YES 10.103
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
| ((fmToList_LE :: (Ord b, Ord c) => FiniteMap (Either b c) a -> Either b c -> [(Either b c,a)]) :: (Ord c, Ord b) => FiniteMap (Either b c) a -> Either b c -> [(Either b c,a)]) |
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 |
|
|
| fmToList :: FiniteMap a b -> [(a,b)]
fmToList | fm | = | foldFM (\key elt rest ->(key,elt) : rest) [] fm |
|
| fmToList_LE :: Ord a => FiniteMap a b -> a -> [(a,b)]
fmToList_LE | fm fr | = | foldFM_LE (\key elt rest ->(key,elt) : rest) [] fr fm |
|
| foldFM :: (b -> a -> c -> c) -> c -> FiniteMap b a -> 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
|
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→(key,elt) : rest
is transformed to
fmToList_LE0 | key elt rest | = (key,elt) : rest |
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
mainModule FiniteMap
| ((fmToList_LE :: (Ord b, Ord c) => FiniteMap (Either b c) a -> Either b c -> [(Either b c,a)]) :: (Ord b, Ord c) => FiniteMap (Either b c) a -> Either b c -> [(Either b c,a)]) |
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 |
|
|
| fmToList :: FiniteMap b a -> [(b,a)]
fmToList | fm | = | foldFM fmToList0 [] fm |
|
|
fmToList0 | key elt rest | = | (key,elt) : rest |
|
| fmToList_LE :: Ord a => FiniteMap a b -> a -> [(a,b)]
fmToList_LE | fm fr | = | foldFM_LE fmToList_LE0 [] fr fm |
|
|
fmToList_LE0 | 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
| ((fmToList_LE :: (Ord b, Ord a) => FiniteMap (Either a b) c -> Either a b -> [(Either a b,c)]) :: (Ord b, Ord a) => FiniteMap (Either a b) c -> Either a b -> [(Either a b,c)]) |
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 |
|
|
| fmToList :: FiniteMap b a -> [(b,a)]
fmToList | fm | = | foldFM fmToList0 [] fm |
|
|
fmToList0 | key elt rest | = | (key,elt) : rest |
|
| fmToList_LE :: Ord b => FiniteMap b a -> b -> [(b,a)]
fmToList_LE | fm fr | = | foldFM_LE fmToList_LE0 [] fr fm |
|
|
fmToList_LE0 | 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 -> 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 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
| ((fmToList_LE :: (Ord a, Ord c) => FiniteMap (Either c a) b -> Either c a -> [(Either c a,b)]) :: (Ord a, Ord c) => FiniteMap (Either c a) b -> Either c a -> [(Either c 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 a b) where
|
|
(==) | fm_1 fm_2 | = | sizeFM fm_1 == sizeFM fm_2 && fmToList fm_1 == fmToList fm_2 |
|
|
| fmToList :: FiniteMap b a -> [(b,a)]
fmToList | fm | = | foldFM fmToList0 [] fm |
|
|
fmToList0 | key elt rest | = | (key,elt) : rest |
|
| fmToList_LE :: Ord b => FiniteMap b a -> b -> [(b,a)]
fmToList_LE | fm fr | = | foldFM_LE fmToList_LE0 [] fr fm |
|
|
fmToList_LE0 | 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 a b -> 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
| ((fmToList_LE :: (Ord b, Ord a) => FiniteMap (Either a b) c -> Either a b -> [(Either a b,c)]) :: (Ord a, Ord b) => FiniteMap (Either a b) c -> Either a b -> [(Either a b,c)]) |
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 |
|
|
| fmToList :: FiniteMap a b -> [(a,b)]
fmToList | fm | = | foldFM fmToList0 [] fm |
|
|
fmToList0 | key elt rest | = | (key,elt) : rest |
|
| fmToList_LE :: Ord b => FiniteMap b a -> b -> [(b,a)]
fmToList_LE | fm fr | = | foldFM_LE fmToList_LE0 [] fr fm |
|
|
fmToList_LE0 | key elt rest | = | (key,elt) : rest |
|
| foldFM :: (b -> a -> c -> c) -> c -> FiniteMap b a -> c
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 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 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 a b -> 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_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_LE0 | k z fr key elt vx fm_l fm_r True | = foldFM_LE k z fr fm_l |
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
absReal1 | x True | = x |
absReal1 | x False | = absReal0 x otherwise |
absReal0 | x True | = `negate` x |
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
| ((fmToList_LE :: (Ord c, Ord a) => FiniteMap (Either a c) b -> Either a c -> [(Either a c,b)]) :: (Ord a, Ord c) => FiniteMap (Either a c) b -> Either a c -> [(Either a c,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 |
|
|
| fmToList :: FiniteMap a b -> [(a,b)]
fmToList | fm | = | foldFM fmToList0 [] fm |
|
|
fmToList0 | key elt rest | = | (key,elt) : rest |
|
| fmToList_LE :: Ord b => FiniteMap b a -> b -> [(b,a)]
fmToList_LE | fm fr | = | foldFM_LE fmToList_LE0 [] fr fm |
|
|
fmToList_LE0 | 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 a b -> 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) |
reduce2Reduce1 | vyw vyx x y True | = error [] |
reduce2Reduce1 | vyw vyx x y False | = reduce2Reduce0 vyw vyx x y otherwise |
reduce2D | vyw vyx | = gcd vyw vyx |
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'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 |
gcd0Gcd'1 | True x vvy | = x |
gcd0Gcd'1 | vvz vwu vwv | = gcd0Gcd'0 vwu vwv |
gcd0Gcd'0 | x y | = gcd0Gcd' y (x `rem` y) |
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
mainModule FiniteMap
| ((fmToList_LE :: (Ord a, Ord b) => FiniteMap (Either b a) c -> Either b a -> [(Either b a,c)]) :: (Ord b, Ord a) => FiniteMap (Either b a) c -> Either b a -> [(Either b a,c)]) |
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 |
|
|
| fmToList :: FiniteMap a b -> [(a,b)]
fmToList | fm | = | foldFM fmToList0 [] fm |
|
|
fmToList0 | key elt rest | = | (key,elt) : rest |
|
| fmToList_LE :: Ord a => FiniteMap a b -> a -> [(a,b)]
fmToList_LE | fm fr | = | foldFM_LE fmToList_LE0 [] fr fm |
|
|
fmToList_LE0 | key elt rest | = | (key,elt) : rest |
|
| foldFM :: (b -> a -> c -> c) -> c -> FiniteMap b a -> c
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 a => (a -> b -> c -> c) -> c -> a -> FiniteMap a b -> 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
| (fmToList_LE :: (Ord c, Ord b) => FiniteMap (Either c b) a -> Either c b -> [(Either c 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 |
|
|
| fmToList :: FiniteMap b a -> [(b,a)]
fmToList | fm | = | foldFM fmToList0 [] fm |
|
|
fmToList0 | key elt rest | = | (key,elt) : rest |
|
| fmToList_LE :: Ord b => FiniteMap b a -> b -> [(b,a)]
fmToList_LE | fm fr | = | foldFM_LE fmToList_LE0 [] fr fm |
|
|
fmToList_LE0 | 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 c => (c -> b -> a -> a) -> a -> c -> FiniteMap c b -> 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 a b -> 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_foldFM(vyy590, vyy591, vyy96, Branch(vyy5930, vyy5931, vyy5932, vyy5933, vyy5934), h, ba) → new_foldFM(vyy5930, vyy5931, new_foldFM0(vyy590, vyy591, vyy96, vyy5934, h, ba), vyy5933, h, ba)
new_foldFM(vyy590, vyy591, vyy96, Branch(vyy5930, vyy5931, vyy5932, vyy5933, vyy5934), h, ba) → new_foldFM(vyy590, vyy591, vyy96, vyy5934, h, ba)
The TRS R consists of the following rules:
new_foldFM0(vyy590, vyy591, vyy96, EmptyFM, h, ba) → :(@2(vyy590, vyy591), vyy96)
new_foldFM0(vyy590, vyy591, vyy96, Branch(vyy5930, vyy5931, vyy5932, vyy5933, vyy5934), h, ba) → new_foldFM0(vyy5930, vyy5931, new_foldFM0(vyy590, vyy591, vyy96, vyy5934, h, ba), vyy5933, h, ba)
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)
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(vyy590, vyy591, vyy96, Branch(vyy5930, vyy5931, vyy5932, vyy5933, vyy5934), h, ba) → new_foldFM(vyy5930, vyy5931, new_foldFM0(vyy590, vyy591, vyy96, vyy5934, h, ba), vyy5933, h, ba)
The graph contains the following edges 4 > 1, 4 > 2, 4 > 4, 5 >= 5, 6 >= 6
- new_foldFM(vyy590, vyy591, vyy96, Branch(vyy5930, vyy5931, vyy5932, vyy5933, vyy5934), h, ba) → new_foldFM(vyy590, vyy591, vyy96, vyy5934, 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
↳ QDPSizeChangeProof
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_foldFM1(Branch(vyy590, vyy591, vyy592, vyy593, vyy594), h, ba) → new_foldFM1(vyy594, 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(vyy590, vyy591, vyy592, vyy593, vyy594), h, ba) → new_foldFM1(vyy594, 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
↳ QDPSizeChangeProof
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_primPlusNat(Succ(vyy9700), Succ(vyy401000)) → new_primPlusNat(vyy9700, 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(vyy9700), Succ(vyy401000)) → new_primPlusNat(vyy9700, 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
↳ QDPSizeChangeProof
↳ QDP
↳ 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
↳ QDPSizeChangeProof
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_primEqNat(Succ(vyy5800), Succ(vyy5900)) → new_primEqNat(vyy5800, vyy5900)
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(vyy5800), Succ(vyy5900)) → new_primEqNat(vyy5800, vyy5900)
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
↳ Rewriting
↳ QDP
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_esEs2(Just(vyy580), Just(vyy590), app(app(app(ty_@3, hg), hh), baa)) → new_esEs1(vyy580, vyy590, hg, hh, baa)
new_esEs3(Right(vyy580), Right(vyy590), bcc, app(app(ty_@2, bde), bdf)) → new_esEs4(vyy580, vyy590, bde, bdf)
new_esEs3(Right(vyy580), Right(vyy590), bcc, app(ty_[], bcf)) → new_esEs(vyy580, vyy590, bcf)
new_esEs4(@2(vyy580, vyy581), @2(vyy590, vyy591), app(app(app(ty_@3, bfg), bfh), bga), bfe) → new_esEs1(vyy580, vyy590, bfg, bfh, bga)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), cf, app(app(app(ty_@3, eh), fa), fb), ef) → new_esEs1(vyy581, vyy591, eh, fa, fb)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), cf, cg, app(app(ty_FiniteMap, da), db)) → new_esEs0(vyy582, vyy592, da, db)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), cf, app(app(ty_Either, fd), ff), ef) → new_esEs3(vyy581, vyy591, fd, ff)
new_esEs3(Right(vyy580), Right(vyy590), bcc, app(app(ty_Either, bdc), bdd)) → new_esEs3(vyy580, vyy590, bdc, bdd)
new_esEs4(@2(vyy580, vyy581), @2(vyy590, vyy591), bdg, app(app(ty_FiniteMap, bdh), bea)) → new_esEs0(vyy581, vyy591, bdh, bea)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), cf, cg, app(app(app(ty_@3, dd), de), df)) → new_esEs1(vyy582, vyy592, dd, de, df)
new_esEs3(Left(vyy580), Left(vyy590), app(app(app(ty_@3, bbc), bbd), bbe), bba) → new_esEs1(vyy580, vyy590, bbc, bbd, bbe)
new_esEs2(Just(vyy580), Just(vyy590), app(ty_Maybe, bab)) → new_esEs2(vyy580, vyy590, bab)
new_esEs3(Left(vyy580), Left(vyy590), app(app(ty_Either, bbg), bbh), bba) → new_esEs3(vyy580, vyy590, bbg, bbh)
new_esEs2(Just(vyy580), Just(vyy590), app(app(ty_FiniteMap, hd), he)) → new_esEs0(vyy580, vyy590, hd, he)
new_esEs4(@2(vyy580, vyy581), @2(vyy590, vyy591), bdg, app(app(ty_Either, beg), beh)) → new_esEs3(vyy581, vyy591, beg, beh)
new_esEs(:(vyy580, vyy581), :(vyy590, vyy591), app(app(ty_Either, bh), ca)) → new_esEs3(vyy580, vyy590, bh, ca)
new_esEs4(@2(vyy580, vyy581), @2(vyy590, vyy591), bdg, app(ty_Maybe, bef)) → new_esEs2(vyy581, vyy591, bef)
new_esEs3(Left(vyy580), Left(vyy590), app(app(ty_@2, bca), bcb), bba) → new_esEs4(vyy580, vyy590, bca, bcb)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), cf, cg, app(app(ty_@2, eb), ec)) → new_esEs4(vyy582, vyy592, eb, ec)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), app(ty_Maybe, gg), cg, ef) → new_esEs2(vyy580, vyy590, gg)
new_esEs3(Right(vyy580), Right(vyy590), bcc, app(ty_Maybe, bdb)) → new_esEs2(vyy580, vyy590, bdb)
new_esEs(:(vyy580, vyy581), :(vyy590, vyy591), app(app(ty_@2, cb), cc)) → new_esEs4(vyy580, vyy590, cb, cc)
new_esEs2(Just(vyy580), Just(vyy590), app(app(ty_Either, bac), bad)) → new_esEs3(vyy580, vyy590, bac, bad)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), cf, cg, app(ty_[], dc)) → new_esEs(vyy582, vyy592, dc)
new_esEs4(@2(vyy580, vyy581), @2(vyy590, vyy591), bdg, app(app(ty_@2, bfa), bfb)) → new_esEs4(vyy581, vyy591, bfa, bfb)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), cf, app(ty_[], eg), ef) → new_esEs(vyy581, vyy591, eg)
new_esEs0(vyy58, vyy59, cd, ce) → new_esEs(new_fmToList(vyy58, cd, ce), new_fmToList(vyy59, cd, ce), app(app(ty_@2, cd), ce))
new_esEs4(@2(vyy580, vyy581), @2(vyy590, vyy591), app(ty_Maybe, bgb), bfe) → new_esEs2(vyy580, vyy590, bgb)
new_esEs2(Just(vyy580), Just(vyy590), app(ty_[], hf)) → new_esEs(vyy580, vyy590, hf)
new_esEs3(Left(vyy580), Left(vyy590), app(app(ty_FiniteMap, bag), bah), bba) → new_esEs0(vyy580, vyy590, bag, bah)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), cf, app(app(ty_FiniteMap, ed), ee), ef) → new_esEs0(vyy581, vyy591, ed, ee)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), cf, cg, app(app(ty_Either, dh), ea)) → new_esEs3(vyy582, vyy592, dh, ea)
new_esEs4(@2(vyy580, vyy581), @2(vyy590, vyy591), app(app(ty_@2, bge), bgf), bfe) → new_esEs4(vyy580, vyy590, bge, bgf)
new_esEs3(Right(vyy580), Right(vyy590), bcc, app(app(app(ty_@3, bcg), bch), bda)) → new_esEs1(vyy580, vyy590, bcg, bch, bda)
new_esEs3(Left(vyy580), Left(vyy590), app(ty_[], bbb), bba) → new_esEs(vyy580, vyy590, bbb)
new_esEs3(Right(vyy580), Right(vyy590), bcc, app(app(ty_FiniteMap, bcd), bce)) → new_esEs0(vyy580, vyy590, bcd, bce)
new_esEs(:(vyy580, vyy581), :(vyy590, vyy591), app(ty_Maybe, bg)) → new_esEs2(vyy580, vyy590, bg)
new_esEs4(@2(vyy580, vyy581), @2(vyy590, vyy591), bdg, app(ty_[], beb)) → new_esEs(vyy581, vyy591, beb)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), app(app(ty_FiniteMap, ga), gb), cg, ef) → new_esEs0(vyy580, vyy590, ga, gb)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), app(app(app(ty_@3, gd), ge), gf), cg, ef) → new_esEs1(vyy580, vyy590, gd, ge, gf)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), cf, app(app(ty_@2, fg), fh), ef) → new_esEs4(vyy581, vyy591, fg, fh)
new_esEs3(Left(vyy580), Left(vyy590), app(ty_Maybe, bbf), bba) → new_esEs2(vyy580, vyy590, bbf)
new_esEs(:(vyy580, vyy581), :(vyy590, vyy591), h) → new_esEs(vyy581, vyy591, h)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), cf, app(ty_Maybe, fc), ef) → new_esEs2(vyy581, vyy591, fc)
new_esEs(:(vyy580, vyy581), :(vyy590, vyy591), app(app(app(ty_@3, bd), be), bf)) → new_esEs1(vyy580, vyy590, bd, be, bf)
new_esEs4(@2(vyy580, vyy581), @2(vyy590, vyy591), app(app(ty_FiniteMap, bfc), bfd), bfe) → new_esEs0(vyy580, vyy590, bfc, bfd)
new_esEs4(@2(vyy580, vyy581), @2(vyy590, vyy591), bdg, app(app(app(ty_@3, bec), bed), bee)) → new_esEs1(vyy581, vyy591, bec, bed, bee)
new_esEs4(@2(vyy580, vyy581), @2(vyy590, vyy591), app(ty_[], bff), bfe) → new_esEs(vyy580, vyy590, bff)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), app(app(ty_@2, hb), hc), cg, ef) → new_esEs4(vyy580, vyy590, hb, hc)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), cf, cg, app(ty_Maybe, dg)) → new_esEs2(vyy582, vyy592, dg)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), app(ty_[], gc), cg, ef) → new_esEs(vyy580, vyy590, gc)
new_esEs4(@2(vyy580, vyy581), @2(vyy590, vyy591), app(app(ty_Either, bgc), bgd), bfe) → new_esEs3(vyy580, vyy590, bgc, bgd)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), app(app(ty_Either, gh), ha), cg, ef) → new_esEs3(vyy580, vyy590, gh, ha)
new_esEs2(Just(vyy580), Just(vyy590), app(app(ty_@2, bae), baf)) → new_esEs4(vyy580, vyy590, bae, baf)
new_esEs(:(vyy580, vyy581), :(vyy590, vyy591), app(ty_[], bc)) → new_esEs(vyy580, vyy590, bc)
new_esEs(:(vyy580, vyy581), :(vyy590, vyy591), app(app(ty_FiniteMap, ba), bb)) → new_esEs0(vyy580, vyy590, ba, bb)
The TRS R consists of the following rules:
new_foldFM0(vyy590, vyy591, vyy96, EmptyFM, cd, ce) → :(@2(vyy590, vyy591), vyy96)
new_foldFM0(vyy590, vyy591, vyy96, Branch(vyy5930, vyy5931, vyy5932, vyy5933, vyy5934), cd, ce) → new_foldFM0(vyy5930, vyy5931, new_foldFM0(vyy590, vyy591, vyy96, vyy5934, cd, ce), vyy5933, cd, ce)
new_fmToList(vyy59, cd, ce) → new_foldFM2(vyy59, cd, ce)
new_foldFM2(Branch(vyy590, vyy591, vyy592, vyy593, vyy594), cd, ce) → new_foldFM0(vyy590, vyy591, new_foldFM2(vyy594, cd, ce), vyy593, cd, ce)
new_foldFM2(EmptyFM, cd, ce) → []
The set Q consists of the following terms:
new_fmToList(x0, x1, x2)
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_foldFM2(EmptyFM, x0, x1)
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_esEs0(vyy58, vyy59, cd, ce) → new_esEs(new_fmToList(vyy58, cd, ce), new_fmToList(vyy59, cd, ce), app(app(ty_@2, cd), ce)) at position [0] we obtained the following new rules:
new_esEs0(vyy58, vyy59, cd, ce) → new_esEs(new_foldFM2(vyy58, cd, ce), new_fmToList(vyy59, cd, ce), app(app(ty_@2, cd), ce))
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ Rewriting
↳ QDP
↳ Rewriting
↳ QDP
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_esEs3(Right(vyy580), Right(vyy590), bcc, app(app(ty_@2, bde), bdf)) → new_esEs4(vyy580, vyy590, bde, bdf)
new_esEs2(Just(vyy580), Just(vyy590), app(app(app(ty_@3, hg), hh), baa)) → new_esEs1(vyy580, vyy590, hg, hh, baa)
new_esEs3(Right(vyy580), Right(vyy590), bcc, app(ty_[], bcf)) → new_esEs(vyy580, vyy590, bcf)
new_esEs4(@2(vyy580, vyy581), @2(vyy590, vyy591), app(app(app(ty_@3, bfg), bfh), bga), bfe) → new_esEs1(vyy580, vyy590, bfg, bfh, bga)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), cf, cg, app(app(ty_FiniteMap, da), db)) → new_esEs0(vyy582, vyy592, da, db)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), cf, app(app(app(ty_@3, eh), fa), fb), ef) → new_esEs1(vyy581, vyy591, eh, fa, fb)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), cf, app(app(ty_Either, fd), ff), ef) → new_esEs3(vyy581, vyy591, fd, ff)
new_esEs4(@2(vyy580, vyy581), @2(vyy590, vyy591), bdg, app(app(ty_FiniteMap, bdh), bea)) → new_esEs0(vyy581, vyy591, bdh, bea)
new_esEs3(Right(vyy580), Right(vyy590), bcc, app(app(ty_Either, bdc), bdd)) → new_esEs3(vyy580, vyy590, bdc, bdd)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), cf, cg, app(app(app(ty_@3, dd), de), df)) → new_esEs1(vyy582, vyy592, dd, de, df)
new_esEs3(Left(vyy580), Left(vyy590), app(app(app(ty_@3, bbc), bbd), bbe), bba) → new_esEs1(vyy580, vyy590, bbc, bbd, bbe)
new_esEs2(Just(vyy580), Just(vyy590), app(ty_Maybe, bab)) → new_esEs2(vyy580, vyy590, bab)
new_esEs2(Just(vyy580), Just(vyy590), app(app(ty_FiniteMap, hd), he)) → new_esEs0(vyy580, vyy590, hd, he)
new_esEs3(Left(vyy580), Left(vyy590), app(app(ty_Either, bbg), bbh), bba) → new_esEs3(vyy580, vyy590, bbg, bbh)
new_esEs4(@2(vyy580, vyy581), @2(vyy590, vyy591), bdg, app(app(ty_Either, beg), beh)) → new_esEs3(vyy581, vyy591, beg, beh)
new_esEs(:(vyy580, vyy581), :(vyy590, vyy591), app(app(ty_Either, bh), ca)) → new_esEs3(vyy580, vyy590, bh, ca)
new_esEs4(@2(vyy580, vyy581), @2(vyy590, vyy591), bdg, app(ty_Maybe, bef)) → new_esEs2(vyy581, vyy591, bef)
new_esEs3(Left(vyy580), Left(vyy590), app(app(ty_@2, bca), bcb), bba) → new_esEs4(vyy580, vyy590, bca, bcb)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), cf, cg, app(app(ty_@2, eb), ec)) → new_esEs4(vyy582, vyy592, eb, ec)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), app(ty_Maybe, gg), cg, ef) → new_esEs2(vyy580, vyy590, gg)
new_esEs3(Right(vyy580), Right(vyy590), bcc, app(ty_Maybe, bdb)) → new_esEs2(vyy580, vyy590, bdb)
new_esEs(:(vyy580, vyy581), :(vyy590, vyy591), app(app(ty_@2, cb), cc)) → new_esEs4(vyy580, vyy590, cb, cc)
new_esEs4(@2(vyy580, vyy581), @2(vyy590, vyy591), bdg, app(app(ty_@2, bfa), bfb)) → new_esEs4(vyy581, vyy591, bfa, bfb)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), cf, cg, app(ty_[], dc)) → new_esEs(vyy582, vyy592, dc)
new_esEs2(Just(vyy580), Just(vyy590), app(app(ty_Either, bac), bad)) → new_esEs3(vyy580, vyy590, bac, bad)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), cf, app(ty_[], eg), ef) → new_esEs(vyy581, vyy591, eg)
new_esEs4(@2(vyy580, vyy581), @2(vyy590, vyy591), app(ty_Maybe, bgb), bfe) → new_esEs2(vyy580, vyy590, bgb)
new_esEs2(Just(vyy580), Just(vyy590), app(ty_[], hf)) → new_esEs(vyy580, vyy590, hf)
new_esEs3(Left(vyy580), Left(vyy590), app(app(ty_FiniteMap, bag), bah), bba) → new_esEs0(vyy580, vyy590, bag, bah)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), cf, app(app(ty_FiniteMap, ed), ee), ef) → new_esEs0(vyy581, vyy591, ed, ee)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), cf, cg, app(app(ty_Either, dh), ea)) → new_esEs3(vyy582, vyy592, dh, ea)
new_esEs4(@2(vyy580, vyy581), @2(vyy590, vyy591), app(app(ty_@2, bge), bgf), bfe) → new_esEs4(vyy580, vyy590, bge, bgf)
new_esEs3(Right(vyy580), Right(vyy590), bcc, app(app(app(ty_@3, bcg), bch), bda)) → new_esEs1(vyy580, vyy590, bcg, bch, bda)
new_esEs3(Left(vyy580), Left(vyy590), app(ty_[], bbb), bba) → new_esEs(vyy580, vyy590, bbb)
new_esEs3(Right(vyy580), Right(vyy590), bcc, app(app(ty_FiniteMap, bcd), bce)) → new_esEs0(vyy580, vyy590, bcd, bce)
new_esEs4(@2(vyy580, vyy581), @2(vyy590, vyy591), bdg, app(ty_[], beb)) → new_esEs(vyy581, vyy591, beb)
new_esEs(:(vyy580, vyy581), :(vyy590, vyy591), app(ty_Maybe, bg)) → new_esEs2(vyy580, vyy590, bg)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), app(app(ty_FiniteMap, ga), gb), cg, ef) → new_esEs0(vyy580, vyy590, ga, gb)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), cf, app(app(ty_@2, fg), fh), ef) → new_esEs4(vyy581, vyy591, fg, fh)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), app(app(app(ty_@3, gd), ge), gf), cg, ef) → new_esEs1(vyy580, vyy590, gd, ge, gf)
new_esEs3(Left(vyy580), Left(vyy590), app(ty_Maybe, bbf), bba) → new_esEs2(vyy580, vyy590, bbf)
new_esEs(:(vyy580, vyy581), :(vyy590, vyy591), h) → new_esEs(vyy581, vyy591, h)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), cf, app(ty_Maybe, fc), ef) → new_esEs2(vyy581, vyy591, fc)
new_esEs(:(vyy580, vyy581), :(vyy590, vyy591), app(app(app(ty_@3, bd), be), bf)) → new_esEs1(vyy580, vyy590, bd, be, bf)
new_esEs4(@2(vyy580, vyy581), @2(vyy590, vyy591), app(app(ty_FiniteMap, bfc), bfd), bfe) → new_esEs0(vyy580, vyy590, bfc, bfd)
new_esEs4(@2(vyy580, vyy581), @2(vyy590, vyy591), bdg, app(app(app(ty_@3, bec), bed), bee)) → new_esEs1(vyy581, vyy591, bec, bed, bee)
new_esEs0(vyy58, vyy59, cd, ce) → new_esEs(new_foldFM2(vyy58, cd, ce), new_fmToList(vyy59, cd, ce), app(app(ty_@2, cd), ce))
new_esEs4(@2(vyy580, vyy581), @2(vyy590, vyy591), app(ty_[], bff), bfe) → new_esEs(vyy580, vyy590, bff)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), app(app(ty_@2, hb), hc), cg, ef) → new_esEs4(vyy580, vyy590, hb, hc)
new_esEs4(@2(vyy580, vyy581), @2(vyy590, vyy591), app(app(ty_Either, bgc), bgd), bfe) → new_esEs3(vyy580, vyy590, bgc, bgd)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), app(ty_[], gc), cg, ef) → new_esEs(vyy580, vyy590, gc)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), cf, cg, app(ty_Maybe, dg)) → new_esEs2(vyy582, vyy592, dg)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), app(app(ty_Either, gh), ha), cg, ef) → new_esEs3(vyy580, vyy590, gh, ha)
new_esEs2(Just(vyy580), Just(vyy590), app(app(ty_@2, bae), baf)) → new_esEs4(vyy580, vyy590, bae, baf)
new_esEs(:(vyy580, vyy581), :(vyy590, vyy591), app(ty_[], bc)) → new_esEs(vyy580, vyy590, bc)
new_esEs(:(vyy580, vyy581), :(vyy590, vyy591), app(app(ty_FiniteMap, ba), bb)) → new_esEs0(vyy580, vyy590, ba, bb)
The TRS R consists of the following rules:
new_foldFM0(vyy590, vyy591, vyy96, EmptyFM, cd, ce) → :(@2(vyy590, vyy591), vyy96)
new_foldFM0(vyy590, vyy591, vyy96, Branch(vyy5930, vyy5931, vyy5932, vyy5933, vyy5934), cd, ce) → new_foldFM0(vyy5930, vyy5931, new_foldFM0(vyy590, vyy591, vyy96, vyy5934, cd, ce), vyy5933, cd, ce)
new_fmToList(vyy59, cd, ce) → new_foldFM2(vyy59, cd, ce)
new_foldFM2(Branch(vyy590, vyy591, vyy592, vyy593, vyy594), cd, ce) → new_foldFM0(vyy590, vyy591, new_foldFM2(vyy594, cd, ce), vyy593, cd, ce)
new_foldFM2(EmptyFM, cd, ce) → []
The set Q consists of the following terms:
new_fmToList(x0, x1, x2)
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_foldFM2(EmptyFM, x0, x1)
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_esEs0(vyy58, vyy59, cd, ce) → new_esEs(new_foldFM2(vyy58, cd, ce), new_fmToList(vyy59, cd, ce), app(app(ty_@2, cd), ce)) at position [1] we obtained the following new rules:
new_esEs0(vyy58, vyy59, cd, ce) → new_esEs(new_foldFM2(vyy58, cd, ce), new_foldFM2(vyy59, cd, ce), app(app(ty_@2, cd), ce))
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ Rewriting
↳ QDP
↳ Rewriting
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_esEs2(Just(vyy580), Just(vyy590), app(app(app(ty_@3, hg), hh), baa)) → new_esEs1(vyy580, vyy590, hg, hh, baa)
new_esEs3(Right(vyy580), Right(vyy590), bcc, app(app(ty_@2, bde), bdf)) → new_esEs4(vyy580, vyy590, bde, bdf)
new_esEs3(Right(vyy580), Right(vyy590), bcc, app(ty_[], bcf)) → new_esEs(vyy580, vyy590, bcf)
new_esEs4(@2(vyy580, vyy581), @2(vyy590, vyy591), app(app(app(ty_@3, bfg), bfh), bga), bfe) → new_esEs1(vyy580, vyy590, bfg, bfh, bga)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), cf, app(app(app(ty_@3, eh), fa), fb), ef) → new_esEs1(vyy581, vyy591, eh, fa, fb)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), cf, cg, app(app(ty_FiniteMap, da), db)) → new_esEs0(vyy582, vyy592, da, db)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), cf, app(app(ty_Either, fd), ff), ef) → new_esEs3(vyy581, vyy591, fd, ff)
new_esEs3(Right(vyy580), Right(vyy590), bcc, app(app(ty_Either, bdc), bdd)) → new_esEs3(vyy580, vyy590, bdc, bdd)
new_esEs4(@2(vyy580, vyy581), @2(vyy590, vyy591), bdg, app(app(ty_FiniteMap, bdh), bea)) → new_esEs0(vyy581, vyy591, bdh, bea)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), cf, cg, app(app(app(ty_@3, dd), de), df)) → new_esEs1(vyy582, vyy592, dd, de, df)
new_esEs3(Left(vyy580), Left(vyy590), app(app(app(ty_@3, bbc), bbd), bbe), bba) → new_esEs1(vyy580, vyy590, bbc, bbd, bbe)
new_esEs2(Just(vyy580), Just(vyy590), app(ty_Maybe, bab)) → new_esEs2(vyy580, vyy590, bab)
new_esEs3(Left(vyy580), Left(vyy590), app(app(ty_Either, bbg), bbh), bba) → new_esEs3(vyy580, vyy590, bbg, bbh)
new_esEs2(Just(vyy580), Just(vyy590), app(app(ty_FiniteMap, hd), he)) → new_esEs0(vyy580, vyy590, hd, he)
new_esEs4(@2(vyy580, vyy581), @2(vyy590, vyy591), bdg, app(app(ty_Either, beg), beh)) → new_esEs3(vyy581, vyy591, beg, beh)
new_esEs(:(vyy580, vyy581), :(vyy590, vyy591), app(app(ty_Either, bh), ca)) → new_esEs3(vyy580, vyy590, bh, ca)
new_esEs0(vyy58, vyy59, cd, ce) → new_esEs(new_foldFM2(vyy58, cd, ce), new_foldFM2(vyy59, cd, ce), app(app(ty_@2, cd), ce))
new_esEs4(@2(vyy580, vyy581), @2(vyy590, vyy591), bdg, app(ty_Maybe, bef)) → new_esEs2(vyy581, vyy591, bef)
new_esEs3(Left(vyy580), Left(vyy590), app(app(ty_@2, bca), bcb), bba) → new_esEs4(vyy580, vyy590, bca, bcb)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), cf, cg, app(app(ty_@2, eb), ec)) → new_esEs4(vyy582, vyy592, eb, ec)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), app(ty_Maybe, gg), cg, ef) → new_esEs2(vyy580, vyy590, gg)
new_esEs3(Right(vyy580), Right(vyy590), bcc, app(ty_Maybe, bdb)) → new_esEs2(vyy580, vyy590, bdb)
new_esEs(:(vyy580, vyy581), :(vyy590, vyy591), app(app(ty_@2, cb), cc)) → new_esEs4(vyy580, vyy590, cb, cc)
new_esEs2(Just(vyy580), Just(vyy590), app(app(ty_Either, bac), bad)) → new_esEs3(vyy580, vyy590, bac, bad)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), cf, cg, app(ty_[], dc)) → new_esEs(vyy582, vyy592, dc)
new_esEs4(@2(vyy580, vyy581), @2(vyy590, vyy591), bdg, app(app(ty_@2, bfa), bfb)) → new_esEs4(vyy581, vyy591, bfa, bfb)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), cf, app(ty_[], eg), ef) → new_esEs(vyy581, vyy591, eg)
new_esEs4(@2(vyy580, vyy581), @2(vyy590, vyy591), app(ty_Maybe, bgb), bfe) → new_esEs2(vyy580, vyy590, bgb)
new_esEs2(Just(vyy580), Just(vyy590), app(ty_[], hf)) → new_esEs(vyy580, vyy590, hf)
new_esEs3(Left(vyy580), Left(vyy590), app(app(ty_FiniteMap, bag), bah), bba) → new_esEs0(vyy580, vyy590, bag, bah)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), cf, app(app(ty_FiniteMap, ed), ee), ef) → new_esEs0(vyy581, vyy591, ed, ee)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), cf, cg, app(app(ty_Either, dh), ea)) → new_esEs3(vyy582, vyy592, dh, ea)
new_esEs4(@2(vyy580, vyy581), @2(vyy590, vyy591), app(app(ty_@2, bge), bgf), bfe) → new_esEs4(vyy580, vyy590, bge, bgf)
new_esEs3(Right(vyy580), Right(vyy590), bcc, app(app(app(ty_@3, bcg), bch), bda)) → new_esEs1(vyy580, vyy590, bcg, bch, bda)
new_esEs3(Left(vyy580), Left(vyy590), app(ty_[], bbb), bba) → new_esEs(vyy580, vyy590, bbb)
new_esEs3(Right(vyy580), Right(vyy590), bcc, app(app(ty_FiniteMap, bcd), bce)) → new_esEs0(vyy580, vyy590, bcd, bce)
new_esEs(:(vyy580, vyy581), :(vyy590, vyy591), app(ty_Maybe, bg)) → new_esEs2(vyy580, vyy590, bg)
new_esEs4(@2(vyy580, vyy581), @2(vyy590, vyy591), bdg, app(ty_[], beb)) → new_esEs(vyy581, vyy591, beb)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), app(app(ty_FiniteMap, ga), gb), cg, ef) → new_esEs0(vyy580, vyy590, ga, gb)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), app(app(app(ty_@3, gd), ge), gf), cg, ef) → new_esEs1(vyy580, vyy590, gd, ge, gf)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), cf, app(app(ty_@2, fg), fh), ef) → new_esEs4(vyy581, vyy591, fg, fh)
new_esEs3(Left(vyy580), Left(vyy590), app(ty_Maybe, bbf), bba) → new_esEs2(vyy580, vyy590, bbf)
new_esEs(:(vyy580, vyy581), :(vyy590, vyy591), h) → new_esEs(vyy581, vyy591, h)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), cf, app(ty_Maybe, fc), ef) → new_esEs2(vyy581, vyy591, fc)
new_esEs(:(vyy580, vyy581), :(vyy590, vyy591), app(app(app(ty_@3, bd), be), bf)) → new_esEs1(vyy580, vyy590, bd, be, bf)
new_esEs4(@2(vyy580, vyy581), @2(vyy590, vyy591), app(app(ty_FiniteMap, bfc), bfd), bfe) → new_esEs0(vyy580, vyy590, bfc, bfd)
new_esEs4(@2(vyy580, vyy581), @2(vyy590, vyy591), bdg, app(app(app(ty_@3, bec), bed), bee)) → new_esEs1(vyy581, vyy591, bec, bed, bee)
new_esEs4(@2(vyy580, vyy581), @2(vyy590, vyy591), app(ty_[], bff), bfe) → new_esEs(vyy580, vyy590, bff)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), app(app(ty_@2, hb), hc), cg, ef) → new_esEs4(vyy580, vyy590, hb, hc)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), cf, cg, app(ty_Maybe, dg)) → new_esEs2(vyy582, vyy592, dg)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), app(ty_[], gc), cg, ef) → new_esEs(vyy580, vyy590, gc)
new_esEs4(@2(vyy580, vyy581), @2(vyy590, vyy591), app(app(ty_Either, bgc), bgd), bfe) → new_esEs3(vyy580, vyy590, bgc, bgd)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), app(app(ty_Either, gh), ha), cg, ef) → new_esEs3(vyy580, vyy590, gh, ha)
new_esEs2(Just(vyy580), Just(vyy590), app(app(ty_@2, bae), baf)) → new_esEs4(vyy580, vyy590, bae, baf)
new_esEs(:(vyy580, vyy581), :(vyy590, vyy591), app(ty_[], bc)) → new_esEs(vyy580, vyy590, bc)
new_esEs(:(vyy580, vyy581), :(vyy590, vyy591), app(app(ty_FiniteMap, ba), bb)) → new_esEs0(vyy580, vyy590, ba, bb)
The TRS R consists of the following rules:
new_foldFM0(vyy590, vyy591, vyy96, EmptyFM, cd, ce) → :(@2(vyy590, vyy591), vyy96)
new_foldFM0(vyy590, vyy591, vyy96, Branch(vyy5930, vyy5931, vyy5932, vyy5933, vyy5934), cd, ce) → new_foldFM0(vyy5930, vyy5931, new_foldFM0(vyy590, vyy591, vyy96, vyy5934, cd, ce), vyy5933, cd, ce)
new_fmToList(vyy59, cd, ce) → new_foldFM2(vyy59, cd, ce)
new_foldFM2(Branch(vyy590, vyy591, vyy592, vyy593, vyy594), cd, ce) → new_foldFM0(vyy590, vyy591, new_foldFM2(vyy594, cd, ce), vyy593, cd, ce)
new_foldFM2(EmptyFM, cd, ce) → []
The set Q consists of the following terms:
new_fmToList(x0, x1, x2)
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_foldFM2(EmptyFM, x0, x1)
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
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
↳ Rewriting
↳ QDP
↳ Rewriting
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QReductionProof
↳ QDP
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_esEs2(Just(vyy580), Just(vyy590), app(app(app(ty_@3, hg), hh), baa)) → new_esEs1(vyy580, vyy590, hg, hh, baa)
new_esEs3(Right(vyy580), Right(vyy590), bcc, app(app(ty_@2, bde), bdf)) → new_esEs4(vyy580, vyy590, bde, bdf)
new_esEs3(Right(vyy580), Right(vyy590), bcc, app(ty_[], bcf)) → new_esEs(vyy580, vyy590, bcf)
new_esEs4(@2(vyy580, vyy581), @2(vyy590, vyy591), app(app(app(ty_@3, bfg), bfh), bga), bfe) → new_esEs1(vyy580, vyy590, bfg, bfh, bga)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), cf, app(app(app(ty_@3, eh), fa), fb), ef) → new_esEs1(vyy581, vyy591, eh, fa, fb)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), cf, cg, app(app(ty_FiniteMap, da), db)) → new_esEs0(vyy582, vyy592, da, db)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), cf, app(app(ty_Either, fd), ff), ef) → new_esEs3(vyy581, vyy591, fd, ff)
new_esEs3(Right(vyy580), Right(vyy590), bcc, app(app(ty_Either, bdc), bdd)) → new_esEs3(vyy580, vyy590, bdc, bdd)
new_esEs4(@2(vyy580, vyy581), @2(vyy590, vyy591), bdg, app(app(ty_FiniteMap, bdh), bea)) → new_esEs0(vyy581, vyy591, bdh, bea)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), cf, cg, app(app(app(ty_@3, dd), de), df)) → new_esEs1(vyy582, vyy592, dd, de, df)
new_esEs3(Left(vyy580), Left(vyy590), app(app(app(ty_@3, bbc), bbd), bbe), bba) → new_esEs1(vyy580, vyy590, bbc, bbd, bbe)
new_esEs2(Just(vyy580), Just(vyy590), app(ty_Maybe, bab)) → new_esEs2(vyy580, vyy590, bab)
new_esEs3(Left(vyy580), Left(vyy590), app(app(ty_Either, bbg), bbh), bba) → new_esEs3(vyy580, vyy590, bbg, bbh)
new_esEs2(Just(vyy580), Just(vyy590), app(app(ty_FiniteMap, hd), he)) → new_esEs0(vyy580, vyy590, hd, he)
new_esEs4(@2(vyy580, vyy581), @2(vyy590, vyy591), bdg, app(app(ty_Either, beg), beh)) → new_esEs3(vyy581, vyy591, beg, beh)
new_esEs(:(vyy580, vyy581), :(vyy590, vyy591), app(app(ty_Either, bh), ca)) → new_esEs3(vyy580, vyy590, bh, ca)
new_esEs0(vyy58, vyy59, cd, ce) → new_esEs(new_foldFM2(vyy58, cd, ce), new_foldFM2(vyy59, cd, ce), app(app(ty_@2, cd), ce))
new_esEs4(@2(vyy580, vyy581), @2(vyy590, vyy591), bdg, app(ty_Maybe, bef)) → new_esEs2(vyy581, vyy591, bef)
new_esEs3(Left(vyy580), Left(vyy590), app(app(ty_@2, bca), bcb), bba) → new_esEs4(vyy580, vyy590, bca, bcb)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), cf, cg, app(app(ty_@2, eb), ec)) → new_esEs4(vyy582, vyy592, eb, ec)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), app(ty_Maybe, gg), cg, ef) → new_esEs2(vyy580, vyy590, gg)
new_esEs3(Right(vyy580), Right(vyy590), bcc, app(ty_Maybe, bdb)) → new_esEs2(vyy580, vyy590, bdb)
new_esEs(:(vyy580, vyy581), :(vyy590, vyy591), app(app(ty_@2, cb), cc)) → new_esEs4(vyy580, vyy590, cb, cc)
new_esEs2(Just(vyy580), Just(vyy590), app(app(ty_Either, bac), bad)) → new_esEs3(vyy580, vyy590, bac, bad)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), cf, cg, app(ty_[], dc)) → new_esEs(vyy582, vyy592, dc)
new_esEs4(@2(vyy580, vyy581), @2(vyy590, vyy591), bdg, app(app(ty_@2, bfa), bfb)) → new_esEs4(vyy581, vyy591, bfa, bfb)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), cf, app(ty_[], eg), ef) → new_esEs(vyy581, vyy591, eg)
new_esEs4(@2(vyy580, vyy581), @2(vyy590, vyy591), app(ty_Maybe, bgb), bfe) → new_esEs2(vyy580, vyy590, bgb)
new_esEs2(Just(vyy580), Just(vyy590), app(ty_[], hf)) → new_esEs(vyy580, vyy590, hf)
new_esEs3(Left(vyy580), Left(vyy590), app(app(ty_FiniteMap, bag), bah), bba) → new_esEs0(vyy580, vyy590, bag, bah)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), cf, app(app(ty_FiniteMap, ed), ee), ef) → new_esEs0(vyy581, vyy591, ed, ee)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), cf, cg, app(app(ty_Either, dh), ea)) → new_esEs3(vyy582, vyy592, dh, ea)
new_esEs4(@2(vyy580, vyy581), @2(vyy590, vyy591), app(app(ty_@2, bge), bgf), bfe) → new_esEs4(vyy580, vyy590, bge, bgf)
new_esEs3(Right(vyy580), Right(vyy590), bcc, app(app(app(ty_@3, bcg), bch), bda)) → new_esEs1(vyy580, vyy590, bcg, bch, bda)
new_esEs3(Left(vyy580), Left(vyy590), app(ty_[], bbb), bba) → new_esEs(vyy580, vyy590, bbb)
new_esEs3(Right(vyy580), Right(vyy590), bcc, app(app(ty_FiniteMap, bcd), bce)) → new_esEs0(vyy580, vyy590, bcd, bce)
new_esEs(:(vyy580, vyy581), :(vyy590, vyy591), app(ty_Maybe, bg)) → new_esEs2(vyy580, vyy590, bg)
new_esEs4(@2(vyy580, vyy581), @2(vyy590, vyy591), bdg, app(ty_[], beb)) → new_esEs(vyy581, vyy591, beb)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), app(app(ty_FiniteMap, ga), gb), cg, ef) → new_esEs0(vyy580, vyy590, ga, gb)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), app(app(app(ty_@3, gd), ge), gf), cg, ef) → new_esEs1(vyy580, vyy590, gd, ge, gf)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), cf, app(app(ty_@2, fg), fh), ef) → new_esEs4(vyy581, vyy591, fg, fh)
new_esEs3(Left(vyy580), Left(vyy590), app(ty_Maybe, bbf), bba) → new_esEs2(vyy580, vyy590, bbf)
new_esEs(:(vyy580, vyy581), :(vyy590, vyy591), h) → new_esEs(vyy581, vyy591, h)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), cf, app(ty_Maybe, fc), ef) → new_esEs2(vyy581, vyy591, fc)
new_esEs(:(vyy580, vyy581), :(vyy590, vyy591), app(app(app(ty_@3, bd), be), bf)) → new_esEs1(vyy580, vyy590, bd, be, bf)
new_esEs4(@2(vyy580, vyy581), @2(vyy590, vyy591), app(app(ty_FiniteMap, bfc), bfd), bfe) → new_esEs0(vyy580, vyy590, bfc, bfd)
new_esEs4(@2(vyy580, vyy581), @2(vyy590, vyy591), bdg, app(app(app(ty_@3, bec), bed), bee)) → new_esEs1(vyy581, vyy591, bec, bed, bee)
new_esEs4(@2(vyy580, vyy581), @2(vyy590, vyy591), app(ty_[], bff), bfe) → new_esEs(vyy580, vyy590, bff)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), app(app(ty_@2, hb), hc), cg, ef) → new_esEs4(vyy580, vyy590, hb, hc)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), cf, cg, app(ty_Maybe, dg)) → new_esEs2(vyy582, vyy592, dg)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), app(ty_[], gc), cg, ef) → new_esEs(vyy580, vyy590, gc)
new_esEs4(@2(vyy580, vyy581), @2(vyy590, vyy591), app(app(ty_Either, bgc), bgd), bfe) → new_esEs3(vyy580, vyy590, bgc, bgd)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), app(app(ty_Either, gh), ha), cg, ef) → new_esEs3(vyy580, vyy590, gh, ha)
new_esEs2(Just(vyy580), Just(vyy590), app(app(ty_@2, bae), baf)) → new_esEs4(vyy580, vyy590, bae, baf)
new_esEs(:(vyy580, vyy581), :(vyy590, vyy591), app(ty_[], bc)) → new_esEs(vyy580, vyy590, bc)
new_esEs(:(vyy580, vyy581), :(vyy590, vyy591), app(app(ty_FiniteMap, ba), bb)) → new_esEs0(vyy580, vyy590, ba, bb)
The TRS R consists of the following rules:
new_foldFM2(Branch(vyy590, vyy591, vyy592, vyy593, vyy594), cd, ce) → new_foldFM0(vyy590, vyy591, new_foldFM2(vyy594, cd, ce), vyy593, cd, ce)
new_foldFM2(EmptyFM, cd, ce) → []
new_foldFM0(vyy590, vyy591, vyy96, EmptyFM, cd, ce) → :(@2(vyy590, vyy591), vyy96)
new_foldFM0(vyy590, vyy591, vyy96, Branch(vyy5930, vyy5931, vyy5932, vyy5933, vyy5934), cd, ce) → new_foldFM0(vyy5930, vyy5931, new_foldFM0(vyy590, vyy591, vyy96, vyy5934, cd, ce), vyy5933, cd, ce)
The set Q consists of the following terms:
new_fmToList(x0, x1, x2)
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_foldFM2(EmptyFM, x0, x1)
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
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
↳ Rewriting
↳ QDP
↳ Rewriting
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QReductionProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_esEs2(Just(vyy580), Just(vyy590), app(app(app(ty_@3, hg), hh), baa)) → new_esEs1(vyy580, vyy590, hg, hh, baa)
new_esEs3(Right(vyy580), Right(vyy590), bcc, app(app(ty_@2, bde), bdf)) → new_esEs4(vyy580, vyy590, bde, bdf)
new_esEs3(Right(vyy580), Right(vyy590), bcc, app(ty_[], bcf)) → new_esEs(vyy580, vyy590, bcf)
new_esEs4(@2(vyy580, vyy581), @2(vyy590, vyy591), app(app(app(ty_@3, bfg), bfh), bga), bfe) → new_esEs1(vyy580, vyy590, bfg, bfh, bga)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), cf, app(app(app(ty_@3, eh), fa), fb), ef) → new_esEs1(vyy581, vyy591, eh, fa, fb)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), cf, cg, app(app(ty_FiniteMap, da), db)) → new_esEs0(vyy582, vyy592, da, db)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), cf, app(app(ty_Either, fd), ff), ef) → new_esEs3(vyy581, vyy591, fd, ff)
new_esEs3(Right(vyy580), Right(vyy590), bcc, app(app(ty_Either, bdc), bdd)) → new_esEs3(vyy580, vyy590, bdc, bdd)
new_esEs4(@2(vyy580, vyy581), @2(vyy590, vyy591), bdg, app(app(ty_FiniteMap, bdh), bea)) → new_esEs0(vyy581, vyy591, bdh, bea)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), cf, cg, app(app(app(ty_@3, dd), de), df)) → new_esEs1(vyy582, vyy592, dd, de, df)
new_esEs3(Left(vyy580), Left(vyy590), app(app(app(ty_@3, bbc), bbd), bbe), bba) → new_esEs1(vyy580, vyy590, bbc, bbd, bbe)
new_esEs2(Just(vyy580), Just(vyy590), app(ty_Maybe, bab)) → new_esEs2(vyy580, vyy590, bab)
new_esEs2(Just(vyy580), Just(vyy590), app(app(ty_FiniteMap, hd), he)) → new_esEs0(vyy580, vyy590, hd, he)
new_esEs3(Left(vyy580), Left(vyy590), app(app(ty_Either, bbg), bbh), bba) → new_esEs3(vyy580, vyy590, bbg, bbh)
new_esEs4(@2(vyy580, vyy581), @2(vyy590, vyy591), bdg, app(app(ty_Either, beg), beh)) → new_esEs3(vyy581, vyy591, beg, beh)
new_esEs(:(vyy580, vyy581), :(vyy590, vyy591), app(app(ty_Either, bh), ca)) → new_esEs3(vyy580, vyy590, bh, ca)
new_esEs0(vyy58, vyy59, cd, ce) → new_esEs(new_foldFM2(vyy58, cd, ce), new_foldFM2(vyy59, cd, ce), app(app(ty_@2, cd), ce))
new_esEs4(@2(vyy580, vyy581), @2(vyy590, vyy591), bdg, app(ty_Maybe, bef)) → new_esEs2(vyy581, vyy591, bef)
new_esEs3(Left(vyy580), Left(vyy590), app(app(ty_@2, bca), bcb), bba) → new_esEs4(vyy580, vyy590, bca, bcb)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), cf, cg, app(app(ty_@2, eb), ec)) → new_esEs4(vyy582, vyy592, eb, ec)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), app(ty_Maybe, gg), cg, ef) → new_esEs2(vyy580, vyy590, gg)
new_esEs3(Right(vyy580), Right(vyy590), bcc, app(ty_Maybe, bdb)) → new_esEs2(vyy580, vyy590, bdb)
new_esEs(:(vyy580, vyy581), :(vyy590, vyy591), app(app(ty_@2, cb), cc)) → new_esEs4(vyy580, vyy590, cb, cc)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), cf, cg, app(ty_[], dc)) → new_esEs(vyy582, vyy592, dc)
new_esEs2(Just(vyy580), Just(vyy590), app(app(ty_Either, bac), bad)) → new_esEs3(vyy580, vyy590, bac, bad)
new_esEs4(@2(vyy580, vyy581), @2(vyy590, vyy591), bdg, app(app(ty_@2, bfa), bfb)) → new_esEs4(vyy581, vyy591, bfa, bfb)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), cf, app(ty_[], eg), ef) → new_esEs(vyy581, vyy591, eg)
new_esEs4(@2(vyy580, vyy581), @2(vyy590, vyy591), app(ty_Maybe, bgb), bfe) → new_esEs2(vyy580, vyy590, bgb)
new_esEs2(Just(vyy580), Just(vyy590), app(ty_[], hf)) → new_esEs(vyy580, vyy590, hf)
new_esEs3(Left(vyy580), Left(vyy590), app(app(ty_FiniteMap, bag), bah), bba) → new_esEs0(vyy580, vyy590, bag, bah)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), cf, app(app(ty_FiniteMap, ed), ee), ef) → new_esEs0(vyy581, vyy591, ed, ee)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), cf, cg, app(app(ty_Either, dh), ea)) → new_esEs3(vyy582, vyy592, dh, ea)
new_esEs4(@2(vyy580, vyy581), @2(vyy590, vyy591), app(app(ty_@2, bge), bgf), bfe) → new_esEs4(vyy580, vyy590, bge, bgf)
new_esEs3(Right(vyy580), Right(vyy590), bcc, app(app(app(ty_@3, bcg), bch), bda)) → new_esEs1(vyy580, vyy590, bcg, bch, bda)
new_esEs3(Left(vyy580), Left(vyy590), app(ty_[], bbb), bba) → new_esEs(vyy580, vyy590, bbb)
new_esEs3(Right(vyy580), Right(vyy590), bcc, app(app(ty_FiniteMap, bcd), bce)) → new_esEs0(vyy580, vyy590, bcd, bce)
new_esEs(:(vyy580, vyy581), :(vyy590, vyy591), app(ty_Maybe, bg)) → new_esEs2(vyy580, vyy590, bg)
new_esEs4(@2(vyy580, vyy581), @2(vyy590, vyy591), bdg, app(ty_[], beb)) → new_esEs(vyy581, vyy591, beb)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), app(app(ty_FiniteMap, ga), gb), cg, ef) → new_esEs0(vyy580, vyy590, ga, gb)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), app(app(app(ty_@3, gd), ge), gf), cg, ef) → new_esEs1(vyy580, vyy590, gd, ge, gf)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), cf, app(app(ty_@2, fg), fh), ef) → new_esEs4(vyy581, vyy591, fg, fh)
new_esEs3(Left(vyy580), Left(vyy590), app(ty_Maybe, bbf), bba) → new_esEs2(vyy580, vyy590, bbf)
new_esEs(:(vyy580, vyy581), :(vyy590, vyy591), h) → new_esEs(vyy581, vyy591, h)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), cf, app(ty_Maybe, fc), ef) → new_esEs2(vyy581, vyy591, fc)
new_esEs(:(vyy580, vyy581), :(vyy590, vyy591), app(app(app(ty_@3, bd), be), bf)) → new_esEs1(vyy580, vyy590, bd, be, bf)
new_esEs4(@2(vyy580, vyy581), @2(vyy590, vyy591), app(app(ty_FiniteMap, bfc), bfd), bfe) → new_esEs0(vyy580, vyy590, bfc, bfd)
new_esEs4(@2(vyy580, vyy581), @2(vyy590, vyy591), bdg, app(app(app(ty_@3, bec), bed), bee)) → new_esEs1(vyy581, vyy591, bec, bed, bee)
new_esEs4(@2(vyy580, vyy581), @2(vyy590, vyy591), app(ty_[], bff), bfe) → new_esEs(vyy580, vyy590, bff)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), app(app(ty_@2, hb), hc), cg, ef) → new_esEs4(vyy580, vyy590, hb, hc)
new_esEs4(@2(vyy580, vyy581), @2(vyy590, vyy591), app(app(ty_Either, bgc), bgd), bfe) → new_esEs3(vyy580, vyy590, bgc, bgd)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), app(ty_[], gc), cg, ef) → new_esEs(vyy580, vyy590, gc)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), cf, cg, app(ty_Maybe, dg)) → new_esEs2(vyy582, vyy592, dg)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), app(app(ty_Either, gh), ha), cg, ef) → new_esEs3(vyy580, vyy590, gh, ha)
new_esEs2(Just(vyy580), Just(vyy590), app(app(ty_@2, bae), baf)) → new_esEs4(vyy580, vyy590, bae, baf)
new_esEs(:(vyy580, vyy581), :(vyy590, vyy591), app(ty_[], bc)) → new_esEs(vyy580, vyy590, bc)
new_esEs(:(vyy580, vyy581), :(vyy590, vyy591), app(app(ty_FiniteMap, ba), bb)) → new_esEs0(vyy580, vyy590, ba, bb)
The TRS R consists of the following rules:
new_foldFM2(Branch(vyy590, vyy591, vyy592, vyy593, vyy594), cd, ce) → new_foldFM0(vyy590, vyy591, new_foldFM2(vyy594, cd, ce), vyy593, cd, ce)
new_foldFM2(EmptyFM, cd, ce) → []
new_foldFM0(vyy590, vyy591, vyy96, EmptyFM, cd, ce) → :(@2(vyy590, vyy591), vyy96)
new_foldFM0(vyy590, vyy591, vyy96, Branch(vyy5930, vyy5931, vyy5932, vyy5933, vyy5934), cd, ce) → new_foldFM0(vyy5930, vyy5931, new_foldFM0(vyy590, vyy591, vyy96, vyy5934, cd, ce), vyy5933, cd, ce)
The set Q consists of the following terms:
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_foldFM2(EmptyFM, x0, x1)
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
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(vyy580), Right(vyy590), bcc, app(app(ty_@2, bde), bdf)) → new_esEs4(vyy580, vyy590, bde, bdf)
new_esEs3(Right(vyy580), Right(vyy590), bcc, app(ty_[], bcf)) → new_esEs(vyy580, vyy590, bcf)
new_esEs3(Right(vyy580), Right(vyy590), bcc, app(app(ty_Either, bdc), bdd)) → new_esEs3(vyy580, vyy590, bdc, bdd)
new_esEs(:(vyy580, vyy581), :(vyy590, vyy591), app(app(ty_Either, bh), ca)) → new_esEs3(vyy580, vyy590, bh, ca)
new_esEs3(Right(vyy580), Right(vyy590), bcc, app(ty_Maybe, bdb)) → new_esEs2(vyy580, vyy590, bdb)
new_esEs(:(vyy580, vyy581), :(vyy590, vyy591), app(app(ty_@2, cb), cc)) → new_esEs4(vyy580, vyy590, cb, cc)
new_esEs3(Right(vyy580), Right(vyy590), bcc, app(app(app(ty_@3, bcg), bch), bda)) → new_esEs1(vyy580, vyy590, bcg, bch, bda)
new_esEs3(Right(vyy580), Right(vyy590), bcc, app(app(ty_FiniteMap, bcd), bce)) → new_esEs0(vyy580, vyy590, bcd, bce)
new_esEs(:(vyy580, vyy581), :(vyy590, vyy591), app(ty_Maybe, bg)) → new_esEs2(vyy580, vyy590, bg)
new_esEs(:(vyy580, vyy581), :(vyy590, vyy591), h) → new_esEs(vyy581, vyy591, h)
new_esEs(:(vyy580, vyy581), :(vyy590, vyy591), app(app(app(ty_@3, bd), be), bf)) → new_esEs1(vyy580, vyy590, bd, be, bf)
new_esEs(:(vyy580, vyy581), :(vyy590, vyy591), app(ty_[], bc)) → new_esEs(vyy580, vyy590, bc)
new_esEs(:(vyy580, vyy581), :(vyy590, vyy591), app(app(ty_FiniteMap, ba), bb)) → new_esEs0(vyy580, vyy590, ba, bb)
The remaining pairs can at least be oriented weakly.
new_esEs2(Just(vyy580), Just(vyy590), app(app(app(ty_@3, hg), hh), baa)) → new_esEs1(vyy580, vyy590, hg, hh, baa)
new_esEs4(@2(vyy580, vyy581), @2(vyy590, vyy591), app(app(app(ty_@3, bfg), bfh), bga), bfe) → new_esEs1(vyy580, vyy590, bfg, bfh, bga)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), cf, app(app(app(ty_@3, eh), fa), fb), ef) → new_esEs1(vyy581, vyy591, eh, fa, fb)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), cf, cg, app(app(ty_FiniteMap, da), db)) → new_esEs0(vyy582, vyy592, da, db)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), cf, app(app(ty_Either, fd), ff), ef) → new_esEs3(vyy581, vyy591, fd, ff)
new_esEs4(@2(vyy580, vyy581), @2(vyy590, vyy591), bdg, app(app(ty_FiniteMap, bdh), bea)) → new_esEs0(vyy581, vyy591, bdh, bea)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), cf, cg, app(app(app(ty_@3, dd), de), df)) → new_esEs1(vyy582, vyy592, dd, de, df)
new_esEs3(Left(vyy580), Left(vyy590), app(app(app(ty_@3, bbc), bbd), bbe), bba) → new_esEs1(vyy580, vyy590, bbc, bbd, bbe)
new_esEs2(Just(vyy580), Just(vyy590), app(ty_Maybe, bab)) → new_esEs2(vyy580, vyy590, bab)
new_esEs2(Just(vyy580), Just(vyy590), app(app(ty_FiniteMap, hd), he)) → new_esEs0(vyy580, vyy590, hd, he)
new_esEs3(Left(vyy580), Left(vyy590), app(app(ty_Either, bbg), bbh), bba) → new_esEs3(vyy580, vyy590, bbg, bbh)
new_esEs4(@2(vyy580, vyy581), @2(vyy590, vyy591), bdg, app(app(ty_Either, beg), beh)) → new_esEs3(vyy581, vyy591, beg, beh)
new_esEs0(vyy58, vyy59, cd, ce) → new_esEs(new_foldFM2(vyy58, cd, ce), new_foldFM2(vyy59, cd, ce), app(app(ty_@2, cd), ce))
new_esEs4(@2(vyy580, vyy581), @2(vyy590, vyy591), bdg, app(ty_Maybe, bef)) → new_esEs2(vyy581, vyy591, bef)
new_esEs3(Left(vyy580), Left(vyy590), app(app(ty_@2, bca), bcb), bba) → new_esEs4(vyy580, vyy590, bca, bcb)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), cf, cg, app(app(ty_@2, eb), ec)) → new_esEs4(vyy582, vyy592, eb, ec)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), app(ty_Maybe, gg), cg, ef) → new_esEs2(vyy580, vyy590, gg)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), cf, cg, app(ty_[], dc)) → new_esEs(vyy582, vyy592, dc)
new_esEs2(Just(vyy580), Just(vyy590), app(app(ty_Either, bac), bad)) → new_esEs3(vyy580, vyy590, bac, bad)
new_esEs4(@2(vyy580, vyy581), @2(vyy590, vyy591), bdg, app(app(ty_@2, bfa), bfb)) → new_esEs4(vyy581, vyy591, bfa, bfb)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), cf, app(ty_[], eg), ef) → new_esEs(vyy581, vyy591, eg)
new_esEs4(@2(vyy580, vyy581), @2(vyy590, vyy591), app(ty_Maybe, bgb), bfe) → new_esEs2(vyy580, vyy590, bgb)
new_esEs2(Just(vyy580), Just(vyy590), app(ty_[], hf)) → new_esEs(vyy580, vyy590, hf)
new_esEs3(Left(vyy580), Left(vyy590), app(app(ty_FiniteMap, bag), bah), bba) → new_esEs0(vyy580, vyy590, bag, bah)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), cf, app(app(ty_FiniteMap, ed), ee), ef) → new_esEs0(vyy581, vyy591, ed, ee)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), cf, cg, app(app(ty_Either, dh), ea)) → new_esEs3(vyy582, vyy592, dh, ea)
new_esEs4(@2(vyy580, vyy581), @2(vyy590, vyy591), app(app(ty_@2, bge), bgf), bfe) → new_esEs4(vyy580, vyy590, bge, bgf)
new_esEs3(Left(vyy580), Left(vyy590), app(ty_[], bbb), bba) → new_esEs(vyy580, vyy590, bbb)
new_esEs4(@2(vyy580, vyy581), @2(vyy590, vyy591), bdg, app(ty_[], beb)) → new_esEs(vyy581, vyy591, beb)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), app(app(ty_FiniteMap, ga), gb), cg, ef) → new_esEs0(vyy580, vyy590, ga, gb)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), app(app(app(ty_@3, gd), ge), gf), cg, ef) → new_esEs1(vyy580, vyy590, gd, ge, gf)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), cf, app(app(ty_@2, fg), fh), ef) → new_esEs4(vyy581, vyy591, fg, fh)
new_esEs3(Left(vyy580), Left(vyy590), app(ty_Maybe, bbf), bba) → new_esEs2(vyy580, vyy590, bbf)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), cf, app(ty_Maybe, fc), ef) → new_esEs2(vyy581, vyy591, fc)
new_esEs4(@2(vyy580, vyy581), @2(vyy590, vyy591), app(app(ty_FiniteMap, bfc), bfd), bfe) → new_esEs0(vyy580, vyy590, bfc, bfd)
new_esEs4(@2(vyy580, vyy581), @2(vyy590, vyy591), bdg, app(app(app(ty_@3, bec), bed), bee)) → new_esEs1(vyy581, vyy591, bec, bed, bee)
new_esEs4(@2(vyy580, vyy581), @2(vyy590, vyy591), app(ty_[], bff), bfe) → new_esEs(vyy580, vyy590, bff)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), app(app(ty_@2, hb), hc), cg, ef) → new_esEs4(vyy580, vyy590, hb, hc)
new_esEs4(@2(vyy580, vyy581), @2(vyy590, vyy591), app(app(ty_Either, bgc), bgd), bfe) → new_esEs3(vyy580, vyy590, bgc, bgd)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), app(ty_[], gc), cg, ef) → new_esEs(vyy580, vyy590, gc)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), cf, cg, app(ty_Maybe, dg)) → new_esEs2(vyy582, vyy592, dg)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), app(app(ty_Either, gh), ha), cg, ef) → new_esEs3(vyy580, vyy590, gh, ha)
new_esEs2(Just(vyy580), Just(vyy590), app(app(ty_@2, bae), baf)) → new_esEs4(vyy580, vyy590, bae, baf)
Used ordering: Polynomial interpretation [25]:
POL(:(x1, x2)) = 1 + x1 + x2
POL(@2(x1, x2)) = x1 + x2
POL(@3(x1, x2, x3)) = x1 + x2 + x3
POL(Branch(x1, x2, x3, x4, x5)) = 1 + x1 + x2 + x4 + x5
POL(EmptyFM) = 0
POL(Just(x1)) = x1
POL(Left(x1)) = x1
POL(Right(x1)) = 1 + x1
POL([]) = 0
POL(app(x1, x2)) = 0
POL(new_esEs(x1, x2, x3)) = x1
POL(new_esEs0(x1, x2, x3, x4)) = x1
POL(new_esEs1(x1, x2, x3, x4, x5)) = x1
POL(new_esEs2(x1, x2, x3)) = x1
POL(new_esEs3(x1, x2, x3, x4)) = x1
POL(new_esEs4(x1, x2, x3, x4)) = x1
POL(new_foldFM0(x1, x2, x3, x4, x5, x6)) = 1 + x1 + x2 + x3 + x4
POL(new_foldFM2(x1, x2, x3)) = x1
POL(ty_@2) = 0
POL(ty_@3) = 0
POL(ty_Either) = 0
POL(ty_FiniteMap) = 0
POL(ty_Maybe) = 0
POL(ty_[]) = 0
The following usable rules [17] were oriented:
new_foldFM2(Branch(vyy590, vyy591, vyy592, vyy593, vyy594), cd, ce) → new_foldFM0(vyy590, vyy591, new_foldFM2(vyy594, cd, ce), vyy593, cd, ce)
new_foldFM0(vyy590, vyy591, vyy96, Branch(vyy5930, vyy5931, vyy5932, vyy5933, vyy5934), cd, ce) → new_foldFM0(vyy5930, vyy5931, new_foldFM0(vyy590, vyy591, vyy96, vyy5934, cd, ce), vyy5933, cd, ce)
new_foldFM2(EmptyFM, cd, ce) → []
new_foldFM0(vyy590, vyy591, vyy96, EmptyFM, cd, ce) → :(@2(vyy590, vyy591), vyy96)
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ Rewriting
↳ QDP
↳ Rewriting
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QReductionProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_esEs2(Just(vyy580), Just(vyy590), app(app(app(ty_@3, hg), hh), baa)) → new_esEs1(vyy580, vyy590, hg, hh, baa)
new_esEs4(@2(vyy580, vyy581), @2(vyy590, vyy591), app(ty_Maybe, bgb), bfe) → new_esEs2(vyy580, vyy590, bgb)
new_esEs4(@2(vyy580, vyy581), @2(vyy590, vyy591), app(app(app(ty_@3, bfg), bfh), bga), bfe) → new_esEs1(vyy580, vyy590, bfg, bfh, bga)
new_esEs2(Just(vyy580), Just(vyy590), app(ty_[], hf)) → new_esEs(vyy580, vyy590, hf)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), cf, cg, app(app(ty_FiniteMap, da), db)) → new_esEs0(vyy582, vyy592, da, db)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), cf, app(app(app(ty_@3, eh), fa), fb), ef) → new_esEs1(vyy581, vyy591, eh, fa, fb)
new_esEs3(Left(vyy580), Left(vyy590), app(app(ty_FiniteMap, bag), bah), bba) → new_esEs0(vyy580, vyy590, bag, bah)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), cf, app(app(ty_Either, fd), ff), ef) → new_esEs3(vyy581, vyy591, fd, ff)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), cf, app(app(ty_FiniteMap, ed), ee), ef) → new_esEs0(vyy581, vyy591, ed, ee)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), cf, cg, app(app(ty_Either, dh), ea)) → new_esEs3(vyy582, vyy592, dh, ea)
new_esEs4(@2(vyy580, vyy581), @2(vyy590, vyy591), app(app(ty_@2, bge), bgf), bfe) → new_esEs4(vyy580, vyy590, bge, bgf)
new_esEs4(@2(vyy580, vyy581), @2(vyy590, vyy591), bdg, app(app(ty_FiniteMap, bdh), bea)) → new_esEs0(vyy581, vyy591, bdh, bea)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), cf, cg, app(app(app(ty_@3, dd), de), df)) → new_esEs1(vyy582, vyy592, dd, de, df)
new_esEs3(Left(vyy580), Left(vyy590), app(app(app(ty_@3, bbc), bbd), bbe), bba) → new_esEs1(vyy580, vyy590, bbc, bbd, bbe)
new_esEs3(Left(vyy580), Left(vyy590), app(ty_[], bbb), bba) → new_esEs(vyy580, vyy590, bbb)
new_esEs2(Just(vyy580), Just(vyy590), app(ty_Maybe, bab)) → new_esEs2(vyy580, vyy590, bab)
new_esEs3(Left(vyy580), Left(vyy590), app(app(ty_Either, bbg), bbh), bba) → new_esEs3(vyy580, vyy590, bbg, bbh)
new_esEs2(Just(vyy580), Just(vyy590), app(app(ty_FiniteMap, hd), he)) → new_esEs0(vyy580, vyy590, hd, he)
new_esEs4(@2(vyy580, vyy581), @2(vyy590, vyy591), bdg, app(ty_[], beb)) → new_esEs(vyy581, vyy591, beb)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), app(app(ty_FiniteMap, ga), gb), cg, ef) → new_esEs0(vyy580, vyy590, ga, gb)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), cf, app(app(ty_@2, fg), fh), ef) → new_esEs4(vyy581, vyy591, fg, fh)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), app(app(app(ty_@3, gd), ge), gf), cg, ef) → new_esEs1(vyy580, vyy590, gd, ge, gf)
new_esEs3(Left(vyy580), Left(vyy590), app(ty_Maybe, bbf), bba) → new_esEs2(vyy580, vyy590, bbf)
new_esEs4(@2(vyy580, vyy581), @2(vyy590, vyy591), bdg, app(app(ty_Either, beg), beh)) → new_esEs3(vyy581, vyy591, beg, beh)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), cf, app(ty_Maybe, fc), ef) → new_esEs2(vyy581, vyy591, fc)
new_esEs4(@2(vyy580, vyy581), @2(vyy590, vyy591), app(app(ty_FiniteMap, bfc), bfd), bfe) → new_esEs0(vyy580, vyy590, bfc, bfd)
new_esEs0(vyy58, vyy59, cd, ce) → new_esEs(new_foldFM2(vyy58, cd, ce), new_foldFM2(vyy59, cd, ce), app(app(ty_@2, cd), ce))
new_esEs4(@2(vyy580, vyy581), @2(vyy590, vyy591), bdg, app(app(app(ty_@3, bec), bed), bee)) → new_esEs1(vyy581, vyy591, bec, bed, bee)
new_esEs4(@2(vyy580, vyy581), @2(vyy590, vyy591), app(ty_[], bff), bfe) → new_esEs(vyy580, vyy590, bff)
new_esEs4(@2(vyy580, vyy581), @2(vyy590, vyy591), bdg, app(ty_Maybe, bef)) → new_esEs2(vyy581, vyy591, bef)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), app(app(ty_@2, hb), hc), cg, ef) → new_esEs4(vyy580, vyy590, hb, hc)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), cf, cg, app(ty_Maybe, dg)) → new_esEs2(vyy582, vyy592, dg)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), app(ty_[], gc), cg, ef) → new_esEs(vyy580, vyy590, gc)
new_esEs4(@2(vyy580, vyy581), @2(vyy590, vyy591), app(app(ty_Either, bgc), bgd), bfe) → new_esEs3(vyy580, vyy590, bgc, bgd)
new_esEs3(Left(vyy580), Left(vyy590), app(app(ty_@2, bca), bcb), bba) → new_esEs4(vyy580, vyy590, bca, bcb)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), cf, cg, app(app(ty_@2, eb), ec)) → new_esEs4(vyy582, vyy592, eb, ec)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), app(ty_Maybe, gg), cg, ef) → new_esEs2(vyy580, vyy590, gg)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), app(app(ty_Either, gh), ha), cg, ef) → new_esEs3(vyy580, vyy590, gh, ha)
new_esEs2(Just(vyy580), Just(vyy590), app(app(ty_@2, bae), baf)) → new_esEs4(vyy580, vyy590, bae, baf)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), cf, cg, app(ty_[], dc)) → new_esEs(vyy582, vyy592, dc)
new_esEs2(Just(vyy580), Just(vyy590), app(app(ty_Either, bac), bad)) → new_esEs3(vyy580, vyy590, bac, bad)
new_esEs4(@2(vyy580, vyy581), @2(vyy590, vyy591), bdg, app(app(ty_@2, bfa), bfb)) → new_esEs4(vyy581, vyy591, bfa, bfb)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), cf, app(ty_[], eg), ef) → new_esEs(vyy581, vyy591, eg)
The TRS R consists of the following rules:
new_foldFM2(Branch(vyy590, vyy591, vyy592, vyy593, vyy594), cd, ce) → new_foldFM0(vyy590, vyy591, new_foldFM2(vyy594, cd, ce), vyy593, cd, ce)
new_foldFM2(EmptyFM, cd, ce) → []
new_foldFM0(vyy590, vyy591, vyy96, EmptyFM, cd, ce) → :(@2(vyy590, vyy591), vyy96)
new_foldFM0(vyy590, vyy591, vyy96, Branch(vyy5930, vyy5931, vyy5932, vyy5933, vyy5934), cd, ce) → new_foldFM0(vyy5930, vyy5931, new_foldFM0(vyy590, vyy591, vyy96, vyy5934, cd, ce), vyy5933, cd, ce)
The set Q consists of the following terms:
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_foldFM2(EmptyFM, x0, x1)
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph [15,17,22] contains 1 SCC with 15 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
↳ Rewriting
↳ QDP
↳ Rewriting
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QReductionProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_esEs2(Just(vyy580), Just(vyy590), app(app(app(ty_@3, hg), hh), baa)) → new_esEs1(vyy580, vyy590, hg, hh, baa)
new_esEs4(@2(vyy580, vyy581), @2(vyy590, vyy591), app(ty_Maybe, bgb), bfe) → new_esEs2(vyy580, vyy590, bgb)
new_esEs4(@2(vyy580, vyy581), @2(vyy590, vyy591), app(app(app(ty_@3, bfg), bfh), bga), bfe) → new_esEs1(vyy580, vyy590, bfg, bfh, bga)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), cf, app(app(app(ty_@3, eh), fa), fb), ef) → new_esEs1(vyy581, vyy591, eh, fa, fb)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), cf, app(app(ty_Either, fd), ff), ef) → new_esEs3(vyy581, vyy591, fd, ff)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), cf, cg, app(app(ty_Either, dh), ea)) → new_esEs3(vyy582, vyy592, dh, ea)
new_esEs4(@2(vyy580, vyy581), @2(vyy590, vyy591), app(app(ty_@2, bge), bgf), bfe) → new_esEs4(vyy580, vyy590, bge, bgf)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), cf, cg, app(app(app(ty_@3, dd), de), df)) → new_esEs1(vyy582, vyy592, dd, de, df)
new_esEs3(Left(vyy580), Left(vyy590), app(app(app(ty_@3, bbc), bbd), bbe), bba) → new_esEs1(vyy580, vyy590, bbc, bbd, bbe)
new_esEs2(Just(vyy580), Just(vyy590), app(ty_Maybe, bab)) → new_esEs2(vyy580, vyy590, bab)
new_esEs3(Left(vyy580), Left(vyy590), app(app(ty_Either, bbg), bbh), bba) → new_esEs3(vyy580, vyy590, bbg, bbh)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), app(app(app(ty_@3, gd), ge), gf), cg, ef) → new_esEs1(vyy580, vyy590, gd, ge, gf)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), cf, app(app(ty_@2, fg), fh), ef) → new_esEs4(vyy581, vyy591, fg, fh)
new_esEs3(Left(vyy580), Left(vyy590), app(ty_Maybe, bbf), bba) → new_esEs2(vyy580, vyy590, bbf)
new_esEs4(@2(vyy580, vyy581), @2(vyy590, vyy591), bdg, app(app(ty_Either, beg), beh)) → new_esEs3(vyy581, vyy591, beg, beh)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), cf, app(ty_Maybe, fc), ef) → new_esEs2(vyy581, vyy591, fc)
new_esEs4(@2(vyy580, vyy581), @2(vyy590, vyy591), bdg, app(app(app(ty_@3, bec), bed), bee)) → new_esEs1(vyy581, vyy591, bec, bed, bee)
new_esEs4(@2(vyy580, vyy581), @2(vyy590, vyy591), bdg, app(ty_Maybe, bef)) → new_esEs2(vyy581, vyy591, bef)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), app(app(ty_@2, hb), hc), cg, ef) → new_esEs4(vyy580, vyy590, hb, hc)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), cf, cg, app(ty_Maybe, dg)) → new_esEs2(vyy582, vyy592, dg)
new_esEs3(Left(vyy580), Left(vyy590), app(app(ty_@2, bca), bcb), bba) → new_esEs4(vyy580, vyy590, bca, bcb)
new_esEs4(@2(vyy580, vyy581), @2(vyy590, vyy591), app(app(ty_Either, bgc), bgd), bfe) → new_esEs3(vyy580, vyy590, bgc, bgd)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), cf, cg, app(app(ty_@2, eb), ec)) → new_esEs4(vyy582, vyy592, eb, ec)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), app(ty_Maybe, gg), cg, ef) → new_esEs2(vyy580, vyy590, gg)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), app(app(ty_Either, gh), ha), cg, ef) → new_esEs3(vyy580, vyy590, gh, ha)
new_esEs2(Just(vyy580), Just(vyy590), app(app(ty_@2, bae), baf)) → new_esEs4(vyy580, vyy590, bae, baf)
new_esEs2(Just(vyy580), Just(vyy590), app(app(ty_Either, bac), bad)) → new_esEs3(vyy580, vyy590, bac, bad)
new_esEs4(@2(vyy580, vyy581), @2(vyy590, vyy591), bdg, app(app(ty_@2, bfa), bfb)) → new_esEs4(vyy581, vyy591, bfa, bfb)
The TRS R consists of the following rules:
new_foldFM2(Branch(vyy590, vyy591, vyy592, vyy593, vyy594), cd, ce) → new_foldFM0(vyy590, vyy591, new_foldFM2(vyy594, cd, ce), vyy593, cd, ce)
new_foldFM2(EmptyFM, cd, ce) → []
new_foldFM0(vyy590, vyy591, vyy96, EmptyFM, cd, ce) → :(@2(vyy590, vyy591), vyy96)
new_foldFM0(vyy590, vyy591, vyy96, Branch(vyy5930, vyy5931, vyy5932, vyy5933, vyy5934), cd, ce) → new_foldFM0(vyy5930, vyy5931, new_foldFM0(vyy590, vyy591, vyy96, vyy5934, cd, ce), vyy5933, cd, ce)
The set Q consists of the following terms:
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_foldFM2(EmptyFM, x0, x1)
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
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
↳ Rewriting
↳ QDP
↳ Rewriting
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QReductionProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QReductionProof
↳ QDP
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_esEs2(Just(vyy580), Just(vyy590), app(app(app(ty_@3, hg), hh), baa)) → new_esEs1(vyy580, vyy590, hg, hh, baa)
new_esEs4(@2(vyy580, vyy581), @2(vyy590, vyy591), app(ty_Maybe, bgb), bfe) → new_esEs2(vyy580, vyy590, bgb)
new_esEs4(@2(vyy580, vyy581), @2(vyy590, vyy591), app(app(app(ty_@3, bfg), bfh), bga), bfe) → new_esEs1(vyy580, vyy590, bfg, bfh, bga)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), cf, app(app(app(ty_@3, eh), fa), fb), ef) → new_esEs1(vyy581, vyy591, eh, fa, fb)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), cf, app(app(ty_Either, fd), ff), ef) → new_esEs3(vyy581, vyy591, fd, ff)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), cf, cg, app(app(ty_Either, dh), ea)) → new_esEs3(vyy582, vyy592, dh, ea)
new_esEs4(@2(vyy580, vyy581), @2(vyy590, vyy591), app(app(ty_@2, bge), bgf), bfe) → new_esEs4(vyy580, vyy590, bge, bgf)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), cf, cg, app(app(app(ty_@3, dd), de), df)) → new_esEs1(vyy582, vyy592, dd, de, df)
new_esEs3(Left(vyy580), Left(vyy590), app(app(app(ty_@3, bbc), bbd), bbe), bba) → new_esEs1(vyy580, vyy590, bbc, bbd, bbe)
new_esEs2(Just(vyy580), Just(vyy590), app(ty_Maybe, bab)) → new_esEs2(vyy580, vyy590, bab)
new_esEs3(Left(vyy580), Left(vyy590), app(app(ty_Either, bbg), bbh), bba) → new_esEs3(vyy580, vyy590, bbg, bbh)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), app(app(app(ty_@3, gd), ge), gf), cg, ef) → new_esEs1(vyy580, vyy590, gd, ge, gf)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), cf, app(app(ty_@2, fg), fh), ef) → new_esEs4(vyy581, vyy591, fg, fh)
new_esEs3(Left(vyy580), Left(vyy590), app(ty_Maybe, bbf), bba) → new_esEs2(vyy580, vyy590, bbf)
new_esEs4(@2(vyy580, vyy581), @2(vyy590, vyy591), bdg, app(app(ty_Either, beg), beh)) → new_esEs3(vyy581, vyy591, beg, beh)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), cf, app(ty_Maybe, fc), ef) → new_esEs2(vyy581, vyy591, fc)
new_esEs4(@2(vyy580, vyy581), @2(vyy590, vyy591), bdg, app(app(app(ty_@3, bec), bed), bee)) → new_esEs1(vyy581, vyy591, bec, bed, bee)
new_esEs4(@2(vyy580, vyy581), @2(vyy590, vyy591), bdg, app(ty_Maybe, bef)) → new_esEs2(vyy581, vyy591, bef)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), app(app(ty_@2, hb), hc), cg, ef) → new_esEs4(vyy580, vyy590, hb, hc)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), cf, cg, app(ty_Maybe, dg)) → new_esEs2(vyy582, vyy592, dg)
new_esEs3(Left(vyy580), Left(vyy590), app(app(ty_@2, bca), bcb), bba) → new_esEs4(vyy580, vyy590, bca, bcb)
new_esEs4(@2(vyy580, vyy581), @2(vyy590, vyy591), app(app(ty_Either, bgc), bgd), bfe) → new_esEs3(vyy580, vyy590, bgc, bgd)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), cf, cg, app(app(ty_@2, eb), ec)) → new_esEs4(vyy582, vyy592, eb, ec)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), app(ty_Maybe, gg), cg, ef) → new_esEs2(vyy580, vyy590, gg)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), app(app(ty_Either, gh), ha), cg, ef) → new_esEs3(vyy580, vyy590, gh, ha)
new_esEs2(Just(vyy580), Just(vyy590), app(app(ty_@2, bae), baf)) → new_esEs4(vyy580, vyy590, bae, baf)
new_esEs2(Just(vyy580), Just(vyy590), app(app(ty_Either, bac), bad)) → new_esEs3(vyy580, vyy590, bac, bad)
new_esEs4(@2(vyy580, vyy581), @2(vyy590, vyy591), bdg, app(app(ty_@2, bfa), bfb)) → new_esEs4(vyy581, vyy591, bfa, bfb)
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_foldFM2(EmptyFM, x0, x1)
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
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_foldFM2(EmptyFM, x0, x1)
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ Rewriting
↳ QDP
↳ Rewriting
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QReductionProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QReductionProof
↳ QDP
↳ QDPSizeChangeProof
↳ QDP
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_esEs2(Just(vyy580), Just(vyy590), app(app(app(ty_@3, hg), hh), baa)) → new_esEs1(vyy580, vyy590, hg, hh, baa)
new_esEs4(@2(vyy580, vyy581), @2(vyy590, vyy591), app(ty_Maybe, bgb), bfe) → new_esEs2(vyy580, vyy590, bgb)
new_esEs4(@2(vyy580, vyy581), @2(vyy590, vyy591), app(app(app(ty_@3, bfg), bfh), bga), bfe) → new_esEs1(vyy580, vyy590, bfg, bfh, bga)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), cf, app(app(app(ty_@3, eh), fa), fb), ef) → new_esEs1(vyy581, vyy591, eh, fa, fb)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), cf, app(app(ty_Either, fd), ff), ef) → new_esEs3(vyy581, vyy591, fd, ff)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), cf, cg, app(app(ty_Either, dh), ea)) → new_esEs3(vyy582, vyy592, dh, ea)
new_esEs4(@2(vyy580, vyy581), @2(vyy590, vyy591), app(app(ty_@2, bge), bgf), bfe) → new_esEs4(vyy580, vyy590, bge, bgf)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), cf, cg, app(app(app(ty_@3, dd), de), df)) → new_esEs1(vyy582, vyy592, dd, de, df)
new_esEs3(Left(vyy580), Left(vyy590), app(app(app(ty_@3, bbc), bbd), bbe), bba) → new_esEs1(vyy580, vyy590, bbc, bbd, bbe)
new_esEs2(Just(vyy580), Just(vyy590), app(ty_Maybe, bab)) → new_esEs2(vyy580, vyy590, bab)
new_esEs3(Left(vyy580), Left(vyy590), app(app(ty_Either, bbg), bbh), bba) → new_esEs3(vyy580, vyy590, bbg, bbh)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), cf, app(app(ty_@2, fg), fh), ef) → new_esEs4(vyy581, vyy591, fg, fh)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), app(app(app(ty_@3, gd), ge), gf), cg, ef) → new_esEs1(vyy580, vyy590, gd, ge, gf)
new_esEs3(Left(vyy580), Left(vyy590), app(ty_Maybe, bbf), bba) → new_esEs2(vyy580, vyy590, bbf)
new_esEs4(@2(vyy580, vyy581), @2(vyy590, vyy591), bdg, app(app(ty_Either, beg), beh)) → new_esEs3(vyy581, vyy591, beg, beh)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), cf, app(ty_Maybe, fc), ef) → new_esEs2(vyy581, vyy591, fc)
new_esEs4(@2(vyy580, vyy581), @2(vyy590, vyy591), bdg, app(app(app(ty_@3, bec), bed), bee)) → new_esEs1(vyy581, vyy591, bec, bed, bee)
new_esEs4(@2(vyy580, vyy581), @2(vyy590, vyy591), bdg, app(ty_Maybe, bef)) → new_esEs2(vyy581, vyy591, bef)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), app(app(ty_@2, hb), hc), cg, ef) → new_esEs4(vyy580, vyy590, hb, hc)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), cf, cg, app(ty_Maybe, dg)) → new_esEs2(vyy582, vyy592, dg)
new_esEs3(Left(vyy580), Left(vyy590), app(app(ty_@2, bca), bcb), bba) → new_esEs4(vyy580, vyy590, bca, bcb)
new_esEs4(@2(vyy580, vyy581), @2(vyy590, vyy591), app(app(ty_Either, bgc), bgd), bfe) → new_esEs3(vyy580, vyy590, bgc, bgd)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), cf, cg, app(app(ty_@2, eb), ec)) → new_esEs4(vyy582, vyy592, eb, ec)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), app(ty_Maybe, gg), cg, ef) → new_esEs2(vyy580, vyy590, gg)
new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), app(app(ty_Either, gh), ha), cg, ef) → new_esEs3(vyy580, vyy590, gh, ha)
new_esEs2(Just(vyy580), Just(vyy590), app(app(ty_@2, bae), baf)) → new_esEs4(vyy580, vyy590, bae, baf)
new_esEs4(@2(vyy580, vyy581), @2(vyy590, vyy591), bdg, app(app(ty_@2, bfa), bfb)) → new_esEs4(vyy581, vyy591, bfa, bfb)
new_esEs2(Just(vyy580), Just(vyy590), app(app(ty_Either, bac), bad)) → new_esEs3(vyy580, vyy590, bac, bad)
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_esEs2(Just(vyy580), Just(vyy590), app(ty_Maybe, bab)) → new_esEs2(vyy580, vyy590, bab)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
- new_esEs2(Just(vyy580), Just(vyy590), app(app(ty_@2, bae), baf)) → new_esEs4(vyy580, vyy590, bae, baf)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
- new_esEs2(Just(vyy580), Just(vyy590), app(app(app(ty_@3, hg), hh), baa)) → new_esEs1(vyy580, vyy590, hg, hh, baa)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
- new_esEs2(Just(vyy580), Just(vyy590), app(app(ty_Either, bac), bad)) → new_esEs3(vyy580, vyy590, bac, bad)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
- new_esEs3(Left(vyy580), Left(vyy590), app(ty_Maybe, bbf), bba) → new_esEs2(vyy580, vyy590, bbf)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
- new_esEs3(Left(vyy580), Left(vyy590), app(app(ty_@2, bca), bcb), bba) → new_esEs4(vyy580, vyy590, bca, bcb)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
- new_esEs3(Left(vyy580), Left(vyy590), app(app(app(ty_@3, bbc), bbd), bbe), bba) → new_esEs1(vyy580, vyy590, bbc, bbd, bbe)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
- new_esEs3(Left(vyy580), Left(vyy590), app(app(ty_Either, bbg), bbh), bba) → new_esEs3(vyy580, vyy590, bbg, bbh)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
- new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), cf, app(ty_Maybe, fc), ef) → new_esEs2(vyy581, vyy591, fc)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
- new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), cf, cg, app(ty_Maybe, dg)) → new_esEs2(vyy582, vyy592, dg)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3
- new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), app(ty_Maybe, gg), cg, ef) → new_esEs2(vyy580, vyy590, gg)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
- new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), cf, app(app(ty_@2, fg), fh), ef) → new_esEs4(vyy581, vyy591, fg, fh)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
- new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), app(app(ty_@2, hb), hc), cg, ef) → new_esEs4(vyy580, vyy590, hb, hc)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
- new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), cf, cg, app(app(ty_@2, eb), ec)) → new_esEs4(vyy582, vyy592, eb, ec)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4
- new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), cf, app(app(app(ty_@3, eh), fa), fb), ef) → new_esEs1(vyy581, vyy591, eh, fa, fb)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5
- new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), cf, cg, app(app(app(ty_@3, dd), de), df)) → new_esEs1(vyy582, vyy592, dd, de, df)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4, 5 > 5
- new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), app(app(app(ty_@3, gd), ge), gf), cg, ef) → new_esEs1(vyy580, vyy590, gd, ge, gf)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
- new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), cf, app(app(ty_Either, fd), ff), ef) → new_esEs3(vyy581, vyy591, fd, ff)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
- new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), cf, cg, app(app(ty_Either, dh), ea)) → new_esEs3(vyy582, vyy592, dh, ea)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4
- new_esEs1(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), app(app(ty_Either, gh), ha), cg, ef) → new_esEs3(vyy580, vyy590, gh, ha)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
- new_esEs4(@2(vyy580, vyy581), @2(vyy590, vyy591), app(ty_Maybe, bgb), bfe) → new_esEs2(vyy580, vyy590, bgb)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
- new_esEs4(@2(vyy580, vyy581), @2(vyy590, vyy591), bdg, app(ty_Maybe, bef)) → new_esEs2(vyy581, vyy591, bef)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
- new_esEs4(@2(vyy580, vyy581), @2(vyy590, vyy591), app(app(ty_@2, bge), bgf), bfe) → new_esEs4(vyy580, vyy590, bge, bgf)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
- new_esEs4(@2(vyy580, vyy581), @2(vyy590, vyy591), bdg, app(app(ty_@2, bfa), bfb)) → new_esEs4(vyy581, vyy591, bfa, bfb)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
- new_esEs4(@2(vyy580, vyy581), @2(vyy590, vyy591), app(app(app(ty_@3, bfg), bfh), bga), bfe) → new_esEs1(vyy580, vyy590, bfg, bfh, bga)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
- new_esEs4(@2(vyy580, vyy581), @2(vyy590, vyy591), bdg, app(app(app(ty_@3, bec), bed), bee)) → new_esEs1(vyy581, vyy591, bec, bed, bee)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5
- new_esEs4(@2(vyy580, vyy581), @2(vyy590, vyy591), bdg, app(app(ty_Either, beg), beh)) → new_esEs3(vyy581, vyy591, beg, beh)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
- new_esEs4(@2(vyy580, vyy581), @2(vyy590, vyy591), app(app(ty_Either, bgc), bgd), bfe) → new_esEs3(vyy580, vyy590, bgc, bgd)
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
↳ QDPSizeChangeProof
↳ 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
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDPSizeChangeProof
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_ltEs1(:(vyy3000, vyy3001), :(vyy400, vyy401), gb) → new_compare(vyy3001, vyy401, gb)
new_compare2(vyy3000, vyy400, False, cb, cc) → new_ltEs(vyy3000, vyy400, cb, cc)
new_ltEs0(Right(vyy3000), Right(vyy400), eg, app(app(app(ty_@3, fg), fh), ga)) → new_ltEs3(vyy3000, vyy400, fg, fh, ga)
new_ltEs0(Left(vyy3000), Left(vyy400), app(app(app(ty_@3, ed), ee), ef), dg) → new_ltEs3(vyy3000, vyy400, ed, ee, ef)
new_ltEs(@2(vyy3000, vyy3001), @2(vyy400, vyy401), h, app(ty_[], be)) → new_ltEs1(vyy3001, vyy401, be)
new_ltEs2(Just(vyy3000), Just(vyy400), app(app(ty_Either, hf), hg)) → new_ltEs0(vyy3000, vyy400, hf, hg)
new_ltEs(@2(vyy3000, vyy3001), @2(vyy400, vyy401), h, app(ty_Maybe, bf)) → new_ltEs2(vyy3001, vyy401, bf)
new_ltEs(@2(vyy3000, vyy3001), @2(vyy400, vyy401), app(app(ty_@2, cb), cc), cd) → new_compare2(vyy3000, vyy400, new_esEs5(vyy3000, vyy400, cb, cc), cb, cc)
new_ltEs3(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), app(app(ty_@2, bdb), bdc), baf, bcb) → new_lt(vyy3000, vyy400, bdb, bdc)
new_compare1(vyy3000, vyy400, cb, cc) → new_compare2(vyy3000, vyy400, new_esEs5(vyy3000, vyy400, cb, cc), cb, cc)
new_compare22(vyy3000, vyy400, False, db, dc, dd) → new_ltEs3(vyy3000, vyy400, db, dc, dd)
new_ltEs0(Left(vyy3000), Left(vyy400), app(ty_[], eb), dg) → new_ltEs1(vyy3000, vyy400, eb)
new_ltEs0(Left(vyy3000), Left(vyy400), app(app(ty_Either, dh), ea), dg) → new_ltEs0(vyy3000, vyy400, dh, ea)
new_compare5(vyy3000, vyy400, db, dc, dd) → new_compare22(vyy3000, vyy400, new_esEs8(vyy3000, vyy400, db, dc, dd), db, dc, dd)
new_primCompAux(vyy3000, vyy400, vyy78, app(ty_[], gg)) → new_compare(vyy3000, vyy400, gg)
new_ltEs(@2(vyy3000, vyy3001), @2(vyy400, vyy401), app(ty_[], cg), cd) → new_compare(vyy3000, vyy400, cg)
new_ltEs3(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), app(ty_Maybe, bdg), baf, bcb) → new_lt2(vyy3000, vyy400, bdg)
new_compare3(vyy3000, vyy400, ce, cf) → new_compare20(vyy3000, vyy400, new_esEs6(vyy3000, vyy400, ce, cf), ce, cf)
new_ltEs3(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), bae, baf, app(app(ty_Either, bba), bbb)) → new_ltEs0(vyy3002, vyy402, bba, bbb)
new_ltEs0(Right(vyy3000), Right(vyy400), eg, app(app(ty_@2, eh), fa)) → new_ltEs(vyy3000, vyy400, eh, fa)
new_ltEs3(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), bae, baf, app(ty_Maybe, bbd)) → new_ltEs2(vyy3002, vyy402, bbd)
new_compare20(vyy3000, vyy400, False, ce, cf) → new_ltEs0(vyy3000, vyy400, ce, cf)
new_ltEs0(Left(vyy3000), Left(vyy400), app(app(ty_@2, de), df), dg) → new_ltEs(vyy3000, vyy400, de, df)
new_lt2(vyy3000, vyy400, da) → new_compare21(vyy3000, vyy400, new_esEs7(vyy3000, vyy400, da), da)
new_ltEs(@2(vyy3000, vyy3001), @2(vyy400, vyy401), h, app(app(app(ty_@3, bg), bh), ca)) → new_ltEs3(vyy3001, vyy401, bg, bh, ca)
new_ltEs2(Just(vyy3000), Just(vyy400), app(ty_[], hh)) → new_ltEs1(vyy3000, vyy400, hh)
new_ltEs2(Just(vyy3000), Just(vyy400), app(app(app(ty_@3, bab), bac), bad)) → new_ltEs3(vyy3000, vyy400, bab, bac, bad)
new_ltEs3(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), bae, baf, app(app(ty_@2, bag), bah)) → new_ltEs(vyy3002, vyy402, bag, bah)
new_lt3(vyy3000, vyy400, db, dc, dd) → new_compare22(vyy3000, vyy400, new_esEs8(vyy3000, vyy400, db, dc, dd), db, dc, dd)
new_ltEs0(Right(vyy3000), Right(vyy400), eg, app(app(ty_Either, fb), fc)) → new_ltEs0(vyy3000, vyy400, fb, fc)
new_lt1(vyy3000, vyy400, cg) → new_compare(vyy3000, vyy400, cg)
new_ltEs0(Right(vyy3000), Right(vyy400), eg, app(ty_Maybe, ff)) → new_ltEs2(vyy3000, vyy400, ff)
new_ltEs3(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), bae, app(app(ty_@2, bbh), bca), bcb) → new_lt(vyy3001, vyy401, bbh, bca)
new_ltEs(@2(vyy3000, vyy3001), @2(vyy400, vyy401), app(ty_Maybe, da), cd) → new_compare21(vyy3000, vyy400, new_esEs7(vyy3000, vyy400, da), da)
new_ltEs2(Just(vyy3000), Just(vyy400), app(app(ty_@2, hd), he)) → new_ltEs(vyy3000, vyy400, hd, he)
new_ltEs3(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), bae, baf, app(app(app(ty_@3, bbe), bbf), bbg)) → new_ltEs3(vyy3002, vyy402, bbe, bbf, bbg)
new_ltEs3(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), app(ty_[], bdf), baf, bcb) → new_lt1(vyy3000, vyy400, bdf)
new_primCompAux(vyy3000, vyy400, vyy78, app(app(app(ty_@3, ha), hb), hc)) → new_compare5(vyy3000, vyy400, ha, hb, hc)
new_ltEs3(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), app(app(app(ty_@3, bdh), bea), beb), baf, bcb) → new_lt3(vyy3000, vyy400, bdh, bea, beb)
new_ltEs2(Just(vyy3000), Just(vyy400), app(ty_Maybe, baa)) → new_ltEs2(vyy3000, vyy400, baa)
new_compare(:(vyy3000, vyy3001), :(vyy400, vyy401), gb) → new_compare(vyy3001, vyy401, gb)
new_compare21(vyy3000, vyy400, False, da) → new_ltEs2(vyy3000, vyy400, da)
new_lt0(vyy3000, vyy400, ce, cf) → new_compare20(vyy3000, vyy400, new_esEs6(vyy3000, vyy400, ce, cf), ce, cf)
new_ltEs0(Left(vyy3000), Left(vyy400), app(ty_Maybe, ec), dg) → new_ltEs2(vyy3000, vyy400, ec)
new_primCompAux(vyy3000, vyy400, vyy78, app(app(ty_Either, ge), gf)) → new_compare3(vyy3000, vyy400, ge, gf)
new_compare(:(vyy3000, vyy3001), :(vyy400, vyy401), gb) → new_primCompAux(vyy3000, vyy400, new_compare0(vyy3001, vyy401, gb), gb)
new_ltEs(@2(vyy3000, vyy3001), @2(vyy400, vyy401), h, app(app(ty_@2, ba), bb)) → new_ltEs(vyy3001, vyy401, ba, bb)
new_ltEs0(Right(vyy3000), Right(vyy400), eg, app(ty_[], fd)) → new_ltEs1(vyy3000, vyy400, fd)
new_compare4(vyy3000, vyy400, da) → new_compare21(vyy3000, vyy400, new_esEs7(vyy3000, vyy400, da), da)
new_ltEs3(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), bae, app(app(app(ty_@3, bcg), bch), bda), bcb) → new_lt3(vyy3001, vyy401, bcg, bch, bda)
new_ltEs3(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), bae, app(app(ty_Either, bcc), bcd), bcb) → new_lt0(vyy3001, vyy401, bcc, bcd)
new_primCompAux(vyy3000, vyy400, vyy78, app(ty_Maybe, gh)) → new_compare4(vyy3000, vyy400, gh)
new_ltEs(@2(vyy3000, vyy3001), @2(vyy400, vyy401), h, app(app(ty_Either, bc), bd)) → new_ltEs0(vyy3001, vyy401, bc, bd)
new_ltEs1(:(vyy3000, vyy3001), :(vyy400, vyy401), gb) → new_primCompAux(vyy3000, vyy400, new_compare0(vyy3001, vyy401, gb), gb)
new_ltEs3(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), bae, baf, app(ty_[], bbc)) → new_ltEs1(vyy3002, vyy402, bbc)
new_ltEs3(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), bae, app(ty_Maybe, bcf), bcb) → new_lt2(vyy3001, vyy401, bcf)
new_primCompAux(vyy3000, vyy400, vyy78, app(app(ty_@2, gc), gd)) → new_compare1(vyy3000, vyy400, gc, gd)
new_ltEs3(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), app(app(ty_Either, bdd), bde), baf, bcb) → new_lt0(vyy3000, vyy400, bdd, bde)
new_ltEs(@2(vyy3000, vyy3001), @2(vyy400, vyy401), app(app(ty_Either, ce), cf), cd) → new_compare20(vyy3000, vyy400, new_esEs6(vyy3000, vyy400, ce, cf), ce, cf)
new_lt(vyy3000, vyy400, cb, cc) → new_compare2(vyy3000, vyy400, new_esEs5(vyy3000, vyy400, cb, cc), cb, cc)
new_ltEs3(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), bae, app(ty_[], bce), bcb) → new_lt1(vyy3001, vyy401, bce)
new_ltEs(@2(vyy3000, vyy3001), @2(vyy400, vyy401), app(app(app(ty_@3, db), dc), dd), cd) → new_compare22(vyy3000, vyy400, new_esEs8(vyy3000, vyy400, db, dc, dd), db, dc, dd)
The TRS R consists of the following rules:
new_esEs23(GT, LT) → False
new_esEs23(LT, GT) → False
new_esEs7(Just(vyy580), Just(vyy590), app(ty_Maybe, bhd)) → new_esEs7(vyy580, vyy590, bhd)
new_ltEs19(vyy3001, vyy401, ty_Integer) → new_ltEs16(vyy3001, vyy401)
new_esEs28(vyy581, vyy591, app(ty_[], dcb)) → new_esEs19(vyy581, vyy591, dcb)
new_lt16(vyy3000, vyy400) → new_esEs9(new_compare26(vyy3000, vyy400))
new_compare16(vyy3000, vyy400) → new_compare211(vyy3000, vyy400, new_esEs21(vyy3000, vyy400))
new_ltEs4(EQ, GT) → True
new_esEs26(vyy580, vyy590, app(app(ty_FiniteMap, cdc), cdd)) → new_esEs17(vyy580, vyy590, cdc, cdd)
new_lt5(vyy3001, vyy401, ty_Char) → new_lt19(vyy3001, vyy401)
new_esEs29(vyy580, vyy590, app(app(app(ty_@3, ddg), ddh), dea)) → new_esEs8(vyy580, vyy590, ddg, ddh, dea)
new_esEs27(vyy582, vyy592, ty_Char) → new_esEs22(vyy582, vyy592)
new_ltEs8(vyy3002, vyy402, ty_Int) → new_ltEs9(vyy3002, vyy402)
new_esEs29(vyy580, vyy590, app(ty_[], ddf)) → new_esEs19(vyy580, vyy590, ddf)
new_compare14(vyy3000, vyy400, ty_Bool) → new_compare16(vyy3000, vyy400)
new_esEs16(vyy58, vyy59, ty_Char) → new_esEs22(vyy58, vyy59)
new_esEs11(Integer(vyy580), Integer(vyy590)) → new_primEqInt(vyy580, vyy590)
new_esEs27(vyy582, vyy592, app(ty_Maybe, dbb)) → new_esEs7(vyy582, vyy592, dbb)
new_esEs28(vyy581, vyy591, ty_Integer) → new_esEs11(vyy581, vyy591)
new_esEs26(vyy580, vyy590, ty_Integer) → new_esEs11(vyy580, vyy590)
new_esEs16(vyy58, vyy59, app(ty_Ratio, bec)) → new_esEs12(vyy58, vyy59, bec)
new_esEs24(vyy580, vyy590, app(app(ty_FiniteMap, cab), cac)) → new_esEs17(vyy580, vyy590, cab, cac)
new_ltEs6(True, False) → False
new_ltEs13(Right(vyy3000), Right(vyy400), eg, app(app(app(ty_@3, fg), fh), ga)) → new_ltEs7(vyy3000, vyy400, fg, fh, ga)
new_esEs7(Just(vyy580), Just(vyy590), app(app(ty_Either, bhe), bhf)) → new_esEs6(vyy580, vyy590, bhe, bhf)
new_primMulNat0(Zero, Zero) → Zero
new_ltEs13(Left(vyy3000), Left(vyy400), app(app(ty_@2, de), df), dg) → new_ltEs10(vyy3000, vyy400, de, df)
new_esEs25(vyy581, vyy591, app(app(ty_Either, ccg), cch)) → new_esEs6(vyy581, vyy591, ccg, cch)
new_lt6(vyy3000, vyy400, app(ty_Ratio, beh)) → new_lt15(vyy3000, vyy400, beh)
new_esEs29(vyy580, vyy590, ty_Char) → new_esEs22(vyy580, vyy590)
new_lt20(vyy3000, vyy400, app(app(ty_@2, cb), cc)) → new_lt8(vyy3000, vyy400, cb, cc)
new_esEs9(LT) → True
new_lt20(vyy3000, vyy400, app(app(app(ty_@3, db), dc), dd)) → new_lt4(vyy3000, vyy400, db, dc, dd)
new_esEs29(vyy580, vyy590, ty_@0) → new_esEs20(vyy580, vyy590)
new_lt19(vyy3000, vyy400) → new_esEs9(new_compare28(vyy3000, vyy400))
new_not(GT) → False
new_esEs26(vyy580, vyy590, app(ty_[], cdf)) → new_esEs19(vyy580, vyy590, cdf)
new_lt5(vyy3001, vyy401, ty_Ordering) → new_lt13(vyy3001, vyy401)
new_esEs6(Left(vyy580), Left(vyy590), app(app(app(ty_@3, cfe), cff), cfg), bfh) → new_esEs8(vyy580, vyy590, cfe, cff, cfg)
new_esEs29(vyy580, vyy590, app(ty_Maybe, deb)) → new_esEs7(vyy580, vyy590, deb)
new_lt20(vyy3000, vyy400, ty_Double) → new_lt14(vyy3000, vyy400)
new_esEs16(vyy58, vyy59, ty_Ordering) → new_esEs23(vyy58, vyy59)
new_lt5(vyy3001, vyy401, app(ty_Ratio, beg)) → new_lt15(vyy3001, vyy401, beg)
new_esEs16(vyy58, vyy59, ty_Integer) → new_esEs11(vyy58, vyy59)
new_esEs16(vyy58, vyy59, app(app(ty_Either, bfg), bfh)) → new_esEs6(vyy58, vyy59, bfg, bfh)
new_lt6(vyy3000, vyy400, app(app(ty_@2, bdb), bdc)) → new_lt8(vyy3000, vyy400, bdb, bdc)
new_compare0(:(vyy3000, vyy3001), :(vyy400, vyy401), gb) → new_primCompAux0(vyy3000, vyy400, new_compare0(vyy3001, vyy401, gb), gb)
new_ltEs17(Just(vyy3000), Just(vyy400), app(ty_Ratio, bgd)) → new_ltEs15(vyy3000, vyy400, bgd)
new_compare18(Double(vyy3000, vyy3001), Double(vyy400, vyy401)) → new_compare9(new_sr(vyy3000, vyy400), new_sr(vyy3001, vyy401))
new_ltEs13(Right(vyy3000), Right(vyy400), eg, app(ty_Maybe, ff)) → new_ltEs17(vyy3000, vyy400, ff)
new_esEs24(vyy580, vyy590, app(app(ty_@2, cbd), cbe)) → new_esEs5(vyy580, vyy590, cbd, cbe)
new_lt20(vyy3000, vyy400, ty_Integer) → new_lt16(vyy3000, vyy400)
new_esEs26(vyy580, vyy590, ty_Float) → new_esEs18(vyy580, vyy590)
new_esEs25(vyy581, vyy591, ty_Double) → new_esEs15(vyy581, vyy591)
new_esEs26(vyy580, vyy590, app(app(app(ty_@3, cdg), cdh), cea)) → new_esEs8(vyy580, vyy590, cdg, cdh, cea)
new_lt6(vyy3000, vyy400, ty_Char) → new_lt19(vyy3000, vyy400)
new_esEs25(vyy581, vyy591, ty_Bool) → new_esEs21(vyy581, vyy591)
new_esEs29(vyy580, vyy590, ty_Float) → new_esEs18(vyy580, vyy590)
new_esEs28(vyy581, vyy591, ty_Bool) → new_esEs21(vyy581, vyy591)
new_ltEs13(Right(vyy3000), Right(vyy400), eg, app(ty_Ratio, dab)) → new_ltEs15(vyy3000, vyy400, dab)
new_foldFM0(vyy590, vyy591, vyy96, EmptyFM, bed, bee) → :(@2(vyy590, vyy591), vyy96)
new_esEs16(vyy58, vyy59, ty_Float) → new_esEs18(vyy58, vyy59)
new_ltEs19(vyy3001, vyy401, ty_Char) → new_ltEs18(vyy3001, vyy401)
new_esEs28(vyy581, vyy591, app(app(app(ty_@3, dcc), dcd), dce)) → new_esEs8(vyy581, vyy591, dcc, dcd, dce)
new_esEs7(Just(vyy580), Just(vyy590), ty_Int) → new_esEs10(vyy580, vyy590)
new_ltEs14(vyy300, vyy40) → new_not(new_compare18(vyy300, vyy40))
new_esEs20(@0, @0) → True
new_esEs5(@2(vyy580, vyy581), @2(vyy590, vyy591), bga, bgb) → new_asAs(new_esEs26(vyy580, vyy590, bga), new_esEs25(vyy581, vyy591, bgb))
new_esEs22(Char(vyy580), Char(vyy590)) → new_primEqNat0(vyy580, vyy590)
new_ltEs13(Left(vyy3000), Left(vyy400), app(ty_[], eb), dg) → new_ltEs5(vyy3000, vyy400, eb)
new_esEs28(vyy581, vyy591, ty_Float) → new_esEs18(vyy581, vyy591)
new_lt20(vyy3000, vyy400, ty_Float) → new_lt10(vyy3000, vyy400)
new_compare14(vyy3000, vyy400, ty_Int) → new_compare9(vyy3000, vyy400)
new_ltEs17(Just(vyy3000), Nothing, bgc) → False
new_lt6(vyy3000, vyy400, ty_Ordering) → new_lt13(vyy3000, vyy400)
new_esEs24(vyy580, vyy590, app(ty_Maybe, cba)) → new_esEs7(vyy580, vyy590, cba)
new_lt4(vyy3000, vyy400, db, dc, dd) → new_esEs9(new_compare7(vyy3000, vyy400, db, dc, dd))
new_lt6(vyy3000, vyy400, ty_Integer) → new_lt16(vyy3000, vyy400)
new_esEs6(Right(vyy580), Right(vyy590), bfg, app(app(ty_FiniteMap, cge), cgf)) → new_esEs17(vyy580, vyy590, cge, cgf)
new_ltEs17(Just(vyy3000), Just(vyy400), app(ty_[], hh)) → new_ltEs5(vyy3000, vyy400, hh)
new_compare9(vyy300, vyy40) → new_primCmpInt(vyy300, vyy40)
new_esEs28(vyy581, vyy591, ty_@0) → new_esEs20(vyy581, vyy591)
new_ltEs8(vyy3002, vyy402, app(app(ty_@2, bag), bah)) → new_ltEs10(vyy3002, vyy402, bag, bah)
new_compare15(@0, @0) → EQ
new_ltEs13(Left(vyy3000), Left(vyy400), ty_Int, dg) → new_ltEs9(vyy3000, vyy400)
new_primCompAux0(vyy3000, vyy400, vyy78, gb) → new_primCompAux00(vyy78, new_compare14(vyy3000, vyy400, gb))
new_compare13(vyy3000, vyy400, False, ce, cf) → GT
new_esEs24(vyy580, vyy590, app(ty_[], cae)) → new_esEs19(vyy580, vyy590, cae)
new_lt6(vyy3000, vyy400, ty_@0) → new_lt9(vyy3000, vyy400)
new_ltEs15(vyy300, vyy40, cbf) → new_not(new_compare19(vyy300, vyy40, cbf))
new_esEs6(Right(vyy580), Right(vyy590), bfg, app(app(app(ty_@3, cha), chb), chc)) → new_esEs8(vyy580, vyy590, cha, chb, chc)
new_primCmpNat0(Zero, Succ(vyy4000)) → LT
new_ltEs19(vyy3001, vyy401, app(ty_Ratio, ceg)) → new_ltEs15(vyy3001, vyy401, ceg)
new_esEs6(Left(vyy580), Left(vyy590), ty_Integer, bfh) → new_esEs11(vyy580, vyy590)
new_ltEs8(vyy3002, vyy402, ty_Double) → new_ltEs14(vyy3002, vyy402)
new_compare6(vyy3000, vyy400, cb, cc) → new_compare23(vyy3000, vyy400, new_esEs5(vyy3000, vyy400, cb, cc), cb, cc)
new_ltEs19(vyy3001, vyy401, ty_Bool) → new_ltEs6(vyy3001, vyy401)
new_esEs13(vyy581, vyy591, ty_Integer) → new_esEs11(vyy581, vyy591)
new_esEs6(Right(vyy580), Left(vyy590), bfg, bfh) → False
new_esEs6(Left(vyy580), Right(vyy590), bfg, bfh) → False
new_compare7(vyy3000, vyy400, db, dc, dd) → new_compare29(vyy3000, vyy400, new_esEs8(vyy3000, vyy400, db, dc, dd), db, dc, dd)
new_lt20(vyy3000, vyy400, ty_Char) → new_lt19(vyy3000, vyy400)
new_compare14(vyy3000, vyy400, app(ty_[], gg)) → new_compare0(vyy3000, vyy400, gg)
new_lt17(vyy3000, vyy400, cg) → new_esEs9(new_compare0(vyy3000, vyy400, cg))
new_esEs28(vyy581, vyy591, ty_Double) → new_esEs15(vyy581, vyy591)
new_esEs6(Right(vyy580), Right(vyy590), bfg, ty_Bool) → new_esEs21(vyy580, vyy590)
new_ltEs17(Just(vyy3000), Just(vyy400), app(app(ty_@2, hd), he)) → new_ltEs10(vyy3000, vyy400, hd, he)
new_esEs21(True, True) → True
new_esEs15(Double(vyy580, vyy581), Double(vyy590, vyy591)) → new_esEs10(new_sr(vyy580, vyy590), new_sr(vyy581, vyy591))
new_compare0([], [], gb) → EQ
new_esEs16(vyy58, vyy59, ty_Bool) → new_esEs21(vyy58, vyy59)
new_primEqNat0(Zero, Zero) → True
new_esEs8(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), bfc, bfd, bfe) → new_asAs(new_esEs29(vyy580, vyy590, bfc), new_asAs(new_esEs28(vyy581, vyy591, bfd), new_esEs27(vyy582, vyy592, bfe)))
new_esEs28(vyy581, vyy591, ty_Ordering) → new_esEs23(vyy581, vyy591)
new_ltEs13(Right(vyy3000), Right(vyy400), eg, ty_Double) → new_ltEs14(vyy3000, vyy400)
new_esEs6(Left(vyy580), Left(vyy590), app(ty_[], cfd), bfh) → new_esEs19(vyy580, vyy590, cfd)
new_esEs14(vyy580, vyy590, ty_Int) → new_esEs10(vyy580, vyy590)
new_esEs6(Left(vyy580), Left(vyy590), ty_@0, bfh) → new_esEs20(vyy580, vyy590)
new_compare19(:%(vyy3000, vyy3001), :%(vyy400, vyy401), ty_Integer) → new_compare26(new_sr0(vyy3000, vyy401), new_sr0(vyy400, vyy3001))
new_compare29(vyy3000, vyy400, False, db, dc, dd) → new_compare110(vyy3000, vyy400, new_ltEs7(vyy3000, vyy400, db, dc, dd), db, dc, dd)
new_esEs6(Right(vyy580), Right(vyy590), bfg, app(app(ty_Either, che), chf)) → new_esEs6(vyy580, vyy590, che, chf)
new_esEs6(Left(vyy580), Left(vyy590), ty_Double, bfh) → new_esEs15(vyy580, vyy590)
new_ltEs7(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), bae, baf, bcb) → new_pePe(new_lt6(vyy3000, vyy400, bae), vyy3000, vyy400, new_pePe(new_lt5(vyy3001, vyy401, baf), vyy3001, vyy401, new_ltEs8(vyy3002, vyy402, bcb), baf), bae)
new_esEs19([], [], bfb) → True
new_esEs25(vyy581, vyy591, app(ty_[], ccb)) → new_esEs19(vyy581, vyy591, ccb)
new_esEs12(:%(vyy580, vyy581), :%(vyy590, vyy591), bec) → new_asAs(new_esEs14(vyy580, vyy590, bec), new_esEs13(vyy581, vyy591, bec))
new_sr(vyy3001, vyy401) → new_primMulInt(vyy3001, vyy401)
new_esEs16(vyy58, vyy59, ty_@0) → new_esEs20(vyy58, vyy59)
new_esEs28(vyy581, vyy591, app(app(ty_Either, dcg), dch)) → new_esEs6(vyy581, vyy591, dcg, dch)
new_ltEs8(vyy3002, vyy402, ty_@0) → new_ltEs11(vyy3002, vyy402)
new_ltEs18(vyy300, vyy40) → new_not(new_compare28(vyy300, vyy40))
new_esEs6(Right(vyy580), Right(vyy590), bfg, ty_Double) → new_esEs15(vyy580, vyy590)
new_ltEs13(Right(vyy3000), Right(vyy400), eg, ty_Float) → new_ltEs12(vyy3000, vyy400)
new_esEs27(vyy582, vyy592, ty_@0) → new_esEs20(vyy582, vyy592)
new_primPlusNat0(Succ(vyy970), vyy40100) → Succ(Succ(new_primPlusNat1(vyy970, vyy40100)))
new_esEs7(Just(vyy580), Just(vyy590), ty_Char) → new_esEs22(vyy580, vyy590)
new_esEs27(vyy582, vyy592, app(app(ty_FiniteMap, dac), dad)) → new_esEs17(vyy582, vyy592, dac, dad)
new_esEs6(Right(vyy580), Right(vyy590), bfg, ty_Float) → new_esEs18(vyy580, vyy590)
new_lt6(vyy3000, vyy400, app(app(ty_Either, bdd), bde)) → new_lt11(vyy3000, vyy400, bdd, bde)
new_esEs19(:(vyy580, vyy581), [], bfb) → False
new_esEs19([], :(vyy590, vyy591), bfb) → False
new_ltEs8(vyy3002, vyy402, app(app(app(ty_@3, bbe), bbf), bbg)) → new_ltEs7(vyy3002, vyy402, bbe, bbf, bbg)
new_compare29(vyy3000, vyy400, True, db, dc, dd) → EQ
new_ltEs8(vyy3002, vyy402, ty_Ordering) → new_ltEs4(vyy3002, vyy402)
new_esEs26(vyy580, vyy590, ty_Ordering) → new_esEs23(vyy580, vyy590)
new_primEqInt(Neg(Succ(vyy5800)), Neg(Succ(vyy5900))) → new_primEqNat0(vyy5800, vyy5900)
new_ltEs19(vyy3001, vyy401, app(app(ty_@2, ba), bb)) → new_ltEs10(vyy3001, vyy401, ba, bb)
new_compare13(vyy3000, vyy400, True, ce, cf) → LT
new_esEs9(GT) → False
new_ltEs17(Just(vyy3000), Just(vyy400), app(app(app(ty_@3, bab), bac), bad)) → new_ltEs7(vyy3000, vyy400, bab, bac, bad)
new_primPlusNat1(Zero, Succ(vyy401000)) → Succ(vyy401000)
new_primPlusNat1(Succ(vyy9700), Zero) → Succ(vyy9700)
new_lt5(vyy3001, vyy401, ty_Int) → new_lt7(vyy3001, vyy401)
new_esEs9(EQ) → False
new_esEs16(vyy58, vyy59, app(app(ty_FiniteMap, bed), bee)) → new_esEs17(vyy58, vyy59, bed, bee)
new_esEs7(Just(vyy580), Just(vyy590), ty_@0) → new_esEs20(vyy580, vyy590)
new_ltEs13(Right(vyy3000), Right(vyy400), eg, ty_Int) → new_ltEs9(vyy3000, vyy400)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_lt20(vyy3000, vyy400, app(ty_Maybe, da)) → new_lt18(vyy3000, vyy400, da)
new_esEs23(EQ, EQ) → True
new_ltEs19(vyy3001, vyy401, ty_Ordering) → new_ltEs4(vyy3001, vyy401)
new_ltEs8(vyy3002, vyy402, ty_Bool) → new_ltEs6(vyy3002, vyy402)
new_esEs6(Right(vyy580), Right(vyy590), bfg, app(ty_[], cgh)) → new_esEs19(vyy580, vyy590, cgh)
new_lt11(vyy3000, vyy400, ce, cf) → new_esEs9(new_compare12(vyy3000, vyy400, ce, cf))
new_primEqInt(Neg(Zero), Neg(Succ(vyy5900))) → False
new_primEqInt(Neg(Succ(vyy5800)), Neg(Zero)) → False
new_compare14(vyy3000, vyy400, app(app(app(ty_@3, ha), hb), hc)) → new_compare7(vyy3000, vyy400, ha, hb, hc)
new_esEs16(vyy58, vyy59, app(app(app(ty_@3, bfc), bfd), bfe)) → new_esEs8(vyy58, vyy59, bfc, bfd, bfe)
new_esEs6(Left(vyy580), Left(vyy590), ty_Char, bfh) → new_esEs22(vyy580, vyy590)
new_lt5(vyy3001, vyy401, ty_@0) → new_lt9(vyy3001, vyy401)
new_compare111(vyy3000, vyy400, True, da) → LT
new_lt5(vyy3001, vyy401, app(ty_[], bce)) → new_lt17(vyy3001, vyy401, bce)
new_lt20(vyy3000, vyy400, ty_Ordering) → new_lt13(vyy3000, vyy400)
new_esEs7(Just(vyy580), Just(vyy590), ty_Bool) → new_esEs21(vyy580, vyy590)
new_esEs24(vyy580, vyy590, ty_Ordering) → new_esEs23(vyy580, vyy590)
new_foldFM0(vyy590, vyy591, vyy96, Branch(vyy5930, vyy5931, vyy5932, vyy5933, vyy5934), bed, bee) → new_foldFM0(vyy5930, vyy5931, new_foldFM0(vyy590, vyy591, vyy96, vyy5934, bed, bee), vyy5933, bed, bee)
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_esEs25(vyy581, vyy591, ty_Ordering) → new_esEs23(vyy581, vyy591)
new_ltEs4(EQ, LT) → False
new_lt10(vyy3000, vyy400) → new_esEs9(new_compare8(vyy3000, vyy400))
new_esEs7(Just(vyy580), Just(vyy590), ty_Integer) → new_esEs11(vyy580, vyy590)
new_primCmpNat0(Succ(vyy30000), Succ(vyy4000)) → new_primCmpNat0(vyy30000, vyy4000)
new_ltEs19(vyy3001, vyy401, ty_@0) → new_ltEs11(vyy3001, vyy401)
new_esEs7(Just(vyy580), Just(vyy590), app(app(ty_FiniteMap, bge), bgf)) → new_esEs17(vyy580, vyy590, bge, bgf)
new_esEs7(Just(vyy580), Just(vyy590), ty_Ordering) → new_esEs23(vyy580, vyy590)
new_sizeFM(EmptyFM, bed, bee) → Pos(Zero)
new_compare112(vyy3000, vyy400, True) → LT
new_ltEs8(vyy3002, vyy402, app(ty_Ratio, bef)) → new_ltEs15(vyy3002, vyy402, bef)
new_primEqInt(Pos(Succ(vyy5800)), Pos(Succ(vyy5900))) → new_primEqNat0(vyy5800, vyy5900)
new_ltEs19(vyy3001, vyy401, app(app(app(ty_@3, bg), bh), ca)) → new_ltEs7(vyy3001, vyy401, bg, bh, ca)
new_esEs16(vyy58, vyy59, ty_Int) → new_esEs10(vyy58, vyy59)
new_ltEs17(Just(vyy3000), Just(vyy400), ty_@0) → new_ltEs11(vyy3000, vyy400)
new_lt20(vyy3000, vyy400, ty_Int) → new_lt7(vyy3000, vyy400)
new_ltEs6(False, True) → True
new_primEqNat0(Succ(vyy5800), Succ(vyy5900)) → new_primEqNat0(vyy5800, vyy5900)
new_ltEs6(True, True) → True
new_esEs27(vyy582, vyy592, app(app(app(ty_@3, dag), dah), dba)) → new_esEs8(vyy582, vyy592, dag, dah, dba)
new_ltEs19(vyy3001, vyy401, app(app(ty_Either, bc), bd)) → new_ltEs13(vyy3001, vyy401, bc, bd)
new_lt5(vyy3001, vyy401, ty_Bool) → new_lt12(vyy3001, vyy401)
new_esEs6(Right(vyy580), Right(vyy590), bfg, app(app(ty_@2, chg), chh)) → new_esEs5(vyy580, vyy590, chg, chh)
new_ltEs19(vyy3001, vyy401, ty_Double) → new_ltEs14(vyy3001, vyy401)
new_esEs29(vyy580, vyy590, ty_Int) → new_esEs10(vyy580, vyy590)
new_ltEs4(GT, EQ) → False
new_primCompAux00(vyy82, LT) → LT
new_esEs24(vyy580, vyy590, app(ty_Ratio, cad)) → new_esEs12(vyy580, vyy590, cad)
new_primCmpInt(Neg(Succ(vyy30000)), Neg(vyy400)) → new_primCmpNat0(vyy400, Succ(vyy30000))
new_esEs7(Nothing, Nothing, bff) → True
new_esEs23(GT, GT) → True
new_primEqInt(Pos(Zero), Pos(Succ(vyy5900))) → False
new_primEqInt(Pos(Succ(vyy5800)), Pos(Zero)) → False
new_compare24(vyy3000, vyy400, False) → new_compare10(vyy3000, vyy400, new_ltEs4(vyy3000, vyy400))
new_ltEs4(EQ, EQ) → True
new_lt5(vyy3001, vyy401, app(app(ty_Either, bcc), bcd)) → new_lt11(vyy3001, vyy401, bcc, bcd)
new_lt7(vyy3000, vyy400) → new_esEs9(new_compare9(vyy3000, vyy400))
new_primCmpNat0(Zero, Zero) → EQ
new_ltEs13(Left(vyy3000), Left(vyy400), app(app(app(ty_@3, ed), ee), ef), dg) → new_ltEs7(vyy3000, vyy400, ed, ee, ef)
new_esEs6(Right(vyy580), Right(vyy590), bfg, app(ty_Maybe, chd)) → new_esEs7(vyy580, vyy590, chd)
new_primCmpNat0(Succ(vyy30000), Zero) → GT
new_esEs14(vyy580, vyy590, ty_Integer) → new_esEs11(vyy580, vyy590)
new_esEs7(Just(vyy580), Just(vyy590), app(app(app(ty_@3, bha), bhb), bhc)) → new_esEs8(vyy580, vyy590, bha, bhb, bhc)
new_primCmpInt(Neg(Zero), Pos(Succ(vyy4000))) → LT
new_compare11(vyy3000, vyy400, True, cb, cc) → LT
new_esEs6(Right(vyy580), Right(vyy590), bfg, ty_@0) → new_esEs20(vyy580, vyy590)
new_ltEs4(GT, LT) → False
new_sr0(Integer(vyy4000), Integer(vyy30010)) → Integer(new_primMulInt(vyy4000, vyy30010))
new_primPlusNat1(Succ(vyy9700), Succ(vyy401000)) → Succ(Succ(new_primPlusNat1(vyy9700, vyy401000)))
new_compare27(vyy3000, vyy400, da) → new_compare210(vyy3000, vyy400, new_esEs7(vyy3000, vyy400, da), da)
new_primEqInt(Neg(Succ(vyy5800)), Pos(vyy590)) → False
new_primEqInt(Pos(Succ(vyy5800)), Neg(vyy590)) → False
new_esEs25(vyy581, vyy591, ty_Int) → new_esEs10(vyy581, vyy591)
new_esEs7(Nothing, Just(vyy590), bff) → False
new_esEs7(Just(vyy580), Nothing, bff) → False
new_compare210(vyy3000, vyy400, True, da) → EQ
new_esEs26(vyy580, vyy590, ty_Char) → new_esEs22(vyy580, vyy590)
new_foldFM2(EmptyFM, bed, bee) → []
new_ltEs17(Just(vyy3000), Just(vyy400), ty_Integer) → new_ltEs16(vyy3000, vyy400)
new_esEs29(vyy580, vyy590, app(app(ty_@2, dee), def)) → new_esEs5(vyy580, vyy590, dee, def)
new_ltEs13(Right(vyy3000), Right(vyy400), eg, app(ty_[], fd)) → new_ltEs5(vyy3000, vyy400, fd)
new_ltEs13(Right(vyy3000), Right(vyy400), eg, ty_@0) → new_ltEs11(vyy3000, vyy400)
new_esEs26(vyy580, vyy590, ty_Int) → new_esEs10(vyy580, vyy590)
new_primEqInt(Neg(Zero), Pos(Succ(vyy5900))) → False
new_primEqInt(Pos(Zero), Neg(Succ(vyy5900))) → False
new_esEs29(vyy580, vyy590, ty_Integer) → new_esEs11(vyy580, vyy590)
new_primCmpInt(Pos(Zero), Pos(Succ(vyy4000))) → new_primCmpNat0(Zero, Succ(vyy4000))
new_primCompAux00(vyy82, EQ) → vyy82
new_compare24(vyy3000, vyy400, True) → EQ
new_esEs7(Just(vyy580), Just(vyy590), ty_Float) → new_esEs18(vyy580, vyy590)
new_ltEs13(Left(vyy3000), Left(vyy400), ty_Float, dg) → new_ltEs12(vyy3000, vyy400)
new_esEs26(vyy580, vyy590, app(app(ty_@2, cee), cef)) → new_esEs5(vyy580, vyy590, cee, cef)
new_ltEs17(Just(vyy3000), Just(vyy400), ty_Ordering) → new_ltEs4(vyy3000, vyy400)
new_ltEs8(vyy3002, vyy402, ty_Float) → new_ltEs12(vyy3002, vyy402)
new_ltEs17(Just(vyy3000), Just(vyy400), ty_Int) → new_ltEs9(vyy3000, vyy400)
new_esEs26(vyy580, vyy590, ty_Bool) → new_esEs21(vyy580, vyy590)
new_esEs6(Left(vyy580), Left(vyy590), app(app(ty_Either, cga), cgb), bfh) → new_esEs6(vyy580, vyy590, cga, cgb)
new_esEs6(Left(vyy580), Left(vyy590), app(ty_Ratio, cfc), bfh) → new_esEs12(vyy580, vyy590, cfc)
new_primPlusNat0(Zero, vyy40100) → Succ(vyy40100)
new_primCmpInt(Pos(Succ(vyy30000)), Pos(vyy400)) → new_primCmpNat0(Succ(vyy30000), vyy400)
new_lt6(vyy3000, vyy400, app(app(app(ty_@3, bdh), bea), beb)) → new_lt4(vyy3000, vyy400, bdh, bea, beb)
new_esEs24(vyy580, vyy590, app(app(ty_Either, cbb), cbc)) → new_esEs6(vyy580, vyy590, cbb, cbc)
new_esEs25(vyy581, vyy591, ty_Float) → new_esEs18(vyy581, vyy591)
new_compare14(vyy3000, vyy400, app(ty_Maybe, gh)) → new_compare27(vyy3000, vyy400, gh)
new_compare14(vyy3000, vyy400, app(app(ty_@2, gc), gd)) → new_compare6(vyy3000, vyy400, gc, gd)
new_ltEs13(Left(vyy3000), Left(vyy400), ty_Bool, dg) → new_ltEs6(vyy3000, vyy400)
new_not0 → True
new_esEs28(vyy581, vyy591, app(app(ty_@2, dda), ddb)) → new_esEs5(vyy581, vyy591, dda, ddb)
new_compare0(:(vyy3000, vyy3001), [], gb) → GT
new_esEs24(vyy580, vyy590, ty_Bool) → new_esEs21(vyy580, vyy590)
new_esEs27(vyy582, vyy592, app(app(ty_Either, dbc), dbd)) → new_esEs6(vyy582, vyy592, dbc, dbd)
new_ltEs13(Left(vyy3000), Left(vyy400), app(ty_Ratio, daa), dg) → new_ltEs15(vyy3000, vyy400, daa)
new_esEs18(Float(vyy580, vyy581), Float(vyy590, vyy591)) → new_esEs10(new_sr(vyy580, vyy590), new_sr(vyy581, vyy591))
new_esEs28(vyy581, vyy591, app(app(ty_FiniteMap, dbg), dbh)) → new_esEs17(vyy581, vyy591, dbg, dbh)
new_esEs6(Right(vyy580), Right(vyy590), bfg, app(ty_Ratio, cgg)) → new_esEs12(vyy580, vyy590, cgg)
new_compare11(vyy3000, vyy400, False, cb, cc) → GT
new_lt15(vyy3000, vyy400, ceh) → new_esEs9(new_compare19(vyy3000, vyy400, ceh))
new_esEs25(vyy581, vyy591, ty_Integer) → new_esEs11(vyy581, vyy591)
new_primCmpInt(Pos(Succ(vyy30000)), Neg(vyy400)) → GT
new_ltEs19(vyy3001, vyy401, ty_Int) → new_ltEs9(vyy3001, vyy401)
new_esEs28(vyy581, vyy591, app(ty_Maybe, dcf)) → new_esEs7(vyy581, vyy591, dcf)
new_esEs24(vyy580, vyy590, ty_Float) → new_esEs18(vyy580, vyy590)
new_lt12(vyy3000, vyy400) → new_esEs9(new_compare16(vyy3000, vyy400))
new_esEs24(vyy580, vyy590, ty_Double) → new_esEs15(vyy580, vyy590)
new_primMulInt(Pos(vyy30010), Pos(vyy4010)) → Pos(new_primMulNat0(vyy30010, vyy4010))
new_ltEs5(vyy300, vyy40, gb) → new_not(new_compare0(vyy300, vyy40, gb))
new_esEs21(False, False) → True
new_esEs24(vyy580, vyy590, ty_Integer) → new_esEs11(vyy580, vyy590)
new_compare25(vyy3000, vyy400, False, ce, cf) → new_compare13(vyy3000, vyy400, new_ltEs13(vyy3000, vyy400, ce, cf), ce, cf)
new_lt8(vyy3000, vyy400, cb, cc) → new_esEs9(new_compare6(vyy3000, vyy400, cb, cc))
new_esEs6(Left(vyy580), Left(vyy590), app(app(ty_@2, cgc), cgd), bfh) → new_esEs5(vyy580, vyy590, cgc, cgd)
new_compare14(vyy3000, vyy400, app(app(ty_Either, ge), gf)) → new_compare12(vyy3000, vyy400, ge, gf)
new_ltEs17(Nothing, Just(vyy400), bgc) → True
new_esEs27(vyy582, vyy592, ty_Double) → new_esEs15(vyy582, vyy592)
new_primMulInt(Neg(vyy30010), Neg(vyy4010)) → Pos(new_primMulNat0(vyy30010, vyy4010))
new_lt6(vyy3000, vyy400, app(ty_[], bdf)) → new_lt17(vyy3000, vyy400, bdf)
new_ltEs17(Just(vyy3000), Just(vyy400), app(app(ty_Either, hf), hg)) → new_ltEs13(vyy3000, vyy400, hf, hg)
new_lt6(vyy3000, vyy400, app(ty_Maybe, bdg)) → new_lt18(vyy3000, vyy400, bdg)
new_primEqNat0(Succ(vyy5800), Zero) → False
new_primEqNat0(Zero, Succ(vyy5900)) → False
new_lt5(vyy3001, vyy401, ty_Float) → new_lt10(vyy3001, vyy401)
new_lt20(vyy3000, vyy400, app(ty_Ratio, ceh)) → new_lt15(vyy3000, vyy400, ceh)
new_lt18(vyy3000, vyy400, da) → new_esEs9(new_compare27(vyy3000, vyy400, da))
new_compare25(vyy3000, vyy400, True, ce, cf) → EQ
new_compare211(vyy3000, vyy400, False) → new_compare112(vyy3000, vyy400, new_ltEs6(vyy3000, vyy400))
new_compare23(vyy3000, vyy400, False, cb, cc) → new_compare11(vyy3000, vyy400, new_ltEs10(vyy3000, vyy400, cb, cc), cb, cc)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_compare17(vyy3000, vyy400) → new_compare24(vyy3000, vyy400, new_esEs23(vyy3000, vyy400))
new_ltEs8(vyy3002, vyy402, ty_Char) → new_ltEs18(vyy3002, vyy402)
new_esEs27(vyy582, vyy592, app(app(ty_@2, dbe), dbf)) → new_esEs5(vyy582, vyy592, dbe, dbf)
new_ltEs17(Nothing, Nothing, bgc) → True
new_esEs25(vyy581, vyy591, app(app(app(ty_@3, ccc), ccd), cce)) → new_esEs8(vyy581, vyy591, ccc, ccd, cce)
new_lt5(vyy3001, vyy401, ty_Integer) → new_lt16(vyy3001, vyy401)
new_sizeFM(Branch(vyy590, vyy591, vyy592, vyy593, vyy594), bed, bee) → vyy592
new_esEs29(vyy580, vyy590, app(app(ty_Either, dec), ded)) → new_esEs6(vyy580, vyy590, dec, ded)
new_ltEs17(Just(vyy3000), Just(vyy400), ty_Bool) → new_ltEs6(vyy3000, vyy400)
new_pePe(True, vyy58, vyy59, vyy60, bfa) → True
new_ltEs4(LT, GT) → True
new_foldFM2(Branch(vyy590, vyy591, vyy592, vyy593, vyy594), bed, bee) → new_foldFM0(vyy590, vyy591, new_foldFM2(vyy594, bed, bee), vyy593, bed, bee)
new_lt20(vyy3000, vyy400, app(app(ty_Either, ce), cf)) → new_lt11(vyy3000, vyy400, ce, cf)
new_lt5(vyy3001, vyy401, ty_Double) → new_lt14(vyy3001, vyy401)
new_ltEs19(vyy3001, vyy401, app(ty_Maybe, bf)) → new_ltEs17(vyy3001, vyy401, bf)
new_lt20(vyy3000, vyy400, ty_@0) → new_lt9(vyy3000, vyy400)
new_lt6(vyy3000, vyy400, ty_Int) → new_lt7(vyy3000, vyy400)
new_primCmpInt(Neg(Zero), Neg(Succ(vyy4000))) → new_primCmpNat0(Succ(vyy4000), Zero)
new_compare23(vyy3000, vyy400, True, cb, cc) → EQ
new_primCmpInt(Pos(Zero), Neg(Succ(vyy4000))) → GT
new_esEs6(Left(vyy580), Left(vyy590), app(ty_Maybe, cfh), bfh) → new_esEs7(vyy580, vyy590, cfh)
new_ltEs13(Left(vyy3000), Left(vyy400), ty_Char, dg) → new_ltEs18(vyy3000, vyy400)
new_ltEs13(Left(vyy3000), Left(vyy400), app(ty_Maybe, ec), dg) → new_ltEs17(vyy3000, vyy400, ec)
new_esEs16(vyy58, vyy59, app(ty_[], bfb)) → new_esEs19(vyy58, vyy59, bfb)
new_esEs28(vyy581, vyy591, app(ty_Ratio, dca)) → new_esEs12(vyy581, vyy591, dca)
new_ltEs13(Left(vyy3000), Left(vyy400), ty_@0, dg) → new_ltEs11(vyy3000, vyy400)
new_esEs6(Right(vyy580), Right(vyy590), bfg, ty_Integer) → new_esEs11(vyy580, vyy590)
new_ltEs8(vyy3002, vyy402, app(ty_[], bbc)) → new_ltEs5(vyy3002, vyy402, bbc)
new_esEs25(vyy581, vyy591, app(app(ty_FiniteMap, cbg), cbh)) → new_esEs17(vyy581, vyy591, cbg, cbh)
new_esEs27(vyy582, vyy592, app(ty_Ratio, dae)) → new_esEs12(vyy582, vyy592, dae)
new_ltEs13(Left(vyy3000), Left(vyy400), app(app(ty_Either, dh), ea), dg) → new_ltEs13(vyy3000, vyy400, dh, ea)
new_esEs6(Right(vyy580), Right(vyy590), bfg, ty_Char) → new_esEs22(vyy580, vyy590)
new_esEs25(vyy581, vyy591, app(ty_Maybe, ccf)) → new_esEs7(vyy581, vyy591, ccf)
new_ltEs13(Left(vyy3000), Left(vyy400), ty_Integer, dg) → new_ltEs16(vyy3000, vyy400)
new_ltEs13(Right(vyy3000), Right(vyy400), eg, app(app(ty_Either, fb), fc)) → new_ltEs13(vyy3000, vyy400, fb, fc)
new_compare8(Float(vyy3000, vyy3001), Float(vyy400, vyy401)) → new_compare9(new_sr(vyy3000, vyy400), new_sr(vyy3001, vyy401))
new_ltEs13(Right(vyy3000), Right(vyy400), eg, ty_Ordering) → new_ltEs4(vyy3000, vyy400)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_ltEs4(LT, EQ) → True
new_compare14(vyy3000, vyy400, ty_Ordering) → new_compare17(vyy3000, vyy400)
new_compare26(Integer(vyy3000), Integer(vyy400)) → new_primCmpInt(vyy3000, vyy400)
new_esEs6(Left(vyy580), Left(vyy590), app(app(ty_FiniteMap, cfa), cfb), bfh) → new_esEs17(vyy580, vyy590, cfa, cfb)
new_compare19(:%(vyy3000, vyy3001), :%(vyy400, vyy401), ty_Int) → new_compare9(new_sr(vyy3000, vyy401), new_sr(vyy400, vyy3001))
new_esEs24(vyy580, vyy590, ty_Int) → new_esEs10(vyy580, vyy590)
new_esEs27(vyy582, vyy592, ty_Float) → new_esEs18(vyy582, vyy592)
new_compare14(vyy3000, vyy400, ty_Float) → new_compare8(vyy3000, vyy400)
new_asAs(False, vyy73) → False
new_esEs6(Left(vyy580), Left(vyy590), ty_Ordering, bfh) → new_esEs23(vyy580, vyy590)
new_esEs29(vyy580, vyy590, app(app(ty_FiniteMap, ddc), ddd)) → new_esEs17(vyy580, vyy590, ddc, ddd)
new_ltEs17(Just(vyy3000), Just(vyy400), ty_Double) → new_ltEs14(vyy3000, vyy400)
new_primMulInt(Neg(vyy30010), Pos(vyy4010)) → Neg(new_primMulNat0(vyy30010, vyy4010))
new_primMulInt(Pos(vyy30010), Neg(vyy4010)) → Neg(new_primMulNat0(vyy30010, vyy4010))
new_ltEs13(Right(vyy3000), Right(vyy400), eg, ty_Bool) → new_ltEs6(vyy3000, vyy400)
new_compare12(vyy3000, vyy400, ce, cf) → new_compare25(vyy3000, vyy400, new_esEs6(vyy3000, vyy400, ce, cf), ce, cf)
new_primMulNat0(Zero, Succ(vyy40100)) → Zero
new_primMulNat0(Succ(vyy300100), Zero) → Zero
new_ltEs13(Left(vyy3000), Right(vyy400), eg, dg) → True
new_esEs25(vyy581, vyy591, ty_Char) → new_esEs22(vyy581, vyy591)
new_compare14(vyy3000, vyy400, ty_Double) → new_compare18(vyy3000, vyy400)
new_esEs27(vyy582, vyy592, ty_Ordering) → new_esEs23(vyy582, vyy592)
new_esEs23(GT, EQ) → False
new_esEs23(EQ, GT) → False
new_esEs26(vyy580, vyy590, app(ty_Maybe, ceb)) → new_esEs7(vyy580, vyy590, ceb)
new_esEs23(EQ, LT) → False
new_esEs23(LT, EQ) → False
new_ltEs12(vyy300, vyy40) → new_not(new_compare8(vyy300, vyy40))
new_ltEs9(vyy300, vyy40) → new_not(new_compare9(vyy300, vyy40))
new_compare110(vyy3000, vyy400, True, db, dc, dd) → LT
new_not(EQ) → new_not0
new_lt20(vyy3000, vyy400, app(ty_[], cg)) → new_lt17(vyy3000, vyy400, cg)
new_ltEs8(vyy3002, vyy402, app(app(ty_Either, bba), bbb)) → new_ltEs13(vyy3002, vyy402, bba, bbb)
new_lt6(vyy3000, vyy400, ty_Double) → new_lt14(vyy3000, vyy400)
new_compare14(vyy3000, vyy400, ty_Integer) → new_compare26(vyy3000, vyy400)
new_esEs6(Right(vyy580), Right(vyy590), bfg, ty_Int) → new_esEs10(vyy580, vyy590)
new_ltEs13(Left(vyy3000), Left(vyy400), ty_Ordering, dg) → new_ltEs4(vyy3000, vyy400)
new_esEs29(vyy580, vyy590, app(ty_Ratio, dde)) → new_esEs12(vyy580, vyy590, dde)
new_esEs19(:(vyy580, vyy581), :(vyy590, vyy591), bfb) → new_asAs(new_esEs24(vyy580, vyy590, bfb), new_esEs19(vyy581, vyy591, bfb))
new_ltEs13(Right(vyy3000), Right(vyy400), eg, app(app(ty_@2, eh), fa)) → new_ltEs10(vyy3000, vyy400, eh, fa)
new_esEs29(vyy580, vyy590, ty_Ordering) → new_esEs23(vyy580, vyy590)
new_esEs28(vyy581, vyy591, ty_Char) → new_esEs22(vyy581, vyy591)
new_compare111(vyy3000, vyy400, False, da) → GT
new_esEs24(vyy580, vyy590, ty_Char) → new_esEs22(vyy580, vyy590)
new_ltEs13(Right(vyy3000), Left(vyy400), eg, dg) → False
new_compare210(vyy3000, vyy400, False, da) → new_compare111(vyy3000, vyy400, new_ltEs17(vyy3000, vyy400, da), da)
new_esEs26(vyy580, vyy590, app(ty_Ratio, cde)) → new_esEs12(vyy580, vyy590, cde)
new_esEs29(vyy580, vyy590, ty_Double) → new_esEs15(vyy580, vyy590)
new_esEs23(LT, LT) → True
new_esEs16(vyy58, vyy59, app(ty_Maybe, bff)) → new_esEs7(vyy58, vyy59, bff)
new_ltEs17(Just(vyy3000), Just(vyy400), ty_Float) → new_ltEs12(vyy3000, vyy400)
new_compare14(vyy3000, vyy400, ty_Char) → new_compare28(vyy3000, vyy400)
new_esEs27(vyy582, vyy592, ty_Bool) → new_esEs21(vyy582, vyy592)
new_ltEs13(Right(vyy3000), Right(vyy400), eg, ty_Char) → new_ltEs18(vyy3000, vyy400)
new_ltEs4(LT, LT) → True
new_ltEs16(vyy300, vyy40) → new_not(new_compare26(vyy300, vyy40))
new_compare14(vyy3000, vyy400, app(ty_Ratio, caa)) → new_compare19(vyy3000, vyy400, caa)
new_esEs25(vyy581, vyy591, app(app(ty_@2, cda), cdb)) → new_esEs5(vyy581, vyy591, cda, cdb)
new_esEs16(vyy58, vyy59, app(app(ty_@2, bga), bgb)) → new_esEs5(vyy58, vyy59, bga, bgb)
new_not(LT) → new_not0
new_lt5(vyy3001, vyy401, app(ty_Maybe, bcf)) → new_lt18(vyy3001, vyy401, bcf)
new_lt20(vyy3000, vyy400, ty_Bool) → new_lt12(vyy3000, vyy400)
new_compare112(vyy3000, vyy400, False) → GT
new_lt5(vyy3001, vyy401, app(app(app(ty_@3, bcg), bch), bda)) → new_lt4(vyy3001, vyy401, bcg, bch, bda)
new_esEs7(Just(vyy580), Just(vyy590), app(app(ty_@2, bhg), bhh)) → new_esEs5(vyy580, vyy590, bhg, bhh)
new_ltEs11(vyy300, vyy40) → new_not(new_compare15(vyy300, vyy40))
new_esEs28(vyy581, vyy591, ty_Int) → new_esEs10(vyy581, vyy591)
new_ltEs8(vyy3002, vyy402, app(ty_Maybe, bbd)) → new_ltEs17(vyy3002, vyy402, bbd)
new_ltEs17(Just(vyy3000), Just(vyy400), app(ty_Maybe, baa)) → new_ltEs17(vyy3000, vyy400, baa)
new_esEs29(vyy580, vyy590, ty_Bool) → new_esEs21(vyy580, vyy590)
new_esEs26(vyy580, vyy590, app(app(ty_Either, cec), ced)) → new_esEs6(vyy580, vyy590, cec, ced)
new_esEs27(vyy582, vyy592, app(ty_[], daf)) → new_esEs19(vyy582, vyy592, daf)
new_primPlusNat1(Zero, Zero) → Zero
new_compare0([], :(vyy400, vyy401), gb) → LT
new_ltEs13(Left(vyy3000), Left(vyy400), ty_Double, dg) → new_ltEs14(vyy3000, vyy400)
new_lt14(vyy3000, vyy400) → new_esEs9(new_compare18(vyy3000, vyy400))
new_ltEs17(Just(vyy3000), Just(vyy400), ty_Char) → new_ltEs18(vyy3000, vyy400)
new_esEs7(Just(vyy580), Just(vyy590), app(ty_[], bgh)) → new_esEs19(vyy580, vyy590, bgh)
new_asAs(True, vyy73) → vyy73
new_primMulNat0(Succ(vyy300100), Succ(vyy40100)) → new_primPlusNat0(new_primMulNat0(vyy300100, Succ(vyy40100)), vyy40100)
new_lt13(vyy3000, vyy400) → new_esEs9(new_compare17(vyy3000, vyy400))
new_esEs6(Left(vyy580), Left(vyy590), ty_Float, bfh) → new_esEs18(vyy580, vyy590)
new_lt5(vyy3001, vyy401, app(app(ty_@2, bbh), bca)) → new_lt8(vyy3001, vyy401, bbh, bca)
new_esEs27(vyy582, vyy592, ty_Integer) → new_esEs11(vyy582, vyy592)
new_pePe(False, vyy58, vyy59, vyy60, bfa) → new_asAs(new_esEs16(vyy58, vyy59, bfa), vyy60)
new_ltEs19(vyy3001, vyy401, ty_Float) → new_ltEs12(vyy3001, vyy401)
new_lt6(vyy3000, vyy400, ty_Float) → new_lt10(vyy3000, vyy400)
new_esEs26(vyy580, vyy590, ty_Double) → new_esEs15(vyy580, vyy590)
new_esEs27(vyy582, vyy592, ty_Int) → new_esEs10(vyy582, vyy592)
new_esEs7(Just(vyy580), Just(vyy590), ty_Double) → new_esEs15(vyy580, vyy590)
new_compare211(vyy3000, vyy400, True) → EQ
new_fmToList(vyy59, bed, bee) → new_foldFM2(vyy59, bed, bee)
new_ltEs10(@2(vyy3000, vyy3001), @2(vyy400, vyy401), h, cd) → new_pePe(new_lt20(vyy3000, vyy400, h), vyy3000, vyy400, new_ltEs19(vyy3001, vyy401, cd), h)
new_esEs21(False, True) → False
new_esEs21(True, False) → False
new_ltEs6(False, False) → True
new_ltEs8(vyy3002, vyy402, ty_Integer) → new_ltEs16(vyy3002, vyy402)
new_compare10(vyy3000, vyy400, True) → LT
new_ltEs4(GT, GT) → True
new_esEs26(vyy580, vyy590, ty_@0) → new_esEs20(vyy580, vyy590)
new_compare14(vyy3000, vyy400, ty_@0) → new_compare15(vyy3000, vyy400)
new_compare110(vyy3000, vyy400, False, db, dc, dd) → GT
new_ltEs19(vyy3001, vyy401, app(ty_[], be)) → new_ltEs5(vyy3001, vyy401, be)
new_compare10(vyy3000, vyy400, False) → GT
new_esEs6(Left(vyy580), Left(vyy590), ty_Bool, bfh) → new_esEs21(vyy580, vyy590)
new_esEs25(vyy581, vyy591, ty_@0) → new_esEs20(vyy581, vyy591)
new_lt6(vyy3000, vyy400, ty_Bool) → new_lt12(vyy3000, vyy400)
new_esEs10(vyy58, vyy59) → new_primEqInt(vyy58, vyy59)
new_primCompAux00(vyy82, GT) → GT
new_ltEs13(Right(vyy3000), Right(vyy400), eg, ty_Integer) → new_ltEs16(vyy3000, vyy400)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_compare28(Char(vyy3000), Char(vyy400)) → new_primCmpNat0(vyy3000, vyy400)
new_esEs6(Right(vyy580), Right(vyy590), bfg, ty_Ordering) → new_esEs23(vyy580, vyy590)
new_esEs24(vyy580, vyy590, app(app(app(ty_@3, caf), cag), cah)) → new_esEs8(vyy580, vyy590, caf, cag, cah)
new_esEs16(vyy58, vyy59, ty_Double) → new_esEs15(vyy58, vyy59)
new_lt9(vyy3000, vyy400) → new_esEs9(new_compare15(vyy3000, vyy400))
new_esEs25(vyy581, vyy591, app(ty_Ratio, cca)) → new_esEs12(vyy581, vyy591, cca)
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_esEs7(Just(vyy580), Just(vyy590), app(ty_Ratio, bgg)) → new_esEs12(vyy580, vyy590, bgg)
new_primCmpInt(Neg(Succ(vyy30000)), Pos(vyy400)) → LT
new_esEs6(Left(vyy580), Left(vyy590), ty_Int, bfh) → new_esEs10(vyy580, vyy590)
new_esEs24(vyy580, vyy590, ty_@0) → new_esEs20(vyy580, vyy590)
new_esEs17(vyy58, vyy59, bed, bee) → new_asAs(new_esEs10(new_sizeFM(vyy58, bed, bee), new_sizeFM(vyy59, bed, bee)), new_esEs19(new_fmToList(vyy58, bed, bee), new_fmToList(vyy59, bed, bee), app(app(ty_@2, bed), bee)))
new_esEs13(vyy581, vyy591, ty_Int) → new_esEs10(vyy581, vyy591)
The set Q consists of the following terms:
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_lt5(x0, x1, ty_Integer)
new_esEs25(x0, x1, ty_@0)
new_lt20(x0, x1, ty_Integer)
new_primEqNat0(Succ(x0), Zero)
new_compare11(x0, x1, False, x2, x3)
new_ltEs13(Right(x0), Right(x1), x2, ty_@0)
new_ltEs13(Right(x0), Right(x1), x2, ty_Ordering)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_compare111(x0, x1, False, x2)
new_esEs6(Left(x0), Left(x1), ty_@0, x2)
new_compare9(x0, x1)
new_esEs6(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_lt9(x0, x1)
new_esEs6(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_lt16(x0, x1)
new_ltEs13(Left(x0), Left(x1), ty_Int, x2)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_lt6(x0, x1, ty_Float)
new_lt15(x0, x1, x2)
new_esEs16(x0, x1, ty_Float)
new_compare15(@0, @0)
new_ltEs17(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_esEs23(LT, EQ)
new_esEs23(EQ, LT)
new_compare29(x0, x1, False, x2, x3, x4)
new_esEs26(x0, x1, ty_Char)
new_ltEs13(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_ltEs8(x0, x1, ty_Int)
new_esEs29(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs23(EQ, EQ)
new_esEs9(EQ)
new_esEs6(Right(x0), Right(x1), x2, ty_Int)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_lt6(x0, x1, app(ty_[], x2))
new_esEs23(EQ, GT)
new_esEs23(GT, EQ)
new_esEs16(x0, x1, app(app(ty_Either, x2), x3))
new_esEs29(x0, x1, ty_Float)
new_esEs16(x0, x1, ty_Int)
new_ltEs13(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs17(Just(x0), Just(x1), app(ty_Maybe, x2))
new_ltEs13(Right(x0), Right(x1), x2, ty_Bool)
new_esEs19([], [], x0)
new_primMulNat0(Zero, Succ(x0))
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpNat0(Succ(x0), Zero)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt6(x0, x1, ty_Int)
new_lt5(x0, x1, ty_Double)
new_esEs10(x0, x1)
new_compare110(x0, x1, False, x2, x3, x4)
new_esEs29(x0, x1, ty_Bool)
new_compare14(x0, x1, app(ty_Ratio, x2))
new_lt5(x0, x1, app(ty_[], x2))
new_ltEs13(Right(x0), Right(x1), x2, ty_Integer)
new_esEs16(x0, x1, ty_@0)
new_esEs24(x0, x1, ty_Double)
new_esEs12(:%(x0, x1), :%(x2, x3), x4)
new_lt19(x0, x1)
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs17(Just(x0), Just(x1), ty_@0)
new_ltEs13(Left(x0), Left(x1), ty_Bool, x2)
new_compare14(x0, x1, ty_Integer)
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs13(Left(x0), Left(x1), ty_Float, x2)
new_ltEs14(x0, x1)
new_esEs7(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs26(x0, x1, ty_Ordering)
new_ltEs17(Nothing, Just(x0), x1)
new_ltEs13(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs17(Just(x0), Just(x1), ty_Ordering)
new_ltEs17(Just(x0), Just(x1), ty_Double)
new_ltEs13(Left(x0), Left(x1), ty_Ordering, x2)
new_compare210(x0, x1, False, x2)
new_esEs29(x0, x1, ty_Char)
new_esEs7(Just(x0), Just(x1), ty_@0)
new_esEs25(x0, x1, ty_Bool)
new_esEs7(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs8(x0, x1, app(ty_Ratio, x2))
new_ltEs6(True, True)
new_esEs7(Nothing, Just(x0), x1)
new_sr(x0, x1)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs26(x0, x1, ty_@0)
new_pePe(False, x0, x1, x2, x3)
new_compare26(Integer(x0), Integer(x1))
new_esEs19([], :(x0, x1), x2)
new_ltEs8(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs17(x0, x1, x2, x3)
new_compare24(x0, x1, False)
new_lt5(x0, x1, app(app(ty_Either, x2), x3))
new_lt20(x0, x1, ty_Bool)
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_FiniteMap, x3), x4))
new_compare0(:(x0, x1), :(x2, x3), x4)
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_compare211(x0, x1, True)
new_esEs6(Left(x0), Left(x1), app(app(ty_FiniteMap, x2), x3), x4)
new_ltEs19(x0, x1, ty_Ordering)
new_esEs24(x0, x1, ty_Integer)
new_compare111(x0, x1, True, x2)
new_lt20(x0, x1, ty_@0)
new_lt6(x0, x1, ty_@0)
new_ltEs17(Just(x0), Just(x1), ty_Int)
new_lt20(x0, x1, ty_Float)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_esEs6(Right(x0), Right(x1), x2, ty_Integer)
new_primEqNat0(Zero, Zero)
new_esEs27(x0, x1, ty_Double)
new_lt5(x0, x1, ty_Char)
new_esEs7(Just(x0), Just(x1), ty_Ordering)
new_primCmpNat0(Succ(x0), Succ(x1))
new_esEs6(Right(x0), Right(x1), x2, ty_@0)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_lt5(x0, x1, ty_Bool)
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_ltEs15(x0, x1, x2)
new_compare112(x0, x1, True)
new_esEs16(x0, x1, app(ty_Ratio, x2))
new_esEs7(Just(x0), Just(x1), ty_Float)
new_lt4(x0, x1, x2, x3, x4)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, ty_Bool)
new_esEs16(x0, x1, app(ty_[], x2))
new_primPlusNat1(Zero, Succ(x0))
new_primMulNat0(Zero, Zero)
new_primMulInt(Pos(x0), Pos(x1))
new_compare14(x0, x1, ty_Int)
new_compare13(x0, x1, True, x2, x3)
new_ltEs8(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs17(Just(x0), Just(x1), ty_Bool)
new_ltEs13(Right(x0), Right(x1), x2, ty_Double)
new_compare110(x0, x1, True, x2, x3, x4)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_ltEs5(x0, x1, x2)
new_ltEs4(GT, GT)
new_ltEs13(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs6(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_lt20(x0, x1, ty_Int)
new_foldFM2(EmptyFM, x0, x1)
new_esEs27(x0, x1, ty_Float)
new_esEs7(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_ltEs13(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_esEs25(x0, x1, ty_Ordering)
new_esEs7(Nothing, Nothing, x0)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_compare19(:%(x0, x1), :%(x2, x3), ty_Integer)
new_esEs28(x0, x1, ty_Integer)
new_primMulNat0(Succ(x0), Succ(x1))
new_ltEs17(Just(x0), Just(x1), ty_Float)
new_lt17(x0, x1, x2)
new_ltEs16(x0, x1)
new_esEs6(Right(x0), Left(x1), x2, x3)
new_esEs6(Left(x0), Right(x1), x2, x3)
new_esEs6(Left(x0), Left(x1), ty_Char, x2)
new_ltEs13(Left(x0), Left(x1), ty_@0, x2)
new_esEs28(x0, x1, ty_Float)
new_compare14(x0, x1, app(app(ty_@2, x2), x3))
new_esEs28(x0, x1, ty_Int)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_lt20(x0, x1, app(ty_Ratio, x2))
new_lt14(x0, x1)
new_compare12(x0, x1, x2, x3)
new_compare14(x0, x1, ty_Ordering)
new_lt6(x0, x1, ty_Double)
new_esEs28(x0, x1, app(ty_[], x2))
new_esEs19(:(x0, x1), [], x2)
new_ltEs13(Right(x0), Right(x1), x2, ty_Char)
new_compare10(x0, x1, False)
new_esEs24(x0, x1, ty_Bool)
new_compare14(x0, x1, ty_Char)
new_primPlusNat1(Succ(x0), Succ(x1))
new_lt8(x0, x1, x2, x3)
new_esEs27(x0, x1, ty_Ordering)
new_esEs7(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs19(x0, x1, ty_Integer)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_esEs24(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_compare13(x0, x1, False, x2, x3)
new_compare0([], [], x0)
new_esEs23(GT, LT)
new_esEs23(LT, GT)
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_ltEs19(x0, x1, ty_Int)
new_ltEs13(Left(x0), Left(x1), ty_Double, x2)
new_ltEs19(x0, x1, ty_Double)
new_compare18(Double(x0, x1), Double(x2, x3))
new_esEs5(@2(x0, x1), @2(x2, x3), x4, x5)
new_primPlusNat1(Zero, Zero)
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_not0
new_primMulNat0(Succ(x0), Zero)
new_ltEs12(x0, x1)
new_ltEs7(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs7(Just(x0), Nothing, x1)
new_esEs25(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs9(GT)
new_esEs27(x0, x1, ty_Int)
new_esEs7(Just(x0), Just(x1), ty_Char)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_esEs24(x0, x1, app(ty_[], x2))
new_ltEs8(x0, x1, ty_Float)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs4(EQ, EQ)
new_compare14(x0, x1, ty_Float)
new_ltEs18(x0, x1)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_lt20(x0, x1, app(ty_Maybe, x2))
new_ltEs6(True, False)
new_ltEs6(False, True)
new_ltEs13(Right(x0), Right(x1), x2, ty_Float)
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, ty_Bool)
new_compare24(x0, x1, True)
new_compare14(x0, x1, ty_Double)
new_sizeFM(EmptyFM, x0, x1)
new_esEs25(x0, x1, ty_Char)
new_primCompAux0(x0, x1, x2, x3)
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs4(EQ, LT)
new_ltEs4(LT, EQ)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_ltEs8(x0, x1, app(ty_[], x2))
new_ltEs17(Nothing, Nothing, x0)
new_not(GT)
new_ltEs8(x0, x1, ty_@0)
new_esEs26(x0, x1, ty_Int)
new_compare210(x0, x1, True, x2)
new_esEs24(x0, x1, ty_Int)
new_esEs16(x0, x1, ty_Double)
new_lt5(x0, x1, app(app(ty_@2, x2), x3))
new_primEqInt(Neg(Zero), Pos(Zero))
new_primEqInt(Pos(Zero), Neg(Zero))
new_lt5(x0, x1, ty_@0)
new_ltEs13(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs7(Just(x0), Just(x1), ty_Bool)
new_esEs27(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs13(x0, x1, ty_Int)
new_ltEs17(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_lt6(x0, x1, ty_Char)
new_compare25(x0, x1, False, x2, x3)
new_compare6(x0, x1, x2, x3)
new_lt7(x0, x1)
new_compare10(x0, x1, True)
new_ltEs19(x0, x1, app(ty_[], x2))
new_primCompAux00(x0, LT)
new_esEs16(x0, x1, app(app(ty_@2, x2), x3))
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_ltEs13(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_ltEs6(False, False)
new_primPlusNat1(Succ(x0), Zero)
new_esEs16(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs7(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_primCompAux00(x0, GT)
new_esEs23(LT, LT)
new_lt5(x0, x1, app(ty_Ratio, x2))
new_ltEs10(@2(x0, x1), @2(x2, x3), x4, x5)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs16(x0, x1, app(ty_Maybe, x2))
new_compare14(x0, x1, app(ty_Maybe, x2))
new_esEs6(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs19(x0, x1, ty_Bool)
new_primEqInt(Neg(Zero), Neg(Zero))
new_primPlusNat0(Succ(x0), x1)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_compare19(:%(x0, x1), :%(x2, x3), ty_Int)
new_compare11(x0, x1, True, x2, x3)
new_esEs28(x0, x1, ty_Bool)
new_ltEs13(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_ltEs13(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_lt5(x0, x1, ty_Float)
new_ltEs4(LT, LT)
new_esEs14(x0, x1, ty_Int)
new_ltEs13(Left(x0), Left(x1), ty_Integer, x2)
new_fmToList(x0, x1, x2)
new_esEs27(x0, x1, ty_Char)
new_ltEs8(x0, x1, ty_Double)
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs11(x0, x1)
new_pePe(True, x0, x1, x2, x3)
new_compare0([], :(x0, x1), x2)
new_compare29(x0, x1, True, x2, x3, x4)
new_esEs26(x0, x1, ty_Float)
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs16(x0, x1, ty_Ordering)
new_lt20(x0, x1, app(ty_[], x2))
new_compare7(x0, x1, x2, x3, x4)
new_esEs6(Right(x0), Right(x1), x2, ty_Char)
new_compare28(Char(x0), Char(x1))
new_esEs9(LT)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_ltEs13(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_esEs29(x0, x1, ty_Ordering)
new_esEs18(Float(x0, x1), Float(x2, x3))
new_esEs6(Left(x0), Left(x1), ty_Double, x2)
new_ltEs17(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare14(x0, x1, app(app(ty_Either, x2), x3))
new_esEs6(Left(x0), Left(x1), ty_Ordering, x2)
new_asAs(False, x0)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_lt6(x0, x1, app(ty_Ratio, x2))
new_primPlusNat0(Zero, x0)
new_compare8(Float(x0, x1), Float(x2, x3))
new_esEs7(Just(x0), Just(x1), ty_Double)
new_compare14(x0, x1, app(ty_[], x2))
new_primCmpNat0(Zero, Zero)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs29(x0, x1, ty_Int)
new_ltEs13(Left(x0), Left(x1), ty_Char, x2)
new_esEs15(Double(x0, x1), Double(x2, x3))
new_lt20(x0, x1, ty_Ordering)
new_esEs7(Just(x0), Just(x1), ty_Int)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_compare17(x0, x1)
new_compare23(x0, x1, True, x2, x3)
new_ltEs8(x0, x1, app(ty_Maybe, x2))
new_esEs6(Right(x0), Right(x1), x2, ty_Float)
new_ltEs8(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs17(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_compare211(x0, x1, False)
new_lt13(x0, x1)
new_esEs19(:(x0, x1), :(x2, x3), x4)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_lt11(x0, x1, x2, x3)
new_esEs13(x0, x1, ty_Integer)
new_lt12(x0, x1)
new_esEs7(Just(x0), Just(x1), app(ty_Ratio, x2))
new_ltEs13(Right(x0), Left(x1), x2, x3)
new_ltEs13(Left(x0), Right(x1), x2, x3)
new_compare0(:(x0, x1), [], x2)
new_ltEs8(x0, x1, ty_Ordering)
new_compare27(x0, x1, x2)
new_esEs8(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_ltEs19(x0, x1, ty_@0)
new_ltEs13(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs6(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
new_esEs6(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs6(Left(x0), Left(x1), ty_Int, x2)
new_esEs28(x0, x1, ty_Double)
new_esEs26(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_lt10(x0, x1)
new_lt5(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs13(Right(x0), Right(x1), x2, ty_Int)
new_esEs25(x0, x1, app(ty_[], x2))
new_lt6(x0, x1, app(ty_Maybe, x2))
new_primEqNat0(Zero, Succ(x0))
new_esEs6(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs16(x0, x1, ty_Bool)
new_esEs21(True, True)
new_ltEs4(EQ, GT)
new_ltEs4(GT, EQ)
new_lt5(x0, x1, app(ty_Maybe, x2))
new_esEs24(x0, x1, ty_Ordering)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs6(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_not(EQ)
new_ltEs17(Just(x0), Just(x1), ty_Integer)
new_esEs14(x0, x1, ty_Integer)
new_lt6(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs27(x0, x1, app(ty_[], x2))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_esEs25(x0, x1, ty_Int)
new_lt18(x0, x1, x2)
new_esEs22(Char(x0), Char(x1))
new_ltEs19(x0, x1, ty_Char)
new_lt6(x0, x1, ty_Bool)
new_esEs26(x0, x1, ty_Double)
new_lt5(x0, x1, ty_Int)
new_esEs24(x0, x1, ty_@0)
new_esEs11(Integer(x0), Integer(x1))
new_esEs21(False, True)
new_esEs21(True, False)
new_lt6(x0, x1, ty_Ordering)
new_esEs7(Just(x0), Just(x1), app(app(ty_FiniteMap, x2), x3))
new_esEs24(x0, x1, ty_Char)
new_esEs6(Left(x0), Left(x1), ty_Integer, x2)
new_esEs6(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs20(@0, @0)
new_esEs24(x0, x1, ty_Float)
new_ltEs17(Just(x0), Nothing, x1)
new_ltEs13(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs25(x0, x1, ty_Float)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs16(x0, x1, ty_Char)
new_esEs6(Right(x0), Right(x1), x2, ty_Double)
new_esEs29(x0, x1, ty_@0)
new_esEs29(x0, x1, app(ty_[], x2))
new_esEs26(x0, x1, ty_Integer)
new_esEs6(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs29(x0, x1, ty_Integer)
new_compare14(x0, x1, ty_Bool)
new_esEs28(x0, x1, ty_Ordering)
new_lt5(x0, x1, ty_Ordering)
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_esEs28(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs6(Right(x0), Right(x1), x2, ty_Bool)
new_compare25(x0, x1, True, x2, x3)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_esEs16(x0, x1, ty_Integer)
new_compare16(x0, x1)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_ltEs8(x0, x1, ty_Char)
new_primCompAux00(x0, EQ)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sr0(Integer(x0), Integer(x1))
new_esEs6(Left(x0), Left(x1), ty_Bool, x2)
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_ltEs9(x0, x1)
new_compare14(x0, x1, ty_@0)
new_ltEs19(x0, x1, ty_Float)
new_esEs28(x0, x1, ty_@0)
new_esEs25(x0, x1, ty_Double)
new_esEs16(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs8(x0, x1, ty_Integer)
new_esEs21(False, False)
new_compare23(x0, x1, False, x2, x3)
new_primEqInt(Pos(Zero), Pos(Zero))
new_esEs27(x0, x1, ty_Integer)
new_asAs(True, x0)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_lt6(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs17(Just(x0), Just(x1), app(ty_[], x2))
new_esEs28(x0, x1, ty_Char)
new_esEs7(Just(x0), Just(x1), ty_Integer)
new_compare112(x0, x1, False)
new_compare14(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt6(x0, x1, ty_Integer)
new_lt20(x0, x1, ty_Char)
new_esEs26(x0, x1, app(ty_[], x2))
new_esEs6(Left(x0), Left(x1), ty_Float, x2)
new_ltEs4(GT, LT)
new_ltEs4(LT, GT)
new_esEs27(x0, x1, ty_@0)
new_ltEs17(Just(x0), Just(x1), ty_Char)
new_lt6(x0, x1, app(app(ty_Either, x2), x3))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs6(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs29(x0, x1, ty_Double)
new_lt20(x0, x1, ty_Double)
new_esEs25(x0, x1, ty_Integer)
new_ltEs8(x0, x1, ty_Bool)
new_esEs23(GT, GT)
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_not(LT)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
We have to consider all minimal (P,Q,R)-chains.
By using the subterm criterion [20] together with the size-change analysis [32] we have proven that there are no infinite chains for this DP problem. From the DPs we obtained the following set of size-change graphs:
- new_ltEs(@2(vyy3000, vyy3001), @2(vyy400, vyy401), h, app(ty_[], be)) → new_ltEs1(vyy3001, vyy401, be)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
- new_ltEs(@2(vyy3000, vyy3001), @2(vyy400, vyy401), app(app(ty_@2, cb), cc), cd) → new_compare2(vyy3000, vyy400, new_esEs5(vyy3000, vyy400, cb, cc), cb, cc)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 4, 3 > 5
- new_ltEs3(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), bae, baf, app(ty_[], bbc)) → new_ltEs1(vyy3002, vyy402, bbc)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3
- new_ltEs(@2(vyy3000, vyy3001), @2(vyy400, vyy401), h, app(app(ty_Either, bc), bd)) → new_ltEs0(vyy3001, vyy401, bc, bd)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
- new_ltEs3(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), bae, baf, app(app(ty_Either, bba), bbb)) → new_ltEs0(vyy3002, vyy402, bba, bbb)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4
- new_ltEs(@2(vyy3000, vyy3001), @2(vyy400, vyy401), h, app(app(ty_@2, ba), bb)) → new_ltEs(vyy3001, vyy401, ba, bb)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
- new_ltEs3(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), bae, baf, app(app(ty_@2, bag), bah)) → new_ltEs(vyy3002, vyy402, bag, bah)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4
- new_ltEs2(Just(vyy3000), Just(vyy400), app(ty_[], hh)) → new_ltEs1(vyy3000, vyy400, hh)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
- new_ltEs(@2(vyy3000, vyy3001), @2(vyy400, vyy401), h, app(ty_Maybe, bf)) → new_ltEs2(vyy3001, vyy401, bf)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
- new_ltEs3(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), bae, baf, app(ty_Maybe, bbd)) → new_ltEs2(vyy3002, vyy402, bbd)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3
- new_ltEs2(Just(vyy3000), Just(vyy400), app(app(ty_Either, hf), hg)) → new_ltEs0(vyy3000, vyy400, hf, hg)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
- new_compare20(vyy3000, vyy400, False, ce, cf) → new_ltEs0(vyy3000, vyy400, ce, cf)
The graph contains the following edges 1 >= 1, 2 >= 2, 4 >= 3, 5 >= 4
- new_ltEs2(Just(vyy3000), Just(vyy400), app(app(ty_@2, hd), he)) → new_ltEs(vyy3000, vyy400, hd, he)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
- new_compare2(vyy3000, vyy400, False, cb, cc) → new_ltEs(vyy3000, vyy400, cb, cc)
The graph contains the following edges 1 >= 1, 2 >= 2, 4 >= 3, 5 >= 4
- new_ltEs2(Just(vyy3000), Just(vyy400), app(ty_Maybe, baa)) → new_ltEs2(vyy3000, vyy400, baa)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
- new_compare21(vyy3000, vyy400, False, da) → new_ltEs2(vyy3000, vyy400, da)
The graph contains the following edges 1 >= 1, 2 >= 2, 4 >= 3
- new_ltEs2(Just(vyy3000), Just(vyy400), app(app(app(ty_@3, bab), bac), bad)) → new_ltEs3(vyy3000, vyy400, bab, bac, bad)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
- new_ltEs(@2(vyy3000, vyy3001), @2(vyy400, vyy401), h, app(app(app(ty_@3, bg), bh), ca)) → new_ltEs3(vyy3001, vyy401, bg, bh, ca)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5
- new_lt(vyy3000, vyy400, cb, cc) → new_compare2(vyy3000, vyy400, new_esEs5(vyy3000, vyy400, cb, cc), cb, cc)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 4, 4 >= 5
- new_compare1(vyy3000, vyy400, cb, cc) → new_compare2(vyy3000, vyy400, new_esEs5(vyy3000, vyy400, cb, cc), cb, cc)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 4, 4 >= 5
- new_ltEs3(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), bae, baf, app(app(app(ty_@3, bbe), bbf), bbg)) → new_ltEs3(vyy3002, vyy402, bbe, bbf, bbg)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4, 5 > 5
- new_compare22(vyy3000, vyy400, False, db, dc, dd) → new_ltEs3(vyy3000, vyy400, db, dc, dd)
The graph contains the following edges 1 >= 1, 2 >= 2, 4 >= 3, 5 >= 4, 6 >= 5
- new_primCompAux(vyy3000, vyy400, vyy78, app(app(ty_@2, gc), gd)) → new_compare1(vyy3000, vyy400, gc, gd)
The graph contains the following edges 1 >= 1, 2 >= 2, 4 > 3, 4 > 4
- new_ltEs(@2(vyy3000, vyy3001), @2(vyy400, vyy401), app(app(app(ty_@3, db), dc), dd), cd) → new_compare22(vyy3000, vyy400, new_esEs8(vyy3000, vyy400, db, dc, dd), db, dc, dd)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 4, 3 > 5, 3 > 6
- new_primCompAux(vyy3000, vyy400, vyy78, app(app(app(ty_@3, ha), hb), hc)) → new_compare5(vyy3000, vyy400, ha, hb, hc)
The graph contains the following edges 1 >= 1, 2 >= 2, 4 > 3, 4 > 4, 4 > 5
- new_compare(:(vyy3000, vyy3001), :(vyy400, vyy401), gb) → new_primCompAux(vyy3000, vyy400, new_compare0(vyy3001, vyy401, gb), gb)
The graph contains the following edges 1 > 1, 2 > 2, 3 >= 4
- new_compare(:(vyy3000, vyy3001), :(vyy400, vyy401), gb) → new_compare(vyy3001, vyy401, gb)
The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3
- new_ltEs1(:(vyy3000, vyy3001), :(vyy400, vyy401), gb) → new_primCompAux(vyy3000, vyy400, new_compare0(vyy3001, vyy401, gb), gb)
The graph contains the following edges 1 > 1, 2 > 2, 3 >= 4
- new_ltEs1(:(vyy3000, vyy3001), :(vyy400, vyy401), gb) → new_compare(vyy3001, vyy401, gb)
The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3
- new_lt2(vyy3000, vyy400, da) → new_compare21(vyy3000, vyy400, new_esEs7(vyy3000, vyy400, da), da)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 4
- new_primCompAux(vyy3000, vyy400, vyy78, app(app(ty_Either, ge), gf)) → new_compare3(vyy3000, vyy400, ge, gf)
The graph contains the following edges 1 >= 1, 2 >= 2, 4 > 3, 4 > 4
- new_ltEs(@2(vyy3000, vyy3001), @2(vyy400, vyy401), app(app(ty_Either, ce), cf), cd) → new_compare20(vyy3000, vyy400, new_esEs6(vyy3000, vyy400, ce, cf), ce, cf)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 4, 3 > 5
- new_lt1(vyy3000, vyy400, cg) → new_compare(vyy3000, vyy400, cg)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3
- new_compare5(vyy3000, vyy400, db, dc, dd) → new_compare22(vyy3000, vyy400, new_esEs8(vyy3000, vyy400, db, dc, dd), db, dc, dd)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 4, 4 >= 5, 5 >= 6
- new_lt3(vyy3000, vyy400, db, dc, dd) → new_compare22(vyy3000, vyy400, new_esEs8(vyy3000, vyy400, db, dc, dd), db, dc, dd)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 4, 4 >= 5, 5 >= 6
- new_ltEs(@2(vyy3000, vyy3001), @2(vyy400, vyy401), app(ty_[], cg), cd) → new_compare(vyy3000, vyy400, cg)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
- new_ltEs(@2(vyy3000, vyy3001), @2(vyy400, vyy401), app(ty_Maybe, da), cd) → new_compare21(vyy3000, vyy400, new_esEs7(vyy3000, vyy400, da), da)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 4
- new_primCompAux(vyy3000, vyy400, vyy78, app(ty_[], gg)) → new_compare(vyy3000, vyy400, gg)
The graph contains the following edges 1 >= 1, 2 >= 2, 4 > 3
- new_compare4(vyy3000, vyy400, da) → new_compare21(vyy3000, vyy400, new_esEs7(vyy3000, vyy400, da), da)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 4
- new_primCompAux(vyy3000, vyy400, vyy78, app(ty_Maybe, gh)) → new_compare4(vyy3000, vyy400, gh)
The graph contains the following edges 1 >= 1, 2 >= 2, 4 > 3
- new_compare3(vyy3000, vyy400, ce, cf) → new_compare20(vyy3000, vyy400, new_esEs6(vyy3000, vyy400, ce, cf), ce, cf)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 4, 4 >= 5
- new_lt0(vyy3000, vyy400, ce, cf) → new_compare20(vyy3000, vyy400, new_esEs6(vyy3000, vyy400, ce, cf), ce, cf)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 4, 4 >= 5
- new_ltEs0(Left(vyy3000), Left(vyy400), app(ty_[], eb), dg) → new_ltEs1(vyy3000, vyy400, eb)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
- new_ltEs0(Right(vyy3000), Right(vyy400), eg, app(ty_[], fd)) → new_ltEs1(vyy3000, vyy400, fd)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
- new_ltEs3(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), app(ty_Maybe, bdg), baf, bcb) → new_lt2(vyy3000, vyy400, bdg)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
- new_ltEs3(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), bae, app(ty_Maybe, bcf), bcb) → new_lt2(vyy3001, vyy401, bcf)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
- new_ltEs3(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), app(app(app(ty_@3, bdh), bea), beb), baf, bcb) → new_lt3(vyy3000, vyy400, bdh, bea, beb)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
- new_ltEs3(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), bae, app(app(app(ty_@3, bcg), bch), bda), bcb) → new_lt3(vyy3001, vyy401, bcg, bch, bda)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5
- new_ltEs3(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), app(ty_[], bdf), baf, bcb) → new_lt1(vyy3000, vyy400, bdf)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
- new_ltEs3(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), bae, app(ty_[], bce), bcb) → new_lt1(vyy3001, vyy401, bce)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
- new_ltEs3(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), bae, app(app(ty_Either, bcc), bcd), bcb) → new_lt0(vyy3001, vyy401, bcc, bcd)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
- new_ltEs3(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), app(app(ty_Either, bdd), bde), baf, bcb) → new_lt0(vyy3000, vyy400, bdd, bde)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
- new_ltEs3(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), app(app(ty_@2, bdb), bdc), baf, bcb) → new_lt(vyy3000, vyy400, bdb, bdc)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
- new_ltEs3(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), bae, app(app(ty_@2, bbh), bca), bcb) → new_lt(vyy3001, vyy401, bbh, bca)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
- new_ltEs0(Left(vyy3000), Left(vyy400), app(app(ty_Either, dh), ea), dg) → new_ltEs0(vyy3000, vyy400, dh, ea)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
- new_ltEs0(Right(vyy3000), Right(vyy400), eg, app(app(ty_Either, fb), fc)) → new_ltEs0(vyy3000, vyy400, fb, fc)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
- new_ltEs0(Right(vyy3000), Right(vyy400), eg, app(app(ty_@2, eh), fa)) → new_ltEs(vyy3000, vyy400, eh, fa)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
- new_ltEs0(Left(vyy3000), Left(vyy400), app(app(ty_@2, de), df), dg) → new_ltEs(vyy3000, vyy400, de, df)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
- new_ltEs0(Right(vyy3000), Right(vyy400), eg, app(ty_Maybe, ff)) → new_ltEs2(vyy3000, vyy400, ff)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
- new_ltEs0(Left(vyy3000), Left(vyy400), app(ty_Maybe, ec), dg) → new_ltEs2(vyy3000, vyy400, ec)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
- new_ltEs0(Right(vyy3000), Right(vyy400), eg, app(app(app(ty_@3, fg), fh), ga)) → new_ltEs3(vyy3000, vyy400, fg, fh, ga)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5
- new_ltEs0(Left(vyy3000), Left(vyy400), app(app(app(ty_@3, ed), ee), ef), dg) → new_ltEs3(vyy3000, vyy400, ed, ee, ef)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 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
↳ QDPSizeChangeProof
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_foldFM_LE1(vyy51, vyy40, vyy340, vyy341, vyy342, vyy343, Branch(vyy3440, vyy3441, vyy3442, vyy3443, vyy3444), True, h, ba, bb) → new_foldFM_LE2(vyy340, vyy341, new_foldFM_LE0(vyy51, vyy40, vyy343, h, ba, bb), vyy40, vyy3440, vyy3441, vyy3442, vyy3443, vyy3444, h, ba, bb)
new_foldFM_LE2(vyy340, vyy341, vyy67, vyy40, vyy3440, vyy3441, vyy3442, vyy3443, vyy3444, h, ba, bb) → new_foldFM_LE1(new_fmToList_LE0(vyy340, vyy341, vyy67, h, ba, bb), vyy40, vyy3440, vyy3441, vyy3442, vyy3443, vyy3444, new_ltEs13(vyy3440, Right(vyy40), h, ba), h, ba, bb)
new_foldFM_LE1(vyy51, vyy40, vyy340, vyy341, vyy342, vyy343, Branch(vyy3440, vyy3441, vyy3442, vyy3443, vyy3444), True, h, ba, bb) → new_foldFM_LE(vyy51, vyy40, vyy343, h, ba, bb)
new_foldFM_LE1(vyy51, vyy40, vyy340, vyy341, vyy342, Branch(vyy3430, vyy3431, vyy3432, vyy3433, vyy3434), vyy344, False, h, ba, bb) → new_foldFM_LE1(vyy51, vyy40, vyy3430, vyy3431, vyy3432, vyy3433, vyy3434, new_ltEs13(vyy3430, Right(vyy40), h, ba), h, ba, bb)
new_foldFM_LE1(vyy51, vyy40, vyy340, vyy341, vyy342, vyy343, EmptyFM, True, h, ba, bb) → new_foldFM_LE(vyy51, vyy40, vyy343, h, ba, bb)
new_foldFM_LE(vyy51, vyy40, Branch(vyy3430, vyy3431, vyy3432, vyy3433, vyy3434), h, ba, bb) → new_foldFM_LE1(vyy51, vyy40, vyy3430, vyy3431, vyy3432, vyy3433, vyy3434, new_ltEs13(vyy3430, Right(vyy40), h, ba), h, ba, bb)
The TRS R consists of the following rules:
new_esEs23(GT, LT) → False
new_esEs23(LT, GT) → False
new_esEs7(Just(vyy580), Just(vyy590), app(ty_Maybe, bce)) → new_esEs7(vyy580, vyy590, bce)
new_ltEs19(vyy3001, vyy401, ty_Integer) → new_ltEs16(vyy3001, vyy401)
new_esEs28(vyy581, vyy591, app(ty_[], dce)) → new_esEs19(vyy581, vyy591, dce)
new_lt16(vyy3000, vyy400) → new_esEs9(new_compare26(vyy3000, vyy400))
new_compare16(vyy3000, vyy400) → new_compare211(vyy3000, vyy400, new_esEs21(vyy3000, vyy400))
new_ltEs4(EQ, GT) → True
new_esEs26(vyy580, vyy590, app(app(ty_FiniteMap, bhg), bhh)) → new_esEs17(vyy580, vyy590, bhg, bhh)
new_lt5(vyy3001, vyy401, ty_Char) → new_lt19(vyy3001, vyy401)
new_esEs29(vyy580, vyy590, app(app(app(ty_@3, deb), dec), ded)) → new_esEs8(vyy580, vyy590, deb, dec, ded)
new_esEs27(vyy582, vyy592, ty_Char) → new_esEs22(vyy582, vyy592)
new_ltEs8(vyy3002, vyy402, ty_Int) → new_ltEs9(vyy3002, vyy402)
new_esEs29(vyy580, vyy590, app(ty_[], dea)) → new_esEs19(vyy580, vyy590, dea)
new_compare14(vyy3000, vyy400, ty_Bool) → new_compare16(vyy3000, vyy400)
new_esEs16(vyy58, vyy59, ty_Char) → new_esEs22(vyy58, vyy59)
new_esEs11(Integer(vyy580), Integer(vyy590)) → new_primEqInt(vyy580, vyy590)
new_esEs27(vyy582, vyy592, app(ty_Maybe, dbe)) → new_esEs7(vyy582, vyy592, dbe)
new_esEs28(vyy581, vyy591, ty_Integer) → new_esEs11(vyy581, vyy591)
new_esEs26(vyy580, vyy590, ty_Integer) → new_esEs11(vyy580, vyy590)
new_fmToList_LE0(vyy340, vyy341, vyy66, h, ba, bb) → :(@2(vyy340, vyy341), vyy66)
new_esEs16(vyy58, vyy59, app(ty_Ratio, bh)) → new_esEs12(vyy58, vyy59, bh)
new_esEs24(vyy580, vyy590, app(app(ty_FiniteMap, bed), bee)) → new_esEs17(vyy580, vyy590, bed, bee)
new_ltEs6(True, False) → False
new_ltEs13(Right(vyy3000), Right(vyy400), chc, app(app(app(ty_@3, dac), dad), dae)) → new_ltEs7(vyy3000, vyy400, dac, dad, dae)
new_esEs7(Just(vyy580), Just(vyy590), app(app(ty_Either, bcf), bcg)) → new_esEs6(vyy580, vyy590, bcf, bcg)
new_primMulNat0(Zero, Zero) → Zero
new_ltEs13(Left(vyy3000), Left(vyy400), app(app(ty_@2, cga), cgb), cfh) → new_ltEs10(vyy3000, vyy400, cga, cgb)
new_esEs25(vyy581, vyy591, app(app(ty_Either, bhc), bhd)) → new_esEs6(vyy581, vyy591, bhc, bhd)
new_lt6(vyy3000, vyy400, app(ty_Ratio, ga)) → new_lt15(vyy3000, vyy400, ga)
new_esEs29(vyy580, vyy590, ty_Char) → new_esEs22(vyy580, vyy590)
new_lt20(vyy3000, vyy400, app(app(ty_@2, bc), bd)) → new_lt8(vyy3000, vyy400, bc, bd)
new_esEs9(LT) → True
new_lt20(vyy3000, vyy400, app(app(app(ty_@3, be), bf), bg)) → new_lt4(vyy3000, vyy400, be, bf, bg)
new_esEs29(vyy580, vyy590, ty_@0) → new_esEs20(vyy580, vyy590)
new_lt19(vyy3000, vyy400) → new_esEs9(new_compare28(vyy3000, vyy400))
new_not(GT) → False
new_esEs26(vyy580, vyy590, app(ty_[], cab)) → new_esEs19(vyy580, vyy590, cab)
new_lt5(vyy3001, vyy401, ty_Ordering) → new_lt13(vyy3001, vyy401)
new_esEs6(Left(vyy580), Left(vyy590), app(app(app(ty_@3, cdd), cde), cdf), hf) → new_esEs8(vyy580, vyy590, cdd, cde, cdf)
new_esEs29(vyy580, vyy590, app(ty_Maybe, dee)) → new_esEs7(vyy580, vyy590, dee)
new_lt20(vyy3000, vyy400, ty_Double) → new_lt14(vyy3000, vyy400)
new_esEs16(vyy58, vyy59, ty_Ordering) → new_esEs23(vyy58, vyy59)
new_lt5(vyy3001, vyy401, app(ty_Ratio, ef)) → new_lt15(vyy3001, vyy401, ef)
new_esEs16(vyy58, vyy59, ty_Integer) → new_esEs11(vyy58, vyy59)
new_esEs16(vyy58, vyy59, app(app(ty_Either, he), hf)) → new_esEs6(vyy58, vyy59, he, hf)
new_lt6(vyy3000, vyy400, app(app(ty_@2, fd), ff)) → new_lt8(vyy3000, vyy400, fd, ff)
new_compare0(:(vyy3000, vyy3001), :(vyy400, vyy401), ca) → new_primCompAux0(vyy3000, vyy400, new_compare0(vyy3001, vyy401, ca), ca)
new_ltEs17(Just(vyy3000), Just(vyy400), app(ty_Ratio, bah)) → new_ltEs15(vyy3000, vyy400, bah)
new_compare18(Double(vyy3000, vyy3001), Double(vyy400, vyy401)) → new_compare9(new_sr(vyy3000, vyy400), new_sr(vyy3001, vyy401))
new_ltEs13(Right(vyy3000), Right(vyy400), chc, app(ty_Maybe, dab)) → new_ltEs17(vyy3000, vyy400, dab)
new_esEs24(vyy580, vyy590, app(app(ty_@2, bff), bfg)) → new_esEs5(vyy580, vyy590, bff, bfg)
new_lt20(vyy3000, vyy400, ty_Integer) → new_lt16(vyy3000, vyy400)
new_esEs26(vyy580, vyy590, ty_Float) → new_esEs18(vyy580, vyy590)
new_esEs25(vyy581, vyy591, ty_Double) → new_esEs15(vyy581, vyy591)
new_esEs26(vyy580, vyy590, app(app(app(ty_@3, cac), cad), cae)) → new_esEs8(vyy580, vyy590, cac, cad, cae)
new_lt6(vyy3000, vyy400, ty_Char) → new_lt19(vyy3000, vyy400)
new_esEs25(vyy581, vyy591, ty_Bool) → new_esEs21(vyy581, vyy591)
new_esEs29(vyy580, vyy590, ty_Float) → new_esEs18(vyy580, vyy590)
new_esEs28(vyy581, vyy591, ty_Bool) → new_esEs21(vyy581, vyy591)
new_ltEs13(Right(vyy3000), Right(vyy400), chc, app(ty_Ratio, chh)) → new_ltEs15(vyy3000, vyy400, chh)
new_foldFM0(vyy590, vyy591, vyy96, EmptyFM, cb, cc) → :(@2(vyy590, vyy591), vyy96)
new_esEs16(vyy58, vyy59, ty_Float) → new_esEs18(vyy58, vyy59)
new_ltEs19(vyy3001, vyy401, ty_Char) → new_ltEs18(vyy3001, vyy401)
new_esEs28(vyy581, vyy591, app(app(app(ty_@3, dcf), dcg), dch)) → new_esEs8(vyy581, vyy591, dcf, dcg, dch)
new_esEs7(Just(vyy580), Just(vyy590), ty_Int) → new_esEs10(vyy580, vyy590)
new_ltEs14(vyy300, vyy40) → new_not(new_compare18(vyy300, vyy40))
new_esEs20(@0, @0) → True
new_esEs5(@2(vyy580, vyy581), @2(vyy590, vyy591), hg, hh) → new_asAs(new_esEs26(vyy580, vyy590, hg), new_esEs25(vyy581, vyy591, hh))
new_esEs22(Char(vyy580), Char(vyy590)) → new_primEqNat0(vyy580, vyy590)
new_ltEs13(Left(vyy3000), Left(vyy400), app(ty_[], cgf), cfh) → new_ltEs5(vyy3000, vyy400, cgf)
new_esEs28(vyy581, vyy591, ty_Float) → new_esEs18(vyy581, vyy591)
new_lt20(vyy3000, vyy400, ty_Float) → new_lt10(vyy3000, vyy400)
new_compare14(vyy3000, vyy400, ty_Int) → new_compare9(vyy3000, vyy400)
new_ltEs17(Just(vyy3000), Nothing, bac) → False
new_lt6(vyy3000, vyy400, ty_Ordering) → new_lt13(vyy3000, vyy400)
new_esEs24(vyy580, vyy590, app(ty_Maybe, bfc)) → new_esEs7(vyy580, vyy590, bfc)
new_foldFM_LE10(vyy51, vyy40, vyy340, vyy341, vyy342, vyy343, Branch(vyy3440, vyy3441, vyy3442, vyy3443, vyy3444), True, h, ba, bb) → new_foldFM_LE20(vyy340, vyy341, new_foldFM_LE0(vyy51, vyy40, vyy343, h, ba, bb), vyy40, vyy3440, vyy3441, vyy3442, vyy3443, vyy3444, h, ba, bb)
new_lt4(vyy3000, vyy400, be, bf, bg) → new_esEs9(new_compare7(vyy3000, vyy400, be, bf, bg))
new_lt6(vyy3000, vyy400, ty_Integer) → new_lt16(vyy3000, vyy400)
new_esEs6(Right(vyy580), Right(vyy590), he, app(app(ty_FiniteMap, ced), cee)) → new_esEs17(vyy580, vyy590, ced, cee)
new_ltEs17(Just(vyy3000), Just(vyy400), app(ty_[], bba)) → new_ltEs5(vyy3000, vyy400, bba)
new_compare9(vyy300, vyy40) → new_primCmpInt(vyy300, vyy40)
new_esEs28(vyy581, vyy591, ty_@0) → new_esEs20(vyy581, vyy591)
new_ltEs8(vyy3002, vyy402, app(app(ty_@2, cg), da)) → new_ltEs10(vyy3002, vyy402, cg, da)
new_compare15(@0, @0) → EQ
new_ltEs13(Left(vyy3000), Left(vyy400), ty_Int, cfh) → new_ltEs9(vyy3000, vyy400)
new_primCompAux0(vyy3000, vyy400, vyy78, ca) → new_primCompAux00(vyy78, new_compare14(vyy3000, vyy400, ca))
new_compare13(vyy3000, vyy400, False, baa, bab) → GT
new_esEs24(vyy580, vyy590, app(ty_[], beg)) → new_esEs19(vyy580, vyy590, beg)
new_lt6(vyy3000, vyy400, ty_@0) → new_lt9(vyy3000, vyy400)
new_ltEs15(vyy300, vyy40, bfh) → new_not(new_compare19(vyy300, vyy40, bfh))
new_esEs6(Right(vyy580), Right(vyy590), he, app(app(app(ty_@3, ceh), cfa), cfb)) → new_esEs8(vyy580, vyy590, ceh, cfa, cfb)
new_primCmpNat0(Zero, Succ(vyy4000)) → LT
new_ltEs19(vyy3001, vyy401, app(ty_Ratio, cca)) → new_ltEs15(vyy3001, vyy401, cca)
new_esEs6(Left(vyy580), Left(vyy590), ty_Integer, hf) → new_esEs11(vyy580, vyy590)
new_ltEs8(vyy3002, vyy402, ty_Double) → new_ltEs14(vyy3002, vyy402)
new_compare6(vyy3000, vyy400, bc, bd) → new_compare23(vyy3000, vyy400, new_esEs5(vyy3000, vyy400, bc, bd), bc, bd)
new_ltEs19(vyy3001, vyy401, ty_Bool) → new_ltEs6(vyy3001, vyy401)
new_esEs13(vyy581, vyy591, ty_Integer) → new_esEs11(vyy581, vyy591)
new_esEs6(Right(vyy580), Left(vyy590), he, hf) → False
new_esEs6(Left(vyy580), Right(vyy590), he, hf) → False
new_compare7(vyy3000, vyy400, be, bf, bg) → new_compare29(vyy3000, vyy400, new_esEs8(vyy3000, vyy400, be, bf, bg), be, bf, bg)
new_lt20(vyy3000, vyy400, ty_Char) → new_lt19(vyy3000, vyy400)
new_compare14(vyy3000, vyy400, app(ty_[], bdg)) → new_compare0(vyy3000, vyy400, bdg)
new_lt17(vyy3000, vyy400, bgb) → new_esEs9(new_compare0(vyy3000, vyy400, bgb))
new_esEs28(vyy581, vyy591, ty_Double) → new_esEs15(vyy581, vyy591)
new_esEs6(Right(vyy580), Right(vyy590), he, ty_Bool) → new_esEs21(vyy580, vyy590)
new_ltEs17(Just(vyy3000), Just(vyy400), app(app(ty_@2, bad), bae)) → new_ltEs10(vyy3000, vyy400, bad, bae)
new_esEs21(True, True) → True
new_esEs15(Double(vyy580, vyy581), Double(vyy590, vyy591)) → new_esEs10(new_sr(vyy580, vyy590), new_sr(vyy581, vyy591))
new_compare0([], [], ca) → EQ
new_esEs16(vyy58, vyy59, ty_Bool) → new_esEs21(vyy58, vyy59)
new_primEqNat0(Zero, Zero) → True
new_esEs8(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), ha, hb, hc) → new_asAs(new_esEs29(vyy580, vyy590, ha), new_asAs(new_esEs28(vyy581, vyy591, hb), new_esEs27(vyy582, vyy592, hc)))
new_esEs28(vyy581, vyy591, ty_Ordering) → new_esEs23(vyy581, vyy591)
new_ltEs13(Right(vyy3000), Right(vyy400), chc, ty_Double) → new_ltEs14(vyy3000, vyy400)
new_esEs6(Left(vyy580), Left(vyy590), app(ty_[], cdc), hf) → new_esEs19(vyy580, vyy590, cdc)
new_esEs14(vyy580, vyy590, ty_Int) → new_esEs10(vyy580, vyy590)
new_esEs6(Left(vyy580), Left(vyy590), ty_@0, hf) → new_esEs20(vyy580, vyy590)
new_compare19(:%(vyy3000, vyy3001), :%(vyy400, vyy401), ty_Integer) → new_compare26(new_sr0(vyy3000, vyy401), new_sr0(vyy400, vyy3001))
new_compare29(vyy3000, vyy400, False, be, bf, bg) → new_compare110(vyy3000, vyy400, new_ltEs7(vyy3000, vyy400, be, bf, bg), be, bf, bg)
new_esEs6(Right(vyy580), Right(vyy590), he, app(app(ty_Either, cfd), cfe)) → new_esEs6(vyy580, vyy590, cfd, cfe)
new_esEs6(Left(vyy580), Left(vyy590), ty_Double, hf) → new_esEs15(vyy580, vyy590)
new_ltEs7(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), cd, ce, cf) → new_pePe(new_lt6(vyy3000, vyy400, cd), vyy3000, vyy400, new_pePe(new_lt5(vyy3001, vyy401, ce), vyy3001, vyy401, new_ltEs8(vyy3002, vyy402, cf), ce), cd)
new_esEs19([], [], gh) → True
new_esEs25(vyy581, vyy591, app(ty_[], bgf)) → new_esEs19(vyy581, vyy591, bgf)
new_esEs12(:%(vyy580, vyy581), :%(vyy590, vyy591), bh) → new_asAs(new_esEs14(vyy580, vyy590, bh), new_esEs13(vyy581, vyy591, bh))
new_sr(vyy3001, vyy401) → new_primMulInt(vyy3001, vyy401)
new_esEs16(vyy58, vyy59, ty_@0) → new_esEs20(vyy58, vyy59)
new_esEs28(vyy581, vyy591, app(app(ty_Either, ddb), ddc)) → new_esEs6(vyy581, vyy591, ddb, ddc)
new_ltEs8(vyy3002, vyy402, ty_@0) → new_ltEs11(vyy3002, vyy402)
new_ltEs18(vyy300, vyy40) → new_not(new_compare28(vyy300, vyy40))
new_esEs6(Right(vyy580), Right(vyy590), he, ty_Double) → new_esEs15(vyy580, vyy590)
new_ltEs13(Right(vyy3000), Right(vyy400), chc, ty_Float) → new_ltEs12(vyy3000, vyy400)
new_esEs27(vyy582, vyy592, ty_@0) → new_esEs20(vyy582, vyy592)
new_primPlusNat0(Succ(vyy970), vyy40100) → Succ(Succ(new_primPlusNat1(vyy970, vyy40100)))
new_esEs7(Just(vyy580), Just(vyy590), ty_Char) → new_esEs22(vyy580, vyy590)
new_esEs27(vyy582, vyy592, app(app(ty_FiniteMap, daf), dag)) → new_esEs17(vyy582, vyy592, daf, dag)
new_esEs6(Right(vyy580), Right(vyy590), he, ty_Float) → new_esEs18(vyy580, vyy590)
new_lt6(vyy3000, vyy400, app(app(ty_Either, fg), fh)) → new_lt11(vyy3000, vyy400, fg, fh)
new_esEs19(:(vyy580, vyy581), [], gh) → False
new_esEs19([], :(vyy590, vyy591), gh) → False
new_ltEs8(vyy3002, vyy402, app(app(app(ty_@3, dg), dh), ea)) → new_ltEs7(vyy3002, vyy402, dg, dh, ea)
new_compare29(vyy3000, vyy400, True, be, bf, bg) → EQ
new_ltEs8(vyy3002, vyy402, ty_Ordering) → new_ltEs4(vyy3002, vyy402)
new_esEs26(vyy580, vyy590, ty_Ordering) → new_esEs23(vyy580, vyy590)
new_primEqInt(Neg(Succ(vyy5800)), Neg(Succ(vyy5900))) → new_primEqNat0(vyy5800, vyy5900)
new_ltEs19(vyy3001, vyy401, app(app(ty_@2, cbe), cbf)) → new_ltEs10(vyy3001, vyy401, cbe, cbf)
new_foldFM_LE10(vyy51, vyy40, vyy340, vyy341, vyy342, vyy343, EmptyFM, True, h, ba, bb) → new_foldFM_LE3(vyy340, vyy341, new_foldFM_LE0(vyy51, vyy40, vyy343, h, ba, bb), vyy40, h, ba, bb)
new_compare13(vyy3000, vyy400, True, baa, bab) → LT
new_esEs9(GT) → False
new_ltEs17(Just(vyy3000), Just(vyy400), app(app(app(ty_@3, bbc), bbd), bbe)) → new_ltEs7(vyy3000, vyy400, bbc, bbd, bbe)
new_primPlusNat1(Zero, Succ(vyy401000)) → Succ(vyy401000)
new_primPlusNat1(Succ(vyy9700), Zero) → Succ(vyy9700)
new_lt5(vyy3001, vyy401, ty_Int) → new_lt7(vyy3001, vyy401)
new_esEs9(EQ) → False
new_esEs16(vyy58, vyy59, app(app(ty_FiniteMap, cb), cc)) → new_esEs17(vyy58, vyy59, cb, cc)
new_esEs7(Just(vyy580), Just(vyy590), ty_@0) → new_esEs20(vyy580, vyy590)
new_ltEs13(Right(vyy3000), Right(vyy400), chc, ty_Int) → new_ltEs9(vyy3000, vyy400)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_lt20(vyy3000, vyy400, app(ty_Maybe, bga)) → new_lt18(vyy3000, vyy400, bga)
new_esEs23(EQ, EQ) → True
new_ltEs19(vyy3001, vyy401, ty_Ordering) → new_ltEs4(vyy3001, vyy401)
new_ltEs8(vyy3002, vyy402, ty_Bool) → new_ltEs6(vyy3002, vyy402)
new_esEs6(Right(vyy580), Right(vyy590), he, app(ty_[], ceg)) → new_esEs19(vyy580, vyy590, ceg)
new_lt11(vyy3000, vyy400, baa, bab) → new_esEs9(new_compare12(vyy3000, vyy400, baa, bab))
new_primEqInt(Neg(Zero), Neg(Succ(vyy5900))) → False
new_primEqInt(Neg(Succ(vyy5800)), Neg(Zero)) → False
new_compare14(vyy3000, vyy400, app(app(app(ty_@3, bea), beb), bec)) → new_compare7(vyy3000, vyy400, bea, beb, bec)
new_esEs16(vyy58, vyy59, app(app(app(ty_@3, ha), hb), hc)) → new_esEs8(vyy58, vyy59, ha, hb, hc)
new_esEs6(Left(vyy580), Left(vyy590), ty_Char, hf) → new_esEs22(vyy580, vyy590)
new_lt5(vyy3001, vyy401, ty_@0) → new_lt9(vyy3001, vyy401)
new_compare111(vyy3000, vyy400, True, bga) → LT
new_lt5(vyy3001, vyy401, app(ty_[], eg)) → new_lt17(vyy3001, vyy401, eg)
new_lt20(vyy3000, vyy400, ty_Ordering) → new_lt13(vyy3000, vyy400)
new_esEs7(Just(vyy580), Just(vyy590), ty_Bool) → new_esEs21(vyy580, vyy590)
new_esEs24(vyy580, vyy590, ty_Ordering) → new_esEs23(vyy580, vyy590)
new_foldFM0(vyy590, vyy591, vyy96, Branch(vyy5930, vyy5931, vyy5932, vyy5933, vyy5934), cb, cc) → new_foldFM0(vyy5930, vyy5931, new_foldFM0(vyy590, vyy591, vyy96, vyy5934, cb, cc), vyy5933, cb, cc)
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_esEs25(vyy581, vyy591, ty_Ordering) → new_esEs23(vyy581, vyy591)
new_ltEs4(EQ, LT) → False
new_lt10(vyy3000, vyy400) → new_esEs9(new_compare8(vyy3000, vyy400))
new_esEs7(Just(vyy580), Just(vyy590), ty_Integer) → new_esEs11(vyy580, vyy590)
new_primCmpNat0(Succ(vyy30000), Succ(vyy4000)) → new_primCmpNat0(vyy30000, vyy4000)
new_ltEs19(vyy3001, vyy401, ty_@0) → new_ltEs11(vyy3001, vyy401)
new_esEs7(Just(vyy580), Just(vyy590), app(app(ty_FiniteMap, bbf), bbg)) → new_esEs17(vyy580, vyy590, bbf, bbg)
new_esEs7(Just(vyy580), Just(vyy590), ty_Ordering) → new_esEs23(vyy580, vyy590)
new_sizeFM(EmptyFM, cb, cc) → Pos(Zero)
new_compare112(vyy3000, vyy400, True) → LT
new_ltEs8(vyy3002, vyy402, app(ty_Ratio, dd)) → new_ltEs15(vyy3002, vyy402, dd)
new_primEqInt(Pos(Succ(vyy5800)), Pos(Succ(vyy5900))) → new_primEqNat0(vyy5800, vyy5900)
new_ltEs19(vyy3001, vyy401, app(app(app(ty_@3, ccd), cce), ccf)) → new_ltEs7(vyy3001, vyy401, ccd, cce, ccf)
new_esEs16(vyy58, vyy59, ty_Int) → new_esEs10(vyy58, vyy59)
new_ltEs17(Just(vyy3000), Just(vyy400), ty_@0) → new_ltEs11(vyy3000, vyy400)
new_lt20(vyy3000, vyy400, ty_Int) → new_lt7(vyy3000, vyy400)
new_ltEs6(False, True) → True
new_primEqNat0(Succ(vyy5800), Succ(vyy5900)) → new_primEqNat0(vyy5800, vyy5900)
new_ltEs6(True, True) → True
new_esEs27(vyy582, vyy592, app(app(app(ty_@3, dbb), dbc), dbd)) → new_esEs8(vyy582, vyy592, dbb, dbc, dbd)
new_foldFM_LE0(vyy51, vyy40, EmptyFM, h, ba, bb) → vyy51
new_ltEs19(vyy3001, vyy401, app(app(ty_Either, cbg), cbh)) → new_ltEs13(vyy3001, vyy401, cbg, cbh)
new_lt5(vyy3001, vyy401, ty_Bool) → new_lt12(vyy3001, vyy401)
new_esEs6(Right(vyy580), Right(vyy590), he, app(app(ty_@2, cff), cfg)) → new_esEs5(vyy580, vyy590, cff, cfg)
new_ltEs19(vyy3001, vyy401, ty_Double) → new_ltEs14(vyy3001, vyy401)
new_esEs29(vyy580, vyy590, ty_Int) → new_esEs10(vyy580, vyy590)
new_ltEs4(GT, EQ) → False
new_primCompAux00(vyy82, LT) → LT
new_esEs24(vyy580, vyy590, app(ty_Ratio, bef)) → new_esEs12(vyy580, vyy590, bef)
new_primCmpInt(Neg(Succ(vyy30000)), Neg(vyy400)) → new_primCmpNat0(vyy400, Succ(vyy30000))
new_esEs7(Nothing, Nothing, hd) → True
new_esEs23(GT, GT) → True
new_primEqInt(Pos(Zero), Pos(Succ(vyy5900))) → False
new_primEqInt(Pos(Succ(vyy5800)), Pos(Zero)) → False
new_compare24(vyy3000, vyy400, False) → new_compare10(vyy3000, vyy400, new_ltEs4(vyy3000, vyy400))
new_ltEs4(EQ, EQ) → True
new_lt5(vyy3001, vyy401, app(app(ty_Either, ed), ee)) → new_lt11(vyy3001, vyy401, ed, ee)
new_lt7(vyy3000, vyy400) → new_esEs9(new_compare9(vyy3000, vyy400))
new_primCmpNat0(Zero, Zero) → EQ
new_ltEs13(Left(vyy3000), Left(vyy400), app(app(app(ty_@3, cgh), cha), chb), cfh) → new_ltEs7(vyy3000, vyy400, cgh, cha, chb)
new_esEs6(Right(vyy580), Right(vyy590), he, app(ty_Maybe, cfc)) → new_esEs7(vyy580, vyy590, cfc)
new_primCmpNat0(Succ(vyy30000), Zero) → GT
new_esEs14(vyy580, vyy590, ty_Integer) → new_esEs11(vyy580, vyy590)
new_esEs7(Just(vyy580), Just(vyy590), app(app(app(ty_@3, bcb), bcc), bcd)) → new_esEs8(vyy580, vyy590, bcb, bcc, bcd)
new_primCmpInt(Neg(Zero), Pos(Succ(vyy4000))) → LT
new_compare11(vyy3000, vyy400, True, bc, bd) → LT
new_esEs6(Right(vyy580), Right(vyy590), he, ty_@0) → new_esEs20(vyy580, vyy590)
new_ltEs4(GT, LT) → False
new_sr0(Integer(vyy4000), Integer(vyy30010)) → Integer(new_primMulInt(vyy4000, vyy30010))
new_primPlusNat1(Succ(vyy9700), Succ(vyy401000)) → Succ(Succ(new_primPlusNat1(vyy9700, vyy401000)))
new_compare27(vyy3000, vyy400, bga) → new_compare210(vyy3000, vyy400, new_esEs7(vyy3000, vyy400, bga), bga)
new_primEqInt(Neg(Succ(vyy5800)), Pos(vyy590)) → False
new_primEqInt(Pos(Succ(vyy5800)), Neg(vyy590)) → False
new_esEs25(vyy581, vyy591, ty_Int) → new_esEs10(vyy581, vyy591)
new_esEs7(Nothing, Just(vyy590), hd) → False
new_esEs7(Just(vyy580), Nothing, hd) → False
new_compare210(vyy3000, vyy400, True, bga) → EQ
new_esEs26(vyy580, vyy590, ty_Char) → new_esEs22(vyy580, vyy590)
new_foldFM2(EmptyFM, cb, cc) → []
new_ltEs17(Just(vyy3000), Just(vyy400), ty_Integer) → new_ltEs16(vyy3000, vyy400)
new_esEs29(vyy580, vyy590, app(app(ty_@2, deh), dfa)) → new_esEs5(vyy580, vyy590, deh, dfa)
new_ltEs13(Right(vyy3000), Right(vyy400), chc, app(ty_[], daa)) → new_ltEs5(vyy3000, vyy400, daa)
new_ltEs13(Right(vyy3000), Right(vyy400), chc, ty_@0) → new_ltEs11(vyy3000, vyy400)
new_esEs26(vyy580, vyy590, ty_Int) → new_esEs10(vyy580, vyy590)
new_primEqInt(Neg(Zero), Pos(Succ(vyy5900))) → False
new_primEqInt(Pos(Zero), Neg(Succ(vyy5900))) → False
new_esEs29(vyy580, vyy590, ty_Integer) → new_esEs11(vyy580, vyy590)
new_primCmpInt(Pos(Zero), Pos(Succ(vyy4000))) → new_primCmpNat0(Zero, Succ(vyy4000))
new_primCompAux00(vyy82, EQ) → vyy82
new_compare24(vyy3000, vyy400, True) → EQ
new_esEs7(Just(vyy580), Just(vyy590), ty_Float) → new_esEs18(vyy580, vyy590)
new_ltEs13(Left(vyy3000), Left(vyy400), ty_Float, cfh) → new_ltEs12(vyy3000, vyy400)
new_esEs26(vyy580, vyy590, app(app(ty_@2, cba), cbb)) → new_esEs5(vyy580, vyy590, cba, cbb)
new_ltEs17(Just(vyy3000), Just(vyy400), ty_Ordering) → new_ltEs4(vyy3000, vyy400)
new_ltEs8(vyy3002, vyy402, ty_Float) → new_ltEs12(vyy3002, vyy402)
new_ltEs17(Just(vyy3000), Just(vyy400), ty_Int) → new_ltEs9(vyy3000, vyy400)
new_esEs26(vyy580, vyy590, ty_Bool) → new_esEs21(vyy580, vyy590)
new_foldFM_LE0(vyy51, vyy40, Branch(vyy3430, vyy3431, vyy3432, vyy3433, vyy3434), h, ba, bb) → new_foldFM_LE10(vyy51, vyy40, vyy3430, vyy3431, vyy3432, vyy3433, vyy3434, new_ltEs13(vyy3430, Right(vyy40), h, ba), h, ba, bb)
new_esEs6(Left(vyy580), Left(vyy590), app(app(ty_Either, cdh), cea), hf) → new_esEs6(vyy580, vyy590, cdh, cea)
new_esEs6(Left(vyy580), Left(vyy590), app(ty_Ratio, cdb), hf) → new_esEs12(vyy580, vyy590, cdb)
new_primPlusNat0(Zero, vyy40100) → Succ(vyy40100)
new_primCmpInt(Pos(Succ(vyy30000)), Pos(vyy400)) → new_primCmpNat0(Succ(vyy30000), vyy400)
new_lt6(vyy3000, vyy400, app(app(app(ty_@3, gd), ge), gf)) → new_lt4(vyy3000, vyy400, gd, ge, gf)
new_esEs24(vyy580, vyy590, app(app(ty_Either, bfd), bfe)) → new_esEs6(vyy580, vyy590, bfd, bfe)
new_esEs25(vyy581, vyy591, ty_Float) → new_esEs18(vyy581, vyy591)
new_compare14(vyy3000, vyy400, app(ty_Maybe, bdh)) → new_compare27(vyy3000, vyy400, bdh)
new_compare14(vyy3000, vyy400, app(app(ty_@2, bdb), bdc)) → new_compare6(vyy3000, vyy400, bdb, bdc)
new_ltEs13(Left(vyy3000), Left(vyy400), ty_Bool, cfh) → new_ltEs6(vyy3000, vyy400)
new_not0 → True
new_esEs28(vyy581, vyy591, app(app(ty_@2, ddd), dde)) → new_esEs5(vyy581, vyy591, ddd, dde)
new_compare0(:(vyy3000, vyy3001), [], ca) → GT
new_esEs24(vyy580, vyy590, ty_Bool) → new_esEs21(vyy580, vyy590)
new_esEs27(vyy582, vyy592, app(app(ty_Either, dbf), dbg)) → new_esEs6(vyy582, vyy592, dbf, dbg)
new_ltEs13(Left(vyy3000), Left(vyy400), app(ty_Ratio, cge), cfh) → new_ltEs15(vyy3000, vyy400, cge)
new_esEs18(Float(vyy580, vyy581), Float(vyy590, vyy591)) → new_esEs10(new_sr(vyy580, vyy590), new_sr(vyy581, vyy591))
new_esEs28(vyy581, vyy591, app(app(ty_FiniteMap, dcb), dcc)) → new_esEs17(vyy581, vyy591, dcb, dcc)
new_esEs6(Right(vyy580), Right(vyy590), he, app(ty_Ratio, cef)) → new_esEs12(vyy580, vyy590, cef)
new_compare11(vyy3000, vyy400, False, bc, bd) → GT
new_lt15(vyy3000, vyy400, ccg) → new_esEs9(new_compare19(vyy3000, vyy400, ccg))
new_esEs25(vyy581, vyy591, ty_Integer) → new_esEs11(vyy581, vyy591)
new_primCmpInt(Pos(Succ(vyy30000)), Neg(vyy400)) → GT
new_ltEs19(vyy3001, vyy401, ty_Int) → new_ltEs9(vyy3001, vyy401)
new_esEs28(vyy581, vyy591, app(ty_Maybe, dda)) → new_esEs7(vyy581, vyy591, dda)
new_esEs24(vyy580, vyy590, ty_Float) → new_esEs18(vyy580, vyy590)
new_lt12(vyy3000, vyy400) → new_esEs9(new_compare16(vyy3000, vyy400))
new_esEs24(vyy580, vyy590, ty_Double) → new_esEs15(vyy580, vyy590)
new_primMulInt(Pos(vyy30010), Pos(vyy4010)) → Pos(new_primMulNat0(vyy30010, vyy4010))
new_ltEs5(vyy300, vyy40, ca) → new_not(new_compare0(vyy300, vyy40, ca))
new_esEs21(False, False) → True
new_esEs24(vyy580, vyy590, ty_Integer) → new_esEs11(vyy580, vyy590)
new_compare25(vyy3000, vyy400, False, baa, bab) → new_compare13(vyy3000, vyy400, new_ltEs13(vyy3000, vyy400, baa, bab), baa, bab)
new_lt8(vyy3000, vyy400, bc, bd) → new_esEs9(new_compare6(vyy3000, vyy400, bc, bd))
new_esEs6(Left(vyy580), Left(vyy590), app(app(ty_@2, ceb), cec), hf) → new_esEs5(vyy580, vyy590, ceb, cec)
new_compare14(vyy3000, vyy400, app(app(ty_Either, bdd), bde)) → new_compare12(vyy3000, vyy400, bdd, bde)
new_ltEs17(Nothing, Just(vyy400), bac) → True
new_esEs27(vyy582, vyy592, ty_Double) → new_esEs15(vyy582, vyy592)
new_primMulInt(Neg(vyy30010), Neg(vyy4010)) → Pos(new_primMulNat0(vyy30010, vyy4010))
new_lt6(vyy3000, vyy400, app(ty_[], gb)) → new_lt17(vyy3000, vyy400, gb)
new_ltEs17(Just(vyy3000), Just(vyy400), app(app(ty_Either, baf), bag)) → new_ltEs13(vyy3000, vyy400, baf, bag)
new_lt6(vyy3000, vyy400, app(ty_Maybe, gc)) → new_lt18(vyy3000, vyy400, gc)
new_primEqNat0(Succ(vyy5800), Zero) → False
new_primEqNat0(Zero, Succ(vyy5900)) → False
new_lt5(vyy3001, vyy401, ty_Float) → new_lt10(vyy3001, vyy401)
new_lt20(vyy3000, vyy400, app(ty_Ratio, ccg)) → new_lt15(vyy3000, vyy400, ccg)
new_lt18(vyy3000, vyy400, bga) → new_esEs9(new_compare27(vyy3000, vyy400, bga))
new_compare25(vyy3000, vyy400, True, baa, bab) → EQ
new_compare23(vyy3000, vyy400, False, bc, bd) → new_compare11(vyy3000, vyy400, new_ltEs10(vyy3000, vyy400, bc, bd), bc, bd)
new_compare211(vyy3000, vyy400, False) → new_compare112(vyy3000, vyy400, new_ltEs6(vyy3000, vyy400))
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_compare17(vyy3000, vyy400) → new_compare24(vyy3000, vyy400, new_esEs23(vyy3000, vyy400))
new_ltEs8(vyy3002, vyy402, ty_Char) → new_ltEs18(vyy3002, vyy402)
new_esEs27(vyy582, vyy592, app(app(ty_@2, dbh), dca)) → new_esEs5(vyy582, vyy592, dbh, dca)
new_ltEs17(Nothing, Nothing, bac) → True
new_esEs25(vyy581, vyy591, app(app(app(ty_@3, bgg), bgh), bha)) → new_esEs8(vyy581, vyy591, bgg, bgh, bha)
new_lt5(vyy3001, vyy401, ty_Integer) → new_lt16(vyy3001, vyy401)
new_sizeFM(Branch(vyy590, vyy591, vyy592, vyy593, vyy594), cb, cc) → vyy592
new_esEs29(vyy580, vyy590, app(app(ty_Either, def), deg)) → new_esEs6(vyy580, vyy590, def, deg)
new_ltEs17(Just(vyy3000), Just(vyy400), ty_Bool) → new_ltEs6(vyy3000, vyy400)
new_pePe(True, vyy58, vyy59, vyy60, gg) → True
new_ltEs4(LT, GT) → True
new_foldFM_LE10(vyy51, vyy40, vyy340, vyy341, vyy342, vyy343, vyy344, False, h, ba, bb) → new_foldFM_LE0(vyy51, vyy40, vyy343, h, ba, bb)
new_foldFM2(Branch(vyy590, vyy591, vyy592, vyy593, vyy594), cb, cc) → new_foldFM0(vyy590, vyy591, new_foldFM2(vyy594, cb, cc), vyy593, cb, cc)
new_lt20(vyy3000, vyy400, app(app(ty_Either, baa), bab)) → new_lt11(vyy3000, vyy400, baa, bab)
new_lt5(vyy3001, vyy401, ty_Double) → new_lt14(vyy3001, vyy401)
new_ltEs19(vyy3001, vyy401, app(ty_Maybe, ccc)) → new_ltEs17(vyy3001, vyy401, ccc)
new_lt20(vyy3000, vyy400, ty_@0) → new_lt9(vyy3000, vyy400)
new_lt6(vyy3000, vyy400, ty_Int) → new_lt7(vyy3000, vyy400)
new_primCmpInt(Neg(Zero), Neg(Succ(vyy4000))) → new_primCmpNat0(Succ(vyy4000), Zero)
new_compare23(vyy3000, vyy400, True, bc, bd) → EQ
new_primCmpInt(Pos(Zero), Neg(Succ(vyy4000))) → GT
new_esEs6(Left(vyy580), Left(vyy590), app(ty_Maybe, cdg), hf) → new_esEs7(vyy580, vyy590, cdg)
new_ltEs13(Left(vyy3000), Left(vyy400), ty_Char, cfh) → new_ltEs18(vyy3000, vyy400)
new_ltEs13(Left(vyy3000), Left(vyy400), app(ty_Maybe, cgg), cfh) → new_ltEs17(vyy3000, vyy400, cgg)
new_esEs16(vyy58, vyy59, app(ty_[], gh)) → new_esEs19(vyy58, vyy59, gh)
new_esEs28(vyy581, vyy591, app(ty_Ratio, dcd)) → new_esEs12(vyy581, vyy591, dcd)
new_ltEs13(Left(vyy3000), Left(vyy400), ty_@0, cfh) → new_ltEs11(vyy3000, vyy400)
new_esEs6(Right(vyy580), Right(vyy590), he, ty_Integer) → new_esEs11(vyy580, vyy590)
new_ltEs8(vyy3002, vyy402, app(ty_[], de)) → new_ltEs5(vyy3002, vyy402, de)
new_esEs25(vyy581, vyy591, app(app(ty_FiniteMap, bgc), bgd)) → new_esEs17(vyy581, vyy591, bgc, bgd)
new_esEs27(vyy582, vyy592, app(ty_Ratio, dah)) → new_esEs12(vyy582, vyy592, dah)
new_ltEs13(Left(vyy3000), Left(vyy400), app(app(ty_Either, cgc), cgd), cfh) → new_ltEs13(vyy3000, vyy400, cgc, cgd)
new_esEs6(Right(vyy580), Right(vyy590), he, ty_Char) → new_esEs22(vyy580, vyy590)
new_esEs25(vyy581, vyy591, app(ty_Maybe, bhb)) → new_esEs7(vyy581, vyy591, bhb)
new_ltEs13(Left(vyy3000), Left(vyy400), ty_Integer, cfh) → new_ltEs16(vyy3000, vyy400)
new_ltEs13(Right(vyy3000), Right(vyy400), chc, app(app(ty_Either, chf), chg)) → new_ltEs13(vyy3000, vyy400, chf, chg)
new_compare8(Float(vyy3000, vyy3001), Float(vyy400, vyy401)) → new_compare9(new_sr(vyy3000, vyy400), new_sr(vyy3001, vyy401))
new_ltEs13(Right(vyy3000), Right(vyy400), chc, ty_Ordering) → new_ltEs4(vyy3000, vyy400)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_ltEs4(LT, EQ) → True
new_compare14(vyy3000, vyy400, ty_Ordering) → new_compare17(vyy3000, vyy400)
new_compare26(Integer(vyy3000), Integer(vyy400)) → new_primCmpInt(vyy3000, vyy400)
new_esEs6(Left(vyy580), Left(vyy590), app(app(ty_FiniteMap, cch), cda), hf) → new_esEs17(vyy580, vyy590, cch, cda)
new_compare19(:%(vyy3000, vyy3001), :%(vyy400, vyy401), ty_Int) → new_compare9(new_sr(vyy3000, vyy401), new_sr(vyy400, vyy3001))
new_esEs24(vyy580, vyy590, ty_Int) → new_esEs10(vyy580, vyy590)
new_esEs27(vyy582, vyy592, ty_Float) → new_esEs18(vyy582, vyy592)
new_compare14(vyy3000, vyy400, ty_Float) → new_compare8(vyy3000, vyy400)
new_asAs(False, vyy73) → False
new_esEs6(Left(vyy580), Left(vyy590), ty_Ordering, hf) → new_esEs23(vyy580, vyy590)
new_esEs29(vyy580, vyy590, app(app(ty_FiniteMap, ddf), ddg)) → new_esEs17(vyy580, vyy590, ddf, ddg)
new_ltEs17(Just(vyy3000), Just(vyy400), ty_Double) → new_ltEs14(vyy3000, vyy400)
new_primMulInt(Neg(vyy30010), Pos(vyy4010)) → Neg(new_primMulNat0(vyy30010, vyy4010))
new_primMulInt(Pos(vyy30010), Neg(vyy4010)) → Neg(new_primMulNat0(vyy30010, vyy4010))
new_ltEs13(Right(vyy3000), Right(vyy400), chc, ty_Bool) → new_ltEs6(vyy3000, vyy400)
new_compare12(vyy3000, vyy400, baa, bab) → new_compare25(vyy3000, vyy400, new_esEs6(vyy3000, vyy400, baa, bab), baa, bab)
new_primMulNat0(Zero, Succ(vyy40100)) → Zero
new_primMulNat0(Succ(vyy300100), Zero) → Zero
new_ltEs13(Left(vyy3000), Right(vyy400), chc, cfh) → True
new_esEs25(vyy581, vyy591, ty_Char) → new_esEs22(vyy581, vyy591)
new_compare14(vyy3000, vyy400, ty_Double) → new_compare18(vyy3000, vyy400)
new_esEs27(vyy582, vyy592, ty_Ordering) → new_esEs23(vyy582, vyy592)
new_esEs23(GT, EQ) → False
new_esEs23(EQ, GT) → False
new_esEs26(vyy580, vyy590, app(ty_Maybe, caf)) → new_esEs7(vyy580, vyy590, caf)
new_esEs23(EQ, LT) → False
new_esEs23(LT, EQ) → False
new_ltEs12(vyy300, vyy40) → new_not(new_compare8(vyy300, vyy40))
new_foldFM_LE3(vyy340, vyy341, vyy66, vyy40, h, ba, bb) → new_fmToList_LE0(vyy340, vyy341, vyy66, h, ba, bb)
new_ltEs9(vyy300, vyy40) → new_not(new_compare9(vyy300, vyy40))
new_compare110(vyy3000, vyy400, True, be, bf, bg) → LT
new_not(EQ) → new_not0
new_lt20(vyy3000, vyy400, app(ty_[], bgb)) → new_lt17(vyy3000, vyy400, bgb)
new_ltEs8(vyy3002, vyy402, app(app(ty_Either, db), dc)) → new_ltEs13(vyy3002, vyy402, db, dc)
new_lt6(vyy3000, vyy400, ty_Double) → new_lt14(vyy3000, vyy400)
new_compare14(vyy3000, vyy400, ty_Integer) → new_compare26(vyy3000, vyy400)
new_esEs6(Right(vyy580), Right(vyy590), he, ty_Int) → new_esEs10(vyy580, vyy590)
new_ltEs13(Left(vyy3000), Left(vyy400), ty_Ordering, cfh) → new_ltEs4(vyy3000, vyy400)
new_esEs29(vyy580, vyy590, app(ty_Ratio, ddh)) → new_esEs12(vyy580, vyy590, ddh)
new_esEs19(:(vyy580, vyy581), :(vyy590, vyy591), gh) → new_asAs(new_esEs24(vyy580, vyy590, gh), new_esEs19(vyy581, vyy591, gh))
new_ltEs13(Right(vyy3000), Right(vyy400), chc, app(app(ty_@2, chd), che)) → new_ltEs10(vyy3000, vyy400, chd, che)
new_esEs29(vyy580, vyy590, ty_Ordering) → new_esEs23(vyy580, vyy590)
new_esEs28(vyy581, vyy591, ty_Char) → new_esEs22(vyy581, vyy591)
new_compare111(vyy3000, vyy400, False, bga) → GT
new_esEs24(vyy580, vyy590, ty_Char) → new_esEs22(vyy580, vyy590)
new_ltEs13(Right(vyy3000), Left(vyy400), chc, cfh) → False
new_compare210(vyy3000, vyy400, False, bga) → new_compare111(vyy3000, vyy400, new_ltEs17(vyy3000, vyy400, bga), bga)
new_esEs26(vyy580, vyy590, app(ty_Ratio, caa)) → new_esEs12(vyy580, vyy590, caa)
new_esEs29(vyy580, vyy590, ty_Double) → new_esEs15(vyy580, vyy590)
new_esEs23(LT, LT) → True
new_esEs16(vyy58, vyy59, app(ty_Maybe, hd)) → new_esEs7(vyy58, vyy59, hd)
new_ltEs17(Just(vyy3000), Just(vyy400), ty_Float) → new_ltEs12(vyy3000, vyy400)
new_compare14(vyy3000, vyy400, ty_Char) → new_compare28(vyy3000, vyy400)
new_esEs27(vyy582, vyy592, ty_Bool) → new_esEs21(vyy582, vyy592)
new_ltEs13(Right(vyy3000), Right(vyy400), chc, ty_Char) → new_ltEs18(vyy3000, vyy400)
new_ltEs4(LT, LT) → True
new_ltEs16(vyy300, vyy40) → new_not(new_compare26(vyy300, vyy40))
new_foldFM_LE20(vyy340, vyy341, vyy67, vyy40, vyy3440, vyy3441, vyy3442, vyy3443, vyy3444, h, ba, bb) → new_foldFM_LE10(new_fmToList_LE0(vyy340, vyy341, vyy67, h, ba, bb), vyy40, vyy3440, vyy3441, vyy3442, vyy3443, vyy3444, new_ltEs13(vyy3440, Right(vyy40), h, ba), h, ba, bb)
new_compare14(vyy3000, vyy400, app(ty_Ratio, bdf)) → new_compare19(vyy3000, vyy400, bdf)
new_esEs25(vyy581, vyy591, app(app(ty_@2, bhe), bhf)) → new_esEs5(vyy581, vyy591, bhe, bhf)
new_esEs16(vyy58, vyy59, app(app(ty_@2, hg), hh)) → new_esEs5(vyy58, vyy59, hg, hh)
new_not(LT) → new_not0
new_lt5(vyy3001, vyy401, app(ty_Maybe, eh)) → new_lt18(vyy3001, vyy401, eh)
new_lt20(vyy3000, vyy400, ty_Bool) → new_lt12(vyy3000, vyy400)
new_compare112(vyy3000, vyy400, False) → GT
new_lt5(vyy3001, vyy401, app(app(app(ty_@3, fa), fb), fc)) → new_lt4(vyy3001, vyy401, fa, fb, fc)
new_esEs7(Just(vyy580), Just(vyy590), app(app(ty_@2, bch), bda)) → new_esEs5(vyy580, vyy590, bch, bda)
new_ltEs11(vyy300, vyy40) → new_not(new_compare15(vyy300, vyy40))
new_esEs28(vyy581, vyy591, ty_Int) → new_esEs10(vyy581, vyy591)
new_ltEs8(vyy3002, vyy402, app(ty_Maybe, df)) → new_ltEs17(vyy3002, vyy402, df)
new_ltEs17(Just(vyy3000), Just(vyy400), app(ty_Maybe, bbb)) → new_ltEs17(vyy3000, vyy400, bbb)
new_esEs29(vyy580, vyy590, ty_Bool) → new_esEs21(vyy580, vyy590)
new_esEs26(vyy580, vyy590, app(app(ty_Either, cag), cah)) → new_esEs6(vyy580, vyy590, cag, cah)
new_esEs27(vyy582, vyy592, app(ty_[], dba)) → new_esEs19(vyy582, vyy592, dba)
new_primPlusNat1(Zero, Zero) → Zero
new_compare0([], :(vyy400, vyy401), ca) → LT
new_ltEs13(Left(vyy3000), Left(vyy400), ty_Double, cfh) → new_ltEs14(vyy3000, vyy400)
new_lt14(vyy3000, vyy400) → new_esEs9(new_compare18(vyy3000, vyy400))
new_ltEs17(Just(vyy3000), Just(vyy400), ty_Char) → new_ltEs18(vyy3000, vyy400)
new_esEs7(Just(vyy580), Just(vyy590), app(ty_[], bca)) → new_esEs19(vyy580, vyy590, bca)
new_asAs(True, vyy73) → vyy73
new_primMulNat0(Succ(vyy300100), Succ(vyy40100)) → new_primPlusNat0(new_primMulNat0(vyy300100, Succ(vyy40100)), vyy40100)
new_lt13(vyy3000, vyy400) → new_esEs9(new_compare17(vyy3000, vyy400))
new_esEs6(Left(vyy580), Left(vyy590), ty_Float, hf) → new_esEs18(vyy580, vyy590)
new_lt5(vyy3001, vyy401, app(app(ty_@2, eb), ec)) → new_lt8(vyy3001, vyy401, eb, ec)
new_esEs27(vyy582, vyy592, ty_Integer) → new_esEs11(vyy582, vyy592)
new_pePe(False, vyy58, vyy59, vyy60, gg) → new_asAs(new_esEs16(vyy58, vyy59, gg), vyy60)
new_ltEs19(vyy3001, vyy401, ty_Float) → new_ltEs12(vyy3001, vyy401)
new_lt6(vyy3000, vyy400, ty_Float) → new_lt10(vyy3000, vyy400)
new_esEs26(vyy580, vyy590, ty_Double) → new_esEs15(vyy580, vyy590)
new_esEs27(vyy582, vyy592, ty_Int) → new_esEs10(vyy582, vyy592)
new_esEs7(Just(vyy580), Just(vyy590), ty_Double) → new_esEs15(vyy580, vyy590)
new_compare211(vyy3000, vyy400, True) → EQ
new_fmToList(vyy59, cb, cc) → new_foldFM2(vyy59, cb, cc)
new_ltEs10(@2(vyy3000, vyy3001), @2(vyy400, vyy401), cbc, cbd) → new_pePe(new_lt20(vyy3000, vyy400, cbc), vyy3000, vyy400, new_ltEs19(vyy3001, vyy401, cbd), cbc)
new_esEs21(False, True) → False
new_esEs21(True, False) → False
new_ltEs6(False, False) → True
new_ltEs8(vyy3002, vyy402, ty_Integer) → new_ltEs16(vyy3002, vyy402)
new_compare10(vyy3000, vyy400, True) → LT
new_ltEs4(GT, GT) → True
new_esEs26(vyy580, vyy590, ty_@0) → new_esEs20(vyy580, vyy590)
new_compare14(vyy3000, vyy400, ty_@0) → new_compare15(vyy3000, vyy400)
new_compare110(vyy3000, vyy400, False, be, bf, bg) → GT
new_ltEs19(vyy3001, vyy401, app(ty_[], ccb)) → new_ltEs5(vyy3001, vyy401, ccb)
new_compare10(vyy3000, vyy400, False) → GT
new_esEs6(Left(vyy580), Left(vyy590), ty_Bool, hf) → new_esEs21(vyy580, vyy590)
new_esEs25(vyy581, vyy591, ty_@0) → new_esEs20(vyy581, vyy591)
new_lt6(vyy3000, vyy400, ty_Bool) → new_lt12(vyy3000, vyy400)
new_esEs10(vyy58, vyy59) → new_primEqInt(vyy58, vyy59)
new_primCompAux00(vyy82, GT) → GT
new_ltEs13(Right(vyy3000), Right(vyy400), chc, ty_Integer) → new_ltEs16(vyy3000, vyy400)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_compare28(Char(vyy3000), Char(vyy400)) → new_primCmpNat0(vyy3000, vyy400)
new_esEs6(Right(vyy580), Right(vyy590), he, ty_Ordering) → new_esEs23(vyy580, vyy590)
new_esEs24(vyy580, vyy590, app(app(app(ty_@3, beh), bfa), bfb)) → new_esEs8(vyy580, vyy590, beh, bfa, bfb)
new_esEs16(vyy58, vyy59, ty_Double) → new_esEs15(vyy58, vyy59)
new_lt9(vyy3000, vyy400) → new_esEs9(new_compare15(vyy3000, vyy400))
new_esEs25(vyy581, vyy591, app(ty_Ratio, bge)) → new_esEs12(vyy581, vyy591, bge)
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_esEs7(Just(vyy580), Just(vyy590), app(ty_Ratio, bbh)) → new_esEs12(vyy580, vyy590, bbh)
new_primCmpInt(Neg(Succ(vyy30000)), Pos(vyy400)) → LT
new_esEs6(Left(vyy580), Left(vyy590), ty_Int, hf) → new_esEs10(vyy580, vyy590)
new_esEs24(vyy580, vyy590, ty_@0) → new_esEs20(vyy580, vyy590)
new_esEs17(vyy58, vyy59, cb, cc) → new_asAs(new_esEs10(new_sizeFM(vyy58, cb, cc), new_sizeFM(vyy59, cb, cc)), new_esEs19(new_fmToList(vyy58, cb, cc), new_fmToList(vyy59, cb, cc), app(app(ty_@2, cb), cc)))
new_esEs13(vyy581, vyy591, ty_Int) → new_esEs10(vyy581, vyy591)
The set Q consists of the following terms:
new_ltEs17(Just(x0), Just(x1), app(ty_Ratio, x2))
new_lt5(x0, x1, ty_Integer)
new_esEs25(x0, x1, ty_@0)
new_lt20(x0, x1, ty_Integer)
new_primEqNat0(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_compare9(x0, x1)
new_compare11(x0, x1, False, x2, x3)
new_compare13(x0, x1, True, x2, x3)
new_lt9(x0, x1)
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_lt16(x0, x1)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_compare210(x0, x1, True, x2)
new_lt6(x0, x1, ty_Float)
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_esEs6(Right(x0), Right(x1), x2, ty_Bool)
new_esEs16(x0, x1, ty_Float)
new_compare15(@0, @0)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_lt5(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs23(LT, EQ)
new_esEs23(EQ, LT)
new_lt5(x0, x1, app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, ty_Char)
new_ltEs8(x0, x1, ty_Int)
new_esEs23(EQ, EQ)
new_esEs9(EQ)
new_ltEs13(Right(x0), Left(x1), x2, x3)
new_ltEs13(Left(x0), Right(x1), x2, x3)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs23(EQ, GT)
new_esEs23(GT, EQ)
new_esEs29(x0, x1, ty_Float)
new_esEs16(x0, x1, ty_Int)
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_esEs12(:%(x0, x1), :%(x2, x3), x4)
new_esEs24(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_primMulNat0(Zero, Succ(x0))
new_primCmpNat0(Zero, Succ(x0))
new_primCmpNat0(Succ(x0), Zero)
new_compare0([], [], x0)
new_lt6(x0, x1, ty_Int)
new_lt6(x0, x1, app(ty_Maybe, x2))
new_lt5(x0, x1, ty_Double)
new_esEs10(x0, x1)
new_foldFM_LE10(x0, x1, x2, x3, x4, x5, Branch(x6, x7, x8, x9, x10), True, x11, x12, x13)
new_esEs29(x0, x1, ty_Bool)
new_esEs27(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs16(x0, x1, ty_@0)
new_esEs24(x0, x1, ty_Double)
new_esEs25(x0, x1, app(ty_[], x2))
new_ltEs13(Right(x0), Right(x1), x2, ty_Integer)
new_esEs6(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_lt19(x0, x1)
new_ltEs17(Just(x0), Just(x1), ty_@0)
new_compare14(x0, x1, ty_Integer)
new_lt5(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs8(x0, x1, app(ty_[], x2))
new_ltEs14(x0, x1)
new_ltEs13(Left(x0), Left(x1), ty_Char, x2)
new_esEs26(x0, x1, ty_Ordering)
new_ltEs17(Just(x0), Just(x1), ty_Ordering)
new_esEs29(x0, x1, app(ty_[], x2))
new_ltEs17(Just(x0), Just(x1), ty_Double)
new_esEs29(x0, x1, ty_Char)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs17(Just(x0), Just(x1), app(ty_[], x2))
new_esEs7(Just(x0), Just(x1), ty_@0)
new_esEs25(x0, x1, ty_Bool)
new_ltEs19(x0, x1, app(ty_[], x2))
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs13(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_ltEs6(True, True)
new_ltEs17(Nothing, Nothing, x0)
new_sr(x0, x1)
new_lt5(x0, x1, app(ty_[], x2))
new_esEs26(x0, x1, ty_@0)
new_compare26(Integer(x0), Integer(x1))
new_compare111(x0, x1, True, x2)
new_compare24(x0, x1, False)
new_lt8(x0, x1, x2, x3)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs13(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs13(Right(x0), Right(x1), x2, ty_Bool)
new_lt20(x0, x1, ty_Bool)
new_ltEs13(Left(x0), Left(x1), app(ty_[], x2), x3)
new_ltEs13(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs6(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare211(x0, x1, True)
new_ltEs19(x0, x1, ty_Ordering)
new_esEs24(x0, x1, ty_Integer)
new_esEs7(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, ty_@0)
new_lt6(x0, x1, ty_@0)
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_esEs7(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_ltEs17(Just(x0), Just(x1), ty_Int)
new_lt20(x0, x1, ty_Float)
new_ltEs13(Left(x0), Left(x1), ty_Integer, x2)
new_primEqNat0(Zero, Zero)
new_esEs27(x0, x1, ty_Double)
new_lt5(x0, x1, ty_Char)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_esEs7(Just(x0), Just(x1), ty_Ordering)
new_compare210(x0, x1, False, x2)
new_primCmpNat0(Succ(x0), Succ(x1))
new_lt6(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs13(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_lt5(x0, x1, ty_Bool)
new_esEs7(Just(x0), Just(x1), app(app(ty_FiniteMap, x2), x3))
new_compare112(x0, x1, True)
new_esEs7(Just(x0), Just(x1), ty_Float)
new_compare0([], :(x0, x1), x2)
new_esEs27(x0, x1, ty_Bool)
new_primPlusNat1(Zero, Succ(x0))
new_ltEs13(Right(x0), Right(x1), x2, ty_Double)
new_primMulNat0(Zero, Zero)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs28(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs6(Left(x0), Left(x1), ty_Char, x2)
new_compare14(x0, x1, ty_Int)
new_sizeFM(EmptyFM, x0, x1)
new_ltEs17(Just(x0), Just(x1), ty_Bool)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_pePe(True, x0, x1, x2, x3)
new_ltEs5(x0, x1, x2)
new_ltEs4(GT, GT)
new_esEs6(Left(x0), Left(x1), ty_Float, x2)
new_lt15(x0, x1, x2)
new_compare14(x0, x1, app(ty_Ratio, x2))
new_lt20(x0, x1, ty_Int)
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_esEs27(x0, x1, ty_Float)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs8(x0, x1, app(app(ty_@2, x2), x3))
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, app(ty_Ratio, x2))
new_foldFM_LE10(x0, x1, x2, x3, x4, x5, EmptyFM, True, x6, x7, x8)
new_esEs25(x0, x1, ty_Ordering)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_compare14(x0, x1, app(ty_Maybe, x2))
new_lt20(x0, x1, app(ty_Maybe, x2))
new_lt20(x0, x1, app(ty_[], x2))
new_compare19(:%(x0, x1), :%(x2, x3), ty_Integer)
new_esEs28(x0, x1, ty_Integer)
new_esEs16(x0, x1, app(ty_Maybe, x2))
new_ltEs10(@2(x0, x1), @2(x2, x3), x4, x5)
new_primMulNat0(Succ(x0), Succ(x1))
new_ltEs17(Just(x0), Just(x1), ty_Float)
new_ltEs13(Right(x0), Right(x1), x2, ty_Char)
new_ltEs16(x0, x1)
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_esEs28(x0, x1, ty_Float)
new_esEs24(x0, x1, app(ty_[], x2))
new_esEs28(x0, x1, ty_Int)
new_lt14(x0, x1)
new_ltEs17(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_compare14(x0, x1, ty_Ordering)
new_lt6(x0, x1, ty_Double)
new_compare23(x0, x1, False, x2, x3)
new_lt5(x0, x1, app(ty_Maybe, x2))
new_lt6(x0, x1, app(app(ty_@2, x2), x3))
new_esEs6(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_lt4(x0, x1, x2, x3, x4)
new_esEs16(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_compare10(x0, x1, False)
new_esEs24(x0, x1, ty_Bool)
new_compare14(x0, x1, ty_Char)
new_compare25(x0, x1, False, x2, x3)
new_esEs29(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_primPlusNat1(Succ(x0), Succ(x1))
new_lt11(x0, x1, x2, x3)
new_esEs27(x0, x1, ty_Ordering)
new_ltEs19(x0, x1, ty_Integer)
new_esEs23(GT, LT)
new_esEs23(LT, GT)
new_foldFM_LE10(x0, x1, x2, x3, x4, x5, x6, False, x7, x8, x9)
new_ltEs15(x0, x1, x2)
new_ltEs19(x0, x1, ty_Int)
new_esEs6(Left(x0), Left(x1), ty_Int, x2)
new_ltEs19(x0, x1, ty_Double)
new_ltEs13(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs7(Just(x0), Just(x1), app(ty_[], x2))
new_compare18(Double(x0, x1), Double(x2, x3))
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_compare14(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs13(Left(x0), Left(x1), ty_Bool, x2)
new_esEs5(@2(x0, x1), @2(x2, x3), x4, x5)
new_primPlusNat1(Zero, Zero)
new_ltEs17(Just(x0), Nothing, x1)
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_not0
new_primMulNat0(Succ(x0), Zero)
new_ltEs12(x0, x1)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_compare29(x0, x1, True, x2, x3, x4)
new_ltEs13(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs9(GT)
new_ltEs13(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_compare0(:(x0, x1), :(x2, x3), x4)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs13(Left(x0), Left(x1), ty_Ordering, x2)
new_ltEs17(Just(x0), Just(x1), app(ty_Maybe, x2))
new_compare25(x0, x1, True, x2, x3)
new_esEs27(x0, x1, ty_Int)
new_esEs7(Just(x0), Just(x1), ty_Char)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_esEs6(Left(x0), Left(x1), ty_@0, x2)
new_ltEs8(x0, x1, ty_Float)
new_ltEs4(EQ, EQ)
new_compare12(x0, x1, x2, x3)
new_esEs7(Nothing, Just(x0), x1)
new_compare7(x0, x1, x2, x3, x4)
new_compare14(x0, x1, ty_Float)
new_fmToList_LE0(x0, x1, x2, x3, x4, x5)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_ltEs18(x0, x1)
new_esEs8(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs17(x0, x1, x2, x3)
new_ltEs6(True, False)
new_ltEs6(False, True)
new_compare27(x0, x1, x2)
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_esEs26(x0, x1, ty_Bool)
new_compare24(x0, x1, True)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_compare14(x0, x1, ty_Double)
new_esEs6(Left(x0), Left(x1), ty_Bool, x2)
new_esEs25(x0, x1, ty_Char)
new_esEs6(Right(x0), Right(x1), x2, ty_@0)
new_ltEs4(EQ, LT)
new_lt6(x0, x1, app(ty_[], x2))
new_ltEs4(LT, EQ)
new_lt17(x0, x1, x2)
new_not(GT)
new_esEs26(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_ltEs8(x0, x1, ty_@0)
new_compare110(x0, x1, True, x2, x3, x4)
new_esEs26(x0, x1, ty_Int)
new_esEs24(x0, x1, ty_Int)
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_foldFM_LE0(x0, x1, EmptyFM, x2, x3, x4)
new_esEs16(x0, x1, ty_Double)
new_esEs6(Right(x0), Right(x1), x2, app(ty_[], x3))
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_primCompAux0(x0, x1, x2, x3)
new_esEs6(Left(x0), Left(x1), ty_Double, x2)
new_esEs16(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt6(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs13(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_foldFM2(EmptyFM, x0, x1)
new_primEqInt(Neg(Zero), Pos(Zero))
new_primEqInt(Pos(Zero), Neg(Zero))
new_lt5(x0, x1, ty_@0)
new_esEs7(Just(x0), Just(x1), ty_Bool)
new_ltEs13(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_ltEs13(Right(x0), Right(x1), x2, ty_Float)
new_esEs13(x0, x1, ty_Int)
new_lt6(x0, x1, ty_Char)
new_esEs7(Just(x0), Nothing, x1)
new_lt7(x0, x1)
new_compare10(x0, x1, True)
new_primCompAux00(x0, LT)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_compare29(x0, x1, False, x2, x3, x4)
new_esEs6(Right(x0), Right(x1), x2, ty_Char)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_ltEs6(False, False)
new_primPlusNat1(Succ(x0), Zero)
new_esEs28(x0, x1, app(ty_[], x2))
new_primCompAux00(x0, GT)
new_esEs23(LT, LT)
new_lt6(x0, x1, app(ty_Ratio, x2))
new_ltEs19(x0, x1, ty_Bool)
new_primEqInt(Neg(Zero), Neg(Zero))
new_esEs6(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_ltEs17(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_primPlusNat0(Succ(x0), x1)
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
new_esEs16(x0, x1, app(ty_Ratio, x2))
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_compare19(:%(x0, x1), :%(x2, x3), ty_Int)
new_foldFM_LE20(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_esEs28(x0, x1, ty_Bool)
new_lt5(x0, x1, ty_Float)
new_esEs19(:(x0, x1), :(x2, x3), x4)
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_ltEs4(LT, LT)
new_esEs14(x0, x1, ty_Int)
new_compare13(x0, x1, False, x2, x3)
new_esEs27(x0, x1, ty_Char)
new_ltEs8(x0, x1, ty_Double)
new_ltEs11(x0, x1)
new_esEs25(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs26(x0, x1, ty_Float)
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs16(x0, x1, ty_Ordering)
new_compare6(x0, x1, x2, x3)
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare28(Char(x0), Char(x1))
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_ltEs13(Right(x0), Right(x1), x2, ty_Int)
new_esEs6(Right(x0), Right(x1), x2, ty_Integer)
new_esEs9(LT)
new_ltEs7(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_compare111(x0, x1, False, x2)
new_esEs6(Right(x0), Left(x1), x2, x3)
new_esEs6(Left(x0), Right(x1), x2, x3)
new_ltEs13(Right(x0), Right(x1), x2, ty_@0)
new_esEs29(x0, x1, ty_Ordering)
new_esEs18(Float(x0, x1), Float(x2, x3))
new_foldFM_LE3(x0, x1, x2, x3, x4, x5, x6)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs6(Left(x0), Left(x1), ty_Ordering, x2)
new_compare110(x0, x1, False, x2, x3, x4)
new_ltEs17(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_asAs(False, x0)
new_esEs7(Nothing, Nothing, x0)
new_primPlusNat0(Zero, x0)
new_compare8(Float(x0, x1), Float(x2, x3))
new_esEs7(Just(x0), Just(x1), ty_Double)
new_primCmpNat0(Zero, Zero)
new_esEs29(x0, x1, ty_Int)
new_esEs16(x0, x1, app(ty_[], x2))
new_esEs15(Double(x0, x1), Double(x2, x3))
new_lt20(x0, x1, ty_Ordering)
new_esEs6(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs7(Just(x0), Just(x1), ty_Int)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_compare17(x0, x1)
new_compare211(x0, x1, False)
new_esEs6(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_compare14(x0, x1, app(ty_[], x2))
new_lt13(x0, x1)
new_compare14(x0, x1, app(app(ty_Either, x2), x3))
new_esEs6(Right(x0), Right(x1), x2, ty_Int)
new_ltEs8(x0, x1, app(ty_Maybe, x2))
new_esEs13(x0, x1, ty_Integer)
new_lt12(x0, x1)
new_esEs6(Right(x0), Right(x1), x2, ty_Double)
new_ltEs8(x0, x1, ty_Ordering)
new_pePe(False, x0, x1, x2, x3)
new_esEs6(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_ltEs19(x0, x1, ty_@0)
new_esEs28(x0, x1, ty_Double)
new_foldFM_LE0(x0, x1, Branch(x2, x3, x4, x5, x6), x7, x8, x9)
new_lt10(x0, x1)
new_ltEs13(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs19([], [], x0)
new_primEqNat0(Zero, Succ(x0))
new_esEs16(x0, x1, ty_Bool)
new_esEs21(True, True)
new_ltEs4(EQ, GT)
new_ltEs4(GT, EQ)
new_ltEs17(Nothing, Just(x0), x1)
new_esEs24(x0, x1, ty_Ordering)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_not(EQ)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_compare23(x0, x1, True, x2, x3)
new_ltEs17(Just(x0), Just(x1), ty_Integer)
new_esEs14(x0, x1, ty_Integer)
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_esEs6(Left(x0), Left(x1), ty_Integer, x2)
new_esEs25(x0, x1, ty_Int)
new_ltEs8(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs22(Char(x0), Char(x1))
new_ltEs19(x0, x1, ty_Char)
new_compare14(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs8(x0, x1, app(ty_Ratio, x2))
new_ltEs13(Left(x0), Left(x1), ty_Int, x2)
new_ltEs13(Left(x0), Left(x1), ty_Float, x2)
new_esEs7(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_lt6(x0, x1, ty_Bool)
new_esEs26(x0, x1, ty_Double)
new_esEs27(x0, x1, app(ty_[], x2))
new_lt5(x0, x1, ty_Int)
new_esEs16(x0, x1, app(app(ty_Either, x2), x3))
new_esEs24(x0, x1, ty_@0)
new_esEs11(Integer(x0), Integer(x1))
new_esEs21(False, True)
new_esEs21(True, False)
new_lt6(x0, x1, ty_Ordering)
new_esEs6(Left(x0), Left(x1), app(app(ty_FiniteMap, x2), x3), x4)
new_lt5(x0, x1, app(ty_Ratio, x2))
new_esEs24(x0, x1, ty_Char)
new_esEs20(@0, @0)
new_esEs24(x0, x1, ty_Float)
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs19(:(x0, x1), [], x2)
new_esEs25(x0, x1, ty_Float)
new_esEs16(x0, x1, ty_Char)
new_ltEs13(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs29(x0, x1, ty_@0)
new_esEs6(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs26(x0, x1, ty_Integer)
new_esEs29(x0, x1, ty_Integer)
new_compare14(x0, x1, ty_Bool)
new_esEs6(Right(x0), Right(x1), x2, ty_Float)
new_ltEs8(x0, x1, app(app(ty_Either, x2), x3))
new_esEs28(x0, x1, ty_Ordering)
new_lt5(x0, x1, ty_Ordering)
new_esEs26(x0, x1, app(ty_[], x2))
new_esEs16(x0, x1, ty_Integer)
new_esEs7(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_compare16(x0, x1)
new_esEs6(Left(x0), Left(x1), app(ty_[], x2), x3)
new_ltEs8(x0, x1, ty_Char)
new_compare0(:(x0, x1), [], x2)
new_primCompAux00(x0, EQ)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sr0(Integer(x0), Integer(x1))
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_esEs6(Right(x0), Right(x1), x2, ty_Ordering)
new_compare11(x0, x1, True, x2, x3)
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_FiniteMap, x3), x4))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_ltEs9(x0, x1)
new_compare14(x0, x1, ty_@0)
new_ltEs19(x0, x1, ty_Float)
new_esEs28(x0, x1, ty_@0)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_esEs25(x0, x1, ty_Double)
new_ltEs8(x0, x1, ty_Integer)
new_esEs21(False, False)
new_primEqInt(Pos(Zero), Pos(Zero))
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs27(x0, x1, ty_Integer)
new_asAs(True, x0)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs28(x0, x1, ty_Char)
new_esEs7(Just(x0), Just(x1), ty_Integer)
new_ltEs13(Left(x0), Left(x1), ty_@0, x2)
new_ltEs13(Right(x0), Right(x1), x2, ty_Ordering)
new_compare112(x0, x1, False)
new_lt6(x0, x1, ty_Integer)
new_lt20(x0, x1, ty_Char)
new_ltEs4(GT, LT)
new_ltEs4(LT, GT)
new_esEs16(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs27(x0, x1, ty_@0)
new_ltEs17(Just(x0), Just(x1), ty_Char)
new_primMulInt(Neg(x0), Neg(x1))
new_ltEs13(Left(x0), Left(x1), ty_Double, x2)
new_esEs29(x0, x1, ty_Double)
new_lt20(x0, x1, ty_Double)
new_esEs25(x0, x1, ty_Integer)
new_fmToList(x0, x1, x2)
new_ltEs8(x0, x1, ty_Bool)
new_esEs23(GT, GT)
new_esEs19([], :(x0, x1), x2)
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
new_not(LT)
new_lt18(x0, x1, x2)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_esEs7(Just(x0), Just(x1), app(ty_Ratio, 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_LE1(vyy51, vyy40, vyy340, vyy341, vyy342, vyy343, Branch(vyy3440, vyy3441, vyy3442, vyy3443, vyy3444), True, h, ba, bb) → new_foldFM_LE2(vyy340, vyy341, new_foldFM_LE0(vyy51, vyy40, vyy343, h, ba, bb), vyy40, vyy3440, vyy3441, vyy3442, vyy3443, vyy3444, h, ba, bb)
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, 11 >= 12
- new_foldFM_LE1(vyy51, vyy40, vyy340, vyy341, vyy342, Branch(vyy3430, vyy3431, vyy3432, vyy3433, vyy3434), vyy344, False, h, ba, bb) → new_foldFM_LE1(vyy51, vyy40, vyy3430, vyy3431, vyy3432, vyy3433, vyy3434, new_ltEs13(vyy3430, Right(vyy40), h, ba), h, ba, bb)
The graph contains the following edges 1 >= 1, 2 >= 2, 6 > 3, 6 > 4, 6 > 5, 6 > 6, 6 > 7, 9 >= 9, 10 >= 10, 11 >= 11
- new_foldFM_LE2(vyy340, vyy341, vyy67, vyy40, vyy3440, vyy3441, vyy3442, vyy3443, vyy3444, h, ba, bb) → new_foldFM_LE1(new_fmToList_LE0(vyy340, vyy341, vyy67, h, ba, bb), vyy40, vyy3440, vyy3441, vyy3442, vyy3443, vyy3444, new_ltEs13(vyy3440, Right(vyy40), h, ba), h, ba, bb)
The graph contains the following edges 4 >= 2, 5 >= 3, 6 >= 4, 7 >= 5, 8 >= 6, 9 >= 7, 10 >= 9, 11 >= 10, 12 >= 11
- new_foldFM_LE(vyy51, vyy40, Branch(vyy3430, vyy3431, vyy3432, vyy3433, vyy3434), h, ba, bb) → new_foldFM_LE1(vyy51, vyy40, vyy3430, vyy3431, vyy3432, vyy3433, vyy3434, new_ltEs13(vyy3430, Right(vyy40), h, ba), h, ba, bb)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 3 > 4, 3 > 5, 3 > 6, 3 > 7, 4 >= 9, 5 >= 10, 6 >= 11
- new_foldFM_LE1(vyy51, vyy40, vyy340, vyy341, vyy342, vyy343, Branch(vyy3440, vyy3441, vyy3442, vyy3443, vyy3444), True, h, ba, bb) → new_foldFM_LE(vyy51, vyy40, vyy343, h, ba, bb)
The graph contains the following edges 1 >= 1, 2 >= 2, 6 >= 3, 9 >= 4, 10 >= 5, 11 >= 6
- new_foldFM_LE1(vyy51, vyy40, vyy340, vyy341, vyy342, vyy343, EmptyFM, True, h, ba, bb) → new_foldFM_LE(vyy51, vyy40, vyy343, h, ba, bb)
The graph contains the following edges 1 >= 1, 2 >= 2, 6 >= 3, 9 >= 4, 10 >= 5, 11 >= 6
↳ 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
↳ QDPSizeChangeProof
Q DP problem:
The TRS P consists of the following rules:
new_foldFM_LE21(vyy76, vyy13, vyy1840, vyy1841, vyy1842, vyy1843, vyy1844, h, ba, bb) → new_foldFM_LE11(vyy76, vyy13, vyy1840, vyy1841, vyy1842, vyy1843, vyy1844, new_ltEs13(vyy1840, Left(vyy13), h, ba), h, ba, bb)
new_foldFM_LE4(vyy65, vyy13, Branch(vyy1830, vyy1831, vyy1832, vyy1833, vyy1834), h, ba, bb) → new_foldFM_LE21(vyy65, vyy13, vyy1830, vyy1831, vyy1832, vyy1833, vyy1834, h, ba, bb)
new_foldFM_LE11(vyy65, vyy13, vyy180, vyy181, vyy182, vyy183, Branch(vyy1840, vyy1841, vyy1842, vyy1843, vyy1844), True, h, ba, bb) → new_foldFM_LE4(vyy65, vyy13, vyy183, h, ba, bb)
new_foldFM_LE11(vyy65, vyy13, vyy180, vyy181, vyy182, vyy183, Branch(vyy1840, vyy1841, vyy1842, vyy1843, vyy1844), True, h, ba, bb) → new_foldFM_LE21(new_fmToList_LE0(vyy180, vyy181, new_foldFM_LE5(vyy65, vyy13, vyy183, h, ba, bb), h, ba, bb), vyy13, vyy1840, vyy1841, vyy1842, vyy1843, vyy1844, h, ba, bb)
new_foldFM_LE11(vyy65, vyy13, vyy180, vyy181, vyy182, Branch(vyy1830, vyy1831, vyy1832, vyy1833, vyy1834), vyy184, False, h, ba, bb) → new_foldFM_LE21(vyy65, vyy13, vyy1830, vyy1831, vyy1832, vyy1833, vyy1834, h, ba, bb)
new_foldFM_LE11(vyy65, vyy13, vyy180, vyy181, vyy182, vyy183, EmptyFM, True, h, ba, bb) → new_foldFM_LE4(vyy65, vyy13, vyy183, h, ba, bb)
The TRS R consists of the following rules:
new_esEs23(GT, LT) → False
new_esEs23(LT, GT) → False
new_esEs7(Just(vyy580), Just(vyy590), app(ty_Maybe, bce)) → new_esEs7(vyy580, vyy590, bce)
new_ltEs19(vyy3001, vyy401, ty_Integer) → new_ltEs16(vyy3001, vyy401)
new_esEs28(vyy581, vyy591, app(ty_[], dch)) → new_esEs19(vyy581, vyy591, dch)
new_lt16(vyy3000, vyy400) → new_esEs9(new_compare26(vyy3000, vyy400))
new_compare16(vyy3000, vyy400) → new_compare211(vyy3000, vyy400, new_esEs21(vyy3000, vyy400))
new_ltEs4(EQ, GT) → True
new_esEs26(vyy580, vyy590, app(app(ty_FiniteMap, cab), cac)) → new_esEs17(vyy580, vyy590, cab, cac)
new_lt5(vyy3001, vyy401, ty_Char) → new_lt19(vyy3001, vyy401)
new_esEs29(vyy580, vyy590, app(app(app(ty_@3, dee), def), deg)) → new_esEs8(vyy580, vyy590, dee, def, deg)
new_esEs27(vyy582, vyy592, ty_Char) → new_esEs22(vyy582, vyy592)
new_ltEs8(vyy3002, vyy402, ty_Int) → new_ltEs9(vyy3002, vyy402)
new_esEs29(vyy580, vyy590, app(ty_[], ded)) → new_esEs19(vyy580, vyy590, ded)
new_compare14(vyy3000, vyy400, ty_Bool) → new_compare16(vyy3000, vyy400)
new_esEs16(vyy58, vyy59, ty_Char) → new_esEs22(vyy58, vyy59)
new_esEs11(Integer(vyy580), Integer(vyy590)) → new_primEqInt(vyy580, vyy590)
new_foldFM_LE12(vyy65, vyy13, vyy180, vyy181, vyy182, vyy183, Branch(vyy1840, vyy1841, vyy1842, vyy1843, vyy1844), True, h, ba, bb) → new_foldFM_LE22(new_fmToList_LE0(vyy180, vyy181, new_foldFM_LE5(vyy65, vyy13, vyy183, h, ba, bb), h, ba, bb), vyy13, vyy1840, vyy1841, vyy1842, vyy1843, vyy1844, h, ba, bb)
new_esEs27(vyy582, vyy592, app(ty_Maybe, dbh)) → new_esEs7(vyy582, vyy592, dbh)
new_esEs28(vyy581, vyy591, ty_Integer) → new_esEs11(vyy581, vyy591)
new_esEs26(vyy580, vyy590, ty_Integer) → new_esEs11(vyy580, vyy590)
new_foldFM_LE30(vyy74, vyy13, h, ba, bb) → vyy74
new_fmToList_LE0(vyy340, vyy341, vyy66, bgc, bgd, bge) → :(@2(vyy340, vyy341), vyy66)
new_esEs16(vyy58, vyy59, app(ty_Ratio, bh)) → new_esEs12(vyy58, vyy59, bh)
new_esEs24(vyy580, vyy590, app(app(ty_FiniteMap, bed), bee)) → new_esEs17(vyy580, vyy590, bed, bee)
new_ltEs6(True, False) → False
new_ltEs13(Right(vyy3000), Right(vyy400), chf, app(app(app(ty_@3, daf), dag), dah)) → new_ltEs7(vyy3000, vyy400, daf, dag, dah)
new_esEs7(Just(vyy580), Just(vyy590), app(app(ty_Either, bcf), bcg)) → new_esEs6(vyy580, vyy590, bcf, bcg)
new_primMulNat0(Zero, Zero) → Zero
new_ltEs13(Left(vyy3000), Left(vyy400), app(app(ty_@2, cgd), cge), cgc) → new_ltEs10(vyy3000, vyy400, cgd, cge)
new_esEs25(vyy581, vyy591, app(app(ty_Either, bhf), bhg)) → new_esEs6(vyy581, vyy591, bhf, bhg)
new_lt6(vyy3000, vyy400, app(ty_Ratio, ga)) → new_lt15(vyy3000, vyy400, ga)
new_esEs29(vyy580, vyy590, ty_Char) → new_esEs22(vyy580, vyy590)
new_lt20(vyy3000, vyy400, app(app(ty_@2, bc), bd)) → new_lt8(vyy3000, vyy400, bc, bd)
new_esEs9(LT) → True
new_lt20(vyy3000, vyy400, app(app(app(ty_@3, be), bf), bg)) → new_lt4(vyy3000, vyy400, be, bf, bg)
new_esEs29(vyy580, vyy590, ty_@0) → new_esEs20(vyy580, vyy590)
new_lt19(vyy3000, vyy400) → new_esEs9(new_compare28(vyy3000, vyy400))
new_foldFM_LE22(vyy76, vyy13, vyy1840, vyy1841, vyy1842, vyy1843, vyy1844, h, ba, bb) → new_foldFM_LE12(vyy76, vyy13, vyy1840, vyy1841, vyy1842, vyy1843, vyy1844, new_ltEs13(vyy1840, Left(vyy13), h, ba), h, ba, bb)
new_not(GT) → False
new_esEs26(vyy580, vyy590, app(ty_[], cae)) → new_esEs19(vyy580, vyy590, cae)
new_lt5(vyy3001, vyy401, ty_Ordering) → new_lt13(vyy3001, vyy401)
new_esEs6(Left(vyy580), Left(vyy590), app(app(app(ty_@3, cdg), cdh), cea), hf) → new_esEs8(vyy580, vyy590, cdg, cdh, cea)
new_esEs29(vyy580, vyy590, app(ty_Maybe, deh)) → new_esEs7(vyy580, vyy590, deh)
new_lt20(vyy3000, vyy400, ty_Double) → new_lt14(vyy3000, vyy400)
new_esEs16(vyy58, vyy59, ty_Ordering) → new_esEs23(vyy58, vyy59)
new_lt5(vyy3001, vyy401, app(ty_Ratio, ef)) → new_lt15(vyy3001, vyy401, ef)
new_esEs16(vyy58, vyy59, ty_Integer) → new_esEs11(vyy58, vyy59)
new_esEs16(vyy58, vyy59, app(app(ty_Either, he), hf)) → new_esEs6(vyy58, vyy59, he, hf)
new_lt6(vyy3000, vyy400, app(app(ty_@2, fd), ff)) → new_lt8(vyy3000, vyy400, fd, ff)
new_compare0(:(vyy3000, vyy3001), :(vyy400, vyy401), ca) → new_primCompAux0(vyy3000, vyy400, new_compare0(vyy3001, vyy401, ca), ca)
new_ltEs17(Just(vyy3000), Just(vyy400), app(ty_Ratio, bah)) → new_ltEs15(vyy3000, vyy400, bah)
new_compare18(Double(vyy3000, vyy3001), Double(vyy400, vyy401)) → new_compare9(new_sr(vyy3000, vyy400), new_sr(vyy3001, vyy401))
new_ltEs13(Right(vyy3000), Right(vyy400), chf, app(ty_Maybe, dae)) → new_ltEs17(vyy3000, vyy400, dae)
new_esEs24(vyy580, vyy590, app(app(ty_@2, bff), bfg)) → new_esEs5(vyy580, vyy590, bff, bfg)
new_lt20(vyy3000, vyy400, ty_Integer) → new_lt16(vyy3000, vyy400)
new_esEs26(vyy580, vyy590, ty_Float) → new_esEs18(vyy580, vyy590)
new_esEs25(vyy581, vyy591, ty_Double) → new_esEs15(vyy581, vyy591)
new_esEs26(vyy580, vyy590, app(app(app(ty_@3, caf), cag), cah)) → new_esEs8(vyy580, vyy590, caf, cag, cah)
new_lt6(vyy3000, vyy400, ty_Char) → new_lt19(vyy3000, vyy400)
new_esEs25(vyy581, vyy591, ty_Bool) → new_esEs21(vyy581, vyy591)
new_esEs29(vyy580, vyy590, ty_Float) → new_esEs18(vyy580, vyy590)
new_esEs28(vyy581, vyy591, ty_Bool) → new_esEs21(vyy581, vyy591)
new_ltEs13(Right(vyy3000), Right(vyy400), chf, app(ty_Ratio, dac)) → new_ltEs15(vyy3000, vyy400, dac)
new_foldFM0(vyy590, vyy591, vyy96, EmptyFM, cb, cc) → :(@2(vyy590, vyy591), vyy96)
new_esEs16(vyy58, vyy59, ty_Float) → new_esEs18(vyy58, vyy59)
new_ltEs19(vyy3001, vyy401, ty_Char) → new_ltEs18(vyy3001, vyy401)
new_esEs28(vyy581, vyy591, app(app(app(ty_@3, dda), ddb), ddc)) → new_esEs8(vyy581, vyy591, dda, ddb, ddc)
new_esEs7(Just(vyy580), Just(vyy590), ty_Int) → new_esEs10(vyy580, vyy590)
new_ltEs14(vyy300, vyy40) → new_not(new_compare18(vyy300, vyy40))
new_esEs20(@0, @0) → True
new_esEs5(@2(vyy580, vyy581), @2(vyy590, vyy591), hg, hh) → new_asAs(new_esEs26(vyy580, vyy590, hg), new_esEs25(vyy581, vyy591, hh))
new_esEs22(Char(vyy580), Char(vyy590)) → new_primEqNat0(vyy580, vyy590)
new_ltEs13(Left(vyy3000), Left(vyy400), app(ty_[], cha), cgc) → new_ltEs5(vyy3000, vyy400, cha)
new_esEs28(vyy581, vyy591, ty_Float) → new_esEs18(vyy581, vyy591)
new_lt20(vyy3000, vyy400, ty_Float) → new_lt10(vyy3000, vyy400)
new_compare14(vyy3000, vyy400, ty_Int) → new_compare9(vyy3000, vyy400)
new_ltEs17(Just(vyy3000), Nothing, bac) → False
new_lt6(vyy3000, vyy400, ty_Ordering) → new_lt13(vyy3000, vyy400)
new_esEs24(vyy580, vyy590, app(ty_Maybe, bfc)) → new_esEs7(vyy580, vyy590, bfc)
new_lt4(vyy3000, vyy400, be, bf, bg) → new_esEs9(new_compare7(vyy3000, vyy400, be, bf, bg))
new_lt6(vyy3000, vyy400, ty_Integer) → new_lt16(vyy3000, vyy400)
new_esEs6(Right(vyy580), Right(vyy590), he, app(app(ty_FiniteMap, ceg), ceh)) → new_esEs17(vyy580, vyy590, ceg, ceh)
new_ltEs17(Just(vyy3000), Just(vyy400), app(ty_[], bba)) → new_ltEs5(vyy3000, vyy400, bba)
new_compare9(vyy300, vyy40) → new_primCmpInt(vyy300, vyy40)
new_esEs28(vyy581, vyy591, ty_@0) → new_esEs20(vyy581, vyy591)
new_ltEs8(vyy3002, vyy402, app(app(ty_@2, cg), da)) → new_ltEs10(vyy3002, vyy402, cg, da)
new_compare15(@0, @0) → EQ
new_ltEs13(Left(vyy3000), Left(vyy400), ty_Int, cgc) → new_ltEs9(vyy3000, vyy400)
new_primCompAux0(vyy3000, vyy400, vyy78, ca) → new_primCompAux00(vyy78, new_compare14(vyy3000, vyy400, ca))
new_compare13(vyy3000, vyy400, False, baa, bab) → GT
new_esEs24(vyy580, vyy590, app(ty_[], beg)) → new_esEs19(vyy580, vyy590, beg)
new_lt6(vyy3000, vyy400, ty_@0) → new_lt9(vyy3000, vyy400)
new_ltEs15(vyy300, vyy40, bfh) → new_not(new_compare19(vyy300, vyy40, bfh))
new_esEs6(Right(vyy580), Right(vyy590), he, app(app(app(ty_@3, cfc), cfd), cfe)) → new_esEs8(vyy580, vyy590, cfc, cfd, cfe)
new_primCmpNat0(Zero, Succ(vyy4000)) → LT
new_ltEs19(vyy3001, vyy401, app(ty_Ratio, ccd)) → new_ltEs15(vyy3001, vyy401, ccd)
new_esEs6(Left(vyy580), Left(vyy590), ty_Integer, hf) → new_esEs11(vyy580, vyy590)
new_ltEs8(vyy3002, vyy402, ty_Double) → new_ltEs14(vyy3002, vyy402)
new_compare6(vyy3000, vyy400, bc, bd) → new_compare23(vyy3000, vyy400, new_esEs5(vyy3000, vyy400, bc, bd), bc, bd)
new_ltEs19(vyy3001, vyy401, ty_Bool) → new_ltEs6(vyy3001, vyy401)
new_esEs13(vyy581, vyy591, ty_Integer) → new_esEs11(vyy581, vyy591)
new_esEs6(Right(vyy580), Left(vyy590), he, hf) → False
new_esEs6(Left(vyy580), Right(vyy590), he, hf) → False
new_compare7(vyy3000, vyy400, be, bf, bg) → new_compare29(vyy3000, vyy400, new_esEs8(vyy3000, vyy400, be, bf, bg), be, bf, bg)
new_lt20(vyy3000, vyy400, ty_Char) → new_lt19(vyy3000, vyy400)
new_compare14(vyy3000, vyy400, app(ty_[], bdg)) → new_compare0(vyy3000, vyy400, bdg)
new_lt17(vyy3000, vyy400, bgb) → new_esEs9(new_compare0(vyy3000, vyy400, bgb))
new_esEs28(vyy581, vyy591, ty_Double) → new_esEs15(vyy581, vyy591)
new_esEs6(Right(vyy580), Right(vyy590), he, ty_Bool) → new_esEs21(vyy580, vyy590)
new_ltEs17(Just(vyy3000), Just(vyy400), app(app(ty_@2, bad), bae)) → new_ltEs10(vyy3000, vyy400, bad, bae)
new_esEs21(True, True) → True
new_esEs15(Double(vyy580, vyy581), Double(vyy590, vyy591)) → new_esEs10(new_sr(vyy580, vyy590), new_sr(vyy581, vyy591))
new_compare0([], [], ca) → EQ
new_esEs16(vyy58, vyy59, ty_Bool) → new_esEs21(vyy58, vyy59)
new_primEqNat0(Zero, Zero) → True
new_esEs8(@3(vyy580, vyy581, vyy582), @3(vyy590, vyy591, vyy592), ha, hb, hc) → new_asAs(new_esEs29(vyy580, vyy590, ha), new_asAs(new_esEs28(vyy581, vyy591, hb), new_esEs27(vyy582, vyy592, hc)))
new_esEs28(vyy581, vyy591, ty_Ordering) → new_esEs23(vyy581, vyy591)
new_ltEs13(Right(vyy3000), Right(vyy400), chf, ty_Double) → new_ltEs14(vyy3000, vyy400)
new_esEs6(Left(vyy580), Left(vyy590), app(ty_[], cdf), hf) → new_esEs19(vyy580, vyy590, cdf)
new_esEs14(vyy580, vyy590, ty_Int) → new_esEs10(vyy580, vyy590)
new_esEs6(Left(vyy580), Left(vyy590), ty_@0, hf) → new_esEs20(vyy580, vyy590)
new_compare19(:%(vyy3000, vyy3001), :%(vyy400, vyy401), ty_Integer) → new_compare26(new_sr0(vyy3000, vyy401), new_sr0(vyy400, vyy3001))
new_compare29(vyy3000, vyy400, False, be, bf, bg) → new_compare110(vyy3000, vyy400, new_ltEs7(vyy3000, vyy400, be, bf, bg), be, bf, bg)
new_esEs6(Right(vyy580), Right(vyy590), he, app(app(ty_Either, cfg), cfh)) → new_esEs6(vyy580, vyy590, cfg, cfh)
new_esEs6(Left(vyy580), Left(vyy590), ty_Double, hf) → new_esEs15(vyy580, vyy590)
new_ltEs7(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), cd, ce, cf) → new_pePe(new_lt6(vyy3000, vyy400, cd), vyy3000, vyy400, new_pePe(new_lt5(vyy3001, vyy401, ce), vyy3001, vyy401, new_ltEs8(vyy3002, vyy402, cf), ce), cd)
new_esEs19([], [], gh) → True
new_esEs25(vyy581, vyy591, app(ty_[], bha)) → new_esEs19(vyy581, vyy591, bha)
new_esEs12(:%(vyy580, vyy581), :%(vyy590, vyy591), bh) → new_asAs(new_esEs14(vyy580, vyy590, bh), new_esEs13(vyy581, vyy591, bh))
new_sr(vyy3001, vyy401) → new_primMulInt(vyy3001, vyy401)
new_esEs16(vyy58, vyy59, ty_@0) → new_esEs20(vyy58, vyy59)
new_foldFM_LE12(vyy65, vyy13, vyy180, vyy181, vyy182, vyy183, EmptyFM, True, h, ba, bb) → new_foldFM_LE30(new_fmToList_LE0(vyy180, vyy181, new_foldFM_LE5(vyy65, vyy13, vyy183, h, ba, bb), h, ba, bb), vyy13, h, ba, bb)
new_esEs28(vyy581, vyy591, app(app(ty_Either, dde), ddf)) → new_esEs6(vyy581, vyy591, dde, ddf)
new_ltEs8(vyy3002, vyy402, ty_@0) → new_ltEs11(vyy3002, vyy402)
new_ltEs18(vyy300, vyy40) → new_not(new_compare28(vyy300, vyy40))
new_esEs6(Right(vyy580), Right(vyy590), he, ty_Double) → new_esEs15(vyy580, vyy590)
new_ltEs13(Right(vyy3000), Right(vyy400), chf, ty_Float) → new_ltEs12(vyy3000, vyy400)
new_esEs27(vyy582, vyy592, ty_@0) → new_esEs20(vyy582, vyy592)
new_primPlusNat0(Succ(vyy970), vyy40100) → Succ(Succ(new_primPlusNat1(vyy970, vyy40100)))
new_esEs7(Just(vyy580), Just(vyy590), ty_Char) → new_esEs22(vyy580, vyy590)
new_esEs27(vyy582, vyy592, app(app(ty_FiniteMap, dba), dbb)) → new_esEs17(vyy582, vyy592, dba, dbb)
new_esEs6(Right(vyy580), Right(vyy590), he, ty_Float) → new_esEs18(vyy580, vyy590)
new_lt6(vyy3000, vyy400, app(app(ty_Either, fg), fh)) → new_lt11(vyy3000, vyy400, fg, fh)
new_esEs19(:(vyy580, vyy581), [], gh) → False
new_esEs19([], :(vyy590, vyy591), gh) → False
new_ltEs8(vyy3002, vyy402, app(app(app(ty_@3, dg), dh), ea)) → new_ltEs7(vyy3002, vyy402, dg, dh, ea)
new_compare29(vyy3000, vyy400, True, be, bf, bg) → EQ
new_ltEs8(vyy3002, vyy402, ty_Ordering) → new_ltEs4(vyy3002, vyy402)
new_esEs26(vyy580, vyy590, ty_Ordering) → new_esEs23(vyy580, vyy590)
new_primEqInt(Neg(Succ(vyy5800)), Neg(Succ(vyy5900))) → new_primEqNat0(vyy5800, vyy5900)
new_ltEs19(vyy3001, vyy401, app(app(ty_@2, cbh), cca)) → new_ltEs10(vyy3001, vyy401, cbh, cca)
new_compare13(vyy3000, vyy400, True, baa, bab) → LT
new_esEs9(GT) → False
new_ltEs17(Just(vyy3000), Just(vyy400), app(app(app(ty_@3, bbc), bbd), bbe)) → new_ltEs7(vyy3000, vyy400, bbc, bbd, bbe)
new_primPlusNat1(Zero, Succ(vyy401000)) → Succ(vyy401000)
new_primPlusNat1(Succ(vyy9700), Zero) → Succ(vyy9700)
new_foldFM_LE5(vyy65, vyy13, Branch(vyy1830, vyy1831, vyy1832, vyy1833, vyy1834), h, ba, bb) → new_foldFM_LE22(vyy65, vyy13, vyy1830, vyy1831, vyy1832, vyy1833, vyy1834, h, ba, bb)
new_lt5(vyy3001, vyy401, ty_Int) → new_lt7(vyy3001, vyy401)
new_esEs9(EQ) → False
new_esEs16(vyy58, vyy59, app(app(ty_FiniteMap, cb), cc)) → new_esEs17(vyy58, vyy59, cb, cc)
new_esEs7(Just(vyy580), Just(vyy590), ty_@0) → new_esEs20(vyy580, vyy590)
new_ltEs13(Right(vyy3000), Right(vyy400), chf, ty_Int) → new_ltEs9(vyy3000, vyy400)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_lt20(vyy3000, vyy400, app(ty_Maybe, bga)) → new_lt18(vyy3000, vyy400, bga)
new_esEs23(EQ, EQ) → True
new_ltEs19(vyy3001, vyy401, ty_Ordering) → new_ltEs4(vyy3001, vyy401)
new_ltEs8(vyy3002, vyy402, ty_Bool) → new_ltEs6(vyy3002, vyy402)
new_esEs6(Right(vyy580), Right(vyy590), he, app(ty_[], cfb)) → new_esEs19(vyy580, vyy590, cfb)
new_lt11(vyy3000, vyy400, baa, bab) → new_esEs9(new_compare12(vyy3000, vyy400, baa, bab))
new_primEqInt(Neg(Zero), Neg(Succ(vyy5900))) → False
new_primEqInt(Neg(Succ(vyy5800)), Neg(Zero)) → False
new_compare14(vyy3000, vyy400, app(app(app(ty_@3, bea), beb), bec)) → new_compare7(vyy3000, vyy400, bea, beb, bec)
new_esEs16(vyy58, vyy59, app(app(app(ty_@3, ha), hb), hc)) → new_esEs8(vyy58, vyy59, ha, hb, hc)
new_esEs6(Left(vyy580), Left(vyy590), ty_Char, hf) → new_esEs22(vyy580, vyy590)
new_lt5(vyy3001, vyy401, ty_@0) → new_lt9(vyy3001, vyy401)
new_compare111(vyy3000, vyy400, True, bga) → LT
new_lt5(vyy3001, vyy401, app(ty_[], eg)) → new_lt17(vyy3001, vyy401, eg)
new_lt20(vyy3000, vyy400, ty_Ordering) → new_lt13(vyy3000, vyy400)
new_esEs7(Just(vyy580), Just(vyy590), ty_Bool) → new_esEs21(vyy580, vyy590)
new_esEs24(vyy580, vyy590, ty_Ordering) → new_esEs23(vyy580, vyy590)
new_foldFM0(vyy590, vyy591, vyy96, Branch(vyy5930, vyy5931, vyy5932, vyy5933, vyy5934), cb, cc) → new_foldFM0(vyy5930, vyy5931, new_foldFM0(vyy590, vyy591, vyy96, vyy5934, cb, cc), vyy5933, cb, cc)
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_esEs25(vyy581, vyy591, ty_Ordering) → new_esEs23(vyy581, vyy591)
new_ltEs4(EQ, LT) → False
new_lt10(vyy3000, vyy400) → new_esEs9(new_compare8(vyy3000, vyy400))
new_esEs7(Just(vyy580), Just(vyy590), ty_Integer) → new_esEs11(vyy580, vyy590)
new_primCmpNat0(Succ(vyy30000), Succ(vyy4000)) → new_primCmpNat0(vyy30000, vyy4000)
new_ltEs19(vyy3001, vyy401, ty_@0) → new_ltEs11(vyy3001, vyy401)
new_esEs7(Just(vyy580), Just(vyy590), app(app(ty_FiniteMap, bbf), bbg)) → new_esEs17(vyy580, vyy590, bbf, bbg)
new_esEs7(Just(vyy580), Just(vyy590), ty_Ordering) → new_esEs23(vyy580, vyy590)
new_sizeFM(EmptyFM, cb, cc) → Pos(Zero)
new_compare112(vyy3000, vyy400, True) → LT
new_ltEs8(vyy3002, vyy402, app(ty_Ratio, dd)) → new_ltEs15(vyy3002, vyy402, dd)
new_primEqInt(Pos(Succ(vyy5800)), Pos(Succ(vyy5900))) → new_primEqNat0(vyy5800, vyy5900)
new_ltEs19(vyy3001, vyy401, app(app(app(ty_@3, ccg), cch), cda)) → new_ltEs7(vyy3001, vyy401, ccg, cch, cda)
new_esEs16(vyy58, vyy59, ty_Int) → new_esEs10(vyy58, vyy59)
new_ltEs17(Just(vyy3000), Just(vyy400), ty_@0) → new_ltEs11(vyy3000, vyy400)
new_foldFM_LE5(vyy65, vyy13, EmptyFM, h, ba, bb) → new_foldFM_LE30(vyy65, vyy13, h, ba, bb)
new_lt20(vyy3000, vyy400, ty_Int) → new_lt7(vyy3000, vyy400)
new_ltEs6(False, True) → True
new_primEqNat0(Succ(vyy5800), Succ(vyy5900)) → new_primEqNat0(vyy5800, vyy5900)
new_ltEs6(True, True) → True
new_esEs27(vyy582, vyy592, app(app(app(ty_@3, dbe), dbf), dbg)) → new_esEs8(vyy582, vyy592, dbe, dbf, dbg)
new_ltEs19(vyy3001, vyy401, app(app(ty_Either, ccb), ccc)) → new_ltEs13(vyy3001, vyy401, ccb, ccc)
new_lt5(vyy3001, vyy401, ty_Bool) → new_lt12(vyy3001, vyy401)
new_esEs6(Right(vyy580), Right(vyy590), he, app(app(ty_@2, cga), cgb)) → new_esEs5(vyy580, vyy590, cga, cgb)
new_ltEs19(vyy3001, vyy401, ty_Double) → new_ltEs14(vyy3001, vyy401)
new_esEs29(vyy580, vyy590, ty_Int) → new_esEs10(vyy580, vyy590)
new_ltEs4(GT, EQ) → False
new_primCompAux00(vyy82, LT) → LT
new_esEs24(vyy580, vyy590, app(ty_Ratio, bef)) → new_esEs12(vyy580, vyy590, bef)
new_primCmpInt(Neg(Succ(vyy30000)), Neg(vyy400)) → new_primCmpNat0(vyy400, Succ(vyy30000))
new_esEs7(Nothing, Nothing, hd) → True
new_esEs23(GT, GT) → True
new_primEqInt(Pos(Zero), Pos(Succ(vyy5900))) → False
new_primEqInt(Pos(Succ(vyy5800)), Pos(Zero)) → False
new_compare24(vyy3000, vyy400, False) → new_compare10(vyy3000, vyy400, new_ltEs4(vyy3000, vyy400))
new_ltEs4(EQ, EQ) → True
new_lt5(vyy3001, vyy401, app(app(ty_Either, ed), ee)) → new_lt11(vyy3001, vyy401, ed, ee)
new_lt7(vyy3000, vyy400) → new_esEs9(new_compare9(vyy3000, vyy400))
new_primCmpNat0(Zero, Zero) → EQ
new_ltEs13(Left(vyy3000), Left(vyy400), app(app(app(ty_@3, chc), chd), che), cgc) → new_ltEs7(vyy3000, vyy400, chc, chd, che)
new_esEs6(Right(vyy580), Right(vyy590), he, app(ty_Maybe, cff)) → new_esEs7(vyy580, vyy590, cff)
new_primCmpNat0(Succ(vyy30000), Zero) → GT
new_esEs14(vyy580, vyy590, ty_Integer) → new_esEs11(vyy580, vyy590)
new_esEs7(Just(vyy580), Just(vyy590), app(app(app(ty_@3, bcb), bcc), bcd)) → new_esEs8(vyy580, vyy590, bcb, bcc, bcd)
new_primCmpInt(Neg(Zero), Pos(Succ(vyy4000))) → LT
new_compare11(vyy3000, vyy400, True, bc, bd) → LT
new_esEs6(Right(vyy580), Right(vyy590), he, ty_@0) → new_esEs20(vyy580, vyy590)
new_ltEs4(GT, LT) → False
new_sr0(Integer(vyy4000), Integer(vyy30010)) → Integer(new_primMulInt(vyy4000, vyy30010))
new_primPlusNat1(Succ(vyy9700), Succ(vyy401000)) → Succ(Succ(new_primPlusNat1(vyy9700, vyy401000)))
new_compare27(vyy3000, vyy400, bga) → new_compare210(vyy3000, vyy400, new_esEs7(vyy3000, vyy400, bga), bga)
new_primEqInt(Neg(Succ(vyy5800)), Pos(vyy590)) → False
new_primEqInt(Pos(Succ(vyy5800)), Neg(vyy590)) → False
new_esEs25(vyy581, vyy591, ty_Int) → new_esEs10(vyy581, vyy591)
new_esEs7(Nothing, Just(vyy590), hd) → False
new_esEs7(Just(vyy580), Nothing, hd) → False
new_compare210(vyy3000, vyy400, True, bga) → EQ
new_esEs26(vyy580, vyy590, ty_Char) → new_esEs22(vyy580, vyy590)
new_foldFM2(EmptyFM, cb, cc) → []
new_ltEs17(Just(vyy3000), Just(vyy400), ty_Integer) → new_ltEs16(vyy3000, vyy400)
new_esEs29(vyy580, vyy590, app(app(ty_@2, dfc), dfd)) → new_esEs5(vyy580, vyy590, dfc, dfd)
new_ltEs13(Right(vyy3000), Right(vyy400), chf, app(ty_[], dad)) → new_ltEs5(vyy3000, vyy400, dad)
new_ltEs13(Right(vyy3000), Right(vyy400), chf, ty_@0) → new_ltEs11(vyy3000, vyy400)
new_esEs26(vyy580, vyy590, ty_Int) → new_esEs10(vyy580, vyy590)
new_primEqInt(Neg(Zero), Pos(Succ(vyy5900))) → False
new_primEqInt(Pos(Zero), Neg(Succ(vyy5900))) → False
new_esEs29(vyy580, vyy590, ty_Integer) → new_esEs11(vyy580, vyy590)
new_primCmpInt(Pos(Zero), Pos(Succ(vyy4000))) → new_primCmpNat0(Zero, Succ(vyy4000))
new_primCompAux00(vyy82, EQ) → vyy82
new_foldFM_LE12(vyy65, vyy13, vyy180, vyy181, vyy182, vyy183, vyy184, False, h, ba, bb) → new_foldFM_LE5(vyy65, vyy13, vyy183, h, ba, bb)
new_compare24(vyy3000, vyy400, True) → EQ
new_esEs7(Just(vyy580), Just(vyy590), ty_Float) → new_esEs18(vyy580, vyy590)
new_ltEs13(Left(vyy3000), Left(vyy400), ty_Float, cgc) → new_ltEs12(vyy3000, vyy400)
new_esEs26(vyy580, vyy590, app(app(ty_@2, cbd), cbe)) → new_esEs5(vyy580, vyy590, cbd, cbe)
new_ltEs17(Just(vyy3000), Just(vyy400), ty_Ordering) → new_ltEs4(vyy3000, vyy400)
new_ltEs8(vyy3002, vyy402, ty_Float) → new_ltEs12(vyy3002, vyy402)
new_ltEs17(Just(vyy3000), Just(vyy400), ty_Int) → new_ltEs9(vyy3000, vyy400)
new_esEs26(vyy580, vyy590, ty_Bool) → new_esEs21(vyy580, vyy590)
new_esEs6(Left(vyy580), Left(vyy590), app(app(ty_Either, cec), ced), hf) → new_esEs6(vyy580, vyy590, cec, ced)
new_esEs6(Left(vyy580), Left(vyy590), app(ty_Ratio, cde), hf) → new_esEs12(vyy580, vyy590, cde)
new_primPlusNat0(Zero, vyy40100) → Succ(vyy40100)
new_primCmpInt(Pos(Succ(vyy30000)), Pos(vyy400)) → new_primCmpNat0(Succ(vyy30000), vyy400)
new_lt6(vyy3000, vyy400, app(app(app(ty_@3, gd), ge), gf)) → new_lt4(vyy3000, vyy400, gd, ge, gf)
new_esEs24(vyy580, vyy590, app(app(ty_Either, bfd), bfe)) → new_esEs6(vyy580, vyy590, bfd, bfe)
new_esEs25(vyy581, vyy591, ty_Float) → new_esEs18(vyy581, vyy591)
new_compare14(vyy3000, vyy400, app(ty_Maybe, bdh)) → new_compare27(vyy3000, vyy400, bdh)
new_compare14(vyy3000, vyy400, app(app(ty_@2, bdb), bdc)) → new_compare6(vyy3000, vyy400, bdb, bdc)
new_ltEs13(Left(vyy3000), Left(vyy400), ty_Bool, cgc) → new_ltEs6(vyy3000, vyy400)
new_not0 → True
new_esEs28(vyy581, vyy591, app(app(ty_@2, ddg), ddh)) → new_esEs5(vyy581, vyy591, ddg, ddh)
new_compare0(:(vyy3000, vyy3001), [], ca) → GT
new_esEs24(vyy580, vyy590, ty_Bool) → new_esEs21(vyy580, vyy590)
new_esEs27(vyy582, vyy592, app(app(ty_Either, dca), dcb)) → new_esEs6(vyy582, vyy592, dca, dcb)
new_ltEs13(Left(vyy3000), Left(vyy400), app(ty_Ratio, cgh), cgc) → new_ltEs15(vyy3000, vyy400, cgh)
new_esEs18(Float(vyy580, vyy581), Float(vyy590, vyy591)) → new_esEs10(new_sr(vyy580, vyy590), new_sr(vyy581, vyy591))
new_esEs28(vyy581, vyy591, app(app(ty_FiniteMap, dce), dcf)) → new_esEs17(vyy581, vyy591, dce, dcf)
new_esEs6(Right(vyy580), Right(vyy590), he, app(ty_Ratio, cfa)) → new_esEs12(vyy580, vyy590, cfa)
new_compare11(vyy3000, vyy400, False, bc, bd) → GT
new_lt15(vyy3000, vyy400, cdb) → new_esEs9(new_compare19(vyy3000, vyy400, cdb))
new_esEs25(vyy581, vyy591, ty_Integer) → new_esEs11(vyy581, vyy591)
new_primCmpInt(Pos(Succ(vyy30000)), Neg(vyy400)) → GT
new_ltEs19(vyy3001, vyy401, ty_Int) → new_ltEs9(vyy3001, vyy401)
new_esEs28(vyy581, vyy591, app(ty_Maybe, ddd)) → new_esEs7(vyy581, vyy591, ddd)
new_esEs24(vyy580, vyy590, ty_Float) → new_esEs18(vyy580, vyy590)
new_lt12(vyy3000, vyy400) → new_esEs9(new_compare16(vyy3000, vyy400))
new_esEs24(vyy580, vyy590, ty_Double) → new_esEs15(vyy580, vyy590)
new_primMulInt(Pos(vyy30010), Pos(vyy4010)) → Pos(new_primMulNat0(vyy30010, vyy4010))
new_ltEs5(vyy300, vyy40, ca) → new_not(new_compare0(vyy300, vyy40, ca))
new_esEs21(False, False) → True
new_esEs24(vyy580, vyy590, ty_Integer) → new_esEs11(vyy580, vyy590)
new_compare25(vyy3000, vyy400, False, baa, bab) → new_compare13(vyy3000, vyy400, new_ltEs13(vyy3000, vyy400, baa, bab), baa, bab)
new_lt8(vyy3000, vyy400, bc, bd) → new_esEs9(new_compare6(vyy3000, vyy400, bc, bd))
new_esEs6(Left(vyy580), Left(vyy590), app(app(ty_@2, cee), cef), hf) → new_esEs5(vyy580, vyy590, cee, cef)
new_compare14(vyy3000, vyy400, app(app(ty_Either, bdd), bde)) → new_compare12(vyy3000, vyy400, bdd, bde)
new_ltEs17(Nothing, Just(vyy400), bac) → True
new_esEs27(vyy582, vyy592, ty_Double) → new_esEs15(vyy582, vyy592)
new_primMulInt(Neg(vyy30010), Neg(vyy4010)) → Pos(new_primMulNat0(vyy30010, vyy4010))
new_lt6(vyy3000, vyy400, app(ty_[], gb)) → new_lt17(vyy3000, vyy400, gb)
new_ltEs17(Just(vyy3000), Just(vyy400), app(app(ty_Either, baf), bag)) → new_ltEs13(vyy3000, vyy400, baf, bag)
new_lt6(vyy3000, vyy400, app(ty_Maybe, gc)) → new_lt18(vyy3000, vyy400, gc)
new_primEqNat0(Succ(vyy5800), Zero) → False
new_primEqNat0(Zero, Succ(vyy5900)) → False
new_lt5(vyy3001, vyy401, ty_Float) → new_lt10(vyy3001, vyy401)
new_lt20(vyy3000, vyy400, app(ty_Ratio, cdb)) → new_lt15(vyy3000, vyy400, cdb)
new_lt18(vyy3000, vyy400, bga) → new_esEs9(new_compare27(vyy3000, vyy400, bga))
new_compare25(vyy3000, vyy400, True, baa, bab) → EQ
new_compare23(vyy3000, vyy400, False, bc, bd) → new_compare11(vyy3000, vyy400, new_ltEs10(vyy3000, vyy400, bc, bd), bc, bd)
new_compare211(vyy3000, vyy400, False) → new_compare112(vyy3000, vyy400, new_ltEs6(vyy3000, vyy400))
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_compare17(vyy3000, vyy400) → new_compare24(vyy3000, vyy400, new_esEs23(vyy3000, vyy400))
new_ltEs8(vyy3002, vyy402, ty_Char) → new_ltEs18(vyy3002, vyy402)
new_esEs27(vyy582, vyy592, app(app(ty_@2, dcc), dcd)) → new_esEs5(vyy582, vyy592, dcc, dcd)
new_ltEs17(Nothing, Nothing, bac) → True
new_esEs25(vyy581, vyy591, app(app(app(ty_@3, bhb), bhc), bhd)) → new_esEs8(vyy581, vyy591, bhb, bhc, bhd)
new_lt5(vyy3001, vyy401, ty_Integer) → new_lt16(vyy3001, vyy401)
new_sizeFM(Branch(vyy590, vyy591, vyy592, vyy593, vyy594), cb, cc) → vyy592
new_esEs29(vyy580, vyy590, app(app(ty_Either, dfa), dfb)) → new_esEs6(vyy580, vyy590, dfa, dfb)
new_ltEs17(Just(vyy3000), Just(vyy400), ty_Bool) → new_ltEs6(vyy3000, vyy400)
new_pePe(True, vyy58, vyy59, vyy60, gg) → True
new_ltEs4(LT, GT) → True
new_foldFM2(Branch(vyy590, vyy591, vyy592, vyy593, vyy594), cb, cc) → new_foldFM0(vyy590, vyy591, new_foldFM2(vyy594, cb, cc), vyy593, cb, cc)
new_lt20(vyy3000, vyy400, app(app(ty_Either, baa), bab)) → new_lt11(vyy3000, vyy400, baa, bab)
new_lt5(vyy3001, vyy401, ty_Double) → new_lt14(vyy3001, vyy401)
new_ltEs19(vyy3001, vyy401, app(ty_Maybe, ccf)) → new_ltEs17(vyy3001, vyy401, ccf)
new_lt20(vyy3000, vyy400, ty_@0) → new_lt9(vyy3000, vyy400)
new_lt6(vyy3000, vyy400, ty_Int) → new_lt7(vyy3000, vyy400)
new_primCmpInt(Neg(Zero), Neg(Succ(vyy4000))) → new_primCmpNat0(Succ(vyy4000), Zero)
new_compare23(vyy3000, vyy400, True, bc, bd) → EQ
new_primCmpInt(Pos(Zero), Neg(Succ(vyy4000))) → GT
new_esEs6(Left(vyy580), Left(vyy590), app(ty_Maybe, ceb), hf) → new_esEs7(vyy580, vyy590, ceb)
new_ltEs13(Left(vyy3000), Left(vyy400), ty_Char, cgc) → new_ltEs18(vyy3000, vyy400)
new_ltEs13(Left(vyy3000), Left(vyy400), app(ty_Maybe, chb), cgc) → new_ltEs17(vyy3000, vyy400, chb)
new_esEs16(vyy58, vyy59, app(ty_[], gh)) → new_esEs19(vyy58, vyy59, gh)
new_esEs28(vyy581, vyy591, app(ty_Ratio, dcg)) → new_esEs12(vyy581, vyy591, dcg)
new_ltEs13(Left(vyy3000), Left(vyy400), ty_@0, cgc) → new_ltEs11(vyy3000, vyy400)
new_esEs6(Right(vyy580), Right(vyy590), he, ty_Integer) → new_esEs11(vyy580, vyy590)
new_ltEs8(vyy3002, vyy402, app(ty_[], de)) → new_ltEs5(vyy3002, vyy402, de)
new_esEs25(vyy581, vyy591, app(app(ty_FiniteMap, bgf), bgg)) → new_esEs17(vyy581, vyy591, bgf, bgg)
new_esEs27(vyy582, vyy592, app(ty_Ratio, dbc)) → new_esEs12(vyy582, vyy592, dbc)
new_ltEs13(Left(vyy3000), Left(vyy400), app(app(ty_Either, cgf), cgg), cgc) → new_ltEs13(vyy3000, vyy400, cgf, cgg)
new_esEs6(Right(vyy580), Right(vyy590), he, ty_Char) → new_esEs22(vyy580, vyy590)
new_esEs25(vyy581, vyy591, app(ty_Maybe, bhe)) → new_esEs7(vyy581, vyy591, bhe)
new_ltEs13(Left(vyy3000), Left(vyy400), ty_Integer, cgc) → new_ltEs16(vyy3000, vyy400)
new_ltEs13(Right(vyy3000), Right(vyy400), chf, app(app(ty_Either, daa), dab)) → new_ltEs13(vyy3000, vyy400, daa, dab)
new_compare8(Float(vyy3000, vyy3001), Float(vyy400, vyy401)) → new_compare9(new_sr(vyy3000, vyy400), new_sr(vyy3001, vyy401))
new_ltEs13(Right(vyy3000), Right(vyy400), chf, ty_Ordering) → new_ltEs4(vyy3000, vyy400)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_ltEs4(LT, EQ) → True
new_compare14(vyy3000, vyy400, ty_Ordering) → new_compare17(vyy3000, vyy400)
new_compare26(Integer(vyy3000), Integer(vyy400)) → new_primCmpInt(vyy3000, vyy400)
new_esEs6(Left(vyy580), Left(vyy590), app(app(ty_FiniteMap, cdc), cdd), hf) → new_esEs17(vyy580, vyy590, cdc, cdd)
new_compare19(:%(vyy3000, vyy3001), :%(vyy400, vyy401), ty_Int) → new_compare9(new_sr(vyy3000, vyy401), new_sr(vyy400, vyy3001))
new_esEs24(vyy580, vyy590, ty_Int) → new_esEs10(vyy580, vyy590)
new_esEs27(vyy582, vyy592, ty_Float) → new_esEs18(vyy582, vyy592)
new_compare14(vyy3000, vyy400, ty_Float) → new_compare8(vyy3000, vyy400)
new_asAs(False, vyy73) → False
new_esEs6(Left(vyy580), Left(vyy590), ty_Ordering, hf) → new_esEs23(vyy580, vyy590)
new_esEs29(vyy580, vyy590, app(app(ty_FiniteMap, dea), deb)) → new_esEs17(vyy580, vyy590, dea, deb)
new_ltEs17(Just(vyy3000), Just(vyy400), ty_Double) → new_ltEs14(vyy3000, vyy400)
new_primMulInt(Neg(vyy30010), Pos(vyy4010)) → Neg(new_primMulNat0(vyy30010, vyy4010))
new_primMulInt(Pos(vyy30010), Neg(vyy4010)) → Neg(new_primMulNat0(vyy30010, vyy4010))
new_ltEs13(Right(vyy3000), Right(vyy400), chf, ty_Bool) → new_ltEs6(vyy3000, vyy400)
new_compare12(vyy3000, vyy400, baa, bab) → new_compare25(vyy3000, vyy400, new_esEs6(vyy3000, vyy400, baa, bab), baa, bab)
new_primMulNat0(Zero, Succ(vyy40100)) → Zero
new_primMulNat0(Succ(vyy300100), Zero) → Zero
new_ltEs13(Left(vyy3000), Right(vyy400), chf, cgc) → True
new_esEs25(vyy581, vyy591, ty_Char) → new_esEs22(vyy581, vyy591)
new_compare14(vyy3000, vyy400, ty_Double) → new_compare18(vyy3000, vyy400)
new_esEs27(vyy582, vyy592, ty_Ordering) → new_esEs23(vyy582, vyy592)
new_esEs23(GT, EQ) → False
new_esEs23(EQ, GT) → False
new_esEs26(vyy580, vyy590, app(ty_Maybe, cba)) → new_esEs7(vyy580, vyy590, cba)
new_esEs23(EQ, LT) → False
new_esEs23(LT, EQ) → False
new_ltEs12(vyy300, vyy40) → new_not(new_compare8(vyy300, vyy40))
new_ltEs9(vyy300, vyy40) → new_not(new_compare9(vyy300, vyy40))
new_compare110(vyy3000, vyy400, True, be, bf, bg) → LT
new_not(EQ) → new_not0
new_lt20(vyy3000, vyy400, app(ty_[], bgb)) → new_lt17(vyy3000, vyy400, bgb)
new_ltEs8(vyy3002, vyy402, app(app(ty_Either, db), dc)) → new_ltEs13(vyy3002, vyy402, db, dc)
new_lt6(vyy3000, vyy400, ty_Double) → new_lt14(vyy3000, vyy400)
new_compare14(vyy3000, vyy400, ty_Integer) → new_compare26(vyy3000, vyy400)
new_esEs6(Right(vyy580), Right(vyy590), he, ty_Int) → new_esEs10(vyy580, vyy590)
new_ltEs13(Left(vyy3000), Left(vyy400), ty_Ordering, cgc) → new_ltEs4(vyy3000, vyy400)
new_esEs29(vyy580, vyy590, app(ty_Ratio, dec)) → new_esEs12(vyy580, vyy590, dec)
new_esEs19(:(vyy580, vyy581), :(vyy590, vyy591), gh) → new_asAs(new_esEs24(vyy580, vyy590, gh), new_esEs19(vyy581, vyy591, gh))
new_ltEs13(Right(vyy3000), Right(vyy400), chf, app(app(ty_@2, chg), chh)) → new_ltEs10(vyy3000, vyy400, chg, chh)
new_esEs29(vyy580, vyy590, ty_Ordering) → new_esEs23(vyy580, vyy590)
new_esEs28(vyy581, vyy591, ty_Char) → new_esEs22(vyy581, vyy591)
new_compare111(vyy3000, vyy400, False, bga) → GT
new_esEs24(vyy580, vyy590, ty_Char) → new_esEs22(vyy580, vyy590)
new_ltEs13(Right(vyy3000), Left(vyy400), chf, cgc) → False
new_compare210(vyy3000, vyy400, False, bga) → new_compare111(vyy3000, vyy400, new_ltEs17(vyy3000, vyy400, bga), bga)
new_esEs26(vyy580, vyy590, app(ty_Ratio, cad)) → new_esEs12(vyy580, vyy590, cad)
new_esEs29(vyy580, vyy590, ty_Double) → new_esEs15(vyy580, vyy590)
new_esEs23(LT, LT) → True
new_esEs16(vyy58, vyy59, app(ty_Maybe, hd)) → new_esEs7(vyy58, vyy59, hd)
new_ltEs17(Just(vyy3000), Just(vyy400), ty_Float) → new_ltEs12(vyy3000, vyy400)
new_compare14(vyy3000, vyy400, ty_Char) → new_compare28(vyy3000, vyy400)
new_esEs27(vyy582, vyy592, ty_Bool) → new_esEs21(vyy582, vyy592)
new_ltEs13(Right(vyy3000), Right(vyy400), chf, ty_Char) → new_ltEs18(vyy3000, vyy400)
new_ltEs4(LT, LT) → True
new_ltEs16(vyy300, vyy40) → new_not(new_compare26(vyy300, vyy40))
new_compare14(vyy3000, vyy400, app(ty_Ratio, bdf)) → new_compare19(vyy3000, vyy400, bdf)
new_esEs25(vyy581, vyy591, app(app(ty_@2, bhh), caa)) → new_esEs5(vyy581, vyy591, bhh, caa)
new_esEs16(vyy58, vyy59, app(app(ty_@2, hg), hh)) → new_esEs5(vyy58, vyy59, hg, hh)
new_not(LT) → new_not0
new_lt5(vyy3001, vyy401, app(ty_Maybe, eh)) → new_lt18(vyy3001, vyy401, eh)
new_lt20(vyy3000, vyy400, ty_Bool) → new_lt12(vyy3000, vyy400)
new_compare112(vyy3000, vyy400, False) → GT
new_lt5(vyy3001, vyy401, app(app(app(ty_@3, fa), fb), fc)) → new_lt4(vyy3001, vyy401, fa, fb, fc)
new_esEs7(Just(vyy580), Just(vyy590), app(app(ty_@2, bch), bda)) → new_esEs5(vyy580, vyy590, bch, bda)
new_ltEs11(vyy300, vyy40) → new_not(new_compare15(vyy300, vyy40))
new_esEs28(vyy581, vyy591, ty_Int) → new_esEs10(vyy581, vyy591)
new_ltEs8(vyy3002, vyy402, app(ty_Maybe, df)) → new_ltEs17(vyy3002, vyy402, df)
new_ltEs17(Just(vyy3000), Just(vyy400), app(ty_Maybe, bbb)) → new_ltEs17(vyy3000, vyy400, bbb)
new_esEs29(vyy580, vyy590, ty_Bool) → new_esEs21(vyy580, vyy590)
new_esEs26(vyy580, vyy590, app(app(ty_Either, cbb), cbc)) → new_esEs6(vyy580, vyy590, cbb, cbc)
new_esEs27(vyy582, vyy592, app(ty_[], dbd)) → new_esEs19(vyy582, vyy592, dbd)
new_primPlusNat1(Zero, Zero) → Zero
new_compare0([], :(vyy400, vyy401), ca) → LT
new_ltEs13(Left(vyy3000), Left(vyy400), ty_Double, cgc) → new_ltEs14(vyy3000, vyy400)
new_lt14(vyy3000, vyy400) → new_esEs9(new_compare18(vyy3000, vyy400))
new_ltEs17(Just(vyy3000), Just(vyy400), ty_Char) → new_ltEs18(vyy3000, vyy400)
new_esEs7(Just(vyy580), Just(vyy590), app(ty_[], bca)) → new_esEs19(vyy580, vyy590, bca)
new_asAs(True, vyy73) → vyy73
new_primMulNat0(Succ(vyy300100), Succ(vyy40100)) → new_primPlusNat0(new_primMulNat0(vyy300100, Succ(vyy40100)), vyy40100)
new_lt13(vyy3000, vyy400) → new_esEs9(new_compare17(vyy3000, vyy400))
new_esEs6(Left(vyy580), Left(vyy590), ty_Float, hf) → new_esEs18(vyy580, vyy590)
new_lt5(vyy3001, vyy401, app(app(ty_@2, eb), ec)) → new_lt8(vyy3001, vyy401, eb, ec)
new_esEs27(vyy582, vyy592, ty_Integer) → new_esEs11(vyy582, vyy592)
new_pePe(False, vyy58, vyy59, vyy60, gg) → new_asAs(new_esEs16(vyy58, vyy59, gg), vyy60)
new_ltEs19(vyy3001, vyy401, ty_Float) → new_ltEs12(vyy3001, vyy401)
new_lt6(vyy3000, vyy400, ty_Float) → new_lt10(vyy3000, vyy400)
new_esEs26(vyy580, vyy590, ty_Double) → new_esEs15(vyy580, vyy590)
new_esEs27(vyy582, vyy592, ty_Int) → new_esEs10(vyy582, vyy592)
new_esEs7(Just(vyy580), Just(vyy590), ty_Double) → new_esEs15(vyy580, vyy590)
new_compare211(vyy3000, vyy400, True) → EQ
new_fmToList(vyy59, cb, cc) → new_foldFM2(vyy59, cb, cc)
new_ltEs10(@2(vyy3000, vyy3001), @2(vyy400, vyy401), cbf, cbg) → new_pePe(new_lt20(vyy3000, vyy400, cbf), vyy3000, vyy400, new_ltEs19(vyy3001, vyy401, cbg), cbf)
new_esEs21(False, True) → False
new_esEs21(True, False) → False
new_ltEs6(False, False) → True
new_ltEs8(vyy3002, vyy402, ty_Integer) → new_ltEs16(vyy3002, vyy402)
new_compare10(vyy3000, vyy400, True) → LT
new_ltEs4(GT, GT) → True
new_esEs26(vyy580, vyy590, ty_@0) → new_esEs20(vyy580, vyy590)
new_compare14(vyy3000, vyy400, ty_@0) → new_compare15(vyy3000, vyy400)
new_compare110(vyy3000, vyy400, False, be, bf, bg) → GT
new_ltEs19(vyy3001, vyy401, app(ty_[], cce)) → new_ltEs5(vyy3001, vyy401, cce)
new_compare10(vyy3000, vyy400, False) → GT
new_esEs6(Left(vyy580), Left(vyy590), ty_Bool, hf) → new_esEs21(vyy580, vyy590)
new_esEs25(vyy581, vyy591, ty_@0) → new_esEs20(vyy581, vyy591)
new_lt6(vyy3000, vyy400, ty_Bool) → new_lt12(vyy3000, vyy400)
new_esEs10(vyy58, vyy59) → new_primEqInt(vyy58, vyy59)
new_primCompAux00(vyy82, GT) → GT
new_ltEs13(Right(vyy3000), Right(vyy400), chf, ty_Integer) → new_ltEs16(vyy3000, vyy400)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_compare28(Char(vyy3000), Char(vyy400)) → new_primCmpNat0(vyy3000, vyy400)
new_esEs6(Right(vyy580), Right(vyy590), he, ty_Ordering) → new_esEs23(vyy580, vyy590)
new_esEs24(vyy580, vyy590, app(app(app(ty_@3, beh), bfa), bfb)) → new_esEs8(vyy580, vyy590, beh, bfa, bfb)
new_esEs16(vyy58, vyy59, ty_Double) → new_esEs15(vyy58, vyy59)
new_lt9(vyy3000, vyy400) → new_esEs9(new_compare15(vyy3000, vyy400))
new_esEs25(vyy581, vyy591, app(ty_Ratio, bgh)) → new_esEs12(vyy581, vyy591, bgh)
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_esEs7(Just(vyy580), Just(vyy590), app(ty_Ratio, bbh)) → new_esEs12(vyy580, vyy590, bbh)
new_primCmpInt(Neg(Succ(vyy30000)), Pos(vyy400)) → LT
new_esEs6(Left(vyy580), Left(vyy590), ty_Int, hf) → new_esEs10(vyy580, vyy590)
new_esEs24(vyy580, vyy590, ty_@0) → new_esEs20(vyy580, vyy590)
new_esEs17(vyy58, vyy59, cb, cc) → new_asAs(new_esEs10(new_sizeFM(vyy58, cb, cc), new_sizeFM(vyy59, cb, cc)), new_esEs19(new_fmToList(vyy58, cb, cc), new_fmToList(vyy59, cb, cc), app(app(ty_@2, cb), cc)))
new_esEs13(vyy581, vyy591, ty_Int) → new_esEs10(vyy581, vyy591)
The set Q consists of the following terms:
new_ltEs17(Just(x0), Just(x1), app(ty_Ratio, x2))
new_lt5(x0, x1, ty_Integer)
new_ltEs13(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_ltEs13(Right(x0), Right(x1), x2, ty_Int)
new_esEs25(x0, x1, ty_@0)
new_lt20(x0, x1, ty_Integer)
new_primEqNat0(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_compare9(x0, x1)
new_compare11(x0, x1, False, x2, x3)
new_compare13(x0, x1, True, x2, x3)
new_lt9(x0, x1)
new_lt16(x0, x1)
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_compare210(x0, x1, True, x2)
new_lt6(x0, x1, ty_Float)
new_esEs6(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs13(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs16(x0, x1, ty_Float)
new_compare15(@0, @0)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_lt5(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs23(LT, EQ)
new_esEs23(EQ, LT)
new_lt5(x0, x1, app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, ty_Char)
new_ltEs8(x0, x1, ty_Int)
new_esEs23(EQ, EQ)
new_esEs9(EQ)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs23(EQ, GT)
new_esEs23(GT, EQ)
new_esEs29(x0, x1, ty_Float)
new_esEs16(x0, x1, ty_Int)
new_esEs12(:%(x0, x1), :%(x2, x3), x4)
new_esEs24(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_primMulNat0(Zero, Succ(x0))
new_primCmpNat0(Zero, Succ(x0))
new_primCmpNat0(Succ(x0), Zero)
new_compare0([], [], x0)
new_ltEs13(Left(x0), Left(x1), ty_Int, x2)
new_lt6(x0, x1, ty_Int)
new_esEs6(Left(x0), Left(x1), app(app(ty_FiniteMap, x2), x3), x4)
new_ltEs13(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs6(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_lt6(x0, x1, app(ty_Maybe, x2))
new_lt5(x0, x1, ty_Double)
new_esEs10(x0, x1)
new_esEs29(x0, x1, ty_Bool)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_esEs16(x0, x1, ty_@0)
new_esEs24(x0, x1, ty_Double)
new_lt19(x0, x1)
new_esEs6(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_ltEs17(Just(x0), Just(x1), ty_@0)
new_compare14(x0, x1, ty_Integer)
new_lt5(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs8(x0, x1, app(ty_[], x2))
new_ltEs13(Left(x0), Left(x1), ty_@0, x2)
new_ltEs14(x0, x1)
new_esEs26(x0, x1, ty_Ordering)
new_ltEs17(Just(x0), Just(x1), ty_Ordering)
new_ltEs17(Just(x0), Just(x1), ty_Double)
new_esEs28(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs29(x0, x1, ty_Char)
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs17(Just(x0), Just(x1), app(ty_[], x2))
new_esEs7(Just(x0), Just(x1), ty_@0)
new_esEs25(x0, x1, ty_Bool)
new_ltEs6(True, True)
new_ltEs17(Nothing, Nothing, x0)
new_sr(x0, x1)
new_lt5(x0, x1, app(ty_[], x2))
new_esEs26(x0, x1, ty_@0)
new_compare26(Integer(x0), Integer(x1))
new_compare111(x0, x1, True, x2)
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_compare24(x0, x1, False)
new_lt8(x0, x1, x2, x3)
new_lt20(x0, x1, ty_Bool)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare211(x0, x1, True)
new_ltEs19(x0, x1, ty_Ordering)
new_esEs24(x0, x1, ty_Integer)
new_esEs7(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, ty_@0)
new_lt6(x0, x1, ty_@0)
new_esEs7(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_lt20(x0, x1, app(ty_Ratio, x2))
new_ltEs17(Just(x0), Just(x1), ty_Int)
new_lt20(x0, x1, ty_Float)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_primEqNat0(Zero, Zero)
new_esEs27(x0, x1, ty_Double)
new_lt5(x0, x1, ty_Char)
new_esEs7(Just(x0), Just(x1), ty_Ordering)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare210(x0, x1, False, x2)
new_primCmpNat0(Succ(x0), Succ(x1))
new_lt6(x0, x1, app(app(ty_Either, x2), x3))
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_lt5(x0, x1, ty_Bool)
new_ltEs13(Left(x0), Left(x1), ty_Integer, x2)
new_esEs7(Just(x0), Just(x1), app(app(ty_FiniteMap, x2), x3))
new_esEs6(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_compare112(x0, x1, True)
new_esEs7(Just(x0), Just(x1), ty_Float)
new_compare0([], :(x0, x1), x2)
new_esEs27(x0, x1, ty_Bool)
new_lt15(x0, x1, x2)
new_primPlusNat1(Zero, Succ(x0))
new_primMulNat0(Zero, Zero)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs6(Left(x0), Left(x1), ty_Char, x2)
new_ltEs13(Left(x0), Left(x1), ty_Ordering, x2)
new_compare14(x0, x1, ty_Int)
new_sizeFM(EmptyFM, x0, x1)
new_ltEs13(Left(x0), Left(x1), ty_Char, x2)
new_ltEs17(Just(x0), Just(x1), ty_Bool)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_pePe(True, x0, x1, x2, x3)
new_ltEs5(x0, x1, x2)
new_ltEs4(GT, GT)
new_esEs6(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs6(Left(x0), Left(x1), ty_Float, x2)
new_compare14(x0, x1, app(ty_Ratio, x2))
new_lt20(x0, x1, ty_Int)
new_ltEs13(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs27(x0, x1, ty_Float)
new_ltEs8(x0, x1, app(app(ty_@2, x2), x3))
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs25(x0, x1, ty_Ordering)
new_compare14(x0, x1, app(ty_Maybe, x2))
new_lt20(x0, x1, app(ty_Maybe, x2))
new_lt20(x0, x1, app(ty_[], x2))
new_compare19(:%(x0, x1), :%(x2, x3), ty_Integer)
new_foldFM_LE30(x0, x1, x2, x3, x4)
new_esEs28(x0, x1, ty_Integer)
new_foldFM_LE12(x0, x1, x2, x3, x4, x5, x6, False, x7, x8, x9)
new_esEs16(x0, x1, app(ty_Maybe, x2))
new_primMulNat0(Succ(x0), Succ(x1))
new_ltEs17(Just(x0), Just(x1), ty_Float)
new_esEs27(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_foldFM_LE12(x0, x1, x2, x3, x4, x5, Branch(x6, x7, x8, x9, x10), True, x11, x12, x13)
new_ltEs16(x0, x1)
new_esEs28(x0, x1, ty_Float)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_esEs24(x0, x1, app(ty_[], x2))
new_esEs28(x0, x1, ty_Int)
new_foldFM_LE5(x0, x1, EmptyFM, x2, x3, x4)
new_lt14(x0, x1)
new_ltEs17(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_lt6(x0, x1, ty_Double)
new_compare14(x0, x1, ty_Ordering)
new_compare23(x0, x1, False, x2, x3)
new_lt5(x0, x1, app(ty_Maybe, x2))
new_lt6(x0, x1, app(app(ty_@2, x2), x3))
new_lt4(x0, x1, x2, x3, x4)
new_esEs16(x0, x1, app(app(ty_@2, x2), x3))
new_compare10(x0, x1, False)
new_esEs24(x0, x1, ty_Bool)
new_compare14(x0, x1, ty_Char)
new_compare25(x0, x1, False, x2, x3)
new_primPlusNat1(Succ(x0), Succ(x1))
new_lt11(x0, x1, x2, x3)
new_esEs27(x0, x1, ty_Ordering)
new_ltEs19(x0, x1, ty_Integer)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_esEs6(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_ltEs13(Right(x0), Right(x1), x2, ty_@0)
new_esEs23(GT, LT)
new_esEs23(LT, GT)
new_ltEs15(x0, x1, x2)
new_ltEs19(x0, x1, ty_Int)
new_esEs6(Left(x0), Left(x1), ty_Int, x2)
new_ltEs19(x0, x1, ty_Double)
new_esEs25(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs7(Just(x0), Just(x1), app(ty_[], x2))
new_compare18(Double(x0, x1), Double(x2, x3))
new_ltEs13(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_compare14(x0, x1, app(app(ty_@2, x2), x3))
new_esEs5(@2(x0, x1), @2(x2, x3), x4, x5)
new_primPlusNat1(Zero, Zero)
new_ltEs17(Just(x0), Nothing, x1)
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_not0
new_ltEs13(Left(x0), Left(x1), ty_Float, x2)
new_primMulNat0(Succ(x0), Zero)
new_ltEs12(x0, x1)
new_compare29(x0, x1, True, x2, x3, x4)
new_esEs9(GT)
new_compare0(:(x0, x1), :(x2, x3), x4)
new_ltEs17(Just(x0), Just(x1), app(ty_Maybe, x2))
new_compare25(x0, x1, True, x2, x3)
new_esEs27(x0, x1, ty_Int)
new_esEs7(Just(x0), Just(x1), ty_Char)
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_esEs6(Left(x0), Left(x1), ty_@0, x2)
new_ltEs8(x0, x1, ty_Float)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs4(EQ, EQ)
new_compare12(x0, x1, x2, x3)
new_esEs7(Nothing, Just(x0), x1)
new_compare7(x0, x1, x2, x3, x4)
new_compare14(x0, x1, ty_Float)
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs18(x0, x1)
new_esEs8(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs17(x0, x1, x2, x3)
new_ltEs6(True, False)
new_ltEs6(False, True)
new_compare27(x0, x1, x2)
new_esEs26(x0, x1, ty_Bool)
new_compare24(x0, x1, True)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_compare14(x0, x1, ty_Double)
new_esEs6(Left(x0), Left(x1), ty_Bool, x2)
new_esEs25(x0, x1, ty_Char)
new_esEs6(Right(x0), Right(x1), x2, ty_@0)
new_ltEs4(EQ, LT)
new_lt6(x0, x1, app(ty_[], x2))
new_ltEs4(LT, EQ)
new_lt17(x0, x1, x2)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_not(GT)
new_ltEs8(x0, x1, ty_@0)
new_compare110(x0, x1, True, x2, x3, x4)
new_esEs26(x0, x1, ty_Int)
new_esEs24(x0, x1, ty_Int)
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_FiniteMap, x3), x4))
new_esEs16(x0, x1, ty_Double)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs26(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_primCompAux0(x0, x1, x2, x3)
new_esEs6(Left(x0), Left(x1), ty_Double, x2)
new_esEs16(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt6(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_foldFM2(EmptyFM, x0, x1)
new_primEqInt(Neg(Zero), Pos(Zero))
new_primEqInt(Pos(Zero), Neg(Zero))
new_lt5(x0, x1, ty_@0)
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_fmToList_LE0(x0, x1, x2, x3, x4, x5)
new_esEs7(Just(x0), Just(x1), ty_Bool)
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_esEs13(x0, x1, ty_Int)
new_lt6(x0, x1, ty_Char)
new_esEs7(Just(x0), Nothing, x1)
new_lt7(x0, x1)
new_compare10(x0, x1, True)
new_primCompAux00(x0, LT)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_compare29(x0, x1, False, x2, x3, x4)
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_esEs6(Right(x0), Right(x1), x2, ty_Char)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_ltEs6(False, False)
new_primPlusNat1(Succ(x0), Zero)
new_primCompAux00(x0, GT)
new_esEs23(LT, LT)
new_lt6(x0, x1, app(ty_Ratio, x2))
new_ltEs19(x0, x1, ty_Bool)
new_primEqInt(Neg(Zero), Neg(Zero))
new_ltEs17(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_primPlusNat0(Succ(x0), x1)
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
new_esEs16(x0, x1, app(ty_Ratio, x2))
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_esEs6(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_compare19(:%(x0, x1), :%(x2, x3), ty_Int)
new_ltEs19(x0, x1, app(ty_[], x2))
new_foldFM_LE22(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9)
new_esEs28(x0, x1, ty_Bool)
new_lt5(x0, x1, ty_Float)
new_esEs19(:(x0, x1), :(x2, x3), x4)
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_ltEs4(LT, LT)
new_esEs14(x0, x1, ty_Int)
new_compare13(x0, x1, False, x2, x3)
new_esEs27(x0, x1, ty_Char)
new_ltEs8(x0, x1, ty_Double)
new_ltEs11(x0, x1)
new_foldFM_LE12(x0, x1, x2, x3, x4, x5, EmptyFM, True, x6, x7, x8)
new_esEs26(x0, x1, ty_Float)
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs16(x0, x1, ty_Ordering)
new_ltEs13(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs26(x0, x1, app(ty_[], x2))
new_compare6(x0, x1, x2, x3)
new_ltEs13(Right(x0), Right(x1), x2, ty_Char)
new_compare28(Char(x0), Char(x1))
new_esEs6(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs6(Right(x0), Right(x1), x2, ty_Integer)
new_esEs9(LT)
new_ltEs7(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_compare111(x0, x1, False, x2)
new_esEs6(Right(x0), Left(x1), x2, x3)
new_esEs6(Left(x0), Right(x1), x2, x3)
new_ltEs13(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs29(x0, x1, ty_Ordering)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_esEs18(Float(x0, x1), Float(x2, x3))
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs6(Left(x0), Left(x1), ty_Ordering, x2)
new_compare110(x0, x1, False, x2, x3, x4)
new_ltEs17(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_asAs(False, x0)
new_esEs7(Nothing, Nothing, x0)
new_primPlusNat0(Zero, x0)
new_compare8(Float(x0, x1), Float(x2, x3))
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(Just(x0), Just(x1), ty_Double)
new_primCmpNat0(Zero, Zero)
new_esEs29(x0, x1, ty_Int)
new_esEs16(x0, x1, app(ty_[], x2))
new_ltEs13(Left(x0), Left(x1), ty_Bool, x2)
new_esEs15(Double(x0, x1), Double(x2, x3))
new_lt20(x0, x1, ty_Ordering)
new_esEs7(Just(x0), Just(x1), ty_Int)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_compare17(x0, x1)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_compare211(x0, x1, False)
new_compare14(x0, x1, app(ty_[], x2))
new_lt13(x0, x1)
new_compare14(x0, x1, app(app(ty_Either, x2), x3))
new_esEs6(Right(x0), Right(x1), x2, ty_Int)
new_ltEs8(x0, x1, app(ty_Maybe, x2))
new_esEs13(x0, x1, ty_Integer)
new_lt12(x0, x1)
new_esEs6(Right(x0), Right(x1), x2, ty_Double)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs13(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs6(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_ltEs8(x0, x1, ty_Ordering)
new_pePe(False, x0, x1, x2, x3)
new_ltEs19(x0, x1, ty_@0)
new_ltEs13(Right(x0), Right(x1), x2, ty_Integer)
new_esEs28(x0, x1, ty_Double)
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_lt10(x0, x1)
new_esEs19([], [], x0)
new_ltEs13(Left(x0), Left(x1), ty_Double, x2)
new_primEqNat0(Zero, Succ(x0))
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_esEs16(x0, x1, ty_Bool)
new_esEs21(True, True)
new_ltEs4(EQ, GT)
new_ltEs4(GT, EQ)
new_ltEs17(Nothing, Just(x0), x1)
new_esEs24(x0, x1, ty_Ordering)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_not(EQ)
new_ltEs13(Right(x0), Right(x1), x2, ty_Float)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare23(x0, x1, True, x2, x3)
new_ltEs17(Just(x0), Just(x1), ty_Integer)
new_esEs14(x0, x1, ty_Integer)
new_esEs29(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_ltEs13(Right(x0), Left(x1), x2, x3)
new_ltEs13(Left(x0), Right(x1), x2, x3)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_esEs6(Left(x0), Left(x1), ty_Integer, x2)
new_esEs25(x0, x1, ty_Int)
new_ltEs8(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs22(Char(x0), Char(x1))
new_ltEs13(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_ltEs19(x0, x1, ty_Char)
new_esEs6(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_compare14(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs8(x0, x1, app(ty_Ratio, x2))
new_ltEs13(Right(x0), Right(x1), x2, ty_Bool)
new_esEs7(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_lt6(x0, x1, ty_Bool)
new_esEs26(x0, x1, ty_Double)
new_lt5(x0, x1, ty_Int)
new_esEs16(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs13(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs24(x0, x1, ty_@0)
new_esEs11(Integer(x0), Integer(x1))
new_esEs21(False, True)
new_esEs21(True, False)
new_lt6(x0, x1, ty_Ordering)
new_lt5(x0, x1, app(ty_Ratio, x2))
new_esEs24(x0, x1, ty_Char)
new_ltEs13(Right(x0), Right(x1), x2, ty_Double)
new_esEs20(@0, @0)
new_esEs24(x0, x1, ty_Float)
new_esEs28(x0, x1, app(ty_[], x2))
new_esEs6(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs27(x0, x1, app(ty_[], x2))
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs19(:(x0, x1), [], x2)
new_esEs25(x0, x1, ty_Float)
new_esEs16(x0, x1, ty_Char)
new_esEs29(x0, x1, ty_@0)
new_foldFM_LE5(x0, x1, Branch(x2, x3, x4, x5, x6), x7, x8, x9)
new_ltEs13(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs26(x0, x1, ty_Integer)
new_esEs29(x0, x1, ty_Integer)
new_compare14(x0, x1, ty_Bool)
new_esEs6(Right(x0), Right(x1), x2, ty_Float)
new_ltEs8(x0, x1, app(app(ty_Either, x2), x3))
new_esEs28(x0, x1, ty_Ordering)
new_lt5(x0, x1, ty_Ordering)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_esEs16(x0, x1, ty_Integer)
new_esEs7(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs25(x0, x1, app(ty_[], x2))
new_compare16(x0, x1)
new_ltEs13(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_ltEs8(x0, x1, ty_Char)
new_compare0(:(x0, x1), [], x2)
new_primCompAux00(x0, EQ)
new_ltEs10(@2(x0, x1), @2(x2, x3), x4, x5)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sr0(Integer(x0), Integer(x1))
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_esEs6(Right(x0), Right(x1), x2, ty_Ordering)
new_compare11(x0, x1, True, x2, x3)
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_ltEs9(x0, x1)
new_compare14(x0, x1, ty_@0)
new_ltEs19(x0, x1, ty_Float)
new_esEs28(x0, x1, ty_@0)
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs29(x0, x1, app(ty_[], x2))
new_esEs25(x0, x1, ty_Double)
new_ltEs8(x0, x1, ty_Integer)
new_esEs21(False, False)
new_primEqInt(Pos(Zero), Pos(Zero))
new_esEs27(x0, x1, ty_Integer)
new_asAs(True, x0)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs28(x0, x1, ty_Char)
new_esEs7(Just(x0), Just(x1), ty_Integer)
new_compare112(x0, x1, False)
new_lt6(x0, x1, ty_Integer)
new_lt20(x0, x1, ty_Char)
new_ltEs4(GT, LT)
new_ltEs4(LT, GT)
new_esEs16(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs27(x0, x1, ty_@0)
new_ltEs17(Just(x0), Just(x1), ty_Char)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs29(x0, x1, ty_Double)
new_ltEs13(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_lt20(x0, x1, ty_Double)
new_esEs25(x0, x1, ty_Integer)
new_fmToList(x0, x1, x2)
new_ltEs8(x0, x1, ty_Bool)
new_esEs23(GT, GT)
new_esEs19([], :(x0, x1), x2)
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
new_not(LT)
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_lt18(x0, x1, x2)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_esEs7(Just(x0), Just(x1), app(ty_Ratio, 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_LE4(vyy65, vyy13, Branch(vyy1830, vyy1831, vyy1832, vyy1833, vyy1834), h, ba, bb) → new_foldFM_LE21(vyy65, vyy13, vyy1830, vyy1831, vyy1832, vyy1833, vyy1834, h, ba, bb)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 3 > 4, 3 > 5, 3 > 6, 3 > 7, 4 >= 8, 5 >= 9, 6 >= 10
- new_foldFM_LE21(vyy76, vyy13, vyy1840, vyy1841, vyy1842, vyy1843, vyy1844, h, ba, bb) → new_foldFM_LE11(vyy76, vyy13, vyy1840, vyy1841, vyy1842, vyy1843, vyy1844, new_ltEs13(vyy1840, Left(vyy13), h, ba), h, ba, bb)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 9, 9 >= 10, 10 >= 11
- new_foldFM_LE11(vyy65, vyy13, vyy180, vyy181, vyy182, vyy183, Branch(vyy1840, vyy1841, vyy1842, vyy1843, vyy1844), True, h, ba, bb) → new_foldFM_LE21(new_fmToList_LE0(vyy180, vyy181, new_foldFM_LE5(vyy65, vyy13, vyy183, h, ba, bb), h, ba, bb), vyy13, vyy1840, vyy1841, vyy1842, vyy1843, vyy1844, h, ba, bb)
The graph contains the following edges 2 >= 2, 7 > 3, 7 > 4, 7 > 5, 7 > 6, 7 > 7, 9 >= 8, 10 >= 9, 11 >= 10
- new_foldFM_LE11(vyy65, vyy13, vyy180, vyy181, vyy182, Branch(vyy1830, vyy1831, vyy1832, vyy1833, vyy1834), vyy184, False, h, ba, bb) → new_foldFM_LE21(vyy65, vyy13, vyy1830, vyy1831, vyy1832, vyy1833, vyy1834, h, ba, bb)
The graph contains the following edges 1 >= 1, 2 >= 2, 6 > 3, 6 > 4, 6 > 5, 6 > 6, 6 > 7, 9 >= 8, 10 >= 9, 11 >= 10
- new_foldFM_LE11(vyy65, vyy13, vyy180, vyy181, vyy182, vyy183, Branch(vyy1840, vyy1841, vyy1842, vyy1843, vyy1844), True, h, ba, bb) → new_foldFM_LE4(vyy65, vyy13, vyy183, h, ba, bb)
The graph contains the following edges 1 >= 1, 2 >= 2, 6 >= 3, 9 >= 4, 10 >= 5, 11 >= 6
- new_foldFM_LE11(vyy65, vyy13, vyy180, vyy181, vyy182, vyy183, EmptyFM, True, h, ba, bb) → new_foldFM_LE4(vyy65, vyy13, vyy183, h, ba, bb)
The graph contains the following edges 1 >= 1, 2 >= 2, 6 >= 3, 9 >= 4, 10 >= 5, 11 >= 6