxw4000, cgc, cgd)
new_esEs24(vxw300, vxw4000, ty_Int) → new_esEs16(vxw300, vxw4000)
new_esEs24(vxw300, vxw4000, ty_Bool) → new_esEs17(vxw300, vxw4000)
new_esEs24(vxw300, vxw4000, ty_Char) → new_esEs12(vxw300, vxw4000)
new_esEs24(vxw300, vxw4000, app(app(app(ty_@3, cfe), cff), cfg)) → new_esEs6(vxw300, vxw4000, cfe, cff, cfg)
new_esEs24(vxw300, vxw4000, ty_Ordering) → new_esEs8(vxw300, vxw4000)
new_esEs24(vxw300, vxw4000, ty_@0) → new_esEs15(vxw300, vxw4000)
new_esEs24(vxw300, vxw4000, app(ty_Ratio, cfh)) → new_esEs13(vxw300, vxw4000, cfh)
new_esEs24(vxw300, vxw4000, ty_Double) → new_esEs9(vxw300, vxw4000)
new_esEs24(vxw300, vxw4000, app(ty_[], cga)) → new_esEs14(vxw300, vxw4000, cga)
new_esEs24(vxw300, vxw4000, ty_Integer) → new_esEs11(vxw300, vxw4000)
new_esEs24(vxw300, vxw4000, ty_Float) → new_esEs10(vxw300, vxw4000)
new_esEs10(Float(vxw300, vxw301), Float(vxw4000, vxw4001)) → new_esEs16(new_sr(vxw300, vxw4000), new_sr(vxw301, vxw4001))
new_esEs11(Integer(vxw300), Integer(vxw4000)) → new_primEqInt(vxw300, vxw4000)
new_esEs13(:%(vxw300, vxw301), :%(vxw4000, vxw4001), bbc) → new_asAs(new_esEs19(vxw300, vxw4000, bbc), new_esEs18(vxw301, vxw4001, bbc))
new_esEs19(vxw300, vxw4000, ty_Integer) → new_esEs11(vxw300, vxw4000)
new_esEs19(vxw300, vxw4000, ty_Int) → new_esEs16(vxw300, vxw4000)
new_esEs18(vxw301, vxw4001, ty_Integer) → new_esEs11(vxw301, vxw4001)
new_esEs18(vxw301, vxw4001, ty_Int) → new_esEs16(vxw301, vxw4001)
new_esEs15(@0, @0) → True
new_esEs8(LT, LT) → True
new_esEs8(GT, LT) → False
new_esEs8(EQ, EQ) → True
new_esEs8(LT, EQ) → False
new_esEs8(EQ, LT) → False
new_esEs8(GT, EQ) → False
new_esEs6(@3(vxw300, vxw301, vxw302), @3(vxw4000, vxw4001, vxw4002), bah, bba, bbb) → new_asAs(new_esEs22(vxw300, vxw4000, bah), new_asAs(new_esEs21(vxw301, vxw4001, bba), new_esEs20(vxw302, vxw4002, bbb)))
new_esEs22(vxw300, vxw4000, ty_Char) → new_esEs12(vxw300, vxw4000)
new_esEs22(vxw300, vxw4000, app(app(ty_@2, bge), bgf)) → new_esEs5(vxw300, vxw4000, bge, bgf)
new_esEs22(vxw300, vxw4000, app(ty_[], bhc)) → new_esEs14(vxw300, vxw4000, bhc)
new_esEs22(vxw300, vxw4000, app(app(ty_Either, bhe), bhf)) → new_esEs7(vxw300, vxw4000, bhe, bhf)
new_esEs22(vxw300, vxw4000, ty_@0) → new_esEs15(vxw300, vxw4000)
new_esEs22(vxw300, vxw4000, ty_Ordering) → new_esEs8(vxw300, vxw4000)
new_esEs22(vxw300, vxw4000, ty_Double) → new_esEs9(vxw300, vxw4000)
new_esEs22(vxw300, vxw4000, app(app(app(ty_@3, bgg), bgh), bha)) → new_esEs6(vxw300, vxw4000, bgg, bgh, bha)
new_esEs22(vxw300, vxw4000, app(ty_Maybe, bhd)) → new_esEs4(vxw300, vxw4000, bhd)
new_esEs22(vxw300, vxw4000, app(ty_Ratio, bhb)) → new_esEs13(vxw300, vxw4000, bhb)
new_esEs22(vxw300, vxw4000, ty_Bool) → new_esEs17(vxw300, vxw4000)
new_esEs22(vxw300, vxw4000, ty_Integer) → new_esEs11(vxw300, vxw4000)
new_esEs22(vxw300, vxw4000, ty_Float) → new_esEs10(vxw300, vxw4000)
new_esEs22(vxw300, vxw4000, ty_Int) → new_esEs16(vxw300, vxw4000)
new_esEs21(vxw301, vxw4001, ty_Bool) → new_esEs17(vxw301, vxw4001)
new_esEs21(vxw301, vxw4001, app(ty_Ratio, bfh)) → new_esEs13(vxw301, vxw4001, bfh)
new_esEs21(vxw301, vxw4001, ty_Char) → new_esEs12(vxw301, vxw4001)
new_esEs21(vxw301, vxw4001, ty_@0) → new_esEs15(vxw301, vxw4001)
new_esEs21(vxw301, vxw4001, ty_Integer) → new_esEs11(vxw301, vxw4001)
new_esEs21(vxw301, vxw4001, ty_Float) → new_esEs10(vxw301, vxw4001)
new_esEs21(vxw301, vxw4001, app(ty_[], bga)) → new_esEs14(vxw301, vxw4001, bga)
new_esEs21(vxw301, vxw4001, app(app(ty_@2, bfc), bfd)) → new_esEs5(vxw301, vxw4001, bfc, bfd)
new_esEs21(vxw301, vxw4001, app(app(ty_Either, bgc), bgd)) → new_esEs7(vxw301, vxw4001, bgc, bgd)
new_esEs21(vxw301, vxw4001, app(ty_Maybe, bgb)) → new_esEs4(vxw301, vxw4001, bgb)
new_esEs21(vxw301, vxw4001, ty_Double) → new_esEs9(vxw301, vxw4001)
new_esEs21(vxw301, vxw4001, ty_Ordering) → new_esEs8(vxw301, vxw4001)
new_esEs21(vxw301, vxw4001, ty_Int) → new_esEs16(vxw301, vxw4001)
new_esEs21(vxw301, vxw4001, app(app(app(ty_@3, bfe), bff), bfg)) → new_esEs6(vxw301, vxw4001, bfe, bff, bfg)
new_esEs20(vxw302, vxw4002, app(ty_Maybe, beh)) → new_esEs4(vxw302, vxw4002, beh)
new_esEs20(vxw302, vxw4002, app(ty_Ratio, bef)) → new_esEs13(vxw302, vxw4002, bef)
new_esEs20(vxw302, vxw4002, ty_Int) → new_esEs16(vxw302, vxw4002)
new_esEs20(vxw302, vxw4002, ty_Char) → new_esEs12(vxw302, vxw4002)
new_esEs20(vxw302, vxw4002, app(app(ty_@2, bea), beb)) → new_esEs5(vxw302, vxw4002, bea, beb)
new_esEs20(vxw302, vxw4002, ty_Integer) → new_esEs11(vxw302, vxw4002)
new_esEs20(vxw302, vxw4002, app(app(app(ty_@3, bec), bed), bee)) → new_esEs6(vxw302, vxw4002, bec, bed, bee)
new_esEs20(vxw302, vxw4002, ty_Bool) → new_esEs17(vxw302, vxw4002)
new_esEs20(vxw302, vxw4002, ty_Ordering) → new_esEs8(vxw302, vxw4002)
new_esEs20(vxw302, vxw4002, ty_Float) → new_esEs10(vxw302, vxw4002)
new_esEs20(vxw302, vxw4002, ty_@0) → new_esEs15(vxw302, vxw4002)
new_esEs20(vxw302, vxw4002, app(app(ty_Either, bfa), bfb)) → new_esEs7(vxw302, vxw4002, bfa, bfb)
new_esEs20(vxw302, vxw4002, ty_Double) → new_esEs9(vxw302, vxw4002)
new_esEs20(vxw302, vxw4002, app(ty_[], beg)) → new_esEs14(vxw302, vxw4002, beg)
new_esEs17(True, True) → True
new_esEs17(False, False) → True
new_esEs17(False, True) → False
new_esEs17(True, False) → False
new_esEs5(@2(vxw300, vxw301), @2(vxw4000, vxw4001), baf, bag) → new_asAs(new_esEs28(vxw300, vxw4000, baf), new_esEs27(vxw301, vxw4001, bag))
new_esEs28(vxw300, vxw4000, ty_Integer) → new_esEs11(vxw300, vxw4000)
new_esEs28(vxw300, vxw4000, ty_@0) → new_esEs15(vxw300, vxw4000)
new_esEs28(vxw300, vxw4000, ty_Float) → new_esEs10(vxw300, vxw4000)
new_esEs28(vxw300, vxw4000, app(ty_Maybe, ded)) → new_esEs4(vxw300, vxw4000, ded)
new_esEs28(vxw300, vxw4000, ty_Int) → new_esEs16(vxw300, vxw4000)
new_esEs28(vxw300, vxw4000, app(ty_[], dec)) → new_esEs14(vxw300, vxw4000, dec)
new_esEs28(vxw300, vxw4000, ty_Ordering) → new_esEs8(vxw300, vxw4000)
new_esEs28(vxw300, vxw4000, app(app(ty_Either, dee), def)) → new_esEs7(vxw300, vxw4000, dee, def)
new_esEs28(vxw300, vxw4000, app(app(ty_@2, dde), ddf)) → new_esEs5(vxw300, vxw4000, dde, ddf)
new_esEs28(vxw300, vxw4000, ty_Double) → new_esEs9(vxw300, vxw4000)
new_esEs28(vxw300, vxw4000, app(app(app(ty_@3, ddg), ddh), dea)) → new_esEs6(vxw300, vxw4000, ddg, ddh, dea)
new_esEs28(vxw300, vxw4000, ty_Bool) → new_esEs17(vxw300, vxw4000)
new_esEs28(vxw300, vxw4000, app(ty_Ratio, deb)) → new_esEs13(vxw300, vxw4000, deb)
new_esEs28(vxw300, vxw4000, ty_Char) → new_esEs12(vxw300, vxw4000)
new_esEs27(vxw301, vxw4001, ty_Bool) → new_esEs17(vxw301, vxw4001)
new_esEs27(vxw301, vxw4001, app(app(ty_Either, ddc), ddd)) → new_esEs7(vxw301, vxw4001, ddc, ddd)
new_esEs27(vxw301, vxw4001, app(ty_Ratio, dch)) → new_esEs13(vxw301, vxw4001, dch)
new_esEs27(vxw301, vxw4001, ty_Char) → new_esEs12(vxw301, vxw4001)
new_esEs27(vxw301, vxw4001, ty_Ordering) → new_esEs8(vxw301, vxw4001)
new_esEs27(vxw301, vxw4001, ty_Double) → new_esEs9(vxw301, vxw4001)
new_esEs27(vxw301, vxw4001, ty_Float) → new_esEs10(vxw301, vxw4001)
new_esEs27(vxw301, vxw4001, ty_@0) → new_esEs15(vxw301, vxw4001)
new_esEs27(vxw301, vxw4001, app(app(app(ty_@3, dce), dcf), dcg)) → new_esEs6(vxw301, vxw4001, dce, dcf, dcg)
new_esEs27(vxw301, vxw4001, app(app(ty_@2, dcc), dcd)) → new_esEs5(vxw301, vxw4001, dcc, dcd)
new_esEs27(vxw301, vxw4001, app(ty_Maybe, ddb)) → new_esEs4(vxw301, vxw4001, ddb)
new_esEs27(vxw301, vxw4001, ty_Int) → new_esEs16(vxw301, vxw4001)
new_esEs27(vxw301, vxw4001, app(ty_[], dda)) → new_esEs14(vxw301, vxw4001, dda)
new_esEs27(vxw301, vxw4001, ty_Integer) → new_esEs11(vxw301, vxw4001)
new_esEs12(Char(vxw300), Char(vxw4000)) → new_primEqNat0(vxw300, vxw4000)
new_compare111(vxw110, vxw100, False, cdg, cdh) → GT
new_compare111(vxw110, vxw100, True, cdg, cdh) → LT
new_compare16(vxw110, vxw100) → new_compare211(vxw110, vxw100, new_esEs8(vxw110, vxw100))
new_compare211(vxw110, vxw100, False) → new_compare110(vxw110, vxw100, new_ltEs10(vxw110, vxw100))
new_compare211(vxw110, vxw100, True) → EQ
new_compare110(vxw110, vxw100, True) → LT
new_compare110(vxw110, vxw100, False) → GT
new_compare13(vxw110, vxw100, dh, ea) → new_compare23(vxw110, vxw100, new_esEs5(vxw110, vxw100, dh, ea), dh, ea)
new_compare23(vxw110, vxw100, False, dh, ea) → new_compare10(vxw110, vxw100, new_ltEs4(vxw110, vxw100, dh, ea), dh, ea)
new_compare23(vxw110, vxw100, True, dh, ea) → EQ
new_compare10(vxw110, vxw100, True, dh, ea) → LT
new_compare10(vxw110, vxw100, False, dh, ea) → GT
new_compare7(@0, @0) → EQ
new_compare18(vxw110, vxw100) → new_compare24(vxw110, vxw100, new_esEs17(vxw110, vxw100))
new_compare24(vxw110, vxw100, True) → EQ
new_compare24(vxw110, vxw100, False) → new_compare11(vxw110, vxw100, new_ltEs5(vxw110, vxw100))
new_compare11(vxw110, vxw100, False) → GT
new_compare11(vxw110, vxw100, True) → LT
new_compare8(vxw110, vxw100, cd) → new_compare210(vxw110, vxw100, new_esEs4(vxw110, vxw100, cd), cd)
new_compare210(vxw110, vxw100, False, cd) → new_compare112(vxw110, vxw100, new_ltEs7(vxw110, vxw100, cd), cd)
new_compare210(vxw110, vxw100, True, cd) → EQ
new_compare112(vxw110, vxw100, True, cd) → LT
new_compare112(vxw110, vxw100, False, cd) → GT
new_compare19(vxw110, vxw100, ha, hb, hc) → new_compare25(vxw110, vxw100, new_esEs6(vxw110, vxw100, ha, hb, hc), ha, hb, hc)
new_compare25(vxw110, vxw100, True, ha, hb, hc) → EQ
new_compare25(vxw110, vxw100, False, ha, hb, hc) → new_compare12(vxw110, vxw100, new_ltEs6(vxw110, vxw100, ha, hb, hc), ha, hb, hc)
new_ltEs6(@3(vxw110, vxw111, vxw112), @3(vxw100, vxw101, vxw102), bdd, bde, bdf) → new_pePe(new_lt20(vxw110, vxw100, bdd), new_asAs(new_esEs26(vxw110, vxw100, bdd), new_pePe(new_lt19(vxw111, vxw101, bde), new_asAs(new_esEs25(vxw111, vxw101, bde), new_ltEs19(vxw112, vxw102, bdf)))))
new_compare12(vxw110, vxw100, True, ha, hb, hc) → LT
new_compare12(vxw110, vxw100, False, ha, hb, hc) → GT
new_lt20(vxw110, vxw100, ty_Integer) → new_lt4(vxw110, vxw100)
new_lt20(vxw110, vxw100, ty_@0) → new_lt8(vxw110, vxw100)
new_lt20(vxw110, vxw100, app(app(ty_@2, dbb), dbc)) → new_lt11(vxw110, vxw100, dbb, dbc)
new_lt20(vxw110, vxw100, ty_Float) → new_lt17(vxw110, vxw100)
new_lt20(vxw110, vxw100, ty_Ordering) → new_lt6(vxw110, vxw100)
new_lt20(vxw110, vxw100, ty_Bool) → new_lt9(vxw110, vxw100)
new_lt20(vxw110, vxw100, app(ty_Maybe, dba)) → new_lt5(vxw110, vxw100, dba)
new_lt20(vxw110, vxw100, ty_Int) → new_lt7(vxw110, vxw100)
new_lt20(vxw110, vxw100, ty_Double) → new_lt13(vxw110, vxw100)
new_lt20(vxw110, vxw100, app(ty_Ratio, dbd)) → new_lt14(vxw110, vxw100, dbd)
new_lt20(vxw110, vxw100, app(app(ty_Either, dca), dcb)) → new_lt18(vxw110, vxw100, dca, dcb)
new_lt20(vxw110, vxw100, app(ty_[], dbe)) → new_lt15(vxw110, vxw100, dbe)
new_lt20(vxw110, vxw100, app(app(app(ty_@3, dbf), dbg), dbh)) → new_lt16(vxw110, vxw100, dbf, dbg, dbh)
new_lt20(vxw110, vxw100, ty_Char) → new_lt12(vxw110, vxw100)
new_esEs26(vxw110, vxw100, ty_@0) → new_esEs15(vxw110, vxw100)
new_esEs26(vxw110, vxw100, ty_Float) → new_esEs10(vxw110, vxw100)
new_esEs26(vxw110, vxw100, ty_Integer) → new_esEs11(vxw110, vxw100)
new_esEs26(vxw110, vxw100, app(ty_Maybe, dba)) → new_esEs4(vxw110, vxw100, dba)
new_esEs26(vxw110, vxw100, ty_Char) → new_esEs12(vxw110, vxw100)
new_esEs26(vxw110, vxw100, app(ty_Ratio, dbd)) → new_esEs13(vxw110, vxw100, dbd)
new_esEs26(vxw110, vxw100, ty_Ordering) → new_esEs8(vxw110, vxw100)
new_esEs26(vxw110, vxw100, app(app(app(ty_@3, dbf), dbg), dbh)) → new_esEs6(vxw110, vxw100, dbf, dbg, dbh)
new_esEs26(vxw110, vxw100, app(ty_[], dbe)) → new_esEs14(vxw110, vxw100, dbe)
new_esEs26(vxw110, vxw100, app(app(ty_Either, dca), dcb)) → new_esEs7(vxw110, vxw100, dca, dcb)
new_esEs26(vxw110, vxw100, app(app(ty_@2, dbb), dbc)) → new_esEs5(vxw110, vxw100, dbb, dbc)
new_esEs26(vxw110, vxw100, ty_Int) → new_esEs16(vxw110, vxw100)
new_esEs26(vxw110, vxw100, ty_Double) → new_esEs9(vxw110, vxw100)
new_esEs26(vxw110, vxw100, ty_Bool) → new_esEs17(vxw110, vxw100)
new_lt19(vxw111, vxw101, app(app(ty_Either, dag), dah)) → new_lt18(vxw111, vxw101, dag, dah)
new_lt19(vxw111, vxw101, ty_@0) → new_lt8(vxw111, vxw101)
new_lt19(vxw111, vxw101, ty_Ordering) → new_lt6(vxw111, vxw101)
new_lt19(vxw111, vxw101, ty_Bool) → new_lt9(vxw111, vxw101)
new_lt19(vxw111, vxw101, app(app(ty_@2, chh), daa)) → new_lt11(vxw111, vxw101, chh, daa)
new_lt19(vxw111, vxw101, ty_Double) → new_lt13(vxw111, vxw101)
new_lt19(vxw111, vxw101, ty_Float) → new_lt17(vxw111, vxw101)
new_lt19(vxw111, vxw101, ty_Char) → new_lt12(vxw111, vxw101)
new_lt19(vxw111, vxw101, ty_Int) → new_lt7(vxw111, vxw101)
new_lt19(vxw111, vxw101, ty_Integer) → new_lt4(vxw111, vxw101)
new_lt19(vxw111, vxw101, app(app(app(ty_@3, dad), dae), daf)) → new_lt16(vxw111, vxw101, dad, dae, daf)
new_lt19(vxw111, vxw101, app(ty_[], dac)) → new_lt15(vxw111, vxw101, dac)
new_lt19(vxw111, vxw101, app(ty_Maybe, chg)) → new_lt5(vxw111, vxw101, chg)
new_lt19(vxw111, vxw101, app(ty_Ratio, dab)) → new_lt14(vxw111, vxw101, dab)
new_esEs25(vxw111, vxw101, app(ty_[], dac)) → new_esEs14(vxw111, vxw101, dac)
new_esEs25(vxw111, vxw101, ty_Bool) → new_esEs17(vxw111, vxw101)
new_esEs25(vxw111, vxw101, ty_Double) → new_esEs9(vxw111, vxw101)
new_esEs25(vxw111, vxw101, ty_Ordering) → new_esEs8(vxw111, vxw101)
new_esEs25(vxw111, vxw101, app(ty_Ratio, dab)) → new_esEs13(vxw111, vxw101, dab)
new_esEs25(vxw111, vxw101, app(ty_Maybe, chg)) → new_esEs4(vxw111, vxw101, chg)
new_esEs25(vxw111, vxw101, ty_Char) → new_esEs12(vxw111, vxw101)
new_esEs25(vxw111, vxw101, ty_Float) → new_esEs10(vxw111, vxw101)
new_esEs25(vxw111, vxw101, ty_@0) → new_esEs15(vxw111, vxw101)
new_esEs25(vxw111, vxw101, ty_Integer) → new_esEs11(vxw111, vxw101)
new_esEs25(vxw111, vxw101, ty_Int) → new_esEs16(vxw111, vxw101)
new_esEs25(vxw111, vxw101, app(app(app(ty_@3, dad), dae), daf)) → new_esEs6(vxw111, vxw101, dad, dae, daf)
new_esEs25(vxw111, vxw101, app(app(ty_@2, chh), daa)) → new_esEs5(vxw111, vxw101, chh, daa)
new_esEs25(vxw111, vxw101, app(app(ty_Either, dag), dah)) → new_esEs7(vxw111, vxw101, dag, dah)
new_ltEs19(vxw112, vxw102, app(ty_Ratio, cgh)) → new_ltEs11(vxw112, vxw102, cgh)
new_ltEs19(vxw112, vxw102, ty_Double) → new_ltEs9(vxw112, vxw102)
new_ltEs19(vxw112, vxw102, ty_Ordering) → new_ltEs10(vxw112, vxw102)
new_ltEs19(vxw112, vxw102, app(app(ty_@2, cgf), cgg)) → new_ltEs4(vxw112, vxw102, cgf, cgg)
new_ltEs19(vxw112, vxw102, ty_Float) → new_ltEs15(vxw112, vxw102)
new_ltEs19(vxw112, vxw102, app(app(ty_Either, che), chf)) → new_ltEs17(vxw112, vxw102, che, chf)
new_ltEs19(vxw112, vxw102, ty_Char) → new_ltEs8(vxw112, vxw102)
new_ltEs19(vxw112, vxw102, app(ty_[], cha)) → new_ltEs12(vxw112, vxw102, cha)
new_ltEs19(vxw112, vxw102, app(app(app(ty_@3, chb), chc), chd)) → new_ltEs6(vxw112, vxw102, chb, chc, chd)
new_ltEs19(vxw112, vxw102, ty_Int) → new_ltEs16(vxw112, vxw102)
new_ltEs19(vxw112, vxw102, ty_@0) → new_ltEs14(vxw112, vxw102)
new_ltEs19(vxw112, vxw102, ty_Bool) → new_ltEs5(vxw112, vxw102)
new_ltEs19(vxw112, vxw102, app(ty_Maybe, cge)) → new_ltEs7(vxw112, vxw102, cge)
new_ltEs19(vxw112, vxw102, ty_Integer) → new_ltEs13(vxw112, vxw102)
new_ltEs13(vxw11, vxw10) → new_not(new_esEs8(new_compare6(vxw11, vxw10), GT))
new_ltEs14(vxw11, vxw10) → new_not(new_esEs8(new_compare7(vxw11, vxw10), GT))
new_ltEs16(vxw11, vxw10) → new_not(new_esEs8(new_compare27(vxw11, vxw10), GT))
new_ltEs8(vxw11, vxw10) → new_not(new_esEs8(new_compare14(vxw11, vxw10), GT))
new_ltEs11(vxw11, vxw10, bda) → new_not(new_esEs8(new_compare17(vxw11, vxw10, bda), GT))
new_lt14(vxw110, vxw100, cde) → new_esEs8(new_compare17(vxw110, vxw100, cde), LT)
new_lt5(vxw110, vxw100, cd) → new_esEs8(new_compare8(vxw110, vxw100, cd), LT)
new_lt15(vxw110, vxw100, cdf) → new_esEs8(new_compare0(vxw110, vxw100, cdf), LT)
new_lt16(vxw110, vxw100, ha, hb, hc) → new_esEs8(new_compare19(vxw110, vxw100, ha, hb, hc), LT)
new_lt4(vxw110, vxw100) → new_esEs8(new_compare6(vxw110, vxw100), LT)
new_lt7(vxw110, vxw100) → new_esEs8(new_compare27(vxw110, vxw100), LT)
new_lt12(vxw110, vxw100) → new_esEs8(new_compare14(vxw110, vxw100), LT)
new_lt17(vxw110, vxw100) → new_esEs8(new_compare26(vxw110, vxw100), LT)
new_lt13(vxw110, vxw100) → new_esEs8(new_compare15(vxw110, vxw100), LT)
new_lt11(vxw110, vxw100, dh, ea) → new_esEs8(new_compare13(vxw110, vxw100, dh, ea), LT)
new_lt9(vxw110, vxw100) → new_esEs8(new_compare18(vxw110, vxw100), LT)
new_lt6(vxw110, vxw100) → new_esEs8(new_compare16(vxw110, vxw100), LT)
new_lt8(vxw110, vxw100) → new_esEs8(new_compare7(vxw110, vxw100), LT)
new_lt18(vxw110, vxw100, cdg, cdh) → new_esEs8(new_compare28(vxw110, vxw100, cdg, cdh), LT)
new_esEs30(vxw30, vxw400, app(ty_[], dd)) → new_esEs14(vxw30, vxw400, dd)
new_esEs30(vxw30, vxw400, app(app(ty_Either, df), dg)) → new_esEs7(vxw30, vxw400, df, dg)
new_esEs30(vxw30, vxw400, ty_Float) → new_esEs10(vxw30, vxw400)
new_esEs30(vxw30, vxw400, ty_Char) → new_esEs12(vxw30, vxw400)
new_esEs30(vxw30, vxw400, ty_Bool) → new_esEs17(vxw30, vxw400)
new_esEs30(vxw30, vxw400, app(ty_Maybe, de)) → new_esEs4(vxw30, vxw400, de)
new_esEs30(vxw30, vxw400, ty_Integer) → new_esEs11(vxw30, vxw400)
new_esEs30(vxw30, vxw400, ty_@0) → new_esEs15(vxw30, vxw400)
new_esEs30(vxw30, vxw400, ty_Int) → new_esEs16(vxw30, vxw400)
new_esEs30(vxw30, vxw400, app(app(ty_@2, ce), cf)) → new_esEs5(vxw30, vxw400, ce, cf)
new_esEs30(vxw30, vxw400, app(ty_Ratio, dc)) → new_esEs13(vxw30, vxw400, dc)
new_esEs30(vxw30, vxw400, ty_Ordering) → new_esEs8(vxw30, vxw400)
new_esEs30(vxw30, vxw400, ty_Double) → new_esEs9(vxw30, vxw400)
new_esEs30(vxw30, vxw400, app(app(app(ty_@3, cg), da), db)) → new_esEs6(vxw30, vxw400, cg, da, db)

The set Q consists of the following terms:

new_esEs11(Integer(x0), Integer(x1))
new_compare12(x0, x1, True, x2, x3, x4)
new_esEs4(Just(x0), Just(x1), ty_Int)
new_ltEs17(Left(x0), Left(x1), ty_@0, x2)
new_ltEs13(x0, x1)
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(Left(x0), Left(x1), ty_Int, x2)
new_asAs(True, x0)
new_lt5(x0, x1, x2)
new_ltEs17(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs21(x0, x1, ty_Ordering)
new_primMulNat0(Zero, Succ(x0))
new_esEs7(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_ltEs17(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_ltEs17(Left(x0), Left(x1), ty_Int, x2)
new_lt10(x0, x1, ty_Int)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_compare11(x0, x1, True)
new_ltEs21(x0, x1, ty_Bool)
new_primCmpNat0(Succ(x0), Zero)
new_lt18(x0, x1, x2, x3)
new_esEs7(Left(x0), Left(x1), ty_Integer, x2)
new_lt20(x0, x1, ty_Integer)
new_ltEs19(x0, x1, ty_@0)
new_ltEs21(x0, x1, app(ty_Maybe, x2))
new_esEs30(x0, x1, app(ty_Maybe, x2))
new_lt19(x0, x1, ty_Int)
new_esEs23(x0, x1, ty_Float)
new_ltEs18(x0, x1, ty_Float)
new_ltEs17(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_compare9(x0, x1, ty_Bool)
new_esEs25(x0, x1, ty_Bool)
new_compare9(x0, x1, ty_Float)
new_esEs7(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs7(Right(x0), Right(x1), x2, ty_Char)
new_ltEs10(LT, LT)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_esEs14(:(x0, x1), :(x2, x3), x4)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs17(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs23(x0, x1, ty_Ordering)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt10(x0, x1, app(app(ty_Either, x2), x3))
new_lt4(x0, x1)
new_esEs9(Double(x0, x1), Double(x2, x3))
new_esEs5(@2(x0, x1), @2(x2, x3), x4, x5)
new_lt20(x0, x1, ty_Double)
new_esEs27(x0, x1, ty_@0)
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs30(x0, x1, ty_Integer)
new_ltEs18(x0, x1, ty_Double)
new_ltEs6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs23(x0, x1, ty_Char)
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs18(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_esEs8(GT, GT)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_ltEs18(x0, x1, app(ty_[], x2))
new_ltEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs17(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs22(x0, x1, ty_Ordering)
new_compare25(x0, x1, True, x2, x3, x4)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs24(x0, x1, ty_Char)
new_ltEs7(Just(x0), Just(x1), app(ty_[], x2))
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_esEs22(x0, x1, app(ty_[], x2))
new_compare6(Integer(x0), Integer(x1))
new_esEs8(LT, LT)
new_primMulNat0(Succ(x0), Succ(x1))
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs7(Just(x0), Just(x1), ty_Integer)
new_ltEs12(x0, x1, x2)
new_esEs21(x0, x1, ty_Double)
new_esEs17(False, False)
new_esEs21(x0, x1, ty_Integer)
new_primEqNat0(Succ(x0), Zero)
new_esEs26(x0, x1, ty_Bool)
new_ltEs5(False, False)
new_ltEs11(x0, x1, x2)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_esEs22(x0, x1, ty_Bool)
new_lt11(x0, x1, x2, x3)
new_esEs30(x0, x1, ty_Double)
new_esEs7(Right(x0), Right(x1), x2, ty_Integer)
new_esEs7(Left(x0), Left(x1), ty_Double, x2)
new_esEs7(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs20(x0, x1, ty_Float)
new_compare0(:(x0, x1), [], x2)
new_ltEs21(x0, x1, app(ty_Ratio, x2))
new_esEs27(x0, x1, ty_Ordering)
new_esEs24(x0, x1, ty_@0)
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_esEs7(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_compare9(x0, x1, app(ty_Maybe, x2))
new_esEs7(Left(x0), Left(x1), ty_@0, x2)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs7(Right(x0), Right(x1), x2, ty_Ordering)
new_lt7(x0, x1)
new_ltEs18(x0, x1, app(ty_Ratio, x2))
new_lt10(x0, x1, app(ty_[], x2))
new_compare211(x0, x1, True)
new_compare8(x0, x1, x2)
new_esEs7(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_primEqNat0(Zero, Zero)
new_compare9(x0, x1, ty_Integer)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_esEs21(x0, x1, ty_Bool)
new_lt10(x0, x1, ty_Integer)
new_esEs21(x0, x1, ty_Char)
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_esEs4(Just(x0), Just(x1), ty_Bool)
new_compare210(x0, x1, False, x2)
new_esEs14([], :(x0, x1), x2)
new_ltEs7(Just(x0), Just(x1), ty_Double)
new_esEs22(x0, x1, ty_Int)
new_lt20(x0, x1, ty_Float)
new_ltEs7(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_esEs7(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs4(Just(x0), Just(x1), ty_Ordering)
new_esEs25(x0, x1, ty_Float)
new_compare23(x0, x1, False, x2, x3)
new_esEs7(Left(x0), Left(x1), ty_Bool, x2)
new_primMulNat0(Zero, Zero)
new_ltEs18(x0, x1, ty_Int)
new_esEs21(x0, x1, ty_Float)
new_esEs7(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs17(Left(x0), Left(x1), ty_Ordering, x2)
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_ltEs10(EQ, LT)
new_ltEs10(LT, EQ)
new_compare23(x0, x1, True, x2, x3)
new_ltEs21(x0, x1, ty_@0)
new_esEs21(x0, x1, app(ty_[], x2))
new_ltEs17(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_esEs18(x0, x1, ty_Integer)
new_lt14(x0, x1, x2)
new_primCompAux00(x0, EQ)
new_compare10(x0, x1, True, x2, x3)
new_esEs13(:%(x0, x1), :%(x2, x3), x4)
new_compare210(x0, x1, True, x2)
new_pePe(True, x0)
new_esEs20(x0, x1, ty_Ordering)
new_ltEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, ty_Ordering)
new_esEs28(x0, x1, ty_Int)
new_esEs12(Char(x0), Char(x1))
new_lt19(x0, x1, ty_Char)
new_compare110(x0, x1, False)
new_esEs4(Just(x0), Just(x1), ty_@0)
new_lt10(x0, x1, ty_Ordering)
new_esEs22(x0, x1, ty_Char)
new_esEs30(x0, x1, ty_Bool)
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs26(x0, x1, ty_@0)
new_esEs24(x0, x1, ty_Integer)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs25(x0, x1, ty_Ordering)
new_esEs4(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, app(ty_[], x2))
new_primCompAux00(x0, LT)
new_ltEs21(x0, x1, ty_Ordering)
new_ltEs19(x0, x1, ty_Integer)
new_ltEs17(Left(x0), Left(x1), ty_Bool, x2)
new_ltEs17(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs17(Left(x0), Left(x1), ty_Float, x2)
new_ltEs19(x0, x1, ty_Int)
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs25(x0, x1, ty_Double)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs7(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_esEs27(x0, x1, ty_Double)
new_esEs26(x0, x1, ty_Integer)
new_esEs19(x0, x1, ty_Integer)
new_esEs23(x0, x1, ty_Integer)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_compare13(x0, x1, x2, x3)
new_lt6(x0, x1)
new_compare0([], [], x0)
new_esEs4(Just(x0), Just(x1), app(ty_Maybe, x2))
new_compare9(x0, x1, ty_@0)
new_esEs4(Just(x0), Just(x1), ty_Double)
new_ltEs17(Right(x0), Right(x1), x2, ty_Float)
new_lt10(x0, x1, app(ty_Maybe, x2))
new_ltEs19(x0, x1, ty_Bool)
new_esEs28(x0, x1, ty_@0)
new_lt20(x0, x1, ty_Bool)
new_ltEs15(x0, x1)
new_lt10(x0, x1, app(app(ty_@2, x2), x3))
new_compare11(x0, x1, False)
new_lt10(x0, x1, ty_Double)
new_compare111(x0, x1, True, x2, x3)
new_lt19(x0, x1, ty_@0)
new_esEs30(x0, x1, app(ty_Ratio, x2))
new_ltEs18(x0, x1, ty_Char)
new_esEs4(Just(x0), Nothing, x1)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_compare25(x0, x1, False, x2, x3, x4)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_compare27(x0, x1)
new_primPlusNat1(Zero, Zero)
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_compare0(:(x0, x1), :(x2, x3), x4)
new_sr(x0, x1)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_esEs20(x0, x1, ty_@0)
new_esEs7(Left(x0), Left(x1), ty_Float, x2)
new_ltEs18(x0, x1, app(app(ty_Either, x2), x3))
new_esEs16(x0, x1)
new_esEs25(x0, x1, app(ty_[], x2))
new_esEs24(x0, x1, ty_Float)
new_esEs4(Nothing, Just(x0), x1)
new_compare9(x0, x1, ty_Ordering)
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare28(x0, x1, x2, x3)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_ltEs7(Just(x0), Just(x1), ty_Int)
new_esEs28(x0, x1, ty_Float)
new_esEs23(x0, x1, ty_@0)
new_ltEs18(x0, x1, ty_Ordering)
new_esEs23(x0, x1, ty_Int)
new_esEs7(Right(x0), Right(x1), x2, ty_Double)
new_compare10(x0, x1, False, x2, x3)
new_esEs26(x0, x1, ty_Double)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs24(x0, x1, ty_Bool)
new_esEs23(x0, x1, app(ty_[], x2))
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs21(x0, x1, ty_Float)
new_primMulInt(Pos(x0), Pos(x1))
new_ltEs7(Just(x0), Just(x1), ty_Char)
new_compare112(x0, x1, True, x2)
new_compare9(x0, x1, app(app(ty_Either, x2), x3))
new_primPlusNat0(Succ(x0), x1)
new_ltEs10(GT, LT)
new_ltEs10(LT, GT)
new_ltEs17(Right(x0), Right(x1), x2, ty_@0)
new_ltEs7(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_sr0(Integer(x0), Integer(x1))
new_esEs23(x0, x1, ty_Double)
new_compare9(x0, x1, app(ty_[], x2))
new_esEs25(x0, x1, ty_Integer)
new_esEs20(x0, x1, ty_Char)
new_ltEs7(Nothing, Just(x0), x1)
new_primEqNat0(Zero, Succ(x0))
new_esEs27(x0, x1, ty_Bool)
new_esEs30(x0, x1, ty_Int)
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare17(:%(x0, x1), :%(x2, x3), ty_Int)
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_lt9(x0, x1)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_primMulInt(Neg(x0), Neg(x1))
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_esEs4(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, ty_Char)
new_compare211(x0, x1, False)
new_ltEs17(Left(x0), Left(x1), ty_Double, x2)
new_compare29(x0, x1, False, x2, x3)
new_ltEs9(x0, x1)
new_esEs7(Right(x0), Right(x1), x2, ty_Float)
new_ltEs17(Right(x0), Right(x1), x2, ty_Ordering)
new_lt10(x0, x1, ty_@0)
new_esEs30(x0, x1, ty_Ordering)
new_ltEs7(Just(x0), Nothing, x1)
new_esEs4(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_compare112(x0, x1, False, x2)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs18(x0, x1, ty_Integer)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_esEs27(x0, x1, ty_Float)
new_ltEs19(x0, x1, ty_Double)
new_ltEs21(x0, x1, ty_Double)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Neg(Zero), Neg(Zero))
new_ltEs19(x0, x1, ty_Ordering)
new_ltEs21(x0, x1, ty_Integer)
new_ltEs14(x0, x1)
new_ltEs17(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_ltEs7(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_compare29(x0, x1, True, x2, x3)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs24(x0, x1, ty_Ordering)
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs26(x0, x1, app(ty_[], x2))
new_ltEs17(Right(x0), Right(x1), x2, ty_Bool)
new_compare9(x0, x1, app(ty_Ratio, x2))
new_esEs30(x0, x1, ty_@0)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_compare7(@0, @0)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_esEs18(x0, x1, ty_Int)
new_ltEs17(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_lt19(x0, x1, app(ty_Maybe, x2))
new_primCompAux00(x0, GT)
new_ltEs21(x0, x1, ty_Int)
new_lt19(x0, x1, ty_Double)
new_esEs26(x0, x1, ty_Float)
new_esEs30(x0, x1, app(ty_[], x2))
new_ltEs7(Just(x0), Just(x1), ty_Ordering)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_esEs4(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs16(x0, x1)
new_esEs21(x0, x1, ty_@0)
new_compare18(x0, x1)
new_lt19(x0, x1, ty_Ordering)
new_esEs4(Nothing, Nothing, x0)
new_esEs30(x0, x1, ty_Char)
new_esEs7(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_ltEs21(x0, x1, app(app(ty_@2, x2), x3))
new_asAs(False, x0)
new_lt10(x0, x1, ty_Char)
new_esEs20(x0, x1, ty_Int)
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat1(Succ(x0), Zero)
new_esEs8(GT, EQ)
new_esEs8(EQ, GT)
new_esEs22(x0, x1, ty_Integer)
new_lt15(x0, x1, x2)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_compare17(:%(x0, x1), :%(x2, x3), ty_Integer)
new_primPlusNat0(Zero, x0)
new_esEs20(x0, x1, ty_Integer)
new_compare26(Float(x0, x1), Float(x2, x3))
new_ltEs17(Left(x0), Left(x1), ty_Char, x2)
new_primCmpNat0(Zero, Zero)
new_lt10(x0, x1, ty_Bool)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs7(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_ltEs17(Left(x0), Left(x1), ty_Integer, x2)
new_compare111(x0, x1, False, x2, x3)
new_ltEs7(Nothing, Nothing, x0)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs15(@0, @0)
new_compare16(x0, x1)
new_compare9(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare9(x0, x1, app(app(ty_@2, x2), x3))
new_lt16(x0, x1, x2, x3, x4)
new_esEs23(x0, x1, ty_Bool)
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs7(Left(x0), Left(x1), ty_Char, x2)
new_primCmpNat0(Zero, Succ(x0))
new_esEs27(x0, x1, ty_Integer)
new_esEs21(x0, x1, ty_Int)
new_esEs24(x0, x1, ty_Double)
new_esEs24(x0, x1, app(ty_[], x2))
new_esEs20(x0, x1, ty_Bool)
new_lt10(x0, x1, app(ty_Ratio, x2))
new_lt19(x0, x1, ty_Integer)
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_ltEs10(GT, GT)
new_esEs27(x0, x1, app(ty_[], x2))
new_ltEs7(Just(x0), Just(x1), ty_Float)
new_lt17(x0, x1)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_compare15(Double(x0, x1), Double(x2, x3))
new_esEs22(x0, x1, ty_Float)
new_lt13(x0, x1)
new_ltEs17(Right(x0), Right(x1), x2, ty_Double)
new_esEs30(x0, x1, app(app(ty_Either, x2), x3))
new_primCompAux0(x0, x1, x2, x3)
new_compare9(x0, x1, ty_Char)
new_ltEs5(True, True)
new_esEs7(Right(x0), Right(x1), x2, ty_@0)
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_compare14(Char(x0), Char(x1))
new_lt19(x0, x1, app(ty_Ratio, x2))
new_ltEs17(Right(x0), Right(x1), x2, ty_Integer)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_not(True)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_ltEs7(Just(x0), Just(x1), ty_@0)
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs28(x0, x1, ty_Double)
new_esEs26(x0, x1, ty_Ordering)
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs17(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs27(x0, x1, ty_Int)
new_esEs6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_lt10(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_not(False)
new_esEs4(Just(x0), Just(x1), ty_Integer)
new_ltEs17(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_lt20(x0, x1, ty_Char)
new_lt19(x0, x1, ty_Bool)
new_primCmpNat0(Succ(x0), Succ(x1))
new_ltEs10(EQ, GT)
new_ltEs10(GT, EQ)
new_esEs22(x0, x1, ty_Double)
new_esEs10(Float(x0, x1), Float(x2, x3))
new_esEs26(x0, x1, ty_Int)
new_esEs4(Just(x0), Just(x1), ty_Float)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_compare24(x0, x1, True)
new_ltEs17(Right(x0), Right(x1), x2, ty_Int)
new_esEs25(x0, x1, ty_@0)
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_compare9(x0, x1, ty_Int)
new_ltEs21(x0, x1, app(ty_[], x2))
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primMulNat0(Succ(x0), Zero)
new_esEs28(x0, x1, ty_Bool)
new_lt19(x0, x1, ty_Float)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs8(EQ, LT)
new_esEs8(LT, EQ)
new_lt20(x0, x1, ty_@0)
new_compare0([], :(x0, x1), x2)
new_lt19(x0, x1, app(ty_[], x2))
new_esEs7(Right(x0), Right(x1), x2, ty_Int)
new_esEs7(Left(x0), Left(x1), ty_Ordering, x2)
new_compare19(x0, x1, x2, x3, x4)
new_ltEs4(@2(x0, x1), @2(x2, x3), x4, x5)
new_lt8(x0, x1)
new_esEs25(x0, x1, ty_Int)
new_esEs4(Just(x0), Just(x1), app(ty_Ratio, x2))
new_ltEs7(Just(x0), Just(x1), ty_Bool)
new_compare12(x0, x1, False, x2, x3, x4)
new_esEs17(False, True)
new_esEs17(True, False)
new_ltEs17(Right(x0), Right(x1), x2, ty_Char)
new_esEs28(x0, x1, app(ty_[], x2))
new_compare110(x0, x1, True)
new_ltEs7(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs30(x0, x1, ty_Float)
new_ltEs8(x0, x1)
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_compare24(x0, x1, False)
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_esEs28(x0, x1, ty_Char)
new_esEs26(x0, x1, ty_Char)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare9(x0, x1, ty_Double)
new_ltEs17(Left(x0), Right(x1), x2, x3)
new_ltEs17(Right(x0), Left(x1), x2, x3)
new_esEs14([], [], x0)
new_primEqInt(Pos(Zero), Pos(Zero))
new_esEs17(True, True)
new_ltEs21(x0, x1, app(app(ty_Either, x2), x3))
new_lt12(x0, x1)
new_ltEs18(x0, x1, app(ty_Maybe, x2))
new_ltEs21(x0, x1, ty_Char)
new_ltEs18(x0, x1, ty_@0)
new_esEs20(x0, x1, ty_Double)
new_lt10(x0, x1, ty_Float)
new_esEs25(x0, x1, ty_Char)
new_ltEs19(x0, x1, ty_Char)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs28(x0, x1, ty_Ordering)
new_ltEs17(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_ltEs5(True, False)
new_ltEs5(False, True)
new_ltEs19(x0, x1, app(ty_[], x2))
new_esEs19(x0, x1, ty_Int)
new_esEs24(x0, x1, ty_Int)
new_ltEs18(x0, x1, ty_Bool)
new_esEs4(Just(x0), Just(x1), ty_Char)
new_ltEs7(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs7(Right(x0), Left(x1), x2, x3)
new_esEs7(Left(x0), Right(x1), x2, x3)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, ty_Int)
new_pePe(False, x0)
new_esEs30(x0, x1, app(app(ty_@2, x2), x3))
new_esEs22(x0, x1, ty_@0)
new_ltEs19(x0, x1, ty_Float)
new_esEs14(:(x0, x1), [], x2)
new_esEs28(x0, x1, ty_Integer)
new_ltEs10(EQ, EQ)
new_esEs20(x0, x1, app(ty_[], 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: