YES 9.032 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
  ↳ LR

mainModule List
  ((group :: (Eq b, Eq a) => [Either a b]  ->  [[Either a b]]) :: (Eq a, Eq b) => [Either a b]  ->  [[Either a b]])

module List where
  import qualified Maybe
import qualified Prelude
  group :: Eq a => [a]  ->  [[a]]
group = groupBy (==)

  groupBy :: (a  ->  a  ->  Bool)  ->  [a]  ->  [[a]]
groupBy _ [] = []
groupBy eq (x : xs) = 
(x : ys) : groupBy eq zs where 
vv10 = span (eq x) xs
ys = (\(ys,_) ->ys) vv10
zs = (\(_,zs) ->zs) vv10


module Maybe where
  import qualified List
import qualified Prelude


Lambda Reductions:
The following Lambda expression
\(_,zs)→zs

is transformed to
zs0 (_,zs) = zs

The following Lambda expression
\(ys,_)→ys

is transformed to
ys0 (ys,_) = ys

The following Lambda expression
\(_,zs)→zs

is transformed to
zs1 (_,zs) = zs

The following Lambda expression
\(ys,_)→ys

is transformed to
ys1 (ys,_) = ys



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ BR

mainModule List
  ((group :: (Eq a, Eq b) => [Either a b]  ->  [[Either a b]]) :: (Eq b, Eq a) => [Either a b]  ->  [[Either a b]])

module List where
  import qualified Maybe
import qualified Prelude
  group :: Eq a => [a]  ->  [[a]]
group = groupBy (==)

  groupBy :: (a  ->  a  ->  Bool)  ->  [a]  ->  [[a]]
groupBy _ [] = []
groupBy eq (x : xs) = 
(x : ys) : groupBy eq zs where 
vv10 = span (eq x) xs
ys = ys0 vv10
ys0 (ys,_) = ys
zs = zs0 vv10
zs0 (_,zs) = zs


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
xs@(ww : wx)

is replaced by the following term
ww : wx



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR

mainModule List
  ((group :: (Eq a, Eq b) => [Either a b]  ->  [[Either a b]]) :: (Eq b, Eq a) => [Either a b]  ->  [[Either a b]])

module List where
  import qualified Maybe
import qualified Prelude
  group :: Eq a => [a]  ->  [[a]]
group = groupBy (==)

  groupBy :: (a  ->  a  ->  Bool)  ->  [a]  ->  [[a]]
groupBy vw [] = []
groupBy eq (x : xs) = 
(x : ys) : groupBy eq zs where 
vv10 = span (eq x) xs
ys = ys0 vv10
ys0 (ys,vx) = ys
zs = zs0 vv10
zs0 (vy,zs) = zs


module Maybe where
  import qualified List
import qualified Prelude


Cond Reductions:
The following Function with conditions
undefined 
 | False
 = undefined

is transformed to
undefined  = undefined1

undefined0 True = undefined

undefined1  = undefined0 False

The following Function with conditions
span p [] = ([],[])
span p (ww : wx)
 | p ww
 = (ww : ys,zs)
 | otherwise
 = ([],ww : wx)
where 
vu43  = span p wx
ys  = ys1 vu43
ys1 (ys,wz) = ys
zs  = zs1 vu43
zs1 (wy,zs) = zs

is transformed to
span p [] = span3 p []
span p (ww : wx) = span2 p (ww : wx)

span2 p (ww : wx) = 
span1 p ww wx (p ww)
where 
span0 p ww wx True = ([],ww : wx)
span1 p ww wx True = (ww : ys,zs)
span1 p ww wx False = span0 p ww wx otherwise
vu43  = span p wx
ys  = ys1 vu43
ys1 (ys,wz) = ys
zs  = zs1 vu43
zs1 (wy,zs) = zs

span3 p [] = ([],[])
span3 yz zu = span2 yz zu



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ LetRed

mainModule List
  ((group :: (Eq a, Eq b) => [Either b a]  ->  [[Either b a]]) :: (Eq a, Eq b) => [Either b a]  ->  [[Either b a]])

module List where
  import qualified Maybe
import qualified Prelude
  group :: Eq a => [a]  ->  [[a]]
group = groupBy (==)

  groupBy :: (a  ->  a  ->  Bool)  ->  [a]  ->  [[a]]
groupBy vw [] = []
groupBy eq (x : xs) = 
(x : ys) : groupBy eq zs where 
vv10 = span (eq x) xs
ys = ys0 vv10
ys0 (ys,vx) = ys
zs = zs0 vv10
zs0 (vy,zs) = zs


module Maybe where
  import qualified List
import qualified Prelude


Let/Where Reductions:
The bindings of the following Let/Where expression
(x : ys) : groupBy eq zs
where 
vv10  = span (eq x) xs
ys  = ys0 vv10
ys0 (ys,vx) = ys
zs  = zs0 vv10
zs0 (vy,zs) = zs

are unpacked to the following functions on top level
groupByZs zv zw zx = groupByZs0 zv zw zx (groupByVv10 zv zw zx)

groupByZs0 zv zw zx (vy,zs) = zs

groupByVv10 zv zw zx = span (zv zw) zx

groupByYs0 zv zw zx (ys,vx) = ys

groupByYs zv zw zx = groupByYs0 zv zw zx (groupByVv10 zv zw zx)

The bindings of the following Let/Where expression
span1 p ww wx (p ww)
where 
span0 p ww wx True = ([],ww : wx)
span1 p ww wx True = (ww : ys,zs)
span1 p ww wx False = span0 p ww wx otherwise
vu43  = span p wx
ys  = ys1 vu43
ys1 (ys,wz) = ys
zs  = zs1 vu43
zs1 (wy,zs) = zs

are unpacked to the following functions on top level
span2Vu43 zy zz = span zy zz

span2Zs1 zy zz (wy,zs) = zs

span2Span1 zy zz p ww wx True = (ww : span2Ys zy zz,span2Zs zy zz)
span2Span1 zy zz p ww wx False = span2Span0 zy zz p ww wx otherwise

span2Span0 zy zz p ww wx True = ([],ww : wx)

span2Zs zy zz = span2Zs1 zy zz (span2Vu43 zy zz)

span2Ys1 zy zz (ys,wz) = ys

span2Ys zy zz = span2Ys1 zy zz (span2Vu43 zy zz)



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ LetRed
                ↳ HASKELL
                  ↳ Narrow

mainModule List
  (group :: (Eq a, Eq b) => [Either a b]  ->  [[Either a b]])

module List where
  import qualified Maybe
import qualified Prelude
  group :: Eq a => [a]  ->  [[a]]
group = groupBy (==)

  groupBy :: (a  ->  a  ->  Bool)  ->  [a]  ->  [[a]]
groupBy vw [] = []
groupBy eq (x : xs) = (x : groupByYs eq x xs) : groupBy eq (groupByZs eq x xs)

  
groupByVv10 zv zw zx = span (zv zw) zx

  
groupByYs zv zw zx = groupByYs0 zv zw zx (groupByVv10 zv zw zx)

  
groupByYs0 zv zw zx (ys,vx) = ys

  
groupByZs zv zw zx = groupByZs0 zv zw zx (groupByVv10 zv zw zx)

  
groupByZs0 zv zw zx (vy,zs) = zs


module Maybe where
  import qualified List
import qualified Prelude


Haskell To QDPs


↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ LetRed
                ↳ HASKELL
                  ↳ Narrow
                    ↳ AND
                      ↳ QDP
                        ↳ QDPSizeChangeProof
                      ↳ QDP
                      ↳ QDP
                      ↳ QDP
                      ↳ QDP
                      ↳ QDP
                      ↳ QDP

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

new_primPlusNat(Succ(vuu6500), Succ(vuu31001000)) → new_primPlusNat(vuu6500, vuu31001000)

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
  ↳ LR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ LetRed
                ↳ HASKELL
                  ↳ Narrow
                    ↳ AND
                      ↳ QDP
                      ↳ QDP
                        ↳ QDPSizeChangeProof
                      ↳ QDP
                      ↳ QDP
                      ↳ QDP
                      ↳ QDP
                      ↳ QDP

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

new_primMulNat(Succ(vuu300100), Succ(vuu3100100)) → new_primMulNat(vuu300100, Succ(vuu3100100))

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
  ↳ LR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ LetRed
                ↳ HASKELL
                  ↳ Narrow
                    ↳ AND
                      ↳ QDP
                      ↳ QDP
                      ↳ QDP
                        ↳ QDPSizeChangeProof
                      ↳ QDP
                      ↳ QDP
                      ↳ QDP
                      ↳ QDP

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

new_primEqNat(Succ(vuu30000), Succ(vuu310000)) → new_primEqNat(vuu30000, vuu310000)

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
  ↳ LR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ LetRed
                ↳ HASKELL
                  ↳ Narrow
                    ↳ AND
                      ↳ QDP
                      ↳ QDP
                      ↳ QDP
                      ↳ QDP
                        ↳ QDPSizeChangeProof
                      ↳ QDP
                      ↳ QDP
                      ↳ QDP

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

new_esEs1(@3(vuu3000, vuu3001, vuu3002), @3(vuu31000, vuu31001, vuu31002), eh, app(app(ty_@2, ga), gb), dg) → new_esEs3(vuu3001, vuu31001, ga, gb)
new_esEs0(:(vuu3000, vuu3001), :(vuu31000, vuu31001), app(app(ty_@2, db), dc)) → new_esEs3(vuu3000, vuu31000, db, dc)
new_esEs1(@3(vuu3000, vuu3001, vuu3002), @3(vuu31000, vuu31001, vuu31002), eh, app(ty_Maybe, fa), dg) → new_esEs(vuu3001, vuu31001, fa)
new_esEs1(@3(vuu3000, vuu3001, vuu3002), @3(vuu31000, vuu31001, vuu31002), eh, app(app(app(ty_@3, fc), fd), ff), dg) → new_esEs1(vuu3001, vuu31001, fc, fd, ff)
new_esEs2(Left(vuu3000), Left(vuu31000), app(app(ty_@2, bad), bae), he) → new_esEs3(vuu3000, vuu31000, bad, bae)
new_esEs1(@3(vuu3000, vuu3001, vuu3002), @3(vuu31000, vuu31001, vuu31002), eh, df, app(app(ty_Either, gh), ha)) → new_esEs2(vuu3002, vuu31002, gh, ha)
new_esEs1(@3(vuu3000, vuu3001, vuu3002), @3(vuu31000, vuu31001, vuu31002), app(app(ty_Either, ed), ee), df, dg) → new_esEs2(vuu3000, vuu31000, ed, ee)
new_esEs1(@3(vuu3000, vuu3001, vuu3002), @3(vuu31000, vuu31001, vuu31002), app(ty_[], dh), df, dg) → new_esEs0(vuu3000, vuu31000, dh)
new_esEs(Just(vuu3000), Just(vuu31000), app(app(ty_Either, bf), bg)) → new_esEs2(vuu3000, vuu31000, bf, bg)
new_esEs1(@3(vuu3000, vuu3001, vuu3002), @3(vuu31000, vuu31001, vuu31002), eh, df, app(app(app(ty_@3, ge), gf), gg)) → new_esEs1(vuu3002, vuu31002, ge, gf, gg)
new_esEs(Just(vuu3000), Just(vuu31000), app(ty_Maybe, ba)) → new_esEs(vuu3000, vuu31000, ba)
new_esEs2(Left(vuu3000), Left(vuu31000), app(app(ty_Either, bab), bac), he) → new_esEs2(vuu3000, vuu31000, bab, bac)
new_esEs2(Right(vuu3000), Right(vuu31000), baf, app(app(ty_@2, bbf), bbg)) → new_esEs3(vuu3000, vuu31000, bbf, bbg)
new_esEs0(:(vuu3000, vuu3001), :(vuu31000, vuu31001), app(ty_Maybe, cb)) → new_esEs(vuu3000, vuu31000, cb)
new_esEs1(@3(vuu3000, vuu3001, vuu3002), @3(vuu31000, vuu31001, vuu31002), eh, app(app(ty_Either, fg), fh), dg) → new_esEs2(vuu3001, vuu31001, fg, fh)
new_esEs3(@2(vuu3000, vuu3001), @2(vuu31000, vuu31001), app(app(app(ty_@3, bcc), bcd), bce), bca) → new_esEs1(vuu3000, vuu31000, bcc, bcd, bce)
new_esEs(Just(vuu3000), Just(vuu31000), app(ty_[], bb)) → new_esEs0(vuu3000, vuu31000, bb)
new_esEs2(Right(vuu3000), Right(vuu31000), baf, app(app(app(ty_@3, bba), bbb), bbc)) → new_esEs1(vuu3000, vuu31000, bba, bbb, bbc)
new_esEs1(@3(vuu3000, vuu3001, vuu3002), @3(vuu31000, vuu31001, vuu31002), app(ty_Maybe, de), df, dg) → new_esEs(vuu3000, vuu31000, de)
new_esEs3(@2(vuu3000, vuu3001), @2(vuu31000, vuu31001), bdb, app(app(ty_@2, beb), bec)) → new_esEs3(vuu3001, vuu31001, beb, bec)
new_esEs(Just(vuu3000), Just(vuu31000), app(app(ty_@2, bh), ca)) → new_esEs3(vuu3000, vuu31000, bh, ca)
new_esEs2(Left(vuu3000), Left(vuu31000), app(ty_Maybe, hd), he) → new_esEs(vuu3000, vuu31000, hd)
new_esEs1(@3(vuu3000, vuu3001, vuu3002), @3(vuu31000, vuu31001, vuu31002), eh, df, app(ty_[], gd)) → new_esEs0(vuu3002, vuu31002, gd)
new_esEs1(@3(vuu3000, vuu3001, vuu3002), @3(vuu31000, vuu31001, vuu31002), app(app(app(ty_@3, ea), eb), ec), df, dg) → new_esEs1(vuu3000, vuu31000, ea, eb, ec)
new_esEs2(Left(vuu3000), Left(vuu31000), app(app(app(ty_@3, hg), hh), baa), he) → new_esEs1(vuu3000, vuu31000, hg, hh, baa)
new_esEs1(@3(vuu3000, vuu3001, vuu3002), @3(vuu31000, vuu31001, vuu31002), app(app(ty_@2, ef), eg), df, dg) → new_esEs3(vuu3000, vuu31000, ef, eg)
new_esEs0(:(vuu3000, vuu3001), :(vuu31000, vuu31001), app(app(app(ty_@3, cd), ce), cf)) → new_esEs1(vuu3000, vuu31000, cd, ce, cf)
new_esEs0(:(vuu3000, vuu3001), :(vuu31000, vuu31001), app(app(ty_Either, cg), da)) → new_esEs2(vuu3000, vuu31000, cg, da)
new_esEs1(@3(vuu3000, vuu3001, vuu3002), @3(vuu31000, vuu31001, vuu31002), eh, app(ty_[], fb), dg) → new_esEs0(vuu3001, vuu31001, fb)
new_esEs2(Right(vuu3000), Right(vuu31000), baf, app(ty_Maybe, bag)) → new_esEs(vuu3000, vuu31000, bag)
new_esEs2(Right(vuu3000), Right(vuu31000), baf, app(ty_[], bah)) → new_esEs0(vuu3000, vuu31000, bah)
new_esEs2(Right(vuu3000), Right(vuu31000), baf, app(app(ty_Either, bbd), bbe)) → new_esEs2(vuu3000, vuu31000, bbd, bbe)
new_esEs3(@2(vuu3000, vuu3001), @2(vuu31000, vuu31001), app(app(ty_@2, bch), bda), bca) → new_esEs3(vuu3000, vuu31000, bch, bda)
new_esEs3(@2(vuu3000, vuu3001), @2(vuu31000, vuu31001), bdb, app(ty_Maybe, bdc)) → new_esEs(vuu3001, vuu31001, bdc)
new_esEs3(@2(vuu3000, vuu3001), @2(vuu31000, vuu31001), bdb, app(ty_[], bdd)) → new_esEs0(vuu3001, vuu31001, bdd)
new_esEs3(@2(vuu3000, vuu3001), @2(vuu31000, vuu31001), bdb, app(app(app(ty_@3, bde), bdf), bdg)) → new_esEs1(vuu3001, vuu31001, bde, bdf, bdg)
new_esEs0(:(vuu3000, vuu3001), :(vuu31000, vuu31001), app(ty_[], cc)) → new_esEs0(vuu3000, vuu31000, cc)
new_esEs1(@3(vuu3000, vuu3001, vuu3002), @3(vuu31000, vuu31001, vuu31002), eh, df, app(app(ty_@2, hb), hc)) → new_esEs3(vuu3002, vuu31002, hb, hc)
new_esEs2(Left(vuu3000), Left(vuu31000), app(ty_[], hf), he) → new_esEs0(vuu3000, vuu31000, hf)
new_esEs3(@2(vuu3000, vuu3001), @2(vuu31000, vuu31001), app(app(ty_Either, bcf), bcg), bca) → new_esEs2(vuu3000, vuu31000, bcf, bcg)
new_esEs3(@2(vuu3000, vuu3001), @2(vuu31000, vuu31001), bdb, app(app(ty_Either, bdh), bea)) → new_esEs2(vuu3001, vuu31001, bdh, bea)
new_esEs3(@2(vuu3000, vuu3001), @2(vuu31000, vuu31001), app(ty_[], bcb), bca) → new_esEs0(vuu3000, vuu31000, bcb)
new_esEs(Just(vuu3000), Just(vuu31000), app(app(app(ty_@3, bc), bd), be)) → new_esEs1(vuu3000, vuu31000, bc, bd, be)
new_esEs0(:(vuu3000, vuu3001), :(vuu31000, vuu31001), dd) → new_esEs0(vuu3001, vuu31001, dd)
new_esEs3(@2(vuu3000, vuu3001), @2(vuu31000, vuu31001), app(ty_Maybe, bbh), bca) → new_esEs(vuu3000, vuu31000, bbh)
new_esEs1(@3(vuu3000, vuu3001, vuu3002), @3(vuu31000, vuu31001, vuu31002), eh, df, app(ty_Maybe, gc)) → new_esEs(vuu3002, vuu31002, gc)

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
  ↳ LR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ LetRed
                ↳ HASKELL
                  ↳ Narrow
                    ↳ AND
                      ↳ QDP
                      ↳ QDP
                      ↳ QDP
                      ↳ QDP
                      ↳ QDP
                        ↳ QDPSizeChangeProof
                      ↳ QDP
                      ↳ QDP

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

new_span2Zs1(vuu36, vuu380, vuu381, True, ba, bb) → new_span2Ys(vuu36, vuu381, ba, bb)
new_span2Zs(vuu36, :(vuu380, vuu381), ba, bb) → new_span2Zs1(vuu36, vuu380, vuu381, new_esEs4(Right(vuu36), vuu380, ba, bb), ba, bb)
new_span2Zs1(vuu36, vuu380, vuu381, True, ba, bb) → new_span2Zs(vuu36, vuu381, ba, bb)
new_span2Ys(vuu18, :(vuu200, vuu201), bc, bd) → new_span2Ys1(vuu18, vuu200, vuu201, new_esEs4(Right(vuu18), vuu200, bc, bd), bc, bd)
new_span2Ys1(vuu18, vuu200, vuu201, True, bc, bd) → new_span2Zs(vuu18, vuu201, bc, bd)
new_span2Ys1(vuu18, vuu200, vuu201, True, bc, bd) → new_span2Ys(vuu18, vuu201, bc, bd)

The TRS R consists of the following rules:

new_esEs4(Left(vuu3000), Left(vuu31000), ty_Ordering, bf) → new_esEs11(vuu3000, vuu31000)
new_esEs4(Left(vuu3000), Left(vuu31000), app(ty_[], bh), bf) → new_esEs9(vuu3000, vuu31000, bh)
new_esEs20(vuu3002, vuu31002, app(ty_Ratio, hd)) → new_esEs7(vuu3002, vuu31002, hd)
new_esEs25(vuu3000, vuu31000, ty_Integer) → new_esEs12(vuu3000, vuu31000)
new_esEs19(vuu3001, vuu31001, app(ty_Ratio, gb)) → new_esEs7(vuu3001, vuu31001, gb)
new_primEqInt(Neg(Succ(vuu30000)), Pos(vuu31000)) → False
new_primEqInt(Pos(Succ(vuu30000)), Neg(vuu31000)) → False
new_esEs4(Left(vuu3000), Left(vuu31000), ty_Bool, bf) → new_esEs14(vuu3000, vuu31000)
new_esEs4(Right(vuu3000), Right(vuu31000), da, ty_Integer) → new_esEs12(vuu3000, vuu31000)
new_esEs4(Right(vuu3000), Right(vuu31000), da, ty_Bool) → new_esEs14(vuu3000, vuu31000)
new_esEs9([], [], beh) → True
new_esEs10(Char(vuu3000), Char(vuu31000)) → new_primEqNat0(vuu3000, vuu31000)
new_primEqInt(Neg(Zero), Pos(Succ(vuu310000))) → False
new_primEqInt(Pos(Zero), Neg(Succ(vuu310000))) → False
new_esEs18(vuu3000, vuu31000, app(app(ty_@2, fh), ga)) → new_esEs17(vuu3000, vuu31000, fh, ga)
new_esEs8(Just(vuu3000), Just(vuu31000), ty_Ordering) → new_esEs11(vuu3000, vuu31000)
new_esEs21(vuu3000, vuu31000, ty_Ordering) → new_esEs11(vuu3000, vuu31000)
new_esEs4(Left(vuu3000), Left(vuu31000), ty_Integer, bf) → new_esEs12(vuu3000, vuu31000)
new_esEs11(EQ, EQ) → True
new_esEs8(Just(vuu3000), Just(vuu31000), ty_Float) → new_esEs16(vuu3000, vuu31000)
new_primMulNat0(Zero, Zero) → Zero
new_esEs20(vuu3002, vuu31002, ty_Ordering) → new_esEs11(vuu3002, vuu31002)
new_esEs4(Left(vuu3000), Left(vuu31000), app(app(ty_@2, cf), cg), bf) → new_esEs17(vuu3000, vuu31000, cf, cg)
new_esEs11(GT, LT) → False
new_esEs11(LT, GT) → False
new_esEs25(vuu3000, vuu31000, ty_Ordering) → new_esEs11(vuu3000, vuu31000)
new_esEs21(vuu3000, vuu31000, ty_Int) → new_esEs6(vuu3000, vuu31000)
new_esEs4(Left(vuu3000), Left(vuu31000), ty_Char, bf) → new_esEs10(vuu3000, vuu31000)
new_esEs21(vuu3000, vuu31000, app(app(ty_@2, bbh), bca)) → new_esEs17(vuu3000, vuu31000, bbh, bca)
new_esEs25(vuu3000, vuu31000, ty_@0) → new_esEs15(vuu3000, vuu31000)
new_esEs20(vuu3002, vuu31002, ty_Int) → new_esEs6(vuu3002, vuu31002)
new_sr(Neg(vuu30010), Pos(vuu310010)) → Neg(new_primMulNat0(vuu30010, vuu310010))
new_sr(Pos(vuu30010), Neg(vuu310010)) → Neg(new_primMulNat0(vuu30010, vuu310010))
new_esEs24(vuu3001, vuu31001, ty_Integer) → new_esEs12(vuu3001, vuu31001)
new_esEs11(EQ, LT) → False
new_esEs11(LT, EQ) → False
new_esEs20(vuu3002, vuu31002, app(app(ty_Either, bab), bac)) → new_esEs4(vuu3002, vuu31002, bab, bac)
new_esEs4(Left(vuu3000), Left(vuu31000), ty_Int, bf) → new_esEs6(vuu3000, vuu31000)
new_esEs18(vuu3000, vuu31000, app(app(ty_Either, ff), fg)) → new_esEs4(vuu3000, vuu31000, ff, fg)
new_esEs6(vuu300, vuu3100) → new_primEqInt(vuu300, vuu3100)
new_esEs20(vuu3002, vuu31002, ty_Char) → new_esEs10(vuu3002, vuu31002)
new_esEs8(Just(vuu3000), Just(vuu31000), ty_Char) → new_esEs10(vuu3000, vuu31000)
new_esEs20(vuu3002, vuu31002, app(app(ty_@2, bad), bae)) → new_esEs17(vuu3002, vuu31002, bad, bae)
new_esEs25(vuu3000, vuu31000, ty_Int) → new_esEs6(vuu3000, vuu31000)
new_esEs23(vuu3000, vuu31000, ty_Integer) → new_esEs12(vuu3000, vuu31000)
new_esEs12(Integer(vuu3000), Integer(vuu31000)) → new_primEqInt(vuu3000, vuu31000)
new_esEs21(vuu3000, vuu31000, ty_Char) → new_esEs10(vuu3000, vuu31000)
new_primEqNat0(Zero, Succ(vuu310000)) → False
new_primEqNat0(Succ(vuu30000), Zero) → False
new_primPlusNat0(Zero, Zero) → Zero
new_esEs19(vuu3001, vuu31001, ty_Double) → new_esEs5(vuu3001, vuu31001)
new_esEs4(Right(vuu3000), Right(vuu31000), da, app(ty_[], dd)) → new_esEs9(vuu3000, vuu31000, dd)
new_esEs20(vuu3002, vuu31002, ty_Bool) → new_esEs14(vuu3002, vuu31002)
new_esEs20(vuu3002, vuu31002, ty_@0) → new_esEs15(vuu3002, vuu31002)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs4(Left(vuu3000), Left(vuu31000), ty_Float, bf) → new_esEs16(vuu3000, vuu31000)
new_esEs25(vuu3000, vuu31000, app(app(ty_Either, bfg), bfh)) → new_esEs4(vuu3000, vuu31000, bfg, bfh)
new_esEs17(@2(vuu3000, vuu3001), @2(vuu31000, vuu31001), baf, bag) → new_asAs(new_esEs21(vuu3000, vuu31000, baf), new_esEs22(vuu3001, vuu31001, bag))
new_esEs19(vuu3001, vuu31001, ty_@0) → new_esEs15(vuu3001, vuu31001)
new_esEs22(vuu3001, vuu31001, app(app(ty_Either, bch), bda)) → new_esEs4(vuu3001, vuu31001, bch, bda)
new_esEs21(vuu3000, vuu31000, ty_Double) → new_esEs5(vuu3000, vuu31000)
new_esEs25(vuu3000, vuu31000, ty_Bool) → new_esEs14(vuu3000, vuu31000)
new_esEs25(vuu3000, vuu31000, app(app(ty_@2, bga), bgb)) → new_esEs17(vuu3000, vuu31000, bga, bgb)
new_primPlusNat1(Succ(vuu650), vuu3100100) → Succ(Succ(new_primPlusNat0(vuu650, vuu3100100)))
new_esEs23(vuu3000, vuu31000, ty_Int) → new_esEs6(vuu3000, vuu31000)
new_esEs22(vuu3001, vuu31001, ty_@0) → new_esEs15(vuu3001, vuu31001)
new_esEs19(vuu3001, vuu31001, app(ty_[], gd)) → new_esEs9(vuu3001, vuu31001, gd)
new_esEs8(Just(vuu3000), Just(vuu31000), ty_@0) → new_esEs15(vuu3000, vuu31000)
new_esEs22(vuu3001, vuu31001, ty_Integer) → new_esEs12(vuu3001, vuu31001)
new_esEs4(Left(vuu3000), Left(vuu31000), app(ty_Maybe, bg), bf) → new_esEs8(vuu3000, vuu31000, bg)
new_esEs21(vuu3000, vuu31000, app(app(app(ty_@3, bbc), bbd), bbe)) → new_esEs13(vuu3000, vuu31000, bbc, bbd, bbe)
new_esEs19(vuu3001, vuu31001, ty_Float) → new_esEs16(vuu3001, vuu31001)
new_esEs18(vuu3000, vuu31000, app(app(app(ty_@3, fb), fc), fd)) → new_esEs13(vuu3000, vuu31000, fb, fc, fd)
new_esEs4(Right(vuu3000), Right(vuu31000), da, ty_Double) → new_esEs5(vuu3000, vuu31000)
new_esEs25(vuu3000, vuu31000, app(ty_[], bfc)) → new_esEs9(vuu3000, vuu31000, bfc)
new_esEs21(vuu3000, vuu31000, ty_Bool) → new_esEs14(vuu3000, vuu31000)
new_esEs18(vuu3000, vuu31000, ty_Integer) → new_esEs12(vuu3000, vuu31000)
new_esEs8(Nothing, Nothing, bde) → True
new_esEs11(GT, GT) → True
new_esEs18(vuu3000, vuu31000, ty_Ordering) → new_esEs11(vuu3000, vuu31000)
new_esEs22(vuu3001, vuu31001, app(ty_Ratio, bcb)) → new_esEs7(vuu3001, vuu31001, bcb)
new_sr(Neg(vuu30010), Neg(vuu310010)) → Pos(new_primMulNat0(vuu30010, vuu310010))
new_esEs15(@0, @0) → True
new_esEs18(vuu3000, vuu31000, ty_Int) → new_esEs6(vuu3000, vuu31000)
new_esEs5(Double(vuu3000, vuu3001), Double(vuu31000, vuu31001)) → new_esEs6(new_sr(vuu3000, vuu31000), new_sr(vuu3001, vuu31001))
new_sr(Pos(vuu30010), Pos(vuu310010)) → Pos(new_primMulNat0(vuu30010, vuu310010))
new_asAs(False, vuu52) → False
new_primEqNat0(Zero, Zero) → True
new_esEs24(vuu3001, vuu31001, ty_Int) → new_esEs6(vuu3001, vuu31001)
new_esEs22(vuu3001, vuu31001, app(ty_Maybe, bcc)) → new_esEs8(vuu3001, vuu31001, bcc)
new_primMulNat0(Zero, Succ(vuu3100100)) → Zero
new_primMulNat0(Succ(vuu300100), Zero) → Zero
new_esEs4(Left(vuu3000), Left(vuu31000), app(ty_Ratio, be), bf) → new_esEs7(vuu3000, vuu31000, be)
new_primMulNat0(Succ(vuu300100), Succ(vuu3100100)) → new_primPlusNat1(new_primMulNat0(vuu300100, Succ(vuu3100100)), vuu3100100)
new_esEs8(Just(vuu3000), Just(vuu31000), ty_Bool) → new_esEs14(vuu3000, vuu31000)
new_esEs4(Right(vuu3000), Right(vuu31000), da, app(app(ty_@2, eb), ec)) → new_esEs17(vuu3000, vuu31000, eb, ec)
new_esEs18(vuu3000, vuu31000, app(ty_[], fa)) → new_esEs9(vuu3000, vuu31000, fa)
new_esEs4(Right(vuu3000), Right(vuu31000), da, app(app(app(ty_@3, de), df), dg)) → new_esEs13(vuu3000, vuu31000, de, df, dg)
new_esEs20(vuu3002, vuu31002, ty_Float) → new_esEs16(vuu3002, vuu31002)
new_esEs22(vuu3001, vuu31001, app(app(app(ty_@3, bce), bcf), bcg)) → new_esEs13(vuu3001, vuu31001, bce, bcf, bcg)
new_esEs22(vuu3001, vuu31001, ty_Char) → new_esEs10(vuu3001, vuu31001)
new_esEs18(vuu3000, vuu31000, ty_Char) → new_esEs10(vuu3000, vuu31000)
new_esEs18(vuu3000, vuu31000, app(ty_Maybe, eh)) → new_esEs8(vuu3000, vuu31000, eh)
new_esEs21(vuu3000, vuu31000, app(ty_Maybe, bba)) → new_esEs8(vuu3000, vuu31000, bba)
new_esEs8(Just(vuu3000), Just(vuu31000), app(app(ty_@2, bef), beg)) → new_esEs17(vuu3000, vuu31000, bef, beg)
new_esEs19(vuu3001, vuu31001, ty_Ordering) → new_esEs11(vuu3001, vuu31001)
new_esEs25(vuu3000, vuu31000, ty_Double) → new_esEs5(vuu3000, vuu31000)
new_esEs4(Right(vuu3000), Right(vuu31000), da, app(ty_Ratio, db)) → new_esEs7(vuu3000, vuu31000, db)
new_esEs18(vuu3000, vuu31000, ty_Double) → new_esEs5(vuu3000, vuu31000)
new_esEs22(vuu3001, vuu31001, app(ty_[], bcd)) → new_esEs9(vuu3001, vuu31001, bcd)
new_esEs25(vuu3000, vuu31000, ty_Float) → new_esEs16(vuu3000, vuu31000)
new_esEs19(vuu3001, vuu31001, ty_Int) → new_esEs6(vuu3001, vuu31001)
new_esEs14(True, True) → True
new_esEs20(vuu3002, vuu31002, ty_Integer) → new_esEs12(vuu3002, vuu31002)
new_esEs16(Float(vuu3000, vuu3001), Float(vuu31000, vuu31001)) → new_esEs6(new_sr(vuu3000, vuu31000), new_sr(vuu3001, vuu31001))
new_esEs19(vuu3001, vuu31001, app(app(app(ty_@3, ge), gf), gg)) → new_esEs13(vuu3001, vuu31001, ge, gf, gg)
new_esEs25(vuu3000, vuu31000, app(app(app(ty_@3, bfd), bfe), bff)) → new_esEs13(vuu3000, vuu31000, bfd, bfe, bff)
new_esEs8(Just(vuu3000), Nothing, bde) → False
new_esEs8(Nothing, Just(vuu31000), bde) → False
new_esEs7(:%(vuu3000, vuu3001), :%(vuu31000, vuu31001), bdd) → new_asAs(new_esEs23(vuu3000, vuu31000, bdd), new_esEs24(vuu3001, vuu31001, bdd))
new_esEs22(vuu3001, vuu31001, ty_Float) → new_esEs16(vuu3001, vuu31001)
new_esEs4(Right(vuu3000), Right(vuu31000), da, app(app(ty_Either, dh), ea)) → new_esEs4(vuu3000, vuu31000, dh, ea)
new_primEqInt(Neg(Succ(vuu30000)), Neg(Succ(vuu310000))) → new_primEqNat0(vuu30000, vuu310000)
new_esEs9([], :(vuu31000, vuu31001), beh) → False
new_esEs9(:(vuu3000, vuu3001), [], beh) → False
new_esEs4(Right(vuu3000), Right(vuu31000), da, ty_@0) → new_esEs15(vuu3000, vuu31000)
new_esEs4(Left(vuu3000), Left(vuu31000), app(app(ty_Either, cd), ce), bf) → new_esEs4(vuu3000, vuu31000, cd, ce)
new_esEs4(Right(vuu3000), Right(vuu31000), da, ty_Float) → new_esEs16(vuu3000, vuu31000)
new_esEs4(Right(vuu3000), Right(vuu31000), da, ty_Ordering) → new_esEs11(vuu3000, vuu31000)
new_esEs9(:(vuu3000, vuu3001), :(vuu31000, vuu31001), beh) → new_asAs(new_esEs25(vuu3000, vuu31000, beh), new_esEs9(vuu3001, vuu31001, beh))
new_esEs21(vuu3000, vuu31000, ty_@0) → new_esEs15(vuu3000, vuu31000)
new_esEs18(vuu3000, vuu31000, app(ty_Ratio, eg)) → new_esEs7(vuu3000, vuu31000, eg)
new_esEs4(Right(vuu3000), Right(vuu31000), da, ty_Int) → new_esEs6(vuu3000, vuu31000)
new_esEs4(Left(vuu3000), Left(vuu31000), app(app(app(ty_@3, ca), cb), cc), bf) → new_esEs13(vuu3000, vuu31000, ca, cb, cc)
new_esEs19(vuu3001, vuu31001, app(app(ty_@2, hb), hc)) → new_esEs17(vuu3001, vuu31001, hb, hc)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs25(vuu3000, vuu31000, app(ty_Ratio, bfa)) → new_esEs7(vuu3000, vuu31000, bfa)
new_esEs8(Just(vuu3000), Just(vuu31000), app(app(ty_Either, bed), bee)) → new_esEs4(vuu3000, vuu31000, bed, bee)
new_esEs19(vuu3001, vuu31001, ty_Bool) → new_esEs14(vuu3001, vuu31001)
new_esEs14(False, False) → True
new_esEs19(vuu3001, vuu31001, ty_Integer) → new_esEs12(vuu3001, vuu31001)
new_primEqInt(Neg(Zero), Neg(Succ(vuu310000))) → False
new_primEqInt(Neg(Succ(vuu30000)), Neg(Zero)) → False
new_esEs4(Left(vuu3000), Left(vuu31000), ty_Double, bf) → new_esEs5(vuu3000, vuu31000)
new_primPlusNat1(Zero, vuu3100100) → Succ(vuu3100100)
new_esEs20(vuu3002, vuu31002, app(app(app(ty_@3, hg), hh), baa)) → new_esEs13(vuu3002, vuu31002, hg, hh, baa)
new_esEs18(vuu3000, vuu31000, ty_Bool) → new_esEs14(vuu3000, vuu31000)
new_esEs21(vuu3000, vuu31000, app(app(ty_Either, bbf), bbg)) → new_esEs4(vuu3000, vuu31000, bbf, bbg)
new_primPlusNat0(Succ(vuu6500), Succ(vuu31001000)) → Succ(Succ(new_primPlusNat0(vuu6500, vuu31001000)))
new_esEs22(vuu3001, vuu31001, ty_Double) → new_esEs5(vuu3001, vuu31001)
new_esEs4(Right(vuu3000), Right(vuu31000), da, app(ty_Maybe, dc)) → new_esEs8(vuu3000, vuu31000, dc)
new_esEs19(vuu3001, vuu31001, app(ty_Maybe, gc)) → new_esEs8(vuu3001, vuu31001, gc)
new_esEs8(Just(vuu3000), Just(vuu31000), ty_Int) → new_esEs6(vuu3000, vuu31000)
new_asAs(True, vuu52) → vuu52
new_esEs8(Just(vuu3000), Just(vuu31000), app(ty_[], bdh)) → new_esEs9(vuu3000, vuu31000, bdh)
new_esEs20(vuu3002, vuu31002, ty_Double) → new_esEs5(vuu3002, vuu31002)
new_esEs8(Just(vuu3000), Just(vuu31000), ty_Double) → new_esEs5(vuu3000, vuu31000)
new_esEs19(vuu3001, vuu31001, app(app(ty_Either, gh), ha)) → new_esEs4(vuu3001, vuu31001, gh, ha)
new_esEs4(Left(vuu3000), Right(vuu31000), da, bf) → False
new_esEs4(Right(vuu3000), Left(vuu31000), da, bf) → False
new_esEs13(@3(vuu3000, vuu3001, vuu3002), @3(vuu31000, vuu31001, vuu31002), ed, ee, ef) → new_asAs(new_esEs18(vuu3000, vuu31000, ed), new_asAs(new_esEs19(vuu3001, vuu31001, ee), new_esEs20(vuu3002, vuu31002, ef)))
new_esEs11(LT, LT) → True
new_esEs22(vuu3001, vuu31001, app(app(ty_@2, bdb), bdc)) → new_esEs17(vuu3001, vuu31001, bdb, bdc)
new_esEs8(Just(vuu3000), Just(vuu31000), app(ty_Maybe, bdg)) → new_esEs8(vuu3000, vuu31000, bdg)
new_primEqInt(Pos(Succ(vuu30000)), Pos(Succ(vuu310000))) → new_primEqNat0(vuu30000, vuu310000)
new_esEs8(Just(vuu3000), Just(vuu31000), app(app(app(ty_@3, bea), beb), bec)) → new_esEs13(vuu3000, vuu31000, bea, beb, bec)
new_esEs4(Left(vuu3000), Left(vuu31000), ty_@0, bf) → new_esEs15(vuu3000, vuu31000)
new_esEs18(vuu3000, vuu31000, ty_@0) → new_esEs15(vuu3000, vuu31000)
new_esEs19(vuu3001, vuu31001, ty_Char) → new_esEs10(vuu3001, vuu31001)
new_esEs20(vuu3002, vuu31002, app(ty_Maybe, he)) → new_esEs8(vuu3002, vuu31002, he)
new_esEs14(True, False) → False
new_esEs14(False, True) → False
new_esEs8(Just(vuu3000), Just(vuu31000), ty_Integer) → new_esEs12(vuu3000, vuu31000)
new_esEs21(vuu3000, vuu31000, ty_Integer) → new_esEs12(vuu3000, vuu31000)
new_esEs25(vuu3000, vuu31000, ty_Char) → new_esEs10(vuu3000, vuu31000)
new_primEqNat0(Succ(vuu30000), Succ(vuu310000)) → new_primEqNat0(vuu30000, vuu310000)
new_esEs11(GT, EQ) → False
new_esEs11(EQ, GT) → False
new_esEs8(Just(vuu3000), Just(vuu31000), app(ty_Ratio, bdf)) → new_esEs7(vuu3000, vuu31000, bdf)
new_esEs4(Right(vuu3000), Right(vuu31000), da, ty_Char) → new_esEs10(vuu3000, vuu31000)
new_esEs22(vuu3001, vuu31001, ty_Int) → new_esEs6(vuu3001, vuu31001)
new_esEs22(vuu3001, vuu31001, ty_Bool) → new_esEs14(vuu3001, vuu31001)
new_esEs21(vuu3000, vuu31000, ty_Float) → new_esEs16(vuu3000, vuu31000)
new_esEs21(vuu3000, vuu31000, app(ty_Ratio, bah)) → new_esEs7(vuu3000, vuu31000, bah)
new_esEs25(vuu3000, vuu31000, app(ty_Maybe, bfb)) → new_esEs8(vuu3000, vuu31000, bfb)
new_esEs21(vuu3000, vuu31000, app(ty_[], bbb)) → new_esEs9(vuu3000, vuu31000, bbb)
new_primEqInt(Pos(Zero), Pos(Succ(vuu310000))) → False
new_primEqInt(Pos(Succ(vuu30000)), Pos(Zero)) → False
new_esEs20(vuu3002, vuu31002, app(ty_[], hf)) → new_esEs9(vuu3002, vuu31002, hf)
new_esEs22(vuu3001, vuu31001, ty_Ordering) → new_esEs11(vuu3001, vuu31001)
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primPlusNat0(Zero, Succ(vuu31001000)) → Succ(vuu31001000)
new_primPlusNat0(Succ(vuu6500), Zero) → Succ(vuu6500)
new_esEs18(vuu3000, vuu31000, ty_Float) → new_esEs16(vuu3000, vuu31000)

The set Q consists of the following terms:

new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_esEs21(x0, x1, app(ty_[], x2))
new_esEs18(x0, x1, ty_Integer)
new_primMulNat0(Succ(x0), Zero)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs22(x0, x1, ty_Ordering)
new_esEs18(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, ty_@0)
new_primEqNat0(Zero, Succ(x0))
new_esEs9([], [], x0)
new_asAs(False, x0)
new_esEs9([], :(x0, x1), x2)
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_esEs18(x0, x1, ty_Double)
new_esEs22(x0, x1, ty_Bool)
new_esEs8(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs4(Right(x0), Right(x1), x2, ty_Char)
new_esEs18(x0, x1, app(app(ty_Either, x2), x3))
new_esEs16(Float(x0, x1), Float(x2, x3))
new_esEs25(x0, x1, ty_Ordering)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs22(x0, x1, ty_Integer)
new_esEs4(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs4(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs11(LT, EQ)
new_esEs11(EQ, LT)
new_esEs22(x0, x1, ty_@0)
new_esEs20(x0, x1, ty_@0)
new_esEs17(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_esEs18(x0, x1, ty_Bool)
new_primEqInt(Neg(Zero), Neg(Zero))
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_esEs22(x0, x1, ty_Int)
new_esEs8(Just(x0), Just(x1), ty_Double)
new_esEs14(False, True)
new_esEs14(True, False)
new_esEs4(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_esEs19(x0, x1, ty_Int)
new_esEs10(Char(x0), Char(x1))
new_sr(Neg(x0), Neg(x1))
new_esEs4(Right(x0), Right(x1), x2, ty_Float)
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, ty_Integer)
new_esEs25(x0, x1, ty_Float)
new_esEs8(Nothing, Nothing, x0)
new_esEs4(Right(x0), Right(x1), x2, ty_Double)
new_esEs21(x0, x1, ty_Bool)
new_esEs8(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs21(x0, x1, ty_Float)
new_esEs8(Just(x0), Just(x1), ty_Float)
new_esEs19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs19(x0, x1, ty_Ordering)
new_esEs8(Just(x0), Just(x1), app(ty_[], x2))
new_esEs9(:(x0, x1), :(x2, x3), x4)
new_esEs4(Left(x0), Left(x1), ty_Integer, x2)
new_esEs8(Just(x0), Just(x1), ty_Char)
new_esEs25(x0, x1, ty_Double)
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs21(x0, x1, ty_Int)
new_esEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, ty_Ordering)
new_esEs11(EQ, GT)
new_esEs11(GT, EQ)
new_esEs24(x0, x1, ty_Integer)
new_esEs19(x0, x1, app(ty_Maybe, x2))
new_esEs19(x0, x1, ty_Float)
new_esEs14(True, True)
new_esEs18(x0, x1, ty_Float)
new_esEs22(x0, x1, app(ty_[], x2))
new_esEs21(x0, x1, ty_Integer)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs8(Just(x0), Just(x1), ty_@0)
new_primEqNat0(Zero, Zero)
new_esEs5(Double(x0, x1), Double(x2, x3))
new_esEs15(@0, @0)
new_esEs8(Just(x0), Nothing, x1)
new_esEs8(Just(x0), Just(x1), ty_Int)
new_esEs4(Right(x0), Left(x1), x2, x3)
new_esEs4(Left(x0), Right(x1), x2, x3)
new_sr(Pos(x0), Pos(x1))
new_esEs22(x0, x1, ty_Char)
new_esEs4(Left(x0), Left(x1), ty_Double, x2)
new_esEs20(x0, x1, app(ty_[], x2))
new_esEs21(x0, x1, ty_Char)
new_primPlusNat0(Succ(x0), Succ(x1))
new_primMulNat0(Zero, Zero)
new_sr(Pos(x0), Neg(x1))
new_sr(Neg(x0), Pos(x1))
new_esEs8(Just(x0), Just(x1), app(ty_Ratio, x2))
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs4(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs19(x0, x1, ty_Bool)
new_esEs11(GT, GT)
new_esEs20(x0, x1, ty_Bool)
new_esEs4(Right(x0), Right(x1), x2, ty_Integer)
new_esEs22(x0, x1, ty_Double)
new_esEs23(x0, x1, ty_Integer)
new_primMulNat0(Zero, Succ(x0))
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_esEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs19(x0, x1, app(ty_Ratio, x2))
new_esEs11(GT, LT)
new_esEs11(LT, GT)
new_primEqNat0(Succ(x0), Zero)
new_esEs19(x0, x1, ty_@0)
new_esEs25(x0, x1, app(ty_[], x2))
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_esEs20(x0, x1, ty_Char)
new_esEs20(x0, x1, ty_Integer)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs20(x0, x1, ty_Double)
new_esEs19(x0, x1, ty_Double)
new_esEs20(x0, x1, ty_Float)
new_esEs20(x0, x1, ty_Ordering)
new_esEs8(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs6(x0, x1)
new_esEs18(x0, x1, app(ty_Ratio, x2))
new_esEs4(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs12(Integer(x0), Integer(x1))
new_esEs8(Nothing, Just(x0), x1)
new_esEs19(x0, x1, app(ty_[], x2))
new_esEs4(Left(x0), Left(x1), ty_@0, x2)
new_esEs18(x0, x1, app(ty_[], x2))
new_primPlusNat1(Succ(x0), x1)
new_esEs20(x0, x1, ty_Int)
new_esEs4(Right(x0), Right(x1), x2, ty_Int)
new_esEs18(x0, x1, ty_@0)
new_primMulNat0(Succ(x0), Succ(x1))
new_esEs4(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs21(x0, x1, ty_@0)
new_esEs4(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs19(x0, x1, ty_Char)
new_primPlusNat0(Zero, Succ(x0))
new_esEs4(Left(x0), Left(x1), ty_Int, x2)
new_esEs4(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs11(LT, LT)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_esEs8(Just(x0), Just(x1), ty_Ordering)
new_asAs(True, x0)
new_esEs9(:(x0, x1), [], x2)
new_primPlusNat0(Zero, Zero)
new_esEs25(x0, x1, ty_Char)
new_esEs24(x0, x1, ty_Int)
new_esEs8(Just(x0), Just(x1), ty_Bool)
new_esEs18(x0, x1, ty_Int)
new_esEs4(Left(x0), Left(x1), ty_Char, x2)
new_esEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs25(x0, x1, ty_Bool)
new_esEs14(False, False)
new_esEs23(x0, x1, ty_Int)
new_primEqInt(Pos(Zero), Pos(Zero))
new_esEs11(EQ, EQ)
new_esEs4(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs4(Right(x0), Right(x1), x2, ty_Bool)
new_esEs4(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs18(x0, x1, ty_Char)
new_esEs18(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(:%(x0, x1), :%(x2, x3), x4)
new_primPlusNat0(Succ(x0), Zero)
new_esEs4(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs21(x0, x1, ty_Double)
new_esEs4(Right(x0), Right(x1), x2, ty_@0)
new_esEs13(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs8(Just(x0), Just(x1), ty_Integer)
new_esEs18(x0, x1, ty_Ordering)
new_esEs25(x0, x1, ty_Int)
new_esEs19(x0, x1, ty_Integer)
new_esEs4(Left(x0), Left(x1), ty_Bool, x2)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs4(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_primPlusNat1(Zero, x0)
new_esEs8(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs22(x0, x1, ty_Float)
new_esEs4(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs4(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_esEs4(Left(x0), Left(x1), ty_Float, 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
  ↳ LR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ LetRed
                ↳ HASKELL
                  ↳ Narrow
                    ↳ AND
                      ↳ QDP
                      ↳ QDP
                      ↳ QDP
                      ↳ QDP
                      ↳ QDP
                      ↳ QDP
                        ↳ QDPSizeChangeProof
                      ↳ QDP

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

new_span2Ys10(vuu9, vuu110, vuu111, True, ba, bb) → new_span2Zs0(vuu9, vuu111, ba, bb)
new_span2Zs0(vuu27, :(vuu290, vuu291), bc, bd) → new_span2Zs10(vuu27, vuu290, vuu291, new_esEs4(Left(vuu27), vuu290, bc, bd), bc, bd)
new_span2Zs10(vuu27, vuu290, vuu291, True, bc, bd) → new_span2Zs0(vuu27, vuu291, bc, bd)
new_span2Zs10(vuu27, vuu290, vuu291, True, bc, bd) → new_span2Ys0(vuu27, vuu291, bc, bd)
new_span2Ys10(vuu9, vuu110, vuu111, True, ba, bb) → new_span2Ys0(vuu9, vuu111, ba, bb)
new_span2Ys0(vuu9, :(vuu110, vuu111), ba, bb) → new_span2Ys10(vuu9, vuu110, vuu111, new_esEs4(Left(vuu9), vuu110, ba, bb), ba, bb)

The TRS R consists of the following rules:

new_esEs4(Left(vuu3000), Left(vuu31000), ty_Ordering, bf) → new_esEs11(vuu3000, vuu31000)
new_esEs4(Left(vuu3000), Left(vuu31000), app(ty_[], bh), bf) → new_esEs9(vuu3000, vuu31000, bh)
new_esEs20(vuu3002, vuu31002, app(ty_Ratio, hd)) → new_esEs7(vuu3002, vuu31002, hd)
new_esEs25(vuu3000, vuu31000, ty_Integer) → new_esEs12(vuu3000, vuu31000)
new_esEs19(vuu3001, vuu31001, app(ty_Ratio, gb)) → new_esEs7(vuu3001, vuu31001, gb)
new_primEqInt(Neg(Succ(vuu30000)), Pos(vuu31000)) → False
new_primEqInt(Pos(Succ(vuu30000)), Neg(vuu31000)) → False
new_esEs4(Left(vuu3000), Left(vuu31000), ty_Bool, bf) → new_esEs14(vuu3000, vuu31000)
new_esEs4(Right(vuu3000), Right(vuu31000), da, ty_Integer) → new_esEs12(vuu3000, vuu31000)
new_esEs4(Right(vuu3000), Right(vuu31000), da, ty_Bool) → new_esEs14(vuu3000, vuu31000)
new_esEs9([], [], beh) → True
new_esEs10(Char(vuu3000), Char(vuu31000)) → new_primEqNat0(vuu3000, vuu31000)
new_primEqInt(Neg(Zero), Pos(Succ(vuu310000))) → False
new_primEqInt(Pos(Zero), Neg(Succ(vuu310000))) → False
new_esEs18(vuu3000, vuu31000, app(app(ty_@2, fh), ga)) → new_esEs17(vuu3000, vuu31000, fh, ga)
new_esEs8(Just(vuu3000), Just(vuu31000), ty_Ordering) → new_esEs11(vuu3000, vuu31000)
new_esEs21(vuu3000, vuu31000, ty_Ordering) → new_esEs11(vuu3000, vuu31000)
new_esEs4(Left(vuu3000), Left(vuu31000), ty_Integer, bf) → new_esEs12(vuu3000, vuu31000)
new_esEs11(EQ, EQ) → True
new_esEs8(Just(vuu3000), Just(vuu31000), ty_Float) → new_esEs16(vuu3000, vuu31000)
new_primMulNat0(Zero, Zero) → Zero
new_esEs20(vuu3002, vuu31002, ty_Ordering) → new_esEs11(vuu3002, vuu31002)
new_esEs4(Left(vuu3000), Left(vuu31000), app(app(ty_@2, cf), cg), bf) → new_esEs17(vuu3000, vuu31000, cf, cg)
new_esEs11(GT, LT) → False
new_esEs11(LT, GT) → False
new_esEs25(vuu3000, vuu31000, ty_Ordering) → new_esEs11(vuu3000, vuu31000)
new_esEs21(vuu3000, vuu31000, ty_Int) → new_esEs6(vuu3000, vuu31000)
new_esEs4(Left(vuu3000), Left(vuu31000), ty_Char, bf) → new_esEs10(vuu3000, vuu31000)
new_esEs21(vuu3000, vuu31000, app(app(ty_@2, bbh), bca)) → new_esEs17(vuu3000, vuu31000, bbh, bca)
new_esEs25(vuu3000, vuu31000, ty_@0) → new_esEs15(vuu3000, vuu31000)
new_esEs20(vuu3002, vuu31002, ty_Int) → new_esEs6(vuu3002, vuu31002)
new_sr(Neg(vuu30010), Pos(vuu310010)) → Neg(new_primMulNat0(vuu30010, vuu310010))
new_sr(Pos(vuu30010), Neg(vuu310010)) → Neg(new_primMulNat0(vuu30010, vuu310010))
new_esEs24(vuu3001, vuu31001, ty_Integer) → new_esEs12(vuu3001, vuu31001)
new_esEs11(EQ, LT) → False
new_esEs11(LT, EQ) → False
new_esEs20(vuu3002, vuu31002, app(app(ty_Either, bab), bac)) → new_esEs4(vuu3002, vuu31002, bab, bac)
new_esEs4(Left(vuu3000), Left(vuu31000), ty_Int, bf) → new_esEs6(vuu3000, vuu31000)
new_esEs18(vuu3000, vuu31000, app(app(ty_Either, ff), fg)) → new_esEs4(vuu3000, vuu31000, ff, fg)
new_esEs6(vuu300, vuu3100) → new_primEqInt(vuu300, vuu3100)
new_esEs20(vuu3002, vuu31002, ty_Char) → new_esEs10(vuu3002, vuu31002)
new_esEs8(Just(vuu3000), Just(vuu31000), ty_Char) → new_esEs10(vuu3000, vuu31000)
new_esEs20(vuu3002, vuu31002, app(app(ty_@2, bad), bae)) → new_esEs17(vuu3002, vuu31002, bad, bae)
new_esEs25(vuu3000, vuu31000, ty_Int) → new_esEs6(vuu3000, vuu31000)
new_esEs23(vuu3000, vuu31000, ty_Integer) → new_esEs12(vuu3000, vuu31000)
new_esEs12(Integer(vuu3000), Integer(vuu31000)) → new_primEqInt(vuu3000, vuu31000)
new_esEs21(vuu3000, vuu31000, ty_Char) → new_esEs10(vuu3000, vuu31000)
new_primEqNat0(Zero, Succ(vuu310000)) → False
new_primEqNat0(Succ(vuu30000), Zero) → False
new_primPlusNat0(Zero, Zero) → Zero
new_esEs19(vuu3001, vuu31001, ty_Double) → new_esEs5(vuu3001, vuu31001)
new_esEs4(Right(vuu3000), Right(vuu31000), da, app(ty_[], dd)) → new_esEs9(vuu3000, vuu31000, dd)
new_esEs20(vuu3002, vuu31002, ty_Bool) → new_esEs14(vuu3002, vuu31002)
new_esEs20(vuu3002, vuu31002, ty_@0) → new_esEs15(vuu3002, vuu31002)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs4(Left(vuu3000), Left(vuu31000), ty_Float, bf) → new_esEs16(vuu3000, vuu31000)
new_esEs25(vuu3000, vuu31000, app(app(ty_Either, bfg), bfh)) → new_esEs4(vuu3000, vuu31000, bfg, bfh)
new_esEs17(@2(vuu3000, vuu3001), @2(vuu31000, vuu31001), baf, bag) → new_asAs(new_esEs21(vuu3000, vuu31000, baf), new_esEs22(vuu3001, vuu31001, bag))
new_esEs19(vuu3001, vuu31001, ty_@0) → new_esEs15(vuu3001, vuu31001)
new_esEs22(vuu3001, vuu31001, app(app(ty_Either, bch), bda)) → new_esEs4(vuu3001, vuu31001, bch, bda)
new_esEs21(vuu3000, vuu31000, ty_Double) → new_esEs5(vuu3000, vuu31000)
new_esEs25(vuu3000, vuu31000, ty_Bool) → new_esEs14(vuu3000, vuu31000)
new_esEs25(vuu3000, vuu31000, app(app(ty_@2, bga), bgb)) → new_esEs17(vuu3000, vuu31000, bga, bgb)
new_primPlusNat1(Succ(vuu650), vuu3100100) → Succ(Succ(new_primPlusNat0(vuu650, vuu3100100)))
new_esEs23(vuu3000, vuu31000, ty_Int) → new_esEs6(vuu3000, vuu31000)
new_esEs22(vuu3001, vuu31001, ty_@0) → new_esEs15(vuu3001, vuu31001)
new_esEs19(vuu3001, vuu31001, app(ty_[], gd)) → new_esEs9(vuu3001, vuu31001, gd)
new_esEs8(Just(vuu3000), Just(vuu31000), ty_@0) → new_esEs15(vuu3000, vuu31000)
new_esEs22(vuu3001, vuu31001, ty_Integer) → new_esEs12(vuu3001, vuu31001)
new_esEs4(Left(vuu3000), Left(vuu31000), app(ty_Maybe, bg), bf) → new_esEs8(vuu3000, vuu31000, bg)
new_esEs21(vuu3000, vuu31000, app(app(app(ty_@3, bbc), bbd), bbe)) → new_esEs13(vuu3000, vuu31000, bbc, bbd, bbe)
new_esEs19(vuu3001, vuu31001, ty_Float) → new_esEs16(vuu3001, vuu31001)
new_esEs18(vuu3000, vuu31000, app(app(app(ty_@3, fb), fc), fd)) → new_esEs13(vuu3000, vuu31000, fb, fc, fd)
new_esEs4(Right(vuu3000), Right(vuu31000), da, ty_Double) → new_esEs5(vuu3000, vuu31000)
new_esEs25(vuu3000, vuu31000, app(ty_[], bfc)) → new_esEs9(vuu3000, vuu31000, bfc)
new_esEs21(vuu3000, vuu31000, ty_Bool) → new_esEs14(vuu3000, vuu31000)
new_esEs18(vuu3000, vuu31000, ty_Integer) → new_esEs12(vuu3000, vuu31000)
new_esEs8(Nothing, Nothing, bde) → True
new_esEs11(GT, GT) → True
new_esEs18(vuu3000, vuu31000, ty_Ordering) → new_esEs11(vuu3000, vuu31000)
new_esEs22(vuu3001, vuu31001, app(ty_Ratio, bcb)) → new_esEs7(vuu3001, vuu31001, bcb)
new_sr(Neg(vuu30010), Neg(vuu310010)) → Pos(new_primMulNat0(vuu30010, vuu310010))
new_esEs15(@0, @0) → True
new_esEs18(vuu3000, vuu31000, ty_Int) → new_esEs6(vuu3000, vuu31000)
new_esEs5(Double(vuu3000, vuu3001), Double(vuu31000, vuu31001)) → new_esEs6(new_sr(vuu3000, vuu31000), new_sr(vuu3001, vuu31001))
new_sr(Pos(vuu30010), Pos(vuu310010)) → Pos(new_primMulNat0(vuu30010, vuu310010))
new_asAs(False, vuu52) → False
new_primEqNat0(Zero, Zero) → True
new_esEs24(vuu3001, vuu31001, ty_Int) → new_esEs6(vuu3001, vuu31001)
new_esEs22(vuu3001, vuu31001, app(ty_Maybe, bcc)) → new_esEs8(vuu3001, vuu31001, bcc)
new_primMulNat0(Zero, Succ(vuu3100100)) → Zero
new_primMulNat0(Succ(vuu300100), Zero) → Zero
new_esEs4(Left(vuu3000), Left(vuu31000), app(ty_Ratio, be), bf) → new_esEs7(vuu3000, vuu31000, be)
new_primMulNat0(Succ(vuu300100), Succ(vuu3100100)) → new_primPlusNat1(new_primMulNat0(vuu300100, Succ(vuu3100100)), vuu3100100)
new_esEs8(Just(vuu3000), Just(vuu31000), ty_Bool) → new_esEs14(vuu3000, vuu31000)
new_esEs4(Right(vuu3000), Right(vuu31000), da, app(app(ty_@2, eb), ec)) → new_esEs17(vuu3000, vuu31000, eb, ec)
new_esEs18(vuu3000, vuu31000, app(ty_[], fa)) → new_esEs9(vuu3000, vuu31000, fa)
new_esEs4(Right(vuu3000), Right(vuu31000), da, app(app(app(ty_@3, de), df), dg)) → new_esEs13(vuu3000, vuu31000, de, df, dg)
new_esEs20(vuu3002, vuu31002, ty_Float) → new_esEs16(vuu3002, vuu31002)
new_esEs22(vuu3001, vuu31001, app(app(app(ty_@3, bce), bcf), bcg)) → new_esEs13(vuu3001, vuu31001, bce, bcf, bcg)
new_esEs22(vuu3001, vuu31001, ty_Char) → new_esEs10(vuu3001, vuu31001)
new_esEs18(vuu3000, vuu31000, ty_Char) → new_esEs10(vuu3000, vuu31000)
new_esEs18(vuu3000, vuu31000, app(ty_Maybe, eh)) → new_esEs8(vuu3000, vuu31000, eh)
new_esEs21(vuu3000, vuu31000, app(ty_Maybe, bba)) → new_esEs8(vuu3000, vuu31000, bba)
new_esEs8(Just(vuu3000), Just(vuu31000), app(app(ty_@2, bef), beg)) → new_esEs17(vuu3000, vuu31000, bef, beg)
new_esEs19(vuu3001, vuu31001, ty_Ordering) → new_esEs11(vuu3001, vuu31001)
new_esEs25(vuu3000, vuu31000, ty_Double) → new_esEs5(vuu3000, vuu31000)
new_esEs4(Right(vuu3000), Right(vuu31000), da, app(ty_Ratio, db)) → new_esEs7(vuu3000, vuu31000, db)
new_esEs18(vuu3000, vuu31000, ty_Double) → new_esEs5(vuu3000, vuu31000)
new_esEs22(vuu3001, vuu31001, app(ty_[], bcd)) → new_esEs9(vuu3001, vuu31001, bcd)
new_esEs25(vuu3000, vuu31000, ty_Float) → new_esEs16(vuu3000, vuu31000)
new_esEs19(vuu3001, vuu31001, ty_Int) → new_esEs6(vuu3001, vuu31001)
new_esEs14(True, True) → True
new_esEs20(vuu3002, vuu31002, ty_Integer) → new_esEs12(vuu3002, vuu31002)
new_esEs16(Float(vuu3000, vuu3001), Float(vuu31000, vuu31001)) → new_esEs6(new_sr(vuu3000, vuu31000), new_sr(vuu3001, vuu31001))
new_esEs19(vuu3001, vuu31001, app(app(app(ty_@3, ge), gf), gg)) → new_esEs13(vuu3001, vuu31001, ge, gf, gg)
new_esEs25(vuu3000, vuu31000, app(app(app(ty_@3, bfd), bfe), bff)) → new_esEs13(vuu3000, vuu31000, bfd, bfe, bff)
new_esEs8(Just(vuu3000), Nothing, bde) → False
new_esEs8(Nothing, Just(vuu31000), bde) → False
new_esEs7(:%(vuu3000, vuu3001), :%(vuu31000, vuu31001), bdd) → new_asAs(new_esEs23(vuu3000, vuu31000, bdd), new_esEs24(vuu3001, vuu31001, bdd))
new_esEs22(vuu3001, vuu31001, ty_Float) → new_esEs16(vuu3001, vuu31001)
new_esEs4(Right(vuu3000), Right(vuu31000), da, app(app(ty_Either, dh), ea)) → new_esEs4(vuu3000, vuu31000, dh, ea)
new_primEqInt(Neg(Succ(vuu30000)), Neg(Succ(vuu310000))) → new_primEqNat0(vuu30000, vuu310000)
new_esEs9([], :(vuu31000, vuu31001), beh) → False
new_esEs9(:(vuu3000, vuu3001), [], beh) → False
new_esEs4(Right(vuu3000), Right(vuu31000), da, ty_@0) → new_esEs15(vuu3000, vuu31000)
new_esEs4(Left(vuu3000), Left(vuu31000), app(app(ty_Either, cd), ce), bf) → new_esEs4(vuu3000, vuu31000, cd, ce)
new_esEs4(Right(vuu3000), Right(vuu31000), da, ty_Float) → new_esEs16(vuu3000, vuu31000)
new_esEs4(Right(vuu3000), Right(vuu31000), da, ty_Ordering) → new_esEs11(vuu3000, vuu31000)
new_esEs9(:(vuu3000, vuu3001), :(vuu31000, vuu31001), beh) → new_asAs(new_esEs25(vuu3000, vuu31000, beh), new_esEs9(vuu3001, vuu31001, beh))
new_esEs21(vuu3000, vuu31000, ty_@0) → new_esEs15(vuu3000, vuu31000)
new_esEs18(vuu3000, vuu31000, app(ty_Ratio, eg)) → new_esEs7(vuu3000, vuu31000, eg)
new_esEs4(Right(vuu3000), Right(vuu31000), da, ty_Int) → new_esEs6(vuu3000, vuu31000)
new_esEs4(Left(vuu3000), Left(vuu31000), app(app(app(ty_@3, ca), cb), cc), bf) → new_esEs13(vuu3000, vuu31000, ca, cb, cc)
new_esEs19(vuu3001, vuu31001, app(app(ty_@2, hb), hc)) → new_esEs17(vuu3001, vuu31001, hb, hc)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs25(vuu3000, vuu31000, app(ty_Ratio, bfa)) → new_esEs7(vuu3000, vuu31000, bfa)
new_esEs8(Just(vuu3000), Just(vuu31000), app(app(ty_Either, bed), bee)) → new_esEs4(vuu3000, vuu31000, bed, bee)
new_esEs19(vuu3001, vuu31001, ty_Bool) → new_esEs14(vuu3001, vuu31001)
new_esEs14(False, False) → True
new_esEs19(vuu3001, vuu31001, ty_Integer) → new_esEs12(vuu3001, vuu31001)
new_primEqInt(Neg(Zero), Neg(Succ(vuu310000))) → False
new_primEqInt(Neg(Succ(vuu30000)), Neg(Zero)) → False
new_esEs4(Left(vuu3000), Left(vuu31000), ty_Double, bf) → new_esEs5(vuu3000, vuu31000)
new_primPlusNat1(Zero, vuu3100100) → Succ(vuu3100100)
new_esEs20(vuu3002, vuu31002, app(app(app(ty_@3, hg), hh), baa)) → new_esEs13(vuu3002, vuu31002, hg, hh, baa)
new_esEs18(vuu3000, vuu31000, ty_Bool) → new_esEs14(vuu3000, vuu31000)
new_esEs21(vuu3000, vuu31000, app(app(ty_Either, bbf), bbg)) → new_esEs4(vuu3000, vuu31000, bbf, bbg)
new_primPlusNat0(Succ(vuu6500), Succ(vuu31001000)) → Succ(Succ(new_primPlusNat0(vuu6500, vuu31001000)))
new_esEs22(vuu3001, vuu31001, ty_Double) → new_esEs5(vuu3001, vuu31001)
new_esEs4(Right(vuu3000), Right(vuu31000), da, app(ty_Maybe, dc)) → new_esEs8(vuu3000, vuu31000, dc)
new_esEs19(vuu3001, vuu31001, app(ty_Maybe, gc)) → new_esEs8(vuu3001, vuu31001, gc)
new_esEs8(Just(vuu3000), Just(vuu31000), ty_Int) → new_esEs6(vuu3000, vuu31000)
new_asAs(True, vuu52) → vuu52
new_esEs8(Just(vuu3000), Just(vuu31000), app(ty_[], bdh)) → new_esEs9(vuu3000, vuu31000, bdh)
new_esEs20(vuu3002, vuu31002, ty_Double) → new_esEs5(vuu3002, vuu31002)
new_esEs8(Just(vuu3000), Just(vuu31000), ty_Double) → new_esEs5(vuu3000, vuu31000)
new_esEs19(vuu3001, vuu31001, app(app(ty_Either, gh), ha)) → new_esEs4(vuu3001, vuu31001, gh, ha)
new_esEs4(Left(vuu3000), Right(vuu31000), da, bf) → False
new_esEs4(Right(vuu3000), Left(vuu31000), da, bf) → False
new_esEs13(@3(vuu3000, vuu3001, vuu3002), @3(vuu31000, vuu31001, vuu31002), ed, ee, ef) → new_asAs(new_esEs18(vuu3000, vuu31000, ed), new_asAs(new_esEs19(vuu3001, vuu31001, ee), new_esEs20(vuu3002, vuu31002, ef)))
new_esEs11(LT, LT) → True
new_esEs22(vuu3001, vuu31001, app(app(ty_@2, bdb), bdc)) → new_esEs17(vuu3001, vuu31001, bdb, bdc)
new_esEs8(Just(vuu3000), Just(vuu31000), app(ty_Maybe, bdg)) → new_esEs8(vuu3000, vuu31000, bdg)
new_primEqInt(Pos(Succ(vuu30000)), Pos(Succ(vuu310000))) → new_primEqNat0(vuu30000, vuu310000)
new_esEs8(Just(vuu3000), Just(vuu31000), app(app(app(ty_@3, bea), beb), bec)) → new_esEs13(vuu3000, vuu31000, bea, beb, bec)
new_esEs4(Left(vuu3000), Left(vuu31000), ty_@0, bf) → new_esEs15(vuu3000, vuu31000)
new_esEs18(vuu3000, vuu31000, ty_@0) → new_esEs15(vuu3000, vuu31000)
new_esEs19(vuu3001, vuu31001, ty_Char) → new_esEs10(vuu3001, vuu31001)
new_esEs20(vuu3002, vuu31002, app(ty_Maybe, he)) → new_esEs8(vuu3002, vuu31002, he)
new_esEs14(True, False) → False
new_esEs14(False, True) → False
new_esEs8(Just(vuu3000), Just(vuu31000), ty_Integer) → new_esEs12(vuu3000, vuu31000)
new_esEs21(vuu3000, vuu31000, ty_Integer) → new_esEs12(vuu3000, vuu31000)
new_esEs25(vuu3000, vuu31000, ty_Char) → new_esEs10(vuu3000, vuu31000)
new_primEqNat0(Succ(vuu30000), Succ(vuu310000)) → new_primEqNat0(vuu30000, vuu310000)
new_esEs11(GT, EQ) → False
new_esEs11(EQ, GT) → False
new_esEs8(Just(vuu3000), Just(vuu31000), app(ty_Ratio, bdf)) → new_esEs7(vuu3000, vuu31000, bdf)
new_esEs4(Right(vuu3000), Right(vuu31000), da, ty_Char) → new_esEs10(vuu3000, vuu31000)
new_esEs22(vuu3001, vuu31001, ty_Int) → new_esEs6(vuu3001, vuu31001)
new_esEs22(vuu3001, vuu31001, ty_Bool) → new_esEs14(vuu3001, vuu31001)
new_esEs21(vuu3000, vuu31000, ty_Float) → new_esEs16(vuu3000, vuu31000)
new_esEs21(vuu3000, vuu31000, app(ty_Ratio, bah)) → new_esEs7(vuu3000, vuu31000, bah)
new_esEs25(vuu3000, vuu31000, app(ty_Maybe, bfb)) → new_esEs8(vuu3000, vuu31000, bfb)
new_esEs21(vuu3000, vuu31000, app(ty_[], bbb)) → new_esEs9(vuu3000, vuu31000, bbb)
new_primEqInt(Pos(Zero), Pos(Succ(vuu310000))) → False
new_primEqInt(Pos(Succ(vuu30000)), Pos(Zero)) → False
new_esEs20(vuu3002, vuu31002, app(ty_[], hf)) → new_esEs9(vuu3002, vuu31002, hf)
new_esEs22(vuu3001, vuu31001, ty_Ordering) → new_esEs11(vuu3001, vuu31001)
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primPlusNat0(Zero, Succ(vuu31001000)) → Succ(vuu31001000)
new_primPlusNat0(Succ(vuu6500), Zero) → Succ(vuu6500)
new_esEs18(vuu3000, vuu31000, ty_Float) → new_esEs16(vuu3000, vuu31000)

The set Q consists of the following terms:

new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_esEs21(x0, x1, app(ty_[], x2))
new_esEs18(x0, x1, ty_Integer)
new_primMulNat0(Succ(x0), Zero)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs22(x0, x1, ty_Ordering)
new_esEs18(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, ty_@0)
new_primEqNat0(Zero, Succ(x0))
new_esEs9([], [], x0)
new_asAs(False, x0)
new_esEs9([], :(x0, x1), x2)
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_esEs18(x0, x1, ty_Double)
new_esEs22(x0, x1, ty_Bool)
new_esEs8(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs4(Right(x0), Right(x1), x2, ty_Char)
new_esEs18(x0, x1, app(app(ty_Either, x2), x3))
new_esEs16(Float(x0, x1), Float(x2, x3))
new_esEs25(x0, x1, ty_Ordering)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs22(x0, x1, ty_Integer)
new_esEs4(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs4(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs11(LT, EQ)
new_esEs11(EQ, LT)
new_esEs22(x0, x1, ty_@0)
new_esEs20(x0, x1, ty_@0)
new_esEs17(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_esEs18(x0, x1, ty_Bool)
new_primEqInt(Neg(Zero), Neg(Zero))
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_esEs22(x0, x1, ty_Int)
new_esEs8(Just(x0), Just(x1), ty_Double)
new_esEs14(False, True)
new_esEs14(True, False)
new_esEs4(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_esEs19(x0, x1, ty_Int)
new_esEs10(Char(x0), Char(x1))
new_sr(Neg(x0), Neg(x1))
new_esEs4(Right(x0), Right(x1), x2, ty_Float)
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, ty_Integer)
new_esEs25(x0, x1, ty_Float)
new_esEs8(Nothing, Nothing, x0)
new_esEs4(Right(x0), Right(x1), x2, ty_Double)
new_esEs21(x0, x1, ty_Bool)
new_esEs8(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs21(x0, x1, ty_Float)
new_esEs8(Just(x0), Just(x1), ty_Float)
new_esEs19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs19(x0, x1, ty_Ordering)
new_esEs8(Just(x0), Just(x1), app(ty_[], x2))
new_esEs9(:(x0, x1), :(x2, x3), x4)
new_esEs4(Left(x0), Left(x1), ty_Integer, x2)
new_esEs8(Just(x0), Just(x1), ty_Char)
new_esEs25(x0, x1, ty_Double)
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs21(x0, x1, ty_Int)
new_esEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, ty_Ordering)
new_esEs11(EQ, GT)
new_esEs11(GT, EQ)
new_esEs24(x0, x1, ty_Integer)
new_esEs19(x0, x1, app(ty_Maybe, x2))
new_esEs19(x0, x1, ty_Float)
new_esEs14(True, True)
new_esEs18(x0, x1, ty_Float)
new_esEs22(x0, x1, app(ty_[], x2))
new_esEs21(x0, x1, ty_Integer)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs8(Just(x0), Just(x1), ty_@0)
new_primEqNat0(Zero, Zero)
new_esEs5(Double(x0, x1), Double(x2, x3))
new_esEs15(@0, @0)
new_esEs8(Just(x0), Nothing, x1)
new_esEs8(Just(x0), Just(x1), ty_Int)
new_esEs4(Right(x0), Left(x1), x2, x3)
new_esEs4(Left(x0), Right(x1), x2, x3)
new_sr(Pos(x0), Pos(x1))
new_esEs22(x0, x1, ty_Char)
new_esEs4(Left(x0), Left(x1), ty_Double, x2)
new_esEs20(x0, x1, app(ty_[], x2))
new_esEs21(x0, x1, ty_Char)
new_primPlusNat0(Succ(x0), Succ(x1))
new_primMulNat0(Zero, Zero)
new_sr(Pos(x0), Neg(x1))
new_sr(Neg(x0), Pos(x1))
new_esEs8(Just(x0), Just(x1), app(ty_Ratio, x2))
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs4(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs19(x0, x1, ty_Bool)
new_esEs11(GT, GT)
new_esEs20(x0, x1, ty_Bool)
new_esEs4(Right(x0), Right(x1), x2, ty_Integer)
new_esEs22(x0, x1, ty_Double)
new_esEs23(x0, x1, ty_Integer)
new_primMulNat0(Zero, Succ(x0))
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_esEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs19(x0, x1, app(ty_Ratio, x2))
new_esEs11(GT, LT)
new_esEs11(LT, GT)
new_primEqNat0(Succ(x0), Zero)
new_esEs19(x0, x1, ty_@0)
new_esEs25(x0, x1, app(ty_[], x2))
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_esEs20(x0, x1, ty_Char)
new_esEs20(x0, x1, ty_Integer)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs20(x0, x1, ty_Double)
new_esEs19(x0, x1, ty_Double)
new_esEs20(x0, x1, ty_Float)
new_esEs20(x0, x1, ty_Ordering)
new_esEs8(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs6(x0, x1)
new_esEs18(x0, x1, app(ty_Ratio, x2))
new_esEs4(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs12(Integer(x0), Integer(x1))
new_esEs8(Nothing, Just(x0), x1)
new_esEs19(x0, x1, app(ty_[], x2))
new_esEs4(Left(x0), Left(x1), ty_@0, x2)
new_esEs18(x0, x1, app(ty_[], x2))
new_primPlusNat1(Succ(x0), x1)
new_esEs20(x0, x1, ty_Int)
new_esEs4(Right(x0), Right(x1), x2, ty_Int)
new_esEs18(x0, x1, ty_@0)
new_primMulNat0(Succ(x0), Succ(x1))
new_esEs4(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs21(x0, x1, ty_@0)
new_esEs4(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs19(x0, x1, ty_Char)
new_primPlusNat0(Zero, Succ(x0))
new_esEs4(Left(x0), Left(x1), ty_Int, x2)
new_esEs4(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs11(LT, LT)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_esEs8(Just(x0), Just(x1), ty_Ordering)
new_asAs(True, x0)
new_esEs9(:(x0, x1), [], x2)
new_primPlusNat0(Zero, Zero)
new_esEs25(x0, x1, ty_Char)
new_esEs24(x0, x1, ty_Int)
new_esEs8(Just(x0), Just(x1), ty_Bool)
new_esEs18(x0, x1, ty_Int)
new_esEs4(Left(x0), Left(x1), ty_Char, x2)
new_esEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs25(x0, x1, ty_Bool)
new_esEs14(False, False)
new_esEs23(x0, x1, ty_Int)
new_primEqInt(Pos(Zero), Pos(Zero))
new_esEs11(EQ, EQ)
new_esEs4(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs4(Right(x0), Right(x1), x2, ty_Bool)
new_esEs4(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs18(x0, x1, ty_Char)
new_esEs18(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(:%(x0, x1), :%(x2, x3), x4)
new_primPlusNat0(Succ(x0), Zero)
new_esEs4(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs21(x0, x1, ty_Double)
new_esEs4(Right(x0), Right(x1), x2, ty_@0)
new_esEs13(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs8(Just(x0), Just(x1), ty_Integer)
new_esEs18(x0, x1, ty_Ordering)
new_esEs25(x0, x1, ty_Int)
new_esEs19(x0, x1, ty_Integer)
new_esEs4(Left(x0), Left(x1), ty_Bool, x2)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs4(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_primPlusNat1(Zero, x0)
new_esEs8(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs22(x0, x1, ty_Float)
new_esEs4(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs4(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_esEs4(Left(x0), Left(x1), ty_Float, 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
  ↳ LR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ LetRed
                ↳ HASKELL
                  ↳ Narrow
                    ↳ AND
                      ↳ QDP
                      ↳ QDP
                      ↳ QDP
                      ↳ QDP
                      ↳ QDP
                      ↳ QDP
                      ↳ QDP
                        ↳ QDPOrderProof

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

new_groupBy(:(vuu30, vuu31), ba, bb) → new_groupBy(new_groupByZs0(vuu30, vuu31, ba, bb), ba, bb)

The TRS R consists of the following rules:

new_esEs26(vuu300, vuu3100, ty_@0) → new_esEs15(vuu300, vuu3100)
new_esEs4(Left(vuu3000), Left(vuu31000), ty_Ordering, bd) → new_esEs11(vuu3000, vuu31000)
new_esEs4(Left(vuu3000), Left(vuu31000), app(ty_[], bf), bd) → new_esEs9(vuu3000, vuu31000, bf)
new_esEs20(vuu3002, vuu31002, app(ty_Ratio, bbe)) → new_esEs7(vuu3002, vuu31002, bbe)
new_esEs25(vuu3000, vuu31000, ty_Integer) → new_esEs12(vuu3000, vuu31000)
new_esEs19(vuu3001, vuu31001, app(ty_Ratio, bac)) → new_esEs7(vuu3001, vuu31001, bac)
new_primEqInt(Neg(Succ(vuu30000)), Pos(vuu31000)) → False
new_primEqInt(Pos(Succ(vuu30000)), Neg(vuu31000)) → False
new_esEs27(vuu300, vuu3100, ty_Ordering) → new_esEs11(vuu300, vuu3100)
new_span2Ys2(vuu18, :(vuu200, vuu201), ed, ee) → new_span2Ys11(vuu18, vuu200, vuu201, new_esEs4(Right(vuu18), vuu200, ed, ee), ed, ee)
new_esEs27(vuu300, vuu3100, app(app(ty_@2, bgg), bgh)) → new_esEs17(vuu300, vuu3100, bgg, bgh)
new_esEs4(Left(vuu3000), Left(vuu31000), ty_Bool, bd) → new_esEs14(vuu3000, vuu31000)
new_esEs4(Right(vuu3000), Right(vuu31000), cf, ty_Integer) → new_esEs12(vuu3000, vuu31000)
new_esEs4(Right(vuu3000), Right(vuu31000), cf, ty_Bool) → new_esEs14(vuu3000, vuu31000)
new_esEs9([], [], eh) → True
new_esEs18(vuu3000, vuu31000, app(app(ty_@2, baa), bab)) → new_esEs17(vuu3000, vuu31000, baa, bab)
new_primEqInt(Pos(Zero), Neg(Succ(vuu310000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(vuu310000))) → False
new_esEs10(Char(vuu3000), Char(vuu31000)) → new_primEqNat0(vuu3000, vuu31000)
new_span2Zs3(vuu27, [], ef, eg) → []
new_esEs8(Just(vuu3000), Just(vuu31000), ty_Ordering) → new_esEs11(vuu3000, vuu31000)
new_esEs21(vuu3000, vuu31000, ty_Ordering) → new_esEs11(vuu3000, vuu31000)
new_esEs4(Left(vuu3000), Left(vuu31000), ty_Integer, bd) → new_esEs12(vuu3000, vuu31000)
new_esEs11(EQ, EQ) → True
new_esEs8(Just(vuu3000), Just(vuu31000), ty_Float) → new_esEs16(vuu3000, vuu31000)
new_primMulNat0(Zero, Zero) → Zero
new_esEs27(vuu300, vuu3100, app(ty_Maybe, bfh)) → new_esEs8(vuu300, vuu3100, bfh)
new_esEs26(vuu300, vuu3100, ty_Float) → new_esEs16(vuu300, vuu3100)
new_esEs20(vuu3002, vuu31002, ty_Ordering) → new_esEs11(vuu3002, vuu31002)
new_esEs26(vuu300, vuu3100, app(ty_Ratio, bfe)) → new_esEs7(vuu300, vuu3100, bfe)
new_esEs4(Left(vuu3000), Left(vuu31000), app(app(ty_@2, cd), ce), bd) → new_esEs17(vuu3000, vuu31000, cd, ce)
new_esEs26(vuu300, vuu3100, app(ty_[], eh)) → new_esEs9(vuu300, vuu3100, eh)
new_esEs11(GT, LT) → False
new_esEs11(LT, GT) → False
new_esEs25(vuu3000, vuu31000, ty_Ordering) → new_esEs11(vuu3000, vuu31000)
new_esEs27(vuu300, vuu3100, ty_Integer) → new_esEs12(vuu300, vuu3100)
new_span2Ys13(vuu9, vuu110, vuu111, False, gd, ge) → []
new_esEs21(vuu3000, vuu31000, ty_Int) → new_esEs6(vuu3000, vuu31000)
new_esEs4(Left(vuu3000), Left(vuu31000), ty_Char, bd) → new_esEs10(vuu3000, vuu31000)
new_span2Ys3(vuu9, [], gd, ge) → []
new_esEs26(vuu300, vuu3100, ty_Bool) → new_esEs14(vuu300, vuu3100)
new_esEs21(vuu3000, vuu31000, app(app(ty_@2, bea), beb)) → new_esEs17(vuu3000, vuu31000, bea, beb)
new_esEs25(vuu3000, vuu31000, ty_@0) → new_esEs15(vuu3000, vuu31000)
new_esEs20(vuu3002, vuu31002, ty_Int) → new_esEs6(vuu3002, vuu31002)
new_esEs24(vuu3001, vuu31001, ty_Integer) → new_esEs12(vuu3001, vuu31001)
new_sr(Pos(vuu30010), Neg(vuu310010)) → Neg(new_primMulNat0(vuu30010, vuu310010))
new_sr(Neg(vuu30010), Pos(vuu310010)) → Neg(new_primMulNat0(vuu30010, vuu310010))
new_esEs11(EQ, LT) → False
new_esEs11(LT, EQ) → False
new_esEs20(vuu3002, vuu31002, app(app(ty_Either, bcc), bcd)) → new_esEs4(vuu3002, vuu31002, bcc, bcd)
new_esEs18(vuu3000, vuu31000, app(app(ty_Either, hg), hh)) → new_esEs4(vuu3000, vuu31000, hg, hh)
new_esEs4(Left(vuu3000), Left(vuu31000), ty_Int, bd) → new_esEs6(vuu3000, vuu31000)
new_esEs6(vuu300, vuu3100) → new_primEqInt(vuu300, vuu3100)
new_span2Zs12(vuu27, vuu290, vuu291, vuu62, vuu61, ef, eg) → vuu61
new_esEs27(vuu300, vuu3100, ty_@0) → new_esEs15(vuu300, vuu3100)
new_groupByZs01(vuu27, vuu28, vuu29, False, ef, eg) → :(Left(vuu28), vuu29)
new_esEs20(vuu3002, vuu31002, ty_Char) → new_esEs10(vuu3002, vuu31002)
new_esEs20(vuu3002, vuu31002, app(app(ty_@2, bce), bcf)) → new_esEs17(vuu3002, vuu31002, bce, bcf)
new_esEs8(Just(vuu3000), Just(vuu31000), ty_Char) → new_esEs10(vuu3000, vuu31000)
new_esEs25(vuu3000, vuu31000, ty_Int) → new_esEs6(vuu3000, vuu31000)
new_esEs23(vuu3000, vuu31000, ty_Integer) → new_esEs12(vuu3000, vuu31000)
new_span2Zs11(vuu27, vuu290, vuu291, False, ef, eg) → :(vuu290, vuu291)
new_esEs27(vuu300, vuu3100, app(ty_Ratio, bfg)) → new_esEs7(vuu300, vuu3100, bfg)
new_esEs27(vuu300, vuu3100, ty_Double) → new_esEs5(vuu300, vuu3100)
new_esEs12(Integer(vuu3000), Integer(vuu31000)) → new_primEqInt(vuu3000, vuu31000)
new_esEs21(vuu3000, vuu31000, ty_Char) → new_esEs10(vuu3000, vuu31000)
new_primEqNat0(Succ(vuu30000), Zero) → False
new_primEqNat0(Zero, Succ(vuu310000)) → False
new_span2Ys11(vuu18, vuu200, vuu201, True, ed, ee) → new_span2Ys12(vuu18, vuu200, vuu201, new_span2Ys2(vuu18, vuu201, ed, ee), new_span2Zs2(vuu18, vuu201, ed, ee), ed, ee)
new_esEs19(vuu3001, vuu31001, ty_Double) → new_esEs5(vuu3001, vuu31001)
new_primPlusNat0(Zero, Zero) → Zero
new_esEs4(Right(vuu3000), Right(vuu31000), cf, app(ty_[], db)) → new_esEs9(vuu3000, vuu31000, db)
new_esEs20(vuu3002, vuu31002, ty_Bool) → new_esEs14(vuu3002, vuu31002)
new_esEs20(vuu3002, vuu31002, ty_@0) → new_esEs15(vuu3002, vuu31002)
new_esEs26(vuu300, vuu3100, ty_Ordering) → new_esEs11(vuu300, vuu3100)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_groupByZs0(vuu30, [], ba, bb) → []
new_esEs27(vuu300, vuu3100, app(app(ty_Either, bge), bgf)) → new_esEs4(vuu300, vuu3100, bge, bgf)
new_esEs4(Left(vuu3000), Left(vuu31000), ty_Float, bd) → new_esEs16(vuu3000, vuu31000)
new_esEs25(vuu3000, vuu31000, app(app(ty_Either, fh), ga)) → new_esEs4(vuu3000, vuu31000, fh, ga)
new_esEs17(@2(vuu3000, vuu3001), @2(vuu31000, vuu31001), bcg, bch) → new_asAs(new_esEs21(vuu3000, vuu31000, bcg), new_esEs22(vuu3001, vuu31001, bch))
new_esEs19(vuu3001, vuu31001, ty_@0) → new_esEs15(vuu3001, vuu31001)
new_esEs26(vuu300, vuu3100, app(app(app(ty_@3, gf), gg), gh)) → new_esEs13(vuu300, vuu3100, gf, gg, gh)
new_esEs22(vuu3001, vuu31001, app(app(ty_Either, bfa), bfb)) → new_esEs4(vuu3001, vuu31001, bfa, bfb)
new_esEs21(vuu3000, vuu31000, ty_Double) → new_esEs5(vuu3000, vuu31000)
new_esEs27(vuu300, vuu3100, app(app(app(ty_@3, bgb), bgc), bgd)) → new_esEs13(vuu300, vuu3100, bgb, bgc, bgd)
new_esEs25(vuu3000, vuu31000, ty_Bool) → new_esEs14(vuu3000, vuu31000)
new_esEs25(vuu3000, vuu31000, app(app(ty_@2, gb), gc)) → new_esEs17(vuu3000, vuu31000, gb, gc)
new_primPlusNat1(Succ(vuu650), vuu3100100) → Succ(Succ(new_primPlusNat0(vuu650, vuu3100100)))
new_esEs22(vuu3001, vuu31001, ty_@0) → new_esEs15(vuu3001, vuu31001)
new_esEs19(vuu3001, vuu31001, app(ty_[], bae)) → new_esEs9(vuu3001, vuu31001, bae)
new_esEs23(vuu3000, vuu31000, ty_Int) → new_esEs6(vuu3000, vuu31000)
new_esEs22(vuu3001, vuu31001, ty_Integer) → new_esEs12(vuu3001, vuu31001)
new_esEs4(Left(vuu3000), Left(vuu31000), app(ty_Maybe, be), bd) → new_esEs8(vuu3000, vuu31000, be)
new_esEs8(Just(vuu3000), Just(vuu31000), ty_@0) → new_esEs15(vuu3000, vuu31000)
new_esEs21(vuu3000, vuu31000, app(app(app(ty_@3, bdd), bde), bdf)) → new_esEs13(vuu3000, vuu31000, bdd, bde, bdf)
new_esEs26(vuu300, vuu3100, ty_Double) → new_esEs5(vuu300, vuu3100)
new_esEs19(vuu3001, vuu31001, ty_Float) → new_esEs16(vuu3001, vuu31001)
new_span2Ys13(vuu9, vuu110, vuu111, True, gd, ge) → new_span2Ys14(vuu9, vuu110, vuu111, new_span2Ys3(vuu9, vuu111, gd, ge), new_span2Zs3(vuu9, vuu111, gd, ge), gd, ge)
new_esEs18(vuu3000, vuu31000, app(app(app(ty_@3, hd), he), hf)) → new_esEs13(vuu3000, vuu31000, hd, he, hf)
new_esEs4(Right(vuu3000), Right(vuu31000), cf, ty_Double) → new_esEs5(vuu3000, vuu31000)
new_esEs27(vuu300, vuu3100, app(ty_[], bga)) → new_esEs9(vuu300, vuu3100, bga)
new_esEs25(vuu3000, vuu31000, app(ty_[], fc)) → new_esEs9(vuu3000, vuu31000, fc)
new_esEs21(vuu3000, vuu31000, ty_Bool) → new_esEs14(vuu3000, vuu31000)
new_esEs18(vuu3000, vuu31000, ty_Integer) → new_esEs12(vuu3000, vuu31000)
new_esEs26(vuu300, vuu3100, ty_Int) → new_esEs6(vuu300, vuu3100)
new_groupByZs0(Left(vuu300), :(Left(vuu3100), vuu311), ba, bb) → new_groupByZs01(vuu300, vuu3100, vuu311, new_esEs26(vuu300, vuu3100, ba), ba, bb)
new_span2Zs3(vuu27, :(vuu290, vuu291), ef, eg) → new_span2Zs11(vuu27, vuu290, vuu291, new_esEs4(Left(vuu27), vuu290, ef, eg), ef, eg)
new_esEs8(Nothing, Nothing, bff) → True
new_esEs18(vuu3000, vuu31000, ty_Ordering) → new_esEs11(vuu3000, vuu31000)
new_esEs11(GT, GT) → True
new_esEs22(vuu3001, vuu31001, app(ty_Ratio, bec)) → new_esEs7(vuu3001, vuu31001, bec)
new_sr(Neg(vuu30010), Neg(vuu310010)) → Pos(new_primMulNat0(vuu30010, vuu310010))
new_esEs15(@0, @0) → True
new_esEs18(vuu3000, vuu31000, ty_Int) → new_esEs6(vuu3000, vuu31000)
new_groupByZs0(Left(vuu300), :(Right(vuu3100), vuu311), ba, bb) → :(Right(vuu3100), vuu311)
new_esEs5(Double(vuu3000, vuu3001), Double(vuu31000, vuu31001)) → new_esEs6(new_sr(vuu3000, vuu31000), new_sr(vuu3001, vuu31001))
new_asAs(False, vuu52) → False
new_sr(Pos(vuu30010), Pos(vuu310010)) → Pos(new_primMulNat0(vuu30010, vuu310010))
new_span2Zs2(vuu36, :(vuu380, vuu381), eb, ec) → new_span2Zs13(vuu36, vuu380, vuu381, new_esEs4(Right(vuu36), vuu380, eb, ec), eb, ec)
new_primEqNat0(Zero, Zero) → True
new_esEs24(vuu3001, vuu31001, ty_Int) → new_esEs6(vuu3001, vuu31001)
new_esEs22(vuu3001, vuu31001, app(ty_Maybe, bed)) → new_esEs8(vuu3001, vuu31001, bed)
new_primMulNat0(Zero, Succ(vuu3100100)) → Zero
new_primMulNat0(Succ(vuu300100), Zero) → Zero
new_esEs4(Left(vuu3000), Left(vuu31000), app(ty_Ratio, bc), bd) → new_esEs7(vuu3000, vuu31000, bc)
new_primMulNat0(Succ(vuu300100), Succ(vuu3100100)) → new_primPlusNat1(new_primMulNat0(vuu300100, Succ(vuu3100100)), vuu3100100)
new_esEs8(Just(vuu3000), Just(vuu31000), ty_Bool) → new_esEs14(vuu3000, vuu31000)
new_esEs4(Right(vuu3000), Right(vuu31000), cf, app(app(ty_@2, dh), ea)) → new_esEs17(vuu3000, vuu31000, dh, ea)
new_esEs18(vuu3000, vuu31000, app(ty_[], hc)) → new_esEs9(vuu3000, vuu31000, hc)
new_span2Ys2(vuu18, [], ed, ee) → []
new_esEs20(vuu3002, vuu31002, ty_Float) → new_esEs16(vuu3002, vuu31002)
new_esEs4(Right(vuu3000), Right(vuu31000), cf, app(app(app(ty_@3, dc), dd), de)) → new_esEs13(vuu3000, vuu31000, dc, dd, de)
new_esEs22(vuu3001, vuu31001, app(app(app(ty_@3, bef), beg), beh)) → new_esEs13(vuu3001, vuu31001, bef, beg, beh)
new_span2Zs13(vuu36, vuu380, vuu381, True, eb, ec) → new_span2Zs14(vuu36, vuu380, vuu381, new_span2Ys2(vuu36, vuu381, eb, ec), new_span2Zs2(vuu36, vuu381, eb, ec), eb, ec)
new_esEs22(vuu3001, vuu31001, ty_Char) → new_esEs10(vuu3001, vuu31001)
new_esEs18(vuu3000, vuu31000, ty_Char) → new_esEs10(vuu3000, vuu31000)
new_span2Ys3(vuu9, :(vuu110, vuu111), gd, ge) → new_span2Ys13(vuu9, vuu110, vuu111, new_esEs4(Left(vuu9), vuu110, gd, ge), gd, ge)
new_esEs18(vuu3000, vuu31000, app(ty_Maybe, hb)) → new_esEs8(vuu3000, vuu31000, hb)
new_esEs21(vuu3000, vuu31000, app(ty_Maybe, bdb)) → new_esEs8(vuu3000, vuu31000, bdb)
new_esEs8(Just(vuu3000), Just(vuu31000), app(app(ty_@2, caa), cab)) → new_esEs17(vuu3000, vuu31000, caa, cab)
new_esEs19(vuu3001, vuu31001, ty_Ordering) → new_esEs11(vuu3001, vuu31001)
new_esEs25(vuu3000, vuu31000, ty_Double) → new_esEs5(vuu3000, vuu31000)
new_esEs4(Right(vuu3000), Right(vuu31000), cf, app(ty_Ratio, cg)) → new_esEs7(vuu3000, vuu31000, cg)
new_groupByZs00(vuu36, vuu37, vuu38, True, eb, ec) → new_span2Zs2(vuu36, vuu38, eb, ec)
new_esEs18(vuu3000, vuu31000, ty_Double) → new_esEs5(vuu3000, vuu31000)
new_esEs22(vuu3001, vuu31001, app(ty_[], bee)) → new_esEs9(vuu3001, vuu31001, bee)
new_esEs27(vuu300, vuu3100, ty_Char) → new_esEs10(vuu300, vuu3100)
new_esEs25(vuu3000, vuu31000, ty_Float) → new_esEs16(vuu3000, vuu31000)
new_esEs19(vuu3001, vuu31001, ty_Int) → new_esEs6(vuu3001, vuu31001)
new_esEs14(True, True) → True
new_esEs20(vuu3002, vuu31002, ty_Integer) → new_esEs12(vuu3002, vuu31002)
new_esEs27(vuu300, vuu3100, ty_Bool) → new_esEs14(vuu300, vuu3100)
new_esEs19(vuu3001, vuu31001, app(app(app(ty_@3, baf), bag), bah)) → new_esEs13(vuu3001, vuu31001, baf, bag, bah)
new_esEs16(Float(vuu3000, vuu3001), Float(vuu31000, vuu31001)) → new_esEs6(new_sr(vuu3000, vuu31000), new_sr(vuu3001, vuu31001))
new_span2Ys14(vuu9, vuu110, vuu111, vuu58, vuu57, gd, ge) → :(vuu110, vuu58)
new_esEs25(vuu3000, vuu31000, app(app(app(ty_@3, fd), ff), fg)) → new_esEs13(vuu3000, vuu31000, fd, ff, fg)
new_esEs26(vuu300, vuu3100, ty_Integer) → new_esEs12(vuu300, vuu3100)
new_esEs8(Nothing, Just(vuu31000), bff) → False
new_esEs8(Just(vuu3000), Nothing, bff) → False
new_esEs7(:%(vuu3000, vuu3001), :%(vuu31000, vuu31001), bfe) → new_asAs(new_esEs23(vuu3000, vuu31000, bfe), new_esEs24(vuu3001, vuu31001, bfe))
new_esEs22(vuu3001, vuu31001, ty_Float) → new_esEs16(vuu3001, vuu31001)
new_esEs4(Right(vuu3000), Right(vuu31000), cf, app(app(ty_Either, df), dg)) → new_esEs4(vuu3000, vuu31000, df, dg)
new_primEqInt(Neg(Succ(vuu30000)), Neg(Succ(vuu310000))) → new_primEqNat0(vuu30000, vuu310000)
new_esEs26(vuu300, vuu3100, app(ty_Maybe, bff)) → new_esEs8(vuu300, vuu3100, bff)
new_esEs9(:(vuu3000, vuu3001), [], eh) → False
new_esEs9([], :(vuu31000, vuu31001), eh) → False
new_esEs4(Right(vuu3000), Right(vuu31000), cf, ty_@0) → new_esEs15(vuu3000, vuu31000)
new_span2Zs2(vuu36, [], eb, ec) → []
new_esEs4(Left(vuu3000), Left(vuu31000), app(app(ty_Either, cb), cc), bd) → new_esEs4(vuu3000, vuu31000, cb, cc)
new_esEs4(Right(vuu3000), Right(vuu31000), cf, ty_Float) → new_esEs16(vuu3000, vuu31000)
new_esEs4(Right(vuu3000), Right(vuu31000), cf, ty_Ordering) → new_esEs11(vuu3000, vuu31000)
new_groupByZs0(Right(vuu300), :(Left(vuu3100), vuu311), ba, bb) → :(Left(vuu3100), vuu311)
new_esEs9(:(vuu3000, vuu3001), :(vuu31000, vuu31001), eh) → new_asAs(new_esEs25(vuu3000, vuu31000, eh), new_esEs9(vuu3001, vuu31001, eh))
new_esEs21(vuu3000, vuu31000, ty_@0) → new_esEs15(vuu3000, vuu31000)
new_esEs18(vuu3000, vuu31000, app(ty_Ratio, ha)) → new_esEs7(vuu3000, vuu31000, ha)
new_esEs4(Right(vuu3000), Right(vuu31000), cf, ty_Int) → new_esEs6(vuu3000, vuu31000)
new_esEs4(Left(vuu3000), Left(vuu31000), app(app(app(ty_@3, bg), bh), ca), bd) → new_esEs13(vuu3000, vuu31000, bg, bh, ca)
new_esEs19(vuu3001, vuu31001, app(app(ty_@2, bbc), bbd)) → new_esEs17(vuu3001, vuu31001, bbc, bbd)
new_span2Zs11(vuu27, vuu290, vuu291, True, ef, eg) → new_span2Zs12(vuu27, vuu290, vuu291, new_span2Ys3(vuu27, vuu291, ef, eg), new_span2Zs3(vuu27, vuu291, ef, eg), ef, eg)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs25(vuu3000, vuu31000, app(ty_Ratio, fa)) → new_esEs7(vuu3000, vuu31000, fa)
new_esEs26(vuu300, vuu3100, ty_Char) → new_esEs10(vuu300, vuu3100)
new_esEs8(Just(vuu3000), Just(vuu31000), app(app(ty_Either, bhg), bhh)) → new_esEs4(vuu3000, vuu31000, bhg, bhh)
new_esEs19(vuu3001, vuu31001, ty_Bool) → new_esEs14(vuu3001, vuu31001)
new_span2Zs14(vuu36, vuu380, vuu381, vuu64, vuu63, eb, ec) → vuu63
new_esEs14(False, False) → True
new_esEs19(vuu3001, vuu31001, ty_Integer) → new_esEs12(vuu3001, vuu31001)
new_esEs4(Left(vuu3000), Left(vuu31000), ty_Double, bd) → new_esEs5(vuu3000, vuu31000)
new_primEqInt(Neg(Succ(vuu30000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(vuu310000))) → False
new_primPlusNat1(Zero, vuu3100100) → Succ(vuu3100100)
new_esEs20(vuu3002, vuu31002, app(app(app(ty_@3, bbh), bca), bcb)) → new_esEs13(vuu3002, vuu31002, bbh, bca, bcb)
new_esEs18(vuu3000, vuu31000, ty_Bool) → new_esEs14(vuu3000, vuu31000)
new_esEs21(vuu3000, vuu31000, app(app(ty_Either, bdg), bdh)) → new_esEs4(vuu3000, vuu31000, bdg, bdh)
new_primPlusNat0(Succ(vuu6500), Succ(vuu31001000)) → Succ(Succ(new_primPlusNat0(vuu6500, vuu31001000)))
new_esEs22(vuu3001, vuu31001, ty_Double) → new_esEs5(vuu3001, vuu31001)
new_esEs4(Right(vuu3000), Right(vuu31000), cf, app(ty_Maybe, da)) → new_esEs8(vuu3000, vuu31000, da)
new_span2Zs13(vuu36, vuu380, vuu381, False, eb, ec) → :(vuu380, vuu381)
new_esEs19(vuu3001, vuu31001, app(ty_Maybe, bad)) → new_esEs8(vuu3001, vuu31001, bad)
new_esEs26(vuu300, vuu3100, app(app(ty_Either, cf), bd)) → new_esEs4(vuu300, vuu3100, cf, bd)
new_esEs8(Just(vuu3000), Just(vuu31000), ty_Int) → new_esEs6(vuu3000, vuu31000)
new_asAs(True, vuu52) → vuu52
new_esEs20(vuu3002, vuu31002, ty_Double) → new_esEs5(vuu3002, vuu31002)
new_esEs8(Just(vuu3000), Just(vuu31000), app(ty_[], bhc)) → new_esEs9(vuu3000, vuu31000, bhc)
new_esEs19(vuu3001, vuu31001, app(app(ty_Either, bba), bbb)) → new_esEs4(vuu3001, vuu31001, bba, bbb)
new_groupByZs00(vuu36, vuu37, vuu38, False, eb, ec) → :(Right(vuu37), vuu38)
new_esEs8(Just(vuu3000), Just(vuu31000), ty_Double) → new_esEs5(vuu3000, vuu31000)
new_esEs27(vuu300, vuu3100, ty_Float) → new_esEs16(vuu300, vuu3100)
new_esEs4(Left(vuu3000), Right(vuu31000), cf, bd) → False
new_esEs4(Right(vuu3000), Left(vuu31000), cf, bd) → False
new_esEs13(@3(vuu3000, vuu3001, vuu3002), @3(vuu31000, vuu31001, vuu31002), gf, gg, gh) → new_asAs(new_esEs18(vuu3000, vuu31000, gf), new_asAs(new_esEs19(vuu3001, vuu31001, gg), new_esEs20(vuu3002, vuu31002, gh)))
new_esEs11(LT, LT) → True
new_esEs22(vuu3001, vuu31001, app(app(ty_@2, bfc), bfd)) → new_esEs17(vuu3001, vuu31001, bfc, bfd)
new_esEs8(Just(vuu3000), Just(vuu31000), app(ty_Maybe, bhb)) → new_esEs8(vuu3000, vuu31000, bhb)
new_primEqInt(Pos(Succ(vuu30000)), Pos(Succ(vuu310000))) → new_primEqNat0(vuu30000, vuu310000)
new_groupByZs0(Right(vuu300), :(Right(vuu3100), vuu311), ba, bb) → new_groupByZs00(vuu300, vuu3100, vuu311, new_esEs27(vuu300, vuu3100, bb), ba, bb)
new_esEs18(vuu3000, vuu31000, ty_@0) → new_esEs15(vuu3000, vuu31000)
new_esEs4(Left(vuu3000), Left(vuu31000), ty_@0, bd) → new_esEs15(vuu3000, vuu31000)
new_span2Ys11(vuu18, vuu200, vuu201, False, ed, ee) → []
new_esEs8(Just(vuu3000), Just(vuu31000), app(app(app(ty_@3, bhd), bhe), bhf)) → new_esEs13(vuu3000, vuu31000, bhd, bhe, bhf)
new_esEs19(vuu3001, vuu31001, ty_Char) → new_esEs10(vuu3001, vuu31001)
new_esEs20(vuu3002, vuu31002, app(ty_Maybe, bbf)) → new_esEs8(vuu3002, vuu31002, bbf)
new_esEs14(False, True) → False
new_esEs14(True, False) → False
new_esEs8(Just(vuu3000), Just(vuu31000), ty_Integer) → new_esEs12(vuu3000, vuu31000)
new_esEs21(vuu3000, vuu31000, ty_Integer) → new_esEs12(vuu3000, vuu31000)
new_esEs25(vuu3000, vuu31000, ty_Char) → new_esEs10(vuu3000, vuu31000)
new_primEqNat0(Succ(vuu30000), Succ(vuu310000)) → new_primEqNat0(vuu30000, vuu310000)
new_esEs11(GT, EQ) → False
new_esEs11(EQ, GT) → False
new_esEs8(Just(vuu3000), Just(vuu31000), app(ty_Ratio, bha)) → new_esEs7(vuu3000, vuu31000, bha)
new_esEs4(Right(vuu3000), Right(vuu31000), cf, ty_Char) → new_esEs10(vuu3000, vuu31000)
new_esEs26(vuu300, vuu3100, app(app(ty_@2, bcg), bch)) → new_esEs17(vuu300, vuu3100, bcg, bch)
new_esEs22(vuu3001, vuu31001, ty_Int) → new_esEs6(vuu3001, vuu31001)
new_esEs22(vuu3001, vuu31001, ty_Bool) → new_esEs14(vuu3001, vuu31001)
new_esEs21(vuu3000, vuu31000, ty_Float) → new_esEs16(vuu3000, vuu31000)
new_esEs21(vuu3000, vuu31000, app(ty_Ratio, bda)) → new_esEs7(vuu3000, vuu31000, bda)
new_esEs25(vuu3000, vuu31000, app(ty_Maybe, fb)) → new_esEs8(vuu3000, vuu31000, fb)
new_esEs27(vuu300, vuu3100, ty_Int) → new_esEs6(vuu300, vuu3100)
new_esEs21(vuu3000, vuu31000, app(ty_[], bdc)) → new_esEs9(vuu3000, vuu31000, bdc)
new_esEs20(vuu3002, vuu31002, app(ty_[], bbg)) → new_esEs9(vuu3002, vuu31002, bbg)
new_primEqInt(Pos(Zero), Pos(Succ(vuu310000))) → False
new_primEqInt(Pos(Succ(vuu30000)), Pos(Zero)) → False
new_esEs22(vuu3001, vuu31001, ty_Ordering) → new_esEs11(vuu3001, vuu31001)
new_groupByZs01(vuu27, vuu28, vuu29, True, ef, eg) → new_span2Zs3(vuu27, vuu29, ef, eg)
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primPlusNat0(Zero, Succ(vuu31001000)) → Succ(vuu31001000)
new_primPlusNat0(Succ(vuu6500), Zero) → Succ(vuu6500)
new_esEs18(vuu3000, vuu31000, ty_Float) → new_esEs16(vuu3000, vuu31000)
new_span2Ys12(vuu18, vuu200, vuu201, vuu60, vuu59, ed, ee) → :(vuu200, vuu60)

The set Q consists of the following terms:

new_groupByZs0(Right(x0), :(Left(x1), x2), x3, x4)
new_esEs4(Right(x0), Right(x1), x2, ty_Float)
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_esEs18(x0, x1, ty_Integer)
new_primMulNat0(Succ(x0), Zero)
new_esEs22(x0, x1, ty_Ordering)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_esEs25(x0, x1, ty_@0)
new_primEqNat0(Zero, Succ(x0))
new_asAs(False, x0)
new_esEs26(x0, x1, ty_Integer)
new_esEs27(x0, x1, ty_Bool)
new_esEs4(Right(x0), Right(x1), x2, app(ty_[], x3))
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_esEs22(x0, x1, ty_Bool)
new_esEs18(x0, x1, ty_Double)
new_esEs26(x0, x1, ty_Int)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_esEs16(Float(x0, x1), Float(x2, x3))
new_esEs27(x0, x1, ty_Char)
new_esEs25(x0, x1, ty_Ordering)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_groupByZs00(x0, x1, x2, True, x3, x4)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs22(x0, x1, ty_Integer)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_esEs19(x0, x1, app(ty_[], x2))
new_esEs11(LT, EQ)
new_esEs11(EQ, LT)
new_esEs22(x0, x1, ty_@0)
new_esEs20(x0, x1, ty_@0)
new_esEs4(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_esEs27(x0, x1, app(ty_[], x2))
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_span2Ys14(x0, x1, x2, x3, x4, x5, x6)
new_esEs17(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs18(x0, x1, ty_Bool)
new_span2Zs11(x0, x1, x2, True, x3, x4)
new_primEqInt(Neg(Zero), Neg(Zero))
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_groupByZs0(Left(x0), :(Left(x1), x2), x3, x4)
new_esEs4(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs4(Left(x0), Right(x1), x2, x3)
new_esEs4(Right(x0), Left(x1), x2, x3)
new_esEs4(Left(x0), Left(x1), ty_Integer, x2)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(:%(x0, x1), :%(x2, x3), x4)
new_esEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs22(x0, x1, ty_Int)
new_groupByZs0(Left(x0), :(Right(x1), x2), x3, x4)
new_esEs8(Just(x0), Just(x1), ty_Double)
new_esEs4(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs14(False, True)
new_esEs14(True, False)
new_span2Ys3(x0, [], x1, x2)
new_esEs8(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_groupByZs00(x0, x1, x2, False, x3, x4)
new_esEs19(x0, x1, ty_Int)
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_esEs10(Char(x0), Char(x1))
new_sr(Neg(x0), Neg(x1))
new_esEs25(x0, x1, ty_Integer)
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_span2Zs11(x0, x1, x2, False, x3, x4)
new_esEs25(x0, x1, ty_Float)
new_esEs9([], [], x0)
new_span2Ys11(x0, x1, x2, True, x3, x4)
new_groupByZs01(x0, x1, x2, False, x3, x4)
new_esEs8(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs4(Right(x0), Right(x1), x2, ty_Double)
new_esEs8(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_span2Ys13(x0, x1, x2, True, x3, x4)
new_esEs4(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs21(x0, x1, ty_Bool)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_esEs4(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs8(Just(x0), Just(x1), app(ty_[], x2))
new_esEs21(x0, x1, ty_Float)
new_esEs4(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs8(Just(x0), Just(x1), ty_Float)
new_span2Zs3(x0, [], x1, x2)
new_esEs19(x0, x1, ty_Ordering)
new_span2Zs14(x0, x1, x2, x3, x4, x5, x6)
new_esEs4(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs26(x0, x1, ty_Double)
new_esEs19(x0, x1, app(ty_Maybe, x2))
new_esEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs19(x0, x1, app(ty_Ratio, x2))
new_esEs8(Just(x0), Just(x1), ty_Char)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs25(x0, x1, ty_Double)
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_esEs21(x0, x1, app(ty_[], x2))
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_esEs21(x0, x1, ty_Int)
new_esEs27(x0, x1, ty_@0)
new_esEs26(x0, x1, ty_Bool)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, ty_Ordering)
new_esEs11(GT, EQ)
new_esEs11(EQ, GT)
new_esEs4(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs24(x0, x1, ty_Integer)
new_span2Ys2(x0, :(x1, x2), x3, x4)
new_esEs4(Right(x0), Right(x1), x2, ty_@0)
new_esEs19(x0, x1, ty_Float)
new_esEs14(True, True)
new_esEs18(x0, x1, ty_Float)
new_groupByZs01(x0, x1, x2, True, x3, x4)
new_esEs21(x0, x1, ty_Integer)
new_esEs8(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_esEs4(Left(x0), Left(x1), ty_Ordering, x2)
new_span2Ys12(x0, x1, x2, x3, x4, x5, x6)
new_esEs8(Just(x0), Just(x1), ty_@0)
new_esEs8(Nothing, Nothing, x0)
new_primEqNat0(Zero, Zero)
new_esEs15(@0, @0)
new_esEs5(Double(x0, x1), Double(x2, x3))
new_esEs27(x0, x1, ty_Ordering)
new_esEs4(Left(x0), Left(x1), ty_Double, x2)
new_esEs8(Just(x0), Just(x1), ty_Int)
new_esEs18(x0, x1, app(ty_[], x2))
new_sr(Pos(x0), Pos(x1))
new_esEs27(x0, x1, ty_Double)
new_esEs22(x0, x1, ty_Char)
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs13(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_esEs4(Right(x0), Right(x1), x2, ty_Bool)
new_esEs21(x0, x1, ty_Char)
new_primPlusNat0(Succ(x0), Succ(x1))
new_esEs4(Right(x0), Right(x1), x2, ty_Integer)
new_primMulNat0(Zero, Zero)
new_sr(Neg(x0), Pos(x1))
new_sr(Pos(x0), Neg(x1))
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_span2Zs12(x0, x1, x2, x3, x4, x5, x6)
new_esEs4(Left(x0), Left(x1), ty_Char, x2)
new_esEs19(x0, x1, ty_Bool)
new_esEs11(GT, GT)
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_esEs25(x0, x1, app(ty_[], x2))
new_esEs20(x0, x1, ty_Bool)
new_esEs9(:(x0, x1), [], x2)
new_esEs4(Left(x0), Left(x1), ty_@0, x2)
new_span2Zs2(x0, [], x1, x2)
new_esEs22(x0, x1, ty_Double)
new_esEs4(Left(x0), Left(x1), ty_Int, x2)
new_esEs27(x0, x1, ty_Float)
new_esEs23(x0, x1, ty_Integer)
new_esEs22(x0, x1, app(ty_[], x2))
new_primMulNat0(Zero, Succ(x0))
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_span2Zs3(x0, :(x1, x2), x3, x4)
new_esEs11(LT, GT)
new_esEs11(GT, LT)
new_span2Ys3(x0, :(x1, x2), x3, x4)
new_primEqNat0(Succ(x0), Zero)
new_esEs19(x0, x1, ty_@0)
new_span2Ys2(x0, [], x1, x2)
new_esEs27(x0, x1, ty_Integer)
new_esEs26(x0, x1, ty_Float)
new_esEs26(x0, x1, ty_Ordering)
new_esEs20(x0, x1, ty_Char)
new_esEs20(x0, x1, ty_Integer)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs8(Nothing, Just(x0), x1)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs20(x0, x1, ty_Double)
new_esEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs19(x0, x1, ty_Double)
new_esEs20(x0, x1, ty_Float)
new_esEs26(x0, x1, ty_@0)
new_span2Ys13(x0, x1, x2, False, x3, x4)
new_esEs4(Left(x0), Left(x1), ty_Float, x2)
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs20(x0, x1, ty_Ordering)
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(x0, x1)
new_esEs4(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_span2Zs2(x0, :(x1, x2), x3, x4)
new_esEs18(x0, x1, app(app(ty_@2, x2), x3))
new_esEs20(x0, x1, app(ty_[], x2))
new_esEs12(Integer(x0), Integer(x1))
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_esEs4(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_primPlusNat1(Succ(x0), x1)
new_esEs20(x0, x1, ty_Int)
new_esEs4(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs18(x0, x1, ty_@0)
new_esEs4(Left(x0), Left(x1), ty_Bool, x2)
new_primMulNat0(Succ(x0), Succ(x1))
new_esEs21(x0, x1, ty_@0)
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs19(x0, x1, ty_Char)
new_primPlusNat0(Zero, Succ(x0))
new_esEs26(x0, x1, app(ty_[], x2))
new_esEs11(LT, LT)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_esEs8(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs8(Just(x0), Just(x1), ty_Ordering)
new_asAs(True, x0)
new_esEs8(Just(x0), Nothing, x1)
new_groupByZs0(Right(x0), :(Right(x1), x2), x3, x4)
new_primPlusNat0(Zero, Zero)
new_esEs27(x0, x1, ty_Int)
new_esEs25(x0, x1, ty_Char)
new_esEs9([], :(x0, x1), x2)
new_esEs4(Right(x0), Right(x1), x2, ty_Char)
new_esEs24(x0, x1, ty_Int)
new_esEs8(Just(x0), Just(x1), ty_Bool)
new_esEs4(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs18(x0, x1, ty_Int)
new_esEs25(x0, x1, ty_Bool)
new_esEs14(False, False)
new_esEs23(x0, x1, ty_Int)
new_primEqInt(Pos(Zero), Pos(Zero))
new_esEs26(x0, x1, ty_Char)
new_esEs11(EQ, EQ)
new_esEs18(x0, x1, ty_Char)
new_esEs18(x0, x1, app(app(ty_Either, x2), x3))
new_span2Zs13(x0, x1, x2, True, x3, x4)
new_primPlusNat0(Succ(x0), Zero)
new_esEs21(x0, x1, ty_Double)
new_esEs4(Right(x0), Right(x1), x2, ty_Int)
new_esEs8(Just(x0), Just(x1), ty_Integer)
new_esEs25(x0, x1, ty_Int)
new_esEs18(x0, x1, ty_Ordering)
new_esEs19(x0, x1, ty_Integer)
new_esEs18(x0, x1, app(ty_Maybe, x2))
new_span2Zs13(x0, x1, x2, False, x3, x4)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_groupByZs0(x0, [], x1, x2)
new_span2Ys11(x0, x1, x2, False, x3, x4)
new_esEs9(:(x0, x1), :(x2, x3), x4)
new_esEs18(x0, x1, app(ty_Ratio, x2))
new_primPlusNat1(Zero, x0)
new_esEs22(x0, x1, ty_Float)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))

We have to consider all minimal (P,Q,R)-chains.
We use the reduction pair processor [15].


The following pairs can be oriented strictly and are deleted.


new_groupBy(:(vuu30, vuu31), ba, bb) → new_groupBy(new_groupByZs0(vuu30, vuu31, ba, bb), ba, bb)
The remaining pairs can at least be oriented weakly.
none
Used ordering: Polynomial interpretation [25]:

POL(:(x1, x2)) = 1 + x2   
POL(:%(x1, x2)) = 0   
POL(@0) = 0   
POL(@2(x1, x2)) = 0   
POL(@3(x1, x2, x3)) = 0   
POL(Char(x1)) = 0   
POL(Double(x1, x2)) = 0   
POL(EQ) = 0   
POL(False) = 0   
POL(Float(x1, x2)) = 0   
POL(GT) = 0   
POL(Integer(x1)) = 0   
POL(Just(x1)) = 0   
POL(LT) = 0   
POL(Left(x1)) = 0   
POL(Neg(x1)) = 0   
POL(Nothing) = 0   
POL(Pos(x1)) = 0   
POL(Right(x1)) = 0   
POL(Succ(x1)) = 0   
POL(True) = 0   
POL(Zero) = 0   
POL([]) = 0   
POL(app(x1, x2)) = x2   
POL(new_asAs(x1, x2)) = 0   
POL(new_esEs10(x1, x2)) = 0   
POL(new_esEs11(x1, x2)) = 0   
POL(new_esEs12(x1, x2)) = 1   
POL(new_esEs13(x1, x2, x3, x4, x5)) = 0   
POL(new_esEs14(x1, x2)) = 1   
POL(new_esEs15(x1, x2)) = 1   
POL(new_esEs16(x1, x2)) = 0   
POL(new_esEs17(x1, x2, x3, x4)) = 0   
POL(new_esEs18(x1, x2, x3)) = 0   
POL(new_esEs19(x1, x2, x3)) = 1 + x1 + x3   
POL(new_esEs20(x1, x2, x3)) = 1 + x2 + x3   
POL(new_esEs21(x1, x2, x3)) = 0   
POL(new_esEs22(x1, x2, x3)) = x1 + x3   
POL(new_esEs23(x1, x2, x3)) = 0   
POL(new_esEs24(x1, x2, x3)) = 1 + x1 + x2 + x3   
POL(new_esEs25(x1, x2, x3)) = 0   
POL(new_esEs26(x1, x2, x3)) = 0   
POL(new_esEs27(x1, x2, x3)) = 0   
POL(new_esEs4(x1, x2, x3, x4)) = 0   
POL(new_esEs5(x1, x2)) = 1   
POL(new_esEs6(x1, x2)) = 0   
POL(new_esEs7(x1, x2, x3)) = 0   
POL(new_esEs8(x1, x2, x3)) = 0   
POL(new_esEs9(x1, x2, x3)) = 0   
POL(new_groupBy(x1, x2, x3)) = x1   
POL(new_groupByZs0(x1, x2, x3, x4)) = x2   
POL(new_groupByZs00(x1, x2, x3, x4, x5, x6)) = 1 + x3   
POL(new_groupByZs01(x1, x2, x3, x4, x5, x6)) = 1 + x3   
POL(new_primEqInt(x1, x2)) = 0   
POL(new_primEqNat0(x1, x2)) = 0   
POL(new_primMulNat0(x1, x2)) = 0   
POL(new_primPlusNat0(x1, x2)) = 0   
POL(new_primPlusNat1(x1, x2)) = 0   
POL(new_span2Ys11(x1, x2, x3, x4, x5, x6)) = 1 + x3   
POL(new_span2Ys12(x1, x2, x3, x4, x5, x6, x7)) = 1 + x4   
POL(new_span2Ys13(x1, x2, x3, x4, x5, x6)) = 1 + x3 + x5   
POL(new_span2Ys14(x1, x2, x3, x4, x5, x6, x7)) = 1 + x4   
POL(new_span2Ys2(x1, x2, x3, x4)) = x2   
POL(new_span2Ys3(x1, x2, x3, x4)) = x2 + x3   
POL(new_span2Zs11(x1, x2, x3, x4, x5, x6)) = 1 + x3   
POL(new_span2Zs12(x1, x2, x3, x4, x5, x6, x7)) = x5   
POL(new_span2Zs13(x1, x2, x3, x4, x5, x6)) = 1 + x3   
POL(new_span2Zs14(x1, x2, x3, x4, x5, x6, x7)) = x5   
POL(new_span2Zs2(x1, x2, x3, x4)) = x2   
POL(new_span2Zs3(x1, x2, x3, x4)) = x2   
POL(new_sr(x1, x2)) = 0   
POL(ty_@0) = 1   
POL(ty_@2) = 0   
POL(ty_@3) = 0   
POL(ty_Bool) = 1   
POL(ty_Char) = 1   
POL(ty_Double) = 1   
POL(ty_Either) = 0   
POL(ty_Float) = 1   
POL(ty_Int) = 0   
POL(ty_Integer) = 1   
POL(ty_Maybe) = 0   
POL(ty_Ordering) = 1   
POL(ty_Ratio) = 0   
POL(ty_[]) = 0   

The following usable rules [17] were oriented:

new_groupByZs01(vuu27, vuu28, vuu29, False, ef, eg) → :(Left(vuu28), vuu29)
new_groupByZs0(Left(vuu300), :(Left(vuu3100), vuu311), ba, bb) → new_groupByZs01(vuu300, vuu3100, vuu311, new_esEs26(vuu300, vuu3100, ba), ba, bb)
new_span2Zs3(vuu27, [], ef, eg) → []
new_span2Ys13(vuu9, vuu110, vuu111, False, gd, ge) → []
new_span2Ys2(vuu18, [], ed, ee) → []
new_groupByZs01(vuu27, vuu28, vuu29, True, ef, eg) → new_span2Zs3(vuu27, vuu29, ef, eg)
new_span2Zs14(vuu36, vuu380, vuu381, vuu64, vuu63, eb, ec) → vuu63
new_span2Ys3(vuu9, [], gd, ge) → []
new_span2Ys11(vuu18, vuu200, vuu201, True, ed, ee) → new_span2Ys12(vuu18, vuu200, vuu201, new_span2Ys2(vuu18, vuu201, ed, ee), new_span2Zs2(vuu18, vuu201, ed, ee), ed, ee)
new_groupByZs0(Right(vuu300), :(Right(vuu3100), vuu311), ba, bb) → new_groupByZs00(vuu300, vuu3100, vuu311, new_esEs27(vuu300, vuu3100, bb), ba, bb)
new_span2Zs13(vuu36, vuu380, vuu381, True, eb, ec) → new_span2Zs14(vuu36, vuu380, vuu381, new_span2Ys2(vuu36, vuu381, eb, ec), new_span2Zs2(vuu36, vuu381, eb, ec), eb, ec)
new_span2Zs12(vuu27, vuu290, vuu291, vuu62, vuu61, ef, eg) → vuu61
new_groupByZs00(vuu36, vuu37, vuu38, True, eb, ec) → new_span2Zs2(vuu36, vuu38, eb, ec)
new_groupByZs00(vuu36, vuu37, vuu38, False, eb, ec) → :(Right(vuu37), vuu38)
new_span2Zs11(vuu27, vuu290, vuu291, False, ef, eg) → :(vuu290, vuu291)
new_groupByZs0(Left(vuu300), :(Right(vuu3100), vuu311), ba, bb) → :(Right(vuu3100), vuu311)
new_span2Zs11(vuu27, vuu290, vuu291, True, ef, eg) → new_span2Zs12(vuu27, vuu290, vuu291, new_span2Ys3(vuu27, vuu291, ef, eg), new_span2Zs3(vuu27, vuu291, ef, eg), ef, eg)
new_span2Zs13(vuu36, vuu380, vuu381, False, eb, ec) → :(vuu380, vuu381)
new_span2Zs2(vuu36, :(vuu380, vuu381), eb, ec) → new_span2Zs13(vuu36, vuu380, vuu381, new_esEs4(Right(vuu36), vuu380, eb, ec), eb, ec)
new_span2Ys3(vuu9, :(vuu110, vuu111), gd, ge) → new_span2Ys13(vuu9, vuu110, vuu111, new_esEs4(Left(vuu9), vuu110, gd, ge), gd, ge)
new_span2Ys13(vuu9, vuu110, vuu111, True, gd, ge) → new_span2Ys14(vuu9, vuu110, vuu111, new_span2Ys3(vuu9, vuu111, gd, ge), new_span2Zs3(vuu9, vuu111, gd, ge), gd, ge)
new_span2Ys2(vuu18, :(vuu200, vuu201), ed, ee) → new_span2Ys11(vuu18, vuu200, vuu201, new_esEs4(Right(vuu18), vuu200, ed, ee), ed, ee)
new_groupByZs0(vuu30, [], ba, bb) → []
new_span2Ys14(vuu9, vuu110, vuu111, vuu58, vuu57, gd, ge) → :(vuu110, vuu58)
new_span2Ys11(vuu18, vuu200, vuu201, False, ed, ee) → []
new_groupByZs0(Right(vuu300), :(Left(vuu3100), vuu311), ba, bb) → :(Left(vuu3100), vuu311)
new_span2Ys12(vuu18, vuu200, vuu201, vuu60, vuu59, ed, ee) → :(vuu200, vuu60)
new_span2Zs2(vuu36, [], eb, ec) → []
new_span2Zs3(vuu27, :(vuu290, vuu291), ef, eg) → new_span2Zs11(vuu27, vuu290, vuu291, new_esEs4(Left(vuu27), vuu290, ef, eg), ef, eg)



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ LetRed
                ↳ HASKELL
                  ↳ Narrow
                    ↳ AND
                      ↳ QDP
                      ↳ QDP
                      ↳ QDP
                      ↳ QDP
                      ↳ QDP
                      ↳ QDP
                      ↳ QDP
                        ↳ QDPOrderProof
                          ↳ QDP
                            ↳ PisEmptyProof

Q DP problem:
P is empty.
The TRS R consists of the following rules:

new_esEs26(vuu300, vuu3100, ty_@0) → new_esEs15(vuu300, vuu3100)
new_esEs4(Left(vuu3000), Left(vuu31000), ty_Ordering, bd) → new_esEs11(vuu3000, vuu31000)
new_esEs4(Left(vuu3000), Left(vuu31000), app(ty_[], bf), bd) → new_esEs9(vuu3000, vuu31000, bf)
new_esEs20(vuu3002, vuu31002, app(ty_Ratio, bbe)) → new_esEs7(vuu3002, vuu31002, bbe)
new_esEs25(vuu3000, vuu31000, ty_Integer) → new_esEs12(vuu3000, vuu31000)
new_esEs19(vuu3001, vuu31001, app(ty_Ratio, bac)) → new_esEs7(vuu3001, vuu31001, bac)
new_primEqInt(Neg(Succ(vuu30000)), Pos(vuu31000)) → False
new_primEqInt(Pos(Succ(vuu30000)), Neg(vuu31000)) → False
new_esEs27(vuu300, vuu3100, ty_Ordering) → new_esEs11(vuu300, vuu3100)
new_span2Ys2(vuu18, :(vuu200, vuu201), ed, ee) → new_span2Ys11(vuu18, vuu200, vuu201, new_esEs4(Right(vuu18), vuu200, ed, ee), ed, ee)
new_esEs27(vuu300, vuu3100, app(app(ty_@2, bgg), bgh)) → new_esEs17(vuu300, vuu3100, bgg, bgh)
new_esEs4(Left(vuu3000), Left(vuu31000), ty_Bool, bd) → new_esEs14(vuu3000, vuu31000)
new_esEs4(Right(vuu3000), Right(vuu31000), cf, ty_Integer) → new_esEs12(vuu3000, vuu31000)
new_esEs4(Right(vuu3000), Right(vuu31000), cf, ty_Bool) → new_esEs14(vuu3000, vuu31000)
new_esEs9([], [], eh) → True
new_esEs18(vuu3000, vuu31000, app(app(ty_@2, baa), bab)) → new_esEs17(vuu3000, vuu31000, baa, bab)
new_primEqInt(Pos(Zero), Neg(Succ(vuu310000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(vuu310000))) → False
new_esEs10(Char(vuu3000), Char(vuu31000)) → new_primEqNat0(vuu3000, vuu31000)
new_span2Zs3(vuu27, [], ef, eg) → []
new_esEs8(Just(vuu3000), Just(vuu31000), ty_Ordering) → new_esEs11(vuu3000, vuu31000)
new_esEs21(vuu3000, vuu31000, ty_Ordering) → new_esEs11(vuu3000, vuu31000)
new_esEs4(Left(vuu3000), Left(vuu31000), ty_Integer, bd) → new_esEs12(vuu3000, vuu31000)
new_esEs11(EQ, EQ) → True
new_esEs8(Just(vuu3000), Just(vuu31000), ty_Float) → new_esEs16(vuu3000, vuu31000)
new_primMulNat0(Zero, Zero) → Zero
new_esEs27(vuu300, vuu3100, app(ty_Maybe, bfh)) → new_esEs8(vuu300, vuu3100, bfh)
new_esEs26(vuu300, vuu3100, ty_Float) → new_esEs16(vuu300, vuu3100)
new_esEs20(vuu3002, vuu31002, ty_Ordering) → new_esEs11(vuu3002, vuu31002)
new_esEs26(vuu300, vuu3100, app(ty_Ratio, bfe)) → new_esEs7(vuu300, vuu3100, bfe)
new_esEs4(Left(vuu3000), Left(vuu31000), app(app(ty_@2, cd), ce), bd) → new_esEs17(vuu3000, vuu31000, cd, ce)
new_esEs26(vuu300, vuu3100, app(ty_[], eh)) → new_esEs9(vuu300, vuu3100, eh)
new_esEs11(GT, LT) → False
new_esEs11(LT, GT) → False
new_esEs25(vuu3000, vuu31000, ty_Ordering) → new_esEs11(vuu3000, vuu31000)
new_esEs27(vuu300, vuu3100, ty_Integer) → new_esEs12(vuu300, vuu3100)
new_span2Ys13(vuu9, vuu110, vuu111, False, gd, ge) → []
new_esEs21(vuu3000, vuu31000, ty_Int) → new_esEs6(vuu3000, vuu31000)
new_esEs4(Left(vuu3000), Left(vuu31000), ty_Char, bd) → new_esEs10(vuu3000, vuu31000)
new_span2Ys3(vuu9, [], gd, ge) → []
new_esEs26(vuu300, vuu3100, ty_Bool) → new_esEs14(vuu300, vuu3100)
new_esEs21(vuu3000, vuu31000, app(app(ty_@2, bea), beb)) → new_esEs17(vuu3000, vuu31000, bea, beb)
new_esEs25(vuu3000, vuu31000, ty_@0) → new_esEs15(vuu3000, vuu31000)
new_esEs20(vuu3002, vuu31002, ty_Int) → new_esEs6(vuu3002, vuu31002)
new_esEs24(vuu3001, vuu31001, ty_Integer) → new_esEs12(vuu3001, vuu31001)
new_sr(Pos(vuu30010), Neg(vuu310010)) → Neg(new_primMulNat0(vuu30010, vuu310010))
new_sr(Neg(vuu30010), Pos(vuu310010)) → Neg(new_primMulNat0(vuu30010, vuu310010))
new_esEs11(EQ, LT) → False
new_esEs11(LT, EQ) → False
new_esEs20(vuu3002, vuu31002, app(app(ty_Either, bcc), bcd)) → new_esEs4(vuu3002, vuu31002, bcc, bcd)
new_esEs18(vuu3000, vuu31000, app(app(ty_Either, hg), hh)) → new_esEs4(vuu3000, vuu31000, hg, hh)
new_esEs4(Left(vuu3000), Left(vuu31000), ty_Int, bd) → new_esEs6(vuu3000, vuu31000)
new_esEs6(vuu300, vuu3100) → new_primEqInt(vuu300, vuu3100)
new_span2Zs12(vuu27, vuu290, vuu291, vuu62, vuu61, ef, eg) → vuu61
new_esEs27(vuu300, vuu3100, ty_@0) → new_esEs15(vuu300, vuu3100)
new_groupByZs01(vuu27, vuu28, vuu29, False, ef, eg) → :(Left(vuu28), vuu29)
new_esEs20(vuu3002, vuu31002, ty_Char) → new_esEs10(vuu3002, vuu31002)
new_esEs20(vuu3002, vuu31002, app(app(ty_@2, bce), bcf)) → new_esEs17(vuu3002, vuu31002, bce, bcf)
new_esEs8(Just(vuu3000), Just(vuu31000), ty_Char) → new_esEs10(vuu3000, vuu31000)
new_esEs25(vuu3000, vuu31000, ty_Int) → new_esEs6(vuu3000, vuu31000)
new_esEs23(vuu3000, vuu31000, ty_Integer) → new_esEs12(vuu3000, vuu31000)
new_span2Zs11(vuu27, vuu290, vuu291, False, ef, eg) → :(vuu290, vuu291)
new_esEs27(vuu300, vuu3100, app(ty_Ratio, bfg)) → new_esEs7(vuu300, vuu3100, bfg)
new_esEs27(vuu300, vuu3100, ty_Double) → new_esEs5(vuu300, vuu3100)
new_esEs12(Integer(vuu3000), Integer(vuu31000)) → new_primEqInt(vuu3000, vuu31000)
new_esEs21(vuu3000, vuu31000, ty_Char) → new_esEs10(vuu3000, vuu31000)
new_primEqNat0(Succ(vuu30000), Zero) → False
new_primEqNat0(Zero, Succ(vuu310000)) → False
new_span2Ys11(vuu18, vuu200, vuu201, True, ed, ee) → new_span2Ys12(vuu18, vuu200, vuu201, new_span2Ys2(vuu18, vuu201, ed, ee), new_span2Zs2(vuu18, vuu201, ed, ee), ed, ee)
new_esEs19(vuu3001, vuu31001, ty_Double) → new_esEs5(vuu3001, vuu31001)
new_primPlusNat0(Zero, Zero) → Zero
new_esEs4(Right(vuu3000), Right(vuu31000), cf, app(ty_[], db)) → new_esEs9(vuu3000, vuu31000, db)
new_esEs20(vuu3002, vuu31002, ty_Bool) → new_esEs14(vuu3002, vuu31002)
new_esEs20(vuu3002, vuu31002, ty_@0) → new_esEs15(vuu3002, vuu31002)
new_esEs26(vuu300, vuu3100, ty_Ordering) → new_esEs11(vuu300, vuu3100)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_groupByZs0(vuu30, [], ba, bb) → []
new_esEs27(vuu300, vuu3100, app(app(ty_Either, bge), bgf)) → new_esEs4(vuu300, vuu3100, bge, bgf)
new_esEs4(Left(vuu3000), Left(vuu31000), ty_Float, bd) → new_esEs16(vuu3000, vuu31000)
new_esEs25(vuu3000, vuu31000, app(app(ty_Either, fh), ga)) → new_esEs4(vuu3000, vuu31000, fh, ga)
new_esEs17(@2(vuu3000, vuu3001), @2(vuu31000, vuu31001), bcg, bch) → new_asAs(new_esEs21(vuu3000, vuu31000, bcg), new_esEs22(vuu3001, vuu31001, bch))
new_esEs19(vuu3001, vuu31001, ty_@0) → new_esEs15(vuu3001, vuu31001)
new_esEs26(vuu300, vuu3100, app(app(app(ty_@3, gf), gg), gh)) → new_esEs13(vuu300, vuu3100, gf, gg, gh)
new_esEs22(vuu3001, vuu31001, app(app(ty_Either, bfa), bfb)) → new_esEs4(vuu3001, vuu31001, bfa, bfb)
new_esEs21(vuu3000, vuu31000, ty_Double) → new_esEs5(vuu3000, vuu31000)
new_esEs27(vuu300, vuu3100, app(app(app(ty_@3, bgb), bgc), bgd)) → new_esEs13(vuu300, vuu3100, bgb, bgc, bgd)
new_esEs25(vuu3000, vuu31000, ty_Bool) → new_esEs14(vuu3000, vuu31000)
new_esEs25(vuu3000, vuu31000, app(app(ty_@2, gb), gc)) → new_esEs17(vuu3000, vuu31000, gb, gc)
new_primPlusNat1(Succ(vuu650), vuu3100100) → Succ(Succ(new_primPlusNat0(vuu650, vuu3100100)))
new_esEs22(vuu3001, vuu31001, ty_@0) → new_esEs15(vuu3001, vuu31001)
new_esEs19(vuu3001, vuu31001, app(ty_[], bae)) → new_esEs9(vuu3001, vuu31001, bae)
new_esEs23(vuu3000, vuu31000, ty_Int) → new_esEs6(vuu3000, vuu31000)
new_esEs22(vuu3001, vuu31001, ty_Integer) → new_esEs12(vuu3001, vuu31001)
new_esEs4(Left(vuu3000), Left(vuu31000), app(ty_Maybe, be), bd) → new_esEs8(vuu3000, vuu31000, be)
new_esEs8(Just(vuu3000), Just(vuu31000), ty_@0) → new_esEs15(vuu3000, vuu31000)
new_esEs21(vuu3000, vuu31000, app(app(app(ty_@3, bdd), bde), bdf)) → new_esEs13(vuu3000, vuu31000, bdd, bde, bdf)
new_esEs26(vuu300, vuu3100, ty_Double) → new_esEs5(vuu300, vuu3100)
new_esEs19(vuu3001, vuu31001, ty_Float) → new_esEs16(vuu3001, vuu31001)
new_span2Ys13(vuu9, vuu110, vuu111, True, gd, ge) → new_span2Ys14(vuu9, vuu110, vuu111, new_span2Ys3(vuu9, vuu111, gd, ge), new_span2Zs3(vuu9, vuu111, gd, ge), gd, ge)
new_esEs18(vuu3000, vuu31000, app(app(app(ty_@3, hd), he), hf)) → new_esEs13(vuu3000, vuu31000, hd, he, hf)
new_esEs4(Right(vuu3000), Right(vuu31000), cf, ty_Double) → new_esEs5(vuu3000, vuu31000)
new_esEs27(vuu300, vuu3100, app(ty_[], bga)) → new_esEs9(vuu300, vuu3100, bga)
new_esEs25(vuu3000, vuu31000, app(ty_[], fc)) → new_esEs9(vuu3000, vuu31000, fc)
new_esEs21(vuu3000, vuu31000, ty_Bool) → new_esEs14(vuu3000, vuu31000)
new_esEs18(vuu3000, vuu31000, ty_Integer) → new_esEs12(vuu3000, vuu31000)
new_esEs26(vuu300, vuu3100, ty_Int) → new_esEs6(vuu300, vuu3100)
new_groupByZs0(Left(vuu300), :(Left(vuu3100), vuu311), ba, bb) → new_groupByZs01(vuu300, vuu3100, vuu311, new_esEs26(vuu300, vuu3100, ba), ba, bb)
new_span2Zs3(vuu27, :(vuu290, vuu291), ef, eg) → new_span2Zs11(vuu27, vuu290, vuu291, new_esEs4(Left(vuu27), vuu290, ef, eg), ef, eg)
new_esEs8(Nothing, Nothing, bff) → True
new_esEs18(vuu3000, vuu31000, ty_Ordering) → new_esEs11(vuu3000, vuu31000)
new_esEs11(GT, GT) → True
new_esEs22(vuu3001, vuu31001, app(ty_Ratio, bec)) → new_esEs7(vuu3001, vuu31001, bec)
new_sr(Neg(vuu30010), Neg(vuu310010)) → Pos(new_primMulNat0(vuu30010, vuu310010))
new_esEs15(@0, @0) → True
new_esEs18(vuu3000, vuu31000, ty_Int) → new_esEs6(vuu3000, vuu31000)
new_groupByZs0(Left(vuu300), :(Right(vuu3100), vuu311), ba, bb) → :(Right(vuu3100), vuu311)
new_esEs5(Double(vuu3000, vuu3001), Double(vuu31000, vuu31001)) → new_esEs6(new_sr(vuu3000, vuu31000), new_sr(vuu3001, vuu31001))
new_asAs(False, vuu52) → False
new_sr(Pos(vuu30010), Pos(vuu310010)) → Pos(new_primMulNat0(vuu30010, vuu310010))
new_span2Zs2(vuu36, :(vuu380, vuu381), eb, ec) → new_span2Zs13(vuu36, vuu380, vuu381, new_esEs4(Right(vuu36), vuu380, eb, ec), eb, ec)
new_primEqNat0(Zero, Zero) → True
new_esEs24(vuu3001, vuu31001, ty_Int) → new_esEs6(vuu3001, vuu31001)
new_esEs22(vuu3001, vuu31001, app(ty_Maybe, bed)) → new_esEs8(vuu3001, vuu31001, bed)
new_primMulNat0(Zero, Succ(vuu3100100)) → Zero
new_primMulNat0(Succ(vuu300100), Zero) → Zero
new_esEs4(Left(vuu3000), Left(vuu31000), app(ty_Ratio, bc), bd) → new_esEs7(vuu3000, vuu31000, bc)
new_primMulNat0(Succ(vuu300100), Succ(vuu3100100)) → new_primPlusNat1(new_primMulNat0(vuu300100, Succ(vuu3100100)), vuu3100100)
new_esEs8(Just(vuu3000), Just(vuu31000), ty_Bool) → new_esEs14(vuu3000, vuu31000)
new_esEs4(Right(vuu3000), Right(vuu31000), cf, app(app(ty_@2, dh), ea)) → new_esEs17(vuu3000, vuu31000, dh, ea)
new_esEs18(vuu3000, vuu31000, app(ty_[], hc)) → new_esEs9(vuu3000, vuu31000, hc)
new_span2Ys2(vuu18, [], ed, ee) → []
new_esEs20(vuu3002, vuu31002, ty_Float) → new_esEs16(vuu3002, vuu31002)
new_esEs4(Right(vuu3000), Right(vuu31000), cf, app(app(app(ty_@3, dc), dd), de)) → new_esEs13(vuu3000, vuu31000, dc, dd, de)
new_esEs22(vuu3001, vuu31001, app(app(app(ty_@3, bef), beg), beh)) → new_esEs13(vuu3001, vuu31001, bef, beg, beh)
new_span2Zs13(vuu36, vuu380, vuu381, True, eb, ec) → new_span2Zs14(vuu36, vuu380, vuu381, new_span2Ys2(vuu36, vuu381, eb, ec), new_span2Zs2(vuu36, vuu381, eb, ec), eb, ec)
new_esEs22(vuu3001, vuu31001, ty_Char) → new_esEs10(vuu3001, vuu31001)
new_esEs18(vuu3000, vuu31000, ty_Char) → new_esEs10(vuu3000, vuu31000)
new_span2Ys3(vuu9, :(vuu110, vuu111), gd, ge) → new_span2Ys13(vuu9, vuu110, vuu111, new_esEs4(Left(vuu9), vuu110, gd, ge), gd, ge)
new_esEs18(vuu3000, vuu31000, app(ty_Maybe, hb)) → new_esEs8(vuu3000, vuu31000, hb)
new_esEs21(vuu3000, vuu31000, app(ty_Maybe, bdb)) → new_esEs8(vuu3000, vuu31000, bdb)
new_esEs8(Just(vuu3000), Just(vuu31000), app(app(ty_@2, caa), cab)) → new_esEs17(vuu3000, vuu31000, caa, cab)
new_esEs19(vuu3001, vuu31001, ty_Ordering) → new_esEs11(vuu3001, vuu31001)
new_esEs25(vuu3000, vuu31000, ty_Double) → new_esEs5(vuu3000, vuu31000)
new_esEs4(Right(vuu3000), Right(vuu31000), cf, app(ty_Ratio, cg)) → new_esEs7(vuu3000, vuu31000, cg)
new_groupByZs00(vuu36, vuu37, vuu38, True, eb, ec) → new_span2Zs2(vuu36, vuu38, eb, ec)
new_esEs18(vuu3000, vuu31000, ty_Double) → new_esEs5(vuu3000, vuu31000)
new_esEs22(vuu3001, vuu31001, app(ty_[], bee)) → new_esEs9(vuu3001, vuu31001, bee)
new_esEs27(vuu300, vuu3100, ty_Char) → new_esEs10(vuu300, vuu3100)
new_esEs25(vuu3000, vuu31000, ty_Float) → new_esEs16(vuu3000, vuu31000)
new_esEs19(vuu3001, vuu31001, ty_Int) → new_esEs6(vuu3001, vuu31001)
new_esEs14(True, True) → True
new_esEs20(vuu3002, vuu31002, ty_Integer) → new_esEs12(vuu3002, vuu31002)
new_esEs27(vuu300, vuu3100, ty_Bool) → new_esEs14(vuu300, vuu3100)
new_esEs19(vuu3001, vuu31001, app(app(app(ty_@3, baf), bag), bah)) → new_esEs13(vuu3001, vuu31001, baf, bag, bah)
new_esEs16(Float(vuu3000, vuu3001), Float(vuu31000, vuu31001)) → new_esEs6(new_sr(vuu3000, vuu31000), new_sr(vuu3001, vuu31001))
new_span2Ys14(vuu9, vuu110, vuu111, vuu58, vuu57, gd, ge) → :(vuu110, vuu58)
new_esEs25(vuu3000, vuu31000, app(app(app(ty_@3, fd), ff), fg)) → new_esEs13(vuu3000, vuu31000, fd, ff, fg)
new_esEs26(vuu300, vuu3100, ty_Integer) → new_esEs12(vuu300, vuu3100)
new_esEs8(Nothing, Just(vuu31000), bff) → False
new_esEs8(Just(vuu3000), Nothing, bff) → False
new_esEs7(:%(vuu3000, vuu3001), :%(vuu31000, vuu31001), bfe) → new_asAs(new_esEs23(vuu3000, vuu31000, bfe), new_esEs24(vuu3001, vuu31001, bfe))
new_esEs22(vuu3001, vuu31001, ty_Float) → new_esEs16(vuu3001, vuu31001)
new_esEs4(Right(vuu3000), Right(vuu31000), cf, app(app(ty_Either, df), dg)) → new_esEs4(vuu3000, vuu31000, df, dg)
new_primEqInt(Neg(Succ(vuu30000)), Neg(Succ(vuu310000))) → new_primEqNat0(vuu30000, vuu310000)
new_esEs26(vuu300, vuu3100, app(ty_Maybe, bff)) → new_esEs8(vuu300, vuu3100, bff)
new_esEs9(:(vuu3000, vuu3001), [], eh) → False
new_esEs9([], :(vuu31000, vuu31001), eh) → False
new_esEs4(Right(vuu3000), Right(vuu31000), cf, ty_@0) → new_esEs15(vuu3000, vuu31000)
new_span2Zs2(vuu36, [], eb, ec) → []
new_esEs4(Left(vuu3000), Left(vuu31000), app(app(ty_Either, cb), cc), bd) → new_esEs4(vuu3000, vuu31000, cb, cc)
new_esEs4(Right(vuu3000), Right(vuu31000), cf, ty_Float) → new_esEs16(vuu3000, vuu31000)
new_esEs4(Right(vuu3000), Right(vuu31000), cf, ty_Ordering) → new_esEs11(vuu3000, vuu31000)
new_groupByZs0(Right(vuu300), :(Left(vuu3100), vuu311), ba, bb) → :(Left(vuu3100), vuu311)
new_esEs9(:(vuu3000, vuu3001), :(vuu31000, vuu31001), eh) → new_asAs(new_esEs25(vuu3000, vuu31000, eh), new_esEs9(vuu3001, vuu31001, eh))
new_esEs21(vuu3000, vuu31000, ty_@0) → new_esEs15(vuu3000, vuu31000)
new_esEs18(vuu3000, vuu31000, app(ty_Ratio, ha)) → new_esEs7(vuu3000, vuu31000, ha)
new_esEs4(Right(vuu3000), Right(vuu31000), cf, ty_Int) → new_esEs6(vuu3000, vuu31000)
new_esEs4(Left(vuu3000), Left(vuu31000), app(app(app(ty_@3, bg), bh), ca), bd) → new_esEs13(vuu3000, vuu31000, bg, bh, ca)
new_esEs19(vuu3001, vuu31001, app(app(ty_@2, bbc), bbd)) → new_esEs17(vuu3001, vuu31001, bbc, bbd)
new_span2Zs11(vuu27, vuu290, vuu291, True, ef, eg) → new_span2Zs12(vuu27, vuu290, vuu291, new_span2Ys3(vuu27, vuu291, ef, eg), new_span2Zs3(vuu27, vuu291, ef, eg), ef, eg)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs25(vuu3000, vuu31000, app(ty_Ratio, fa)) → new_esEs7(vuu3000, vuu31000, fa)
new_esEs26(vuu300, vuu3100, ty_Char) → new_esEs10(vuu300, vuu3100)
new_esEs8(Just(vuu3000), Just(vuu31000), app(app(ty_Either, bhg), bhh)) → new_esEs4(vuu3000, vuu31000, bhg, bhh)
new_esEs19(vuu3001, vuu31001, ty_Bool) → new_esEs14(vuu3001, vuu31001)
new_span2Zs14(vuu36, vuu380, vuu381, vuu64, vuu63, eb, ec) → vuu63
new_esEs14(False, False) → True
new_esEs19(vuu3001, vuu31001, ty_Integer) → new_esEs12(vuu3001, vuu31001)
new_esEs4(Left(vuu3000), Left(vuu31000), ty_Double, bd) → new_esEs5(vuu3000, vuu31000)
new_primEqInt(Neg(Succ(vuu30000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(vuu310000))) → False
new_primPlusNat1(Zero, vuu3100100) → Succ(vuu3100100)
new_esEs20(vuu3002, vuu31002, app(app(app(ty_@3, bbh), bca), bcb)) → new_esEs13(vuu3002, vuu31002, bbh, bca, bcb)
new_esEs18(vuu3000, vuu31000, ty_Bool) → new_esEs14(vuu3000, vuu31000)
new_esEs21(vuu3000, vuu31000, app(app(ty_Either, bdg), bdh)) → new_esEs4(vuu3000, vuu31000, bdg, bdh)
new_primPlusNat0(Succ(vuu6500), Succ(vuu31001000)) → Succ(Succ(new_primPlusNat0(vuu6500, vuu31001000)))
new_esEs22(vuu3001, vuu31001, ty_Double) → new_esEs5(vuu3001, vuu31001)
new_esEs4(Right(vuu3000), Right(vuu31000), cf, app(ty_Maybe, da)) → new_esEs8(vuu3000, vuu31000, da)
new_span2Zs13(vuu36, vuu380, vuu381, False, eb, ec) → :(vuu380, vuu381)
new_esEs19(vuu3001, vuu31001, app(ty_Maybe, bad)) → new_esEs8(vuu3001, vuu31001, bad)
new_esEs26(vuu300, vuu3100, app(app(ty_Either, cf), bd)) → new_esEs4(vuu300, vuu3100, cf, bd)
new_esEs8(Just(vuu3000), Just(vuu31000), ty_Int) → new_esEs6(vuu3000, vuu31000)
new_asAs(True, vuu52) → vuu52
new_esEs20(vuu3002, vuu31002, ty_Double) → new_esEs5(vuu3002, vuu31002)
new_esEs8(Just(vuu3000), Just(vuu31000), app(ty_[], bhc)) → new_esEs9(vuu3000, vuu31000, bhc)
new_esEs19(vuu3001, vuu31001, app(app(ty_Either, bba), bbb)) → new_esEs4(vuu3001, vuu31001, bba, bbb)
new_groupByZs00(vuu36, vuu37, vuu38, False, eb, ec) → :(Right(vuu37), vuu38)
new_esEs8(Just(vuu3000), Just(vuu31000), ty_Double) → new_esEs5(vuu3000, vuu31000)
new_esEs27(vuu300, vuu3100, ty_Float) → new_esEs16(vuu300, vuu3100)
new_esEs4(Left(vuu3000), Right(vuu31000), cf, bd) → False
new_esEs4(Right(vuu3000), Left(vuu31000), cf, bd) → False
new_esEs13(@3(vuu3000, vuu3001, vuu3002), @3(vuu31000, vuu31001, vuu31002), gf, gg, gh) → new_asAs(new_esEs18(vuu3000, vuu31000, gf), new_asAs(new_esEs19(vuu3001, vuu31001, gg), new_esEs20(vuu3002, vuu31002, gh)))
new_esEs11(LT, LT) → True
new_esEs22(vuu3001, vuu31001, app(app(ty_@2, bfc), bfd)) → new_esEs17(vuu3001, vuu31001, bfc, bfd)
new_esEs8(Just(vuu3000), Just(vuu31000), app(ty_Maybe, bhb)) → new_esEs8(vuu3000, vuu31000, bhb)
new_primEqInt(Pos(Succ(vuu30000)), Pos(Succ(vuu310000))) → new_primEqNat0(vuu30000, vuu310000)
new_groupByZs0(Right(vuu300), :(Right(vuu3100), vuu311), ba, bb) → new_groupByZs00(vuu300, vuu3100, vuu311, new_esEs27(vuu300, vuu3100, bb), ba, bb)
new_esEs18(vuu3000, vuu31000, ty_@0) → new_esEs15(vuu3000, vuu31000)
new_esEs4(Left(vuu3000), Left(vuu31000), ty_@0, bd) → new_esEs15(vuu3000, vuu31000)
new_span2Ys11(vuu18, vuu200, vuu201, False, ed, ee) → []
new_esEs8(Just(vuu3000), Just(vuu31000), app(app(app(ty_@3, bhd), bhe), bhf)) → new_esEs13(vuu3000, vuu31000, bhd, bhe, bhf)
new_esEs19(vuu3001, vuu31001, ty_Char) → new_esEs10(vuu3001, vuu31001)
new_esEs20(vuu3002, vuu31002, app(ty_Maybe, bbf)) → new_esEs8(vuu3002, vuu31002, bbf)
new_esEs14(False, True) → False
new_esEs14(True, False) → False
new_esEs8(Just(vuu3000), Just(vuu31000), ty_Integer) → new_esEs12(vuu3000, vuu31000)
new_esEs21(vuu3000, vuu31000, ty_Integer) → new_esEs12(vuu3000, vuu31000)
new_esEs25(vuu3000, vuu31000, ty_Char) → new_esEs10(vuu3000, vuu31000)
new_primEqNat0(Succ(vuu30000), Succ(vuu310000)) → new_primEqNat0(vuu30000, vuu310000)
new_esEs11(GT, EQ) → False
new_esEs11(EQ, GT) → False
new_esEs8(Just(vuu3000), Just(vuu31000), app(ty_Ratio, bha)) → new_esEs7(vuu3000, vuu31000, bha)
new_esEs4(Right(vuu3000), Right(vuu31000), cf, ty_Char) → new_esEs10(vuu3000, vuu31000)
new_esEs26(vuu300, vuu3100, app(app(ty_@2, bcg), bch)) → new_esEs17(vuu300, vuu3100, bcg, bch)
new_esEs22(vuu3001, vuu31001, ty_Int) → new_esEs6(vuu3001, vuu31001)
new_esEs22(vuu3001, vuu31001, ty_Bool) → new_esEs14(vuu3001, vuu31001)
new_esEs21(vuu3000, vuu31000, ty_Float) → new_esEs16(vuu3000, vuu31000)
new_esEs21(vuu3000, vuu31000, app(ty_Ratio, bda)) → new_esEs7(vuu3000, vuu31000, bda)
new_esEs25(vuu3000, vuu31000, app(ty_Maybe, fb)) → new_esEs8(vuu3000, vuu31000, fb)
new_esEs27(vuu300, vuu3100, ty_Int) → new_esEs6(vuu300, vuu3100)
new_esEs21(vuu3000, vuu31000, app(ty_[], bdc)) → new_esEs9(vuu3000, vuu31000, bdc)
new_esEs20(vuu3002, vuu31002, app(ty_[], bbg)) → new_esEs9(vuu3002, vuu31002, bbg)
new_primEqInt(Pos(Zero), Pos(Succ(vuu310000))) → False
new_primEqInt(Pos(Succ(vuu30000)), Pos(Zero)) → False
new_esEs22(vuu3001, vuu31001, ty_Ordering) → new_esEs11(vuu3001, vuu31001)
new_groupByZs01(vuu27, vuu28, vuu29, True, ef, eg) → new_span2Zs3(vuu27, vuu29, ef, eg)
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primPlusNat0(Zero, Succ(vuu31001000)) → Succ(vuu31001000)
new_primPlusNat0(Succ(vuu6500), Zero) → Succ(vuu6500)
new_esEs18(vuu3000, vuu31000, ty_Float) → new_esEs16(vuu3000, vuu31000)
new_span2Ys12(vuu18, vuu200, vuu201, vuu60, vuu59, ed, ee) → :(vuu200, vuu60)

The set Q consists of the following terms:

new_groupByZs0(Right(x0), :(Left(x1), x2), x3, x4)
new_esEs4(Right(x0), Right(x1), x2, ty_Float)
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_esEs18(x0, x1, ty_Integer)
new_primMulNat0(Succ(x0), Zero)
new_esEs22(x0, x1, ty_Ordering)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_esEs25(x0, x1, ty_@0)
new_primEqNat0(Zero, Succ(x0))
new_asAs(False, x0)
new_esEs26(x0, x1, ty_Integer)
new_esEs27(x0, x1, ty_Bool)
new_esEs4(Right(x0), Right(x1), x2, app(ty_[], x3))
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_esEs22(x0, x1, ty_Bool)
new_esEs18(x0, x1, ty_Double)
new_esEs26(x0, x1, ty_Int)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_esEs16(Float(x0, x1), Float(x2, x3))
new_esEs27(x0, x1, ty_Char)
new_esEs25(x0, x1, ty_Ordering)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_groupByZs00(x0, x1, x2, True, x3, x4)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs22(x0, x1, ty_Integer)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_esEs19(x0, x1, app(ty_[], x2))
new_esEs11(LT, EQ)
new_esEs11(EQ, LT)
new_esEs22(x0, x1, ty_@0)
new_esEs20(x0, x1, ty_@0)
new_esEs4(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_esEs27(x0, x1, app(ty_[], x2))
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_span2Ys14(x0, x1, x2, x3, x4, x5, x6)
new_esEs17(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs18(x0, x1, ty_Bool)
new_span2Zs11(x0, x1, x2, True, x3, x4)
new_primEqInt(Neg(Zero), Neg(Zero))
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_groupByZs0(Left(x0), :(Left(x1), x2), x3, x4)
new_esEs4(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs4(Left(x0), Right(x1), x2, x3)
new_esEs4(Right(x0), Left(x1), x2, x3)
new_esEs4(Left(x0), Left(x1), ty_Integer, x2)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(:%(x0, x1), :%(x2, x3), x4)
new_esEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs22(x0, x1, ty_Int)
new_groupByZs0(Left(x0), :(Right(x1), x2), x3, x4)
new_esEs8(Just(x0), Just(x1), ty_Double)
new_esEs4(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs14(False, True)
new_esEs14(True, False)
new_span2Ys3(x0, [], x1, x2)
new_esEs8(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_groupByZs00(x0, x1, x2, False, x3, x4)
new_esEs19(x0, x1, ty_Int)
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_esEs10(Char(x0), Char(x1))
new_sr(Neg(x0), Neg(x1))
new_esEs25(x0, x1, ty_Integer)
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_span2Zs11(x0, x1, x2, False, x3, x4)
new_esEs25(x0, x1, ty_Float)
new_esEs9([], [], x0)
new_span2Ys11(x0, x1, x2, True, x3, x4)
new_groupByZs01(x0, x1, x2, False, x3, x4)
new_esEs8(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs4(Right(x0), Right(x1), x2, ty_Double)
new_esEs8(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_span2Ys13(x0, x1, x2, True, x3, x4)
new_esEs4(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs21(x0, x1, ty_Bool)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_esEs4(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs8(Just(x0), Just(x1), app(ty_[], x2))
new_esEs21(x0, x1, ty_Float)
new_esEs4(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs8(Just(x0), Just(x1), ty_Float)
new_span2Zs3(x0, [], x1, x2)
new_esEs19(x0, x1, ty_Ordering)
new_span2Zs14(x0, x1, x2, x3, x4, x5, x6)
new_esEs4(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs26(x0, x1, ty_Double)
new_esEs19(x0, x1, app(ty_Maybe, x2))
new_esEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs19(x0, x1, app(ty_Ratio, x2))
new_esEs8(Just(x0), Just(x1), ty_Char)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs25(x0, x1, ty_Double)
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_esEs21(x0, x1, app(ty_[], x2))
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_esEs21(x0, x1, ty_Int)
new_esEs27(x0, x1, ty_@0)
new_esEs26(x0, x1, ty_Bool)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, ty_Ordering)
new_esEs11(GT, EQ)
new_esEs11(EQ, GT)
new_esEs4(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs24(x0, x1, ty_Integer)
new_span2Ys2(x0, :(x1, x2), x3, x4)
new_esEs4(Right(x0), Right(x1), x2, ty_@0)
new_esEs19(x0, x1, ty_Float)
new_esEs14(True, True)
new_esEs18(x0, x1, ty_Float)
new_groupByZs01(x0, x1, x2, True, x3, x4)
new_esEs21(x0, x1, ty_Integer)
new_esEs8(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_esEs4(Left(x0), Left(x1), ty_Ordering, x2)
new_span2Ys12(x0, x1, x2, x3, x4, x5, x6)
new_esEs8(Just(x0), Just(x1), ty_@0)
new_esEs8(Nothing, Nothing, x0)
new_primEqNat0(Zero, Zero)
new_esEs15(@0, @0)
new_esEs5(Double(x0, x1), Double(x2, x3))
new_esEs27(x0, x1, ty_Ordering)
new_esEs4(Left(x0), Left(x1), ty_Double, x2)
new_esEs8(Just(x0), Just(x1), ty_Int)
new_esEs18(x0, x1, app(ty_[], x2))
new_sr(Pos(x0), Pos(x1))
new_esEs27(x0, x1, ty_Double)
new_esEs22(x0, x1, ty_Char)
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs13(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_esEs4(Right(x0), Right(x1), x2, ty_Bool)
new_esEs21(x0, x1, ty_Char)
new_primPlusNat0(Succ(x0), Succ(x1))
new_esEs4(Right(x0), Right(x1), x2, ty_Integer)
new_primMulNat0(Zero, Zero)
new_sr(Neg(x0), Pos(x1))
new_sr(Pos(x0), Neg(x1))
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_span2Zs12(x0, x1, x2, x3, x4, x5, x6)
new_esEs4(Left(x0), Left(x1), ty_Char, x2)
new_esEs19(x0, x1, ty_Bool)
new_esEs11(GT, GT)
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_esEs25(x0, x1, app(ty_[], x2))
new_esEs20(x0, x1, ty_Bool)
new_esEs9(:(x0, x1), [], x2)
new_esEs4(Left(x0), Left(x1), ty_@0, x2)
new_span2Zs2(x0, [], x1, x2)
new_esEs22(x0, x1, ty_Double)
new_esEs4(Left(x0), Left(x1), ty_Int, x2)
new_esEs27(x0, x1, ty_Float)
new_esEs23(x0, x1, ty_Integer)
new_esEs22(x0, x1, app(ty_[], x2))
new_primMulNat0(Zero, Succ(x0))
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_span2Zs3(x0, :(x1, x2), x3, x4)
new_esEs11(LT, GT)
new_esEs11(GT, LT)
new_span2Ys3(x0, :(x1, x2), x3, x4)
new_primEqNat0(Succ(x0), Zero)
new_esEs19(x0, x1, ty_@0)
new_span2Ys2(x0, [], x1, x2)
new_esEs27(x0, x1, ty_Integer)
new_esEs26(x0, x1, ty_Float)
new_esEs26(x0, x1, ty_Ordering)
new_esEs20(x0, x1, ty_Char)
new_esEs20(x0, x1, ty_Integer)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs8(Nothing, Just(x0), x1)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs20(x0, x1, ty_Double)
new_esEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs19(x0, x1, ty_Double)
new_esEs20(x0, x1, ty_Float)
new_esEs26(x0, x1, ty_@0)
new_span2Ys13(x0, x1, x2, False, x3, x4)
new_esEs4(Left(x0), Left(x1), ty_Float, x2)
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs20(x0, x1, ty_Ordering)
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(x0, x1)
new_esEs4(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_span2Zs2(x0, :(x1, x2), x3, x4)
new_esEs18(x0, x1, app(app(ty_@2, x2), x3))
new_esEs20(x0, x1, app(ty_[], x2))
new_esEs12(Integer(x0), Integer(x1))
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_esEs4(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_primPlusNat1(Succ(x0), x1)
new_esEs20(x0, x1, ty_Int)
new_esEs4(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs18(x0, x1, ty_@0)
new_esEs4(Left(x0), Left(x1), ty_Bool, x2)
new_primMulNat0(Succ(x0), Succ(x1))
new_esEs21(x0, x1, ty_@0)
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs19(x0, x1, ty_Char)
new_primPlusNat0(Zero, Succ(x0))
new_esEs26(x0, x1, app(ty_[], x2))
new_esEs11(LT, LT)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_esEs8(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs8(Just(x0), Just(x1), ty_Ordering)
new_asAs(True, x0)
new_esEs8(Just(x0), Nothing, x1)
new_groupByZs0(Right(x0), :(Right(x1), x2), x3, x4)
new_primPlusNat0(Zero, Zero)
new_esEs27(x0, x1, ty_Int)
new_esEs25(x0, x1, ty_Char)
new_esEs9([], :(x0, x1), x2)
new_esEs4(Right(x0), Right(x1), x2, ty_Char)
new_esEs24(x0, x1, ty_Int)
new_esEs8(Just(x0), Just(x1), ty_Bool)
new_esEs4(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs18(x0, x1, ty_Int)
new_esEs25(x0, x1, ty_Bool)
new_esEs14(False, False)
new_esEs23(x0, x1, ty_Int)
new_primEqInt(Pos(Zero), Pos(Zero))
new_esEs26(x0, x1, ty_Char)
new_esEs11(EQ, EQ)
new_esEs18(x0, x1, ty_Char)
new_esEs18(x0, x1, app(app(ty_Either, x2), x3))
new_span2Zs13(x0, x1, x2, True, x3, x4)
new_primPlusNat0(Succ(x0), Zero)
new_esEs21(x0, x1, ty_Double)
new_esEs4(Right(x0), Right(x1), x2, ty_Int)
new_esEs8(Just(x0), Just(x1), ty_Integer)
new_esEs25(x0, x1, ty_Int)
new_esEs18(x0, x1, ty_Ordering)
new_esEs19(x0, x1, ty_Integer)
new_esEs18(x0, x1, app(ty_Maybe, x2))
new_span2Zs13(x0, x1, x2, False, x3, x4)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_groupByZs0(x0, [], x1, x2)
new_span2Ys11(x0, x1, x2, False, x3, x4)
new_esEs9(:(x0, x1), :(x2, x3), x4)
new_esEs18(x0, x1, app(ty_Ratio, x2))
new_primPlusNat1(Zero, x0)
new_esEs22(x0, x1, ty_Float)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))

We have to consider all minimal (P,Q,R)-chains.
The TRS P is empty. Hence, there is no (P,Q,R) chain.