YES
H-Termination proof of ../tpdb/FP/full_haskell/List_union_12.hs
H-Termination of the given Haskell-Program with start terms could successfully be proven:
↳ HASKELL
↳ IFR
mainModule Main
|
| ((List.union :: (Eq b, Eq a) => [(b,a)] -> [(b,a)] -> [(b,a)]) :: (Eq b, Eq a) => [(b,a)] -> [(b,a)] -> [(b,a)]) |
module List where
| | import qualified Main
import qualified Maybe
import qualified Prelude
|
| | deleteBy :: (a -> a -> Bool) -> a -> [a] -> [a]
| deleteBy | _ _ [] | = | [] |
| deleteBy | eq x (y : ys) | = | if x `eq` y then ys else y : deleteBy eq x ys |
|
| | elem_by :: (a -> a -> Bool) -> a -> [a] -> Bool
| elem_by | _ _ [] | = | False |
| elem_by | eq y (x : xs) | = | x `eq` y || elem_by eq y xs |
|
| | nubBy :: (a -> a -> Bool) -> [a] -> [a]
| nubBy | eq l | = |
| nubBy' l [] | where |
| nubBy' | [] _ | = | [] |
| nubBy' | (y : ys) xs | |
| | | elem_by eq y xs | = |
|
| | | otherwise | = |
|
|
|
|
|
|
| | union :: Eq a => [a] -> [a] -> [a]
|
| | unionBy :: (a -> a -> Bool) -> [a] -> [a] -> [a]
| unionBy | eq xs ys | = | xs ++ foldl (flip (deleteBy eq)) (nubBy eq ys) xs |
|
module Main where
| | import qualified List
import qualified Maybe
import qualified Prelude
|
module Maybe where
| | import qualified List
import qualified Main
import qualified Prelude
|
If Reductions:
The following If expression
if eq x y then ys else y : deleteBy eq x ys
is transformed to
| deleteBy0 | ys y eq x True | = ys |
| deleteBy0 | ys y eq x False | = y : deleteBy eq x ys |
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
mainModule Main
|
| ((List.union :: (Eq b, Eq a) => [(a,b)] -> [(a,b)] -> [(a,b)]) :: (Eq b, Eq a) => [(a,b)] -> [(a,b)] -> [(a,b)]) |
module List where
| | import qualified Main
import qualified Maybe
import qualified Prelude
|
| | deleteBy :: (a -> a -> Bool) -> a -> [a] -> [a]
| deleteBy | _ _ [] | = | [] |
| deleteBy | eq x (y : ys) | = | deleteBy0 ys y eq x (x `eq` y) |
|
| |
| deleteBy0 | ys y eq x True | = | ys |
| deleteBy0 | ys y eq x False | = | y : deleteBy eq x ys |
|
| | elem_by :: (a -> a -> Bool) -> a -> [a] -> Bool
| elem_by | _ _ [] | = | False |
| elem_by | eq y (x : xs) | = | x `eq` y || elem_by eq y xs |
|
| | nubBy :: (a -> a -> Bool) -> [a] -> [a]
| nubBy | eq l | = |
| nubBy' l [] | where |
| nubBy' | [] _ | = | [] |
| nubBy' | (y : ys) xs | |
| | | elem_by eq y xs | = |
|
| | | otherwise | = |
|
|
|
|
|
|
| | union :: Eq a => [a] -> [a] -> [a]
|
| | unionBy :: (a -> a -> Bool) -> [a] -> [a] -> [a]
| unionBy | eq xs ys | = | xs ++ foldl (flip (deleteBy eq)) (nubBy eq ys) xs |
|
module Main where
| | import qualified List
import qualified Maybe
import qualified Prelude
|
module Maybe where
| | import qualified List
import qualified Main
import qualified Prelude
|
Replaced joker patterns by fresh variables and removed binding patterns.
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
mainModule Main
|
| ((List.union :: (Eq b, Eq a) => [(a,b)] -> [(a,b)] -> [(a,b)]) :: (Eq a, Eq b) => [(a,b)] -> [(a,b)] -> [(a,b)]) |
module List where
| | import qualified Main
import qualified Maybe
import qualified Prelude
|
| | deleteBy :: (a -> a -> Bool) -> a -> [a] -> [a]
| deleteBy | vw vx [] | = | [] |
| deleteBy | eq x (y : ys) | = | deleteBy0 ys y eq x (x `eq` y) |
|
| |
| deleteBy0 | ys y eq x True | = | ys |
| deleteBy0 | ys y eq x False | = | y : deleteBy eq x ys |
|
| | elem_by :: (a -> a -> Bool) -> a -> [a] -> Bool
| elem_by | vz wu [] | = | False |
| elem_by | eq y (x : xs) | = | x `eq` y || elem_by eq y xs |
|
| | nubBy :: (a -> a -> Bool) -> [a] -> [a]
| nubBy | eq l | = |
| nubBy' l [] | where |
| nubBy' | [] vy | = | [] |
| nubBy' | (y : ys) xs | |
| | | elem_by eq y xs | = |
|
| | | otherwise | = |
|
|
|
|
|
|
| | union :: Eq a => [a] -> [a] -> [a]
|
| | unionBy :: (a -> a -> Bool) -> [a] -> [a] -> [a]
| unionBy | eq xs ys | = | xs ++ foldl (flip (deleteBy eq)) (nubBy eq ys) xs |
|
module Main where
| | import qualified List
import qualified Maybe
import qualified Prelude
|
module Maybe where
| | import qualified List
import qualified Main
import qualified Prelude
|
Cond Reductions:
The following Function with conditions
| nubBy' | [] vy | = [] |
| nubBy' | (y : ys) xs |
| | | elem_by eq y xs | |
| | | otherwise | |
|
is transformed to
| nubBy' | [] vy | = nubBy'3 [] vy |
| nubBy' | (y : ys) xs | = nubBy'2 (y : ys) xs |
| nubBy'0 | y ys xs True | = y : nubBy' ys (y : xs) |
| nubBy'1 | y ys xs True | = nubBy' ys xs |
| nubBy'1 | y ys xs False | = nubBy'0 y ys xs otherwise |
| nubBy'2 | (y : ys) xs | = nubBy'1 y ys xs (elem_by eq y xs) |
| nubBy'3 | [] vy | = [] |
| nubBy'3 | yx yy | = nubBy'2 yx yy |
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
mainModule Main
|
| ((List.union :: (Eq a, Eq b) => [(a,b)] -> [(a,b)] -> [(a,b)]) :: (Eq a, Eq b) => [(a,b)] -> [(a,b)] -> [(a,b)]) |
module List where
| | import qualified Main
import qualified Maybe
import qualified Prelude
|
| | deleteBy :: (a -> a -> Bool) -> a -> [a] -> [a]
| deleteBy | vw vx [] | = | [] |
| deleteBy | eq x (y : ys) | = | deleteBy0 ys y eq x (x `eq` y) |
|
| |
| deleteBy0 | ys y eq x True | = | ys |
| deleteBy0 | ys y eq x False | = | y : deleteBy eq x ys |
|
| | elem_by :: (a -> a -> Bool) -> a -> [a] -> Bool
| elem_by | vz wu [] | = | False |
| elem_by | eq y (x : xs) | = | x `eq` y || elem_by eq y xs |
|
| | nubBy :: (a -> a -> Bool) -> [a] -> [a]
| nubBy | eq l | = |
| nubBy' l [] | where |
| nubBy' | [] vy | = | nubBy'3 [] vy |
| nubBy' | (y : ys) xs | = | nubBy'2 (y : ys) xs |
|
| nubBy'0 | y ys xs True | = | y : nubBy' ys (y : xs) |
|
| nubBy'1 | y ys xs True | = | nubBy' ys xs |
| nubBy'1 | y ys xs False | = | nubBy'0 y ys xs otherwise |
|
| nubBy'2 | (y : ys) xs | = | nubBy'1 y ys xs (elem_by eq y xs) |
|
| nubBy'3 | [] vy | = | [] |
| nubBy'3 | yx yy | = | nubBy'2 yx yy |
|
|
|
|
| | union :: Eq a => [a] -> [a] -> [a]
|
| | unionBy :: (a -> a -> Bool) -> [a] -> [a] -> [a]
| unionBy | eq xs ys | = | xs ++ foldl (flip (deleteBy eq)) (nubBy eq ys) xs |
|
module Main where
| | import qualified List
import qualified Maybe
import qualified Prelude
|
module Maybe where
| | import qualified List
import qualified Main
import qualified Prelude
|
Let/Where Reductions:
The bindings of the following Let/Where expression
| nubBy' l [] |
| where |
| nubBy' | [] vy | = nubBy'3 [] vy |
| nubBy' | (y : ys) xs | = nubBy'2 (y : ys) xs |
|
|
| nubBy'0 | y ys xs True | = y : nubBy' ys (y : xs) |
|
|
| nubBy'1 | y ys xs True | = nubBy' ys xs |
| nubBy'1 | y ys xs False | = nubBy'0 y ys xs otherwise |
|
|
| nubBy'2 | (y : ys) xs | = nubBy'1 y ys xs (elem_by eq y xs) |
|
|
| nubBy'3 | [] vy | = [] |
| nubBy'3 | yx yy | = nubBy'2 yx yy |
|
are unpacked to the following functions on top level
| nubByNubBy' | yz [] vy | = nubByNubBy'3 yz [] vy |
| nubByNubBy' | yz (y : ys) xs | = nubByNubBy'2 yz (y : ys) xs |
| nubByNubBy'3 | yz [] vy | = [] |
| nubByNubBy'3 | yz yx yy | = nubByNubBy'2 yz yx yy |
| nubByNubBy'1 | yz y ys xs True | = nubByNubBy' yz ys xs |
| nubByNubBy'1 | yz y ys xs False | = nubByNubBy'0 yz y ys xs otherwise |
| nubByNubBy'2 | yz (y : ys) xs | = nubByNubBy'1 yz y ys xs (elem_by yz y xs) |
| nubByNubBy'0 | yz y ys xs True | = y : nubByNubBy' yz ys (y : xs) |
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
mainModule Main
|
| ((List.union :: (Eq b, Eq a) => [(b,a)] -> [(b,a)] -> [(b,a)]) :: (Eq b, Eq a) => [(b,a)] -> [(b,a)] -> [(b,a)]) |
module List where
| | import qualified Main
import qualified Maybe
import qualified Prelude
|
| | deleteBy :: (a -> a -> Bool) -> a -> [a] -> [a]
| deleteBy | vw vx [] | = | [] |
| deleteBy | eq x (y : ys) | = | deleteBy0 ys y eq x (x `eq` y) |
|
| |
| deleteBy0 | ys y eq x True | = | ys |
| deleteBy0 | ys y eq x False | = | y : deleteBy eq x ys |
|
| | elem_by :: (a -> a -> Bool) -> a -> [a] -> Bool
| elem_by | vz wu [] | = | False |
| elem_by | eq y (x : xs) | = | x `eq` y || elem_by eq y xs |
|
| | nubBy :: (a -> a -> Bool) -> [a] -> [a]
| nubBy | eq l | = | nubByNubBy' eq l [] |
|
| |
| nubByNubBy' | yz [] vy | = | nubByNubBy'3 yz [] vy |
| nubByNubBy' | yz (y : ys) xs | = | nubByNubBy'2 yz (y : ys) xs |
|
| |
| nubByNubBy'0 | yz y ys xs True | = | y : nubByNubBy' yz ys (y : xs) |
|
| |
| nubByNubBy'1 | yz y ys xs True | = | nubByNubBy' yz ys xs |
| nubByNubBy'1 | yz y ys xs False | = | nubByNubBy'0 yz y ys xs otherwise |
|
| |
| nubByNubBy'2 | yz (y : ys) xs | = | nubByNubBy'1 yz y ys xs (elem_by yz y xs) |
|
| |
| nubByNubBy'3 | yz [] vy | = | [] |
| nubByNubBy'3 | yz yx yy | = | nubByNubBy'2 yz yx yy |
|
| | union :: Eq a => [a] -> [a] -> [a]
|
| | unionBy :: (a -> a -> Bool) -> [a] -> [a] -> [a]
| unionBy | eq xs ys | = | xs ++ foldl (flip (deleteBy eq)) (nubBy eq ys) xs |
|
module Main where
| | import qualified List
import qualified Maybe
import qualified Prelude
|
module Maybe where
| | import qualified List
import qualified Main
import qualified Prelude
|
Num Reduction:All numbers are transformed to thier corresponding representation with Succ, Pred and Zero.
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
mainModule Main
|
| (List.union :: (Eq b, Eq a) => [(a,b)] -> [(a,b)] -> [(a,b)]) |
module List where
| | import qualified Main
import qualified Maybe
import qualified Prelude
|
| | deleteBy :: (a -> a -> Bool) -> a -> [a] -> [a]
| deleteBy | vw vx [] | = | [] |
| deleteBy | eq x (y : ys) | = | deleteBy0 ys y eq x (x `eq` y) |
|
| |
| deleteBy0 | ys y eq x True | = | ys |
| deleteBy0 | ys y eq x False | = | y : deleteBy eq x ys |
|
| | elem_by :: (a -> a -> Bool) -> a -> [a] -> Bool
| elem_by | vz wu [] | = | False |
| elem_by | eq y (x : xs) | = | x `eq` y || elem_by eq y xs |
|
| | nubBy :: (a -> a -> Bool) -> [a] -> [a]
| nubBy | eq l | = | nubByNubBy' eq l [] |
|
| |
| nubByNubBy' | yz [] vy | = | nubByNubBy'3 yz [] vy |
| nubByNubBy' | yz (y : ys) xs | = | nubByNubBy'2 yz (y : ys) xs |
|
| |
| nubByNubBy'0 | yz y ys xs True | = | y : nubByNubBy' yz ys (y : xs) |
|
| |
| nubByNubBy'1 | yz y ys xs True | = | nubByNubBy' yz ys xs |
| nubByNubBy'1 | yz y ys xs False | = | nubByNubBy'0 yz y ys xs otherwise |
|
| |
| nubByNubBy'2 | yz (y : ys) xs | = | nubByNubBy'1 yz y ys xs (elem_by yz y xs) |
|
| |
| nubByNubBy'3 | yz [] vy | = | [] |
| nubByNubBy'3 | yz yx yy | = | nubByNubBy'2 yz yx yy |
|
| | union :: Eq a => [a] -> [a] -> [a]
|
| | unionBy :: (a -> a -> Bool) -> [a] -> [a] -> [a]
| unionBy | eq xs ys | = | xs ++ foldl (flip (deleteBy eq)) (nubBy eq ys) xs |
|
module Main where
| | import qualified List
import qualified Maybe
import qualified Prelude
|
module Maybe where
| | import qualified List
import qualified Main
import qualified Prelude
|
Haskell To QDPs
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDPSizeChangeProof
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_primMulNat(Succ(zu31100100), Succ(zu4800100)) → new_primMulNat(zu31100100, Succ(zu4800100))
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(zu31100100), Succ(zu4800100)) → new_primMulNat(zu31100100, Succ(zu4800100))
The graph contains the following edges 1 > 1, 2 >= 2
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDPSizeChangeProof
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_primPlusNat(Succ(zu9100), Succ(zu48001000)) → new_primPlusNat(zu9100, zu48001000)
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(zu9100), Succ(zu48001000)) → new_primPlusNat(zu9100, zu48001000)
The graph contains the following edges 1 > 1, 2 > 2
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDPSizeChangeProof
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_foldl(zu48, :(zu3110, zu3111), ba, bb) → new_foldl(new_deleteBy1(zu3110, zu48, ba, bb), zu3111, ba, bb)
The TRS R consists of the following rules:
new_esEs28(zu31101, zu4801, ty_Char) → new_esEs21(zu31101, zu4801)
new_esEs24(zu311000, zu48000, ty_Float) → new_esEs12(zu311000, zu48000)
new_primPlusNat1(Succ(zu9100), Succ(zu48001000)) → Succ(Succ(new_primPlusNat1(zu9100, zu48001000)))
new_primEqInt(Neg(Succ(zu3110000)), Pos(zu48000)) → False
new_primEqInt(Pos(Succ(zu3110000)), Neg(zu48000)) → False
new_esEs27(zu31100, zu4800, ty_Ordering) → new_esEs11(zu31100, zu4800)
new_esEs18(Just(zu311000), Just(zu48000), app(app(ty_Either, bdb), bdc)) → new_esEs14(zu311000, zu48000, bdb, bdc)
new_esEs14(Right(zu311000), Right(zu48000), bh, ty_Ordering) → new_esEs11(zu311000, zu48000)
new_esEs14(Right(zu311000), Right(zu48000), bh, app(app(ty_@2, bba), bbb)) → new_esEs10(zu311000, zu48000, bba, bbb)
new_esEs14(Right(zu311000), Left(zu48000), bh, ca) → False
new_esEs14(Left(zu311000), Right(zu48000), bh, ca) → False
new_esEs25(zu311001, zu48001, ty_@0) → new_esEs13(zu311001, zu48001)
new_esEs23(zu311001, zu48001, ty_Integer) → new_esEs19(zu311001, zu48001)
new_esEs28(zu31101, zu4801, app(ty_Maybe, df)) → new_esEs18(zu31101, zu4801, df)
new_esEs14(Right(zu311000), Right(zu48000), bh, ty_Integer) → new_esEs19(zu311000, zu48000)
new_esEs14(Right(zu311000), Right(zu48000), bh, app(app(app(ty_@3, bbc), bbd), bbe)) → new_esEs6(zu311000, zu48000, bbc, bbd, bbe)
new_esEs14(Right(zu311000), Right(zu48000), bh, ty_Char) → new_esEs21(zu311000, zu48000)
new_esEs9(zu311002, zu48002, ty_Ordering) → new_esEs11(zu311002, zu48002)
new_esEs7(zu311000, zu48000, ty_Int) → new_esEs15(zu311000, zu48000)
new_esEs9(zu311002, zu48002, ty_@0) → new_esEs13(zu311002, zu48002)
new_esEs24(zu311000, zu48000, ty_Ordering) → new_esEs11(zu311000, zu48000)
new_primEqInt(Neg(Zero), Pos(Succ(zu480000))) → False
new_primEqInt(Pos(Zero), Neg(Succ(zu480000))) → False
new_esEs26(zu311000, zu48000, app(ty_[], bhb)) → new_esEs17(zu311000, zu48000, bhb)
new_esEs14(Right(zu311000), Right(zu48000), bh, ty_@0) → new_esEs13(zu311000, zu48000)
new_esEs13(@0, @0) → True
new_esEs28(zu31101, zu4801, ty_Bool) → new_esEs5(zu31101, zu4801)
new_esEs26(zu311000, zu48000, ty_Float) → new_esEs12(zu311000, zu48000)
new_esEs14(Right(zu311000), Right(zu48000), bh, ty_Float) → new_esEs12(zu311000, zu48000)
new_esEs28(zu31101, zu4801, ty_Integer) → new_esEs19(zu31101, zu4801)
new_esEs24(zu311000, zu48000, app(ty_Maybe, beg)) → new_esEs18(zu311000, zu48000, beg)
new_esEs16(Double(zu311000, zu311001), Double(zu48000, zu48001)) → new_esEs15(new_sr(zu311000, zu48000), new_sr(zu311001, zu48001))
new_esEs11(EQ, EQ) → True
new_esEs27(zu31100, zu4800, ty_Double) → new_esEs16(zu31100, zu4800)
new_esEs28(zu31101, zu4801, ty_Float) → new_esEs12(zu31101, zu4801)
new_esEs8(zu311001, zu48001, ty_Int) → new_esEs15(zu311001, zu48001)
new_primMulNat0(Zero, Zero) → Zero
new_esEs14(Left(zu311000), Left(zu48000), ty_Double, ca) → new_esEs16(zu311000, zu48000)
new_esEs28(zu31101, zu4801, ty_Ordering) → new_esEs11(zu31101, zu4801)
new_esEs25(zu311001, zu48001, ty_Float) → new_esEs12(zu311001, zu48001)
new_esEs24(zu311000, zu48000, ty_@0) → new_esEs13(zu311000, zu48000)
new_esEs18(Just(zu311000), Just(zu48000), app(ty_Ratio, bdf)) → new_esEs20(zu311000, zu48000, bdf)
new_esEs17(:(zu311000, zu311001), :(zu48000, zu48001), cb) → new_asAs(new_esEs26(zu311000, zu48000, cb), new_esEs17(zu311001, zu48001, cb))
new_esEs8(zu311001, zu48001, app(app(app(ty_@3, fd), ff), fg)) → new_esEs6(zu311001, zu48001, fd, ff, fg)
new_esEs8(zu311001, zu48001, ty_Float) → new_esEs12(zu311001, zu48001)
new_esEs9(zu311002, zu48002, ty_Float) → new_esEs12(zu311002, zu48002)
new_esEs8(zu311001, zu48001, app(ty_Ratio, gd)) → new_esEs20(zu311001, zu48001, gd)
new_esEs9(zu311002, zu48002, app(app(ty_@2, ge), gf)) → new_esEs10(zu311002, zu48002, ge, gf)
new_primPlusNat0(Zero, zu4800100) → Succ(zu4800100)
new_esEs18(Just(zu311000), Just(zu48000), ty_Ordering) → new_esEs11(zu311000, zu48000)
new_esEs11(LT, GT) → False
new_esEs11(GT, LT) → False
new_esEs19(Integer(zu311000), Integer(zu48000)) → new_primEqInt(zu311000, zu48000)
new_esEs25(zu311001, zu48001, ty_Ordering) → new_esEs11(zu311001, zu48001)
new_esEs28(zu31101, zu4801, ty_Int) → new_esEs15(zu31101, zu4801)
new_esEs18(Just(zu311000), Just(zu48000), ty_Integer) → new_esEs19(zu311000, zu48000)
new_esEs7(zu311000, zu48000, app(ty_[], eg)) → new_esEs17(zu311000, zu48000, eg)
new_deleteBy1(zu3110, [], ba, bb) → []
new_esEs25(zu311001, zu48001, ty_Double) → new_esEs16(zu311001, zu48001)
new_sr(Neg(zu3110010), Pos(zu480010)) → Neg(new_primMulNat0(zu3110010, zu480010))
new_sr(Pos(zu3110010), Neg(zu480010)) → Neg(new_primMulNat0(zu3110010, zu480010))
new_esEs11(LT, EQ) → False
new_esEs11(EQ, LT) → False
new_esEs24(zu311000, zu48000, app(ty_[], bef)) → new_esEs17(zu311000, zu48000, bef)
new_esEs24(zu311000, zu48000, ty_Int) → new_esEs15(zu311000, zu48000)
new_esEs8(zu311001, zu48001, ty_Double) → new_esEs16(zu311001, zu48001)
new_esEs27(zu31100, zu4800, app(ty_Maybe, cc)) → new_esEs18(zu31100, zu4800, cc)
new_esEs24(zu311000, zu48000, app(app(ty_Either, bed), bee)) → new_esEs14(zu311000, zu48000, bed, bee)
new_esEs18(Just(zu311000), Just(zu48000), ty_Char) → new_esEs21(zu311000, zu48000)
new_esEs9(zu311002, zu48002, ty_Char) → new_esEs21(zu311002, zu48002)
new_esEs26(zu311000, zu48000, app(app(ty_Either, bgh), bha)) → new_esEs14(zu311000, zu48000, bgh, bha)
new_esEs8(zu311001, zu48001, ty_Bool) → new_esEs5(zu311001, zu48001)
new_esEs18(Just(zu311000), Just(zu48000), ty_Int) → new_esEs15(zu311000, zu48000)
new_esEs14(Left(zu311000), Left(zu48000), app(ty_Ratio, bah), ca) → new_esEs20(zu311000, zu48000, bah)
new_esEs8(zu311001, zu48001, ty_Ordering) → new_esEs11(zu311001, zu48001)
new_primEqNat0(Zero, Succ(zu4800000)) → False
new_primEqNat0(Succ(zu31100000), Zero) → False
new_esEs14(Left(zu311000), Left(zu48000), ty_Int, ca) → new_esEs15(zu311000, zu48000)
new_esEs14(Right(zu311000), Right(zu48000), bh, ty_Int) → new_esEs15(zu311000, zu48000)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs26(zu311000, zu48000, ty_Ordering) → new_esEs11(zu311000, zu48000)
new_esEs14(Right(zu311000), Right(zu48000), bh, ty_Double) → new_esEs16(zu311000, zu48000)
new_esEs28(zu31101, zu4801, app(app(app(ty_@3, cg), da), db)) → new_esEs6(zu31101, zu4801, cg, da, db)
new_esEs8(zu311001, zu48001, app(ty_Maybe, gc)) → new_esEs18(zu311001, zu48001, gc)
new_esEs26(zu311000, zu48000, app(ty_Maybe, bhc)) → new_esEs18(zu311000, zu48000, bhc)
new_esEs27(zu31100, zu4800, app(app(app(ty_@3, be), bf), bg)) → new_esEs6(zu31100, zu4800, be, bf, bg)
new_esEs8(zu311001, zu48001, ty_Char) → new_esEs21(zu311001, zu48001)
new_esEs18(Just(zu311000), Just(zu48000), app(app(app(ty_@3, bcg), bch), bda)) → new_esEs6(zu311000, zu48000, bcg, bch, bda)
new_esEs15(zu31100, zu4800) → new_primEqInt(zu31100, zu4800)
new_esEs28(zu31101, zu4801, ty_@0) → new_esEs13(zu31101, zu4801)
new_esEs26(zu311000, zu48000, ty_@0) → new_esEs13(zu311000, zu48000)
new_esEs24(zu311000, zu48000, ty_Integer) → new_esEs19(zu311000, zu48000)
new_esEs27(zu31100, zu4800, app(ty_Ratio, cd)) → new_esEs20(zu31100, zu4800, cd)
new_esEs14(Left(zu311000), Left(zu48000), app(ty_[], baf), ca) → new_esEs17(zu311000, zu48000, baf)
new_deleteBy1(@2(zu31100, zu31101), :(@2(zu4800, zu4801), zu481), ba, bb) → new_deleteBy00(zu481, zu4800, zu4801, zu31100, zu31101, new_asAs(new_esEs27(zu31100, zu4800, ba), new_esEs28(zu31101, zu4801, bb)), ba, bb)
new_esEs28(zu31101, zu4801, app(app(ty_@2, ce), cf)) → new_esEs10(zu31101, zu4801, ce, cf)
new_esEs24(zu311000, zu48000, ty_Char) → new_esEs21(zu311000, zu48000)
new_esEs26(zu311000, zu48000, ty_Bool) → new_esEs5(zu311000, zu48000)
new_esEs27(zu31100, zu4800, app(ty_[], cb)) → new_esEs17(zu31100, zu4800, cb)
new_esEs8(zu311001, zu48001, ty_Integer) → new_esEs19(zu311001, zu48001)
new_deleteBy00(zu70, zu71, zu72, zu73, zu74, True, bcc, bcd) → zu70
new_esEs18(Nothing, Nothing, cc) → True
new_esEs14(Right(zu311000), Right(zu48000), bh, app(app(ty_Either, bbf), bbg)) → new_esEs14(zu311000, zu48000, bbf, bbg)
new_esEs7(zu311000, zu48000, ty_Bool) → new_esEs5(zu311000, zu48000)
new_esEs14(Left(zu311000), Left(zu48000), app(app(ty_Either, bad), bae), ca) → new_esEs14(zu311000, zu48000, bad, bae)
new_esEs7(zu311000, zu48000, ty_Integer) → new_esEs19(zu311000, zu48000)
new_esEs7(zu311000, zu48000, app(app(ty_@2, dh), ea)) → new_esEs10(zu311000, zu48000, dh, ea)
new_esEs7(zu311000, zu48000, ty_Ordering) → new_esEs11(zu311000, zu48000)
new_esEs28(zu31101, zu4801, ty_Double) → new_esEs16(zu31101, zu4801)
new_esEs18(Just(zu311000), Just(zu48000), ty_Bool) → new_esEs5(zu311000, zu48000)
new_esEs11(GT, GT) → True
new_sr(Neg(zu3110010), Neg(zu480010)) → Pos(new_primMulNat0(zu3110010, zu480010))
new_esEs14(Right(zu311000), Right(zu48000), bh, ty_Bool) → new_esEs5(zu311000, zu48000)
new_asAs(False, zu89) → False
new_sr(Pos(zu3110010), Pos(zu480010)) → Pos(new_primMulNat0(zu3110010, zu480010))
new_esEs27(zu31100, zu4800, app(app(ty_@2, bc), bd)) → new_esEs10(zu31100, zu4800, bc, bd)
new_esEs6(@3(zu311000, zu311001, zu311002), @3(zu48000, zu48001, zu48002), be, bf, bg) → new_asAs(new_esEs7(zu311000, zu48000, be), new_asAs(new_esEs8(zu311001, zu48001, bf), new_esEs9(zu311002, zu48002, bg)))
new_primEqNat0(Zero, Zero) → True
new_esEs27(zu31100, zu4800, app(app(ty_Either, bh), ca)) → new_esEs14(zu31100, zu4800, bh, ca)
new_primMulNat0(Succ(zu31100100), Zero) → Zero
new_primMulNat0(Zero, Succ(zu4800100)) → Zero
new_esEs7(zu311000, zu48000, ty_Double) → new_esEs16(zu311000, zu48000)
new_esEs7(zu311000, zu48000, app(ty_Ratio, fa)) → new_esEs20(zu311000, zu48000, fa)
new_esEs14(Left(zu311000), Left(zu48000), ty_Float, ca) → new_esEs12(zu311000, zu48000)
new_esEs18(Just(zu311000), Nothing, cc) → False
new_esEs18(Nothing, Just(zu48000), cc) → False
new_esEs9(zu311002, zu48002, ty_Bool) → new_esEs5(zu311002, zu48002)
new_esEs25(zu311001, zu48001, ty_Bool) → new_esEs5(zu311001, zu48001)
new_esEs25(zu311001, zu48001, ty_Int) → new_esEs15(zu311001, zu48001)
new_esEs5(False, False) → True
new_esEs5(True, False) → False
new_esEs5(False, True) → False
new_esEs27(zu31100, zu4800, ty_@0) → new_esEs13(zu31100, zu4800)
new_esEs20(:%(zu311000, zu311001), :%(zu48000, zu48001), cd) → new_asAs(new_esEs22(zu311000, zu48000, cd), new_esEs23(zu311001, zu48001, cd))
new_esEs7(zu311000, zu48000, app(app(ty_Either, ee), ef)) → new_esEs14(zu311000, zu48000, ee, ef)
new_esEs25(zu311001, zu48001, app(ty_[], bfh)) → new_esEs17(zu311001, zu48001, bfh)
new_esEs26(zu311000, zu48000, app(app(ty_@2, bgc), bgd)) → new_esEs10(zu311000, zu48000, bgc, bgd)
new_esEs24(zu311000, zu48000, ty_Double) → new_esEs16(zu311000, zu48000)
new_esEs7(zu311000, zu48000, ty_@0) → new_esEs13(zu311000, zu48000)
new_esEs25(zu311001, zu48001, app(app(app(ty_@3, bfc), bfd), bfe)) → new_esEs6(zu311001, zu48001, bfc, bfd, bfe)
new_esEs27(zu31100, zu4800, ty_Integer) → new_esEs19(zu31100, zu4800)
new_esEs9(zu311002, zu48002, ty_Integer) → new_esEs19(zu311002, zu48002)
new_esEs8(zu311001, zu48001, app(app(ty_@2, fb), fc)) → new_esEs10(zu311001, zu48001, fb, fc)
new_primPlusNat0(Succ(zu910), zu4800100) → Succ(Succ(new_primPlusNat1(zu910, zu4800100)))
new_esEs26(zu311000, zu48000, app(app(app(ty_@3, bge), bgf), bgg)) → new_esEs6(zu311000, zu48000, bge, bgf, bgg)
new_esEs25(zu311001, zu48001, ty_Integer) → new_esEs19(zu311001, zu48001)
new_esEs5(True, True) → True
new_esEs25(zu311001, zu48001, ty_Char) → new_esEs21(zu311001, zu48001)
new_esEs27(zu31100, zu4800, ty_Bool) → new_esEs5(zu31100, zu4800)
new_deleteBy00(zu70, zu71, zu72, zu73, zu74, False, bcc, bcd) → :(@2(zu71, zu72), new_deleteBy1(@2(zu73, zu74), zu70, bcc, bcd))
new_esEs21(Char(zu311000), Char(zu48000)) → new_primEqInt(zu311000, zu48000)
new_primEqInt(Neg(Succ(zu3110000)), Neg(Succ(zu480000))) → new_primEqNat0(zu3110000, zu480000)
new_esEs28(zu31101, zu4801, app(ty_[], de)) → new_esEs17(zu31101, zu4801, de)
new_esEs23(zu311001, zu48001, ty_Int) → new_esEs15(zu311001, zu48001)
new_esEs27(zu31100, zu4800, ty_Char) → new_esEs21(zu31100, zu4800)
new_esEs28(zu31101, zu4801, app(ty_Ratio, dg)) → new_esEs20(zu31101, zu4801, dg)
new_primPlusNat1(Succ(zu9100), Zero) → Succ(zu9100)
new_primPlusNat1(Zero, Succ(zu48001000)) → Succ(zu48001000)
new_esEs27(zu31100, zu4800, ty_Int) → new_esEs15(zu31100, zu4800)
new_esEs14(Left(zu311000), Left(zu48000), ty_Integer, ca) → new_esEs19(zu311000, zu48000)
new_esEs14(Left(zu311000), Left(zu48000), app(ty_Maybe, bag), ca) → new_esEs18(zu311000, zu48000, bag)
new_esEs12(Float(zu311000, zu311001), Float(zu48000, zu48001)) → new_esEs15(new_sr(zu311000, zu48000), new_sr(zu311001, zu48001))
new_esEs22(zu311000, zu48000, ty_Int) → new_esEs15(zu311000, zu48000)
new_esEs28(zu31101, zu4801, app(app(ty_Either, dc), dd)) → new_esEs14(zu31101, zu4801, dc, dd)
new_esEs10(@2(zu311000, zu311001), @2(zu48000, zu48001), bc, bd) → new_asAs(new_esEs24(zu311000, zu48000, bc), new_esEs25(zu311001, zu48001, bd))
new_esEs14(Left(zu311000), Left(zu48000), ty_Bool, ca) → new_esEs5(zu311000, zu48000)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs26(zu311000, zu48000, ty_Integer) → new_esEs19(zu311000, zu48000)
new_esEs24(zu311000, zu48000, app(app(app(ty_@3, bea), beb), bec)) → new_esEs6(zu311000, zu48000, bea, beb, bec)
new_esEs9(zu311002, zu48002, ty_Double) → new_esEs16(zu311002, zu48002)
new_esEs9(zu311002, zu48002, app(ty_Ratio, hf)) → new_esEs20(zu311002, zu48002, hf)
new_primEqInt(Neg(Zero), Neg(Succ(zu480000))) → False
new_primEqInt(Neg(Succ(zu3110000)), Neg(Zero)) → False
new_esEs9(zu311002, zu48002, app(ty_[], hd)) → new_esEs17(zu311002, zu48002, hd)
new_esEs22(zu311000, zu48000, ty_Integer) → new_esEs19(zu311000, zu48000)
new_esEs8(zu311001, zu48001, app(ty_[], gb)) → new_esEs17(zu311001, zu48001, gb)
new_esEs14(Left(zu311000), Left(zu48000), app(app(app(ty_@3, baa), bab), bac), ca) → new_esEs6(zu311000, zu48000, baa, bab, bac)
new_esEs9(zu311002, zu48002, app(app(app(ty_@3, gg), gh), ha)) → new_esEs6(zu311002, zu48002, gg, gh, ha)
new_esEs7(zu311000, zu48000, ty_Char) → new_esEs21(zu311000, zu48000)
new_esEs14(Right(zu311000), Right(zu48000), bh, app(ty_[], bbh)) → new_esEs17(zu311000, zu48000, bbh)
new_primPlusNat1(Zero, Zero) → Zero
new_esEs9(zu311002, zu48002, app(app(ty_Either, hb), hc)) → new_esEs14(zu311002, zu48002, hb, hc)
new_esEs25(zu311001, zu48001, app(app(ty_@2, bfa), bfb)) → new_esEs10(zu311001, zu48001, bfa, bfb)
new_asAs(True, zu89) → zu89
new_primMulNat0(Succ(zu31100100), Succ(zu4800100)) → new_primPlusNat0(new_primMulNat0(zu31100100, Succ(zu4800100)), zu4800100)
new_esEs18(Just(zu311000), Just(zu48000), ty_Double) → new_esEs16(zu311000, zu48000)
new_esEs11(LT, LT) → True
new_esEs24(zu311000, zu48000, app(app(ty_@2, bdg), bdh)) → new_esEs10(zu311000, zu48000, bdg, bdh)
new_esEs8(zu311001, zu48001, ty_@0) → new_esEs13(zu311001, zu48001)
new_esEs18(Just(zu311000), Just(zu48000), app(app(ty_@2, bce), bcf)) → new_esEs10(zu311000, zu48000, bce, bcf)
new_primEqInt(Pos(Succ(zu3110000)), Pos(Succ(zu480000))) → new_primEqNat0(zu3110000, zu480000)
new_esEs14(Left(zu311000), Left(zu48000), app(app(ty_@2, hg), hh), ca) → new_esEs10(zu311000, zu48000, hg, hh)
new_esEs7(zu311000, zu48000, app(ty_Maybe, eh)) → new_esEs18(zu311000, zu48000, eh)
new_esEs17([], [], cb) → True
new_esEs17(:(zu311000, zu311001), [], cb) → False
new_esEs17([], :(zu48000, zu48001), cb) → False
new_esEs26(zu311000, zu48000, ty_Double) → new_esEs16(zu311000, zu48000)
new_esEs24(zu311000, zu48000, app(ty_Ratio, beh)) → new_esEs20(zu311000, zu48000, beh)
new_esEs9(zu311002, zu48002, ty_Int) → new_esEs15(zu311002, zu48002)
new_esEs18(Just(zu311000), Just(zu48000), ty_@0) → new_esEs13(zu311000, zu48000)
new_esEs25(zu311001, zu48001, app(app(ty_Either, bff), bfg)) → new_esEs14(zu311001, zu48001, bff, bfg)
new_esEs24(zu311000, zu48000, ty_Bool) → new_esEs5(zu311000, zu48000)
new_primEqNat0(Succ(zu31100000), Succ(zu4800000)) → new_primEqNat0(zu31100000, zu4800000)
new_esEs11(EQ, GT) → False
new_esEs11(GT, EQ) → False
new_esEs18(Just(zu311000), Just(zu48000), app(ty_[], bdd)) → new_esEs17(zu311000, zu48000, bdd)
new_esEs14(Right(zu311000), Right(zu48000), bh, app(ty_Maybe, bca)) → new_esEs18(zu311000, zu48000, bca)
new_esEs14(Right(zu311000), Right(zu48000), bh, app(ty_Ratio, bcb)) → new_esEs20(zu311000, zu48000, bcb)
new_esEs26(zu311000, zu48000, ty_Int) → new_esEs15(zu311000, zu48000)
new_esEs27(zu31100, zu4800, ty_Float) → new_esEs12(zu31100, zu4800)
new_esEs8(zu311001, zu48001, app(app(ty_Either, fh), ga)) → new_esEs14(zu311001, zu48001, fh, ga)
new_esEs9(zu311002, zu48002, app(ty_Maybe, he)) → new_esEs18(zu311002, zu48002, he)
new_esEs18(Just(zu311000), Just(zu48000), app(ty_Maybe, bde)) → new_esEs18(zu311000, zu48000, bde)
new_esEs18(Just(zu311000), Just(zu48000), ty_Float) → new_esEs12(zu311000, zu48000)
new_primEqInt(Pos(Zero), Pos(Succ(zu480000))) → False
new_primEqInt(Pos(Succ(zu3110000)), Pos(Zero)) → False
new_esEs14(Left(zu311000), Left(zu48000), ty_Ordering, ca) → new_esEs11(zu311000, zu48000)
new_esEs7(zu311000, zu48000, app(app(app(ty_@3, eb), ec), ed)) → new_esEs6(zu311000, zu48000, eb, ec, ed)
new_esEs25(zu311001, zu48001, app(ty_Ratio, bgb)) → new_esEs20(zu311001, zu48001, bgb)
new_esEs25(zu311001, zu48001, app(ty_Maybe, bga)) → new_esEs18(zu311001, zu48001, bga)
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_esEs14(Left(zu311000), Left(zu48000), ty_@0, ca) → new_esEs13(zu311000, zu48000)
new_esEs26(zu311000, zu48000, ty_Char) → new_esEs21(zu311000, zu48000)
new_esEs14(Left(zu311000), Left(zu48000), ty_Char, ca) → new_esEs21(zu311000, zu48000)
new_esEs26(zu311000, zu48000, app(ty_Ratio, bhd)) → new_esEs20(zu311000, zu48000, bhd)
new_esEs7(zu311000, zu48000, ty_Float) → new_esEs12(zu311000, zu48000)
The set Q consists of the following terms:
new_esEs24(x0, x1, ty_@0)
new_esEs14(Left(x0), Left(x1), ty_Bool, x2)
new_esEs14(Right(x0), Right(x1), x2, ty_Double)
new_esEs13(@0, @0)
new_esEs25(x0, x1, ty_Char)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs28(x0, x1, ty_Integer)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_esEs24(x0, x1, ty_Char)
new_esEs28(x0, x1, app(ty_[], x2))
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_esEs26(x0, x1, ty_Double)
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_esEs26(x0, x1, ty_Char)
new_deleteBy00(x0, x1, x2, x3, x4, False, x5, x6)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_esEs14(Left(x0), Left(x1), ty_Double, x2)
new_esEs7(x0, x1, ty_Float)
new_esEs19(Integer(x0), Integer(x1))
new_deleteBy1(x0, [], x1, x2)
new_primEqInt(Neg(Zero), Pos(Zero))
new_primEqInt(Pos(Zero), Neg(Zero))
new_esEs8(x0, x1, app(app(ty_@2, x2), x3))
new_esEs14(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs7(x0, x1, ty_@0)
new_sr(Pos(x0), Pos(x1))
new_esEs18(Just(x0), Just(x1), ty_Float)
new_esEs7(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs24(x0, x1, ty_Bool)
new_esEs11(LT, EQ)
new_esEs11(EQ, LT)
new_esEs18(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs8(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs7(x0, x1, app(app(ty_@2, x2), x3))
new_esEs8(x0, x1, ty_Float)
new_esEs8(x0, x1, ty_Char)
new_primEqInt(Neg(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs14(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs8(x0, x1, ty_@0)
new_esEs24(x0, x1, ty_Ordering)
new_esEs27(x0, x1, ty_Integer)
new_esEs18(Just(x0), Just(x1), app(ty_[], x2))
new_esEs27(x0, x1, ty_Int)
new_esEs14(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_primEqNat0(Zero, Succ(x0))
new_esEs7(x0, x1, app(ty_[], x2))
new_primPlusNat1(Succ(x0), Zero)
new_esEs6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs17(:(x0, x1), :(x2, x3), x4)
new_sr(Neg(x0), Neg(x1))
new_esEs28(x0, x1, ty_@0)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs25(x0, x1, ty_Float)
new_esEs14(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs25(x0, x1, ty_@0)
new_esEs5(False, True)
new_esEs5(True, False)
new_esEs20(:%(x0, x1), :%(x2, x3), x4)
new_esEs27(x0, x1, app(ty_[], x2))
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs14(Left(x0), Left(x1), ty_Float, x2)
new_esEs26(x0, x1, app(ty_[], x2))
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_esEs16(Double(x0, x1), Double(x2, x3))
new_primEqNat0(Succ(x0), Zero)
new_esEs18(Just(x0), Just(x1), ty_Int)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs14(Left(x0), Right(x1), x2, x3)
new_esEs14(Right(x0), Left(x1), x2, x3)
new_esEs8(x0, x1, ty_Ordering)
new_esEs27(x0, x1, ty_Double)
new_esEs24(x0, x1, app(ty_[], x2))
new_esEs24(x0, x1, ty_Int)
new_primMulNat0(Zero, Succ(x0))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_esEs14(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs14(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_esEs9(x0, x1, app(app(ty_@2, x2), x3))
new_esEs18(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs11(EQ, GT)
new_esEs11(GT, EQ)
new_esEs26(x0, x1, ty_@0)
new_esEs28(x0, x1, ty_Float)
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, ty_Float)
new_esEs14(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs5(True, True)
new_esEs14(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs17(:(x0, x1), [], x2)
new_primEqNat0(Zero, Zero)
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_esEs24(x0, x1, ty_Integer)
new_esEs8(x0, x1, ty_Bool)
new_esEs25(x0, x1, app(ty_[], x2))
new_esEs8(x0, x1, ty_Integer)
new_esEs9(x0, x1, ty_Double)
new_esEs9(x0, x1, app(ty_Ratio, x2))
new_esEs26(x0, x1, ty_Ordering)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs9(x0, x1, ty_Char)
new_esEs5(False, False)
new_esEs18(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs14(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs25(x0, x1, ty_Double)
new_esEs23(x0, x1, ty_Int)
new_esEs7(x0, x1, ty_Char)
new_esEs14(Left(x0), Left(x1), ty_Integer, x2)
new_esEs7(x0, x1, ty_Ordering)
new_esEs25(x0, x1, ty_Int)
new_esEs14(Left(x0), Left(x1), ty_@0, x2)
new_esEs27(x0, x1, ty_Ordering)
new_primMulNat0(Zero, Zero)
new_esEs14(Left(x0), Left(x1), ty_Char, x2)
new_esEs9(x0, x1, app(ty_[], x2))
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_esEs28(x0, x1, ty_Int)
new_esEs9(x0, x1, ty_@0)
new_esEs7(x0, x1, ty_Integer)
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_esEs24(x0, x1, ty_Double)
new_deleteBy00(x0, x1, x2, x3, x4, True, x5, x6)
new_esEs11(GT, GT)
new_primPlusNat0(Zero, x0)
new_esEs7(x0, x1, app(ty_Ratio, x2))
new_primMulNat0(Succ(x0), Succ(x1))
new_esEs25(x0, x1, ty_Ordering)
new_esEs26(x0, x1, ty_Int)
new_esEs26(x0, x1, ty_Bool)
new_esEs18(Just(x0), Just(x1), ty_Char)
new_esEs14(Right(x0), Right(x1), x2, ty_Integer)
new_esEs8(x0, x1, app(ty_Ratio, x2))
new_esEs7(x0, x1, ty_Bool)
new_esEs17([], [], x0)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_esEs18(Just(x0), Just(x1), ty_Bool)
new_esEs27(x0, x1, ty_Char)
new_esEs11(LT, GT)
new_esEs11(GT, LT)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_asAs(True, x0)
new_esEs18(Just(x0), Just(x1), app(ty_Ratio, x2))
new_asAs(False, x0)
new_esEs14(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs24(x0, x1, ty_Float)
new_esEs21(Char(x0), Char(x1))
new_sr(Neg(x0), Pos(x1))
new_sr(Pos(x0), Neg(x1))
new_esEs14(Right(x0), Right(x1), x2, ty_Char)
new_esEs27(x0, x1, ty_@0)
new_esEs18(Nothing, Nothing, x0)
new_esEs9(x0, x1, ty_Int)
new_esEs7(x0, x1, ty_Int)
new_esEs10(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs26(x0, x1, ty_Integer)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_esEs9(x0, x1, ty_Integer)
new_esEs18(Just(x0), Just(x1), ty_Integer)
new_esEs9(x0, x1, ty_Float)
new_esEs9(x0, x1, app(app(ty_Either, x2), x3))
new_esEs7(x0, x1, ty_Double)
new_esEs7(x0, x1, app(ty_Maybe, x2))
new_esEs15(x0, x1)
new_esEs14(Right(x0), Right(x1), x2, ty_@0)
new_esEs26(x0, x1, ty_Float)
new_esEs8(x0, x1, ty_Double)
new_esEs28(x0, x1, ty_Char)
new_esEs23(x0, x1, ty_Integer)
new_esEs17([], :(x0, x1), x2)
new_esEs28(x0, x1, ty_Double)
new_esEs18(Nothing, Just(x0), x1)
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_esEs18(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs18(Just(x0), Nothing, x1)
new_esEs14(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs9(x0, x1, ty_Ordering)
new_esEs22(x0, x1, ty_Integer)
new_esEs11(LT, LT)
new_esEs8(x0, x1, ty_Int)
new_esEs9(x0, x1, ty_Bool)
new_esEs7(x0, x1, app(app(ty_Either, x2), x3))
new_esEs14(Left(x0), Left(x1), ty_Int, x2)
new_primPlusNat1(Zero, Zero)
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_primMulNat0(Succ(x0), Zero)
new_esEs14(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs14(Right(x0), Right(x1), x2, ty_Int)
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_esEs28(x0, x1, ty_Bool)
new_esEs14(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs14(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_primEqInt(Pos(Zero), Pos(Zero))
new_esEs8(x0, x1, app(ty_[], x2))
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs11(EQ, EQ)
new_esEs18(Just(x0), Just(x1), ty_Ordering)
new_esEs27(x0, x1, ty_Bool)
new_esEs25(x0, x1, ty_Integer)
new_primPlusNat1(Zero, Succ(x0))
new_esEs9(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs18(Just(x0), Just(x1), ty_@0)
new_esEs12(Float(x0, x1), Float(x2, x3))
new_esEs14(Right(x0), Right(x1), x2, ty_Bool)
new_esEs14(Right(x0), Right(x1), x2, ty_Float)
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_deleteBy1(@2(x0, x1), :(@2(x2, x3), x4), x5, x6)
new_esEs8(x0, x1, app(ty_Maybe, x2))
new_esEs22(x0, x1, ty_Int)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_esEs28(x0, x1, ty_Ordering)
new_esEs8(x0, x1, app(app(ty_Either, x2), x3))
new_esEs9(x0, x1, app(ty_Maybe, x2))
new_primPlusNat0(Succ(x0), x1)
new_esEs25(x0, x1, ty_Bool)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_esEs18(Just(x0), Just(x1), ty_Double)
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_foldl(zu48, :(zu3110, zu3111), ba, bb) → new_foldl(new_deleteBy1(zu3110, zu48, ba, bb), zu3111, ba, bb)
The graph contains the following edges 2 > 2, 3 >= 3, 4 >= 4
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDPSizeChangeProof
↳ QDP
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_psPs(:(zu311111110, zu311111111), zu45, ba, bb) → new_psPs(zu311111111, zu45, ba, bb)
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_psPs(:(zu311111110, zu311111111), zu45, ba, bb) → new_psPs(zu311111111, zu45, ba, bb)
The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3, 4 >= 4
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDPSizeChangeProof
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_esEs(@2(zu311000, zu311001), @2(zu48000, zu48001), app(app(ty_@2, ba), bb), bc) → new_esEs(zu311000, zu48000, ba, bb)
new_esEs1(Right(zu311000), Right(zu48000), bag, app(ty_Maybe, bbh)) → new_esEs3(zu311000, zu48000, bbh)
new_esEs0(@3(zu311000, zu311001, zu311002), @3(zu48000, zu48001, zu48002), fa, dh, app(app(ty_Either, ha), hb)) → new_esEs1(zu311002, zu48002, ha, hb)
new_esEs(@2(zu311000, zu311001), @2(zu48000, zu48001), cc, app(app(app(ty_@3, cf), cg), da)) → new_esEs0(zu311001, zu48001, cf, cg, da)
new_esEs0(@3(zu311000, zu311001, zu311002), @3(zu48000, zu48001, zu48002), app(ty_Maybe, eh), dh, ea) → new_esEs3(zu311000, zu48000, eh)
new_esEs(@2(zu311000, zu311001), @2(zu48000, zu48001), cc, app(ty_[], dd)) → new_esEs2(zu311001, zu48001, dd)
new_esEs2(:(zu311000, zu311001), :(zu48000, zu48001), app(ty_Maybe, bda)) → new_esEs3(zu311000, zu48000, bda)
new_esEs0(@3(zu311000, zu311001, zu311002), @3(zu48000, zu48001, zu48002), fa, dh, app(app(ty_@2, gd), ge)) → new_esEs(zu311002, zu48002, gd, ge)
new_esEs1(Left(zu311000), Left(zu48000), app(app(app(ty_@3, hh), baa), bab), hg) → new_esEs0(zu311000, zu48000, hh, baa, bab)
new_esEs1(Left(zu311000), Left(zu48000), app(ty_[], bae), hg) → new_esEs2(zu311000, zu48000, bae)
new_esEs3(Just(zu311000), Just(zu48000), app(ty_[], beb)) → new_esEs2(zu311000, zu48000, beb)
new_esEs(@2(zu311000, zu311001), @2(zu48000, zu48001), app(ty_Maybe, cb), bc) → new_esEs3(zu311000, zu48000, cb)
new_esEs0(@3(zu311000, zu311001, zu311002), @3(zu48000, zu48001, zu48002), app(app(ty_Either, ee), ef), dh, ea) → new_esEs1(zu311000, zu48000, ee, ef)
new_esEs2(:(zu311000, zu311001), :(zu48000, zu48001), app(app(app(ty_@3, bcc), bcd), bce)) → new_esEs0(zu311000, zu48000, bcc, bcd, bce)
new_esEs0(@3(zu311000, zu311001, zu311002), @3(zu48000, zu48001, zu48002), app(ty_[], eg), dh, ea) → new_esEs2(zu311000, zu48000, eg)
new_esEs1(Right(zu311000), Right(zu48000), bag, app(app(app(ty_@3, bbb), bbc), bbd)) → new_esEs0(zu311000, zu48000, bbb, bbc, bbd)
new_esEs0(@3(zu311000, zu311001, zu311002), @3(zu48000, zu48001, zu48002), fa, app(app(ty_@2, fb), fc), ea) → new_esEs(zu311001, zu48001, fb, fc)
new_esEs1(Left(zu311000), Left(zu48000), app(app(ty_Either, bac), bad), hg) → new_esEs1(zu311000, zu48000, bac, bad)
new_esEs1(Right(zu311000), Right(zu48000), bag, app(app(ty_Either, bbe), bbf)) → new_esEs1(zu311000, zu48000, bbe, bbf)
new_esEs0(@3(zu311000, zu311001, zu311002), @3(zu48000, zu48001, zu48002), fa, app(app(app(ty_@3, fd), ff), fg), ea) → new_esEs0(zu311001, zu48001, fd, ff, fg)
new_esEs0(@3(zu311000, zu311001, zu311002), @3(zu48000, zu48001, zu48002), fa, app(app(ty_Either, fh), ga), ea) → new_esEs1(zu311001, zu48001, fh, ga)
new_esEs0(@3(zu311000, zu311001, zu311002), @3(zu48000, zu48001, zu48002), app(app(ty_@2, df), dg), dh, ea) → new_esEs(zu311000, zu48000, df, dg)
new_esEs(@2(zu311000, zu311001), @2(zu48000, zu48001), cc, app(ty_Maybe, de)) → new_esEs3(zu311001, zu48001, de)
new_esEs3(Just(zu311000), Just(zu48000), app(app(app(ty_@3, bde), bdf), bdg)) → new_esEs0(zu311000, zu48000, bde, bdf, bdg)
new_esEs0(@3(zu311000, zu311001, zu311002), @3(zu48000, zu48001, zu48002), fa, app(ty_Maybe, gc), ea) → new_esEs3(zu311001, zu48001, gc)
new_esEs0(@3(zu311000, zu311001, zu311002), @3(zu48000, zu48001, zu48002), fa, dh, app(ty_Maybe, hd)) → new_esEs3(zu311002, zu48002, hd)
new_esEs0(@3(zu311000, zu311001, zu311002), @3(zu48000, zu48001, zu48002), fa, app(ty_[], gb), ea) → new_esEs2(zu311001, zu48001, gb)
new_esEs0(@3(zu311000, zu311001, zu311002), @3(zu48000, zu48001, zu48002), fa, dh, app(app(app(ty_@3, gf), gg), gh)) → new_esEs0(zu311002, zu48002, gf, gg, gh)
new_esEs1(Right(zu311000), Right(zu48000), bag, app(app(ty_@2, bah), bba)) → new_esEs(zu311000, zu48000, bah, bba)
new_esEs(@2(zu311000, zu311001), @2(zu48000, zu48001), cc, app(app(ty_Either, db), dc)) → new_esEs1(zu311001, zu48001, db, dc)
new_esEs2(:(zu311000, zu311001), :(zu48000, zu48001), app(app(ty_Either, bcf), bcg)) → new_esEs1(zu311000, zu48000, bcf, bcg)
new_esEs2(:(zu311000, zu311001), :(zu48000, zu48001), bdb) → new_esEs2(zu311001, zu48001, bdb)
new_esEs3(Just(zu311000), Just(zu48000), app(ty_Maybe, bec)) → new_esEs3(zu311000, zu48000, bec)
new_esEs2(:(zu311000, zu311001), :(zu48000, zu48001), app(app(ty_@2, bca), bcb)) → new_esEs(zu311000, zu48000, bca, bcb)
new_esEs3(Just(zu311000), Just(zu48000), app(app(ty_@2, bdc), bdd)) → new_esEs(zu311000, zu48000, bdc, bdd)
new_esEs0(@3(zu311000, zu311001, zu311002), @3(zu48000, zu48001, zu48002), fa, dh, app(ty_[], hc)) → new_esEs2(zu311002, zu48002, hc)
new_esEs(@2(zu311000, zu311001), @2(zu48000, zu48001), cc, app(app(ty_@2, cd), ce)) → new_esEs(zu311001, zu48001, cd, ce)
new_esEs2(:(zu311000, zu311001), :(zu48000, zu48001), app(ty_[], bch)) → new_esEs2(zu311000, zu48000, bch)
new_esEs1(Left(zu311000), Left(zu48000), app(ty_Maybe, baf), hg) → new_esEs3(zu311000, zu48000, baf)
new_esEs1(Left(zu311000), Left(zu48000), app(app(ty_@2, he), hf), hg) → new_esEs(zu311000, zu48000, he, hf)
new_esEs1(Right(zu311000), Right(zu48000), bag, app(ty_[], bbg)) → new_esEs2(zu311000, zu48000, bbg)
new_esEs(@2(zu311000, zu311001), @2(zu48000, zu48001), app(app(app(ty_@3, bd), be), bf), bc) → new_esEs0(zu311000, zu48000, bd, be, bf)
new_esEs3(Just(zu311000), Just(zu48000), app(app(ty_Either, bdh), bea)) → new_esEs1(zu311000, zu48000, bdh, bea)
new_esEs(@2(zu311000, zu311001), @2(zu48000, zu48001), app(app(ty_Either, bg), bh), bc) → new_esEs1(zu311000, zu48000, bg, bh)
new_esEs0(@3(zu311000, zu311001, zu311002), @3(zu48000, zu48001, zu48002), app(app(app(ty_@3, eb), ec), ed), dh, ea) → new_esEs0(zu311000, zu48000, eb, ec, ed)
new_esEs(@2(zu311000, zu311001), @2(zu48000, zu48001), app(ty_[], ca), bc) → new_esEs2(zu311000, zu48000, ca)
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_esEs3(Just(zu311000), Just(zu48000), app(app(ty_@2, bdc), bdd)) → new_esEs(zu311000, zu48000, bdc, bdd)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
- new_esEs3(Just(zu311000), Just(zu48000), app(app(ty_Either, bdh), bea)) → new_esEs1(zu311000, zu48000, bdh, bea)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
- new_esEs2(:(zu311000, zu311001), :(zu48000, zu48001), app(app(ty_@2, bca), bcb)) → new_esEs(zu311000, zu48000, bca, bcb)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
- new_esEs3(Just(zu311000), Just(zu48000), app(app(app(ty_@3, bde), bdf), bdg)) → new_esEs0(zu311000, zu48000, bde, bdf, bdg)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
- new_esEs2(:(zu311000, zu311001), :(zu48000, zu48001), app(app(ty_Either, bcf), bcg)) → new_esEs1(zu311000, zu48000, bcf, bcg)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
- new_esEs2(:(zu311000, zu311001), :(zu48000, zu48001), app(app(app(ty_@3, bcc), bcd), bce)) → new_esEs0(zu311000, zu48000, bcc, bcd, bce)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
- new_esEs3(Just(zu311000), Just(zu48000), app(ty_[], beb)) → new_esEs2(zu311000, zu48000, beb)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
- new_esEs3(Just(zu311000), Just(zu48000), app(ty_Maybe, bec)) → new_esEs3(zu311000, zu48000, bec)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
- new_esEs2(:(zu311000, zu311001), :(zu48000, zu48001), app(ty_Maybe, bda)) → new_esEs3(zu311000, zu48000, bda)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
- new_esEs(@2(zu311000, zu311001), @2(zu48000, zu48001), app(app(ty_@2, ba), bb), bc) → new_esEs(zu311000, zu48000, ba, bb)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
- new_esEs(@2(zu311000, zu311001), @2(zu48000, zu48001), cc, app(app(ty_@2, cd), ce)) → new_esEs(zu311001, zu48001, cd, ce)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
- new_esEs(@2(zu311000, zu311001), @2(zu48000, zu48001), cc, app(app(ty_Either, db), dc)) → new_esEs1(zu311001, zu48001, db, dc)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
- new_esEs(@2(zu311000, zu311001), @2(zu48000, zu48001), app(app(ty_Either, bg), bh), bc) → new_esEs1(zu311000, zu48000, bg, bh)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
- new_esEs(@2(zu311000, zu311001), @2(zu48000, zu48001), cc, app(app(app(ty_@3, cf), cg), da)) → new_esEs0(zu311001, zu48001, cf, cg, da)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5
- new_esEs(@2(zu311000, zu311001), @2(zu48000, zu48001), app(app(app(ty_@3, bd), be), bf), bc) → new_esEs0(zu311000, zu48000, bd, be, bf)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
- new_esEs(@2(zu311000, zu311001), @2(zu48000, zu48001), cc, app(ty_[], dd)) → new_esEs2(zu311001, zu48001, dd)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
- new_esEs(@2(zu311000, zu311001), @2(zu48000, zu48001), app(ty_[], ca), bc) → new_esEs2(zu311000, zu48000, ca)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
- new_esEs(@2(zu311000, zu311001), @2(zu48000, zu48001), app(ty_Maybe, cb), bc) → new_esEs3(zu311000, zu48000, cb)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
- new_esEs(@2(zu311000, zu311001), @2(zu48000, zu48001), cc, app(ty_Maybe, de)) → new_esEs3(zu311001, zu48001, de)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
- new_esEs0(@3(zu311000, zu311001, zu311002), @3(zu48000, zu48001, zu48002), fa, dh, app(app(ty_@2, gd), ge)) → new_esEs(zu311002, zu48002, gd, ge)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4
- new_esEs0(@3(zu311000, zu311001, zu311002), @3(zu48000, zu48001, zu48002), fa, app(app(ty_@2, fb), fc), ea) → new_esEs(zu311001, zu48001, fb, fc)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
- new_esEs0(@3(zu311000, zu311001, zu311002), @3(zu48000, zu48001, zu48002), app(app(ty_@2, df), dg), dh, ea) → new_esEs(zu311000, zu48000, df, dg)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
- new_esEs1(Right(zu311000), Right(zu48000), bag, app(app(ty_@2, bah), bba)) → new_esEs(zu311000, zu48000, bah, bba)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
- new_esEs1(Left(zu311000), Left(zu48000), app(app(ty_@2, he), hf), hg) → new_esEs(zu311000, zu48000, he, hf)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
- new_esEs0(@3(zu311000, zu311001, zu311002), @3(zu48000, zu48001, zu48002), fa, dh, app(app(ty_Either, ha), hb)) → new_esEs1(zu311002, zu48002, ha, hb)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4
- new_esEs0(@3(zu311000, zu311001, zu311002), @3(zu48000, zu48001, zu48002), app(app(ty_Either, ee), ef), dh, ea) → new_esEs1(zu311000, zu48000, ee, ef)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
- new_esEs0(@3(zu311000, zu311001, zu311002), @3(zu48000, zu48001, zu48002), fa, app(app(ty_Either, fh), ga), ea) → new_esEs1(zu311001, zu48001, fh, ga)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
- new_esEs1(Left(zu311000), Left(zu48000), app(app(ty_Either, bac), bad), hg) → new_esEs1(zu311000, zu48000, bac, bad)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
- new_esEs1(Right(zu311000), Right(zu48000), bag, app(app(ty_Either, bbe), bbf)) → new_esEs1(zu311000, zu48000, bbe, bbf)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
- new_esEs0(@3(zu311000, zu311001, zu311002), @3(zu48000, zu48001, zu48002), fa, app(app(app(ty_@3, fd), ff), fg), ea) → new_esEs0(zu311001, zu48001, fd, ff, fg)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5
- new_esEs0(@3(zu311000, zu311001, zu311002), @3(zu48000, zu48001, zu48002), fa, dh, app(app(app(ty_@3, gf), gg), gh)) → new_esEs0(zu311002, zu48002, gf, gg, gh)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4, 5 > 5
- new_esEs0(@3(zu311000, zu311001, zu311002), @3(zu48000, zu48001, zu48002), app(app(app(ty_@3, eb), ec), ed), dh, ea) → new_esEs0(zu311000, zu48000, eb, ec, ed)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
- new_esEs0(@3(zu311000, zu311001, zu311002), @3(zu48000, zu48001, zu48002), app(ty_[], eg), dh, ea) → new_esEs2(zu311000, zu48000, eg)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
- new_esEs0(@3(zu311000, zu311001, zu311002), @3(zu48000, zu48001, zu48002), fa, app(ty_[], gb), ea) → new_esEs2(zu311001, zu48001, gb)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
- new_esEs0(@3(zu311000, zu311001, zu311002), @3(zu48000, zu48001, zu48002), fa, dh, app(ty_[], hc)) → new_esEs2(zu311002, zu48002, hc)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3
- new_esEs0(@3(zu311000, zu311001, zu311002), @3(zu48000, zu48001, zu48002), app(ty_Maybe, eh), dh, ea) → new_esEs3(zu311000, zu48000, eh)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
- new_esEs0(@3(zu311000, zu311001, zu311002), @3(zu48000, zu48001, zu48002), fa, app(ty_Maybe, gc), ea) → new_esEs3(zu311001, zu48001, gc)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
- new_esEs0(@3(zu311000, zu311001, zu311002), @3(zu48000, zu48001, zu48002), fa, dh, app(ty_Maybe, hd)) → new_esEs3(zu311002, zu48002, hd)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3
- new_esEs1(Left(zu311000), Left(zu48000), app(app(app(ty_@3, hh), baa), bab), hg) → new_esEs0(zu311000, zu48000, hh, baa, bab)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
- new_esEs1(Right(zu311000), Right(zu48000), bag, app(app(app(ty_@3, bbb), bbc), bbd)) → new_esEs0(zu311000, zu48000, bbb, bbc, bbd)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5
- new_esEs1(Left(zu311000), Left(zu48000), app(ty_[], bae), hg) → new_esEs2(zu311000, zu48000, bae)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
- new_esEs1(Right(zu311000), Right(zu48000), bag, app(ty_[], bbg)) → new_esEs2(zu311000, zu48000, bbg)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
- new_esEs1(Right(zu311000), Right(zu48000), bag, app(ty_Maybe, bbh)) → new_esEs3(zu311000, zu48000, bbh)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
- new_esEs1(Left(zu311000), Left(zu48000), app(ty_Maybe, baf), hg) → new_esEs3(zu311000, zu48000, baf)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
- new_esEs2(:(zu311000, zu311001), :(zu48000, zu48001), bdb) → new_esEs2(zu311001, zu48001, bdb)
The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3
- new_esEs2(:(zu311000, zu311001), :(zu48000, zu48001), app(ty_[], bch)) → new_esEs2(zu311000, zu48000, bch)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDPSizeChangeProof
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_primEqNat(Succ(zu31100000), Succ(zu4800000)) → new_primEqNat(zu31100000, zu4800000)
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(zu31100000), Succ(zu4800000)) → new_primEqNat(zu31100000, zu4800000)
The graph contains the following edges 1 > 1, 2 > 2
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDPSizeChangeProof
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_deleteBy0(zu70, zu71, zu72, zu73, zu74, False, ba, bb) → new_deleteBy(@2(zu73, zu74), zu70, ba, bb)
new_deleteBy(@2(zu31100, zu31101), :(@2(zu4800, zu4801), zu481), bc, bd) → new_deleteBy0(zu481, zu4800, zu4801, zu31100, zu31101, new_asAs(new_esEs27(zu31100, zu4800, bc), new_esEs28(zu31101, zu4801, bd)), bc, bd)
The TRS R consists of the following rules:
new_esEs28(zu31101, zu4801, ty_Char) → new_esEs21(zu31101, zu4801)
new_esEs24(zu311000, zu48000, ty_Float) → new_esEs12(zu311000, zu48000)
new_primPlusNat1(Succ(zu9100), Succ(zu48001000)) → Succ(Succ(new_primPlusNat1(zu9100, zu48001000)))
new_primEqInt(Neg(Succ(zu3110000)), Pos(zu48000)) → False
new_primEqInt(Pos(Succ(zu3110000)), Neg(zu48000)) → False
new_esEs27(zu31100, zu4800, ty_Ordering) → new_esEs11(zu31100, zu4800)
new_esEs18(Just(zu311000), Just(zu48000), app(app(ty_Either, bbh), bca)) → new_esEs14(zu311000, zu48000, bbh, bca)
new_esEs14(Right(zu311000), Right(zu48000), cb, ty_Ordering) → new_esEs11(zu311000, zu48000)
new_esEs14(Left(zu311000), Right(zu48000), cb, cc) → False
new_esEs14(Right(zu311000), Left(zu48000), cb, cc) → False
new_esEs14(Right(zu311000), Right(zu48000), cb, app(app(ty_@2, baa), bab)) → new_esEs10(zu311000, zu48000, baa, bab)
new_esEs25(zu311001, zu48001, ty_@0) → new_esEs13(zu311001, zu48001)
new_esEs23(zu311001, zu48001, ty_Integer) → new_esEs19(zu311001, zu48001)
new_esEs28(zu31101, zu4801, app(ty_Maybe, bga)) → new_esEs18(zu31101, zu4801, bga)
new_esEs14(Right(zu311000), Right(zu48000), cb, ty_Integer) → new_esEs19(zu311000, zu48000)
new_esEs14(Right(zu311000), Right(zu48000), cb, app(app(app(ty_@3, bac), bad), bae)) → new_esEs6(zu311000, zu48000, bac, bad, bae)
new_esEs14(Right(zu311000), Right(zu48000), cb, ty_Char) → new_esEs21(zu311000, zu48000)
new_esEs9(zu311002, zu48002, ty_Ordering) → new_esEs11(zu311002, zu48002)
new_esEs7(zu311000, zu48000, ty_Int) → new_esEs15(zu311000, zu48000)
new_esEs9(zu311002, zu48002, ty_@0) → new_esEs13(zu311002, zu48002)
new_esEs24(zu311000, zu48000, ty_Ordering) → new_esEs11(zu311000, zu48000)
new_primEqInt(Neg(Zero), Pos(Succ(zu480000))) → False
new_primEqInt(Pos(Zero), Neg(Succ(zu480000))) → False
new_esEs26(zu311000, zu48000, app(ty_[], bhb)) → new_esEs17(zu311000, zu48000, bhb)
new_esEs14(Right(zu311000), Right(zu48000), cb, ty_@0) → new_esEs13(zu311000, zu48000)
new_esEs13(@0, @0) → True
new_esEs28(zu31101, zu4801, ty_Bool) → new_esEs5(zu31101, zu4801)
new_esEs26(zu311000, zu48000, ty_Float) → new_esEs12(zu311000, zu48000)
new_esEs28(zu31101, zu4801, ty_Integer) → new_esEs19(zu31101, zu4801)
new_esEs14(Right(zu311000), Right(zu48000), cb, ty_Float) → new_esEs12(zu311000, zu48000)
new_esEs24(zu311000, zu48000, app(ty_Maybe, bde)) → new_esEs18(zu311000, zu48000, bde)
new_esEs16(Double(zu311000, zu311001), Double(zu48000, zu48001)) → new_esEs15(new_sr(zu311000, zu48000), new_sr(zu311001, zu48001))
new_esEs11(EQ, EQ) → True
new_esEs28(zu31101, zu4801, ty_Float) → new_esEs12(zu31101, zu4801)
new_esEs27(zu31100, zu4800, ty_Double) → new_esEs16(zu31100, zu4800)
new_esEs8(zu311001, zu48001, ty_Int) → new_esEs15(zu311001, zu48001)
new_primMulNat0(Zero, Zero) → Zero
new_esEs14(Left(zu311000), Left(zu48000), ty_Double, cc) → new_esEs16(zu311000, zu48000)
new_esEs28(zu31101, zu4801, ty_Ordering) → new_esEs11(zu31101, zu4801)
new_esEs25(zu311001, zu48001, ty_Float) → new_esEs12(zu311001, zu48001)
new_esEs24(zu311000, zu48000, ty_@0) → new_esEs13(zu311000, zu48000)
new_esEs18(Just(zu311000), Just(zu48000), app(ty_Ratio, bcd)) → new_esEs20(zu311000, zu48000, bcd)
new_esEs17(:(zu311000, zu311001), :(zu48000, zu48001), cd) → new_asAs(new_esEs26(zu311000, zu48000, cd), new_esEs17(zu311001, zu48001, cd))
new_esEs8(zu311001, zu48001, app(app(app(ty_@3, ed), ee), ef)) → new_esEs6(zu311001, zu48001, ed, ee, ef)
new_esEs8(zu311001, zu48001, ty_Float) → new_esEs12(zu311001, zu48001)
new_esEs9(zu311002, zu48002, ty_Float) → new_esEs12(zu311002, zu48002)
new_esEs8(zu311001, zu48001, app(ty_Ratio, fc)) → new_esEs20(zu311001, zu48001, fc)
new_esEs9(zu311002, zu48002, app(app(ty_@2, fd), ff)) → new_esEs10(zu311002, zu48002, fd, ff)
new_primPlusNat0(Zero, zu4800100) → Succ(zu4800100)
new_esEs18(Just(zu311000), Just(zu48000), ty_Ordering) → new_esEs11(zu311000, zu48000)
new_esEs11(LT, GT) → False
new_esEs11(GT, LT) → False
new_esEs19(Integer(zu311000), Integer(zu48000)) → new_primEqInt(zu311000, zu48000)
new_esEs25(zu311001, zu48001, ty_Ordering) → new_esEs11(zu311001, zu48001)
new_esEs28(zu31101, zu4801, ty_Int) → new_esEs15(zu31101, zu4801)
new_esEs18(Just(zu311000), Just(zu48000), ty_Integer) → new_esEs19(zu311000, zu48000)
new_esEs7(zu311000, zu48000, app(ty_[], dg)) → new_esEs17(zu311000, zu48000, dg)
new_esEs25(zu311001, zu48001, ty_Double) → new_esEs16(zu311001, zu48001)
new_sr(Neg(zu3110010), Pos(zu480010)) → Neg(new_primMulNat0(zu3110010, zu480010))
new_sr(Pos(zu3110010), Neg(zu480010)) → Neg(new_primMulNat0(zu3110010, zu480010))
new_esEs11(LT, EQ) → False
new_esEs11(EQ, LT) → False
new_esEs24(zu311000, zu48000, app(ty_[], bdd)) → new_esEs17(zu311000, zu48000, bdd)
new_esEs24(zu311000, zu48000, ty_Int) → new_esEs15(zu311000, zu48000)
new_esEs8(zu311001, zu48001, ty_Double) → new_esEs16(zu311001, zu48001)
new_esEs27(zu31100, zu4800, app(ty_Maybe, ce)) → new_esEs18(zu31100, zu4800, ce)
new_esEs24(zu311000, zu48000, app(app(ty_Either, bdb), bdc)) → new_esEs14(zu311000, zu48000, bdb, bdc)
new_esEs18(Just(zu311000), Just(zu48000), ty_Char) → new_esEs21(zu311000, zu48000)
new_esEs9(zu311002, zu48002, ty_Char) → new_esEs21(zu311002, zu48002)
new_esEs26(zu311000, zu48000, app(app(ty_Either, bgh), bha)) → new_esEs14(zu311000, zu48000, bgh, bha)
new_esEs8(zu311001, zu48001, ty_Bool) → new_esEs5(zu311001, zu48001)
new_esEs18(Just(zu311000), Just(zu48000), ty_Int) → new_esEs15(zu311000, zu48000)
new_esEs8(zu311001, zu48001, ty_Ordering) → new_esEs11(zu311001, zu48001)
new_esEs14(Left(zu311000), Left(zu48000), app(ty_Ratio, hh), cc) → new_esEs20(zu311000, zu48000, hh)
new_primEqNat0(Zero, Succ(zu4800000)) → False
new_primEqNat0(Succ(zu31100000), Zero) → False
new_esEs14(Left(zu311000), Left(zu48000), ty_Int, cc) → new_esEs15(zu311000, zu48000)
new_esEs14(Right(zu311000), Right(zu48000), cb, ty_Int) → new_esEs15(zu311000, zu48000)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs26(zu311000, zu48000, ty_Ordering) → new_esEs11(zu311000, zu48000)
new_esEs28(zu31101, zu4801, app(app(app(ty_@3, bfc), bfd), bfe)) → new_esEs6(zu31101, zu4801, bfc, bfd, bfe)
new_esEs14(Right(zu311000), Right(zu48000), cb, ty_Double) → new_esEs16(zu311000, zu48000)
new_esEs8(zu311001, zu48001, app(ty_Maybe, fb)) → new_esEs18(zu311001, zu48001, fb)
new_esEs26(zu311000, zu48000, app(ty_Maybe, bhc)) → new_esEs18(zu311000, zu48000, bhc)
new_esEs27(zu31100, zu4800, app(app(app(ty_@3, bg), bh), ca)) → new_esEs6(zu31100, zu4800, bg, bh, ca)
new_esEs8(zu311001, zu48001, ty_Char) → new_esEs21(zu311001, zu48001)
new_esEs18(Just(zu311000), Just(zu48000), app(app(app(ty_@3, bbe), bbf), bbg)) → new_esEs6(zu311000, zu48000, bbe, bbf, bbg)
new_esEs15(zu31100, zu4800) → new_primEqInt(zu31100, zu4800)
new_esEs28(zu31101, zu4801, ty_@0) → new_esEs13(zu31101, zu4801)
new_esEs26(zu311000, zu48000, ty_@0) → new_esEs13(zu311000, zu48000)
new_esEs24(zu311000, zu48000, ty_Integer) → new_esEs19(zu311000, zu48000)
new_esEs27(zu31100, zu4800, app(ty_Ratio, cf)) → new_esEs20(zu31100, zu4800, cf)
new_esEs14(Left(zu311000), Left(zu48000), app(ty_[], hf), cc) → new_esEs17(zu311000, zu48000, hf)
new_esEs28(zu31101, zu4801, app(app(ty_@2, bfa), bfb)) → new_esEs10(zu31101, zu4801, bfa, bfb)
new_esEs24(zu311000, zu48000, ty_Char) → new_esEs21(zu311000, zu48000)
new_esEs26(zu311000, zu48000, ty_Bool) → new_esEs5(zu311000, zu48000)
new_esEs27(zu31100, zu4800, app(ty_[], cd)) → new_esEs17(zu31100, zu4800, cd)
new_esEs8(zu311001, zu48001, ty_Integer) → new_esEs19(zu311001, zu48001)
new_esEs18(Nothing, Nothing, ce) → True
new_esEs14(Right(zu311000), Right(zu48000), cb, app(app(ty_Either, baf), bag)) → new_esEs14(zu311000, zu48000, baf, bag)
new_esEs7(zu311000, zu48000, ty_Bool) → new_esEs5(zu311000, zu48000)
new_esEs14(Left(zu311000), Left(zu48000), app(app(ty_Either, hd), he), cc) → new_esEs14(zu311000, zu48000, hd, he)
new_esEs7(zu311000, zu48000, ty_Integer) → new_esEs19(zu311000, zu48000)
new_esEs7(zu311000, zu48000, app(app(ty_@2, cg), da)) → new_esEs10(zu311000, zu48000, cg, da)
new_esEs7(zu311000, zu48000, ty_Ordering) → new_esEs11(zu311000, zu48000)
new_esEs28(zu31101, zu4801, ty_Double) → new_esEs16(zu31101, zu4801)
new_esEs18(Just(zu311000), Just(zu48000), ty_Bool) → new_esEs5(zu311000, zu48000)
new_esEs11(GT, GT) → True
new_sr(Neg(zu3110010), Neg(zu480010)) → Pos(new_primMulNat0(zu3110010, zu480010))
new_esEs14(Right(zu311000), Right(zu48000), cb, ty_Bool) → new_esEs5(zu311000, zu48000)
new_asAs(False, zu89) → False
new_sr(Pos(zu3110010), Pos(zu480010)) → Pos(new_primMulNat0(zu3110010, zu480010))
new_esEs27(zu31100, zu4800, app(app(ty_@2, be), bf)) → new_esEs10(zu31100, zu4800, be, bf)
new_esEs6(@3(zu311000, zu311001, zu311002), @3(zu48000, zu48001, zu48002), bg, bh, ca) → new_asAs(new_esEs7(zu311000, zu48000, bg), new_asAs(new_esEs8(zu311001, zu48001, bh), new_esEs9(zu311002, zu48002, ca)))
new_primEqNat0(Zero, Zero) → True
new_esEs27(zu31100, zu4800, app(app(ty_Either, cb), cc)) → new_esEs14(zu31100, zu4800, cb, cc)
new_primMulNat0(Succ(zu31100100), Zero) → Zero
new_primMulNat0(Zero, Succ(zu4800100)) → Zero
new_esEs7(zu311000, zu48000, ty_Double) → new_esEs16(zu311000, zu48000)
new_esEs7(zu311000, zu48000, app(ty_Ratio, ea)) → new_esEs20(zu311000, zu48000, ea)
new_esEs14(Left(zu311000), Left(zu48000), ty_Float, cc) → new_esEs12(zu311000, zu48000)
new_esEs18(Just(zu311000), Nothing, ce) → False
new_esEs18(Nothing, Just(zu48000), ce) → False
new_esEs9(zu311002, zu48002, ty_Bool) → new_esEs5(zu311002, zu48002)
new_esEs25(zu311001, zu48001, ty_Bool) → new_esEs5(zu311001, zu48001)
new_esEs25(zu311001, zu48001, ty_Int) → new_esEs15(zu311001, zu48001)
new_esEs5(False, False) → True
new_esEs5(False, True) → False
new_esEs5(True, False) → False
new_esEs27(zu31100, zu4800, ty_@0) → new_esEs13(zu31100, zu4800)
new_esEs20(:%(zu311000, zu311001), :%(zu48000, zu48001), cf) → new_asAs(new_esEs22(zu311000, zu48000, cf), new_esEs23(zu311001, zu48001, cf))
new_esEs7(zu311000, zu48000, app(app(ty_Either, de), df)) → new_esEs14(zu311000, zu48000, de, df)
new_esEs25(zu311001, zu48001, app(ty_[], bef)) → new_esEs17(zu311001, zu48001, bef)
new_esEs26(zu311000, zu48000, app(app(ty_@2, bgc), bgd)) → new_esEs10(zu311000, zu48000, bgc, bgd)
new_esEs24(zu311000, zu48000, ty_Double) → new_esEs16(zu311000, zu48000)
new_esEs7(zu311000, zu48000, ty_@0) → new_esEs13(zu311000, zu48000)
new_esEs25(zu311001, zu48001, app(app(app(ty_@3, bea), beb), bec)) → new_esEs6(zu311001, zu48001, bea, beb, bec)
new_esEs27(zu31100, zu4800, ty_Integer) → new_esEs19(zu31100, zu4800)
new_esEs9(zu311002, zu48002, ty_Integer) → new_esEs19(zu311002, zu48002)
new_esEs8(zu311001, zu48001, app(app(ty_@2, eb), ec)) → new_esEs10(zu311001, zu48001, eb, ec)
new_primPlusNat0(Succ(zu910), zu4800100) → Succ(Succ(new_primPlusNat1(zu910, zu4800100)))
new_esEs26(zu311000, zu48000, app(app(app(ty_@3, bge), bgf), bgg)) → new_esEs6(zu311000, zu48000, bge, bgf, bgg)
new_esEs25(zu311001, zu48001, ty_Integer) → new_esEs19(zu311001, zu48001)
new_esEs5(True, True) → True
new_esEs25(zu311001, zu48001, ty_Char) → new_esEs21(zu311001, zu48001)
new_esEs27(zu31100, zu4800, ty_Bool) → new_esEs5(zu31100, zu4800)
new_esEs21(Char(zu311000), Char(zu48000)) → new_primEqInt(zu311000, zu48000)
new_primEqInt(Neg(Succ(zu3110000)), Neg(Succ(zu480000))) → new_primEqNat0(zu3110000, zu480000)
new_esEs28(zu31101, zu4801, app(ty_[], bfh)) → new_esEs17(zu31101, zu4801, bfh)
new_esEs23(zu311001, zu48001, ty_Int) → new_esEs15(zu311001, zu48001)
new_esEs27(zu31100, zu4800, ty_Char) → new_esEs21(zu31100, zu4800)
new_esEs28(zu31101, zu4801, app(ty_Ratio, bgb)) → new_esEs20(zu31101, zu4801, bgb)
new_primPlusNat1(Succ(zu9100), Zero) → Succ(zu9100)
new_primPlusNat1(Zero, Succ(zu48001000)) → Succ(zu48001000)
new_esEs27(zu31100, zu4800, ty_Int) → new_esEs15(zu31100, zu4800)
new_esEs14(Left(zu311000), Left(zu48000), app(ty_Maybe, hg), cc) → new_esEs18(zu311000, zu48000, hg)
new_esEs14(Left(zu311000), Left(zu48000), ty_Integer, cc) → new_esEs19(zu311000, zu48000)
new_esEs12(Float(zu311000, zu311001), Float(zu48000, zu48001)) → new_esEs15(new_sr(zu311000, zu48000), new_sr(zu311001, zu48001))
new_esEs22(zu311000, zu48000, ty_Int) → new_esEs15(zu311000, zu48000)
new_esEs28(zu31101, zu4801, app(app(ty_Either, bff), bfg)) → new_esEs14(zu31101, zu4801, bff, bfg)
new_esEs10(@2(zu311000, zu311001), @2(zu48000, zu48001), be, bf) → new_asAs(new_esEs24(zu311000, zu48000, be), new_esEs25(zu311001, zu48001, bf))
new_esEs14(Left(zu311000), Left(zu48000), ty_Bool, cc) → new_esEs5(zu311000, zu48000)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs26(zu311000, zu48000, ty_Integer) → new_esEs19(zu311000, zu48000)
new_esEs24(zu311000, zu48000, app(app(app(ty_@3, bcg), bch), bda)) → new_esEs6(zu311000, zu48000, bcg, bch, bda)
new_esEs9(zu311002, zu48002, ty_Double) → new_esEs16(zu311002, zu48002)
new_esEs9(zu311002, zu48002, app(ty_Ratio, gf)) → new_esEs20(zu311002, zu48002, gf)
new_primEqInt(Neg(Zero), Neg(Succ(zu480000))) → False
new_primEqInt(Neg(Succ(zu3110000)), Neg(Zero)) → False
new_esEs9(zu311002, zu48002, app(ty_[], gd)) → new_esEs17(zu311002, zu48002, gd)
new_esEs22(zu311000, zu48000, ty_Integer) → new_esEs19(zu311000, zu48000)
new_esEs8(zu311001, zu48001, app(ty_[], fa)) → new_esEs17(zu311001, zu48001, fa)
new_esEs14(Left(zu311000), Left(zu48000), app(app(app(ty_@3, ha), hb), hc), cc) → new_esEs6(zu311000, zu48000, ha, hb, hc)
new_esEs9(zu311002, zu48002, app(app(app(ty_@3, fg), fh), ga)) → new_esEs6(zu311002, zu48002, fg, fh, ga)
new_esEs7(zu311000, zu48000, ty_Char) → new_esEs21(zu311000, zu48000)
new_esEs14(Right(zu311000), Right(zu48000), cb, app(ty_[], bah)) → new_esEs17(zu311000, zu48000, bah)
new_primPlusNat1(Zero, Zero) → Zero
new_esEs9(zu311002, zu48002, app(app(ty_Either, gb), gc)) → new_esEs14(zu311002, zu48002, gb, gc)
new_esEs25(zu311001, zu48001, app(app(ty_@2, bdg), bdh)) → new_esEs10(zu311001, zu48001, bdg, bdh)
new_asAs(True, zu89) → zu89
new_primMulNat0(Succ(zu31100100), Succ(zu4800100)) → new_primPlusNat0(new_primMulNat0(zu31100100, Succ(zu4800100)), zu4800100)
new_esEs11(LT, LT) → True
new_esEs18(Just(zu311000), Just(zu48000), ty_Double) → new_esEs16(zu311000, zu48000)
new_esEs24(zu311000, zu48000, app(app(ty_@2, bce), bcf)) → new_esEs10(zu311000, zu48000, bce, bcf)
new_esEs8(zu311001, zu48001, ty_@0) → new_esEs13(zu311001, zu48001)
new_esEs18(Just(zu311000), Just(zu48000), app(app(ty_@2, bbc), bbd)) → new_esEs10(zu311000, zu48000, bbc, bbd)
new_primEqInt(Pos(Succ(zu3110000)), Pos(Succ(zu480000))) → new_primEqNat0(zu3110000, zu480000)
new_esEs14(Left(zu311000), Left(zu48000), app(app(ty_@2, gg), gh), cc) → new_esEs10(zu311000, zu48000, gg, gh)
new_esEs7(zu311000, zu48000, app(ty_Maybe, dh)) → new_esEs18(zu311000, zu48000, dh)
new_esEs17([], [], cd) → True
new_esEs17(:(zu311000, zu311001), [], cd) → False
new_esEs17([], :(zu48000, zu48001), cd) → False
new_esEs26(zu311000, zu48000, ty_Double) → new_esEs16(zu311000, zu48000)
new_esEs24(zu311000, zu48000, app(ty_Ratio, bdf)) → new_esEs20(zu311000, zu48000, bdf)
new_esEs9(zu311002, zu48002, ty_Int) → new_esEs15(zu311002, zu48002)
new_esEs18(Just(zu311000), Just(zu48000), ty_@0) → new_esEs13(zu311000, zu48000)
new_esEs25(zu311001, zu48001, app(app(ty_Either, bed), bee)) → new_esEs14(zu311001, zu48001, bed, bee)
new_esEs24(zu311000, zu48000, ty_Bool) → new_esEs5(zu311000, zu48000)
new_primEqNat0(Succ(zu31100000), Succ(zu4800000)) → new_primEqNat0(zu31100000, zu4800000)
new_esEs11(EQ, GT) → False
new_esEs11(GT, EQ) → False
new_esEs18(Just(zu311000), Just(zu48000), app(ty_[], bcb)) → new_esEs17(zu311000, zu48000, bcb)
new_esEs14(Right(zu311000), Right(zu48000), cb, app(ty_Maybe, bba)) → new_esEs18(zu311000, zu48000, bba)
new_esEs14(Right(zu311000), Right(zu48000), cb, app(ty_Ratio, bbb)) → new_esEs20(zu311000, zu48000, bbb)
new_esEs26(zu311000, zu48000, ty_Int) → new_esEs15(zu311000, zu48000)
new_esEs27(zu31100, zu4800, ty_Float) → new_esEs12(zu31100, zu4800)
new_esEs8(zu311001, zu48001, app(app(ty_Either, eg), eh)) → new_esEs14(zu311001, zu48001, eg, eh)
new_esEs9(zu311002, zu48002, app(ty_Maybe, ge)) → new_esEs18(zu311002, zu48002, ge)
new_esEs18(Just(zu311000), Just(zu48000), app(ty_Maybe, bcc)) → new_esEs18(zu311000, zu48000, bcc)
new_esEs18(Just(zu311000), Just(zu48000), ty_Float) → new_esEs12(zu311000, zu48000)
new_primEqInt(Pos(Zero), Pos(Succ(zu480000))) → False
new_primEqInt(Pos(Succ(zu3110000)), Pos(Zero)) → False
new_esEs14(Left(zu311000), Left(zu48000), ty_Ordering, cc) → new_esEs11(zu311000, zu48000)
new_esEs7(zu311000, zu48000, app(app(app(ty_@3, db), dc), dd)) → new_esEs6(zu311000, zu48000, db, dc, dd)
new_esEs25(zu311001, zu48001, app(ty_Ratio, beh)) → new_esEs20(zu311001, zu48001, beh)
new_esEs25(zu311001, zu48001, app(ty_Maybe, beg)) → new_esEs18(zu311001, zu48001, beg)
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_esEs14(Left(zu311000), Left(zu48000), ty_@0, cc) → new_esEs13(zu311000, zu48000)
new_esEs26(zu311000, zu48000, ty_Char) → new_esEs21(zu311000, zu48000)
new_esEs14(Left(zu311000), Left(zu48000), ty_Char, cc) → new_esEs21(zu311000, zu48000)
new_esEs26(zu311000, zu48000, app(ty_Ratio, bhd)) → new_esEs20(zu311000, zu48000, bhd)
new_esEs7(zu311000, zu48000, ty_Float) → new_esEs12(zu311000, zu48000)
The set Q consists of the following terms:
new_esEs24(x0, x1, ty_@0)
new_esEs13(@0, @0)
new_esEs25(x0, x1, ty_Char)
new_esEs28(x0, x1, ty_Integer)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs24(x0, x1, ty_Char)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_esEs26(x0, x1, ty_Double)
new_esEs14(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs17(:(x0, x1), [], x2)
new_esEs26(x0, x1, ty_Char)
new_esEs20(:%(x0, x1), :%(x2, x3), x4)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs7(x0, x1, ty_Float)
new_esEs19(Integer(x0), Integer(x1))
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_primEqInt(Neg(Zero), Pos(Zero))
new_primEqInt(Pos(Zero), Neg(Zero))
new_esEs17(:(x0, x1), :(x2, x3), x4)
new_esEs7(x0, x1, ty_@0)
new_esEs9(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_esEs18(Just(x0), Just(x1), app(ty_Ratio, x2))
new_sr(Pos(x0), Pos(x1))
new_esEs18(Just(x0), Just(x1), ty_Float)
new_esEs14(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs24(x0, x1, ty_Bool)
new_esEs11(LT, EQ)
new_esEs11(EQ, LT)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs8(x0, x1, ty_Float)
new_esEs8(x0, x1, ty_Char)
new_primEqInt(Neg(Zero), Neg(Zero))
new_esEs14(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs27(x0, x1, app(ty_[], x2))
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs8(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs14(Right(x0), Right(x1), x2, ty_Int)
new_esEs14(Right(x0), Right(x1), x2, ty_Integer)
new_esEs8(x0, x1, ty_@0)
new_esEs24(x0, x1, ty_Ordering)
new_esEs27(x0, x1, ty_Integer)
new_esEs27(x0, x1, ty_Int)
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_primEqNat0(Zero, Succ(x0))
new_esEs9(x0, x1, app(ty_Ratio, x2))
new_primPlusNat1(Succ(x0), Zero)
new_esEs14(Left(x0), Left(x1), ty_Float, x2)
new_sr(Neg(x0), Neg(x1))
new_esEs28(x0, x1, ty_@0)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs25(x0, x1, ty_Float)
new_esEs14(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs18(Nothing, Nothing, x0)
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_esEs14(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs14(Right(x0), Right(x1), x2, ty_Float)
new_esEs18(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs25(x0, x1, ty_@0)
new_esEs5(True, False)
new_esEs5(False, True)
new_esEs14(Left(x0), Left(x1), ty_Char, x2)
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs26(x0, x1, app(ty_[], x2))
new_esEs17([], :(x0, x1), x2)
new_esEs18(Just(x0), Nothing, x1)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_esEs16(Double(x0, x1), Double(x2, x3))
new_primEqNat0(Succ(x0), Zero)
new_esEs18(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs18(Just(x0), Just(x1), ty_Int)
new_esEs24(x0, x1, app(ty_[], x2))
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs7(x0, x1, app(app(ty_Either, x2), x3))
new_esEs8(x0, x1, ty_Ordering)
new_esEs27(x0, x1, ty_Double)
new_esEs14(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs24(x0, x1, ty_Int)
new_primMulNat0(Zero, Succ(x0))
new_esEs14(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs7(x0, x1, app(app(ty_@2, x2), x3))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_esEs11(EQ, GT)
new_esEs11(GT, EQ)
new_esEs26(x0, x1, ty_@0)
new_esEs14(Left(x0), Left(x1), ty_Bool, x2)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_esEs28(x0, x1, ty_Float)
new_esEs7(x0, x1, app(ty_[], x2))
new_esEs27(x0, x1, ty_Float)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_esEs5(True, True)
new_esEs14(Left(x0), Left(x1), ty_Int, x2)
new_esEs18(Nothing, Just(x0), x1)
new_esEs17([], [], x0)
new_primEqNat0(Zero, Zero)
new_esEs24(x0, x1, ty_Integer)
new_esEs8(x0, x1, ty_Bool)
new_esEs8(x0, x1, ty_Integer)
new_esEs9(x0, x1, ty_Double)
new_esEs26(x0, x1, ty_Ordering)
new_esEs8(x0, x1, app(ty_Ratio, x2))
new_esEs25(x0, x1, app(ty_[], x2))
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_esEs14(Left(x0), Left(x1), ty_@0, x2)
new_esEs9(x0, x1, ty_Char)
new_esEs5(False, False)
new_esEs14(Right(x0), Right(x1), x2, ty_Bool)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_esEs8(x0, x1, app(ty_Maybe, x2))
new_esEs14(Left(x0), Left(x1), ty_Double, x2)
new_esEs25(x0, x1, ty_Double)
new_esEs23(x0, x1, ty_Int)
new_esEs7(x0, x1, ty_Char)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(x0, x1, app(ty_Ratio, x2))
new_esEs14(Right(x0), Left(x1), x2, x3)
new_esEs14(Left(x0), Right(x1), x2, x3)
new_esEs7(x0, x1, ty_Ordering)
new_esEs25(x0, x1, ty_Int)
new_esEs27(x0, x1, ty_Ordering)
new_primMulNat0(Zero, Zero)
new_esEs14(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs14(Left(x0), Left(x1), ty_Integer, x2)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs28(x0, x1, ty_Int)
new_esEs9(x0, x1, ty_@0)
new_esEs7(x0, x1, ty_Integer)
new_esEs24(x0, x1, ty_Double)
new_esEs11(GT, GT)
new_primPlusNat0(Zero, x0)
new_esEs14(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs14(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_primMulNat0(Succ(x0), Succ(x1))
new_esEs7(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs25(x0, x1, ty_Ordering)
new_esEs26(x0, x1, ty_Int)
new_esEs26(x0, x1, ty_Bool)
new_esEs18(Just(x0), Just(x1), ty_Char)
new_esEs18(Just(x0), Just(x1), app(ty_[], x2))
new_esEs7(x0, x1, ty_Bool)
new_esEs28(x0, x1, app(ty_[], x2))
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_esEs18(Just(x0), Just(x1), ty_Bool)
new_esEs27(x0, x1, ty_Char)
new_esEs11(LT, GT)
new_esEs11(GT, LT)
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_asAs(True, x0)
new_asAs(False, x0)
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs24(x0, x1, ty_Float)
new_esEs21(Char(x0), Char(x1))
new_esEs9(x0, x1, app(app(ty_@2, x2), x3))
new_esEs14(Right(x0), Right(x1), x2, ty_Double)
new_sr(Neg(x0), Pos(x1))
new_sr(Pos(x0), Neg(x1))
new_esEs9(x0, x1, app(ty_Maybe, x2))
new_esEs27(x0, x1, ty_@0)
new_esEs9(x0, x1, ty_Int)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_esEs7(x0, x1, ty_Int)
new_esEs26(x0, x1, ty_Integer)
new_esEs9(x0, x1, ty_Integer)
new_esEs18(Just(x0), Just(x1), ty_Integer)
new_esEs9(x0, x1, ty_Float)
new_esEs7(x0, x1, ty_Double)
new_esEs15(x0, x1)
new_esEs26(x0, x1, ty_Float)
new_esEs14(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs18(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs8(x0, x1, ty_Double)
new_esEs28(x0, x1, ty_Char)
new_esEs8(x0, x1, app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, ty_Integer)
new_esEs14(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs8(x0, x1, app(ty_[], x2))
new_esEs28(x0, x1, ty_Double)
new_esEs7(x0, x1, app(ty_Maybe, x2))
new_esEs14(Right(x0), Right(x1), x2, ty_Char)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_esEs18(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs9(x0, x1, ty_Ordering)
new_esEs22(x0, x1, ty_Integer)
new_esEs11(LT, LT)
new_esEs8(x0, x1, ty_Int)
new_esEs9(x0, x1, ty_Bool)
new_primPlusNat1(Zero, Zero)
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs9(x0, x1, app(app(ty_Either, x2), x3))
new_primMulNat0(Succ(x0), Zero)
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_esEs28(x0, x1, ty_Bool)
new_esEs8(x0, x1, app(app(ty_@2, x2), x3))
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_primEqInt(Pos(Zero), Pos(Zero))
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs11(EQ, EQ)
new_esEs18(Just(x0), Just(x1), ty_Ordering)
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_esEs10(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs27(x0, x1, ty_Bool)
new_esEs9(x0, x1, app(ty_[], x2))
new_esEs25(x0, x1, ty_Integer)
new_primPlusNat1(Zero, Succ(x0))
new_esEs14(Right(x0), Right(x1), x2, ty_@0)
new_esEs18(Just(x0), Just(x1), ty_@0)
new_esEs14(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs12(Float(x0, x1), Float(x2, x3))
new_esEs14(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs22(x0, x1, ty_Int)
new_esEs28(x0, x1, ty_Ordering)
new_primPlusNat0(Succ(x0), x1)
new_esEs25(x0, x1, ty_Bool)
new_esEs18(Just(x0), Just(x1), ty_Double)
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_deleteBy(@2(zu31100, zu31101), :(@2(zu4800, zu4801), zu481), bc, bd) → new_deleteBy0(zu481, zu4800, zu4801, zu31100, zu31101, new_asAs(new_esEs27(zu31100, zu4800, bc), new_esEs28(zu31101, zu4801, bd)), bc, bd)
The graph contains the following edges 2 > 1, 2 > 2, 2 > 3, 1 > 4, 1 > 5, 3 >= 7, 4 >= 8
- new_deleteBy0(zu70, zu71, zu72, zu73, zu74, False, ba, bb) → new_deleteBy(@2(zu73, zu74), zu70, ba, bb)
The graph contains the following edges 1 >= 2, 7 >= 3, 8 >= 4
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ DependencyGraphProof
Q DP problem:
The TRS P consists of the following rules:
new_nubByNubBy'1(zu199, zu200, zu201, zu202, False, :(zu2040, zu2041), ba) → new_nubByNubBy'1(zu199, zu200, zu201, zu202, new_esEs4(zu2040, zu199, ba), zu2041, ba)
new_nubByNubBy'10(zu199, zu200, zu201, zu202, [], ba) → new_nubByNubBy'(zu200, zu199, :(zu201, zu202), ba)
new_nubByNubBy'1(zu199, :(zu2000, zu2001), zu201, zu202, True, zu204, ba) → new_nubByNubBy'10(zu2000, zu2001, zu201, zu202, :(zu201, zu202), ba)
new_nubByNubBy'1(zu199, zu200, zu201, zu202, False, [], ba) → new_nubByNubBy'(zu200, zu199, :(zu201, zu202), ba)
new_nubByNubBy'10(zu199, zu200, zu201, zu202, :(zu2040, zu2041), ba) → new_nubByNubBy'1(zu199, zu200, zu201, zu202, new_esEs4(zu2040, zu199, ba), zu2041, ba)
new_nubByNubBy'(:(zu2000, zu2001), zu201, zu202, ba) → new_nubByNubBy'10(zu2000, zu2001, zu201, zu202, :(zu201, zu202), ba)
The TRS R consists of the following rules:
new_esEs24(zu311000, zu48000, ty_Float) → new_esEs12(zu311000, zu48000)
new_primPlusNat1(Succ(zu9100), Succ(zu48001000)) → Succ(Succ(new_primPlusNat1(zu9100, zu48001000)))
new_primEqInt(Neg(Succ(zu3110000)), Pos(zu48000)) → False
new_primEqInt(Pos(Succ(zu3110000)), Neg(zu48000)) → False
new_esEs18(Just(zu311000), Just(zu48000), app(app(ty_Either, bbb), bbc)) → new_esEs14(zu311000, zu48000, bbb, bbc)
new_esEs14(Right(zu311000), Right(zu48000), ha, ty_Ordering) → new_esEs11(zu311000, zu48000)
new_esEs14(Left(zu311000), Right(zu48000), ha, fh) → False
new_esEs14(Right(zu311000), Left(zu48000), ha, fh) → False
new_esEs14(Right(zu311000), Right(zu48000), ha, app(app(ty_@2, hb), hc)) → new_esEs10(zu311000, zu48000, hb, hc)
new_esEs25(zu311001, zu48001, ty_@0) → new_esEs13(zu311001, zu48001)
new_esEs23(zu311001, zu48001, ty_Integer) → new_esEs19(zu311001, zu48001)
new_esEs4(zu2040, zu199, app(app(app(ty_@3, beg), beh), bfa)) → new_esEs6(zu2040, zu199, beg, beh, bfa)
new_esEs14(Right(zu311000), Right(zu48000), ha, ty_Integer) → new_esEs19(zu311000, zu48000)
new_esEs14(Right(zu311000), Right(zu48000), ha, app(app(app(ty_@3, hd), he), hf)) → new_esEs6(zu311000, zu48000, hd, he, hf)
new_esEs14(Right(zu311000), Right(zu48000), ha, ty_Char) → new_esEs21(zu311000, zu48000)
new_esEs9(zu311002, zu48002, ty_Ordering) → new_esEs11(zu311002, zu48002)
new_esEs9(zu311002, zu48002, ty_@0) → new_esEs13(zu311002, zu48002)
new_esEs7(zu311000, zu48000, ty_Int) → new_esEs15(zu311000, zu48000)
new_esEs24(zu311000, zu48000, ty_Ordering) → new_esEs11(zu311000, zu48000)
new_primEqInt(Neg(Zero), Pos(Succ(zu480000))) → False
new_primEqInt(Pos(Zero), Neg(Succ(zu480000))) → False
new_esEs26(zu311000, zu48000, app(ty_[], bgg)) → new_esEs17(zu311000, zu48000, bgg)
new_esEs14(Right(zu311000), Right(zu48000), ha, ty_@0) → new_esEs13(zu311000, zu48000)
new_esEs13(@0, @0) → True
new_esEs26(zu311000, zu48000, ty_Float) → new_esEs12(zu311000, zu48000)
new_esEs4(zu2040, zu199, app(app(ty_@2, bee), bef)) → new_esEs10(zu2040, zu199, bee, bef)
new_esEs14(Right(zu311000), Right(zu48000), ha, ty_Float) → new_esEs12(zu311000, zu48000)
new_esEs24(zu311000, zu48000, app(ty_Maybe, bda)) → new_esEs18(zu311000, zu48000, bda)
new_esEs16(Double(zu311000, zu311001), Double(zu48000, zu48001)) → new_esEs15(new_sr(zu311000, zu48000), new_sr(zu311001, zu48001))
new_esEs11(EQ, EQ) → True
new_esEs8(zu311001, zu48001, ty_Int) → new_esEs15(zu311001, zu48001)
new_primMulNat0(Zero, Zero) → Zero
new_esEs4(zu2040, zu199, app(ty_[], bfd)) → new_esEs17(zu2040, zu199, bfd)
new_esEs14(Left(zu311000), Left(zu48000), ty_Double, fh) → new_esEs16(zu311000, zu48000)
new_esEs25(zu311001, zu48001, ty_Float) → new_esEs12(zu311001, zu48001)
new_esEs24(zu311000, zu48000, ty_@0) → new_esEs13(zu311000, zu48000)
new_esEs18(Just(zu311000), Just(zu48000), app(ty_Ratio, bbf)) → new_esEs20(zu311000, zu48000, bbf)
new_esEs17(:(zu311000, zu311001), :(zu48000, zu48001), bfg) → new_asAs(new_esEs26(zu311000, zu48000, bfg), new_esEs17(zu311001, zu48001, bfg))
new_esEs8(zu311001, zu48001, app(app(app(ty_@3, db), dc), dd)) → new_esEs6(zu311001, zu48001, db, dc, dd)
new_esEs8(zu311001, zu48001, ty_Float) → new_esEs12(zu311001, zu48001)
new_esEs4(zu2040, zu199, ty_Char) → new_esEs21(zu2040, zu199)
new_esEs9(zu311002, zu48002, ty_Float) → new_esEs12(zu311002, zu48002)
new_esEs8(zu311001, zu48001, app(ty_Ratio, ea)) → new_esEs20(zu311001, zu48001, ea)
new_esEs9(zu311002, zu48002, app(app(ty_@2, eb), ec)) → new_esEs10(zu311002, zu48002, eb, ec)
new_primPlusNat0(Zero, zu4800100) → Succ(zu4800100)
new_esEs18(Just(zu311000), Just(zu48000), ty_Ordering) → new_esEs11(zu311000, zu48000)
new_esEs11(GT, LT) → False
new_esEs11(LT, GT) → False
new_esEs19(Integer(zu311000), Integer(zu48000)) → new_primEqInt(zu311000, zu48000)
new_esEs25(zu311001, zu48001, ty_Ordering) → new_esEs11(zu311001, zu48001)
new_esEs18(Just(zu311000), Just(zu48000), ty_Integer) → new_esEs19(zu311000, zu48000)
new_esEs7(zu311000, zu48000, app(ty_[], cd)) → new_esEs17(zu311000, zu48000, cd)
new_esEs25(zu311001, zu48001, ty_Double) → new_esEs16(zu311001, zu48001)
new_sr(Neg(zu3110010), Pos(zu480010)) → Neg(new_primMulNat0(zu3110010, zu480010))
new_sr(Pos(zu3110010), Neg(zu480010)) → Neg(new_primMulNat0(zu3110010, zu480010))
new_esEs11(EQ, LT) → False
new_esEs11(LT, EQ) → False
new_esEs24(zu311000, zu48000, app(ty_[], bch)) → new_esEs17(zu311000, zu48000, bch)
new_esEs24(zu311000, zu48000, ty_Int) → new_esEs15(zu311000, zu48000)
new_esEs8(zu311001, zu48001, ty_Double) → new_esEs16(zu311001, zu48001)
new_esEs24(zu311000, zu48000, app(app(ty_Either, bcf), bcg)) → new_esEs14(zu311000, zu48000, bcf, bcg)
new_esEs18(Just(zu311000), Just(zu48000), ty_Char) → new_esEs21(zu311000, zu48000)
new_esEs9(zu311002, zu48002, ty_Char) → new_esEs21(zu311002, zu48002)
new_esEs4(zu2040, zu199, ty_Ordering) → new_esEs11(zu2040, zu199)
new_esEs26(zu311000, zu48000, app(app(ty_Either, bge), bgf)) → new_esEs14(zu311000, zu48000, bge, bgf)
new_esEs8(zu311001, zu48001, ty_Bool) → new_esEs5(zu311001, zu48001)
new_esEs18(Just(zu311000), Just(zu48000), ty_Int) → new_esEs15(zu311000, zu48000)
new_esEs8(zu311001, zu48001, ty_Ordering) → new_esEs11(zu311001, zu48001)
new_esEs14(Left(zu311000), Left(zu48000), app(ty_Ratio, gh), fh) → new_esEs20(zu311000, zu48000, gh)
new_primEqNat0(Zero, Succ(zu4800000)) → False
new_primEqNat0(Succ(zu31100000), Zero) → False
new_esEs14(Left(zu311000), Left(zu48000), ty_Int, fh) → new_esEs15(zu311000, zu48000)
new_esEs14(Right(zu311000), Right(zu48000), ha, ty_Int) → new_esEs15(zu311000, zu48000)
new_esEs26(zu311000, zu48000, ty_Ordering) → new_esEs11(zu311000, zu48000)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs14(Right(zu311000), Right(zu48000), ha, ty_Double) → new_esEs16(zu311000, zu48000)
new_esEs8(zu311001, zu48001, app(ty_Maybe, dh)) → new_esEs18(zu311001, zu48001, dh)
new_esEs26(zu311000, zu48000, app(ty_Maybe, bgh)) → new_esEs18(zu311000, zu48000, bgh)
new_esEs8(zu311001, zu48001, ty_Char) → new_esEs21(zu311001, zu48001)
new_esEs18(Just(zu311000), Just(zu48000), app(app(app(ty_@3, bag), bah), bba)) → new_esEs6(zu311000, zu48000, bag, bah, bba)
new_esEs15(zu31100, zu4800) → new_primEqInt(zu31100, zu4800)
new_esEs26(zu311000, zu48000, ty_@0) → new_esEs13(zu311000, zu48000)
new_esEs24(zu311000, zu48000, ty_Integer) → new_esEs19(zu311000, zu48000)
new_esEs14(Left(zu311000), Left(zu48000), app(ty_[], gf), fh) → new_esEs17(zu311000, zu48000, gf)
new_esEs24(zu311000, zu48000, ty_Char) → new_esEs21(zu311000, zu48000)
new_esEs26(zu311000, zu48000, ty_Bool) → new_esEs5(zu311000, zu48000)
new_esEs8(zu311001, zu48001, ty_Integer) → new_esEs19(zu311001, zu48001)
new_esEs18(Nothing, Nothing, bad) → True
new_esEs4(zu2040, zu199, ty_@0) → new_esEs13(zu2040, zu199)
new_esEs14(Right(zu311000), Right(zu48000), ha, app(app(ty_Either, hg), hh)) → new_esEs14(zu311000, zu48000, hg, hh)
new_esEs7(zu311000, zu48000, ty_Bool) → new_esEs5(zu311000, zu48000)
new_esEs14(Left(zu311000), Left(zu48000), app(app(ty_Either, gd), ge), fh) → new_esEs14(zu311000, zu48000, gd, ge)
new_esEs7(zu311000, zu48000, app(app(ty_@2, be), bf)) → new_esEs10(zu311000, zu48000, be, bf)
new_esEs7(zu311000, zu48000, ty_Integer) → new_esEs19(zu311000, zu48000)
new_esEs7(zu311000, zu48000, ty_Ordering) → new_esEs11(zu311000, zu48000)
new_esEs11(GT, GT) → True
new_esEs18(Just(zu311000), Just(zu48000), ty_Bool) → new_esEs5(zu311000, zu48000)
new_sr(Neg(zu3110010), Neg(zu480010)) → Pos(new_primMulNat0(zu3110010, zu480010))
new_esEs14(Right(zu311000), Right(zu48000), ha, ty_Bool) → new_esEs5(zu311000, zu48000)
new_asAs(False, zu89) → False
new_sr(Pos(zu3110010), Pos(zu480010)) → Pos(new_primMulNat0(zu3110010, zu480010))
new_esEs6(@3(zu311000, zu311001, zu311002), @3(zu48000, zu48001, zu48002), bb, bc, bd) → new_asAs(new_esEs7(zu311000, zu48000, bb), new_asAs(new_esEs8(zu311001, zu48001, bc), new_esEs9(zu311002, zu48002, bd)))
new_primEqNat0(Zero, Zero) → True
new_primMulNat0(Succ(zu31100100), Zero) → Zero
new_primMulNat0(Zero, Succ(zu4800100)) → Zero
new_esEs7(zu311000, zu48000, ty_Double) → new_esEs16(zu311000, zu48000)
new_esEs7(zu311000, zu48000, app(ty_Ratio, cf)) → new_esEs20(zu311000, zu48000, cf)
new_esEs14(Left(zu311000), Left(zu48000), ty_Float, fh) → new_esEs12(zu311000, zu48000)
new_esEs18(Just(zu311000), Nothing, bad) → False
new_esEs18(Nothing, Just(zu48000), bad) → False
new_esEs9(zu311002, zu48002, ty_Bool) → new_esEs5(zu311002, zu48002)
new_esEs25(zu311001, zu48001, ty_Bool) → new_esEs5(zu311001, zu48001)
new_esEs25(zu311001, zu48001, ty_Int) → new_esEs15(zu311001, zu48001)
new_esEs5(False, False) → True
new_esEs5(True, False) → False
new_esEs5(False, True) → False
new_esEs20(:%(zu311000, zu311001), :%(zu48000, zu48001), fd) → new_asAs(new_esEs22(zu311000, zu48000, fd), new_esEs23(zu311001, zu48001, fd))
new_esEs7(zu311000, zu48000, app(app(ty_Either, cb), cc)) → new_esEs14(zu311000, zu48000, cb, cc)
new_esEs25(zu311001, zu48001, app(ty_[], beb)) → new_esEs17(zu311001, zu48001, beb)
new_esEs26(zu311000, zu48000, app(app(ty_@2, bfh), bga)) → new_esEs10(zu311000, zu48000, bfh, bga)
new_esEs24(zu311000, zu48000, ty_Double) → new_esEs16(zu311000, zu48000)
new_esEs7(zu311000, zu48000, ty_@0) → new_esEs13(zu311000, zu48000)
new_esEs25(zu311001, zu48001, app(app(app(ty_@3, bde), bdf), bdg)) → new_esEs6(zu311001, zu48001, bde, bdf, bdg)
new_esEs9(zu311002, zu48002, ty_Integer) → new_esEs19(zu311002, zu48002)
new_primPlusNat0(Succ(zu910), zu4800100) → Succ(Succ(new_primPlusNat1(zu910, zu4800100)))
new_esEs8(zu311001, zu48001, app(app(ty_@2, cg), da)) → new_esEs10(zu311001, zu48001, cg, da)
new_esEs26(zu311000, zu48000, app(app(app(ty_@3, bgb), bgc), bgd)) → new_esEs6(zu311000, zu48000, bgb, bgc, bgd)
new_esEs4(zu2040, zu199, app(ty_Ratio, bff)) → new_esEs20(zu2040, zu199, bff)
new_esEs25(zu311001, zu48001, ty_Integer) → new_esEs19(zu311001, zu48001)
new_esEs4(zu2040, zu199, ty_Bool) → new_esEs5(zu2040, zu199)
new_esEs5(True, True) → True
new_esEs25(zu311001, zu48001, ty_Char) → new_esEs21(zu311001, zu48001)
new_esEs21(Char(zu311000), Char(zu48000)) → new_primEqInt(zu311000, zu48000)
new_primEqInt(Neg(Succ(zu3110000)), Neg(Succ(zu480000))) → new_primEqNat0(zu3110000, zu480000)
new_esEs23(zu311001, zu48001, ty_Int) → new_esEs15(zu311001, zu48001)
new_esEs4(zu2040, zu199, app(app(ty_Either, bfb), bfc)) → new_esEs14(zu2040, zu199, bfb, bfc)
new_primPlusNat1(Succ(zu9100), Zero) → Succ(zu9100)
new_primPlusNat1(Zero, Succ(zu48001000)) → Succ(zu48001000)
new_esEs14(Left(zu311000), Left(zu48000), app(ty_Maybe, gg), fh) → new_esEs18(zu311000, zu48000, gg)
new_esEs14(Left(zu311000), Left(zu48000), ty_Integer, fh) → new_esEs19(zu311000, zu48000)
new_esEs12(Float(zu311000, zu311001), Float(zu48000, zu48001)) → new_esEs15(new_sr(zu311000, zu48000), new_sr(zu311001, zu48001))
new_esEs22(zu311000, zu48000, ty_Int) → new_esEs15(zu311000, zu48000)
new_esEs10(@2(zu311000, zu311001), @2(zu48000, zu48001), bbg, bbh) → new_asAs(new_esEs24(zu311000, zu48000, bbg), new_esEs25(zu311001, zu48001, bbh))
new_esEs14(Left(zu311000), Left(zu48000), ty_Bool, fh) → new_esEs5(zu311000, zu48000)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs26(zu311000, zu48000, ty_Integer) → new_esEs19(zu311000, zu48000)
new_esEs24(zu311000, zu48000, app(app(app(ty_@3, bcc), bcd), bce)) → new_esEs6(zu311000, zu48000, bcc, bcd, bce)
new_esEs4(zu2040, zu199, ty_Float) → new_esEs12(zu2040, zu199)
new_esEs9(zu311002, zu48002, ty_Double) → new_esEs16(zu311002, zu48002)
new_esEs4(zu2040, zu199, ty_Integer) → new_esEs19(zu2040, zu199)
new_esEs9(zu311002, zu48002, app(ty_Ratio, fc)) → new_esEs20(zu311002, zu48002, fc)
new_primEqInt(Neg(Zero), Neg(Succ(zu480000))) → False
new_primEqInt(Neg(Succ(zu3110000)), Neg(Zero)) → False
new_esEs9(zu311002, zu48002, app(ty_[], fa)) → new_esEs17(zu311002, zu48002, fa)
new_esEs22(zu311000, zu48000, ty_Integer) → new_esEs19(zu311000, zu48000)
new_esEs8(zu311001, zu48001, app(ty_[], dg)) → new_esEs17(zu311001, zu48001, dg)
new_esEs14(Left(zu311000), Left(zu48000), app(app(app(ty_@3, ga), gb), gc), fh) → new_esEs6(zu311000, zu48000, ga, gb, gc)
new_esEs9(zu311002, zu48002, app(app(app(ty_@3, ed), ee), ef)) → new_esEs6(zu311002, zu48002, ed, ee, ef)
new_esEs7(zu311000, zu48000, ty_Char) → new_esEs21(zu311000, zu48000)
new_esEs14(Right(zu311000), Right(zu48000), ha, app(ty_[], baa)) → new_esEs17(zu311000, zu48000, baa)
new_primPlusNat1(Zero, Zero) → Zero
new_esEs9(zu311002, zu48002, app(app(ty_Either, eg), eh)) → new_esEs14(zu311002, zu48002, eg, eh)
new_esEs4(zu2040, zu199, ty_Int) → new_esEs15(zu2040, zu199)
new_esEs25(zu311001, zu48001, app(app(ty_@2, bdc), bdd)) → new_esEs10(zu311001, zu48001, bdc, bdd)
new_asAs(True, zu89) → zu89
new_primMulNat0(Succ(zu31100100), Succ(zu4800100)) → new_primPlusNat0(new_primMulNat0(zu31100100, Succ(zu4800100)), zu4800100)
new_esEs11(LT, LT) → True
new_esEs18(Just(zu311000), Just(zu48000), ty_Double) → new_esEs16(zu311000, zu48000)
new_esEs24(zu311000, zu48000, app(app(ty_@2, bca), bcb)) → new_esEs10(zu311000, zu48000, bca, bcb)
new_esEs8(zu311001, zu48001, ty_@0) → new_esEs13(zu311001, zu48001)
new_esEs18(Just(zu311000), Just(zu48000), app(app(ty_@2, bae), baf)) → new_esEs10(zu311000, zu48000, bae, baf)
new_primEqInt(Pos(Succ(zu3110000)), Pos(Succ(zu480000))) → new_primEqNat0(zu3110000, zu480000)
new_esEs14(Left(zu311000), Left(zu48000), app(app(ty_@2, ff), fg), fh) → new_esEs10(zu311000, zu48000, ff, fg)
new_esEs17([], [], bfg) → True
new_esEs7(zu311000, zu48000, app(ty_Maybe, ce)) → new_esEs18(zu311000, zu48000, ce)
new_esEs17([], :(zu48000, zu48001), bfg) → False
new_esEs17(:(zu311000, zu311001), [], bfg) → False
new_esEs26(zu311000, zu48000, ty_Double) → new_esEs16(zu311000, zu48000)
new_esEs24(zu311000, zu48000, app(ty_Ratio, bdb)) → new_esEs20(zu311000, zu48000, bdb)
new_esEs9(zu311002, zu48002, ty_Int) → new_esEs15(zu311002, zu48002)
new_esEs18(Just(zu311000), Just(zu48000), ty_@0) → new_esEs13(zu311000, zu48000)
new_esEs25(zu311001, zu48001, app(app(ty_Either, bdh), bea)) → new_esEs14(zu311001, zu48001, bdh, bea)
new_esEs24(zu311000, zu48000, ty_Bool) → new_esEs5(zu311000, zu48000)
new_primEqNat0(Succ(zu31100000), Succ(zu4800000)) → new_primEqNat0(zu31100000, zu4800000)
new_esEs11(GT, EQ) → False
new_esEs11(EQ, GT) → False
new_esEs18(Just(zu311000), Just(zu48000), app(ty_[], bbd)) → new_esEs17(zu311000, zu48000, bbd)
new_esEs14(Right(zu311000), Right(zu48000), ha, app(ty_Maybe, bab)) → new_esEs18(zu311000, zu48000, bab)
new_esEs14(Right(zu311000), Right(zu48000), ha, app(ty_Ratio, bac)) → new_esEs20(zu311000, zu48000, bac)
new_esEs26(zu311000, zu48000, ty_Int) → new_esEs15(zu311000, zu48000)
new_esEs8(zu311001, zu48001, app(app(ty_Either, de), df)) → new_esEs14(zu311001, zu48001, de, df)
new_esEs9(zu311002, zu48002, app(ty_Maybe, fb)) → new_esEs18(zu311002, zu48002, fb)
new_esEs4(zu2040, zu199, ty_Double) → new_esEs16(zu2040, zu199)
new_esEs18(Just(zu311000), Just(zu48000), app(ty_Maybe, bbe)) → new_esEs18(zu311000, zu48000, bbe)
new_esEs18(Just(zu311000), Just(zu48000), ty_Float) → new_esEs12(zu311000, zu48000)
new_esEs14(Left(zu311000), Left(zu48000), ty_Ordering, fh) → new_esEs11(zu311000, zu48000)
new_primEqInt(Pos(Succ(zu3110000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(zu480000))) → False
new_esEs7(zu311000, zu48000, app(app(app(ty_@3, bg), bh), ca)) → new_esEs6(zu311000, zu48000, bg, bh, ca)
new_esEs25(zu311001, zu48001, app(ty_Ratio, bed)) → new_esEs20(zu311001, zu48001, bed)
new_esEs25(zu311001, zu48001, app(ty_Maybe, bec)) → new_esEs18(zu311001, zu48001, bec)
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_esEs14(Left(zu311000), Left(zu48000), ty_@0, fh) → new_esEs13(zu311000, zu48000)
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_esEs26(zu311000, zu48000, ty_Char) → new_esEs21(zu311000, zu48000)
new_esEs14(Left(zu311000), Left(zu48000), ty_Char, fh) → new_esEs21(zu311000, zu48000)
new_esEs26(zu311000, zu48000, app(ty_Ratio, bha)) → new_esEs20(zu311000, zu48000, bha)
new_esEs7(zu311000, zu48000, ty_Float) → new_esEs12(zu311000, zu48000)
new_esEs4(zu2040, zu199, app(ty_Maybe, bfe)) → new_esEs18(zu2040, zu199, bfe)
The set Q consists of the following terms:
new_esEs24(x0, x1, ty_@0)
new_esEs9(x0, x1, app(ty_Maybe, x2))
new_esEs13(@0, @0)
new_esEs25(x0, x1, ty_Char)
new_esEs9(x0, x1, app(ty_Ratio, x2))
new_esEs24(x0, x1, ty_Char)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_esEs26(x0, x1, ty_Double)
new_esEs26(x0, x1, ty_Char)
new_esEs7(x0, x1, app(app(ty_@2, x2), x3))
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs7(x0, x1, ty_Float)
new_esEs19(Integer(x0), Integer(x1))
new_esEs7(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primEqInt(Neg(Zero), Pos(Zero))
new_primEqInt(Pos(Zero), Neg(Zero))
new_esEs14(Left(x0), Left(x1), ty_Integer, x2)
new_esEs7(x0, x1, ty_@0)
new_esEs17([], [], x0)
new_sr(Pos(x0), Pos(x1))
new_esEs18(Just(x0), Just(x1), ty_Float)
new_esEs24(x0, x1, ty_Bool)
new_esEs9(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs11(EQ, LT)
new_esEs11(LT, EQ)
new_esEs17(:(x0, x1), :(x2, x3), x4)
new_esEs4(x0, x1, ty_Integer)
new_esEs4(x0, x1, ty_Int)
new_esEs17([], :(x0, x1), x2)
new_esEs14(Right(x0), Right(x1), x2, ty_Int)
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_esEs8(x0, x1, ty_Float)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs8(x0, x1, ty_Char)
new_primEqInt(Neg(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs8(x0, x1, ty_@0)
new_esEs4(x0, x1, app(app(ty_@2, x2), x3))
new_esEs24(x0, x1, ty_Ordering)
new_esEs14(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs8(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primEqNat0(Zero, Succ(x0))
new_primPlusNat1(Succ(x0), Zero)
new_sr(Neg(x0), Neg(x1))
new_esEs14(Right(x0), Right(x1), x2, ty_@0)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs25(x0, x1, ty_Float)
new_esEs14(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs26(x0, x1, app(ty_[], x2))
new_esEs8(x0, x1, app(app(ty_@2, x2), x3))
new_esEs14(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs25(x0, x1, ty_@0)
new_esEs4(x0, x1, app(ty_[], x2))
new_esEs10(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs5(False, True)
new_esEs5(True, False)
new_esEs4(x0, x1, ty_Double)
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs7(x0, x1, app(ty_Maybe, x2))
new_esEs4(x0, x1, app(ty_Maybe, x2))
new_esEs14(Left(x0), Left(x1), ty_Ordering, x2)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_esEs16(Double(x0, x1), Double(x2, x3))
new_primEqNat0(Succ(x0), Zero)
new_esEs4(x0, x1, ty_Ordering)
new_esEs14(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs18(Just(x0), Just(x1), ty_Int)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs8(x0, x1, ty_Ordering)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_esEs24(x0, x1, ty_Int)
new_primMulNat0(Zero, Succ(x0))
new_esEs14(Left(x0), Left(x1), ty_@0, x2)
new_esEs8(x0, x1, app(ty_Maybe, x2))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs11(EQ, GT)
new_esEs11(GT, EQ)
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_esEs26(x0, x1, ty_@0)
new_esEs14(Right(x0), Right(x1), x2, ty_Double)
new_esEs14(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs5(True, True)
new_primEqNat0(Zero, Zero)
new_esEs24(x0, x1, ty_Integer)
new_esEs8(x0, x1, ty_Bool)
new_esEs8(x0, x1, ty_Integer)
new_esEs8(x0, x1, app(ty_Ratio, x2))
new_esEs9(x0, x1, ty_Double)
new_esEs26(x0, x1, ty_Ordering)
new_esEs18(Nothing, Nothing, x0)
new_esEs14(Left(x0), Left(x1), ty_Char, x2)
new_esEs9(x0, x1, ty_Char)
new_esEs14(Left(x0), Left(x1), ty_Float, x2)
new_esEs5(False, False)
new_esEs14(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs18(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs14(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs25(x0, x1, ty_Double)
new_esEs23(x0, x1, ty_Int)
new_esEs7(x0, x1, ty_Char)
new_esEs4(x0, x1, ty_Bool)
new_esEs14(Right(x0), Right(x1), x2, ty_Float)
new_esEs20(:%(x0, x1), :%(x2, x3), x4)
new_esEs7(x0, x1, ty_Ordering)
new_esEs25(x0, x1, ty_Int)
new_primMulNat0(Zero, Zero)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs4(x0, x1, ty_@0)
new_esEs9(x0, x1, ty_@0)
new_esEs7(x0, x1, ty_Integer)
new_esEs7(x0, x1, app(app(ty_Either, x2), x3))
new_esEs24(x0, x1, ty_Double)
new_esEs11(GT, GT)
new_primPlusNat0(Zero, x0)
new_esEs24(x0, x1, app(ty_[], x2))
new_esEs8(x0, x1, app(app(ty_Either, x2), x3))
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_esEs4(x0, x1, app(app(ty_Either, x2), x3))
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_primMulNat0(Succ(x0), Succ(x1))
new_esEs25(x0, x1, ty_Ordering)
new_esEs18(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs26(x0, x1, ty_Int)
new_esEs14(Left(x0), Left(x1), ty_Double, x2)
new_esEs26(x0, x1, ty_Bool)
new_esEs18(Just(x0), Just(x1), ty_Char)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs18(Just(x0), Nothing, x1)
new_esEs7(x0, x1, ty_Bool)
new_esEs18(Just(x0), Just(x1), ty_Bool)
new_esEs11(LT, GT)
new_esEs11(GT, LT)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_asAs(True, x0)
new_asAs(False, x0)
new_esEs24(x0, x1, ty_Float)
new_esEs14(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs21(Char(x0), Char(x1))
new_esEs4(x0, x1, app(ty_Ratio, x2))
new_sr(Neg(x0), Pos(x1))
new_sr(Pos(x0), Neg(x1))
new_esEs14(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs18(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs7(x0, x1, ty_Int)
new_esEs9(x0, x1, ty_Int)
new_esEs26(x0, x1, ty_Integer)
new_esEs14(Right(x0), Right(x1), x2, ty_Integer)
new_esEs18(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs14(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs9(x0, x1, ty_Integer)
new_esEs18(Just(x0), Just(x1), ty_Integer)
new_esEs9(x0, x1, ty_Float)
new_esEs14(Left(x0), Left(x1), ty_Bool, x2)
new_esEs7(x0, x1, ty_Double)
new_esEs14(Right(x0), Left(x1), x2, x3)
new_esEs14(Left(x0), Right(x1), x2, x3)
new_esEs15(x0, x1)
new_esEs14(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs7(x0, x1, app(ty_[], x2))
new_esEs26(x0, x1, ty_Float)
new_esEs8(x0, x1, ty_Double)
new_esEs23(x0, x1, ty_Integer)
new_esEs25(x0, x1, app(ty_[], x2))
new_esEs14(Left(x0), Left(x1), ty_Int, x2)
new_esEs14(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs17(:(x0, x1), [], x2)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_esEs14(Right(x0), Right(x1), x2, ty_Char)
new_esEs8(x0, x1, app(ty_[], x2))
new_esEs9(x0, x1, app(ty_[], x2))
new_esEs9(x0, x1, ty_Ordering)
new_esEs22(x0, x1, ty_Integer)
new_esEs11(LT, LT)
new_esEs8(x0, x1, ty_Int)
new_esEs9(x0, x1, ty_Bool)
new_esEs18(Nothing, Just(x0), x1)
new_esEs9(x0, x1, app(app(ty_Either, x2), x3))
new_primPlusNat1(Zero, Zero)
new_esEs7(x0, x1, app(ty_Ratio, x2))
new_esEs9(x0, x1, app(app(ty_@2, x2), x3))
new_primMulNat0(Succ(x0), Zero)
new_esEs4(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs4(x0, x1, ty_Float)
new_primEqInt(Pos(Zero), Pos(Zero))
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs11(EQ, EQ)
new_esEs18(Just(x0), Just(x1), ty_Ordering)
new_esEs25(x0, x1, ty_Integer)
new_esEs4(x0, x1, ty_Char)
new_primPlusNat1(Zero, Succ(x0))
new_esEs12(Float(x0, x1), Float(x2, x3))
new_esEs18(Just(x0), Just(x1), ty_@0)
new_esEs14(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs18(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs14(Right(x0), Right(x1), x2, ty_Bool)
new_esEs22(x0, x1, ty_Int)
new_primPlusNat0(Succ(x0), x1)
new_esEs18(Just(x0), Just(x1), app(ty_[], x2))
new_esEs25(x0, x1, ty_Bool)
new_esEs18(Just(x0), Just(x1), ty_Double)
We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph [15,17,22] contains 1 SCC with 1 less node.
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPSizeChangeProof
Q DP problem:
The TRS P consists of the following rules:
new_nubByNubBy'1(zu199, zu200, zu201, zu202, False, :(zu2040, zu2041), ba) → new_nubByNubBy'1(zu199, zu200, zu201, zu202, new_esEs4(zu2040, zu199, ba), zu2041, ba)
new_nubByNubBy'1(zu199, :(zu2000, zu2001), zu201, zu202, True, zu204, ba) → new_nubByNubBy'10(zu2000, zu2001, zu201, zu202, :(zu201, zu202), ba)
new_nubByNubBy'1(zu199, zu200, zu201, zu202, False, [], ba) → new_nubByNubBy'(zu200, zu199, :(zu201, zu202), ba)
new_nubByNubBy'10(zu199, zu200, zu201, zu202, :(zu2040, zu2041), ba) → new_nubByNubBy'1(zu199, zu200, zu201, zu202, new_esEs4(zu2040, zu199, ba), zu2041, ba)
new_nubByNubBy'(:(zu2000, zu2001), zu201, zu202, ba) → new_nubByNubBy'10(zu2000, zu2001, zu201, zu202, :(zu201, zu202), ba)
The TRS R consists of the following rules:
new_esEs24(zu311000, zu48000, ty_Float) → new_esEs12(zu311000, zu48000)
new_primPlusNat1(Succ(zu9100), Succ(zu48001000)) → Succ(Succ(new_primPlusNat1(zu9100, zu48001000)))
new_primEqInt(Neg(Succ(zu3110000)), Pos(zu48000)) → False
new_primEqInt(Pos(Succ(zu3110000)), Neg(zu48000)) → False
new_esEs18(Just(zu311000), Just(zu48000), app(app(ty_Either, bbb), bbc)) → new_esEs14(zu311000, zu48000, bbb, bbc)
new_esEs14(Right(zu311000), Right(zu48000), ha, ty_Ordering) → new_esEs11(zu311000, zu48000)
new_esEs14(Left(zu311000), Right(zu48000), ha, fh) → False
new_esEs14(Right(zu311000), Left(zu48000), ha, fh) → False
new_esEs14(Right(zu311000), Right(zu48000), ha, app(app(ty_@2, hb), hc)) → new_esEs10(zu311000, zu48000, hb, hc)
new_esEs25(zu311001, zu48001, ty_@0) → new_esEs13(zu311001, zu48001)
new_esEs23(zu311001, zu48001, ty_Integer) → new_esEs19(zu311001, zu48001)
new_esEs4(zu2040, zu199, app(app(app(ty_@3, beg), beh), bfa)) → new_esEs6(zu2040, zu199, beg, beh, bfa)
new_esEs14(Right(zu311000), Right(zu48000), ha, ty_Integer) → new_esEs19(zu311000, zu48000)
new_esEs14(Right(zu311000), Right(zu48000), ha, app(app(app(ty_@3, hd), he), hf)) → new_esEs6(zu311000, zu48000, hd, he, hf)
new_esEs14(Right(zu311000), Right(zu48000), ha, ty_Char) → new_esEs21(zu311000, zu48000)
new_esEs9(zu311002, zu48002, ty_Ordering) → new_esEs11(zu311002, zu48002)
new_esEs9(zu311002, zu48002, ty_@0) → new_esEs13(zu311002, zu48002)
new_esEs7(zu311000, zu48000, ty_Int) → new_esEs15(zu311000, zu48000)
new_esEs24(zu311000, zu48000, ty_Ordering) → new_esEs11(zu311000, zu48000)
new_primEqInt(Neg(Zero), Pos(Succ(zu480000))) → False
new_primEqInt(Pos(Zero), Neg(Succ(zu480000))) → False
new_esEs26(zu311000, zu48000, app(ty_[], bgg)) → new_esEs17(zu311000, zu48000, bgg)
new_esEs14(Right(zu311000), Right(zu48000), ha, ty_@0) → new_esEs13(zu311000, zu48000)
new_esEs13(@0, @0) → True
new_esEs26(zu311000, zu48000, ty_Float) → new_esEs12(zu311000, zu48000)
new_esEs4(zu2040, zu199, app(app(ty_@2, bee), bef)) → new_esEs10(zu2040, zu199, bee, bef)
new_esEs14(Right(zu311000), Right(zu48000), ha, ty_Float) → new_esEs12(zu311000, zu48000)
new_esEs24(zu311000, zu48000, app(ty_Maybe, bda)) → new_esEs18(zu311000, zu48000, bda)
new_esEs16(Double(zu311000, zu311001), Double(zu48000, zu48001)) → new_esEs15(new_sr(zu311000, zu48000), new_sr(zu311001, zu48001))
new_esEs11(EQ, EQ) → True
new_esEs8(zu311001, zu48001, ty_Int) → new_esEs15(zu311001, zu48001)
new_primMulNat0(Zero, Zero) → Zero
new_esEs4(zu2040, zu199, app(ty_[], bfd)) → new_esEs17(zu2040, zu199, bfd)
new_esEs14(Left(zu311000), Left(zu48000), ty_Double, fh) → new_esEs16(zu311000, zu48000)
new_esEs25(zu311001, zu48001, ty_Float) → new_esEs12(zu311001, zu48001)
new_esEs24(zu311000, zu48000, ty_@0) → new_esEs13(zu311000, zu48000)
new_esEs18(Just(zu311000), Just(zu48000), app(ty_Ratio, bbf)) → new_esEs20(zu311000, zu48000, bbf)
new_esEs17(:(zu311000, zu311001), :(zu48000, zu48001), bfg) → new_asAs(new_esEs26(zu311000, zu48000, bfg), new_esEs17(zu311001, zu48001, bfg))
new_esEs8(zu311001, zu48001, app(app(app(ty_@3, db), dc), dd)) → new_esEs6(zu311001, zu48001, db, dc, dd)
new_esEs8(zu311001, zu48001, ty_Float) → new_esEs12(zu311001, zu48001)
new_esEs4(zu2040, zu199, ty_Char) → new_esEs21(zu2040, zu199)
new_esEs9(zu311002, zu48002, ty_Float) → new_esEs12(zu311002, zu48002)
new_esEs8(zu311001, zu48001, app(ty_Ratio, ea)) → new_esEs20(zu311001, zu48001, ea)
new_esEs9(zu311002, zu48002, app(app(ty_@2, eb), ec)) → new_esEs10(zu311002, zu48002, eb, ec)
new_primPlusNat0(Zero, zu4800100) → Succ(zu4800100)
new_esEs18(Just(zu311000), Just(zu48000), ty_Ordering) → new_esEs11(zu311000, zu48000)
new_esEs11(GT, LT) → False
new_esEs11(LT, GT) → False
new_esEs19(Integer(zu311000), Integer(zu48000)) → new_primEqInt(zu311000, zu48000)
new_esEs25(zu311001, zu48001, ty_Ordering) → new_esEs11(zu311001, zu48001)
new_esEs18(Just(zu311000), Just(zu48000), ty_Integer) → new_esEs19(zu311000, zu48000)
new_esEs7(zu311000, zu48000, app(ty_[], cd)) → new_esEs17(zu311000, zu48000, cd)
new_esEs25(zu311001, zu48001, ty_Double) → new_esEs16(zu311001, zu48001)
new_sr(Neg(zu3110010), Pos(zu480010)) → Neg(new_primMulNat0(zu3110010, zu480010))
new_sr(Pos(zu3110010), Neg(zu480010)) → Neg(new_primMulNat0(zu3110010, zu480010))
new_esEs11(EQ, LT) → False
new_esEs11(LT, EQ) → False
new_esEs24(zu311000, zu48000, app(ty_[], bch)) → new_esEs17(zu311000, zu48000, bch)
new_esEs24(zu311000, zu48000, ty_Int) → new_esEs15(zu311000, zu48000)
new_esEs8(zu311001, zu48001, ty_Double) → new_esEs16(zu311001, zu48001)
new_esEs24(zu311000, zu48000, app(app(ty_Either, bcf), bcg)) → new_esEs14(zu311000, zu48000, bcf, bcg)
new_esEs18(Just(zu311000), Just(zu48000), ty_Char) → new_esEs21(zu311000, zu48000)
new_esEs9(zu311002, zu48002, ty_Char) → new_esEs21(zu311002, zu48002)
new_esEs4(zu2040, zu199, ty_Ordering) → new_esEs11(zu2040, zu199)
new_esEs26(zu311000, zu48000, app(app(ty_Either, bge), bgf)) → new_esEs14(zu311000, zu48000, bge, bgf)
new_esEs8(zu311001, zu48001, ty_Bool) → new_esEs5(zu311001, zu48001)
new_esEs18(Just(zu311000), Just(zu48000), ty_Int) → new_esEs15(zu311000, zu48000)
new_esEs8(zu311001, zu48001, ty_Ordering) → new_esEs11(zu311001, zu48001)
new_esEs14(Left(zu311000), Left(zu48000), app(ty_Ratio, gh), fh) → new_esEs20(zu311000, zu48000, gh)
new_primEqNat0(Zero, Succ(zu4800000)) → False
new_primEqNat0(Succ(zu31100000), Zero) → False
new_esEs14(Left(zu311000), Left(zu48000), ty_Int, fh) → new_esEs15(zu311000, zu48000)
new_esEs14(Right(zu311000), Right(zu48000), ha, ty_Int) → new_esEs15(zu311000, zu48000)
new_esEs26(zu311000, zu48000, ty_Ordering) → new_esEs11(zu311000, zu48000)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs14(Right(zu311000), Right(zu48000), ha, ty_Double) → new_esEs16(zu311000, zu48000)
new_esEs8(zu311001, zu48001, app(ty_Maybe, dh)) → new_esEs18(zu311001, zu48001, dh)
new_esEs26(zu311000, zu48000, app(ty_Maybe, bgh)) → new_esEs18(zu311000, zu48000, bgh)
new_esEs8(zu311001, zu48001, ty_Char) → new_esEs21(zu311001, zu48001)
new_esEs18(Just(zu311000), Just(zu48000), app(app(app(ty_@3, bag), bah), bba)) → new_esEs6(zu311000, zu48000, bag, bah, bba)
new_esEs15(zu31100, zu4800) → new_primEqInt(zu31100, zu4800)
new_esEs26(zu311000, zu48000, ty_@0) → new_esEs13(zu311000, zu48000)
new_esEs24(zu311000, zu48000, ty_Integer) → new_esEs19(zu311000, zu48000)
new_esEs14(Left(zu311000), Left(zu48000), app(ty_[], gf), fh) → new_esEs17(zu311000, zu48000, gf)
new_esEs24(zu311000, zu48000, ty_Char) → new_esEs21(zu311000, zu48000)
new_esEs26(zu311000, zu48000, ty_Bool) → new_esEs5(zu311000, zu48000)
new_esEs8(zu311001, zu48001, ty_Integer) → new_esEs19(zu311001, zu48001)
new_esEs18(Nothing, Nothing, bad) → True
new_esEs4(zu2040, zu199, ty_@0) → new_esEs13(zu2040, zu199)
new_esEs14(Right(zu311000), Right(zu48000), ha, app(app(ty_Either, hg), hh)) → new_esEs14(zu311000, zu48000, hg, hh)
new_esEs7(zu311000, zu48000, ty_Bool) → new_esEs5(zu311000, zu48000)
new_esEs14(Left(zu311000), Left(zu48000), app(app(ty_Either, gd), ge), fh) → new_esEs14(zu311000, zu48000, gd, ge)
new_esEs7(zu311000, zu48000, app(app(ty_@2, be), bf)) → new_esEs10(zu311000, zu48000, be, bf)
new_esEs7(zu311000, zu48000, ty_Integer) → new_esEs19(zu311000, zu48000)
new_esEs7(zu311000, zu48000, ty_Ordering) → new_esEs11(zu311000, zu48000)
new_esEs11(GT, GT) → True
new_esEs18(Just(zu311000), Just(zu48000), ty_Bool) → new_esEs5(zu311000, zu48000)
new_sr(Neg(zu3110010), Neg(zu480010)) → Pos(new_primMulNat0(zu3110010, zu480010))
new_esEs14(Right(zu311000), Right(zu48000), ha, ty_Bool) → new_esEs5(zu311000, zu48000)
new_asAs(False, zu89) → False
new_sr(Pos(zu3110010), Pos(zu480010)) → Pos(new_primMulNat0(zu3110010, zu480010))
new_esEs6(@3(zu311000, zu311001, zu311002), @3(zu48000, zu48001, zu48002), bb, bc, bd) → new_asAs(new_esEs7(zu311000, zu48000, bb), new_asAs(new_esEs8(zu311001, zu48001, bc), new_esEs9(zu311002, zu48002, bd)))
new_primEqNat0(Zero, Zero) → True
new_primMulNat0(Succ(zu31100100), Zero) → Zero
new_primMulNat0(Zero, Succ(zu4800100)) → Zero
new_esEs7(zu311000, zu48000, ty_Double) → new_esEs16(zu311000, zu48000)
new_esEs7(zu311000, zu48000, app(ty_Ratio, cf)) → new_esEs20(zu311000, zu48000, cf)
new_esEs14(Left(zu311000), Left(zu48000), ty_Float, fh) → new_esEs12(zu311000, zu48000)
new_esEs18(Just(zu311000), Nothing, bad) → False
new_esEs18(Nothing, Just(zu48000), bad) → False
new_esEs9(zu311002, zu48002, ty_Bool) → new_esEs5(zu311002, zu48002)
new_esEs25(zu311001, zu48001, ty_Bool) → new_esEs5(zu311001, zu48001)
new_esEs25(zu311001, zu48001, ty_Int) → new_esEs15(zu311001, zu48001)
new_esEs5(False, False) → True
new_esEs5(True, False) → False
new_esEs5(False, True) → False
new_esEs20(:%(zu311000, zu311001), :%(zu48000, zu48001), fd) → new_asAs(new_esEs22(zu311000, zu48000, fd), new_esEs23(zu311001, zu48001, fd))
new_esEs7(zu311000, zu48000, app(app(ty_Either, cb), cc)) → new_esEs14(zu311000, zu48000, cb, cc)
new_esEs25(zu311001, zu48001, app(ty_[], beb)) → new_esEs17(zu311001, zu48001, beb)
new_esEs26(zu311000, zu48000, app(app(ty_@2, bfh), bga)) → new_esEs10(zu311000, zu48000, bfh, bga)
new_esEs24(zu311000, zu48000, ty_Double) → new_esEs16(zu311000, zu48000)
new_esEs7(zu311000, zu48000, ty_@0) → new_esEs13(zu311000, zu48000)
new_esEs25(zu311001, zu48001, app(app(app(ty_@3, bde), bdf), bdg)) → new_esEs6(zu311001, zu48001, bde, bdf, bdg)
new_esEs9(zu311002, zu48002, ty_Integer) → new_esEs19(zu311002, zu48002)
new_primPlusNat0(Succ(zu910), zu4800100) → Succ(Succ(new_primPlusNat1(zu910, zu4800100)))
new_esEs8(zu311001, zu48001, app(app(ty_@2, cg), da)) → new_esEs10(zu311001, zu48001, cg, da)
new_esEs26(zu311000, zu48000, app(app(app(ty_@3, bgb), bgc), bgd)) → new_esEs6(zu311000, zu48000, bgb, bgc, bgd)
new_esEs4(zu2040, zu199, app(ty_Ratio, bff)) → new_esEs20(zu2040, zu199, bff)
new_esEs25(zu311001, zu48001, ty_Integer) → new_esEs19(zu311001, zu48001)
new_esEs4(zu2040, zu199, ty_Bool) → new_esEs5(zu2040, zu199)
new_esEs5(True, True) → True
new_esEs25(zu311001, zu48001, ty_Char) → new_esEs21(zu311001, zu48001)
new_esEs21(Char(zu311000), Char(zu48000)) → new_primEqInt(zu311000, zu48000)
new_primEqInt(Neg(Succ(zu3110000)), Neg(Succ(zu480000))) → new_primEqNat0(zu3110000, zu480000)
new_esEs23(zu311001, zu48001, ty_Int) → new_esEs15(zu311001, zu48001)
new_esEs4(zu2040, zu199, app(app(ty_Either, bfb), bfc)) → new_esEs14(zu2040, zu199, bfb, bfc)
new_primPlusNat1(Succ(zu9100), Zero) → Succ(zu9100)
new_primPlusNat1(Zero, Succ(zu48001000)) → Succ(zu48001000)
new_esEs14(Left(zu311000), Left(zu48000), app(ty_Maybe, gg), fh) → new_esEs18(zu311000, zu48000, gg)
new_esEs14(Left(zu311000), Left(zu48000), ty_Integer, fh) → new_esEs19(zu311000, zu48000)
new_esEs12(Float(zu311000, zu311001), Float(zu48000, zu48001)) → new_esEs15(new_sr(zu311000, zu48000), new_sr(zu311001, zu48001))
new_esEs22(zu311000, zu48000, ty_Int) → new_esEs15(zu311000, zu48000)
new_esEs10(@2(zu311000, zu311001), @2(zu48000, zu48001), bbg, bbh) → new_asAs(new_esEs24(zu311000, zu48000, bbg), new_esEs25(zu311001, zu48001, bbh))
new_esEs14(Left(zu311000), Left(zu48000), ty_Bool, fh) → new_esEs5(zu311000, zu48000)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs26(zu311000, zu48000, ty_Integer) → new_esEs19(zu311000, zu48000)
new_esEs24(zu311000, zu48000, app(app(app(ty_@3, bcc), bcd), bce)) → new_esEs6(zu311000, zu48000, bcc, bcd, bce)
new_esEs4(zu2040, zu199, ty_Float) → new_esEs12(zu2040, zu199)
new_esEs9(zu311002, zu48002, ty_Double) → new_esEs16(zu311002, zu48002)
new_esEs4(zu2040, zu199, ty_Integer) → new_esEs19(zu2040, zu199)
new_esEs9(zu311002, zu48002, app(ty_Ratio, fc)) → new_esEs20(zu311002, zu48002, fc)
new_primEqInt(Neg(Zero), Neg(Succ(zu480000))) → False
new_primEqInt(Neg(Succ(zu3110000)), Neg(Zero)) → False
new_esEs9(zu311002, zu48002, app(ty_[], fa)) → new_esEs17(zu311002, zu48002, fa)
new_esEs22(zu311000, zu48000, ty_Integer) → new_esEs19(zu311000, zu48000)
new_esEs8(zu311001, zu48001, app(ty_[], dg)) → new_esEs17(zu311001, zu48001, dg)
new_esEs14(Left(zu311000), Left(zu48000), app(app(app(ty_@3, ga), gb), gc), fh) → new_esEs6(zu311000, zu48000, ga, gb, gc)
new_esEs9(zu311002, zu48002, app(app(app(ty_@3, ed), ee), ef)) → new_esEs6(zu311002, zu48002, ed, ee, ef)
new_esEs7(zu311000, zu48000, ty_Char) → new_esEs21(zu311000, zu48000)
new_esEs14(Right(zu311000), Right(zu48000), ha, app(ty_[], baa)) → new_esEs17(zu311000, zu48000, baa)
new_primPlusNat1(Zero, Zero) → Zero
new_esEs9(zu311002, zu48002, app(app(ty_Either, eg), eh)) → new_esEs14(zu311002, zu48002, eg, eh)
new_esEs4(zu2040, zu199, ty_Int) → new_esEs15(zu2040, zu199)
new_esEs25(zu311001, zu48001, app(app(ty_@2, bdc), bdd)) → new_esEs10(zu311001, zu48001, bdc, bdd)
new_asAs(True, zu89) → zu89
new_primMulNat0(Succ(zu31100100), Succ(zu4800100)) → new_primPlusNat0(new_primMulNat0(zu31100100, Succ(zu4800100)), zu4800100)
new_esEs11(LT, LT) → True
new_esEs18(Just(zu311000), Just(zu48000), ty_Double) → new_esEs16(zu311000, zu48000)
new_esEs24(zu311000, zu48000, app(app(ty_@2, bca), bcb)) → new_esEs10(zu311000, zu48000, bca, bcb)
new_esEs8(zu311001, zu48001, ty_@0) → new_esEs13(zu311001, zu48001)
new_esEs18(Just(zu311000), Just(zu48000), app(app(ty_@2, bae), baf)) → new_esEs10(zu311000, zu48000, bae, baf)
new_primEqInt(Pos(Succ(zu3110000)), Pos(Succ(zu480000))) → new_primEqNat0(zu3110000, zu480000)
new_esEs14(Left(zu311000), Left(zu48000), app(app(ty_@2, ff), fg), fh) → new_esEs10(zu311000, zu48000, ff, fg)
new_esEs17([], [], bfg) → True
new_esEs7(zu311000, zu48000, app(ty_Maybe, ce)) → new_esEs18(zu311000, zu48000, ce)
new_esEs17([], :(zu48000, zu48001), bfg) → False
new_esEs17(:(zu311000, zu311001), [], bfg) → False
new_esEs26(zu311000, zu48000, ty_Double) → new_esEs16(zu311000, zu48000)
new_esEs24(zu311000, zu48000, app(ty_Ratio, bdb)) → new_esEs20(zu311000, zu48000, bdb)
new_esEs9(zu311002, zu48002, ty_Int) → new_esEs15(zu311002, zu48002)
new_esEs18(Just(zu311000), Just(zu48000), ty_@0) → new_esEs13(zu311000, zu48000)
new_esEs25(zu311001, zu48001, app(app(ty_Either, bdh), bea)) → new_esEs14(zu311001, zu48001, bdh, bea)
new_esEs24(zu311000, zu48000, ty_Bool) → new_esEs5(zu311000, zu48000)
new_primEqNat0(Succ(zu31100000), Succ(zu4800000)) → new_primEqNat0(zu31100000, zu4800000)
new_esEs11(GT, EQ) → False
new_esEs11(EQ, GT) → False
new_esEs18(Just(zu311000), Just(zu48000), app(ty_[], bbd)) → new_esEs17(zu311000, zu48000, bbd)
new_esEs14(Right(zu311000), Right(zu48000), ha, app(ty_Maybe, bab)) → new_esEs18(zu311000, zu48000, bab)
new_esEs14(Right(zu311000), Right(zu48000), ha, app(ty_Ratio, bac)) → new_esEs20(zu311000, zu48000, bac)
new_esEs26(zu311000, zu48000, ty_Int) → new_esEs15(zu311000, zu48000)
new_esEs8(zu311001, zu48001, app(app(ty_Either, de), df)) → new_esEs14(zu311001, zu48001, de, df)
new_esEs9(zu311002, zu48002, app(ty_Maybe, fb)) → new_esEs18(zu311002, zu48002, fb)
new_esEs4(zu2040, zu199, ty_Double) → new_esEs16(zu2040, zu199)
new_esEs18(Just(zu311000), Just(zu48000), app(ty_Maybe, bbe)) → new_esEs18(zu311000, zu48000, bbe)
new_esEs18(Just(zu311000), Just(zu48000), ty_Float) → new_esEs12(zu311000, zu48000)
new_esEs14(Left(zu311000), Left(zu48000), ty_Ordering, fh) → new_esEs11(zu311000, zu48000)
new_primEqInt(Pos(Succ(zu3110000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(zu480000))) → False
new_esEs7(zu311000, zu48000, app(app(app(ty_@3, bg), bh), ca)) → new_esEs6(zu311000, zu48000, bg, bh, ca)
new_esEs25(zu311001, zu48001, app(ty_Ratio, bed)) → new_esEs20(zu311001, zu48001, bed)
new_esEs25(zu311001, zu48001, app(ty_Maybe, bec)) → new_esEs18(zu311001, zu48001, bec)
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_esEs14(Left(zu311000), Left(zu48000), ty_@0, fh) → new_esEs13(zu311000, zu48000)
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_esEs26(zu311000, zu48000, ty_Char) → new_esEs21(zu311000, zu48000)
new_esEs14(Left(zu311000), Left(zu48000), ty_Char, fh) → new_esEs21(zu311000, zu48000)
new_esEs26(zu311000, zu48000, app(ty_Ratio, bha)) → new_esEs20(zu311000, zu48000, bha)
new_esEs7(zu311000, zu48000, ty_Float) → new_esEs12(zu311000, zu48000)
new_esEs4(zu2040, zu199, app(ty_Maybe, bfe)) → new_esEs18(zu2040, zu199, bfe)
The set Q consists of the following terms:
new_esEs24(x0, x1, ty_@0)
new_esEs9(x0, x1, app(ty_Maybe, x2))
new_esEs13(@0, @0)
new_esEs25(x0, x1, ty_Char)
new_esEs9(x0, x1, app(ty_Ratio, x2))
new_esEs24(x0, x1, ty_Char)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_esEs26(x0, x1, ty_Double)
new_esEs26(x0, x1, ty_Char)
new_esEs7(x0, x1, app(app(ty_@2, x2), x3))
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs7(x0, x1, ty_Float)
new_esEs19(Integer(x0), Integer(x1))
new_esEs7(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primEqInt(Neg(Zero), Pos(Zero))
new_primEqInt(Pos(Zero), Neg(Zero))
new_esEs14(Left(x0), Left(x1), ty_Integer, x2)
new_esEs7(x0, x1, ty_@0)
new_esEs17([], [], x0)
new_sr(Pos(x0), Pos(x1))
new_esEs18(Just(x0), Just(x1), ty_Float)
new_esEs24(x0, x1, ty_Bool)
new_esEs9(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs11(EQ, LT)
new_esEs11(LT, EQ)
new_esEs17(:(x0, x1), :(x2, x3), x4)
new_esEs4(x0, x1, ty_Integer)
new_esEs4(x0, x1, ty_Int)
new_esEs17([], :(x0, x1), x2)
new_esEs14(Right(x0), Right(x1), x2, ty_Int)
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_esEs8(x0, x1, ty_Float)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs8(x0, x1, ty_Char)
new_primEqInt(Neg(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs8(x0, x1, ty_@0)
new_esEs4(x0, x1, app(app(ty_@2, x2), x3))
new_esEs24(x0, x1, ty_Ordering)
new_esEs14(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs8(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primEqNat0(Zero, Succ(x0))
new_primPlusNat1(Succ(x0), Zero)
new_sr(Neg(x0), Neg(x1))
new_esEs14(Right(x0), Right(x1), x2, ty_@0)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs25(x0, x1, ty_Float)
new_esEs14(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs26(x0, x1, app(ty_[], x2))
new_esEs8(x0, x1, app(app(ty_@2, x2), x3))
new_esEs14(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs25(x0, x1, ty_@0)
new_esEs4(x0, x1, app(ty_[], x2))
new_esEs10(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs5(False, True)
new_esEs5(True, False)
new_esEs4(x0, x1, ty_Double)
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs7(x0, x1, app(ty_Maybe, x2))
new_esEs4(x0, x1, app(ty_Maybe, x2))
new_esEs14(Left(x0), Left(x1), ty_Ordering, x2)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_esEs16(Double(x0, x1), Double(x2, x3))
new_primEqNat0(Succ(x0), Zero)
new_esEs4(x0, x1, ty_Ordering)
new_esEs14(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs18(Just(x0), Just(x1), ty_Int)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs8(x0, x1, ty_Ordering)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_esEs24(x0, x1, ty_Int)
new_primMulNat0(Zero, Succ(x0))
new_esEs14(Left(x0), Left(x1), ty_@0, x2)
new_esEs8(x0, x1, app(ty_Maybe, x2))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs11(EQ, GT)
new_esEs11(GT, EQ)
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_esEs26(x0, x1, ty_@0)
new_esEs14(Right(x0), Right(x1), x2, ty_Double)
new_esEs14(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs5(True, True)
new_primEqNat0(Zero, Zero)
new_esEs24(x0, x1, ty_Integer)
new_esEs8(x0, x1, ty_Bool)
new_esEs8(x0, x1, ty_Integer)
new_esEs8(x0, x1, app(ty_Ratio, x2))
new_esEs9(x0, x1, ty_Double)
new_esEs26(x0, x1, ty_Ordering)
new_esEs18(Nothing, Nothing, x0)
new_esEs14(Left(x0), Left(x1), ty_Char, x2)
new_esEs9(x0, x1, ty_Char)
new_esEs14(Left(x0), Left(x1), ty_Float, x2)
new_esEs5(False, False)
new_esEs14(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs18(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs14(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs25(x0, x1, ty_Double)
new_esEs23(x0, x1, ty_Int)
new_esEs7(x0, x1, ty_Char)
new_esEs4(x0, x1, ty_Bool)
new_esEs14(Right(x0), Right(x1), x2, ty_Float)
new_esEs20(:%(x0, x1), :%(x2, x3), x4)
new_esEs7(x0, x1, ty_Ordering)
new_esEs25(x0, x1, ty_Int)
new_primMulNat0(Zero, Zero)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs4(x0, x1, ty_@0)
new_esEs9(x0, x1, ty_@0)
new_esEs7(x0, x1, ty_Integer)
new_esEs7(x0, x1, app(app(ty_Either, x2), x3))
new_esEs24(x0, x1, ty_Double)
new_esEs11(GT, GT)
new_primPlusNat0(Zero, x0)
new_esEs24(x0, x1, app(ty_[], x2))
new_esEs8(x0, x1, app(app(ty_Either, x2), x3))
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_esEs4(x0, x1, app(app(ty_Either, x2), x3))
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_primMulNat0(Succ(x0), Succ(x1))
new_esEs25(x0, x1, ty_Ordering)
new_esEs18(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs26(x0, x1, ty_Int)
new_esEs14(Left(x0), Left(x1), ty_Double, x2)
new_esEs26(x0, x1, ty_Bool)
new_esEs18(Just(x0), Just(x1), ty_Char)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs18(Just(x0), Nothing, x1)
new_esEs7(x0, x1, ty_Bool)
new_esEs18(Just(x0), Just(x1), ty_Bool)
new_esEs11(LT, GT)
new_esEs11(GT, LT)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_asAs(True, x0)
new_asAs(False, x0)
new_esEs24(x0, x1, ty_Float)
new_esEs14(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs21(Char(x0), Char(x1))
new_esEs4(x0, x1, app(ty_Ratio, x2))
new_sr(Neg(x0), Pos(x1))
new_sr(Pos(x0), Neg(x1))
new_esEs14(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs18(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs7(x0, x1, ty_Int)
new_esEs9(x0, x1, ty_Int)
new_esEs26(x0, x1, ty_Integer)
new_esEs14(Right(x0), Right(x1), x2, ty_Integer)
new_esEs18(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs14(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs9(x0, x1, ty_Integer)
new_esEs18(Just(x0), Just(x1), ty_Integer)
new_esEs9(x0, x1, ty_Float)
new_esEs14(Left(x0), Left(x1), ty_Bool, x2)
new_esEs7(x0, x1, ty_Double)
new_esEs14(Right(x0), Left(x1), x2, x3)
new_esEs14(Left(x0), Right(x1), x2, x3)
new_esEs15(x0, x1)
new_esEs14(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs7(x0, x1, app(ty_[], x2))
new_esEs26(x0, x1, ty_Float)
new_esEs8(x0, x1, ty_Double)
new_esEs23(x0, x1, ty_Integer)
new_esEs25(x0, x1, app(ty_[], x2))
new_esEs14(Left(x0), Left(x1), ty_Int, x2)
new_esEs14(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs17(:(x0, x1), [], x2)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_esEs14(Right(x0), Right(x1), x2, ty_Char)
new_esEs8(x0, x1, app(ty_[], x2))
new_esEs9(x0, x1, app(ty_[], x2))
new_esEs9(x0, x1, ty_Ordering)
new_esEs22(x0, x1, ty_Integer)
new_esEs11(LT, LT)
new_esEs8(x0, x1, ty_Int)
new_esEs9(x0, x1, ty_Bool)
new_esEs18(Nothing, Just(x0), x1)
new_esEs9(x0, x1, app(app(ty_Either, x2), x3))
new_primPlusNat1(Zero, Zero)
new_esEs7(x0, x1, app(ty_Ratio, x2))
new_esEs9(x0, x1, app(app(ty_@2, x2), x3))
new_primMulNat0(Succ(x0), Zero)
new_esEs4(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs4(x0, x1, ty_Float)
new_primEqInt(Pos(Zero), Pos(Zero))
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs11(EQ, EQ)
new_esEs18(Just(x0), Just(x1), ty_Ordering)
new_esEs25(x0, x1, ty_Integer)
new_esEs4(x0, x1, ty_Char)
new_primPlusNat1(Zero, Succ(x0))
new_esEs12(Float(x0, x1), Float(x2, x3))
new_esEs18(Just(x0), Just(x1), ty_@0)
new_esEs14(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs18(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs14(Right(x0), Right(x1), x2, ty_Bool)
new_esEs22(x0, x1, ty_Int)
new_primPlusNat0(Succ(x0), x1)
new_esEs18(Just(x0), Just(x1), app(ty_[], x2))
new_esEs25(x0, x1, ty_Bool)
new_esEs18(Just(x0), Just(x1), ty_Double)
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_nubByNubBy'10(zu199, zu200, zu201, zu202, :(zu2040, zu2041), ba) → new_nubByNubBy'1(zu199, zu200, zu201, zu202, new_esEs4(zu2040, zu199, ba), zu2041, ba)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 > 6, 6 >= 7
- new_nubByNubBy'1(zu199, zu200, zu201, zu202, False, :(zu2040, zu2041), ba) → new_nubByNubBy'1(zu199, zu200, zu201, zu202, new_esEs4(zu2040, zu199, ba), zu2041, ba)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 6 > 6, 7 >= 7
- new_nubByNubBy'1(zu199, :(zu2000, zu2001), zu201, zu202, True, zu204, ba) → new_nubByNubBy'10(zu2000, zu2001, zu201, zu202, :(zu201, zu202), ba)
The graph contains the following edges 2 > 1, 2 > 2, 3 >= 3, 4 >= 4, 7 >= 6
- new_nubByNubBy'1(zu199, zu200, zu201, zu202, False, [], ba) → new_nubByNubBy'(zu200, zu199, :(zu201, zu202), ba)
The graph contains the following edges 2 >= 1, 1 >= 2, 7 >= 4
- new_nubByNubBy'(:(zu2000, zu2001), zu201, zu202, ba) → new_nubByNubBy'10(zu2000, zu2001, zu201, zu202, :(zu201, zu202), ba)
The graph contains the following edges 1 > 1, 1 > 2, 2 >= 3, 3 >= 4, 4 >= 6