YES 2.024
↳ HASKELL
↳ BR
((foldFM_LE :: (Int -> a -> b -> b) -> b -> Int -> FiniteMap Int a -> b) :: (Int -> a -> b -> b) -> b -> Int -> FiniteMap Int a -> b) |
import qualified Maybe import qualified Prelude |
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data FiniteMap a b = EmptyFM | Branch a b Int (FiniteMap a b) (FiniteMap a b) |
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instance (Eq a, Eq b) => Eq (FiniteMap b a) where |
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foldFM_LE :: Ord c => (c -> a -> b -> b) -> b -> c -> FiniteMap c a -> b
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import qualified FiniteMap import qualified Prelude |
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
((foldFM_LE :: (Int -> b -> a -> a) -> a -> Int -> FiniteMap Int b -> a) :: (Int -> b -> a -> a) -> a -> Int -> FiniteMap Int b -> a) |
import qualified Maybe import qualified Prelude |
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data FiniteMap a b = EmptyFM | Branch a b Int (FiniteMap a b) (FiniteMap a b) |
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instance (Eq a, Eq b) => Eq (FiniteMap b a) where |
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foldFM_LE :: Ord b => (b -> c -> a -> a) -> a -> b -> FiniteMap b c -> a
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import qualified FiniteMap import qualified Prelude |
foldFM_LE k z fr EmptyFM = z foldFM_LE k z fr (Branch key elt vw fm_l fm_r)
| key <= fr
= foldFM_LE k (k key elt (foldFM_LE k z fr fm_l)) fr fm_r | otherwise
= foldFM_LE k z fr fm_l
foldFM_LE k z fr EmptyFM = foldFM_LE3 k z fr EmptyFM foldFM_LE k z fr (Branch key elt vw fm_l fm_r) = foldFM_LE2 k z fr (Branch key elt vw fm_l fm_r)
foldFM_LE1 k z fr key elt vw fm_l fm_r True = foldFM_LE k (k key elt (foldFM_LE k z fr fm_l)) fr fm_r foldFM_LE1 k z fr key elt vw fm_l fm_r False = foldFM_LE0 k z fr key elt vw fm_l fm_r otherwise
foldFM_LE0 k z fr key elt vw fm_l fm_r True = foldFM_LE k z fr fm_l
foldFM_LE2 k z fr (Branch key elt vw fm_l fm_r) = foldFM_LE1 k z fr key elt vw fm_l fm_r (key <= fr)
foldFM_LE3 k z fr EmptyFM = z foldFM_LE3 wv ww wx wy = foldFM_LE2 wv ww wx wy
undefined
| False
= undefined
undefined = undefined1
undefined0 True = undefined
undefined1 = undefined0 False
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ Narrow
(foldFM_LE :: (Int -> b -> a -> a) -> a -> Int -> FiniteMap Int b -> a) |
import qualified Maybe import qualified Prelude |
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data FiniteMap a b = EmptyFM | Branch a b Int (FiniteMap a b) (FiniteMap a b) |
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instance (Eq a, Eq b) => Eq (FiniteMap b a) where |
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foldFM_LE :: Ord c => (c -> b -> a -> a) -> a -> c -> FiniteMap c b -> a
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import qualified FiniteMap import qualified Prelude |
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ Narrow
↳ QDP
↳ DependencyGraphProof
new_foldFM_LE(wz3, Pos(Zero), Branch(Pos(Succ(wz6000)), wz61, wz62, wz63, wz64), bb, bc) → new_foldFM_LE(wz3, Pos(Zero), wz63, bb, bc)
new_foldFM_LE(wz3, Neg(Zero), Branch(Neg(Succ(wz6000)), wz61, wz62, wz63, wz64), bb, bc) → new_foldFM_LE(wz3, Neg(Zero), wz63, bb, bc)
new_foldFM_LE(wz3, Pos(Zero), Branch(Neg(Zero), wz61, wz62, wz63, wz64), bb, bc) → new_foldFM_LE(wz3, Pos(Zero), wz64, bb, bc)
new_foldFM_LE(wz3, Pos(Succ(wz500)), Branch(Neg(Zero), wz61, wz62, wz63, wz64), bb, bc) → new_foldFM_LE(wz3, Pos(Succ(wz500)), wz63, bb, bc)
new_foldFM_LE(wz3, Pos(Zero), Branch(Pos(Zero), wz61, wz62, wz63, wz64), bb, bc) → new_foldFM_LE(wz3, Pos(Zero), wz64, bb, bc)
new_foldFM_LE12(wz160, wz162, wz163, wz164, wz165, wz166, wz167, bd, be) → new_foldFM_LE(wz160, Neg(Succ(wz162)), wz167, bd, be)
new_foldFM_LE(wz3, Neg(Zero), Branch(Neg(Succ(wz6000)), wz61, wz62, wz63, wz64), bb, bc) → new_foldFM_LE(wz3, Neg(Zero), wz64, bb, bc)
new_foldFM_LE(wz3, Pos(Zero), Branch(Neg(Zero), wz61, wz62, wz63, wz64), bb, bc) → new_foldFM_LE(wz3, Pos(Zero), wz63, bb, bc)
new_foldFM_LE(wz3, Neg(wz50), Branch(Pos(Succ(wz6000)), wz61, wz62, wz63, wz64), bb, bc) → new_foldFM_LE(wz3, Neg(wz50), wz63, bb, bc)
new_foldFM_LE(wz3, Neg(Succ(wz500)), Branch(Pos(Zero), wz61, wz62, wz63, wz64), bb, bc) → new_foldFM_LE(wz3, Neg(Succ(wz500)), wz63, bb, bc)
new_foldFM_LE11(wz160, wz162, wz163, wz164, wz165, wz166, wz167, Succ(wz1680), Zero, bd, be) → new_foldFM_LE(wz160, Neg(Succ(wz162)), wz166, bd, be)
new_foldFM_LE11(wz160, wz162, wz163, wz164, wz165, wz166, wz167, Zero, Succ(wz1690), bd, be) → new_foldFM_LE(wz160, Neg(Succ(wz162)), wz166, bd, be)
new_foldFM_LE(wz3, Neg(Zero), Branch(Neg(Zero), wz61, wz62, wz63, wz64), bb, bc) → new_foldFM_LE(wz3, Neg(Zero), wz64, bb, bc)
new_foldFM_LE(wz3, Pos(wz50), Branch(Neg(Succ(wz6000)), wz61, wz62, wz63, wz64), bb, bc) → new_foldFM_LE(wz3, Pos(wz50), wz64, bb, bc)
new_foldFM_LE(wz3, Pos(Zero), Branch(Pos(Zero), wz61, wz62, wz63, wz64), bb, bc) → new_foldFM_LE(wz3, Pos(Zero), wz63, bb, bc)
new_foldFM_LE1(wz149, wz151, wz152, wz153, wz154, wz155, wz156, Zero, Zero, h, ba) → new_foldFM_LE10(wz149, wz151, wz152, wz153, wz154, wz155, wz156, h, ba)
new_foldFM_LE(wz3, Neg(Zero), Branch(Pos(Zero), wz61, wz62, wz63, wz64), bb, bc) → new_foldFM_LE(wz3, Neg(Zero), wz64, bb, bc)
new_foldFM_LE(wz3, Neg(Succ(wz500)), Branch(Neg(Succ(wz6000)), wz61, wz62, wz63, wz64), bb, bc) → new_foldFM_LE11(wz3, wz500, wz6000, wz61, wz62, wz63, wz64, wz500, wz6000, bb, bc)
new_foldFM_LE11(wz160, wz162, wz163, wz164, wz165, wz166, wz167, Zero, Succ(wz1690), bd, be) → new_foldFM_LE(wz160, Neg(Succ(wz162)), wz167, bd, be)
new_foldFM_LE10(wz149, wz151, wz152, wz153, wz154, wz155, wz156, h, ba) → new_foldFM_LE(wz149, Pos(Succ(wz151)), wz155, h, ba)
new_foldFM_LE12(wz160, wz162, wz163, wz164, wz165, wz166, wz167, bd, be) → new_foldFM_LE(wz160, Neg(Succ(wz162)), wz166, bd, be)
new_foldFM_LE1(wz149, wz151, wz152, wz153, wz154, wz155, wz156, Zero, Succ(wz1580), h, ba) → new_foldFM_LE(wz149, Pos(Succ(wz151)), wz155, h, ba)
new_foldFM_LE1(wz149, wz151, wz152, wz153, wz154, wz155, wz156, Succ(wz1570), Zero, h, ba) → new_foldFM_LE(wz149, Pos(Succ(wz151)), wz155, h, ba)
new_foldFM_LE(wz3, Pos(wz50), Branch(Neg(Succ(wz6000)), wz61, wz62, wz63, wz64), bb, bc) → new_foldFM_LE(wz3, Pos(wz50), wz63, bb, bc)
new_foldFM_LE(wz3, Pos(Succ(wz500)), Branch(Neg(Zero), wz61, wz62, wz63, wz64), bb, bc) → new_foldFM_LE(wz3, Pos(Succ(wz500)), wz64, bb, bc)
new_foldFM_LE11(wz160, wz162, wz163, wz164, wz165, wz166, wz167, Succ(wz1680), Succ(wz1690), bd, be) → new_foldFM_LE11(wz160, wz162, wz163, wz164, wz165, wz166, wz167, wz1680, wz1690, bd, be)
new_foldFM_LE(wz3, Pos(Succ(wz500)), Branch(Pos(Zero), wz61, wz62, wz63, wz64), bb, bc) → new_foldFM_LE(wz3, Pos(Succ(wz500)), wz64, bb, bc)
new_foldFM_LE10(wz149, wz151, wz152, wz153, wz154, wz155, wz156, h, ba) → new_foldFM_LE(wz149, Pos(Succ(wz151)), wz156, h, ba)
new_foldFM_LE1(wz149, wz151, wz152, wz153, wz154, wz155, wz156, Zero, Succ(wz1580), h, ba) → new_foldFM_LE(wz149, Pos(Succ(wz151)), wz156, h, ba)
new_foldFM_LE(wz3, Neg(Succ(wz500)), Branch(Neg(Zero), wz61, wz62, wz63, wz64), bb, bc) → new_foldFM_LE(wz3, Neg(Succ(wz500)), wz63, bb, bc)
new_foldFM_LE(wz3, Pos(Succ(wz500)), Branch(Pos(Succ(wz6000)), wz61, wz62, wz63, wz64), bb, bc) → new_foldFM_LE1(wz3, wz500, wz6000, wz61, wz62, wz63, wz64, wz6000, wz500, bb, bc)
new_foldFM_LE(wz3, Neg(Zero), Branch(Neg(Zero), wz61, wz62, wz63, wz64), bb, bc) → new_foldFM_LE(wz3, Neg(Zero), wz63, bb, bc)
new_foldFM_LE11(wz160, wz162, wz163, wz164, wz165, wz166, wz167, Zero, Zero, bd, be) → new_foldFM_LE12(wz160, wz162, wz163, wz164, wz165, wz166, wz167, bd, be)
new_foldFM_LE1(wz149, wz151, wz152, wz153, wz154, wz155, wz156, Succ(wz1570), Succ(wz1580), h, ba) → new_foldFM_LE1(wz149, wz151, wz152, wz153, wz154, wz155, wz156, wz1570, wz1580, h, ba)
new_foldFM_LE(wz3, Neg(Zero), Branch(Pos(Zero), wz61, wz62, wz63, wz64), bb, bc) → new_foldFM_LE(wz3, Neg(Zero), wz63, bb, bc)
new_foldFM_LE(wz3, Pos(Succ(wz500)), Branch(Pos(Zero), wz61, wz62, wz63, wz64), bb, bc) → new_foldFM_LE(wz3, Pos(Succ(wz500)), wz63, bb, bc)
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ Narrow
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPSizeChangeProof
↳ QDP
new_foldFM_LE(wz3, Neg(Zero), Branch(Pos(Zero), wz61, wz62, wz63, wz64), bb, bc) → new_foldFM_LE(wz3, Neg(Zero), wz64, bb, bc)
new_foldFM_LE(wz3, Neg(Zero), Branch(Neg(Succ(wz6000)), wz61, wz62, wz63, wz64), bb, bc) → new_foldFM_LE(wz3, Neg(Zero), wz63, bb, bc)
new_foldFM_LE(wz3, Neg(Succ(wz500)), Branch(Neg(Succ(wz6000)), wz61, wz62, wz63, wz64), bb, bc) → new_foldFM_LE11(wz3, wz500, wz6000, wz61, wz62, wz63, wz64, wz500, wz6000, bb, bc)
new_foldFM_LE11(wz160, wz162, wz163, wz164, wz165, wz166, wz167, Zero, Succ(wz1690), bd, be) → new_foldFM_LE(wz160, Neg(Succ(wz162)), wz167, bd, be)
new_foldFM_LE12(wz160, wz162, wz163, wz164, wz165, wz166, wz167, bd, be) → new_foldFM_LE(wz160, Neg(Succ(wz162)), wz166, bd, be)
new_foldFM_LE11(wz160, wz162, wz163, wz164, wz165, wz166, wz167, Succ(wz1680), Succ(wz1690), bd, be) → new_foldFM_LE11(wz160, wz162, wz163, wz164, wz165, wz166, wz167, wz1680, wz1690, bd, be)
new_foldFM_LE12(wz160, wz162, wz163, wz164, wz165, wz166, wz167, bd, be) → new_foldFM_LE(wz160, Neg(Succ(wz162)), wz167, bd, be)
new_foldFM_LE(wz3, Neg(Zero), Branch(Neg(Succ(wz6000)), wz61, wz62, wz63, wz64), bb, bc) → new_foldFM_LE(wz3, Neg(Zero), wz64, bb, bc)
new_foldFM_LE(wz3, Neg(Succ(wz500)), Branch(Neg(Zero), wz61, wz62, wz63, wz64), bb, bc) → new_foldFM_LE(wz3, Neg(Succ(wz500)), wz63, bb, bc)
new_foldFM_LE(wz3, Neg(wz50), Branch(Pos(Succ(wz6000)), wz61, wz62, wz63, wz64), bb, bc) → new_foldFM_LE(wz3, Neg(wz50), wz63, bb, bc)
new_foldFM_LE(wz3, Neg(Succ(wz500)), Branch(Pos(Zero), wz61, wz62, wz63, wz64), bb, bc) → new_foldFM_LE(wz3, Neg(Succ(wz500)), wz63, bb, bc)
new_foldFM_LE(wz3, Neg(Zero), Branch(Neg(Zero), wz61, wz62, wz63, wz64), bb, bc) → new_foldFM_LE(wz3, Neg(Zero), wz63, bb, bc)
new_foldFM_LE11(wz160, wz162, wz163, wz164, wz165, wz166, wz167, Zero, Zero, bd, be) → new_foldFM_LE12(wz160, wz162, wz163, wz164, wz165, wz166, wz167, bd, be)
new_foldFM_LE11(wz160, wz162, wz163, wz164, wz165, wz166, wz167, Zero, Succ(wz1690), bd, be) → new_foldFM_LE(wz160, Neg(Succ(wz162)), wz166, bd, be)
new_foldFM_LE11(wz160, wz162, wz163, wz164, wz165, wz166, wz167, Succ(wz1680), Zero, bd, be) → new_foldFM_LE(wz160, Neg(Succ(wz162)), wz166, bd, be)
new_foldFM_LE(wz3, Neg(Zero), Branch(Pos(Zero), wz61, wz62, wz63, wz64), bb, bc) → new_foldFM_LE(wz3, Neg(Zero), wz63, bb, bc)
new_foldFM_LE(wz3, Neg(Zero), Branch(Neg(Zero), wz61, wz62, wz63, wz64), bb, bc) → new_foldFM_LE(wz3, Neg(Zero), wz64, bb, bc)
From the DPs we obtained the following set of size-change graphs:
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ Narrow
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPSizeChangeProof
new_foldFM_LE(wz3, Pos(Zero), Branch(Pos(Succ(wz6000)), wz61, wz62, wz63, wz64), bb, bc) → new_foldFM_LE(wz3, Pos(Zero), wz63, bb, bc)
new_foldFM_LE(wz3, Pos(wz50), Branch(Neg(Succ(wz6000)), wz61, wz62, wz63, wz64), bb, bc) → new_foldFM_LE(wz3, Pos(wz50), wz64, bb, bc)
new_foldFM_LE(wz3, Pos(Zero), Branch(Pos(Zero), wz61, wz62, wz63, wz64), bb, bc) → new_foldFM_LE(wz3, Pos(Zero), wz63, bb, bc)
new_foldFM_LE1(wz149, wz151, wz152, wz153, wz154, wz155, wz156, Zero, Zero, h, ba) → new_foldFM_LE10(wz149, wz151, wz152, wz153, wz154, wz155, wz156, h, ba)
new_foldFM_LE(wz3, Pos(Zero), Branch(Neg(Zero), wz61, wz62, wz63, wz64), bb, bc) → new_foldFM_LE(wz3, Pos(Zero), wz64, bb, bc)
new_foldFM_LE1(wz149, wz151, wz152, wz153, wz154, wz155, wz156, Succ(wz1570), Zero, h, ba) → new_foldFM_LE(wz149, Pos(Succ(wz151)), wz155, h, ba)
new_foldFM_LE1(wz149, wz151, wz152, wz153, wz154, wz155, wz156, Zero, Succ(wz1580), h, ba) → new_foldFM_LE(wz149, Pos(Succ(wz151)), wz155, h, ba)
new_foldFM_LE(wz3, Pos(wz50), Branch(Neg(Succ(wz6000)), wz61, wz62, wz63, wz64), bb, bc) → new_foldFM_LE(wz3, Pos(wz50), wz63, bb, bc)
new_foldFM_LE(wz3, Pos(Succ(wz500)), Branch(Neg(Zero), wz61, wz62, wz63, wz64), bb, bc) → new_foldFM_LE(wz3, Pos(Succ(wz500)), wz64, bb, bc)
new_foldFM_LE10(wz149, wz151, wz152, wz153, wz154, wz155, wz156, h, ba) → new_foldFM_LE(wz149, Pos(Succ(wz151)), wz155, h, ba)
new_foldFM_LE(wz3, Pos(Succ(wz500)), Branch(Neg(Zero), wz61, wz62, wz63, wz64), bb, bc) → new_foldFM_LE(wz3, Pos(Succ(wz500)), wz63, bb, bc)
new_foldFM_LE(wz3, Pos(Succ(wz500)), Branch(Pos(Zero), wz61, wz62, wz63, wz64), bb, bc) → new_foldFM_LE(wz3, Pos(Succ(wz500)), wz64, bb, bc)
new_foldFM_LE10(wz149, wz151, wz152, wz153, wz154, wz155, wz156, h, ba) → new_foldFM_LE(wz149, Pos(Succ(wz151)), wz156, h, ba)
new_foldFM_LE(wz3, Pos(Zero), Branch(Pos(Zero), wz61, wz62, wz63, wz64), bb, bc) → new_foldFM_LE(wz3, Pos(Zero), wz64, bb, bc)
new_foldFM_LE1(wz149, wz151, wz152, wz153, wz154, wz155, wz156, Zero, Succ(wz1580), h, ba) → new_foldFM_LE(wz149, Pos(Succ(wz151)), wz156, h, ba)
new_foldFM_LE(wz3, Pos(Zero), Branch(Neg(Zero), wz61, wz62, wz63, wz64), bb, bc) → new_foldFM_LE(wz3, Pos(Zero), wz63, bb, bc)
new_foldFM_LE(wz3, Pos(Succ(wz500)), Branch(Pos(Succ(wz6000)), wz61, wz62, wz63, wz64), bb, bc) → new_foldFM_LE1(wz3, wz500, wz6000, wz61, wz62, wz63, wz64, wz6000, wz500, bb, bc)
new_foldFM_LE1(wz149, wz151, wz152, wz153, wz154, wz155, wz156, Succ(wz1570), Succ(wz1580), h, ba) → new_foldFM_LE1(wz149, wz151, wz152, wz153, wz154, wz155, wz156, wz1570, wz1580, h, ba)
new_foldFM_LE(wz3, Pos(Succ(wz500)), Branch(Pos(Zero), wz61, wz62, wz63, wz64), bb, bc) → new_foldFM_LE(wz3, Pos(Succ(wz500)), wz63, bb, bc)
From the DPs we obtained the following set of size-change graphs: