YES 4.138
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
↳ BR
mainModule List
|
| ((nub :: Eq a => [Maybe a] -> [Maybe a]) :: Eq a => [Maybe a] -> [Maybe a]) |
module List where
| | import qualified Maybe
import qualified Prelude
|
| | nub :: Eq a => [a] -> [a]
| nub | l | = |
| nub' l [] | where |
| nub' | [] _ | = | [] |
| nub' | (x : xs) ls | |
| | | x `elem` ls | = |
|
| | | otherwise | = |
|
|
|
|
|
|
module Maybe where
| | import qualified List
import qualified Prelude
|
Replaced joker patterns by fresh variables and removed binding patterns.
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
mainModule List
|
| ((nub :: Eq a => [Maybe a] -> [Maybe a]) :: Eq a => [Maybe a] -> [Maybe a]) |
module List where
| | import qualified Maybe
import qualified Prelude
|
| | nub :: Eq a => [a] -> [a]
| nub | l | = |
| nub' l [] | where |
| nub' | [] vw | = | [] |
| nub' | (x : xs) ls | |
| | | x `elem` ls | = |
|
| | | otherwise | = |
|
|
|
|
|
|
module Maybe where
| | import qualified List
import qualified Prelude
|
Cond Reductions:
The following Function with conditions
| nub' | [] vw | = [] |
| nub' | (x : xs) ls |
| | | x `elem` ls | |
| | | otherwise | |
|
is transformed to
| nub' | [] vw | = nub'3 [] vw |
| nub' | (x : xs) ls | = nub'2 (x : xs) ls |
| nub'0 | x xs ls True | = x : nub' xs (x : ls) |
| nub'1 | x xs ls True | = nub' xs ls |
| nub'1 | x xs ls False | = nub'0 x xs ls otherwise |
| nub'2 | (x : xs) ls | = nub'1 x xs ls (x `elem` ls) |
| nub'3 | [] vw | = [] |
| nub'3 | xz yu | = nub'2 xz yu |
The following Function with conditions
is transformed to
| undefined0 | True | = undefined |
| undefined1 | | = undefined0 False |
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
mainModule List
|
| ((nub :: Eq a => [Maybe a] -> [Maybe a]) :: Eq a => [Maybe a] -> [Maybe a]) |
module List where
| | import qualified Maybe
import qualified Prelude
|
| | nub :: Eq a => [a] -> [a]
| nub | l | = |
| nub' l [] | where |
| nub' | [] vw | = | nub'3 [] vw |
| nub' | (x : xs) ls | = | nub'2 (x : xs) ls |
|
| nub'0 | x xs ls True | = | x : nub' xs (x : ls) |
|
| nub'1 | x xs ls True | = | nub' xs ls |
| nub'1 | x xs ls False | = | nub'0 x xs ls otherwise |
|
| nub'2 | (x : xs) ls | = | nub'1 x xs ls (x `elem` ls) |
|
| nub'3 | [] vw | = | [] |
| nub'3 | xz yu | = | nub'2 xz yu |
|
|
|
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module Maybe where
| | import qualified List
import qualified Prelude
|
Let/Where Reductions:
The bindings of the following Let/Where expression
| nub' l [] |
| where |
| nub' | [] vw | = nub'3 [] vw |
| nub' | (x : xs) ls | = nub'2 (x : xs) ls |
|
|
| nub'0 | x xs ls True | = x : nub' xs (x : ls) |
|
|
| nub'1 | x xs ls True | = nub' xs ls |
| nub'1 | x xs ls False | = nub'0 x xs ls otherwise |
|
|
| nub'2 | (x : xs) ls | = nub'1 x xs ls (x `elem` ls) |
|
|
| nub'3 | [] vw | = [] |
| nub'3 | xz yu | = nub'2 xz yu |
|
are unpacked to the following functions on top level
| nubNub'0 | x xs ls True | = x : nubNub' xs (x : ls) |
| nubNub'2 | (x : xs) ls | = nubNub'1 x xs ls (x `elem` ls) |
| nubNub'3 | [] vw | = [] |
| nubNub'3 | xz yu | = nubNub'2 xz yu |
| nubNub' | [] vw | = nubNub'3 [] vw |
| nubNub' | (x : xs) ls | = nubNub'2 (x : xs) ls |
| nubNub'1 | x xs ls True | = nubNub' xs ls |
| nubNub'1 | x xs ls False | = nubNub'0 x xs ls otherwise |
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ Narrow
mainModule List
|
| (nub :: Eq a => [Maybe a] -> [Maybe a]) |
module List where
| | import qualified Maybe
import qualified Prelude
|
| | nub :: Eq a => [a] -> [a]
|
| |
| nubNub' | [] vw | = | nubNub'3 [] vw |
| nubNub' | (x : xs) ls | = | nubNub'2 (x : xs) ls |
|
| |
| nubNub'0 | x xs ls True | = | x : nubNub' xs (x : ls) |
|
| |
| nubNub'1 | x xs ls True | = | nubNub' xs ls |
| nubNub'1 | x xs ls False | = | nubNub'0 x xs ls otherwise |
|
| |
| nubNub'2 | (x : xs) ls | = | nubNub'1 x xs ls (x `elem` ls) |
|
| |
| nubNub'3 | [] vw | = | [] |
| nubNub'3 | xz yu | = | nubNub'2 xz yu |
|
module Maybe where
| | import qualified List
import qualified Prelude
|
Haskell To QDPs
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDPSizeChangeProof
↳ QDP
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_primPlusNat(Succ(yv19500), Succ(yv1671000)) → new_primPlusNat(yv19500, yv1671000)
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(yv19500), Succ(yv1671000)) → new_primPlusNat(yv19500, yv1671000)
The graph contains the following edges 1 > 1, 2 > 2
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDPSizeChangeProof
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_primMulNat(Succ(yv163100), Succ(yv167100)) → new_primMulNat(yv163100, Succ(yv167100))
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(yv163100), Succ(yv167100)) → new_primMulNat(yv163100, Succ(yv167100))
The graph contains the following edges 1 > 1, 2 >= 2
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDPSizeChangeProof
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_primEqNat(Succ(yv16300), Succ(yv16700)) → new_primEqNat(yv16300, yv16700)
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(yv16300), Succ(yv16700)) → new_primEqNat(yv16300, yv16700)
The graph contains the following edges 1 > 1, 2 > 2
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDPSizeChangeProof
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_esEs1(@3(yv1630, yv1631, yv1632), @3(yv1670, yv1671, yv1672), gc, app(ty_Maybe, gd), fa) → new_esEs(yv1631, yv1671, gd)
new_esEs3(:(yv1630, yv1631), :(yv1670, yv1671), app(app(ty_@2, bdc), bdd)) → new_esEs0(yv1630, yv1670, bdc, bdd)
new_esEs1(@3(yv1630, yv1631, yv1632), @3(yv1670, yv1671, yv1672), gc, app(app(app(ty_@3, gg), gh), ha), fa) → new_esEs1(yv1631, yv1671, gg, gh, ha)
new_esEs1(@3(yv1630, yv1631, yv1632), @3(yv1670, yv1671, yv1672), gc, eh, app(app(ty_Either, bac), bad)) → new_esEs2(yv1632, yv1672, bac, bad)
new_esEs3(:(yv1630, yv1631), :(yv1670, yv1671), app(ty_[], beb)) → new_esEs3(yv1630, yv1670, beb)
new_esEs2(Left(yv1630), Left(yv1670), app(app(ty_@2, bah), bba), bag) → new_esEs0(yv1630, yv1670, bah, bba)
new_esEs1(@3(yv1630, yv1631, yv1632), @3(yv1670, yv1671, yv1672), app(app(ty_Either, fh), ga), eh, fa) → new_esEs2(yv1630, yv1670, fh, ga)
new_esEs0(@2(yv1630, yv1631), @2(yv1670, yv1671), app(app(ty_Either, db), dc), cc) → new_esEs2(yv1630, yv1670, db, dc)
new_esEs1(@3(yv1630, yv1631, yv1632), @3(yv1670, yv1671, yv1672), gc, eh, app(ty_[], bae)) → new_esEs3(yv1632, yv1672, bae)
new_esEs(Just(yv1630), Just(yv1670), app(app(ty_Either, bg), bh)) → new_esEs2(yv1630, yv1670, bg, bh)
new_esEs(Just(yv1630), Just(yv1670), app(ty_[], ca)) → new_esEs3(yv1630, yv1670, ca)
new_esEs0(@2(yv1630, yv1631), @2(yv1670, yv1671), de, app(app(app(ty_@3, ea), eb), ec)) → new_esEs1(yv1631, yv1671, ea, eb, ec)
new_esEs1(@3(yv1630, yv1631, yv1632), @3(yv1670, yv1671, yv1672), gc, eh, app(app(app(ty_@3, hh), baa), bab)) → new_esEs1(yv1632, yv1672, hh, baa, bab)
new_esEs2(Left(yv1630), Left(yv1670), app(app(ty_Either, bbe), bbf), bag) → new_esEs2(yv1630, yv1670, bbe, bbf)
new_esEs1(@3(yv1630, yv1631, yv1632), @3(yv1670, yv1671, yv1672), gc, eh, app(app(ty_@2, hf), hg)) → new_esEs0(yv1632, yv1672, hf, hg)
new_esEs(Just(yv1630), Just(yv1670), app(ty_Maybe, ba)) → new_esEs(yv1630, yv1670, ba)
new_esEs0(@2(yv1630, yv1631), @2(yv1670, yv1671), de, app(ty_[], ef)) → new_esEs3(yv1631, yv1671, ef)
new_esEs0(@2(yv1630, yv1631), @2(yv1670, yv1671), app(ty_[], dd), cc) → new_esEs3(yv1630, yv1670, dd)
new_esEs1(@3(yv1630, yv1631, yv1632), @3(yv1670, yv1671, yv1672), gc, app(app(ty_Either, hb), hc), fa) → new_esEs2(yv1631, yv1671, hb, hc)
new_esEs1(@3(yv1630, yv1631, yv1632), @3(yv1670, yv1671, yv1672), app(app(ty_@2, fb), fc), eh, fa) → new_esEs0(yv1630, yv1670, fb, fc)
new_esEs2(Right(yv1630), Right(yv1670), bbh, app(app(ty_@2, bcb), bcc)) → new_esEs0(yv1630, yv1670, bcb, bcc)
new_esEs1(@3(yv1630, yv1631, yv1632), @3(yv1670, yv1671, yv1672), app(ty_[], gb), eh, fa) → new_esEs3(yv1630, yv1670, gb)
new_esEs3(:(yv1630, yv1631), :(yv1670, yv1671), bec) → new_esEs3(yv1631, yv1671, bec)
new_esEs1(@3(yv1630, yv1631, yv1632), @3(yv1670, yv1671, yv1672), app(ty_Maybe, eg), eh, fa) → new_esEs(yv1630, yv1670, eg)
new_esEs2(Right(yv1630), Right(yv1670), bbh, app(app(app(ty_@3, bcd), bce), bcf)) → new_esEs1(yv1630, yv1670, bcd, bce, bcf)
new_esEs2(Left(yv1630), Left(yv1670), app(ty_[], bbg), bag) → new_esEs3(yv1630, yv1670, bbg)
new_esEs2(Left(yv1630), Left(yv1670), app(ty_Maybe, baf), bag) → new_esEs(yv1630, yv1670, baf)
new_esEs1(@3(yv1630, yv1631, yv1632), @3(yv1670, yv1671, yv1672), gc, app(ty_[], hd), fa) → new_esEs3(yv1631, yv1671, hd)
new_esEs1(@3(yv1630, yv1631, yv1632), @3(yv1670, yv1671, yv1672), app(app(app(ty_@3, fd), ff), fg), eh, fa) → new_esEs1(yv1630, yv1670, fd, ff, fg)
new_esEs(Just(yv1630), Just(yv1670), app(app(ty_@2, bb), bc)) → new_esEs0(yv1630, yv1670, bb, bc)
new_esEs2(Left(yv1630), Left(yv1670), app(app(app(ty_@3, bbb), bbc), bbd), bag) → new_esEs1(yv1630, yv1670, bbb, bbc, bbd)
new_esEs0(@2(yv1630, yv1631), @2(yv1670, yv1671), de, app(app(ty_Either, ed), ee)) → new_esEs2(yv1631, yv1671, ed, ee)
new_esEs2(Right(yv1630), Right(yv1670), bbh, app(ty_Maybe, bca)) → new_esEs(yv1630, yv1670, bca)
new_esEs0(@2(yv1630, yv1631), @2(yv1670, yv1671), app(ty_Maybe, cb), cc) → new_esEs(yv1630, yv1670, cb)
new_esEs2(Right(yv1630), Right(yv1670), bbh, app(app(ty_Either, bcg), bch)) → new_esEs2(yv1630, yv1670, bcg, bch)
new_esEs0(@2(yv1630, yv1631), @2(yv1670, yv1671), de, app(ty_Maybe, df)) → new_esEs(yv1631, yv1671, df)
new_esEs0(@2(yv1630, yv1631), @2(yv1670, yv1671), app(app(ty_@2, cd), ce), cc) → new_esEs0(yv1630, yv1670, cd, ce)
new_esEs2(Right(yv1630), Right(yv1670), bbh, app(ty_[], bda)) → new_esEs3(yv1630, yv1670, bda)
new_esEs3(:(yv1630, yv1631), :(yv1670, yv1671), app(app(ty_Either, bdh), bea)) → new_esEs2(yv1630, yv1670, bdh, bea)
new_esEs0(@2(yv1630, yv1631), @2(yv1670, yv1671), app(app(app(ty_@3, cf), cg), da), cc) → new_esEs1(yv1630, yv1670, cf, cg, da)
new_esEs1(@3(yv1630, yv1631, yv1632), @3(yv1670, yv1671, yv1672), gc, app(app(ty_@2, ge), gf), fa) → new_esEs0(yv1631, yv1671, ge, gf)
new_esEs0(@2(yv1630, yv1631), @2(yv1670, yv1671), de, app(app(ty_@2, dg), dh)) → new_esEs0(yv1631, yv1671, dg, dh)
new_esEs(Just(yv1630), Just(yv1670), app(app(app(ty_@3, bd), be), bf)) → new_esEs1(yv1630, yv1670, bd, be, bf)
new_esEs3(:(yv1630, yv1631), :(yv1670, yv1671), app(ty_Maybe, bdb)) → new_esEs(yv1630, yv1670, bdb)
new_esEs3(:(yv1630, yv1631), :(yv1670, yv1671), app(app(app(ty_@3, bde), bdf), bdg)) → new_esEs1(yv1630, yv1670, bde, bdf, bdg)
new_esEs1(@3(yv1630, yv1631, yv1632), @3(yv1670, yv1671, yv1672), gc, eh, app(ty_Maybe, he)) → new_esEs(yv1632, yv1672, he)
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_esEs(Just(yv1630), Just(yv1670), app(ty_[], ca)) → new_esEs3(yv1630, yv1670, ca)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
- new_esEs(Just(yv1630), Just(yv1670), app(app(app(ty_@3, bd), be), bf)) → new_esEs1(yv1630, yv1670, bd, be, bf)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
- new_esEs3(:(yv1630, yv1631), :(yv1670, yv1671), app(app(app(ty_@3, bde), bdf), bdg)) → new_esEs1(yv1630, yv1670, bde, bdf, bdg)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
- new_esEs(Just(yv1630), Just(yv1670), app(app(ty_Either, bg), bh)) → new_esEs2(yv1630, yv1670, bg, bh)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
- new_esEs3(:(yv1630, yv1631), :(yv1670, yv1671), app(app(ty_Either, bdh), bea)) → new_esEs2(yv1630, yv1670, bdh, bea)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
- new_esEs(Just(yv1630), Just(yv1670), app(app(ty_@2, bb), bc)) → new_esEs0(yv1630, yv1670, bb, bc)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
- new_esEs(Just(yv1630), Just(yv1670), app(ty_Maybe, ba)) → new_esEs(yv1630, yv1670, ba)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
- new_esEs3(:(yv1630, yv1631), :(yv1670, yv1671), app(app(ty_@2, bdc), bdd)) → new_esEs0(yv1630, yv1670, bdc, bdd)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
- new_esEs3(:(yv1630, yv1631), :(yv1670, yv1671), app(ty_Maybe, bdb)) → new_esEs(yv1630, yv1670, bdb)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
- new_esEs0(@2(yv1630, yv1631), @2(yv1670, yv1671), de, app(ty_[], ef)) → new_esEs3(yv1631, yv1671, ef)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
- new_esEs0(@2(yv1630, yv1631), @2(yv1670, yv1671), app(ty_[], dd), cc) → new_esEs3(yv1630, yv1670, dd)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
- new_esEs0(@2(yv1630, yv1631), @2(yv1670, yv1671), de, app(app(app(ty_@3, ea), eb), ec)) → new_esEs1(yv1631, yv1671, ea, eb, ec)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5
- new_esEs0(@2(yv1630, yv1631), @2(yv1670, yv1671), app(app(app(ty_@3, cf), cg), da), cc) → new_esEs1(yv1630, yv1670, cf, cg, da)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
- new_esEs0(@2(yv1630, yv1631), @2(yv1670, yv1671), app(app(ty_Either, db), dc), cc) → new_esEs2(yv1630, yv1670, db, dc)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
- new_esEs0(@2(yv1630, yv1631), @2(yv1670, yv1671), de, app(app(ty_Either, ed), ee)) → new_esEs2(yv1631, yv1671, ed, ee)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
- new_esEs0(@2(yv1630, yv1631), @2(yv1670, yv1671), app(app(ty_@2, cd), ce), cc) → new_esEs0(yv1630, yv1670, cd, ce)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
- new_esEs0(@2(yv1630, yv1631), @2(yv1670, yv1671), de, app(app(ty_@2, dg), dh)) → new_esEs0(yv1631, yv1671, dg, dh)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
- new_esEs0(@2(yv1630, yv1631), @2(yv1670, yv1671), app(ty_Maybe, cb), cc) → new_esEs(yv1630, yv1670, cb)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
- new_esEs0(@2(yv1630, yv1631), @2(yv1670, yv1671), de, app(ty_Maybe, df)) → new_esEs(yv1631, yv1671, df)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
- new_esEs1(@3(yv1630, yv1631, yv1632), @3(yv1670, yv1671, yv1672), gc, eh, app(ty_[], bae)) → new_esEs3(yv1632, yv1672, bae)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3
- new_esEs1(@3(yv1630, yv1631, yv1632), @3(yv1670, yv1671, yv1672), app(ty_[], gb), eh, fa) → new_esEs3(yv1630, yv1670, gb)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
- new_esEs1(@3(yv1630, yv1631, yv1632), @3(yv1670, yv1671, yv1672), gc, app(ty_[], hd), fa) → new_esEs3(yv1631, yv1671, hd)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
- new_esEs2(Left(yv1630), Left(yv1670), app(ty_[], bbg), bag) → new_esEs3(yv1630, yv1670, bbg)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
- new_esEs2(Right(yv1630), Right(yv1670), bbh, app(ty_[], bda)) → new_esEs3(yv1630, yv1670, bda)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
- new_esEs3(:(yv1630, yv1631), :(yv1670, yv1671), app(ty_[], beb)) → new_esEs3(yv1630, yv1670, beb)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
- new_esEs3(:(yv1630, yv1631), :(yv1670, yv1671), bec) → new_esEs3(yv1631, yv1671, bec)
The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3
- new_esEs1(@3(yv1630, yv1631, yv1632), @3(yv1670, yv1671, yv1672), gc, app(app(app(ty_@3, gg), gh), ha), fa) → new_esEs1(yv1631, yv1671, gg, gh, ha)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5
- new_esEs1(@3(yv1630, yv1631, yv1632), @3(yv1670, yv1671, yv1672), gc, eh, app(app(app(ty_@3, hh), baa), bab)) → new_esEs1(yv1632, yv1672, hh, baa, bab)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4, 5 > 5
- new_esEs1(@3(yv1630, yv1631, yv1632), @3(yv1670, yv1671, yv1672), app(app(app(ty_@3, fd), ff), fg), eh, fa) → new_esEs1(yv1630, yv1670, fd, ff, fg)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
- new_esEs2(Right(yv1630), Right(yv1670), bbh, app(app(app(ty_@3, bcd), bce), bcf)) → new_esEs1(yv1630, yv1670, bcd, bce, bcf)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5
- new_esEs2(Left(yv1630), Left(yv1670), app(app(app(ty_@3, bbb), bbc), bbd), bag) → new_esEs1(yv1630, yv1670, bbb, bbc, bbd)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
- new_esEs1(@3(yv1630, yv1631, yv1632), @3(yv1670, yv1671, yv1672), gc, eh, app(app(ty_Either, bac), bad)) → new_esEs2(yv1632, yv1672, bac, bad)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4
- new_esEs1(@3(yv1630, yv1631, yv1632), @3(yv1670, yv1671, yv1672), app(app(ty_Either, fh), ga), eh, fa) → new_esEs2(yv1630, yv1670, fh, ga)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
- new_esEs1(@3(yv1630, yv1631, yv1632), @3(yv1670, yv1671, yv1672), gc, app(app(ty_Either, hb), hc), fa) → new_esEs2(yv1631, yv1671, hb, hc)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
- new_esEs1(@3(yv1630, yv1631, yv1632), @3(yv1670, yv1671, yv1672), gc, eh, app(app(ty_@2, hf), hg)) → new_esEs0(yv1632, yv1672, hf, hg)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4
- new_esEs1(@3(yv1630, yv1631, yv1632), @3(yv1670, yv1671, yv1672), app(app(ty_@2, fb), fc), eh, fa) → new_esEs0(yv1630, yv1670, fb, fc)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
- new_esEs1(@3(yv1630, yv1631, yv1632), @3(yv1670, yv1671, yv1672), gc, app(app(ty_@2, ge), gf), fa) → new_esEs0(yv1631, yv1671, ge, gf)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
- new_esEs1(@3(yv1630, yv1631, yv1632), @3(yv1670, yv1671, yv1672), gc, app(ty_Maybe, gd), fa) → new_esEs(yv1631, yv1671, gd)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
- new_esEs1(@3(yv1630, yv1631, yv1632), @3(yv1670, yv1671, yv1672), app(ty_Maybe, eg), eh, fa) → new_esEs(yv1630, yv1670, eg)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
- new_esEs1(@3(yv1630, yv1631, yv1632), @3(yv1670, yv1671, yv1672), gc, eh, app(ty_Maybe, he)) → new_esEs(yv1632, yv1672, he)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3
- new_esEs2(Left(yv1630), Left(yv1670), app(app(ty_Either, bbe), bbf), bag) → new_esEs2(yv1630, yv1670, bbe, bbf)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
- new_esEs2(Right(yv1630), Right(yv1670), bbh, app(app(ty_Either, bcg), bch)) → new_esEs2(yv1630, yv1670, bcg, bch)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
- new_esEs2(Left(yv1630), Left(yv1670), app(app(ty_@2, bah), bba), bag) → new_esEs0(yv1630, yv1670, bah, bba)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
- new_esEs2(Right(yv1630), Right(yv1670), bbh, app(app(ty_@2, bcb), bcc)) → new_esEs0(yv1630, yv1670, bcb, bcc)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
- new_esEs2(Left(yv1630), Left(yv1670), app(ty_Maybe, baf), bag) → new_esEs(yv1630, yv1670, baf)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
- new_esEs2(Right(yv1630), Right(yv1670), bbh, app(ty_Maybe, bca)) → new_esEs(yv1630, yv1670, bca)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDPSizeChangeProof
Q DP problem:
The TRS P consists of the following rules:
new_nubNub'10(yv176, yv177, yv178, yv179, True, yv181, bb) → new_nubNub'(yv177, yv178, yv179, bb)
new_nubNub'1(yv163, yv164, yv165, yv166, yv167, yv168, ba) → new_nubNub'10(yv163, yv164, yv165, yv166, new_esEs4(yv163, yv167, ba), yv168, ba)
new_nubNub'10(yv176, yv177, yv178, yv179, False, :(yv1810, yv1811), bb) → new_nubNub'1(yv176, yv177, yv178, yv179, yv1810, yv1811, bb)
new_nubNub'10(yv176, yv177, yv178, yv179, False, [], bb) → new_nubNub'(yv177, yv176, :(yv178, yv179), bb)
new_nubNub'(:(yv700, yv701), yv71, yv72, bc) → new_nubNub'1(yv700, yv701, yv71, yv72, yv71, yv72, bc)
The TRS R consists of the following rules:
new_esEs26(yv1632, yv1672, app(ty_[], bef)) → new_esEs8(yv1632, yv1672, bef)
new_esEs22(yv1630, yv1670, app(app(ty_@2, gd), ge)) → new_esEs15(yv1630, yv1670, gd, ge)
new_esEs24(yv1630, yv1670, app(ty_Maybe, bba)) → new_esEs13(yv1630, yv1670, bba)
new_esEs13(Just(yv1630), Just(yv1670), ty_Float) → new_esEs5(yv1630, yv1670)
new_esEs22(yv1630, yv1670, app(ty_Maybe, gb)) → new_esEs13(yv1630, yv1670, gb)
new_esEs22(yv1630, yv1670, ty_Double) → new_esEs11(yv1630, yv1670)
new_esEs23(yv1631, yv1671, ty_Float) → new_esEs5(yv1631, yv1671)
new_esEs25(yv1631, yv1671, ty_Integer) → new_esEs12(yv1631, yv1671)
new_esEs25(yv1631, yv1671, app(app(app(ty_@3, bcg), bch), bda)) → new_esEs16(yv1631, yv1671, bcg, bch, bda)
new_primEqInt(Neg(Succ(yv16300)), Pos(yv1670)) → False
new_primEqInt(Pos(Succ(yv16300)), Neg(yv1670)) → False
new_esEs18(Left(yv1630), Left(yv1670), app(app(ty_Either, dh), ea), cg) → new_esEs18(yv1630, yv1670, dh, ea)
new_esEs22(yv1630, yv1670, ty_Ordering) → new_esEs7(yv1630, yv1670)
new_esEs24(yv1630, yv1670, app(app(ty_Either, bbh), bca)) → new_esEs18(yv1630, yv1670, bbh, bca)
new_esEs10(Char(yv1630), Char(yv1670)) → new_primEqNat0(yv1630, yv1670)
new_primEqInt(Neg(Zero), Pos(Succ(yv16700))) → False
new_primEqInt(Pos(Zero), Neg(Succ(yv16700))) → False
new_esEs24(yv1630, yv1670, ty_Float) → new_esEs5(yv1630, yv1670)
new_esEs18(Right(yv1630), Right(yv1670), ec, ty_Double) → new_esEs11(yv1630, yv1670)
new_esEs18(Left(yv1630), Left(yv1670), ty_Double, cg) → new_esEs11(yv1630, yv1670)
new_esEs23(yv1631, yv1671, ty_Char) → new_esEs10(yv1631, yv1671)
new_esEs24(yv1630, yv1670, ty_Ordering) → new_esEs7(yv1630, yv1670)
new_esEs18(Left(yv1630), Left(yv1670), app(app(ty_@2, dc), dd), cg) → new_esEs15(yv1630, yv1670, dc, dd)
new_esEs26(yv1632, yv1672, app(app(ty_@2, bdg), bdh)) → new_esEs15(yv1632, yv1672, bdg, bdh)
new_esEs7(GT, LT) → False
new_esEs7(LT, GT) → False
new_primMulNat0(Zero, Zero) → Zero
new_esEs13(Just(yv1630), Just(yv1670), ty_Integer) → new_esEs12(yv1630, yv1670)
new_esEs13(Nothing, Nothing, beg) → True
new_esEs22(yv1630, yv1670, app(app(ty_Either, ha), hb)) → new_esEs18(yv1630, yv1670, ha, hb)
new_esEs13(Just(yv1630), Just(yv1670), app(app(ty_Either, bfg), bfh)) → new_esEs18(yv1630, yv1670, bfg, bfh)
new_esEs26(yv1632, yv1672, ty_@0) → new_esEs19(yv1632, yv1672)
new_esEs26(yv1632, yv1672, app(ty_Ratio, bdf)) → new_esEs14(yv1632, yv1672, bdf)
new_esEs25(yv1631, yv1671, app(app(ty_@2, bce), bcf)) → new_esEs15(yv1631, yv1671, bce, bcf)
new_esEs22(yv1630, yv1670, ty_Bool) → new_esEs17(yv1630, yv1670)
new_esEs18(Right(yv1630), Right(yv1670), ec, app(ty_Maybe, ed)) → new_esEs13(yv1630, yv1670, ed)
new_esEs24(yv1630, yv1670, ty_@0) → new_esEs19(yv1630, yv1670)
new_esEs13(Just(yv1630), Just(yv1670), ty_Char) → new_esEs10(yv1630, yv1670)
new_esEs25(yv1631, yv1671, ty_Bool) → new_esEs17(yv1631, yv1671)
new_esEs21(yv1631, yv1671, ty_Int) → new_esEs6(yv1631, yv1671)
new_esEs23(yv1631, yv1671, ty_Double) → new_esEs11(yv1631, yv1671)
new_esEs24(yv1630, yv1670, app(ty_[], bcb)) → new_esEs8(yv1630, yv1670, bcb)
new_esEs20(yv1630, yv1670, ty_Int) → new_esEs6(yv1630, yv1670)
new_esEs24(yv1630, yv1670, ty_Integer) → new_esEs12(yv1630, yv1670)
new_sr(Pos(yv16310), Neg(yv16710)) → Neg(new_primMulNat0(yv16310, yv16710))
new_sr(Neg(yv16310), Pos(yv16710)) → Neg(new_primMulNat0(yv16310, yv16710))
new_esEs18(Right(yv1630), Right(yv1670), ec, app(ty_Ratio, ee)) → new_esEs14(yv1630, yv1670, ee)
new_esEs17(True, True) → True
new_esEs18(Left(yv1630), Left(yv1670), app(ty_Maybe, da), cg) → new_esEs13(yv1630, yv1670, da)
new_esEs6(yv163, yv167) → new_primEqInt(yv163, yv167)
new_esEs18(Left(yv1630), Left(yv1670), ty_Char, cg) → new_esEs10(yv1630, yv1670)
new_esEs9(yv1630, yv1670, ty_Float) → new_esEs5(yv1630, yv1670)
new_esEs18(Left(yv1630), Left(yv1670), ty_Bool, cg) → new_esEs17(yv1630, yv1670)
new_esEs22(yv1630, yv1670, app(ty_Ratio, gc)) → new_esEs14(yv1630, yv1670, gc)
new_esEs4(yv163, yv167, app(app(app(ty_@3, baf), bag), bah)) → new_esEs16(yv163, yv167, baf, bag, bah)
new_esEs7(LT, LT) → True
new_esEs25(yv1631, yv1671, ty_Int) → new_esEs6(yv1631, yv1671)
new_esEs23(yv1631, yv1671, ty_Integer) → new_esEs12(yv1631, yv1671)
new_esEs12(Integer(yv1630), Integer(yv1670)) → new_primEqInt(yv1630, yv1670)
new_esEs22(yv1630, yv1670, ty_Float) → new_esEs5(yv1630, yv1670)
new_esEs4(yv163, yv167, ty_Ordering) → new_esEs7(yv163, yv167)
new_esEs18(Right(yv1630), Right(yv1670), ec, ty_Integer) → new_esEs12(yv1630, yv1670)
new_esEs22(yv1630, yv1670, app(ty_[], hc)) → new_esEs8(yv1630, yv1670, hc)
new_esEs18(Left(yv1630), Left(yv1670), ty_@0, cg) → new_esEs19(yv1630, yv1670)
new_primEqNat0(Zero, Succ(yv16700)) → False
new_primEqNat0(Succ(yv16300), Zero) → False
new_esEs18(Right(yv1630), Right(yv1670), ec, ty_@0) → new_esEs19(yv1630, yv1670)
new_primPlusNat0(Zero, Zero) → Zero
new_esEs4(yv163, yv167, app(ty_Ratio, fg)) → new_esEs14(yv163, yv167, fg)
new_esEs9(yv1630, yv1670, app(app(ty_Either, cd), ce)) → new_esEs18(yv1630, yv1670, cd, ce)
new_esEs13(Just(yv1630), Nothing, beg) → False
new_esEs13(Nothing, Just(yv1670), beg) → False
new_esEs23(yv1631, yv1671, app(app(app(ty_@3, hh), baa), bab)) → new_esEs16(yv1631, yv1671, hh, baa, bab)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs24(yv1630, yv1670, app(app(app(ty_@3, bbe), bbf), bbg)) → new_esEs16(yv1630, yv1670, bbe, bbf, bbg)
new_esEs24(yv1630, yv1670, app(ty_Ratio, bbb)) → new_esEs14(yv1630, yv1670, bbb)
new_esEs23(yv1631, yv1671, ty_@0) → new_esEs19(yv1631, yv1671)
new_esEs18(Left(yv1630), Left(yv1670), app(ty_[], eb), cg) → new_esEs8(yv1630, yv1670, eb)
new_esEs5(Float(yv1630, yv1631), Float(yv1670, yv1671)) → new_esEs6(new_sr(yv1630, yv1670), new_sr(yv1631, yv1671))
new_esEs18(Left(yv1630), Left(yv1670), ty_Float, cg) → new_esEs5(yv1630, yv1670)
new_esEs13(Just(yv1630), Just(yv1670), app(app(app(ty_@3, bfd), bfe), bff)) → new_esEs16(yv1630, yv1670, bfd, bfe, bff)
new_esEs4(yv163, yv167, ty_Double) → new_esEs11(yv163, yv167)
new_esEs9(yv1630, yv1670, ty_Integer) → new_esEs12(yv1630, yv1670)
new_esEs25(yv1631, yv1671, ty_Double) → new_esEs11(yv1631, yv1671)
new_esEs9(yv1630, yv1670, app(app(ty_@2, bg), bh)) → new_esEs15(yv1630, yv1670, bg, bh)
new_primPlusNat1(Succ(yv1950), yv167100) → Succ(Succ(new_primPlusNat0(yv1950, yv167100)))
new_esEs8(:(yv1630, yv1631), :(yv1670, yv1671), bd) → new_asAs(new_esEs9(yv1630, yv1670, bd), new_esEs8(yv1631, yv1671, bd))
new_esEs18(Right(yv1630), Right(yv1670), ec, app(ty_[], ff)) → new_esEs8(yv1630, yv1670, ff)
new_esEs23(yv1631, yv1671, ty_Int) → new_esEs6(yv1631, yv1671)
new_esEs22(yv1630, yv1670, ty_Integer) → new_esEs12(yv1630, yv1670)
new_esEs24(yv1630, yv1670, ty_Double) → new_esEs11(yv1630, yv1670)
new_esEs7(EQ, EQ) → True
new_esEs23(yv1631, yv1671, ty_Bool) → new_esEs17(yv1631, yv1671)
new_esEs23(yv1631, yv1671, ty_Ordering) → new_esEs7(yv1631, yv1671)
new_esEs25(yv1631, yv1671, app(ty_Ratio, bcd)) → new_esEs14(yv1631, yv1671, bcd)
new_esEs11(Double(yv1630, yv1631), Double(yv1670, yv1671)) → new_esEs6(new_sr(yv1630, yv1670), new_sr(yv1631, yv1671))
new_esEs9(yv1630, yv1670, ty_Bool) → new_esEs17(yv1630, yv1670)
new_esEs9(yv1630, yv1670, app(ty_Maybe, be)) → new_esEs13(yv1630, yv1670, be)
new_esEs9(yv1630, yv1670, app(app(app(ty_@3, ca), cb), cc)) → new_esEs16(yv1630, yv1670, ca, cb, cc)
new_esEs26(yv1632, yv1672, ty_Int) → new_esEs6(yv1632, yv1672)
new_esEs18(Right(yv1630), Right(yv1670), ec, app(app(ty_@2, ef), eg)) → new_esEs15(yv1630, yv1670, ef, eg)
new_esEs9(yv1630, yv1670, ty_Ordering) → new_esEs7(yv1630, yv1670)
new_esEs7(GT, EQ) → False
new_esEs7(EQ, GT) → False
new_esEs16(@3(yv1630, yv1631, yv1632), @3(yv1670, yv1671, yv1672), baf, bag, bah) → new_asAs(new_esEs24(yv1630, yv1670, baf), new_asAs(new_esEs25(yv1631, yv1671, bag), new_esEs26(yv1632, yv1672, bah)))
new_esEs26(yv1632, yv1672, ty_Ordering) → new_esEs7(yv1632, yv1672)
new_esEs13(Just(yv1630), Just(yv1670), ty_Double) → new_esEs11(yv1630, yv1670)
new_esEs9(yv1630, yv1670, app(ty_Ratio, bf)) → new_esEs14(yv1630, yv1670, bf)
new_sr(Neg(yv16310), Neg(yv16710)) → Pos(new_primMulNat0(yv16310, yv16710))
new_esEs23(yv1631, yv1671, app(ty_Maybe, hd)) → new_esEs13(yv1631, yv1671, hd)
new_esEs9(yv1630, yv1670, ty_Char) → new_esEs10(yv1630, yv1670)
new_sr(Pos(yv16310), Pos(yv16710)) → Pos(new_primMulNat0(yv16310, yv16710))
new_asAs(False, yv194) → False
new_primEqNat0(Zero, Zero) → True
new_esEs4(yv163, yv167, app(app(ty_@2, fh), ga)) → new_esEs15(yv163, yv167, fh, ga)
new_esEs24(yv1630, yv1670, ty_Int) → new_esEs6(yv1630, yv1670)
new_esEs4(yv163, yv167, app(ty_Maybe, beg)) → new_esEs13(yv163, yv167, beg)
new_esEs4(yv163, yv167, app(ty_[], bd)) → new_esEs8(yv163, yv167, bd)
new_esEs13(Just(yv1630), Just(yv1670), ty_Bool) → new_esEs17(yv1630, yv1670)
new_primMulNat0(Zero, Succ(yv167100)) → Zero
new_primMulNat0(Succ(yv163100), Zero) → Zero
new_esEs4(yv163, yv167, ty_@0) → new_esEs19(yv163, yv167)
new_esEs18(Left(yv1630), Left(yv1670), app(ty_Ratio, db), cg) → new_esEs14(yv1630, yv1670, db)
new_esEs18(Left(yv1630), Left(yv1670), ty_Ordering, cg) → new_esEs7(yv1630, yv1670)
new_primMulNat0(Succ(yv163100), Succ(yv167100)) → new_primPlusNat1(new_primMulNat0(yv163100, Succ(yv167100)), yv167100)
new_esEs25(yv1631, yv1671, ty_Ordering) → new_esEs7(yv1631, yv1671)
new_esEs18(Right(yv1630), Right(yv1670), ec, app(app(ty_Either, fc), fd)) → new_esEs18(yv1630, yv1670, fc, fd)
new_esEs18(Right(yv1630), Right(yv1670), ec, ty_Bool) → new_esEs17(yv1630, yv1670)
new_esEs25(yv1631, yv1671, app(app(ty_Either, bdb), bdc)) → new_esEs18(yv1631, yv1671, bdb, bdc)
new_esEs24(yv1630, yv1670, ty_Char) → new_esEs10(yv1630, yv1670)
new_esEs17(False, False) → True
new_esEs18(Right(yv1630), Right(yv1670), ec, app(app(app(ty_@3, eh), fa), fb)) → new_esEs16(yv1630, yv1670, eh, fa, fb)
new_esEs17(True, False) → False
new_esEs17(False, True) → False
new_esEs13(Just(yv1630), Just(yv1670), app(app(ty_@2, bfb), bfc)) → new_esEs15(yv1630, yv1670, bfb, bfc)
new_esEs4(yv163, yv167, ty_Integer) → new_esEs12(yv163, yv167)
new_esEs18(Right(yv1630), Right(yv1670), ec, ty_Ordering) → new_esEs7(yv1630, yv1670)
new_esEs22(yv1630, yv1670, ty_Char) → new_esEs10(yv1630, yv1670)
new_esEs13(Just(yv1630), Just(yv1670), app(ty_Maybe, beh)) → new_esEs13(yv1630, yv1670, beh)
new_esEs9(yv1630, yv1670, ty_Double) → new_esEs11(yv1630, yv1670)
new_esEs18(Left(yv1630), Right(yv1670), ec, cg) → False
new_esEs18(Right(yv1630), Left(yv1670), ec, cg) → False
new_esEs24(yv1630, yv1670, ty_Bool) → new_esEs17(yv1630, yv1670)
new_esEs4(yv163, yv167, ty_Int) → new_esEs6(yv163, yv167)
new_esEs13(Just(yv1630), Just(yv1670), app(ty_Ratio, bfa)) → new_esEs14(yv1630, yv1670, bfa)
new_esEs13(Just(yv1630), Just(yv1670), app(ty_[], bga)) → new_esEs8(yv1630, yv1670, bga)
new_esEs18(Right(yv1630), Right(yv1670), ec, ty_Int) → new_esEs6(yv1630, yv1670)
new_esEs20(yv1630, yv1670, ty_Integer) → new_esEs12(yv1630, yv1670)
new_esEs9(yv1630, yv1670, ty_Int) → new_esEs6(yv1630, yv1670)
new_esEs26(yv1632, yv1672, ty_Integer) → new_esEs12(yv1632, yv1672)
new_primEqInt(Neg(Succ(yv16300)), Neg(Succ(yv16700))) → new_primEqNat0(yv16300, yv16700)
new_esEs13(Just(yv1630), Just(yv1670), ty_Int) → new_esEs6(yv1630, yv1670)
new_esEs26(yv1632, yv1672, ty_Bool) → new_esEs17(yv1632, yv1672)
new_esEs18(Right(yv1630), Right(yv1670), ec, ty_Float) → new_esEs5(yv1630, yv1670)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs26(yv1632, yv1672, ty_Char) → new_esEs10(yv1632, yv1672)
new_esEs9(yv1630, yv1670, ty_@0) → new_esEs19(yv1630, yv1670)
new_esEs25(yv1631, yv1671, ty_Float) → new_esEs5(yv1631, yv1671)
new_esEs18(Left(yv1630), Left(yv1670), app(app(app(ty_@3, de), df), dg), cg) → new_esEs16(yv1630, yv1670, de, df, dg)
new_esEs8([], [], bd) → True
new_esEs25(yv1631, yv1671, app(ty_Maybe, bcc)) → new_esEs13(yv1631, yv1671, bcc)
new_esEs26(yv1632, yv1672, app(app(app(ty_@3, bea), beb), bec)) → new_esEs16(yv1632, yv1672, bea, beb, bec)
new_esEs23(yv1631, yv1671, app(app(ty_Either, bac), bad)) → new_esEs18(yv1631, yv1671, bac, bad)
new_esEs7(EQ, LT) → False
new_esEs7(LT, EQ) → False
new_primEqInt(Neg(Succ(yv16300)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(yv16700))) → False
new_primPlusNat1(Zero, yv167100) → Succ(yv167100)
new_primPlusNat0(Succ(yv19500), Succ(yv1671000)) → Succ(Succ(new_primPlusNat0(yv19500, yv1671000)))
new_esEs18(Left(yv1630), Left(yv1670), ty_Integer, cg) → new_esEs12(yv1630, yv1670)
new_esEs19(@0, @0) → True
new_esEs26(yv1632, yv1672, app(ty_Maybe, bde)) → new_esEs13(yv1632, yv1672, bde)
new_asAs(True, yv194) → yv194
new_esEs13(Just(yv1630), Just(yv1670), ty_@0) → new_esEs19(yv1630, yv1670)
new_esEs26(yv1632, yv1672, ty_Double) → new_esEs11(yv1632, yv1672)
new_esEs22(yv1630, yv1670, ty_@0) → new_esEs19(yv1630, yv1670)
new_esEs14(:%(yv1630, yv1631), :%(yv1670, yv1671), fg) → new_asAs(new_esEs20(yv1630, yv1670, fg), new_esEs21(yv1631, yv1671, fg))
new_esEs18(Right(yv1630), Right(yv1670), ec, ty_Char) → new_esEs10(yv1630, yv1670)
new_primEqInt(Pos(Succ(yv16300)), Pos(Succ(yv16700))) → new_primEqNat0(yv16300, yv16700)
new_esEs9(yv1630, yv1670, app(ty_[], cf)) → new_esEs8(yv1630, yv1670, cf)
new_esEs25(yv1631, yv1671, app(ty_[], bdd)) → new_esEs8(yv1631, yv1671, bdd)
new_esEs26(yv1632, yv1672, ty_Float) → new_esEs5(yv1632, yv1672)
new_esEs13(Just(yv1630), Just(yv1670), ty_Ordering) → new_esEs7(yv1630, yv1670)
new_esEs21(yv1631, yv1671, ty_Integer) → new_esEs12(yv1631, yv1671)
new_esEs15(@2(yv1630, yv1631), @2(yv1670, yv1671), fh, ga) → new_asAs(new_esEs22(yv1630, yv1670, fh), new_esEs23(yv1631, yv1671, ga))
new_esEs26(yv1632, yv1672, app(app(ty_Either, bed), bee)) → new_esEs18(yv1632, yv1672, bed, bee)
new_esEs25(yv1631, yv1671, ty_Char) → new_esEs10(yv1631, yv1671)
new_primEqNat0(Succ(yv16300), Succ(yv16700)) → new_primEqNat0(yv16300, yv16700)
new_esEs22(yv1630, yv1670, app(app(app(ty_@3, gf), gg), gh)) → new_esEs16(yv1630, yv1670, gf, gg, gh)
new_esEs4(yv163, yv167, ty_Char) → new_esEs10(yv163, yv167)
new_esEs23(yv1631, yv1671, app(ty_[], bae)) → new_esEs8(yv1631, yv1671, bae)
new_esEs23(yv1631, yv1671, app(ty_Ratio, he)) → new_esEs14(yv1631, yv1671, he)
new_esEs18(Left(yv1630), Left(yv1670), ty_Int, cg) → new_esEs6(yv1630, yv1670)
new_esEs22(yv1630, yv1670, ty_Int) → new_esEs6(yv1630, yv1670)
new_esEs25(yv1631, yv1671, ty_@0) → new_esEs19(yv1631, yv1671)
new_esEs7(GT, GT) → True
new_esEs4(yv163, yv167, ty_Bool) → new_esEs17(yv163, yv167)
new_esEs23(yv1631, yv1671, app(app(ty_@2, hf), hg)) → new_esEs15(yv1631, yv1671, hf, hg)
new_esEs24(yv1630, yv1670, app(app(ty_@2, bbc), bbd)) → new_esEs15(yv1630, yv1670, bbc, bbd)
new_esEs8([], :(yv1670, yv1671), bd) → False
new_esEs8(:(yv1630, yv1631), [], bd) → False
new_primEqInt(Pos(Zero), Pos(Succ(yv16700))) → False
new_primEqInt(Pos(Succ(yv16300)), Pos(Zero)) → False
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primPlusNat0(Succ(yv19500), Zero) → Succ(yv19500)
new_primPlusNat0(Zero, Succ(yv1671000)) → Succ(yv1671000)
new_esEs4(yv163, yv167, app(app(ty_Either, ec), cg)) → new_esEs18(yv163, yv167, ec, cg)
new_esEs4(yv163, yv167, ty_Float) → new_esEs5(yv163, yv167)
The set Q consists of the following terms:
new_esEs18(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs23(x0, x1, ty_Int)
new_esEs4(x0, x1, ty_Bool)
new_esEs18(Right(x0), Right(x1), x2, ty_Bool)
new_esEs7(LT, EQ)
new_esEs7(EQ, LT)
new_esEs26(x0, x1, ty_Int)
new_esEs18(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs13(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs8(:(x0, x1), [], x2)
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, ty_@0)
new_esEs9(x0, x1, ty_Float)
new_sr(Neg(x0), Pos(x1))
new_sr(Pos(x0), Neg(x1))
new_primEqNat0(Succ(x0), Zero)
new_primEqInt(Neg(Zero), Pos(Zero))
new_primEqInt(Pos(Zero), Neg(Zero))
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, ty_Char)
new_sr(Neg(x0), Neg(x1))
new_esEs24(x0, x1, ty_Integer)
new_esEs12(Integer(x0), Integer(x1))
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs4(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_esEs4(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_esEs9(x0, x1, ty_Int)
new_esEs7(LT, LT)
new_esEs8([], :(x0, x1), x2)
new_esEs22(x0, x1, ty_Double)
new_esEs22(x0, x1, ty_Ordering)
new_esEs25(x0, x1, ty_Float)
new_esEs4(x0, x1, ty_@0)
new_primEqInt(Neg(Zero), Neg(Zero))
new_esEs20(x0, x1, ty_Int)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_esEs4(x0, x1, app(ty_Ratio, x2))
new_esEs24(x0, x1, ty_Double)
new_esEs7(LT, GT)
new_esEs7(GT, LT)
new_esEs24(x0, x1, ty_Ordering)
new_esEs22(x0, x1, ty_Float)
new_esEs24(x0, x1, ty_@0)
new_esEs26(x0, x1, ty_Float)
new_esEs9(x0, x1, ty_@0)
new_esEs26(x0, x1, ty_Integer)
new_esEs25(x0, x1, ty_Double)
new_esEs23(x0, x1, ty_Double)
new_esEs9(x0, x1, ty_Double)
new_esEs24(x0, x1, app(ty_[], x2))
new_primMulNat0(Succ(x0), Zero)
new_esEs13(Just(x0), Just(x1), ty_Ordering)
new_esEs25(x0, x1, ty_Integer)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_primPlusNat1(Zero, x0)
new_esEs10(Char(x0), Char(x1))
new_esEs13(Just(x0), Just(x1), ty_Char)
new_primEqNat0(Zero, Succ(x0))
new_esEs17(False, False)
new_esEs13(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs9(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs13(Just(x0), Just(x1), ty_Bool)
new_esEs18(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_esEs13(Nothing, Just(x0), x1)
new_esEs9(x0, x1, ty_Char)
new_esEs26(x0, x1, app(ty_[], x2))
new_esEs9(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, app(ty_[], x2))
new_esEs9(x0, x1, ty_Ordering)
new_esEs18(Right(x0), Right(x1), x2, ty_Int)
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs18(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs8([], [], x0)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs18(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs4(x0, x1, ty_Float)
new_esEs21(x0, x1, ty_Int)
new_esEs4(x0, x1, app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_esEs6(x0, x1)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs22(x0, x1, app(ty_[], x2))
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(GT, GT)
new_esEs4(x0, x1, ty_Integer)
new_primEqNat0(Zero, Zero)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs22(x0, x1, ty_Bool)
new_esEs13(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs24(x0, x1, ty_Float)
new_primMulNat0(Succ(x0), Succ(x1))
new_esEs18(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs18(Right(x0), Left(x1), x2, x3)
new_esEs18(Left(x0), Right(x1), x2, x3)
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_esEs26(x0, x1, ty_@0)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_esEs18(Right(x0), Right(x1), x2, ty_Double)
new_esEs20(x0, x1, ty_Integer)
new_esEs13(Just(x0), Nothing, x1)
new_esEs18(Left(x0), Left(x1), ty_Integer, x2)
new_esEs18(Left(x0), Left(x1), ty_Double, x2)
new_esEs13(Nothing, Nothing, x0)
new_primMulNat0(Zero, Zero)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs22(x0, x1, ty_Char)
new_esEs26(x0, x1, ty_Ordering)
new_esEs18(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs18(Right(x0), Right(x1), x2, ty_@0)
new_esEs13(Just(x0), Just(x1), ty_Double)
new_esEs9(x0, x1, app(ty_Ratio, x2))
new_esEs24(x0, x1, ty_Char)
new_primPlusNat1(Succ(x0), x1)
new_esEs23(x0, x1, ty_Ordering)
new_esEs18(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs18(Right(x0), Right(x1), x2, ty_Integer)
new_esEs18(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs9(x0, x1, app(app(ty_Either, x2), x3))
new_primPlusNat0(Zero, Succ(x0))
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_esEs18(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs23(x0, x1, ty_Bool)
new_esEs25(x0, x1, ty_Int)
new_esEs13(Just(x0), Just(x1), ty_@0)
new_esEs7(EQ, GT)
new_esEs7(GT, EQ)
new_esEs14(:%(x0, x1), :%(x2, x3), x4)
new_esEs15(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs25(x0, x1, app(ty_[], x2))
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_esEs24(x0, x1, ty_Bool)
new_esEs25(x0, x1, ty_Bool)
new_asAs(False, x0)
new_esEs13(Just(x0), Just(x1), ty_Float)
new_esEs26(x0, x1, ty_Double)
new_esEs18(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs18(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs18(Left(x0), Left(x1), ty_Char, x2)
new_esEs16(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs18(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs22(x0, x1, ty_@0)
new_esEs22(x0, x1, ty_Int)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs13(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_esEs26(x0, x1, ty_Bool)
new_primPlusNat0(Succ(x0), Zero)
new_esEs24(x0, x1, ty_Int)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_esEs18(Right(x0), Right(x1), x2, ty_Char)
new_esEs4(x0, x1, app(ty_[], x2))
new_esEs4(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_esEs4(x0, x1, ty_Double)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs5(Float(x0, x1), Float(x2, x3))
new_esEs23(x0, x1, ty_@0)
new_esEs18(Left(x0), Left(x1), ty_Int, x2)
new_esEs25(x0, x1, ty_Ordering)
new_esEs4(x0, x1, ty_Char)
new_esEs9(x0, x1, ty_Bool)
new_esEs9(x0, x1, ty_Integer)
new_esEs17(False, True)
new_esEs17(True, False)
new_esEs8(:(x0, x1), :(x2, x3), x4)
new_esEs9(x0, x1, app(ty_[], x2))
new_esEs9(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, ty_Char)
new_esEs13(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs4(x0, x1, ty_Ordering)
new_esEs18(Right(x0), Right(x1), x2, ty_Float)
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_esEs18(Left(x0), Left(x1), ty_Float, x2)
new_primPlusNat0(Zero, Zero)
new_sr(Pos(x0), Pos(x1))
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_esEs13(Just(x0), Just(x1), app(ty_[], x2))
new_esEs13(Just(x0), Just(x1), ty_Integer)
new_primEqInt(Pos(Zero), Pos(Zero))
new_esEs18(Left(x0), Left(x1), ty_@0, x2)
new_esEs17(True, True)
new_esEs7(EQ, EQ)
new_esEs23(x0, x1, ty_Integer)
new_esEs22(x0, x1, ty_Integer)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs25(x0, x1, ty_Char)
new_esEs18(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs21(x0, x1, ty_Integer)
new_esEs11(Double(x0, x1), Double(x2, x3))
new_primPlusNat0(Succ(x0), Succ(x1))
new_primMulNat0(Zero, Succ(x0))
new_esEs19(@0, @0)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_esEs13(Just(x0), Just(x1), ty_Int)
new_esEs18(Left(x0), Left(x1), ty_Bool, x2)
new_esEs23(x0, x1, ty_Float)
new_asAs(True, x0)
new_esEs4(x0, x1, ty_Int)
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_nubNub'(:(yv700, yv701), yv71, yv72, bc) → new_nubNub'1(yv700, yv701, yv71, yv72, yv71, yv72, bc)
The graph contains the following edges 1 > 1, 1 > 2, 2 >= 3, 3 >= 4, 2 >= 5, 3 >= 6, 4 >= 7
- new_nubNub'1(yv163, yv164, yv165, yv166, yv167, yv168, ba) → new_nubNub'10(yv163, yv164, yv165, yv166, new_esEs4(yv163, yv167, ba), yv168, ba)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 6 >= 6, 7 >= 7
- new_nubNub'10(yv176, yv177, yv178, yv179, False, :(yv1810, yv1811), bb) → new_nubNub'1(yv176, yv177, yv178, yv179, yv1810, yv1811, bb)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 6 > 5, 6 > 6, 7 >= 7
- new_nubNub'10(yv176, yv177, yv178, yv179, True, yv181, bb) → new_nubNub'(yv177, yv178, yv179, bb)
The graph contains the following edges 2 >= 1, 3 >= 2, 4 >= 3, 7 >= 4
- new_nubNub'10(yv176, yv177, yv178, yv179, False, [], bb) → new_nubNub'(yv177, yv176, :(yv178, yv179), bb)
The graph contains the following edges 2 >= 1, 1 >= 2, 7 >= 4