YES 4.022
H-Termination proof of /home/matraf/haskell/eval_FullyBlown_Fast/empty.hs
H-Termination of the given Haskell-Program with start terms could successfully be proven:
↳ HASKELL
↳ CR
mainModule Main
| ((max :: Ord a => a -> a -> a) :: Ord a => a -> a -> a) |
module Main where
Case Reductions:
The following Case expression
case | compare x y of |
| EQ | → o |
| LT | → LT |
| GT | → GT |
is transformed to
primCompAux0 | o EQ | = o |
primCompAux0 | o LT | = LT |
primCompAux0 | o GT | = GT |
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
mainModule Main
| ((max :: Ord a => a -> a -> a) :: Ord a => a -> a -> a) |
module Main where
If Reductions:
The following If expression
if primGEqNatS x y then Succ (primDivNatS (primMinusNatS x y) (Succ y)) else Zero
is transformed to
primDivNatS0 | x y True | = Succ (primDivNatS (primMinusNatS x y) (Succ y)) |
primDivNatS0 | x y False | = Zero |
The following If expression
if primGEqNatS x y then primModNatS (primMinusNatS x y) (Succ y) else Succ x
is transformed to
primModNatS0 | x y True | = primModNatS (primMinusNatS x y) (Succ y) |
primModNatS0 | x y False | = Succ x |
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
mainModule Main
| ((max :: Ord a => a -> a -> a) :: Ord a => a -> a -> a) |
module Main where
Replaced joker patterns by fresh variables and removed binding patterns.
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
mainModule Main
| ((max :: Ord a => a -> a -> a) :: Ord a => a -> a -> a) |
module Main where
Cond Reductions:
The following Function with conditions
is transformed to
max1 | x y True | = y |
max1 | x y False | = max0 x y otherwise |
max2 | x y | = max1 x y (x <= y) |
The following Function with conditions
compare | x y |
| | x == y | |
| | x <= y | |
| | otherwise | |
|
is transformed to
compare | x y | = compare3 x y |
compare1 | x y True | = LT |
compare1 | x y False | = compare0 x y otherwise |
compare2 | x y True | = EQ |
compare2 | x y False | = compare1 x y (x <= y) |
compare3 | x y | = compare2 x y (x == y) |
The following Function with conditions
gcd' | x 0 | = x |
gcd' | x y | = gcd' y (x `rem` y) |
is transformed to
gcd' | x zx | = gcd'2 x zx |
gcd' | x y | = gcd'0 x y |
gcd'0 | x y | = gcd' y (x `rem` y) |
gcd'1 | True x zx | = x |
gcd'1 | zy zz vuu | = gcd'0 zz vuu |
gcd'2 | x zx | = gcd'1 (zx == 0) x zx |
gcd'2 | vuv vuw | = gcd'0 vuv vuw |
The following Function with conditions
gcd | 0 0 | = error [] |
gcd | x y | =
gcd' (abs x) (abs y) |
where |
gcd' | x 0 | = x |
gcd' | x y | = gcd' y (x `rem` y) |
|
|
is transformed to
gcd | vux vuy | = gcd3 vux vuy |
gcd | x y | = gcd0 x y |
gcd0 | x y | =
gcd' (abs x) (abs y) |
where |
gcd' | x zx | = gcd'2 x zx |
gcd' | x y | = gcd'0 x y |
|
|
gcd'0 | x y | = gcd' y (x `rem` y) |
|
|
gcd'1 | True x zx | = x |
gcd'1 | zy zz vuu | = gcd'0 zz vuu |
|
|
gcd'2 | x zx | = gcd'1 (zx == 0) x zx |
gcd'2 | vuv vuw | = gcd'0 vuv vuw |
|
|
gcd1 | True vux vuy | = error [] |
gcd1 | vuz vvu vvv | = gcd0 vvu vvv |
gcd2 | True vux vuy | = gcd1 (vuy == 0) vux vuy |
gcd2 | vvw vvx vvy | = gcd0 vvx vvy |
gcd3 | vux vuy | = gcd2 (vux == 0) vux vuy |
gcd3 | vvz vwu | = gcd0 vvz vwu |
The following Function with conditions
is transformed to
absReal0 | x True | = `negate` x |
absReal1 | x True | = x |
absReal1 | x False | = absReal0 x otherwise |
absReal2 | x | = absReal1 x (x >= 0) |
The following Function with conditions
is transformed to
undefined0 | True | = undefined |
undefined1 | | = undefined0 False |
The following Function with conditions
reduce | x y |
| | y == 0 | |
| | otherwise |
= | x `quot` d :% (y `quot` d) |
|
|
where | |
|
is transformed to
reduce2 | x y | =
reduce1 x y (y == 0) |
where | |
|
reduce0 | x y True | = x `quot` d :% (y `quot` d) |
|
|
reduce1 | x y True | = error [] |
reduce1 | x y False | = reduce0 x y otherwise |
|
|
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
mainModule Main
| ((max :: Ord a => a -> a -> a) :: Ord a => a -> a -> a) |
module Main where
Let/Where Reductions:
The bindings of the following Let/Where expression
reduce1 x y (y == 0) |
where | |
|
reduce0 | x y True | = x `quot` d :% (y `quot` d) |
|
|
reduce1 | x y True | = error [] |
reduce1 | x y False | = reduce0 x y otherwise |
|
are unpacked to the following functions on top level
reduce2Reduce0 | vwv vww x y True | = x `quot` reduce2D vwv vww :% (y `quot` reduce2D vwv vww) |
reduce2D | vwv vww | = gcd vwv vww |
reduce2Reduce1 | vwv vww x y True | = error [] |
reduce2Reduce1 | vwv vww x y False | = reduce2Reduce0 vwv vww x y otherwise |
The bindings of the following Let/Where expression
gcd' (abs x) (abs y) |
where |
gcd' | x zx | = gcd'2 x zx |
gcd' | x y | = gcd'0 x y |
|
|
gcd'0 | x y | = gcd' y (x `rem` y) |
|
|
gcd'1 | True x zx | = x |
gcd'1 | zy zz vuu | = gcd'0 zz vuu |
|
|
gcd'2 | x zx | = gcd'1 (zx == 0) x zx |
gcd'2 | vuv vuw | = gcd'0 vuv vuw |
|
are unpacked to the following functions on top level
gcd0Gcd' | x zx | = gcd0Gcd'2 x zx |
gcd0Gcd' | x y | = gcd0Gcd'0 x y |
gcd0Gcd'0 | x y | = gcd0Gcd' y (x `rem` y) |
gcd0Gcd'2 | x zx | = gcd0Gcd'1 (zx == 0) x zx |
gcd0Gcd'2 | vuv vuw | = gcd0Gcd'0 vuv vuw |
gcd0Gcd'1 | True x zx | = x |
gcd0Gcd'1 | zy zz vuu | = gcd0Gcd'0 zz vuu |
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
mainModule Main
| ((max :: Ord a => a -> a -> a) :: Ord a => a -> a -> a) |
module Main where
Num Reduction: All numbers are transformed to thier corresponding representation with Pos, Neg, Succ and Zero.
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
mainModule Main
| (max :: Ord a => a -> a -> a) |
module Main where
Haskell To QDPs
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDPSizeChangeProof
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_primEqNat(Succ(vwx13200), Succ(vwx13300)) → new_primEqNat(vwx13200, vwx13300)
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:
- new_primEqNat(Succ(vwx13200), Succ(vwx13300)) → new_primEqNat(vwx13200, vwx13300)
The graph contains the following edges 1 > 1, 2 > 2
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDPSizeChangeProof
↳ QDP
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_primPlusNat(Succ(vwx22200), Succ(vwx41000)) → new_primPlusNat(vwx22200, vwx41000)
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:
- new_primPlusNat(Succ(vwx22200), Succ(vwx41000)) → new_primPlusNat(vwx22200, vwx41000)
The graph contains the following edges 1 > 1, 2 > 2
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDPSizeChangeProof
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_primMulNat(Succ(vwx3000), Succ(vwx4100)) → new_primMulNat(vwx3000, Succ(vwx4100))
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:
- new_primMulNat(Succ(vwx3000), Succ(vwx4100)) → new_primMulNat(vwx3000, Succ(vwx4100))
The graph contains the following edges 1 > 1, 2 >= 2
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDPSizeChangeProof
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_primCmpNat(Succ(vwx3000), Succ(vwx4000)) → new_primCmpNat(vwx3000, vwx4000)
R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By using the subterm criterion [20] together with the size-change analysis [32] we have proven that there are no infinite chains for this DP problem. From the DPs we obtained the following set of size-change graphs:
- new_primCmpNat(Succ(vwx3000), Succ(vwx4000)) → new_primCmpNat(vwx3000, vwx4000)
The graph contains the following edges 1 > 1, 2 > 2
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDPSizeChangeProof
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_esEs1(Just(vwx1320), Just(vwx1330), app(app(app(ty_@3, gc), gd), ge)) → new_esEs(vwx1320, vwx1330, gc, gd, ge)
new_esEs3(Right(vwx1320), Right(vwx1330), bdb, app(app(ty_@2, bdh), bea)) → new_esEs2(vwx1320, vwx1330, bdh, bea)
new_esEs(@3(vwx1320, vwx1321, vwx1322), @3(vwx1330, vwx1331, vwx1332), cd, app(ty_[], da), be) → new_esEs0(vwx1321, vwx1331, da)
new_esEs(@3(vwx1320, vwx1321, vwx1322), @3(vwx1330, vwx1331, vwx1332), cd, bd, app(ty_Maybe, ec)) → new_esEs1(vwx1322, vwx1332, ec)
new_esEs(@3(vwx1320, vwx1321, vwx1322), @3(vwx1330, vwx1331, vwx1332), app(app(ty_Either, cb), cc), bd, be) → new_esEs3(vwx1320, vwx1330, cb, cc)
new_esEs2(@2(vwx1320, vwx1321), @2(vwx1330, vwx1331), app(ty_[], hh), hg) → new_esEs0(vwx1320, vwx1330, hh)
new_esEs2(@2(vwx1320, vwx1321), @2(vwx1330, vwx1331), baf, app(ty_Maybe, bbc)) → new_esEs1(vwx1321, vwx1331, bbc)
new_esEs2(@2(vwx1320, vwx1321), @2(vwx1330, vwx1331), baf, app(app(ty_@2, bbd), bbe)) → new_esEs2(vwx1321, vwx1331, bbd, bbe)
new_esEs(@3(vwx1320, vwx1321, vwx1322), @3(vwx1330, vwx1331, vwx1332), cd, bd, app(ty_[], eb)) → new_esEs0(vwx1322, vwx1332, eb)
new_esEs3(Left(vwx1320), Left(vwx1330), app(ty_Maybe, bce), bcc) → new_esEs1(vwx1320, vwx1330, bce)
new_esEs2(@2(vwx1320, vwx1321), @2(vwx1330, vwx1331), app(ty_Maybe, baa), hg) → new_esEs1(vwx1320, vwx1330, baa)
new_esEs3(Right(vwx1320), Right(vwx1330), bdb, app(app(ty_Either, beb), bec)) → new_esEs3(vwx1320, vwx1330, beb, bec)
new_esEs2(@2(vwx1320, vwx1321), @2(vwx1330, vwx1331), app(app(ty_@2, bab), bac), hg) → new_esEs2(vwx1320, vwx1330, bab, bac)
new_esEs0(:(vwx1320, vwx1321), :(vwx1330, vwx1331), app(app(app(ty_@3, eh), fa), fb)) → new_esEs(vwx1320, vwx1330, eh, fa, fb)
new_esEs(@3(vwx1320, vwx1321, vwx1322), @3(vwx1330, vwx1331, vwx1332), app(app(app(ty_@3, ba), bb), bc), bd, be) → new_esEs(vwx1320, vwx1330, ba, bb, bc)
new_esEs2(@2(vwx1320, vwx1321), @2(vwx1330, vwx1331), baf, app(app(app(ty_@3, bag), bah), bba)) → new_esEs(vwx1321, vwx1331, bag, bah, bba)
new_esEs1(Just(vwx1320), Just(vwx1330), app(ty_[], gf)) → new_esEs0(vwx1320, vwx1330, gf)
new_esEs3(Left(vwx1320), Left(vwx1330), app(app(ty_Either, bch), bda), bcc) → new_esEs3(vwx1320, vwx1330, bch, bda)
new_esEs0(:(vwx1320, vwx1321), :(vwx1330, vwx1331), app(app(ty_Either, fh), ga)) → new_esEs3(vwx1320, vwx1330, fh, ga)
new_esEs1(Just(vwx1320), Just(vwx1330), app(app(ty_Either, hb), hc)) → new_esEs3(vwx1320, vwx1330, hb, hc)
new_esEs(@3(vwx1320, vwx1321, vwx1322), @3(vwx1330, vwx1331, vwx1332), app(ty_Maybe, bg), bd, be) → new_esEs1(vwx1320, vwx1330, bg)
new_esEs(@3(vwx1320, vwx1321, vwx1322), @3(vwx1330, vwx1331, vwx1332), cd, app(ty_Maybe, db), be) → new_esEs1(vwx1321, vwx1331, db)
new_esEs(@3(vwx1320, vwx1321, vwx1322), @3(vwx1330, vwx1331, vwx1332), app(app(ty_@2, bh), ca), bd, be) → new_esEs2(vwx1320, vwx1330, bh, ca)
new_esEs0(:(vwx1320, vwx1321), :(vwx1330, vwx1331), app(ty_Maybe, fd)) → new_esEs1(vwx1320, vwx1330, fd)
new_esEs3(Right(vwx1320), Right(vwx1330), bdb, app(app(app(ty_@3, bdc), bdd), bde)) → new_esEs(vwx1320, vwx1330, bdc, bdd, bde)
new_esEs3(Left(vwx1320), Left(vwx1330), app(app(ty_@2, bcf), bcg), bcc) → new_esEs2(vwx1320, vwx1330, bcf, bcg)
new_esEs2(@2(vwx1320, vwx1321), @2(vwx1330, vwx1331), app(app(app(ty_@3, hd), he), hf), hg) → new_esEs(vwx1320, vwx1330, hd, he, hf)
new_esEs3(Left(vwx1320), Left(vwx1330), app(ty_[], bcd), bcc) → new_esEs0(vwx1320, vwx1330, bcd)
new_esEs2(@2(vwx1320, vwx1321), @2(vwx1330, vwx1331), baf, app(app(ty_Either, bbf), bbg)) → new_esEs3(vwx1321, vwx1331, bbf, bbg)
new_esEs(@3(vwx1320, vwx1321, vwx1322), @3(vwx1330, vwx1331, vwx1332), cd, app(app(ty_@2, dc), dd), be) → new_esEs2(vwx1321, vwx1331, dc, dd)
new_esEs3(Right(vwx1320), Right(vwx1330), bdb, app(ty_[], bdf)) → new_esEs0(vwx1320, vwx1330, bdf)
new_esEs(@3(vwx1320, vwx1321, vwx1322), @3(vwx1330, vwx1331, vwx1332), cd, app(app(app(ty_@3, ce), cf), cg), be) → new_esEs(vwx1321, vwx1331, ce, cf, cg)
new_esEs3(Right(vwx1320), Right(vwx1330), bdb, app(ty_Maybe, bdg)) → new_esEs1(vwx1320, vwx1330, bdg)
new_esEs1(Just(vwx1320), Just(vwx1330), app(ty_Maybe, gg)) → new_esEs1(vwx1320, vwx1330, gg)
new_esEs1(Just(vwx1320), Just(vwx1330), app(app(ty_@2, gh), ha)) → new_esEs2(vwx1320, vwx1330, gh, ha)
new_esEs(@3(vwx1320, vwx1321, vwx1322), @3(vwx1330, vwx1331, vwx1332), app(ty_[], bf), bd, be) → new_esEs0(vwx1320, vwx1330, bf)
new_esEs(@3(vwx1320, vwx1321, vwx1322), @3(vwx1330, vwx1331, vwx1332), cd, bd, app(app(ty_@2, ed), ee)) → new_esEs2(vwx1322, vwx1332, ed, ee)
new_esEs2(@2(vwx1320, vwx1321), @2(vwx1330, vwx1331), baf, app(ty_[], bbb)) → new_esEs0(vwx1321, vwx1331, bbb)
new_esEs0(:(vwx1320, vwx1321), :(vwx1330, vwx1331), app(ty_[], fc)) → new_esEs0(vwx1320, vwx1330, fc)
new_esEs(@3(vwx1320, vwx1321, vwx1322), @3(vwx1330, vwx1331, vwx1332), cd, app(app(ty_Either, de), df), be) → new_esEs3(vwx1321, vwx1331, de, df)
new_esEs2(@2(vwx1320, vwx1321), @2(vwx1330, vwx1331), app(app(ty_Either, bad), bae), hg) → new_esEs3(vwx1320, vwx1330, bad, bae)
new_esEs0(:(vwx1320, vwx1321), :(vwx1330, vwx1331), app(app(ty_@2, ff), fg)) → new_esEs2(vwx1320, vwx1330, ff, fg)
new_esEs3(Left(vwx1320), Left(vwx1330), app(app(app(ty_@3, bbh), bca), bcb), bcc) → new_esEs(vwx1320, vwx1330, bbh, bca, bcb)
new_esEs0(:(vwx1320, vwx1321), :(vwx1330, vwx1331), gb) → new_esEs0(vwx1321, vwx1331, gb)
new_esEs(@3(vwx1320, vwx1321, vwx1322), @3(vwx1330, vwx1331, vwx1332), cd, bd, app(app(ty_Either, ef), eg)) → new_esEs3(vwx1322, vwx1332, ef, eg)
new_esEs(@3(vwx1320, vwx1321, vwx1322), @3(vwx1330, vwx1331, vwx1332), cd, bd, app(app(app(ty_@3, dg), dh), ea)) → new_esEs(vwx1322, vwx1332, dg, dh, ea)
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:
- new_esEs0(:(vwx1320, vwx1321), :(vwx1330, vwx1331), app(ty_Maybe, fd)) → new_esEs1(vwx1320, vwx1330, fd)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
- new_esEs0(:(vwx1320, vwx1321), :(vwx1330, vwx1331), app(app(ty_Either, fh), ga)) → new_esEs3(vwx1320, vwx1330, fh, ga)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
- new_esEs0(:(vwx1320, vwx1321), :(vwx1330, vwx1331), app(app(app(ty_@3, eh), fa), fb)) → new_esEs(vwx1320, vwx1330, eh, fa, fb)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
- new_esEs1(Just(vwx1320), Just(vwx1330), app(ty_Maybe, gg)) → new_esEs1(vwx1320, vwx1330, gg)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
- new_esEs1(Just(vwx1320), Just(vwx1330), app(app(ty_Either, hb), hc)) → new_esEs3(vwx1320, vwx1330, hb, hc)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
- new_esEs1(Just(vwx1320), Just(vwx1330), app(app(app(ty_@3, gc), gd), ge)) → new_esEs(vwx1320, vwx1330, gc, gd, ge)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
- new_esEs0(:(vwx1320, vwx1321), :(vwx1330, vwx1331), app(app(ty_@2, ff), fg)) → new_esEs2(vwx1320, vwx1330, ff, fg)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
- new_esEs1(Just(vwx1320), Just(vwx1330), app(app(ty_@2, gh), ha)) → new_esEs2(vwx1320, vwx1330, gh, ha)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
- new_esEs1(Just(vwx1320), Just(vwx1330), app(ty_[], gf)) → new_esEs0(vwx1320, vwx1330, gf)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
- new_esEs(@3(vwx1320, vwx1321, vwx1322), @3(vwx1330, vwx1331, vwx1332), cd, bd, app(ty_Maybe, ec)) → new_esEs1(vwx1322, vwx1332, ec)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3
- new_esEs(@3(vwx1320, vwx1321, vwx1322), @3(vwx1330, vwx1331, vwx1332), app(ty_Maybe, bg), bd, be) → new_esEs1(vwx1320, vwx1330, bg)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
- new_esEs(@3(vwx1320, vwx1321, vwx1322), @3(vwx1330, vwx1331, vwx1332), cd, app(ty_Maybe, db), be) → new_esEs1(vwx1321, vwx1331, db)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
- new_esEs(@3(vwx1320, vwx1321, vwx1322), @3(vwx1330, vwx1331, vwx1332), app(app(ty_Either, cb), cc), bd, be) → new_esEs3(vwx1320, vwx1330, cb, cc)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
- new_esEs(@3(vwx1320, vwx1321, vwx1322), @3(vwx1330, vwx1331, vwx1332), cd, app(app(ty_Either, de), df), be) → new_esEs3(vwx1321, vwx1331, de, df)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
- new_esEs(@3(vwx1320, vwx1321, vwx1322), @3(vwx1330, vwx1331, vwx1332), cd, bd, app(app(ty_Either, ef), eg)) → new_esEs3(vwx1322, vwx1332, ef, eg)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4
- new_esEs(@3(vwx1320, vwx1321, vwx1322), @3(vwx1330, vwx1331, vwx1332), app(app(app(ty_@3, ba), bb), bc), bd, be) → new_esEs(vwx1320, vwx1330, ba, bb, bc)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
- new_esEs(@3(vwx1320, vwx1321, vwx1322), @3(vwx1330, vwx1331, vwx1332), cd, app(app(app(ty_@3, ce), cf), cg), be) → new_esEs(vwx1321, vwx1331, ce, cf, cg)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5
- new_esEs(@3(vwx1320, vwx1321, vwx1322), @3(vwx1330, vwx1331, vwx1332), cd, bd, app(app(app(ty_@3, dg), dh), ea)) → new_esEs(vwx1322, vwx1332, dg, dh, ea)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4, 5 > 5
- new_esEs(@3(vwx1320, vwx1321, vwx1322), @3(vwx1330, vwx1331, vwx1332), app(app(ty_@2, bh), ca), bd, be) → new_esEs2(vwx1320, vwx1330, bh, ca)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
- new_esEs(@3(vwx1320, vwx1321, vwx1322), @3(vwx1330, vwx1331, vwx1332), cd, app(app(ty_@2, dc), dd), be) → new_esEs2(vwx1321, vwx1331, dc, dd)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
- new_esEs(@3(vwx1320, vwx1321, vwx1322), @3(vwx1330, vwx1331, vwx1332), cd, bd, app(app(ty_@2, ed), ee)) → new_esEs2(vwx1322, vwx1332, ed, ee)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4
- new_esEs(@3(vwx1320, vwx1321, vwx1322), @3(vwx1330, vwx1331, vwx1332), cd, app(ty_[], da), be) → new_esEs0(vwx1321, vwx1331, da)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
- new_esEs(@3(vwx1320, vwx1321, vwx1322), @3(vwx1330, vwx1331, vwx1332), cd, bd, app(ty_[], eb)) → new_esEs0(vwx1322, vwx1332, eb)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3
- new_esEs(@3(vwx1320, vwx1321, vwx1322), @3(vwx1330, vwx1331, vwx1332), app(ty_[], bf), bd, be) → new_esEs0(vwx1320, vwx1330, bf)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
- new_esEs2(@2(vwx1320, vwx1321), @2(vwx1330, vwx1331), baf, app(ty_Maybe, bbc)) → new_esEs1(vwx1321, vwx1331, bbc)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
- new_esEs2(@2(vwx1320, vwx1321), @2(vwx1330, vwx1331), app(ty_Maybe, baa), hg) → new_esEs1(vwx1320, vwx1330, baa)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
- new_esEs3(Left(vwx1320), Left(vwx1330), app(ty_Maybe, bce), bcc) → new_esEs1(vwx1320, vwx1330, bce)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
- new_esEs3(Right(vwx1320), Right(vwx1330), bdb, app(ty_Maybe, bdg)) → new_esEs1(vwx1320, vwx1330, bdg)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
- new_esEs2(@2(vwx1320, vwx1321), @2(vwx1330, vwx1331), baf, app(app(ty_Either, bbf), bbg)) → new_esEs3(vwx1321, vwx1331, bbf, bbg)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
- new_esEs2(@2(vwx1320, vwx1321), @2(vwx1330, vwx1331), app(app(ty_Either, bad), bae), hg) → new_esEs3(vwx1320, vwx1330, bad, bae)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
- new_esEs2(@2(vwx1320, vwx1321), @2(vwx1330, vwx1331), baf, app(app(app(ty_@3, bag), bah), bba)) → new_esEs(vwx1321, vwx1331, bag, bah, bba)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5
- new_esEs2(@2(vwx1320, vwx1321), @2(vwx1330, vwx1331), app(app(app(ty_@3, hd), he), hf), hg) → new_esEs(vwx1320, vwx1330, hd, he, hf)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
- new_esEs2(@2(vwx1320, vwx1321), @2(vwx1330, vwx1331), baf, app(app(ty_@2, bbd), bbe)) → new_esEs2(vwx1321, vwx1331, bbd, bbe)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
- new_esEs2(@2(vwx1320, vwx1321), @2(vwx1330, vwx1331), app(app(ty_@2, bab), bac), hg) → new_esEs2(vwx1320, vwx1330, bab, bac)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
- new_esEs2(@2(vwx1320, vwx1321), @2(vwx1330, vwx1331), app(ty_[], hh), hg) → new_esEs0(vwx1320, vwx1330, hh)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
- new_esEs2(@2(vwx1320, vwx1321), @2(vwx1330, vwx1331), baf, app(ty_[], bbb)) → new_esEs0(vwx1321, vwx1331, bbb)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
- new_esEs3(Right(vwx1320), Right(vwx1330), bdb, app(app(ty_Either, beb), bec)) → new_esEs3(vwx1320, vwx1330, beb, bec)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
- new_esEs3(Left(vwx1320), Left(vwx1330), app(app(ty_Either, bch), bda), bcc) → new_esEs3(vwx1320, vwx1330, bch, bda)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
- new_esEs0(:(vwx1320, vwx1321), :(vwx1330, vwx1331), app(ty_[], fc)) → new_esEs0(vwx1320, vwx1330, fc)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
- new_esEs0(:(vwx1320, vwx1321), :(vwx1330, vwx1331), gb) → new_esEs0(vwx1321, vwx1331, gb)
The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3
- new_esEs3(Right(vwx1320), Right(vwx1330), bdb, app(app(app(ty_@3, bdc), bdd), bde)) → new_esEs(vwx1320, vwx1330, bdc, bdd, bde)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5
- new_esEs3(Left(vwx1320), Left(vwx1330), app(app(app(ty_@3, bbh), bca), bcb), bcc) → new_esEs(vwx1320, vwx1330, bbh, bca, bcb)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
- new_esEs3(Right(vwx1320), Right(vwx1330), bdb, app(app(ty_@2, bdh), bea)) → new_esEs2(vwx1320, vwx1330, bdh, bea)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
- new_esEs3(Left(vwx1320), Left(vwx1330), app(app(ty_@2, bcf), bcg), bcc) → new_esEs2(vwx1320, vwx1330, bcf, bcg)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
- new_esEs3(Left(vwx1320), Left(vwx1330), app(ty_[], bcd), bcc) → new_esEs0(vwx1320, vwx1330, bcd)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
- new_esEs3(Right(vwx1320), Right(vwx1330), bdb, app(ty_[], bdf)) → new_esEs0(vwx1320, vwx1330, bdf)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDPSizeChangeProof
Q DP problem:
The TRS P consists of the following rules:
new_ltEs0(@2(vwx300, vwx301), @2(vwx400, vwx401), app(app(ty_@2, dg), dh), df) → new_lt0(vwx300, vwx400, dg, dh)
new_ltEs2(Right(vwx300), Right(vwx400), bac, app(ty_Maybe, bad)) → new_ltEs(vwx300, vwx400, bad)
new_compare3(vwx30, vwx40, bfc, bfd, bfe) → new_compare23(vwx30, vwx40, new_esEs7(vwx30, vwx40, bfc, bfd, bfe), bfc, bfd, bfe)
new_ltEs2(Left(vwx300), Left(vwx400), app(app(app(ty_@3, hh), baa), bab), hb) → new_ltEs3(vwx300, vwx400, hh, baa, bab)
new_lt3(vwx30, vwx40, bfc, bfd, bfe) → new_compare23(vwx30, vwx40, new_esEs7(vwx30, vwx40, bfc, bfd, bfe), bfc, bfd, bfe)
new_ltEs3(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), bbe, app(app(ty_Either, bde), bdf), bda) → new_lt2(vwx301, vwx401, bde, bdf)
new_ltEs0(@2(vwx300, vwx301), @2(vwx400, vwx401), cb, app(app(app(ty_@3, db), dc), dd)) → new_ltEs3(vwx301, vwx401, db, dc, dd)
new_ltEs1(vwx30, vwx40, eg) → new_compare(vwx30, vwx40, eg)
new_primCompAux(vwx30, vwx40, vwx31, vwx41, app(app(app(ty_@3, ga), gb), gc)) → new_compare3(vwx30, vwx40, ga, gb, gc)
new_ltEs2(Left(vwx300), Left(vwx400), app(app(ty_Either, hf), hg), hb) → new_ltEs2(vwx300, vwx400, hf, hg)
new_ltEs0(@2(vwx300, vwx301), @2(vwx400, vwx401), cb, app(ty_Maybe, cc)) → new_ltEs(vwx301, vwx401, cc)
new_ltEs2(Left(vwx300), Left(vwx400), app(ty_Maybe, ha), hb) → new_ltEs(vwx300, vwx400, ha)
new_compare(:(vwx300, vwx301), :(vwx400, vwx401), eh) → new_primCompAux(vwx300, vwx400, vwx301, vwx401, eh)
new_ltEs(Just(vwx300), Just(vwx400), app(app(ty_@2, bb), bc)) → new_ltEs0(vwx300, vwx400, bb, bc)
new_compare21(vwx30, vwx40, False, ge, gf) → new_ltEs0(vwx30, vwx40, ge, gf)
new_ltEs2(Left(vwx300), Left(vwx400), app(app(ty_@2, hc), hd), hb) → new_ltEs0(vwx300, vwx400, hc, hd)
new_ltEs(Just(vwx300), Just(vwx400), app(ty_Maybe, ba)) → new_ltEs(vwx300, vwx400, ba)
new_ltEs3(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), bbe, bbf, app(ty_Maybe, bbg)) → new_ltEs(vwx302, vwx402, bbg)
new_lt1(:(vwx300, vwx301), :(vwx400, vwx401), eh) → new_primCompAux(vwx300, vwx400, vwx301, vwx401, eh)
new_compare2(vwx30, vwx40, gg, gh) → new_compare22(vwx30, vwx40, new_esEs6(vwx30, vwx40, gg, gh), gg, gh)
new_ltEs3(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), app(app(ty_@2, bec), bed), bbf, bda) → new_lt0(vwx300, vwx400, bec, bed)
new_ltEs3(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), app(ty_Maybe, beb), bbf, bda) → new_lt(vwx300, vwx400, beb)
new_ltEs3(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), bbe, app(app(ty_@2, bdb), bdc), bda) → new_lt0(vwx301, vwx401, bdb, bdc)
new_lt(vwx30, vwx40, gd) → new_compare20(vwx30, vwx40, new_esEs4(vwx30, vwx40, gd), gd)
new_ltEs3(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), app(app(ty_Either, bef), beg), bbf, bda) → new_lt2(vwx300, vwx400, bef, beg)
new_ltEs2(Right(vwx300), Right(vwx400), bac, app(ty_[], bag)) → new_ltEs1(vwx300, vwx400, bag)
new_compare1(vwx30, vwx40, ge, gf) → new_compare21(vwx30, vwx40, new_esEs5(vwx30, vwx40, ge, gf), ge, gf)
new_ltEs2(Right(vwx300), Right(vwx400), bac, app(app(ty_Either, bah), bba)) → new_ltEs2(vwx300, vwx400, bah, bba)
new_ltEs(Just(vwx300), Just(vwx400), app(app(ty_Either, be), bf)) → new_ltEs2(vwx300, vwx400, be, bf)
new_primCompAux(vwx30, vwx40, vwx31, vwx41, app(ty_[], ff)) → new_compare(vwx30, vwx40, ff)
new_ltEs0(@2(vwx300, vwx301), @2(vwx400, vwx401), cb, app(app(ty_@2, cd), ce)) → new_ltEs0(vwx301, vwx401, cd, ce)
new_ltEs0(@2(vwx300, vwx301), @2(vwx400, vwx401), cb, app(ty_[], cf)) → new_ltEs1(vwx301, vwx401, cf)
new_ltEs3(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), bbe, bbf, app(app(app(ty_@3, bce), bcf), bcg)) → new_ltEs3(vwx302, vwx402, bce, bcf, bcg)
new_ltEs3(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), app(ty_[], bee), bbf, bda) → new_lt1(vwx300, vwx400, bee)
new_ltEs0(@2(vwx300, vwx301), @2(vwx400, vwx401), app(ty_Maybe, de), df) → new_lt(vwx300, vwx400, de)
new_ltEs0(@2(vwx300, vwx301), @2(vwx400, vwx401), app(ty_[], ea), df) → new_lt1(vwx300, vwx400, ea)
new_compare0(vwx30, vwx40, gd) → new_compare20(vwx30, vwx40, new_esEs4(vwx30, vwx40, gd), gd)
new_ltEs0(@2(vwx300, vwx301), @2(vwx400, vwx401), cb, app(app(ty_Either, cg), da)) → new_ltEs2(vwx301, vwx401, cg, da)
new_ltEs3(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), bbe, app(ty_Maybe, bch), bda) → new_lt(vwx301, vwx401, bch)
new_ltEs3(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), app(app(app(ty_@3, beh), bfa), bfb), bbf, bda) → new_lt3(vwx300, vwx400, beh, bfa, bfb)
new_ltEs(Just(vwx300), Just(vwx400), app(ty_[], bd)) → new_ltEs1(vwx300, vwx400, bd)
new_primCompAux(vwx30, vwx40, vwx31, vwx41, app(app(ty_Either, fg), fh)) → new_compare2(vwx30, vwx40, fg, fh)
new_ltEs3(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), bbe, app(app(app(ty_@3, bdg), bdh), bea), bda) → new_lt3(vwx301, vwx401, bdg, bdh, bea)
new_primCompAux(vwx30, vwx40, vwx31, vwx41, fa) → new_compare(vwx31, vwx41, fa)
new_ltEs2(Right(vwx300), Right(vwx400), bac, app(app(ty_@2, bae), baf)) → new_ltEs0(vwx300, vwx400, bae, baf)
new_ltEs3(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), bbe, bbf, app(app(ty_Either, bcc), bcd)) → new_ltEs2(vwx302, vwx402, bcc, bcd)
new_lt2(vwx30, vwx40, gg, gh) → new_compare22(vwx30, vwx40, new_esEs6(vwx30, vwx40, gg, gh), gg, gh)
new_ltEs3(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), bbe, bbf, app(app(ty_@2, bbh), bca)) → new_ltEs0(vwx302, vwx402, bbh, bca)
new_ltEs3(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), bbe, bbf, app(ty_[], bcb)) → new_ltEs1(vwx302, vwx402, bcb)
new_compare22(vwx30, vwx40, False, gg, gh) → new_ltEs2(vwx30, vwx40, gg, gh)
new_lt0(vwx30, vwx40, ge, gf) → new_compare21(vwx30, vwx40, new_esEs5(vwx30, vwx40, ge, gf), ge, gf)
new_primCompAux(vwx30, vwx40, vwx31, vwx41, app(app(ty_@2, fc), fd)) → new_compare1(vwx30, vwx40, fc, fd)
new_ltEs(Just(vwx300), Just(vwx400), app(app(app(ty_@3, bg), bh), ca)) → new_ltEs3(vwx300, vwx400, bg, bh, ca)
new_ltEs0(@2(vwx300, vwx301), @2(vwx400, vwx401), app(app(ty_Either, eb), ec), df) → new_lt2(vwx300, vwx400, eb, ec)
new_ltEs2(Right(vwx300), Right(vwx400), bac, app(app(app(ty_@3, bbb), bbc), bbd)) → new_ltEs3(vwx300, vwx400, bbb, bbc, bbd)
new_compare23(vwx30, vwx40, False, bfc, bfd, bfe) → new_ltEs3(vwx30, vwx40, bfc, bfd, bfe)
new_ltEs3(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), bbe, app(ty_[], bdd), bda) → new_lt1(vwx301, vwx401, bdd)
new_ltEs2(Left(vwx300), Left(vwx400), app(ty_[], he), hb) → new_ltEs1(vwx300, vwx400, he)
new_ltEs0(@2(vwx300, vwx301), @2(vwx400, vwx401), app(app(app(ty_@3, ed), ee), ef), df) → new_lt3(vwx300, vwx400, ed, ee, ef)
new_primCompAux(vwx30, vwx40, vwx31, vwx41, app(ty_Maybe, fb)) → new_compare0(vwx30, vwx40, fb)
new_compare20(vwx30, vwx40, False, gd) → new_ltEs(vwx30, vwx40, gd)
The TRS R consists of the following rules:
new_esEs4(Just(vwx1320), Just(vwx1330), app(ty_Maybe, bgd)) → new_esEs4(vwx1320, vwx1330, bgd)
new_esEs23(vwx1322, vwx1332, app(app(ty_@2, dbe), dbf)) → new_esEs5(vwx1322, vwx1332, dbe, dbf)
new_esEs21(vwx1320, vwx1330, ty_@0) → new_esEs13(vwx1320, vwx1330)
new_esEs19(vwx1320, vwx1330, ty_@0) → new_esEs13(vwx1320, vwx1330)
new_esEs18(vwx1320, vwx1330, ty_Ordering) → new_esEs9(vwx1320, vwx1330)
new_esEs6(Right(vwx1320), Right(vwx1330), cad, ty_Double) → new_esEs14(vwx1320, vwx1330)
new_esEs18(vwx1320, vwx1330, app(app(app(ty_@3, cbh), cca), ccb)) → new_esEs7(vwx1320, vwx1330, cbh, cca, ccb)
new_primPlusNat1(Succ(vwx22200), Succ(vwx41000)) → Succ(Succ(new_primPlusNat1(vwx22200, vwx41000)))
new_primEqInt(Neg(Succ(vwx13200)), Pos(vwx1330)) → False
new_primEqInt(Pos(Succ(vwx13200)), Neg(vwx1330)) → False
new_esEs9(LT, GT) → False
new_esEs9(GT, LT) → False
new_esEs6(Left(vwx1320), Left(vwx1330), app(ty_Maybe, bhg), bha) → new_esEs4(vwx1320, vwx1330, bhg)
new_esEs6(Left(vwx1320), Left(vwx1330), ty_@0, bha) → new_esEs13(vwx1320, vwx1330)
new_primEqInt(Neg(Zero), Pos(Succ(vwx13300))) → False
new_primEqInt(Pos(Zero), Neg(Succ(vwx13300))) → False
new_esEs4(Just(vwx1320), Nothing, bff) → False
new_esEs4(Nothing, Just(vwx1330), bff) → False
new_esEs10(Char(vwx1320), Char(vwx1330)) → new_primEqNat0(vwx1320, vwx1330)
new_esEs13(@0, @0) → True
new_esEs6(Left(vwx1320), Left(vwx1330), ty_Ordering, bha) → new_esEs9(vwx1320, vwx1330)
new_esEs23(vwx1322, vwx1332, ty_Char) → new_esEs10(vwx1322, vwx1332)
new_esEs6(Left(vwx1320), Left(vwx1330), app(ty_[], bhe), bha) → new_esEs15(vwx1320, vwx1330, bhe)
new_esEs22(vwx1321, vwx1331, ty_Ordering) → new_esEs9(vwx1321, vwx1331)
new_esEs18(vwx1320, vwx1330, ty_Integer) → new_esEs8(vwx1320, vwx1330)
new_esEs21(vwx1320, vwx1330, ty_Int) → new_esEs12(vwx1320, vwx1330)
new_primMulNat0(Zero, Zero) → Zero
new_esEs21(vwx1320, vwx1330, app(app(ty_@2, cha), chb)) → new_esEs5(vwx1320, vwx1330, cha, chb)
new_esEs6(Left(vwx1320), Left(vwx1330), app(app(app(ty_@3, bhb), bhc), bhd), bha) → new_esEs7(vwx1320, vwx1330, bhb, bhc, bhd)
new_esEs23(vwx1322, vwx1332, ty_Float) → new_esEs11(vwx1322, vwx1332)
new_esEs19(vwx1320, vwx1330, ty_Ordering) → new_esEs9(vwx1320, vwx1330)
new_esEs6(Left(vwx1320), Left(vwx1330), app(app(ty_Either, cab), cac), bha) → new_esEs6(vwx1320, vwx1330, cab, cac)
new_esEs20(vwx1321, vwx1331, app(ty_Maybe, cfc)) → new_esEs4(vwx1321, vwx1331, cfc)
new_esEs20(vwx1321, vwx1331, app(ty_Ratio, cfb)) → new_esEs16(vwx1321, vwx1331, cfb)
new_esEs6(Left(vwx1320), Left(vwx1330), app(ty_Ratio, bhf), bha) → new_esEs16(vwx1320, vwx1330, bhf)
new_esEs15(:(vwx1320, vwx1321), :(vwx1330, vwx1331), cbg) → new_asAs(new_esEs18(vwx1320, vwx1330, cbg), new_esEs15(vwx1321, vwx1331, cbg))
new_esEs21(vwx1320, vwx1330, ty_Bool) → new_esEs17(vwx1320, vwx1330)
new_primPlusNat0(Zero, vwx4100) → Succ(vwx4100)
new_esEs18(vwx1320, vwx1330, ty_Bool) → new_esEs17(vwx1320, vwx1330)
new_esEs22(vwx1321, vwx1331, ty_Float) → new_esEs11(vwx1321, vwx1331)
new_esEs21(vwx1320, vwx1330, app(ty_[], cgf)) → new_esEs15(vwx1320, vwx1330, cgf)
new_esEs22(vwx1321, vwx1331, ty_Bool) → new_esEs17(vwx1321, vwx1331)
new_esEs9(GT, GT) → True
new_esEs24(vwx1320, vwx1330, ty_Integer) → new_esEs8(vwx1320, vwx1330)
new_esEs23(vwx1322, vwx1332, app(ty_Maybe, dbd)) → new_esEs4(vwx1322, vwx1332, dbd)
new_esEs6(Right(vwx1320), Right(vwx1330), cad, ty_Float) → new_esEs11(vwx1320, vwx1330)
new_esEs19(vwx1320, vwx1330, app(app(app(ty_@3, cdd), cde), cdf)) → new_esEs7(vwx1320, vwx1330, cdd, cde, cdf)
new_esEs20(vwx1321, vwx1331, ty_Float) → new_esEs11(vwx1321, vwx1331)
new_esEs18(vwx1320, vwx1330, app(ty_Maybe, cce)) → new_esEs4(vwx1320, vwx1330, cce)
new_esEs17(True, True) → True
new_esEs23(vwx1322, vwx1332, ty_@0) → new_esEs13(vwx1322, vwx1332)
new_esEs22(vwx1321, vwx1331, app(app(ty_@2, dac), dad)) → new_esEs5(vwx1321, vwx1331, dac, dad)
new_esEs22(vwx1321, vwx1331, app(app(app(ty_@3, che), chf), chg)) → new_esEs7(vwx1321, vwx1331, che, chf, chg)
new_esEs20(vwx1321, vwx1331, ty_Integer) → new_esEs8(vwx1321, vwx1331)
new_esEs21(vwx1320, vwx1330, app(app(app(ty_@3, cgc), cgd), cge)) → new_esEs7(vwx1320, vwx1330, cgc, cgd, cge)
new_esEs20(vwx1321, vwx1331, ty_Char) → new_esEs10(vwx1321, vwx1331)
new_primMulInt(Pos(vwx300), Pos(vwx410)) → Pos(new_primMulNat0(vwx300, vwx410))
new_esEs21(vwx1320, vwx1330, app(app(ty_Either, chc), chd)) → new_esEs6(vwx1320, vwx1330, chc, chd)
new_esEs6(Left(vwx1320), Left(vwx1330), ty_Bool, bha) → new_esEs17(vwx1320, vwx1330)
new_esEs7(@3(vwx1320, vwx1321, vwx1322), @3(vwx1330, vwx1331, vwx1332), cfh, cga, cgb) → new_asAs(new_esEs21(vwx1320, vwx1330, cfh), new_asAs(new_esEs22(vwx1321, vwx1331, cga), new_esEs23(vwx1322, vwx1332, cgb)))
new_esEs6(Left(vwx1320), Left(vwx1330), app(app(ty_@2, bhh), caa), bha) → new_esEs5(vwx1320, vwx1330, bhh, caa)
new_esEs18(vwx1320, vwx1330, ty_Float) → new_esEs11(vwx1320, vwx1330)
new_esEs23(vwx1322, vwx1332, ty_Ordering) → new_esEs9(vwx1322, vwx1332)
new_primMulInt(Neg(vwx300), Neg(vwx410)) → Pos(new_primMulNat0(vwx300, vwx410))
new_esEs21(vwx1320, vwx1330, ty_Char) → new_esEs10(vwx1320, vwx1330)
new_esEs4(Just(vwx1320), Just(vwx1330), app(ty_[], bgb)) → new_esEs15(vwx1320, vwx1330, bgb)
new_primEqNat0(Zero, Succ(vwx13300)) → False
new_primEqNat0(Succ(vwx13200), Zero) → False
new_esEs6(Left(vwx1320), Left(vwx1330), ty_Float, bha) → new_esEs11(vwx1320, vwx1330)
new_esEs18(vwx1320, vwx1330, ty_Int) → new_esEs12(vwx1320, vwx1330)
new_esEs6(Left(vwx1320), Left(vwx1330), ty_Int, bha) → new_esEs12(vwx1320, vwx1330)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs22(vwx1321, vwx1331, ty_Double) → new_esEs14(vwx1321, vwx1331)
new_esEs4(Just(vwx1320), Just(vwx1330), ty_Int) → new_esEs12(vwx1320, vwx1330)
new_esEs4(Nothing, Nothing, bff) → True
new_esEs6(Right(vwx1320), Right(vwx1330), cad, ty_@0) → new_esEs13(vwx1320, vwx1330)
new_esEs25(vwx1321, vwx1331, ty_Int) → new_esEs12(vwx1321, vwx1331)
new_esEs4(Just(vwx1320), Just(vwx1330), app(ty_Ratio, bgc)) → new_esEs16(vwx1320, vwx1330, bgc)
new_esEs20(vwx1321, vwx1331, app(app(ty_Either, cff), cfg)) → new_esEs6(vwx1321, vwx1331, cff, cfg)
new_esEs22(vwx1321, vwx1331, app(ty_[], chh)) → new_esEs15(vwx1321, vwx1331, chh)
new_esEs23(vwx1322, vwx1332, ty_Bool) → new_esEs17(vwx1322, vwx1332)
new_esEs11(Float(vwx1320, vwx1321), Float(vwx1330, vwx1331)) → new_esEs12(new_sr(vwx1320, vwx1330), new_sr(vwx1321, vwx1331))
new_esEs12(vwx132, vwx133) → new_primEqInt(vwx132, vwx133)
new_esEs9(EQ, GT) → False
new_esEs9(GT, EQ) → False
new_esEs20(vwx1321, vwx1331, app(app(ty_@2, cfd), cfe)) → new_esEs5(vwx1321, vwx1331, cfd, cfe)
new_esEs19(vwx1320, vwx1330, ty_Double) → new_esEs14(vwx1320, vwx1330)
new_esEs15(:(vwx1320, vwx1321), [], cbg) → False
new_esEs15([], :(vwx1330, vwx1331), cbg) → False
new_esEs18(vwx1320, vwx1330, app(app(ty_Either, cch), cda)) → new_esEs6(vwx1320, vwx1330, cch, cda)
new_esEs19(vwx1320, vwx1330, ty_Float) → new_esEs11(vwx1320, vwx1330)
new_esEs23(vwx1322, vwx1332, ty_Double) → new_esEs14(vwx1322, vwx1332)
new_esEs23(vwx1322, vwx1332, app(app(app(ty_@3, dag), dah), dba)) → new_esEs7(vwx1322, vwx1332, dag, dah, dba)
new_esEs21(vwx1320, vwx1330, app(ty_Maybe, cgh)) → new_esEs4(vwx1320, vwx1330, cgh)
new_esEs23(vwx1322, vwx1332, ty_Integer) → new_esEs8(vwx1322, vwx1332)
new_esEs23(vwx1322, vwx1332, app(ty_Ratio, dbc)) → new_esEs16(vwx1322, vwx1332, dbc)
new_esEs22(vwx1321, vwx1331, app(ty_Ratio, daa)) → new_esEs16(vwx1321, vwx1331, daa)
new_esEs6(Left(vwx1320), Right(vwx1330), cad, bha) → False
new_esEs6(Right(vwx1320), Left(vwx1330), cad, bha) → False
new_esEs18(vwx1320, vwx1330, ty_@0) → new_esEs13(vwx1320, vwx1330)
new_esEs19(vwx1320, vwx1330, app(ty_Maybe, cea)) → new_esEs4(vwx1320, vwx1330, cea)
new_esEs19(vwx1320, vwx1330, app(app(ty_@2, ceb), cec)) → new_esEs5(vwx1320, vwx1330, ceb, cec)
new_esEs19(vwx1320, vwx1330, app(ty_Ratio, cdh)) → new_esEs16(vwx1320, vwx1330, cdh)
new_esEs24(vwx1320, vwx1330, ty_Int) → new_esEs12(vwx1320, vwx1330)
new_esEs4(Just(vwx1320), Just(vwx1330), ty_Integer) → new_esEs8(vwx1320, vwx1330)
new_esEs4(Just(vwx1320), Just(vwx1330), ty_Float) → new_esEs11(vwx1320, vwx1330)
new_esEs19(vwx1320, vwx1330, ty_Integer) → new_esEs8(vwx1320, vwx1330)
new_esEs4(Just(vwx1320), Just(vwx1330), ty_Double) → new_esEs14(vwx1320, vwx1330)
new_esEs6(Right(vwx1320), Right(vwx1330), cad, ty_Ordering) → new_esEs9(vwx1320, vwx1330)
new_asAs(False, vwx152) → False
new_esEs18(vwx1320, vwx1330, app(ty_Ratio, ccd)) → new_esEs16(vwx1320, vwx1330, ccd)
new_esEs14(Double(vwx1320, vwx1321), Double(vwx1330, vwx1331)) → new_esEs12(new_sr(vwx1320, vwx1330), new_sr(vwx1321, vwx1331))
new_primEqNat0(Zero, Zero) → True
new_primMulInt(Neg(vwx300), Pos(vwx410)) → Neg(new_primMulNat0(vwx300, vwx410))
new_primMulInt(Pos(vwx300), Neg(vwx410)) → Neg(new_primMulNat0(vwx300, vwx410))
new_primMulNat0(Succ(vwx3000), Zero) → Zero
new_primMulNat0(Zero, Succ(vwx4100)) → Zero
new_esEs23(vwx1322, vwx1332, app(app(ty_Either, dbg), dbh)) → new_esEs6(vwx1322, vwx1332, dbg, dbh)
new_esEs25(vwx1321, vwx1331, ty_Integer) → new_esEs8(vwx1321, vwx1331)
new_esEs19(vwx1320, vwx1330, ty_Int) → new_esEs12(vwx1320, vwx1330)
new_esEs6(Right(vwx1320), Right(vwx1330), cad, app(ty_Ratio, cba)) → new_esEs16(vwx1320, vwx1330, cba)
new_esEs6(Left(vwx1320), Left(vwx1330), ty_Double, bha) → new_esEs14(vwx1320, vwx1330)
new_esEs6(Right(vwx1320), Right(vwx1330), cad, app(app(ty_Either, cbe), cbf)) → new_esEs6(vwx1320, vwx1330, cbe, cbf)
new_esEs17(False, False) → True
new_esEs17(True, False) → False
new_esEs17(False, True) → False
new_esEs5(@2(vwx1320, vwx1321), @2(vwx1330, vwx1331), cdb, cdc) → new_asAs(new_esEs19(vwx1320, vwx1330, cdb), new_esEs20(vwx1321, vwx1331, cdc))
new_esEs8(Integer(vwx1320), Integer(vwx1330)) → new_primEqInt(vwx1320, vwx1330)
new_esEs22(vwx1321, vwx1331, ty_Char) → new_esEs10(vwx1321, vwx1331)
new_esEs18(vwx1320, vwx1330, ty_Char) → new_esEs10(vwx1320, vwx1330)
new_esEs6(Right(vwx1320), Right(vwx1330), cad, ty_Bool) → new_esEs17(vwx1320, vwx1330)
new_esEs6(Right(vwx1320), Right(vwx1330), cad, app(ty_[], cah)) → new_esEs15(vwx1320, vwx1330, cah)
new_esEs18(vwx1320, vwx1330, app(app(ty_@2, ccf), ccg)) → new_esEs5(vwx1320, vwx1330, ccf, ccg)
new_sr(vwx30, vwx40) → new_primMulInt(vwx30, vwx40)
new_esEs20(vwx1321, vwx1331, app(ty_[], cfa)) → new_esEs15(vwx1321, vwx1331, cfa)
new_esEs23(vwx1322, vwx1332, app(ty_[], dbb)) → new_esEs15(vwx1322, vwx1332, dbb)
new_esEs16(:%(vwx1320, vwx1321), :%(vwx1330, vwx1331), dca) → new_asAs(new_esEs24(vwx1320, vwx1330, dca), new_esEs25(vwx1321, vwx1331, dca))
new_esEs6(Right(vwx1320), Right(vwx1330), cad, ty_Char) → new_esEs10(vwx1320, vwx1330)
new_esEs4(Just(vwx1320), Just(vwx1330), ty_Bool) → new_esEs17(vwx1320, vwx1330)
new_primPlusNat0(Succ(vwx2220), vwx4100) → Succ(Succ(new_primPlusNat1(vwx2220, vwx4100)))
new_esEs20(vwx1321, vwx1331, app(app(app(ty_@3, cef), ceg), ceh)) → new_esEs7(vwx1321, vwx1331, cef, ceg, ceh)
new_esEs20(vwx1321, vwx1331, ty_Bool) → new_esEs17(vwx1321, vwx1331)
new_esEs21(vwx1320, vwx1330, app(ty_Ratio, cgg)) → new_esEs16(vwx1320, vwx1330, cgg)
new_esEs23(vwx1322, vwx1332, ty_Int) → new_esEs12(vwx1322, vwx1332)
new_esEs20(vwx1321, vwx1331, ty_Ordering) → new_esEs9(vwx1321, vwx1331)
new_esEs21(vwx1320, vwx1330, ty_Ordering) → new_esEs9(vwx1320, vwx1330)
new_esEs9(EQ, EQ) → True
new_primEqInt(Neg(Succ(vwx13200)), Neg(Succ(vwx13300))) → new_primEqNat0(vwx13200, vwx13300)
new_esEs6(Right(vwx1320), Right(vwx1330), cad, app(app(app(ty_@3, cae), caf), cag)) → new_esEs7(vwx1320, vwx1330, cae, caf, cag)
new_primPlusNat1(Zero, Succ(vwx41000)) → Succ(vwx41000)
new_primPlusNat1(Succ(vwx22200), Zero) → Succ(vwx22200)
new_esEs20(vwx1321, vwx1331, ty_Int) → new_esEs12(vwx1321, vwx1331)
new_esEs9(LT, EQ) → False
new_esEs9(EQ, LT) → False
new_esEs6(Left(vwx1320), Left(vwx1330), ty_Integer, bha) → new_esEs8(vwx1320, vwx1330)
new_esEs21(vwx1320, vwx1330, ty_Double) → new_esEs14(vwx1320, vwx1330)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs22(vwx1321, vwx1331, app(app(ty_Either, dae), daf)) → new_esEs6(vwx1321, vwx1331, dae, daf)
new_esEs6(Right(vwx1320), Right(vwx1330), cad, ty_Int) → new_esEs12(vwx1320, vwx1330)
new_esEs19(vwx1320, vwx1330, ty_Bool) → new_esEs17(vwx1320, vwx1330)
new_esEs4(Just(vwx1320), Just(vwx1330), ty_Ordering) → new_esEs9(vwx1320, vwx1330)
new_esEs6(Right(vwx1320), Right(vwx1330), cad, ty_Integer) → new_esEs8(vwx1320, vwx1330)
new_primEqInt(Neg(Zero), Neg(Succ(vwx13300))) → False
new_primEqInt(Neg(Succ(vwx13200)), Neg(Zero)) → False
new_esEs22(vwx1321, vwx1331, ty_Integer) → new_esEs8(vwx1321, vwx1331)
new_esEs21(vwx1320, vwx1330, ty_Float) → new_esEs11(vwx1320, vwx1330)
new_esEs4(Just(vwx1320), Just(vwx1330), ty_@0) → new_esEs13(vwx1320, vwx1330)
new_esEs22(vwx1321, vwx1331, ty_@0) → new_esEs13(vwx1321, vwx1331)
new_esEs6(Left(vwx1320), Left(vwx1330), ty_Char, bha) → new_esEs10(vwx1320, vwx1330)
new_esEs22(vwx1321, vwx1331, ty_Int) → new_esEs12(vwx1321, vwx1331)
new_primPlusNat1(Zero, Zero) → Zero
new_asAs(True, vwx152) → vwx152
new_esEs21(vwx1320, vwx1330, ty_Integer) → new_esEs8(vwx1320, vwx1330)
new_primMulNat0(Succ(vwx3000), Succ(vwx4100)) → new_primPlusNat0(new_primMulNat0(vwx3000, Succ(vwx4100)), vwx4100)
new_esEs22(vwx1321, vwx1331, app(ty_Maybe, dab)) → new_esEs4(vwx1321, vwx1331, dab)
new_esEs18(vwx1320, vwx1330, ty_Double) → new_esEs14(vwx1320, vwx1330)
new_primEqInt(Pos(Succ(vwx13200)), Pos(Succ(vwx13300))) → new_primEqNat0(vwx13200, vwx13300)
new_esEs19(vwx1320, vwx1330, ty_Char) → new_esEs10(vwx1320, vwx1330)
new_esEs4(Just(vwx1320), Just(vwx1330), app(app(ty_Either, bgg), bgh)) → new_esEs6(vwx1320, vwx1330, bgg, bgh)
new_esEs4(Just(vwx1320), Just(vwx1330), app(app(ty_@2, bge), bgf)) → new_esEs5(vwx1320, vwx1330, bge, bgf)
new_esEs19(vwx1320, vwx1330, app(app(ty_Either, ced), cee)) → new_esEs6(vwx1320, vwx1330, ced, cee)
new_esEs6(Right(vwx1320), Right(vwx1330), cad, app(ty_Maybe, cbb)) → new_esEs4(vwx1320, vwx1330, cbb)
new_esEs4(Just(vwx1320), Just(vwx1330), app(app(app(ty_@3, bfg), bfh), bga)) → new_esEs7(vwx1320, vwx1330, bfg, bfh, bga)
new_primEqNat0(Succ(vwx13200), Succ(vwx13300)) → new_primEqNat0(vwx13200, vwx13300)
new_esEs4(Just(vwx1320), Just(vwx1330), ty_Char) → new_esEs10(vwx1320, vwx1330)
new_esEs20(vwx1321, vwx1331, ty_Double) → new_esEs14(vwx1321, vwx1331)
new_esEs6(Right(vwx1320), Right(vwx1330), cad, app(app(ty_@2, cbc), cbd)) → new_esEs5(vwx1320, vwx1330, cbc, cbd)
new_esEs9(LT, LT) → True
new_esEs18(vwx1320, vwx1330, app(ty_[], ccc)) → new_esEs15(vwx1320, vwx1330, ccc)
new_esEs20(vwx1321, vwx1331, ty_@0) → new_esEs13(vwx1321, vwx1331)
new_esEs15([], [], cbg) → True
new_primEqInt(Pos(Zero), Pos(Succ(vwx13300))) → False
new_primEqInt(Pos(Succ(vwx13200)), Pos(Zero)) → False
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_esEs19(vwx1320, vwx1330, app(ty_[], cdg)) → new_esEs15(vwx1320, vwx1330, cdg)
The set Q consists of the following terms:
new_esEs4(Just(x0), Just(x1), app(ty_[], x2))
new_esEs20(x0, x1, ty_Integer)
new_esEs23(x0, x1, app(ty_[], x2))
new_esEs13(@0, @0)
new_esEs22(x0, x1, ty_@0)
new_esEs23(x0, x1, ty_Char)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_esEs9(GT, GT)
new_esEs20(x0, x1, ty_Double)
new_primPlusNat0(Zero, x0)
new_primMulNat0(Zero, Succ(x0))
new_esEs21(x0, x1, ty_@0)
new_esEs6(Right(x0), Right(x1), x2, ty_@0)
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_esEs19(x0, x1, ty_Char)
new_esEs18(x0, x1, ty_Bool)
new_esEs21(x0, x1, ty_Ordering)
new_primEqInt(Neg(Zero), Pos(Zero))
new_primEqInt(Pos(Zero), Neg(Zero))
new_esEs6(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs4(Just(x0), Just(x1), app(ty_Maybe, x2))
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_esEs21(x0, x1, ty_Int)
new_esEs22(x0, x1, ty_Ordering)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_esEs6(Left(x0), Left(x1), ty_Double, x2)
new_esEs4(Just(x0), Just(x1), ty_Ordering)
new_esEs6(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs9(EQ, EQ)
new_esEs6(Right(x0), Right(x1), x2, ty_Double)
new_esEs6(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs19(x0, x1, ty_Bool)
new_primEqInt(Neg(Zero), Neg(Zero))
new_esEs19(x0, x1, ty_Integer)
new_esEs21(x0, x1, ty_Char)
new_esEs6(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs18(x0, x1, app(app(ty_@2, x2), x3))
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs14(Double(x0, x1), Double(x2, x3))
new_esEs21(x0, x1, ty_Float)
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_esEs19(x0, x1, ty_Ordering)
new_esEs18(x0, x1, app(ty_Ratio, x2))
new_esEs18(x0, x1, ty_Integer)
new_esEs11(Float(x0, x1), Float(x2, x3))
new_esEs23(x0, x1, ty_Ordering)
new_esEs21(x0, x1, ty_Double)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, ty_Integer)
new_esEs6(Right(x0), Right(x1), x2, ty_Char)
new_esEs6(Right(x0), Left(x1), x2, x3)
new_esEs6(Left(x0), Right(x1), x2, x3)
new_esEs4(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs4(Just(x0), Just(x1), ty_Double)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs9(GT, LT)
new_esEs9(LT, GT)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs6(Left(x0), Left(x1), ty_@0, x2)
new_esEs6(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs20(x0, x1, ty_Char)
new_esEs22(x0, x1, ty_Int)
new_esEs18(x0, x1, app(ty_Maybe, x2))
new_esEs6(Left(x0), Left(x1), ty_Float, x2)
new_esEs19(x0, x1, app(ty_Maybe, x2))
new_esEs6(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs22(x0, x1, ty_Bool)
new_esEs7(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs19(x0, x1, ty_@0)
new_esEs17(False, False)
new_esEs9(EQ, GT)
new_esEs9(GT, EQ)
new_esEs4(Nothing, Just(x0), x1)
new_esEs19(x0, x1, app(ty_Ratio, x2))
new_esEs19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs20(x0, x1, ty_Bool)
new_esEs6(Left(x0), Left(x1), ty_Integer, x2)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Right(x0), Right(x1), x2, ty_Float)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs18(x0, x1, app(ty_[], x2))
new_esEs23(x0, x1, ty_Bool)
new_esEs6(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs4(Just(x0), Just(x1), ty_Int)
new_esEs6(Right(x0), Right(x1), x2, ty_Int)
new_esEs23(x0, x1, ty_Double)
new_esEs18(x0, x1, ty_Ordering)
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_esEs4(Just(x0), Just(x1), ty_Integer)
new_asAs(False, x0)
new_esEs4(Just(x0), Just(x1), ty_Char)
new_primEqNat0(Succ(x0), Zero)
new_esEs24(x0, x1, ty_Integer)
new_primMulNat0(Succ(x0), Succ(x1))
new_primPlusNat1(Succ(x0), Zero)
new_primEqNat0(Zero, Zero)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_esEs15(:(x0, x1), [], x2)
new_primPlusNat1(Zero, Succ(x0))
new_esEs18(x0, x1, ty_Double)
new_esEs4(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_sr(x0, x1)
new_primMulInt(Pos(x0), Pos(x1))
new_primMulNat0(Zero, Zero)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_esEs18(x0, x1, ty_Int)
new_esEs18(x0, x1, app(app(ty_Either, x2), x3))
new_primMulNat0(Succ(x0), Zero)
new_esEs20(x0, x1, ty_Ordering)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_esEs25(x0, x1, ty_Integer)
new_esEs21(x0, x1, app(ty_[], x2))
new_esEs6(Right(x0), Right(x1), x2, ty_Integer)
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs6(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs22(x0, x1, app(ty_[], x2))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_esEs12(x0, x1)
new_esEs4(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs25(x0, x1, ty_Int)
new_asAs(True, x0)
new_esEs21(x0, x1, ty_Bool)
new_esEs5(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs6(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs23(x0, x1, ty_@0)
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_esEs9(EQ, LT)
new_esEs9(LT, EQ)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs18(x0, x1, ty_Char)
new_esEs4(Nothing, Nothing, x0)
new_esEs4(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, ty_Char)
new_esEs19(x0, x1, ty_Float)
new_esEs20(x0, x1, ty_Float)
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs22(x0, x1, ty_Float)
new_primEqNat0(Zero, Succ(x0))
new_esEs6(Left(x0), Left(x1), ty_Bool, x2)
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs21(x0, x1, ty_Integer)
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs22(x0, x1, ty_Double)
new_esEs4(Just(x0), Just(x1), ty_@0)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_esEs16(:%(x0, x1), :%(x2, x3), x4)
new_esEs18(x0, x1, ty_Float)
new_esEs8(Integer(x0), Integer(x1))
new_esEs18(x0, x1, ty_@0)
new_esEs10(Char(x0), Char(x1))
new_esEs6(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs6(Left(x0), Left(x1), ty_Int, x2)
new_esEs4(Just(x0), Just(x1), ty_Bool)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_esEs17(False, True)
new_esEs17(True, False)
new_esEs6(Left(x0), Left(x1), ty_Char, x2)
new_esEs23(x0, x1, ty_Float)
new_esEs23(x0, x1, ty_Int)
new_primPlusNat1(Zero, Zero)
new_primPlusNat0(Succ(x0), x1)
new_esEs19(x0, x1, ty_Int)
new_esEs20(x0, x1, ty_Int)
new_esEs15([], [], x0)
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs4(Just(x0), Just(x1), ty_Float)
new_esEs4(Just(x0), Nothing, x1)
new_esEs6(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs6(Right(x0), Right(x1), x2, ty_Bool)
new_esEs6(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs19(x0, x1, app(ty_[], x2))
new_primEqInt(Pos(Zero), Pos(Zero))
new_esEs17(True, True)
new_esEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs15([], :(x0, x1), x2)
new_esEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs20(x0, x1, app(ty_[], x2))
new_esEs19(x0, x1, ty_Double)
new_esEs15(:(x0, x1), :(x2, x3), x4)
new_esEs24(x0, x1, ty_Int)
new_esEs22(x0, x1, ty_Integer)
new_esEs9(LT, LT)
new_esEs20(x0, x1, ty_@0)
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:
- new_lt0(vwx30, vwx40, ge, gf) → new_compare21(vwx30, vwx40, new_esEs5(vwx30, vwx40, ge, gf), ge, gf)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 4, 4 >= 5
- new_ltEs(Just(vwx300), Just(vwx400), app(app(ty_@2, bb), bc)) → new_ltEs0(vwx300, vwx400, bb, bc)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
- new_ltEs(Just(vwx300), Just(vwx400), app(app(ty_Either, be), bf)) → new_ltEs2(vwx300, vwx400, be, bf)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
- new_compare23(vwx30, vwx40, False, bfc, bfd, bfe) → new_ltEs3(vwx30, vwx40, bfc, bfd, bfe)
The graph contains the following edges 1 >= 1, 2 >= 2, 4 >= 3, 5 >= 4, 6 >= 5
- new_primCompAux(vwx30, vwx40, vwx31, vwx41, app(app(app(ty_@3, ga), gb), gc)) → new_compare3(vwx30, vwx40, ga, gb, gc)
The graph contains the following edges 1 >= 1, 2 >= 2, 5 > 3, 5 > 4, 5 > 5
- new_ltEs3(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), bbe, bbf, app(app(ty_@2, bbh), bca)) → new_ltEs0(vwx302, vwx402, bbh, bca)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4
- new_ltEs3(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), bbe, bbf, app(app(ty_Either, bcc), bcd)) → new_ltEs2(vwx302, vwx402, bcc, bcd)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4
- new_ltEs0(@2(vwx300, vwx301), @2(vwx400, vwx401), app(app(app(ty_@3, ed), ee), ef), df) → new_lt3(vwx300, vwx400, ed, ee, ef)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
- new_ltEs(Just(vwx300), Just(vwx400), app(app(app(ty_@3, bg), bh), ca)) → new_ltEs3(vwx300, vwx400, bg, bh, ca)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
- new_ltEs3(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), bbe, bbf, app(app(app(ty_@3, bce), bcf), bcg)) → new_ltEs3(vwx302, vwx402, bce, bcf, bcg)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4, 5 > 5
- new_lt2(vwx30, vwx40, gg, gh) → new_compare22(vwx30, vwx40, new_esEs6(vwx30, vwx40, gg, gh), gg, gh)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 4, 4 >= 5
- new_ltEs(Just(vwx300), Just(vwx400), app(ty_[], bd)) → new_ltEs1(vwx300, vwx400, bd)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
- new_ltEs(Just(vwx300), Just(vwx400), app(ty_Maybe, ba)) → new_ltEs(vwx300, vwx400, ba)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
- new_ltEs3(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), bbe, bbf, app(ty_[], bcb)) → new_ltEs1(vwx302, vwx402, bcb)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3
- new_compare(:(vwx300, vwx301), :(vwx400, vwx401), eh) → new_primCompAux(vwx300, vwx400, vwx301, vwx401, eh)
The graph contains the following edges 1 > 1, 2 > 2, 1 > 3, 2 > 4, 3 >= 5
- new_compare3(vwx30, vwx40, bfc, bfd, bfe) → new_compare23(vwx30, vwx40, new_esEs7(vwx30, vwx40, bfc, bfd, bfe), bfc, bfd, bfe)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 4, 4 >= 5, 5 >= 6
- new_lt1(:(vwx300, vwx301), :(vwx400, vwx401), eh) → new_primCompAux(vwx300, vwx400, vwx301, vwx401, eh)
The graph contains the following edges 1 > 1, 2 > 2, 1 > 3, 2 > 4, 3 >= 5
- new_ltEs0(@2(vwx300, vwx301), @2(vwx400, vwx401), cb, app(app(app(ty_@3, db), dc), dd)) → new_ltEs3(vwx301, vwx401, db, dc, dd)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5
- new_ltEs0(@2(vwx300, vwx301), @2(vwx400, vwx401), cb, app(ty_[], cf)) → new_ltEs1(vwx301, vwx401, cf)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
- new_ltEs1(vwx30, vwx40, eg) → new_compare(vwx30, vwx40, eg)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3
- new_ltEs0(@2(vwx300, vwx301), @2(vwx400, vwx401), cb, app(app(ty_@2, cd), ce)) → new_ltEs0(vwx301, vwx401, cd, ce)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
- new_compare21(vwx30, vwx40, False, ge, gf) → new_ltEs0(vwx30, vwx40, ge, gf)
The graph contains the following edges 1 >= 1, 2 >= 2, 4 >= 3, 5 >= 4
- new_ltEs0(@2(vwx300, vwx301), @2(vwx400, vwx401), cb, app(app(ty_Either, cg), da)) → new_ltEs2(vwx301, vwx401, cg, da)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
- new_compare22(vwx30, vwx40, False, gg, gh) → new_ltEs2(vwx30, vwx40, gg, gh)
The graph contains the following edges 1 >= 1, 2 >= 2, 4 >= 3, 5 >= 4
- new_ltEs3(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), bbe, bbf, app(ty_Maybe, bbg)) → new_ltEs(vwx302, vwx402, bbg)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3
- new_ltEs0(@2(vwx300, vwx301), @2(vwx400, vwx401), cb, app(ty_Maybe, cc)) → new_ltEs(vwx301, vwx401, cc)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
- new_compare20(vwx30, vwx40, False, gd) → new_ltEs(vwx30, vwx40, gd)
The graph contains the following edges 1 >= 1, 2 >= 2, 4 >= 3
- new_compare1(vwx30, vwx40, ge, gf) → new_compare21(vwx30, vwx40, new_esEs5(vwx30, vwx40, ge, gf), ge, gf)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 4, 4 >= 5
- new_ltEs0(@2(vwx300, vwx301), @2(vwx400, vwx401), app(ty_[], ea), df) → new_lt1(vwx300, vwx400, ea)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
- new_primCompAux(vwx30, vwx40, vwx31, vwx41, app(app(ty_Either, fg), fh)) → new_compare2(vwx30, vwx40, fg, fh)
The graph contains the following edges 1 >= 1, 2 >= 2, 5 > 3, 5 > 4
- new_lt(vwx30, vwx40, gd) → new_compare20(vwx30, vwx40, new_esEs4(vwx30, vwx40, gd), gd)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 4
- new_ltEs0(@2(vwx300, vwx301), @2(vwx400, vwx401), app(ty_Maybe, de), df) → new_lt(vwx300, vwx400, de)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
- new_primCompAux(vwx30, vwx40, vwx31, vwx41, app(app(ty_@2, fc), fd)) → new_compare1(vwx30, vwx40, fc, fd)
The graph contains the following edges 1 >= 1, 2 >= 2, 5 > 3, 5 > 4
- new_primCompAux(vwx30, vwx40, vwx31, vwx41, app(ty_Maybe, fb)) → new_compare0(vwx30, vwx40, fb)
The graph contains the following edges 1 >= 1, 2 >= 2, 5 > 3
- new_lt3(vwx30, vwx40, bfc, bfd, bfe) → new_compare23(vwx30, vwx40, new_esEs7(vwx30, vwx40, bfc, bfd, bfe), bfc, bfd, bfe)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 4, 4 >= 5, 5 >= 6
- new_compare2(vwx30, vwx40, gg, gh) → new_compare22(vwx30, vwx40, new_esEs6(vwx30, vwx40, gg, gh), gg, gh)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 4, 4 >= 5
- new_compare0(vwx30, vwx40, gd) → new_compare20(vwx30, vwx40, new_esEs4(vwx30, vwx40, gd), gd)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 4
- new_ltEs0(@2(vwx300, vwx301), @2(vwx400, vwx401), app(app(ty_Either, eb), ec), df) → new_lt2(vwx300, vwx400, eb, ec)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
- new_ltEs0(@2(vwx300, vwx301), @2(vwx400, vwx401), app(app(ty_@2, dg), dh), df) → new_lt0(vwx300, vwx400, dg, dh)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
- new_ltEs2(Left(vwx300), Left(vwx400), app(app(ty_@2, hc), hd), hb) → new_ltEs0(vwx300, vwx400, hc, hd)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
- new_ltEs2(Right(vwx300), Right(vwx400), bac, app(app(ty_@2, bae), baf)) → new_ltEs0(vwx300, vwx400, bae, baf)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
- new_ltEs2(Left(vwx300), Left(vwx400), app(app(ty_Either, hf), hg), hb) → new_ltEs2(vwx300, vwx400, hf, hg)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
- new_ltEs2(Right(vwx300), Right(vwx400), bac, app(app(ty_Either, bah), bba)) → new_ltEs2(vwx300, vwx400, bah, bba)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
- new_ltEs3(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), app(app(app(ty_@3, beh), bfa), bfb), bbf, bda) → new_lt3(vwx300, vwx400, beh, bfa, bfb)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
- new_ltEs3(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), bbe, app(app(app(ty_@3, bdg), bdh), bea), bda) → new_lt3(vwx301, vwx401, bdg, bdh, bea)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5
- new_ltEs3(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), app(ty_[], bee), bbf, bda) → new_lt1(vwx300, vwx400, bee)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
- new_ltEs3(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), bbe, app(ty_[], bdd), bda) → new_lt1(vwx301, vwx401, bdd)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
- new_ltEs3(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), app(ty_Maybe, beb), bbf, bda) → new_lt(vwx300, vwx400, beb)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
- new_ltEs3(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), bbe, app(ty_Maybe, bch), bda) → new_lt(vwx301, vwx401, bch)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
- new_ltEs3(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), bbe, app(app(ty_Either, bde), bdf), bda) → new_lt2(vwx301, vwx401, bde, bdf)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
- new_ltEs3(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), app(app(ty_Either, bef), beg), bbf, bda) → new_lt2(vwx300, vwx400, bef, beg)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
- new_ltEs3(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), app(app(ty_@2, bec), bed), bbf, bda) → new_lt0(vwx300, vwx400, bec, bed)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
- new_ltEs3(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), bbe, app(app(ty_@2, bdb), bdc), bda) → new_lt0(vwx301, vwx401, bdb, bdc)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
- new_ltEs2(Left(vwx300), Left(vwx400), app(app(app(ty_@3, hh), baa), bab), hb) → new_ltEs3(vwx300, vwx400, hh, baa, bab)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
- new_ltEs2(Right(vwx300), Right(vwx400), bac, app(app(app(ty_@3, bbb), bbc), bbd)) → new_ltEs3(vwx300, vwx400, bbb, bbc, bbd)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5
- new_ltEs2(Right(vwx300), Right(vwx400), bac, app(ty_[], bag)) → new_ltEs1(vwx300, vwx400, bag)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
- new_ltEs2(Left(vwx300), Left(vwx400), app(ty_[], he), hb) → new_ltEs1(vwx300, vwx400, he)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
- new_ltEs2(Right(vwx300), Right(vwx400), bac, app(ty_Maybe, bad)) → new_ltEs(vwx300, vwx400, bad)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
- new_ltEs2(Left(vwx300), Left(vwx400), app(ty_Maybe, ha), hb) → new_ltEs(vwx300, vwx400, ha)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
- new_primCompAux(vwx30, vwx40, vwx31, vwx41, app(ty_[], ff)) → new_compare(vwx30, vwx40, ff)
The graph contains the following edges 1 >= 1, 2 >= 2, 5 > 3
- new_primCompAux(vwx30, vwx40, vwx31, vwx41, fa) → new_compare(vwx31, vwx41, fa)
The graph contains the following edges 3 >= 1, 4 >= 2, 5 >= 3