YES 15.818
H-Termination proof of /home/matraf/haskell/eval_FullyBlown_Fast/List.hs
H-Termination of the given Haskell-Program with start terms could successfully be proven:
↳ HASKELL
↳ IFR
mainModule List
| ((delete :: Float -> [Float] -> [Float]) :: Float -> [Float] -> [Float]) |
module List where
| import qualified Maybe import qualified Prelude
|
| delete :: Eq a => a -> [a] -> [a]
|
| 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 |
|
module Maybe where
| import qualified List 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 List
| ((delete :: Float -> [Float] -> [Float]) :: Float -> [Float] -> [Float]) |
module List where
| import qualified Maybe import qualified Prelude
|
| delete :: Eq a => a -> [a] -> [a]
|
| 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 |
|
module Maybe where
| import qualified List import qualified Prelude
|
Replaced joker patterns by fresh variables and removed binding patterns.
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
mainModule List
| ((delete :: Float -> [Float] -> [Float]) :: Float -> [Float] -> [Float]) |
module List where
| import qualified Maybe import qualified Prelude
|
| delete :: Eq a => a -> [a] -> [a]
|
| 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 |
|
module Maybe where
| import qualified List import qualified Prelude
|
Cond Reductions:
The following Function with conditions
is transformed to
undefined0 | True | = undefined |
undefined1 | | = undefined0 False |
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ Narrow
mainModule List
| (delete :: Float -> [Float] -> [Float]) |
module List where
| import qualified Maybe import qualified Prelude
|
| delete :: Eq a => a -> [a] -> [a]
|
| 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 |
|
module Maybe where
| import qualified List import qualified Prelude
|
Haskell To QDPs
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDPSizeChangeProof
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_primPlusNat(Succ(ww5200), Succ(ww400000)) → new_primPlusNat(ww5200, ww400000)
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(ww5200), Succ(ww400000)) → new_primPlusNat(ww5200, ww400000)
The graph contains the following edges 1 > 1, 2 > 2
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDPSizeChangeProof
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_primMulNat(Succ(ww30000), ww40000) → new_primMulNat(ww30000, ww40000)
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(ww30000), ww40000) → new_primMulNat(ww30000, ww40000)
The graph contains the following edges 1 > 1, 2 >= 2
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ DependencyGraphProof
Q DP problem:
The TRS P consists of the following rules:
new_deleteBy14(:(ww410, ww411)) → new_deleteBy01(ww411, ww410, Float(Neg(Zero), Neg(Succ(Succ(Zero)))))
new_deleteBy0111(ww23, ww24, ww2500, ww26, ww2700, Succ(ww1630)) → new_deleteBy0115(ww23, ww24, Succ(ww2500), ww26, Succ(ww2700))
new_deleteBy01(ww41, Float(Pos(Zero), Neg(Succ(ww40100))), Float(Pos(Zero), Pos(Succ(Succ(Succ(ww310000)))))) → new_deleteBy027(ww41, ww40100, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
new_deleteBy01(ww41, Float(Neg(Zero), Pos(Succ(ww40100))), Float(Neg(Succ(ww3000)), Neg(Succ(Succ(Zero))))) → new_deleteBy089(ww41, ww40100, ww3000, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy01(ww41, Float(Neg(Succ(ww40000)), Neg(Succ(ww40100))), Float(Pos(Zero), Neg(Succ(Succ(Succ(ww310000)))))) → new_deleteBy048(ww41, ww40000, ww40100, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
new_deleteBy0(:(ww170, ww171), ww18, Neg(ww190), ww20, Pos(ww210), Succ(ww530)) → new_deleteBy01(ww171, ww170, Float(Pos(Succ(ww20)), Pos(ww210)))
new_deleteBy01(ww41, Float(Neg(Zero), Neg(Succ(ww40100))), Float(Neg(Zero), Neg(Succ(Succ(Zero))))) → new_deleteBy0107(ww41, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy0143(ww42, ww43, ww4400, ww45, ww4600, Zero, Succ(ww34100)) → new_deleteBy0144(ww42, ww43, ww4400, ww45, ww4600)
new_deleteBy0143(ww42, ww43, ww4400, ww45, ww4600, Succ(ww30800), Zero) → new_deleteBy0144(ww42, ww43, ww4400, ww45, ww4600)
new_deleteBy0(ww17, ww18, Pos(Zero), ww20, Pos(Zero), Succ(ww530)) → new_deleteBy(ww20, Zero, ww17)
new_deleteBy0122(ww36, ww37, ww3800, ww39, ww4000, Zero, Succ(Succ(ww25000))) → new_deleteBy0131(ww36, ww37, ww3800, ww39, ww4000)
new_deleteBy096(ww41, ww40000, ww40100, ww310000, Succ(ww3630)) → new_deleteBy13(ww310000, ww41)
new_deleteBy0106(ww41, ww40100, ww310000, Succ(ww3930)) → new_deleteBy13(ww310000, ww41)
new_deleteBy0114(ww23, ww24, ww2500, ww26, ww2700, Succ(ww1690)) → new_deleteBy0120(ww23, ww24, Succ(ww2500), ww26, Succ(ww2700))
new_deleteBy0122(ww36, ww37, ww3800, ww39, ww4000, Succ(ww21900), Succ(Zero)) → new_deleteBy0131(ww36, ww37, ww3800, ww39, ww4000)
new_deleteBy01(ww41, Float(Neg(Zero), Neg(Succ(ww40100))), Float(Neg(Succ(ww3000)), Neg(Succ(Succ(Succ(ww310000)))))) → new_deleteBy090(ww41, ww40100, ww3000, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
new_deleteBy01(ww41, Float(Pos(Zero), Pos(Succ(ww40100))), Float(Pos(Succ(ww3000)), Pos(Succ(Succ(Zero))))) → new_deleteBy010(ww41, ww40100, ww3000, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy0(ww17, ww18, Pos(Succ(ww1900)), ww20, Neg(Succ(ww2100)), Zero) → new_deleteBy05(ww17, ww18, ww1900, ww20, ww2100, new_primPlusNat0(new_primMulNat0(ww2100, ww1900), Succ(ww1900)))
new_deleteBy01(ww41, Float(Pos(Zero), Pos(Succ(ww40100))), Float(Pos(Succ(ww3000)), Pos(Succ(Succ(Succ(ww310000)))))) → new_deleteBy09(ww41, ww40100, ww3000, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
new_deleteBy0121(ww36, ww37, ww3800, ww39, ww4000, ww2190, Zero) → new_deleteBy4(ww39, Succ(ww4000), ww36)
new_deleteBy0126(ww36, ww37, ww3800, ww39, ww4000, Succ(ww2580)) → new_deleteBy0132(ww36, ww37, Succ(ww3800), ww39, Succ(ww4000))
new_deleteBy0133(ww42, ww43, ww4400, ww45, ww4600, ww3080, Zero) → new_deleteBy4(ww45, Succ(ww4600), ww42)
new_deleteBy022(:(ww410, ww411), ww40000, ww40100, Succ(ww960)) → new_deleteBy01(ww411, ww410, Float(Pos(Zero), Neg(Succ(Succ(Zero)))))
new_deleteBy097(ww41, ww40000, ww40100, Succ(ww3670)) → new_deleteBy14(ww41)
new_deleteBy0131(ww36, ww37, ww3800, ww39, ww4000) → new_deleteBy5(ww39, Succ(ww4000), ww36)
new_deleteBy077(ww41, ww40100, ww310000, Succ(ww2900)) → new_deleteBy11(ww310000, ww41)
new_deleteBy083(ww42, ww43, Pos(Succ(ww4400)), ww45, Pos(Succ(ww4600)), Succ(ww3080)) → new_deleteBy0133(ww42, ww43, ww4400, ww45, ww4600, ww3080, new_primPlusNat0(new_primMulNat0(ww4600, ww4400), Succ(ww4400)))
new_deleteBy020(ww41, ww40000, ww40100, Succ(ww900)) → new_deleteBy0108(ww41, Float(Pos(Succ(ww40000)), Neg(Succ(ww40100))))
new_deleteBy01(ww41, Float(Pos(Succ(ww40000)), ww401), Float(Neg(Succ(ww3000)), ww31)) → new_deleteBy058(ww41, ww40000, ww401, ww3000, ww31, new_primPlusNat0(new_primMulNat0(ww3000, ww40000), Succ(ww40000)))
new_deleteBy01(ww41, Float(Pos(Zero), Pos(Succ(ww40100))), Float(Neg(Succ(ww3000)), Pos(Succ(Succ(Zero))))) → new_deleteBy060(ww41, ww40100, ww3000, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy00(ww17, ww18, ww1900, ww20, ww2100, Succ(ww5300), Succ(Zero)) → new_deleteBy08(ww17, ww18, ww1900, ww20, ww2100)
new_deleteBy01(ww41, Float(Pos(Succ(ww40000)), Pos(Succ(ww40100))), Float(Neg(Zero), Neg(Succ(Succ(Zero))))) → new_deleteBy072(ww41, ww40000, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy01(ww41, Float(Neg(Zero), Neg(Succ(ww40100))), Float(Pos(Zero), Pos(Succ(Succ(Zero))))) → new_deleteBy053(ww41, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy058(:(ww360, ww361), ww37, Pos(ww380), ww39, Pos(ww400), Succ(ww2190)) → new_deleteBy01(ww361, ww360, Float(Neg(Succ(ww39)), Pos(ww400)))
new_deleteBy033(ww23, ww24, Neg(Zero), ww26, Pos(Succ(ww2700)), Succ(ww1280)) → new_deleteBy(ww26, Succ(ww2700), ww23)
new_deleteBy0139(ww42, ww43, ww4400, ww45, ww4600, Succ(ww30800), Succ(ww33900)) → new_deleteBy0139(ww42, ww43, ww4400, ww45, ww4600, ww30800, ww33900)
new_deleteBy058(ww36, ww37, Neg(Succ(ww3800)), ww39, Pos(Zero), Succ(ww2190)) → new_deleteBy4(ww39, Zero, ww36)
new_deleteBy01(ww41, Float(Neg(Zero), Neg(Succ(ww40100))), Float(Pos(Succ(ww3000)), Neg(Succ(Succ(Zero))))) → new_deleteBy041(ww41, ww40100, ww3000, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy0147(ww17, ww18, ww1900, ww20, ww2100, Succ(ww5300), Succ(ww8000)) → new_deleteBy0147(ww17, ww18, ww1900, ww20, ww2100, ww5300, ww8000)
new_deleteBy090(ww41, ww40100, ww3000, ww310000, Succ(ww3330)) → new_deleteBy5(ww3000, Succ(Succ(Succ(ww310000))), ww41)
new_deleteBy0107(ww41, ww40100, Succ(ww3970)) → new_deleteBy14(ww41)
new_deleteBy034(ww41, ww40100, ww3000, ww310000, Succ(ww1350)) → new_deleteBy(ww3000, Succ(Succ(Succ(ww310000))), ww41)
new_deleteBy068(:(ww410, ww411), ww40000, ww40100, Succ(ww2640)) → new_deleteBy01(ww411, ww410, Float(Neg(Zero), Pos(Succ(Succ(Zero)))))
new_deleteBy058(ww36, ww37, Pos(Zero), ww39, Neg(Succ(ww4000)), Succ(ww2190)) → new_deleteBy5(ww39, Succ(ww4000), ww36)
new_deleteBy01(ww41, Float(Pos(Succ(ww40000)), Neg(Succ(ww40100))), Float(Pos(Zero), Pos(Succ(Succ(Zero))))) → new_deleteBy020(ww41, ww40000, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy01(ww41, Float(Pos(Succ(ww40000)), Neg(Succ(ww40100))), Float(Pos(Zero), Neg(Succ(Succ(Zero))))) → new_deleteBy024(ww41, ww40000, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy01(ww41, Float(Neg(Succ(ww40000)), ww401), Float(Neg(Succ(ww3000)), ww31)) → new_deleteBy083(ww41, ww40000, ww401, ww3000, ww31, new_primPlusNat0(new_primMulNat0(ww3000, ww40000), Succ(ww40000)))
new_deleteBy00(ww17, ww18, ww1900, ww20, ww2100, ww530, Zero) → new_deleteBy(ww20, Succ(ww2100), ww17)
new_deleteBy057(ww41, ww40100, Succ(ww2170)) → new_deleteBy10(ww41)
new_deleteBy0129(ww36, ww37, ww3800, ww39, ww4000) → new_deleteBy4(ww39, Succ(ww4000), ww36)
new_deleteBy2(:(ww410, ww411)) → new_deleteBy01(ww411, ww410, Float(Pos(Zero), Pos(Succ(Zero))))
new_deleteBy01(ww41, Float(Neg(Zero), Pos(Succ(ww40100))), Float(Neg(Succ(ww3000)), Pos(Succ(Zero)))) → new_deleteBy4(ww3000, Succ(Zero), ww41)
new_deleteBy01(ww41, Float(Pos(Succ(ww40000)), Neg(Succ(ww40100))), Float(Neg(Zero), Neg(Succ(Succ(Zero))))) → new_deleteBy074(ww41, ww40000, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy01(ww41, Float(Pos(Zero), Neg(Succ(ww40100))), Float(Neg(Succ(ww3000)), Pos(Succ(Zero)))) → new_deleteBy4(ww3000, Succ(Zero), ww41)
new_deleteBy033(ww23, ww24, Neg(Succ(ww2500)), ww26, Pos(Succ(ww2700)), Zero) → new_deleteBy0112(ww23, ww24, ww2500, ww26, ww2700, new_primPlusNat0(new_primMulNat0(ww2700, ww2500), Succ(ww2500)))
new_deleteBy030(ww41, ww40100, Succ(ww1200)) → new_deleteBy10(ww41)
new_deleteBy02(ww17, ww18, ww1900, ww20, ww2100, Zero, Succ(Succ(ww8000))) → new_deleteBy0148(ww17, ww18, ww1900, ww20, ww2100)
new_deleteBy0125(ww36, ww37, ww3800, ww39, ww4000, Succ(ww2560)) → new_deleteBy0131(ww36, ww37, ww3800, ww39, ww4000)
new_deleteBy01(ww41, Float(Pos(Zero), Pos(Succ(ww40100))), Float(Pos(Succ(ww3000)), Pos(Succ(Zero)))) → new_deleteBy(ww3000, Succ(Zero), ww41)
new_deleteBy0(ww17, ww18, Neg(Succ(ww1900)), ww20, Pos(Succ(ww2100)), Zero) → new_deleteBy04(ww17, ww18, ww1900, ww20, ww2100, new_primPlusNat0(new_primMulNat0(ww2100, ww1900), Succ(ww1900)))
new_deleteBy079(ww41, ww40100, ww310000, Succ(ww2960)) → new_deleteBy13(ww310000, ww41)
new_deleteBy058(ww36, ww37, Neg(Succ(ww3800)), ww39, Neg(Succ(ww4000)), Zero) → new_deleteBy0126(ww36, ww37, ww3800, ww39, ww4000, new_primPlusNat0(new_primMulNat0(ww4000, ww3800), Succ(ww3800)))
new_deleteBy05(ww17, ww18, ww1900, ww20, ww2100, Succ(ww860)) → new_deleteBy0146(ww17, ww18, Succ(ww1900), ww20, Succ(ww2100))
new_deleteBy01(ww41, Float(Neg(Zero), Pos(Succ(ww40100))), Float(Neg(Zero), Pos(Succ(Zero)))) → new_deleteBy6(ww41)
new_deleteBy01(ww41, Float(Pos(Zero), Neg(Succ(ww40100))), Float(Neg(Zero), Pos(Succ(Zero)))) → new_deleteBy6(ww41)
new_deleteBy092(ww41, ww40000, ww40100, ww310000, Succ(ww3510)) → new_deleteBy11(ww310000, ww41)
new_deleteBy015(ww41, ww40100, ww3000, ww310000, Succ(ww620)) → new_deleteBy1(ww3000, Succ(Succ(Succ(ww310000))), ww41)
new_deleteBy01(ww41, Float(Neg(Succ(ww40000)), Neg(Succ(ww40100))), Float(Pos(Zero), Pos(Succ(Succ(Zero))))) → new_deleteBy045(ww41, ww40000, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy064(ww41, ww40100, ww3000, Succ(ww2400)) → new_deleteBy5(ww3000, Succ(Succ(Zero)), ww41)
new_deleteBy01(ww41, Float(Neg(Succ(ww40000)), Pos(Succ(ww40100))), Float(Pos(Zero), Pos(Succ(Succ(Succ(ww310000)))))) → new_deleteBy042(ww41, ww40000, ww40100, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
new_deleteBy058(ww36, ww37, Neg(Zero), ww39, Pos(Zero), Succ(ww2190)) → new_deleteBy4(ww39, Zero, ww36)
new_deleteBy083(ww42, ww43, Neg(Succ(ww4400)), ww45, Neg(Zero), Succ(ww3080)) → new_deleteBy5(ww45, Zero, ww42)
new_deleteBy053(ww41, ww40100, Succ(ww2050)) → new_deleteBy0108(ww41, Float(Neg(Zero), Neg(Succ(ww40100))))
new_deleteBy066(ww41, ww40100, ww3000, Succ(ww2460)) → new_deleteBy5(ww3000, Succ(Succ(Zero)), ww41)
new_deleteBy12(:(ww410, ww411)) → new_deleteBy01(ww411, ww410, Float(Neg(Zero), Pos(Succ(Succ(Zero)))))
new_deleteBy6(:(ww410, ww411)) → new_deleteBy01(ww411, ww410, Float(Neg(Zero), Pos(Succ(Zero))))
new_deleteBy088(ww41, ww40100, ww3000, ww310000, Succ(ww3270)) → new_deleteBy5(ww3000, Succ(Succ(Succ(ww310000))), ww41)
new_deleteBy0137(ww42, ww43, ww4400, ww45, ww4600, Succ(ww3470)) → new_deleteBy0142(ww42, ww43, Succ(ww4400), ww45, Succ(ww4600))
new_deleteBy073(ww41, ww40000, ww40100, ww310000, Succ(ww2780)) → new_deleteBy13(ww310000, ww41)
new_deleteBy4(ww39, ww400, :(ww360, ww361)) → new_deleteBy01(ww361, ww360, Float(Neg(Succ(ww39)), Pos(ww400)))
new_deleteBy01(ww41, Float(Pos(Succ(ww40000)), Pos(Succ(ww40100))), Float(Pos(Zero), Pos(Succ(Succ(Succ(ww310000)))))) → new_deleteBy017(ww41, ww40000, ww40100, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
new_deleteBy061(ww41, ww40100, ww3000, ww310000, Succ(ww2300)) → new_deleteBy4(ww3000, Succ(Succ(Succ(ww310000))), ww41)
new_deleteBy01(ww41, Float(Neg(Zero), Pos(Succ(ww40100))), Float(Pos(Succ(ww3000)), Neg(Succ(Succ(Succ(ww310000)))))) → new_deleteBy038(ww41, ww40100, ww3000, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
new_deleteBy099(ww41, ww40000, ww40100, Succ(ww3730)) → new_deleteBy14(ww41)
new_deleteBy01(ww41, Float(Neg(Succ(ww40000)), Pos(Succ(ww40100))), Float(Pos(Zero), Neg(Succ(Succ(Zero))))) → new_deleteBy047(ww41, ww40000, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy01(ww41, Float(Pos(Zero), Neg(Succ(ww40100))), Float(Pos(Succ(ww3000)), Neg(Succ(Succ(Zero))))) → new_deleteBy016(ww41, ww40100, ww3000, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy01(ww41, Float(Neg(Succ(ww40000)), Pos(Succ(ww40100))), Float(Neg(Zero), Neg(Succ(Succ(Zero))))) → new_deleteBy097(ww41, ww40000, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy0133(ww42, ww43, ww4400, ww45, ww4600, Succ(ww30800), Succ(Zero)) → new_deleteBy0140(ww42, ww43, ww4400, ww45, ww4600)
new_deleteBy01(ww41, Float(Pos(Succ(ww40000)), Pos(Succ(ww40100))), Float(Pos(Zero), Neg(Succ(Succ(Succ(ww310000)))))) → new_deleteBy021(ww41, ww40000, ww40100, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
new_deleteBy01(ww41, Float(Pos(Zero), Neg(Succ(ww40100))), Float(Neg(Zero), Pos(Succ(Succ(Zero))))) → new_deleteBy078(ww41, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy01(ww41, Float(Neg(Succ(ww40000)), Neg(Succ(ww40100))), Float(Pos(Zero), Neg(Succ(Zero)))) → new_deleteBy3(ww41)
new_deleteBy01(ww41, Float(Neg(Zero), Pos(Succ(ww40100))), Float(Neg(Succ(ww3000)), Neg(Succ(Zero)))) → new_deleteBy5(ww3000, Succ(Zero), ww41)
new_deleteBy01(ww41, Float(Pos(Zero), Neg(Succ(ww40100))), Float(Neg(Succ(ww3000)), Neg(Succ(Zero)))) → new_deleteBy5(ww3000, Succ(Zero), ww41)
new_deleteBy0133(ww42, ww43, ww4400, ww45, ww4600, Zero, Succ(Succ(ww33900))) → new_deleteBy0140(ww42, ww43, ww4400, ww45, ww4600)
new_deleteBy11(ww310000, :(ww410, ww411)) → new_deleteBy01(ww411, ww410, Float(Neg(Zero), Pos(Succ(Succ(Succ(ww310000))))))
new_deleteBy069(ww41, ww40000, ww40100, ww310000, Succ(ww2660)) → new_deleteBy11(ww310000, ww41)
new_deleteBy065(ww41, ww40100, ww3000, ww310000, Succ(ww2420)) → new_deleteBy5(ww3000, Succ(Succ(Succ(ww310000))), ww41)
new_deleteBy0136(ww42, ww43, ww4400, ww45, ww4600, Succ(ww3450)) → new_deleteBy0141(ww42, ww43, Succ(ww4400), ww45, Succ(ww4600))
new_deleteBy01(ww41, Float(Pos(Succ(ww40000)), Neg(Succ(ww40100))), Float(Neg(Zero), Pos(Succ(Succ(Succ(ww310000)))))) → new_deleteBy069(ww41, ww40000, ww40100, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
new_deleteBy01(ww41, Float(Neg(Zero), Neg(Succ(ww40100))), Float(Pos(Succ(ww3000)), Pos(Succ(Zero)))) → new_deleteBy(ww3000, Succ(Zero), ww41)
new_deleteBy01(ww41, Float(Neg(Zero), Neg(Succ(ww40100))), Float(Pos(Zero), Neg(Succ(Succ(Succ(ww310000)))))) → new_deleteBy056(ww41, ww40100, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
new_deleteBy01(ww41, Float(Pos(Zero), Neg(Succ(ww40100))), Float(Pos(Succ(ww3000)), Pos(Succ(Succ(Zero))))) → new_deleteBy012(ww41, ww40100, ww3000, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy01(ww41, Float(Pos(Succ(ww40000)), Pos(Succ(ww40100))), Float(Pos(Zero), Neg(Succ(Succ(Zero))))) → new_deleteBy022(ww41, ww40000, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy01(ww41, Float(Pos(Succ(ww40000)), Pos(Succ(ww40100))), Float(Neg(Zero), Pos(Succ(Succ(Zero))))) → new_deleteBy068(ww41, ww40000, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy01(ww41, Float(Neg(Zero), Neg(Succ(ww40100))), Float(Neg(Zero), Neg(Succ(Zero)))) → new_deleteBy7(ww41)
new_deleteBy01(ww41, Float(Neg(Zero), Pos(Succ(ww40100))), Float(Pos(Succ(ww3000)), Pos(Succ(Succ(Succ(ww310000)))))) → new_deleteBy034(ww41, ww40100, ww3000, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
new_deleteBy017(:(ww410, ww411), ww40000, ww40100, ww310000, Succ(ww680)) → new_deleteBy01(ww411, ww410, Float(Pos(Zero), Pos(Succ(Succ(Succ(ww310000))))))
new_deleteBy0121(ww36, ww37, ww3800, ww39, ww4000, Zero, Succ(Succ(ww24800))) → new_deleteBy0129(ww36, ww37, ww3800, ww39, ww4000)
new_deleteBy011(ww41, ww40100, ww3000, ww310000, Succ(ww4030)) → new_deleteBy(ww3000, Succ(Succ(Succ(ww310000))), ww41)
new_deleteBy02(ww17, ww18, ww1900, ww20, ww2100, Succ(ww5300), Succ(Zero)) → new_deleteBy0148(ww17, ww18, ww1900, ww20, ww2100)
new_deleteBy0110(ww23, ww24, ww2500, ww26, ww2700, Succ(ww12800), Succ(Succ(ww16100))) → new_deleteBy0118(ww23, ww24, ww2500, ww26, ww2700, ww12800, ww16100)
new_deleteBy0115(ww23, ww24, ww250, ww26, ww270) → new_deleteBy(ww26, ww270, ww23)
new_deleteBy0110(ww23, ww24, ww2500, ww26, ww2700, ww1280, Zero) → new_deleteBy1(ww26, Succ(ww2700), ww23)
new_deleteBy01(ww41, Float(Pos(Zero), Pos(Succ(ww40100))), Float(Neg(Succ(ww3000)), Pos(Succ(Succ(Succ(ww310000)))))) → new_deleteBy059(ww41, ww40100, ww3000, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
new_deleteBy01(:(ww410, ww411), Float(Pos(Succ(ww40000)), Pos(Succ(ww40100))), Float(Neg(Zero), Neg(Succ(Zero)))) → new_deleteBy01(ww411, ww410, Float(Neg(Zero), Neg(Succ(Zero))))
new_deleteBy083(ww42, ww43, Pos(Zero), ww45, Pos(Zero), Succ(ww3080)) → new_deleteBy4(ww45, Zero, ww42)
new_deleteBy043(ww41, ww40000, ww40100, Succ(ww1750)) → new_deleteBy0108(ww41, Float(Neg(Succ(ww40000)), Pos(Succ(ww40100))))
new_deleteBy0134(ww42, ww43, ww4400, ww45, ww4600, Succ(ww30800), Succ(Succ(ww34100))) → new_deleteBy0143(ww42, ww43, ww4400, ww45, ww4600, ww30800, ww34100)
new_deleteBy01(ww41, Float(Neg(Zero), Neg(Succ(ww40100))), Float(Neg(Zero), Pos(Succ(Succ(Zero))))) → new_deleteBy0103(ww41, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy01(ww41, Float(Pos(Succ(ww40000)), Neg(Succ(ww40100))), Float(Neg(Zero), Neg(Succ(Zero)))) → new_deleteBy7(ww41)
new_deleteBy01(ww41, Float(Neg(Succ(ww40000)), Pos(Succ(ww40100))), Float(Neg(Zero), Neg(Succ(Zero)))) → new_deleteBy7(ww41)
new_deleteBy0148(ww17, ww18, ww1900, ww20, ww2100) → new_deleteBy1(ww20, Succ(ww2100), ww17)
new_deleteBy0138(ww42, ww43, ww4400, ww45, ww4600, Succ(ww3490)) → new_deleteBy0144(ww42, ww43, ww4400, ww45, ww4600)
new_deleteBy039(ww41, ww40100, ww3000, Succ(ww1510)) → new_deleteBy1(ww3000, Succ(Succ(Zero)), ww41)
new_deleteBy040(ww41, ww40100, ww3000, ww310000, Succ(ww1530)) → new_deleteBy1(ww3000, Succ(Succ(Succ(ww310000))), ww41)
new_deleteBy0(ww17, ww18, Neg(Succ(ww1900)), ww20, Neg(Succ(ww2100)), Zero) → new_deleteBy06(ww17, ww18, ww1900, ww20, ww2100, new_primPlusNat0(new_primMulNat0(ww2100, ww1900), Succ(ww1900)))
new_deleteBy01(ww41, Float(Neg(Zero), Neg(Succ(ww40100))), Float(Neg(Zero), Neg(Succ(Succ(Succ(ww310000)))))) → new_deleteBy0106(ww41, ww40100, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
new_deleteBy0(ww17, ww18, Pos(Succ(ww1900)), ww20, Pos(Zero), Succ(ww530)) → new_deleteBy(ww20, Zero, ww17)
new_deleteBy051(ww41, ww40100, Succ(ww1990)) → new_deleteBy0108(ww41, Float(Neg(Zero), Pos(Succ(ww40100))))
new_deleteBy01(ww41, Float(Pos(Zero), Pos(Succ(ww40100))), Float(Pos(Zero), Neg(Succ(Succ(Zero))))) → new_deleteBy030(ww41, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy0(:(ww170, ww171), ww18, Pos(ww190), ww20, Neg(ww210), Succ(ww530)) → new_deleteBy01(ww171, ww170, Float(Pos(Succ(ww20)), Neg(ww210)))
new_deleteBy01(ww41, Float(Neg(Zero), Pos(Succ(ww40100))), Float(Pos(Succ(ww3000)), Neg(Succ(Zero)))) → new_deleteBy1(ww3000, Succ(Zero), ww41)
new_deleteBy01(ww41, Float(Pos(Zero), Neg(Succ(ww40100))), Float(Pos(Succ(ww3000)), Neg(Succ(Zero)))) → new_deleteBy1(ww3000, Succ(Zero), ww41)
new_deleteBy00(ww17, ww18, ww1900, ww20, ww2100, Succ(ww5300), Succ(Succ(ww7800))) → new_deleteBy07(ww17, ww18, ww1900, ww20, ww2100, ww5300, ww7800)
new_deleteBy01(ww41, Float(Pos(Zero), Neg(Succ(ww40100))), Float(Neg(Succ(ww3000)), Neg(Succ(Succ(Zero))))) → new_deleteBy066(ww41, ww40100, ww3000, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy01(ww41, Float(Neg(Zero), Pos(Succ(ww40100))), Float(Neg(Zero), Pos(Succ(Succ(Succ(ww310000)))))) → new_deleteBy0100(ww41, ww40100, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
new_deleteBy083(ww42, ww43, Pos(ww440), ww45, Neg(ww460), Succ(ww3080)) → new_deleteBy5(ww45, ww460, ww42)
new_deleteBy058(:(ww360, ww361), ww37, Neg(ww380), ww39, Neg(ww400), Succ(ww2190)) → new_deleteBy01(ww361, ww360, Float(Neg(Succ(ww39)), Neg(ww400)))
new_deleteBy01(ww41, Float(Pos(Succ(ww40000)), Neg(Succ(ww40100))), Float(Neg(Zero), Pos(Succ(Succ(Zero))))) → new_deleteBy070(ww41, ww40000, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy01(ww41, Float(Neg(Zero), Pos(Succ(ww40100))), Float(Pos(Succ(ww3000)), Pos(Succ(Succ(Zero))))) → new_deleteBy035(ww41, ww40100, ww3000, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy085(ww41, ww40100, ww3000, Succ(ww3190)) → new_deleteBy4(ww3000, Succ(Succ(Zero)), ww41)
new_deleteBy027(ww41, ww40100, ww310000, Succ(ww1100)) → new_deleteBy8(ww310000, ww41)
new_deleteBy01(ww41, Float(Neg(Succ(ww40000)), Neg(Succ(ww40100))), Float(Neg(Zero), Neg(Succ(Zero)))) → new_deleteBy7(ww41)
new_deleteBy036(ww41, ww40100, ww3000, ww310000, Succ(ww1410)) → new_deleteBy(ww3000, Succ(Succ(Succ(ww310000))), ww41)
new_deleteBy01(ww41, Float(Neg(Zero), Neg(Succ(ww40100))), Float(Pos(Succ(ww3000)), Pos(Succ(Succ(Succ(ww310000)))))) → new_deleteBy036(ww41, ww40100, ww3000, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
new_deleteBy0143(ww42, ww43, ww4400, ww45, ww4600, Succ(ww30800), Succ(ww34100)) → new_deleteBy0143(ww42, ww43, ww4400, ww45, ww4600, ww30800, ww34100)
new_deleteBy049(ww41, ww40000, ww40100, Succ(ww1930)) → new_deleteBy10(ww41)
new_deleteBy01(ww41, Float(Pos(Zero), Pos(Succ(ww40100))), Float(Neg(Zero), Neg(Succ(Zero)))) → new_deleteBy7(ww41)
new_deleteBy01(ww41, Float(Pos(Zero), Neg(Succ(ww40100))), Float(Pos(Succ(ww3000)), Neg(Succ(Succ(Succ(ww310000)))))) → new_deleteBy015(ww41, ww40100, ww3000, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
new_deleteBy07(ww17, ww18, ww1900, ww20, ww2100, Zero, Succ(ww7800)) → new_deleteBy08(ww17, ww18, ww1900, ww20, ww2100)
new_deleteBy07(ww17, ww18, ww1900, ww20, ww2100, Succ(ww5300), Zero) → new_deleteBy08(ww17, ww18, ww1900, ww20, ww2100)
new_deleteBy01(ww41, Float(Pos(Zero), Pos(Succ(ww40100))), Float(Pos(Zero), Neg(Succ(Zero)))) → new_deleteBy3(ww41)
new_deleteBy033(ww23, ww24, Neg(Succ(ww2500)), ww26, Neg(Succ(ww2700)), Zero) → new_deleteBy0114(ww23, ww24, ww2500, ww26, ww2700, new_primPlusNat0(new_primMulNat0(ww2700, ww2500), Succ(ww2500)))
new_deleteBy045(ww41, ww40000, ww40100, Succ(ww1810)) → new_deleteBy0108(ww41, Float(Neg(Succ(ww40000)), Neg(Succ(ww40100))))
new_deleteBy0134(ww42, ww43, ww4400, ww45, ww4600, Zero, Succ(Succ(ww34100))) → new_deleteBy0144(ww42, ww43, ww4400, ww45, ww4600)
new_deleteBy01(ww41, Float(Pos(Zero), Pos(Succ(ww40100))), Float(Pos(Zero), Pos(Succ(Succ(Succ(ww310000)))))) → new_deleteBy025(ww41, ww40100, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
new_deleteBy0101(ww41, ww40100, Succ(ww3790)) → new_deleteBy12(ww41)
new_deleteBy0139(ww42, ww43, ww4400, ww45, ww4600, Zero, Succ(ww33900)) → new_deleteBy0140(ww42, ww43, ww4400, ww45, ww4600)
new_deleteBy0139(ww42, ww43, ww4400, ww45, ww4600, Succ(ww30800), Zero) → new_deleteBy0140(ww42, ww43, ww4400, ww45, ww4600)
new_deleteBy01(ww41, Float(Neg(Zero), Neg(Succ(ww40100))), Float(Neg(Succ(ww3000)), Neg(Succ(Zero)))) → new_deleteBy5(ww3000, Succ(Zero), ww41)
new_deleteBy0(ww17, ww18, Neg(Succ(ww1900)), ww20, Neg(Succ(ww2100)), Succ(ww530)) → new_deleteBy02(ww17, ww18, ww1900, ww20, ww2100, ww530, new_primPlusNat0(new_primMulNat0(ww2100, ww1900), Succ(ww1900)))
new_deleteBy075(ww41, ww40100, ww310000, Succ(ww2840)) → new_deleteBy11(ww310000, ww41)
new_deleteBy033(ww23, ww24, Pos(Succ(ww2500)), ww26, Neg(Succ(ww2700)), Succ(ww1280)) → new_deleteBy0110(ww23, ww24, ww2500, ww26, ww2700, ww1280, new_primPlusNat0(new_primMulNat0(ww2700, ww2500), Succ(ww2500)))
new_deleteBy01(ww41, Float(Pos(Zero), Neg(Succ(ww40100))), Float(Pos(Zero), Neg(Succ(Succ(Succ(ww310000)))))) → new_deleteBy031(ww41, ww40100, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
new_deleteBy01(ww41, Float(Pos(Zero), Neg(Succ(ww40100))), Float(Neg(Zero), Neg(Succ(Zero)))) → new_deleteBy7(ww41)
new_deleteBy01(ww41, Float(Neg(Zero), Pos(Succ(ww40100))), Float(Neg(Zero), Neg(Succ(Zero)))) → new_deleteBy7(ww41)
new_deleteBy033(ww23, ww24, Neg(ww250), ww26, Neg(ww270), Succ(ww1280)) → new_deleteBy1(ww26, ww270, ww23)
new_deleteBy0(ww17, ww18, Neg(Zero), ww20, Neg(Zero), Succ(ww530)) → new_deleteBy1(ww20, Zero, ww17)
new_deleteBy080(ww41, ww40100, Succ(ww3000)) → new_deleteBy14(ww41)
new_deleteBy01(ww41, Float(Neg(Zero), Pos(Succ(ww40100))), Float(Neg(Succ(ww3000)), Neg(Succ(Succ(Succ(ww310000)))))) → new_deleteBy088(ww41, ww40100, ww3000, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
new_deleteBy041(ww41, ww40100, ww3000, Succ(ww1570)) → new_deleteBy1(ww3000, Succ(Succ(Zero)), ww41)
new_deleteBy098(ww41, ww40000, ww40100, ww310000, Succ(ww3690)) → new_deleteBy13(ww310000, ww41)
new_deleteBy052(ww41, ww40100, ww310000, Succ(ww2010)) → new_deleteBy8(ww310000, ww41)
new_deleteBy0134(ww42, ww43, ww4400, ww45, ww4600, ww3080, Zero) → new_deleteBy5(ww45, Succ(ww4600), ww42)
new_deleteBy3(:(ww410, ww411)) → new_deleteBy01(ww411, ww410, Float(Pos(Zero), Neg(Succ(Zero))))
new_deleteBy01(ww41, Float(Neg(Succ(ww40000)), Pos(Succ(ww40100))), Float(Pos(Zero), Neg(Succ(Zero)))) → new_deleteBy3(ww41)
new_deleteBy01(ww41, Float(Pos(Succ(ww40000)), Neg(Succ(ww40100))), Float(Pos(Zero), Neg(Succ(Zero)))) → new_deleteBy3(ww41)
new_deleteBy0127(:(ww360, ww361), ww37, ww380, ww39, ww400) → new_deleteBy01(ww361, ww360, Float(Neg(Succ(ww39)), Pos(ww400)))
new_deleteBy0117(ww23, ww24, ww2500, ww26, ww2700) → new_deleteBy(ww26, Succ(ww2700), ww23)
new_deleteBy0135(ww42, ww43, ww4400, ww45, ww4600, Succ(ww3430)) → new_deleteBy0140(ww42, ww43, ww4400, ww45, ww4600)
new_deleteBy01(ww41, Float(Neg(Succ(ww40000)), ww401), Float(Pos(Succ(ww3000)), ww31)) → new_deleteBy033(ww41, ww40000, ww401, ww3000, ww31, new_primPlusNat0(new_primMulNat0(ww3000, ww40000), Succ(ww40000)))
new_deleteBy083(ww42, ww43, Pos(Succ(ww4400)), ww45, Pos(Zero), Succ(ww3080)) → new_deleteBy4(ww45, Zero, ww42)
new_deleteBy01(ww41, Float(Neg(Succ(ww40000)), Neg(Succ(ww40100))), Float(Neg(Zero), Neg(Succ(Succ(Succ(ww310000)))))) → new_deleteBy098(ww41, ww40000, ww40100, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
new_deleteBy083(ww42, ww43, Neg(Succ(ww4400)), ww45, Neg(Succ(ww4600)), Succ(ww3080)) → new_deleteBy0134(ww42, ww43, ww4400, ww45, ww4600, ww3080, new_primPlusNat0(new_primMulNat0(ww4600, ww4400), Succ(ww4400)))
new_deleteBy083(ww42, ww43, Neg(Succ(ww4400)), ww45, Neg(Succ(ww4600)), Zero) → new_deleteBy0138(ww42, ww43, ww4400, ww45, ww4600, new_primPlusNat0(new_primMulNat0(ww4600, ww4400), Succ(ww4400)))
new_deleteBy01(ww41, Float(Pos(Succ(ww40000)), Pos(Succ(ww40100))), Float(Neg(Zero), Neg(Succ(Succ(Succ(ww310000)))))) → new_deleteBy071(ww41, ww40000, ww40100, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
new_deleteBy054(ww41, ww40100, ww310000, Succ(ww2070)) → new_deleteBy9(ww310000, ww41)
new_deleteBy0108(:(ww4070, ww4071), ww408) → new_deleteBy01(ww4071, ww4070, Float(Pos(Zero), Pos(Succ(Succ(Zero)))))
new_deleteBy01(ww41, Float(Pos(Zero), Neg(Succ(ww40100))), Float(Neg(Zero), Pos(Succ(Succ(Succ(ww310000)))))) → new_deleteBy077(ww41, ww40100, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
new_deleteBy01(ww41, Float(Neg(Zero), Pos(Succ(ww40100))), Float(Neg(Succ(ww3000)), Pos(Succ(Succ(Zero))))) → new_deleteBy085(ww41, ww40100, ww3000, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy084(ww41, ww40100, ww3000, ww310000, Succ(ww3150)) → new_deleteBy4(ww3000, Succ(Succ(Succ(ww310000))), ww41)
new_deleteBy0134(ww42, ww43, ww4400, ww45, ww4600, Succ(ww30800), Succ(Zero)) → new_deleteBy0144(ww42, ww43, ww4400, ww45, ww4600)
new_deleteBy0121(ww36, ww37, ww3800, ww39, ww4000, Succ(ww21900), Succ(Succ(ww24800))) → new_deleteBy0128(ww36, ww37, ww3800, ww39, ww4000, ww21900, ww24800)
new_deleteBy01(ww41, Float(Neg(Zero), Pos(Succ(ww40100))), Float(Pos(Zero), Pos(Succ(Succ(Succ(ww310000)))))) → new_deleteBy050(ww41, ww40100, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
new_deleteBy01(ww41, Float(Pos(Succ(ww40000)), Pos(Succ(ww40100))), Float(Pos(Zero), Pos(Succ(Succ(Zero))))) → new_deleteBy018(ww41, ww40000, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy093(ww41, ww40000, ww40100, Succ(ww3550)) → new_deleteBy12(ww41)
new_deleteBy01(ww41, Float(Neg(Zero), Neg(Succ(ww40100))), Float(Pos(Zero), Neg(Succ(Succ(Zero))))) → new_deleteBy057(ww41, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy0146(:(ww170, ww171), ww18, ww190, ww20, ww210) → new_deleteBy01(ww171, ww170, Float(Pos(Succ(ww20)), Neg(ww210)))
new_deleteBy01(ww41, Float(Neg(Zero), Neg(Succ(ww40100))), Float(Pos(Zero), Pos(Succ(Zero)))) → new_deleteBy2(ww41)
new_deleteBy050(ww41, ww40100, ww310000, Succ(ww1950)) → new_deleteBy8(ww310000, ww41)
new_deleteBy044(ww41, ww40000, ww40100, ww310000, Succ(ww1770)) → new_deleteBy8(ww310000, ww41)
new_deleteBy033(ww23, ww24, Pos(Succ(ww2500)), ww26, Pos(Succ(ww2700)), Zero) → new_deleteBy0111(ww23, ww24, ww2500, ww26, ww2700, new_primPlusNat0(new_primMulNat0(ww2700, ww2500), Succ(ww2500)))
new_deleteBy0123(ww36, ww37, ww3800, ww39, ww4000, Succ(ww2520)) → new_deleteBy0127(ww36, ww37, Succ(ww3800), ww39, Succ(ww4000))
new_deleteBy082(ww41, ww40100, Succ(ww3060)) → new_deleteBy14(ww41)
new_deleteBy01(ww41, Float(Pos(Zero), Pos(Succ(ww40100))), Float(Neg(Succ(ww3000)), Neg(Succ(Succ(Succ(ww310000)))))) → new_deleteBy063(ww41, ww40100, ww3000, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
new_deleteBy01(ww41, Float(Pos(Zero), Neg(Succ(ww40100))), Float(Pos(Zero), Neg(Succ(Succ(Zero))))) → new_deleteBy032(ww41, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy01(ww41, Float(Neg(Succ(ww40000)), Pos(Succ(ww40100))), Float(Pos(Zero), Pos(Succ(Succ(Zero))))) → new_deleteBy043(ww41, ww40000, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy01(ww41, Float(Pos(Zero), Neg(Succ(ww40100))), Float(Neg(Zero), Neg(Succ(Succ(Succ(ww310000)))))) → new_deleteBy081(ww41, ww40100, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
new_deleteBy058(ww36, ww37, Pos(Succ(ww3800)), ww39, Neg(Succ(ww4000)), Zero) → new_deleteBy0125(ww36, ww37, ww3800, ww39, ww4000, new_primPlusNat0(new_primMulNat0(ww4000, ww3800), Succ(ww3800)))
new_deleteBy0128(ww36, ww37, ww3800, ww39, ww4000, Succ(ww21900), Succ(ww24800)) → new_deleteBy0128(ww36, ww37, ww3800, ww39, ww4000, ww21900, ww24800)
new_deleteBy086(ww41, ww40100, ww3000, ww310000, Succ(ww3210)) → new_deleteBy4(ww3000, Succ(Succ(Succ(ww310000))), ww41)
new_deleteBy0121(ww36, ww37, ww3800, ww39, ww4000, Succ(ww21900), Succ(Zero)) → new_deleteBy0129(ww36, ww37, ww3800, ww39, ww4000)
new_deleteBy0140(ww42, ww43, ww4400, ww45, ww4600) → new_deleteBy4(ww45, Succ(ww4600), ww42)
new_deleteBy01(ww41, Float(Pos(Succ(ww40000)), Pos(Succ(ww40100))), Float(Neg(Zero), Pos(Succ(Succ(Succ(ww310000)))))) → new_deleteBy067(ww41, ww40000, ww40100, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
new_deleteBy01(ww41, Float(Neg(Succ(ww40000)), Neg(Succ(ww40100))), Float(Pos(Zero), Pos(Succ(Zero)))) → new_deleteBy2(ww41)
new_deleteBy0109(ww23, ww24, ww2500, ww26, ww2700, Zero, Succ(Succ(ww15900))) → new_deleteBy0117(ww23, ww24, ww2500, ww26, ww2700)
new_deleteBy01(ww41, Float(Neg(Succ(ww40000)), Pos(Succ(ww40100))), Float(Neg(Zero), Pos(Succ(Zero)))) → new_deleteBy6(ww41)
new_deleteBy01(ww41, Float(Pos(Succ(ww40000)), Neg(Succ(ww40100))), Float(Neg(Zero), Pos(Succ(Zero)))) → new_deleteBy6(ww41)
new_deleteBy0100(ww41, ww40100, ww310000, Succ(ww3750)) → new_deleteBy11(ww310000, ww41)
new_deleteBy047(ww41, ww40000, ww40100, Succ(ww1870)) → new_deleteBy10(ww41)
new_deleteBy033(ww23, ww24, Pos(Zero), ww26, Neg(Succ(ww2700)), Succ(ww1280)) → new_deleteBy1(ww26, Succ(ww2700), ww23)
new_deleteBy01(ww41, Float(Pos(Zero), Pos(Succ(ww40100))), Float(Pos(Succ(ww3000)), Neg(Succ(Succ(Zero))))) → new_deleteBy014(ww41, ww40100, ww3000, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy01(ww41, Float(Neg(Succ(ww40000)), Neg(Succ(ww40100))), Float(Pos(Zero), Pos(Succ(Succ(Succ(ww310000)))))) → new_deleteBy044(ww41, ww40000, ww40100, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
new_deleteBy0118(ww23, ww24, ww2500, ww26, ww2700, Succ(ww12800), Zero) → new_deleteBy0119(ww23, ww24, ww2500, ww26, ww2700)
new_deleteBy0118(ww23, ww24, ww2500, ww26, ww2700, Zero, Succ(ww16100)) → new_deleteBy0119(ww23, ww24, ww2500, ww26, ww2700)
new_deleteBy095(ww41, ww40000, ww40100, Succ(ww3610)) → new_deleteBy12(ww41)
new_deleteBy070(ww41, ww40000, ww40100, Succ(ww2700)) → new_deleteBy12(ww41)
new_deleteBy038(ww41, ww40100, ww3000, ww310000, Succ(ww1470)) → new_deleteBy1(ww3000, Succ(Succ(Succ(ww310000))), ww41)
new_deleteBy01(ww41, Float(Pos(Zero), Pos(Succ(ww40100))), Float(Neg(Zero), Neg(Succ(Succ(Succ(ww310000)))))) → new_deleteBy079(ww41, ww40100, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
new_deleteBy01(ww41, Float(Neg(Succ(ww40000)), Neg(Succ(ww40100))), Float(Neg(Zero), Pos(Succ(Zero)))) → new_deleteBy6(ww41)
new_deleteBy01(ww41, Float(Pos(Zero), Neg(Succ(ww40100))), Float(Neg(Zero), Neg(Succ(Succ(Zero))))) → new_deleteBy082(ww41, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy01(ww41, Float(Pos(Zero), Pos(Succ(ww40100))), Float(Neg(Zero), Pos(Succ(Zero)))) → new_deleteBy6(ww41)
new_deleteBy078(ww41, ww40100, Succ(ww2940)) → new_deleteBy12(ww41)
new_deleteBy01(ww41, Float(Pos(Zero), Pos(Succ(ww40100))), Float(Pos(Zero), Neg(Succ(Succ(Succ(ww310000)))))) → new_deleteBy029(ww41, ww40100, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
new_deleteBy0147(ww17, ww18, ww1900, ww20, ww2100, Zero, Succ(ww8000)) → new_deleteBy0148(ww17, ww18, ww1900, ww20, ww2100)
new_deleteBy0147(ww17, ww18, ww1900, ww20, ww2100, Succ(ww5300), Zero) → new_deleteBy0148(ww17, ww18, ww1900, ww20, ww2100)
new_deleteBy01(ww41, Float(Pos(Zero), Pos(Succ(ww40100))), Float(Neg(Succ(ww3000)), Neg(Succ(Succ(Zero))))) → new_deleteBy064(ww41, ww40100, ww3000, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy01(ww41, Float(Neg(Zero), Pos(Succ(ww40100))), Float(Neg(Zero), Pos(Succ(Succ(Zero))))) → new_deleteBy0101(ww41, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy01(ww41, Float(Neg(Zero), Pos(Succ(ww40100))), Float(Neg(Zero), Neg(Succ(Succ(Zero))))) → new_deleteBy0105(ww41, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy0109(ww23, ww24, ww2500, ww26, ww2700, ww1280, Zero) → new_deleteBy(ww26, Succ(ww2700), ww23)
new_deleteBy058(ww36, ww37, Neg(Zero), ww39, Pos(Succ(ww4000)), Succ(ww2190)) → new_deleteBy4(ww39, Succ(ww4000), ww36)
new_deleteBy0124(ww36, ww37, ww3800, ww39, ww4000, Succ(ww2540)) → new_deleteBy0129(ww36, ww37, ww3800, ww39, ww4000)
new_deleteBy01(ww41, Float(Pos(Zero), Pos(Succ(ww40100))), Float(Neg(Zero), Pos(Succ(Succ(Succ(ww310000)))))) → new_deleteBy075(ww41, ww40100, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
new_deleteBy01(ww41, Float(Pos(Succ(ww40000)), Neg(Succ(ww40100))), Float(Pos(Zero), Pos(Succ(Zero)))) → new_deleteBy2(ww41)
new_deleteBy01(ww41, Float(Neg(Succ(ww40000)), Pos(Succ(ww40100))), Float(Pos(Zero), Pos(Succ(Zero)))) → new_deleteBy2(ww41)
new_deleteBy0102(ww41, ww40100, ww310000, Succ(ww3810)) → new_deleteBy11(ww310000, ww41)
new_deleteBy01(ww41, Float(Pos(Zero), Neg(Succ(ww40100))), Float(Pos(Succ(ww3000)), Pos(Succ(Zero)))) → new_deleteBy(ww3000, Succ(Zero), ww41)
new_deleteBy01(ww41, Float(Neg(Zero), Pos(Succ(ww40100))), Float(Pos(Succ(ww3000)), Pos(Succ(Zero)))) → new_deleteBy(ww3000, Succ(Zero), ww41)
new_deleteBy037(ww41, ww40100, ww3000, Succ(ww1450)) → new_deleteBy(ww3000, Succ(Succ(Zero)), ww41)
new_deleteBy5(ww39, ww400, :(ww360, ww361)) → new_deleteBy01(ww361, ww360, Float(Neg(Succ(ww39)), Neg(ww400)))
new_deleteBy058(ww36, ww37, Pos(Succ(ww3800)), ww39, Neg(Succ(ww4000)), Succ(ww2190)) → new_deleteBy0122(ww36, ww37, ww3800, ww39, ww4000, ww2190, new_primPlusNat0(new_primMulNat0(ww4000, ww3800), Succ(ww3800)))
new_deleteBy062(ww41, ww40100, ww3000, Succ(ww2340)) → new_deleteBy4(ww3000, Succ(Succ(Zero)), ww41)
new_deleteBy01(ww41, Float(Pos(Zero), Pos(Succ(ww40100))), Float(Pos(Zero), Pos(Succ(Zero)))) → new_deleteBy2(ww41)
new_deleteBy01(ww41, Float(Neg(Zero), Neg(Succ(ww40100))), Float(Pos(Zero), Pos(Succ(Succ(Succ(ww310000)))))) → new_deleteBy052(ww41, ww40100, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
new_deleteBy0110(ww23, ww24, ww2500, ww26, ww2700, Succ(ww12800), Succ(Zero)) → new_deleteBy0119(ww23, ww24, ww2500, ww26, ww2700)
new_deleteBy0120(ww23, ww24, ww250, ww26, ww270) → new_deleteBy1(ww26, ww270, ww23)
new_deleteBy063(ww41, ww40100, ww3000, ww310000, Succ(ww2360)) → new_deleteBy5(ww3000, Succ(Succ(Succ(ww310000))), ww41)
new_deleteBy01(ww41, Float(Pos(Succ(ww40000)), Neg(Succ(ww40100))), Float(Neg(Zero), Neg(Succ(Succ(Succ(ww310000)))))) → new_deleteBy073(ww41, ww40000, ww40100, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
new_deleteBy031(ww41, ww40100, ww310000, Succ(ww1220)) → new_deleteBy9(ww310000, ww41)
new_deleteBy0116(ww23, ww24, ww2500, ww26, ww2700, Succ(ww12800), Succ(ww15900)) → new_deleteBy0116(ww23, ww24, ww2500, ww26, ww2700, ww12800, ww15900)
new_deleteBy0119(ww23, ww24, ww2500, ww26, ww2700) → new_deleteBy1(ww26, Succ(ww2700), ww23)
new_deleteBy09(ww41, ww40100, ww3000, ww310000, Succ(ww3990)) → new_deleteBy(ww3000, Succ(Succ(Succ(ww310000))), ww41)
new_deleteBy033(ww23, ww24, Pos(Succ(ww2500)), ww26, Neg(Succ(ww2700)), Zero) → new_deleteBy0113(ww23, ww24, ww2500, ww26, ww2700, new_primPlusNat0(new_primMulNat0(ww2700, ww2500), Succ(ww2500)))
new_deleteBy1(ww20, ww210, :(ww170, ww171)) → new_deleteBy01(ww171, ww170, Float(Pos(Succ(ww20)), Neg(ww210)))
new_deleteBy01(ww41, Float(Neg(Zero), Pos(Succ(ww40100))), Float(Neg(Succ(ww3000)), Pos(Succ(Succ(Succ(ww310000)))))) → new_deleteBy084(ww41, ww40100, ww3000, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
new_deleteBy0132(:(ww360, ww361), ww37, ww380, ww39, ww400) → new_deleteBy01(ww361, ww360, Float(Neg(Succ(ww39)), Neg(ww400)))
new_deleteBy0109(ww23, ww24, ww2500, ww26, ww2700, Succ(ww12800), Succ(Zero)) → new_deleteBy0117(ww23, ww24, ww2500, ww26, ww2700)
new_deleteBy012(ww41, ww40100, ww3000, Succ(ww540)) → new_deleteBy(ww3000, Succ(Succ(Zero)), ww41)
new_deleteBy046(ww41, ww40000, ww40100, ww310000, Succ(ww1830)) → new_deleteBy9(ww310000, ww41)
new_deleteBy01(ww41, Float(Neg(Zero), Neg(Succ(ww40100))), Float(Neg(Zero), Pos(Succ(Succ(Succ(ww310000)))))) → new_deleteBy0102(ww41, ww40100, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
new_deleteBy01(ww41, Float(Pos(Zero), Neg(Succ(ww40100))), Float(Pos(Zero), Neg(Succ(Zero)))) → new_deleteBy3(ww41)
new_deleteBy01(ww41, Float(Neg(Zero), Pos(Succ(ww40100))), Float(Pos(Zero), Neg(Succ(Zero)))) → new_deleteBy3(ww41)
new_deleteBy01(ww41, Float(Neg(Zero), Neg(Succ(ww40100))), Float(Pos(Succ(ww3000)), Neg(Succ(Zero)))) → new_deleteBy1(ww3000, Succ(Zero), ww41)
new_deleteBy033(ww23, ww24, Neg(Zero), ww26, Pos(Zero), Succ(ww1280)) → new_deleteBy(ww26, Zero, ww23)
new_deleteBy01(:(ww410, ww411), Float(Pos(Succ(ww40000)), Pos(Succ(ww40100))), Float(Pos(Zero), Pos(Succ(Zero)))) → new_deleteBy01(ww411, ww410, Float(Pos(Zero), Pos(Succ(Zero))))
new_deleteBy042(ww41, ww40000, ww40100, ww310000, Succ(ww1710)) → new_deleteBy8(ww310000, ww41)
new_deleteBy01(ww41, Float(Pos(Zero), Pos(Succ(ww40100))), Float(Pos(Succ(ww3000)), Neg(Succ(Zero)))) → new_deleteBy1(ww3000, Succ(Zero), ww41)
new_deleteBy01(ww41, Float(Pos(Zero), Pos(Succ(ww40100))), Float(Neg(Succ(ww3000)), Neg(Succ(Zero)))) → new_deleteBy5(ww3000, Succ(Zero), ww41)
new_deleteBy013(ww41, ww40100, ww3000, ww310000, Succ(ww560)) → new_deleteBy1(ww3000, Succ(Succ(Succ(ww310000))), ww41)
new_deleteBy094(ww41, ww40000, ww40100, ww310000, Succ(ww3570)) → new_deleteBy11(ww310000, ww41)
new_deleteBy0145(:(ww170, ww171), ww18, ww190, ww20, ww210) → new_deleteBy01(ww171, ww170, Float(Pos(Succ(ww20)), Pos(ww210)))
new_deleteBy048(ww41, ww40000, ww40100, ww310000, Succ(ww1890)) → new_deleteBy9(ww310000, ww41)
new_deleteBy06(ww17, ww18, ww1900, ww20, ww2100, Succ(ww880)) → new_deleteBy0148(ww17, ww18, ww1900, ww20, ww2100)
new_deleteBy01(ww41, Float(Pos(Succ(ww40000)), ww401), Float(Pos(Succ(ww3000)), ww31)) → new_deleteBy0(ww41, ww40000, ww401, ww3000, ww31, new_primPlusNat1(new_primMulNat0(ww3000, ww40000), ww40000))
new_deleteBy091(ww41, ww40100, ww3000, Succ(ww3370)) → new_deleteBy5(ww3000, Succ(Succ(Zero)), ww41)
new_deleteBy02(ww17, ww18, ww1900, ww20, ww2100, Succ(ww5300), Succ(Succ(ww8000))) → new_deleteBy0147(ww17, ww18, ww1900, ww20, ww2100, ww5300, ww8000)
new_deleteBy025(ww41, ww40100, ww310000, Succ(ww1040)) → new_deleteBy8(ww310000, ww41)
new_deleteBy083(ww42, ww43, Pos(Zero), ww45, Pos(Succ(ww4600)), Succ(ww3080)) → new_deleteBy4(ww45, Succ(ww4600), ww42)
new_deleteBy0104(ww41, ww40100, ww310000, Succ(ww3870)) → new_deleteBy13(ww310000, ww41)
new_deleteBy01(:(ww410, ww411), Float(Pos(Succ(ww40000)), Pos(Succ(ww40100))), Float(Neg(Zero), Pos(Succ(Zero)))) → new_deleteBy01(ww411, ww410, Float(Neg(Zero), Pos(Succ(Zero))))
new_deleteBy01(:(ww410, ww411), Float(Pos(Succ(ww40000)), Pos(Succ(ww40100))), Float(Pos(Zero), Neg(Succ(Zero)))) → new_deleteBy01(ww411, ww410, Float(Pos(Zero), Neg(Succ(Zero))))
new_deleteBy0(ww17, ww18, Neg(Zero), ww20, Neg(Succ(ww2100)), Succ(ww530)) → new_deleteBy1(ww20, Succ(ww2100), ww17)
new_deleteBy010(ww41, ww40100, ww3000, Succ(ww4020)) → new_deleteBy(ww3000, Succ(Succ(Zero)), ww41)
new_deleteBy067(:(ww410, ww411), ww40000, ww40100, ww310000, Succ(ww2600)) → new_deleteBy01(ww411, ww410, Float(Neg(Zero), Pos(Succ(Succ(Succ(ww310000))))))
new_deleteBy0110(ww23, ww24, ww2500, ww26, ww2700, Zero, Succ(Succ(ww16100))) → new_deleteBy0119(ww23, ww24, ww2500, ww26, ww2700)
new_deleteBy00(ww17, ww18, ww1900, ww20, ww2100, Zero, Succ(Succ(ww7800))) → new_deleteBy08(ww17, ww18, ww1900, ww20, ww2100)
new_deleteBy083(ww42, ww43, Neg(Zero), ww45, Neg(Zero), Succ(ww3080)) → new_deleteBy5(ww45, Zero, ww42)
new_deleteBy023(ww41, ww40000, ww40100, ww310000, Succ(ww980)) → new_deleteBy9(ww310000, ww41)
new_deleteBy0122(ww36, ww37, ww3800, ww39, ww4000, Succ(ww21900), Succ(Succ(ww25000))) → new_deleteBy0130(ww36, ww37, ww3800, ww39, ww4000, ww21900, ww25000)
new_deleteBy074(ww41, ww40000, ww40100, Succ(ww2820)) → new_deleteBy14(ww41)
new_deleteBy033(ww23, ww24, Pos(ww250), ww26, Pos(ww270), Succ(ww1280)) → new_deleteBy(ww26, ww270, ww23)
new_deleteBy019(ww41, ww40000, ww40100, ww310000, Succ(ww740)) → new_deleteBy8(ww310000, ww41)
new_deleteBy029(ww41, ww40100, ww310000, Succ(ww1160)) → new_deleteBy9(ww310000, ww41)
new_deleteBy032(ww41, ww40100, Succ(ww1260)) → new_deleteBy10(ww41)
new_deleteBy081(ww41, ww40100, ww310000, Succ(ww3020)) → new_deleteBy13(ww310000, ww41)
new_deleteBy018(ww41, ww40000, ww40100, Succ(ww720)) → new_deleteBy0108(ww41, Float(Pos(Succ(ww40000)), Pos(Succ(ww40100))))
new_deleteBy033(ww23, ww24, Neg(Succ(ww2500)), ww26, Pos(Succ(ww2700)), Succ(ww1280)) → new_deleteBy0109(ww23, ww24, ww2500, ww26, ww2700, ww1280, new_primPlusNat0(new_primMulNat0(ww2700, ww2500), Succ(ww2500)))
new_deleteBy083(ww42, ww43, Pos(Succ(ww4400)), ww45, Pos(Succ(ww4600)), Zero) → new_deleteBy0135(ww42, ww43, ww4400, ww45, ww4600, new_primPlusNat0(new_primMulNat0(ww4600, ww4400), Succ(ww4400)))
new_deleteBy02(ww17, ww18, ww1900, ww20, ww2100, ww530, Zero) → new_deleteBy1(ww20, Succ(ww2100), ww17)
new_deleteBy0122(ww36, ww37, ww3800, ww39, ww4000, ww2190, Zero) → new_deleteBy5(ww39, Succ(ww4000), ww36)
new_deleteBy01(ww41, Float(Neg(Succ(ww40000)), Neg(Succ(ww40100))), Float(Neg(Zero), Pos(Succ(Succ(Succ(ww310000)))))) → new_deleteBy094(ww41, ww40000, ww40100, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
new_deleteBy01(ww41, Float(Pos(Zero), Neg(Succ(ww40100))), Float(Neg(Succ(ww3000)), Pos(Succ(Succ(Succ(ww310000)))))) → new_deleteBy061(ww41, ww40100, ww3000, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
new_deleteBy0118(ww23, ww24, ww2500, ww26, ww2700, Succ(ww12800), Succ(ww16100)) → new_deleteBy0118(ww23, ww24, ww2500, ww26, ww2700, ww12800, ww16100)
new_deleteBy083(ww42, ww43, Pos(Succ(ww4400)), ww45, Neg(Succ(ww4600)), Zero) → new_deleteBy0137(ww42, ww43, ww4400, ww45, ww4600, new_primPlusNat0(new_primMulNat0(ww4600, ww4400), Succ(ww4400)))
new_deleteBy08(ww17, ww18, ww1900, ww20, ww2100) → new_deleteBy(ww20, Succ(ww2100), ww17)
new_deleteBy01(ww41, Float(Pos(Zero), Neg(Succ(ww40100))), Float(Neg(Succ(ww3000)), Neg(Succ(Succ(Succ(ww310000)))))) → new_deleteBy065(ww41, ww40100, ww3000, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
new_deleteBy055(ww41, ww40100, Succ(ww2110)) → new_deleteBy10(ww41)
new_deleteBy04(ww17, ww18, ww1900, ww20, ww2100, Succ(ww840)) → new_deleteBy0145(ww17, ww18, Succ(ww1900), ww20, Succ(ww2100))
new_deleteBy01(ww41, Float(Neg(Zero), Neg(Succ(ww40100))), Float(Neg(Succ(ww3000)), Neg(Succ(Succ(Zero))))) → new_deleteBy091(ww41, ww40100, ww3000, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy072(:(ww410, ww411), ww40000, ww40100, Succ(ww2760)) → new_deleteBy01(ww411, ww410, Float(Neg(Zero), Neg(Succ(Succ(Zero)))))
new_deleteBy083(ww42, ww43, Neg(ww440), ww45, Pos(ww460), Succ(ww3080)) → new_deleteBy4(ww45, ww460, ww42)
new_deleteBy0144(ww42, ww43, ww4400, ww45, ww4600) → new_deleteBy5(ww45, Succ(ww4600), ww42)
new_deleteBy026(ww41, ww40100, Succ(ww1080)) → new_deleteBy0108(ww41, Float(Pos(Zero), Pos(Succ(ww40100))))
new_deleteBy(ww20, ww210, :(ww170, ww171)) → new_deleteBy01(ww171, ww170, Float(Pos(Succ(ww20)), Pos(ww210)))
new_deleteBy0130(ww36, ww37, ww3800, ww39, ww4000, Succ(ww21900), Succ(ww25000)) → new_deleteBy0130(ww36, ww37, ww3800, ww39, ww4000, ww21900, ww25000)
new_deleteBy01(ww41, Float(Neg(Zero), Neg(Succ(ww40100))), Float(Neg(Succ(ww3000)), Pos(Succ(Succ(Zero))))) → new_deleteBy087(ww41, ww40100, ww3000, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy0112(ww23, ww24, ww2500, ww26, ww2700, Succ(ww1650)) → new_deleteBy0117(ww23, ww24, ww2500, ww26, ww2700)
new_deleteBy087(ww41, ww40100, ww3000, Succ(ww3250)) → new_deleteBy4(ww3000, Succ(Succ(Zero)), ww41)
new_deleteBy01(ww41, Float(Neg(Zero), Pos(Succ(ww40100))), Float(Pos(Zero), Pos(Succ(Succ(Zero))))) → new_deleteBy051(ww41, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy033(ww23, ww24, Neg(Succ(ww2500)), ww26, Pos(Zero), Succ(ww1280)) → new_deleteBy(ww26, Zero, ww23)
new_deleteBy058(ww36, ww37, Pos(Succ(ww3800)), ww39, Neg(Zero), Succ(ww2190)) → new_deleteBy5(ww39, Zero, ww36)
new_deleteBy016(ww41, ww40100, ww3000, Succ(ww660)) → new_deleteBy1(ww3000, Succ(Succ(Zero)), ww41)
new_deleteBy0128(ww36, ww37, ww3800, ww39, ww4000, Succ(ww21900), Zero) → new_deleteBy0129(ww36, ww37, ww3800, ww39, ww4000)
new_deleteBy0128(ww36, ww37, ww3800, ww39, ww4000, Zero, Succ(ww24800)) → new_deleteBy0129(ww36, ww37, ww3800, ww39, ww4000)
new_deleteBy089(ww41, ww40100, ww3000, Succ(ww3310)) → new_deleteBy5(ww3000, Succ(Succ(Zero)), ww41)
new_deleteBy01(ww41, Float(Neg(Succ(ww40000)), Pos(Succ(ww40100))), Float(Pos(Zero), Neg(Succ(Succ(Succ(ww310000)))))) → new_deleteBy046(ww41, ww40000, ww40100, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
new_deleteBy071(:(ww410, ww411), ww40000, ww40100, ww310000, Succ(ww2720)) → new_deleteBy01(ww411, ww410, Float(Neg(Zero), Neg(Succ(Succ(Succ(ww310000))))))
new_deleteBy014(ww41, ww40100, ww3000, Succ(ww600)) → new_deleteBy1(ww3000, Succ(Succ(Zero)), ww41)
new_deleteBy0(ww17, ww18, Pos(Succ(ww1900)), ww20, Pos(Succ(ww2100)), Succ(ww530)) → new_deleteBy00(ww17, ww18, ww1900, ww20, ww2100, ww530, new_primPlusNat0(new_primMulNat0(ww2100, ww1900), Succ(ww1900)))
new_deleteBy01(ww41, Float(Neg(Succ(ww40000)), Pos(Succ(ww40100))), Float(Neg(Zero), Neg(Succ(Succ(Succ(ww310000)))))) → new_deleteBy096(ww41, ww40000, ww40100, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
new_deleteBy083(ww42, ww43, Neg(Zero), ww45, Neg(Succ(ww4600)), Succ(ww3080)) → new_deleteBy5(ww45, Succ(ww4600), ww42)
new_deleteBy01(ww41, Float(Neg(Zero), Neg(Succ(ww40100))), Float(Neg(Succ(ww3000)), Pos(Succ(Succ(Succ(ww310000)))))) → new_deleteBy086(ww41, ww40100, ww3000, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
new_deleteBy01(ww41, Float(Neg(Zero), Neg(Succ(ww40100))), Float(Pos(Succ(ww3000)), Neg(Succ(Succ(Succ(ww310000)))))) → new_deleteBy040(ww41, ww40100, ww3000, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
new_deleteBy01(ww41, Float(Neg(Zero), Neg(Succ(ww40100))), Float(Pos(Zero), Neg(Succ(Zero)))) → new_deleteBy3(ww41)
new_deleteBy01(ww41, Float(Neg(Zero), Neg(Succ(ww40100))), Float(Neg(Zero), Pos(Succ(Zero)))) → new_deleteBy6(ww41)
new_deleteBy01(ww41, Float(Neg(Succ(ww40000)), Neg(Succ(ww40100))), Float(Pos(Zero), Neg(Succ(Succ(Zero))))) → new_deleteBy049(ww41, ww40000, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy024(ww41, ww40000, ww40100, Succ(ww1020)) → new_deleteBy10(ww41)
new_deleteBy9(ww310000, :(ww410, ww411)) → new_deleteBy01(ww411, ww410, Float(Pos(Zero), Neg(Succ(Succ(Succ(ww310000))))))
new_deleteBy01(ww41, Float(Pos(Succ(ww40000)), Neg(Succ(ww40100))), Float(Pos(Zero), Neg(Succ(Succ(Succ(ww310000)))))) → new_deleteBy023(ww41, ww40000, ww40100, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
new_deleteBy01(ww41, Float(Neg(Succ(ww40000)), Neg(Succ(ww40100))), Float(Neg(Zero), Neg(Succ(Succ(Zero))))) → new_deleteBy099(ww41, ww40000, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy083(ww42, ww43, Neg(Succ(ww4400)), ww45, Pos(Succ(ww4600)), Zero) → new_deleteBy0136(ww42, ww43, ww4400, ww45, ww4600, new_primPlusNat0(new_primMulNat0(ww4600, ww4400), Succ(ww4400)))
new_deleteBy13(ww310000, :(ww410, ww411)) → new_deleteBy01(ww411, ww410, Float(Neg(Zero), Neg(Succ(Succ(Succ(ww310000))))))
new_deleteBy058(ww36, ww37, Neg(Succ(ww3800)), ww39, Pos(Succ(ww4000)), Zero) → new_deleteBy0124(ww36, ww37, ww3800, ww39, ww4000, new_primPlusNat0(new_primMulNat0(ww4000, ww3800), Succ(ww3800)))
new_deleteBy058(ww36, ww37, Pos(Zero), ww39, Neg(Zero), Succ(ww2190)) → new_deleteBy5(ww39, Zero, ww36)
new_deleteBy01(ww41, Float(Neg(Zero), Pos(Succ(ww40100))), Float(Neg(Zero), Neg(Succ(Succ(Succ(ww310000)))))) → new_deleteBy0104(ww41, ww40100, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
new_deleteBy01(ww41, Float(Pos(Zero), Pos(Succ(ww40100))), Float(Neg(Succ(ww3000)), Pos(Succ(Zero)))) → new_deleteBy4(ww3000, Succ(Zero), ww41)
new_deleteBy01(ww41, Float(Neg(Zero), Pos(Succ(ww40100))), Float(Pos(Succ(ww3000)), Neg(Succ(Succ(Zero))))) → new_deleteBy039(ww41, ww40100, ww3000, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy059(ww41, ww40100, ww3000, ww310000, Succ(ww2240)) → new_deleteBy4(ww3000, Succ(Succ(Succ(ww310000))), ww41)
new_deleteBy01(ww41, Float(Pos(Zero), Pos(Succ(ww40100))), Float(Pos(Zero), Pos(Succ(Succ(Zero))))) → new_deleteBy026(ww41, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy01(ww41, Float(Neg(Succ(ww40000)), Pos(Succ(ww40100))), Float(Neg(Zero), Pos(Succ(Succ(Succ(ww310000)))))) → new_deleteBy092(ww41, ww40000, ww40100, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
new_deleteBy01(ww41, Float(Pos(Succ(ww40000)), Neg(Succ(ww40100))), Float(Pos(Zero), Pos(Succ(Succ(Succ(ww310000)))))) → new_deleteBy019(ww41, ww40000, ww40100, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
new_deleteBy0(ww17, ww18, Pos(Succ(ww1900)), ww20, Pos(Succ(ww2100)), Zero) → new_deleteBy03(ww17, ww18, ww1900, ww20, ww2100, new_primPlusNat0(new_primMulNat0(ww2100, ww1900), Succ(ww1900)))
new_deleteBy033(ww23, ww24, Pos(Succ(ww2500)), ww26, Neg(Zero), Succ(ww1280)) → new_deleteBy1(ww26, Zero, ww23)
new_deleteBy01(ww41, Float(Pos(Zero), Neg(Succ(ww40100))), Float(Pos(Zero), Pos(Succ(Zero)))) → new_deleteBy2(ww41)
new_deleteBy01(ww41, Float(Neg(Zero), Pos(Succ(ww40100))), Float(Pos(Zero), Pos(Succ(Zero)))) → new_deleteBy2(ww41)
new_deleteBy076(ww41, ww40100, Succ(ww2880)) → new_deleteBy12(ww41)
new_deleteBy10(:(ww410, ww411)) → new_deleteBy01(ww411, ww410, Float(Pos(Zero), Neg(Succ(Succ(Zero)))))
new_deleteBy01(ww41, Float(Pos(Zero), Neg(Succ(ww40100))), Float(Neg(Succ(ww3000)), Pos(Succ(Succ(Zero))))) → new_deleteBy062(ww41, ww40100, ww3000, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy0130(ww36, ww37, ww3800, ww39, ww4000, Succ(ww21900), Zero) → new_deleteBy0131(ww36, ww37, ww3800, ww39, ww4000)
new_deleteBy0130(ww36, ww37, ww3800, ww39, ww4000, Zero, Succ(ww25000)) → new_deleteBy0131(ww36, ww37, ww3800, ww39, ww4000)
new_deleteBy056(ww41, ww40100, ww310000, Succ(ww2130)) → new_deleteBy9(ww310000, ww41)
new_deleteBy7(:(ww410, ww411)) → new_deleteBy01(ww411, ww410, Float(Neg(Zero), Neg(Succ(Zero))))
new_deleteBy0116(ww23, ww24, ww2500, ww26, ww2700, Succ(ww12800), Zero) → new_deleteBy0117(ww23, ww24, ww2500, ww26, ww2700)
new_deleteBy0116(ww23, ww24, ww2500, ww26, ww2700, Zero, Succ(ww15900)) → new_deleteBy0117(ww23, ww24, ww2500, ww26, ww2700)
new_deleteBy058(ww36, ww37, Neg(Succ(ww3800)), ww39, Pos(Succ(ww4000)), Succ(ww2190)) → new_deleteBy0121(ww36, ww37, ww3800, ww39, ww4000, ww2190, new_primPlusNat0(new_primMulNat0(ww4000, ww3800), Succ(ww3800)))
new_deleteBy01(ww41, Float(Pos(Zero), Pos(Succ(ww40100))), Float(Neg(Zero), Neg(Succ(Succ(Zero))))) → new_deleteBy080(ww41, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy0109(ww23, ww24, ww2500, ww26, ww2700, Succ(ww12800), Succ(Succ(ww15900))) → new_deleteBy0116(ww23, ww24, ww2500, ww26, ww2700, ww12800, ww15900)
new_deleteBy01(ww41, Float(Neg(Zero), Pos(Succ(ww40100))), Float(Pos(Zero), Neg(Succ(Succ(Succ(ww310000)))))) → new_deleteBy054(ww41, ww40100, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
new_deleteBy0113(ww23, ww24, ww2500, ww26, ww2700, Succ(ww1670)) → new_deleteBy0119(ww23, ww24, ww2500, ww26, ww2700)
new_deleteBy0141(ww42, ww43, ww440, ww45, ww460) → new_deleteBy4(ww45, ww460, ww42)
new_deleteBy060(ww41, ww40100, ww3000, Succ(ww2280)) → new_deleteBy4(ww3000, Succ(Succ(Zero)), ww41)
new_deleteBy021(:(ww410, ww411), ww40000, ww40100, ww310000, Succ(ww920)) → new_deleteBy01(ww411, ww410, Float(Pos(Zero), Neg(Succ(Succ(Succ(ww310000))))))
new_deleteBy0(ww17, ww18, Neg(Succ(ww1900)), ww20, Neg(Zero), Succ(ww530)) → new_deleteBy1(ww20, Zero, ww17)
new_deleteBy01(ww41, Float(Neg(Zero), Neg(Succ(ww40100))), Float(Pos(Succ(ww3000)), Pos(Succ(Succ(Zero))))) → new_deleteBy037(ww41, ww40100, ww3000, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy028(ww41, ww40100, Succ(ww1140)) → new_deleteBy0108(ww41, Float(Pos(Zero), Neg(Succ(ww40100))))
new_deleteBy01(ww41, Float(Neg(Succ(ww40000)), Pos(Succ(ww40100))), Float(Neg(Zero), Pos(Succ(Succ(Zero))))) → new_deleteBy093(ww41, ww40000, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy0142(ww42, ww43, ww440, ww45, ww460) → new_deleteBy5(ww45, ww460, ww42)
new_deleteBy01(ww41, Float(Pos(Zero), Pos(Succ(ww40100))), Float(Pos(Succ(ww3000)), Neg(Succ(Succ(Succ(ww310000)))))) → new_deleteBy013(ww41, ww40100, ww3000, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
new_deleteBy01(ww41, Float(Pos(Zero), Neg(Succ(ww40100))), Float(Pos(Zero), Pos(Succ(Succ(Zero))))) → new_deleteBy028(ww41, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy8(ww310000, :(ww410, ww411)) → new_deleteBy01(ww411, ww410, Float(Pos(Zero), Pos(Succ(Succ(Succ(ww310000))))))
new_deleteBy0(ww17, ww18, Pos(Zero), ww20, Pos(Succ(ww2100)), Succ(ww530)) → new_deleteBy(ww20, Succ(ww2100), ww17)
new_deleteBy0133(ww42, ww43, ww4400, ww45, ww4600, Succ(ww30800), Succ(Succ(ww33900))) → new_deleteBy0139(ww42, ww43, ww4400, ww45, ww4600, ww30800, ww33900)
new_deleteBy058(ww36, ww37, Pos(Succ(ww3800)), ww39, Pos(Succ(ww4000)), Zero) → new_deleteBy0123(ww36, ww37, ww3800, ww39, ww4000, new_primPlusNat0(new_primMulNat0(ww4000, ww3800), Succ(ww3800)))
new_deleteBy07(ww17, ww18, ww1900, ww20, ww2100, Succ(ww5300), Succ(ww7800)) → new_deleteBy07(ww17, ww18, ww1900, ww20, ww2100, ww5300, ww7800)
new_deleteBy03(ww17, ww18, ww1900, ww20, ww2100, Succ(ww820)) → new_deleteBy08(ww17, ww18, ww1900, ww20, ww2100)
new_deleteBy035(ww41, ww40100, ww3000, Succ(ww1390)) → new_deleteBy(ww3000, Succ(Succ(Zero)), ww41)
new_deleteBy01(ww41, Float(Neg(Zero), Pos(Succ(ww40100))), Float(Pos(Zero), Neg(Succ(Succ(Zero))))) → new_deleteBy055(ww41, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy01(ww41, Float(Pos(Zero), Pos(Succ(ww40100))), Float(Neg(Zero), Pos(Succ(Succ(Zero))))) → new_deleteBy076(ww41, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy01(ww41, Float(Neg(Succ(ww40000)), Neg(Succ(ww40100))), Float(Neg(Zero), Pos(Succ(Succ(Zero))))) → new_deleteBy095(ww41, ww40000, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy0103(ww41, ww40100, Succ(ww3850)) → new_deleteBy12(ww41)
new_deleteBy01(ww41, Float(Neg(Zero), Neg(Succ(ww40100))), Float(Neg(Succ(ww3000)), Pos(Succ(Zero)))) → new_deleteBy4(ww3000, Succ(Zero), ww41)
new_deleteBy0105(ww41, ww40100, Succ(ww3910)) → new_deleteBy14(ww41)
new_deleteBy033(ww23, ww24, Pos(Zero), ww26, Neg(Zero), Succ(ww1280)) → new_deleteBy1(ww26, Zero, ww23)
new_deleteBy01(ww41, Float(Pos(Zero), Neg(Succ(ww40100))), Float(Pos(Succ(ww3000)), Pos(Succ(Succ(Succ(ww310000)))))) → new_deleteBy011(ww41, ww40100, ww3000, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
The TRS R consists of the following rules:
new_primPlusNat1(Zero, ww40000) → Succ(ww40000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, ww40000) → Zero
new_primPlusNat1(Succ(ww520), ww40000) → Succ(Succ(new_primPlusNat0(ww520, ww40000)))
new_primPlusNat0(Succ(ww5200), Zero) → Succ(ww5200)
new_primPlusNat0(Zero, Succ(ww400000)) → Succ(ww400000)
new_primPlusNat0(Succ(ww5200), Succ(ww400000)) → Succ(Succ(new_primPlusNat0(ww5200, ww400000)))
new_primMulNat0(Succ(ww30000), ww40000) → new_primPlusNat1(new_primMulNat0(ww30000, ww40000), ww40000)
The set Q consists of the following terms:
new_primMulNat0(Succ(x0), x1)
new_primMulNat0(Zero, x0)
new_primPlusNat1(Succ(x0), x1)
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph [15,17,22] contains 14 SCCs.
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_deleteBy01(ww41, Float(Neg(Succ(ww40000)), Neg(Succ(ww40100))), Float(Neg(Zero), Neg(Succ(Zero)))) → new_deleteBy7(ww41)
new_deleteBy01(:(ww410, ww411), Float(Pos(Succ(ww40000)), Pos(Succ(ww40100))), Float(Neg(Zero), Neg(Succ(Zero)))) → new_deleteBy01(ww411, ww410, Float(Neg(Zero), Neg(Succ(Zero))))
new_deleteBy01(ww41, Float(Neg(Zero), Neg(Succ(ww40100))), Float(Neg(Zero), Neg(Succ(Zero)))) → new_deleteBy7(ww41)
new_deleteBy01(ww41, Float(Pos(Zero), Pos(Succ(ww40100))), Float(Neg(Zero), Neg(Succ(Zero)))) → new_deleteBy7(ww41)
new_deleteBy01(ww41, Float(Pos(Succ(ww40000)), Neg(Succ(ww40100))), Float(Neg(Zero), Neg(Succ(Zero)))) → new_deleteBy7(ww41)
new_deleteBy01(ww41, Float(Neg(Succ(ww40000)), Pos(Succ(ww40100))), Float(Neg(Zero), Neg(Succ(Zero)))) → new_deleteBy7(ww41)
new_deleteBy7(:(ww410, ww411)) → new_deleteBy01(ww411, ww410, Float(Neg(Zero), Neg(Succ(Zero))))
new_deleteBy01(ww41, Float(Pos(Zero), Neg(Succ(ww40100))), Float(Neg(Zero), Neg(Succ(Zero)))) → new_deleteBy7(ww41)
new_deleteBy01(ww41, Float(Neg(Zero), Pos(Succ(ww40100))), Float(Neg(Zero), Neg(Succ(Zero)))) → new_deleteBy7(ww41)
The TRS R consists of the following rules:
new_primPlusNat1(Zero, ww40000) → Succ(ww40000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, ww40000) → Zero
new_primPlusNat1(Succ(ww520), ww40000) → Succ(Succ(new_primPlusNat0(ww520, ww40000)))
new_primPlusNat0(Succ(ww5200), Zero) → Succ(ww5200)
new_primPlusNat0(Zero, Succ(ww400000)) → Succ(ww400000)
new_primPlusNat0(Succ(ww5200), Succ(ww400000)) → Succ(Succ(new_primPlusNat0(ww5200, ww400000)))
new_primMulNat0(Succ(ww30000), ww40000) → new_primPlusNat1(new_primMulNat0(ww30000, ww40000), ww40000)
The set Q consists of the following terms:
new_primMulNat0(Succ(x0), x1)
new_primMulNat0(Zero, x0)
new_primPlusNat1(Succ(x0), x1)
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
We have to consider all minimal (P,Q,R)-chains.
As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [15] we can delete all non-usable rules [17] from R.
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QReductionProof
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_deleteBy01(ww41, Float(Neg(Succ(ww40000)), Neg(Succ(ww40100))), Float(Neg(Zero), Neg(Succ(Zero)))) → new_deleteBy7(ww41)
new_deleteBy01(:(ww410, ww411), Float(Pos(Succ(ww40000)), Pos(Succ(ww40100))), Float(Neg(Zero), Neg(Succ(Zero)))) → new_deleteBy01(ww411, ww410, Float(Neg(Zero), Neg(Succ(Zero))))
new_deleteBy01(ww41, Float(Neg(Zero), Neg(Succ(ww40100))), Float(Neg(Zero), Neg(Succ(Zero)))) → new_deleteBy7(ww41)
new_deleteBy01(ww41, Float(Pos(Zero), Pos(Succ(ww40100))), Float(Neg(Zero), Neg(Succ(Zero)))) → new_deleteBy7(ww41)
new_deleteBy01(ww41, Float(Pos(Succ(ww40000)), Neg(Succ(ww40100))), Float(Neg(Zero), Neg(Succ(Zero)))) → new_deleteBy7(ww41)
new_deleteBy01(ww41, Float(Neg(Succ(ww40000)), Pos(Succ(ww40100))), Float(Neg(Zero), Neg(Succ(Zero)))) → new_deleteBy7(ww41)
new_deleteBy7(:(ww410, ww411)) → new_deleteBy01(ww411, ww410, Float(Neg(Zero), Neg(Succ(Zero))))
new_deleteBy01(ww41, Float(Pos(Zero), Neg(Succ(ww40100))), Float(Neg(Zero), Neg(Succ(Zero)))) → new_deleteBy7(ww41)
new_deleteBy01(ww41, Float(Neg(Zero), Pos(Succ(ww40100))), Float(Neg(Zero), Neg(Succ(Zero)))) → new_deleteBy7(ww41)
R is empty.
The set Q consists of the following terms:
new_primMulNat0(Succ(x0), x1)
new_primMulNat0(Zero, x0)
new_primPlusNat1(Succ(x0), x1)
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
We have to consider all minimal (P,Q,R)-chains.
We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.
new_primMulNat0(Succ(x0), x1)
new_primMulNat0(Zero, x0)
new_primPlusNat1(Succ(x0), x1)
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QReductionProof
↳ QDP
↳ QDPSizeChangeProof
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_deleteBy01(ww41, Float(Neg(Succ(ww40000)), Neg(Succ(ww40100))), Float(Neg(Zero), Neg(Succ(Zero)))) → new_deleteBy7(ww41)
new_deleteBy01(ww41, Float(Neg(Zero), Neg(Succ(ww40100))), Float(Neg(Zero), Neg(Succ(Zero)))) → new_deleteBy7(ww41)
new_deleteBy01(:(ww410, ww411), Float(Pos(Succ(ww40000)), Pos(Succ(ww40100))), Float(Neg(Zero), Neg(Succ(Zero)))) → new_deleteBy01(ww411, ww410, Float(Neg(Zero), Neg(Succ(Zero))))
new_deleteBy01(ww41, Float(Pos(Zero), Pos(Succ(ww40100))), Float(Neg(Zero), Neg(Succ(Zero)))) → new_deleteBy7(ww41)
new_deleteBy01(ww41, Float(Neg(Succ(ww40000)), Pos(Succ(ww40100))), Float(Neg(Zero), Neg(Succ(Zero)))) → new_deleteBy7(ww41)
new_deleteBy01(ww41, Float(Pos(Succ(ww40000)), Neg(Succ(ww40100))), Float(Neg(Zero), Neg(Succ(Zero)))) → new_deleteBy7(ww41)
new_deleteBy7(:(ww410, ww411)) → new_deleteBy01(ww411, ww410, Float(Neg(Zero), Neg(Succ(Zero))))
new_deleteBy01(ww41, Float(Neg(Zero), Pos(Succ(ww40100))), Float(Neg(Zero), Neg(Succ(Zero)))) → new_deleteBy7(ww41)
new_deleteBy01(ww41, Float(Pos(Zero), Neg(Succ(ww40100))), Float(Neg(Zero), Neg(Succ(Zero)))) → new_deleteBy7(ww41)
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_deleteBy7(:(ww410, ww411)) → new_deleteBy01(ww411, ww410, Float(Neg(Zero), Neg(Succ(Zero))))
The graph contains the following edges 1 > 1, 1 > 2
- new_deleteBy01(:(ww410, ww411), Float(Pos(Succ(ww40000)), Pos(Succ(ww40100))), Float(Neg(Zero), Neg(Succ(Zero)))) → new_deleteBy01(ww411, ww410, Float(Neg(Zero), Neg(Succ(Zero))))
The graph contains the following edges 1 > 1, 1 > 2, 3 >= 3
- new_deleteBy01(ww41, Float(Neg(Succ(ww40000)), Neg(Succ(ww40100))), Float(Neg(Zero), Neg(Succ(Zero)))) → new_deleteBy7(ww41)
The graph contains the following edges 1 >= 1
- new_deleteBy01(ww41, Float(Neg(Zero), Neg(Succ(ww40100))), Float(Neg(Zero), Neg(Succ(Zero)))) → new_deleteBy7(ww41)
The graph contains the following edges 1 >= 1
- new_deleteBy01(ww41, Float(Pos(Zero), Pos(Succ(ww40100))), Float(Neg(Zero), Neg(Succ(Zero)))) → new_deleteBy7(ww41)
The graph contains the following edges 1 >= 1
- new_deleteBy01(ww41, Float(Pos(Succ(ww40000)), Neg(Succ(ww40100))), Float(Neg(Zero), Neg(Succ(Zero)))) → new_deleteBy7(ww41)
The graph contains the following edges 1 >= 1
- new_deleteBy01(ww41, Float(Neg(Succ(ww40000)), Pos(Succ(ww40100))), Float(Neg(Zero), Neg(Succ(Zero)))) → new_deleteBy7(ww41)
The graph contains the following edges 1 >= 1
- new_deleteBy01(ww41, Float(Pos(Zero), Neg(Succ(ww40100))), Float(Neg(Zero), Neg(Succ(Zero)))) → new_deleteBy7(ww41)
The graph contains the following edges 1 >= 1
- new_deleteBy01(ww41, Float(Neg(Zero), Pos(Succ(ww40100))), Float(Neg(Zero), Neg(Succ(Zero)))) → new_deleteBy7(ww41)
The graph contains the following edges 1 >= 1
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_deleteBy01(ww41, Float(Neg(Zero), Pos(Succ(ww40100))), Float(Pos(Zero), Neg(Succ(Zero)))) → new_deleteBy3(ww41)
new_deleteBy01(ww41, Float(Pos(Zero), Neg(Succ(ww40100))), Float(Pos(Zero), Neg(Succ(Zero)))) → new_deleteBy3(ww41)
new_deleteBy3(:(ww410, ww411)) → new_deleteBy01(ww411, ww410, Float(Pos(Zero), Neg(Succ(Zero))))
new_deleteBy01(ww41, Float(Neg(Zero), Neg(Succ(ww40100))), Float(Pos(Zero), Neg(Succ(Zero)))) → new_deleteBy3(ww41)
new_deleteBy01(:(ww410, ww411), Float(Pos(Succ(ww40000)), Pos(Succ(ww40100))), Float(Pos(Zero), Neg(Succ(Zero)))) → new_deleteBy01(ww411, ww410, Float(Pos(Zero), Neg(Succ(Zero))))
new_deleteBy01(ww41, Float(Neg(Succ(ww40000)), Pos(Succ(ww40100))), Float(Pos(Zero), Neg(Succ(Zero)))) → new_deleteBy3(ww41)
new_deleteBy01(ww41, Float(Pos(Succ(ww40000)), Neg(Succ(ww40100))), Float(Pos(Zero), Neg(Succ(Zero)))) → new_deleteBy3(ww41)
new_deleteBy01(ww41, Float(Neg(Succ(ww40000)), Neg(Succ(ww40100))), Float(Pos(Zero), Neg(Succ(Zero)))) → new_deleteBy3(ww41)
new_deleteBy01(ww41, Float(Pos(Zero), Pos(Succ(ww40100))), Float(Pos(Zero), Neg(Succ(Zero)))) → new_deleteBy3(ww41)
The TRS R consists of the following rules:
new_primPlusNat1(Zero, ww40000) → Succ(ww40000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, ww40000) → Zero
new_primPlusNat1(Succ(ww520), ww40000) → Succ(Succ(new_primPlusNat0(ww520, ww40000)))
new_primPlusNat0(Succ(ww5200), Zero) → Succ(ww5200)
new_primPlusNat0(Zero, Succ(ww400000)) → Succ(ww400000)
new_primPlusNat0(Succ(ww5200), Succ(ww400000)) → Succ(Succ(new_primPlusNat0(ww5200, ww400000)))
new_primMulNat0(Succ(ww30000), ww40000) → new_primPlusNat1(new_primMulNat0(ww30000, ww40000), ww40000)
The set Q consists of the following terms:
new_primMulNat0(Succ(x0), x1)
new_primMulNat0(Zero, x0)
new_primPlusNat1(Succ(x0), x1)
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
We have to consider all minimal (P,Q,R)-chains.
As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [15] we can delete all non-usable rules [17] from R.
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QReductionProof
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_deleteBy01(ww41, Float(Neg(Zero), Pos(Succ(ww40100))), Float(Pos(Zero), Neg(Succ(Zero)))) → new_deleteBy3(ww41)
new_deleteBy01(ww41, Float(Pos(Zero), Neg(Succ(ww40100))), Float(Pos(Zero), Neg(Succ(Zero)))) → new_deleteBy3(ww41)
new_deleteBy3(:(ww410, ww411)) → new_deleteBy01(ww411, ww410, Float(Pos(Zero), Neg(Succ(Zero))))
new_deleteBy01(ww41, Float(Neg(Zero), Neg(Succ(ww40100))), Float(Pos(Zero), Neg(Succ(Zero)))) → new_deleteBy3(ww41)
new_deleteBy01(:(ww410, ww411), Float(Pos(Succ(ww40000)), Pos(Succ(ww40100))), Float(Pos(Zero), Neg(Succ(Zero)))) → new_deleteBy01(ww411, ww410, Float(Pos(Zero), Neg(Succ(Zero))))
new_deleteBy01(ww41, Float(Neg(Succ(ww40000)), Pos(Succ(ww40100))), Float(Pos(Zero), Neg(Succ(Zero)))) → new_deleteBy3(ww41)
new_deleteBy01(ww41, Float(Pos(Succ(ww40000)), Neg(Succ(ww40100))), Float(Pos(Zero), Neg(Succ(Zero)))) → new_deleteBy3(ww41)
new_deleteBy01(ww41, Float(Neg(Succ(ww40000)), Neg(Succ(ww40100))), Float(Pos(Zero), Neg(Succ(Zero)))) → new_deleteBy3(ww41)
new_deleteBy01(ww41, Float(Pos(Zero), Pos(Succ(ww40100))), Float(Pos(Zero), Neg(Succ(Zero)))) → new_deleteBy3(ww41)
R is empty.
The set Q consists of the following terms:
new_primMulNat0(Succ(x0), x1)
new_primMulNat0(Zero, x0)
new_primPlusNat1(Succ(x0), x1)
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
We have to consider all minimal (P,Q,R)-chains.
We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.
new_primMulNat0(Succ(x0), x1)
new_primMulNat0(Zero, x0)
new_primPlusNat1(Succ(x0), x1)
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QReductionProof
↳ QDP
↳ QDPSizeChangeProof
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_deleteBy01(ww41, Float(Pos(Zero), Neg(Succ(ww40100))), Float(Pos(Zero), Neg(Succ(Zero)))) → new_deleteBy3(ww41)
new_deleteBy01(ww41, Float(Neg(Zero), Pos(Succ(ww40100))), Float(Pos(Zero), Neg(Succ(Zero)))) → new_deleteBy3(ww41)
new_deleteBy3(:(ww410, ww411)) → new_deleteBy01(ww411, ww410, Float(Pos(Zero), Neg(Succ(Zero))))
new_deleteBy01(ww41, Float(Neg(Zero), Neg(Succ(ww40100))), Float(Pos(Zero), Neg(Succ(Zero)))) → new_deleteBy3(ww41)
new_deleteBy01(:(ww410, ww411), Float(Pos(Succ(ww40000)), Pos(Succ(ww40100))), Float(Pos(Zero), Neg(Succ(Zero)))) → new_deleteBy01(ww411, ww410, Float(Pos(Zero), Neg(Succ(Zero))))
new_deleteBy01(ww41, Float(Pos(Succ(ww40000)), Neg(Succ(ww40100))), Float(Pos(Zero), Neg(Succ(Zero)))) → new_deleteBy3(ww41)
new_deleteBy01(ww41, Float(Neg(Succ(ww40000)), Pos(Succ(ww40100))), Float(Pos(Zero), Neg(Succ(Zero)))) → new_deleteBy3(ww41)
new_deleteBy01(ww41, Float(Neg(Succ(ww40000)), Neg(Succ(ww40100))), Float(Pos(Zero), Neg(Succ(Zero)))) → new_deleteBy3(ww41)
new_deleteBy01(ww41, Float(Pos(Zero), Pos(Succ(ww40100))), Float(Pos(Zero), Neg(Succ(Zero)))) → new_deleteBy3(ww41)
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_deleteBy3(:(ww410, ww411)) → new_deleteBy01(ww411, ww410, Float(Pos(Zero), Neg(Succ(Zero))))
The graph contains the following edges 1 > 1, 1 > 2
- new_deleteBy01(:(ww410, ww411), Float(Pos(Succ(ww40000)), Pos(Succ(ww40100))), Float(Pos(Zero), Neg(Succ(Zero)))) → new_deleteBy01(ww411, ww410, Float(Pos(Zero), Neg(Succ(Zero))))
The graph contains the following edges 1 > 1, 1 > 2, 3 >= 3
- new_deleteBy01(ww41, Float(Neg(Zero), Pos(Succ(ww40100))), Float(Pos(Zero), Neg(Succ(Zero)))) → new_deleteBy3(ww41)
The graph contains the following edges 1 >= 1
- new_deleteBy01(ww41, Float(Pos(Zero), Neg(Succ(ww40100))), Float(Pos(Zero), Neg(Succ(Zero)))) → new_deleteBy3(ww41)
The graph contains the following edges 1 >= 1
- new_deleteBy01(ww41, Float(Neg(Zero), Neg(Succ(ww40100))), Float(Pos(Zero), Neg(Succ(Zero)))) → new_deleteBy3(ww41)
The graph contains the following edges 1 >= 1
- new_deleteBy01(ww41, Float(Neg(Succ(ww40000)), Pos(Succ(ww40100))), Float(Pos(Zero), Neg(Succ(Zero)))) → new_deleteBy3(ww41)
The graph contains the following edges 1 >= 1
- new_deleteBy01(ww41, Float(Pos(Succ(ww40000)), Neg(Succ(ww40100))), Float(Pos(Zero), Neg(Succ(Zero)))) → new_deleteBy3(ww41)
The graph contains the following edges 1 >= 1
- new_deleteBy01(ww41, Float(Neg(Succ(ww40000)), Neg(Succ(ww40100))), Float(Pos(Zero), Neg(Succ(Zero)))) → new_deleteBy3(ww41)
The graph contains the following edges 1 >= 1
- new_deleteBy01(ww41, Float(Pos(Zero), Pos(Succ(ww40100))), Float(Pos(Zero), Neg(Succ(Zero)))) → new_deleteBy3(ww41)
The graph contains the following edges 1 >= 1
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_deleteBy6(:(ww410, ww411)) → new_deleteBy01(ww411, ww410, Float(Neg(Zero), Pos(Succ(Zero))))
new_deleteBy01(ww41, Float(Pos(Succ(ww40000)), Neg(Succ(ww40100))), Float(Neg(Zero), Pos(Succ(Zero)))) → new_deleteBy6(ww41)
new_deleteBy01(ww41, Float(Neg(Succ(ww40000)), Pos(Succ(ww40100))), Float(Neg(Zero), Pos(Succ(Zero)))) → new_deleteBy6(ww41)
new_deleteBy01(:(ww410, ww411), Float(Pos(Succ(ww40000)), Pos(Succ(ww40100))), Float(Neg(Zero), Pos(Succ(Zero)))) → new_deleteBy01(ww411, ww410, Float(Neg(Zero), Pos(Succ(Zero))))
new_deleteBy01(ww41, Float(Neg(Zero), Neg(Succ(ww40100))), Float(Neg(Zero), Pos(Succ(Zero)))) → new_deleteBy6(ww41)
new_deleteBy01(ww41, Float(Pos(Zero), Neg(Succ(ww40100))), Float(Neg(Zero), Pos(Succ(Zero)))) → new_deleteBy6(ww41)
new_deleteBy01(ww41, Float(Neg(Zero), Pos(Succ(ww40100))), Float(Neg(Zero), Pos(Succ(Zero)))) → new_deleteBy6(ww41)
new_deleteBy01(ww41, Float(Neg(Succ(ww40000)), Neg(Succ(ww40100))), Float(Neg(Zero), Pos(Succ(Zero)))) → new_deleteBy6(ww41)
new_deleteBy01(ww41, Float(Pos(Zero), Pos(Succ(ww40100))), Float(Neg(Zero), Pos(Succ(Zero)))) → new_deleteBy6(ww41)
The TRS R consists of the following rules:
new_primPlusNat1(Zero, ww40000) → Succ(ww40000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, ww40000) → Zero
new_primPlusNat1(Succ(ww520), ww40000) → Succ(Succ(new_primPlusNat0(ww520, ww40000)))
new_primPlusNat0(Succ(ww5200), Zero) → Succ(ww5200)
new_primPlusNat0(Zero, Succ(ww400000)) → Succ(ww400000)
new_primPlusNat0(Succ(ww5200), Succ(ww400000)) → Succ(Succ(new_primPlusNat0(ww5200, ww400000)))
new_primMulNat0(Succ(ww30000), ww40000) → new_primPlusNat1(new_primMulNat0(ww30000, ww40000), ww40000)
The set Q consists of the following terms:
new_primMulNat0(Succ(x0), x1)
new_primMulNat0(Zero, x0)
new_primPlusNat1(Succ(x0), x1)
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
We have to consider all minimal (P,Q,R)-chains.
As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [15] we can delete all non-usable rules [17] from R.
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QReductionProof
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_deleteBy6(:(ww410, ww411)) → new_deleteBy01(ww411, ww410, Float(Neg(Zero), Pos(Succ(Zero))))
new_deleteBy01(ww41, Float(Pos(Succ(ww40000)), Neg(Succ(ww40100))), Float(Neg(Zero), Pos(Succ(Zero)))) → new_deleteBy6(ww41)
new_deleteBy01(ww41, Float(Neg(Succ(ww40000)), Pos(Succ(ww40100))), Float(Neg(Zero), Pos(Succ(Zero)))) → new_deleteBy6(ww41)
new_deleteBy01(:(ww410, ww411), Float(Pos(Succ(ww40000)), Pos(Succ(ww40100))), Float(Neg(Zero), Pos(Succ(Zero)))) → new_deleteBy01(ww411, ww410, Float(Neg(Zero), Pos(Succ(Zero))))
new_deleteBy01(ww41, Float(Neg(Zero), Neg(Succ(ww40100))), Float(Neg(Zero), Pos(Succ(Zero)))) → new_deleteBy6(ww41)
new_deleteBy01(ww41, Float(Pos(Zero), Neg(Succ(ww40100))), Float(Neg(Zero), Pos(Succ(Zero)))) → new_deleteBy6(ww41)
new_deleteBy01(ww41, Float(Neg(Zero), Pos(Succ(ww40100))), Float(Neg(Zero), Pos(Succ(Zero)))) → new_deleteBy6(ww41)
new_deleteBy01(ww41, Float(Neg(Succ(ww40000)), Neg(Succ(ww40100))), Float(Neg(Zero), Pos(Succ(Zero)))) → new_deleteBy6(ww41)
new_deleteBy01(ww41, Float(Pos(Zero), Pos(Succ(ww40100))), Float(Neg(Zero), Pos(Succ(Zero)))) → new_deleteBy6(ww41)
R is empty.
The set Q consists of the following terms:
new_primMulNat0(Succ(x0), x1)
new_primMulNat0(Zero, x0)
new_primPlusNat1(Succ(x0), x1)
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
We have to consider all minimal (P,Q,R)-chains.
We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.
new_primMulNat0(Succ(x0), x1)
new_primMulNat0(Zero, x0)
new_primPlusNat1(Succ(x0), x1)
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QReductionProof
↳ QDP
↳ QDPSizeChangeProof
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_deleteBy6(:(ww410, ww411)) → new_deleteBy01(ww411, ww410, Float(Neg(Zero), Pos(Succ(Zero))))
new_deleteBy01(ww41, Float(Neg(Succ(ww40000)), Pos(Succ(ww40100))), Float(Neg(Zero), Pos(Succ(Zero)))) → new_deleteBy6(ww41)
new_deleteBy01(ww41, Float(Pos(Succ(ww40000)), Neg(Succ(ww40100))), Float(Neg(Zero), Pos(Succ(Zero)))) → new_deleteBy6(ww41)
new_deleteBy01(:(ww410, ww411), Float(Pos(Succ(ww40000)), Pos(Succ(ww40100))), Float(Neg(Zero), Pos(Succ(Zero)))) → new_deleteBy01(ww411, ww410, Float(Neg(Zero), Pos(Succ(Zero))))
new_deleteBy01(ww41, Float(Neg(Zero), Neg(Succ(ww40100))), Float(Neg(Zero), Pos(Succ(Zero)))) → new_deleteBy6(ww41)
new_deleteBy01(ww41, Float(Neg(Zero), Pos(Succ(ww40100))), Float(Neg(Zero), Pos(Succ(Zero)))) → new_deleteBy6(ww41)
new_deleteBy01(ww41, Float(Pos(Zero), Neg(Succ(ww40100))), Float(Neg(Zero), Pos(Succ(Zero)))) → new_deleteBy6(ww41)
new_deleteBy01(ww41, Float(Neg(Succ(ww40000)), Neg(Succ(ww40100))), Float(Neg(Zero), Pos(Succ(Zero)))) → new_deleteBy6(ww41)
new_deleteBy01(ww41, Float(Pos(Zero), Pos(Succ(ww40100))), Float(Neg(Zero), Pos(Succ(Zero)))) → new_deleteBy6(ww41)
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_deleteBy01(:(ww410, ww411), Float(Pos(Succ(ww40000)), Pos(Succ(ww40100))), Float(Neg(Zero), Pos(Succ(Zero)))) → new_deleteBy01(ww411, ww410, Float(Neg(Zero), Pos(Succ(Zero))))
The graph contains the following edges 1 > 1, 1 > 2, 3 >= 3
- new_deleteBy6(:(ww410, ww411)) → new_deleteBy01(ww411, ww410, Float(Neg(Zero), Pos(Succ(Zero))))
The graph contains the following edges 1 > 1, 1 > 2
- new_deleteBy01(ww41, Float(Pos(Succ(ww40000)), Neg(Succ(ww40100))), Float(Neg(Zero), Pos(Succ(Zero)))) → new_deleteBy6(ww41)
The graph contains the following edges 1 >= 1
- new_deleteBy01(ww41, Float(Neg(Succ(ww40000)), Pos(Succ(ww40100))), Float(Neg(Zero), Pos(Succ(Zero)))) → new_deleteBy6(ww41)
The graph contains the following edges 1 >= 1
- new_deleteBy01(ww41, Float(Neg(Zero), Neg(Succ(ww40100))), Float(Neg(Zero), Pos(Succ(Zero)))) → new_deleteBy6(ww41)
The graph contains the following edges 1 >= 1
- new_deleteBy01(ww41, Float(Pos(Zero), Neg(Succ(ww40100))), Float(Neg(Zero), Pos(Succ(Zero)))) → new_deleteBy6(ww41)
The graph contains the following edges 1 >= 1
- new_deleteBy01(ww41, Float(Neg(Zero), Pos(Succ(ww40100))), Float(Neg(Zero), Pos(Succ(Zero)))) → new_deleteBy6(ww41)
The graph contains the following edges 1 >= 1
- new_deleteBy01(ww41, Float(Neg(Succ(ww40000)), Neg(Succ(ww40100))), Float(Neg(Zero), Pos(Succ(Zero)))) → new_deleteBy6(ww41)
The graph contains the following edges 1 >= 1
- new_deleteBy01(ww41, Float(Pos(Zero), Pos(Succ(ww40100))), Float(Neg(Zero), Pos(Succ(Zero)))) → new_deleteBy6(ww41)
The graph contains the following edges 1 >= 1
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_deleteBy2(:(ww410, ww411)) → new_deleteBy01(ww411, ww410, Float(Pos(Zero), Pos(Succ(Zero))))
new_deleteBy01(ww41, Float(Neg(Zero), Neg(Succ(ww40100))), Float(Pos(Zero), Pos(Succ(Zero)))) → new_deleteBy2(ww41)
new_deleteBy01(ww41, Float(Neg(Zero), Pos(Succ(ww40100))), Float(Pos(Zero), Pos(Succ(Zero)))) → new_deleteBy2(ww41)
new_deleteBy01(ww41, Float(Pos(Zero), Neg(Succ(ww40100))), Float(Pos(Zero), Pos(Succ(Zero)))) → new_deleteBy2(ww41)
new_deleteBy01(ww41, Float(Neg(Succ(ww40000)), Neg(Succ(ww40100))), Float(Pos(Zero), Pos(Succ(Zero)))) → new_deleteBy2(ww41)
new_deleteBy01(ww41, Float(Neg(Succ(ww40000)), Pos(Succ(ww40100))), Float(Pos(Zero), Pos(Succ(Zero)))) → new_deleteBy2(ww41)
new_deleteBy01(ww41, Float(Pos(Succ(ww40000)), Neg(Succ(ww40100))), Float(Pos(Zero), Pos(Succ(Zero)))) → new_deleteBy2(ww41)
new_deleteBy01(ww41, Float(Pos(Zero), Pos(Succ(ww40100))), Float(Pos(Zero), Pos(Succ(Zero)))) → new_deleteBy2(ww41)
new_deleteBy01(:(ww410, ww411), Float(Pos(Succ(ww40000)), Pos(Succ(ww40100))), Float(Pos(Zero), Pos(Succ(Zero)))) → new_deleteBy01(ww411, ww410, Float(Pos(Zero), Pos(Succ(Zero))))
The TRS R consists of the following rules:
new_primPlusNat1(Zero, ww40000) → Succ(ww40000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, ww40000) → Zero
new_primPlusNat1(Succ(ww520), ww40000) → Succ(Succ(new_primPlusNat0(ww520, ww40000)))
new_primPlusNat0(Succ(ww5200), Zero) → Succ(ww5200)
new_primPlusNat0(Zero, Succ(ww400000)) → Succ(ww400000)
new_primPlusNat0(Succ(ww5200), Succ(ww400000)) → Succ(Succ(new_primPlusNat0(ww5200, ww400000)))
new_primMulNat0(Succ(ww30000), ww40000) → new_primPlusNat1(new_primMulNat0(ww30000, ww40000), ww40000)
The set Q consists of the following terms:
new_primMulNat0(Succ(x0), x1)
new_primMulNat0(Zero, x0)
new_primPlusNat1(Succ(x0), x1)
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
We have to consider all minimal (P,Q,R)-chains.
As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [15] we can delete all non-usable rules [17] from R.
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QReductionProof
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_deleteBy2(:(ww410, ww411)) → new_deleteBy01(ww411, ww410, Float(Pos(Zero), Pos(Succ(Zero))))
new_deleteBy01(ww41, Float(Neg(Zero), Neg(Succ(ww40100))), Float(Pos(Zero), Pos(Succ(Zero)))) → new_deleteBy2(ww41)
new_deleteBy01(ww41, Float(Neg(Zero), Pos(Succ(ww40100))), Float(Pos(Zero), Pos(Succ(Zero)))) → new_deleteBy2(ww41)
new_deleteBy01(ww41, Float(Pos(Zero), Neg(Succ(ww40100))), Float(Pos(Zero), Pos(Succ(Zero)))) → new_deleteBy2(ww41)
new_deleteBy01(ww41, Float(Neg(Succ(ww40000)), Neg(Succ(ww40100))), Float(Pos(Zero), Pos(Succ(Zero)))) → new_deleteBy2(ww41)
new_deleteBy01(ww41, Float(Neg(Succ(ww40000)), Pos(Succ(ww40100))), Float(Pos(Zero), Pos(Succ(Zero)))) → new_deleteBy2(ww41)
new_deleteBy01(ww41, Float(Pos(Succ(ww40000)), Neg(Succ(ww40100))), Float(Pos(Zero), Pos(Succ(Zero)))) → new_deleteBy2(ww41)
new_deleteBy01(ww41, Float(Pos(Zero), Pos(Succ(ww40100))), Float(Pos(Zero), Pos(Succ(Zero)))) → new_deleteBy2(ww41)
new_deleteBy01(:(ww410, ww411), Float(Pos(Succ(ww40000)), Pos(Succ(ww40100))), Float(Pos(Zero), Pos(Succ(Zero)))) → new_deleteBy01(ww411, ww410, Float(Pos(Zero), Pos(Succ(Zero))))
R is empty.
The set Q consists of the following terms:
new_primMulNat0(Succ(x0), x1)
new_primMulNat0(Zero, x0)
new_primPlusNat1(Succ(x0), x1)
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
We have to consider all minimal (P,Q,R)-chains.
We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.
new_primMulNat0(Succ(x0), x1)
new_primMulNat0(Zero, x0)
new_primPlusNat1(Succ(x0), x1)
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QReductionProof
↳ QDP
↳ QDPSizeChangeProof
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_deleteBy01(ww41, Float(Neg(Zero), Neg(Succ(ww40100))), Float(Pos(Zero), Pos(Succ(Zero)))) → new_deleteBy2(ww41)
new_deleteBy2(:(ww410, ww411)) → new_deleteBy01(ww411, ww410, Float(Pos(Zero), Pos(Succ(Zero))))
new_deleteBy01(ww41, Float(Neg(Succ(ww40000)), Neg(Succ(ww40100))), Float(Pos(Zero), Pos(Succ(Zero)))) → new_deleteBy2(ww41)
new_deleteBy01(ww41, Float(Pos(Zero), Neg(Succ(ww40100))), Float(Pos(Zero), Pos(Succ(Zero)))) → new_deleteBy2(ww41)
new_deleteBy01(ww41, Float(Neg(Zero), Pos(Succ(ww40100))), Float(Pos(Zero), Pos(Succ(Zero)))) → new_deleteBy2(ww41)
new_deleteBy01(ww41, Float(Pos(Succ(ww40000)), Neg(Succ(ww40100))), Float(Pos(Zero), Pos(Succ(Zero)))) → new_deleteBy2(ww41)
new_deleteBy01(ww41, Float(Neg(Succ(ww40000)), Pos(Succ(ww40100))), Float(Pos(Zero), Pos(Succ(Zero)))) → new_deleteBy2(ww41)
new_deleteBy01(ww41, Float(Pos(Zero), Pos(Succ(ww40100))), Float(Pos(Zero), Pos(Succ(Zero)))) → new_deleteBy2(ww41)
new_deleteBy01(:(ww410, ww411), Float(Pos(Succ(ww40000)), Pos(Succ(ww40100))), Float(Pos(Zero), Pos(Succ(Zero)))) → new_deleteBy01(ww411, ww410, Float(Pos(Zero), Pos(Succ(Zero))))
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_deleteBy01(:(ww410, ww411), Float(Pos(Succ(ww40000)), Pos(Succ(ww40100))), Float(Pos(Zero), Pos(Succ(Zero)))) → new_deleteBy01(ww411, ww410, Float(Pos(Zero), Pos(Succ(Zero))))
The graph contains the following edges 1 > 1, 1 > 2, 3 >= 3
- new_deleteBy2(:(ww410, ww411)) → new_deleteBy01(ww411, ww410, Float(Pos(Zero), Pos(Succ(Zero))))
The graph contains the following edges 1 > 1, 1 > 2
- new_deleteBy01(ww41, Float(Neg(Zero), Neg(Succ(ww40100))), Float(Pos(Zero), Pos(Succ(Zero)))) → new_deleteBy2(ww41)
The graph contains the following edges 1 >= 1
- new_deleteBy01(ww41, Float(Neg(Zero), Pos(Succ(ww40100))), Float(Pos(Zero), Pos(Succ(Zero)))) → new_deleteBy2(ww41)
The graph contains the following edges 1 >= 1
- new_deleteBy01(ww41, Float(Pos(Zero), Neg(Succ(ww40100))), Float(Pos(Zero), Pos(Succ(Zero)))) → new_deleteBy2(ww41)
The graph contains the following edges 1 >= 1
- new_deleteBy01(ww41, Float(Neg(Succ(ww40000)), Neg(Succ(ww40100))), Float(Pos(Zero), Pos(Succ(Zero)))) → new_deleteBy2(ww41)
The graph contains the following edges 1 >= 1
- new_deleteBy01(ww41, Float(Neg(Succ(ww40000)), Pos(Succ(ww40100))), Float(Pos(Zero), Pos(Succ(Zero)))) → new_deleteBy2(ww41)
The graph contains the following edges 1 >= 1
- new_deleteBy01(ww41, Float(Pos(Succ(ww40000)), Neg(Succ(ww40100))), Float(Pos(Zero), Pos(Succ(Zero)))) → new_deleteBy2(ww41)
The graph contains the following edges 1 >= 1
- new_deleteBy01(ww41, Float(Pos(Zero), Pos(Succ(ww40100))), Float(Pos(Zero), Pos(Succ(Zero)))) → new_deleteBy2(ww41)
The graph contains the following edges 1 >= 1
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_deleteBy078(ww41, ww40100, Succ(ww2940)) → new_deleteBy12(ww41)
new_deleteBy076(ww41, ww40100, Succ(ww2880)) → new_deleteBy12(ww41)
new_deleteBy093(ww41, ww40000, ww40100, Succ(ww3550)) → new_deleteBy12(ww41)
new_deleteBy01(ww41, Float(Neg(Zero), Pos(Succ(ww40100))), Float(Neg(Zero), Pos(Succ(Succ(Zero))))) → new_deleteBy0101(ww41, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy01(ww41, Float(Pos(Succ(ww40000)), Neg(Succ(ww40100))), Float(Neg(Zero), Pos(Succ(Succ(Zero))))) → new_deleteBy070(ww41, ww40000, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy068(:(ww410, ww411), ww40000, ww40100, Succ(ww2640)) → new_deleteBy01(ww411, ww410, Float(Neg(Zero), Pos(Succ(Succ(Zero)))))
new_deleteBy01(ww41, Float(Neg(Succ(ww40000)), Pos(Succ(ww40100))), Float(Neg(Zero), Pos(Succ(Succ(Zero))))) → new_deleteBy093(ww41, ww40000, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy095(ww41, ww40000, ww40100, Succ(ww3610)) → new_deleteBy12(ww41)
new_deleteBy01(ww41, Float(Pos(Succ(ww40000)), Pos(Succ(ww40100))), Float(Neg(Zero), Pos(Succ(Succ(Zero))))) → new_deleteBy068(ww41, ww40000, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy01(ww41, Float(Neg(Zero), Neg(Succ(ww40100))), Float(Neg(Zero), Pos(Succ(Succ(Zero))))) → new_deleteBy0103(ww41, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy070(ww41, ww40000, ww40100, Succ(ww2700)) → new_deleteBy12(ww41)
new_deleteBy01(ww41, Float(Pos(Zero), Pos(Succ(ww40100))), Float(Neg(Zero), Pos(Succ(Succ(Zero))))) → new_deleteBy076(ww41, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy0101(ww41, ww40100, Succ(ww3790)) → new_deleteBy12(ww41)
new_deleteBy01(ww41, Float(Neg(Succ(ww40000)), Neg(Succ(ww40100))), Float(Neg(Zero), Pos(Succ(Succ(Zero))))) → new_deleteBy095(ww41, ww40000, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy0103(ww41, ww40100, Succ(ww3850)) → new_deleteBy12(ww41)
new_deleteBy01(ww41, Float(Pos(Zero), Neg(Succ(ww40100))), Float(Neg(Zero), Pos(Succ(Succ(Zero))))) → new_deleteBy078(ww41, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy12(:(ww410, ww411)) → new_deleteBy01(ww411, ww410, Float(Neg(Zero), Pos(Succ(Succ(Zero)))))
The TRS R consists of the following rules:
new_primPlusNat1(Zero, ww40000) → Succ(ww40000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, ww40000) → Zero
new_primPlusNat1(Succ(ww520), ww40000) → Succ(Succ(new_primPlusNat0(ww520, ww40000)))
new_primPlusNat0(Succ(ww5200), Zero) → Succ(ww5200)
new_primPlusNat0(Zero, Succ(ww400000)) → Succ(ww400000)
new_primPlusNat0(Succ(ww5200), Succ(ww400000)) → Succ(Succ(new_primPlusNat0(ww5200, ww400000)))
new_primMulNat0(Succ(ww30000), ww40000) → new_primPlusNat1(new_primMulNat0(ww30000, ww40000), ww40000)
The set Q consists of the following terms:
new_primMulNat0(Succ(x0), x1)
new_primMulNat0(Zero, x0)
new_primPlusNat1(Succ(x0), x1)
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
We have to consider all minimal (P,Q,R)-chains.
As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [15] we can delete all non-usable rules [17] from R.
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QReductionProof
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_deleteBy078(ww41, ww40100, Succ(ww2940)) → new_deleteBy12(ww41)
new_deleteBy076(ww41, ww40100, Succ(ww2880)) → new_deleteBy12(ww41)
new_deleteBy093(ww41, ww40000, ww40100, Succ(ww3550)) → new_deleteBy12(ww41)
new_deleteBy01(ww41, Float(Neg(Zero), Pos(Succ(ww40100))), Float(Neg(Zero), Pos(Succ(Succ(Zero))))) → new_deleteBy0101(ww41, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy01(ww41, Float(Pos(Succ(ww40000)), Neg(Succ(ww40100))), Float(Neg(Zero), Pos(Succ(Succ(Zero))))) → new_deleteBy070(ww41, ww40000, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy068(:(ww410, ww411), ww40000, ww40100, Succ(ww2640)) → new_deleteBy01(ww411, ww410, Float(Neg(Zero), Pos(Succ(Succ(Zero)))))
new_deleteBy01(ww41, Float(Neg(Succ(ww40000)), Pos(Succ(ww40100))), Float(Neg(Zero), Pos(Succ(Succ(Zero))))) → new_deleteBy093(ww41, ww40000, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy095(ww41, ww40000, ww40100, Succ(ww3610)) → new_deleteBy12(ww41)
new_deleteBy01(ww41, Float(Pos(Succ(ww40000)), Pos(Succ(ww40100))), Float(Neg(Zero), Pos(Succ(Succ(Zero))))) → new_deleteBy068(ww41, ww40000, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy01(ww41, Float(Neg(Zero), Neg(Succ(ww40100))), Float(Neg(Zero), Pos(Succ(Succ(Zero))))) → new_deleteBy0103(ww41, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy070(ww41, ww40000, ww40100, Succ(ww2700)) → new_deleteBy12(ww41)
new_deleteBy01(ww41, Float(Pos(Zero), Pos(Succ(ww40100))), Float(Neg(Zero), Pos(Succ(Succ(Zero))))) → new_deleteBy076(ww41, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy0101(ww41, ww40100, Succ(ww3790)) → new_deleteBy12(ww41)
new_deleteBy01(ww41, Float(Neg(Succ(ww40000)), Neg(Succ(ww40100))), Float(Neg(Zero), Pos(Succ(Succ(Zero))))) → new_deleteBy095(ww41, ww40000, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy0103(ww41, ww40100, Succ(ww3850)) → new_deleteBy12(ww41)
new_deleteBy01(ww41, Float(Pos(Zero), Neg(Succ(ww40100))), Float(Neg(Zero), Pos(Succ(Succ(Zero))))) → new_deleteBy078(ww41, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy12(:(ww410, ww411)) → new_deleteBy01(ww411, ww410, Float(Neg(Zero), Pos(Succ(Succ(Zero)))))
The TRS R consists of the following rules:
new_primPlusNat0(Zero, Succ(ww400000)) → Succ(ww400000)
new_primPlusNat0(Succ(ww5200), Succ(ww400000)) → Succ(Succ(new_primPlusNat0(ww5200, ww400000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(ww5200), Zero) → Succ(ww5200)
The set Q consists of the following terms:
new_primMulNat0(Succ(x0), x1)
new_primMulNat0(Zero, x0)
new_primPlusNat1(Succ(x0), x1)
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
We have to consider all minimal (P,Q,R)-chains.
We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.
new_primMulNat0(Succ(x0), x1)
new_primMulNat0(Zero, x0)
new_primPlusNat1(Succ(x0), x1)
new_primPlusNat1(Zero, x0)
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QReductionProof
↳ QDP
↳ QDPSizeChangeProof
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_deleteBy078(ww41, ww40100, Succ(ww2940)) → new_deleteBy12(ww41)
new_deleteBy076(ww41, ww40100, Succ(ww2880)) → new_deleteBy12(ww41)
new_deleteBy093(ww41, ww40000, ww40100, Succ(ww3550)) → new_deleteBy12(ww41)
new_deleteBy01(ww41, Float(Neg(Zero), Pos(Succ(ww40100))), Float(Neg(Zero), Pos(Succ(Succ(Zero))))) → new_deleteBy0101(ww41, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy01(ww41, Float(Pos(Succ(ww40000)), Neg(Succ(ww40100))), Float(Neg(Zero), Pos(Succ(Succ(Zero))))) → new_deleteBy070(ww41, ww40000, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy068(:(ww410, ww411), ww40000, ww40100, Succ(ww2640)) → new_deleteBy01(ww411, ww410, Float(Neg(Zero), Pos(Succ(Succ(Zero)))))
new_deleteBy01(ww41, Float(Neg(Succ(ww40000)), Pos(Succ(ww40100))), Float(Neg(Zero), Pos(Succ(Succ(Zero))))) → new_deleteBy093(ww41, ww40000, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy095(ww41, ww40000, ww40100, Succ(ww3610)) → new_deleteBy12(ww41)
new_deleteBy01(ww41, Float(Pos(Succ(ww40000)), Pos(Succ(ww40100))), Float(Neg(Zero), Pos(Succ(Succ(Zero))))) → new_deleteBy068(ww41, ww40000, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy01(ww41, Float(Neg(Zero), Neg(Succ(ww40100))), Float(Neg(Zero), Pos(Succ(Succ(Zero))))) → new_deleteBy0103(ww41, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy070(ww41, ww40000, ww40100, Succ(ww2700)) → new_deleteBy12(ww41)
new_deleteBy01(ww41, Float(Pos(Zero), Pos(Succ(ww40100))), Float(Neg(Zero), Pos(Succ(Succ(Zero))))) → new_deleteBy076(ww41, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy0101(ww41, ww40100, Succ(ww3790)) → new_deleteBy12(ww41)
new_deleteBy0103(ww41, ww40100, Succ(ww3850)) → new_deleteBy12(ww41)
new_deleteBy01(ww41, Float(Neg(Succ(ww40000)), Neg(Succ(ww40100))), Float(Neg(Zero), Pos(Succ(Succ(Zero))))) → new_deleteBy095(ww41, ww40000, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy01(ww41, Float(Pos(Zero), Neg(Succ(ww40100))), Float(Neg(Zero), Pos(Succ(Succ(Zero))))) → new_deleteBy078(ww41, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy12(:(ww410, ww411)) → new_deleteBy01(ww411, ww410, Float(Neg(Zero), Pos(Succ(Succ(Zero)))))
The TRS R consists of the following rules:
new_primPlusNat0(Zero, Succ(ww400000)) → Succ(ww400000)
new_primPlusNat0(Succ(ww5200), Succ(ww400000)) → Succ(Succ(new_primPlusNat0(ww5200, ww400000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(ww5200), Zero) → Succ(ww5200)
The set Q consists of the following terms:
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), Zero)
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_deleteBy12(:(ww410, ww411)) → new_deleteBy01(ww411, ww410, Float(Neg(Zero), Pos(Succ(Succ(Zero)))))
The graph contains the following edges 1 > 1, 1 > 2
- new_deleteBy01(ww41, Float(Pos(Zero), Neg(Succ(ww40100))), Float(Neg(Zero), Pos(Succ(Succ(Zero))))) → new_deleteBy078(ww41, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
The graph contains the following edges 1 >= 1, 2 > 2
- new_deleteBy01(ww41, Float(Pos(Zero), Pos(Succ(ww40100))), Float(Neg(Zero), Pos(Succ(Succ(Zero))))) → new_deleteBy076(ww41, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
The graph contains the following edges 1 >= 1, 2 > 2
- new_deleteBy01(ww41, Float(Neg(Succ(ww40000)), Pos(Succ(ww40100))), Float(Neg(Zero), Pos(Succ(Succ(Zero))))) → new_deleteBy093(ww41, ww40000, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
The graph contains the following edges 1 >= 1, 2 > 2, 2 > 3
- new_deleteBy0101(ww41, ww40100, Succ(ww3790)) → new_deleteBy12(ww41)
The graph contains the following edges 1 >= 1
- new_deleteBy068(:(ww410, ww411), ww40000, ww40100, Succ(ww2640)) → new_deleteBy01(ww411, ww410, Float(Neg(Zero), Pos(Succ(Succ(Zero)))))
The graph contains the following edges 1 > 1, 1 > 2
- new_deleteBy070(ww41, ww40000, ww40100, Succ(ww2700)) → new_deleteBy12(ww41)
The graph contains the following edges 1 >= 1
- new_deleteBy01(ww41, Float(Pos(Succ(ww40000)), Pos(Succ(ww40100))), Float(Neg(Zero), Pos(Succ(Succ(Zero))))) → new_deleteBy068(ww41, ww40000, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
The graph contains the following edges 1 >= 1, 2 > 2, 2 > 3
- new_deleteBy093(ww41, ww40000, ww40100, Succ(ww3550)) → new_deleteBy12(ww41)
The graph contains the following edges 1 >= 1
- new_deleteBy01(ww41, Float(Neg(Succ(ww40000)), Neg(Succ(ww40100))), Float(Neg(Zero), Pos(Succ(Succ(Zero))))) → new_deleteBy095(ww41, ww40000, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
The graph contains the following edges 1 >= 1, 2 > 2, 2 > 3
- new_deleteBy0103(ww41, ww40100, Succ(ww3850)) → new_deleteBy12(ww41)
The graph contains the following edges 1 >= 1
- new_deleteBy01(ww41, Float(Pos(Succ(ww40000)), Neg(Succ(ww40100))), Float(Neg(Zero), Pos(Succ(Succ(Zero))))) → new_deleteBy070(ww41, ww40000, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
The graph contains the following edges 1 >= 1, 2 > 2, 2 > 3
- new_deleteBy076(ww41, ww40100, Succ(ww2880)) → new_deleteBy12(ww41)
The graph contains the following edges 1 >= 1
- new_deleteBy01(ww41, Float(Neg(Zero), Pos(Succ(ww40100))), Float(Neg(Zero), Pos(Succ(Succ(Zero))))) → new_deleteBy0101(ww41, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
The graph contains the following edges 1 >= 1, 2 > 2
- new_deleteBy01(ww41, Float(Neg(Zero), Neg(Succ(ww40100))), Float(Neg(Zero), Pos(Succ(Succ(Zero))))) → new_deleteBy0103(ww41, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
The graph contains the following edges 1 >= 1, 2 > 2
- new_deleteBy095(ww41, ww40000, ww40100, Succ(ww3610)) → new_deleteBy12(ww41)
The graph contains the following edges 1 >= 1
- new_deleteBy078(ww41, ww40100, Succ(ww2940)) → new_deleteBy12(ww41)
The graph contains the following edges 1 >= 1
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_deleteBy01(ww41, Float(Neg(Succ(ww40000)), Pos(Succ(ww40100))), Float(Pos(Zero), Pos(Succ(Succ(Zero))))) → new_deleteBy043(ww41, ww40000, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy01(ww41, Float(Neg(Succ(ww40000)), Neg(Succ(ww40100))), Float(Pos(Zero), Pos(Succ(Succ(Zero))))) → new_deleteBy045(ww41, ww40000, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy018(ww41, ww40000, ww40100, Succ(ww720)) → new_deleteBy0108(ww41, Float(Pos(Succ(ww40000)), Pos(Succ(ww40100))))
new_deleteBy0108(:(ww4070, ww4071), ww408) → new_deleteBy01(ww4071, ww4070, Float(Pos(Zero), Pos(Succ(Succ(Zero)))))
new_deleteBy01(ww41, Float(Pos(Succ(ww40000)), Pos(Succ(ww40100))), Float(Pos(Zero), Pos(Succ(Succ(Zero))))) → new_deleteBy018(ww41, ww40000, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy01(ww41, Float(Neg(Zero), Neg(Succ(ww40100))), Float(Pos(Zero), Pos(Succ(Succ(Zero))))) → new_deleteBy053(ww41, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy026(ww41, ww40100, Succ(ww1080)) → new_deleteBy0108(ww41, Float(Pos(Zero), Pos(Succ(ww40100))))
new_deleteBy028(ww41, ww40100, Succ(ww1140)) → new_deleteBy0108(ww41, Float(Pos(Zero), Neg(Succ(ww40100))))
new_deleteBy045(ww41, ww40000, ww40100, Succ(ww1810)) → new_deleteBy0108(ww41, Float(Neg(Succ(ww40000)), Neg(Succ(ww40100))))
new_deleteBy043(ww41, ww40000, ww40100, Succ(ww1750)) → new_deleteBy0108(ww41, Float(Neg(Succ(ww40000)), Pos(Succ(ww40100))))
new_deleteBy051(ww41, ww40100, Succ(ww1990)) → new_deleteBy0108(ww41, Float(Neg(Zero), Pos(Succ(ww40100))))
new_deleteBy01(ww41, Float(Pos(Succ(ww40000)), Neg(Succ(ww40100))), Float(Pos(Zero), Pos(Succ(Succ(Zero))))) → new_deleteBy020(ww41, ww40000, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy01(ww41, Float(Pos(Zero), Pos(Succ(ww40100))), Float(Pos(Zero), Pos(Succ(Succ(Zero))))) → new_deleteBy026(ww41, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy053(ww41, ww40100, Succ(ww2050)) → new_deleteBy0108(ww41, Float(Neg(Zero), Neg(Succ(ww40100))))
new_deleteBy01(ww41, Float(Neg(Zero), Pos(Succ(ww40100))), Float(Pos(Zero), Pos(Succ(Succ(Zero))))) → new_deleteBy051(ww41, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy020(ww41, ww40000, ww40100, Succ(ww900)) → new_deleteBy0108(ww41, Float(Pos(Succ(ww40000)), Neg(Succ(ww40100))))
new_deleteBy01(ww41, Float(Pos(Zero), Neg(Succ(ww40100))), Float(Pos(Zero), Pos(Succ(Succ(Zero))))) → new_deleteBy028(ww41, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
The TRS R consists of the following rules:
new_primPlusNat1(Zero, ww40000) → Succ(ww40000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, ww40000) → Zero
new_primPlusNat1(Succ(ww520), ww40000) → Succ(Succ(new_primPlusNat0(ww520, ww40000)))
new_primPlusNat0(Succ(ww5200), Zero) → Succ(ww5200)
new_primPlusNat0(Zero, Succ(ww400000)) → Succ(ww400000)
new_primPlusNat0(Succ(ww5200), Succ(ww400000)) → Succ(Succ(new_primPlusNat0(ww5200, ww400000)))
new_primMulNat0(Succ(ww30000), ww40000) → new_primPlusNat1(new_primMulNat0(ww30000, ww40000), ww40000)
The set Q consists of the following terms:
new_primMulNat0(Succ(x0), x1)
new_primMulNat0(Zero, x0)
new_primPlusNat1(Succ(x0), x1)
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
We have to consider all minimal (P,Q,R)-chains.
As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [15] we can delete all non-usable rules [17] from R.
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QReductionProof
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_deleteBy01(ww41, Float(Neg(Succ(ww40000)), Pos(Succ(ww40100))), Float(Pos(Zero), Pos(Succ(Succ(Zero))))) → new_deleteBy043(ww41, ww40000, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy01(ww41, Float(Neg(Succ(ww40000)), Neg(Succ(ww40100))), Float(Pos(Zero), Pos(Succ(Succ(Zero))))) → new_deleteBy045(ww41, ww40000, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy018(ww41, ww40000, ww40100, Succ(ww720)) → new_deleteBy0108(ww41, Float(Pos(Succ(ww40000)), Pos(Succ(ww40100))))
new_deleteBy0108(:(ww4070, ww4071), ww408) → new_deleteBy01(ww4071, ww4070, Float(Pos(Zero), Pos(Succ(Succ(Zero)))))
new_deleteBy01(ww41, Float(Pos(Succ(ww40000)), Pos(Succ(ww40100))), Float(Pos(Zero), Pos(Succ(Succ(Zero))))) → new_deleteBy018(ww41, ww40000, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy01(ww41, Float(Neg(Zero), Neg(Succ(ww40100))), Float(Pos(Zero), Pos(Succ(Succ(Zero))))) → new_deleteBy053(ww41, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy026(ww41, ww40100, Succ(ww1080)) → new_deleteBy0108(ww41, Float(Pos(Zero), Pos(Succ(ww40100))))
new_deleteBy028(ww41, ww40100, Succ(ww1140)) → new_deleteBy0108(ww41, Float(Pos(Zero), Neg(Succ(ww40100))))
new_deleteBy045(ww41, ww40000, ww40100, Succ(ww1810)) → new_deleteBy0108(ww41, Float(Neg(Succ(ww40000)), Neg(Succ(ww40100))))
new_deleteBy043(ww41, ww40000, ww40100, Succ(ww1750)) → new_deleteBy0108(ww41, Float(Neg(Succ(ww40000)), Pos(Succ(ww40100))))
new_deleteBy051(ww41, ww40100, Succ(ww1990)) → new_deleteBy0108(ww41, Float(Neg(Zero), Pos(Succ(ww40100))))
new_deleteBy01(ww41, Float(Pos(Succ(ww40000)), Neg(Succ(ww40100))), Float(Pos(Zero), Pos(Succ(Succ(Zero))))) → new_deleteBy020(ww41, ww40000, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy01(ww41, Float(Pos(Zero), Pos(Succ(ww40100))), Float(Pos(Zero), Pos(Succ(Succ(Zero))))) → new_deleteBy026(ww41, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy053(ww41, ww40100, Succ(ww2050)) → new_deleteBy0108(ww41, Float(Neg(Zero), Neg(Succ(ww40100))))
new_deleteBy01(ww41, Float(Neg(Zero), Pos(Succ(ww40100))), Float(Pos(Zero), Pos(Succ(Succ(Zero))))) → new_deleteBy051(ww41, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy020(ww41, ww40000, ww40100, Succ(ww900)) → new_deleteBy0108(ww41, Float(Pos(Succ(ww40000)), Neg(Succ(ww40100))))
new_deleteBy01(ww41, Float(Pos(Zero), Neg(Succ(ww40100))), Float(Pos(Zero), Pos(Succ(Succ(Zero))))) → new_deleteBy028(ww41, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
The TRS R consists of the following rules:
new_primPlusNat0(Zero, Succ(ww400000)) → Succ(ww400000)
new_primPlusNat0(Succ(ww5200), Succ(ww400000)) → Succ(Succ(new_primPlusNat0(ww5200, ww400000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(ww5200), Zero) → Succ(ww5200)
The set Q consists of the following terms:
new_primMulNat0(Succ(x0), x1)
new_primMulNat0(Zero, x0)
new_primPlusNat1(Succ(x0), x1)
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
We have to consider all minimal (P,Q,R)-chains.
We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.
new_primMulNat0(Succ(x0), x1)
new_primMulNat0(Zero, x0)
new_primPlusNat1(Succ(x0), x1)
new_primPlusNat1(Zero, x0)
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QReductionProof
↳ QDP
↳ QDPSizeChangeProof
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_deleteBy01(ww41, Float(Neg(Succ(ww40000)), Pos(Succ(ww40100))), Float(Pos(Zero), Pos(Succ(Succ(Zero))))) → new_deleteBy043(ww41, ww40000, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy01(ww41, Float(Neg(Succ(ww40000)), Neg(Succ(ww40100))), Float(Pos(Zero), Pos(Succ(Succ(Zero))))) → new_deleteBy045(ww41, ww40000, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy018(ww41, ww40000, ww40100, Succ(ww720)) → new_deleteBy0108(ww41, Float(Pos(Succ(ww40000)), Pos(Succ(ww40100))))
new_deleteBy0108(:(ww4070, ww4071), ww408) → new_deleteBy01(ww4071, ww4070, Float(Pos(Zero), Pos(Succ(Succ(Zero)))))
new_deleteBy01(ww41, Float(Pos(Succ(ww40000)), Pos(Succ(ww40100))), Float(Pos(Zero), Pos(Succ(Succ(Zero))))) → new_deleteBy018(ww41, ww40000, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy01(ww41, Float(Neg(Zero), Neg(Succ(ww40100))), Float(Pos(Zero), Pos(Succ(Succ(Zero))))) → new_deleteBy053(ww41, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy026(ww41, ww40100, Succ(ww1080)) → new_deleteBy0108(ww41, Float(Pos(Zero), Pos(Succ(ww40100))))
new_deleteBy028(ww41, ww40100, Succ(ww1140)) → new_deleteBy0108(ww41, Float(Pos(Zero), Neg(Succ(ww40100))))
new_deleteBy045(ww41, ww40000, ww40100, Succ(ww1810)) → new_deleteBy0108(ww41, Float(Neg(Succ(ww40000)), Neg(Succ(ww40100))))
new_deleteBy043(ww41, ww40000, ww40100, Succ(ww1750)) → new_deleteBy0108(ww41, Float(Neg(Succ(ww40000)), Pos(Succ(ww40100))))
new_deleteBy051(ww41, ww40100, Succ(ww1990)) → new_deleteBy0108(ww41, Float(Neg(Zero), Pos(Succ(ww40100))))
new_deleteBy01(ww41, Float(Pos(Succ(ww40000)), Neg(Succ(ww40100))), Float(Pos(Zero), Pos(Succ(Succ(Zero))))) → new_deleteBy020(ww41, ww40000, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy053(ww41, ww40100, Succ(ww2050)) → new_deleteBy0108(ww41, Float(Neg(Zero), Neg(Succ(ww40100))))
new_deleteBy01(ww41, Float(Pos(Zero), Pos(Succ(ww40100))), Float(Pos(Zero), Pos(Succ(Succ(Zero))))) → new_deleteBy026(ww41, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy01(ww41, Float(Neg(Zero), Pos(Succ(ww40100))), Float(Pos(Zero), Pos(Succ(Succ(Zero))))) → new_deleteBy051(ww41, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy020(ww41, ww40000, ww40100, Succ(ww900)) → new_deleteBy0108(ww41, Float(Pos(Succ(ww40000)), Neg(Succ(ww40100))))
new_deleteBy01(ww41, Float(Pos(Zero), Neg(Succ(ww40100))), Float(Pos(Zero), Pos(Succ(Succ(Zero))))) → new_deleteBy028(ww41, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
The TRS R consists of the following rules:
new_primPlusNat0(Zero, Succ(ww400000)) → Succ(ww400000)
new_primPlusNat0(Succ(ww5200), Succ(ww400000)) → Succ(Succ(new_primPlusNat0(ww5200, ww400000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(ww5200), Zero) → Succ(ww5200)
The set Q consists of the following terms:
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), Zero)
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_deleteBy043(ww41, ww40000, ww40100, Succ(ww1750)) → new_deleteBy0108(ww41, Float(Neg(Succ(ww40000)), Pos(Succ(ww40100))))
The graph contains the following edges 1 >= 1
- new_deleteBy0108(:(ww4070, ww4071), ww408) → new_deleteBy01(ww4071, ww4070, Float(Pos(Zero), Pos(Succ(Succ(Zero)))))
The graph contains the following edges 1 > 1, 1 > 2
- new_deleteBy045(ww41, ww40000, ww40100, Succ(ww1810)) → new_deleteBy0108(ww41, Float(Neg(Succ(ww40000)), Neg(Succ(ww40100))))
The graph contains the following edges 1 >= 1
- new_deleteBy01(ww41, Float(Pos(Succ(ww40000)), Pos(Succ(ww40100))), Float(Pos(Zero), Pos(Succ(Succ(Zero))))) → new_deleteBy018(ww41, ww40000, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
The graph contains the following edges 1 >= 1, 2 > 2, 2 > 3
- new_deleteBy018(ww41, ww40000, ww40100, Succ(ww720)) → new_deleteBy0108(ww41, Float(Pos(Succ(ww40000)), Pos(Succ(ww40100))))
The graph contains the following edges 1 >= 1
- new_deleteBy053(ww41, ww40100, Succ(ww2050)) → new_deleteBy0108(ww41, Float(Neg(Zero), Neg(Succ(ww40100))))
The graph contains the following edges 1 >= 1
- new_deleteBy01(ww41, Float(Pos(Zero), Pos(Succ(ww40100))), Float(Pos(Zero), Pos(Succ(Succ(Zero))))) → new_deleteBy026(ww41, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
The graph contains the following edges 1 >= 1, 2 > 2
- new_deleteBy01(ww41, Float(Pos(Zero), Neg(Succ(ww40100))), Float(Pos(Zero), Pos(Succ(Succ(Zero))))) → new_deleteBy028(ww41, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
The graph contains the following edges 1 >= 1, 2 > 2
- new_deleteBy01(ww41, Float(Neg(Succ(ww40000)), Neg(Succ(ww40100))), Float(Pos(Zero), Pos(Succ(Succ(Zero))))) → new_deleteBy045(ww41, ww40000, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
The graph contains the following edges 1 >= 1, 2 > 2, 2 > 3
- new_deleteBy01(ww41, Float(Neg(Succ(ww40000)), Pos(Succ(ww40100))), Float(Pos(Zero), Pos(Succ(Succ(Zero))))) → new_deleteBy043(ww41, ww40000, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
The graph contains the following edges 1 >= 1, 2 > 2, 2 > 3
- new_deleteBy01(ww41, Float(Neg(Zero), Pos(Succ(ww40100))), Float(Pos(Zero), Pos(Succ(Succ(Zero))))) → new_deleteBy051(ww41, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
The graph contains the following edges 1 >= 1, 2 > 2
- new_deleteBy020(ww41, ww40000, ww40100, Succ(ww900)) → new_deleteBy0108(ww41, Float(Pos(Succ(ww40000)), Neg(Succ(ww40100))))
The graph contains the following edges 1 >= 1
- new_deleteBy026(ww41, ww40100, Succ(ww1080)) → new_deleteBy0108(ww41, Float(Pos(Zero), Pos(Succ(ww40100))))
The graph contains the following edges 1 >= 1
- new_deleteBy01(ww41, Float(Neg(Zero), Neg(Succ(ww40100))), Float(Pos(Zero), Pos(Succ(Succ(Zero))))) → new_deleteBy053(ww41, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
The graph contains the following edges 1 >= 1, 2 > 2
- new_deleteBy01(ww41, Float(Pos(Succ(ww40000)), Neg(Succ(ww40100))), Float(Pos(Zero), Pos(Succ(Succ(Zero))))) → new_deleteBy020(ww41, ww40000, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
The graph contains the following edges 1 >= 1, 2 > 2, 2 > 3
- new_deleteBy051(ww41, ww40100, Succ(ww1990)) → new_deleteBy0108(ww41, Float(Neg(Zero), Pos(Succ(ww40100))))
The graph contains the following edges 1 >= 1
- new_deleteBy028(ww41, ww40100, Succ(ww1140)) → new_deleteBy0108(ww41, Float(Pos(Zero), Neg(Succ(ww40100))))
The graph contains the following edges 1 >= 1
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDPSizeChangeProof
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_deleteBy01(ww41, Float(Pos(Succ(ww40000)), Pos(Succ(ww40100))), Float(Neg(Zero), Pos(Succ(Succ(Succ(ww310000)))))) → new_deleteBy067(ww41, ww40000, ww40100, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
new_deleteBy092(ww41, ww40000, ww40100, ww310000, Succ(ww3510)) → new_deleteBy11(ww310000, ww41)
new_deleteBy0100(ww41, ww40100, ww310000, Succ(ww3750)) → new_deleteBy11(ww310000, ww41)
new_deleteBy094(ww41, ww40000, ww40100, ww310000, Succ(ww3570)) → new_deleteBy11(ww310000, ww41)
new_deleteBy075(ww41, ww40100, ww310000, Succ(ww2840)) → new_deleteBy11(ww310000, ww41)
new_deleteBy01(ww41, Float(Neg(Zero), Pos(Succ(ww40100))), Float(Neg(Zero), Pos(Succ(Succ(Succ(ww310000)))))) → new_deleteBy0100(ww41, ww40100, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
new_deleteBy01(ww41, Float(Pos(Succ(ww40000)), Neg(Succ(ww40100))), Float(Neg(Zero), Pos(Succ(Succ(Succ(ww310000)))))) → new_deleteBy069(ww41, ww40000, ww40100, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
new_deleteBy067(:(ww410, ww411), ww40000, ww40100, ww310000, Succ(ww2600)) → new_deleteBy01(ww411, ww410, Float(Neg(Zero), Pos(Succ(Succ(Succ(ww310000))))))
new_deleteBy01(ww41, Float(Pos(Zero), Neg(Succ(ww40100))), Float(Neg(Zero), Pos(Succ(Succ(Succ(ww310000)))))) → new_deleteBy077(ww41, ww40100, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
new_deleteBy01(ww41, Float(Neg(Zero), Neg(Succ(ww40100))), Float(Neg(Zero), Pos(Succ(Succ(Succ(ww310000)))))) → new_deleteBy0102(ww41, ww40100, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
new_deleteBy01(ww41, Float(Pos(Zero), Pos(Succ(ww40100))), Float(Neg(Zero), Pos(Succ(Succ(Succ(ww310000)))))) → new_deleteBy075(ww41, ww40100, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
new_deleteBy077(ww41, ww40100, ww310000, Succ(ww2900)) → new_deleteBy11(ww310000, ww41)
new_deleteBy01(ww41, Float(Neg(Succ(ww40000)), Pos(Succ(ww40100))), Float(Neg(Zero), Pos(Succ(Succ(Succ(ww310000)))))) → new_deleteBy092(ww41, ww40000, ww40100, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
new_deleteBy01(ww41, Float(Neg(Succ(ww40000)), Neg(Succ(ww40100))), Float(Neg(Zero), Pos(Succ(Succ(Succ(ww310000)))))) → new_deleteBy094(ww41, ww40000, ww40100, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
new_deleteBy0102(ww41, ww40100, ww310000, Succ(ww3810)) → new_deleteBy11(ww310000, ww41)
new_deleteBy11(ww310000, :(ww410, ww411)) → new_deleteBy01(ww411, ww410, Float(Neg(Zero), Pos(Succ(Succ(Succ(ww310000))))))
new_deleteBy069(ww41, ww40000, ww40100, ww310000, Succ(ww2660)) → new_deleteBy11(ww310000, ww41)
The TRS R consists of the following rules:
new_primPlusNat1(Zero, ww40000) → Succ(ww40000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, ww40000) → Zero
new_primPlusNat1(Succ(ww520), ww40000) → Succ(Succ(new_primPlusNat0(ww520, ww40000)))
new_primPlusNat0(Succ(ww5200), Zero) → Succ(ww5200)
new_primPlusNat0(Zero, Succ(ww400000)) → Succ(ww400000)
new_primPlusNat0(Succ(ww5200), Succ(ww400000)) → Succ(Succ(new_primPlusNat0(ww5200, ww400000)))
new_primMulNat0(Succ(ww30000), ww40000) → new_primPlusNat1(new_primMulNat0(ww30000, ww40000), ww40000)
The set Q consists of the following terms:
new_primMulNat0(Succ(x0), x1)
new_primMulNat0(Zero, x0)
new_primPlusNat1(Succ(x0), x1)
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
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_deleteBy069(ww41, ww40000, ww40100, ww310000, Succ(ww2660)) → new_deleteBy11(ww310000, ww41)
The graph contains the following edges 4 >= 1, 1 >= 2
- new_deleteBy01(ww41, Float(Pos(Succ(ww40000)), Neg(Succ(ww40100))), Float(Neg(Zero), Pos(Succ(Succ(Succ(ww310000)))))) → new_deleteBy069(ww41, ww40000, ww40100, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
The graph contains the following edges 1 >= 1, 2 > 2, 2 > 3, 3 > 4
- new_deleteBy11(ww310000, :(ww410, ww411)) → new_deleteBy01(ww411, ww410, Float(Neg(Zero), Pos(Succ(Succ(Succ(ww310000))))))
The graph contains the following edges 2 > 1, 2 > 2
- new_deleteBy067(:(ww410, ww411), ww40000, ww40100, ww310000, Succ(ww2600)) → new_deleteBy01(ww411, ww410, Float(Neg(Zero), Pos(Succ(Succ(Succ(ww310000))))))
The graph contains the following edges 1 > 1, 1 > 2
- new_deleteBy0100(ww41, ww40100, ww310000, Succ(ww3750)) → new_deleteBy11(ww310000, ww41)
The graph contains the following edges 3 >= 1, 1 >= 2
- new_deleteBy01(ww41, Float(Neg(Zero), Pos(Succ(ww40100))), Float(Neg(Zero), Pos(Succ(Succ(Succ(ww310000)))))) → new_deleteBy0100(ww41, ww40100, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
The graph contains the following edges 1 >= 1, 2 > 2, 3 > 3
- new_deleteBy077(ww41, ww40100, ww310000, Succ(ww2900)) → new_deleteBy11(ww310000, ww41)
The graph contains the following edges 3 >= 1, 1 >= 2
- new_deleteBy01(ww41, Float(Pos(Zero), Neg(Succ(ww40100))), Float(Neg(Zero), Pos(Succ(Succ(Succ(ww310000)))))) → new_deleteBy077(ww41, ww40100, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
The graph contains the following edges 1 >= 1, 2 > 2, 3 > 3
- new_deleteBy01(ww41, Float(Pos(Succ(ww40000)), Pos(Succ(ww40100))), Float(Neg(Zero), Pos(Succ(Succ(Succ(ww310000)))))) → new_deleteBy067(ww41, ww40000, ww40100, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
The graph contains the following edges 1 >= 1, 2 > 2, 2 > 3, 3 > 4
- new_deleteBy075(ww41, ww40100, ww310000, Succ(ww2840)) → new_deleteBy11(ww310000, ww41)
The graph contains the following edges 3 >= 1, 1 >= 2
- new_deleteBy01(ww41, Float(Pos(Zero), Pos(Succ(ww40100))), Float(Neg(Zero), Pos(Succ(Succ(Succ(ww310000)))))) → new_deleteBy075(ww41, ww40100, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
The graph contains the following edges 1 >= 1, 2 > 2, 3 > 3
- new_deleteBy0102(ww41, ww40100, ww310000, Succ(ww3810)) → new_deleteBy11(ww310000, ww41)
The graph contains the following edges 3 >= 1, 1 >= 2
- new_deleteBy01(ww41, Float(Neg(Zero), Neg(Succ(ww40100))), Float(Neg(Zero), Pos(Succ(Succ(Succ(ww310000)))))) → new_deleteBy0102(ww41, ww40100, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
The graph contains the following edges 1 >= 1, 2 > 2, 3 > 3
- new_deleteBy094(ww41, ww40000, ww40100, ww310000, Succ(ww3570)) → new_deleteBy11(ww310000, ww41)
The graph contains the following edges 4 >= 1, 1 >= 2
- new_deleteBy092(ww41, ww40000, ww40100, ww310000, Succ(ww3510)) → new_deleteBy11(ww310000, ww41)
The graph contains the following edges 4 >= 1, 1 >= 2
- new_deleteBy01(ww41, Float(Neg(Succ(ww40000)), Neg(Succ(ww40100))), Float(Neg(Zero), Pos(Succ(Succ(Succ(ww310000)))))) → new_deleteBy094(ww41, ww40000, ww40100, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
The graph contains the following edges 1 >= 1, 2 > 2, 2 > 3, 3 > 4
- new_deleteBy01(ww41, Float(Neg(Succ(ww40000)), Pos(Succ(ww40100))), Float(Neg(Zero), Pos(Succ(Succ(Succ(ww310000)))))) → new_deleteBy092(ww41, ww40000, ww40100, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
The graph contains the following edges 1 >= 1, 2 > 2, 2 > 3, 3 > 4
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_deleteBy055(ww41, ww40100, Succ(ww2110)) → new_deleteBy10(ww41)
new_deleteBy049(ww41, ww40000, ww40100, Succ(ww1930)) → new_deleteBy10(ww41)
new_deleteBy01(ww41, Float(Neg(Succ(ww40000)), Pos(Succ(ww40100))), Float(Pos(Zero), Neg(Succ(Succ(Zero))))) → new_deleteBy047(ww41, ww40000, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy047(ww41, ww40000, ww40100, Succ(ww1870)) → new_deleteBy10(ww41)
new_deleteBy10(:(ww410, ww411)) → new_deleteBy01(ww411, ww410, Float(Pos(Zero), Neg(Succ(Succ(Zero)))))
new_deleteBy01(ww41, Float(Neg(Succ(ww40000)), Neg(Succ(ww40100))), Float(Pos(Zero), Neg(Succ(Succ(Zero))))) → new_deleteBy049(ww41, ww40000, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy024(ww41, ww40000, ww40100, Succ(ww1020)) → new_deleteBy10(ww41)
new_deleteBy01(ww41, Float(Neg(Zero), Neg(Succ(ww40100))), Float(Pos(Zero), Neg(Succ(Succ(Zero))))) → new_deleteBy057(ww41, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy030(ww41, ww40100, Succ(ww1200)) → new_deleteBy10(ww41)
new_deleteBy022(:(ww410, ww411), ww40000, ww40100, Succ(ww960)) → new_deleteBy01(ww411, ww410, Float(Pos(Zero), Neg(Succ(Succ(Zero)))))
new_deleteBy01(ww41, Float(Pos(Succ(ww40000)), Pos(Succ(ww40100))), Float(Pos(Zero), Neg(Succ(Succ(Zero))))) → new_deleteBy022(ww41, ww40000, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy01(ww41, Float(Pos(Succ(ww40000)), Neg(Succ(ww40100))), Float(Pos(Zero), Neg(Succ(Succ(Zero))))) → new_deleteBy024(ww41, ww40000, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy01(ww41, Float(Pos(Zero), Pos(Succ(ww40100))), Float(Pos(Zero), Neg(Succ(Succ(Zero))))) → new_deleteBy030(ww41, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy01(ww41, Float(Neg(Zero), Pos(Succ(ww40100))), Float(Pos(Zero), Neg(Succ(Succ(Zero))))) → new_deleteBy055(ww41, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy057(ww41, ww40100, Succ(ww2170)) → new_deleteBy10(ww41)
new_deleteBy01(ww41, Float(Pos(Zero), Neg(Succ(ww40100))), Float(Pos(Zero), Neg(Succ(Succ(Zero))))) → new_deleteBy032(ww41, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy032(ww41, ww40100, Succ(ww1260)) → new_deleteBy10(ww41)
The TRS R consists of the following rules:
new_primPlusNat1(Zero, ww40000) → Succ(ww40000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, ww40000) → Zero
new_primPlusNat1(Succ(ww520), ww40000) → Succ(Succ(new_primPlusNat0(ww520, ww40000)))
new_primPlusNat0(Succ(ww5200), Zero) → Succ(ww5200)
new_primPlusNat0(Zero, Succ(ww400000)) → Succ(ww400000)
new_primPlusNat0(Succ(ww5200), Succ(ww400000)) → Succ(Succ(new_primPlusNat0(ww5200, ww400000)))
new_primMulNat0(Succ(ww30000), ww40000) → new_primPlusNat1(new_primMulNat0(ww30000, ww40000), ww40000)
The set Q consists of the following terms:
new_primMulNat0(Succ(x0), x1)
new_primMulNat0(Zero, x0)
new_primPlusNat1(Succ(x0), x1)
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
We have to consider all minimal (P,Q,R)-chains.
As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [15] we can delete all non-usable rules [17] from R.
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QReductionProof
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_deleteBy055(ww41, ww40100, Succ(ww2110)) → new_deleteBy10(ww41)
new_deleteBy049(ww41, ww40000, ww40100, Succ(ww1930)) → new_deleteBy10(ww41)
new_deleteBy01(ww41, Float(Neg(Succ(ww40000)), Pos(Succ(ww40100))), Float(Pos(Zero), Neg(Succ(Succ(Zero))))) → new_deleteBy047(ww41, ww40000, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy047(ww41, ww40000, ww40100, Succ(ww1870)) → new_deleteBy10(ww41)
new_deleteBy10(:(ww410, ww411)) → new_deleteBy01(ww411, ww410, Float(Pos(Zero), Neg(Succ(Succ(Zero)))))
new_deleteBy01(ww41, Float(Neg(Succ(ww40000)), Neg(Succ(ww40100))), Float(Pos(Zero), Neg(Succ(Succ(Zero))))) → new_deleteBy049(ww41, ww40000, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy024(ww41, ww40000, ww40100, Succ(ww1020)) → new_deleteBy10(ww41)
new_deleteBy01(ww41, Float(Neg(Zero), Neg(Succ(ww40100))), Float(Pos(Zero), Neg(Succ(Succ(Zero))))) → new_deleteBy057(ww41, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy030(ww41, ww40100, Succ(ww1200)) → new_deleteBy10(ww41)
new_deleteBy022(:(ww410, ww411), ww40000, ww40100, Succ(ww960)) → new_deleteBy01(ww411, ww410, Float(Pos(Zero), Neg(Succ(Succ(Zero)))))
new_deleteBy01(ww41, Float(Pos(Succ(ww40000)), Pos(Succ(ww40100))), Float(Pos(Zero), Neg(Succ(Succ(Zero))))) → new_deleteBy022(ww41, ww40000, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy01(ww41, Float(Pos(Succ(ww40000)), Neg(Succ(ww40100))), Float(Pos(Zero), Neg(Succ(Succ(Zero))))) → new_deleteBy024(ww41, ww40000, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy01(ww41, Float(Pos(Zero), Pos(Succ(ww40100))), Float(Pos(Zero), Neg(Succ(Succ(Zero))))) → new_deleteBy030(ww41, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy01(ww41, Float(Neg(Zero), Pos(Succ(ww40100))), Float(Pos(Zero), Neg(Succ(Succ(Zero))))) → new_deleteBy055(ww41, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy057(ww41, ww40100, Succ(ww2170)) → new_deleteBy10(ww41)
new_deleteBy01(ww41, Float(Pos(Zero), Neg(Succ(ww40100))), Float(Pos(Zero), Neg(Succ(Succ(Zero))))) → new_deleteBy032(ww41, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy032(ww41, ww40100, Succ(ww1260)) → new_deleteBy10(ww41)
The TRS R consists of the following rules:
new_primPlusNat0(Zero, Succ(ww400000)) → Succ(ww400000)
new_primPlusNat0(Succ(ww5200), Succ(ww400000)) → Succ(Succ(new_primPlusNat0(ww5200, ww400000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(ww5200), Zero) → Succ(ww5200)
The set Q consists of the following terms:
new_primMulNat0(Succ(x0), x1)
new_primMulNat0(Zero, x0)
new_primPlusNat1(Succ(x0), x1)
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
We have to consider all minimal (P,Q,R)-chains.
We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.
new_primMulNat0(Succ(x0), x1)
new_primMulNat0(Zero, x0)
new_primPlusNat1(Succ(x0), x1)
new_primPlusNat1(Zero, x0)
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QReductionProof
↳ QDP
↳ QDPSizeChangeProof
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_deleteBy055(ww41, ww40100, Succ(ww2110)) → new_deleteBy10(ww41)
new_deleteBy049(ww41, ww40000, ww40100, Succ(ww1930)) → new_deleteBy10(ww41)
new_deleteBy01(ww41, Float(Neg(Succ(ww40000)), Pos(Succ(ww40100))), Float(Pos(Zero), Neg(Succ(Succ(Zero))))) → new_deleteBy047(ww41, ww40000, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy047(ww41, ww40000, ww40100, Succ(ww1870)) → new_deleteBy10(ww41)
new_deleteBy10(:(ww410, ww411)) → new_deleteBy01(ww411, ww410, Float(Pos(Zero), Neg(Succ(Succ(Zero)))))
new_deleteBy01(ww41, Float(Neg(Succ(ww40000)), Neg(Succ(ww40100))), Float(Pos(Zero), Neg(Succ(Succ(Zero))))) → new_deleteBy049(ww41, ww40000, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy024(ww41, ww40000, ww40100, Succ(ww1020)) → new_deleteBy10(ww41)
new_deleteBy01(ww41, Float(Neg(Zero), Neg(Succ(ww40100))), Float(Pos(Zero), Neg(Succ(Succ(Zero))))) → new_deleteBy057(ww41, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy030(ww41, ww40100, Succ(ww1200)) → new_deleteBy10(ww41)
new_deleteBy022(:(ww410, ww411), ww40000, ww40100, Succ(ww960)) → new_deleteBy01(ww411, ww410, Float(Pos(Zero), Neg(Succ(Succ(Zero)))))
new_deleteBy01(ww41, Float(Pos(Succ(ww40000)), Pos(Succ(ww40100))), Float(Pos(Zero), Neg(Succ(Succ(Zero))))) → new_deleteBy022(ww41, ww40000, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy01(ww41, Float(Pos(Succ(ww40000)), Neg(Succ(ww40100))), Float(Pos(Zero), Neg(Succ(Succ(Zero))))) → new_deleteBy024(ww41, ww40000, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy01(ww41, Float(Pos(Zero), Pos(Succ(ww40100))), Float(Pos(Zero), Neg(Succ(Succ(Zero))))) → new_deleteBy030(ww41, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy01(ww41, Float(Neg(Zero), Pos(Succ(ww40100))), Float(Pos(Zero), Neg(Succ(Succ(Zero))))) → new_deleteBy055(ww41, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy057(ww41, ww40100, Succ(ww2170)) → new_deleteBy10(ww41)
new_deleteBy032(ww41, ww40100, Succ(ww1260)) → new_deleteBy10(ww41)
new_deleteBy01(ww41, Float(Pos(Zero), Neg(Succ(ww40100))), Float(Pos(Zero), Neg(Succ(Succ(Zero))))) → new_deleteBy032(ww41, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
The TRS R consists of the following rules:
new_primPlusNat0(Zero, Succ(ww400000)) → Succ(ww400000)
new_primPlusNat0(Succ(ww5200), Succ(ww400000)) → Succ(Succ(new_primPlusNat0(ww5200, ww400000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(ww5200), Zero) → Succ(ww5200)
The set Q consists of the following terms:
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), Zero)
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_deleteBy10(:(ww410, ww411)) → new_deleteBy01(ww411, ww410, Float(Pos(Zero), Neg(Succ(Succ(Zero)))))
The graph contains the following edges 1 > 1, 1 > 2
- new_deleteBy01(ww41, Float(Neg(Zero), Pos(Succ(ww40100))), Float(Pos(Zero), Neg(Succ(Succ(Zero))))) → new_deleteBy055(ww41, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
The graph contains the following edges 1 >= 1, 2 > 2
- new_deleteBy01(ww41, Float(Neg(Succ(ww40000)), Neg(Succ(ww40100))), Float(Pos(Zero), Neg(Succ(Succ(Zero))))) → new_deleteBy049(ww41, ww40000, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
The graph contains the following edges 1 >= 1, 2 > 2, 2 > 3
- new_deleteBy047(ww41, ww40000, ww40100, Succ(ww1870)) → new_deleteBy10(ww41)
The graph contains the following edges 1 >= 1
- new_deleteBy022(:(ww410, ww411), ww40000, ww40100, Succ(ww960)) → new_deleteBy01(ww411, ww410, Float(Pos(Zero), Neg(Succ(Succ(Zero)))))
The graph contains the following edges 1 > 1, 1 > 2
- new_deleteBy01(ww41, Float(Neg(Succ(ww40000)), Pos(Succ(ww40100))), Float(Pos(Zero), Neg(Succ(Succ(Zero))))) → new_deleteBy047(ww41, ww40000, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
The graph contains the following edges 1 >= 1, 2 > 2, 2 > 3
- new_deleteBy049(ww41, ww40000, ww40100, Succ(ww1930)) → new_deleteBy10(ww41)
The graph contains the following edges 1 >= 1
- new_deleteBy01(ww41, Float(Pos(Succ(ww40000)), Neg(Succ(ww40100))), Float(Pos(Zero), Neg(Succ(Succ(Zero))))) → new_deleteBy024(ww41, ww40000, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
The graph contains the following edges 1 >= 1, 2 > 2, 2 > 3
- new_deleteBy057(ww41, ww40100, Succ(ww2170)) → new_deleteBy10(ww41)
The graph contains the following edges 1 >= 1
- new_deleteBy01(ww41, Float(Pos(Zero), Pos(Succ(ww40100))), Float(Pos(Zero), Neg(Succ(Succ(Zero))))) → new_deleteBy030(ww41, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
The graph contains the following edges 1 >= 1, 2 > 2
- new_deleteBy01(ww41, Float(Pos(Succ(ww40000)), Pos(Succ(ww40100))), Float(Pos(Zero), Neg(Succ(Succ(Zero))))) → new_deleteBy022(ww41, ww40000, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
The graph contains the following edges 1 >= 1, 2 > 2, 2 > 3
- new_deleteBy024(ww41, ww40000, ww40100, Succ(ww1020)) → new_deleteBy10(ww41)
The graph contains the following edges 1 >= 1
- new_deleteBy030(ww41, ww40100, Succ(ww1200)) → new_deleteBy10(ww41)
The graph contains the following edges 1 >= 1
- new_deleteBy055(ww41, ww40100, Succ(ww2110)) → new_deleteBy10(ww41)
The graph contains the following edges 1 >= 1
- new_deleteBy032(ww41, ww40100, Succ(ww1260)) → new_deleteBy10(ww41)
The graph contains the following edges 1 >= 1
- new_deleteBy01(ww41, Float(Neg(Zero), Neg(Succ(ww40100))), Float(Pos(Zero), Neg(Succ(Succ(Zero))))) → new_deleteBy057(ww41, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
The graph contains the following edges 1 >= 1, 2 > 2
- new_deleteBy01(ww41, Float(Pos(Zero), Neg(Succ(ww40100))), Float(Pos(Zero), Neg(Succ(Succ(Zero))))) → new_deleteBy032(ww41, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
The graph contains the following edges 1 >= 1, 2 > 2
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDPSizeChangeProof
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_deleteBy081(ww41, ww40100, ww310000, Succ(ww3020)) → new_deleteBy13(ww310000, ww41)
new_deleteBy01(ww41, Float(Pos(Succ(ww40000)), Pos(Succ(ww40100))), Float(Neg(Zero), Neg(Succ(Succ(Succ(ww310000)))))) → new_deleteBy071(ww41, ww40000, ww40100, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
new_deleteBy01(ww41, Float(Neg(Zero), Pos(Succ(ww40100))), Float(Neg(Zero), Neg(Succ(Succ(Succ(ww310000)))))) → new_deleteBy0104(ww41, ww40100, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
new_deleteBy01(ww41, Float(Pos(Zero), Neg(Succ(ww40100))), Float(Neg(Zero), Neg(Succ(Succ(Succ(ww310000)))))) → new_deleteBy081(ww41, ww40100, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
new_deleteBy0104(ww41, ww40100, ww310000, Succ(ww3870)) → new_deleteBy13(ww310000, ww41)
new_deleteBy01(ww41, Float(Neg(Zero), Neg(Succ(ww40100))), Float(Neg(Zero), Neg(Succ(Succ(Succ(ww310000)))))) → new_deleteBy0106(ww41, ww40100, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
new_deleteBy096(ww41, ww40000, ww40100, ww310000, Succ(ww3630)) → new_deleteBy13(ww310000, ww41)
new_deleteBy071(:(ww410, ww411), ww40000, ww40100, ww310000, Succ(ww2720)) → new_deleteBy01(ww411, ww410, Float(Neg(Zero), Neg(Succ(Succ(Succ(ww310000))))))
new_deleteBy079(ww41, ww40100, ww310000, Succ(ww2960)) → new_deleteBy13(ww310000, ww41)
new_deleteBy01(ww41, Float(Pos(Succ(ww40000)), Neg(Succ(ww40100))), Float(Neg(Zero), Neg(Succ(Succ(Succ(ww310000)))))) → new_deleteBy073(ww41, ww40000, ww40100, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
new_deleteBy0106(ww41, ww40100, ww310000, Succ(ww3930)) → new_deleteBy13(ww310000, ww41)
new_deleteBy073(ww41, ww40000, ww40100, ww310000, Succ(ww2780)) → new_deleteBy13(ww310000, ww41)
new_deleteBy01(ww41, Float(Neg(Succ(ww40000)), Neg(Succ(ww40100))), Float(Neg(Zero), Neg(Succ(Succ(Succ(ww310000)))))) → new_deleteBy098(ww41, ww40000, ww40100, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
new_deleteBy13(ww310000, :(ww410, ww411)) → new_deleteBy01(ww411, ww410, Float(Neg(Zero), Neg(Succ(Succ(Succ(ww310000))))))
new_deleteBy01(ww41, Float(Neg(Succ(ww40000)), Pos(Succ(ww40100))), Float(Neg(Zero), Neg(Succ(Succ(Succ(ww310000)))))) → new_deleteBy096(ww41, ww40000, ww40100, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
new_deleteBy01(ww41, Float(Pos(Zero), Pos(Succ(ww40100))), Float(Neg(Zero), Neg(Succ(Succ(Succ(ww310000)))))) → new_deleteBy079(ww41, ww40100, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
new_deleteBy098(ww41, ww40000, ww40100, ww310000, Succ(ww3690)) → new_deleteBy13(ww310000, ww41)
The TRS R consists of the following rules:
new_primPlusNat1(Zero, ww40000) → Succ(ww40000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, ww40000) → Zero
new_primPlusNat1(Succ(ww520), ww40000) → Succ(Succ(new_primPlusNat0(ww520, ww40000)))
new_primPlusNat0(Succ(ww5200), Zero) → Succ(ww5200)
new_primPlusNat0(Zero, Succ(ww400000)) → Succ(ww400000)
new_primPlusNat0(Succ(ww5200), Succ(ww400000)) → Succ(Succ(new_primPlusNat0(ww5200, ww400000)))
new_primMulNat0(Succ(ww30000), ww40000) → new_primPlusNat1(new_primMulNat0(ww30000, ww40000), ww40000)
The set Q consists of the following terms:
new_primMulNat0(Succ(x0), x1)
new_primMulNat0(Zero, x0)
new_primPlusNat1(Succ(x0), x1)
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
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_deleteBy0106(ww41, ww40100, ww310000, Succ(ww3930)) → new_deleteBy13(ww310000, ww41)
The graph contains the following edges 3 >= 1, 1 >= 2
- new_deleteBy01(ww41, Float(Neg(Zero), Neg(Succ(ww40100))), Float(Neg(Zero), Neg(Succ(Succ(Succ(ww310000)))))) → new_deleteBy0106(ww41, ww40100, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
The graph contains the following edges 1 >= 1, 2 > 2, 3 > 3
- new_deleteBy13(ww310000, :(ww410, ww411)) → new_deleteBy01(ww411, ww410, Float(Neg(Zero), Neg(Succ(Succ(Succ(ww310000))))))
The graph contains the following edges 2 > 1, 2 > 2
- new_deleteBy071(:(ww410, ww411), ww40000, ww40100, ww310000, Succ(ww2720)) → new_deleteBy01(ww411, ww410, Float(Neg(Zero), Neg(Succ(Succ(Succ(ww310000))))))
The graph contains the following edges 1 > 1, 1 > 2
- new_deleteBy098(ww41, ww40000, ww40100, ww310000, Succ(ww3690)) → new_deleteBy13(ww310000, ww41)
The graph contains the following edges 4 >= 1, 1 >= 2
- new_deleteBy01(ww41, Float(Neg(Succ(ww40000)), Neg(Succ(ww40100))), Float(Neg(Zero), Neg(Succ(Succ(Succ(ww310000)))))) → new_deleteBy098(ww41, ww40000, ww40100, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
The graph contains the following edges 1 >= 1, 2 > 2, 2 > 3, 3 > 4
- new_deleteBy01(ww41, Float(Pos(Succ(ww40000)), Pos(Succ(ww40100))), Float(Neg(Zero), Neg(Succ(Succ(Succ(ww310000)))))) → new_deleteBy071(ww41, ww40000, ww40100, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
The graph contains the following edges 1 >= 1, 2 > 2, 2 > 3, 3 > 4
- new_deleteBy081(ww41, ww40100, ww310000, Succ(ww3020)) → new_deleteBy13(ww310000, ww41)
The graph contains the following edges 3 >= 1, 1 >= 2
- new_deleteBy01(ww41, Float(Pos(Zero), Neg(Succ(ww40100))), Float(Neg(Zero), Neg(Succ(Succ(Succ(ww310000)))))) → new_deleteBy081(ww41, ww40100, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
The graph contains the following edges 1 >= 1, 2 > 2, 3 > 3
- new_deleteBy079(ww41, ww40100, ww310000, Succ(ww2960)) → new_deleteBy13(ww310000, ww41)
The graph contains the following edges 3 >= 1, 1 >= 2
- new_deleteBy01(ww41, Float(Pos(Zero), Pos(Succ(ww40100))), Float(Neg(Zero), Neg(Succ(Succ(Succ(ww310000)))))) → new_deleteBy079(ww41, ww40100, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
The graph contains the following edges 1 >= 1, 2 > 2, 3 > 3
- new_deleteBy073(ww41, ww40000, ww40100, ww310000, Succ(ww2780)) → new_deleteBy13(ww310000, ww41)
The graph contains the following edges 4 >= 1, 1 >= 2
- new_deleteBy01(ww41, Float(Pos(Succ(ww40000)), Neg(Succ(ww40100))), Float(Neg(Zero), Neg(Succ(Succ(Succ(ww310000)))))) → new_deleteBy073(ww41, ww40000, ww40100, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
The graph contains the following edges 1 >= 1, 2 > 2, 2 > 3, 3 > 4
- new_deleteBy096(ww41, ww40000, ww40100, ww310000, Succ(ww3630)) → new_deleteBy13(ww310000, ww41)
The graph contains the following edges 4 >= 1, 1 >= 2
- new_deleteBy0104(ww41, ww40100, ww310000, Succ(ww3870)) → new_deleteBy13(ww310000, ww41)
The graph contains the following edges 3 >= 1, 1 >= 2
- new_deleteBy01(ww41, Float(Neg(Succ(ww40000)), Pos(Succ(ww40100))), Float(Neg(Zero), Neg(Succ(Succ(Succ(ww310000)))))) → new_deleteBy096(ww41, ww40000, ww40100, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
The graph contains the following edges 1 >= 1, 2 > 2, 2 > 3, 3 > 4
- new_deleteBy01(ww41, Float(Neg(Zero), Pos(Succ(ww40100))), Float(Neg(Zero), Neg(Succ(Succ(Succ(ww310000)))))) → new_deleteBy0104(ww41, ww40100, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
The graph contains the following edges 1 >= 1, 2 > 2, 3 > 3
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDPSizeChangeProof
↳ QDP
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_deleteBy01(ww41, Float(Neg(Zero), Pos(Succ(ww40100))), Float(Pos(Zero), Neg(Succ(Succ(Succ(ww310000)))))) → new_deleteBy054(ww41, ww40100, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
new_deleteBy01(ww41, Float(Pos(Zero), Pos(Succ(ww40100))), Float(Pos(Zero), Neg(Succ(Succ(Succ(ww310000)))))) → new_deleteBy029(ww41, ww40100, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
new_deleteBy054(ww41, ww40100, ww310000, Succ(ww2070)) → new_deleteBy9(ww310000, ww41)
new_deleteBy01(ww41, Float(Neg(Succ(ww40000)), Neg(Succ(ww40100))), Float(Pos(Zero), Neg(Succ(Succ(Succ(ww310000)))))) → new_deleteBy048(ww41, ww40000, ww40100, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
new_deleteBy056(ww41, ww40100, ww310000, Succ(ww2130)) → new_deleteBy9(ww310000, ww41)
new_deleteBy048(ww41, ww40000, ww40100, ww310000, Succ(ww1890)) → new_deleteBy9(ww310000, ww41)
new_deleteBy01(ww41, Float(Neg(Succ(ww40000)), Pos(Succ(ww40100))), Float(Pos(Zero), Neg(Succ(Succ(Succ(ww310000)))))) → new_deleteBy046(ww41, ww40000, ww40100, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
new_deleteBy9(ww310000, :(ww410, ww411)) → new_deleteBy01(ww411, ww410, Float(Pos(Zero), Neg(Succ(Succ(Succ(ww310000))))))
new_deleteBy021(:(ww410, ww411), ww40000, ww40100, ww310000, Succ(ww920)) → new_deleteBy01(ww411, ww410, Float(Pos(Zero), Neg(Succ(Succ(Succ(ww310000))))))
new_deleteBy01(ww41, Float(Pos(Zero), Neg(Succ(ww40100))), Float(Pos(Zero), Neg(Succ(Succ(Succ(ww310000)))))) → new_deleteBy031(ww41, ww40100, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
new_deleteBy046(ww41, ww40000, ww40100, ww310000, Succ(ww1830)) → new_deleteBy9(ww310000, ww41)
new_deleteBy01(ww41, Float(Neg(Zero), Neg(Succ(ww40100))), Float(Pos(Zero), Neg(Succ(Succ(Succ(ww310000)))))) → new_deleteBy056(ww41, ww40100, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
new_deleteBy023(ww41, ww40000, ww40100, ww310000, Succ(ww980)) → new_deleteBy9(ww310000, ww41)
new_deleteBy01(ww41, Float(Pos(Succ(ww40000)), Neg(Succ(ww40100))), Float(Pos(Zero), Neg(Succ(Succ(Succ(ww310000)))))) → new_deleteBy023(ww41, ww40000, ww40100, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
new_deleteBy031(ww41, ww40100, ww310000, Succ(ww1220)) → new_deleteBy9(ww310000, ww41)
new_deleteBy01(ww41, Float(Pos(Succ(ww40000)), Pos(Succ(ww40100))), Float(Pos(Zero), Neg(Succ(Succ(Succ(ww310000)))))) → new_deleteBy021(ww41, ww40000, ww40100, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
new_deleteBy029(ww41, ww40100, ww310000, Succ(ww1160)) → new_deleteBy9(ww310000, ww41)
The TRS R consists of the following rules:
new_primPlusNat1(Zero, ww40000) → Succ(ww40000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, ww40000) → Zero
new_primPlusNat1(Succ(ww520), ww40000) → Succ(Succ(new_primPlusNat0(ww520, ww40000)))
new_primPlusNat0(Succ(ww5200), Zero) → Succ(ww5200)
new_primPlusNat0(Zero, Succ(ww400000)) → Succ(ww400000)
new_primPlusNat0(Succ(ww5200), Succ(ww400000)) → Succ(Succ(new_primPlusNat0(ww5200, ww400000)))
new_primMulNat0(Succ(ww30000), ww40000) → new_primPlusNat1(new_primMulNat0(ww30000, ww40000), ww40000)
The set Q consists of the following terms:
new_primMulNat0(Succ(x0), x1)
new_primMulNat0(Zero, x0)
new_primPlusNat1(Succ(x0), x1)
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
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_deleteBy9(ww310000, :(ww410, ww411)) → new_deleteBy01(ww411, ww410, Float(Pos(Zero), Neg(Succ(Succ(Succ(ww310000))))))
The graph contains the following edges 2 > 1, 2 > 2
- new_deleteBy01(ww41, Float(Neg(Succ(ww40000)), Neg(Succ(ww40100))), Float(Pos(Zero), Neg(Succ(Succ(Succ(ww310000)))))) → new_deleteBy048(ww41, ww40000, ww40100, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
The graph contains the following edges 1 >= 1, 2 > 2, 2 > 3, 3 > 4
- new_deleteBy021(:(ww410, ww411), ww40000, ww40100, ww310000, Succ(ww920)) → new_deleteBy01(ww411, ww410, Float(Pos(Zero), Neg(Succ(Succ(Succ(ww310000))))))
The graph contains the following edges 1 > 1, 1 > 2
- new_deleteBy048(ww41, ww40000, ww40100, ww310000, Succ(ww1890)) → new_deleteBy9(ww310000, ww41)
The graph contains the following edges 4 >= 1, 1 >= 2
- new_deleteBy01(ww41, Float(Pos(Succ(ww40000)), Pos(Succ(ww40100))), Float(Pos(Zero), Neg(Succ(Succ(Succ(ww310000)))))) → new_deleteBy021(ww41, ww40000, ww40100, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
The graph contains the following edges 1 >= 1, 2 > 2, 2 > 3, 3 > 4
- new_deleteBy056(ww41, ww40100, ww310000, Succ(ww2130)) → new_deleteBy9(ww310000, ww41)
The graph contains the following edges 3 >= 1, 1 >= 2
- new_deleteBy01(ww41, Float(Neg(Zero), Neg(Succ(ww40100))), Float(Pos(Zero), Neg(Succ(Succ(Succ(ww310000)))))) → new_deleteBy056(ww41, ww40100, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
The graph contains the following edges 1 >= 1, 2 > 2, 3 > 3
- new_deleteBy031(ww41, ww40100, ww310000, Succ(ww1220)) → new_deleteBy9(ww310000, ww41)
The graph contains the following edges 3 >= 1, 1 >= 2
- new_deleteBy01(ww41, Float(Pos(Zero), Neg(Succ(ww40100))), Float(Pos(Zero), Neg(Succ(Succ(Succ(ww310000)))))) → new_deleteBy031(ww41, ww40100, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
The graph contains the following edges 1 >= 1, 2 > 2, 3 > 3
- new_deleteBy029(ww41, ww40100, ww310000, Succ(ww1160)) → new_deleteBy9(ww310000, ww41)
The graph contains the following edges 3 >= 1, 1 >= 2
- new_deleteBy01(ww41, Float(Pos(Zero), Pos(Succ(ww40100))), Float(Pos(Zero), Neg(Succ(Succ(Succ(ww310000)))))) → new_deleteBy029(ww41, ww40100, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
The graph contains the following edges 1 >= 1, 2 > 2, 3 > 3
- new_deleteBy046(ww41, ww40000, ww40100, ww310000, Succ(ww1830)) → new_deleteBy9(ww310000, ww41)
The graph contains the following edges 4 >= 1, 1 >= 2
- new_deleteBy01(ww41, Float(Neg(Succ(ww40000)), Pos(Succ(ww40100))), Float(Pos(Zero), Neg(Succ(Succ(Succ(ww310000)))))) → new_deleteBy046(ww41, ww40000, ww40100, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
The graph contains the following edges 1 >= 1, 2 > 2, 2 > 3, 3 > 4
- new_deleteBy023(ww41, ww40000, ww40100, ww310000, Succ(ww980)) → new_deleteBy9(ww310000, ww41)
The graph contains the following edges 4 >= 1, 1 >= 2
- new_deleteBy054(ww41, ww40100, ww310000, Succ(ww2070)) → new_deleteBy9(ww310000, ww41)
The graph contains the following edges 3 >= 1, 1 >= 2
- new_deleteBy01(ww41, Float(Pos(Succ(ww40000)), Neg(Succ(ww40100))), Float(Pos(Zero), Neg(Succ(Succ(Succ(ww310000)))))) → new_deleteBy023(ww41, ww40000, ww40100, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
The graph contains the following edges 1 >= 1, 2 > 2, 2 > 3, 3 > 4
- new_deleteBy01(ww41, Float(Neg(Zero), Pos(Succ(ww40100))), Float(Pos(Zero), Neg(Succ(Succ(Succ(ww310000)))))) → new_deleteBy054(ww41, ww40100, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
The graph contains the following edges 1 >= 1, 2 > 2, 3 > 3
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDPSizeChangeProof
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_deleteBy0121(ww36, ww37, ww3800, ww39, ww4000, Succ(ww21900), Succ(Succ(ww24800))) → new_deleteBy0128(ww36, ww37, ww3800, ww39, ww4000, ww21900, ww24800)
new_deleteBy083(ww42, ww43, Pos(Succ(ww4400)), ww45, Pos(Succ(ww4600)), Zero) → new_deleteBy0135(ww42, ww43, ww4400, ww45, ww4600, new_primPlusNat0(new_primMulNat0(ww4600, ww4400), Succ(ww4400)))
new_deleteBy01(ww41, Float(Neg(Zero), Pos(Succ(ww40100))), Float(Neg(Succ(ww3000)), Neg(Succ(Succ(Zero))))) → new_deleteBy089(ww41, ww40100, ww3000, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy065(ww41, ww40100, ww3000, ww310000, Succ(ww2420)) → new_deleteBy5(ww3000, Succ(Succ(Succ(ww310000))), ww41)
new_deleteBy0136(ww42, ww43, ww4400, ww45, ww4600, Succ(ww3450)) → new_deleteBy0141(ww42, ww43, Succ(ww4400), ww45, Succ(ww4600))
new_deleteBy0143(ww42, ww43, ww4400, ww45, ww4600, Zero, Succ(ww34100)) → new_deleteBy0144(ww42, ww43, ww4400, ww45, ww4600)
new_deleteBy0143(ww42, ww43, ww4400, ww45, ww4600, Succ(ww30800), Zero) → new_deleteBy0144(ww42, ww43, ww4400, ww45, ww4600)
new_deleteBy0122(ww36, ww37, ww3800, ww39, ww4000, Zero, Succ(Succ(ww25000))) → new_deleteBy0131(ww36, ww37, ww3800, ww39, ww4000)
new_deleteBy0122(ww36, ww37, ww3800, ww39, ww4000, ww2190, Zero) → new_deleteBy5(ww39, Succ(ww4000), ww36)
new_deleteBy0121(ww36, ww37, ww3800, ww39, ww4000, Zero, Succ(Succ(ww24800))) → new_deleteBy0129(ww36, ww37, ww3800, ww39, ww4000)
new_deleteBy0123(ww36, ww37, ww3800, ww39, ww4000, Succ(ww2520)) → new_deleteBy0127(ww36, ww37, Succ(ww3800), ww39, Succ(ww4000))
new_deleteBy01(ww41, Float(Pos(Zero), Pos(Succ(ww40100))), Float(Neg(Succ(ww3000)), Neg(Succ(Succ(Succ(ww310000)))))) → new_deleteBy063(ww41, ww40100, ww3000, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
new_deleteBy0122(ww36, ww37, ww3800, ww39, ww4000, Succ(ww21900), Succ(Zero)) → new_deleteBy0131(ww36, ww37, ww3800, ww39, ww4000)
new_deleteBy01(ww41, Float(Pos(Zero), Neg(Succ(ww40100))), Float(Neg(Succ(ww3000)), Pos(Succ(Succ(Succ(ww310000)))))) → new_deleteBy061(ww41, ww40100, ww3000, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
new_deleteBy083(ww42, ww43, Pos(Succ(ww4400)), ww45, Neg(Succ(ww4600)), Zero) → new_deleteBy0137(ww42, ww43, ww4400, ww45, ww4600, new_primPlusNat0(new_primMulNat0(ww4600, ww4400), Succ(ww4400)))
new_deleteBy01(ww41, Float(Pos(Zero), Neg(Succ(ww40100))), Float(Neg(Succ(ww3000)), Neg(Succ(Succ(Succ(ww310000)))))) → new_deleteBy065(ww41, ww40100, ww3000, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
new_deleteBy01(ww41, Float(Neg(Zero), Neg(Succ(ww40100))), Float(Neg(Succ(ww3000)), Neg(Succ(Succ(Succ(ww310000)))))) → new_deleteBy090(ww41, ww40100, ww3000, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
new_deleteBy01(ww41, Float(Pos(Zero), Pos(Succ(ww40100))), Float(Neg(Succ(ww3000)), Pos(Succ(Succ(Succ(ww310000)))))) → new_deleteBy059(ww41, ww40100, ww3000, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
new_deleteBy01(ww41, Float(Neg(Zero), Neg(Succ(ww40100))), Float(Neg(Succ(ww3000)), Neg(Succ(Succ(Zero))))) → new_deleteBy091(ww41, ww40100, ww3000, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy083(ww42, ww43, Neg(ww440), ww45, Pos(ww460), Succ(ww3080)) → new_deleteBy4(ww45, ww460, ww42)
new_deleteBy058(ww36, ww37, Pos(Succ(ww3800)), ww39, Neg(Succ(ww4000)), Zero) → new_deleteBy0125(ww36, ww37, ww3800, ww39, ww4000, new_primPlusNat0(new_primMulNat0(ww4000, ww3800), Succ(ww3800)))
new_deleteBy0128(ww36, ww37, ww3800, ww39, ww4000, Succ(ww21900), Succ(ww24800)) → new_deleteBy0128(ww36, ww37, ww3800, ww39, ww4000, ww21900, ww24800)
new_deleteBy0121(ww36, ww37, ww3800, ww39, ww4000, ww2190, Zero) → new_deleteBy4(ww39, Succ(ww4000), ww36)
new_deleteBy086(ww41, ww40100, ww3000, ww310000, Succ(ww3210)) → new_deleteBy4(ww3000, Succ(Succ(Succ(ww310000))), ww41)
new_deleteBy0144(ww42, ww43, ww4400, ww45, ww4600) → new_deleteBy5(ww45, Succ(ww4600), ww42)
new_deleteBy0126(ww36, ww37, ww3800, ww39, ww4000, Succ(ww2580)) → new_deleteBy0132(ww36, ww37, Succ(ww3800), ww39, Succ(ww4000))
new_deleteBy0133(ww42, ww43, ww4400, ww45, ww4600, ww3080, Zero) → new_deleteBy4(ww45, Succ(ww4600), ww42)
new_deleteBy083(ww42, ww43, Pos(Zero), ww45, Pos(Zero), Succ(ww3080)) → new_deleteBy4(ww45, Zero, ww42)
new_deleteBy0121(ww36, ww37, ww3800, ww39, ww4000, Succ(ww21900), Succ(Zero)) → new_deleteBy0129(ww36, ww37, ww3800, ww39, ww4000)
new_deleteBy0140(ww42, ww43, ww4400, ww45, ww4600) → new_deleteBy4(ww45, Succ(ww4600), ww42)
new_deleteBy0131(ww36, ww37, ww3800, ww39, ww4000) → new_deleteBy5(ww39, Succ(ww4000), ww36)
new_deleteBy0130(ww36, ww37, ww3800, ww39, ww4000, Succ(ww21900), Succ(ww25000)) → new_deleteBy0130(ww36, ww37, ww3800, ww39, ww4000, ww21900, ww25000)
new_deleteBy01(ww41, Float(Neg(Zero), Neg(Succ(ww40100))), Float(Neg(Succ(ww3000)), Pos(Succ(Succ(Zero))))) → new_deleteBy087(ww41, ww40100, ww3000, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy0134(ww42, ww43, ww4400, ww45, ww4600, Succ(ww30800), Succ(Succ(ww34100))) → new_deleteBy0143(ww42, ww43, ww4400, ww45, ww4600, ww30800, ww34100)
new_deleteBy083(ww42, ww43, Pos(Succ(ww4400)), ww45, Pos(Succ(ww4600)), Succ(ww3080)) → new_deleteBy0133(ww42, ww43, ww4400, ww45, ww4600, ww3080, new_primPlusNat0(new_primMulNat0(ww4600, ww4400), Succ(ww4400)))
new_deleteBy087(ww41, ww40100, ww3000, Succ(ww3250)) → new_deleteBy4(ww3000, Succ(Succ(Zero)), ww41)
new_deleteBy058(ww36, ww37, Pos(Succ(ww3800)), ww39, Neg(Zero), Succ(ww2190)) → new_deleteBy5(ww39, Zero, ww36)
new_deleteBy0128(ww36, ww37, ww3800, ww39, ww4000, Zero, Succ(ww24800)) → new_deleteBy0129(ww36, ww37, ww3800, ww39, ww4000)
new_deleteBy0128(ww36, ww37, ww3800, ww39, ww4000, Succ(ww21900), Zero) → new_deleteBy0129(ww36, ww37, ww3800, ww39, ww4000)
new_deleteBy089(ww41, ww40100, ww3000, Succ(ww3310)) → new_deleteBy5(ww3000, Succ(Succ(Zero)), ww41)
new_deleteBy01(ww41, Float(Pos(Succ(ww40000)), ww401), Float(Neg(Succ(ww3000)), ww31)) → new_deleteBy058(ww41, ww40000, ww401, ww3000, ww31, new_primPlusNat0(new_primMulNat0(ww3000, ww40000), Succ(ww40000)))
new_deleteBy01(ww41, Float(Pos(Zero), Pos(Succ(ww40100))), Float(Neg(Succ(ww3000)), Pos(Succ(Succ(Zero))))) → new_deleteBy060(ww41, ww40100, ww3000, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy0138(ww42, ww43, ww4400, ww45, ww4600, Succ(ww3490)) → new_deleteBy0144(ww42, ww43, ww4400, ww45, ww4600)
new_deleteBy058(:(ww360, ww361), ww37, Pos(ww380), ww39, Pos(ww400), Succ(ww2190)) → new_deleteBy01(ww361, ww360, Float(Neg(Succ(ww39)), Pos(ww400)))
new_deleteBy0139(ww42, ww43, ww4400, ww45, ww4600, Succ(ww30800), Succ(ww33900)) → new_deleteBy0139(ww42, ww43, ww4400, ww45, ww4600, ww30800, ww33900)
new_deleteBy058(ww36, ww37, Neg(Succ(ww3800)), ww39, Pos(Zero), Succ(ww2190)) → new_deleteBy4(ww39, Zero, ww36)
new_deleteBy083(ww42, ww43, Neg(Zero), ww45, Neg(Succ(ww4600)), Succ(ww3080)) → new_deleteBy5(ww45, Succ(ww4600), ww42)
new_deleteBy01(ww41, Float(Neg(Zero), Neg(Succ(ww40100))), Float(Neg(Succ(ww3000)), Pos(Succ(Succ(Succ(ww310000)))))) → new_deleteBy086(ww41, ww40100, ww3000, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
new_deleteBy01(ww41, Float(Pos(Zero), Neg(Succ(ww40100))), Float(Neg(Succ(ww3000)), Neg(Succ(Succ(Zero))))) → new_deleteBy066(ww41, ww40100, ww3000, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy01(ww41, Float(Pos(Zero), Pos(Succ(ww40100))), Float(Neg(Succ(ww3000)), Neg(Succ(Succ(Zero))))) → new_deleteBy064(ww41, ww40100, ww3000, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy090(ww41, ww40100, ww3000, ww310000, Succ(ww3330)) → new_deleteBy5(ww3000, Succ(Succ(Succ(ww310000))), ww41)
new_deleteBy083(ww42, ww43, Pos(ww440), ww45, Neg(ww460), Succ(ww3080)) → new_deleteBy5(ww45, ww460, ww42)
new_deleteBy058(:(ww360, ww361), ww37, Neg(ww380), ww39, Neg(ww400), Succ(ww2190)) → new_deleteBy01(ww361, ww360, Float(Neg(Succ(ww39)), Neg(ww400)))
new_deleteBy058(ww36, ww37, Neg(Zero), ww39, Pos(Succ(ww4000)), Succ(ww2190)) → new_deleteBy4(ww39, Succ(ww4000), ww36)
new_deleteBy0124(ww36, ww37, ww3800, ww39, ww4000, Succ(ww2540)) → new_deleteBy0129(ww36, ww37, ww3800, ww39, ww4000)
new_deleteBy085(ww41, ww40100, ww3000, Succ(ww3190)) → new_deleteBy4(ww3000, Succ(Succ(Zero)), ww41)
new_deleteBy058(ww36, ww37, Pos(Zero), ww39, Neg(Succ(ww4000)), Succ(ww2190)) → new_deleteBy5(ww39, Succ(ww4000), ww36)
new_deleteBy083(ww42, ww43, Neg(Succ(ww4400)), ww45, Pos(Succ(ww4600)), Zero) → new_deleteBy0136(ww42, ww43, ww4400, ww45, ww4600, new_primPlusNat0(new_primMulNat0(ww4600, ww4400), Succ(ww4400)))
new_deleteBy01(ww41, Float(Neg(Succ(ww40000)), ww401), Float(Neg(Succ(ww3000)), ww31)) → new_deleteBy083(ww41, ww40000, ww401, ww3000, ww31, new_primPlusNat0(new_primMulNat0(ww3000, ww40000), Succ(ww40000)))
new_deleteBy058(ww36, ww37, Neg(Succ(ww3800)), ww39, Pos(Succ(ww4000)), Zero) → new_deleteBy0124(ww36, ww37, ww3800, ww39, ww4000, new_primPlusNat0(new_primMulNat0(ww4000, ww3800), Succ(ww3800)))
new_deleteBy0129(ww36, ww37, ww3800, ww39, ww4000) → new_deleteBy4(ww39, Succ(ww4000), ww36)
new_deleteBy058(ww36, ww37, Pos(Zero), ww39, Neg(Zero), Succ(ww2190)) → new_deleteBy5(ww39, Zero, ww36)
new_deleteBy0143(ww42, ww43, ww4400, ww45, ww4600, Succ(ww30800), Succ(ww34100)) → new_deleteBy0143(ww42, ww43, ww4400, ww45, ww4600, ww30800, ww34100)
new_deleteBy5(ww39, ww400, :(ww360, ww361)) → new_deleteBy01(ww361, ww360, Float(Neg(Succ(ww39)), Neg(ww400)))
new_deleteBy01(ww41, Float(Pos(Zero), Pos(Succ(ww40100))), Float(Neg(Succ(ww3000)), Pos(Succ(Zero)))) → new_deleteBy4(ww3000, Succ(Zero), ww41)
new_deleteBy01(ww41, Float(Pos(Zero), Neg(Succ(ww40100))), Float(Neg(Succ(ww3000)), Pos(Succ(Zero)))) → new_deleteBy4(ww3000, Succ(Zero), ww41)
new_deleteBy01(ww41, Float(Neg(Zero), Pos(Succ(ww40100))), Float(Neg(Succ(ww3000)), Pos(Succ(Zero)))) → new_deleteBy4(ww3000, Succ(Zero), ww41)
new_deleteBy062(ww41, ww40100, ww3000, Succ(ww2340)) → new_deleteBy4(ww3000, Succ(Succ(Zero)), ww41)
new_deleteBy058(ww36, ww37, Pos(Succ(ww3800)), ww39, Neg(Succ(ww4000)), Succ(ww2190)) → new_deleteBy0122(ww36, ww37, ww3800, ww39, ww4000, ww2190, new_primPlusNat0(new_primMulNat0(ww4000, ww3800), Succ(ww3800)))
new_deleteBy059(ww41, ww40100, ww3000, ww310000, Succ(ww2240)) → new_deleteBy4(ww3000, Succ(Succ(Succ(ww310000))), ww41)
new_deleteBy063(ww41, ww40100, ww3000, ww310000, Succ(ww2360)) → new_deleteBy5(ww3000, Succ(Succ(Succ(ww310000))), ww41)
new_deleteBy0125(ww36, ww37, ww3800, ww39, ww4000, Succ(ww2560)) → new_deleteBy0131(ww36, ww37, ww3800, ww39, ww4000)
new_deleteBy0134(ww42, ww43, ww4400, ww45, ww4600, Zero, Succ(Succ(ww34100))) → new_deleteBy0144(ww42, ww43, ww4400, ww45, ww4600)
new_deleteBy058(ww36, ww37, Neg(Succ(ww3800)), ww39, Neg(Succ(ww4000)), Zero) → new_deleteBy0126(ww36, ww37, ww3800, ww39, ww4000, new_primPlusNat0(new_primMulNat0(ww4000, ww3800), Succ(ww3800)))
new_deleteBy0139(ww42, ww43, ww4400, ww45, ww4600, Succ(ww30800), Zero) → new_deleteBy0140(ww42, ww43, ww4400, ww45, ww4600)
new_deleteBy0139(ww42, ww43, ww4400, ww45, ww4600, Zero, Succ(ww33900)) → new_deleteBy0140(ww42, ww43, ww4400, ww45, ww4600)
new_deleteBy01(ww41, Float(Neg(Zero), Neg(Succ(ww40100))), Float(Neg(Succ(ww3000)), Neg(Succ(Zero)))) → new_deleteBy5(ww3000, Succ(Zero), ww41)
new_deleteBy064(ww41, ww40100, ww3000, Succ(ww2400)) → new_deleteBy5(ww3000, Succ(Succ(Zero)), ww41)
new_deleteBy01(ww41, Float(Neg(Zero), Pos(Succ(ww40100))), Float(Neg(Succ(ww3000)), Pos(Succ(Succ(Succ(ww310000)))))) → new_deleteBy084(ww41, ww40100, ww3000, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
new_deleteBy01(ww41, Float(Pos(Zero), Neg(Succ(ww40100))), Float(Neg(Succ(ww3000)), Pos(Succ(Succ(Zero))))) → new_deleteBy062(ww41, ww40100, ww3000, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy0132(:(ww360, ww361), ww37, ww380, ww39, ww400) → new_deleteBy01(ww361, ww360, Float(Neg(Succ(ww39)), Neg(ww400)))
new_deleteBy0130(ww36, ww37, ww3800, ww39, ww4000, Zero, Succ(ww25000)) → new_deleteBy0131(ww36, ww37, ww3800, ww39, ww4000)
new_deleteBy0130(ww36, ww37, ww3800, ww39, ww4000, Succ(ww21900), Zero) → new_deleteBy0131(ww36, ww37, ww3800, ww39, ww4000)
new_deleteBy083(ww42, ww43, Neg(Succ(ww4400)), ww45, Neg(Zero), Succ(ww3080)) → new_deleteBy5(ww45, Zero, ww42)
new_deleteBy058(ww36, ww37, Neg(Zero), ww39, Pos(Zero), Succ(ww2190)) → new_deleteBy4(ww39, Zero, ww36)
new_deleteBy066(ww41, ww40100, ww3000, Succ(ww2460)) → new_deleteBy5(ww3000, Succ(Succ(Zero)), ww41)
new_deleteBy01(ww41, Float(Neg(Zero), Pos(Succ(ww40100))), Float(Neg(Succ(ww3000)), Neg(Succ(Succ(Succ(ww310000)))))) → new_deleteBy088(ww41, ww40100, ww3000, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
new_deleteBy058(ww36, ww37, Neg(Succ(ww3800)), ww39, Pos(Succ(ww4000)), Succ(ww2190)) → new_deleteBy0121(ww36, ww37, ww3800, ww39, ww4000, ww2190, new_primPlusNat0(new_primMulNat0(ww4000, ww3800), Succ(ww3800)))
new_deleteBy0134(ww42, ww43, ww4400, ww45, ww4600, ww3080, Zero) → new_deleteBy5(ww45, Succ(ww4600), ww42)
new_deleteBy088(ww41, ww40100, ww3000, ww310000, Succ(ww3270)) → new_deleteBy5(ww3000, Succ(Succ(Succ(ww310000))), ww41)
new_deleteBy01(ww41, Float(Pos(Zero), Pos(Succ(ww40100))), Float(Neg(Succ(ww3000)), Neg(Succ(Zero)))) → new_deleteBy5(ww3000, Succ(Zero), ww41)
new_deleteBy0141(ww42, ww43, ww440, ww45, ww460) → new_deleteBy4(ww45, ww460, ww42)
new_deleteBy060(ww41, ww40100, ww3000, Succ(ww2280)) → new_deleteBy4(ww3000, Succ(Succ(Zero)), ww41)
new_deleteBy0127(:(ww360, ww361), ww37, ww380, ww39, ww400) → new_deleteBy01(ww361, ww360, Float(Neg(Succ(ww39)), Pos(ww400)))
new_deleteBy0135(ww42, ww43, ww4400, ww45, ww4600, Succ(ww3430)) → new_deleteBy0140(ww42, ww43, ww4400, ww45, ww4600)
new_deleteBy091(ww41, ww40100, ww3000, Succ(ww3370)) → new_deleteBy5(ww3000, Succ(Succ(Zero)), ww41)
new_deleteBy0137(ww42, ww43, ww4400, ww45, ww4600, Succ(ww3470)) → new_deleteBy0142(ww42, ww43, Succ(ww4400), ww45, Succ(ww4600))
new_deleteBy0142(ww42, ww43, ww440, ww45, ww460) → new_deleteBy5(ww45, ww460, ww42)
new_deleteBy083(ww42, ww43, Pos(Succ(ww4400)), ww45, Pos(Zero), Succ(ww3080)) → new_deleteBy4(ww45, Zero, ww42)
new_deleteBy4(ww39, ww400, :(ww360, ww361)) → new_deleteBy01(ww361, ww360, Float(Neg(Succ(ww39)), Pos(ww400)))
new_deleteBy083(ww42, ww43, Neg(Succ(ww4400)), ww45, Neg(Succ(ww4600)), Succ(ww3080)) → new_deleteBy0134(ww42, ww43, ww4400, ww45, ww4600, ww3080, new_primPlusNat0(new_primMulNat0(ww4600, ww4400), Succ(ww4400)))
new_deleteBy083(ww42, ww43, Neg(Succ(ww4400)), ww45, Neg(Succ(ww4600)), Zero) → new_deleteBy0138(ww42, ww43, ww4400, ww45, ww4600, new_primPlusNat0(new_primMulNat0(ww4600, ww4400), Succ(ww4400)))
new_deleteBy0133(ww42, ww43, ww4400, ww45, ww4600, Succ(ww30800), Succ(Succ(ww33900))) → new_deleteBy0139(ww42, ww43, ww4400, ww45, ww4600, ww30800, ww33900)
new_deleteBy061(ww41, ww40100, ww3000, ww310000, Succ(ww2300)) → new_deleteBy4(ww3000, Succ(Succ(Succ(ww310000))), ww41)
new_deleteBy058(ww36, ww37, Pos(Succ(ww3800)), ww39, Pos(Succ(ww4000)), Zero) → new_deleteBy0123(ww36, ww37, ww3800, ww39, ww4000, new_primPlusNat0(new_primMulNat0(ww4000, ww3800), Succ(ww3800)))
new_deleteBy083(ww42, ww43, Pos(Zero), ww45, Pos(Succ(ww4600)), Succ(ww3080)) → new_deleteBy4(ww45, Succ(ww4600), ww42)
new_deleteBy0133(ww42, ww43, ww4400, ww45, ww4600, Succ(ww30800), Succ(Zero)) → new_deleteBy0140(ww42, ww43, ww4400, ww45, ww4600)
new_deleteBy01(ww41, Float(Neg(Zero), Pos(Succ(ww40100))), Float(Neg(Succ(ww3000)), Pos(Succ(Succ(Zero))))) → new_deleteBy085(ww41, ww40100, ww3000, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy084(ww41, ww40100, ww3000, ww310000, Succ(ww3150)) → new_deleteBy4(ww3000, Succ(Succ(Succ(ww310000))), ww41)
new_deleteBy083(ww42, ww43, Neg(Zero), ww45, Neg(Zero), Succ(ww3080)) → new_deleteBy5(ww45, Zero, ww42)
new_deleteBy0122(ww36, ww37, ww3800, ww39, ww4000, Succ(ww21900), Succ(Succ(ww25000))) → new_deleteBy0130(ww36, ww37, ww3800, ww39, ww4000, ww21900, ww25000)
new_deleteBy0134(ww42, ww43, ww4400, ww45, ww4600, Succ(ww30800), Succ(Zero)) → new_deleteBy0144(ww42, ww43, ww4400, ww45, ww4600)
new_deleteBy01(ww41, Float(Neg(Zero), Neg(Succ(ww40100))), Float(Neg(Succ(ww3000)), Pos(Succ(Zero)))) → new_deleteBy4(ww3000, Succ(Zero), ww41)
new_deleteBy0133(ww42, ww43, ww4400, ww45, ww4600, Zero, Succ(Succ(ww33900))) → new_deleteBy0140(ww42, ww43, ww4400, ww45, ww4600)
new_deleteBy01(ww41, Float(Neg(Zero), Pos(Succ(ww40100))), Float(Neg(Succ(ww3000)), Neg(Succ(Zero)))) → new_deleteBy5(ww3000, Succ(Zero), ww41)
new_deleteBy01(ww41, Float(Pos(Zero), Neg(Succ(ww40100))), Float(Neg(Succ(ww3000)), Neg(Succ(Zero)))) → new_deleteBy5(ww3000, Succ(Zero), ww41)
The TRS R consists of the following rules:
new_primPlusNat1(Zero, ww40000) → Succ(ww40000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, ww40000) → Zero
new_primPlusNat1(Succ(ww520), ww40000) → Succ(Succ(new_primPlusNat0(ww520, ww40000)))
new_primPlusNat0(Succ(ww5200), Zero) → Succ(ww5200)
new_primPlusNat0(Zero, Succ(ww400000)) → Succ(ww400000)
new_primPlusNat0(Succ(ww5200), Succ(ww400000)) → Succ(Succ(new_primPlusNat0(ww5200, ww400000)))
new_primMulNat0(Succ(ww30000), ww40000) → new_primPlusNat1(new_primMulNat0(ww30000, ww40000), ww40000)
The set Q consists of the following terms:
new_primMulNat0(Succ(x0), x1)
new_primMulNat0(Zero, x0)
new_primPlusNat1(Succ(x0), x1)
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
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_deleteBy5(ww39, ww400, :(ww360, ww361)) → new_deleteBy01(ww361, ww360, Float(Neg(Succ(ww39)), Neg(ww400)))
The graph contains the following edges 3 > 1, 3 > 2
- new_deleteBy01(ww41, Float(Neg(Zero), Pos(Succ(ww40100))), Float(Neg(Succ(ww3000)), Neg(Succ(Succ(Zero))))) → new_deleteBy089(ww41, ww40100, ww3000, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
The graph contains the following edges 1 >= 1, 2 > 2, 3 > 3
- new_deleteBy089(ww41, ww40100, ww3000, Succ(ww3310)) → new_deleteBy5(ww3000, Succ(Succ(Zero)), ww41)
The graph contains the following edges 3 >= 1, 1 >= 3
- new_deleteBy090(ww41, ww40100, ww3000, ww310000, Succ(ww3330)) → new_deleteBy5(ww3000, Succ(Succ(Succ(ww310000))), ww41)
The graph contains the following edges 3 >= 1, 1 >= 3
- new_deleteBy01(ww41, Float(Neg(Zero), Neg(Succ(ww40100))), Float(Neg(Succ(ww3000)), Neg(Succ(Succ(Succ(ww310000)))))) → new_deleteBy090(ww41, ww40100, ww3000, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
The graph contains the following edges 1 >= 1, 2 > 2, 3 > 3, 3 > 4
- new_deleteBy058(:(ww360, ww361), ww37, Neg(ww380), ww39, Neg(ww400), Succ(ww2190)) → new_deleteBy01(ww361, ww360, Float(Neg(Succ(ww39)), Neg(ww400)))
The graph contains the following edges 1 > 1, 1 > 2
- new_deleteBy0132(:(ww360, ww361), ww37, ww380, ww39, ww400) → new_deleteBy01(ww361, ww360, Float(Neg(Succ(ww39)), Neg(ww400)))
The graph contains the following edges 1 > 1, 1 > 2
- new_deleteBy058(:(ww360, ww361), ww37, Pos(ww380), ww39, Pos(ww400), Succ(ww2190)) → new_deleteBy01(ww361, ww360, Float(Neg(Succ(ww39)), Pos(ww400)))
The graph contains the following edges 1 > 1, 1 > 2
- new_deleteBy01(ww41, Float(Pos(Succ(ww40000)), ww401), Float(Neg(Succ(ww3000)), ww31)) → new_deleteBy058(ww41, ww40000, ww401, ww3000, ww31, new_primPlusNat0(new_primMulNat0(ww3000, ww40000), Succ(ww40000)))
The graph contains the following edges 1 >= 1, 2 > 2, 2 > 3, 3 > 4, 3 > 5
- new_deleteBy01(ww41, Float(Neg(Succ(ww40000)), ww401), Float(Neg(Succ(ww3000)), ww31)) → new_deleteBy083(ww41, ww40000, ww401, ww3000, ww31, new_primPlusNat0(new_primMulNat0(ww3000, ww40000), Succ(ww40000)))
The graph contains the following edges 1 >= 1, 2 > 2, 2 > 3, 3 > 4, 3 > 5
- new_deleteBy060(ww41, ww40100, ww3000, Succ(ww2280)) → new_deleteBy4(ww3000, Succ(Succ(Zero)), ww41)
The graph contains the following edges 3 >= 1, 1 >= 3
- new_deleteBy4(ww39, ww400, :(ww360, ww361)) → new_deleteBy01(ww361, ww360, Float(Neg(Succ(ww39)), Pos(ww400)))
The graph contains the following edges 3 > 1, 3 > 2
- new_deleteBy0127(:(ww360, ww361), ww37, ww380, ww39, ww400) → new_deleteBy01(ww361, ww360, Float(Neg(Succ(ww39)), Pos(ww400)))
The graph contains the following edges 1 > 1, 1 > 2
- new_deleteBy01(ww41, Float(Pos(Zero), Pos(Succ(ww40100))), Float(Neg(Succ(ww3000)), Pos(Succ(Succ(Zero))))) → new_deleteBy060(ww41, ww40100, ww3000, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
The graph contains the following edges 1 >= 1, 2 > 2, 3 > 3
- new_deleteBy0133(ww42, ww43, ww4400, ww45, ww4600, ww3080, Zero) → new_deleteBy4(ww45, Succ(ww4600), ww42)
The graph contains the following edges 4 >= 1, 1 >= 3
- new_deleteBy083(ww42, ww43, Pos(Succ(ww4400)), ww45, Pos(Succ(ww4600)), Succ(ww3080)) → new_deleteBy0133(ww42, ww43, ww4400, ww45, ww4600, ww3080, new_primPlusNat0(new_primMulNat0(ww4600, ww4400), Succ(ww4400)))
The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 >= 4, 5 > 5, 6 > 6
- new_deleteBy0140(ww42, ww43, ww4400, ww45, ww4600) → new_deleteBy4(ww45, Succ(ww4600), ww42)
The graph contains the following edges 4 >= 1, 1 >= 3
- new_deleteBy0133(ww42, ww43, ww4400, ww45, ww4600, Succ(ww30800), Succ(Succ(ww33900))) → new_deleteBy0139(ww42, ww43, ww4400, ww45, ww4600, ww30800, ww33900)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 > 6, 7 > 7
- new_deleteBy0135(ww42, ww43, ww4400, ww45, ww4600, Succ(ww3430)) → new_deleteBy0140(ww42, ww43, ww4400, ww45, ww4600)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5
- new_deleteBy0139(ww42, ww43, ww4400, ww45, ww4600, Succ(ww30800), Succ(ww33900)) → new_deleteBy0139(ww42, ww43, ww4400, ww45, ww4600, ww30800, ww33900)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 > 6, 7 > 7
- new_deleteBy0134(ww42, ww43, ww4400, ww45, ww4600, ww3080, Zero) → new_deleteBy5(ww45, Succ(ww4600), ww42)
The graph contains the following edges 4 >= 1, 1 >= 3
- new_deleteBy083(ww42, ww43, Neg(Succ(ww4400)), ww45, Neg(Succ(ww4600)), Succ(ww3080)) → new_deleteBy0134(ww42, ww43, ww4400, ww45, ww4600, ww3080, new_primPlusNat0(new_primMulNat0(ww4600, ww4400), Succ(ww4400)))
The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 >= 4, 5 > 5, 6 > 6
- new_deleteBy0144(ww42, ww43, ww4400, ww45, ww4600) → new_deleteBy5(ww45, Succ(ww4600), ww42)
The graph contains the following edges 4 >= 1, 1 >= 3
- new_deleteBy0134(ww42, ww43, ww4400, ww45, ww4600, Succ(ww30800), Succ(Succ(ww34100))) → new_deleteBy0143(ww42, ww43, ww4400, ww45, ww4600, ww30800, ww34100)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 > 6, 7 > 7
- new_deleteBy0143(ww42, ww43, ww4400, ww45, ww4600, Succ(ww30800), Succ(ww34100)) → new_deleteBy0143(ww42, ww43, ww4400, ww45, ww4600, ww30800, ww34100)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 > 6, 7 > 7
- new_deleteBy0138(ww42, ww43, ww4400, ww45, ww4600, Succ(ww3490)) → new_deleteBy0144(ww42, ww43, ww4400, ww45, ww4600)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5
- new_deleteBy083(ww42, ww43, Neg(Succ(ww4400)), ww45, Neg(Succ(ww4600)), Zero) → new_deleteBy0138(ww42, ww43, ww4400, ww45, ww4600, new_primPlusNat0(new_primMulNat0(ww4600, ww4400), Succ(ww4400)))
The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 >= 4, 5 > 5
- new_deleteBy083(ww42, ww43, Pos(Succ(ww4400)), ww45, Pos(Succ(ww4600)), Zero) → new_deleteBy0135(ww42, ww43, ww4400, ww45, ww4600, new_primPlusNat0(new_primMulNat0(ww4600, ww4400), Succ(ww4400)))
The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 >= 4, 5 > 5
- new_deleteBy0137(ww42, ww43, ww4400, ww45, ww4600, Succ(ww3470)) → new_deleteBy0142(ww42, ww43, Succ(ww4400), ww45, Succ(ww4600))
The graph contains the following edges 1 >= 1, 2 >= 2, 4 >= 4
- new_deleteBy0142(ww42, ww43, ww440, ww45, ww460) → new_deleteBy5(ww45, ww460, ww42)
The graph contains the following edges 4 >= 1, 5 >= 2, 1 >= 3
- new_deleteBy083(ww42, ww43, Pos(Succ(ww4400)), ww45, Neg(Succ(ww4600)), Zero) → new_deleteBy0137(ww42, ww43, ww4400, ww45, ww4600, new_primPlusNat0(new_primMulNat0(ww4600, ww4400), Succ(ww4400)))
The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 >= 4, 5 > 5
- new_deleteBy083(ww42, ww43, Neg(Succ(ww4400)), ww45, Pos(Succ(ww4600)), Zero) → new_deleteBy0136(ww42, ww43, ww4400, ww45, ww4600, new_primPlusNat0(new_primMulNat0(ww4600, ww4400), Succ(ww4400)))
The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 >= 4, 5 > 5
- new_deleteBy0136(ww42, ww43, ww4400, ww45, ww4600, Succ(ww3450)) → new_deleteBy0141(ww42, ww43, Succ(ww4400), ww45, Succ(ww4600))
The graph contains the following edges 1 >= 1, 2 >= 2, 4 >= 4
- new_deleteBy0141(ww42, ww43, ww440, ww45, ww460) → new_deleteBy4(ww45, ww460, ww42)
The graph contains the following edges 4 >= 1, 5 >= 2, 1 >= 3
- new_deleteBy059(ww41, ww40100, ww3000, ww310000, Succ(ww2240)) → new_deleteBy4(ww3000, Succ(Succ(Succ(ww310000))), ww41)
The graph contains the following edges 3 >= 1, 1 >= 3
- new_deleteBy01(ww41, Float(Pos(Zero), Pos(Succ(ww40100))), Float(Neg(Succ(ww3000)), Pos(Succ(Succ(Succ(ww310000)))))) → new_deleteBy059(ww41, ww40100, ww3000, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
The graph contains the following edges 1 >= 1, 2 > 2, 3 > 3, 3 > 4
- new_deleteBy085(ww41, ww40100, ww3000, Succ(ww3190)) → new_deleteBy4(ww3000, Succ(Succ(Zero)), ww41)
The graph contains the following edges 3 >= 1, 1 >= 3
- new_deleteBy01(ww41, Float(Neg(Zero), Pos(Succ(ww40100))), Float(Neg(Succ(ww3000)), Pos(Succ(Succ(Zero))))) → new_deleteBy085(ww41, ww40100, ww3000, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
The graph contains the following edges 1 >= 1, 2 > 2, 3 > 3
- new_deleteBy084(ww41, ww40100, ww3000, ww310000, Succ(ww3150)) → new_deleteBy4(ww3000, Succ(Succ(Succ(ww310000))), ww41)
The graph contains the following edges 3 >= 1, 1 >= 3
- new_deleteBy01(ww41, Float(Neg(Zero), Pos(Succ(ww40100))), Float(Neg(Succ(ww3000)), Pos(Succ(Succ(Succ(ww310000)))))) → new_deleteBy084(ww41, ww40100, ww3000, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
The graph contains the following edges 1 >= 1, 2 > 2, 3 > 3, 3 > 4
- new_deleteBy061(ww41, ww40100, ww3000, ww310000, Succ(ww2300)) → new_deleteBy4(ww3000, Succ(Succ(Succ(ww310000))), ww41)
The graph contains the following edges 3 >= 1, 1 >= 3
- new_deleteBy01(ww41, Float(Pos(Zero), Neg(Succ(ww40100))), Float(Neg(Succ(ww3000)), Pos(Succ(Succ(Succ(ww310000)))))) → new_deleteBy061(ww41, ww40100, ww3000, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
The graph contains the following edges 1 >= 1, 2 > 2, 3 > 3, 3 > 4
- new_deleteBy087(ww41, ww40100, ww3000, Succ(ww3250)) → new_deleteBy4(ww3000, Succ(Succ(Zero)), ww41)
The graph contains the following edges 3 >= 1, 1 >= 3
- new_deleteBy01(ww41, Float(Neg(Zero), Neg(Succ(ww40100))), Float(Neg(Succ(ww3000)), Pos(Succ(Succ(Zero))))) → new_deleteBy087(ww41, ww40100, ww3000, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
The graph contains the following edges 1 >= 1, 2 > 2, 3 > 3
- new_deleteBy086(ww41, ww40100, ww3000, ww310000, Succ(ww3210)) → new_deleteBy4(ww3000, Succ(Succ(Succ(ww310000))), ww41)
The graph contains the following edges 3 >= 1, 1 >= 3
- new_deleteBy01(ww41, Float(Neg(Zero), Neg(Succ(ww40100))), Float(Neg(Succ(ww3000)), Pos(Succ(Succ(Succ(ww310000)))))) → new_deleteBy086(ww41, ww40100, ww3000, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
The graph contains the following edges 1 >= 1, 2 > 2, 3 > 3, 3 > 4
- new_deleteBy01(ww41, Float(Pos(Zero), Neg(Succ(ww40100))), Float(Neg(Succ(ww3000)), Pos(Succ(Succ(Zero))))) → new_deleteBy062(ww41, ww40100, ww3000, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
The graph contains the following edges 1 >= 1, 2 > 2, 3 > 3
- new_deleteBy062(ww41, ww40100, ww3000, Succ(ww2340)) → new_deleteBy4(ww3000, Succ(Succ(Zero)), ww41)
The graph contains the following edges 3 >= 1, 1 >= 3
- new_deleteBy0126(ww36, ww37, ww3800, ww39, ww4000, Succ(ww2580)) → new_deleteBy0132(ww36, ww37, Succ(ww3800), ww39, Succ(ww4000))
The graph contains the following edges 1 >= 1, 2 >= 2, 4 >= 4
- new_deleteBy058(ww36, ww37, Neg(Succ(ww3800)), ww39, Neg(Succ(ww4000)), Zero) → new_deleteBy0126(ww36, ww37, ww3800, ww39, ww4000, new_primPlusNat0(new_primMulNat0(ww4000, ww3800), Succ(ww3800)))
The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 >= 4, 5 > 5
- new_deleteBy066(ww41, ww40100, ww3000, Succ(ww2460)) → new_deleteBy5(ww3000, Succ(Succ(Zero)), ww41)
The graph contains the following edges 3 >= 1, 1 >= 3
- new_deleteBy01(ww41, Float(Pos(Zero), Neg(Succ(ww40100))), Float(Neg(Succ(ww3000)), Neg(Succ(Succ(Zero))))) → new_deleteBy066(ww41, ww40100, ww3000, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
The graph contains the following edges 1 >= 1, 2 > 2, 3 > 3
- new_deleteBy088(ww41, ww40100, ww3000, ww310000, Succ(ww3270)) → new_deleteBy5(ww3000, Succ(Succ(Succ(ww310000))), ww41)
The graph contains the following edges 3 >= 1, 1 >= 3
- new_deleteBy01(ww41, Float(Neg(Zero), Pos(Succ(ww40100))), Float(Neg(Succ(ww3000)), Neg(Succ(Succ(Succ(ww310000)))))) → new_deleteBy088(ww41, ww40100, ww3000, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
The graph contains the following edges 1 >= 1, 2 > 2, 3 > 3, 3 > 4
- new_deleteBy063(ww41, ww40100, ww3000, ww310000, Succ(ww2360)) → new_deleteBy5(ww3000, Succ(Succ(Succ(ww310000))), ww41)
The graph contains the following edges 3 >= 1, 1 >= 3
- new_deleteBy01(ww41, Float(Pos(Zero), Pos(Succ(ww40100))), Float(Neg(Succ(ww3000)), Neg(Succ(Succ(Succ(ww310000)))))) → new_deleteBy063(ww41, ww40100, ww3000, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
The graph contains the following edges 1 >= 1, 2 > 2, 3 > 3, 3 > 4
- new_deleteBy064(ww41, ww40100, ww3000, Succ(ww2400)) → new_deleteBy5(ww3000, Succ(Succ(Zero)), ww41)
The graph contains the following edges 3 >= 1, 1 >= 3
- new_deleteBy01(ww41, Float(Pos(Zero), Pos(Succ(ww40100))), Float(Neg(Succ(ww3000)), Neg(Succ(Succ(Zero))))) → new_deleteBy064(ww41, ww40100, ww3000, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
The graph contains the following edges 1 >= 1, 2 > 2, 3 > 3
- new_deleteBy065(ww41, ww40100, ww3000, ww310000, Succ(ww2420)) → new_deleteBy5(ww3000, Succ(Succ(Succ(ww310000))), ww41)
The graph contains the following edges 3 >= 1, 1 >= 3
- new_deleteBy01(ww41, Float(Pos(Zero), Neg(Succ(ww40100))), Float(Neg(Succ(ww3000)), Neg(Succ(Succ(Succ(ww310000)))))) → new_deleteBy065(ww41, ww40100, ww3000, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
The graph contains the following edges 1 >= 1, 2 > 2, 3 > 3, 3 > 4
- new_deleteBy01(ww41, Float(Neg(Zero), Neg(Succ(ww40100))), Float(Neg(Succ(ww3000)), Neg(Succ(Succ(Zero))))) → new_deleteBy091(ww41, ww40100, ww3000, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
The graph contains the following edges 1 >= 1, 2 > 2, 3 > 3
- new_deleteBy091(ww41, ww40100, ww3000, Succ(ww3370)) → new_deleteBy5(ww3000, Succ(Succ(Zero)), ww41)
The graph contains the following edges 3 >= 1, 1 >= 3
- new_deleteBy0125(ww36, ww37, ww3800, ww39, ww4000, Succ(ww2560)) → new_deleteBy0131(ww36, ww37, ww3800, ww39, ww4000)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5
- new_deleteBy0131(ww36, ww37, ww3800, ww39, ww4000) → new_deleteBy5(ww39, Succ(ww4000), ww36)
The graph contains the following edges 4 >= 1, 1 >= 3
- new_deleteBy0122(ww36, ww37, ww3800, ww39, ww4000, ww2190, Zero) → new_deleteBy5(ww39, Succ(ww4000), ww36)
The graph contains the following edges 4 >= 1, 1 >= 3
- new_deleteBy058(ww36, ww37, Pos(Succ(ww3800)), ww39, Neg(Succ(ww4000)), Zero) → new_deleteBy0125(ww36, ww37, ww3800, ww39, ww4000, new_primPlusNat0(new_primMulNat0(ww4000, ww3800), Succ(ww3800)))
The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 >= 4, 5 > 5
- new_deleteBy0122(ww36, ww37, ww3800, ww39, ww4000, Succ(ww21900), Succ(Succ(ww25000))) → new_deleteBy0130(ww36, ww37, ww3800, ww39, ww4000, ww21900, ww25000)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 > 6, 7 > 7
- new_deleteBy058(ww36, ww37, Pos(Succ(ww3800)), ww39, Neg(Succ(ww4000)), Succ(ww2190)) → new_deleteBy0122(ww36, ww37, ww3800, ww39, ww4000, ww2190, new_primPlusNat0(new_primMulNat0(ww4000, ww3800), Succ(ww3800)))
The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 >= 4, 5 > 5, 6 > 6
- new_deleteBy0130(ww36, ww37, ww3800, ww39, ww4000, Succ(ww21900), Succ(ww25000)) → new_deleteBy0130(ww36, ww37, ww3800, ww39, ww4000, ww21900, ww25000)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 > 6, 7 > 7
- new_deleteBy0124(ww36, ww37, ww3800, ww39, ww4000, Succ(ww2540)) → new_deleteBy0129(ww36, ww37, ww3800, ww39, ww4000)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5
- new_deleteBy058(ww36, ww37, Neg(Succ(ww3800)), ww39, Pos(Succ(ww4000)), Zero) → new_deleteBy0124(ww36, ww37, ww3800, ww39, ww4000, new_primPlusNat0(new_primMulNat0(ww4000, ww3800), Succ(ww3800)))
The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 >= 4, 5 > 5
- new_deleteBy0129(ww36, ww37, ww3800, ww39, ww4000) → new_deleteBy4(ww39, Succ(ww4000), ww36)
The graph contains the following edges 4 >= 1, 1 >= 3
- new_deleteBy0121(ww36, ww37, ww3800, ww39, ww4000, ww2190, Zero) → new_deleteBy4(ww39, Succ(ww4000), ww36)
The graph contains the following edges 4 >= 1, 1 >= 3
- new_deleteBy0121(ww36, ww37, ww3800, ww39, ww4000, Succ(ww21900), Succ(Succ(ww24800))) → new_deleteBy0128(ww36, ww37, ww3800, ww39, ww4000, ww21900, ww24800)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 > 6, 7 > 7
- new_deleteBy058(ww36, ww37, Neg(Succ(ww3800)), ww39, Pos(Succ(ww4000)), Succ(ww2190)) → new_deleteBy0121(ww36, ww37, ww3800, ww39, ww4000, ww2190, new_primPlusNat0(new_primMulNat0(ww4000, ww3800), Succ(ww3800)))
The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 >= 4, 5 > 5, 6 > 6
- new_deleteBy058(ww36, ww37, Pos(Succ(ww3800)), ww39, Pos(Succ(ww4000)), Zero) → new_deleteBy0123(ww36, ww37, ww3800, ww39, ww4000, new_primPlusNat0(new_primMulNat0(ww4000, ww3800), Succ(ww3800)))
The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 >= 4, 5 > 5
- new_deleteBy0128(ww36, ww37, ww3800, ww39, ww4000, Succ(ww21900), Succ(ww24800)) → new_deleteBy0128(ww36, ww37, ww3800, ww39, ww4000, ww21900, ww24800)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 > 6, 7 > 7
- new_deleteBy0123(ww36, ww37, ww3800, ww39, ww4000, Succ(ww2520)) → new_deleteBy0127(ww36, ww37, Succ(ww3800), ww39, Succ(ww4000))
The graph contains the following edges 1 >= 1, 2 >= 2, 4 >= 4
- new_deleteBy01(ww41, Float(Neg(Zero), Pos(Succ(ww40100))), Float(Neg(Succ(ww3000)), Neg(Succ(Zero)))) → new_deleteBy5(ww3000, Succ(Zero), ww41)
The graph contains the following edges 3 > 1, 3 > 2, 1 >= 3
- new_deleteBy01(ww41, Float(Pos(Zero), Neg(Succ(ww40100))), Float(Neg(Succ(ww3000)), Neg(Succ(Zero)))) → new_deleteBy5(ww3000, Succ(Zero), ww41)
The graph contains the following edges 3 > 1, 3 > 2, 1 >= 3
- new_deleteBy01(ww41, Float(Neg(Zero), Neg(Succ(ww40100))), Float(Neg(Succ(ww3000)), Neg(Succ(Zero)))) → new_deleteBy5(ww3000, Succ(Zero), ww41)
The graph contains the following edges 3 > 1, 3 > 2, 1 >= 3
- new_deleteBy01(ww41, Float(Pos(Zero), Pos(Succ(ww40100))), Float(Neg(Succ(ww3000)), Neg(Succ(Zero)))) → new_deleteBy5(ww3000, Succ(Zero), ww41)
The graph contains the following edges 3 > 1, 3 > 2, 1 >= 3
- new_deleteBy058(ww36, ww37, Pos(Zero), ww39, Neg(Succ(ww4000)), Succ(ww2190)) → new_deleteBy5(ww39, Succ(ww4000), ww36)
The graph contains the following edges 4 >= 1, 5 > 2, 1 >= 3
- new_deleteBy058(ww36, ww37, Pos(Succ(ww3800)), ww39, Neg(Zero), Succ(ww2190)) → new_deleteBy5(ww39, Zero, ww36)
The graph contains the following edges 4 >= 1, 5 > 2, 1 >= 3
- new_deleteBy058(ww36, ww37, Pos(Zero), ww39, Neg(Zero), Succ(ww2190)) → new_deleteBy5(ww39, Zero, ww36)
The graph contains the following edges 4 >= 1, 3 > 2, 5 > 2, 1 >= 3
- new_deleteBy083(ww42, ww43, Neg(Succ(ww4400)), ww45, Neg(Zero), Succ(ww3080)) → new_deleteBy5(ww45, Zero, ww42)
The graph contains the following edges 4 >= 1, 5 > 2, 1 >= 3
- new_deleteBy083(ww42, ww43, Pos(ww440), ww45, Neg(ww460), Succ(ww3080)) → new_deleteBy5(ww45, ww460, ww42)
The graph contains the following edges 4 >= 1, 5 > 2, 1 >= 3
- new_deleteBy083(ww42, ww43, Neg(Zero), ww45, Neg(Zero), Succ(ww3080)) → new_deleteBy5(ww45, Zero, ww42)
The graph contains the following edges 4 >= 1, 3 > 2, 5 > 2, 1 >= 3
- new_deleteBy083(ww42, ww43, Neg(Zero), ww45, Neg(Succ(ww4600)), Succ(ww3080)) → new_deleteBy5(ww45, Succ(ww4600), ww42)
The graph contains the following edges 4 >= 1, 5 > 2, 1 >= 3
- new_deleteBy058(ww36, ww37, Neg(Succ(ww3800)), ww39, Pos(Zero), Succ(ww2190)) → new_deleteBy4(ww39, Zero, ww36)
The graph contains the following edges 4 >= 1, 5 > 2, 1 >= 3
- new_deleteBy058(ww36, ww37, Neg(Zero), ww39, Pos(Zero), Succ(ww2190)) → new_deleteBy4(ww39, Zero, ww36)
The graph contains the following edges 4 >= 1, 3 > 2, 5 > 2, 1 >= 3
- new_deleteBy058(ww36, ww37, Neg(Zero), ww39, Pos(Succ(ww4000)), Succ(ww2190)) → new_deleteBy4(ww39, Succ(ww4000), ww36)
The graph contains the following edges 4 >= 1, 5 > 2, 1 >= 3
- new_deleteBy01(ww41, Float(Neg(Zero), Pos(Succ(ww40100))), Float(Neg(Succ(ww3000)), Pos(Succ(Zero)))) → new_deleteBy4(ww3000, Succ(Zero), ww41)
The graph contains the following edges 3 > 1, 3 > 2, 1 >= 3
- new_deleteBy01(ww41, Float(Pos(Zero), Neg(Succ(ww40100))), Float(Neg(Succ(ww3000)), Pos(Succ(Zero)))) → new_deleteBy4(ww3000, Succ(Zero), ww41)
The graph contains the following edges 3 > 1, 3 > 2, 1 >= 3
- new_deleteBy01(ww41, Float(Pos(Zero), Pos(Succ(ww40100))), Float(Neg(Succ(ww3000)), Pos(Succ(Zero)))) → new_deleteBy4(ww3000, Succ(Zero), ww41)
The graph contains the following edges 3 > 1, 3 > 2, 1 >= 3
- new_deleteBy01(ww41, Float(Neg(Zero), Neg(Succ(ww40100))), Float(Neg(Succ(ww3000)), Pos(Succ(Zero)))) → new_deleteBy4(ww3000, Succ(Zero), ww41)
The graph contains the following edges 3 > 1, 3 > 2, 1 >= 3
- new_deleteBy083(ww42, ww43, Pos(Zero), ww45, Pos(Zero), Succ(ww3080)) → new_deleteBy4(ww45, Zero, ww42)
The graph contains the following edges 4 >= 1, 3 > 2, 5 > 2, 1 >= 3
- new_deleteBy083(ww42, ww43, Pos(Succ(ww4400)), ww45, Pos(Zero), Succ(ww3080)) → new_deleteBy4(ww45, Zero, ww42)
The graph contains the following edges 4 >= 1, 5 > 2, 1 >= 3
- new_deleteBy083(ww42, ww43, Pos(Zero), ww45, Pos(Succ(ww4600)), Succ(ww3080)) → new_deleteBy4(ww45, Succ(ww4600), ww42)
The graph contains the following edges 4 >= 1, 5 > 2, 1 >= 3
- new_deleteBy083(ww42, ww43, Neg(ww440), ww45, Pos(ww460), Succ(ww3080)) → new_deleteBy4(ww45, ww460, ww42)
The graph contains the following edges 4 >= 1, 5 > 2, 1 >= 3
- new_deleteBy0133(ww42, ww43, ww4400, ww45, ww4600, Succ(ww30800), Succ(Zero)) → new_deleteBy0140(ww42, ww43, ww4400, ww45, ww4600)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5
- new_deleteBy0133(ww42, ww43, ww4400, ww45, ww4600, Zero, Succ(Succ(ww33900))) → new_deleteBy0140(ww42, ww43, ww4400, ww45, ww4600)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5
- new_deleteBy0139(ww42, ww43, ww4400, ww45, ww4600, Succ(ww30800), Zero) → new_deleteBy0140(ww42, ww43, ww4400, ww45, ww4600)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5
- new_deleteBy0139(ww42, ww43, ww4400, ww45, ww4600, Zero, Succ(ww33900)) → new_deleteBy0140(ww42, ww43, ww4400, ww45, ww4600)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5
- new_deleteBy0134(ww42, ww43, ww4400, ww45, ww4600, Zero, Succ(Succ(ww34100))) → new_deleteBy0144(ww42, ww43, ww4400, ww45, ww4600)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5
- new_deleteBy0134(ww42, ww43, ww4400, ww45, ww4600, Succ(ww30800), Succ(Zero)) → new_deleteBy0144(ww42, ww43, ww4400, ww45, ww4600)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5
- new_deleteBy0143(ww42, ww43, ww4400, ww45, ww4600, Succ(ww30800), Zero) → new_deleteBy0144(ww42, ww43, ww4400, ww45, ww4600)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5
- new_deleteBy0143(ww42, ww43, ww4400, ww45, ww4600, Zero, Succ(ww34100)) → new_deleteBy0144(ww42, ww43, ww4400, ww45, ww4600)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5
- new_deleteBy0122(ww36, ww37, ww3800, ww39, ww4000, Zero, Succ(Succ(ww25000))) → new_deleteBy0131(ww36, ww37, ww3800, ww39, ww4000)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5
- new_deleteBy0122(ww36, ww37, ww3800, ww39, ww4000, Succ(ww21900), Succ(Zero)) → new_deleteBy0131(ww36, ww37, ww3800, ww39, ww4000)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5
- new_deleteBy0130(ww36, ww37, ww3800, ww39, ww4000, Succ(ww21900), Zero) → new_deleteBy0131(ww36, ww37, ww3800, ww39, ww4000)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5
- new_deleteBy0130(ww36, ww37, ww3800, ww39, ww4000, Zero, Succ(ww25000)) → new_deleteBy0131(ww36, ww37, ww3800, ww39, ww4000)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5
- new_deleteBy0121(ww36, ww37, ww3800, ww39, ww4000, Zero, Succ(Succ(ww24800))) → new_deleteBy0129(ww36, ww37, ww3800, ww39, ww4000)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5
- new_deleteBy0121(ww36, ww37, ww3800, ww39, ww4000, Succ(ww21900), Succ(Zero)) → new_deleteBy0129(ww36, ww37, ww3800, ww39, ww4000)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5
- new_deleteBy0128(ww36, ww37, ww3800, ww39, ww4000, Succ(ww21900), Zero) → new_deleteBy0129(ww36, ww37, ww3800, ww39, ww4000)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5
- new_deleteBy0128(ww36, ww37, ww3800, ww39, ww4000, Zero, Succ(ww24800)) → new_deleteBy0129(ww36, ww37, ww3800, ww39, ww4000)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDPSizeChangeProof
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_deleteBy0111(ww23, ww24, ww2500, ww26, ww2700, Succ(ww1630)) → new_deleteBy0115(ww23, ww24, Succ(ww2500), ww26, Succ(ww2700))
new_deleteBy033(ww23, ww24, Neg(Succ(ww2500)), ww26, Pos(Succ(ww2700)), Succ(ww1280)) → new_deleteBy0109(ww23, ww24, ww2500, ww26, ww2700, ww1280, new_primPlusNat0(new_primMulNat0(ww2700, ww2500), Succ(ww2500)))
new_deleteBy0(:(ww170, ww171), ww18, Neg(ww190), ww20, Pos(ww210), Succ(ww530)) → new_deleteBy01(ww171, ww170, Float(Pos(Succ(ww20)), Pos(ww210)))
new_deleteBy0146(:(ww170, ww171), ww18, ww190, ww20, ww210) → new_deleteBy01(ww171, ww170, Float(Pos(Succ(ww20)), Neg(ww210)))
new_deleteBy0(ww17, ww18, Pos(Zero), ww20, Pos(Zero), Succ(ww530)) → new_deleteBy(ww20, Zero, ww17)
new_deleteBy01(ww41, Float(Neg(Zero), Neg(Succ(ww40100))), Float(Pos(Succ(ww3000)), Pos(Succ(Zero)))) → new_deleteBy(ww3000, Succ(Zero), ww41)
new_deleteBy02(ww17, ww18, ww1900, ww20, ww2100, ww530, Zero) → new_deleteBy1(ww20, Succ(ww2100), ww17)
new_deleteBy01(ww41, Float(Pos(Zero), Neg(Succ(ww40100))), Float(Pos(Succ(ww3000)), Pos(Succ(Succ(Zero))))) → new_deleteBy012(ww41, ww40100, ww3000, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy01(ww41, Float(Neg(Zero), Pos(Succ(ww40100))), Float(Pos(Succ(ww3000)), Pos(Succ(Succ(Succ(ww310000)))))) → new_deleteBy034(ww41, ww40100, ww3000, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
new_deleteBy0114(ww23, ww24, ww2500, ww26, ww2700, Succ(ww1690)) → new_deleteBy0120(ww23, ww24, Succ(ww2500), ww26, Succ(ww2700))
new_deleteBy011(ww41, ww40100, ww3000, ww310000, Succ(ww4030)) → new_deleteBy(ww3000, Succ(Succ(Succ(ww310000))), ww41)
new_deleteBy033(ww23, ww24, Pos(Succ(ww2500)), ww26, Pos(Succ(ww2700)), Zero) → new_deleteBy0111(ww23, ww24, ww2500, ww26, ww2700, new_primPlusNat0(new_primMulNat0(ww2700, ww2500), Succ(ww2500)))
new_deleteBy0118(ww23, ww24, ww2500, ww26, ww2700, Succ(ww12800), Succ(ww16100)) → new_deleteBy0118(ww23, ww24, ww2500, ww26, ww2700, ww12800, ww16100)
new_deleteBy02(ww17, ww18, ww1900, ww20, ww2100, Succ(ww5300), Succ(Zero)) → new_deleteBy0148(ww17, ww18, ww1900, ww20, ww2100)
new_deleteBy08(ww17, ww18, ww1900, ww20, ww2100) → new_deleteBy(ww20, Succ(ww2100), ww17)
new_deleteBy0110(ww23, ww24, ww2500, ww26, ww2700, Succ(ww12800), Succ(Succ(ww16100))) → new_deleteBy0118(ww23, ww24, ww2500, ww26, ww2700, ww12800, ww16100)
new_deleteBy0115(ww23, ww24, ww250, ww26, ww270) → new_deleteBy(ww26, ww270, ww23)
new_deleteBy04(ww17, ww18, ww1900, ww20, ww2100, Succ(ww840)) → new_deleteBy0145(ww17, ww18, Succ(ww1900), ww20, Succ(ww2100))
new_deleteBy01(ww41, Float(Pos(Zero), Pos(Succ(ww40100))), Float(Pos(Succ(ww3000)), Pos(Succ(Succ(Zero))))) → new_deleteBy010(ww41, ww40100, ww3000, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy0110(ww23, ww24, ww2500, ww26, ww2700, ww1280, Zero) → new_deleteBy1(ww26, Succ(ww2700), ww23)
new_deleteBy0(ww17, ww18, Pos(Succ(ww1900)), ww20, Neg(Succ(ww2100)), Zero) → new_deleteBy05(ww17, ww18, ww1900, ww20, ww2100, new_primPlusNat0(new_primMulNat0(ww2100, ww1900), Succ(ww1900)))
new_deleteBy01(ww41, Float(Pos(Zero), Pos(Succ(ww40100))), Float(Pos(Succ(ww3000)), Pos(Succ(Succ(Succ(ww310000)))))) → new_deleteBy09(ww41, ww40100, ww3000, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
new_deleteBy(ww20, ww210, :(ww170, ww171)) → new_deleteBy01(ww171, ww170, Float(Pos(Succ(ww20)), Pos(ww210)))
new_deleteBy0112(ww23, ww24, ww2500, ww26, ww2700, Succ(ww1650)) → new_deleteBy0117(ww23, ww24, ww2500, ww26, ww2700)
new_deleteBy033(ww23, ww24, Neg(Succ(ww2500)), ww26, Pos(Zero), Succ(ww1280)) → new_deleteBy(ww26, Zero, ww23)
new_deleteBy0148(ww17, ww18, ww1900, ww20, ww2100) → new_deleteBy1(ww20, Succ(ww2100), ww17)
new_deleteBy016(ww41, ww40100, ww3000, Succ(ww660)) → new_deleteBy1(ww3000, Succ(Succ(Zero)), ww41)
new_deleteBy0109(ww23, ww24, ww2500, ww26, ww2700, Zero, Succ(Succ(ww15900))) → new_deleteBy0117(ww23, ww24, ww2500, ww26, ww2700)
new_deleteBy00(ww17, ww18, ww1900, ww20, ww2100, Succ(ww5300), Succ(Zero)) → new_deleteBy08(ww17, ww18, ww1900, ww20, ww2100)
new_deleteBy039(ww41, ww40100, ww3000, Succ(ww1510)) → new_deleteBy1(ww3000, Succ(Succ(Zero)), ww41)
new_deleteBy040(ww41, ww40100, ww3000, ww310000, Succ(ww1530)) → new_deleteBy1(ww3000, Succ(Succ(Succ(ww310000))), ww41)
new_deleteBy0(ww17, ww18, Neg(Succ(ww1900)), ww20, Neg(Succ(ww2100)), Zero) → new_deleteBy06(ww17, ww18, ww1900, ww20, ww2100, new_primPlusNat0(new_primMulNat0(ww2100, ww1900), Succ(ww1900)))
new_deleteBy033(ww23, ww24, Pos(Zero), ww26, Neg(Succ(ww2700)), Succ(ww1280)) → new_deleteBy1(ww26, Succ(ww2700), ww23)
new_deleteBy01(ww41, Float(Pos(Zero), Pos(Succ(ww40100))), Float(Pos(Succ(ww3000)), Neg(Succ(Succ(Zero))))) → new_deleteBy014(ww41, ww40100, ww3000, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy0(ww17, ww18, Pos(Succ(ww1900)), ww20, Pos(Zero), Succ(ww530)) → new_deleteBy(ww20, Zero, ww17)
new_deleteBy0118(ww23, ww24, ww2500, ww26, ww2700, Succ(ww12800), Zero) → new_deleteBy0119(ww23, ww24, ww2500, ww26, ww2700)
new_deleteBy0118(ww23, ww24, ww2500, ww26, ww2700, Zero, Succ(ww16100)) → new_deleteBy0119(ww23, ww24, ww2500, ww26, ww2700)
new_deleteBy033(ww23, ww24, Neg(Zero), ww26, Pos(Succ(ww2700)), Succ(ww1280)) → new_deleteBy(ww26, Succ(ww2700), ww23)
new_deleteBy014(ww41, ww40100, ww3000, Succ(ww600)) → new_deleteBy1(ww3000, Succ(Succ(Zero)), ww41)
new_deleteBy0(ww17, ww18, Pos(Succ(ww1900)), ww20, Pos(Succ(ww2100)), Succ(ww530)) → new_deleteBy00(ww17, ww18, ww1900, ww20, ww2100, ww530, new_primPlusNat0(new_primMulNat0(ww2100, ww1900), Succ(ww1900)))
new_deleteBy0(:(ww170, ww171), ww18, Pos(ww190), ww20, Neg(ww210), Succ(ww530)) → new_deleteBy01(ww171, ww170, Float(Pos(Succ(ww20)), Neg(ww210)))
new_deleteBy01(ww41, Float(Neg(Zero), Pos(Succ(ww40100))), Float(Pos(Succ(ww3000)), Neg(Succ(Zero)))) → new_deleteBy1(ww3000, Succ(Zero), ww41)
new_deleteBy01(ww41, Float(Pos(Zero), Neg(Succ(ww40100))), Float(Pos(Succ(ww3000)), Neg(Succ(Zero)))) → new_deleteBy1(ww3000, Succ(Zero), ww41)
new_deleteBy038(ww41, ww40100, ww3000, ww310000, Succ(ww1470)) → new_deleteBy1(ww3000, Succ(Succ(Succ(ww310000))), ww41)
new_deleteBy01(ww41, Float(Neg(Zero), Neg(Succ(ww40100))), Float(Pos(Succ(ww3000)), Neg(Succ(Succ(Zero))))) → new_deleteBy041(ww41, ww40100, ww3000, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy01(ww41, Float(Neg(Zero), Neg(Succ(ww40100))), Float(Pos(Succ(ww3000)), Neg(Succ(Succ(Succ(ww310000)))))) → new_deleteBy040(ww41, ww40100, ww3000, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
new_deleteBy0147(ww17, ww18, ww1900, ww20, ww2100, Succ(ww5300), Succ(ww8000)) → new_deleteBy0147(ww17, ww18, ww1900, ww20, ww2100, ww5300, ww8000)
new_deleteBy00(ww17, ww18, ww1900, ww20, ww2100, Succ(ww5300), Succ(Succ(ww7800))) → new_deleteBy07(ww17, ww18, ww1900, ww20, ww2100, ww5300, ww7800)
new_deleteBy0147(ww17, ww18, ww1900, ww20, ww2100, Zero, Succ(ww8000)) → new_deleteBy0148(ww17, ww18, ww1900, ww20, ww2100)
new_deleteBy0147(ww17, ww18, ww1900, ww20, ww2100, Succ(ww5300), Zero) → new_deleteBy0148(ww17, ww18, ww1900, ww20, ww2100)
new_deleteBy0109(ww23, ww24, ww2500, ww26, ww2700, ww1280, Zero) → new_deleteBy(ww26, Succ(ww2700), ww23)
new_deleteBy034(ww41, ww40100, ww3000, ww310000, Succ(ww1350)) → new_deleteBy(ww3000, Succ(Succ(Succ(ww310000))), ww41)
new_deleteBy01(ww41, Float(Neg(Zero), Pos(Succ(ww40100))), Float(Pos(Succ(ww3000)), Pos(Succ(Succ(Zero))))) → new_deleteBy035(ww41, ww40100, ww3000, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy036(ww41, ww40100, ww3000, ww310000, Succ(ww1410)) → new_deleteBy(ww3000, Succ(Succ(Succ(ww310000))), ww41)
new_deleteBy00(ww17, ww18, ww1900, ww20, ww2100, ww530, Zero) → new_deleteBy(ww20, Succ(ww2100), ww17)
new_deleteBy01(ww41, Float(Neg(Zero), Neg(Succ(ww40100))), Float(Pos(Succ(ww3000)), Pos(Succ(Succ(Succ(ww310000)))))) → new_deleteBy036(ww41, ww40100, ww3000, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
new_deleteBy01(ww41, Float(Neg(Zero), Pos(Succ(ww40100))), Float(Pos(Succ(ww3000)), Pos(Succ(Zero)))) → new_deleteBy(ww3000, Succ(Zero), ww41)
new_deleteBy01(ww41, Float(Pos(Zero), Neg(Succ(ww40100))), Float(Pos(Succ(ww3000)), Pos(Succ(Zero)))) → new_deleteBy(ww3000, Succ(Zero), ww41)
new_deleteBy037(ww41, ww40100, ww3000, Succ(ww1450)) → new_deleteBy(ww3000, Succ(Succ(Zero)), ww41)
new_deleteBy033(ww23, ww24, Neg(Succ(ww2500)), ww26, Pos(Succ(ww2700)), Zero) → new_deleteBy0112(ww23, ww24, ww2500, ww26, ww2700, new_primPlusNat0(new_primMulNat0(ww2700, ww2500), Succ(ww2500)))
new_deleteBy01(ww41, Float(Neg(Zero), Pos(Succ(ww40100))), Float(Pos(Succ(ww3000)), Neg(Succ(Succ(Zero))))) → new_deleteBy039(ww41, ww40100, ww3000, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy01(ww41, Float(Pos(Zero), Neg(Succ(ww40100))), Float(Pos(Succ(ww3000)), Neg(Succ(Succ(Succ(ww310000)))))) → new_deleteBy015(ww41, ww40100, ww3000, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
new_deleteBy0120(ww23, ww24, ww250, ww26, ww270) → new_deleteBy1(ww26, ww270, ww23)
new_deleteBy0110(ww23, ww24, ww2500, ww26, ww2700, Succ(ww12800), Succ(Zero)) → new_deleteBy0119(ww23, ww24, ww2500, ww26, ww2700)
new_deleteBy07(ww17, ww18, ww1900, ww20, ww2100, Succ(ww5300), Zero) → new_deleteBy08(ww17, ww18, ww1900, ww20, ww2100)
new_deleteBy07(ww17, ww18, ww1900, ww20, ww2100, Zero, Succ(ww7800)) → new_deleteBy08(ww17, ww18, ww1900, ww20, ww2100)
new_deleteBy02(ww17, ww18, ww1900, ww20, ww2100, Zero, Succ(Succ(ww8000))) → new_deleteBy0148(ww17, ww18, ww1900, ww20, ww2100)
new_deleteBy033(ww23, ww24, Neg(Succ(ww2500)), ww26, Neg(Succ(ww2700)), Zero) → new_deleteBy0114(ww23, ww24, ww2500, ww26, ww2700, new_primPlusNat0(new_primMulNat0(ww2700, ww2500), Succ(ww2500)))
new_deleteBy01(ww41, Float(Pos(Zero), Pos(Succ(ww40100))), Float(Pos(Succ(ww3000)), Pos(Succ(Zero)))) → new_deleteBy(ww3000, Succ(Zero), ww41)
new_deleteBy0(ww17, ww18, Neg(Succ(ww1900)), ww20, Pos(Succ(ww2100)), Zero) → new_deleteBy04(ww17, ww18, ww1900, ww20, ww2100, new_primPlusNat0(new_primMulNat0(ww2100, ww1900), Succ(ww1900)))
new_deleteBy05(ww17, ww18, ww1900, ww20, ww2100, Succ(ww860)) → new_deleteBy0146(ww17, ww18, Succ(ww1900), ww20, Succ(ww2100))
new_deleteBy0116(ww23, ww24, ww2500, ww26, ww2700, Succ(ww12800), Succ(ww15900)) → new_deleteBy0116(ww23, ww24, ww2500, ww26, ww2700, ww12800, ww15900)
new_deleteBy033(ww23, ww24, Pos(Succ(ww2500)), ww26, Neg(Zero), Succ(ww1280)) → new_deleteBy1(ww26, Zero, ww23)
new_deleteBy0(ww17, ww18, Pos(Succ(ww1900)), ww20, Pos(Succ(ww2100)), Zero) → new_deleteBy03(ww17, ww18, ww1900, ww20, ww2100, new_primPlusNat0(new_primMulNat0(ww2100, ww1900), Succ(ww1900)))
new_deleteBy0119(ww23, ww24, ww2500, ww26, ww2700) → new_deleteBy1(ww26, Succ(ww2700), ww23)
new_deleteBy09(ww41, ww40100, ww3000, ww310000, Succ(ww3990)) → new_deleteBy(ww3000, Succ(Succ(Succ(ww310000))), ww41)
new_deleteBy033(ww23, ww24, Pos(Succ(ww2500)), ww26, Neg(Succ(ww2700)), Zero) → new_deleteBy0113(ww23, ww24, ww2500, ww26, ww2700, new_primPlusNat0(new_primMulNat0(ww2700, ww2500), Succ(ww2500)))
new_deleteBy015(ww41, ww40100, ww3000, ww310000, Succ(ww620)) → new_deleteBy1(ww3000, Succ(Succ(Succ(ww310000))), ww41)
new_deleteBy1(ww20, ww210, :(ww170, ww171)) → new_deleteBy01(ww171, ww170, Float(Pos(Succ(ww20)), Neg(ww210)))
new_deleteBy0(ww17, ww18, Neg(Succ(ww1900)), ww20, Neg(Succ(ww2100)), Succ(ww530)) → new_deleteBy02(ww17, ww18, ww1900, ww20, ww2100, ww530, new_primPlusNat0(new_primMulNat0(ww2100, ww1900), Succ(ww1900)))
new_deleteBy0109(ww23, ww24, ww2500, ww26, ww2700, Succ(ww12800), Succ(Zero)) → new_deleteBy0117(ww23, ww24, ww2500, ww26, ww2700)
new_deleteBy033(ww23, ww24, Pos(Succ(ww2500)), ww26, Neg(Succ(ww2700)), Succ(ww1280)) → new_deleteBy0110(ww23, ww24, ww2500, ww26, ww2700, ww1280, new_primPlusNat0(new_primMulNat0(ww2700, ww2500), Succ(ww2500)))
new_deleteBy012(ww41, ww40100, ww3000, Succ(ww540)) → new_deleteBy(ww3000, Succ(Succ(Zero)), ww41)
new_deleteBy033(ww23, ww24, Neg(ww250), ww26, Neg(ww270), Succ(ww1280)) → new_deleteBy1(ww26, ww270, ww23)
new_deleteBy0(ww17, ww18, Neg(Zero), ww20, Neg(Zero), Succ(ww530)) → new_deleteBy1(ww20, Zero, ww17)
new_deleteBy0116(ww23, ww24, ww2500, ww26, ww2700, Zero, Succ(ww15900)) → new_deleteBy0117(ww23, ww24, ww2500, ww26, ww2700)
new_deleteBy0116(ww23, ww24, ww2500, ww26, ww2700, Succ(ww12800), Zero) → new_deleteBy0117(ww23, ww24, ww2500, ww26, ww2700)
new_deleteBy01(ww41, Float(Neg(Zero), Neg(Succ(ww40100))), Float(Pos(Succ(ww3000)), Neg(Succ(Zero)))) → new_deleteBy1(ww3000, Succ(Zero), ww41)
new_deleteBy041(ww41, ww40100, ww3000, Succ(ww1570)) → new_deleteBy1(ww3000, Succ(Succ(Zero)), ww41)
new_deleteBy033(ww23, ww24, Neg(Zero), ww26, Pos(Zero), Succ(ww1280)) → new_deleteBy(ww26, Zero, ww23)
new_deleteBy01(ww41, Float(Pos(Zero), Pos(Succ(ww40100))), Float(Pos(Succ(ww3000)), Neg(Succ(Zero)))) → new_deleteBy1(ww3000, Succ(Zero), ww41)
new_deleteBy0109(ww23, ww24, ww2500, ww26, ww2700, Succ(ww12800), Succ(Succ(ww15900))) → new_deleteBy0116(ww23, ww24, ww2500, ww26, ww2700, ww12800, ww15900)
new_deleteBy0113(ww23, ww24, ww2500, ww26, ww2700, Succ(ww1670)) → new_deleteBy0119(ww23, ww24, ww2500, ww26, ww2700)
new_deleteBy013(ww41, ww40100, ww3000, ww310000, Succ(ww560)) → new_deleteBy1(ww3000, Succ(Succ(Succ(ww310000))), ww41)
new_deleteBy0145(:(ww170, ww171), ww18, ww190, ww20, ww210) → new_deleteBy01(ww171, ww170, Float(Pos(Succ(ww20)), Pos(ww210)))
new_deleteBy01(ww41, Float(Neg(Zero), Neg(Succ(ww40100))), Float(Pos(Succ(ww3000)), Pos(Succ(Succ(Zero))))) → new_deleteBy037(ww41, ww40100, ww3000, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy0117(ww23, ww24, ww2500, ww26, ww2700) → new_deleteBy(ww26, Succ(ww2700), ww23)
new_deleteBy06(ww17, ww18, ww1900, ww20, ww2100, Succ(ww880)) → new_deleteBy0148(ww17, ww18, ww1900, ww20, ww2100)
new_deleteBy0(ww17, ww18, Neg(Succ(ww1900)), ww20, Neg(Zero), Succ(ww530)) → new_deleteBy1(ww20, Zero, ww17)
new_deleteBy01(ww41, Float(Pos(Succ(ww40000)), ww401), Float(Pos(Succ(ww3000)), ww31)) → new_deleteBy0(ww41, ww40000, ww401, ww3000, ww31, new_primPlusNat1(new_primMulNat0(ww3000, ww40000), ww40000))
new_deleteBy01(ww41, Float(Neg(Succ(ww40000)), ww401), Float(Pos(Succ(ww3000)), ww31)) → new_deleteBy033(ww41, ww40000, ww401, ww3000, ww31, new_primPlusNat0(new_primMulNat0(ww3000, ww40000), Succ(ww40000)))
new_deleteBy02(ww17, ww18, ww1900, ww20, ww2100, Succ(ww5300), Succ(Succ(ww8000))) → new_deleteBy0147(ww17, ww18, ww1900, ww20, ww2100, ww5300, ww8000)
new_deleteBy01(ww41, Float(Pos(Zero), Pos(Succ(ww40100))), Float(Pos(Succ(ww3000)), Neg(Succ(Succ(Succ(ww310000)))))) → new_deleteBy013(ww41, ww40100, ww3000, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
new_deleteBy0(ww17, ww18, Pos(Zero), ww20, Pos(Succ(ww2100)), Succ(ww530)) → new_deleteBy(ww20, Succ(ww2100), ww17)
new_deleteBy01(ww41, Float(Neg(Zero), Pos(Succ(ww40100))), Float(Pos(Succ(ww3000)), Neg(Succ(Succ(Succ(ww310000)))))) → new_deleteBy038(ww41, ww40100, ww3000, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
new_deleteBy01(ww41, Float(Pos(Zero), Neg(Succ(ww40100))), Float(Pos(Succ(ww3000)), Neg(Succ(Succ(Zero))))) → new_deleteBy016(ww41, ww40100, ww3000, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy07(ww17, ww18, ww1900, ww20, ww2100, Succ(ww5300), Succ(ww7800)) → new_deleteBy07(ww17, ww18, ww1900, ww20, ww2100, ww5300, ww7800)
new_deleteBy0(ww17, ww18, Neg(Zero), ww20, Neg(Succ(ww2100)), Succ(ww530)) → new_deleteBy1(ww20, Succ(ww2100), ww17)
new_deleteBy010(ww41, ww40100, ww3000, Succ(ww4020)) → new_deleteBy(ww3000, Succ(Succ(Zero)), ww41)
new_deleteBy03(ww17, ww18, ww1900, ww20, ww2100, Succ(ww820)) → new_deleteBy08(ww17, ww18, ww1900, ww20, ww2100)
new_deleteBy035(ww41, ww40100, ww3000, Succ(ww1390)) → new_deleteBy(ww3000, Succ(Succ(Zero)), ww41)
new_deleteBy0110(ww23, ww24, ww2500, ww26, ww2700, Zero, Succ(Succ(ww16100))) → new_deleteBy0119(ww23, ww24, ww2500, ww26, ww2700)
new_deleteBy00(ww17, ww18, ww1900, ww20, ww2100, Zero, Succ(Succ(ww7800))) → new_deleteBy08(ww17, ww18, ww1900, ww20, ww2100)
new_deleteBy033(ww23, ww24, Pos(ww250), ww26, Pos(ww270), Succ(ww1280)) → new_deleteBy(ww26, ww270, ww23)
new_deleteBy033(ww23, ww24, Pos(Zero), ww26, Neg(Zero), Succ(ww1280)) → new_deleteBy1(ww26, Zero, ww23)
new_deleteBy01(ww41, Float(Pos(Zero), Neg(Succ(ww40100))), Float(Pos(Succ(ww3000)), Pos(Succ(Succ(Succ(ww310000)))))) → new_deleteBy011(ww41, ww40100, ww3000, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
The TRS R consists of the following rules:
new_primPlusNat1(Zero, ww40000) → Succ(ww40000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, ww40000) → Zero
new_primPlusNat1(Succ(ww520), ww40000) → Succ(Succ(new_primPlusNat0(ww520, ww40000)))
new_primPlusNat0(Succ(ww5200), Zero) → Succ(ww5200)
new_primPlusNat0(Zero, Succ(ww400000)) → Succ(ww400000)
new_primPlusNat0(Succ(ww5200), Succ(ww400000)) → Succ(Succ(new_primPlusNat0(ww5200, ww400000)))
new_primMulNat0(Succ(ww30000), ww40000) → new_primPlusNat1(new_primMulNat0(ww30000, ww40000), ww40000)
The set Q consists of the following terms:
new_primMulNat0(Succ(x0), x1)
new_primMulNat0(Zero, x0)
new_primPlusNat1(Succ(x0), x1)
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
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(ww20, ww210, :(ww170, ww171)) → new_deleteBy01(ww171, ww170, Float(Pos(Succ(ww20)), Pos(ww210)))
The graph contains the following edges 3 > 1, 3 > 2
- new_deleteBy0111(ww23, ww24, ww2500, ww26, ww2700, Succ(ww1630)) → new_deleteBy0115(ww23, ww24, Succ(ww2500), ww26, Succ(ww2700))
The graph contains the following edges 1 >= 1, 2 >= 2, 4 >= 4
- new_deleteBy010(ww41, ww40100, ww3000, Succ(ww4020)) → new_deleteBy(ww3000, Succ(Succ(Zero)), ww41)
The graph contains the following edges 3 >= 1, 1 >= 3
- new_deleteBy01(ww41, Float(Pos(Zero), Pos(Succ(ww40100))), Float(Pos(Succ(ww3000)), Pos(Succ(Succ(Zero))))) → new_deleteBy010(ww41, ww40100, ww3000, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
The graph contains the following edges 1 >= 1, 2 > 2, 3 > 3
- new_deleteBy09(ww41, ww40100, ww3000, ww310000, Succ(ww3990)) → new_deleteBy(ww3000, Succ(Succ(Succ(ww310000))), ww41)
The graph contains the following edges 3 >= 1, 1 >= 3
- new_deleteBy01(ww41, Float(Pos(Zero), Pos(Succ(ww40100))), Float(Pos(Succ(ww3000)), Pos(Succ(Succ(Succ(ww310000)))))) → new_deleteBy09(ww41, ww40100, ww3000, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
The graph contains the following edges 1 >= 1, 2 > 2, 3 > 3, 3 > 4
- new_deleteBy012(ww41, ww40100, ww3000, Succ(ww540)) → new_deleteBy(ww3000, Succ(Succ(Zero)), ww41)
The graph contains the following edges 3 >= 1, 1 >= 3
- new_deleteBy01(ww41, Float(Pos(Zero), Neg(Succ(ww40100))), Float(Pos(Succ(ww3000)), Pos(Succ(Succ(Zero))))) → new_deleteBy012(ww41, ww40100, ww3000, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
The graph contains the following edges 1 >= 1, 2 > 2, 3 > 3
- new_deleteBy034(ww41, ww40100, ww3000, ww310000, Succ(ww1350)) → new_deleteBy(ww3000, Succ(Succ(Succ(ww310000))), ww41)
The graph contains the following edges 3 >= 1, 1 >= 3
- new_deleteBy01(ww41, Float(Neg(Zero), Pos(Succ(ww40100))), Float(Pos(Succ(ww3000)), Pos(Succ(Succ(Succ(ww310000)))))) → new_deleteBy034(ww41, ww40100, ww3000, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
The graph contains the following edges 1 >= 1, 2 > 2, 3 > 3, 3 > 4
- new_deleteBy035(ww41, ww40100, ww3000, Succ(ww1390)) → new_deleteBy(ww3000, Succ(Succ(Zero)), ww41)
The graph contains the following edges 3 >= 1, 1 >= 3
- new_deleteBy01(ww41, Float(Neg(Zero), Pos(Succ(ww40100))), Float(Pos(Succ(ww3000)), Pos(Succ(Succ(Zero))))) → new_deleteBy035(ww41, ww40100, ww3000, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
The graph contains the following edges 1 >= 1, 2 > 2, 3 > 3
- new_deleteBy036(ww41, ww40100, ww3000, ww310000, Succ(ww1410)) → new_deleteBy(ww3000, Succ(Succ(Succ(ww310000))), ww41)
The graph contains the following edges 3 >= 1, 1 >= 3
- new_deleteBy01(ww41, Float(Neg(Zero), Neg(Succ(ww40100))), Float(Pos(Succ(ww3000)), Pos(Succ(Succ(Succ(ww310000)))))) → new_deleteBy036(ww41, ww40100, ww3000, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
The graph contains the following edges 1 >= 1, 2 > 2, 3 > 3, 3 > 4
- new_deleteBy01(ww41, Float(Neg(Succ(ww40000)), ww401), Float(Pos(Succ(ww3000)), ww31)) → new_deleteBy033(ww41, ww40000, ww401, ww3000, ww31, new_primPlusNat0(new_primMulNat0(ww3000, ww40000), Succ(ww40000)))
The graph contains the following edges 1 >= 1, 2 > 2, 2 > 3, 3 > 4, 3 > 5
- new_deleteBy0112(ww23, ww24, ww2500, ww26, ww2700, Succ(ww1650)) → new_deleteBy0117(ww23, ww24, ww2500, ww26, ww2700)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5
- new_deleteBy0117(ww23, ww24, ww2500, ww26, ww2700) → new_deleteBy(ww26, Succ(ww2700), ww23)
The graph contains the following edges 4 >= 1, 1 >= 3
- new_deleteBy033(ww23, ww24, Neg(Succ(ww2500)), ww26, Pos(Succ(ww2700)), Zero) → new_deleteBy0112(ww23, ww24, ww2500, ww26, ww2700, new_primPlusNat0(new_primMulNat0(ww2700, ww2500), Succ(ww2500)))
The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 >= 4, 5 > 5
- new_deleteBy0114(ww23, ww24, ww2500, ww26, ww2700, Succ(ww1690)) → new_deleteBy0120(ww23, ww24, Succ(ww2500), ww26, Succ(ww2700))
The graph contains the following edges 1 >= 1, 2 >= 2, 4 >= 4
- new_deleteBy033(ww23, ww24, Neg(Succ(ww2500)), ww26, Neg(Succ(ww2700)), Zero) → new_deleteBy0114(ww23, ww24, ww2500, ww26, ww2700, new_primPlusNat0(new_primMulNat0(ww2700, ww2500), Succ(ww2500)))
The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 >= 4, 5 > 5
- new_deleteBy0120(ww23, ww24, ww250, ww26, ww270) → new_deleteBy1(ww26, ww270, ww23)
The graph contains the following edges 4 >= 1, 5 >= 2, 1 >= 3
- new_deleteBy1(ww20, ww210, :(ww170, ww171)) → new_deleteBy01(ww171, ww170, Float(Pos(Succ(ww20)), Neg(ww210)))
The graph contains the following edges 3 > 1, 3 > 2
- new_deleteBy01(ww41, Float(Pos(Succ(ww40000)), ww401), Float(Pos(Succ(ww3000)), ww31)) → new_deleteBy0(ww41, ww40000, ww401, ww3000, ww31, new_primPlusNat1(new_primMulNat0(ww3000, ww40000), ww40000))
The graph contains the following edges 1 >= 1, 2 > 2, 2 > 3, 3 > 4, 3 > 5
- new_deleteBy041(ww41, ww40100, ww3000, Succ(ww1570)) → new_deleteBy1(ww3000, Succ(Succ(Zero)), ww41)
The graph contains the following edges 3 >= 1, 1 >= 3
- new_deleteBy01(ww41, Float(Neg(Zero), Neg(Succ(ww40100))), Float(Pos(Succ(ww3000)), Neg(Succ(Succ(Zero))))) → new_deleteBy041(ww41, ww40100, ww3000, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
The graph contains the following edges 1 >= 1, 2 > 2, 3 > 3
- new_deleteBy038(ww41, ww40100, ww3000, ww310000, Succ(ww1470)) → new_deleteBy1(ww3000, Succ(Succ(Succ(ww310000))), ww41)
The graph contains the following edges 3 >= 1, 1 >= 3
- new_deleteBy01(ww41, Float(Neg(Zero), Pos(Succ(ww40100))), Float(Pos(Succ(ww3000)), Neg(Succ(Succ(Succ(ww310000)))))) → new_deleteBy038(ww41, ww40100, ww3000, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
The graph contains the following edges 1 >= 1, 2 > 2, 3 > 3, 3 > 4
- new_deleteBy016(ww41, ww40100, ww3000, Succ(ww660)) → new_deleteBy1(ww3000, Succ(Succ(Zero)), ww41)
The graph contains the following edges 3 >= 1, 1 >= 3
- new_deleteBy01(ww41, Float(Pos(Zero), Neg(Succ(ww40100))), Float(Pos(Succ(ww3000)), Neg(Succ(Succ(Zero))))) → new_deleteBy016(ww41, ww40100, ww3000, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
The graph contains the following edges 1 >= 1, 2 > 2, 3 > 3
- new_deleteBy015(ww41, ww40100, ww3000, ww310000, Succ(ww620)) → new_deleteBy1(ww3000, Succ(Succ(Succ(ww310000))), ww41)
The graph contains the following edges 3 >= 1, 1 >= 3
- new_deleteBy01(ww41, Float(Pos(Zero), Neg(Succ(ww40100))), Float(Pos(Succ(ww3000)), Neg(Succ(Succ(Succ(ww310000)))))) → new_deleteBy015(ww41, ww40100, ww3000, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
The graph contains the following edges 1 >= 1, 2 > 2, 3 > 3, 3 > 4
- new_deleteBy014(ww41, ww40100, ww3000, Succ(ww600)) → new_deleteBy1(ww3000, Succ(Succ(Zero)), ww41)
The graph contains the following edges 3 >= 1, 1 >= 3
- new_deleteBy01(ww41, Float(Pos(Zero), Pos(Succ(ww40100))), Float(Pos(Succ(ww3000)), Neg(Succ(Succ(Zero))))) → new_deleteBy014(ww41, ww40100, ww3000, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
The graph contains the following edges 1 >= 1, 2 > 2, 3 > 3
- new_deleteBy0(:(ww170, ww171), ww18, Neg(ww190), ww20, Pos(ww210), Succ(ww530)) → new_deleteBy01(ww171, ww170, Float(Pos(Succ(ww20)), Pos(ww210)))
The graph contains the following edges 1 > 1, 1 > 2
- new_deleteBy0145(:(ww170, ww171), ww18, ww190, ww20, ww210) → new_deleteBy01(ww171, ww170, Float(Pos(Succ(ww20)), Pos(ww210)))
The graph contains the following edges 1 > 1, 1 > 2
- new_deleteBy0(:(ww170, ww171), ww18, Pos(ww190), ww20, Neg(ww210), Succ(ww530)) → new_deleteBy01(ww171, ww170, Float(Pos(Succ(ww20)), Neg(ww210)))
The graph contains the following edges 1 > 1, 1 > 2
- new_deleteBy0146(:(ww170, ww171), ww18, ww190, ww20, ww210) → new_deleteBy01(ww171, ww170, Float(Pos(Succ(ww20)), Neg(ww210)))
The graph contains the following edges 1 > 1, 1 > 2
- new_deleteBy037(ww41, ww40100, ww3000, Succ(ww1450)) → new_deleteBy(ww3000, Succ(Succ(Zero)), ww41)
The graph contains the following edges 3 >= 1, 1 >= 3
- new_deleteBy01(ww41, Float(Neg(Zero), Neg(Succ(ww40100))), Float(Pos(Succ(ww3000)), Pos(Succ(Succ(Zero))))) → new_deleteBy037(ww41, ww40100, ww3000, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
The graph contains the following edges 1 >= 1, 2 > 2, 3 > 3
- new_deleteBy01(ww41, Float(Pos(Zero), Neg(Succ(ww40100))), Float(Pos(Succ(ww3000)), Pos(Succ(Succ(Succ(ww310000)))))) → new_deleteBy011(ww41, ww40100, ww3000, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
The graph contains the following edges 1 >= 1, 2 > 2, 3 > 3, 3 > 4
- new_deleteBy011(ww41, ww40100, ww3000, ww310000, Succ(ww4030)) → new_deleteBy(ww3000, Succ(Succ(Succ(ww310000))), ww41)
The graph contains the following edges 3 >= 1, 1 >= 3
- new_deleteBy05(ww17, ww18, ww1900, ww20, ww2100, Succ(ww860)) → new_deleteBy0146(ww17, ww18, Succ(ww1900), ww20, Succ(ww2100))
The graph contains the following edges 1 >= 1, 2 >= 2, 4 >= 4
- new_deleteBy0(ww17, ww18, Pos(Succ(ww1900)), ww20, Neg(Succ(ww2100)), Zero) → new_deleteBy05(ww17, ww18, ww1900, ww20, ww2100, new_primPlusNat0(new_primMulNat0(ww2100, ww1900), Succ(ww1900)))
The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 >= 4, 5 > 5
- new_deleteBy040(ww41, ww40100, ww3000, ww310000, Succ(ww1530)) → new_deleteBy1(ww3000, Succ(Succ(Succ(ww310000))), ww41)
The graph contains the following edges 3 >= 1, 1 >= 3
- new_deleteBy01(ww41, Float(Neg(Zero), Neg(Succ(ww40100))), Float(Pos(Succ(ww3000)), Neg(Succ(Succ(Succ(ww310000)))))) → new_deleteBy040(ww41, ww40100, ww3000, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
The graph contains the following edges 1 >= 1, 2 > 2, 3 > 3, 3 > 4
- new_deleteBy039(ww41, ww40100, ww3000, Succ(ww1510)) → new_deleteBy1(ww3000, Succ(Succ(Zero)), ww41)
The graph contains the following edges 3 >= 1, 1 >= 3
- new_deleteBy01(ww41, Float(Neg(Zero), Pos(Succ(ww40100))), Float(Pos(Succ(ww3000)), Neg(Succ(Succ(Zero))))) → new_deleteBy039(ww41, ww40100, ww3000, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
The graph contains the following edges 1 >= 1, 2 > 2, 3 > 3
- new_deleteBy01(ww41, Float(Pos(Zero), Pos(Succ(ww40100))), Float(Pos(Succ(ww3000)), Neg(Succ(Succ(Succ(ww310000)))))) → new_deleteBy013(ww41, ww40100, ww3000, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
The graph contains the following edges 1 >= 1, 2 > 2, 3 > 3, 3 > 4
- new_deleteBy013(ww41, ww40100, ww3000, ww310000, Succ(ww560)) → new_deleteBy1(ww3000, Succ(Succ(Succ(ww310000))), ww41)
The graph contains the following edges 3 >= 1, 1 >= 3
- new_deleteBy04(ww17, ww18, ww1900, ww20, ww2100, Succ(ww840)) → new_deleteBy0145(ww17, ww18, Succ(ww1900), ww20, Succ(ww2100))
The graph contains the following edges 1 >= 1, 2 >= 2, 4 >= 4
- new_deleteBy0(ww17, ww18, Neg(Succ(ww1900)), ww20, Pos(Succ(ww2100)), Zero) → new_deleteBy04(ww17, ww18, ww1900, ww20, ww2100, new_primPlusNat0(new_primMulNat0(ww2100, ww1900), Succ(ww1900)))
The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 >= 4, 5 > 5
- new_deleteBy06(ww17, ww18, ww1900, ww20, ww2100, Succ(ww880)) → new_deleteBy0148(ww17, ww18, ww1900, ww20, ww2100)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5
- new_deleteBy0148(ww17, ww18, ww1900, ww20, ww2100) → new_deleteBy1(ww20, Succ(ww2100), ww17)
The graph contains the following edges 4 >= 1, 1 >= 3
- new_deleteBy0(ww17, ww18, Neg(Succ(ww1900)), ww20, Neg(Succ(ww2100)), Zero) → new_deleteBy06(ww17, ww18, ww1900, ww20, ww2100, new_primPlusNat0(new_primMulNat0(ww2100, ww1900), Succ(ww1900)))
The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 >= 4, 5 > 5
- new_deleteBy02(ww17, ww18, ww1900, ww20, ww2100, ww530, Zero) → new_deleteBy1(ww20, Succ(ww2100), ww17)
The graph contains the following edges 4 >= 1, 1 >= 3
- new_deleteBy02(ww17, ww18, ww1900, ww20, ww2100, Succ(ww5300), Succ(Succ(ww8000))) → new_deleteBy0147(ww17, ww18, ww1900, ww20, ww2100, ww5300, ww8000)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 > 6, 7 > 7
- new_deleteBy0(ww17, ww18, Neg(Succ(ww1900)), ww20, Neg(Succ(ww2100)), Succ(ww530)) → new_deleteBy02(ww17, ww18, ww1900, ww20, ww2100, ww530, new_primPlusNat0(new_primMulNat0(ww2100, ww1900), Succ(ww1900)))
The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 >= 4, 5 > 5, 6 > 6
- new_deleteBy0147(ww17, ww18, ww1900, ww20, ww2100, Succ(ww5300), Succ(ww8000)) → new_deleteBy0147(ww17, ww18, ww1900, ww20, ww2100, ww5300, ww8000)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 > 6, 7 > 7
- new_deleteBy00(ww17, ww18, ww1900, ww20, ww2100, ww530, Zero) → new_deleteBy(ww20, Succ(ww2100), ww17)
The graph contains the following edges 4 >= 1, 1 >= 3
- new_deleteBy08(ww17, ww18, ww1900, ww20, ww2100) → new_deleteBy(ww20, Succ(ww2100), ww17)
The graph contains the following edges 4 >= 1, 1 >= 3
- new_deleteBy0(ww17, ww18, Pos(Succ(ww1900)), ww20, Pos(Succ(ww2100)), Succ(ww530)) → new_deleteBy00(ww17, ww18, ww1900, ww20, ww2100, ww530, new_primPlusNat0(new_primMulNat0(ww2100, ww1900), Succ(ww1900)))
The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 >= 4, 5 > 5, 6 > 6
- new_deleteBy0(ww17, ww18, Pos(Succ(ww1900)), ww20, Pos(Succ(ww2100)), Zero) → new_deleteBy03(ww17, ww18, ww1900, ww20, ww2100, new_primPlusNat0(new_primMulNat0(ww2100, ww1900), Succ(ww1900)))
The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 >= 4, 5 > 5
- new_deleteBy00(ww17, ww18, ww1900, ww20, ww2100, Succ(ww5300), Succ(Succ(ww7800))) → new_deleteBy07(ww17, ww18, ww1900, ww20, ww2100, ww5300, ww7800)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 > 6, 7 > 7
- new_deleteBy03(ww17, ww18, ww1900, ww20, ww2100, Succ(ww820)) → new_deleteBy08(ww17, ww18, ww1900, ww20, ww2100)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5
- new_deleteBy07(ww17, ww18, ww1900, ww20, ww2100, Succ(ww5300), Succ(ww7800)) → new_deleteBy07(ww17, ww18, ww1900, ww20, ww2100, ww5300, ww7800)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 > 6, 7 > 7
- new_deleteBy0110(ww23, ww24, ww2500, ww26, ww2700, ww1280, Zero) → new_deleteBy1(ww26, Succ(ww2700), ww23)
The graph contains the following edges 4 >= 1, 1 >= 3
- new_deleteBy0119(ww23, ww24, ww2500, ww26, ww2700) → new_deleteBy1(ww26, Succ(ww2700), ww23)
The graph contains the following edges 4 >= 1, 1 >= 3
- new_deleteBy033(ww23, ww24, Pos(Succ(ww2500)), ww26, Neg(Succ(ww2700)), Succ(ww1280)) → new_deleteBy0110(ww23, ww24, ww2500, ww26, ww2700, ww1280, new_primPlusNat0(new_primMulNat0(ww2700, ww2500), Succ(ww2500)))
The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 >= 4, 5 > 5, 6 > 6
- new_deleteBy0110(ww23, ww24, ww2500, ww26, ww2700, Succ(ww12800), Succ(Succ(ww16100))) → new_deleteBy0118(ww23, ww24, ww2500, ww26, ww2700, ww12800, ww16100)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 > 6, 7 > 7
- new_deleteBy0118(ww23, ww24, ww2500, ww26, ww2700, Succ(ww12800), Succ(ww16100)) → new_deleteBy0118(ww23, ww24, ww2500, ww26, ww2700, ww12800, ww16100)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 > 6, 7 > 7
- new_deleteBy0113(ww23, ww24, ww2500, ww26, ww2700, Succ(ww1670)) → new_deleteBy0119(ww23, ww24, ww2500, ww26, ww2700)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5
- new_deleteBy0115(ww23, ww24, ww250, ww26, ww270) → new_deleteBy(ww26, ww270, ww23)
The graph contains the following edges 4 >= 1, 5 >= 2, 1 >= 3
- new_deleteBy0109(ww23, ww24, ww2500, ww26, ww2700, ww1280, Zero) → new_deleteBy(ww26, Succ(ww2700), ww23)
The graph contains the following edges 4 >= 1, 1 >= 3
- new_deleteBy033(ww23, ww24, Pos(Succ(ww2500)), ww26, Pos(Succ(ww2700)), Zero) → new_deleteBy0111(ww23, ww24, ww2500, ww26, ww2700, new_primPlusNat0(new_primMulNat0(ww2700, ww2500), Succ(ww2500)))
The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 >= 4, 5 > 5
- new_deleteBy033(ww23, ww24, Pos(Succ(ww2500)), ww26, Neg(Succ(ww2700)), Zero) → new_deleteBy0113(ww23, ww24, ww2500, ww26, ww2700, new_primPlusNat0(new_primMulNat0(ww2700, ww2500), Succ(ww2500)))
The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 >= 4, 5 > 5
- new_deleteBy033(ww23, ww24, Neg(Succ(ww2500)), ww26, Pos(Succ(ww2700)), Succ(ww1280)) → new_deleteBy0109(ww23, ww24, ww2500, ww26, ww2700, ww1280, new_primPlusNat0(new_primMulNat0(ww2700, ww2500), Succ(ww2500)))
The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 >= 4, 5 > 5, 6 > 6
- new_deleteBy0109(ww23, ww24, ww2500, ww26, ww2700, Succ(ww12800), Succ(Succ(ww15900))) → new_deleteBy0116(ww23, ww24, ww2500, ww26, ww2700, ww12800, ww15900)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 > 6, 7 > 7
- new_deleteBy0116(ww23, ww24, ww2500, ww26, ww2700, Succ(ww12800), Succ(ww15900)) → new_deleteBy0116(ww23, ww24, ww2500, ww26, ww2700, ww12800, ww15900)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 > 6, 7 > 7
- new_deleteBy01(ww41, Float(Pos(Zero), Pos(Succ(ww40100))), Float(Pos(Succ(ww3000)), Pos(Succ(Zero)))) → new_deleteBy(ww3000, Succ(Zero), ww41)
The graph contains the following edges 3 > 1, 3 > 2, 1 >= 3
- new_deleteBy01(ww41, Float(Neg(Zero), Neg(Succ(ww40100))), Float(Pos(Succ(ww3000)), Pos(Succ(Zero)))) → new_deleteBy(ww3000, Succ(Zero), ww41)
The graph contains the following edges 3 > 1, 3 > 2, 1 >= 3
- new_deleteBy01(ww41, Float(Pos(Zero), Neg(Succ(ww40100))), Float(Pos(Succ(ww3000)), Pos(Succ(Zero)))) → new_deleteBy(ww3000, Succ(Zero), ww41)
The graph contains the following edges 3 > 1, 3 > 2, 1 >= 3
- new_deleteBy01(ww41, Float(Neg(Zero), Pos(Succ(ww40100))), Float(Pos(Succ(ww3000)), Pos(Succ(Zero)))) → new_deleteBy(ww3000, Succ(Zero), ww41)
The graph contains the following edges 3 > 1, 3 > 2, 1 >= 3
- new_deleteBy033(ww23, ww24, Neg(Zero), ww26, Pos(Succ(ww2700)), Succ(ww1280)) → new_deleteBy(ww26, Succ(ww2700), ww23)
The graph contains the following edges 4 >= 1, 5 > 2, 1 >= 3
- new_deleteBy033(ww23, ww24, Neg(Zero), ww26, Pos(Zero), Succ(ww1280)) → new_deleteBy(ww26, Zero, ww23)
The graph contains the following edges 4 >= 1, 3 > 2, 5 > 2, 1 >= 3
- new_deleteBy033(ww23, ww24, Pos(ww250), ww26, Pos(ww270), Succ(ww1280)) → new_deleteBy(ww26, ww270, ww23)
The graph contains the following edges 4 >= 1, 5 > 2, 1 >= 3
- new_deleteBy033(ww23, ww24, Neg(Succ(ww2500)), ww26, Pos(Zero), Succ(ww1280)) → new_deleteBy(ww26, Zero, ww23)
The graph contains the following edges 4 >= 1, 5 > 2, 1 >= 3
- new_deleteBy0(ww17, ww18, Pos(Zero), ww20, Pos(Zero), Succ(ww530)) → new_deleteBy(ww20, Zero, ww17)
The graph contains the following edges 4 >= 1, 3 > 2, 5 > 2, 1 >= 3
- new_deleteBy0(ww17, ww18, Pos(Succ(ww1900)), ww20, Pos(Zero), Succ(ww530)) → new_deleteBy(ww20, Zero, ww17)
The graph contains the following edges 4 >= 1, 5 > 2, 1 >= 3
- new_deleteBy0(ww17, ww18, Pos(Zero), ww20, Pos(Succ(ww2100)), Succ(ww530)) → new_deleteBy(ww20, Succ(ww2100), ww17)
The graph contains the following edges 4 >= 1, 5 > 2, 1 >= 3
- new_deleteBy033(ww23, ww24, Neg(ww250), ww26, Neg(ww270), Succ(ww1280)) → new_deleteBy1(ww26, ww270, ww23)
The graph contains the following edges 4 >= 1, 5 > 2, 1 >= 3
- new_deleteBy033(ww23, ww24, Pos(Zero), ww26, Neg(Succ(ww2700)), Succ(ww1280)) → new_deleteBy1(ww26, Succ(ww2700), ww23)
The graph contains the following edges 4 >= 1, 5 > 2, 1 >= 3
- new_deleteBy033(ww23, ww24, Pos(Succ(ww2500)), ww26, Neg(Zero), Succ(ww1280)) → new_deleteBy1(ww26, Zero, ww23)
The graph contains the following edges 4 >= 1, 5 > 2, 1 >= 3
- new_deleteBy033(ww23, ww24, Pos(Zero), ww26, Neg(Zero), Succ(ww1280)) → new_deleteBy1(ww26, Zero, ww23)
The graph contains the following edges 4 >= 1, 3 > 2, 5 > 2, 1 >= 3
- new_deleteBy0109(ww23, ww24, ww2500, ww26, ww2700, Zero, Succ(Succ(ww15900))) → new_deleteBy0117(ww23, ww24, ww2500, ww26, ww2700)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5
- new_deleteBy0109(ww23, ww24, ww2500, ww26, ww2700, Succ(ww12800), Succ(Zero)) → new_deleteBy0117(ww23, ww24, ww2500, ww26, ww2700)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5
- new_deleteBy0116(ww23, ww24, ww2500, ww26, ww2700, Succ(ww12800), Zero) → new_deleteBy0117(ww23, ww24, ww2500, ww26, ww2700)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5
- new_deleteBy0116(ww23, ww24, ww2500, ww26, ww2700, Zero, Succ(ww15900)) → new_deleteBy0117(ww23, ww24, ww2500, ww26, ww2700)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5
- new_deleteBy01(ww41, Float(Pos(Zero), Neg(Succ(ww40100))), Float(Pos(Succ(ww3000)), Neg(Succ(Zero)))) → new_deleteBy1(ww3000, Succ(Zero), ww41)
The graph contains the following edges 3 > 1, 3 > 2, 1 >= 3
- new_deleteBy01(ww41, Float(Neg(Zero), Pos(Succ(ww40100))), Float(Pos(Succ(ww3000)), Neg(Succ(Zero)))) → new_deleteBy1(ww3000, Succ(Zero), ww41)
The graph contains the following edges 3 > 1, 3 > 2, 1 >= 3
- new_deleteBy01(ww41, Float(Neg(Zero), Neg(Succ(ww40100))), Float(Pos(Succ(ww3000)), Neg(Succ(Zero)))) → new_deleteBy1(ww3000, Succ(Zero), ww41)
The graph contains the following edges 3 > 1, 3 > 2, 1 >= 3
- new_deleteBy01(ww41, Float(Pos(Zero), Pos(Succ(ww40100))), Float(Pos(Succ(ww3000)), Neg(Succ(Zero)))) → new_deleteBy1(ww3000, Succ(Zero), ww41)
The graph contains the following edges 3 > 1, 3 > 2, 1 >= 3
- new_deleteBy0(ww17, ww18, Neg(Zero), ww20, Neg(Zero), Succ(ww530)) → new_deleteBy1(ww20, Zero, ww17)
The graph contains the following edges 4 >= 1, 3 > 2, 5 > 2, 1 >= 3
- new_deleteBy0(ww17, ww18, Neg(Zero), ww20, Neg(Succ(ww2100)), Succ(ww530)) → new_deleteBy1(ww20, Succ(ww2100), ww17)
The graph contains the following edges 4 >= 1, 5 > 2, 1 >= 3
- new_deleteBy0(ww17, ww18, Neg(Succ(ww1900)), ww20, Neg(Zero), Succ(ww530)) → new_deleteBy1(ww20, Zero, ww17)
The graph contains the following edges 4 >= 1, 5 > 2, 1 >= 3
- new_deleteBy02(ww17, ww18, ww1900, ww20, ww2100, Zero, Succ(Succ(ww8000))) → new_deleteBy0148(ww17, ww18, ww1900, ww20, ww2100)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5
- new_deleteBy02(ww17, ww18, ww1900, ww20, ww2100, Succ(ww5300), Succ(Zero)) → new_deleteBy0148(ww17, ww18, ww1900, ww20, ww2100)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5
- new_deleteBy0147(ww17, ww18, ww1900, ww20, ww2100, Zero, Succ(ww8000)) → new_deleteBy0148(ww17, ww18, ww1900, ww20, ww2100)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5
- new_deleteBy0147(ww17, ww18, ww1900, ww20, ww2100, Succ(ww5300), Zero) → new_deleteBy0148(ww17, ww18, ww1900, ww20, ww2100)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5
- new_deleteBy00(ww17, ww18, ww1900, ww20, ww2100, Succ(ww5300), Succ(Zero)) → new_deleteBy08(ww17, ww18, ww1900, ww20, ww2100)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5
- new_deleteBy00(ww17, ww18, ww1900, ww20, ww2100, Zero, Succ(Succ(ww7800))) → new_deleteBy08(ww17, ww18, ww1900, ww20, ww2100)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5
- new_deleteBy07(ww17, ww18, ww1900, ww20, ww2100, Succ(ww5300), Zero) → new_deleteBy08(ww17, ww18, ww1900, ww20, ww2100)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5
- new_deleteBy07(ww17, ww18, ww1900, ww20, ww2100, Zero, Succ(ww7800)) → new_deleteBy08(ww17, ww18, ww1900, ww20, ww2100)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5
- new_deleteBy0110(ww23, ww24, ww2500, ww26, ww2700, Succ(ww12800), Succ(Zero)) → new_deleteBy0119(ww23, ww24, ww2500, ww26, ww2700)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5
- new_deleteBy0110(ww23, ww24, ww2500, ww26, ww2700, Zero, Succ(Succ(ww16100))) → new_deleteBy0119(ww23, ww24, ww2500, ww26, ww2700)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5
- new_deleteBy0118(ww23, ww24, ww2500, ww26, ww2700, Succ(ww12800), Zero) → new_deleteBy0119(ww23, ww24, ww2500, ww26, ww2700)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5
- new_deleteBy0118(ww23, ww24, ww2500, ww26, ww2700, Zero, Succ(ww16100)) → new_deleteBy0119(ww23, ww24, ww2500, ww26, ww2700)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDPSizeChangeProof
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_deleteBy01(ww41, Float(Pos(Zero), Neg(Succ(ww40100))), Float(Pos(Zero), Pos(Succ(Succ(Succ(ww310000)))))) → new_deleteBy027(ww41, ww40100, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
new_deleteBy01(ww41, Float(Neg(Zero), Pos(Succ(ww40100))), Float(Pos(Zero), Pos(Succ(Succ(Succ(ww310000)))))) → new_deleteBy050(ww41, ww40100, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
new_deleteBy01(ww41, Float(Neg(Succ(ww40000)), Pos(Succ(ww40100))), Float(Pos(Zero), Pos(Succ(Succ(Succ(ww310000)))))) → new_deleteBy042(ww41, ww40000, ww40100, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
new_deleteBy01(ww41, Float(Neg(Zero), Neg(Succ(ww40100))), Float(Pos(Zero), Pos(Succ(Succ(Succ(ww310000)))))) → new_deleteBy052(ww41, ww40100, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
new_deleteBy01(ww41, Float(Neg(Succ(ww40000)), Neg(Succ(ww40100))), Float(Pos(Zero), Pos(Succ(Succ(Succ(ww310000)))))) → new_deleteBy044(ww41, ww40000, ww40100, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
new_deleteBy027(ww41, ww40100, ww310000, Succ(ww1100)) → new_deleteBy8(ww310000, ww41)
new_deleteBy01(ww41, Float(Pos(Zero), Pos(Succ(ww40100))), Float(Pos(Zero), Pos(Succ(Succ(Succ(ww310000)))))) → new_deleteBy025(ww41, ww40100, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
new_deleteBy050(ww41, ww40100, ww310000, Succ(ww1950)) → new_deleteBy8(ww310000, ww41)
new_deleteBy017(:(ww410, ww411), ww40000, ww40100, ww310000, Succ(ww680)) → new_deleteBy01(ww411, ww410, Float(Pos(Zero), Pos(Succ(Succ(Succ(ww310000))))))
new_deleteBy01(ww41, Float(Pos(Succ(ww40000)), Neg(Succ(ww40100))), Float(Pos(Zero), Pos(Succ(Succ(Succ(ww310000)))))) → new_deleteBy019(ww41, ww40000, ww40100, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
new_deleteBy044(ww41, ww40000, ww40100, ww310000, Succ(ww1770)) → new_deleteBy8(ww310000, ww41)
new_deleteBy025(ww41, ww40100, ww310000, Succ(ww1040)) → new_deleteBy8(ww310000, ww41)
new_deleteBy052(ww41, ww40100, ww310000, Succ(ww2010)) → new_deleteBy8(ww310000, ww41)
new_deleteBy8(ww310000, :(ww410, ww411)) → new_deleteBy01(ww411, ww410, Float(Pos(Zero), Pos(Succ(Succ(Succ(ww310000))))))
new_deleteBy042(ww41, ww40000, ww40100, ww310000, Succ(ww1710)) → new_deleteBy8(ww310000, ww41)
new_deleteBy019(ww41, ww40000, ww40100, ww310000, Succ(ww740)) → new_deleteBy8(ww310000, ww41)
new_deleteBy01(ww41, Float(Pos(Succ(ww40000)), Pos(Succ(ww40100))), Float(Pos(Zero), Pos(Succ(Succ(Succ(ww310000)))))) → new_deleteBy017(ww41, ww40000, ww40100, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
The TRS R consists of the following rules:
new_primPlusNat1(Zero, ww40000) → Succ(ww40000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, ww40000) → Zero
new_primPlusNat1(Succ(ww520), ww40000) → Succ(Succ(new_primPlusNat0(ww520, ww40000)))
new_primPlusNat0(Succ(ww5200), Zero) → Succ(ww5200)
new_primPlusNat0(Zero, Succ(ww400000)) → Succ(ww400000)
new_primPlusNat0(Succ(ww5200), Succ(ww400000)) → Succ(Succ(new_primPlusNat0(ww5200, ww400000)))
new_primMulNat0(Succ(ww30000), ww40000) → new_primPlusNat1(new_primMulNat0(ww30000, ww40000), ww40000)
The set Q consists of the following terms:
new_primMulNat0(Succ(x0), x1)
new_primMulNat0(Zero, x0)
new_primPlusNat1(Succ(x0), x1)
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
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_deleteBy8(ww310000, :(ww410, ww411)) → new_deleteBy01(ww411, ww410, Float(Pos(Zero), Pos(Succ(Succ(Succ(ww310000))))))
The graph contains the following edges 2 > 1, 2 > 2
- new_deleteBy01(ww41, Float(Pos(Zero), Neg(Succ(ww40100))), Float(Pos(Zero), Pos(Succ(Succ(Succ(ww310000)))))) → new_deleteBy027(ww41, ww40100, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
The graph contains the following edges 1 >= 1, 2 > 2, 3 > 3
- new_deleteBy017(:(ww410, ww411), ww40000, ww40100, ww310000, Succ(ww680)) → new_deleteBy01(ww411, ww410, Float(Pos(Zero), Pos(Succ(Succ(Succ(ww310000))))))
The graph contains the following edges 1 > 1, 1 > 2
- new_deleteBy027(ww41, ww40100, ww310000, Succ(ww1100)) → new_deleteBy8(ww310000, ww41)
The graph contains the following edges 3 >= 1, 1 >= 2
- new_deleteBy042(ww41, ww40000, ww40100, ww310000, Succ(ww1710)) → new_deleteBy8(ww310000, ww41)
The graph contains the following edges 4 >= 1, 1 >= 2
- new_deleteBy01(ww41, Float(Neg(Succ(ww40000)), Pos(Succ(ww40100))), Float(Pos(Zero), Pos(Succ(Succ(Succ(ww310000)))))) → new_deleteBy042(ww41, ww40000, ww40100, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
The graph contains the following edges 1 >= 1, 2 > 2, 2 > 3, 3 > 4
- new_deleteBy01(ww41, Float(Pos(Succ(ww40000)), Pos(Succ(ww40100))), Float(Pos(Zero), Pos(Succ(Succ(Succ(ww310000)))))) → new_deleteBy017(ww41, ww40000, ww40100, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
The graph contains the following edges 1 >= 1, 2 > 2, 2 > 3, 3 > 4
- new_deleteBy025(ww41, ww40100, ww310000, Succ(ww1040)) → new_deleteBy8(ww310000, ww41)
The graph contains the following edges 3 >= 1, 1 >= 2
- new_deleteBy01(ww41, Float(Pos(Zero), Pos(Succ(ww40100))), Float(Pos(Zero), Pos(Succ(Succ(Succ(ww310000)))))) → new_deleteBy025(ww41, ww40100, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
The graph contains the following edges 1 >= 1, 2 > 2, 3 > 3
- new_deleteBy050(ww41, ww40100, ww310000, Succ(ww1950)) → new_deleteBy8(ww310000, ww41)
The graph contains the following edges 3 >= 1, 1 >= 2
- new_deleteBy01(ww41, Float(Neg(Zero), Pos(Succ(ww40100))), Float(Pos(Zero), Pos(Succ(Succ(Succ(ww310000)))))) → new_deleteBy050(ww41, ww40100, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
The graph contains the following edges 1 >= 1, 2 > 2, 3 > 3
- new_deleteBy044(ww41, ww40000, ww40100, ww310000, Succ(ww1770)) → new_deleteBy8(ww310000, ww41)
The graph contains the following edges 4 >= 1, 1 >= 2
- new_deleteBy01(ww41, Float(Neg(Succ(ww40000)), Neg(Succ(ww40100))), Float(Pos(Zero), Pos(Succ(Succ(Succ(ww310000)))))) → new_deleteBy044(ww41, ww40000, ww40100, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
The graph contains the following edges 1 >= 1, 2 > 2, 2 > 3, 3 > 4
- new_deleteBy052(ww41, ww40100, ww310000, Succ(ww2010)) → new_deleteBy8(ww310000, ww41)
The graph contains the following edges 3 >= 1, 1 >= 2
- new_deleteBy019(ww41, ww40000, ww40100, ww310000, Succ(ww740)) → new_deleteBy8(ww310000, ww41)
The graph contains the following edges 4 >= 1, 1 >= 2
- new_deleteBy01(ww41, Float(Neg(Zero), Neg(Succ(ww40100))), Float(Pos(Zero), Pos(Succ(Succ(Succ(ww310000)))))) → new_deleteBy052(ww41, ww40100, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
The graph contains the following edges 1 >= 1, 2 > 2, 3 > 3
- new_deleteBy01(ww41, Float(Pos(Succ(ww40000)), Neg(Succ(ww40100))), Float(Pos(Zero), Pos(Succ(Succ(Succ(ww310000)))))) → new_deleteBy019(ww41, ww40000, ww40100, ww310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(ww310000, ww40100), Succ(ww40100)), Succ(ww40100)), Succ(ww40100)))
The graph contains the following edges 1 >= 1, 2 > 2, 2 > 3, 3 > 4
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ UsableRulesProof
Q DP problem:
The TRS P consists of the following rules:
new_deleteBy01(ww41, Float(Pos(Zero), Pos(Succ(ww40100))), Float(Neg(Zero), Neg(Succ(Succ(Zero))))) → new_deleteBy080(ww41, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy14(:(ww410, ww411)) → new_deleteBy01(ww411, ww410, Float(Neg(Zero), Neg(Succ(Succ(Zero)))))
new_deleteBy099(ww41, ww40000, ww40100, Succ(ww3730)) → new_deleteBy14(ww41)
new_deleteBy01(ww41, Float(Pos(Succ(ww40000)), Neg(Succ(ww40100))), Float(Neg(Zero), Neg(Succ(Succ(Zero))))) → new_deleteBy074(ww41, ww40000, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy01(ww41, Float(Pos(Succ(ww40000)), Pos(Succ(ww40100))), Float(Neg(Zero), Neg(Succ(Succ(Zero))))) → new_deleteBy072(ww41, ww40000, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy072(:(ww410, ww411), ww40000, ww40100, Succ(ww2760)) → new_deleteBy01(ww411, ww410, Float(Neg(Zero), Neg(Succ(Succ(Zero)))))
new_deleteBy01(ww41, Float(Neg(Zero), Neg(Succ(ww40100))), Float(Neg(Zero), Neg(Succ(Succ(Zero))))) → new_deleteBy0107(ww41, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy01(ww41, Float(Neg(Succ(ww40000)), Pos(Succ(ww40100))), Float(Neg(Zero), Neg(Succ(Succ(Zero))))) → new_deleteBy097(ww41, ww40000, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy01(ww41, Float(Neg(Zero), Pos(Succ(ww40100))), Float(Neg(Zero), Neg(Succ(Succ(Zero))))) → new_deleteBy0105(ww41, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy0107(ww41, ww40100, Succ(ww3970)) → new_deleteBy14(ww41)
new_deleteBy097(ww41, ww40000, ww40100, Succ(ww3670)) → new_deleteBy14(ww41)
new_deleteBy080(ww41, ww40100, Succ(ww3000)) → new_deleteBy14(ww41)
new_deleteBy01(ww41, Float(Neg(Succ(ww40000)), Neg(Succ(ww40100))), Float(Neg(Zero), Neg(Succ(Succ(Zero))))) → new_deleteBy099(ww41, ww40000, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy074(ww41, ww40000, ww40100, Succ(ww2820)) → new_deleteBy14(ww41)
new_deleteBy082(ww41, ww40100, Succ(ww3060)) → new_deleteBy14(ww41)
new_deleteBy01(ww41, Float(Pos(Zero), Neg(Succ(ww40100))), Float(Neg(Zero), Neg(Succ(Succ(Zero))))) → new_deleteBy082(ww41, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy0105(ww41, ww40100, Succ(ww3910)) → new_deleteBy14(ww41)
The TRS R consists of the following rules:
new_primPlusNat1(Zero, ww40000) → Succ(ww40000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, ww40000) → Zero
new_primPlusNat1(Succ(ww520), ww40000) → Succ(Succ(new_primPlusNat0(ww520, ww40000)))
new_primPlusNat0(Succ(ww5200), Zero) → Succ(ww5200)
new_primPlusNat0(Zero, Succ(ww400000)) → Succ(ww400000)
new_primPlusNat0(Succ(ww5200), Succ(ww400000)) → Succ(Succ(new_primPlusNat0(ww5200, ww400000)))
new_primMulNat0(Succ(ww30000), ww40000) → new_primPlusNat1(new_primMulNat0(ww30000, ww40000), ww40000)
The set Q consists of the following terms:
new_primMulNat0(Succ(x0), x1)
new_primMulNat0(Zero, x0)
new_primPlusNat1(Succ(x0), x1)
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
We have to consider all minimal (P,Q,R)-chains.
As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [15] we can delete all non-usable rules [17] from R.
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QReductionProof
Q DP problem:
The TRS P consists of the following rules:
new_deleteBy01(ww41, Float(Pos(Zero), Pos(Succ(ww40100))), Float(Neg(Zero), Neg(Succ(Succ(Zero))))) → new_deleteBy080(ww41, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy14(:(ww410, ww411)) → new_deleteBy01(ww411, ww410, Float(Neg(Zero), Neg(Succ(Succ(Zero)))))
new_deleteBy099(ww41, ww40000, ww40100, Succ(ww3730)) → new_deleteBy14(ww41)
new_deleteBy01(ww41, Float(Pos(Succ(ww40000)), Neg(Succ(ww40100))), Float(Neg(Zero), Neg(Succ(Succ(Zero))))) → new_deleteBy074(ww41, ww40000, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy01(ww41, Float(Pos(Succ(ww40000)), Pos(Succ(ww40100))), Float(Neg(Zero), Neg(Succ(Succ(Zero))))) → new_deleteBy072(ww41, ww40000, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy072(:(ww410, ww411), ww40000, ww40100, Succ(ww2760)) → new_deleteBy01(ww411, ww410, Float(Neg(Zero), Neg(Succ(Succ(Zero)))))
new_deleteBy01(ww41, Float(Neg(Zero), Neg(Succ(ww40100))), Float(Neg(Zero), Neg(Succ(Succ(Zero))))) → new_deleteBy0107(ww41, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy01(ww41, Float(Neg(Succ(ww40000)), Pos(Succ(ww40100))), Float(Neg(Zero), Neg(Succ(Succ(Zero))))) → new_deleteBy097(ww41, ww40000, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy01(ww41, Float(Neg(Zero), Pos(Succ(ww40100))), Float(Neg(Zero), Neg(Succ(Succ(Zero))))) → new_deleteBy0105(ww41, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy0107(ww41, ww40100, Succ(ww3970)) → new_deleteBy14(ww41)
new_deleteBy097(ww41, ww40000, ww40100, Succ(ww3670)) → new_deleteBy14(ww41)
new_deleteBy080(ww41, ww40100, Succ(ww3000)) → new_deleteBy14(ww41)
new_deleteBy01(ww41, Float(Neg(Succ(ww40000)), Neg(Succ(ww40100))), Float(Neg(Zero), Neg(Succ(Succ(Zero))))) → new_deleteBy099(ww41, ww40000, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy074(ww41, ww40000, ww40100, Succ(ww2820)) → new_deleteBy14(ww41)
new_deleteBy082(ww41, ww40100, Succ(ww3060)) → new_deleteBy14(ww41)
new_deleteBy01(ww41, Float(Pos(Zero), Neg(Succ(ww40100))), Float(Neg(Zero), Neg(Succ(Succ(Zero))))) → new_deleteBy082(ww41, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy0105(ww41, ww40100, Succ(ww3910)) → new_deleteBy14(ww41)
The TRS R consists of the following rules:
new_primPlusNat0(Zero, Succ(ww400000)) → Succ(ww400000)
new_primPlusNat0(Succ(ww5200), Succ(ww400000)) → Succ(Succ(new_primPlusNat0(ww5200, ww400000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(ww5200), Zero) → Succ(ww5200)
The set Q consists of the following terms:
new_primMulNat0(Succ(x0), x1)
new_primMulNat0(Zero, x0)
new_primPlusNat1(Succ(x0), x1)
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
We have to consider all minimal (P,Q,R)-chains.
We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.
new_primMulNat0(Succ(x0), x1)
new_primMulNat0(Zero, x0)
new_primPlusNat1(Succ(x0), x1)
new_primPlusNat1(Zero, x0)
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QReductionProof
↳ QDP
↳ QDPSizeChangeProof
Q DP problem:
The TRS P consists of the following rules:
new_deleteBy01(ww41, Float(Pos(Zero), Pos(Succ(ww40100))), Float(Neg(Zero), Neg(Succ(Succ(Zero))))) → new_deleteBy080(ww41, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy14(:(ww410, ww411)) → new_deleteBy01(ww411, ww410, Float(Neg(Zero), Neg(Succ(Succ(Zero)))))
new_deleteBy099(ww41, ww40000, ww40100, Succ(ww3730)) → new_deleteBy14(ww41)
new_deleteBy01(ww41, Float(Pos(Succ(ww40000)), Neg(Succ(ww40100))), Float(Neg(Zero), Neg(Succ(Succ(Zero))))) → new_deleteBy074(ww41, ww40000, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy01(ww41, Float(Pos(Succ(ww40000)), Pos(Succ(ww40100))), Float(Neg(Zero), Neg(Succ(Succ(Zero))))) → new_deleteBy072(ww41, ww40000, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy072(:(ww410, ww411), ww40000, ww40100, Succ(ww2760)) → new_deleteBy01(ww411, ww410, Float(Neg(Zero), Neg(Succ(Succ(Zero)))))
new_deleteBy01(ww41, Float(Neg(Zero), Neg(Succ(ww40100))), Float(Neg(Zero), Neg(Succ(Succ(Zero))))) → new_deleteBy0107(ww41, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy01(ww41, Float(Neg(Succ(ww40000)), Pos(Succ(ww40100))), Float(Neg(Zero), Neg(Succ(Succ(Zero))))) → new_deleteBy097(ww41, ww40000, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy01(ww41, Float(Neg(Zero), Pos(Succ(ww40100))), Float(Neg(Zero), Neg(Succ(Succ(Zero))))) → new_deleteBy0105(ww41, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy0107(ww41, ww40100, Succ(ww3970)) → new_deleteBy14(ww41)
new_deleteBy097(ww41, ww40000, ww40100, Succ(ww3670)) → new_deleteBy14(ww41)
new_deleteBy080(ww41, ww40100, Succ(ww3000)) → new_deleteBy14(ww41)
new_deleteBy01(ww41, Float(Neg(Succ(ww40000)), Neg(Succ(ww40100))), Float(Neg(Zero), Neg(Succ(Succ(Zero))))) → new_deleteBy099(ww41, ww40000, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
new_deleteBy074(ww41, ww40000, ww40100, Succ(ww2820)) → new_deleteBy14(ww41)
new_deleteBy082(ww41, ww40100, Succ(ww3060)) → new_deleteBy14(ww41)
new_deleteBy0105(ww41, ww40100, Succ(ww3910)) → new_deleteBy14(ww41)
new_deleteBy01(ww41, Float(Pos(Zero), Neg(Succ(ww40100))), Float(Neg(Zero), Neg(Succ(Succ(Zero))))) → new_deleteBy082(ww41, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
The TRS R consists of the following rules:
new_primPlusNat0(Zero, Succ(ww400000)) → Succ(ww400000)
new_primPlusNat0(Succ(ww5200), Succ(ww400000)) → Succ(Succ(new_primPlusNat0(ww5200, ww400000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(ww5200), Zero) → Succ(ww5200)
The set Q consists of the following terms:
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), Zero)
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_deleteBy080(ww41, ww40100, Succ(ww3000)) → new_deleteBy14(ww41)
The graph contains the following edges 1 >= 1
- new_deleteBy14(:(ww410, ww411)) → new_deleteBy01(ww411, ww410, Float(Neg(Zero), Neg(Succ(Succ(Zero)))))
The graph contains the following edges 1 > 1, 1 > 2
- new_deleteBy072(:(ww410, ww411), ww40000, ww40100, Succ(ww2760)) → new_deleteBy01(ww411, ww410, Float(Neg(Zero), Neg(Succ(Succ(Zero)))))
The graph contains the following edges 1 > 1, 1 > 2
- new_deleteBy01(ww41, Float(Neg(Succ(ww40000)), Neg(Succ(ww40100))), Float(Neg(Zero), Neg(Succ(Succ(Zero))))) → new_deleteBy099(ww41, ww40000, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
The graph contains the following edges 1 >= 1, 2 > 2, 2 > 3
- new_deleteBy074(ww41, ww40000, ww40100, Succ(ww2820)) → new_deleteBy14(ww41)
The graph contains the following edges 1 >= 1
- new_deleteBy01(ww41, Float(Pos(Succ(ww40000)), Pos(Succ(ww40100))), Float(Neg(Zero), Neg(Succ(Succ(Zero))))) → new_deleteBy072(ww41, ww40000, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
The graph contains the following edges 1 >= 1, 2 > 2, 2 > 3
- new_deleteBy0107(ww41, ww40100, Succ(ww3970)) → new_deleteBy14(ww41)
The graph contains the following edges 1 >= 1
- new_deleteBy097(ww41, ww40000, ww40100, Succ(ww3670)) → new_deleteBy14(ww41)
The graph contains the following edges 1 >= 1
- new_deleteBy0105(ww41, ww40100, Succ(ww3910)) → new_deleteBy14(ww41)
The graph contains the following edges 1 >= 1
- new_deleteBy01(ww41, Float(Neg(Zero), Neg(Succ(ww40100))), Float(Neg(Zero), Neg(Succ(Succ(Zero))))) → new_deleteBy0107(ww41, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
The graph contains the following edges 1 >= 1, 2 > 2
- new_deleteBy01(ww41, Float(Neg(Succ(ww40000)), Pos(Succ(ww40100))), Float(Neg(Zero), Neg(Succ(Succ(Zero))))) → new_deleteBy097(ww41, ww40000, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
The graph contains the following edges 1 >= 1, 2 > 2, 2 > 3
- new_deleteBy01(ww41, Float(Pos(Zero), Pos(Succ(ww40100))), Float(Neg(Zero), Neg(Succ(Succ(Zero))))) → new_deleteBy080(ww41, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
The graph contains the following edges 1 >= 1, 2 > 2
- new_deleteBy099(ww41, ww40000, ww40100, Succ(ww3730)) → new_deleteBy14(ww41)
The graph contains the following edges 1 >= 1
- new_deleteBy082(ww41, ww40100, Succ(ww3060)) → new_deleteBy14(ww41)
The graph contains the following edges 1 >= 1
- new_deleteBy01(ww41, Float(Pos(Succ(ww40000)), Neg(Succ(ww40100))), Float(Neg(Zero), Neg(Succ(Succ(Zero))))) → new_deleteBy074(ww41, ww40000, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
The graph contains the following edges 1 >= 1, 2 > 2, 2 > 3
- new_deleteBy01(ww41, Float(Pos(Zero), Neg(Succ(ww40100))), Float(Neg(Zero), Neg(Succ(Succ(Zero))))) → new_deleteBy082(ww41, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
The graph contains the following edges 1 >= 1, 2 > 2
- new_deleteBy01(ww41, Float(Neg(Zero), Pos(Succ(ww40100))), Float(Neg(Zero), Neg(Succ(Succ(Zero))))) → new_deleteBy0105(ww41, ww40100, new_primPlusNat0(new_primPlusNat0(Zero, Succ(ww40100)), Succ(ww40100)))
The graph contains the following edges 1 >= 1, 2 > 2