YES 9.966000000000001
H-Termination proof of /home/matraf/haskell/eval_FullyBlown_Fast/FiniteMap.hs
H-Termination of the given Haskell-Program with start terms could successfully be proven:
↳ HASKELL
↳ LR
mainModule FiniteMap
|
| ((eltsFM_LE :: Ord b => FiniteMap (Maybe b) a -> Maybe b -> [a]) :: Ord b => FiniteMap (Maybe b) a -> Maybe b -> [a]) |
module FiniteMap where
| | import qualified Maybe
import qualified Prelude
|
| | data FiniteMap b a = EmptyFM | Branch b a Int (FiniteMap b a) (FiniteMap b a)
|
| | instance (Eq a, Eq b) => Eq (FiniteMap a b) where
|
|
|
| (==) | fm_1 fm_2 | = | sizeFM fm_1 == sizeFM fm_2 && fmToList fm_1 == fmToList fm_2 |
|
|
| | eltsFM_LE :: Ord b => FiniteMap b a -> b -> [a]
| eltsFM_LE | fm fr | = | foldFM_LE (\key elt rest ->elt : rest) [] fr fm |
|
| | fmToList :: FiniteMap a b -> [(a,b)]
| fmToList | fm | = | foldFM (\key elt rest ->(key,elt) : rest) [] fm |
|
| | foldFM :: (c -> a -> b -> b) -> b -> FiniteMap c a -> b
| foldFM | k z EmptyFM | = | z |
| foldFM | k z (Branch key elt _ fm_l fm_r) | = | foldFM k (k key elt (foldFM k z fm_r)) fm_l |
|
| | foldFM_LE :: Ord b => (b -> a -> c -> c) -> c -> b -> FiniteMap b a -> c
| foldFM_LE | k z fr EmptyFM | = | z |
| foldFM_LE | k z fr (Branch key elt _ fm_l fm_r) | |
| | | key <= fr | = |
| foldFM_LE k (k key elt (foldFM_LE k z fr fm_l)) fr fm_r |
|
| | | otherwise | = |
|
|
|
| | sizeFM :: FiniteMap a b -> Int
| sizeFM | EmptyFM | = | 0 |
| sizeFM | (Branch _ _ size _ _) | = | size |
|
module Maybe where
| | import qualified FiniteMap
import qualified Prelude
|
Lambda Reductions:
The following Lambda expression
\keyeltrest→(key,elt) : rest
is transformed to
| fmToList0 | key elt rest | = (key,elt) : rest |
The following Lambda expression
\keyeltrest→elt : rest
is transformed to
| eltsFM_LE0 | key elt rest | = elt : rest |
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
mainModule FiniteMap
|
| ((eltsFM_LE :: Ord a => FiniteMap (Maybe a) b -> Maybe a -> [b]) :: Ord a => FiniteMap (Maybe a) b -> Maybe a -> [b]) |
module FiniteMap where
| | import qualified Maybe
import qualified Prelude
|
| | data FiniteMap a b = EmptyFM | Branch a b Int (FiniteMap a b) (FiniteMap a b)
|
| | instance (Eq a, Eq b) => Eq (FiniteMap b a) where
|
|
|
| (==) | fm_1 fm_2 | = | sizeFM fm_1 == sizeFM fm_2 && fmToList fm_1 == fmToList fm_2 |
|
|
| | eltsFM_LE :: Ord b => FiniteMap b a -> b -> [a]
| eltsFM_LE | fm fr | = | foldFM_LE eltsFM_LE0 [] fr fm |
|
| |
| eltsFM_LE0 | key elt rest | = | elt : rest |
|
| | fmToList :: FiniteMap b a -> [(b,a)]
| fmToList | fm | = | foldFM fmToList0 [] fm |
|
| |
| fmToList0 | key elt rest | = | (key,elt) : rest |
|
| | foldFM :: (c -> a -> b -> b) -> b -> FiniteMap c a -> b
| foldFM | k z EmptyFM | = | z |
| foldFM | k z (Branch key elt _ fm_l fm_r) | = | foldFM k (k key elt (foldFM k z fm_r)) fm_l |
|
| | foldFM_LE :: Ord b => (b -> c -> a -> a) -> a -> b -> FiniteMap b c -> a
| foldFM_LE | k z fr EmptyFM | = | z |
| foldFM_LE | k z fr (Branch key elt _ fm_l fm_r) | |
| | | key <= fr | = |
| foldFM_LE k (k key elt (foldFM_LE k z fr fm_l)) fr fm_r |
|
| | | otherwise | = |
|
|
|
| | sizeFM :: FiniteMap a b -> Int
| sizeFM | EmptyFM | = | 0 |
| sizeFM | (Branch _ _ size _ _) | = | size |
|
module Maybe where
| | import qualified FiniteMap
import qualified Prelude
|
Case Reductions:
The following Case expression
| case | compare x y of |
| | EQ | → o |
| | LT | → LT |
| | GT | → GT |
is transformed to
| primCompAux0 | o EQ | = o |
| primCompAux0 | o LT | = LT |
| primCompAux0 | o GT | = GT |
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
mainModule FiniteMap
|
| ((eltsFM_LE :: Ord a => FiniteMap (Maybe a) b -> Maybe a -> [b]) :: Ord a => FiniteMap (Maybe a) b -> Maybe a -> [b]) |
module FiniteMap where
| | import qualified Maybe
import qualified Prelude
|
| | data FiniteMap b a = EmptyFM | Branch b a Int (FiniteMap b a) (FiniteMap b a)
|
| | instance (Eq a, Eq b) => Eq (FiniteMap b a) where
|
|
|
| (==) | fm_1 fm_2 | = | sizeFM fm_1 == sizeFM fm_2 && fmToList fm_1 == fmToList fm_2 |
|
|
| | eltsFM_LE :: Ord b => FiniteMap b a -> b -> [a]
| eltsFM_LE | fm fr | = | foldFM_LE eltsFM_LE0 [] fr fm |
|
| |
| eltsFM_LE0 | key elt rest | = | elt : rest |
|
| | fmToList :: FiniteMap a b -> [(a,b)]
| fmToList | fm | = | foldFM fmToList0 [] fm |
|
| |
| fmToList0 | key elt rest | = | (key,elt) : rest |
|
| | foldFM :: (c -> b -> a -> a) -> a -> FiniteMap c b -> a
| foldFM | k z EmptyFM | = | z |
| foldFM | k z (Branch key elt _ fm_l fm_r) | = | foldFM k (k key elt (foldFM k z fm_r)) fm_l |
|
| | foldFM_LE :: Ord a => (a -> c -> b -> b) -> b -> a -> FiniteMap a c -> b
| foldFM_LE | k z fr EmptyFM | = | z |
| foldFM_LE | k z fr (Branch key elt _ fm_l fm_r) | |
| | | key <= fr | = |
| foldFM_LE k (k key elt (foldFM_LE k z fr fm_l)) fr fm_r |
|
| | | otherwise | = |
|
|
|
| | sizeFM :: FiniteMap a b -> Int
| sizeFM | EmptyFM | = | 0 |
| sizeFM | (Branch _ _ size _ _) | = | size |
|
module Maybe where
| | import qualified FiniteMap
import qualified Prelude
|
If Reductions:
The following If expression
if primGEqNatS x y then Succ (primDivNatS (primMinusNatS x y) (Succ y)) else Zero
is transformed to
| primDivNatS0 | x y True | = Succ (primDivNatS (primMinusNatS x y) (Succ y)) |
| primDivNatS0 | x y False | = Zero |
The following If expression
if primGEqNatS x y then primModNatS (primMinusNatS x y) (Succ y) else Succ x
is transformed to
| primModNatS0 | x y True | = primModNatS (primMinusNatS x y) (Succ y) |
| primModNatS0 | x y False | = Succ x |
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
mainModule FiniteMap
|
| ((eltsFM_LE :: Ord b => FiniteMap (Maybe b) a -> Maybe b -> [a]) :: Ord b => FiniteMap (Maybe b) a -> Maybe b -> [a]) |
module FiniteMap where
| | import qualified Maybe
import qualified Prelude
|
| | data FiniteMap b a = EmptyFM | Branch b a Int (FiniteMap b a) (FiniteMap b a)
|
| | instance (Eq a, Eq b) => Eq (FiniteMap b a) where
|
|
|
| (==) | fm_1 fm_2 | = | sizeFM fm_1 == sizeFM fm_2 && fmToList fm_1 == fmToList fm_2 |
|
|
| | eltsFM_LE :: Ord a => FiniteMap a b -> a -> [b]
| eltsFM_LE | fm fr | = | foldFM_LE eltsFM_LE0 [] fr fm |
|
| |
| eltsFM_LE0 | key elt rest | = | elt : rest |
|
| | fmToList :: FiniteMap b a -> [(b,a)]
| fmToList | fm | = | foldFM fmToList0 [] fm |
|
| |
| fmToList0 | key elt rest | = | (key,elt) : rest |
|
| | foldFM :: (a -> b -> c -> c) -> c -> FiniteMap a b -> c
| foldFM | k z EmptyFM | = | z |
| foldFM | k z (Branch key elt _ fm_l fm_r) | = | foldFM k (k key elt (foldFM k z fm_r)) fm_l |
|
| | foldFM_LE :: Ord a => (a -> b -> c -> c) -> c -> a -> FiniteMap a b -> c
| foldFM_LE | k z fr EmptyFM | = | z |
| foldFM_LE | k z fr (Branch key elt _ fm_l fm_r) | |
| | | key <= fr | = |
| foldFM_LE k (k key elt (foldFM_LE k z fr fm_l)) fr fm_r |
|
| | | otherwise | = |
|
|
|
| | sizeFM :: FiniteMap b a -> Int
| sizeFM | EmptyFM | = | 0 |
| sizeFM | (Branch _ _ size _ _) | = | size |
|
module Maybe where
| | import qualified FiniteMap
import qualified Prelude
|
Replaced joker patterns by fresh variables and removed binding patterns.
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
mainModule FiniteMap
|
| ((eltsFM_LE :: Ord b => FiniteMap (Maybe b) a -> Maybe b -> [a]) :: Ord b => FiniteMap (Maybe b) a -> Maybe b -> [a]) |
module FiniteMap where
| | import qualified Maybe
import qualified Prelude
|
| | data FiniteMap b a = EmptyFM | Branch b a Int (FiniteMap b a) (FiniteMap b a)
|
| | instance (Eq a, Eq b) => Eq (FiniteMap a b) where
|
|
|
| (==) | fm_1 fm_2 | = | sizeFM fm_1 == sizeFM fm_2 && fmToList fm_1 == fmToList fm_2 |
|
|
| | eltsFM_LE :: Ord b => FiniteMap b a -> b -> [a]
| eltsFM_LE | fm fr | = | foldFM_LE eltsFM_LE0 [] fr fm |
|
| |
| eltsFM_LE0 | key elt rest | = | elt : rest |
|
| | fmToList :: FiniteMap a b -> [(a,b)]
| fmToList | fm | = | foldFM fmToList0 [] fm |
|
| |
| fmToList0 | key elt rest | = | (key,elt) : rest |
|
| | foldFM :: (a -> c -> b -> b) -> b -> FiniteMap a c -> b
| foldFM | k z EmptyFM | = | z |
| foldFM | k z (Branch key elt vw fm_l fm_r) | = | foldFM k (k key elt (foldFM k z fm_r)) fm_l |
|
| | foldFM_LE :: Ord c => (c -> a -> b -> b) -> b -> c -> FiniteMap c a -> b
| foldFM_LE | k z fr EmptyFM | = | z |
| foldFM_LE | k z fr (Branch key elt vx fm_l fm_r) | |
| | | key <= fr | = |
| foldFM_LE k (k key elt (foldFM_LE k z fr fm_l)) fr fm_r |
|
| | | otherwise | = |
|
|
|
| | sizeFM :: FiniteMap b a -> Int
| sizeFM | EmptyFM | = | 0 |
| sizeFM | (Branch vy vz size wu wv) | = | size |
|
module Maybe where
| | import qualified FiniteMap
import qualified Prelude
|
Cond Reductions:
The following Function with conditions
| foldFM_LE | k z fr EmptyFM | = z |
| foldFM_LE | k z fr (Branch key elt vx fm_l fm_r) |
| | | key <= fr |
| = | foldFM_LE k (k key elt (foldFM_LE k z fr fm_l)) fr fm_r |
|
| | | otherwise | |
|
is transformed to
| foldFM_LE | k z fr EmptyFM | = foldFM_LE3 k z fr EmptyFM |
| foldFM_LE | k z fr (Branch key elt vx fm_l fm_r) | = foldFM_LE2 k z fr (Branch key elt vx fm_l fm_r) |
| foldFM_LE0 | k z fr key elt vx fm_l fm_r True | = foldFM_LE k z fr fm_l |
| foldFM_LE1 | k z fr key elt vx 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 vx fm_l fm_r False | = foldFM_LE0 k z fr key elt vx fm_l fm_r otherwise |
| foldFM_LE2 | k z fr (Branch key elt vx fm_l fm_r) | = foldFM_LE1 k z fr key elt vx fm_l fm_r (key <= fr) |
| foldFM_LE3 | k z fr EmptyFM | = z |
| foldFM_LE3 | vvu vvv vvw vvx | = foldFM_LE2 vvu vvv vvw vvx |
The following Function with conditions
| compare | x y |
| | | x == y | |
| | | x <= y | |
| | | otherwise | |
|
is transformed to
| compare | x y | = compare3 x y |
| compare2 | x y True | = EQ |
| compare2 | x y False | = compare1 x y (x <= y) |
| compare1 | x y True | = LT |
| compare1 | x y False | = compare0 x y otherwise |
| compare3 | x y | = compare2 x y (x == y) |
The following Function with conditions
| gcd' | x 0 | = x |
| gcd' | x y | = gcd' y (x `rem` y) |
is transformed to
| gcd' | x vvy | = gcd'2 x vvy |
| gcd' | x y | = gcd'0 x y |
| gcd'0 | x y | = gcd' y (x `rem` y) |
| gcd'1 | True x vvy | = x |
| gcd'1 | vvz vwu vwv | = gcd'0 vwu vwv |
| gcd'2 | x vvy | = gcd'1 (vvy == 0) x vvy |
| gcd'2 | vww vwx | = gcd'0 vww vwx |
The following Function with conditions
| gcd | 0 0 | = error [] |
| gcd | x y | =
| gcd' (abs x) (abs y) |
| where |
| gcd' | x 0 | = x |
| gcd' | x y | = gcd' y (x `rem` y) |
|
|
is transformed to
| gcd | vwy vwz | = gcd3 vwy vwz |
| gcd | x y | = gcd0 x y |
| gcd0 | x y | =
| gcd' (abs x) (abs y) |
| where |
| gcd' | x vvy | = gcd'2 x vvy |
| gcd' | x y | = gcd'0 x y |
|
|
| gcd'0 | x y | = gcd' y (x `rem` y) |
|
|
| gcd'1 | True x vvy | = x |
| gcd'1 | vvz vwu vwv | = gcd'0 vwu vwv |
|
|
| gcd'2 | x vvy | = gcd'1 (vvy == 0) x vvy |
| gcd'2 | vww vwx | = gcd'0 vww vwx |
|
|
| gcd1 | True vwy vwz | = error [] |
| gcd1 | vxu vxv vxw | = gcd0 vxv vxw |
| gcd2 | True vwy vwz | = gcd1 (vwz == 0) vwy vwz |
| gcd2 | vxx vxy vxz | = gcd0 vxy vxz |
| gcd3 | vwy vwz | = gcd2 (vwy == 0) vwy vwz |
| gcd3 | vyu vyv | = gcd0 vyu vyv |
The following Function with conditions
is transformed to
| absReal0 | x True | = `negate` x |
| absReal1 | x True | = x |
| absReal1 | x False | = absReal0 x otherwise |
| absReal2 | x | = absReal1 x (x >= 0) |
The following Function with conditions
is transformed to
| undefined0 | True | = undefined |
| undefined1 | | = undefined0 False |
The following Function with conditions
| reduce | x y |
| | | y == 0 | |
| | | otherwise |
| = | x `quot` d :% (y `quot` d) |
|
|
| where | |
|
is transformed to
| reduce2 | x y | =
| reduce1 x y (y == 0) |
| where | |
|
| reduce0 | x y True | = x `quot` d :% (y `quot` d) |
|
|
| reduce1 | x y True | = error [] |
| reduce1 | x y False | = reduce0 x y otherwise |
|
|
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
mainModule FiniteMap
|
| ((eltsFM_LE :: Ord a => FiniteMap (Maybe a) b -> Maybe a -> [b]) :: Ord a => FiniteMap (Maybe a) b -> Maybe a -> [b]) |
module FiniteMap where
| | import qualified Maybe
import qualified Prelude
|
| | data FiniteMap a b = EmptyFM | Branch a b Int (FiniteMap a b) (FiniteMap a b)
|
| | instance (Eq a, Eq b) => Eq (FiniteMap a b) where
|
|
|
| (==) | fm_1 fm_2 | = | sizeFM fm_1 == sizeFM fm_2 && fmToList fm_1 == fmToList fm_2 |
|
|
| | eltsFM_LE :: Ord a => FiniteMap a b -> a -> [b]
| eltsFM_LE | fm fr | = | foldFM_LE eltsFM_LE0 [] fr fm |
|
| |
| eltsFM_LE0 | key elt rest | = | elt : rest |
|
| | fmToList :: FiniteMap b a -> [(b,a)]
| fmToList | fm | = | foldFM fmToList0 [] fm |
|
| |
| fmToList0 | key elt rest | = | (key,elt) : rest |
|
| | foldFM :: (c -> b -> a -> a) -> a -> FiniteMap c b -> a
| foldFM | k z EmptyFM | = | z |
| foldFM | k z (Branch key elt vw fm_l fm_r) | = | foldFM k (k key elt (foldFM k z fm_r)) fm_l |
|
| | foldFM_LE :: Ord b => (b -> c -> a -> a) -> a -> b -> FiniteMap b c -> a
| foldFM_LE | k z fr EmptyFM | = | foldFM_LE3 k z fr EmptyFM |
| foldFM_LE | k z fr (Branch key elt vx fm_l fm_r) | = | foldFM_LE2 k z fr (Branch key elt vx fm_l fm_r) |
|
| |
| foldFM_LE0 | k z fr key elt vx fm_l fm_r True | = | foldFM_LE k z fr fm_l |
|
| |
| foldFM_LE1 | k z fr key elt vx 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 vx fm_l fm_r False | = | foldFM_LE0 k z fr key elt vx fm_l fm_r otherwise |
|
| |
| foldFM_LE2 | k z fr (Branch key elt vx fm_l fm_r) | = | foldFM_LE1 k z fr key elt vx fm_l fm_r (key <= fr) |
|
| |
| foldFM_LE3 | k z fr EmptyFM | = | z |
| foldFM_LE3 | vvu vvv vvw vvx | = | foldFM_LE2 vvu vvv vvw vvx |
|
| | sizeFM :: FiniteMap b a -> Int
| sizeFM | EmptyFM | = | 0 |
| sizeFM | (Branch vy vz size wu wv) | = | size |
|
module Maybe where
| | import qualified FiniteMap
import qualified Prelude
|
Let/Where Reductions:
The bindings of the following Let/Where expression
| reduce1 x y (y == 0) |
| where | |
|
| reduce0 | x y True | = x `quot` d :% (y `quot` d) |
|
|
| reduce1 | x y True | = error [] |
| reduce1 | x y False | = reduce0 x y otherwise |
|
are unpacked to the following functions on top level
| reduce2Reduce0 | vyw vyx x y True | = x `quot` reduce2D vyw vyx :% (y `quot` reduce2D vyw vyx) |
| reduce2D | vyw vyx | = gcd vyw vyx |
| reduce2Reduce1 | vyw vyx x y True | = error [] |
| reduce2Reduce1 | vyw vyx x y False | = reduce2Reduce0 vyw vyx x y otherwise |
The bindings of the following Let/Where expression
| gcd' (abs x) (abs y) |
| where |
| gcd' | x vvy | = gcd'2 x vvy |
| gcd' | x y | = gcd'0 x y |
|
|
| gcd'0 | x y | = gcd' y (x `rem` y) |
|
|
| gcd'1 | True x vvy | = x |
| gcd'1 | vvz vwu vwv | = gcd'0 vwu vwv |
|
|
| gcd'2 | x vvy | = gcd'1 (vvy == 0) x vvy |
| gcd'2 | vww vwx | = gcd'0 vww vwx |
|
are unpacked to the following functions on top level
| gcd0Gcd'1 | True x vvy | = x |
| gcd0Gcd'1 | vvz vwu vwv | = gcd0Gcd'0 vwu vwv |
| gcd0Gcd'0 | x y | = gcd0Gcd' y (x `rem` y) |
| gcd0Gcd'2 | x vvy | = gcd0Gcd'1 (vvy == 0) x vvy |
| gcd0Gcd'2 | vww vwx | = gcd0Gcd'0 vww vwx |
| gcd0Gcd' | x vvy | = gcd0Gcd'2 x vvy |
| gcd0Gcd' | x y | = gcd0Gcd'0 x y |
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
mainModule FiniteMap
|
| ((eltsFM_LE :: Ord a => FiniteMap (Maybe a) b -> Maybe a -> [b]) :: Ord a => FiniteMap (Maybe a) b -> Maybe a -> [b]) |
module FiniteMap where
| | import qualified Maybe
import qualified Prelude
|
| | data FiniteMap a b = EmptyFM | Branch a b Int (FiniteMap a b) (FiniteMap a b)
|
| | instance (Eq a, Eq b) => Eq (FiniteMap a b) where
|
|
|
| (==) | fm_1 fm_2 | = | sizeFM fm_1 == sizeFM fm_2 && fmToList fm_1 == fmToList fm_2 |
|
|
| | eltsFM_LE :: Ord b => FiniteMap b a -> b -> [a]
| eltsFM_LE | fm fr | = | foldFM_LE eltsFM_LE0 [] fr fm |
|
| |
| eltsFM_LE0 | key elt rest | = | elt : rest |
|
| | fmToList :: FiniteMap b a -> [(b,a)]
| fmToList | fm | = | foldFM fmToList0 [] fm |
|
| |
| fmToList0 | key elt rest | = | (key,elt) : rest |
|
| | foldFM :: (c -> a -> b -> b) -> b -> FiniteMap c a -> b
| foldFM | k z EmptyFM | = | z |
| foldFM | k z (Branch key elt vw fm_l fm_r) | = | foldFM k (k key elt (foldFM k z fm_r)) fm_l |
|
| | foldFM_LE :: Ord b => (b -> a -> c -> c) -> c -> b -> FiniteMap b a -> c
| foldFM_LE | k z fr EmptyFM | = | foldFM_LE3 k z fr EmptyFM |
| foldFM_LE | k z fr (Branch key elt vx fm_l fm_r) | = | foldFM_LE2 k z fr (Branch key elt vx fm_l fm_r) |
|
| |
| foldFM_LE0 | k z fr key elt vx fm_l fm_r True | = | foldFM_LE k z fr fm_l |
|
| |
| foldFM_LE1 | k z fr key elt vx 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 vx fm_l fm_r False | = | foldFM_LE0 k z fr key elt vx fm_l fm_r otherwise |
|
| |
| foldFM_LE2 | k z fr (Branch key elt vx fm_l fm_r) | = | foldFM_LE1 k z fr key elt vx fm_l fm_r (key <= fr) |
|
| |
| foldFM_LE3 | k z fr EmptyFM | = | z |
| foldFM_LE3 | vvu vvv vvw vvx | = | foldFM_LE2 vvu vvv vvw vvx |
|
| | sizeFM :: FiniteMap b a -> Int
| sizeFM | EmptyFM | = | 0 |
| sizeFM | (Branch vy vz size wu wv) | = | size |
|
module Maybe where
| | import qualified FiniteMap
import qualified Prelude
|
Num Reduction: All numbers are transformed to thier corresponding representation with Pos, Neg, Succ and Zero.
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
mainModule FiniteMap
|
| (eltsFM_LE :: Ord b => FiniteMap (Maybe b) a -> Maybe b -> [a]) |
module FiniteMap where
| | import qualified Maybe
import qualified Prelude
|
| | data FiniteMap b a = EmptyFM | Branch b a Int (FiniteMap b a) (FiniteMap b a)
|
| | instance (Eq a, Eq b) => Eq (FiniteMap b a) where
|
|
|
| (==) | fm_1 fm_2 | = | sizeFM fm_1 == sizeFM fm_2 && fmToList fm_1 == fmToList fm_2 |
|
|
| | eltsFM_LE :: Ord b => FiniteMap b a -> b -> [a]
| eltsFM_LE | fm fr | = | foldFM_LE eltsFM_LE0 [] fr fm |
|
| |
| eltsFM_LE0 | key elt rest | = | elt : rest |
|
| | fmToList :: FiniteMap a b -> [(a,b)]
| fmToList | fm | = | foldFM fmToList0 [] fm |
|
| |
| fmToList0 | key elt rest | = | (key,elt) : rest |
|
| | foldFM :: (a -> c -> b -> b) -> b -> FiniteMap a c -> b
| foldFM | k z EmptyFM | = | z |
| foldFM | k z (Branch key elt vw fm_l fm_r) | = | foldFM k (k key elt (foldFM k z fm_r)) fm_l |
|
| | foldFM_LE :: Ord c => (c -> a -> b -> b) -> b -> c -> FiniteMap c a -> b
| foldFM_LE | k z fr EmptyFM | = | foldFM_LE3 k z fr EmptyFM |
| foldFM_LE | k z fr (Branch key elt vx fm_l fm_r) | = | foldFM_LE2 k z fr (Branch key elt vx fm_l fm_r) |
|
| |
| foldFM_LE0 | k z fr key elt vx fm_l fm_r True | = | foldFM_LE k z fr fm_l |
|
| |
| foldFM_LE1 | k z fr key elt vx 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 vx fm_l fm_r False | = | foldFM_LE0 k z fr key elt vx fm_l fm_r otherwise |
|
| |
| foldFM_LE2 | k z fr (Branch key elt vx fm_l fm_r) | = | foldFM_LE1 k z fr key elt vx fm_l fm_r (key <= fr) |
|
| |
| foldFM_LE3 | k z fr EmptyFM | = | z |
| foldFM_LE3 | vvu vvv vvw vvx | = | foldFM_LE2 vvu vvv vvw vvx |
|
| | sizeFM :: FiniteMap b a -> Int
| sizeFM | EmptyFM | = | Pos Zero |
| sizeFM | (Branch vy vz size wu wv) | = | size |
|
module Maybe where
| | import qualified FiniteMap
import qualified Prelude
|
Haskell To QDPs
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDPSizeChangeProof
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_primCmpNat(Succ(vyy30000), Succ(vyy4000)) → new_primCmpNat(vyy30000, vyy4000)
R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By using the subterm criterion [20] together with the size-change analysis [32] we have proven that there are no infinite chains for this DP problem. From the DPs we obtained the following set of size-change graphs:
- new_primCmpNat(Succ(vyy30000), Succ(vyy4000)) → new_primCmpNat(vyy30000, vyy4000)
The graph contains the following edges 1 > 1, 2 > 2
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDPSizeChangeProof
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_foldFM(vyy410, vyy411, vyy85, Branch(vyy4130, vyy4131, vyy4132, vyy4133, vyy4134), h, ba) → new_foldFM(vyy4130, vyy4131, new_foldFM0(vyy410, vyy411, vyy85, vyy4134, h, ba), vyy4133, h, ba)
new_foldFM(vyy410, vyy411, vyy85, Branch(vyy4130, vyy4131, vyy4132, vyy4133, vyy4134), h, ba) → new_foldFM(vyy410, vyy411, vyy85, vyy4134, h, ba)
The TRS R consists of the following rules:
new_foldFM0(vyy410, vyy411, vyy85, EmptyFM, h, ba) → :(@2(vyy410, vyy411), vyy85)
new_foldFM0(vyy410, vyy411, vyy85, Branch(vyy4130, vyy4131, vyy4132, vyy4133, vyy4134), h, ba) → new_foldFM0(vyy4130, vyy4131, new_foldFM0(vyy410, vyy411, vyy85, vyy4134, h, ba), vyy4133, h, ba)
The set Q consists of the following terms:
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
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_foldFM(vyy410, vyy411, vyy85, Branch(vyy4130, vyy4131, vyy4132, vyy4133, vyy4134), h, ba) → new_foldFM(vyy4130, vyy4131, new_foldFM0(vyy410, vyy411, vyy85, vyy4134, h, ba), vyy4133, h, ba)
The graph contains the following edges 4 > 1, 4 > 2, 4 > 4, 5 >= 5, 6 >= 6
- new_foldFM(vyy410, vyy411, vyy85, Branch(vyy4130, vyy4131, vyy4132, vyy4133, vyy4134), h, ba) → new_foldFM(vyy410, vyy411, vyy85, vyy4134, h, ba)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 > 4, 5 >= 5, 6 >= 6
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDPSizeChangeProof
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_foldFM1(Branch(vyy410, vyy411, vyy412, vyy413, vyy414), h, ba) → new_foldFM1(vyy414, h, ba)
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_foldFM1(Branch(vyy410, vyy411, vyy412, vyy413, vyy414), h, ba) → new_foldFM1(vyy414, h, ba)
The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDPSizeChangeProof
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_primPlusNat(Succ(vyy8600), Succ(vyy401000)) → new_primPlusNat(vyy8600, vyy401000)
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(vyy8600), Succ(vyy401000)) → new_primPlusNat(vyy8600, vyy401000)
The graph contains the following edges 1 > 1, 2 > 2
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDPSizeChangeProof
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_primMulNat(Succ(vyy300100), Succ(vyy40100)) → new_primMulNat(vyy300100, Succ(vyy40100))
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(vyy300100), Succ(vyy40100)) → new_primMulNat(vyy300100, Succ(vyy40100))
The graph contains the following edges 1 > 1, 2 >= 2
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDPSizeChangeProof
↳ QDP
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_primEqNat(Succ(vyy4000), Succ(vyy4100)) → new_primEqNat(vyy4000, vyy4100)
R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By using the subterm criterion [20] together with the size-change analysis [32] we have proven that there are no infinite chains for this DP problem. From the DPs we obtained the following set of size-change graphs:
- new_primEqNat(Succ(vyy4000), Succ(vyy4100)) → new_primEqNat(vyy4000, vyy4100)
The graph contains the following edges 1 > 1, 2 > 2
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ Rewriting
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_esEs3(Right(vyy400), Right(vyy410), bcc, app(app(ty_@2, bde), bdf)) → new_esEs4(vyy400, vyy410, bde, bdf)
new_esEs3(Right(vyy400), Right(vyy410), bcc, app(ty_[], bcd)) → new_esEs(vyy400, vyy410, bcd)
new_esEs4(@2(vyy400, vyy401), @2(vyy410, vyy411), app(app(app(ty_@3, bfe), bff), bfg), bfd) → new_esEs0(vyy400, vyy410, bfe, bff, bfg)
new_esEs1(Just(vyy400), Just(vyy410), app(app(app(ty_@3, hc), hd), he)) → new_esEs0(vyy400, vyy410, hc, hd, he)
new_esEs2(vyy40, vyy41, bae, baf) → new_esEs(new_fmToList(vyy40, bae, baf), new_fmToList(vyy41, bae, baf), app(app(ty_@2, bae), baf))
new_esEs4(@2(vyy400, vyy401), @2(vyy410, vyy411), app(ty_Maybe, bfh), bfd) → new_esEs1(vyy400, vyy410, bfh)
new_esEs3(Right(vyy400), Right(vyy410), bcc, app(app(ty_Either, bdc), bdd)) → new_esEs3(vyy400, vyy410, bdc, bdd)
new_esEs0(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), app(app(ty_@2, gh), ha), ce, ec) → new_esEs4(vyy400, vyy410, gh, ha)
new_esEs0(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), cd, ce, app(ty_[], cf)) → new_esEs(vyy402, vyy412, cf)
new_esEs3(Right(vyy400), Right(vyy410), bcc, app(app(app(ty_@3, bce), bcf), bcg)) → new_esEs0(vyy400, vyy410, bce, bcf, bcg)
new_esEs3(Left(vyy400), Left(vyy410), app(app(ty_Either, bbg), bbh), bah) → new_esEs3(vyy400, vyy410, bbg, bbh)
new_esEs1(Just(vyy400), Just(vyy410), app(app(ty_Either, baa), bab)) → new_esEs3(vyy400, vyy410, baa, bab)
new_esEs4(@2(vyy400, vyy401), @2(vyy410, vyy411), bdg, app(app(app(ty_@3, bea), beb), bec)) → new_esEs0(vyy401, vyy411, bea, beb, bec)
new_esEs(:(vyy400, vyy401), :(vyy410, vyy411), app(app(ty_FiniteMap, bf), bg)) → new_esEs2(vyy400, vyy410, bf, bg)
new_esEs1(Just(vyy400), Just(vyy410), app(ty_[], hb)) → new_esEs(vyy400, vyy410, hb)
new_esEs4(@2(vyy400, vyy401), @2(vyy410, vyy411), bdg, app(app(ty_Either, beg), beh)) → new_esEs3(vyy401, vyy411, beg, beh)
new_esEs(:(vyy400, vyy401), :(vyy410, vyy411), app(app(ty_Either, bh), ca)) → new_esEs3(vyy400, vyy410, bh, ca)
new_esEs0(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), cd, app(ty_[], eb), ec) → new_esEs(vyy401, vyy411, eb)
new_esEs4(@2(vyy400, vyy401), @2(vyy410, vyy411), bdg, app(app(ty_FiniteMap, bee), bef)) → new_esEs2(vyy401, vyy411, bee, bef)
new_esEs3(Left(vyy400), Left(vyy410), app(app(ty_FiniteMap, bbe), bbf), bah) → new_esEs2(vyy400, vyy410, bbe, bbf)
new_esEs3(Left(vyy400), Left(vyy410), app(app(ty_@2, bca), bcb), bah) → new_esEs4(vyy400, vyy410, bca, bcb)
new_esEs1(Just(vyy400), Just(vyy410), app(ty_Maybe, hf)) → new_esEs1(vyy400, vyy410, hf)
new_esEs(:(vyy400, vyy401), :(vyy410, vyy411), app(app(ty_@2, cb), cc)) → new_esEs4(vyy400, vyy410, cb, cc)
new_esEs1(Just(vyy400), Just(vyy410), app(app(ty_FiniteMap, hg), hh)) → new_esEs2(vyy400, vyy410, hg, hh)
new_esEs4(@2(vyy400, vyy401), @2(vyy410, vyy411), bdg, app(app(ty_@2, bfa), bfb)) → new_esEs4(vyy401, vyy411, bfa, bfb)
new_esEs3(Right(vyy400), Right(vyy410), bcc, app(app(ty_FiniteMap, bda), bdb)) → new_esEs2(vyy400, vyy410, bda, bdb)
new_esEs0(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), cd, app(ty_Maybe, eg), ec) → new_esEs1(vyy401, vyy411, eg)
new_esEs0(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), cd, app(app(ty_FiniteMap, eh), fa), ec) → new_esEs2(vyy401, vyy411, eh, fa)
new_esEs1(Just(vyy400), Just(vyy410), app(app(ty_@2, bac), bad)) → new_esEs4(vyy400, vyy410, bac, bad)
new_esEs0(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), cd, ce, app(app(ty_Either, df), dg)) → new_esEs3(vyy402, vyy412, df, dg)
new_esEs3(Left(vyy400), Left(vyy410), app(ty_Maybe, bbd), bah) → new_esEs1(vyy400, vyy410, bbd)
new_esEs4(@2(vyy400, vyy401), @2(vyy410, vyy411), app(app(ty_@2, bge), bgf), bfd) → new_esEs4(vyy400, vyy410, bge, bgf)
new_esEs0(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), cd, app(app(ty_@2, fd), ff), ec) → new_esEs4(vyy401, vyy411, fd, ff)
new_esEs3(Left(vyy400), Left(vyy410), app(ty_[], bag), bah) → new_esEs(vyy400, vyy410, bag)
new_esEs0(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), cd, app(app(app(ty_@3, ed), ee), ef), ec) → new_esEs0(vyy401, vyy411, ed, ee, ef)
new_esEs4(@2(vyy400, vyy401), @2(vyy410, vyy411), bdg, app(ty_[], bdh)) → new_esEs(vyy401, vyy411, bdh)
new_esEs4(@2(vyy400, vyy401), @2(vyy410, vyy411), bdg, app(ty_Maybe, bed)) → new_esEs1(vyy401, vyy411, bed)
new_esEs4(@2(vyy400, vyy401), @2(vyy410, vyy411), app(app(ty_FiniteMap, bga), bgb), bfd) → new_esEs2(vyy400, vyy410, bga, bgb)
new_esEs3(Left(vyy400), Left(vyy410), app(app(app(ty_@3, bba), bbb), bbc), bah) → new_esEs0(vyy400, vyy410, bba, bbb, bbc)
new_esEs0(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), app(ty_[], fg), ce, ec) → new_esEs(vyy400, vyy410, fg)
new_esEs0(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), app(app(ty_FiniteMap, gd), ge), ce, ec) → new_esEs2(vyy400, vyy410, gd, ge)
new_esEs(:(vyy400, vyy401), :(vyy410, vyy411), h) → new_esEs(vyy401, vyy411, h)
new_esEs0(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), cd, ce, app(app(app(ty_@3, cg), da), db)) → new_esEs0(vyy402, vyy412, cg, da, db)
new_esEs0(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), cd, ce, app(ty_Maybe, dc)) → new_esEs1(vyy402, vyy412, dc)
new_esEs4(@2(vyy400, vyy401), @2(vyy410, vyy411), app(ty_[], bfc), bfd) → new_esEs(vyy400, vyy410, bfc)
new_esEs0(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), cd, ce, app(app(ty_FiniteMap, dd), de)) → new_esEs2(vyy402, vyy412, dd, de)
new_esEs3(Right(vyy400), Right(vyy410), bcc, app(ty_Maybe, bch)) → new_esEs1(vyy400, vyy410, bch)
new_esEs0(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), app(app(ty_Either, gf), gg), ce, ec) → new_esEs3(vyy400, vyy410, gf, gg)
new_esEs4(@2(vyy400, vyy401), @2(vyy410, vyy411), app(app(ty_Either, bgc), bgd), bfd) → new_esEs3(vyy400, vyy410, bgc, bgd)
new_esEs(:(vyy400, vyy401), :(vyy410, vyy411), app(app(app(ty_@3, bb), bc), bd)) → new_esEs0(vyy400, vyy410, bb, bc, bd)
new_esEs0(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), app(ty_Maybe, gc), ce, ec) → new_esEs1(vyy400, vyy410, gc)
new_esEs0(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), cd, app(app(ty_Either, fb), fc), ec) → new_esEs3(vyy401, vyy411, fb, fc)
new_esEs(:(vyy400, vyy401), :(vyy410, vyy411), app(ty_[], ba)) → new_esEs(vyy400, vyy410, ba)
new_esEs0(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), cd, ce, app(app(ty_@2, dh), ea)) → new_esEs4(vyy402, vyy412, dh, ea)
new_esEs0(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), app(app(app(ty_@3, fh), ga), gb), ce, ec) → new_esEs0(vyy400, vyy410, fh, ga, gb)
new_esEs(:(vyy400, vyy401), :(vyy410, vyy411), app(ty_Maybe, be)) → new_esEs1(vyy400, vyy410, be)
The TRS R consists of the following rules:
new_foldFM0(vyy410, vyy411, vyy85, EmptyFM, bae, baf) → :(@2(vyy410, vyy411), vyy85)
new_foldFM0(vyy410, vyy411, vyy85, Branch(vyy4130, vyy4131, vyy4132, vyy4133, vyy4134), bae, baf) → new_foldFM0(vyy4130, vyy4131, new_foldFM0(vyy410, vyy411, vyy85, vyy4134, bae, baf), vyy4133, bae, baf)
new_fmToList(vyy41, bae, baf) → new_foldFM2(vyy41, bae, baf)
new_foldFM2(Branch(vyy410, vyy411, vyy412, vyy413, vyy414), bae, baf) → new_foldFM0(vyy410, vyy411, new_foldFM2(vyy414, bae, baf), vyy413, bae, baf)
new_foldFM2(EmptyFM, bae, baf) → []
The set Q consists of the following terms:
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
new_fmToList(x0, x1, x2)
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
new_foldFM2(EmptyFM, x0, x1)
We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_esEs2(vyy40, vyy41, bae, baf) → new_esEs(new_fmToList(vyy40, bae, baf), new_fmToList(vyy41, bae, baf), app(app(ty_@2, bae), baf)) at position [0] we obtained the following new rules:
new_esEs2(vyy40, vyy41, bae, baf) → new_esEs(new_foldFM2(vyy40, bae, baf), new_fmToList(vyy41, bae, baf), app(app(ty_@2, bae), baf))
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ Rewriting
↳ QDP
↳ Rewriting
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_esEs3(Right(vyy400), Right(vyy410), bcc, app(app(ty_@2, bde), bdf)) → new_esEs4(vyy400, vyy410, bde, bdf)
new_esEs3(Right(vyy400), Right(vyy410), bcc, app(ty_[], bcd)) → new_esEs(vyy400, vyy410, bcd)
new_esEs4(@2(vyy400, vyy401), @2(vyy410, vyy411), app(app(app(ty_@3, bfe), bff), bfg), bfd) → new_esEs0(vyy400, vyy410, bfe, bff, bfg)
new_esEs1(Just(vyy400), Just(vyy410), app(app(app(ty_@3, hc), hd), he)) → new_esEs0(vyy400, vyy410, hc, hd, he)
new_esEs3(Right(vyy400), Right(vyy410), bcc, app(app(ty_Either, bdc), bdd)) → new_esEs3(vyy400, vyy410, bdc, bdd)
new_esEs4(@2(vyy400, vyy401), @2(vyy410, vyy411), app(ty_Maybe, bfh), bfd) → new_esEs1(vyy400, vyy410, bfh)
new_esEs0(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), app(app(ty_@2, gh), ha), ce, ec) → new_esEs4(vyy400, vyy410, gh, ha)
new_esEs0(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), cd, ce, app(ty_[], cf)) → new_esEs(vyy402, vyy412, cf)
new_esEs3(Right(vyy400), Right(vyy410), bcc, app(app(app(ty_@3, bce), bcf), bcg)) → new_esEs0(vyy400, vyy410, bce, bcf, bcg)
new_esEs3(Left(vyy400), Left(vyy410), app(app(ty_Either, bbg), bbh), bah) → new_esEs3(vyy400, vyy410, bbg, bbh)
new_esEs4(@2(vyy400, vyy401), @2(vyy410, vyy411), bdg, app(app(app(ty_@3, bea), beb), bec)) → new_esEs0(vyy401, vyy411, bea, beb, bec)
new_esEs1(Just(vyy400), Just(vyy410), app(app(ty_Either, baa), bab)) → new_esEs3(vyy400, vyy410, baa, bab)
new_esEs(:(vyy400, vyy401), :(vyy410, vyy411), app(app(ty_FiniteMap, bf), bg)) → new_esEs2(vyy400, vyy410, bf, bg)
new_esEs1(Just(vyy400), Just(vyy410), app(ty_[], hb)) → new_esEs(vyy400, vyy410, hb)
new_esEs4(@2(vyy400, vyy401), @2(vyy410, vyy411), bdg, app(app(ty_Either, beg), beh)) → new_esEs3(vyy401, vyy411, beg, beh)
new_esEs(:(vyy400, vyy401), :(vyy410, vyy411), app(app(ty_Either, bh), ca)) → new_esEs3(vyy400, vyy410, bh, ca)
new_esEs0(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), cd, app(ty_[], eb), ec) → new_esEs(vyy401, vyy411, eb)
new_esEs3(Left(vyy400), Left(vyy410), app(app(ty_FiniteMap, bbe), bbf), bah) → new_esEs2(vyy400, vyy410, bbe, bbf)
new_esEs4(@2(vyy400, vyy401), @2(vyy410, vyy411), bdg, app(app(ty_FiniteMap, bee), bef)) → new_esEs2(vyy401, vyy411, bee, bef)
new_esEs3(Left(vyy400), Left(vyy410), app(app(ty_@2, bca), bcb), bah) → new_esEs4(vyy400, vyy410, bca, bcb)
new_esEs1(Just(vyy400), Just(vyy410), app(ty_Maybe, hf)) → new_esEs1(vyy400, vyy410, hf)
new_esEs(:(vyy400, vyy401), :(vyy410, vyy411), app(app(ty_@2, cb), cc)) → new_esEs4(vyy400, vyy410, cb, cc)
new_esEs1(Just(vyy400), Just(vyy410), app(app(ty_FiniteMap, hg), hh)) → new_esEs2(vyy400, vyy410, hg, hh)
new_esEs4(@2(vyy400, vyy401), @2(vyy410, vyy411), bdg, app(app(ty_@2, bfa), bfb)) → new_esEs4(vyy401, vyy411, bfa, bfb)
new_esEs2(vyy40, vyy41, bae, baf) → new_esEs(new_foldFM2(vyy40, bae, baf), new_fmToList(vyy41, bae, baf), app(app(ty_@2, bae), baf))
new_esEs3(Right(vyy400), Right(vyy410), bcc, app(app(ty_FiniteMap, bda), bdb)) → new_esEs2(vyy400, vyy410, bda, bdb)
new_esEs0(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), cd, app(ty_Maybe, eg), ec) → new_esEs1(vyy401, vyy411, eg)
new_esEs1(Just(vyy400), Just(vyy410), app(app(ty_@2, bac), bad)) → new_esEs4(vyy400, vyy410, bac, bad)
new_esEs0(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), cd, app(app(ty_FiniteMap, eh), fa), ec) → new_esEs2(vyy401, vyy411, eh, fa)
new_esEs0(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), cd, ce, app(app(ty_Either, df), dg)) → new_esEs3(vyy402, vyy412, df, dg)
new_esEs3(Left(vyy400), Left(vyy410), app(ty_Maybe, bbd), bah) → new_esEs1(vyy400, vyy410, bbd)
new_esEs4(@2(vyy400, vyy401), @2(vyy410, vyy411), app(app(ty_@2, bge), bgf), bfd) → new_esEs4(vyy400, vyy410, bge, bgf)
new_esEs0(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), cd, app(app(ty_@2, fd), ff), ec) → new_esEs4(vyy401, vyy411, fd, ff)
new_esEs3(Left(vyy400), Left(vyy410), app(ty_[], bag), bah) → new_esEs(vyy400, vyy410, bag)
new_esEs0(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), cd, app(app(app(ty_@3, ed), ee), ef), ec) → new_esEs0(vyy401, vyy411, ed, ee, ef)
new_esEs4(@2(vyy400, vyy401), @2(vyy410, vyy411), bdg, app(ty_[], bdh)) → new_esEs(vyy401, vyy411, bdh)
new_esEs4(@2(vyy400, vyy401), @2(vyy410, vyy411), bdg, app(ty_Maybe, bed)) → new_esEs1(vyy401, vyy411, bed)
new_esEs3(Left(vyy400), Left(vyy410), app(app(app(ty_@3, bba), bbb), bbc), bah) → new_esEs0(vyy400, vyy410, bba, bbb, bbc)
new_esEs4(@2(vyy400, vyy401), @2(vyy410, vyy411), app(app(ty_FiniteMap, bga), bgb), bfd) → new_esEs2(vyy400, vyy410, bga, bgb)
new_esEs0(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), app(ty_[], fg), ce, ec) → new_esEs(vyy400, vyy410, fg)
new_esEs(:(vyy400, vyy401), :(vyy410, vyy411), h) → new_esEs(vyy401, vyy411, h)
new_esEs0(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), app(app(ty_FiniteMap, gd), ge), ce, ec) → new_esEs2(vyy400, vyy410, gd, ge)
new_esEs0(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), cd, ce, app(ty_Maybe, dc)) → new_esEs1(vyy402, vyy412, dc)
new_esEs0(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), cd, ce, app(app(app(ty_@3, cg), da), db)) → new_esEs0(vyy402, vyy412, cg, da, db)
new_esEs0(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), cd, ce, app(app(ty_FiniteMap, dd), de)) → new_esEs2(vyy402, vyy412, dd, de)
new_esEs4(@2(vyy400, vyy401), @2(vyy410, vyy411), app(ty_[], bfc), bfd) → new_esEs(vyy400, vyy410, bfc)
new_esEs3(Right(vyy400), Right(vyy410), bcc, app(ty_Maybe, bch)) → new_esEs1(vyy400, vyy410, bch)
new_esEs0(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), app(app(ty_Either, gf), gg), ce, ec) → new_esEs3(vyy400, vyy410, gf, gg)
new_esEs4(@2(vyy400, vyy401), @2(vyy410, vyy411), app(app(ty_Either, bgc), bgd), bfd) → new_esEs3(vyy400, vyy410, bgc, bgd)
new_esEs(:(vyy400, vyy401), :(vyy410, vyy411), app(app(app(ty_@3, bb), bc), bd)) → new_esEs0(vyy400, vyy410, bb, bc, bd)
new_esEs0(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), app(ty_Maybe, gc), ce, ec) → new_esEs1(vyy400, vyy410, gc)
new_esEs0(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), cd, app(app(ty_Either, fb), fc), ec) → new_esEs3(vyy401, vyy411, fb, fc)
new_esEs(:(vyy400, vyy401), :(vyy410, vyy411), app(ty_[], ba)) → new_esEs(vyy400, vyy410, ba)
new_esEs0(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), app(app(app(ty_@3, fh), ga), gb), ce, ec) → new_esEs0(vyy400, vyy410, fh, ga, gb)
new_esEs0(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), cd, ce, app(app(ty_@2, dh), ea)) → new_esEs4(vyy402, vyy412, dh, ea)
new_esEs(:(vyy400, vyy401), :(vyy410, vyy411), app(ty_Maybe, be)) → new_esEs1(vyy400, vyy410, be)
The TRS R consists of the following rules:
new_foldFM0(vyy410, vyy411, vyy85, EmptyFM, bae, baf) → :(@2(vyy410, vyy411), vyy85)
new_foldFM0(vyy410, vyy411, vyy85, Branch(vyy4130, vyy4131, vyy4132, vyy4133, vyy4134), bae, baf) → new_foldFM0(vyy4130, vyy4131, new_foldFM0(vyy410, vyy411, vyy85, vyy4134, bae, baf), vyy4133, bae, baf)
new_fmToList(vyy41, bae, baf) → new_foldFM2(vyy41, bae, baf)
new_foldFM2(Branch(vyy410, vyy411, vyy412, vyy413, vyy414), bae, baf) → new_foldFM0(vyy410, vyy411, new_foldFM2(vyy414, bae, baf), vyy413, bae, baf)
new_foldFM2(EmptyFM, bae, baf) → []
The set Q consists of the following terms:
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
new_fmToList(x0, x1, x2)
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
new_foldFM2(EmptyFM, x0, x1)
We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_esEs2(vyy40, vyy41, bae, baf) → new_esEs(new_foldFM2(vyy40, bae, baf), new_fmToList(vyy41, bae, baf), app(app(ty_@2, bae), baf)) at position [1] we obtained the following new rules:
new_esEs2(vyy40, vyy41, bae, baf) → new_esEs(new_foldFM2(vyy40, bae, baf), new_foldFM2(vyy41, bae, baf), app(app(ty_@2, bae), baf))
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ Rewriting
↳ QDP
↳ Rewriting
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_esEs3(Right(vyy400), Right(vyy410), bcc, app(app(ty_@2, bde), bdf)) → new_esEs4(vyy400, vyy410, bde, bdf)
new_esEs3(Right(vyy400), Right(vyy410), bcc, app(ty_[], bcd)) → new_esEs(vyy400, vyy410, bcd)
new_esEs4(@2(vyy400, vyy401), @2(vyy410, vyy411), app(app(app(ty_@3, bfe), bff), bfg), bfd) → new_esEs0(vyy400, vyy410, bfe, bff, bfg)
new_esEs1(Just(vyy400), Just(vyy410), app(app(app(ty_@3, hc), hd), he)) → new_esEs0(vyy400, vyy410, hc, hd, he)
new_esEs4(@2(vyy400, vyy401), @2(vyy410, vyy411), app(ty_Maybe, bfh), bfd) → new_esEs1(vyy400, vyy410, bfh)
new_esEs3(Right(vyy400), Right(vyy410), bcc, app(app(ty_Either, bdc), bdd)) → new_esEs3(vyy400, vyy410, bdc, bdd)
new_esEs0(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), app(app(ty_@2, gh), ha), ce, ec) → new_esEs4(vyy400, vyy410, gh, ha)
new_esEs0(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), cd, ce, app(ty_[], cf)) → new_esEs(vyy402, vyy412, cf)
new_esEs3(Right(vyy400), Right(vyy410), bcc, app(app(app(ty_@3, bce), bcf), bcg)) → new_esEs0(vyy400, vyy410, bce, bcf, bcg)
new_esEs3(Left(vyy400), Left(vyy410), app(app(ty_Either, bbg), bbh), bah) → new_esEs3(vyy400, vyy410, bbg, bbh)
new_esEs1(Just(vyy400), Just(vyy410), app(app(ty_Either, baa), bab)) → new_esEs3(vyy400, vyy410, baa, bab)
new_esEs4(@2(vyy400, vyy401), @2(vyy410, vyy411), bdg, app(app(app(ty_@3, bea), beb), bec)) → new_esEs0(vyy401, vyy411, bea, beb, bec)
new_esEs(:(vyy400, vyy401), :(vyy410, vyy411), app(app(ty_FiniteMap, bf), bg)) → new_esEs2(vyy400, vyy410, bf, bg)
new_esEs1(Just(vyy400), Just(vyy410), app(ty_[], hb)) → new_esEs(vyy400, vyy410, hb)
new_esEs2(vyy40, vyy41, bae, baf) → new_esEs(new_foldFM2(vyy40, bae, baf), new_foldFM2(vyy41, bae, baf), app(app(ty_@2, bae), baf))
new_esEs4(@2(vyy400, vyy401), @2(vyy410, vyy411), bdg, app(app(ty_Either, beg), beh)) → new_esEs3(vyy401, vyy411, beg, beh)
new_esEs(:(vyy400, vyy401), :(vyy410, vyy411), app(app(ty_Either, bh), ca)) → new_esEs3(vyy400, vyy410, bh, ca)
new_esEs0(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), cd, app(ty_[], eb), ec) → new_esEs(vyy401, vyy411, eb)
new_esEs4(@2(vyy400, vyy401), @2(vyy410, vyy411), bdg, app(app(ty_FiniteMap, bee), bef)) → new_esEs2(vyy401, vyy411, bee, bef)
new_esEs3(Left(vyy400), Left(vyy410), app(app(ty_FiniteMap, bbe), bbf), bah) → new_esEs2(vyy400, vyy410, bbe, bbf)
new_esEs3(Left(vyy400), Left(vyy410), app(app(ty_@2, bca), bcb), bah) → new_esEs4(vyy400, vyy410, bca, bcb)
new_esEs1(Just(vyy400), Just(vyy410), app(ty_Maybe, hf)) → new_esEs1(vyy400, vyy410, hf)
new_esEs(:(vyy400, vyy401), :(vyy410, vyy411), app(app(ty_@2, cb), cc)) → new_esEs4(vyy400, vyy410, cb, cc)
new_esEs1(Just(vyy400), Just(vyy410), app(app(ty_FiniteMap, hg), hh)) → new_esEs2(vyy400, vyy410, hg, hh)
new_esEs4(@2(vyy400, vyy401), @2(vyy410, vyy411), bdg, app(app(ty_@2, bfa), bfb)) → new_esEs4(vyy401, vyy411, bfa, bfb)
new_esEs3(Right(vyy400), Right(vyy410), bcc, app(app(ty_FiniteMap, bda), bdb)) → new_esEs2(vyy400, vyy410, bda, bdb)
new_esEs0(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), cd, app(ty_Maybe, eg), ec) → new_esEs1(vyy401, vyy411, eg)
new_esEs0(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), cd, app(app(ty_FiniteMap, eh), fa), ec) → new_esEs2(vyy401, vyy411, eh, fa)
new_esEs1(Just(vyy400), Just(vyy410), app(app(ty_@2, bac), bad)) → new_esEs4(vyy400, vyy410, bac, bad)
new_esEs0(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), cd, ce, app(app(ty_Either, df), dg)) → new_esEs3(vyy402, vyy412, df, dg)
new_esEs3(Left(vyy400), Left(vyy410), app(ty_Maybe, bbd), bah) → new_esEs1(vyy400, vyy410, bbd)
new_esEs4(@2(vyy400, vyy401), @2(vyy410, vyy411), app(app(ty_@2, bge), bgf), bfd) → new_esEs4(vyy400, vyy410, bge, bgf)
new_esEs0(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), cd, app(app(ty_@2, fd), ff), ec) → new_esEs4(vyy401, vyy411, fd, ff)
new_esEs3(Left(vyy400), Left(vyy410), app(ty_[], bag), bah) → new_esEs(vyy400, vyy410, bag)
new_esEs0(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), cd, app(app(app(ty_@3, ed), ee), ef), ec) → new_esEs0(vyy401, vyy411, ed, ee, ef)
new_esEs4(@2(vyy400, vyy401), @2(vyy410, vyy411), bdg, app(ty_[], bdh)) → new_esEs(vyy401, vyy411, bdh)
new_esEs4(@2(vyy400, vyy401), @2(vyy410, vyy411), bdg, app(ty_Maybe, bed)) → new_esEs1(vyy401, vyy411, bed)
new_esEs4(@2(vyy400, vyy401), @2(vyy410, vyy411), app(app(ty_FiniteMap, bga), bgb), bfd) → new_esEs2(vyy400, vyy410, bga, bgb)
new_esEs3(Left(vyy400), Left(vyy410), app(app(app(ty_@3, bba), bbb), bbc), bah) → new_esEs0(vyy400, vyy410, bba, bbb, bbc)
new_esEs0(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), app(ty_[], fg), ce, ec) → new_esEs(vyy400, vyy410, fg)
new_esEs0(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), app(app(ty_FiniteMap, gd), ge), ce, ec) → new_esEs2(vyy400, vyy410, gd, ge)
new_esEs(:(vyy400, vyy401), :(vyy410, vyy411), h) → new_esEs(vyy401, vyy411, h)
new_esEs0(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), cd, ce, app(app(app(ty_@3, cg), da), db)) → new_esEs0(vyy402, vyy412, cg, da, db)
new_esEs0(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), cd, ce, app(ty_Maybe, dc)) → new_esEs1(vyy402, vyy412, dc)
new_esEs4(@2(vyy400, vyy401), @2(vyy410, vyy411), app(ty_[], bfc), bfd) → new_esEs(vyy400, vyy410, bfc)
new_esEs0(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), cd, ce, app(app(ty_FiniteMap, dd), de)) → new_esEs2(vyy402, vyy412, dd, de)
new_esEs3(Right(vyy400), Right(vyy410), bcc, app(ty_Maybe, bch)) → new_esEs1(vyy400, vyy410, bch)
new_esEs0(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), app(app(ty_Either, gf), gg), ce, ec) → new_esEs3(vyy400, vyy410, gf, gg)
new_esEs4(@2(vyy400, vyy401), @2(vyy410, vyy411), app(app(ty_Either, bgc), bgd), bfd) → new_esEs3(vyy400, vyy410, bgc, bgd)
new_esEs(:(vyy400, vyy401), :(vyy410, vyy411), app(app(app(ty_@3, bb), bc), bd)) → new_esEs0(vyy400, vyy410, bb, bc, bd)
new_esEs0(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), app(ty_Maybe, gc), ce, ec) → new_esEs1(vyy400, vyy410, gc)
new_esEs0(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), cd, app(app(ty_Either, fb), fc), ec) → new_esEs3(vyy401, vyy411, fb, fc)
new_esEs(:(vyy400, vyy401), :(vyy410, vyy411), app(ty_[], ba)) → new_esEs(vyy400, vyy410, ba)
new_esEs0(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), cd, ce, app(app(ty_@2, dh), ea)) → new_esEs4(vyy402, vyy412, dh, ea)
new_esEs0(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), app(app(app(ty_@3, fh), ga), gb), ce, ec) → new_esEs0(vyy400, vyy410, fh, ga, gb)
new_esEs(:(vyy400, vyy401), :(vyy410, vyy411), app(ty_Maybe, be)) → new_esEs1(vyy400, vyy410, be)
The TRS R consists of the following rules:
new_foldFM0(vyy410, vyy411, vyy85, EmptyFM, bae, baf) → :(@2(vyy410, vyy411), vyy85)
new_foldFM0(vyy410, vyy411, vyy85, Branch(vyy4130, vyy4131, vyy4132, vyy4133, vyy4134), bae, baf) → new_foldFM0(vyy4130, vyy4131, new_foldFM0(vyy410, vyy411, vyy85, vyy4134, bae, baf), vyy4133, bae, baf)
new_fmToList(vyy41, bae, baf) → new_foldFM2(vyy41, bae, baf)
new_foldFM2(Branch(vyy410, vyy411, vyy412, vyy413, vyy414), bae, baf) → new_foldFM0(vyy410, vyy411, new_foldFM2(vyy414, bae, baf), vyy413, bae, baf)
new_foldFM2(EmptyFM, bae, baf) → []
The set Q consists of the following terms:
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
new_fmToList(x0, x1, x2)
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
new_foldFM2(EmptyFM, x0, x1)
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
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ Rewriting
↳ QDP
↳ Rewriting
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QReductionProof
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_esEs3(Right(vyy400), Right(vyy410), bcc, app(app(ty_@2, bde), bdf)) → new_esEs4(vyy400, vyy410, bde, bdf)
new_esEs3(Right(vyy400), Right(vyy410), bcc, app(ty_[], bcd)) → new_esEs(vyy400, vyy410, bcd)
new_esEs4(@2(vyy400, vyy401), @2(vyy410, vyy411), app(app(app(ty_@3, bfe), bff), bfg), bfd) → new_esEs0(vyy400, vyy410, bfe, bff, bfg)
new_esEs1(Just(vyy400), Just(vyy410), app(app(app(ty_@3, hc), hd), he)) → new_esEs0(vyy400, vyy410, hc, hd, he)
new_esEs4(@2(vyy400, vyy401), @2(vyy410, vyy411), app(ty_Maybe, bfh), bfd) → new_esEs1(vyy400, vyy410, bfh)
new_esEs3(Right(vyy400), Right(vyy410), bcc, app(app(ty_Either, bdc), bdd)) → new_esEs3(vyy400, vyy410, bdc, bdd)
new_esEs0(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), app(app(ty_@2, gh), ha), ce, ec) → new_esEs4(vyy400, vyy410, gh, ha)
new_esEs0(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), cd, ce, app(ty_[], cf)) → new_esEs(vyy402, vyy412, cf)
new_esEs3(Right(vyy400), Right(vyy410), bcc, app(app(app(ty_@3, bce), bcf), bcg)) → new_esEs0(vyy400, vyy410, bce, bcf, bcg)
new_esEs3(Left(vyy400), Left(vyy410), app(app(ty_Either, bbg), bbh), bah) → new_esEs3(vyy400, vyy410, bbg, bbh)
new_esEs1(Just(vyy400), Just(vyy410), app(app(ty_Either, baa), bab)) → new_esEs3(vyy400, vyy410, baa, bab)
new_esEs4(@2(vyy400, vyy401), @2(vyy410, vyy411), bdg, app(app(app(ty_@3, bea), beb), bec)) → new_esEs0(vyy401, vyy411, bea, beb, bec)
new_esEs(:(vyy400, vyy401), :(vyy410, vyy411), app(app(ty_FiniteMap, bf), bg)) → new_esEs2(vyy400, vyy410, bf, bg)
new_esEs1(Just(vyy400), Just(vyy410), app(ty_[], hb)) → new_esEs(vyy400, vyy410, hb)
new_esEs2(vyy40, vyy41, bae, baf) → new_esEs(new_foldFM2(vyy40, bae, baf), new_foldFM2(vyy41, bae, baf), app(app(ty_@2, bae), baf))
new_esEs4(@2(vyy400, vyy401), @2(vyy410, vyy411), bdg, app(app(ty_Either, beg), beh)) → new_esEs3(vyy401, vyy411, beg, beh)
new_esEs(:(vyy400, vyy401), :(vyy410, vyy411), app(app(ty_Either, bh), ca)) → new_esEs3(vyy400, vyy410, bh, ca)
new_esEs0(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), cd, app(ty_[], eb), ec) → new_esEs(vyy401, vyy411, eb)
new_esEs4(@2(vyy400, vyy401), @2(vyy410, vyy411), bdg, app(app(ty_FiniteMap, bee), bef)) → new_esEs2(vyy401, vyy411, bee, bef)
new_esEs3(Left(vyy400), Left(vyy410), app(app(ty_FiniteMap, bbe), bbf), bah) → new_esEs2(vyy400, vyy410, bbe, bbf)
new_esEs3(Left(vyy400), Left(vyy410), app(app(ty_@2, bca), bcb), bah) → new_esEs4(vyy400, vyy410, bca, bcb)
new_esEs1(Just(vyy400), Just(vyy410), app(ty_Maybe, hf)) → new_esEs1(vyy400, vyy410, hf)
new_esEs(:(vyy400, vyy401), :(vyy410, vyy411), app(app(ty_@2, cb), cc)) → new_esEs4(vyy400, vyy410, cb, cc)
new_esEs1(Just(vyy400), Just(vyy410), app(app(ty_FiniteMap, hg), hh)) → new_esEs2(vyy400, vyy410, hg, hh)
new_esEs4(@2(vyy400, vyy401), @2(vyy410, vyy411), bdg, app(app(ty_@2, bfa), bfb)) → new_esEs4(vyy401, vyy411, bfa, bfb)
new_esEs3(Right(vyy400), Right(vyy410), bcc, app(app(ty_FiniteMap, bda), bdb)) → new_esEs2(vyy400, vyy410, bda, bdb)
new_esEs0(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), cd, app(ty_Maybe, eg), ec) → new_esEs1(vyy401, vyy411, eg)
new_esEs0(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), cd, app(app(ty_FiniteMap, eh), fa), ec) → new_esEs2(vyy401, vyy411, eh, fa)
new_esEs1(Just(vyy400), Just(vyy410), app(app(ty_@2, bac), bad)) → new_esEs4(vyy400, vyy410, bac, bad)
new_esEs0(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), cd, ce, app(app(ty_Either, df), dg)) → new_esEs3(vyy402, vyy412, df, dg)
new_esEs3(Left(vyy400), Left(vyy410), app(ty_Maybe, bbd), bah) → new_esEs1(vyy400, vyy410, bbd)
new_esEs4(@2(vyy400, vyy401), @2(vyy410, vyy411), app(app(ty_@2, bge), bgf), bfd) → new_esEs4(vyy400, vyy410, bge, bgf)
new_esEs0(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), cd, app(app(ty_@2, fd), ff), ec) → new_esEs4(vyy401, vyy411, fd, ff)
new_esEs3(Left(vyy400), Left(vyy410), app(ty_[], bag), bah) → new_esEs(vyy400, vyy410, bag)
new_esEs0(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), cd, app(app(app(ty_@3, ed), ee), ef), ec) → new_esEs0(vyy401, vyy411, ed, ee, ef)
new_esEs4(@2(vyy400, vyy401), @2(vyy410, vyy411), bdg, app(ty_[], bdh)) → new_esEs(vyy401, vyy411, bdh)
new_esEs4(@2(vyy400, vyy401), @2(vyy410, vyy411), bdg, app(ty_Maybe, bed)) → new_esEs1(vyy401, vyy411, bed)
new_esEs4(@2(vyy400, vyy401), @2(vyy410, vyy411), app(app(ty_FiniteMap, bga), bgb), bfd) → new_esEs2(vyy400, vyy410, bga, bgb)
new_esEs3(Left(vyy400), Left(vyy410), app(app(app(ty_@3, bba), bbb), bbc), bah) → new_esEs0(vyy400, vyy410, bba, bbb, bbc)
new_esEs0(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), app(ty_[], fg), ce, ec) → new_esEs(vyy400, vyy410, fg)
new_esEs0(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), app(app(ty_FiniteMap, gd), ge), ce, ec) → new_esEs2(vyy400, vyy410, gd, ge)
new_esEs(:(vyy400, vyy401), :(vyy410, vyy411), h) → new_esEs(vyy401, vyy411, h)
new_esEs0(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), cd, ce, app(app(app(ty_@3, cg), da), db)) → new_esEs0(vyy402, vyy412, cg, da, db)
new_esEs0(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), cd, ce, app(ty_Maybe, dc)) → new_esEs1(vyy402, vyy412, dc)
new_esEs4(@2(vyy400, vyy401), @2(vyy410, vyy411), app(ty_[], bfc), bfd) → new_esEs(vyy400, vyy410, bfc)
new_esEs0(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), cd, ce, app(app(ty_FiniteMap, dd), de)) → new_esEs2(vyy402, vyy412, dd, de)
new_esEs3(Right(vyy400), Right(vyy410), bcc, app(ty_Maybe, bch)) → new_esEs1(vyy400, vyy410, bch)
new_esEs0(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), app(app(ty_Either, gf), gg), ce, ec) → new_esEs3(vyy400, vyy410, gf, gg)
new_esEs4(@2(vyy400, vyy401), @2(vyy410, vyy411), app(app(ty_Either, bgc), bgd), bfd) → new_esEs3(vyy400, vyy410, bgc, bgd)
new_esEs(:(vyy400, vyy401), :(vyy410, vyy411), app(app(app(ty_@3, bb), bc), bd)) → new_esEs0(vyy400, vyy410, bb, bc, bd)
new_esEs0(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), app(ty_Maybe, gc), ce, ec) → new_esEs1(vyy400, vyy410, gc)
new_esEs0(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), cd, app(app(ty_Either, fb), fc), ec) → new_esEs3(vyy401, vyy411, fb, fc)
new_esEs(:(vyy400, vyy401), :(vyy410, vyy411), app(ty_[], ba)) → new_esEs(vyy400, vyy410, ba)
new_esEs0(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), cd, ce, app(app(ty_@2, dh), ea)) → new_esEs4(vyy402, vyy412, dh, ea)
new_esEs0(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), app(app(app(ty_@3, fh), ga), gb), ce, ec) → new_esEs0(vyy400, vyy410, fh, ga, gb)
new_esEs(:(vyy400, vyy401), :(vyy410, vyy411), app(ty_Maybe, be)) → new_esEs1(vyy400, vyy410, be)
The TRS R consists of the following rules:
new_foldFM2(Branch(vyy410, vyy411, vyy412, vyy413, vyy414), bae, baf) → new_foldFM0(vyy410, vyy411, new_foldFM2(vyy414, bae, baf), vyy413, bae, baf)
new_foldFM2(EmptyFM, bae, baf) → []
new_foldFM0(vyy410, vyy411, vyy85, EmptyFM, bae, baf) → :(@2(vyy410, vyy411), vyy85)
new_foldFM0(vyy410, vyy411, vyy85, Branch(vyy4130, vyy4131, vyy4132, vyy4133, vyy4134), bae, baf) → new_foldFM0(vyy4130, vyy4131, new_foldFM0(vyy410, vyy411, vyy85, vyy4134, bae, baf), vyy4133, bae, baf)
The set Q consists of the following terms:
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
new_fmToList(x0, x1, x2)
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
new_foldFM2(EmptyFM, x0, x1)
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_fmToList(x0, x1, x2)
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ Rewriting
↳ QDP
↳ Rewriting
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QReductionProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_esEs3(Right(vyy400), Right(vyy410), bcc, app(app(ty_@2, bde), bdf)) → new_esEs4(vyy400, vyy410, bde, bdf)
new_esEs3(Right(vyy400), Right(vyy410), bcc, app(ty_[], bcd)) → new_esEs(vyy400, vyy410, bcd)
new_esEs4(@2(vyy400, vyy401), @2(vyy410, vyy411), app(app(app(ty_@3, bfe), bff), bfg), bfd) → new_esEs0(vyy400, vyy410, bfe, bff, bfg)
new_esEs1(Just(vyy400), Just(vyy410), app(app(app(ty_@3, hc), hd), he)) → new_esEs0(vyy400, vyy410, hc, hd, he)
new_esEs4(@2(vyy400, vyy401), @2(vyy410, vyy411), app(ty_Maybe, bfh), bfd) → new_esEs1(vyy400, vyy410, bfh)
new_esEs3(Right(vyy400), Right(vyy410), bcc, app(app(ty_Either, bdc), bdd)) → new_esEs3(vyy400, vyy410, bdc, bdd)
new_esEs0(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), app(app(ty_@2, gh), ha), ce, ec) → new_esEs4(vyy400, vyy410, gh, ha)
new_esEs0(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), cd, ce, app(ty_[], cf)) → new_esEs(vyy402, vyy412, cf)
new_esEs3(Right(vyy400), Right(vyy410), bcc, app(app(app(ty_@3, bce), bcf), bcg)) → new_esEs0(vyy400, vyy410, bce, bcf, bcg)
new_esEs3(Left(vyy400), Left(vyy410), app(app(ty_Either, bbg), bbh), bah) → new_esEs3(vyy400, vyy410, bbg, bbh)
new_esEs1(Just(vyy400), Just(vyy410), app(app(ty_Either, baa), bab)) → new_esEs3(vyy400, vyy410, baa, bab)
new_esEs4(@2(vyy400, vyy401), @2(vyy410, vyy411), bdg, app(app(app(ty_@3, bea), beb), bec)) → new_esEs0(vyy401, vyy411, bea, beb, bec)
new_esEs(:(vyy400, vyy401), :(vyy410, vyy411), app(app(ty_FiniteMap, bf), bg)) → new_esEs2(vyy400, vyy410, bf, bg)
new_esEs1(Just(vyy400), Just(vyy410), app(ty_[], hb)) → new_esEs(vyy400, vyy410, hb)
new_esEs2(vyy40, vyy41, bae, baf) → new_esEs(new_foldFM2(vyy40, bae, baf), new_foldFM2(vyy41, bae, baf), app(app(ty_@2, bae), baf))
new_esEs4(@2(vyy400, vyy401), @2(vyy410, vyy411), bdg, app(app(ty_Either, beg), beh)) → new_esEs3(vyy401, vyy411, beg, beh)
new_esEs(:(vyy400, vyy401), :(vyy410, vyy411), app(app(ty_Either, bh), ca)) → new_esEs3(vyy400, vyy410, bh, ca)
new_esEs0(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), cd, app(ty_[], eb), ec) → new_esEs(vyy401, vyy411, eb)
new_esEs3(Left(vyy400), Left(vyy410), app(app(ty_FiniteMap, bbe), bbf), bah) → new_esEs2(vyy400, vyy410, bbe, bbf)
new_esEs4(@2(vyy400, vyy401), @2(vyy410, vyy411), bdg, app(app(ty_FiniteMap, bee), bef)) → new_esEs2(vyy401, vyy411, bee, bef)
new_esEs3(Left(vyy400), Left(vyy410), app(app(ty_@2, bca), bcb), bah) → new_esEs4(vyy400, vyy410, bca, bcb)
new_esEs1(Just(vyy400), Just(vyy410), app(ty_Maybe, hf)) → new_esEs1(vyy400, vyy410, hf)
new_esEs(:(vyy400, vyy401), :(vyy410, vyy411), app(app(ty_@2, cb), cc)) → new_esEs4(vyy400, vyy410, cb, cc)
new_esEs1(Just(vyy400), Just(vyy410), app(app(ty_FiniteMap, hg), hh)) → new_esEs2(vyy400, vyy410, hg, hh)
new_esEs4(@2(vyy400, vyy401), @2(vyy410, vyy411), bdg, app(app(ty_@2, bfa), bfb)) → new_esEs4(vyy401, vyy411, bfa, bfb)
new_esEs3(Right(vyy400), Right(vyy410), bcc, app(app(ty_FiniteMap, bda), bdb)) → new_esEs2(vyy400, vyy410, bda, bdb)
new_esEs0(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), cd, app(ty_Maybe, eg), ec) → new_esEs1(vyy401, vyy411, eg)
new_esEs0(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), cd, app(app(ty_FiniteMap, eh), fa), ec) → new_esEs2(vyy401, vyy411, eh, fa)
new_esEs1(Just(vyy400), Just(vyy410), app(app(ty_@2, bac), bad)) → new_esEs4(vyy400, vyy410, bac, bad)
new_esEs0(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), cd, ce, app(app(ty_Either, df), dg)) → new_esEs3(vyy402, vyy412, df, dg)
new_esEs3(Left(vyy400), Left(vyy410), app(ty_Maybe, bbd), bah) → new_esEs1(vyy400, vyy410, bbd)
new_esEs4(@2(vyy400, vyy401), @2(vyy410, vyy411), app(app(ty_@2, bge), bgf), bfd) → new_esEs4(vyy400, vyy410, bge, bgf)
new_esEs0(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), cd, app(app(ty_@2, fd), ff), ec) → new_esEs4(vyy401, vyy411, fd, ff)
new_esEs3(Left(vyy400), Left(vyy410), app(ty_[], bag), bah) → new_esEs(vyy400, vyy410, bag)
new_esEs0(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), cd, app(app(app(ty_@3, ed), ee), ef), ec) → new_esEs0(vyy401, vyy411, ed, ee, ef)
new_esEs4(@2(vyy400, vyy401), @2(vyy410, vyy411), bdg, app(ty_[], bdh)) → new_esEs(vyy401, vyy411, bdh)
new_esEs4(@2(vyy400, vyy401), @2(vyy410, vyy411), bdg, app(ty_Maybe, bed)) → new_esEs1(vyy401, vyy411, bed)
new_esEs4(@2(vyy400, vyy401), @2(vyy410, vyy411), app(app(ty_FiniteMap, bga), bgb), bfd) → new_esEs2(vyy400, vyy410, bga, bgb)
new_esEs3(Left(vyy400), Left(vyy410), app(app(app(ty_@3, bba), bbb), bbc), bah) → new_esEs0(vyy400, vyy410, bba, bbb, bbc)
new_esEs0(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), app(ty_[], fg), ce, ec) → new_esEs(vyy400, vyy410, fg)
new_esEs0(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), app(app(ty_FiniteMap, gd), ge), ce, ec) → new_esEs2(vyy400, vyy410, gd, ge)
new_esEs(:(vyy400, vyy401), :(vyy410, vyy411), h) → new_esEs(vyy401, vyy411, h)
new_esEs0(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), cd, ce, app(app(app(ty_@3, cg), da), db)) → new_esEs0(vyy402, vyy412, cg, da, db)
new_esEs0(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), cd, ce, app(ty_Maybe, dc)) → new_esEs1(vyy402, vyy412, dc)
new_esEs4(@2(vyy400, vyy401), @2(vyy410, vyy411), app(ty_[], bfc), bfd) → new_esEs(vyy400, vyy410, bfc)
new_esEs0(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), cd, ce, app(app(ty_FiniteMap, dd), de)) → new_esEs2(vyy402, vyy412, dd, de)
new_esEs3(Right(vyy400), Right(vyy410), bcc, app(ty_Maybe, bch)) → new_esEs1(vyy400, vyy410, bch)
new_esEs0(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), app(app(ty_Either, gf), gg), ce, ec) → new_esEs3(vyy400, vyy410, gf, gg)
new_esEs4(@2(vyy400, vyy401), @2(vyy410, vyy411), app(app(ty_Either, bgc), bgd), bfd) → new_esEs3(vyy400, vyy410, bgc, bgd)
new_esEs(:(vyy400, vyy401), :(vyy410, vyy411), app(app(app(ty_@3, bb), bc), bd)) → new_esEs0(vyy400, vyy410, bb, bc, bd)
new_esEs0(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), app(ty_Maybe, gc), ce, ec) → new_esEs1(vyy400, vyy410, gc)
new_esEs0(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), cd, app(app(ty_Either, fb), fc), ec) → new_esEs3(vyy401, vyy411, fb, fc)
new_esEs(:(vyy400, vyy401), :(vyy410, vyy411), app(ty_[], ba)) → new_esEs(vyy400, vyy410, ba)
new_esEs0(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), app(app(app(ty_@3, fh), ga), gb), ce, ec) → new_esEs0(vyy400, vyy410, fh, ga, gb)
new_esEs0(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), cd, ce, app(app(ty_@2, dh), ea)) → new_esEs4(vyy402, vyy412, dh, ea)
new_esEs(:(vyy400, vyy401), :(vyy410, vyy411), app(ty_Maybe, be)) → new_esEs1(vyy400, vyy410, be)
The TRS R consists of the following rules:
new_foldFM2(Branch(vyy410, vyy411, vyy412, vyy413, vyy414), bae, baf) → new_foldFM0(vyy410, vyy411, new_foldFM2(vyy414, bae, baf), vyy413, bae, baf)
new_foldFM2(EmptyFM, bae, baf) → []
new_foldFM0(vyy410, vyy411, vyy85, EmptyFM, bae, baf) → :(@2(vyy410, vyy411), vyy85)
new_foldFM0(vyy410, vyy411, vyy85, Branch(vyy4130, vyy4131, vyy4132, vyy4133, vyy4134), bae, baf) → new_foldFM0(vyy4130, vyy4131, new_foldFM0(vyy410, vyy411, vyy85, vyy4134, bae, baf), vyy4133, bae, baf)
The set Q consists of the following terms:
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
new_foldFM2(EmptyFM, x0, x1)
We have to consider all minimal (P,Q,R)-chains.
We use the reduction pair processor [15].
The following pairs can be oriented strictly and are deleted.
new_esEs3(Right(vyy400), Right(vyy410), bcc, app(app(ty_@2, bde), bdf)) → new_esEs4(vyy400, vyy410, bde, bdf)
new_esEs3(Right(vyy400), Right(vyy410), bcc, app(ty_[], bcd)) → new_esEs(vyy400, vyy410, bcd)
new_esEs1(Just(vyy400), Just(vyy410), app(app(app(ty_@3, hc), hd), he)) → new_esEs0(vyy400, vyy410, hc, hd, he)
new_esEs3(Right(vyy400), Right(vyy410), bcc, app(app(ty_Either, bdc), bdd)) → new_esEs3(vyy400, vyy410, bdc, bdd)
new_esEs0(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), app(app(ty_@2, gh), ha), ce, ec) → new_esEs4(vyy400, vyy410, gh, ha)
new_esEs0(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), cd, ce, app(ty_[], cf)) → new_esEs(vyy402, vyy412, cf)
new_esEs3(Right(vyy400), Right(vyy410), bcc, app(app(app(ty_@3, bce), bcf), bcg)) → new_esEs0(vyy400, vyy410, bce, bcf, bcg)
new_esEs3(Left(vyy400), Left(vyy410), app(app(ty_Either, bbg), bbh), bah) → new_esEs3(vyy400, vyy410, bbg, bbh)
new_esEs1(Just(vyy400), Just(vyy410), app(app(ty_Either, baa), bab)) → new_esEs3(vyy400, vyy410, baa, bab)
new_esEs(:(vyy400, vyy401), :(vyy410, vyy411), app(app(ty_FiniteMap, bf), bg)) → new_esEs2(vyy400, vyy410, bf, bg)
new_esEs1(Just(vyy400), Just(vyy410), app(ty_[], hb)) → new_esEs(vyy400, vyy410, hb)
new_esEs0(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), cd, app(ty_[], eb), ec) → new_esEs(vyy401, vyy411, eb)
new_esEs3(Left(vyy400), Left(vyy410), app(app(ty_FiniteMap, bbe), bbf), bah) → new_esEs2(vyy400, vyy410, bbe, bbf)
new_esEs4(@2(vyy400, vyy401), @2(vyy410, vyy411), bdg, app(app(ty_FiniteMap, bee), bef)) → new_esEs2(vyy401, vyy411, bee, bef)
new_esEs3(Left(vyy400), Left(vyy410), app(app(ty_@2, bca), bcb), bah) → new_esEs4(vyy400, vyy410, bca, bcb)
new_esEs1(Just(vyy400), Just(vyy410), app(ty_Maybe, hf)) → new_esEs1(vyy400, vyy410, hf)
new_esEs1(Just(vyy400), Just(vyy410), app(app(ty_FiniteMap, hg), hh)) → new_esEs2(vyy400, vyy410, hg, hh)
new_esEs3(Right(vyy400), Right(vyy410), bcc, app(app(ty_FiniteMap, bda), bdb)) → new_esEs2(vyy400, vyy410, bda, bdb)
new_esEs0(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), cd, app(ty_Maybe, eg), ec) → new_esEs1(vyy401, vyy411, eg)
new_esEs0(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), cd, app(app(ty_FiniteMap, eh), fa), ec) → new_esEs2(vyy401, vyy411, eh, fa)
new_esEs1(Just(vyy400), Just(vyy410), app(app(ty_@2, bac), bad)) → new_esEs4(vyy400, vyy410, bac, bad)
new_esEs0(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), cd, ce, app(app(ty_Either, df), dg)) → new_esEs3(vyy402, vyy412, df, dg)
new_esEs3(Left(vyy400), Left(vyy410), app(ty_Maybe, bbd), bah) → new_esEs1(vyy400, vyy410, bbd)
new_esEs0(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), cd, app(app(ty_@2, fd), ff), ec) → new_esEs4(vyy401, vyy411, fd, ff)
new_esEs3(Left(vyy400), Left(vyy410), app(ty_[], bag), bah) → new_esEs(vyy400, vyy410, bag)
new_esEs0(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), cd, app(app(app(ty_@3, ed), ee), ef), ec) → new_esEs0(vyy401, vyy411, ed, ee, ef)
new_esEs4(@2(vyy400, vyy401), @2(vyy410, vyy411), bdg, app(ty_[], bdh)) → new_esEs(vyy401, vyy411, bdh)
new_esEs4(@2(vyy400, vyy401), @2(vyy410, vyy411), app(app(ty_FiniteMap, bga), bgb), bfd) → new_esEs2(vyy400, vyy410, bga, bgb)
new_esEs3(Left(vyy400), Left(vyy410), app(app(app(ty_@3, bba), bbb), bbc), bah) → new_esEs0(vyy400, vyy410, bba, bbb, bbc)
new_esEs0(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), app(ty_[], fg), ce, ec) → new_esEs(vyy400, vyy410, fg)
new_esEs0(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), app(app(ty_FiniteMap, gd), ge), ce, ec) → new_esEs2(vyy400, vyy410, gd, ge)
new_esEs0(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), cd, ce, app(app(app(ty_@3, cg), da), db)) → new_esEs0(vyy402, vyy412, cg, da, db)
new_esEs0(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), cd, ce, app(ty_Maybe, dc)) → new_esEs1(vyy402, vyy412, dc)
new_esEs4(@2(vyy400, vyy401), @2(vyy410, vyy411), app(ty_[], bfc), bfd) → new_esEs(vyy400, vyy410, bfc)
new_esEs0(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), cd, ce, app(app(ty_FiniteMap, dd), de)) → new_esEs2(vyy402, vyy412, dd, de)
new_esEs3(Right(vyy400), Right(vyy410), bcc, app(ty_Maybe, bch)) → new_esEs1(vyy400, vyy410, bch)
new_esEs0(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), app(app(ty_Either, gf), gg), ce, ec) → new_esEs3(vyy400, vyy410, gf, gg)
new_esEs0(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), app(ty_Maybe, gc), ce, ec) → new_esEs1(vyy400, vyy410, gc)
new_esEs0(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), cd, app(app(ty_Either, fb), fc), ec) → new_esEs3(vyy401, vyy411, fb, fc)
new_esEs(:(vyy400, vyy401), :(vyy410, vyy411), app(ty_[], ba)) → new_esEs(vyy400, vyy410, ba)
new_esEs0(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), app(app(app(ty_@3, fh), ga), gb), ce, ec) → new_esEs0(vyy400, vyy410, fh, ga, gb)
new_esEs0(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), cd, ce, app(app(ty_@2, dh), ea)) → new_esEs4(vyy402, vyy412, dh, ea)
The remaining pairs can at least be oriented weakly.
new_esEs4(@2(vyy400, vyy401), @2(vyy410, vyy411), app(app(app(ty_@3, bfe), bff), bfg), bfd) → new_esEs0(vyy400, vyy410, bfe, bff, bfg)
new_esEs4(@2(vyy400, vyy401), @2(vyy410, vyy411), app(ty_Maybe, bfh), bfd) → new_esEs1(vyy400, vyy410, bfh)
new_esEs4(@2(vyy400, vyy401), @2(vyy410, vyy411), bdg, app(app(app(ty_@3, bea), beb), bec)) → new_esEs0(vyy401, vyy411, bea, beb, bec)
new_esEs2(vyy40, vyy41, bae, baf) → new_esEs(new_foldFM2(vyy40, bae, baf), new_foldFM2(vyy41, bae, baf), app(app(ty_@2, bae), baf))
new_esEs4(@2(vyy400, vyy401), @2(vyy410, vyy411), bdg, app(app(ty_Either, beg), beh)) → new_esEs3(vyy401, vyy411, beg, beh)
new_esEs(:(vyy400, vyy401), :(vyy410, vyy411), app(app(ty_Either, bh), ca)) → new_esEs3(vyy400, vyy410, bh, ca)
new_esEs(:(vyy400, vyy401), :(vyy410, vyy411), app(app(ty_@2, cb), cc)) → new_esEs4(vyy400, vyy410, cb, cc)
new_esEs4(@2(vyy400, vyy401), @2(vyy410, vyy411), bdg, app(app(ty_@2, bfa), bfb)) → new_esEs4(vyy401, vyy411, bfa, bfb)
new_esEs4(@2(vyy400, vyy401), @2(vyy410, vyy411), app(app(ty_@2, bge), bgf), bfd) → new_esEs4(vyy400, vyy410, bge, bgf)
new_esEs4(@2(vyy400, vyy401), @2(vyy410, vyy411), bdg, app(ty_Maybe, bed)) → new_esEs1(vyy401, vyy411, bed)
new_esEs(:(vyy400, vyy401), :(vyy410, vyy411), h) → new_esEs(vyy401, vyy411, h)
new_esEs4(@2(vyy400, vyy401), @2(vyy410, vyy411), app(app(ty_Either, bgc), bgd), bfd) → new_esEs3(vyy400, vyy410, bgc, bgd)
new_esEs(:(vyy400, vyy401), :(vyy410, vyy411), app(app(app(ty_@3, bb), bc), bd)) → new_esEs0(vyy400, vyy410, bb, bc, bd)
new_esEs(:(vyy400, vyy401), :(vyy410, vyy411), app(ty_Maybe, be)) → new_esEs1(vyy400, vyy410, be)
Used ordering: Polynomial interpretation [25]:
POL(:(x1, x2)) = 0
POL(@2(x1, x2)) = 0
POL(@3(x1, x2, x3)) = 0
POL(Branch(x1, x2, x3, x4, x5)) = 0
POL(EmptyFM) = 0
POL(Just(x1)) = 0
POL(Left(x1)) = 0
POL(Right(x1)) = 0
POL([]) = 0
POL(app(x1, x2)) = x1 + x2
POL(new_esEs(x1, x2, x3)) = x3
POL(new_esEs0(x1, x2, x3, x4, x5)) = 1 + x3 + x4 + x5
POL(new_esEs1(x1, x2, x3)) = 1 + x3
POL(new_esEs2(x1, x2, x3, x4)) = x3 + x4
POL(new_esEs3(x1, x2, x3, x4)) = 1 + x3 + x4
POL(new_esEs4(x1, x2, x3, x4)) = x3 + x4
POL(new_foldFM0(x1, x2, x3, x4, x5, x6)) = 0
POL(new_foldFM2(x1, x2, x3)) = 0
POL(ty_@2) = 0
POL(ty_@3) = 1
POL(ty_Either) = 1
POL(ty_FiniteMap) = 1
POL(ty_Maybe) = 1
POL(ty_[]) = 1
The following usable rules [17] were oriented:
none
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ Rewriting
↳ QDP
↳ Rewriting
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QReductionProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_esEs2(vyy40, vyy41, bae, baf) → new_esEs(new_foldFM2(vyy40, bae, baf), new_foldFM2(vyy41, bae, baf), app(app(ty_@2, bae), baf))
new_esEs4(@2(vyy400, vyy401), @2(vyy410, vyy411), bdg, app(app(ty_Either, beg), beh)) → new_esEs3(vyy401, vyy411, beg, beh)
new_esEs(:(vyy400, vyy401), :(vyy410, vyy411), h) → new_esEs(vyy401, vyy411, h)
new_esEs(:(vyy400, vyy401), :(vyy410, vyy411), app(app(ty_Either, bh), ca)) → new_esEs3(vyy400, vyy410, bh, ca)
new_esEs4(@2(vyy400, vyy401), @2(vyy410, vyy411), app(app(app(ty_@3, bfe), bff), bfg), bfd) → new_esEs0(vyy400, vyy410, bfe, bff, bfg)
new_esEs4(@2(vyy400, vyy401), @2(vyy410, vyy411), app(app(ty_Either, bgc), bgd), bfd) → new_esEs3(vyy400, vyy410, bgc, bgd)
new_esEs4(@2(vyy400, vyy401), @2(vyy410, vyy411), app(app(ty_@2, bge), bgf), bfd) → new_esEs4(vyy400, vyy410, bge, bgf)
new_esEs(:(vyy400, vyy401), :(vyy410, vyy411), app(app(app(ty_@3, bb), bc), bd)) → new_esEs0(vyy400, vyy410, bb, bc, bd)
new_esEs4(@2(vyy400, vyy401), @2(vyy410, vyy411), app(ty_Maybe, bfh), bfd) → new_esEs1(vyy400, vyy410, bfh)
new_esEs(:(vyy400, vyy401), :(vyy410, vyy411), app(app(ty_@2, cb), cc)) → new_esEs4(vyy400, vyy410, cb, cc)
new_esEs4(@2(vyy400, vyy401), @2(vyy410, vyy411), bdg, app(app(ty_@2, bfa), bfb)) → new_esEs4(vyy401, vyy411, bfa, bfb)
new_esEs4(@2(vyy400, vyy401), @2(vyy410, vyy411), bdg, app(app(app(ty_@3, bea), beb), bec)) → new_esEs0(vyy401, vyy411, bea, beb, bec)
new_esEs4(@2(vyy400, vyy401), @2(vyy410, vyy411), bdg, app(ty_Maybe, bed)) → new_esEs1(vyy401, vyy411, bed)
new_esEs(:(vyy400, vyy401), :(vyy410, vyy411), app(ty_Maybe, be)) → new_esEs1(vyy400, vyy410, be)
The TRS R consists of the following rules:
new_foldFM2(Branch(vyy410, vyy411, vyy412, vyy413, vyy414), bae, baf) → new_foldFM0(vyy410, vyy411, new_foldFM2(vyy414, bae, baf), vyy413, bae, baf)
new_foldFM2(EmptyFM, bae, baf) → []
new_foldFM0(vyy410, vyy411, vyy85, EmptyFM, bae, baf) → :(@2(vyy410, vyy411), vyy85)
new_foldFM0(vyy410, vyy411, vyy85, Branch(vyy4130, vyy4131, vyy4132, vyy4133, vyy4134), bae, baf) → new_foldFM0(vyy4130, vyy4131, new_foldFM0(vyy410, vyy411, vyy85, vyy4134, bae, baf), vyy4133, bae, baf)
The set Q consists of the following terms:
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
new_foldFM2(EmptyFM, x0, x1)
We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph [15,17,22] contains 2 SCCs with 11 less nodes.
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ Rewriting
↳ QDP
↳ Rewriting
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QReductionProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_esEs4(@2(vyy400, vyy401), @2(vyy410, vyy411), bdg, app(app(ty_@2, bfa), bfb)) → new_esEs4(vyy401, vyy411, bfa, bfb)
new_esEs4(@2(vyy400, vyy401), @2(vyy410, vyy411), app(app(ty_@2, bge), bgf), bfd) → new_esEs4(vyy400, vyy410, bge, bgf)
The TRS R consists of the following rules:
new_foldFM2(Branch(vyy410, vyy411, vyy412, vyy413, vyy414), bae, baf) → new_foldFM0(vyy410, vyy411, new_foldFM2(vyy414, bae, baf), vyy413, bae, baf)
new_foldFM2(EmptyFM, bae, baf) → []
new_foldFM0(vyy410, vyy411, vyy85, EmptyFM, bae, baf) → :(@2(vyy410, vyy411), vyy85)
new_foldFM0(vyy410, vyy411, vyy85, Branch(vyy4130, vyy4131, vyy4132, vyy4133, vyy4134), bae, baf) → new_foldFM0(vyy4130, vyy4131, new_foldFM0(vyy410, vyy411, vyy85, vyy4134, bae, baf), vyy4133, bae, baf)
The set Q consists of the following terms:
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
new_foldFM2(EmptyFM, x0, x1)
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
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ Rewriting
↳ QDP
↳ Rewriting
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QReductionProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QReductionProof
↳ QDP
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_esEs4(@2(vyy400, vyy401), @2(vyy410, vyy411), bdg, app(app(ty_@2, bfa), bfb)) → new_esEs4(vyy401, vyy411, bfa, bfb)
new_esEs4(@2(vyy400, vyy401), @2(vyy410, vyy411), app(app(ty_@2, bge), bgf), bfd) → new_esEs4(vyy400, vyy410, bge, bgf)
R is empty.
The set Q consists of the following terms:
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
new_foldFM2(EmptyFM, x0, x1)
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_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
new_foldFM2(EmptyFM, x0, x1)
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ Rewriting
↳ QDP
↳ Rewriting
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QReductionProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QReductionProof
↳ QDP
↳ QDPSizeChangeProof
↳ QDP
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_esEs4(@2(vyy400, vyy401), @2(vyy410, vyy411), bdg, app(app(ty_@2, bfa), bfb)) → new_esEs4(vyy401, vyy411, bfa, bfb)
new_esEs4(@2(vyy400, vyy401), @2(vyy410, vyy411), app(app(ty_@2, bge), bgf), bfd) → new_esEs4(vyy400, vyy410, bge, bgf)
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_esEs4(@2(vyy400, vyy401), @2(vyy410, vyy411), bdg, app(app(ty_@2, bfa), bfb)) → new_esEs4(vyy401, vyy411, bfa, bfb)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
- new_esEs4(@2(vyy400, vyy401), @2(vyy410, vyy411), app(app(ty_@2, bge), bgf), bfd) → new_esEs4(vyy400, vyy410, bge, bgf)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ Rewriting
↳ QDP
↳ Rewriting
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QReductionProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_esEs(:(vyy400, vyy401), :(vyy410, vyy411), h) → new_esEs(vyy401, vyy411, h)
The TRS R consists of the following rules:
new_foldFM2(Branch(vyy410, vyy411, vyy412, vyy413, vyy414), bae, baf) → new_foldFM0(vyy410, vyy411, new_foldFM2(vyy414, bae, baf), vyy413, bae, baf)
new_foldFM2(EmptyFM, bae, baf) → []
new_foldFM0(vyy410, vyy411, vyy85, EmptyFM, bae, baf) → :(@2(vyy410, vyy411), vyy85)
new_foldFM0(vyy410, vyy411, vyy85, Branch(vyy4130, vyy4131, vyy4132, vyy4133, vyy4134), bae, baf) → new_foldFM0(vyy4130, vyy4131, new_foldFM0(vyy410, vyy411, vyy85, vyy4134, bae, baf), vyy4133, bae, baf)
The set Q consists of the following terms:
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
new_foldFM2(EmptyFM, x0, x1)
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
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ Rewriting
↳ QDP
↳ Rewriting
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QReductionProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QReductionProof
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_esEs(:(vyy400, vyy401), :(vyy410, vyy411), h) → new_esEs(vyy401, vyy411, h)
R is empty.
The set Q consists of the following terms:
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
new_foldFM2(EmptyFM, x0, x1)
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_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
new_foldFM2(EmptyFM, x0, x1)
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ Rewriting
↳ QDP
↳ Rewriting
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QReductionProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QReductionProof
↳ QDP
↳ QDPSizeChangeProof
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_esEs(:(vyy400, vyy401), :(vyy410, vyy411), h) → new_esEs(vyy401, vyy411, h)
R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By using the subterm criterion [20] together with the size-change analysis [32] we have proven that there are no infinite chains for this DP problem. From the DPs we obtained the following set of size-change graphs:
- new_esEs(:(vyy400, vyy401), :(vyy410, vyy411), h) → new_esEs(vyy401, vyy411, h)
The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDPSizeChangeProof
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_ltEs0(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), app(ty_[], fc), cf, eb) → new_compare0(vyy3000, vyy400, fc)
new_compare0(:(vyy3000, vyy3001), :(vyy400, vyy401), h) → new_primCompAux(vyy3000, vyy400, new_compare(vyy3001, vyy401, h), h)
new_primCompAux(vyy3000, vyy400, vyy67, app(app(app(ty_@3, bb), bc), bd)) → new_compare1(vyy3000, vyy400, bb, bc, bd)
new_ltEs3(@2(vyy3000, vyy3001), @2(vyy400, vyy401), app(app(ty_Either, bdg), bdh), bdb) → new_lt2(vyy3000, vyy400, bdg, bdh)
new_ltEs3(@2(vyy3000, vyy3001), @2(vyy400, vyy401), app(ty_[], bda), bdb) → new_lt(vyy3000, vyy400, bda)
new_compare0(:(vyy3000, vyy3001), :(vyy400, vyy401), h) → new_compare0(vyy3001, vyy401, h)
new_ltEs0(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), app(app(app(ty_@3, cb), cc), cd), cf, eb) → new_compare20(vyy3000, vyy400, new_esEs5(vyy3000, vyy400, cb, cc, cd), cb, cc, cd)
new_ltEs2(Left(vyy3000), Left(vyy400), app(app(ty_Either, baa), bab), hd) → new_ltEs2(vyy3000, vyy400, baa, bab)
new_ltEs0(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), ce, app(app(ty_@2, fa), fb), eb) → new_lt3(vyy3001, vyy401, fa, fb)
new_ltEs0(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), app(app(ty_@2, fh), ga), cf, eb) → new_compare23(vyy3000, vyy400, new_esEs8(vyy3000, vyy400, fh, ga), fh, ga)
new_ltEs1(Just(vyy3000), Just(vyy400), app(ty_Maybe, gf)) → new_ltEs1(vyy3000, vyy400, gf)
new_ltEs2(Right(vyy3000), Right(vyy400), bae, app(ty_[], baf)) → new_ltEs(vyy3000, vyy400, baf)
new_ltEs0(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), ce, app(app(ty_Either, eg), eh), eb) → new_lt2(vyy3001, vyy401, eg, eh)
new_ltEs1(Just(vyy3000), Just(vyy400), app(app(app(ty_@3, gc), gd), ge)) → new_ltEs0(vyy3000, vyy400, gc, gd, ge)
new_ltEs2(Right(vyy3000), Right(vyy400), bae, app(app(app(ty_@3, bag), bah), bba)) → new_ltEs0(vyy3000, vyy400, bag, bah, bba)
new_compare1(vyy3000, vyy400, cb, cc, cd) → new_compare20(vyy3000, vyy400, new_esEs5(vyy3000, vyy400, cb, cc, cd), cb, cc, cd)
new_ltEs2(Left(vyy3000), Left(vyy400), app(app(ty_@2, bac), bad), hd) → new_ltEs3(vyy3000, vyy400, bac, bad)
new_lt2(vyy3000, vyy400, ff, fg) → new_compare22(vyy3000, vyy400, new_esEs7(vyy3000, vyy400, ff, fg), ff, fg)
new_ltEs(:(vyy3000, vyy3001), :(vyy400, vyy401), h) → new_primCompAux(vyy3000, vyy400, new_compare(vyy3001, vyy401, h), h)
new_ltEs0(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), ce, cf, app(app(ty_@2, dg), dh)) → new_ltEs3(vyy3002, vyy402, dg, dh)
new_ltEs0(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), ce, app(ty_[], ea), eb) → new_lt(vyy3001, vyy401, ea)
new_primCompAux(vyy3000, vyy400, vyy67, app(ty_[], ba)) → new_compare0(vyy3000, vyy400, ba)
new_ltEs3(@2(vyy3000, vyy3001), @2(vyy400, vyy401), app(ty_Maybe, bdf), bdb) → new_lt1(vyy3000, vyy400, bdf)
new_ltEs0(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), ce, cf, app(ty_Maybe, dd)) → new_ltEs1(vyy3002, vyy402, dd)
new_ltEs0(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), ce, app(app(app(ty_@3, ec), ed), ee), eb) → new_lt0(vyy3001, vyy401, ec, ed, ee)
new_ltEs1(Just(vyy3000), Just(vyy400), app(ty_[], gb)) → new_ltEs(vyy3000, vyy400, gb)
new_ltEs3(@2(vyy3000, vyy3001), @2(vyy400, vyy401), bbg, app(app(app(ty_@3, bca), bcb), bcc)) → new_ltEs0(vyy3001, vyy401, bca, bcb, bcc)
new_primCompAux(vyy3000, vyy400, vyy67, app(ty_Maybe, be)) → new_compare2(vyy3000, vyy400, be)
new_ltEs3(@2(vyy3000, vyy3001), @2(vyy400, vyy401), bbg, app(app(ty_@2, bcg), bch)) → new_ltEs3(vyy3001, vyy401, bcg, bch)
new_ltEs0(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), ce, cf, app(ty_[], cg)) → new_ltEs(vyy3002, vyy402, cg)
new_lt0(vyy3000, vyy400, cb, cc, cd) → new_compare20(vyy3000, vyy400, new_esEs5(vyy3000, vyy400, cb, cc, cd), cb, cc, cd)
new_ltEs2(Left(vyy3000), Left(vyy400), app(ty_Maybe, hh), hd) → new_ltEs1(vyy3000, vyy400, hh)
new_ltEs2(Right(vyy3000), Right(vyy400), bae, app(app(ty_@2, bbe), bbf)) → new_ltEs3(vyy3000, vyy400, bbe, bbf)
new_ltEs2(Right(vyy3000), Right(vyy400), bae, app(app(ty_Either, bbc), bbd)) → new_ltEs2(vyy3000, vyy400, bbc, bbd)
new_compare2(vyy3000, vyy400, fd) → new_compare21(vyy3000, vyy400, new_esEs6(vyy3000, vyy400, fd), fd)
new_ltEs0(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), ce, cf, app(app(ty_Either, de), df)) → new_ltEs2(vyy3002, vyy402, de, df)
new_lt1(vyy3000, vyy400, fd) → new_compare21(vyy3000, vyy400, new_esEs6(vyy3000, vyy400, fd), fd)
new_compare3(vyy3000, vyy400, ff, fg) → new_compare22(vyy3000, vyy400, new_esEs7(vyy3000, vyy400, ff, fg), ff, fg)
new_ltEs0(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), app(app(ty_Either, ff), fg), cf, eb) → new_compare22(vyy3000, vyy400, new_esEs7(vyy3000, vyy400, ff, fg), ff, fg)
new_ltEs0(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), ce, cf, app(app(app(ty_@3, da), db), dc)) → new_ltEs0(vyy3002, vyy402, da, db, dc)
new_compare23(vyy3000, vyy400, False, fh, ga) → new_ltEs3(vyy3000, vyy400, fh, ga)
new_ltEs3(@2(vyy3000, vyy3001), @2(vyy400, vyy401), app(app(ty_@2, bea), beb), bdb) → new_lt3(vyy3000, vyy400, bea, beb)
new_ltEs(:(vyy3000, vyy3001), :(vyy400, vyy401), h) → new_compare0(vyy3001, vyy401, h)
new_lt3(vyy3000, vyy400, fh, ga) → new_compare23(vyy3000, vyy400, new_esEs8(vyy3000, vyy400, fh, ga), fh, ga)
new_primCompAux(vyy3000, vyy400, vyy67, app(app(ty_Either, bf), bg)) → new_compare3(vyy3000, vyy400, bf, bg)
new_compare4(vyy3000, vyy400, fh, ga) → new_compare23(vyy3000, vyy400, new_esEs8(vyy3000, vyy400, fh, ga), fh, ga)
new_ltEs1(Just(vyy3000), Just(vyy400), app(app(ty_Either, gg), gh)) → new_ltEs2(vyy3000, vyy400, gg, gh)
new_primCompAux(vyy3000, vyy400, vyy67, app(app(ty_@2, bh), ca)) → new_compare4(vyy3000, vyy400, bh, ca)
new_ltEs3(@2(vyy3000, vyy3001), @2(vyy400, vyy401), bbg, app(ty_Maybe, bcd)) → new_ltEs1(vyy3001, vyy401, bcd)
new_lt(vyy3000, vyy400, fc) → new_compare0(vyy3000, vyy400, fc)
new_ltEs3(@2(vyy3000, vyy3001), @2(vyy400, vyy401), bbg, app(ty_[], bbh)) → new_ltEs(vyy3001, vyy401, bbh)
new_ltEs2(Left(vyy3000), Left(vyy400), app(ty_[], hc), hd) → new_ltEs(vyy3000, vyy400, hc)
new_ltEs3(@2(vyy3000, vyy3001), @2(vyy400, vyy401), bbg, app(app(ty_Either, bce), bcf)) → new_ltEs2(vyy3001, vyy401, bce, bcf)
new_ltEs0(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), ce, app(ty_Maybe, ef), eb) → new_lt1(vyy3001, vyy401, ef)
new_compare22(vyy3000, vyy400, False, ff, fg) → new_ltEs2(vyy3000, vyy400, ff, fg)
new_compare20(vyy3000, vyy400, False, cb, cc, cd) → new_ltEs0(vyy3000, vyy400, cb, cc, cd)
new_ltEs1(Just(vyy3000), Just(vyy400), app(app(ty_@2, ha), hb)) → new_ltEs3(vyy3000, vyy400, ha, hb)
new_ltEs2(Left(vyy3000), Left(vyy400), app(app(app(ty_@3, he), hf), hg), hd) → new_ltEs0(vyy3000, vyy400, he, hf, hg)
new_ltEs0(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), app(ty_Maybe, fd), cf, eb) → new_compare21(vyy3000, vyy400, new_esEs6(vyy3000, vyy400, fd), fd)
new_ltEs3(@2(vyy3000, vyy3001), @2(vyy400, vyy401), app(app(app(ty_@3, bdc), bdd), bde), bdb) → new_lt0(vyy3000, vyy400, bdc, bdd, bde)
new_compare21(vyy3000, vyy400, False, fd) → new_ltEs1(vyy3000, vyy400, fd)
new_ltEs2(Right(vyy3000), Right(vyy400), bae, app(ty_Maybe, bbb)) → new_ltEs1(vyy3000, vyy400, bbb)
The TRS R consists of the following rules:
new_esEs28(vyy401, vyy411, ty_Double) → new_esEs21(vyy401, vyy411)
new_esEs10(vyy401, vyy411, ty_Integer) → new_esEs12(vyy401, vyy411)
new_esEs25(vyy402, vyy412, ty_Char) → new_esEs19(vyy402, vyy412)
new_lt19(vyy3000, vyy400) → new_esEs15(new_compare14(vyy3000, vyy400))
new_esEs7(Left(vyy400), Left(vyy410), app(app(ty_Either, dcd), dce), bhc) → new_esEs7(vyy400, vyy410, dcd, dce)
new_lt12(vyy3001, vyy401, ty_@0) → new_lt17(vyy3001, vyy401)
new_compare15(vyy3000, vyy400, app(app(app(ty_@3, bb), bc), bd)) → new_compare16(vyy3000, vyy400, bb, bc, bd)
new_esEs27(vyy400, vyy410, ty_Char) → new_esEs19(vyy400, vyy410)
new_esEs25(vyy402, vyy412, ty_Integer) → new_esEs12(vyy402, vyy412)
new_esEs24(vyy40, vyy41, app(app(app(ty_@3, bgf), bgg), bgh)) → new_esEs5(vyy40, vyy41, bgf, bgg, bgh)
new_esEs6(Just(vyy400), Just(vyy410), ty_Int) → new_esEs13(vyy400, vyy410)
new_esEs7(Right(vyy400), Right(vyy410), bhb, app(ty_[], dda)) → new_esEs17(vyy400, vyy410, dda)
new_compare([], :(vyy400, vyy401), h) → LT
new_esEs18(vyy400, vyy410, app(ty_[], beg)) → new_esEs17(vyy400, vyy410, beg)
new_ltEs10(vyy300, vyy40) → new_not(new_compare19(vyy300, vyy40))
new_esEs15(GT) → False
new_esEs24(vyy40, vyy41, ty_Double) → new_esEs21(vyy40, vyy41)
new_ltEs19(vyy3001, vyy401, ty_Integer) → new_ltEs15(vyy3001, vyy401)
new_compare15(vyy3000, vyy400, ty_Integer) → new_compare7(vyy3000, vyy400)
new_ltEs18(vyy3002, vyy402, app(ty_Ratio, chd)) → new_ltEs12(vyy3002, vyy402, chd)
new_esEs6(Just(vyy400), Just(vyy410), app(app(ty_FiniteMap, dad), dae)) → new_esEs23(vyy400, vyy410, dad, dae)
new_ltEs19(vyy3001, vyy401, app(ty_Ratio, dee)) → new_ltEs12(vyy3001, vyy401, dee)
new_esEs27(vyy400, vyy410, ty_Double) → new_esEs21(vyy400, vyy410)
new_ltEs13(Right(vyy3000), Right(vyy400), bae, app(app(app(ty_@3, bag), bah), bba)) → new_ltEs7(vyy3000, vyy400, bag, bah, bba)
new_primMulNat0(Zero, Zero) → Zero
new_compare9(Float(vyy3000, vyy3001), Float(vyy400, vyy401)) → new_compare8(new_sr(vyy3000, vyy400), new_sr(vyy3001, vyy401))
new_esEs7(Left(vyy400), Left(vyy410), app(app(app(ty_@3, dbf), dbg), dbh), bhc) → new_esEs5(vyy400, vyy410, dbf, dbg, dbh)
new_compare(:(vyy3000, vyy3001), [], h) → GT
new_esEs29(vyy400, vyy410, ty_Float) → new_esEs16(vyy400, vyy410)
new_compare15(vyy3000, vyy400, ty_Char) → new_compare14(vyy3000, vyy400)
new_esEs18(vyy400, vyy410, ty_@0) → new_esEs22(vyy400, vyy410)
new_compare15(vyy3000, vyy400, ty_Double) → new_compare19(vyy3000, vyy400)
new_esEs20(EQ, EQ) → True
new_esEs26(vyy401, vyy411, ty_@0) → new_esEs22(vyy401, vyy411)
new_compare27(:%(vyy3000, vyy3001), :%(vyy400, vyy401), ty_Integer) → new_compare7(new_sr0(vyy3000, vyy401), new_sr0(vyy400, vyy3001))
new_lt20(vyy3000, vyy400, ty_Integer) → new_lt4(vyy3000, vyy400)
new_ltEs7(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), ce, cf, eb) → new_pePe(new_lt13(vyy3000, vyy400, ce), vyy3000, vyy400, new_pePe(new_lt12(vyy3001, vyy401, cf), vyy3001, vyy401, new_ltEs18(vyy3002, vyy402, eb), cf), ce)
new_esEs7(Left(vyy400), Left(vyy410), ty_Bool, bhc) → new_esEs14(vyy400, vyy410)
new_esEs20(EQ, GT) → False
new_esEs20(GT, EQ) → False
new_esEs27(vyy400, vyy410, ty_Integer) → new_esEs12(vyy400, vyy410)
new_not(GT) → False
new_lt5(vyy3000, vyy400) → new_esEs15(new_compare8(vyy3000, vyy400))
new_esEs27(vyy400, vyy410, app(app(ty_@2, cea), ceb)) → new_esEs8(vyy400, vyy410, cea, ceb)
new_esEs6(Just(vyy400), Just(vyy410), ty_Ordering) → new_esEs20(vyy400, vyy410)
new_ltEs5(Just(vyy3000), Just(vyy400), app(app(ty_Either, gg), gh)) → new_ltEs13(vyy3000, vyy400, gg, gh)
new_esEs27(vyy400, vyy410, app(ty_Ratio, cdh)) → new_esEs9(vyy400, vyy410, cdh)
new_lt12(vyy3001, vyy401, ty_Char) → new_lt19(vyy3001, vyy401)
new_esEs7(Right(vyy400), Right(vyy410), bhb, app(app(app(ty_@3, ddb), ddc), ddd)) → new_esEs5(vyy400, vyy410, ddb, ddc, ddd)
new_esEs27(vyy400, vyy410, ty_Ordering) → new_esEs20(vyy400, vyy410)
new_ltEs15(vyy300, vyy40) → new_not(new_compare7(vyy300, vyy40))
new_ltEs13(Left(vyy3000), Left(vyy400), app(app(ty_@2, bac), bad), hd) → new_ltEs17(vyy3000, vyy400, bac, bad)
new_ltEs18(vyy3002, vyy402, ty_Char) → new_ltEs14(vyy3002, vyy402)
new_ltEs19(vyy3001, vyy401, ty_Bool) → new_ltEs4(vyy3001, vyy401)
new_esEs29(vyy400, vyy410, app(app(ty_FiniteMap, cge), cgf)) → new_esEs23(vyy400, vyy410, cge, cgf)
new_esEs27(vyy400, vyy410, app(ty_Maybe, cdc)) → new_esEs6(vyy400, vyy410, cdc)
new_ltEs4(False, True) → True
new_ltEs8(EQ, EQ) → True
new_esEs7(Right(vyy400), Right(vyy410), bhb, app(ty_Ratio, deb)) → new_esEs9(vyy400, vyy410, deb)
new_lt13(vyy3000, vyy400, app(app(ty_Either, ff), fg)) → new_lt18(vyy3000, vyy400, ff, fg)
new_lt13(vyy3000, vyy400, ty_Integer) → new_lt4(vyy3000, vyy400)
new_esEs12(Integer(vyy400), Integer(vyy410)) → new_primEqInt(vyy400, vyy410)
new_ltEs9(vyy300, vyy40) → new_not(new_compare8(vyy300, vyy40))
new_esEs28(vyy401, vyy411, ty_Integer) → new_esEs12(vyy401, vyy411)
new_lt20(vyy3000, vyy400, ty_Ordering) → new_lt15(vyy3000, vyy400)
new_esEs28(vyy401, vyy411, app(app(app(ty_@3, cee), cef), ceg)) → new_esEs5(vyy401, vyy411, cee, cef, ceg)
new_esEs18(vyy400, vyy410, ty_Char) → new_esEs19(vyy400, vyy410)
new_ltEs13(Left(vyy3000), Left(vyy400), ty_Bool, hd) → new_ltEs4(vyy3000, vyy400)
new_foldFM0(vyy410, vyy411, vyy85, EmptyFM, bed, bee) → :(@2(vyy410, vyy411), vyy85)
new_lt12(vyy3001, vyy401, app(ty_Maybe, ef)) → new_lt10(vyy3001, vyy401, ef)
new_ltEs19(vyy3001, vyy401, ty_Float) → new_ltEs16(vyy3001, vyy401)
new_esEs7(Right(vyy400), Right(vyy410), bhb, app(ty_Maybe, dde)) → new_esEs6(vyy400, vyy410, dde)
new_ltEs4(True, True) → True
new_ltEs18(vyy3002, vyy402, app(app(app(ty_@3, da), db), dc)) → new_ltEs7(vyy3002, vyy402, da, db, dc)
new_esEs26(vyy401, vyy411, app(app(ty_@2, cce), ccf)) → new_esEs8(vyy401, vyy411, cce, ccf)
new_esEs7(Left(vyy400), Right(vyy410), bhb, bhc) → False
new_esEs7(Right(vyy400), Left(vyy410), bhb, bhc) → False
new_pePe(False, vyy40, vyy41, vyy57, bge) → new_asAs(new_esEs24(vyy40, vyy41, bge), vyy57)
new_esEs17(:(vyy400, vyy401), :(vyy410, vyy411), bef) → new_asAs(new_esEs18(vyy400, vyy410, bef), new_esEs17(vyy401, vyy411, bef))
new_lt18(vyy3000, vyy400, ff, fg) → new_esEs15(new_compare28(vyy3000, vyy400, ff, fg))
new_compare6(vyy3000, vyy400) → new_compare25(vyy3000, vyy400, new_esEs14(vyy3000, vyy400))
new_esEs20(LT, LT) → True
new_esEs5(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), bgf, bgg, bgh) → new_asAs(new_esEs27(vyy400, vyy410, bgf), new_asAs(new_esEs26(vyy401, vyy411, bgg), new_esEs25(vyy402, vyy412, bgh)))
new_lt16(vyy3000, vyy400) → new_esEs15(new_compare19(vyy3000, vyy400))
new_esEs25(vyy402, vyy412, ty_Bool) → new_esEs14(vyy402, vyy412)
new_esEs27(vyy400, vyy410, app(app(ty_Either, cdf), cdg)) → new_esEs7(vyy400, vyy410, cdf, cdg)
new_esEs11(vyy400, vyy410, ty_Int) → new_esEs13(vyy400, vyy410)
new_esEs18(vyy400, vyy410, app(app(ty_@2, bga), bgb)) → new_esEs8(vyy400, vyy410, bga, bgb)
new_lt13(vyy3000, vyy400, ty_Int) → new_lt5(vyy3000, vyy400)
new_esEs25(vyy402, vyy412, ty_Double) → new_esEs21(vyy402, vyy412)
new_ltEs13(Left(vyy3000), Left(vyy400), ty_Int, hd) → new_ltEs9(vyy3000, vyy400)
new_esEs27(vyy400, vyy410, app(ty_[], ccg)) → new_esEs17(vyy400, vyy410, ccg)
new_ltEs8(EQ, GT) → True
new_compare13(vyy3000, vyy400, False, ff, fg) → GT
new_esEs7(Left(vyy400), Left(vyy410), ty_Int, bhc) → new_esEs13(vyy400, vyy410)
new_ltEs8(GT, GT) → True
new_compare5(vyy3000, vyy400, fh, ga) → new_compare24(vyy3000, vyy400, new_esEs8(vyy3000, vyy400, fh, ga), fh, ga)
new_esEs18(vyy400, vyy410, ty_Int) → new_esEs13(vyy400, vyy410)
new_compare111(vyy3000, vyy400, False) → GT
new_compare111(vyy3000, vyy400, True) → LT
new_compare10(vyy3000, vyy400, True, fd) → LT
new_esEs26(vyy401, vyy411, ty_Char) → new_esEs19(vyy401, vyy411)
new_ltEs18(vyy3002, vyy402, ty_@0) → new_ltEs11(vyy3002, vyy402)
new_esEs6(Just(vyy400), Just(vyy410), app(app(app(ty_@3, chh), daa), dab)) → new_esEs5(vyy400, vyy410, chh, daa, dab)
new_primCmpNat0(Zero, Succ(vyy4000)) → LT
new_compare18(vyy3000, vyy400, fd) → new_compare211(vyy3000, vyy400, new_esEs6(vyy3000, vyy400, fd), fd)
new_ltEs5(Just(vyy3000), Just(vyy400), app(ty_Ratio, bgd)) → new_ltEs12(vyy3000, vyy400, bgd)
new_esEs15(LT) → True
new_ltEs6(vyy300, vyy40, h) → new_not(new_compare(vyy300, vyy40, h))
new_ltEs13(Left(vyy3000), Left(vyy400), ty_Double, hd) → new_ltEs10(vyy3000, vyy400)
new_esEs7(Right(vyy400), Right(vyy410), bhb, ty_Bool) → new_esEs14(vyy400, vyy410)
new_esEs26(vyy401, vyy411, ty_Double) → new_esEs21(vyy401, vyy411)
new_esEs26(vyy401, vyy411, ty_Ordering) → new_esEs20(vyy401, vyy411)
new_lt20(vyy3000, vyy400, ty_Char) → new_lt19(vyy3000, vyy400)
new_ltEs8(LT, EQ) → True
new_lt20(vyy3000, vyy400, ty_Int) → new_lt5(vyy3000, vyy400)
new_lt20(vyy3000, vyy400, app(ty_Ratio, def)) → new_lt9(vyy3000, vyy400, def)
new_ltEs18(vyy3002, vyy402, app(ty_Maybe, dd)) → new_ltEs5(vyy3002, vyy402, dd)
new_esEs18(vyy400, vyy410, app(ty_Ratio, bfh)) → new_esEs9(vyy400, vyy410, bfh)
new_compare10(vyy3000, vyy400, False, fd) → GT
new_esEs24(vyy40, vyy41, app(app(ty_Either, bhb), bhc)) → new_esEs7(vyy40, vyy41, bhb, bhc)
new_esEs15(EQ) → False
new_esEs7(Right(vyy400), Right(vyy410), bhb, ty_Float) → new_esEs16(vyy400, vyy410)
new_primEqNat0(Zero, Zero) → True
new_compare27(:%(vyy3000, vyy3001), :%(vyy400, vyy401), ty_Int) → new_compare8(new_sr(vyy3000, vyy401), new_sr(vyy400, vyy3001))
new_esEs29(vyy400, vyy410, app(ty_Maybe, cgd)) → new_esEs6(vyy400, vyy410, cgd)
new_esEs26(vyy401, vyy411, app(ty_Maybe, cbg)) → new_esEs6(vyy401, vyy411, cbg)
new_compare210(vyy3000, vyy400, False) → new_compare111(vyy3000, vyy400, new_ltEs8(vyy3000, vyy400))
new_compare29(vyy3000, vyy400, False, cb, cc, cd) → new_compare110(vyy3000, vyy400, new_ltEs7(vyy3000, vyy400, cb, cc, cd), cb, cc, cd)
new_esEs29(vyy400, vyy410, ty_Ordering) → new_esEs20(vyy400, vyy410)
new_ltEs8(GT, EQ) → False
new_lt13(vyy3000, vyy400, ty_Float) → new_lt7(vyy3000, vyy400)
new_ltEs8(EQ, LT) → False
new_esEs29(vyy400, vyy410, ty_Int) → new_esEs13(vyy400, vyy410)
new_compare(:(vyy3000, vyy3001), :(vyy400, vyy401), h) → new_primCompAux1(vyy3000, vyy400, new_compare(vyy3001, vyy401, h), h)
new_ltEs17(@2(vyy3000, vyy3001), @2(vyy400, vyy401), bbg, bdb) → new_pePe(new_lt20(vyy3000, vyy400, bbg), vyy3000, vyy400, new_ltEs19(vyy3001, vyy401, bdb), bbg)
new_ltEs13(Left(vyy3000), Left(vyy400), ty_Float, hd) → new_ltEs16(vyy3000, vyy400)
new_sr(vyy3001, vyy401) → new_primMulInt(vyy3001, vyy401)
new_esEs25(vyy402, vyy412, ty_Int) → new_esEs13(vyy402, vyy412)
new_esEs18(vyy400, vyy410, app(app(app(ty_@3, beh), bfa), bfb)) → new_esEs5(vyy400, vyy410, beh, bfa, bfb)
new_compare15(vyy3000, vyy400, app(app(ty_@2, bh), ca)) → new_compare5(vyy3000, vyy400, bh, ca)
new_ltEs5(Just(vyy3000), Just(vyy400), ty_Double) → new_ltEs10(vyy3000, vyy400)
new_lt7(vyy3000, vyy400) → new_esEs15(new_compare9(vyy3000, vyy400))
new_lt12(vyy3001, vyy401, ty_Float) → new_lt7(vyy3001, vyy401)
new_esEs24(vyy40, vyy41, ty_Char) → new_esEs19(vyy40, vyy41)
new_esEs13(vyy40, vyy41) → new_primEqInt(vyy40, vyy41)
new_primPlusNat0(Succ(vyy860), vyy40100) → Succ(Succ(new_primPlusNat1(vyy860, vyy40100)))
new_esEs25(vyy402, vyy412, ty_Float) → new_esEs16(vyy402, vyy412)
new_esEs7(Right(vyy400), Right(vyy410), bhb, app(app(ty_Either, ddh), dea)) → new_esEs7(vyy400, vyy410, ddh, dea)
new_ltEs19(vyy3001, vyy401, ty_Double) → new_ltEs10(vyy3001, vyy401)
new_esEs20(LT, EQ) → False
new_esEs20(EQ, LT) → False
new_ltEs11(vyy300, vyy40) → new_not(new_compare26(vyy300, vyy40))
new_compare29(vyy3000, vyy400, True, cb, cc, cd) → EQ
new_esEs26(vyy401, vyy411, ty_Integer) → new_esEs12(vyy401, vyy411)
new_lt11(vyy3000, vyy400, cb, cc, cd) → new_esEs15(new_compare16(vyy3000, vyy400, cb, cc, cd))
new_esEs28(vyy401, vyy411, ty_Float) → new_esEs16(vyy401, vyy411)
new_compare211(vyy3000, vyy400, True, fd) → EQ
new_compare25(vyy3000, vyy400, True) → EQ
new_primEqInt(Neg(Succ(vyy4000)), Neg(Succ(vyy4100))) → new_primEqNat0(vyy4000, vyy4100)
new_ltEs19(vyy3001, vyy401, app(app(ty_@2, bcg), bch)) → new_ltEs17(vyy3001, vyy401, bcg, bch)
new_esEs7(Right(vyy400), Right(vyy410), bhb, ty_Int) → new_esEs13(vyy400, vyy410)
new_ltEs19(vyy3001, vyy401, ty_Ordering) → new_ltEs8(vyy3001, vyy401)
new_esEs6(Just(vyy400), Just(vyy410), ty_@0) → new_esEs22(vyy400, vyy410)
new_esEs7(Left(vyy400), Left(vyy410), ty_@0, bhc) → new_esEs22(vyy400, vyy410)
new_esEs21(Double(vyy400, vyy401), Double(vyy410, vyy411)) → new_esEs13(new_sr(vyy400, vyy410), new_sr(vyy401, vyy411))
new_compare13(vyy3000, vyy400, True, ff, fg) → LT
new_esEs25(vyy402, vyy412, app(app(ty_@2, cba), cbb)) → new_esEs8(vyy402, vyy412, cba, cbb)
new_compare25(vyy3000, vyy400, False) → new_compare12(vyy3000, vyy400, new_ltEs4(vyy3000, vyy400))
new_ltEs5(Just(vyy3000), Nothing, bgc) → False
new_esEs24(vyy40, vyy41, ty_Bool) → new_esEs14(vyy40, vyy41)
new_primPlusNat1(Succ(vyy8600), Zero) → Succ(vyy8600)
new_primPlusNat1(Zero, Succ(vyy401000)) → Succ(vyy401000)
new_esEs7(Left(vyy400), Left(vyy410), app(app(ty_FiniteMap, dcb), dcc), bhc) → new_esEs23(vyy400, vyy410, dcb, dcc)
new_esEs7(Left(vyy400), Left(vyy410), app(ty_[], dbe), bhc) → new_esEs17(vyy400, vyy410, dbe)
new_ltEs13(Right(vyy3000), Right(vyy400), bae, ty_Integer) → new_ltEs15(vyy3000, vyy400)
new_ltEs13(Right(vyy3000), Right(vyy400), bae, ty_Int) → new_ltEs9(vyy3000, vyy400)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs6(Just(vyy400), Just(vyy410), ty_Integer) → new_esEs12(vyy400, vyy410)
new_ltEs5(Just(vyy3000), Just(vyy400), ty_Int) → new_ltEs9(vyy3000, vyy400)
new_lt13(vyy3000, vyy400, ty_@0) → new_lt17(vyy3000, vyy400)
new_ltEs13(Right(vyy3000), Right(vyy400), bae, ty_Char) → new_ltEs14(vyy3000, vyy400)
new_esEs29(vyy400, vyy410, ty_Double) → new_esEs21(vyy400, vyy410)
new_compare15(vyy3000, vyy400, ty_Int) → new_compare8(vyy3000, vyy400)
new_compare8(vyy300, vyy40) → new_primCmpInt(vyy300, vyy40)
new_primEqInt(Neg(Succ(vyy4000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(vyy4100))) → False
new_primCompAux0(vyy71, GT) → GT
new_lt12(vyy3001, vyy401, ty_Bool) → new_lt8(vyy3001, vyy401)
new_lt13(vyy3000, vyy400, ty_Ordering) → new_lt15(vyy3000, vyy400)
new_compare24(vyy3000, vyy400, True, fh, ga) → EQ
new_esEs28(vyy401, vyy411, ty_Int) → new_esEs13(vyy401, vyy411)
new_compare([], [], h) → EQ
new_ltEs13(Right(vyy3000), Right(vyy400), bae, ty_Double) → new_ltEs10(vyy3000, vyy400)
new_esEs8(@2(vyy400, vyy401), @2(vyy410, vyy411), bhd, bhe) → new_asAs(new_esEs29(vyy400, vyy410, bhd), new_esEs28(vyy401, vyy411, bhe))
new_foldFM0(vyy410, vyy411, vyy85, Branch(vyy4130, vyy4131, vyy4132, vyy4133, vyy4134), bed, bee) → new_foldFM0(vyy4130, vyy4131, new_foldFM0(vyy410, vyy411, vyy85, vyy4134, bed, bee), vyy4133, bed, bee)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_esEs26(vyy401, vyy411, app(app(ty_Either, ccb), ccc)) → new_esEs7(vyy401, vyy411, ccb, ccc)
new_esEs23(vyy40, vyy41, bed, bee) → new_asAs(new_esEs13(new_sizeFM(vyy40, bed, bee), new_sizeFM(vyy41, bed, bee)), new_esEs17(new_fmToList(vyy40, bed, bee), new_fmToList(vyy41, bed, bee), app(app(ty_@2, bed), bee)))
new_compare14(Char(vyy3000), Char(vyy400)) → new_primCmpNat0(vyy3000, vyy400)
new_esEs7(Right(vyy400), Right(vyy410), bhb, ty_@0) → new_esEs22(vyy400, vyy410)
new_ltEs5(Just(vyy3000), Just(vyy400), ty_Char) → new_ltEs14(vyy3000, vyy400)
new_primCmpNat0(Succ(vyy30000), Succ(vyy4000)) → new_primCmpNat0(vyy30000, vyy4000)
new_ltEs19(vyy3001, vyy401, ty_@0) → new_ltEs11(vyy3001, vyy401)
new_sizeFM(EmptyFM, bed, bee) → Pos(Zero)
new_ltEs5(Just(vyy3000), Just(vyy400), app(ty_[], gb)) → new_ltEs6(vyy3000, vyy400, gb)
new_ltEs13(Left(vyy3000), Left(vyy400), app(ty_[], hc), hd) → new_ltEs6(vyy3000, vyy400, hc)
new_esEs6(Nothing, Nothing, bha) → True
new_ltEs18(vyy3002, vyy402, app(app(ty_Either, de), df)) → new_ltEs13(vyy3002, vyy402, de, df)
new_lt12(vyy3001, vyy401, ty_Ordering) → new_lt15(vyy3001, vyy401)
new_ltEs13(Right(vyy3000), Right(vyy400), bae, ty_Ordering) → new_ltEs8(vyy3000, vyy400)
new_primEqInt(Pos(Succ(vyy4000)), Pos(Succ(vyy4100))) → new_primEqNat0(vyy4000, vyy4100)
new_compare15(vyy3000, vyy400, app(ty_[], ba)) → new_compare(vyy3000, vyy400, ba)
new_ltEs19(vyy3001, vyy401, app(app(app(ty_@3, bca), bcb), bcc)) → new_ltEs7(vyy3001, vyy401, bca, bcb, bcc)
new_compare15(vyy3000, vyy400, ty_Float) → new_compare9(vyy3000, vyy400)
new_lt13(vyy3000, vyy400, ty_Char) → new_lt19(vyy3000, vyy400)
new_esEs14(True, False) → False
new_esEs14(False, True) → False
new_ltEs16(vyy300, vyy40) → new_not(new_compare9(vyy300, vyy40))
new_compare15(vyy3000, vyy400, ty_Bool) → new_compare6(vyy3000, vyy400)
new_esEs26(vyy401, vyy411, ty_Int) → new_esEs13(vyy401, vyy411)
new_esEs6(Just(vyy400), Nothing, bha) → False
new_esEs6(Nothing, Just(vyy410), bha) → False
new_ltEs18(vyy3002, vyy402, ty_Bool) → new_ltEs4(vyy3002, vyy402)
new_primEqNat0(Succ(vyy4000), Succ(vyy4100)) → new_primEqNat0(vyy4000, vyy4100)
new_ltEs19(vyy3001, vyy401, app(app(ty_Either, bce), bcf)) → new_ltEs13(vyy3001, vyy401, bce, bcf)
new_ltEs5(Just(vyy3000), Just(vyy400), ty_Bool) → new_ltEs4(vyy3000, vyy400)
new_esEs7(Right(vyy400), Right(vyy410), bhb, ty_Ordering) → new_esEs20(vyy400, vyy410)
new_compare28(vyy3000, vyy400, ff, fg) → new_compare212(vyy3000, vyy400, new_esEs7(vyy3000, vyy400, ff, fg), ff, fg)
new_primCompAux1(vyy3000, vyy400, vyy67, h) → new_primCompAux0(vyy67, new_compare15(vyy3000, vyy400, h))
new_primCmpInt(Neg(Succ(vyy30000)), Neg(vyy400)) → new_primCmpNat0(vyy400, Succ(vyy30000))
new_esEs27(vyy400, vyy410, app(app(app(ty_@3, cch), cda), cdb)) → new_esEs5(vyy400, vyy410, cch, cda, cdb)
new_lt4(vyy3000, vyy400) → new_esEs15(new_compare7(vyy3000, vyy400))
new_primEqInt(Pos(Zero), Pos(Succ(vyy4100))) → False
new_primEqInt(Pos(Succ(vyy4000)), Pos(Zero)) → False
new_ltEs5(Just(vyy3000), Just(vyy400), ty_@0) → new_ltEs11(vyy3000, vyy400)
new_ltEs5(Nothing, Just(vyy400), bgc) → True
new_esEs24(vyy40, vyy41, ty_@0) → new_esEs22(vyy40, vyy41)
new_esEs25(vyy402, vyy412, ty_Ordering) → new_esEs20(vyy402, vyy412)
new_esEs20(GT, GT) → True
new_lt9(vyy3000, vyy400, cec) → new_esEs15(new_compare27(vyy3000, vyy400, cec))
new_lt15(vyy3000, vyy400) → new_esEs15(new_compare17(vyy3000, vyy400))
new_ltEs13(Left(vyy3000), Left(vyy400), app(app(app(ty_@3, he), hf), hg), hd) → new_ltEs7(vyy3000, vyy400, he, hf, hg)
new_primCmpNat0(Zero, Zero) → EQ
new_esEs7(Right(vyy400), Right(vyy410), bhb, app(app(ty_FiniteMap, ddf), ddg)) → new_esEs23(vyy400, vyy410, ddf, ddg)
new_primCmpNat0(Succ(vyy30000), Zero) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(vyy4000))) → LT
new_compare11(vyy3000, vyy400, True, fh, ga) → LT
new_esEs27(vyy400, vyy410, app(app(ty_FiniteMap, cdd), cde)) → new_esEs23(vyy400, vyy410, cdd, cde)
new_sr0(Integer(vyy4000), Integer(vyy30010)) → Integer(new_primMulInt(vyy4000, vyy30010))
new_primPlusNat1(Succ(vyy8600), Succ(vyy401000)) → Succ(Succ(new_primPlusNat1(vyy8600, vyy401000)))
new_primEqInt(Pos(Succ(vyy4000)), Neg(vyy410)) → False
new_primEqInt(Neg(Succ(vyy4000)), Pos(vyy410)) → False
new_esEs29(vyy400, vyy410, ty_Char) → new_esEs19(vyy400, vyy410)
new_lt12(vyy3001, vyy401, app(ty_Ratio, che)) → new_lt9(vyy3001, vyy401, che)
new_foldFM2(EmptyFM, bed, bee) → []
new_ltEs13(Right(vyy3000), Right(vyy400), bae, ty_@0) → new_ltEs11(vyy3000, vyy400)
new_esEs28(vyy401, vyy411, app(ty_Maybe, ceh)) → new_esEs6(vyy401, vyy411, ceh)
new_compare15(vyy3000, vyy400, app(app(ty_Either, bf), bg)) → new_compare28(vyy3000, vyy400, bf, bg)
new_ltEs12(vyy300, vyy40, chf) → new_not(new_compare27(vyy300, vyy40, chf))
new_primEqInt(Pos(Zero), Neg(Succ(vyy4100))) → False
new_primEqInt(Neg(Zero), Pos(Succ(vyy4100))) → False
new_esEs26(vyy401, vyy411, app(ty_[], cbc)) → new_esEs17(vyy401, vyy411, cbc)
new_ltEs14(vyy300, vyy40) → new_not(new_compare14(vyy300, vyy40))
new_primCmpInt(Pos(Zero), Pos(Succ(vyy4000))) → new_primCmpNat0(Zero, Succ(vyy4000))
new_esEs28(vyy401, vyy411, app(app(ty_Either, cfc), cfd)) → new_esEs7(vyy401, vyy411, cfc, cfd)
new_ltEs13(Right(vyy3000), Right(vyy400), bae, app(ty_Ratio, dbd)) → new_ltEs12(vyy3000, vyy400, dbd)
new_ltEs18(vyy3002, vyy402, ty_Int) → new_ltEs9(vyy3002, vyy402)
new_esEs27(vyy400, vyy410, ty_Int) → new_esEs13(vyy400, vyy410)
new_esEs28(vyy401, vyy411, app(app(ty_FiniteMap, cfa), cfb)) → new_esEs23(vyy401, vyy411, cfa, cfb)
new_compare12(vyy3000, vyy400, False) → GT
new_esEs6(Just(vyy400), Just(vyy410), app(app(ty_@2, dba), dbb)) → new_esEs8(vyy400, vyy410, dba, dbb)
new_esEs7(Right(vyy400), Right(vyy410), bhb, ty_Char) → new_esEs19(vyy400, vyy410)
new_ltEs8(GT, LT) → False
new_esEs26(vyy401, vyy411, ty_Float) → new_esEs16(vyy401, vyy411)
new_primCompAux0(vyy71, LT) → LT
new_esEs18(vyy400, vyy410, ty_Ordering) → new_esEs20(vyy400, vyy410)
new_lt20(vyy3000, vyy400, ty_Bool) → new_lt8(vyy3000, vyy400)
new_esEs24(vyy40, vyy41, ty_Int) → new_esEs13(vyy40, vyy41)
new_esEs7(Left(vyy400), Left(vyy410), app(ty_Maybe, dca), bhc) → new_esEs6(vyy400, vyy410, dca)
new_primPlusNat0(Zero, vyy40100) → Succ(vyy40100)
new_esEs27(vyy400, vyy410, ty_@0) → new_esEs22(vyy400, vyy410)
new_primCmpInt(Pos(Succ(vyy30000)), Pos(vyy400)) → new_primCmpNat0(Succ(vyy30000), vyy400)
new_esEs29(vyy400, vyy410, ty_Integer) → new_esEs12(vyy400, vyy410)
new_lt13(vyy3000, vyy400, app(app(app(ty_@3, cb), cc), cd)) → new_lt11(vyy3000, vyy400, cb, cc, cd)
new_esEs29(vyy400, vyy410, app(ty_[], cfh)) → new_esEs17(vyy400, vyy410, cfh)
new_esEs7(Left(vyy400), Left(vyy410), ty_Integer, bhc) → new_esEs12(vyy400, vyy410)
new_esEs29(vyy400, vyy410, app(app(ty_@2, chb), chc)) → new_esEs8(vyy400, vyy410, chb, chc)
new_esEs26(vyy401, vyy411, ty_Bool) → new_esEs14(vyy401, vyy411)
new_lt13(vyy3000, vyy400, app(ty_[], fc)) → new_lt14(vyy3000, vyy400, fc)
new_compare15(vyy3000, vyy400, ty_@0) → new_compare26(vyy3000, vyy400)
new_compare212(vyy3000, vyy400, True, ff, fg) → EQ
new_not0 → True
new_esEs24(vyy40, vyy41, ty_Integer) → new_esEs12(vyy40, vyy41)
new_esEs24(vyy40, vyy41, app(ty_[], bef)) → new_esEs17(vyy40, vyy41, bef)
new_ltEs5(Just(vyy3000), Just(vyy400), ty_Integer) → new_ltEs15(vyy3000, vyy400)
new_compare15(vyy3000, vyy400, app(ty_Ratio, bhf)) → new_compare27(vyy3000, vyy400, bhf)
new_esEs7(Left(vyy400), Left(vyy410), app(ty_Ratio, dcf), bhc) → new_esEs9(vyy400, vyy410, dcf)
new_lt13(vyy3000, vyy400, app(ty_Ratio, cec)) → new_lt9(vyy3000, vyy400, cec)
new_compare11(vyy3000, vyy400, False, fh, ga) → GT
new_primCmpInt(Pos(Succ(vyy30000)), Neg(vyy400)) → GT
new_ltEs19(vyy3001, vyy401, ty_Int) → new_ltEs9(vyy3001, vyy401)
new_ltEs13(Right(vyy3000), Right(vyy400), bae, ty_Float) → new_ltEs16(vyy3000, vyy400)
new_esEs18(vyy400, vyy410, app(app(ty_Either, bff), bfg)) → new_esEs7(vyy400, vyy410, bff, bfg)
new_ltEs13(Right(vyy3000), Right(vyy400), bae, app(app(ty_@2, bbe), bbf)) → new_ltEs17(vyy3000, vyy400, bbe, bbf)
new_primMulInt(Pos(vyy30010), Pos(vyy4010)) → Pos(new_primMulNat0(vyy30010, vyy4010))
new_esEs7(Left(vyy400), Left(vyy410), ty_Ordering, bhc) → new_esEs20(vyy400, vyy410)
new_esEs24(vyy40, vyy41, app(app(ty_FiniteMap, bed), bee)) → new_esEs23(vyy40, vyy41, bed, bee)
new_ltEs13(Left(vyy3000), Left(vyy400), ty_Integer, hd) → new_ltEs15(vyy3000, vyy400)
new_primMulInt(Neg(vyy30010), Neg(vyy4010)) → Pos(new_primMulNat0(vyy30010, vyy4010))
new_esEs20(LT, GT) → False
new_esEs20(GT, LT) → False
new_esEs28(vyy401, vyy411, app(ty_Ratio, cfe)) → new_esEs9(vyy401, vyy411, cfe)
new_compare19(Double(vyy3000, vyy3001), Double(vyy400, vyy401)) → new_compare8(new_sr(vyy3000, vyy400), new_sr(vyy3001, vyy401))
new_lt20(vyy3000, vyy400, app(app(app(ty_@3, bdc), bdd), bde)) → new_lt11(vyy3000, vyy400, bdc, bdd, bde)
new_primEqNat0(Succ(vyy4000), Zero) → False
new_primEqNat0(Zero, Succ(vyy4100)) → False
new_ltEs5(Nothing, Nothing, bgc) → True
new_lt20(vyy3000, vyy400, app(app(ty_Either, bdg), bdh)) → new_lt18(vyy3000, vyy400, bdg, bdh)
new_lt12(vyy3001, vyy401, ty_Double) → new_lt16(vyy3001, vyy401)
new_esEs25(vyy402, vyy412, app(ty_Maybe, cac)) → new_esEs6(vyy402, vyy412, cac)
new_lt20(vyy3000, vyy400, ty_@0) → new_lt17(vyy3000, vyy400)
new_lt20(vyy3000, vyy400, app(ty_Maybe, bdf)) → new_lt10(vyy3000, vyy400, bdf)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_lt6(vyy3000, vyy400, fh, ga) → new_esEs15(new_compare5(vyy3000, vyy400, fh, ga))
new_esEs7(Right(vyy400), Right(vyy410), bhb, app(app(ty_@2, dec), ded)) → new_esEs8(vyy400, vyy410, dec, ded)
new_compare210(vyy3000, vyy400, True) → EQ
new_lt12(vyy3001, vyy401, app(app(ty_@2, fa), fb)) → new_lt6(vyy3001, vyy401, fa, fb)
new_sizeFM(Branch(vyy410, vyy411, vyy412, vyy413, vyy414), bed, bee) → vyy412
new_ltEs18(vyy3002, vyy402, app(app(ty_@2, dg), dh)) → new_ltEs17(vyy3002, vyy402, dg, dh)
new_ltEs4(True, False) → False
new_esEs18(vyy400, vyy410, app(app(ty_FiniteMap, bfd), bfe)) → new_esEs23(vyy400, vyy410, bfd, bfe)
new_esEs6(Just(vyy400), Just(vyy410), ty_Double) → new_esEs21(vyy400, vyy410)
new_pePe(True, vyy40, vyy41, vyy57, bge) → True
new_foldFM2(Branch(vyy410, vyy411, vyy412, vyy413, vyy414), bed, bee) → new_foldFM0(vyy410, vyy411, new_foldFM2(vyy414, bed, bee), vyy413, bed, bee)
new_esEs29(vyy400, vyy410, app(app(app(ty_@3, cga), cgb), cgc)) → new_esEs5(vyy400, vyy410, cga, cgb, cgc)
new_ltEs19(vyy3001, vyy401, app(ty_Maybe, bcd)) → new_ltEs5(vyy3001, vyy401, bcd)
new_lt12(vyy3001, vyy401, app(ty_[], ea)) → new_lt14(vyy3001, vyy401, ea)
new_ltEs13(Right(vyy3000), Right(vyy400), bae, ty_Bool) → new_ltEs4(vyy3000, vyy400)
new_esEs26(vyy401, vyy411, app(app(ty_FiniteMap, cbh), cca)) → new_esEs23(vyy401, vyy411, cbh, cca)
new_primCmpInt(Neg(Zero), Neg(Succ(vyy4000))) → new_primCmpNat0(Succ(vyy4000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(vyy4000))) → GT
new_ltEs13(Left(vyy3000), Left(vyy400), app(ty_Maybe, hh), hd) → new_ltEs5(vyy3000, vyy400, hh)
new_compare24(vyy3000, vyy400, False, fh, ga) → new_compare11(vyy3000, vyy400, new_ltEs17(vyy3000, vyy400, fh, ga), fh, ga)
new_ltEs13(Left(vyy3000), Left(vyy400), ty_@0, hd) → new_ltEs11(vyy3000, vyy400)
new_ltEs5(Just(vyy3000), Just(vyy400), ty_Ordering) → new_ltEs8(vyy3000, vyy400)
new_esEs6(Just(vyy400), Just(vyy410), ty_Bool) → new_esEs14(vyy400, vyy410)
new_lt20(vyy3000, vyy400, app(app(ty_@2, bea), beb)) → new_lt6(vyy3000, vyy400, bea, beb)
new_ltEs13(Left(vyy3000), Left(vyy400), app(ty_Ratio, dbc), hd) → new_ltEs12(vyy3000, vyy400, dbc)
new_ltEs19(vyy3001, vyy401, ty_Char) → new_ltEs14(vyy3001, vyy401)
new_esEs6(Just(vyy400), Just(vyy410), app(ty_[], chg)) → new_esEs17(vyy400, vyy410, chg)
new_lt12(vyy3001, vyy401, ty_Integer) → new_lt4(vyy3001, vyy401)
new_lt20(vyy3000, vyy400, ty_Float) → new_lt7(vyy3000, vyy400)
new_lt12(vyy3001, vyy401, app(app(app(ty_@3, ec), ed), ee)) → new_lt11(vyy3001, vyy401, ec, ed, ee)
new_ltEs13(Left(vyy3000), Left(vyy400), app(app(ty_Either, baa), bab), hd) → new_ltEs13(vyy3000, vyy400, baa, bab)
new_esEs18(vyy400, vyy410, ty_Integer) → new_esEs12(vyy400, vyy410)
new_compare15(vyy3000, vyy400, ty_Ordering) → new_compare17(vyy3000, vyy400)
new_lt20(vyy3000, vyy400, ty_Double) → new_lt16(vyy3000, vyy400)
new_ltEs18(vyy3002, vyy402, app(ty_[], cg)) → new_ltEs6(vyy3002, vyy402, cg)
new_esEs19(Char(vyy400), Char(vyy410)) → new_primEqNat0(vyy400, vyy410)
new_ltEs13(Right(vyy3000), Right(vyy400), bae, app(app(ty_Either, bbc), bbd)) → new_ltEs13(vyy3000, vyy400, bbc, bbd)
new_esEs29(vyy400, vyy410, app(ty_Ratio, cha)) → new_esEs9(vyy400, vyy410, cha)
new_esEs18(vyy400, vyy410, app(ty_Maybe, bfc)) → new_esEs6(vyy400, vyy410, bfc)
new_ltEs13(Left(vyy3000), Left(vyy400), ty_Ordering, hd) → new_ltEs8(vyy3000, vyy400)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_ltEs18(vyy3002, vyy402, ty_Double) → new_ltEs10(vyy3002, vyy402)
new_esEs25(vyy402, vyy412, app(app(ty_FiniteMap, cad), cae)) → new_esEs23(vyy402, vyy412, cad, cae)
new_asAs(False, vyy66) → False
new_ltEs13(Right(vyy3000), Right(vyy400), bae, app(ty_[], baf)) → new_ltEs6(vyy3000, vyy400, baf)
new_esEs25(vyy402, vyy412, app(ty_Ratio, cah)) → new_esEs9(vyy402, vyy412, cah)
new_esEs29(vyy400, vyy410, ty_@0) → new_esEs22(vyy400, vyy410)
new_primMulInt(Pos(vyy30010), Neg(vyy4010)) → Neg(new_primMulNat0(vyy30010, vyy4010))
new_primMulInt(Neg(vyy30010), Pos(vyy4010)) → Neg(new_primMulNat0(vyy30010, vyy4010))
new_esEs7(Left(vyy400), Left(vyy410), app(app(ty_@2, dcg), dch), bhc) → new_esEs8(vyy400, vyy410, dcg, dch)
new_ltEs13(Left(vyy3000), Right(vyy400), bae, hd) → True
new_primMulNat0(Zero, Succ(vyy40100)) → Zero
new_primMulNat0(Succ(vyy300100), Zero) → Zero
new_esEs6(Just(vyy400), Just(vyy410), app(ty_Ratio, dah)) → new_esEs9(vyy400, vyy410, dah)
new_esEs6(Just(vyy400), Just(vyy410), app(ty_Maybe, dac)) → new_esEs6(vyy400, vyy410, dac)
new_lt20(vyy3000, vyy400, app(ty_[], bda)) → new_lt14(vyy3000, vyy400, bda)
new_lt10(vyy3000, vyy400, fd) → new_esEs15(new_compare18(vyy3000, vyy400, fd))
new_esEs28(vyy401, vyy411, ty_Bool) → new_esEs14(vyy401, vyy411)
new_compare12(vyy3000, vyy400, True) → LT
new_esEs18(vyy400, vyy410, ty_Double) → new_esEs21(vyy400, vyy410)
new_ltEs5(Just(vyy3000), Just(vyy400), app(ty_Maybe, gf)) → new_ltEs5(vyy3000, vyy400, gf)
new_esEs24(vyy40, vyy41, ty_Ordering) → new_esEs20(vyy40, vyy41)
new_not(EQ) → new_not0
new_compare110(vyy3000, vyy400, True, cb, cc, cd) → LT
new_esEs26(vyy401, vyy411, app(ty_Ratio, ccd)) → new_esEs9(vyy401, vyy411, ccd)
new_lt13(vyy3000, vyy400, app(app(ty_@2, fh), ga)) → new_lt6(vyy3000, vyy400, fh, ga)
new_esEs25(vyy402, vyy412, app(ty_[], bhg)) → new_esEs17(vyy402, vyy412, bhg)
new_ltEs4(False, False) → True
new_esEs14(True, True) → True
new_esEs27(vyy400, vyy410, ty_Bool) → new_esEs14(vyy400, vyy410)
new_ltEs13(Right(vyy3000), Left(vyy400), bae, hd) → False
new_esEs28(vyy401, vyy411, ty_Char) → new_esEs19(vyy401, vyy411)
new_ltEs8(LT, GT) → True
new_esEs6(Just(vyy400), Just(vyy410), ty_Char) → new_esEs19(vyy400, vyy410)
new_esEs28(vyy401, vyy411, app(ty_[], ced)) → new_esEs17(vyy401, vyy411, ced)
new_ltEs5(Just(vyy3000), Just(vyy400), app(app(ty_@2, ha), hb)) → new_ltEs17(vyy3000, vyy400, ha, hb)
new_compare26(@0, @0) → EQ
new_esEs7(Right(vyy400), Right(vyy410), bhb, ty_Integer) → new_esEs12(vyy400, vyy410)
new_esEs11(vyy400, vyy410, ty_Integer) → new_esEs12(vyy400, vyy410)
new_esEs9(:%(vyy400, vyy401), :%(vyy410, vyy411), bec) → new_asAs(new_esEs11(vyy400, vyy410, bec), new_esEs10(vyy401, vyy411, bec))
new_ltEs5(Just(vyy3000), Just(vyy400), app(app(app(ty_@3, gc), gd), ge)) → new_ltEs7(vyy3000, vyy400, gc, gd, ge)
new_lt13(vyy3000, vyy400, ty_Double) → new_lt16(vyy3000, vyy400)
new_not(LT) → new_not0
new_ltEs18(vyy3002, vyy402, ty_Float) → new_ltEs16(vyy3002, vyy402)
new_compare7(Integer(vyy3000), Integer(vyy400)) → new_primCmpInt(vyy3000, vyy400)
new_esEs25(vyy402, vyy412, ty_@0) → new_esEs22(vyy402, vyy412)
new_esEs25(vyy402, vyy412, app(app(app(ty_@3, bhh), caa), cab)) → new_esEs5(vyy402, vyy412, bhh, caa, cab)
new_ltEs19(vyy3001, vyy401, app(ty_[], bbh)) → new_ltEs6(vyy3001, vyy401, bbh)
new_esEs6(Just(vyy400), Just(vyy410), ty_Float) → new_esEs16(vyy400, vyy410)
new_ltEs5(Just(vyy3000), Just(vyy400), ty_Float) → new_ltEs16(vyy3000, vyy400)
new_lt17(vyy3000, vyy400) → new_esEs15(new_compare26(vyy3000, vyy400))
new_esEs29(vyy400, vyy410, app(app(ty_Either, cgg), cgh)) → new_esEs7(vyy400, vyy410, cgg, cgh)
new_esEs14(False, False) → True
new_esEs10(vyy401, vyy411, ty_Int) → new_esEs13(vyy401, vyy411)
new_lt14(vyy3000, vyy400, fc) → new_esEs15(new_compare(vyy3000, vyy400, fc))
new_compare211(vyy3000, vyy400, False, fd) → new_compare10(vyy3000, vyy400, new_ltEs5(vyy3000, vyy400, fd), fd)
new_esEs18(vyy400, vyy410, ty_Bool) → new_esEs14(vyy400, vyy410)
new_ltEs8(LT, LT) → True
new_esEs28(vyy401, vyy411, app(app(ty_@2, cff), cfg)) → new_esEs8(vyy401, vyy411, cff, cfg)
new_primPlusNat1(Zero, Zero) → Zero
new_esEs28(vyy401, vyy411, ty_@0) → new_esEs22(vyy401, vyy411)
new_asAs(True, vyy66) → vyy66
new_compare17(vyy3000, vyy400) → new_compare210(vyy3000, vyy400, new_esEs20(vyy3000, vyy400))
new_esEs24(vyy40, vyy41, ty_Float) → new_esEs16(vyy40, vyy41)
new_primMulNat0(Succ(vyy300100), Succ(vyy40100)) → new_primPlusNat0(new_primMulNat0(vyy300100, Succ(vyy40100)), vyy40100)
new_esEs27(vyy400, vyy410, ty_Float) → new_esEs16(vyy400, vyy410)
new_esEs26(vyy401, vyy411, app(app(app(ty_@3, cbd), cbe), cbf)) → new_esEs5(vyy401, vyy411, cbd, cbe, cbf)
new_lt12(vyy3001, vyy401, app(app(ty_Either, eg), eh)) → new_lt18(vyy3001, vyy401, eg, eh)
new_esEs6(Just(vyy400), Just(vyy410), app(app(ty_Either, daf), dag)) → new_esEs7(vyy400, vyy410, daf, dag)
new_lt13(vyy3000, vyy400, ty_Bool) → new_lt8(vyy3000, vyy400)
new_esEs17([], [], bef) → True
new_esEs17(:(vyy400, vyy401), [], bef) → False
new_esEs17([], :(vyy410, vyy411), bef) → False
new_esEs16(Float(vyy400, vyy401), Float(vyy410, vyy411)) → new_esEs13(new_sr(vyy400, vyy410), new_sr(vyy401, vyy411))
new_fmToList(vyy41, bed, bee) → new_foldFM2(vyy41, bed, bee)
new_compare16(vyy3000, vyy400, cb, cc, cd) → new_compare29(vyy3000, vyy400, new_esEs5(vyy3000, vyy400, cb, cc, cd), cb, cc, cd)
new_esEs28(vyy401, vyy411, ty_Ordering) → new_esEs20(vyy401, vyy411)
new_ltEs18(vyy3002, vyy402, ty_Integer) → new_ltEs15(vyy3002, vyy402)
new_esEs24(vyy40, vyy41, app(app(ty_@2, bhd), bhe)) → new_esEs8(vyy40, vyy41, bhd, bhe)
new_esEs7(Left(vyy400), Left(vyy410), ty_Double, bhc) → new_esEs21(vyy400, vyy410)
new_ltEs18(vyy3002, vyy402, ty_Ordering) → new_ltEs8(vyy3002, vyy402)
new_esEs24(vyy40, vyy41, app(ty_Maybe, bha)) → new_esEs6(vyy40, vyy41, bha)
new_esEs7(Left(vyy400), Left(vyy410), ty_Char, bhc) → new_esEs19(vyy400, vyy410)
new_esEs29(vyy400, vyy410, ty_Bool) → new_esEs14(vyy400, vyy410)
new_compare110(vyy3000, vyy400, False, cb, cc, cd) → GT
new_esEs7(Right(vyy400), Right(vyy410), bhb, ty_Double) → new_esEs21(vyy400, vyy410)
new_lt13(vyy3000, vyy400, app(ty_Maybe, fd)) → new_lt10(vyy3000, vyy400, fd)
new_esEs25(vyy402, vyy412, app(app(ty_Either, caf), cag)) → new_esEs7(vyy402, vyy412, caf, cag)
new_esEs7(Left(vyy400), Left(vyy410), ty_Float, bhc) → new_esEs16(vyy400, vyy410)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs24(vyy40, vyy41, app(ty_Ratio, bec)) → new_esEs9(vyy40, vyy41, bec)
new_primCompAux0(vyy71, EQ) → vyy71
new_ltEs13(Left(vyy3000), Left(vyy400), ty_Char, hd) → new_ltEs14(vyy3000, vyy400)
new_compare212(vyy3000, vyy400, False, ff, fg) → new_compare13(vyy3000, vyy400, new_ltEs13(vyy3000, vyy400, ff, fg), ff, fg)
new_compare15(vyy3000, vyy400, app(ty_Maybe, be)) → new_compare18(vyy3000, vyy400, be)
new_lt8(vyy3000, vyy400) → new_esEs15(new_compare6(vyy3000, vyy400))
new_esEs22(@0, @0) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_esEs18(vyy400, vyy410, ty_Float) → new_esEs16(vyy400, vyy410)
new_ltEs13(Right(vyy3000), Right(vyy400), bae, app(ty_Maybe, bbb)) → new_ltEs5(vyy3000, vyy400, bbb)
new_primCmpInt(Neg(Succ(vyy30000)), Pos(vyy400)) → LT
new_lt12(vyy3001, vyy401, ty_Int) → new_lt5(vyy3001, vyy401)
The set Q consists of the following terms:
new_ltEs18(x0, x1, ty_Char)
new_esEs18(x0, x1, ty_Char)
new_ltEs13(Right(x0), Right(x1), x2, ty_Double)
new_esEs7(Left(x0), Left(x1), ty_Int, x2)
new_ltEs13(Right(x0), Right(x1), x2, ty_Bool)
new_lt20(x0, x1, ty_Integer)
new_compare15(x0, x1, ty_Int)
new_compare6(x0, x1)
new_compare25(x0, x1, False)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs18(x0, x1, ty_Ordering)
new_esEs7(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_ltEs5(Just(x0), Just(x1), ty_@0)
new_lt16(x0, x1)
new_primEqNat0(Succ(x0), Succ(x1))
new_ltEs13(Left(x0), Left(x1), ty_Int, x2)
new_esEs7(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_lt12(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, ty_Ordering)
new_ltEs13(Left(x0), Left(x1), ty_Double, x2)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_ltEs5(Nothing, Just(x0), x1)
new_ltEs8(EQ, EQ)
new_esEs13(x0, x1)
new_ltEs13(Right(x0), Right(x1), x2, ty_@0)
new_esEs27(x0, x1, ty_Char)
new_compare15(x0, x1, ty_Double)
new_compare15(x0, x1, app(ty_Ratio, x2))
new_ltEs13(Left(x0), Left(x1), ty_@0, x2)
new_ltEs5(Just(x0), Just(x1), ty_Ordering)
new_compare24(x0, x1, True, x2, x3)
new_esEs27(x0, x1, ty_Float)
new_esEs7(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_primMulNat0(Zero, Succ(x0))
new_esEs29(x0, x1, ty_Ordering)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpNat0(Succ(x0), Zero)
new_pePe(False, x0, x1, x2, x3)
new_esEs7(Right(x0), Right(x1), x2, ty_Integer)
new_compare10(x0, x1, False, x2)
new_esEs28(x0, x1, ty_Integer)
new_ltEs13(Left(x0), Left(x1), ty_Float, x2)
new_lt18(x0, x1, x2, x3)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs13(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_ltEs5(Just(x0), Just(x1), ty_Double)
new_compare19(Double(x0, x1), Double(x2, x3))
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_compare8(x0, x1)
new_lt19(x0, x1)
new_ltEs5(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_compare15(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_compare110(x0, x1, False, x2, x3, x4)
new_ltEs5(Just(x0), Just(x1), ty_Int)
new_lt12(x0, x1, app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, ty_Double)
new_ltEs14(x0, x1)
new_asAs(False, x0)
new_ltEs13(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs13(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_ltEs5(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs24(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs7(Right(x0), Right(x1), x2, ty_Float)
new_lt12(x0, x1, ty_Double)
new_ltEs5(Just(x0), Just(x1), app(ty_[], x2))
new_compare24(x0, x1, False, x2, x3)
new_sr(x0, x1)
new_ltEs5(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, x2, x3)
new_ltEs18(x0, x1, ty_Ordering)
new_fmToList(x0, x1, x2)
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_ltEs13(Right(x0), Right(x1), x2, ty_Char)
new_compare10(x0, x1, True, x2)
new_compare([], :(x0, x1), x2)
new_lt20(x0, x1, ty_Bool)
new_esEs10(x0, x1, ty_Integer)
new_esEs28(x0, x1, ty_Char)
new_ltEs19(x0, x1, ty_Ordering)
new_ltEs13(Left(x0), Left(x1), ty_Bool, x2)
new_esEs14(True, True)
new_ltEs5(Just(x0), Just(x1), ty_Char)
new_esEs22(@0, @0)
new_esEs28(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, ty_@0)
new_compare211(x0, x1, True, x2)
new_esEs29(x0, x1, ty_Char)
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_compare15(x0, x1, ty_Bool)
new_esEs7(Left(x0), Left(x1), ty_Float, x2)
new_lt20(x0, x1, ty_Float)
new_esEs7(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_primEqNat0(Zero, Zero)
new_primCmpNat0(Succ(x0), Succ(x1))
new_compare13(x0, x1, True, x2, x3)
new_esEs15(LT)
new_ltEs19(x0, x1, app(ty_[], x2))
new_esEs29(x0, x1, ty_Int)
new_ltEs4(True, True)
new_ltEs13(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_esEs24(x0, x1, ty_Bool)
new_lt12(x0, x1, ty_Float)
new_esEs27(x0, x1, ty_@0)
new_esEs26(x0, x1, ty_Integer)
new_pePe(True, x0, x1, x2, x3)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs19(Char(x0), Char(x1))
new_primPlusNat1(Zero, Succ(x0))
new_primMulNat0(Zero, Zero)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs18(x0, x1, ty_@0)
new_esEs24(x0, x1, ty_@0)
new_compare5(x0, x1, x2, x3)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_esEs7(Left(x0), Left(x1), ty_@0, x2)
new_lt12(x0, x1, ty_@0)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_compare28(x0, x1, x2, x3)
new_esEs28(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_esEs25(x0, x1, ty_Bool)
new_compare12(x0, x1, False)
new_esEs10(x0, x1, ty_Int)
new_lt20(x0, x1, ty_Int)
new_foldFM2(EmptyFM, x0, x1)
new_esEs25(x0, x1, ty_Integer)
new_ltEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs13(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_ltEs13(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_ltEs18(x0, x1, ty_Integer)
new_esEs16(Float(x0, x1), Float(x2, x3))
new_primPlusNat1(Succ(x0), Zero)
new_ltEs18(x0, x1, ty_Int)
new_ltEs13(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs24(x0, x1, ty_Integer)
new_compare15(x0, x1, app(app(ty_@2, x2), x3))
new_primMulNat0(Succ(x0), Succ(x1))
new_ltEs18(x0, x1, app(app(ty_Either, x2), x3))
new_esEs28(x0, x1, ty_Bool)
new_ltEs16(x0, x1)
new_ltEs18(x0, x1, app(ty_[], x2))
new_esEs6(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs20(EQ, GT)
new_esEs20(GT, EQ)
new_esEs7(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs18(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs4(False, False)
new_esEs18(x0, x1, app(ty_[], x2))
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare(:(x0, x1), :(x2, x3), x4)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs24(x0, x1, ty_Ordering)
new_esEs7(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs18(x0, x1, ty_Double)
new_ltEs13(Right(x0), Right(x1), x2, ty_Int)
new_esEs7(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs7(Left(x0), Left(x1), ty_Integer, x2)
new_esEs26(x0, x1, ty_Char)
new_ltEs13(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs25(x0, x1, app(ty_[], x2))
new_esEs27(x0, x1, ty_Int)
new_ltEs19(x0, x1, ty_Integer)
new_esEs20(LT, EQ)
new_esEs20(EQ, LT)
new_compare14(Char(x0), Char(x1))
new_esEs27(x0, x1, ty_Double)
new_ltEs19(x0, x1, ty_Int)
new_compare([], [], x0)
new_ltEs5(Just(x0), Just(x1), app(ty_Maybe, x2))
new_ltEs19(x0, x1, ty_Double)
new_primPlusNat0(Succ(x0), x1)
new_esEs7(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_ltEs5(Just(x0), Just(x1), ty_Integer)
new_lt12(x0, x1, ty_Char)
new_primPlusNat1(Zero, Zero)
new_not0
new_esEs29(x0, x1, ty_@0)
new_compare15(x0, x1, ty_@0)
new_compare18(x0, x1, x2)
new_primMulNat0(Succ(x0), Zero)
new_compare9(Float(x0, x1), Float(x2, x3))
new_esEs18(x0, x1, ty_Bool)
new_ltEs13(Left(x0), Left(x1), ty_Char, x2)
new_esEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Just(x0), Just(x1), ty_@0)
new_esEs17(:(x0, x1), :(x2, x3), x4)
new_ltEs5(Nothing, Nothing, x0)
new_esEs24(x0, x1, app(ty_[], x2))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_esEs26(x0, x1, ty_@0)
new_esEs27(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs17(:(x0, x1), [], x2)
new_ltEs18(x0, x1, ty_Bool)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_lt12(x0, x1, app(ty_[], x2))
new_esEs7(Left(x0), Left(x1), ty_Char, x2)
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs18(x0, x1, ty_Double)
new_ltEs18(x0, x1, app(ty_Ratio, x2))
new_esEs26(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs26(x0, x1, ty_Float)
new_esEs18(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs17([], [], x0)
new_esEs18(x0, x1, app(app(ty_@2, x2), x3))
new_compare13(x0, x1, False, x2, x3)
new_lt5(x0, x1)
new_sizeFM(EmptyFM, x0, x1)
new_ltEs18(x0, x1, ty_Float)
new_ltEs5(Just(x0), Nothing, x1)
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_compare110(x0, x1, True, x2, x3, x4)
new_lt9(x0, x1, x2)
new_not(GT)
new_compare11(x0, x1, False, x2, x3)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare111(x0, x1, True)
new_ltEs10(x0, x1)
new_esEs7(Right(x0), Right(x1), x2, ty_Ordering)
new_compare210(x0, x1, False)
new_ltEs13(Right(x0), Right(x1), x2, ty_Integer)
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_esEs29(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_lt12(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs11(x0, x1, ty_Integer)
new_lt4(x0, x1)
new_esEs26(x0, x1, app(ty_[], x2))
new_lt12(x0, x1, ty_Int)
new_esEs5(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_ltEs13(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs6(Just(x0), Just(x1), ty_Float)
new_lt7(x0, x1)
new_lt12(x0, x1, ty_Integer)
new_ltEs13(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_ltEs13(Right(x0), Right(x1), x2, ty_Float)
new_ltEs8(EQ, LT)
new_ltEs8(LT, EQ)
new_lt20(x0, x1, app(ty_[], x2))
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt6(x0, x1, x2, x3)
new_ltEs18(x0, x1, ty_@0)
new_esEs26(x0, x1, ty_Int)
new_esEs18(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs29(x0, x1, ty_Float)
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_esEs6(Just(x0), Just(x1), app(ty_[], x2))
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs6(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs7(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_compare25(x0, x1, True)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs19(x0, x1, ty_Bool)
new_primEqInt(Neg(Zero), Neg(Zero))
new_compare12(x0, x1, True)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs18(x0, x1, app(ty_Maybe, x2))
new_esEs7(Left(x0), Left(x1), ty_Double, x2)
new_esEs28(x0, x1, ty_Ordering)
new_primCompAux0(x0, EQ)
new_esEs20(LT, LT)
new_esEs26(x0, x1, ty_Bool)
new_compare15(x0, x1, ty_Ordering)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_compare27(:%(x0, x1), :%(x2, x3), ty_Int)
new_ltEs13(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_lt13(x0, x1, app(ty_[], x2))
new_esEs14(False, True)
new_esEs14(True, False)
new_lt11(x0, x1, x2, x3, x4)
new_lt13(x0, x1, ty_Double)
new_esEs24(x0, x1, ty_Int)
new_esEs28(x0, x1, ty_Double)
new_ltEs11(x0, x1)
new_primCompAux0(x0, LT)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_lt15(x0, x1)
new_lt17(x0, x1)
new_esEs20(GT, LT)
new_esEs20(LT, GT)
new_lt12(x0, x1, ty_Bool)
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_esEs7(Right(x0), Right(x1), x2, ty_@0)
new_esEs18(x0, x1, ty_Integer)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs25(x0, x1, ty_Int)
new_esEs6(Just(x0), Just(x1), ty_Char)
new_lt8(x0, x1)
new_primEqNat0(Succ(x0), Zero)
new_esEs27(x0, x1, app(ty_[], x2))
new_esEs6(Just(x0), Just(x1), app(ty_Ratio, x2))
new_lt13(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primEqNat0(Zero, Succ(x0))
new_ltEs18(x0, x1, app(ty_Maybe, x2))
new_ltEs12(x0, x1, x2)
new_esEs7(Right(x0), Right(x1), x2, ty_Char)
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_FiniteMap, x3), x4))
new_primPlusNat0(Zero, x0)
new_lt13(x0, x1, ty_Float)
new_ltEs8(LT, LT)
new_esEs20(GT, GT)
new_esEs7(Left(x0), Left(x1), ty_Bool, x2)
new_esEs7(Right(x0), Right(x1), x2, ty_Double)
new_primCmpNat0(Zero, Zero)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_lt14(x0, x1, x2)
new_esEs6(Just(x0), Just(x1), ty_Integer)
new_lt20(x0, x1, ty_Ordering)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_ltEs4(False, True)
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_ltEs4(True, False)
new_compare17(x0, x1)
new_esEs15(GT)
new_ltEs8(GT, GT)
new_esEs25(x0, x1, ty_Float)
new_ltEs5(Just(x0), Just(x1), ty_Float)
new_primCompAux0(x0, GT)
new_esEs28(x0, x1, ty_Int)
new_compare15(x0, x1, app(ty_Maybe, x2))
new_compare212(x0, x1, False, x2, x3)
new_esEs29(x0, x1, ty_Integer)
new_compare15(x0, x1, ty_Integer)
new_esEs28(x0, x1, ty_@0)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_compare29(x0, x1, True, x2, x3, x4)
new_esEs6(Just(x0), Just(x1), ty_Ordering)
new_lt13(x0, x1, ty_Ordering)
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_esEs27(x0, x1, ty_Ordering)
new_compare16(x0, x1, x2, x3, x4)
new_ltEs19(x0, x1, ty_@0)
new_esEs24(x0, x1, ty_Char)
new_esEs6(Nothing, Just(x0), x1)
new_esEs29(x0, x1, ty_Bool)
new_esEs18(x0, x1, ty_Int)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs24(x0, x1, ty_Double)
new_ltEs13(Right(x0), Left(x1), x2, x3)
new_esEs12(Integer(x0), Integer(x1))
new_ltEs13(Left(x0), Right(x1), x2, x3)
new_compare210(x0, x1, True)
new_lt12(x0, x1, app(ty_Ratio, x2))
new_esEs9(:%(x0, x1), :%(x2, x3), x4)
new_ltEs8(LT, GT)
new_ltEs8(GT, LT)
new_esEs25(x0, x1, ty_Double)
new_esEs6(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_lt13(x0, x1, app(ty_Maybe, x2))
new_esEs27(x0, x1, ty_Integer)
new_esEs6(Nothing, Nothing, x0)
new_esEs18(x0, x1, app(app(ty_Either, x2), x3))
new_esEs8(@2(x0, x1), @2(x2, x3), x4, x5)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_ltEs13(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_esEs6(Just(x0), Nothing, x1)
new_ltEs6(x0, x1, x2)
new_lt13(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs13(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs17(@2(x0, x1), @2(x2, x3), x4, x5)
new_compare29(x0, x1, False, x2, x3, x4)
new_esEs18(x0, x1, ty_Float)
new_not(EQ)
new_ltEs7(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_lt13(x0, x1, ty_@0)
new_esEs6(Just(x0), Just(x1), app(app(ty_FiniteMap, x2), x3))
new_esEs6(Just(x0), Just(x1), ty_Double)
new_esEs29(x0, x1, ty_Double)
new_lt12(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs19(x0, x1, ty_Char)
new_esEs7(Right(x0), Right(x1), x2, ty_Bool)
new_lt12(x0, x1, ty_Ordering)
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_compare11(x0, x1, True, x2, x3)
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_lt13(x0, x1, ty_Integer)
new_compare211(x0, x1, False, x2)
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_lt13(x0, x1, ty_Char)
new_esEs29(x0, x1, app(ty_[], x2))
new_esEs20(EQ, EQ)
new_ltEs13(Left(x0), Left(x1), ty_Integer, x2)
new_esEs11(x0, x1, ty_Int)
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs15(EQ)
new_ltEs15(x0, x1)
new_compare7(Integer(x0), Integer(x1))
new_ltEs5(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs13(Left(x0), Left(x1), ty_Ordering, x2)
new_compare27(:%(x0, x1), :%(x2, x3), ty_Integer)
new_esEs25(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs7(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_compare111(x0, x1, False)
new_esEs25(x0, x1, ty_Ordering)
new_ltEs8(GT, EQ)
new_ltEs8(EQ, GT)
new_esEs21(Double(x0, x1), Double(x2, x3))
new_lt13(x0, x1, app(app(ty_@2, x2), x3))
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_esEs17([], :(x0, x1), x2)
new_ltEs5(Just(x0), Just(x1), ty_Bool)
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sr0(Integer(x0), Integer(x1))
new_esEs25(x0, x1, ty_@0)
new_esEs7(Left(x0), Left(x1), app(app(ty_FiniteMap, x2), x3), x4)
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
new_compare26(@0, @0)
new_ltEs9(x0, x1)
new_ltEs19(x0, x1, ty_Float)
new_esEs28(x0, x1, ty_Float)
new_esEs14(False, False)
new_lt13(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Pos(Zero), Pos(Zero))
new_esEs6(Just(x0), Just(x1), ty_Bool)
new_compare212(x0, x1, True, x2, x3)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs7(Left(x0), Left(x1), ty_Ordering, x2)
new_compare15(x0, x1, app(ty_[], x2))
new_lt13(x0, x1, ty_Bool)
new_primCompAux1(x0, x1, x2, x3)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_lt20(x0, x1, ty_Char)
new_esEs6(Just(x0), Just(x1), app(ty_Maybe, x2))
new_asAs(True, x0)
new_esEs24(x0, x1, ty_Float)
new_compare15(x0, x1, ty_Char)
new_esEs7(Right(x0), Left(x1), x2, x3)
new_esEs7(Left(x0), Right(x1), x2, x3)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs6(Just(x0), Just(x1), ty_Int)
new_compare15(x0, x1, ty_Float)
new_lt20(x0, x1, ty_Double)
new_not(LT)
new_esEs7(Right(x0), Right(x1), x2, ty_Int)
new_esEs25(x0, x1, ty_Char)
new_lt13(x0, x1, ty_Int)
new_esEs27(x0, x1, ty_Bool)
new_compare15(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_compare(:(x0, x1), [], x2)
new_lt10(x0, x1, x2)
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_compare0(:(vyy3000, vyy3001), :(vyy400, vyy401), h) → new_compare0(vyy3001, vyy401, h)
The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3
- new_compare0(:(vyy3000, vyy3001), :(vyy400, vyy401), h) → new_primCompAux(vyy3000, vyy400, new_compare(vyy3001, vyy401, h), h)
The graph contains the following edges 1 > 1, 2 > 2, 3 >= 4
- new_primCompAux(vyy3000, vyy400, vyy67, app(ty_[], ba)) → new_compare0(vyy3000, vyy400, ba)
The graph contains the following edges 1 >= 1, 2 >= 2, 4 > 3
- new_compare1(vyy3000, vyy400, cb, cc, cd) → new_compare20(vyy3000, vyy400, new_esEs5(vyy3000, vyy400, cb, cc, cd), cb, cc, cd)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 4, 4 >= 5, 5 >= 6
- new_ltEs(:(vyy3000, vyy3001), :(vyy400, vyy401), h) → new_primCompAux(vyy3000, vyy400, new_compare(vyy3001, vyy401, h), h)
The graph contains the following edges 1 > 1, 2 > 2, 3 >= 4
- new_lt2(vyy3000, vyy400, ff, fg) → new_compare22(vyy3000, vyy400, new_esEs7(vyy3000, vyy400, ff, fg), ff, fg)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 4, 4 >= 5
- new_lt(vyy3000, vyy400, fc) → new_compare0(vyy3000, vyy400, fc)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3
- new_compare20(vyy3000, vyy400, False, cb, cc, cd) → new_ltEs0(vyy3000, vyy400, cb, cc, cd)
The graph contains the following edges 1 >= 1, 2 >= 2, 4 >= 3, 5 >= 4, 6 >= 5
- new_lt3(vyy3000, vyy400, fh, ga) → new_compare23(vyy3000, vyy400, new_esEs8(vyy3000, vyy400, fh, ga), fh, ga)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 4, 4 >= 5
- new_compare23(vyy3000, vyy400, False, fh, ga) → new_ltEs3(vyy3000, vyy400, fh, ga)
The graph contains the following edges 1 >= 1, 2 >= 2, 4 >= 3, 5 >= 4
- new_ltEs1(Just(vyy3000), Just(vyy400), app(app(app(ty_@3, gc), gd), ge)) → new_ltEs0(vyy3000, vyy400, gc, gd, ge)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
- new_ltEs1(Just(vyy3000), Just(vyy400), app(app(ty_@2, ha), hb)) → new_ltEs3(vyy3000, vyy400, ha, hb)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
- new_ltEs1(Just(vyy3000), Just(vyy400), app(app(ty_Either, gg), gh)) → new_ltEs2(vyy3000, vyy400, gg, gh)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
- new_ltEs1(Just(vyy3000), Just(vyy400), app(ty_Maybe, gf)) → new_ltEs1(vyy3000, vyy400, gf)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
- new_ltEs1(Just(vyy3000), Just(vyy400), app(ty_[], gb)) → new_ltEs(vyy3000, vyy400, gb)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
- new_ltEs(:(vyy3000, vyy3001), :(vyy400, vyy401), h) → new_compare0(vyy3001, vyy401, h)
The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3
- new_ltEs0(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), app(ty_[], fc), cf, eb) → new_compare0(vyy3000, vyy400, fc)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
- new_ltEs0(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), ce, cf, app(app(app(ty_@3, da), db), dc)) → new_ltEs0(vyy3002, vyy402, da, db, dc)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4, 5 > 5
- new_ltEs3(@2(vyy3000, vyy3001), @2(vyy400, vyy401), bbg, app(app(app(ty_@3, bca), bcb), bcc)) → new_ltEs0(vyy3001, vyy401, bca, bcb, bcc)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5
- new_ltEs0(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), ce, cf, app(app(ty_@2, dg), dh)) → new_ltEs3(vyy3002, vyy402, dg, dh)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4
- new_ltEs3(@2(vyy3000, vyy3001), @2(vyy400, vyy401), bbg, app(app(ty_@2, bcg), bch)) → new_ltEs3(vyy3001, vyy401, bcg, bch)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
- new_ltEs0(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), ce, cf, app(app(ty_Either, de), df)) → new_ltEs2(vyy3002, vyy402, de, df)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4
- new_ltEs0(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), ce, cf, app(ty_Maybe, dd)) → new_ltEs1(vyy3002, vyy402, dd)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3
- new_primCompAux(vyy3000, vyy400, vyy67, app(app(app(ty_@3, bb), bc), bd)) → new_compare1(vyy3000, vyy400, bb, bc, bd)
The graph contains the following edges 1 >= 1, 2 >= 2, 4 > 3, 4 > 4, 4 > 5
- new_ltEs3(@2(vyy3000, vyy3001), @2(vyy400, vyy401), bbg, app(app(ty_Either, bce), bcf)) → new_ltEs2(vyy3001, vyy401, bce, bcf)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
- new_compare22(vyy3000, vyy400, False, ff, fg) → new_ltEs2(vyy3000, vyy400, ff, fg)
The graph contains the following edges 1 >= 1, 2 >= 2, 4 >= 3, 5 >= 4
- new_ltEs3(@2(vyy3000, vyy3001), @2(vyy400, vyy401), bbg, app(ty_Maybe, bcd)) → new_ltEs1(vyy3001, vyy401, bcd)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
- new_compare21(vyy3000, vyy400, False, fd) → new_ltEs1(vyy3000, vyy400, fd)
The graph contains the following edges 1 >= 1, 2 >= 2, 4 >= 3
- new_ltEs0(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), ce, app(app(ty_Either, eg), eh), eb) → new_lt2(vyy3001, vyy401, eg, eh)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
- new_ltEs3(@2(vyy3000, vyy3001), @2(vyy400, vyy401), app(app(ty_Either, bdg), bdh), bdb) → new_lt2(vyy3000, vyy400, bdg, bdh)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
- new_ltEs0(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), ce, cf, app(ty_[], cg)) → new_ltEs(vyy3002, vyy402, cg)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3
- new_ltEs3(@2(vyy3000, vyy3001), @2(vyy400, vyy401), bbg, app(ty_[], bbh)) → new_ltEs(vyy3001, vyy401, bbh)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
- new_lt1(vyy3000, vyy400, fd) → new_compare21(vyy3000, vyy400, new_esEs6(vyy3000, vyy400, fd), fd)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 4
- new_lt0(vyy3000, vyy400, cb, cc, cd) → new_compare20(vyy3000, vyy400, new_esEs5(vyy3000, vyy400, cb, cc, cd), cb, cc, cd)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 4, 4 >= 5, 5 >= 6
- new_compare2(vyy3000, vyy400, fd) → new_compare21(vyy3000, vyy400, new_esEs6(vyy3000, vyy400, fd), fd)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 4
- new_ltEs0(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), ce, app(app(app(ty_@3, ec), ed), ee), eb) → new_lt0(vyy3001, vyy401, ec, ed, ee)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5
- new_ltEs3(@2(vyy3000, vyy3001), @2(vyy400, vyy401), app(app(app(ty_@3, bdc), bdd), bde), bdb) → new_lt0(vyy3000, vyy400, bdc, bdd, bde)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
- new_primCompAux(vyy3000, vyy400, vyy67, app(ty_Maybe, be)) → new_compare2(vyy3000, vyy400, be)
The graph contains the following edges 1 >= 1, 2 >= 2, 4 > 3
- new_ltEs0(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), ce, app(ty_Maybe, ef), eb) → new_lt1(vyy3001, vyy401, ef)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
- new_ltEs3(@2(vyy3000, vyy3001), @2(vyy400, vyy401), app(ty_Maybe, bdf), bdb) → new_lt1(vyy3000, vyy400, bdf)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
- new_primCompAux(vyy3000, vyy400, vyy67, app(app(ty_Either, bf), bg)) → new_compare3(vyy3000, vyy400, bf, bg)
The graph contains the following edges 1 >= 1, 2 >= 2, 4 > 3, 4 > 4
- new_primCompAux(vyy3000, vyy400, vyy67, app(app(ty_@2, bh), ca)) → new_compare4(vyy3000, vyy400, bh, ca)
The graph contains the following edges 1 >= 1, 2 >= 2, 4 > 3, 4 > 4
- new_ltEs0(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), app(app(ty_@2, fh), ga), cf, eb) → new_compare23(vyy3000, vyy400, new_esEs8(vyy3000, vyy400, fh, ga), fh, ga)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 4, 3 > 5
- new_compare4(vyy3000, vyy400, fh, ga) → new_compare23(vyy3000, vyy400, new_esEs8(vyy3000, vyy400, fh, ga), fh, ga)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 4, 4 >= 5
- new_compare3(vyy3000, vyy400, ff, fg) → new_compare22(vyy3000, vyy400, new_esEs7(vyy3000, vyy400, ff, fg), ff, fg)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 4, 4 >= 5
- new_ltEs0(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), ce, app(app(ty_@2, fa), fb), eb) → new_lt3(vyy3001, vyy401, fa, fb)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
- new_ltEs3(@2(vyy3000, vyy3001), @2(vyy400, vyy401), app(app(ty_@2, bea), beb), bdb) → new_lt3(vyy3000, vyy400, bea, beb)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
- new_ltEs3(@2(vyy3000, vyy3001), @2(vyy400, vyy401), app(ty_[], bda), bdb) → new_lt(vyy3000, vyy400, bda)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
- new_ltEs0(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), ce, app(ty_[], ea), eb) → new_lt(vyy3001, vyy401, ea)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
- new_ltEs0(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), app(app(ty_Either, ff), fg), cf, eb) → new_compare22(vyy3000, vyy400, new_esEs7(vyy3000, vyy400, ff, fg), ff, fg)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 4, 3 > 5
- new_ltEs0(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), app(app(app(ty_@3, cb), cc), cd), cf, eb) → new_compare20(vyy3000, vyy400, new_esEs5(vyy3000, vyy400, cb, cc, cd), cb, cc, cd)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 4, 3 > 5, 3 > 6
- new_ltEs0(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), app(ty_Maybe, fd), cf, eb) → new_compare21(vyy3000, vyy400, new_esEs6(vyy3000, vyy400, fd), fd)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 4
- new_ltEs2(Right(vyy3000), Right(vyy400), bae, app(app(app(ty_@3, bag), bah), bba)) → new_ltEs0(vyy3000, vyy400, bag, bah, bba)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5
- new_ltEs2(Left(vyy3000), Left(vyy400), app(app(app(ty_@3, he), hf), hg), hd) → new_ltEs0(vyy3000, vyy400, he, hf, hg)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
- new_ltEs2(Left(vyy3000), Left(vyy400), app(app(ty_@2, bac), bad), hd) → new_ltEs3(vyy3000, vyy400, bac, bad)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
- new_ltEs2(Right(vyy3000), Right(vyy400), bae, app(app(ty_@2, bbe), bbf)) → new_ltEs3(vyy3000, vyy400, bbe, bbf)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
- new_ltEs2(Left(vyy3000), Left(vyy400), app(app(ty_Either, baa), bab), hd) → new_ltEs2(vyy3000, vyy400, baa, bab)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
- new_ltEs2(Right(vyy3000), Right(vyy400), bae, app(app(ty_Either, bbc), bbd)) → new_ltEs2(vyy3000, vyy400, bbc, bbd)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
- new_ltEs2(Left(vyy3000), Left(vyy400), app(ty_Maybe, hh), hd) → new_ltEs1(vyy3000, vyy400, hh)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
- new_ltEs2(Right(vyy3000), Right(vyy400), bae, app(ty_Maybe, bbb)) → new_ltEs1(vyy3000, vyy400, bbb)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
- new_ltEs2(Right(vyy3000), Right(vyy400), bae, app(ty_[], baf)) → new_ltEs(vyy3000, vyy400, baf)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
- new_ltEs2(Left(vyy3000), Left(vyy400), app(ty_[], hc), hd) → new_ltEs(vyy3000, vyy400, hc)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDPSizeChangeProof
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_foldFM_LE1(vyy26, vyy40, vyy340, vyy341, vyy342, vyy343, EmptyFM, True, h, ba) → new_foldFM_LE(vyy26, vyy40, vyy343, h, ba)
new_foldFM_LE(vyy26, vyy40, Branch(vyy3430, vyy3431, vyy3432, vyy3433, vyy3434), h, ba) → new_foldFM_LE1(vyy26, vyy40, vyy3430, vyy3431, vyy3432, vyy3433, vyy3434, new_ltEs5(vyy3430, Just(vyy40), ba), h, ba)
new_foldFM_LE2(vyy340, vyy341, vyy30, vyy40, vyy3440, vyy3441, vyy3442, vyy3443, vyy3444, h, ba) → new_foldFM_LE1(new_eltsFM_LE0(vyy340, vyy341, vyy30, h, ba), vyy40, vyy3440, vyy3441, vyy3442, vyy3443, vyy3444, new_ltEs5(vyy3440, Just(vyy40), ba), h, ba)
new_foldFM_LE1(vyy26, vyy40, vyy340, vyy341, vyy342, vyy343, Branch(vyy3440, vyy3441, vyy3442, vyy3443, vyy3444), True, h, ba) → new_foldFM_LE2(vyy340, vyy341, new_foldFM_LE0(vyy26, vyy40, vyy343, h, ba), vyy40, vyy3440, vyy3441, vyy3442, vyy3443, vyy3444, h, ba)
new_foldFM_LE1(vyy26, vyy40, vyy340, vyy341, vyy342, Branch(vyy3430, vyy3431, vyy3432, vyy3433, vyy3434), vyy344, False, h, ba) → new_foldFM_LE1(vyy26, vyy40, vyy3430, vyy3431, vyy3432, vyy3433, vyy3434, new_ltEs5(vyy3430, Just(vyy40), ba), h, ba)
new_foldFM_LE1(vyy26, vyy40, vyy340, vyy341, vyy342, vyy343, Branch(vyy3440, vyy3441, vyy3442, vyy3443, vyy3444), True, h, ba) → new_foldFM_LE(vyy26, vyy40, vyy343, h, ba)
The TRS R consists of the following rules:
new_esEs28(vyy401, vyy411, ty_Double) → new_esEs21(vyy401, vyy411)
new_esEs10(vyy401, vyy411, ty_Integer) → new_esEs12(vyy401, vyy411)
new_esEs25(vyy402, vyy412, ty_Char) → new_esEs19(vyy402, vyy412)
new_lt19(vyy3000, vyy400) → new_esEs15(new_compare14(vyy3000, vyy400))
new_esEs7(Left(vyy400), Left(vyy410), app(app(ty_Either, dab), dac), gb) → new_esEs7(vyy400, vyy410, dab, dac)
new_lt12(vyy3001, vyy401, ty_@0) → new_lt17(vyy3001, vyy401)
new_compare15(vyy3000, vyy400, app(app(app(ty_@3, gg), gh), ha)) → new_compare16(vyy3000, vyy400, gg, gh, ha)
new_esEs27(vyy400, vyy410, ty_Char) → new_esEs19(vyy400, vyy410)
new_esEs25(vyy402, vyy412, ty_Integer) → new_esEs12(vyy402, vyy412)
new_esEs24(vyy40, vyy41, app(app(app(ty_@3, fd), ff), fg)) → new_esEs5(vyy40, vyy41, fd, ff, fg)
new_esEs6(Just(vyy400), Just(vyy410), ty_Int) → new_esEs13(vyy400, vyy410)
new_esEs7(Right(vyy400), Right(vyy410), ga, app(ty_[], dag)) → new_esEs17(vyy400, vyy410, dag)
new_compare([], :(vyy400, vyy401), ge) → LT
new_esEs18(vyy400, vyy410, app(ty_[], cc)) → new_esEs17(vyy400, vyy410, cc)
new_ltEs10(vyy300, vyy40) → new_not(new_compare19(vyy300, vyy40))
new_esEs15(GT) → False
new_esEs24(vyy40, vyy41, ty_Double) → new_esEs21(vyy40, vyy41)
new_ltEs19(vyy3001, vyy401, ty_Integer) → new_ltEs15(vyy3001, vyy401)
new_compare15(vyy3000, vyy400, ty_Integer) → new_compare7(vyy3000, vyy400)
new_ltEs18(vyy3002, vyy402, app(ty_Ratio, cah)) → new_ltEs12(vyy3002, vyy402, cah)
new_esEs6(Just(vyy400), Just(vyy410), app(app(ty_FiniteMap, cdf), cdg)) → new_esEs23(vyy400, vyy410, cdf, cdg)
new_ltEs19(vyy3001, vyy401, app(ty_Ratio, ddb)) → new_ltEs12(vyy3001, vyy401, ddb)
new_esEs27(vyy400, vyy410, ty_Double) → new_esEs21(vyy400, vyy410)
new_ltEs13(Right(vyy3000), Right(vyy400), cfh, app(app(app(ty_@3, cgb), cgc), cgd)) → new_ltEs7(vyy3000, vyy400, cgb, cgc, cgd)
new_primMulNat0(Zero, Zero) → Zero
new_compare9(Float(vyy3000, vyy3001), Float(vyy400, vyy401)) → new_compare8(new_sr(vyy3000, vyy400), new_sr(vyy3001, vyy401))
new_esEs7(Left(vyy400), Left(vyy410), app(app(app(ty_@3, chd), che), chf), gb) → new_esEs5(vyy400, vyy410, chd, che, chf)
new_compare(:(vyy3000, vyy3001), [], ge) → GT
new_esEs29(vyy400, vyy410, ty_Float) → new_esEs16(vyy400, vyy410)
new_compare15(vyy3000, vyy400, ty_Char) → new_compare14(vyy3000, vyy400)
new_esEs18(vyy400, vyy410, ty_@0) → new_esEs22(vyy400, vyy410)
new_compare15(vyy3000, vyy400, ty_Double) → new_compare19(vyy3000, vyy400)
new_esEs20(EQ, EQ) → True
new_esEs26(vyy401, vyy411, ty_@0) → new_esEs22(vyy401, vyy411)
new_compare27(:%(vyy3000, vyy3001), :%(vyy400, vyy401), ty_Integer) → new_compare7(new_sr0(vyy3000, vyy401), new_sr0(vyy400, vyy3001))
new_lt20(vyy3000, vyy400, ty_Integer) → new_lt4(vyy3000, vyy400)
new_ltEs7(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), bhh, caa, cab) → new_pePe(new_lt13(vyy3000, vyy400, bhh), vyy3000, vyy400, new_pePe(new_lt12(vyy3001, vyy401, caa), vyy3001, vyy401, new_ltEs18(vyy3002, vyy402, cab), caa), bhh)
new_esEs7(Left(vyy400), Left(vyy410), ty_Bool, gb) → new_esEs14(vyy400, vyy410)
new_esEs20(EQ, GT) → False
new_esEs20(GT, EQ) → False
new_esEs27(vyy400, vyy410, ty_Integer) → new_esEs12(vyy400, vyy410)
new_not(GT) → False
new_lt5(vyy3000, vyy400) → new_esEs15(new_compare8(vyy3000, vyy400))
new_esEs27(vyy400, vyy410, app(app(ty_@2, bee), bef)) → new_esEs8(vyy400, vyy410, bee, bef)
new_esEs6(Just(vyy400), Just(vyy410), ty_Ordering) → new_esEs20(vyy400, vyy410)
new_ltEs5(Just(vyy3000), Just(vyy400), app(app(ty_Either, eg), eh)) → new_ltEs13(vyy3000, vyy400, eg, eh)
new_esEs27(vyy400, vyy410, app(ty_Ratio, bed)) → new_esEs9(vyy400, vyy410, bed)
new_lt12(vyy3001, vyy401, ty_Char) → new_lt19(vyy3001, vyy401)
new_esEs7(Right(vyy400), Right(vyy410), ga, app(app(app(ty_@3, dah), dba), dbb)) → new_esEs5(vyy400, vyy410, dah, dba, dbb)
new_foldFM_LE20(vyy340, vyy341, vyy30, vyy40, vyy3440, vyy3441, vyy3442, vyy3443, vyy3444, h, ba) → new_foldFM_LE10(new_eltsFM_LE0(vyy340, vyy341, vyy30, h, ba), vyy40, vyy3440, vyy3441, vyy3442, vyy3443, vyy3444, new_ltEs5(vyy3440, Just(vyy40), ba), h, ba)
new_esEs27(vyy400, vyy410, ty_Ordering) → new_esEs20(vyy400, vyy410)
new_ltEs15(vyy300, vyy40) → new_not(new_compare7(vyy300, vyy40))
new_ltEs13(Left(vyy3000), Left(vyy400), app(app(ty_@2, cff), cfg), cef) → new_ltEs17(vyy3000, vyy400, cff, cfg)
new_ltEs18(vyy3002, vyy402, ty_Char) → new_ltEs14(vyy3002, vyy402)
new_ltEs19(vyy3001, vyy401, ty_Bool) → new_ltEs4(vyy3001, vyy401)
new_esEs29(vyy400, vyy410, app(app(ty_FiniteMap, bha), bhb)) → new_esEs23(vyy400, vyy410, bha, bhb)
new_esEs27(vyy400, vyy410, app(ty_Maybe, bdg)) → new_esEs6(vyy400, vyy410, bdg)
new_ltEs4(False, True) → True
new_ltEs8(EQ, EQ) → True
new_esEs7(Right(vyy400), Right(vyy410), ga, app(ty_Ratio, dbh)) → new_esEs9(vyy400, vyy410, dbh)
new_lt13(vyy3000, vyy400, app(app(ty_Either, bf), bg)) → new_lt18(vyy3000, vyy400, bf, bg)
new_lt13(vyy3000, vyy400, ty_Integer) → new_lt4(vyy3000, vyy400)
new_esEs12(Integer(vyy400), Integer(vyy410)) → new_primEqInt(vyy400, vyy410)
new_ltEs9(vyy300, vyy40) → new_not(new_compare8(vyy300, vyy40))
new_esEs28(vyy401, vyy411, ty_Integer) → new_esEs12(vyy401, vyy411)
new_lt20(vyy3000, vyy400, ty_Ordering) → new_lt15(vyy3000, vyy400)
new_esEs28(vyy401, vyy411, app(app(app(ty_@3, bfa), bfb), bfc)) → new_esEs5(vyy401, vyy411, bfa, bfb, bfc)
new_esEs18(vyy400, vyy410, ty_Char) → new_esEs19(vyy400, vyy410)
new_ltEs13(Left(vyy3000), Left(vyy400), ty_Bool, cef) → new_ltEs4(vyy3000, vyy400)
new_foldFM0(vyy410, vyy411, vyy85, EmptyFM, bh, ca) → :(@2(vyy410, vyy411), vyy85)
new_lt12(vyy3001, vyy401, app(ty_Maybe, cca)) → new_lt10(vyy3001, vyy401, cca)
new_ltEs19(vyy3001, vyy401, ty_Float) → new_ltEs16(vyy3001, vyy401)
new_esEs7(Right(vyy400), Right(vyy410), ga, app(ty_Maybe, dbc)) → new_esEs6(vyy400, vyy410, dbc)
new_ltEs4(True, True) → True
new_ltEs18(vyy3002, vyy402, app(app(app(ty_@3, cad), cae), caf)) → new_ltEs7(vyy3002, vyy402, cad, cae, caf)
new_esEs26(vyy401, vyy411, app(app(ty_@2, bda), bdb)) → new_esEs8(vyy401, vyy411, bda, bdb)
new_esEs7(Left(vyy400), Right(vyy410), ga, gb) → False
new_esEs7(Right(vyy400), Left(vyy410), ga, gb) → False
new_pePe(False, vyy40, vyy41, vyy57, fc) → new_asAs(new_esEs24(vyy40, vyy41, fc), vyy57)
new_esEs17(:(vyy400, vyy401), :(vyy410, vyy411), cb) → new_asAs(new_esEs18(vyy400, vyy410, cb), new_esEs17(vyy401, vyy411, cb))
new_lt18(vyy3000, vyy400, bf, bg) → new_esEs15(new_compare28(vyy3000, vyy400, bf, bg))
new_compare6(vyy3000, vyy400) → new_compare25(vyy3000, vyy400, new_esEs14(vyy3000, vyy400))
new_esEs20(LT, LT) → True
new_esEs5(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), fd, ff, fg) → new_asAs(new_esEs27(vyy400, vyy410, fd), new_asAs(new_esEs26(vyy401, vyy411, ff), new_esEs25(vyy402, vyy412, fg)))
new_lt16(vyy3000, vyy400) → new_esEs15(new_compare19(vyy3000, vyy400))
new_esEs25(vyy402, vyy412, ty_Bool) → new_esEs14(vyy402, vyy412)
new_esEs27(vyy400, vyy410, app(app(ty_Either, beb), bec)) → new_esEs7(vyy400, vyy410, beb, bec)
new_esEs11(vyy400, vyy410, ty_Int) → new_esEs13(vyy400, vyy410)
new_esEs18(vyy400, vyy410, app(app(ty_@2, df), dg)) → new_esEs8(vyy400, vyy410, df, dg)
new_lt13(vyy3000, vyy400, ty_Int) → new_lt5(vyy3000, vyy400)
new_esEs25(vyy402, vyy412, ty_Double) → new_esEs21(vyy402, vyy412)
new_ltEs13(Left(vyy3000), Left(vyy400), ty_Int, cef) → new_ltEs9(vyy3000, vyy400)
new_esEs27(vyy400, vyy410, app(ty_[], bdc)) → new_esEs17(vyy400, vyy410, bdc)
new_ltEs8(EQ, GT) → True
new_compare13(vyy3000, vyy400, False, bf, bg) → GT
new_esEs7(Left(vyy400), Left(vyy410), ty_Int, gb) → new_esEs13(vyy400, vyy410)
new_ltEs8(GT, GT) → True
new_compare5(vyy3000, vyy400, bc, bd) → new_compare24(vyy3000, vyy400, new_esEs8(vyy3000, vyy400, bc, bd), bc, bd)
new_esEs18(vyy400, vyy410, ty_Int) → new_esEs13(vyy400, vyy410)
new_compare111(vyy3000, vyy400, False) → GT
new_compare111(vyy3000, vyy400, True) → LT
new_compare10(vyy3000, vyy400, True, bb) → LT
new_esEs26(vyy401, vyy411, ty_Char) → new_esEs19(vyy401, vyy411)
new_ltEs18(vyy3002, vyy402, ty_@0) → new_ltEs11(vyy3002, vyy402)
new_esEs6(Just(vyy400), Just(vyy410), app(app(app(ty_@3, cdb), cdc), cdd)) → new_esEs5(vyy400, vyy410, cdb, cdc, cdd)
new_primCmpNat0(Zero, Succ(vyy4000)) → LT
new_compare18(vyy3000, vyy400, bb) → new_compare211(vyy3000, vyy400, new_esEs6(vyy3000, vyy400, bb), bb)
new_ltEs5(Just(vyy3000), Just(vyy400), app(ty_Ratio, ef)) → new_ltEs12(vyy3000, vyy400, ef)
new_esEs15(LT) → True
new_ltEs6(vyy300, vyy40, ge) → new_not(new_compare(vyy300, vyy40, ge))
new_ltEs13(Left(vyy3000), Left(vyy400), ty_Double, cef) → new_ltEs10(vyy3000, vyy400)
new_esEs7(Right(vyy400), Right(vyy410), ga, ty_Bool) → new_esEs14(vyy400, vyy410)
new_esEs26(vyy401, vyy411, ty_Double) → new_esEs21(vyy401, vyy411)
new_esEs26(vyy401, vyy411, ty_Ordering) → new_esEs20(vyy401, vyy411)
new_lt20(vyy3000, vyy400, ty_Char) → new_lt19(vyy3000, vyy400)
new_ltEs8(LT, EQ) → True
new_lt20(vyy3000, vyy400, ty_Int) → new_lt5(vyy3000, vyy400)
new_lt20(vyy3000, vyy400, app(ty_Ratio, ded)) → new_lt9(vyy3000, vyy400, ded)
new_ltEs18(vyy3002, vyy402, app(ty_Maybe, cag)) → new_ltEs5(vyy3002, vyy402, cag)
new_esEs18(vyy400, vyy410, app(ty_Ratio, de)) → new_esEs9(vyy400, vyy410, de)
new_compare10(vyy3000, vyy400, False, bb) → GT
new_esEs24(vyy40, vyy41, app(app(ty_Either, ga), gb)) → new_esEs7(vyy40, vyy41, ga, gb)
new_esEs15(EQ) → False
new_esEs7(Right(vyy400), Right(vyy410), ga, ty_Float) → new_esEs16(vyy400, vyy410)
new_primEqNat0(Zero, Zero) → True
new_compare27(:%(vyy3000, vyy3001), :%(vyy400, vyy401), ty_Int) → new_compare8(new_sr(vyy3000, vyy401), new_sr(vyy400, vyy3001))
new_esEs29(vyy400, vyy410, app(ty_Maybe, bgh)) → new_esEs6(vyy400, vyy410, bgh)
new_esEs26(vyy401, vyy411, app(ty_Maybe, bcc)) → new_esEs6(vyy401, vyy411, bcc)
new_compare210(vyy3000, vyy400, False) → new_compare111(vyy3000, vyy400, new_ltEs8(vyy3000, vyy400))
new_compare29(vyy3000, vyy400, False, hh, baa, bab) → new_compare110(vyy3000, vyy400, new_ltEs7(vyy3000, vyy400, hh, baa, bab), hh, baa, bab)
new_esEs29(vyy400, vyy410, ty_Ordering) → new_esEs20(vyy400, vyy410)
new_ltEs8(GT, EQ) → False
new_lt13(vyy3000, vyy400, ty_Float) → new_lt7(vyy3000, vyy400)
new_ltEs8(EQ, LT) → False
new_esEs29(vyy400, vyy410, ty_Int) → new_esEs13(vyy400, vyy410)
new_compare(:(vyy3000, vyy3001), :(vyy400, vyy401), ge) → new_primCompAux1(vyy3000, vyy400, new_compare(vyy3001, vyy401, ge), ge)
new_ltEs17(@2(vyy3000, vyy3001), @2(vyy400, vyy401), dcc, dcd) → new_pePe(new_lt20(vyy3000, vyy400, dcc), vyy3000, vyy400, new_ltEs19(vyy3001, vyy401, dcd), dcc)
new_ltEs13(Left(vyy3000), Left(vyy400), ty_Float, cef) → new_ltEs16(vyy3000, vyy400)
new_sr(vyy3001, vyy401) → new_primMulInt(vyy3001, vyy401)
new_esEs25(vyy402, vyy412, ty_Int) → new_esEs13(vyy402, vyy412)
new_esEs18(vyy400, vyy410, app(app(app(ty_@3, cd), ce), cf)) → new_esEs5(vyy400, vyy410, cd, ce, cf)
new_compare15(vyy3000, vyy400, app(app(ty_@2, hf), hg)) → new_compare5(vyy3000, vyy400, hf, hg)
new_ltEs5(Just(vyy3000), Just(vyy400), ty_Double) → new_ltEs10(vyy3000, vyy400)
new_lt7(vyy3000, vyy400) → new_esEs15(new_compare9(vyy3000, vyy400))
new_lt12(vyy3001, vyy401, ty_Float) → new_lt7(vyy3001, vyy401)
new_esEs24(vyy40, vyy41, ty_Char) → new_esEs19(vyy40, vyy41)
new_esEs13(vyy40, vyy41) → new_primEqInt(vyy40, vyy41)
new_primPlusNat0(Succ(vyy860), vyy40100) → Succ(Succ(new_primPlusNat1(vyy860, vyy40100)))
new_esEs25(vyy402, vyy412, ty_Float) → new_esEs16(vyy402, vyy412)
new_esEs7(Right(vyy400), Right(vyy410), ga, app(app(ty_Either, dbf), dbg)) → new_esEs7(vyy400, vyy410, dbf, dbg)
new_ltEs19(vyy3001, vyy401, ty_Double) → new_ltEs10(vyy3001, vyy401)
new_esEs20(LT, EQ) → False
new_esEs20(EQ, LT) → False
new_ltEs11(vyy300, vyy40) → new_not(new_compare26(vyy300, vyy40))
new_compare29(vyy3000, vyy400, True, hh, baa, bab) → EQ
new_esEs26(vyy401, vyy411, ty_Integer) → new_esEs12(vyy401, vyy411)
new_lt11(vyy3000, vyy400, hh, baa, bab) → new_esEs15(new_compare16(vyy3000, vyy400, hh, baa, bab))
new_esEs28(vyy401, vyy411, ty_Float) → new_esEs16(vyy401, vyy411)
new_compare211(vyy3000, vyy400, True, bb) → EQ
new_compare25(vyy3000, vyy400, True) → EQ
new_primEqInt(Neg(Succ(vyy4000)), Neg(Succ(vyy4100))) → new_primEqNat0(vyy4000, vyy4100)
new_ltEs19(vyy3001, vyy401, app(app(ty_@2, dde), ddf)) → new_ltEs17(vyy3001, vyy401, dde, ddf)
new_esEs7(Right(vyy400), Right(vyy410), ga, ty_Int) → new_esEs13(vyy400, vyy410)
new_ltEs19(vyy3001, vyy401, ty_Ordering) → new_ltEs8(vyy3001, vyy401)
new_esEs6(Just(vyy400), Just(vyy410), ty_@0) → new_esEs22(vyy400, vyy410)
new_esEs7(Left(vyy400), Left(vyy410), ty_@0, gb) → new_esEs22(vyy400, vyy410)
new_esEs21(Double(vyy400, vyy401), Double(vyy410, vyy411)) → new_esEs13(new_sr(vyy400, vyy410), new_sr(vyy401, vyy411))
new_compare13(vyy3000, vyy400, True, bf, bg) → LT
new_esEs25(vyy402, vyy412, app(app(ty_@2, bbe), bbf)) → new_esEs8(vyy402, vyy412, bbe, bbf)
new_compare25(vyy3000, vyy400, False) → new_compare12(vyy3000, vyy400, new_ltEs4(vyy3000, vyy400))
new_ltEs5(Just(vyy3000), Nothing, dh) → False
new_esEs24(vyy40, vyy41, ty_Bool) → new_esEs14(vyy40, vyy41)
new_primPlusNat1(Succ(vyy8600), Zero) → Succ(vyy8600)
new_primPlusNat1(Zero, Succ(vyy401000)) → Succ(vyy401000)
new_esEs7(Left(vyy400), Left(vyy410), app(app(ty_FiniteMap, chh), daa), gb) → new_esEs23(vyy400, vyy410, chh, daa)
new_ltEs13(Right(vyy3000), Right(vyy400), cfh, ty_Integer) → new_ltEs15(vyy3000, vyy400)
new_esEs7(Left(vyy400), Left(vyy410), app(ty_[], chc), gb) → new_esEs17(vyy400, vyy410, chc)
new_ltEs13(Right(vyy3000), Right(vyy400), cfh, ty_Int) → new_ltEs9(vyy3000, vyy400)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs6(Just(vyy400), Just(vyy410), ty_Integer) → new_esEs12(vyy400, vyy410)
new_ltEs5(Just(vyy3000), Just(vyy400), ty_Int) → new_ltEs9(vyy3000, vyy400)
new_lt13(vyy3000, vyy400, ty_@0) → new_lt17(vyy3000, vyy400)
new_ltEs13(Right(vyy3000), Right(vyy400), cfh, ty_Char) → new_ltEs14(vyy3000, vyy400)
new_esEs29(vyy400, vyy410, ty_Double) → new_esEs21(vyy400, vyy410)
new_compare15(vyy3000, vyy400, ty_Int) → new_compare8(vyy3000, vyy400)
new_compare8(vyy300, vyy40) → new_primCmpInt(vyy300, vyy40)
new_primEqInt(Neg(Succ(vyy4000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(vyy4100))) → False
new_primCompAux0(vyy71, GT) → GT
new_lt12(vyy3001, vyy401, ty_Bool) → new_lt8(vyy3001, vyy401)
new_lt13(vyy3000, vyy400, ty_Ordering) → new_lt15(vyy3000, vyy400)
new_compare24(vyy3000, vyy400, True, bc, bd) → EQ
new_esEs28(vyy401, vyy411, ty_Int) → new_esEs13(vyy401, vyy411)
new_compare([], [], ge) → EQ
new_ltEs13(Right(vyy3000), Right(vyy400), cfh, ty_Double) → new_ltEs10(vyy3000, vyy400)
new_esEs8(@2(vyy400, vyy401), @2(vyy410, vyy411), gc, gd) → new_asAs(new_esEs29(vyy400, vyy410, gc), new_esEs28(vyy401, vyy411, gd))
new_foldFM0(vyy410, vyy411, vyy85, Branch(vyy4130, vyy4131, vyy4132, vyy4133, vyy4134), bh, ca) → new_foldFM0(vyy4130, vyy4131, new_foldFM0(vyy410, vyy411, vyy85, vyy4134, bh, ca), vyy4133, bh, ca)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_esEs26(vyy401, vyy411, app(app(ty_Either, bcf), bcg)) → new_esEs7(vyy401, vyy411, bcf, bcg)
new_esEs23(vyy40, vyy41, bh, ca) → new_asAs(new_esEs13(new_sizeFM(vyy40, bh, ca), new_sizeFM(vyy41, bh, ca)), new_esEs17(new_fmToList(vyy40, bh, ca), new_fmToList(vyy41, bh, ca), app(app(ty_@2, bh), ca)))
new_compare14(Char(vyy3000), Char(vyy400)) → new_primCmpNat0(vyy3000, vyy400)
new_esEs7(Right(vyy400), Right(vyy410), ga, ty_@0) → new_esEs22(vyy400, vyy410)
new_ltEs5(Just(vyy3000), Just(vyy400), ty_Char) → new_ltEs14(vyy3000, vyy400)
new_primCmpNat0(Succ(vyy30000), Succ(vyy4000)) → new_primCmpNat0(vyy30000, vyy4000)
new_ltEs19(vyy3001, vyy401, ty_@0) → new_ltEs11(vyy3001, vyy401)
new_sizeFM(EmptyFM, bh, ca) → Pos(Zero)
new_ltEs5(Just(vyy3000), Just(vyy400), app(ty_[], ea)) → new_ltEs6(vyy3000, vyy400, ea)
new_ltEs13(Left(vyy3000), Left(vyy400), app(ty_[], cee), cef) → new_ltEs6(vyy3000, vyy400, cee)
new_esEs6(Nothing, Nothing, fh) → True
new_ltEs18(vyy3002, vyy402, app(app(ty_Either, cba), cbb)) → new_ltEs13(vyy3002, vyy402, cba, cbb)
new_lt12(vyy3001, vyy401, ty_Ordering) → new_lt15(vyy3001, vyy401)
new_ltEs13(Right(vyy3000), Right(vyy400), cfh, ty_Ordering) → new_ltEs8(vyy3000, vyy400)
new_primEqInt(Pos(Succ(vyy4000)), Pos(Succ(vyy4100))) → new_primEqNat0(vyy4000, vyy4100)
new_compare15(vyy3000, vyy400, app(ty_[], gf)) → new_compare(vyy3000, vyy400, gf)
new_ltEs19(vyy3001, vyy401, app(app(app(ty_@3, dcf), dcg), dch)) → new_ltEs7(vyy3001, vyy401, dcf, dcg, dch)
new_compare15(vyy3000, vyy400, ty_Float) → new_compare9(vyy3000, vyy400)
new_lt13(vyy3000, vyy400, ty_Char) → new_lt19(vyy3000, vyy400)
new_esEs14(True, False) → False
new_esEs14(False, True) → False
new_ltEs16(vyy300, vyy40) → new_not(new_compare9(vyy300, vyy40))
new_compare15(vyy3000, vyy400, ty_Bool) → new_compare6(vyy3000, vyy400)
new_esEs26(vyy401, vyy411, ty_Int) → new_esEs13(vyy401, vyy411)
new_esEs6(Just(vyy400), Nothing, fh) → False
new_esEs6(Nothing, Just(vyy410), fh) → False
new_ltEs18(vyy3002, vyy402, ty_Bool) → new_ltEs4(vyy3002, vyy402)
new_primEqNat0(Succ(vyy4000), Succ(vyy4100)) → new_primEqNat0(vyy4000, vyy4100)
new_ltEs19(vyy3001, vyy401, app(app(ty_Either, ddc), ddd)) → new_ltEs13(vyy3001, vyy401, ddc, ddd)
new_ltEs5(Just(vyy3000), Just(vyy400), ty_Bool) → new_ltEs4(vyy3000, vyy400)
new_esEs7(Right(vyy400), Right(vyy410), ga, ty_Ordering) → new_esEs20(vyy400, vyy410)
new_compare28(vyy3000, vyy400, bf, bg) → new_compare212(vyy3000, vyy400, new_esEs7(vyy3000, vyy400, bf, bg), bf, bg)
new_primCompAux1(vyy3000, vyy400, vyy67, ge) → new_primCompAux0(vyy67, new_compare15(vyy3000, vyy400, ge))
new_primCmpInt(Neg(Succ(vyy30000)), Neg(vyy400)) → new_primCmpNat0(vyy400, Succ(vyy30000))
new_esEs27(vyy400, vyy410, app(app(app(ty_@3, bdd), bde), bdf)) → new_esEs5(vyy400, vyy410, bdd, bde, bdf)
new_lt4(vyy3000, vyy400) → new_esEs15(new_compare7(vyy3000, vyy400))
new_primEqInt(Pos(Zero), Pos(Succ(vyy4100))) → False
new_primEqInt(Pos(Succ(vyy4000)), Pos(Zero)) → False
new_ltEs5(Just(vyy3000), Just(vyy400), ty_@0) → new_ltEs11(vyy3000, vyy400)
new_ltEs5(Nothing, Just(vyy400), dh) → True
new_esEs24(vyy40, vyy41, ty_@0) → new_esEs22(vyy40, vyy41)
new_esEs25(vyy402, vyy412, ty_Ordering) → new_esEs20(vyy402, vyy412)
new_esEs20(GT, GT) → True
new_lt9(vyy3000, vyy400, beg) → new_esEs15(new_compare27(vyy3000, vyy400, beg))
new_lt15(vyy3000, vyy400) → new_esEs15(new_compare17(vyy3000, vyy400))
new_ltEs13(Left(vyy3000), Left(vyy400), app(app(app(ty_@3, ceg), ceh), cfa), cef) → new_ltEs7(vyy3000, vyy400, ceg, ceh, cfa)
new_primCmpNat0(Zero, Zero) → EQ
new_esEs7(Right(vyy400), Right(vyy410), ga, app(app(ty_FiniteMap, dbd), dbe)) → new_esEs23(vyy400, vyy410, dbd, dbe)
new_primCmpNat0(Succ(vyy30000), Zero) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(vyy4000))) → LT
new_compare11(vyy3000, vyy400, True, bc, bd) → LT
new_esEs27(vyy400, vyy410, app(app(ty_FiniteMap, bdh), bea)) → new_esEs23(vyy400, vyy410, bdh, bea)
new_sr0(Integer(vyy4000), Integer(vyy30010)) → Integer(new_primMulInt(vyy4000, vyy30010))
new_primPlusNat1(Succ(vyy8600), Succ(vyy401000)) → Succ(Succ(new_primPlusNat1(vyy8600, vyy401000)))
new_primEqInt(Pos(Succ(vyy4000)), Neg(vyy410)) → False
new_primEqInt(Neg(Succ(vyy4000)), Pos(vyy410)) → False
new_esEs29(vyy400, vyy410, ty_Char) → new_esEs19(vyy400, vyy410)
new_lt12(vyy3001, vyy401, app(ty_Ratio, ccb)) → new_lt9(vyy3001, vyy401, ccb)
new_foldFM2(EmptyFM, bh, ca) → []
new_foldFM_LE10(vyy26, vyy40, vyy340, vyy341, vyy342, vyy343, vyy344, False, h, ba) → new_foldFM_LE0(vyy26, vyy40, vyy343, h, ba)
new_ltEs13(Right(vyy3000), Right(vyy400), cfh, ty_@0) → new_ltEs11(vyy3000, vyy400)
new_esEs28(vyy401, vyy411, app(ty_Maybe, bfd)) → new_esEs6(vyy401, vyy411, bfd)
new_compare15(vyy3000, vyy400, app(app(ty_Either, hd), he)) → new_compare28(vyy3000, vyy400, hd, he)
new_ltEs12(vyy300, vyy40, cch) → new_not(new_compare27(vyy300, vyy40, cch))
new_primEqInt(Pos(Zero), Neg(Succ(vyy4100))) → False
new_primEqInt(Neg(Zero), Pos(Succ(vyy4100))) → False
new_esEs26(vyy401, vyy411, app(ty_[], bbg)) → new_esEs17(vyy401, vyy411, bbg)
new_ltEs14(vyy300, vyy40) → new_not(new_compare14(vyy300, vyy40))
new_primCmpInt(Pos(Zero), Pos(Succ(vyy4000))) → new_primCmpNat0(Zero, Succ(vyy4000))
new_esEs28(vyy401, vyy411, app(app(ty_Either, bfg), bfh)) → new_esEs7(vyy401, vyy411, bfg, bfh)
new_ltEs13(Right(vyy3000), Right(vyy400), cfh, app(ty_Ratio, cgf)) → new_ltEs12(vyy3000, vyy400, cgf)
new_ltEs18(vyy3002, vyy402, ty_Int) → new_ltEs9(vyy3002, vyy402)
new_esEs27(vyy400, vyy410, ty_Int) → new_esEs13(vyy400, vyy410)
new_esEs28(vyy401, vyy411, app(app(ty_FiniteMap, bfe), bff)) → new_esEs23(vyy401, vyy411, bfe, bff)
new_compare12(vyy3000, vyy400, False) → GT
new_eltsFM_LE0(vyy340, vyy341, vyy27, h, ba) → :(vyy341, vyy27)
new_esEs6(Just(vyy400), Just(vyy410), app(app(ty_@2, cec), ced)) → new_esEs8(vyy400, vyy410, cec, ced)
new_esEs7(Right(vyy400), Right(vyy410), ga, ty_Char) → new_esEs19(vyy400, vyy410)
new_ltEs8(GT, LT) → False
new_esEs26(vyy401, vyy411, ty_Float) → new_esEs16(vyy401, vyy411)
new_primCompAux0(vyy71, LT) → LT
new_esEs18(vyy400, vyy410, ty_Ordering) → new_esEs20(vyy400, vyy410)
new_lt20(vyy3000, vyy400, ty_Bool) → new_lt8(vyy3000, vyy400)
new_esEs24(vyy40, vyy41, ty_Int) → new_esEs13(vyy40, vyy41)
new_esEs7(Left(vyy400), Left(vyy410), app(ty_Maybe, chg), gb) → new_esEs6(vyy400, vyy410, chg)
new_primPlusNat0(Zero, vyy40100) → Succ(vyy40100)
new_esEs27(vyy400, vyy410, ty_@0) → new_esEs22(vyy400, vyy410)
new_primCmpInt(Pos(Succ(vyy30000)), Pos(vyy400)) → new_primCmpNat0(Succ(vyy30000), vyy400)
new_esEs29(vyy400, vyy410, ty_Integer) → new_esEs12(vyy400, vyy410)
new_lt13(vyy3000, vyy400, app(app(app(ty_@3, hh), baa), bab)) → new_lt11(vyy3000, vyy400, hh, baa, bab)
new_esEs29(vyy400, vyy410, app(ty_[], bgd)) → new_esEs17(vyy400, vyy410, bgd)
new_esEs7(Left(vyy400), Left(vyy410), ty_Integer, gb) → new_esEs12(vyy400, vyy410)
new_esEs29(vyy400, vyy410, app(app(ty_@2, bhf), bhg)) → new_esEs8(vyy400, vyy410, bhf, bhg)
new_foldFM_LE0(vyy26, vyy40, Branch(vyy3430, vyy3431, vyy3432, vyy3433, vyy3434), h, ba) → new_foldFM_LE10(vyy26, vyy40, vyy3430, vyy3431, vyy3432, vyy3433, vyy3434, new_ltEs5(vyy3430, Just(vyy40), ba), h, ba)
new_esEs26(vyy401, vyy411, ty_Bool) → new_esEs14(vyy401, vyy411)
new_lt13(vyy3000, vyy400, app(ty_[], ccg)) → new_lt14(vyy3000, vyy400, ccg)
new_compare15(vyy3000, vyy400, ty_@0) → new_compare26(vyy3000, vyy400)
new_compare212(vyy3000, vyy400, True, bf, bg) → EQ
new_not0 → True
new_esEs24(vyy40, vyy41, ty_Integer) → new_esEs12(vyy40, vyy41)
new_esEs24(vyy40, vyy41, app(ty_[], cb)) → new_esEs17(vyy40, vyy41, cb)
new_ltEs5(Just(vyy3000), Just(vyy400), ty_Integer) → new_ltEs15(vyy3000, vyy400)
new_compare15(vyy3000, vyy400, app(ty_Ratio, hc)) → new_compare27(vyy3000, vyy400, hc)
new_esEs7(Left(vyy400), Left(vyy410), app(ty_Ratio, dad), gb) → new_esEs9(vyy400, vyy410, dad)
new_lt13(vyy3000, vyy400, app(ty_Ratio, beg)) → new_lt9(vyy3000, vyy400, beg)
new_compare11(vyy3000, vyy400, False, bc, bd) → GT
new_primCmpInt(Pos(Succ(vyy30000)), Neg(vyy400)) → GT
new_ltEs19(vyy3001, vyy401, ty_Int) → new_ltEs9(vyy3001, vyy401)
new_ltEs13(Right(vyy3000), Right(vyy400), cfh, ty_Float) → new_ltEs16(vyy3000, vyy400)
new_esEs18(vyy400, vyy410, app(app(ty_Either, dc), dd)) → new_esEs7(vyy400, vyy410, dc, dd)
new_ltEs13(Right(vyy3000), Right(vyy400), cfh, app(app(ty_@2, cha), chb)) → new_ltEs17(vyy3000, vyy400, cha, chb)
new_primMulInt(Pos(vyy30010), Pos(vyy4010)) → Pos(new_primMulNat0(vyy30010, vyy4010))
new_esEs7(Left(vyy400), Left(vyy410), ty_Ordering, gb) → new_esEs20(vyy400, vyy410)
new_esEs24(vyy40, vyy41, app(app(ty_FiniteMap, bh), ca)) → new_esEs23(vyy40, vyy41, bh, ca)
new_ltEs13(Left(vyy3000), Left(vyy400), ty_Integer, cef) → new_ltEs15(vyy3000, vyy400)
new_primMulInt(Neg(vyy30010), Neg(vyy4010)) → Pos(new_primMulNat0(vyy30010, vyy4010))
new_esEs20(LT, GT) → False
new_esEs20(GT, LT) → False
new_esEs28(vyy401, vyy411, app(ty_Ratio, bga)) → new_esEs9(vyy401, vyy411, bga)
new_compare19(Double(vyy3000, vyy3001), Double(vyy400, vyy401)) → new_compare8(new_sr(vyy3000, vyy400), new_sr(vyy3001, vyy401))
new_lt20(vyy3000, vyy400, app(app(app(ty_@3, ddh), dea), deb)) → new_lt11(vyy3000, vyy400, ddh, dea, deb)
new_primEqNat0(Succ(vyy4000), Zero) → False
new_primEqNat0(Zero, Succ(vyy4100)) → False
new_ltEs5(Nothing, Nothing, dh) → True
new_lt20(vyy3000, vyy400, app(app(ty_Either, dee), def)) → new_lt18(vyy3000, vyy400, dee, def)
new_lt12(vyy3001, vyy401, ty_Double) → new_lt16(vyy3001, vyy401)
new_esEs25(vyy402, vyy412, app(ty_Maybe, bag)) → new_esEs6(vyy402, vyy412, bag)
new_lt20(vyy3000, vyy400, ty_@0) → new_lt17(vyy3000, vyy400)
new_lt20(vyy3000, vyy400, app(ty_Maybe, dec)) → new_lt10(vyy3000, vyy400, dec)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_lt6(vyy3000, vyy400, bc, bd) → new_esEs15(new_compare5(vyy3000, vyy400, bc, bd))
new_esEs7(Right(vyy400), Right(vyy410), ga, app(app(ty_@2, dca), dcb)) → new_esEs8(vyy400, vyy410, dca, dcb)
new_compare210(vyy3000, vyy400, True) → EQ
new_lt12(vyy3001, vyy401, app(app(ty_@2, cce), ccf)) → new_lt6(vyy3001, vyy401, cce, ccf)
new_sizeFM(Branch(vyy410, vyy411, vyy412, vyy413, vyy414), bh, ca) → vyy412
new_ltEs18(vyy3002, vyy402, app(app(ty_@2, cbc), cbd)) → new_ltEs17(vyy3002, vyy402, cbc, cbd)
new_ltEs4(True, False) → False
new_foldFM_LE10(vyy26, vyy40, vyy340, vyy341, vyy342, vyy343, EmptyFM, True, h, ba) → new_foldFM_LE3(vyy340, vyy341, new_foldFM_LE0(vyy26, vyy40, vyy343, h, ba), vyy40, h, ba)
new_esEs18(vyy400, vyy410, app(app(ty_FiniteMap, da), db)) → new_esEs23(vyy400, vyy410, da, db)
new_esEs6(Just(vyy400), Just(vyy410), ty_Double) → new_esEs21(vyy400, vyy410)
new_pePe(True, vyy40, vyy41, vyy57, fc) → True
new_foldFM2(Branch(vyy410, vyy411, vyy412, vyy413, vyy414), bh, ca) → new_foldFM0(vyy410, vyy411, new_foldFM2(vyy414, bh, ca), vyy413, bh, ca)
new_esEs29(vyy400, vyy410, app(app(app(ty_@3, bge), bgf), bgg)) → new_esEs5(vyy400, vyy410, bge, bgf, bgg)
new_ltEs19(vyy3001, vyy401, app(ty_Maybe, dda)) → new_ltEs5(vyy3001, vyy401, dda)
new_lt12(vyy3001, vyy401, app(ty_[], cbe)) → new_lt14(vyy3001, vyy401, cbe)
new_esEs26(vyy401, vyy411, app(app(ty_FiniteMap, bcd), bce)) → new_esEs23(vyy401, vyy411, bcd, bce)
new_ltEs13(Right(vyy3000), Right(vyy400), cfh, ty_Bool) → new_ltEs4(vyy3000, vyy400)
new_primCmpInt(Neg(Zero), Neg(Succ(vyy4000))) → new_primCmpNat0(Succ(vyy4000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(vyy4000))) → GT
new_ltEs13(Left(vyy3000), Left(vyy400), app(ty_Maybe, cfb), cef) → new_ltEs5(vyy3000, vyy400, cfb)
new_compare24(vyy3000, vyy400, False, bc, bd) → new_compare11(vyy3000, vyy400, new_ltEs17(vyy3000, vyy400, bc, bd), bc, bd)
new_ltEs13(Left(vyy3000), Left(vyy400), ty_@0, cef) → new_ltEs11(vyy3000, vyy400)
new_ltEs5(Just(vyy3000), Just(vyy400), ty_Ordering) → new_ltEs8(vyy3000, vyy400)
new_esEs6(Just(vyy400), Just(vyy410), ty_Bool) → new_esEs14(vyy400, vyy410)
new_lt20(vyy3000, vyy400, app(app(ty_@2, deg), deh)) → new_lt6(vyy3000, vyy400, deg, deh)
new_ltEs13(Left(vyy3000), Left(vyy400), app(ty_Ratio, cfc), cef) → new_ltEs12(vyy3000, vyy400, cfc)
new_ltEs19(vyy3001, vyy401, ty_Char) → new_ltEs14(vyy3001, vyy401)
new_esEs6(Just(vyy400), Just(vyy410), app(ty_[], cda)) → new_esEs17(vyy400, vyy410, cda)
new_lt12(vyy3001, vyy401, ty_Integer) → new_lt4(vyy3001, vyy401)
new_lt20(vyy3000, vyy400, ty_Float) → new_lt7(vyy3000, vyy400)
new_lt12(vyy3001, vyy401, app(app(app(ty_@3, cbf), cbg), cbh)) → new_lt11(vyy3001, vyy401, cbf, cbg, cbh)
new_ltEs13(Left(vyy3000), Left(vyy400), app(app(ty_Either, cfd), cfe), cef) → new_ltEs13(vyy3000, vyy400, cfd, cfe)
new_esEs18(vyy400, vyy410, ty_Integer) → new_esEs12(vyy400, vyy410)
new_compare15(vyy3000, vyy400, ty_Ordering) → new_compare17(vyy3000, vyy400)
new_lt20(vyy3000, vyy400, ty_Double) → new_lt16(vyy3000, vyy400)
new_ltEs18(vyy3002, vyy402, app(ty_[], cac)) → new_ltEs6(vyy3002, vyy402, cac)
new_esEs19(Char(vyy400), Char(vyy410)) → new_primEqNat0(vyy400, vyy410)
new_ltEs13(Right(vyy3000), Right(vyy400), cfh, app(app(ty_Either, cgg), cgh)) → new_ltEs13(vyy3000, vyy400, cgg, cgh)
new_esEs29(vyy400, vyy410, app(ty_Ratio, bhe)) → new_esEs9(vyy400, vyy410, bhe)
new_esEs18(vyy400, vyy410, app(ty_Maybe, cg)) → new_esEs6(vyy400, vyy410, cg)
new_ltEs13(Left(vyy3000), Left(vyy400), ty_Ordering, cef) → new_ltEs8(vyy3000, vyy400)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_ltEs18(vyy3002, vyy402, ty_Double) → new_ltEs10(vyy3002, vyy402)
new_esEs25(vyy402, vyy412, app(app(ty_FiniteMap, bah), bba)) → new_esEs23(vyy402, vyy412, bah, bba)
new_asAs(False, vyy66) → False
new_ltEs13(Right(vyy3000), Right(vyy400), cfh, app(ty_[], cga)) → new_ltEs6(vyy3000, vyy400, cga)
new_esEs25(vyy402, vyy412, app(ty_Ratio, bbd)) → new_esEs9(vyy402, vyy412, bbd)
new_esEs29(vyy400, vyy410, ty_@0) → new_esEs22(vyy400, vyy410)
new_primMulInt(Pos(vyy30010), Neg(vyy4010)) → Neg(new_primMulNat0(vyy30010, vyy4010))
new_primMulInt(Neg(vyy30010), Pos(vyy4010)) → Neg(new_primMulNat0(vyy30010, vyy4010))
new_esEs7(Left(vyy400), Left(vyy410), app(app(ty_@2, dae), daf), gb) → new_esEs8(vyy400, vyy410, dae, daf)
new_ltEs13(Left(vyy3000), Right(vyy400), cfh, cef) → True
new_primMulNat0(Zero, Succ(vyy40100)) → Zero
new_primMulNat0(Succ(vyy300100), Zero) → Zero
new_esEs6(Just(vyy400), Just(vyy410), app(ty_Ratio, ceb)) → new_esEs9(vyy400, vyy410, ceb)
new_esEs6(Just(vyy400), Just(vyy410), app(ty_Maybe, cde)) → new_esEs6(vyy400, vyy410, cde)
new_lt20(vyy3000, vyy400, app(ty_[], ddg)) → new_lt14(vyy3000, vyy400, ddg)
new_lt10(vyy3000, vyy400, bb) → new_esEs15(new_compare18(vyy3000, vyy400, bb))
new_esEs28(vyy401, vyy411, ty_Bool) → new_esEs14(vyy401, vyy411)
new_compare12(vyy3000, vyy400, True) → LT
new_esEs18(vyy400, vyy410, ty_Double) → new_esEs21(vyy400, vyy410)
new_ltEs5(Just(vyy3000), Just(vyy400), app(ty_Maybe, ee)) → new_ltEs5(vyy3000, vyy400, ee)
new_esEs24(vyy40, vyy41, ty_Ordering) → new_esEs20(vyy40, vyy41)
new_not(EQ) → new_not0
new_compare110(vyy3000, vyy400, True, hh, baa, bab) → LT
new_esEs26(vyy401, vyy411, app(ty_Ratio, bch)) → new_esEs9(vyy401, vyy411, bch)
new_lt13(vyy3000, vyy400, app(app(ty_@2, bc), bd)) → new_lt6(vyy3000, vyy400, bc, bd)
new_esEs25(vyy402, vyy412, app(ty_[], bac)) → new_esEs17(vyy402, vyy412, bac)
new_ltEs4(False, False) → True
new_foldFM_LE10(vyy26, vyy40, vyy340, vyy341, vyy342, vyy343, Branch(vyy3440, vyy3441, vyy3442, vyy3443, vyy3444), True, h, ba) → new_foldFM_LE20(vyy340, vyy341, new_foldFM_LE0(vyy26, vyy40, vyy343, h, ba), vyy40, vyy3440, vyy3441, vyy3442, vyy3443, vyy3444, h, ba)
new_esEs14(True, True) → True
new_esEs27(vyy400, vyy410, ty_Bool) → new_esEs14(vyy400, vyy410)
new_ltEs13(Right(vyy3000), Left(vyy400), cfh, cef) → False
new_esEs28(vyy401, vyy411, ty_Char) → new_esEs19(vyy401, vyy411)
new_ltEs8(LT, GT) → True
new_esEs6(Just(vyy400), Just(vyy410), ty_Char) → new_esEs19(vyy400, vyy410)
new_foldFM_LE3(vyy340, vyy341, vyy29, vyy40, h, ba) → new_eltsFM_LE0(vyy340, vyy341, vyy29, h, ba)
new_esEs28(vyy401, vyy411, app(ty_[], beh)) → new_esEs17(vyy401, vyy411, beh)
new_ltEs5(Just(vyy3000), Just(vyy400), app(app(ty_@2, fa), fb)) → new_ltEs17(vyy3000, vyy400, fa, fb)
new_compare26(@0, @0) → EQ
new_esEs7(Right(vyy400), Right(vyy410), ga, ty_Integer) → new_esEs12(vyy400, vyy410)
new_esEs11(vyy400, vyy410, ty_Integer) → new_esEs12(vyy400, vyy410)
new_esEs9(:%(vyy400, vyy401), :%(vyy410, vyy411), be) → new_asAs(new_esEs11(vyy400, vyy410, be), new_esEs10(vyy401, vyy411, be))
new_ltEs5(Just(vyy3000), Just(vyy400), app(app(app(ty_@3, eb), ec), ed)) → new_ltEs7(vyy3000, vyy400, eb, ec, ed)
new_lt13(vyy3000, vyy400, ty_Double) → new_lt16(vyy3000, vyy400)
new_not(LT) → new_not0
new_ltEs18(vyy3002, vyy402, ty_Float) → new_ltEs16(vyy3002, vyy402)
new_compare7(Integer(vyy3000), Integer(vyy400)) → new_primCmpInt(vyy3000, vyy400)
new_esEs25(vyy402, vyy412, ty_@0) → new_esEs22(vyy402, vyy412)
new_esEs25(vyy402, vyy412, app(app(app(ty_@3, bad), bae), baf)) → new_esEs5(vyy402, vyy412, bad, bae, baf)
new_ltEs19(vyy3001, vyy401, app(ty_[], dce)) → new_ltEs6(vyy3001, vyy401, dce)
new_esEs6(Just(vyy400), Just(vyy410), ty_Float) → new_esEs16(vyy400, vyy410)
new_ltEs5(Just(vyy3000), Just(vyy400), ty_Float) → new_ltEs16(vyy3000, vyy400)
new_lt17(vyy3000, vyy400) → new_esEs15(new_compare26(vyy3000, vyy400))
new_esEs29(vyy400, vyy410, app(app(ty_Either, bhc), bhd)) → new_esEs7(vyy400, vyy410, bhc, bhd)
new_esEs14(False, False) → True
new_esEs10(vyy401, vyy411, ty_Int) → new_esEs13(vyy401, vyy411)
new_lt14(vyy3000, vyy400, ccg) → new_esEs15(new_compare(vyy3000, vyy400, ccg))
new_compare211(vyy3000, vyy400, False, bb) → new_compare10(vyy3000, vyy400, new_ltEs5(vyy3000, vyy400, bb), bb)
new_esEs18(vyy400, vyy410, ty_Bool) → new_esEs14(vyy400, vyy410)
new_ltEs8(LT, LT) → True
new_esEs28(vyy401, vyy411, app(app(ty_@2, bgb), bgc)) → new_esEs8(vyy401, vyy411, bgb, bgc)
new_primPlusNat1(Zero, Zero) → Zero
new_esEs28(vyy401, vyy411, ty_@0) → new_esEs22(vyy401, vyy411)
new_asAs(True, vyy66) → vyy66
new_compare17(vyy3000, vyy400) → new_compare210(vyy3000, vyy400, new_esEs20(vyy3000, vyy400))
new_esEs24(vyy40, vyy41, ty_Float) → new_esEs16(vyy40, vyy41)
new_primMulNat0(Succ(vyy300100), Succ(vyy40100)) → new_primPlusNat0(new_primMulNat0(vyy300100, Succ(vyy40100)), vyy40100)
new_esEs27(vyy400, vyy410, ty_Float) → new_esEs16(vyy400, vyy410)
new_esEs26(vyy401, vyy411, app(app(app(ty_@3, bbh), bca), bcb)) → new_esEs5(vyy401, vyy411, bbh, bca, bcb)
new_lt12(vyy3001, vyy401, app(app(ty_Either, ccc), ccd)) → new_lt18(vyy3001, vyy401, ccc, ccd)
new_esEs6(Just(vyy400), Just(vyy410), app(app(ty_Either, cdh), cea)) → new_esEs7(vyy400, vyy410, cdh, cea)
new_lt13(vyy3000, vyy400, ty_Bool) → new_lt8(vyy3000, vyy400)
new_esEs17([], [], cb) → True
new_esEs17(:(vyy400, vyy401), [], cb) → False
new_esEs17([], :(vyy410, vyy411), cb) → False
new_esEs16(Float(vyy400, vyy401), Float(vyy410, vyy411)) → new_esEs13(new_sr(vyy400, vyy410), new_sr(vyy401, vyy411))
new_fmToList(vyy41, bh, ca) → new_foldFM2(vyy41, bh, ca)
new_compare16(vyy3000, vyy400, hh, baa, bab) → new_compare29(vyy3000, vyy400, new_esEs5(vyy3000, vyy400, hh, baa, bab), hh, baa, bab)
new_esEs28(vyy401, vyy411, ty_Ordering) → new_esEs20(vyy401, vyy411)
new_ltEs18(vyy3002, vyy402, ty_Integer) → new_ltEs15(vyy3002, vyy402)
new_esEs24(vyy40, vyy41, app(app(ty_@2, gc), gd)) → new_esEs8(vyy40, vyy41, gc, gd)
new_esEs7(Left(vyy400), Left(vyy410), ty_Double, gb) → new_esEs21(vyy400, vyy410)
new_ltEs18(vyy3002, vyy402, ty_Ordering) → new_ltEs8(vyy3002, vyy402)
new_esEs24(vyy40, vyy41, app(ty_Maybe, fh)) → new_esEs6(vyy40, vyy41, fh)
new_esEs7(Left(vyy400), Left(vyy410), ty_Char, gb) → new_esEs19(vyy400, vyy410)
new_esEs29(vyy400, vyy410, ty_Bool) → new_esEs14(vyy400, vyy410)
new_compare110(vyy3000, vyy400, False, hh, baa, bab) → GT
new_esEs7(Right(vyy400), Right(vyy410), ga, ty_Double) → new_esEs21(vyy400, vyy410)
new_lt13(vyy3000, vyy400, app(ty_Maybe, bb)) → new_lt10(vyy3000, vyy400, bb)
new_esEs25(vyy402, vyy412, app(app(ty_Either, bbb), bbc)) → new_esEs7(vyy402, vyy412, bbb, bbc)
new_esEs7(Left(vyy400), Left(vyy410), ty_Float, gb) → new_esEs16(vyy400, vyy410)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs24(vyy40, vyy41, app(ty_Ratio, be)) → new_esEs9(vyy40, vyy41, be)
new_primCompAux0(vyy71, EQ) → vyy71
new_ltEs13(Left(vyy3000), Left(vyy400), ty_Char, cef) → new_ltEs14(vyy3000, vyy400)
new_compare212(vyy3000, vyy400, False, bf, bg) → new_compare13(vyy3000, vyy400, new_ltEs13(vyy3000, vyy400, bf, bg), bf, bg)
new_compare15(vyy3000, vyy400, app(ty_Maybe, hb)) → new_compare18(vyy3000, vyy400, hb)
new_lt8(vyy3000, vyy400) → new_esEs15(new_compare6(vyy3000, vyy400))
new_foldFM_LE0(vyy26, vyy40, EmptyFM, h, ba) → vyy26
new_esEs22(@0, @0) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_esEs18(vyy400, vyy410, ty_Float) → new_esEs16(vyy400, vyy410)
new_ltEs13(Right(vyy3000), Right(vyy400), cfh, app(ty_Maybe, cge)) → new_ltEs5(vyy3000, vyy400, cge)
new_primCmpInt(Neg(Succ(vyy30000)), Pos(vyy400)) → LT
new_lt12(vyy3001, vyy401, ty_Int) → new_lt5(vyy3001, vyy401)
The set Q consists of the following terms:
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs18(x0, x1, ty_Char)
new_esEs18(x0, x1, ty_Char)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_esEs17([], :(x0, x1), x2)
new_esEs28(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, ty_Integer)
new_esEs7(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs13(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_fmToList(x0, x1, x2)
new_ltEs19(x0, x1, app(ty_[], x2))
new_esEs7(Left(x0), Left(x1), ty_Ordering, x2)
new_compare15(x0, x1, ty_Int)
new_compare6(x0, x1)
new_compare25(x0, x1, False)
new_compare15(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs18(x0, x1, ty_Ordering)
new_esEs7(Right(x0), Right(x1), x2, ty_Int)
new_compare11(x0, x1, False, x2, x3)
new_esEs25(x0, x1, app(ty_[], x2))
new_esEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs5(Just(x0), Just(x1), ty_@0)
new_esEs29(x0, x1, app(ty_[], x2))
new_lt16(x0, x1)
new_primEqNat0(Succ(x0), Succ(x1))
new_ltEs13(Right(x0), Right(x1), x2, ty_@0)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs7(Right(x0), Right(x1), x2, ty_Double)
new_pePe(False, x0, x1, x2, x3)
new_esEs28(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs26(x0, x1, ty_Ordering)
new_ltEs8(EQ, EQ)
new_ltEs5(Just(x0), Just(x1), app(ty_Ratio, x2))
new_ltEs7(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs13(x0, x1)
new_esEs27(x0, x1, ty_Char)
new_ltEs13(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_compare15(x0, x1, ty_Double)
new_foldFM_LE10(x0, x1, x2, x3, x4, x5, EmptyFM, True, x6, x7)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs7(Right(x0), Right(x1), x2, ty_@0)
new_ltEs5(Just(x0), Just(x1), ty_Ordering)
new_esEs27(x0, x1, ty_Float)
new_ltEs5(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_primMulNat0(Zero, Succ(x0))
new_esEs29(x0, x1, ty_Ordering)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_primCmpNat0(Zero, Succ(x0))
new_primCmpNat0(Succ(x0), Zero)
new_esEs28(x0, x1, ty_Integer)
new_ltEs13(Left(x0), Left(x1), ty_Int, x2)
new_compare5(x0, x1, x2, x3)
new_ltEs5(Just(x0), Just(x1), ty_Double)
new_compare19(Double(x0, x1), Double(x2, x3))
new_compare8(x0, x1)
new_lt19(x0, x1)
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare212(x0, x1, True, x2, x3)
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs5(Just(x0), Just(x1), ty_Int)
new_esEs7(Left(x0), Left(x1), ty_Integer, x2)
new_ltEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, ty_Double)
new_ltEs14(x0, x1)
new_asAs(False, x0)
new_ltEs5(Nothing, Just(x0), x1)
new_ltEs13(Right(x0), Right(x1), x2, app(ty_[], x3))
new_lt12(x0, x1, ty_Double)
new_esEs7(Right(x0), Right(x1), x2, ty_Integer)
new_foldFM_LE10(x0, x1, x2, x3, x4, x5, x6, False, x7, x8)
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_sr(x0, x1)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs18(x0, x1, ty_Ordering)
new_lt13(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs18(x0, x1, app(app(ty_Either, x2), x3))
new_esEs26(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_ltEs13(Right(x0), Right(x1), x2, ty_Bool)
new_lt12(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, ty_Bool)
new_esEs10(x0, x1, ty_Integer)
new_esEs28(x0, x1, ty_Char)
new_ltEs19(x0, x1, ty_Ordering)
new_esEs14(True, True)
new_ltEs5(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs5(Just(x0), Just(x1), ty_Char)
new_ltEs18(x0, x1, app(ty_Ratio, x2))
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(@0, @0)
new_lt20(x0, x1, ty_@0)
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_esEs29(x0, x1, ty_Char)
new_compare15(x0, x1, ty_Bool)
new_lt20(x0, x1, ty_Float)
new_primEqNat0(Zero, Zero)
new_esEs6(Just(x0), Just(x1), app(ty_[], x2))
new_esEs7(Right(x0), Right(x1), x2, ty_Float)
new_primCmpNat0(Succ(x0), Succ(x1))
new_esEs7(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs15(LT)
new_ltEs18(x0, x1, app(ty_[], x2))
new_ltEs13(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_ltEs13(Left(x0), Left(x1), ty_Integer, x2)
new_esEs29(x0, x1, ty_Int)
new_ltEs4(True, True)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_esEs24(x0, x1, ty_Bool)
new_lt12(x0, x1, ty_Float)
new_esEs27(x0, x1, ty_@0)
new_esEs26(x0, x1, app(ty_[], x2))
new_esEs7(Left(x0), Left(x1), ty_Char, x2)
new_ltEs13(Left(x0), Left(x1), ty_Char, x2)
new_esEs26(x0, x1, ty_Integer)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_lt13(x0, x1, app(app(ty_Either, x2), x3))
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt13(x0, x1, app(ty_[], x2))
new_foldFM_LE20(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs19(Char(x0), Char(x1))
new_primPlusNat1(Zero, Succ(x0))
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_primMulNat0(Zero, Zero)
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primMulInt(Pos(x0), Pos(x1))
new_lt9(x0, x1, x2)
new_esEs18(x0, x1, ty_@0)
new_esEs24(x0, x1, ty_@0)
new_esEs7(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_compare13(x0, x1, True, x2, x3)
new_lt12(x0, x1, ty_@0)
new_lt12(x0, x1, app(ty_[], x2))
new_esEs7(Left(x0), Left(x1), ty_Float, x2)
new_foldFM_LE0(x0, x1, EmptyFM, x2, x3)
new_esEs27(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs18(x0, x1, app(app(ty_Either, x2), x3))
new_esEs25(x0, x1, ty_Bool)
new_compare15(x0, x1, app(ty_Ratio, x2))
new_compare12(x0, x1, False)
new_esEs10(x0, x1, ty_Int)
new_lt20(x0, x1, ty_Int)
new_esEs25(x0, x1, ty_Integer)
new_ltEs18(x0, x1, ty_Integer)
new_lt13(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs5(Nothing, Nothing, x0)
new_esEs16(Float(x0, x1), Float(x2, x3))
new_primPlusNat1(Succ(x0), Zero)
new_ltEs18(x0, x1, ty_Int)
new_compare29(x0, x1, False, x2, x3, x4)
new_esEs17([], [], x0)
new_esEs7(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_pePe(True, x0, x1, x2, x3)
new_esEs24(x0, x1, ty_Integer)
new_primMulNat0(Succ(x0), Succ(x1))
new_eltsFM_LE0(x0, x1, x2, x3, x4)
new_esEs28(x0, x1, ty_Bool)
new_sizeFM(EmptyFM, x0, x1)
new_ltEs16(x0, x1)
new_esEs20(EQ, GT)
new_esEs20(GT, EQ)
new_ltEs13(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs18(x0, x1, app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_esEs6(Just(x0), Just(x1), app(ty_Maybe, x2))
new_ltEs4(False, False)
new_compare(:(x0, x1), :(x2, x3), x4)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs24(x0, x1, ty_Ordering)
new_esEs18(x0, x1, ty_Double)
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs26(x0, x1, ty_Char)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_esEs27(x0, x1, ty_Int)
new_ltEs19(x0, x1, ty_Integer)
new_compare24(x0, x1, False, x2, x3)
new_esEs20(LT, EQ)
new_esEs20(EQ, LT)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_compare14(Char(x0), Char(x1))
new_esEs27(x0, x1, ty_Double)
new_ltEs19(x0, x1, ty_Int)
new_esEs6(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, ty_Double)
new_primPlusNat0(Succ(x0), x1)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_ltEs5(Just(x0), Just(x1), ty_Integer)
new_lt12(x0, x1, ty_Char)
new_primPlusNat1(Zero, Zero)
new_not0
new_esEs29(x0, x1, ty_@0)
new_compare15(x0, x1, ty_@0)
new_compare16(x0, x1, x2, x3, x4)
new_primMulNat0(Succ(x0), Zero)
new_esEs7(Right(x0), Left(x1), x2, x3)
new_esEs7(Left(x0), Right(x1), x2, x3)
new_compare9(Float(x0, x1), Float(x2, x3))
new_esEs18(x0, x1, ty_Bool)
new_ltEs18(x0, x1, app(ty_Maybe, x2))
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_ltEs5(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_lt10(x0, x1, x2)
new_ltEs13(Left(x0), Left(x1), ty_Float, x2)
new_esEs6(Just(x0), Just(x1), ty_@0)
new_esEs6(Just(x0), Just(x1), app(app(ty_FiniteMap, x2), x3))
new_esEs7(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs13(Left(x0), Left(x1), app(ty_[], x2), x3)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs8(@2(x0, x1), @2(x2, x3), x4, x5)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_esEs7(Left(x0), Left(x1), ty_Double, x2)
new_esEs26(x0, x1, ty_@0)
new_ltEs18(x0, x1, ty_Bool)
new_ltEs18(x0, x1, ty_Double)
new_esEs7(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs26(x0, x1, ty_Float)
new_compare211(x0, x1, True, x2)
new_lt5(x0, x1)
new_ltEs18(x0, x1, ty_Float)
new_ltEs13(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_compare28(x0, x1, x2, x3)
new_ltEs13(Right(x0), Left(x1), x2, x3)
new_ltEs13(Left(x0), Right(x1), x2, x3)
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_ltEs18(x0, x1, app(app(ty_@2, x2), x3))
new_not(GT)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_compare111(x0, x1, True)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_ltEs6(x0, x1, x2)
new_lt14(x0, x1, x2)
new_ltEs10(x0, x1)
new_foldFM2(EmptyFM, x0, x1)
new_compare210(x0, x1, False)
new_foldFM_LE3(x0, x1, x2, x3, x4, x5)
new_esEs18(x0, x1, app(ty_Ratio, x2))
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
new_esEs6(Nothing, Just(x0), x1)
new_ltEs13(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_esEs11(x0, x1, ty_Integer)
new_lt4(x0, x1)
new_compare15(x0, x1, app(app(ty_Either, x2), x3))
new_lt12(x0, x1, ty_Int)
new_esEs7(Left(x0), Left(x1), ty_Bool, x2)
new_esEs6(Just(x0), Just(x1), ty_Float)
new_lt12(x0, x1, app(ty_Ratio, x2))
new_lt7(x0, x1)
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_lt12(x0, x1, ty_Integer)
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs8(EQ, LT)
new_ltEs8(LT, EQ)
new_ltEs17(@2(x0, x1), @2(x2, x3), x4, x5)
new_ltEs18(x0, x1, ty_@0)
new_foldFM_LE10(x0, x1, x2, x3, x4, x5, Branch(x6, x7, x8, x9, x10), True, x11, x12)
new_esEs26(x0, x1, ty_Int)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs29(x0, x1, ty_Float)
new_ltEs13(Right(x0), Right(x1), x2, ty_Char)
new_primPlusNat1(Succ(x0), Succ(x1))
new_compare25(x0, x1, True)
new_ltEs19(x0, x1, ty_Bool)
new_compare12(x0, x1, True)
new_primEqInt(Neg(Zero), Neg(Zero))
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs28(x0, x1, ty_Ordering)
new_primCompAux0(x0, EQ)
new_esEs20(LT, LT)
new_esEs26(x0, x1, ty_Bool)
new_compare15(x0, x1, ty_Ordering)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_ltEs13(Right(x0), Right(x1), x2, ty_Float)
new_compare27(:%(x0, x1), :%(x2, x3), ty_Int)
new_ltEs13(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_esEs14(False, True)
new_esEs14(True, False)
new_compare110(x0, x1, True, x2, x3, x4)
new_lt12(x0, x1, app(app(ty_@2, x2), x3))
new_lt13(x0, x1, ty_Double)
new_esEs24(x0, x1, ty_Int)
new_esEs28(x0, x1, ty_Double)
new_ltEs11(x0, x1)
new_primCompAux0(x0, LT)
new_primCompAux1(x0, x1, x2, x3)
new_lt15(x0, x1)
new_lt17(x0, x1)
new_esEs20(GT, LT)
new_esEs20(LT, GT)
new_esEs24(x0, x1, app(ty_[], x2))
new_compare29(x0, x1, True, x2, x3, x4)
new_esEs7(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_lt12(x0, x1, ty_Bool)
new_esEs7(Left(x0), Left(x1), app(app(ty_FiniteMap, x2), x3), x4)
new_esEs17(:(x0, x1), [], x2)
new_compare13(x0, x1, False, x2, x3)
new_esEs18(x0, x1, ty_Integer)
new_ltEs13(Left(x0), Left(x1), ty_@0, x2)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_ltEs12(x0, x1, x2)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_esEs25(x0, x1, ty_Int)
new_esEs6(Just(x0), Just(x1), ty_Char)
new_ltEs13(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs7(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_lt8(x0, x1)
new_primEqNat0(Succ(x0), Zero)
new_esEs25(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_primEqNat0(Zero, Succ(x0))
new_lt13(x0, x1, app(ty_Maybe, x2))
new_esEs24(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_lt12(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, x2, x3)
new_lt20(x0, x1, app(ty_[], x2))
new_ltEs5(Just(x0), Nothing, x1)
new_esEs7(Left(x0), Left(x1), ty_Int, x2)
new_primPlusNat0(Zero, x0)
new_compare24(x0, x1, True, x2, x3)
new_lt13(x0, x1, ty_Float)
new_ltEs8(LT, LT)
new_esEs20(GT, GT)
new_ltEs13(Right(x0), Right(x1), x2, ty_Int)
new_primCmpNat0(Zero, Zero)
new_esEs18(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
new_esEs6(Just(x0), Just(x1), ty_Integer)
new_esEs7(Left(x0), Left(x1), ty_@0, x2)
new_lt20(x0, x1, ty_Ordering)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_ltEs4(False, True)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_ltEs4(True, False)
new_compare17(x0, x1)
new_esEs15(GT)
new_ltEs8(GT, GT)
new_esEs25(x0, x1, ty_Float)
new_ltEs5(Just(x0), Just(x1), ty_Float)
new_primCompAux0(x0, GT)
new_esEs7(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs28(x0, x1, ty_Int)
new_compare15(x0, x1, app(app(ty_@2, x2), x3))
new_esEs29(x0, x1, ty_Integer)
new_compare15(x0, x1, ty_Integer)
new_esEs7(Right(x0), Right(x1), x2, ty_Char)
new_lt13(x0, x1, app(ty_Ratio, x2))
new_esEs28(x0, x1, ty_@0)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs6(Just(x0), Just(x1), ty_Ordering)
new_lt13(x0, x1, ty_Ordering)
new_ltEs13(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_esEs27(x0, x1, ty_Ordering)
new_compare10(x0, x1, True, x2)
new_ltEs19(x0, x1, ty_@0)
new_esEs24(x0, x1, ty_Char)
new_compare10(x0, x1, False, x2)
new_esEs29(x0, x1, ty_Bool)
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs18(x0, x1, ty_Int)
new_esEs17(:(x0, x1), :(x2, x3), x4)
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_esEs24(x0, x1, ty_Double)
new_esEs12(Integer(x0), Integer(x1))
new_compare18(x0, x1, x2)
new_compare210(x0, x1, True)
new_ltEs8(LT, GT)
new_ltEs8(GT, LT)
new_ltEs13(Left(x0), Left(x1), ty_Bool, x2)
new_esEs25(x0, x1, ty_Double)
new_lt6(x0, x1, x2, x3)
new_esEs6(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, ty_Integer)
new_compare110(x0, x1, False, x2, x3, x4)
new_esEs7(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs6(Nothing, Nothing, x0)
new_esEs27(x0, x1, app(ty_[], x2))
new_esEs6(Just(x0), Nothing, x1)
new_esEs5(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_ltEs13(Right(x0), Right(x1), x2, ty_Double)
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_foldFM_LE0(x0, x1, Branch(x2, x3, x4, x5, x6), x7, x8)
new_esEs18(x0, x1, ty_Float)
new_not(EQ)
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_lt11(x0, x1, x2, x3, x4)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_esEs7(Right(x0), Right(x1), x2, ty_Ordering)
new_lt13(x0, x1, ty_@0)
new_esEs6(Just(x0), Just(x1), ty_Double)
new_esEs29(x0, x1, ty_Double)
new_ltEs19(x0, x1, ty_Char)
new_lt12(x0, x1, ty_Ordering)
new_lt18(x0, x1, x2, x3)
new_lt13(x0, x1, ty_Integer)
new_compare([], [], x0)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_compare212(x0, x1, False, x2, x3)
new_lt13(x0, x1, ty_Char)
new_esEs20(EQ, EQ)
new_esEs9(:%(x0, x1), :%(x2, x3), x4)
new_esEs11(x0, x1, ty_Int)
new_ltEs13(Right(x0), Right(x1), x2, ty_Ordering)
new_compare15(x0, x1, app(ty_Maybe, x2))
new_esEs15(EQ)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_ltEs15(x0, x1)
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_FiniteMap, x3), x4))
new_compare7(Integer(x0), Integer(x1))
new_compare([], :(x0, x1), x2)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_compare27(:%(x0, x1), :%(x2, x3), ty_Integer)
new_ltEs13(Left(x0), Left(x1), ty_Ordering, x2)
new_compare111(x0, x1, False)
new_esEs25(x0, x1, ty_Ordering)
new_ltEs8(GT, EQ)
new_ltEs8(EQ, GT)
new_esEs21(Double(x0, x1), Double(x2, x3))
new_ltEs13(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_ltEs5(Just(x0), Just(x1), ty_Bool)
new_esEs29(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_ltEs13(Left(x0), Left(x1), ty_Double, x2)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sr0(Integer(x0), Integer(x1))
new_compare11(x0, x1, True, x2, x3)
new_esEs6(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs6(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs25(x0, x1, ty_@0)
new_compare26(@0, @0)
new_ltEs9(x0, x1)
new_ltEs19(x0, x1, ty_Float)
new_esEs28(x0, x1, ty_Float)
new_ltEs13(Right(x0), Right(x1), x2, ty_Integer)
new_esEs14(False, False)
new_ltEs5(Just(x0), Just(x1), app(ty_Maybe, x2))
new_primEqInt(Pos(Zero), Pos(Zero))
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Just(x0), Just(x1), ty_Bool)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_lt12(x0, x1, app(app(ty_Either, x2), x3))
new_compare(:(x0, x1), [], x2)
new_lt13(x0, x1, ty_Bool)
new_compare211(x0, x1, False, x2)
new_lt20(x0, x1, ty_Char)
new_esEs18(x0, x1, app(ty_[], x2))
new_asAs(True, x0)
new_esEs24(x0, x1, ty_Float)
new_compare15(x0, x1, ty_Char)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs7(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs6(Just(x0), Just(x1), ty_Int)
new_compare15(x0, x1, ty_Float)
new_lt20(x0, x1, ty_Double)
new_compare15(x0, x1, app(ty_[], x2))
new_ltEs5(Just(x0), Just(x1), app(ty_[], x2))
new_not(LT)
new_esEs25(x0, x1, ty_Char)
new_lt13(x0, x1, ty_Int)
new_esEs27(x0, x1, ty_Bool)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_esEs18(x0, x1, app(ty_Maybe, x2))
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_foldFM_LE(vyy26, vyy40, Branch(vyy3430, vyy3431, vyy3432, vyy3433, vyy3434), h, ba) → new_foldFM_LE1(vyy26, vyy40, vyy3430, vyy3431, vyy3432, vyy3433, vyy3434, new_ltEs5(vyy3430, Just(vyy40), ba), h, ba)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 3 > 4, 3 > 5, 3 > 6, 3 > 7, 4 >= 9, 5 >= 10
- new_foldFM_LE1(vyy26, vyy40, vyy340, vyy341, vyy342, Branch(vyy3430, vyy3431, vyy3432, vyy3433, vyy3434), vyy344, False, h, ba) → new_foldFM_LE1(vyy26, vyy40, vyy3430, vyy3431, vyy3432, vyy3433, vyy3434, new_ltEs5(vyy3430, Just(vyy40), ba), h, ba)
The graph contains the following edges 1 >= 1, 2 >= 2, 6 > 3, 6 > 4, 6 > 5, 6 > 6, 6 > 7, 9 >= 9, 10 >= 10
- new_foldFM_LE2(vyy340, vyy341, vyy30, vyy40, vyy3440, vyy3441, vyy3442, vyy3443, vyy3444, h, ba) → new_foldFM_LE1(new_eltsFM_LE0(vyy340, vyy341, vyy30, h, ba), vyy40, vyy3440, vyy3441, vyy3442, vyy3443, vyy3444, new_ltEs5(vyy3440, Just(vyy40), ba), h, ba)
The graph contains the following edges 4 >= 2, 5 >= 3, 6 >= 4, 7 >= 5, 8 >= 6, 9 >= 7, 10 >= 9, 11 >= 10
- new_foldFM_LE1(vyy26, vyy40, vyy340, vyy341, vyy342, vyy343, Branch(vyy3440, vyy3441, vyy3442, vyy3443, vyy3444), True, h, ba) → new_foldFM_LE2(vyy340, vyy341, new_foldFM_LE0(vyy26, vyy40, vyy343, h, ba), vyy40, vyy3440, vyy3441, vyy3442, vyy3443, vyy3444, h, ba)
The graph contains the following edges 3 >= 1, 4 >= 2, 2 >= 4, 7 > 5, 7 > 6, 7 > 7, 7 > 8, 7 > 9, 9 >= 10, 10 >= 11
- new_foldFM_LE1(vyy26, vyy40, vyy340, vyy341, vyy342, vyy343, EmptyFM, True, h, ba) → new_foldFM_LE(vyy26, vyy40, vyy343, h, ba)
The graph contains the following edges 1 >= 1, 2 >= 2, 6 >= 3, 9 >= 4, 10 >= 5
- new_foldFM_LE1(vyy26, vyy40, vyy340, vyy341, vyy342, vyy343, Branch(vyy3440, vyy3441, vyy3442, vyy3443, vyy3444), True, h, ba) → new_foldFM_LE(vyy26, vyy40, vyy343, h, ba)
The graph contains the following edges 1 >= 1, 2 >= 2, 6 >= 3, 9 >= 4, 10 >= 5
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ UsableRulesProof
Q DP problem:
The TRS P consists of the following rules:
new_foldFM_LE11(vyy24, vyy340, vyy341, vyy342, vyy343, Branch(vyy3440, vyy3441, vyy3442, vyy3443, vyy3444), True, h, ba) → new_foldFM_LE4(vyy24, vyy343, h, ba)
new_foldFM_LE4(vyy24, Branch(vyy3430, vyy3431, vyy3432, vyy3433, vyy3434), h, ba) → new_foldFM_LE11(vyy24, vyy3430, vyy3431, vyy3432, vyy3433, vyy3434, new_ltEs5(vyy3430, Nothing, ba), h, ba)
new_foldFM_LE11(vyy24, vyy340, vyy341, vyy342, Branch(vyy3430, vyy3431, vyy3432, vyy3433, vyy3434), vyy344, False, h, ba) → new_foldFM_LE11(vyy24, vyy3430, vyy3431, vyy3432, vyy3433, vyy3434, new_ltEs5(vyy3430, Nothing, ba), h, ba)
new_foldFM_LE11(vyy24, vyy340, vyy341, vyy342, vyy343, Branch(vyy3440, vyy3441, vyy3442, vyy3443, vyy3444), True, h, ba) → new_foldFM_LE21(vyy340, vyy341, new_foldFM_LE5(vyy24, vyy343, h, ba), vyy3440, vyy3441, vyy3442, vyy3443, vyy3444, h, ba)
new_foldFM_LE21(vyy340, vyy341, vyy28, vyy3440, vyy3441, vyy3442, vyy3443, vyy3444, h, ba) → new_foldFM_LE11(new_eltsFM_LE0(vyy340, vyy341, vyy28, h, ba), vyy3440, vyy3441, vyy3442, vyy3443, vyy3444, new_ltEs5(vyy3440, Nothing, ba), h, ba)
new_foldFM_LE11(vyy24, vyy340, vyy341, vyy342, vyy343, EmptyFM, True, h, ba) → new_foldFM_LE4(vyy24, vyy343, h, ba)
The TRS R consists of the following rules:
new_esEs28(vyy401, vyy411, ty_Double) → new_esEs21(vyy401, vyy411)
new_esEs10(vyy401, vyy411, ty_Integer) → new_esEs12(vyy401, vyy411)
new_esEs25(vyy402, vyy412, ty_Char) → new_esEs19(vyy402, vyy412)
new_lt19(vyy3000, vyy400) → new_esEs15(new_compare14(vyy3000, vyy400))
new_esEs7(Left(vyy400), Left(vyy410), app(app(ty_Either, dab), dac), gb) → new_esEs7(vyy400, vyy410, dab, dac)
new_lt12(vyy3001, vyy401, ty_@0) → new_lt17(vyy3001, vyy401)
new_compare15(vyy3000, vyy400, app(app(app(ty_@3, gg), gh), ha)) → new_compare16(vyy3000, vyy400, gg, gh, ha)
new_esEs27(vyy400, vyy410, ty_Char) → new_esEs19(vyy400, vyy410)
new_esEs25(vyy402, vyy412, ty_Integer) → new_esEs12(vyy402, vyy412)
new_esEs24(vyy40, vyy41, app(app(app(ty_@3, fd), ff), fg)) → new_esEs5(vyy40, vyy41, fd, ff, fg)
new_esEs6(Just(vyy400), Just(vyy410), ty_Int) → new_esEs13(vyy400, vyy410)
new_esEs7(Right(vyy400), Right(vyy410), ga, app(ty_[], dag)) → new_esEs17(vyy400, vyy410, dag)
new_compare([], :(vyy400, vyy401), ge) → LT
new_esEs18(vyy400, vyy410, app(ty_[], cc)) → new_esEs17(vyy400, vyy410, cc)
new_ltEs10(vyy300, vyy40) → new_not(new_compare19(vyy300, vyy40))
new_esEs15(GT) → False
new_esEs24(vyy40, vyy41, ty_Double) → new_esEs21(vyy40, vyy41)
new_ltEs19(vyy3001, vyy401, ty_Integer) → new_ltEs15(vyy3001, vyy401)
new_compare15(vyy3000, vyy400, ty_Integer) → new_compare7(vyy3000, vyy400)
new_ltEs18(vyy3002, vyy402, app(ty_Ratio, cah)) → new_ltEs12(vyy3002, vyy402, cah)
new_esEs6(Just(vyy400), Just(vyy410), app(app(ty_FiniteMap, cdf), cdg)) → new_esEs23(vyy400, vyy410, cdf, cdg)
new_ltEs19(vyy3001, vyy401, app(ty_Ratio, ddb)) → new_ltEs12(vyy3001, vyy401, ddb)
new_esEs27(vyy400, vyy410, ty_Double) → new_esEs21(vyy400, vyy410)
new_ltEs13(Right(vyy3000), Right(vyy400), cfh, app(app(app(ty_@3, cgb), cgc), cgd)) → new_ltEs7(vyy3000, vyy400, cgb, cgc, cgd)
new_primMulNat0(Zero, Zero) → Zero
new_compare9(Float(vyy3000, vyy3001), Float(vyy400, vyy401)) → new_compare8(new_sr(vyy3000, vyy400), new_sr(vyy3001, vyy401))
new_esEs7(Left(vyy400), Left(vyy410), app(app(app(ty_@3, chd), che), chf), gb) → new_esEs5(vyy400, vyy410, chd, che, chf)
new_compare(:(vyy3000, vyy3001), [], ge) → GT
new_esEs29(vyy400, vyy410, ty_Float) → new_esEs16(vyy400, vyy410)
new_compare15(vyy3000, vyy400, ty_Char) → new_compare14(vyy3000, vyy400)
new_esEs18(vyy400, vyy410, ty_@0) → new_esEs22(vyy400, vyy410)
new_compare15(vyy3000, vyy400, ty_Double) → new_compare19(vyy3000, vyy400)
new_esEs20(EQ, EQ) → True
new_esEs26(vyy401, vyy411, ty_@0) → new_esEs22(vyy401, vyy411)
new_compare27(:%(vyy3000, vyy3001), :%(vyy400, vyy401), ty_Integer) → new_compare7(new_sr0(vyy3000, vyy401), new_sr0(vyy400, vyy3001))
new_lt20(vyy3000, vyy400, ty_Integer) → new_lt4(vyy3000, vyy400)
new_ltEs7(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), bhh, caa, cab) → new_pePe(new_lt13(vyy3000, vyy400, bhh), vyy3000, vyy400, new_pePe(new_lt12(vyy3001, vyy401, caa), vyy3001, vyy401, new_ltEs18(vyy3002, vyy402, cab), caa), bhh)
new_esEs7(Left(vyy400), Left(vyy410), ty_Bool, gb) → new_esEs14(vyy400, vyy410)
new_esEs20(EQ, GT) → False
new_esEs20(GT, EQ) → False
new_esEs27(vyy400, vyy410, ty_Integer) → new_esEs12(vyy400, vyy410)
new_not(GT) → False
new_lt5(vyy3000, vyy400) → new_esEs15(new_compare8(vyy3000, vyy400))
new_esEs27(vyy400, vyy410, app(app(ty_@2, bee), bef)) → new_esEs8(vyy400, vyy410, bee, bef)
new_foldFM_LE12(vyy24, vyy340, vyy341, vyy342, vyy343, EmptyFM, True, h, ba) → new_foldFM_LE30(vyy340, vyy341, new_foldFM_LE5(vyy24, vyy343, h, ba), h, ba)
new_esEs6(Just(vyy400), Just(vyy410), ty_Ordering) → new_esEs20(vyy400, vyy410)
new_ltEs5(Just(vyy3000), Just(vyy400), app(app(ty_Either, eg), eh)) → new_ltEs13(vyy3000, vyy400, eg, eh)
new_esEs27(vyy400, vyy410, app(ty_Ratio, bed)) → new_esEs9(vyy400, vyy410, bed)
new_lt12(vyy3001, vyy401, ty_Char) → new_lt19(vyy3001, vyy401)
new_esEs7(Right(vyy400), Right(vyy410), ga, app(app(app(ty_@3, dah), dba), dbb)) → new_esEs5(vyy400, vyy410, dah, dba, dbb)
new_esEs27(vyy400, vyy410, ty_Ordering) → new_esEs20(vyy400, vyy410)
new_ltEs15(vyy300, vyy40) → new_not(new_compare7(vyy300, vyy40))
new_ltEs13(Left(vyy3000), Left(vyy400), app(app(ty_@2, cff), cfg), cef) → new_ltEs17(vyy3000, vyy400, cff, cfg)
new_ltEs18(vyy3002, vyy402, ty_Char) → new_ltEs14(vyy3002, vyy402)
new_foldFM_LE12(vyy24, vyy340, vyy341, vyy342, vyy343, Branch(vyy3440, vyy3441, vyy3442, vyy3443, vyy3444), True, h, ba) → new_foldFM_LE22(vyy340, vyy341, new_foldFM_LE5(vyy24, vyy343, h, ba), vyy3440, vyy3441, vyy3442, vyy3443, vyy3444, h, ba)
new_ltEs19(vyy3001, vyy401, ty_Bool) → new_ltEs4(vyy3001, vyy401)
new_esEs29(vyy400, vyy410, app(app(ty_FiniteMap, bha), bhb)) → new_esEs23(vyy400, vyy410, bha, bhb)
new_esEs27(vyy400, vyy410, app(ty_Maybe, bdg)) → new_esEs6(vyy400, vyy410, bdg)
new_ltEs4(False, True) → True
new_ltEs8(EQ, EQ) → True
new_esEs7(Right(vyy400), Right(vyy410), ga, app(ty_Ratio, dbh)) → new_esEs9(vyy400, vyy410, dbh)
new_lt13(vyy3000, vyy400, app(app(ty_Either, bf), bg)) → new_lt18(vyy3000, vyy400, bf, bg)
new_lt13(vyy3000, vyy400, ty_Integer) → new_lt4(vyy3000, vyy400)
new_esEs12(Integer(vyy400), Integer(vyy410)) → new_primEqInt(vyy400, vyy410)
new_ltEs9(vyy300, vyy40) → new_not(new_compare8(vyy300, vyy40))
new_esEs28(vyy401, vyy411, ty_Integer) → new_esEs12(vyy401, vyy411)
new_lt20(vyy3000, vyy400, ty_Ordering) → new_lt15(vyy3000, vyy400)
new_esEs28(vyy401, vyy411, app(app(app(ty_@3, bfa), bfb), bfc)) → new_esEs5(vyy401, vyy411, bfa, bfb, bfc)
new_esEs18(vyy400, vyy410, ty_Char) → new_esEs19(vyy400, vyy410)
new_ltEs13(Left(vyy3000), Left(vyy400), ty_Bool, cef) → new_ltEs4(vyy3000, vyy400)
new_foldFM0(vyy410, vyy411, vyy85, EmptyFM, bh, ca) → :(@2(vyy410, vyy411), vyy85)
new_lt12(vyy3001, vyy401, app(ty_Maybe, cca)) → new_lt10(vyy3001, vyy401, cca)
new_ltEs19(vyy3001, vyy401, ty_Float) → new_ltEs16(vyy3001, vyy401)
new_esEs7(Right(vyy400), Right(vyy410), ga, app(ty_Maybe, dbc)) → new_esEs6(vyy400, vyy410, dbc)
new_ltEs4(True, True) → True
new_ltEs18(vyy3002, vyy402, app(app(app(ty_@3, cad), cae), caf)) → new_ltEs7(vyy3002, vyy402, cad, cae, caf)
new_esEs26(vyy401, vyy411, app(app(ty_@2, bda), bdb)) → new_esEs8(vyy401, vyy411, bda, bdb)
new_esEs7(Left(vyy400), Right(vyy410), ga, gb) → False
new_esEs7(Right(vyy400), Left(vyy410), ga, gb) → False
new_pePe(False, vyy40, vyy41, vyy57, fc) → new_asAs(new_esEs24(vyy40, vyy41, fc), vyy57)
new_esEs17(:(vyy400, vyy401), :(vyy410, vyy411), cb) → new_asAs(new_esEs18(vyy400, vyy410, cb), new_esEs17(vyy401, vyy411, cb))
new_lt18(vyy3000, vyy400, bf, bg) → new_esEs15(new_compare28(vyy3000, vyy400, bf, bg))
new_compare6(vyy3000, vyy400) → new_compare25(vyy3000, vyy400, new_esEs14(vyy3000, vyy400))
new_esEs20(LT, LT) → True
new_esEs5(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), fd, ff, fg) → new_asAs(new_esEs27(vyy400, vyy410, fd), new_asAs(new_esEs26(vyy401, vyy411, ff), new_esEs25(vyy402, vyy412, fg)))
new_foldFM_LE5(vyy24, Branch(vyy3430, vyy3431, vyy3432, vyy3433, vyy3434), h, ba) → new_foldFM_LE12(vyy24, vyy3430, vyy3431, vyy3432, vyy3433, vyy3434, new_ltEs5(vyy3430, Nothing, ba), h, ba)
new_lt16(vyy3000, vyy400) → new_esEs15(new_compare19(vyy3000, vyy400))
new_esEs25(vyy402, vyy412, ty_Bool) → new_esEs14(vyy402, vyy412)
new_esEs27(vyy400, vyy410, app(app(ty_Either, beb), bec)) → new_esEs7(vyy400, vyy410, beb, bec)
new_esEs11(vyy400, vyy410, ty_Int) → new_esEs13(vyy400, vyy410)
new_esEs18(vyy400, vyy410, app(app(ty_@2, df), dg)) → new_esEs8(vyy400, vyy410, df, dg)
new_lt13(vyy3000, vyy400, ty_Int) → new_lt5(vyy3000, vyy400)
new_esEs25(vyy402, vyy412, ty_Double) → new_esEs21(vyy402, vyy412)
new_ltEs13(Left(vyy3000), Left(vyy400), ty_Int, cef) → new_ltEs9(vyy3000, vyy400)
new_esEs27(vyy400, vyy410, app(ty_[], bdc)) → new_esEs17(vyy400, vyy410, bdc)
new_ltEs8(EQ, GT) → True
new_compare13(vyy3000, vyy400, False, bf, bg) → GT
new_esEs7(Left(vyy400), Left(vyy410), ty_Int, gb) → new_esEs13(vyy400, vyy410)
new_ltEs8(GT, GT) → True
new_compare5(vyy3000, vyy400, bc, bd) → new_compare24(vyy3000, vyy400, new_esEs8(vyy3000, vyy400, bc, bd), bc, bd)
new_esEs18(vyy400, vyy410, ty_Int) → new_esEs13(vyy400, vyy410)
new_compare111(vyy3000, vyy400, False) → GT
new_compare111(vyy3000, vyy400, True) → LT
new_compare10(vyy3000, vyy400, True, bb) → LT
new_esEs26(vyy401, vyy411, ty_Char) → new_esEs19(vyy401, vyy411)
new_ltEs18(vyy3002, vyy402, ty_@0) → new_ltEs11(vyy3002, vyy402)
new_esEs6(Just(vyy400), Just(vyy410), app(app(app(ty_@3, cdb), cdc), cdd)) → new_esEs5(vyy400, vyy410, cdb, cdc, cdd)
new_primCmpNat0(Zero, Succ(vyy4000)) → LT
new_compare18(vyy3000, vyy400, bb) → new_compare211(vyy3000, vyy400, new_esEs6(vyy3000, vyy400, bb), bb)
new_ltEs5(Just(vyy3000), Just(vyy400), app(ty_Ratio, ef)) → new_ltEs12(vyy3000, vyy400, ef)
new_esEs15(LT) → True
new_ltEs6(vyy300, vyy40, ge) → new_not(new_compare(vyy300, vyy40, ge))
new_ltEs13(Left(vyy3000), Left(vyy400), ty_Double, cef) → new_ltEs10(vyy3000, vyy400)
new_esEs7(Right(vyy400), Right(vyy410), ga, ty_Bool) → new_esEs14(vyy400, vyy410)
new_esEs26(vyy401, vyy411, ty_Double) → new_esEs21(vyy401, vyy411)
new_esEs26(vyy401, vyy411, ty_Ordering) → new_esEs20(vyy401, vyy411)
new_lt20(vyy3000, vyy400, ty_Char) → new_lt19(vyy3000, vyy400)
new_ltEs8(LT, EQ) → True
new_lt20(vyy3000, vyy400, ty_Int) → new_lt5(vyy3000, vyy400)
new_lt20(vyy3000, vyy400, app(ty_Ratio, ded)) → new_lt9(vyy3000, vyy400, ded)
new_ltEs18(vyy3002, vyy402, app(ty_Maybe, cag)) → new_ltEs5(vyy3002, vyy402, cag)
new_esEs18(vyy400, vyy410, app(ty_Ratio, de)) → new_esEs9(vyy400, vyy410, de)
new_compare10(vyy3000, vyy400, False, bb) → GT
new_esEs24(vyy40, vyy41, app(app(ty_Either, ga), gb)) → new_esEs7(vyy40, vyy41, ga, gb)
new_esEs15(EQ) → False
new_esEs7(Right(vyy400), Right(vyy410), ga, ty_Float) → new_esEs16(vyy400, vyy410)
new_primEqNat0(Zero, Zero) → True
new_compare27(:%(vyy3000, vyy3001), :%(vyy400, vyy401), ty_Int) → new_compare8(new_sr(vyy3000, vyy401), new_sr(vyy400, vyy3001))
new_esEs29(vyy400, vyy410, app(ty_Maybe, bgh)) → new_esEs6(vyy400, vyy410, bgh)
new_esEs26(vyy401, vyy411, app(ty_Maybe, bcc)) → new_esEs6(vyy401, vyy411, bcc)
new_compare210(vyy3000, vyy400, False) → new_compare111(vyy3000, vyy400, new_ltEs8(vyy3000, vyy400))
new_foldFM_LE5(vyy24, EmptyFM, h, ba) → vyy24
new_compare29(vyy3000, vyy400, False, hh, baa, bab) → new_compare110(vyy3000, vyy400, new_ltEs7(vyy3000, vyy400, hh, baa, bab), hh, baa, bab)
new_esEs29(vyy400, vyy410, ty_Ordering) → new_esEs20(vyy400, vyy410)
new_ltEs8(GT, EQ) → False
new_lt13(vyy3000, vyy400, ty_Float) → new_lt7(vyy3000, vyy400)
new_ltEs8(EQ, LT) → False
new_esEs29(vyy400, vyy410, ty_Int) → new_esEs13(vyy400, vyy410)
new_compare(:(vyy3000, vyy3001), :(vyy400, vyy401), ge) → new_primCompAux1(vyy3000, vyy400, new_compare(vyy3001, vyy401, ge), ge)
new_ltEs17(@2(vyy3000, vyy3001), @2(vyy400, vyy401), dcc, dcd) → new_pePe(new_lt20(vyy3000, vyy400, dcc), vyy3000, vyy400, new_ltEs19(vyy3001, vyy401, dcd), dcc)
new_ltEs13(Left(vyy3000), Left(vyy400), ty_Float, cef) → new_ltEs16(vyy3000, vyy400)
new_sr(vyy3001, vyy401) → new_primMulInt(vyy3001, vyy401)
new_esEs25(vyy402, vyy412, ty_Int) → new_esEs13(vyy402, vyy412)
new_esEs18(vyy400, vyy410, app(app(app(ty_@3, cd), ce), cf)) → new_esEs5(vyy400, vyy410, cd, ce, cf)
new_compare15(vyy3000, vyy400, app(app(ty_@2, hf), hg)) → new_compare5(vyy3000, vyy400, hf, hg)
new_ltEs5(Just(vyy3000), Just(vyy400), ty_Double) → new_ltEs10(vyy3000, vyy400)
new_lt7(vyy3000, vyy400) → new_esEs15(new_compare9(vyy3000, vyy400))
new_lt12(vyy3001, vyy401, ty_Float) → new_lt7(vyy3001, vyy401)
new_esEs24(vyy40, vyy41, ty_Char) → new_esEs19(vyy40, vyy41)
new_esEs13(vyy40, vyy41) → new_primEqInt(vyy40, vyy41)
new_primPlusNat0(Succ(vyy860), vyy40100) → Succ(Succ(new_primPlusNat1(vyy860, vyy40100)))
new_esEs25(vyy402, vyy412, ty_Float) → new_esEs16(vyy402, vyy412)
new_esEs7(Right(vyy400), Right(vyy410), ga, app(app(ty_Either, dbf), dbg)) → new_esEs7(vyy400, vyy410, dbf, dbg)
new_ltEs19(vyy3001, vyy401, ty_Double) → new_ltEs10(vyy3001, vyy401)
new_esEs20(LT, EQ) → False
new_esEs20(EQ, LT) → False
new_ltEs11(vyy300, vyy40) → new_not(new_compare26(vyy300, vyy40))
new_compare29(vyy3000, vyy400, True, hh, baa, bab) → EQ
new_esEs26(vyy401, vyy411, ty_Integer) → new_esEs12(vyy401, vyy411)
new_lt11(vyy3000, vyy400, hh, baa, bab) → new_esEs15(new_compare16(vyy3000, vyy400, hh, baa, bab))
new_esEs28(vyy401, vyy411, ty_Float) → new_esEs16(vyy401, vyy411)
new_compare211(vyy3000, vyy400, True, bb) → EQ
new_compare25(vyy3000, vyy400, True) → EQ
new_primEqInt(Neg(Succ(vyy4000)), Neg(Succ(vyy4100))) → new_primEqNat0(vyy4000, vyy4100)
new_ltEs19(vyy3001, vyy401, app(app(ty_@2, dde), ddf)) → new_ltEs17(vyy3001, vyy401, dde, ddf)
new_esEs7(Right(vyy400), Right(vyy410), ga, ty_Int) → new_esEs13(vyy400, vyy410)
new_ltEs19(vyy3001, vyy401, ty_Ordering) → new_ltEs8(vyy3001, vyy401)
new_esEs6(Just(vyy400), Just(vyy410), ty_@0) → new_esEs22(vyy400, vyy410)
new_esEs7(Left(vyy400), Left(vyy410), ty_@0, gb) → new_esEs22(vyy400, vyy410)
new_esEs21(Double(vyy400, vyy401), Double(vyy410, vyy411)) → new_esEs13(new_sr(vyy400, vyy410), new_sr(vyy401, vyy411))
new_compare13(vyy3000, vyy400, True, bf, bg) → LT
new_esEs25(vyy402, vyy412, app(app(ty_@2, bbe), bbf)) → new_esEs8(vyy402, vyy412, bbe, bbf)
new_compare25(vyy3000, vyy400, False) → new_compare12(vyy3000, vyy400, new_ltEs4(vyy3000, vyy400))
new_ltEs5(Just(vyy3000), Nothing, dh) → False
new_esEs24(vyy40, vyy41, ty_Bool) → new_esEs14(vyy40, vyy41)
new_primPlusNat1(Succ(vyy8600), Zero) → Succ(vyy8600)
new_primPlusNat1(Zero, Succ(vyy401000)) → Succ(vyy401000)
new_esEs7(Left(vyy400), Left(vyy410), app(app(ty_FiniteMap, chh), daa), gb) → new_esEs23(vyy400, vyy410, chh, daa)
new_ltEs13(Right(vyy3000), Right(vyy400), cfh, ty_Integer) → new_ltEs15(vyy3000, vyy400)
new_esEs7(Left(vyy400), Left(vyy410), app(ty_[], chc), gb) → new_esEs17(vyy400, vyy410, chc)
new_ltEs13(Right(vyy3000), Right(vyy400), cfh, ty_Int) → new_ltEs9(vyy3000, vyy400)
new_foldFM_LE12(vyy24, vyy340, vyy341, vyy342, vyy343, vyy344, False, h, ba) → new_foldFM_LE5(vyy24, vyy343, h, ba)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs6(Just(vyy400), Just(vyy410), ty_Integer) → new_esEs12(vyy400, vyy410)
new_ltEs5(Just(vyy3000), Just(vyy400), ty_Int) → new_ltEs9(vyy3000, vyy400)
new_lt13(vyy3000, vyy400, ty_@0) → new_lt17(vyy3000, vyy400)
new_ltEs13(Right(vyy3000), Right(vyy400), cfh, ty_Char) → new_ltEs14(vyy3000, vyy400)
new_esEs29(vyy400, vyy410, ty_Double) → new_esEs21(vyy400, vyy410)
new_compare15(vyy3000, vyy400, ty_Int) → new_compare8(vyy3000, vyy400)
new_compare8(vyy300, vyy40) → new_primCmpInt(vyy300, vyy40)
new_primEqInt(Neg(Succ(vyy4000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(vyy4100))) → False
new_primCompAux0(vyy71, GT) → GT
new_lt12(vyy3001, vyy401, ty_Bool) → new_lt8(vyy3001, vyy401)
new_lt13(vyy3000, vyy400, ty_Ordering) → new_lt15(vyy3000, vyy400)
new_compare24(vyy3000, vyy400, True, bc, bd) → EQ
new_esEs28(vyy401, vyy411, ty_Int) → new_esEs13(vyy401, vyy411)
new_compare([], [], ge) → EQ
new_ltEs13(Right(vyy3000), Right(vyy400), cfh, ty_Double) → new_ltEs10(vyy3000, vyy400)
new_esEs8(@2(vyy400, vyy401), @2(vyy410, vyy411), gc, gd) → new_asAs(new_esEs29(vyy400, vyy410, gc), new_esEs28(vyy401, vyy411, gd))
new_foldFM0(vyy410, vyy411, vyy85, Branch(vyy4130, vyy4131, vyy4132, vyy4133, vyy4134), bh, ca) → new_foldFM0(vyy4130, vyy4131, new_foldFM0(vyy410, vyy411, vyy85, vyy4134, bh, ca), vyy4133, bh, ca)
new_esEs26(vyy401, vyy411, app(app(ty_Either, bcf), bcg)) → new_esEs7(vyy401, vyy411, bcf, bcg)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_esEs23(vyy40, vyy41, bh, ca) → new_asAs(new_esEs13(new_sizeFM(vyy40, bh, ca), new_sizeFM(vyy41, bh, ca)), new_esEs17(new_fmToList(vyy40, bh, ca), new_fmToList(vyy41, bh, ca), app(app(ty_@2, bh), ca)))
new_compare14(Char(vyy3000), Char(vyy400)) → new_primCmpNat0(vyy3000, vyy400)
new_foldFM_LE30(vyy340, vyy341, vyy27, h, ba) → new_eltsFM_LE0(vyy340, vyy341, vyy27, h, ba)
new_esEs7(Right(vyy400), Right(vyy410), ga, ty_@0) → new_esEs22(vyy400, vyy410)
new_ltEs5(Just(vyy3000), Just(vyy400), ty_Char) → new_ltEs14(vyy3000, vyy400)
new_primCmpNat0(Succ(vyy30000), Succ(vyy4000)) → new_primCmpNat0(vyy30000, vyy4000)
new_ltEs19(vyy3001, vyy401, ty_@0) → new_ltEs11(vyy3001, vyy401)
new_sizeFM(EmptyFM, bh, ca) → Pos(Zero)
new_ltEs5(Just(vyy3000), Just(vyy400), app(ty_[], ea)) → new_ltEs6(vyy3000, vyy400, ea)
new_ltEs13(Left(vyy3000), Left(vyy400), app(ty_[], cee), cef) → new_ltEs6(vyy3000, vyy400, cee)
new_esEs6(Nothing, Nothing, fh) → True
new_ltEs18(vyy3002, vyy402, app(app(ty_Either, cba), cbb)) → new_ltEs13(vyy3002, vyy402, cba, cbb)
new_lt12(vyy3001, vyy401, ty_Ordering) → new_lt15(vyy3001, vyy401)
new_ltEs13(Right(vyy3000), Right(vyy400), cfh, ty_Ordering) → new_ltEs8(vyy3000, vyy400)
new_primEqInt(Pos(Succ(vyy4000)), Pos(Succ(vyy4100))) → new_primEqNat0(vyy4000, vyy4100)
new_compare15(vyy3000, vyy400, app(ty_[], gf)) → new_compare(vyy3000, vyy400, gf)
new_ltEs19(vyy3001, vyy401, app(app(app(ty_@3, dcf), dcg), dch)) → new_ltEs7(vyy3001, vyy401, dcf, dcg, dch)
new_compare15(vyy3000, vyy400, ty_Float) → new_compare9(vyy3000, vyy400)
new_lt13(vyy3000, vyy400, ty_Char) → new_lt19(vyy3000, vyy400)
new_esEs14(True, False) → False
new_esEs14(False, True) → False
new_ltEs16(vyy300, vyy40) → new_not(new_compare9(vyy300, vyy40))
new_compare15(vyy3000, vyy400, ty_Bool) → new_compare6(vyy3000, vyy400)
new_esEs26(vyy401, vyy411, ty_Int) → new_esEs13(vyy401, vyy411)
new_esEs6(Just(vyy400), Nothing, fh) → False
new_esEs6(Nothing, Just(vyy410), fh) → False
new_ltEs18(vyy3002, vyy402, ty_Bool) → new_ltEs4(vyy3002, vyy402)
new_primEqNat0(Succ(vyy4000), Succ(vyy4100)) → new_primEqNat0(vyy4000, vyy4100)
new_ltEs19(vyy3001, vyy401, app(app(ty_Either, ddc), ddd)) → new_ltEs13(vyy3001, vyy401, ddc, ddd)
new_ltEs5(Just(vyy3000), Just(vyy400), ty_Bool) → new_ltEs4(vyy3000, vyy400)
new_foldFM_LE22(vyy340, vyy341, vyy28, vyy3440, vyy3441, vyy3442, vyy3443, vyy3444, h, ba) → new_foldFM_LE12(new_eltsFM_LE0(vyy340, vyy341, vyy28, h, ba), vyy3440, vyy3441, vyy3442, vyy3443, vyy3444, new_ltEs5(vyy3440, Nothing, ba), h, ba)
new_esEs7(Right(vyy400), Right(vyy410), ga, ty_Ordering) → new_esEs20(vyy400, vyy410)
new_compare28(vyy3000, vyy400, bf, bg) → new_compare212(vyy3000, vyy400, new_esEs7(vyy3000, vyy400, bf, bg), bf, bg)
new_primCompAux1(vyy3000, vyy400, vyy67, ge) → new_primCompAux0(vyy67, new_compare15(vyy3000, vyy400, ge))
new_primCmpInt(Neg(Succ(vyy30000)), Neg(vyy400)) → new_primCmpNat0(vyy400, Succ(vyy30000))
new_esEs27(vyy400, vyy410, app(app(app(ty_@3, bdd), bde), bdf)) → new_esEs5(vyy400, vyy410, bdd, bde, bdf)
new_lt4(vyy3000, vyy400) → new_esEs15(new_compare7(vyy3000, vyy400))
new_primEqInt(Pos(Succ(vyy4000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(vyy4100))) → False
new_ltEs5(Just(vyy3000), Just(vyy400), ty_@0) → new_ltEs11(vyy3000, vyy400)
new_ltEs5(Nothing, Just(vyy400), dh) → True
new_esEs24(vyy40, vyy41, ty_@0) → new_esEs22(vyy40, vyy41)
new_esEs25(vyy402, vyy412, ty_Ordering) → new_esEs20(vyy402, vyy412)
new_esEs20(GT, GT) → True
new_lt9(vyy3000, vyy400, beg) → new_esEs15(new_compare27(vyy3000, vyy400, beg))
new_lt15(vyy3000, vyy400) → new_esEs15(new_compare17(vyy3000, vyy400))
new_ltEs13(Left(vyy3000), Left(vyy400), app(app(app(ty_@3, ceg), ceh), cfa), cef) → new_ltEs7(vyy3000, vyy400, ceg, ceh, cfa)
new_primCmpNat0(Zero, Zero) → EQ
new_esEs7(Right(vyy400), Right(vyy410), ga, app(app(ty_FiniteMap, dbd), dbe)) → new_esEs23(vyy400, vyy410, dbd, dbe)
new_primCmpNat0(Succ(vyy30000), Zero) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(vyy4000))) → LT
new_compare11(vyy3000, vyy400, True, bc, bd) → LT
new_esEs27(vyy400, vyy410, app(app(ty_FiniteMap, bdh), bea)) → new_esEs23(vyy400, vyy410, bdh, bea)
new_sr0(Integer(vyy4000), Integer(vyy30010)) → Integer(new_primMulInt(vyy4000, vyy30010))
new_primPlusNat1(Succ(vyy8600), Succ(vyy401000)) → Succ(Succ(new_primPlusNat1(vyy8600, vyy401000)))
new_primEqInt(Pos(Succ(vyy4000)), Neg(vyy410)) → False
new_primEqInt(Neg(Succ(vyy4000)), Pos(vyy410)) → False
new_esEs29(vyy400, vyy410, ty_Char) → new_esEs19(vyy400, vyy410)
new_lt12(vyy3001, vyy401, app(ty_Ratio, ccb)) → new_lt9(vyy3001, vyy401, ccb)
new_foldFM2(EmptyFM, bh, ca) → []
new_ltEs13(Right(vyy3000), Right(vyy400), cfh, ty_@0) → new_ltEs11(vyy3000, vyy400)
new_esEs28(vyy401, vyy411, app(ty_Maybe, bfd)) → new_esEs6(vyy401, vyy411, bfd)
new_compare15(vyy3000, vyy400, app(app(ty_Either, hd), he)) → new_compare28(vyy3000, vyy400, hd, he)
new_ltEs12(vyy300, vyy40, cch) → new_not(new_compare27(vyy300, vyy40, cch))
new_primEqInt(Pos(Zero), Neg(Succ(vyy4100))) → False
new_primEqInt(Neg(Zero), Pos(Succ(vyy4100))) → False
new_esEs26(vyy401, vyy411, app(ty_[], bbg)) → new_esEs17(vyy401, vyy411, bbg)
new_ltEs14(vyy300, vyy40) → new_not(new_compare14(vyy300, vyy40))
new_primCmpInt(Pos(Zero), Pos(Succ(vyy4000))) → new_primCmpNat0(Zero, Succ(vyy4000))
new_esEs28(vyy401, vyy411, app(app(ty_Either, bfg), bfh)) → new_esEs7(vyy401, vyy411, bfg, bfh)
new_ltEs13(Right(vyy3000), Right(vyy400), cfh, app(ty_Ratio, cgf)) → new_ltEs12(vyy3000, vyy400, cgf)
new_ltEs18(vyy3002, vyy402, ty_Int) → new_ltEs9(vyy3002, vyy402)
new_esEs27(vyy400, vyy410, ty_Int) → new_esEs13(vyy400, vyy410)
new_esEs28(vyy401, vyy411, app(app(ty_FiniteMap, bfe), bff)) → new_esEs23(vyy401, vyy411, bfe, bff)
new_compare12(vyy3000, vyy400, False) → GT
new_eltsFM_LE0(vyy340, vyy341, vyy27, h, ba) → :(vyy341, vyy27)
new_esEs6(Just(vyy400), Just(vyy410), app(app(ty_@2, cec), ced)) → new_esEs8(vyy400, vyy410, cec, ced)
new_esEs7(Right(vyy400), Right(vyy410), ga, ty_Char) → new_esEs19(vyy400, vyy410)
new_ltEs8(GT, LT) → False
new_esEs26(vyy401, vyy411, ty_Float) → new_esEs16(vyy401, vyy411)
new_primCompAux0(vyy71, LT) → LT
new_esEs18(vyy400, vyy410, ty_Ordering) → new_esEs20(vyy400, vyy410)
new_lt20(vyy3000, vyy400, ty_Bool) → new_lt8(vyy3000, vyy400)
new_esEs24(vyy40, vyy41, ty_Int) → new_esEs13(vyy40, vyy41)
new_esEs7(Left(vyy400), Left(vyy410), app(ty_Maybe, chg), gb) → new_esEs6(vyy400, vyy410, chg)
new_primPlusNat0(Zero, vyy40100) → Succ(vyy40100)
new_esEs27(vyy400, vyy410, ty_@0) → new_esEs22(vyy400, vyy410)
new_primCmpInt(Pos(Succ(vyy30000)), Pos(vyy400)) → new_primCmpNat0(Succ(vyy30000), vyy400)
new_esEs29(vyy400, vyy410, ty_Integer) → new_esEs12(vyy400, vyy410)
new_lt13(vyy3000, vyy400, app(app(app(ty_@3, hh), baa), bab)) → new_lt11(vyy3000, vyy400, hh, baa, bab)
new_esEs29(vyy400, vyy410, app(ty_[], bgd)) → new_esEs17(vyy400, vyy410, bgd)
new_esEs7(Left(vyy400), Left(vyy410), ty_Integer, gb) → new_esEs12(vyy400, vyy410)
new_esEs29(vyy400, vyy410, app(app(ty_@2, bhf), bhg)) → new_esEs8(vyy400, vyy410, bhf, bhg)
new_esEs26(vyy401, vyy411, ty_Bool) → new_esEs14(vyy401, vyy411)
new_lt13(vyy3000, vyy400, app(ty_[], ccg)) → new_lt14(vyy3000, vyy400, ccg)
new_compare15(vyy3000, vyy400, ty_@0) → new_compare26(vyy3000, vyy400)
new_compare212(vyy3000, vyy400, True, bf, bg) → EQ
new_not0 → True
new_esEs24(vyy40, vyy41, ty_Integer) → new_esEs12(vyy40, vyy41)
new_esEs24(vyy40, vyy41, app(ty_[], cb)) → new_esEs17(vyy40, vyy41, cb)
new_ltEs5(Just(vyy3000), Just(vyy400), ty_Integer) → new_ltEs15(vyy3000, vyy400)
new_compare15(vyy3000, vyy400, app(ty_Ratio, hc)) → new_compare27(vyy3000, vyy400, hc)
new_esEs7(Left(vyy400), Left(vyy410), app(ty_Ratio, dad), gb) → new_esEs9(vyy400, vyy410, dad)
new_lt13(vyy3000, vyy400, app(ty_Ratio, beg)) → new_lt9(vyy3000, vyy400, beg)
new_compare11(vyy3000, vyy400, False, bc, bd) → GT
new_primCmpInt(Pos(Succ(vyy30000)), Neg(vyy400)) → GT
new_ltEs19(vyy3001, vyy401, ty_Int) → new_ltEs9(vyy3001, vyy401)
new_esEs18(vyy400, vyy410, app(app(ty_Either, dc), dd)) → new_esEs7(vyy400, vyy410, dc, dd)
new_ltEs13(Right(vyy3000), Right(vyy400), cfh, ty_Float) → new_ltEs16(vyy3000, vyy400)
new_ltEs13(Right(vyy3000), Right(vyy400), cfh, app(app(ty_@2, cha), chb)) → new_ltEs17(vyy3000, vyy400, cha, chb)
new_primMulInt(Pos(vyy30010), Pos(vyy4010)) → Pos(new_primMulNat0(vyy30010, vyy4010))
new_esEs7(Left(vyy400), Left(vyy410), ty_Ordering, gb) → new_esEs20(vyy400, vyy410)
new_esEs24(vyy40, vyy41, app(app(ty_FiniteMap, bh), ca)) → new_esEs23(vyy40, vyy41, bh, ca)
new_ltEs13(Left(vyy3000), Left(vyy400), ty_Integer, cef) → new_ltEs15(vyy3000, vyy400)
new_primMulInt(Neg(vyy30010), Neg(vyy4010)) → Pos(new_primMulNat0(vyy30010, vyy4010))
new_esEs20(LT, GT) → False
new_esEs20(GT, LT) → False
new_esEs28(vyy401, vyy411, app(ty_Ratio, bga)) → new_esEs9(vyy401, vyy411, bga)
new_compare19(Double(vyy3000, vyy3001), Double(vyy400, vyy401)) → new_compare8(new_sr(vyy3000, vyy400), new_sr(vyy3001, vyy401))
new_lt20(vyy3000, vyy400, app(app(app(ty_@3, ddh), dea), deb)) → new_lt11(vyy3000, vyy400, ddh, dea, deb)
new_primEqNat0(Succ(vyy4000), Zero) → False
new_primEqNat0(Zero, Succ(vyy4100)) → False
new_ltEs5(Nothing, Nothing, dh) → True
new_lt20(vyy3000, vyy400, app(app(ty_Either, dee), def)) → new_lt18(vyy3000, vyy400, dee, def)
new_lt12(vyy3001, vyy401, ty_Double) → new_lt16(vyy3001, vyy401)
new_esEs25(vyy402, vyy412, app(ty_Maybe, bag)) → new_esEs6(vyy402, vyy412, bag)
new_lt20(vyy3000, vyy400, ty_@0) → new_lt17(vyy3000, vyy400)
new_lt20(vyy3000, vyy400, app(ty_Maybe, dec)) → new_lt10(vyy3000, vyy400, dec)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_lt6(vyy3000, vyy400, bc, bd) → new_esEs15(new_compare5(vyy3000, vyy400, bc, bd))
new_esEs7(Right(vyy400), Right(vyy410), ga, app(app(ty_@2, dca), dcb)) → new_esEs8(vyy400, vyy410, dca, dcb)
new_compare210(vyy3000, vyy400, True) → EQ
new_lt12(vyy3001, vyy401, app(app(ty_@2, cce), ccf)) → new_lt6(vyy3001, vyy401, cce, ccf)
new_sizeFM(Branch(vyy410, vyy411, vyy412, vyy413, vyy414), bh, ca) → vyy412
new_ltEs18(vyy3002, vyy402, app(app(ty_@2, cbc), cbd)) → new_ltEs17(vyy3002, vyy402, cbc, cbd)
new_ltEs4(True, False) → False
new_esEs18(vyy400, vyy410, app(app(ty_FiniteMap, da), db)) → new_esEs23(vyy400, vyy410, da, db)
new_esEs6(Just(vyy400), Just(vyy410), ty_Double) → new_esEs21(vyy400, vyy410)
new_pePe(True, vyy40, vyy41, vyy57, fc) → True
new_foldFM2(Branch(vyy410, vyy411, vyy412, vyy413, vyy414), bh, ca) → new_foldFM0(vyy410, vyy411, new_foldFM2(vyy414, bh, ca), vyy413, bh, ca)
new_esEs29(vyy400, vyy410, app(app(app(ty_@3, bge), bgf), bgg)) → new_esEs5(vyy400, vyy410, bge, bgf, bgg)
new_ltEs19(vyy3001, vyy401, app(ty_Maybe, dda)) → new_ltEs5(vyy3001, vyy401, dda)
new_lt12(vyy3001, vyy401, app(ty_[], cbe)) → new_lt14(vyy3001, vyy401, cbe)
new_esEs26(vyy401, vyy411, app(app(ty_FiniteMap, bcd), bce)) → new_esEs23(vyy401, vyy411, bcd, bce)
new_ltEs13(Right(vyy3000), Right(vyy400), cfh, ty_Bool) → new_ltEs4(vyy3000, vyy400)
new_primCmpInt(Neg(Zero), Neg(Succ(vyy4000))) → new_primCmpNat0(Succ(vyy4000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(vyy4000))) → GT
new_ltEs13(Left(vyy3000), Left(vyy400), app(ty_Maybe, cfb), cef) → new_ltEs5(vyy3000, vyy400, cfb)
new_compare24(vyy3000, vyy400, False, bc, bd) → new_compare11(vyy3000, vyy400, new_ltEs17(vyy3000, vyy400, bc, bd), bc, bd)
new_ltEs13(Left(vyy3000), Left(vyy400), ty_@0, cef) → new_ltEs11(vyy3000, vyy400)
new_ltEs5(Just(vyy3000), Just(vyy400), ty_Ordering) → new_ltEs8(vyy3000, vyy400)
new_esEs6(Just(vyy400), Just(vyy410), ty_Bool) → new_esEs14(vyy400, vyy410)
new_lt20(vyy3000, vyy400, app(app(ty_@2, deg), deh)) → new_lt6(vyy3000, vyy400, deg, deh)
new_ltEs13(Left(vyy3000), Left(vyy400), app(ty_Ratio, cfc), cef) → new_ltEs12(vyy3000, vyy400, cfc)
new_ltEs19(vyy3001, vyy401, ty_Char) → new_ltEs14(vyy3001, vyy401)
new_esEs6(Just(vyy400), Just(vyy410), app(ty_[], cda)) → new_esEs17(vyy400, vyy410, cda)
new_lt12(vyy3001, vyy401, ty_Integer) → new_lt4(vyy3001, vyy401)
new_lt20(vyy3000, vyy400, ty_Float) → new_lt7(vyy3000, vyy400)
new_lt12(vyy3001, vyy401, app(app(app(ty_@3, cbf), cbg), cbh)) → new_lt11(vyy3001, vyy401, cbf, cbg, cbh)
new_ltEs13(Left(vyy3000), Left(vyy400), app(app(ty_Either, cfd), cfe), cef) → new_ltEs13(vyy3000, vyy400, cfd, cfe)
new_esEs18(vyy400, vyy410, ty_Integer) → new_esEs12(vyy400, vyy410)
new_compare15(vyy3000, vyy400, ty_Ordering) → new_compare17(vyy3000, vyy400)
new_lt20(vyy3000, vyy400, ty_Double) → new_lt16(vyy3000, vyy400)
new_ltEs18(vyy3002, vyy402, app(ty_[], cac)) → new_ltEs6(vyy3002, vyy402, cac)
new_esEs19(Char(vyy400), Char(vyy410)) → new_primEqNat0(vyy400, vyy410)
new_ltEs13(Right(vyy3000), Right(vyy400), cfh, app(app(ty_Either, cgg), cgh)) → new_ltEs13(vyy3000, vyy400, cgg, cgh)
new_esEs29(vyy400, vyy410, app(ty_Ratio, bhe)) → new_esEs9(vyy400, vyy410, bhe)
new_esEs18(vyy400, vyy410, app(ty_Maybe, cg)) → new_esEs6(vyy400, vyy410, cg)
new_ltEs13(Left(vyy3000), Left(vyy400), ty_Ordering, cef) → new_ltEs8(vyy3000, vyy400)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_ltEs18(vyy3002, vyy402, ty_Double) → new_ltEs10(vyy3002, vyy402)
new_esEs25(vyy402, vyy412, app(app(ty_FiniteMap, bah), bba)) → new_esEs23(vyy402, vyy412, bah, bba)
new_asAs(False, vyy66) → False
new_ltEs13(Right(vyy3000), Right(vyy400), cfh, app(ty_[], cga)) → new_ltEs6(vyy3000, vyy400, cga)
new_esEs25(vyy402, vyy412, app(ty_Ratio, bbd)) → new_esEs9(vyy402, vyy412, bbd)
new_esEs29(vyy400, vyy410, ty_@0) → new_esEs22(vyy400, vyy410)
new_primMulInt(Pos(vyy30010), Neg(vyy4010)) → Neg(new_primMulNat0(vyy30010, vyy4010))
new_primMulInt(Neg(vyy30010), Pos(vyy4010)) → Neg(new_primMulNat0(vyy30010, vyy4010))
new_esEs7(Left(vyy400), Left(vyy410), app(app(ty_@2, dae), daf), gb) → new_esEs8(vyy400, vyy410, dae, daf)
new_ltEs13(Left(vyy3000), Right(vyy400), cfh, cef) → True
new_primMulNat0(Zero, Succ(vyy40100)) → Zero
new_primMulNat0(Succ(vyy300100), Zero) → Zero
new_esEs6(Just(vyy400), Just(vyy410), app(ty_Ratio, ceb)) → new_esEs9(vyy400, vyy410, ceb)
new_esEs6(Just(vyy400), Just(vyy410), app(ty_Maybe, cde)) → new_esEs6(vyy400, vyy410, cde)
new_lt20(vyy3000, vyy400, app(ty_[], ddg)) → new_lt14(vyy3000, vyy400, ddg)
new_lt10(vyy3000, vyy400, bb) → new_esEs15(new_compare18(vyy3000, vyy400, bb))
new_esEs28(vyy401, vyy411, ty_Bool) → new_esEs14(vyy401, vyy411)
new_compare12(vyy3000, vyy400, True) → LT
new_esEs18(vyy400, vyy410, ty_Double) → new_esEs21(vyy400, vyy410)
new_ltEs5(Just(vyy3000), Just(vyy400), app(ty_Maybe, ee)) → new_ltEs5(vyy3000, vyy400, ee)
new_esEs24(vyy40, vyy41, ty_Ordering) → new_esEs20(vyy40, vyy41)
new_not(EQ) → new_not0
new_esEs26(vyy401, vyy411, app(ty_Ratio, bch)) → new_esEs9(vyy401, vyy411, bch)
new_compare110(vyy3000, vyy400, True, hh, baa, bab) → LT
new_lt13(vyy3000, vyy400, app(app(ty_@2, bc), bd)) → new_lt6(vyy3000, vyy400, bc, bd)
new_esEs25(vyy402, vyy412, app(ty_[], bac)) → new_esEs17(vyy402, vyy412, bac)
new_ltEs4(False, False) → True
new_esEs14(True, True) → True
new_esEs27(vyy400, vyy410, ty_Bool) → new_esEs14(vyy400, vyy410)
new_ltEs13(Right(vyy3000), Left(vyy400), cfh, cef) → False
new_esEs28(vyy401, vyy411, ty_Char) → new_esEs19(vyy401, vyy411)
new_ltEs8(LT, GT) → True
new_esEs6(Just(vyy400), Just(vyy410), ty_Char) → new_esEs19(vyy400, vyy410)
new_esEs28(vyy401, vyy411, app(ty_[], beh)) → new_esEs17(vyy401, vyy411, beh)
new_ltEs5(Just(vyy3000), Just(vyy400), app(app(ty_@2, fa), fb)) → new_ltEs17(vyy3000, vyy400, fa, fb)
new_compare26(@0, @0) → EQ
new_esEs7(Right(vyy400), Right(vyy410), ga, ty_Integer) → new_esEs12(vyy400, vyy410)
new_esEs11(vyy400, vyy410, ty_Integer) → new_esEs12(vyy400, vyy410)
new_esEs9(:%(vyy400, vyy401), :%(vyy410, vyy411), be) → new_asAs(new_esEs11(vyy400, vyy410, be), new_esEs10(vyy401, vyy411, be))
new_ltEs5(Just(vyy3000), Just(vyy400), app(app(app(ty_@3, eb), ec), ed)) → new_ltEs7(vyy3000, vyy400, eb, ec, ed)
new_lt13(vyy3000, vyy400, ty_Double) → new_lt16(vyy3000, vyy400)
new_not(LT) → new_not0
new_ltEs18(vyy3002, vyy402, ty_Float) → new_ltEs16(vyy3002, vyy402)
new_compare7(Integer(vyy3000), Integer(vyy400)) → new_primCmpInt(vyy3000, vyy400)
new_esEs25(vyy402, vyy412, ty_@0) → new_esEs22(vyy402, vyy412)
new_esEs25(vyy402, vyy412, app(app(app(ty_@3, bad), bae), baf)) → new_esEs5(vyy402, vyy412, bad, bae, baf)
new_ltEs19(vyy3001, vyy401, app(ty_[], dce)) → new_ltEs6(vyy3001, vyy401, dce)
new_esEs6(Just(vyy400), Just(vyy410), ty_Float) → new_esEs16(vyy400, vyy410)
new_ltEs5(Just(vyy3000), Just(vyy400), ty_Float) → new_ltEs16(vyy3000, vyy400)
new_lt17(vyy3000, vyy400) → new_esEs15(new_compare26(vyy3000, vyy400))
new_esEs29(vyy400, vyy410, app(app(ty_Either, bhc), bhd)) → new_esEs7(vyy400, vyy410, bhc, bhd)
new_esEs14(False, False) → True
new_esEs10(vyy401, vyy411, ty_Int) → new_esEs13(vyy401, vyy411)
new_lt14(vyy3000, vyy400, ccg) → new_esEs15(new_compare(vyy3000, vyy400, ccg))
new_compare211(vyy3000, vyy400, False, bb) → new_compare10(vyy3000, vyy400, new_ltEs5(vyy3000, vyy400, bb), bb)
new_esEs18(vyy400, vyy410, ty_Bool) → new_esEs14(vyy400, vyy410)
new_ltEs8(LT, LT) → True
new_esEs28(vyy401, vyy411, app(app(ty_@2, bgb), bgc)) → new_esEs8(vyy401, vyy411, bgb, bgc)
new_primPlusNat1(Zero, Zero) → Zero
new_esEs28(vyy401, vyy411, ty_@0) → new_esEs22(vyy401, vyy411)
new_asAs(True, vyy66) → vyy66
new_compare17(vyy3000, vyy400) → new_compare210(vyy3000, vyy400, new_esEs20(vyy3000, vyy400))
new_esEs24(vyy40, vyy41, ty_Float) → new_esEs16(vyy40, vyy41)
new_primMulNat0(Succ(vyy300100), Succ(vyy40100)) → new_primPlusNat0(new_primMulNat0(vyy300100, Succ(vyy40100)), vyy40100)
new_esEs27(vyy400, vyy410, ty_Float) → new_esEs16(vyy400, vyy410)
new_esEs26(vyy401, vyy411, app(app(app(ty_@3, bbh), bca), bcb)) → new_esEs5(vyy401, vyy411, bbh, bca, bcb)
new_lt12(vyy3001, vyy401, app(app(ty_Either, ccc), ccd)) → new_lt18(vyy3001, vyy401, ccc, ccd)
new_esEs6(Just(vyy400), Just(vyy410), app(app(ty_Either, cdh), cea)) → new_esEs7(vyy400, vyy410, cdh, cea)
new_lt13(vyy3000, vyy400, ty_Bool) → new_lt8(vyy3000, vyy400)
new_esEs17([], [], cb) → True
new_esEs17(:(vyy400, vyy401), [], cb) → False
new_esEs17([], :(vyy410, vyy411), cb) → False
new_esEs16(Float(vyy400, vyy401), Float(vyy410, vyy411)) → new_esEs13(new_sr(vyy400, vyy410), new_sr(vyy401, vyy411))
new_fmToList(vyy41, bh, ca) → new_foldFM2(vyy41, bh, ca)
new_compare16(vyy3000, vyy400, hh, baa, bab) → new_compare29(vyy3000, vyy400, new_esEs5(vyy3000, vyy400, hh, baa, bab), hh, baa, bab)
new_esEs28(vyy401, vyy411, ty_Ordering) → new_esEs20(vyy401, vyy411)
new_ltEs18(vyy3002, vyy402, ty_Integer) → new_ltEs15(vyy3002, vyy402)
new_esEs24(vyy40, vyy41, app(app(ty_@2, gc), gd)) → new_esEs8(vyy40, vyy41, gc, gd)
new_esEs7(Left(vyy400), Left(vyy410), ty_Double, gb) → new_esEs21(vyy400, vyy410)
new_ltEs18(vyy3002, vyy402, ty_Ordering) → new_ltEs8(vyy3002, vyy402)
new_esEs24(vyy40, vyy41, app(ty_Maybe, fh)) → new_esEs6(vyy40, vyy41, fh)
new_esEs7(Left(vyy400), Left(vyy410), ty_Char, gb) → new_esEs19(vyy400, vyy410)
new_esEs29(vyy400, vyy410, ty_Bool) → new_esEs14(vyy400, vyy410)
new_compare110(vyy3000, vyy400, False, hh, baa, bab) → GT
new_esEs7(Right(vyy400), Right(vyy410), ga, ty_Double) → new_esEs21(vyy400, vyy410)
new_lt13(vyy3000, vyy400, app(ty_Maybe, bb)) → new_lt10(vyy3000, vyy400, bb)
new_esEs25(vyy402, vyy412, app(app(ty_Either, bbb), bbc)) → new_esEs7(vyy402, vyy412, bbb, bbc)
new_esEs7(Left(vyy400), Left(vyy410), ty_Float, gb) → new_esEs16(vyy400, vyy410)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs24(vyy40, vyy41, app(ty_Ratio, be)) → new_esEs9(vyy40, vyy41, be)
new_primCompAux0(vyy71, EQ) → vyy71
new_ltEs13(Left(vyy3000), Left(vyy400), ty_Char, cef) → new_ltEs14(vyy3000, vyy400)
new_compare212(vyy3000, vyy400, False, bf, bg) → new_compare13(vyy3000, vyy400, new_ltEs13(vyy3000, vyy400, bf, bg), bf, bg)
new_compare15(vyy3000, vyy400, app(ty_Maybe, hb)) → new_compare18(vyy3000, vyy400, hb)
new_lt8(vyy3000, vyy400) → new_esEs15(new_compare6(vyy3000, vyy400))
new_esEs22(@0, @0) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_esEs18(vyy400, vyy410, ty_Float) → new_esEs16(vyy400, vyy410)
new_ltEs13(Right(vyy3000), Right(vyy400), cfh, app(ty_Maybe, cge)) → new_ltEs5(vyy3000, vyy400, cge)
new_primCmpInt(Neg(Succ(vyy30000)), Pos(vyy400)) → LT
new_lt12(vyy3001, vyy401, ty_Int) → new_lt5(vyy3001, vyy401)
The set Q consists of the following terms:
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs18(x0, x1, ty_Char)
new_esEs18(x0, x1, ty_Char)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_esEs17([], :(x0, x1), x2)
new_esEs28(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, ty_Integer)
new_esEs7(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs13(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_fmToList(x0, x1, x2)
new_ltEs19(x0, x1, app(ty_[], x2))
new_esEs7(Left(x0), Left(x1), ty_Ordering, x2)
new_compare15(x0, x1, ty_Int)
new_compare6(x0, x1)
new_compare25(x0, x1, False)
new_compare15(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs18(x0, x1, ty_Ordering)
new_esEs7(Right(x0), Right(x1), x2, ty_Int)
new_compare11(x0, x1, False, x2, x3)
new_esEs25(x0, x1, app(ty_[], x2))
new_esEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs5(Just(x0), Just(x1), ty_@0)
new_esEs29(x0, x1, app(ty_[], x2))
new_lt16(x0, x1)
new_primEqNat0(Succ(x0), Succ(x1))
new_ltEs13(Right(x0), Right(x1), x2, ty_@0)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs7(Right(x0), Right(x1), x2, ty_Double)
new_pePe(False, x0, x1, x2, x3)
new_esEs28(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs26(x0, x1, ty_Ordering)
new_ltEs8(EQ, EQ)
new_ltEs5(Just(x0), Just(x1), app(ty_Ratio, x2))
new_ltEs7(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs13(x0, x1)
new_esEs27(x0, x1, ty_Char)
new_ltEs13(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_compare15(x0, x1, ty_Double)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs7(Right(x0), Right(x1), x2, ty_@0)
new_ltEs5(Just(x0), Just(x1), ty_Ordering)
new_esEs27(x0, x1, ty_Float)
new_ltEs5(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_primMulNat0(Zero, Succ(x0))
new_esEs29(x0, x1, ty_Ordering)
new_foldFM_LE22(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_primCmpNat0(Zero, Succ(x0))
new_primCmpNat0(Succ(x0), Zero)
new_esEs28(x0, x1, ty_Integer)
new_ltEs13(Left(x0), Left(x1), ty_Int, x2)
new_compare5(x0, x1, x2, x3)
new_ltEs5(Just(x0), Just(x1), ty_Double)
new_compare19(Double(x0, x1), Double(x2, x3))
new_compare8(x0, x1)
new_lt19(x0, x1)
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare212(x0, x1, True, x2, x3)
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs5(Just(x0), Just(x1), ty_Int)
new_esEs7(Left(x0), Left(x1), ty_Integer, x2)
new_ltEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, ty_Double)
new_ltEs14(x0, x1)
new_asAs(False, x0)
new_ltEs5(Nothing, Just(x0), x1)
new_ltEs13(Right(x0), Right(x1), x2, app(ty_[], x3))
new_lt12(x0, x1, ty_Double)
new_esEs7(Right(x0), Right(x1), x2, ty_Integer)
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_sr(x0, x1)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs18(x0, x1, ty_Ordering)
new_lt13(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs18(x0, x1, app(app(ty_Either, x2), x3))
new_esEs26(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_ltEs13(Right(x0), Right(x1), x2, ty_Bool)
new_lt12(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, ty_Bool)
new_esEs10(x0, x1, ty_Integer)
new_esEs28(x0, x1, ty_Char)
new_ltEs19(x0, x1, ty_Ordering)
new_esEs14(True, True)
new_ltEs5(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs5(Just(x0), Just(x1), ty_Char)
new_ltEs18(x0, x1, app(ty_Ratio, x2))
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(@0, @0)
new_lt20(x0, x1, ty_@0)
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_esEs29(x0, x1, ty_Char)
new_compare15(x0, x1, ty_Bool)
new_lt20(x0, x1, ty_Float)
new_primEqNat0(Zero, Zero)
new_esEs6(Just(x0), Just(x1), app(ty_[], x2))
new_esEs7(Right(x0), Right(x1), x2, ty_Float)
new_primCmpNat0(Succ(x0), Succ(x1))
new_esEs7(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs15(LT)
new_ltEs18(x0, x1, app(ty_[], x2))
new_ltEs13(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_ltEs13(Left(x0), Left(x1), ty_Integer, x2)
new_esEs29(x0, x1, ty_Int)
new_ltEs4(True, True)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_esEs24(x0, x1, ty_Bool)
new_lt12(x0, x1, ty_Float)
new_esEs27(x0, x1, ty_@0)
new_esEs26(x0, x1, app(ty_[], x2))
new_esEs7(Left(x0), Left(x1), ty_Char, x2)
new_ltEs13(Left(x0), Left(x1), ty_Char, x2)
new_esEs26(x0, x1, ty_Integer)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_lt13(x0, x1, app(app(ty_Either, x2), x3))
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt13(x0, x1, app(ty_[], x2))
new_esEs19(Char(x0), Char(x1))
new_primPlusNat1(Zero, Succ(x0))
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_primMulNat0(Zero, Zero)
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primMulInt(Pos(x0), Pos(x1))
new_lt9(x0, x1, x2)
new_esEs18(x0, x1, ty_@0)
new_esEs24(x0, x1, ty_@0)
new_esEs7(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_compare13(x0, x1, True, x2, x3)
new_lt12(x0, x1, ty_@0)
new_lt12(x0, x1, app(ty_[], x2))
new_esEs7(Left(x0), Left(x1), ty_Float, x2)
new_esEs27(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs18(x0, x1, app(app(ty_Either, x2), x3))
new_esEs25(x0, x1, ty_Bool)
new_compare15(x0, x1, app(ty_Ratio, x2))
new_compare12(x0, x1, False)
new_esEs10(x0, x1, ty_Int)
new_lt20(x0, x1, ty_Int)
new_esEs25(x0, x1, ty_Integer)
new_ltEs18(x0, x1, ty_Integer)
new_lt13(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs5(Nothing, Nothing, x0)
new_esEs16(Float(x0, x1), Float(x2, x3))
new_primPlusNat1(Succ(x0), Zero)
new_ltEs18(x0, x1, ty_Int)
new_compare29(x0, x1, False, x2, x3, x4)
new_esEs17([], [], x0)
new_esEs7(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_pePe(True, x0, x1, x2, x3)
new_esEs24(x0, x1, ty_Integer)
new_primMulNat0(Succ(x0), Succ(x1))
new_eltsFM_LE0(x0, x1, x2, x3, x4)
new_esEs28(x0, x1, ty_Bool)
new_sizeFM(EmptyFM, x0, x1)
new_ltEs16(x0, x1)
new_esEs20(EQ, GT)
new_esEs20(GT, EQ)
new_ltEs13(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs18(x0, x1, app(app(ty_@2, x2), x3))
new_esEs6(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_ltEs4(False, False)
new_compare(:(x0, x1), :(x2, x3), x4)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs24(x0, x1, ty_Ordering)
new_esEs18(x0, x1, ty_Double)
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs26(x0, x1, ty_Char)
new_foldFM_LE5(x0, EmptyFM, x1, x2)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_esEs27(x0, x1, ty_Int)
new_ltEs19(x0, x1, ty_Integer)
new_compare24(x0, x1, False, x2, x3)
new_esEs20(LT, EQ)
new_esEs20(EQ, LT)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_compare14(Char(x0), Char(x1))
new_esEs27(x0, x1, ty_Double)
new_ltEs19(x0, x1, ty_Int)
new_esEs6(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, ty_Double)
new_primPlusNat0(Succ(x0), x1)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_ltEs5(Just(x0), Just(x1), ty_Integer)
new_lt12(x0, x1, ty_Char)
new_primPlusNat1(Zero, Zero)
new_not0
new_esEs29(x0, x1, ty_@0)
new_compare15(x0, x1, ty_@0)
new_compare16(x0, x1, x2, x3, x4)
new_primMulNat0(Succ(x0), Zero)
new_esEs7(Right(x0), Left(x1), x2, x3)
new_esEs7(Left(x0), Right(x1), x2, x3)
new_foldFM_LE12(x0, x1, x2, x3, x4, EmptyFM, True, x5, x6)
new_compare9(Float(x0, x1), Float(x2, x3))
new_esEs18(x0, x1, ty_Bool)
new_ltEs18(x0, x1, app(ty_Maybe, x2))
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_ltEs5(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_lt10(x0, x1, x2)
new_ltEs13(Left(x0), Left(x1), ty_Float, x2)
new_esEs6(Just(x0), Just(x1), ty_@0)
new_esEs6(Just(x0), Just(x1), app(app(ty_FiniteMap, x2), x3))
new_esEs7(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs13(Left(x0), Left(x1), app(ty_[], x2), x3)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs8(@2(x0, x1), @2(x2, x3), x4, x5)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_esEs7(Left(x0), Left(x1), ty_Double, x2)
new_esEs26(x0, x1, ty_@0)
new_ltEs18(x0, x1, ty_Bool)
new_ltEs18(x0, x1, ty_Double)
new_esEs7(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs26(x0, x1, ty_Float)
new_compare211(x0, x1, True, x2)
new_lt5(x0, x1)
new_ltEs18(x0, x1, ty_Float)
new_ltEs13(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_compare28(x0, x1, x2, x3)
new_ltEs13(Right(x0), Left(x1), x2, x3)
new_ltEs13(Left(x0), Right(x1), x2, x3)
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_ltEs18(x0, x1, app(app(ty_@2, x2), x3))
new_not(GT)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_compare111(x0, x1, True)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_ltEs6(x0, x1, x2)
new_lt14(x0, x1, x2)
new_ltEs10(x0, x1)
new_foldFM2(EmptyFM, x0, x1)
new_compare210(x0, x1, False)
new_esEs18(x0, x1, app(ty_Ratio, x2))
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
new_esEs6(Nothing, Just(x0), x1)
new_ltEs13(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_esEs11(x0, x1, ty_Integer)
new_lt4(x0, x1)
new_compare15(x0, x1, app(app(ty_Either, x2), x3))
new_lt12(x0, x1, ty_Int)
new_esEs7(Left(x0), Left(x1), ty_Bool, x2)
new_esEs6(Just(x0), Just(x1), ty_Float)
new_lt12(x0, x1, app(ty_Ratio, x2))
new_lt7(x0, x1)
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_lt12(x0, x1, ty_Integer)
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs8(EQ, LT)
new_ltEs8(LT, EQ)
new_ltEs17(@2(x0, x1), @2(x2, x3), x4, x5)
new_ltEs18(x0, x1, ty_@0)
new_esEs26(x0, x1, ty_Int)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs29(x0, x1, ty_Float)
new_ltEs13(Right(x0), Right(x1), x2, ty_Char)
new_primPlusNat1(Succ(x0), Succ(x1))
new_compare25(x0, x1, True)
new_ltEs19(x0, x1, ty_Bool)
new_compare12(x0, x1, True)
new_primEqInt(Neg(Zero), Neg(Zero))
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs28(x0, x1, ty_Ordering)
new_primCompAux0(x0, EQ)
new_esEs20(LT, LT)
new_esEs26(x0, x1, ty_Bool)
new_compare15(x0, x1, ty_Ordering)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_ltEs13(Right(x0), Right(x1), x2, ty_Float)
new_foldFM_LE12(x0, x1, x2, x3, x4, x5, False, x6, x7)
new_compare27(:%(x0, x1), :%(x2, x3), ty_Int)
new_ltEs13(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_esEs14(False, True)
new_esEs14(True, False)
new_compare110(x0, x1, True, x2, x3, x4)
new_lt12(x0, x1, app(app(ty_@2, x2), x3))
new_lt13(x0, x1, ty_Double)
new_esEs24(x0, x1, ty_Int)
new_esEs28(x0, x1, ty_Double)
new_ltEs11(x0, x1)
new_primCompAux0(x0, LT)
new_primCompAux1(x0, x1, x2, x3)
new_lt15(x0, x1)
new_lt17(x0, x1)
new_esEs20(GT, LT)
new_esEs20(LT, GT)
new_esEs24(x0, x1, app(ty_[], x2))
new_compare29(x0, x1, True, x2, x3, x4)
new_esEs7(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_lt12(x0, x1, ty_Bool)
new_esEs7(Left(x0), Left(x1), app(app(ty_FiniteMap, x2), x3), x4)
new_esEs17(:(x0, x1), [], x2)
new_compare13(x0, x1, False, x2, x3)
new_esEs18(x0, x1, ty_Integer)
new_ltEs13(Left(x0), Left(x1), ty_@0, x2)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_ltEs12(x0, x1, x2)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_esEs25(x0, x1, ty_Int)
new_esEs6(Just(x0), Just(x1), ty_Char)
new_ltEs13(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs7(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_lt8(x0, x1)
new_primEqNat0(Succ(x0), Zero)
new_esEs25(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_primEqNat0(Zero, Succ(x0))
new_lt13(x0, x1, app(ty_Maybe, x2))
new_esEs24(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_lt12(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, x2, x3)
new_lt20(x0, x1, app(ty_[], x2))
new_ltEs5(Just(x0), Nothing, x1)
new_esEs7(Left(x0), Left(x1), ty_Int, x2)
new_primPlusNat0(Zero, x0)
new_compare24(x0, x1, True, x2, x3)
new_lt13(x0, x1, ty_Float)
new_ltEs8(LT, LT)
new_esEs20(GT, GT)
new_ltEs13(Right(x0), Right(x1), x2, ty_Int)
new_primCmpNat0(Zero, Zero)
new_esEs18(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
new_esEs6(Just(x0), Just(x1), ty_Integer)
new_esEs7(Left(x0), Left(x1), ty_@0, x2)
new_lt20(x0, x1, ty_Ordering)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_ltEs4(False, True)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_ltEs4(True, False)
new_compare17(x0, x1)
new_ltEs8(GT, GT)
new_esEs15(GT)
new_esEs25(x0, x1, ty_Float)
new_ltEs5(Just(x0), Just(x1), ty_Float)
new_primCompAux0(x0, GT)
new_esEs7(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs28(x0, x1, ty_Int)
new_compare15(x0, x1, app(app(ty_@2, x2), x3))
new_esEs29(x0, x1, ty_Integer)
new_compare15(x0, x1, ty_Integer)
new_esEs7(Right(x0), Right(x1), x2, ty_Char)
new_lt13(x0, x1, app(ty_Ratio, x2))
new_esEs28(x0, x1, ty_@0)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_foldFM_LE12(x0, x1, x2, x3, x4, Branch(x5, x6, x7, x8, x9), True, x10, x11)
new_esEs6(Just(x0), Just(x1), ty_Ordering)
new_lt13(x0, x1, ty_Ordering)
new_ltEs13(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_esEs27(x0, x1, ty_Ordering)
new_compare10(x0, x1, True, x2)
new_ltEs19(x0, x1, ty_@0)
new_esEs24(x0, x1, ty_Char)
new_compare10(x0, x1, False, x2)
new_esEs29(x0, x1, ty_Bool)
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs18(x0, x1, ty_Int)
new_esEs17(:(x0, x1), :(x2, x3), x4)
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_esEs24(x0, x1, ty_Double)
new_esEs12(Integer(x0), Integer(x1))
new_compare18(x0, x1, x2)
new_compare210(x0, x1, True)
new_ltEs8(LT, GT)
new_ltEs8(GT, LT)
new_ltEs13(Left(x0), Left(x1), ty_Bool, x2)
new_esEs25(x0, x1, ty_Double)
new_lt6(x0, x1, x2, x3)
new_esEs6(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, ty_Integer)
new_compare110(x0, x1, False, x2, x3, x4)
new_esEs7(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs6(Nothing, Nothing, x0)
new_esEs27(x0, x1, app(ty_[], x2))
new_esEs6(Just(x0), Nothing, x1)
new_esEs5(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_ltEs13(Right(x0), Right(x1), x2, ty_Double)
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs18(x0, x1, ty_Float)
new_not(EQ)
new_foldFM_LE5(x0, Branch(x1, x2, x3, x4, x5), x6, x7)
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_lt11(x0, x1, x2, x3, x4)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_esEs7(Right(x0), Right(x1), x2, ty_Ordering)
new_lt13(x0, x1, ty_@0)
new_esEs6(Just(x0), Just(x1), ty_Double)
new_esEs29(x0, x1, ty_Double)
new_ltEs19(x0, x1, ty_Char)
new_lt12(x0, x1, ty_Ordering)
new_lt18(x0, x1, x2, x3)
new_lt13(x0, x1, ty_Integer)
new_compare([], [], x0)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_compare212(x0, x1, False, x2, x3)
new_lt13(x0, x1, ty_Char)
new_esEs20(EQ, EQ)
new_esEs9(:%(x0, x1), :%(x2, x3), x4)
new_esEs11(x0, x1, ty_Int)
new_ltEs13(Right(x0), Right(x1), x2, ty_Ordering)
new_compare15(x0, x1, app(ty_Maybe, x2))
new_esEs15(EQ)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_ltEs15(x0, x1)
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_FiniteMap, x3), x4))
new_compare7(Integer(x0), Integer(x1))
new_compare([], :(x0, x1), x2)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_compare27(:%(x0, x1), :%(x2, x3), ty_Integer)
new_ltEs13(Left(x0), Left(x1), ty_Ordering, x2)
new_compare111(x0, x1, False)
new_esEs25(x0, x1, ty_Ordering)
new_ltEs8(GT, EQ)
new_ltEs8(EQ, GT)
new_esEs21(Double(x0, x1), Double(x2, x3))
new_ltEs13(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_ltEs5(Just(x0), Just(x1), ty_Bool)
new_esEs29(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_ltEs13(Left(x0), Left(x1), ty_Double, x2)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sr0(Integer(x0), Integer(x1))
new_compare11(x0, x1, True, x2, x3)
new_esEs6(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs6(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs25(x0, x1, ty_@0)
new_compare26(@0, @0)
new_ltEs9(x0, x1)
new_ltEs19(x0, x1, ty_Float)
new_esEs28(x0, x1, ty_Float)
new_ltEs13(Right(x0), Right(x1), x2, ty_Integer)
new_esEs14(False, False)
new_ltEs5(Just(x0), Just(x1), app(ty_Maybe, x2))
new_primEqInt(Pos(Zero), Pos(Zero))
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Just(x0), Just(x1), ty_Bool)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_lt12(x0, x1, app(app(ty_Either, x2), x3))
new_compare(:(x0, x1), [], x2)
new_lt13(x0, x1, ty_Bool)
new_compare211(x0, x1, False, x2)
new_lt20(x0, x1, ty_Char)
new_esEs18(x0, x1, app(ty_[], x2))
new_asAs(True, x0)
new_esEs24(x0, x1, ty_Float)
new_compare15(x0, x1, ty_Char)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs7(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs6(Just(x0), Just(x1), ty_Int)
new_compare15(x0, x1, ty_Float)
new_lt20(x0, x1, ty_Double)
new_compare15(x0, x1, app(ty_[], x2))
new_ltEs5(Just(x0), Just(x1), app(ty_[], x2))
new_not(LT)
new_esEs25(x0, x1, ty_Char)
new_foldFM_LE30(x0, x1, x2, x3, x4)
new_lt13(x0, x1, ty_Int)
new_esEs27(x0, x1, ty_Bool)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_esEs18(x0, x1, app(ty_Maybe, x2))
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
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ 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_foldFM_LE11(vyy24, vyy340, vyy341, vyy342, vyy343, Branch(vyy3440, vyy3441, vyy3442, vyy3443, vyy3444), True, h, ba) → new_foldFM_LE4(vyy24, vyy343, h, ba)
new_foldFM_LE4(vyy24, Branch(vyy3430, vyy3431, vyy3432, vyy3433, vyy3434), h, ba) → new_foldFM_LE11(vyy24, vyy3430, vyy3431, vyy3432, vyy3433, vyy3434, new_ltEs5(vyy3430, Nothing, ba), h, ba)
new_foldFM_LE11(vyy24, vyy340, vyy341, vyy342, Branch(vyy3430, vyy3431, vyy3432, vyy3433, vyy3434), vyy344, False, h, ba) → new_foldFM_LE11(vyy24, vyy3430, vyy3431, vyy3432, vyy3433, vyy3434, new_ltEs5(vyy3430, Nothing, ba), h, ba)
new_foldFM_LE11(vyy24, vyy340, vyy341, vyy342, vyy343, Branch(vyy3440, vyy3441, vyy3442, vyy3443, vyy3444), True, h, ba) → new_foldFM_LE21(vyy340, vyy341, new_foldFM_LE5(vyy24, vyy343, h, ba), vyy3440, vyy3441, vyy3442, vyy3443, vyy3444, h, ba)
new_foldFM_LE21(vyy340, vyy341, vyy28, vyy3440, vyy3441, vyy3442, vyy3443, vyy3444, h, ba) → new_foldFM_LE11(new_eltsFM_LE0(vyy340, vyy341, vyy28, h, ba), vyy3440, vyy3441, vyy3442, vyy3443, vyy3444, new_ltEs5(vyy3440, Nothing, ba), h, ba)
new_foldFM_LE11(vyy24, vyy340, vyy341, vyy342, vyy343, EmptyFM, True, h, ba) → new_foldFM_LE4(vyy24, vyy343, h, ba)
The TRS R consists of the following rules:
new_foldFM_LE5(vyy24, Branch(vyy3430, vyy3431, vyy3432, vyy3433, vyy3434), h, ba) → new_foldFM_LE12(vyy24, vyy3430, vyy3431, vyy3432, vyy3433, vyy3434, new_ltEs5(vyy3430, Nothing, ba), h, ba)
new_foldFM_LE12(vyy24, vyy340, vyy341, vyy342, vyy343, Branch(vyy3440, vyy3441, vyy3442, vyy3443, vyy3444), True, h, ba) → new_foldFM_LE22(vyy340, vyy341, new_foldFM_LE5(vyy24, vyy343, h, ba), vyy3440, vyy3441, vyy3442, vyy3443, vyy3444, h, ba)
new_foldFM_LE12(vyy24, vyy340, vyy341, vyy342, vyy343, vyy344, False, h, ba) → new_foldFM_LE5(vyy24, vyy343, h, ba)
new_foldFM_LE22(vyy340, vyy341, vyy28, vyy3440, vyy3441, vyy3442, vyy3443, vyy3444, h, ba) → new_foldFM_LE12(new_eltsFM_LE0(vyy340, vyy341, vyy28, h, ba), vyy3440, vyy3441, vyy3442, vyy3443, vyy3444, new_ltEs5(vyy3440, Nothing, ba), h, ba)
new_foldFM_LE5(vyy24, EmptyFM, h, ba) → vyy24
new_eltsFM_LE0(vyy340, vyy341, vyy27, h, ba) → :(vyy341, vyy27)
new_ltEs5(Just(vyy3000), Nothing, dh) → False
new_ltEs5(Nothing, Nothing, dh) → True
new_foldFM_LE12(vyy24, vyy340, vyy341, vyy342, vyy343, EmptyFM, True, h, ba) → new_foldFM_LE30(vyy340, vyy341, new_foldFM_LE5(vyy24, vyy343, h, ba), h, ba)
new_foldFM_LE30(vyy340, vyy341, vyy27, h, ba) → new_eltsFM_LE0(vyy340, vyy341, vyy27, h, ba)
The set Q consists of the following terms:
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs18(x0, x1, ty_Char)
new_esEs18(x0, x1, ty_Char)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_esEs17([], :(x0, x1), x2)
new_esEs28(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, ty_Integer)
new_esEs7(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs13(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_fmToList(x0, x1, x2)
new_ltEs19(x0, x1, app(ty_[], x2))
new_esEs7(Left(x0), Left(x1), ty_Ordering, x2)
new_compare15(x0, x1, ty_Int)
new_compare6(x0, x1)
new_compare25(x0, x1, False)
new_compare15(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs18(x0, x1, ty_Ordering)
new_esEs7(Right(x0), Right(x1), x2, ty_Int)
new_compare11(x0, x1, False, x2, x3)
new_esEs25(x0, x1, app(ty_[], x2))
new_esEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs5(Just(x0), Just(x1), ty_@0)
new_esEs29(x0, x1, app(ty_[], x2))
new_lt16(x0, x1)
new_primEqNat0(Succ(x0), Succ(x1))
new_ltEs13(Right(x0), Right(x1), x2, ty_@0)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs7(Right(x0), Right(x1), x2, ty_Double)
new_pePe(False, x0, x1, x2, x3)
new_esEs28(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs26(x0, x1, ty_Ordering)
new_ltEs8(EQ, EQ)
new_ltEs5(Just(x0), Just(x1), app(ty_Ratio, x2))
new_ltEs7(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs13(x0, x1)
new_esEs27(x0, x1, ty_Char)
new_ltEs13(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_compare15(x0, x1, ty_Double)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs7(Right(x0), Right(x1), x2, ty_@0)
new_ltEs5(Just(x0), Just(x1), ty_Ordering)
new_esEs27(x0, x1, ty_Float)
new_ltEs5(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_primMulNat0(Zero, Succ(x0))
new_esEs29(x0, x1, ty_Ordering)
new_foldFM_LE22(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_primCmpNat0(Zero, Succ(x0))
new_primCmpNat0(Succ(x0), Zero)
new_esEs28(x0, x1, ty_Integer)
new_ltEs13(Left(x0), Left(x1), ty_Int, x2)
new_compare5(x0, x1, x2, x3)
new_ltEs5(Just(x0), Just(x1), ty_Double)
new_compare19(Double(x0, x1), Double(x2, x3))
new_compare8(x0, x1)
new_lt19(x0, x1)
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare212(x0, x1, True, x2, x3)
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs5(Just(x0), Just(x1), ty_Int)
new_esEs7(Left(x0), Left(x1), ty_Integer, x2)
new_ltEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, ty_Double)
new_ltEs14(x0, x1)
new_asAs(False, x0)
new_ltEs5(Nothing, Just(x0), x1)
new_ltEs13(Right(x0), Right(x1), x2, app(ty_[], x3))
new_lt12(x0, x1, ty_Double)
new_esEs7(Right(x0), Right(x1), x2, ty_Integer)
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_sr(x0, x1)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs18(x0, x1, ty_Ordering)
new_lt13(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs18(x0, x1, app(app(ty_Either, x2), x3))
new_esEs26(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_ltEs13(Right(x0), Right(x1), x2, ty_Bool)
new_lt12(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, ty_Bool)
new_esEs10(x0, x1, ty_Integer)
new_esEs28(x0, x1, ty_Char)
new_ltEs19(x0, x1, ty_Ordering)
new_esEs14(True, True)
new_ltEs5(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs5(Just(x0), Just(x1), ty_Char)
new_ltEs18(x0, x1, app(ty_Ratio, x2))
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(@0, @0)
new_lt20(x0, x1, ty_@0)
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_esEs29(x0, x1, ty_Char)
new_compare15(x0, x1, ty_Bool)
new_lt20(x0, x1, ty_Float)
new_primEqNat0(Zero, Zero)
new_esEs6(Just(x0), Just(x1), app(ty_[], x2))
new_esEs7(Right(x0), Right(x1), x2, ty_Float)
new_primCmpNat0(Succ(x0), Succ(x1))
new_esEs7(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs15(LT)
new_ltEs18(x0, x1, app(ty_[], x2))
new_ltEs13(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_ltEs13(Left(x0), Left(x1), ty_Integer, x2)
new_esEs29(x0, x1, ty_Int)
new_ltEs4(True, True)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_esEs24(x0, x1, ty_Bool)
new_lt12(x0, x1, ty_Float)
new_esEs27(x0, x1, ty_@0)
new_esEs26(x0, x1, app(ty_[], x2))
new_esEs7(Left(x0), Left(x1), ty_Char, x2)
new_ltEs13(Left(x0), Left(x1), ty_Char, x2)
new_esEs26(x0, x1, ty_Integer)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_lt13(x0, x1, app(app(ty_Either, x2), x3))
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt13(x0, x1, app(ty_[], x2))
new_esEs19(Char(x0), Char(x1))
new_primPlusNat1(Zero, Succ(x0))
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_primMulNat0(Zero, Zero)
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primMulInt(Pos(x0), Pos(x1))
new_lt9(x0, x1, x2)
new_esEs18(x0, x1, ty_@0)
new_esEs24(x0, x1, ty_@0)
new_esEs7(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_compare13(x0, x1, True, x2, x3)
new_lt12(x0, x1, ty_@0)
new_lt12(x0, x1, app(ty_[], x2))
new_esEs7(Left(x0), Left(x1), ty_Float, x2)
new_esEs27(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs18(x0, x1, app(app(ty_Either, x2), x3))
new_esEs25(x0, x1, ty_Bool)
new_compare15(x0, x1, app(ty_Ratio, x2))
new_compare12(x0, x1, False)
new_esEs10(x0, x1, ty_Int)
new_lt20(x0, x1, ty_Int)
new_esEs25(x0, x1, ty_Integer)
new_ltEs18(x0, x1, ty_Integer)
new_lt13(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs5(Nothing, Nothing, x0)
new_esEs16(Float(x0, x1), Float(x2, x3))
new_primPlusNat1(Succ(x0), Zero)
new_ltEs18(x0, x1, ty_Int)
new_compare29(x0, x1, False, x2, x3, x4)
new_esEs17([], [], x0)
new_esEs7(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_pePe(True, x0, x1, x2, x3)
new_esEs24(x0, x1, ty_Integer)
new_primMulNat0(Succ(x0), Succ(x1))
new_eltsFM_LE0(x0, x1, x2, x3, x4)
new_esEs28(x0, x1, ty_Bool)
new_sizeFM(EmptyFM, x0, x1)
new_ltEs16(x0, x1)
new_esEs20(EQ, GT)
new_esEs20(GT, EQ)
new_ltEs13(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs18(x0, x1, app(app(ty_@2, x2), x3))
new_esEs6(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_ltEs4(False, False)
new_compare(:(x0, x1), :(x2, x3), x4)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs24(x0, x1, ty_Ordering)
new_esEs18(x0, x1, ty_Double)
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs26(x0, x1, ty_Char)
new_foldFM_LE5(x0, EmptyFM, x1, x2)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_esEs27(x0, x1, ty_Int)
new_ltEs19(x0, x1, ty_Integer)
new_compare24(x0, x1, False, x2, x3)
new_esEs20(LT, EQ)
new_esEs20(EQ, LT)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_compare14(Char(x0), Char(x1))
new_esEs27(x0, x1, ty_Double)
new_ltEs19(x0, x1, ty_Int)
new_esEs6(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, ty_Double)
new_primPlusNat0(Succ(x0), x1)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_ltEs5(Just(x0), Just(x1), ty_Integer)
new_lt12(x0, x1, ty_Char)
new_primPlusNat1(Zero, Zero)
new_not0
new_esEs29(x0, x1, ty_@0)
new_compare15(x0, x1, ty_@0)
new_compare16(x0, x1, x2, x3, x4)
new_primMulNat0(Succ(x0), Zero)
new_esEs7(Right(x0), Left(x1), x2, x3)
new_esEs7(Left(x0), Right(x1), x2, x3)
new_foldFM_LE12(x0, x1, x2, x3, x4, EmptyFM, True, x5, x6)
new_compare9(Float(x0, x1), Float(x2, x3))
new_esEs18(x0, x1, ty_Bool)
new_ltEs18(x0, x1, app(ty_Maybe, x2))
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_ltEs5(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_lt10(x0, x1, x2)
new_ltEs13(Left(x0), Left(x1), ty_Float, x2)
new_esEs6(Just(x0), Just(x1), ty_@0)
new_esEs6(Just(x0), Just(x1), app(app(ty_FiniteMap, x2), x3))
new_esEs7(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs13(Left(x0), Left(x1), app(ty_[], x2), x3)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs8(@2(x0, x1), @2(x2, x3), x4, x5)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_esEs7(Left(x0), Left(x1), ty_Double, x2)
new_esEs26(x0, x1, ty_@0)
new_ltEs18(x0, x1, ty_Bool)
new_ltEs18(x0, x1, ty_Double)
new_esEs7(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs26(x0, x1, ty_Float)
new_compare211(x0, x1, True, x2)
new_lt5(x0, x1)
new_ltEs18(x0, x1, ty_Float)
new_ltEs13(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_compare28(x0, x1, x2, x3)
new_ltEs13(Right(x0), Left(x1), x2, x3)
new_ltEs13(Left(x0), Right(x1), x2, x3)
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_ltEs18(x0, x1, app(app(ty_@2, x2), x3))
new_not(GT)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_compare111(x0, x1, True)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_ltEs6(x0, x1, x2)
new_lt14(x0, x1, x2)
new_ltEs10(x0, x1)
new_foldFM2(EmptyFM, x0, x1)
new_compare210(x0, x1, False)
new_esEs18(x0, x1, app(ty_Ratio, x2))
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
new_esEs6(Nothing, Just(x0), x1)
new_ltEs13(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_esEs11(x0, x1, ty_Integer)
new_lt4(x0, x1)
new_compare15(x0, x1, app(app(ty_Either, x2), x3))
new_lt12(x0, x1, ty_Int)
new_esEs7(Left(x0), Left(x1), ty_Bool, x2)
new_esEs6(Just(x0), Just(x1), ty_Float)
new_lt12(x0, x1, app(ty_Ratio, x2))
new_lt7(x0, x1)
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_lt12(x0, x1, ty_Integer)
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs8(EQ, LT)
new_ltEs8(LT, EQ)
new_ltEs17(@2(x0, x1), @2(x2, x3), x4, x5)
new_ltEs18(x0, x1, ty_@0)
new_esEs26(x0, x1, ty_Int)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs29(x0, x1, ty_Float)
new_ltEs13(Right(x0), Right(x1), x2, ty_Char)
new_primPlusNat1(Succ(x0), Succ(x1))
new_compare25(x0, x1, True)
new_ltEs19(x0, x1, ty_Bool)
new_compare12(x0, x1, True)
new_primEqInt(Neg(Zero), Neg(Zero))
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs28(x0, x1, ty_Ordering)
new_primCompAux0(x0, EQ)
new_esEs20(LT, LT)
new_esEs26(x0, x1, ty_Bool)
new_compare15(x0, x1, ty_Ordering)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_ltEs13(Right(x0), Right(x1), x2, ty_Float)
new_foldFM_LE12(x0, x1, x2, x3, x4, x5, False, x6, x7)
new_compare27(:%(x0, x1), :%(x2, x3), ty_Int)
new_ltEs13(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_esEs14(False, True)
new_esEs14(True, False)
new_compare110(x0, x1, True, x2, x3, x4)
new_lt12(x0, x1, app(app(ty_@2, x2), x3))
new_lt13(x0, x1, ty_Double)
new_esEs24(x0, x1, ty_Int)
new_esEs28(x0, x1, ty_Double)
new_ltEs11(x0, x1)
new_primCompAux0(x0, LT)
new_primCompAux1(x0, x1, x2, x3)
new_lt15(x0, x1)
new_lt17(x0, x1)
new_esEs20(GT, LT)
new_esEs20(LT, GT)
new_esEs24(x0, x1, app(ty_[], x2))
new_compare29(x0, x1, True, x2, x3, x4)
new_esEs7(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_lt12(x0, x1, ty_Bool)
new_esEs7(Left(x0), Left(x1), app(app(ty_FiniteMap, x2), x3), x4)
new_esEs17(:(x0, x1), [], x2)
new_compare13(x0, x1, False, x2, x3)
new_esEs18(x0, x1, ty_Integer)
new_ltEs13(Left(x0), Left(x1), ty_@0, x2)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_ltEs12(x0, x1, x2)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_esEs25(x0, x1, ty_Int)
new_esEs6(Just(x0), Just(x1), ty_Char)
new_ltEs13(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs7(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_lt8(x0, x1)
new_primEqNat0(Succ(x0), Zero)
new_esEs25(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_primEqNat0(Zero, Succ(x0))
new_lt13(x0, x1, app(ty_Maybe, x2))
new_esEs24(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_lt12(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, x2, x3)
new_lt20(x0, x1, app(ty_[], x2))
new_ltEs5(Just(x0), Nothing, x1)
new_esEs7(Left(x0), Left(x1), ty_Int, x2)
new_primPlusNat0(Zero, x0)
new_compare24(x0, x1, True, x2, x3)
new_lt13(x0, x1, ty_Float)
new_ltEs8(LT, LT)
new_esEs20(GT, GT)
new_ltEs13(Right(x0), Right(x1), x2, ty_Int)
new_primCmpNat0(Zero, Zero)
new_esEs18(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
new_esEs6(Just(x0), Just(x1), ty_Integer)
new_esEs7(Left(x0), Left(x1), ty_@0, x2)
new_lt20(x0, x1, ty_Ordering)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_ltEs4(False, True)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_ltEs4(True, False)
new_compare17(x0, x1)
new_ltEs8(GT, GT)
new_esEs15(GT)
new_esEs25(x0, x1, ty_Float)
new_ltEs5(Just(x0), Just(x1), ty_Float)
new_primCompAux0(x0, GT)
new_esEs7(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs28(x0, x1, ty_Int)
new_compare15(x0, x1, app(app(ty_@2, x2), x3))
new_esEs29(x0, x1, ty_Integer)
new_compare15(x0, x1, ty_Integer)
new_esEs7(Right(x0), Right(x1), x2, ty_Char)
new_lt13(x0, x1, app(ty_Ratio, x2))
new_esEs28(x0, x1, ty_@0)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_foldFM_LE12(x0, x1, x2, x3, x4, Branch(x5, x6, x7, x8, x9), True, x10, x11)
new_esEs6(Just(x0), Just(x1), ty_Ordering)
new_lt13(x0, x1, ty_Ordering)
new_ltEs13(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_esEs27(x0, x1, ty_Ordering)
new_compare10(x0, x1, True, x2)
new_ltEs19(x0, x1, ty_@0)
new_esEs24(x0, x1, ty_Char)
new_compare10(x0, x1, False, x2)
new_esEs29(x0, x1, ty_Bool)
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs18(x0, x1, ty_Int)
new_esEs17(:(x0, x1), :(x2, x3), x4)
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_esEs24(x0, x1, ty_Double)
new_esEs12(Integer(x0), Integer(x1))
new_compare18(x0, x1, x2)
new_compare210(x0, x1, True)
new_ltEs8(LT, GT)
new_ltEs8(GT, LT)
new_ltEs13(Left(x0), Left(x1), ty_Bool, x2)
new_esEs25(x0, x1, ty_Double)
new_lt6(x0, x1, x2, x3)
new_esEs6(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, ty_Integer)
new_compare110(x0, x1, False, x2, x3, x4)
new_esEs7(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs6(Nothing, Nothing, x0)
new_esEs27(x0, x1, app(ty_[], x2))
new_esEs6(Just(x0), Nothing, x1)
new_esEs5(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_ltEs13(Right(x0), Right(x1), x2, ty_Double)
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs18(x0, x1, ty_Float)
new_not(EQ)
new_foldFM_LE5(x0, Branch(x1, x2, x3, x4, x5), x6, x7)
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_lt11(x0, x1, x2, x3, x4)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_esEs7(Right(x0), Right(x1), x2, ty_Ordering)
new_lt13(x0, x1, ty_@0)
new_esEs6(Just(x0), Just(x1), ty_Double)
new_esEs29(x0, x1, ty_Double)
new_ltEs19(x0, x1, ty_Char)
new_lt12(x0, x1, ty_Ordering)
new_lt18(x0, x1, x2, x3)
new_lt13(x0, x1, ty_Integer)
new_compare([], [], x0)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_compare212(x0, x1, False, x2, x3)
new_lt13(x0, x1, ty_Char)
new_esEs20(EQ, EQ)
new_esEs9(:%(x0, x1), :%(x2, x3), x4)
new_esEs11(x0, x1, ty_Int)
new_ltEs13(Right(x0), Right(x1), x2, ty_Ordering)
new_compare15(x0, x1, app(ty_Maybe, x2))
new_esEs15(EQ)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_ltEs15(x0, x1)
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_FiniteMap, x3), x4))
new_compare7(Integer(x0), Integer(x1))
new_compare([], :(x0, x1), x2)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_compare27(:%(x0, x1), :%(x2, x3), ty_Integer)
new_ltEs13(Left(x0), Left(x1), ty_Ordering, x2)
new_compare111(x0, x1, False)
new_esEs25(x0, x1, ty_Ordering)
new_ltEs8(GT, EQ)
new_ltEs8(EQ, GT)
new_esEs21(Double(x0, x1), Double(x2, x3))
new_ltEs13(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_ltEs5(Just(x0), Just(x1), ty_Bool)
new_esEs29(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_ltEs13(Left(x0), Left(x1), ty_Double, x2)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sr0(Integer(x0), Integer(x1))
new_compare11(x0, x1, True, x2, x3)
new_esEs6(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs6(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs25(x0, x1, ty_@0)
new_compare26(@0, @0)
new_ltEs9(x0, x1)
new_ltEs19(x0, x1, ty_Float)
new_esEs28(x0, x1, ty_Float)
new_ltEs13(Right(x0), Right(x1), x2, ty_Integer)
new_esEs14(False, False)
new_ltEs5(Just(x0), Just(x1), app(ty_Maybe, x2))
new_primEqInt(Pos(Zero), Pos(Zero))
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Just(x0), Just(x1), ty_Bool)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_lt12(x0, x1, app(app(ty_Either, x2), x3))
new_compare(:(x0, x1), [], x2)
new_lt13(x0, x1, ty_Bool)
new_compare211(x0, x1, False, x2)
new_lt20(x0, x1, ty_Char)
new_esEs18(x0, x1, app(ty_[], x2))
new_asAs(True, x0)
new_esEs24(x0, x1, ty_Float)
new_compare15(x0, x1, ty_Char)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs7(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs6(Just(x0), Just(x1), ty_Int)
new_compare15(x0, x1, ty_Float)
new_lt20(x0, x1, ty_Double)
new_compare15(x0, x1, app(ty_[], x2))
new_ltEs5(Just(x0), Just(x1), app(ty_[], x2))
new_not(LT)
new_esEs25(x0, x1, ty_Char)
new_foldFM_LE30(x0, x1, x2, x3, x4)
new_lt13(x0, x1, ty_Int)
new_esEs27(x0, x1, ty_Bool)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_esEs18(x0, x1, app(ty_Maybe, x2))
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_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs18(x0, x1, ty_Char)
new_esEs18(x0, x1, ty_Char)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_esEs17([], :(x0, x1), x2)
new_esEs28(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, ty_Integer)
new_esEs7(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs13(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_fmToList(x0, x1, x2)
new_ltEs19(x0, x1, app(ty_[], x2))
new_esEs7(Left(x0), Left(x1), ty_Ordering, x2)
new_compare15(x0, x1, ty_Int)
new_compare6(x0, x1)
new_compare25(x0, x1, False)
new_compare15(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs18(x0, x1, ty_Ordering)
new_esEs7(Right(x0), Right(x1), x2, ty_Int)
new_compare11(x0, x1, False, x2, x3)
new_esEs25(x0, x1, app(ty_[], x2))
new_esEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs29(x0, x1, app(ty_[], x2))
new_lt16(x0, x1)
new_primEqNat0(Succ(x0), Succ(x1))
new_ltEs13(Right(x0), Right(x1), x2, ty_@0)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs7(Right(x0), Right(x1), x2, ty_Double)
new_pePe(False, x0, x1, x2, x3)
new_esEs28(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs26(x0, x1, ty_Ordering)
new_ltEs8(EQ, EQ)
new_ltEs7(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs13(x0, x1)
new_esEs27(x0, x1, ty_Char)
new_ltEs13(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_compare15(x0, x1, ty_Double)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs7(Right(x0), Right(x1), x2, ty_@0)
new_esEs27(x0, x1, ty_Float)
new_primMulNat0(Zero, Succ(x0))
new_esEs29(x0, x1, ty_Ordering)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_primCmpNat0(Zero, Succ(x0))
new_primCmpNat0(Succ(x0), Zero)
new_esEs28(x0, x1, ty_Integer)
new_ltEs13(Left(x0), Left(x1), ty_Int, x2)
new_compare5(x0, x1, x2, x3)
new_compare19(Double(x0, x1), Double(x2, x3))
new_compare8(x0, x1)
new_lt19(x0, x1)
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare212(x0, x1, True, x2, x3)
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs7(Left(x0), Left(x1), ty_Integer, x2)
new_ltEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, ty_Double)
new_ltEs14(x0, x1)
new_asAs(False, x0)
new_ltEs13(Right(x0), Right(x1), x2, app(ty_[], x3))
new_lt12(x0, x1, ty_Double)
new_esEs7(Right(x0), Right(x1), x2, ty_Integer)
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_sr(x0, x1)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs18(x0, x1, ty_Ordering)
new_lt13(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs18(x0, x1, app(app(ty_Either, x2), x3))
new_esEs26(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_ltEs13(Right(x0), Right(x1), x2, ty_Bool)
new_lt12(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, ty_Bool)
new_esEs10(x0, x1, ty_Integer)
new_esEs28(x0, x1, ty_Char)
new_ltEs19(x0, x1, ty_Ordering)
new_esEs14(True, True)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs18(x0, x1, app(ty_Ratio, x2))
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(@0, @0)
new_lt20(x0, x1, ty_@0)
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_esEs29(x0, x1, ty_Char)
new_compare15(x0, x1, ty_Bool)
new_lt20(x0, x1, ty_Float)
new_primEqNat0(Zero, Zero)
new_esEs6(Just(x0), Just(x1), app(ty_[], x2))
new_esEs7(Right(x0), Right(x1), x2, ty_Float)
new_primCmpNat0(Succ(x0), Succ(x1))
new_esEs7(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs15(LT)
new_ltEs18(x0, x1, app(ty_[], x2))
new_ltEs13(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_ltEs13(Left(x0), Left(x1), ty_Integer, x2)
new_esEs29(x0, x1, ty_Int)
new_ltEs4(True, True)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_esEs24(x0, x1, ty_Bool)
new_lt12(x0, x1, ty_Float)
new_esEs27(x0, x1, ty_@0)
new_esEs26(x0, x1, app(ty_[], x2))
new_esEs7(Left(x0), Left(x1), ty_Char, x2)
new_ltEs13(Left(x0), Left(x1), ty_Char, x2)
new_esEs26(x0, x1, ty_Integer)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_lt13(x0, x1, app(app(ty_Either, x2), x3))
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt13(x0, x1, app(ty_[], x2))
new_esEs19(Char(x0), Char(x1))
new_primPlusNat1(Zero, Succ(x0))
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_primMulNat0(Zero, Zero)
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primMulInt(Pos(x0), Pos(x1))
new_lt9(x0, x1, x2)
new_esEs18(x0, x1, ty_@0)
new_esEs24(x0, x1, ty_@0)
new_esEs7(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_compare13(x0, x1, True, x2, x3)
new_lt12(x0, x1, ty_@0)
new_lt12(x0, x1, app(ty_[], x2))
new_esEs7(Left(x0), Left(x1), ty_Float, x2)
new_esEs27(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs18(x0, x1, app(app(ty_Either, x2), x3))
new_esEs25(x0, x1, ty_Bool)
new_compare15(x0, x1, app(ty_Ratio, x2))
new_compare12(x0, x1, False)
new_esEs10(x0, x1, ty_Int)
new_lt20(x0, x1, ty_Int)
new_esEs25(x0, x1, ty_Integer)
new_ltEs18(x0, x1, ty_Integer)
new_lt13(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs16(Float(x0, x1), Float(x2, x3))
new_primPlusNat1(Succ(x0), Zero)
new_ltEs18(x0, x1, ty_Int)
new_compare29(x0, x1, False, x2, x3, x4)
new_esEs17([], [], x0)
new_esEs7(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_pePe(True, x0, x1, x2, x3)
new_esEs24(x0, x1, ty_Integer)
new_primMulNat0(Succ(x0), Succ(x1))
new_esEs28(x0, x1, ty_Bool)
new_sizeFM(EmptyFM, x0, x1)
new_ltEs16(x0, x1)
new_esEs20(EQ, GT)
new_esEs20(GT, EQ)
new_ltEs13(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs18(x0, x1, app(app(ty_@2, x2), x3))
new_esEs6(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_ltEs4(False, False)
new_compare(:(x0, x1), :(x2, x3), x4)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs24(x0, x1, ty_Ordering)
new_esEs18(x0, x1, ty_Double)
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs26(x0, x1, ty_Char)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_esEs27(x0, x1, ty_Int)
new_ltEs19(x0, x1, ty_Integer)
new_compare24(x0, x1, False, x2, x3)
new_esEs20(LT, EQ)
new_esEs20(EQ, LT)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_compare14(Char(x0), Char(x1))
new_esEs27(x0, x1, ty_Double)
new_ltEs19(x0, x1, ty_Int)
new_esEs6(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, ty_Double)
new_primPlusNat0(Succ(x0), x1)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_lt12(x0, x1, ty_Char)
new_primPlusNat1(Zero, Zero)
new_not0
new_esEs29(x0, x1, ty_@0)
new_compare15(x0, x1, ty_@0)
new_compare16(x0, x1, x2, x3, x4)
new_primMulNat0(Succ(x0), Zero)
new_esEs7(Right(x0), Left(x1), x2, x3)
new_esEs7(Left(x0), Right(x1), x2, x3)
new_compare9(Float(x0, x1), Float(x2, x3))
new_esEs18(x0, x1, ty_Bool)
new_ltEs18(x0, x1, app(ty_Maybe, x2))
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_lt10(x0, x1, x2)
new_ltEs13(Left(x0), Left(x1), ty_Float, x2)
new_esEs6(Just(x0), Just(x1), ty_@0)
new_esEs6(Just(x0), Just(x1), app(app(ty_FiniteMap, x2), x3))
new_esEs7(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs13(Left(x0), Left(x1), app(ty_[], x2), x3)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs8(@2(x0, x1), @2(x2, x3), x4, x5)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_esEs7(Left(x0), Left(x1), ty_Double, x2)
new_esEs26(x0, x1, ty_@0)
new_ltEs18(x0, x1, ty_Bool)
new_ltEs18(x0, x1, ty_Double)
new_esEs7(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs26(x0, x1, ty_Float)
new_compare211(x0, x1, True, x2)
new_lt5(x0, x1)
new_ltEs18(x0, x1, ty_Float)
new_ltEs13(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_compare28(x0, x1, x2, x3)
new_ltEs13(Right(x0), Left(x1), x2, x3)
new_ltEs13(Left(x0), Right(x1), x2, x3)
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_ltEs18(x0, x1, app(app(ty_@2, x2), x3))
new_not(GT)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_compare111(x0, x1, True)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_ltEs6(x0, x1, x2)
new_lt14(x0, x1, x2)
new_ltEs10(x0, x1)
new_foldFM2(EmptyFM, x0, x1)
new_compare210(x0, x1, False)
new_esEs18(x0, x1, app(ty_Ratio, x2))
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
new_esEs6(Nothing, Just(x0), x1)
new_ltEs13(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_esEs11(x0, x1, ty_Integer)
new_lt4(x0, x1)
new_compare15(x0, x1, app(app(ty_Either, x2), x3))
new_lt12(x0, x1, ty_Int)
new_esEs7(Left(x0), Left(x1), ty_Bool, x2)
new_esEs6(Just(x0), Just(x1), ty_Float)
new_lt12(x0, x1, app(ty_Ratio, x2))
new_lt7(x0, x1)
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_lt12(x0, x1, ty_Integer)
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs8(EQ, LT)
new_ltEs8(LT, EQ)
new_ltEs17(@2(x0, x1), @2(x2, x3), x4, x5)
new_ltEs18(x0, x1, ty_@0)
new_esEs26(x0, x1, ty_Int)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs29(x0, x1, ty_Float)
new_ltEs13(Right(x0), Right(x1), x2, ty_Char)
new_primPlusNat1(Succ(x0), Succ(x1))
new_compare25(x0, x1, True)
new_ltEs19(x0, x1, ty_Bool)
new_compare12(x0, x1, True)
new_primEqInt(Neg(Zero), Neg(Zero))
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs28(x0, x1, ty_Ordering)
new_primCompAux0(x0, EQ)
new_esEs20(LT, LT)
new_esEs26(x0, x1, ty_Bool)
new_compare15(x0, x1, ty_Ordering)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_ltEs13(Right(x0), Right(x1), x2, ty_Float)
new_compare27(:%(x0, x1), :%(x2, x3), ty_Int)
new_ltEs13(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_esEs14(False, True)
new_esEs14(True, False)
new_compare110(x0, x1, True, x2, x3, x4)
new_lt12(x0, x1, app(app(ty_@2, x2), x3))
new_lt13(x0, x1, ty_Double)
new_esEs24(x0, x1, ty_Int)
new_esEs28(x0, x1, ty_Double)
new_ltEs11(x0, x1)
new_primCompAux0(x0, LT)
new_primCompAux1(x0, x1, x2, x3)
new_lt15(x0, x1)
new_lt17(x0, x1)
new_esEs20(GT, LT)
new_esEs20(LT, GT)
new_esEs24(x0, x1, app(ty_[], x2))
new_compare29(x0, x1, True, x2, x3, x4)
new_esEs7(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_lt12(x0, x1, ty_Bool)
new_esEs7(Left(x0), Left(x1), app(app(ty_FiniteMap, x2), x3), x4)
new_esEs17(:(x0, x1), [], x2)
new_compare13(x0, x1, False, x2, x3)
new_esEs18(x0, x1, ty_Integer)
new_ltEs13(Left(x0), Left(x1), ty_@0, x2)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_ltEs12(x0, x1, x2)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_esEs25(x0, x1, ty_Int)
new_esEs6(Just(x0), Just(x1), ty_Char)
new_ltEs13(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs7(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_lt8(x0, x1)
new_primEqNat0(Succ(x0), Zero)
new_esEs25(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_primEqNat0(Zero, Succ(x0))
new_lt13(x0, x1, app(ty_Maybe, x2))
new_esEs24(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_lt12(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, x2, x3)
new_lt20(x0, x1, app(ty_[], x2))
new_esEs7(Left(x0), Left(x1), ty_Int, x2)
new_primPlusNat0(Zero, x0)
new_compare24(x0, x1, True, x2, x3)
new_lt13(x0, x1, ty_Float)
new_ltEs8(LT, LT)
new_esEs20(GT, GT)
new_ltEs13(Right(x0), Right(x1), x2, ty_Int)
new_primCmpNat0(Zero, Zero)
new_esEs18(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
new_esEs6(Just(x0), Just(x1), ty_Integer)
new_esEs7(Left(x0), Left(x1), ty_@0, x2)
new_lt20(x0, x1, ty_Ordering)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_ltEs4(False, True)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_ltEs4(True, False)
new_compare17(x0, x1)
new_ltEs8(GT, GT)
new_esEs15(GT)
new_esEs25(x0, x1, ty_Float)
new_primCompAux0(x0, GT)
new_esEs7(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs28(x0, x1, ty_Int)
new_compare15(x0, x1, app(app(ty_@2, x2), x3))
new_esEs29(x0, x1, ty_Integer)
new_compare15(x0, x1, ty_Integer)
new_esEs7(Right(x0), Right(x1), x2, ty_Char)
new_lt13(x0, x1, app(ty_Ratio, x2))
new_esEs28(x0, x1, ty_@0)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs6(Just(x0), Just(x1), ty_Ordering)
new_lt13(x0, x1, ty_Ordering)
new_ltEs13(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_esEs27(x0, x1, ty_Ordering)
new_compare10(x0, x1, True, x2)
new_ltEs19(x0, x1, ty_@0)
new_esEs24(x0, x1, ty_Char)
new_compare10(x0, x1, False, x2)
new_esEs29(x0, x1, ty_Bool)
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs18(x0, x1, ty_Int)
new_esEs17(:(x0, x1), :(x2, x3), x4)
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_esEs24(x0, x1, ty_Double)
new_esEs12(Integer(x0), Integer(x1))
new_compare18(x0, x1, x2)
new_compare210(x0, x1, True)
new_ltEs8(LT, GT)
new_ltEs8(GT, LT)
new_ltEs13(Left(x0), Left(x1), ty_Bool, x2)
new_esEs25(x0, x1, ty_Double)
new_lt6(x0, x1, x2, x3)
new_esEs6(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, ty_Integer)
new_compare110(x0, x1, False, x2, x3, x4)
new_esEs7(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs6(Nothing, Nothing, x0)
new_esEs27(x0, x1, app(ty_[], x2))
new_esEs6(Just(x0), Nothing, x1)
new_esEs5(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_ltEs13(Right(x0), Right(x1), x2, ty_Double)
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs18(x0, x1, ty_Float)
new_not(EQ)
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_lt11(x0, x1, x2, x3, x4)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_esEs7(Right(x0), Right(x1), x2, ty_Ordering)
new_lt13(x0, x1, ty_@0)
new_esEs6(Just(x0), Just(x1), ty_Double)
new_esEs29(x0, x1, ty_Double)
new_ltEs19(x0, x1, ty_Char)
new_lt12(x0, x1, ty_Ordering)
new_lt18(x0, x1, x2, x3)
new_lt13(x0, x1, ty_Integer)
new_compare([], [], x0)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_compare212(x0, x1, False, x2, x3)
new_lt13(x0, x1, ty_Char)
new_esEs20(EQ, EQ)
new_esEs9(:%(x0, x1), :%(x2, x3), x4)
new_esEs11(x0, x1, ty_Int)
new_ltEs13(Right(x0), Right(x1), x2, ty_Ordering)
new_compare15(x0, x1, app(ty_Maybe, x2))
new_esEs15(EQ)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_ltEs15(x0, x1)
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_FiniteMap, x3), x4))
new_compare7(Integer(x0), Integer(x1))
new_compare([], :(x0, x1), x2)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_compare27(:%(x0, x1), :%(x2, x3), ty_Integer)
new_ltEs13(Left(x0), Left(x1), ty_Ordering, x2)
new_compare111(x0, x1, False)
new_esEs25(x0, x1, ty_Ordering)
new_ltEs8(GT, EQ)
new_ltEs8(EQ, GT)
new_esEs21(Double(x0, x1), Double(x2, x3))
new_ltEs13(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs29(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_ltEs13(Left(x0), Left(x1), ty_Double, x2)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sr0(Integer(x0), Integer(x1))
new_compare11(x0, x1, True, x2, x3)
new_esEs6(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs6(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs25(x0, x1, ty_@0)
new_compare26(@0, @0)
new_ltEs9(x0, x1)
new_ltEs19(x0, x1, ty_Float)
new_esEs28(x0, x1, ty_Float)
new_ltEs13(Right(x0), Right(x1), x2, ty_Integer)
new_esEs14(False, False)
new_primEqInt(Pos(Zero), Pos(Zero))
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Just(x0), Just(x1), ty_Bool)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_lt12(x0, x1, app(app(ty_Either, x2), x3))
new_compare(:(x0, x1), [], x2)
new_lt13(x0, x1, ty_Bool)
new_compare211(x0, x1, False, x2)
new_lt20(x0, x1, ty_Char)
new_esEs18(x0, x1, app(ty_[], x2))
new_asAs(True, x0)
new_esEs24(x0, x1, ty_Float)
new_compare15(x0, x1, ty_Char)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs7(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs6(Just(x0), Just(x1), ty_Int)
new_compare15(x0, x1, ty_Float)
new_lt20(x0, x1, ty_Double)
new_compare15(x0, x1, app(ty_[], x2))
new_not(LT)
new_esEs25(x0, x1, ty_Char)
new_lt13(x0, x1, ty_Int)
new_esEs27(x0, x1, ty_Bool)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_esEs18(x0, x1, app(ty_Maybe, x2))
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ 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_foldFM_LE11(vyy24, vyy340, vyy341, vyy342, vyy343, Branch(vyy3440, vyy3441, vyy3442, vyy3443, vyy3444), True, h, ba) → new_foldFM_LE4(vyy24, vyy343, h, ba)
new_foldFM_LE4(vyy24, Branch(vyy3430, vyy3431, vyy3432, vyy3433, vyy3434), h, ba) → new_foldFM_LE11(vyy24, vyy3430, vyy3431, vyy3432, vyy3433, vyy3434, new_ltEs5(vyy3430, Nothing, ba), h, ba)
new_foldFM_LE11(vyy24, vyy340, vyy341, vyy342, Branch(vyy3430, vyy3431, vyy3432, vyy3433, vyy3434), vyy344, False, h, ba) → new_foldFM_LE11(vyy24, vyy3430, vyy3431, vyy3432, vyy3433, vyy3434, new_ltEs5(vyy3430, Nothing, ba), h, ba)
new_foldFM_LE11(vyy24, vyy340, vyy341, vyy342, vyy343, Branch(vyy3440, vyy3441, vyy3442, vyy3443, vyy3444), True, h, ba) → new_foldFM_LE21(vyy340, vyy341, new_foldFM_LE5(vyy24, vyy343, h, ba), vyy3440, vyy3441, vyy3442, vyy3443, vyy3444, h, ba)
new_foldFM_LE21(vyy340, vyy341, vyy28, vyy3440, vyy3441, vyy3442, vyy3443, vyy3444, h, ba) → new_foldFM_LE11(new_eltsFM_LE0(vyy340, vyy341, vyy28, h, ba), vyy3440, vyy3441, vyy3442, vyy3443, vyy3444, new_ltEs5(vyy3440, Nothing, ba), h, ba)
new_foldFM_LE11(vyy24, vyy340, vyy341, vyy342, vyy343, EmptyFM, True, h, ba) → new_foldFM_LE4(vyy24, vyy343, h, ba)
The TRS R consists of the following rules:
new_foldFM_LE5(vyy24, Branch(vyy3430, vyy3431, vyy3432, vyy3433, vyy3434), h, ba) → new_foldFM_LE12(vyy24, vyy3430, vyy3431, vyy3432, vyy3433, vyy3434, new_ltEs5(vyy3430, Nothing, ba), h, ba)
new_foldFM_LE12(vyy24, vyy340, vyy341, vyy342, vyy343, Branch(vyy3440, vyy3441, vyy3442, vyy3443, vyy3444), True, h, ba) → new_foldFM_LE22(vyy340, vyy341, new_foldFM_LE5(vyy24, vyy343, h, ba), vyy3440, vyy3441, vyy3442, vyy3443, vyy3444, h, ba)
new_foldFM_LE12(vyy24, vyy340, vyy341, vyy342, vyy343, vyy344, False, h, ba) → new_foldFM_LE5(vyy24, vyy343, h, ba)
new_foldFM_LE22(vyy340, vyy341, vyy28, vyy3440, vyy3441, vyy3442, vyy3443, vyy3444, h, ba) → new_foldFM_LE12(new_eltsFM_LE0(vyy340, vyy341, vyy28, h, ba), vyy3440, vyy3441, vyy3442, vyy3443, vyy3444, new_ltEs5(vyy3440, Nothing, ba), h, ba)
new_foldFM_LE5(vyy24, EmptyFM, h, ba) → vyy24
new_eltsFM_LE0(vyy340, vyy341, vyy27, h, ba) → :(vyy341, vyy27)
new_ltEs5(Just(vyy3000), Nothing, dh) → False
new_ltEs5(Nothing, Nothing, dh) → True
new_foldFM_LE12(vyy24, vyy340, vyy341, vyy342, vyy343, EmptyFM, True, h, ba) → new_foldFM_LE30(vyy340, vyy341, new_foldFM_LE5(vyy24, vyy343, h, ba), h, ba)
new_foldFM_LE30(vyy340, vyy341, vyy27, h, ba) → new_eltsFM_LE0(vyy340, vyy341, vyy27, h, ba)
The set Q consists of the following terms:
new_ltEs5(Just(x0), Just(x1), ty_@0)
new_ltEs5(Just(x0), Just(x1), app(ty_Ratio, x2))
new_ltEs5(Just(x0), Just(x1), ty_Ordering)
new_ltEs5(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_foldFM_LE22(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9)
new_ltEs5(Just(x0), Just(x1), ty_Double)
new_ltEs5(Just(x0), Just(x1), ty_Int)
new_ltEs5(Nothing, Just(x0), x1)
new_ltEs5(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_ltEs5(Just(x0), Just(x1), ty_Char)
new_ltEs5(Nothing, Nothing, x0)
new_eltsFM_LE0(x0, x1, x2, x3, x4)
new_foldFM_LE5(x0, EmptyFM, x1, x2)
new_ltEs5(Just(x0), Just(x1), ty_Integer)
new_foldFM_LE12(x0, x1, x2, x3, x4, EmptyFM, True, x5, x6)
new_ltEs5(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_foldFM_LE12(x0, x1, x2, x3, x4, x5, False, x6, x7)
new_ltEs5(Just(x0), Nothing, x1)
new_ltEs5(Just(x0), Just(x1), ty_Float)
new_foldFM_LE12(x0, x1, x2, x3, x4, Branch(x5, x6, x7, x8, x9), True, x10, x11)
new_foldFM_LE5(x0, Branch(x1, x2, x3, x4, x5), x6, x7)
new_ltEs5(Just(x0), Just(x1), ty_Bool)
new_ltEs5(Just(x0), Just(x1), app(ty_Maybe, x2))
new_ltEs5(Just(x0), Just(x1), app(ty_[], x2))
new_foldFM_LE30(x0, x1, x2, x3, x4)
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_foldFM_LE4(vyy24, Branch(vyy3430, vyy3431, vyy3432, vyy3433, vyy3434), h, ba) → new_foldFM_LE11(vyy24, vyy3430, vyy3431, vyy3432, vyy3433, vyy3434, new_ltEs5(vyy3430, Nothing, ba), h, ba)
The graph contains the following edges 1 >= 1, 2 > 2, 2 > 3, 2 > 4, 2 > 5, 2 > 6, 3 >= 8, 4 >= 9
- new_foldFM_LE11(vyy24, vyy340, vyy341, vyy342, Branch(vyy3430, vyy3431, vyy3432, vyy3433, vyy3434), vyy344, False, h, ba) → new_foldFM_LE11(vyy24, vyy3430, vyy3431, vyy3432, vyy3433, vyy3434, new_ltEs5(vyy3430, Nothing, ba), h, ba)
The graph contains the following edges 1 >= 1, 5 > 2, 5 > 3, 5 > 4, 5 > 5, 5 > 6, 8 >= 8, 9 >= 9
- new_foldFM_LE21(vyy340, vyy341, vyy28, vyy3440, vyy3441, vyy3442, vyy3443, vyy3444, h, ba) → new_foldFM_LE11(new_eltsFM_LE0(vyy340, vyy341, vyy28, h, ba), vyy3440, vyy3441, vyy3442, vyy3443, vyy3444, new_ltEs5(vyy3440, Nothing, ba), h, ba)
The graph contains the following edges 4 >= 2, 5 >= 3, 6 >= 4, 7 >= 5, 8 >= 6, 9 >= 8, 10 >= 9
- new_foldFM_LE11(vyy24, vyy340, vyy341, vyy342, vyy343, Branch(vyy3440, vyy3441, vyy3442, vyy3443, vyy3444), True, h, ba) → new_foldFM_LE21(vyy340, vyy341, new_foldFM_LE5(vyy24, vyy343, h, ba), vyy3440, vyy3441, vyy3442, vyy3443, vyy3444, h, ba)
The graph contains the following edges 2 >= 1, 3 >= 2, 6 > 4, 6 > 5, 6 > 6, 6 > 7, 6 > 8, 8 >= 9, 9 >= 10
- new_foldFM_LE11(vyy24, vyy340, vyy341, vyy342, vyy343, Branch(vyy3440, vyy3441, vyy3442, vyy3443, vyy3444), True, h, ba) → new_foldFM_LE4(vyy24, vyy343, h, ba)
The graph contains the following edges 1 >= 1, 5 >= 2, 8 >= 3, 9 >= 4
- new_foldFM_LE11(vyy24, vyy340, vyy341, vyy342, vyy343, EmptyFM, True, h, ba) → new_foldFM_LE4(vyy24, vyy343, h, ba)
The graph contains the following edges 1 >= 1, 5 >= 2, 8 >= 3, 9 >= 4