YES 11.144
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 => FiniteMap (Maybe b) a -> Maybe b -> [(Maybe b,a)]) :: Ord b => FiniteMap (Maybe b) a -> Maybe b -> [(Maybe b,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 :: (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
|
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 a => FiniteMap (Maybe a) b -> Maybe a -> [(Maybe a,b)]) :: Ord a => FiniteMap (Maybe a) b -> Maybe a -> [(Maybe a,b)]) |
module FiniteMap where
| | import qualified Maybe
import qualified Prelude
|
| | data FiniteMap a b = EmptyFM | Branch a b Int (FiniteMap a b) (FiniteMap a b)
|
| | instance (Eq a, Eq b) => Eq (FiniteMap a b) where
|
|
|
| (==) | fm_1 fm_2 | = | sizeFM fm_1 == sizeFM fm_2 && fmToList fm_1 == fmToList fm_2 |
|
|
| | 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 :: (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 a => (a -> c -> b -> b) -> b -> a -> FiniteMap a c -> b
| foldFM_LE | k z fr EmptyFM | = | z |
| foldFM_LE | k z fr (Branch key elt _ fm_l fm_r) | |
| | | key <= fr | = |
| foldFM_LE k (k key elt (foldFM_LE k z fr fm_l)) fr fm_r |
|
| | | otherwise | = |
|
|
|
| | sizeFM :: FiniteMap b a -> 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 a => FiniteMap (Maybe a) b -> Maybe a -> [(Maybe a,b)]) :: Ord a => FiniteMap (Maybe a) b -> Maybe a -> [(Maybe a,b)]) |
module FiniteMap where
| | import qualified Maybe
import qualified Prelude
|
| | data FiniteMap a b = EmptyFM | Branch a b Int (FiniteMap a b) (FiniteMap a b)
|
| | instance (Eq a, Eq b) => Eq (FiniteMap a b) where
|
|
|
| (==) | fm_1 fm_2 | = | sizeFM fm_1 == sizeFM fm_2 && fmToList fm_1 == fmToList fm_2 |
|
|
| | 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 -> 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 a => (a -> c -> b -> b) -> b -> a -> FiniteMap a c -> b
| foldFM_LE | k z fr EmptyFM | = | z |
| foldFM_LE | k z fr (Branch key elt _ fm_l fm_r) | |
| | | key <= fr | = |
| foldFM_LE k (k key elt (foldFM_LE k z fr fm_l)) fr fm_r |
|
| | | otherwise | = |
|
|
|
| | sizeFM :: FiniteMap b a -> 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 b => FiniteMap (Maybe b) a -> Maybe b -> [(Maybe b,a)]) :: Ord b => FiniteMap (Maybe b) a -> Maybe b -> [(Maybe b,a)]) |
module FiniteMap where
| | import qualified Maybe
import qualified Prelude
|
| | data FiniteMap b a = EmptyFM | Branch b a Int (FiniteMap b a) (FiniteMap b a)
|
| | instance (Eq a, Eq b) => Eq (FiniteMap a b) where
|
|
|
| (==) | fm_1 fm_2 | = | sizeFM fm_1 == sizeFM fm_2 && fmToList fm_1 == fmToList fm_2 |
|
|
| | 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 :: (b -> c -> a -> a) -> a -> FiniteMap b c -> 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 b => (b -> a -> c -> c) -> c -> b -> FiniteMap b a -> c
| foldFM_LE | k z fr EmptyFM | = | z |
| foldFM_LE | k z fr (Branch key elt _ fm_l fm_r) | |
| | | key <= fr | = |
| foldFM_LE k (k key elt (foldFM_LE k z fr fm_l)) fr fm_r |
|
| | | otherwise | = |
|
|
|
| | sizeFM :: FiniteMap a b -> Int
| sizeFM | EmptyFM | = | 0 |
| sizeFM | (Branch _ _ size _ _) | = | size |
|
module Maybe where
| | import qualified FiniteMap
import qualified Prelude
|
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 a => FiniteMap (Maybe a) b -> Maybe a -> [(Maybe a,b)]) :: Ord a => FiniteMap (Maybe a) b -> Maybe a -> [(Maybe a,b)]) |
module FiniteMap where
| | import qualified Maybe
import qualified Prelude
|
| | data FiniteMap b a = EmptyFM | Branch b a Int (FiniteMap b a) (FiniteMap b a)
|
| | instance (Eq a, Eq b) => Eq (FiniteMap 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 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 -> c -> a -> a) -> a -> FiniteMap b c -> 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 c => (c -> a -> b -> b) -> b -> c -> FiniteMap c a -> b
| foldFM_LE | k z fr EmptyFM | = | z |
| foldFM_LE | k z fr (Branch key elt vx fm_l fm_r) | |
| | | key <= fr | = |
| foldFM_LE k (k key elt (foldFM_LE k z fr fm_l)) fr fm_r |
|
| | | otherwise | = |
|
|
|
| | sizeFM :: FiniteMap 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_LE0 | k z fr key elt vx fm_l fm_r True | = foldFM_LE k z fr fm_l |
| foldFM_LE1 | k z fr key elt vx fm_l fm_r True | = foldFM_LE k (k key elt (foldFM_LE k z fr fm_l)) fr fm_r |
| foldFM_LE1 | k z fr key elt vx fm_l fm_r False | = foldFM_LE0 k z fr key elt vx fm_l fm_r otherwise |
| foldFM_LE2 | k z fr (Branch key elt vx fm_l fm_r) | = foldFM_LE1 k z fr key elt vx fm_l fm_r (key <= fr) |
| foldFM_LE3 | k z fr EmptyFM | = z |
| foldFM_LE3 | vvu vvv vvw vvx | = foldFM_LE2 vvu vvv vvw vvx |
The following Function with conditions
| compare | x y |
| | | x == y | |
| | | x <= y | |
| | | otherwise | |
|
is transformed to
| compare | x y | = compare3 x y |
| compare1 | x y True | = LT |
| compare1 | x y False | = compare0 x y otherwise |
| compare2 | x y True | = EQ |
| compare2 | x y False | = compare1 x y (x <= y) |
| 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 a => FiniteMap (Maybe a) b -> Maybe a -> [(Maybe a,b)]) :: Ord a => FiniteMap (Maybe a) b -> Maybe a -> [(Maybe a,b)]) |
module FiniteMap where
| | import qualified Maybe
import qualified Prelude
|
| | data FiniteMap b a = EmptyFM | Branch b a Int (FiniteMap b a) (FiniteMap b a)
|
| | instance (Eq a, Eq b) => Eq (FiniteMap 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 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 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 | = | 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
| reduce2D | vyw vyx | = gcd vyw vyx |
| reduce2Reduce1 | vyw vyx x y True | = error [] |
| reduce2Reduce1 | vyw vyx x y False | = reduce2Reduce0 vyw vyx x y otherwise |
| reduce2Reduce0 | vyw vyx x y True | = x `quot` reduce2D vyw vyx :% (y `quot` reduce2D 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'0 | x y | = gcd0Gcd' y (x `rem` y) |
| gcd0Gcd'2 | x vvy | = gcd0Gcd'1 (vvy == 0) x vvy |
| gcd0Gcd'2 | vww vwx | = gcd0Gcd'0 vww vwx |
| gcd0Gcd'1 | True x vvy | = x |
| gcd0Gcd'1 | vvz vwu vwv | = gcd0Gcd'0 vwu vwv |
| gcd0Gcd' | x vvy | = gcd0Gcd'2 x vvy |
| gcd0Gcd' | x y | = gcd0Gcd'0 x y |
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
mainModule FiniteMap
|
| ((fmToList_LE :: Ord a => FiniteMap (Maybe a) b -> Maybe a -> [(Maybe a,b)]) :: Ord a => FiniteMap (Maybe a) b -> Maybe a -> [(Maybe a,b)]) |
module FiniteMap where
| | import qualified Maybe
import qualified Prelude
|
| | data FiniteMap b a = EmptyFM | Branch b a Int (FiniteMap b a) (FiniteMap b a)
|
| | instance (Eq a, Eq b) => Eq (FiniteMap 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 -> 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
|
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 a => FiniteMap (Maybe a) b -> Maybe a -> [(Maybe a,b)]) |
module FiniteMap where
| | import qualified Maybe
import qualified Prelude
|
| | data FiniteMap a b = EmptyFM | Branch a b Int (FiniteMap a b) (FiniteMap a b)
|
| | instance (Eq a, Eq b) => Eq (FiniteMap a b) where
|
|
|
| (==) | fm_1 fm_2 | = | sizeFM fm_1 == sizeFM fm_2 && fmToList fm_1 == fmToList fm_2 |
|
|
| | 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 :: (b -> c -> a -> a) -> a -> FiniteMap b c -> 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 a => (a -> c -> b -> b) -> b -> a -> FiniteMap a c -> b
| foldFM_LE | k z fr EmptyFM | = | foldFM_LE3 k z fr EmptyFM |
| foldFM_LE | k z fr (Branch key elt vx fm_l fm_r) | = | foldFM_LE2 k z fr (Branch key elt vx fm_l fm_r) |
|
| |
| foldFM_LE0 | k z fr key elt vx fm_l fm_r True | = | foldFM_LE k z fr fm_l |
|
| |
| foldFM_LE1 | k z fr key elt vx fm_l fm_r True | = | foldFM_LE k (k key elt (foldFM_LE k z fr fm_l)) fr fm_r |
| foldFM_LE1 | k z fr key elt vx fm_l fm_r False | = | foldFM_LE0 k z fr key elt vx fm_l fm_r otherwise |
|
| |
| foldFM_LE2 | k z fr (Branch key elt vx fm_l fm_r) | = | foldFM_LE1 k z fr key elt vx fm_l fm_r (key <= fr) |
|
| |
| foldFM_LE3 | k z fr EmptyFM | = | z |
| foldFM_LE3 | vvu vvv vvw vvx | = | foldFM_LE2 vvu vvv vvw vvx |
|
| | sizeFM :: FiniteMap 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_primCmpNat(Succ(vyy30000), Succ(vyy4000)) → new_primCmpNat(vyy30000, vyy4000)
R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By using the subterm criterion [20] together with the size-change analysis [32] we have proven that there are no infinite chains for this DP problem. From the DPs we obtained the following set of size-change graphs:
- new_primCmpNat(Succ(vyy30000), Succ(vyy4000)) → new_primCmpNat(vyy30000, vyy4000)
The graph contains the following edges 1 > 1, 2 > 2
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDPSizeChangeProof
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_foldFM(vyy410, vyy411, vyy85, Branch(vyy4130, vyy4131, vyy4132, vyy4133, vyy4134), h, ba) → new_foldFM(vyy4130, vyy4131, new_foldFM0(vyy410, vyy411, vyy85, vyy4134, h, ba), vyy4133, h, ba)
new_foldFM(vyy410, vyy411, vyy85, Branch(vyy4130, vyy4131, vyy4132, vyy4133, vyy4134), h, ba) → new_foldFM(vyy410, vyy411, vyy85, vyy4134, h, ba)
The TRS R consists of the following rules:
new_foldFM0(vyy410, vyy411, vyy85, EmptyFM, h, ba) → :(@2(vyy410, vyy411), vyy85)
new_foldFM0(vyy410, vyy411, vyy85, Branch(vyy4130, vyy4131, vyy4132, vyy4133, vyy4134), h, ba) → new_foldFM0(vyy4130, vyy4131, new_foldFM0(vyy410, vyy411, vyy85, vyy4134, h, ba), vyy4133, h, ba)
The set Q consists of the following terms:
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
We have to consider all minimal (P,Q,R)-chains.
By using the subterm criterion [20] together with the size-change analysis [32] we have proven that there are no infinite chains for this DP problem. From the DPs we obtained the following set of size-change graphs:
- new_foldFM(vyy410, vyy411, vyy85, Branch(vyy4130, vyy4131, vyy4132, vyy4133, vyy4134), h, ba) → new_foldFM(vyy4130, vyy4131, new_foldFM0(vyy410, vyy411, vyy85, vyy4134, h, ba), vyy4133, h, ba)
The graph contains the following edges 4 > 1, 4 > 2, 4 > 4, 5 >= 5, 6 >= 6
- new_foldFM(vyy410, vyy411, vyy85, Branch(vyy4130, vyy4131, vyy4132, vyy4133, vyy4134), h, ba) → new_foldFM(vyy410, vyy411, vyy85, vyy4134, h, ba)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 > 4, 5 >= 5, 6 >= 6
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDPSizeChangeProof
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_foldFM1(Branch(vyy410, vyy411, vyy412, vyy413, vyy414), h, ba) → new_foldFM1(vyy414, h, ba)
R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By using the subterm criterion [20] together with the size-change analysis [32] we have proven that there are no infinite chains for this DP problem. From the DPs we obtained the following set of size-change graphs:
- new_foldFM1(Branch(vyy410, vyy411, vyy412, vyy413, vyy414), h, ba) → new_foldFM1(vyy414, h, ba)
The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDPSizeChangeProof
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_primPlusNat(Succ(vyy8600), Succ(vyy401000)) → new_primPlusNat(vyy8600, vyy401000)
R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By using the subterm criterion [20] together with the size-change analysis [32] we have proven that there are no infinite chains for this DP problem. From the DPs we obtained the following set of size-change graphs:
- new_primPlusNat(Succ(vyy8600), Succ(vyy401000)) → new_primPlusNat(vyy8600, vyy401000)
The graph contains the following edges 1 > 1, 2 > 2
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDPSizeChangeProof
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_primMulNat(Succ(vyy300100), Succ(vyy40100)) → new_primMulNat(vyy300100, Succ(vyy40100))
R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By using the subterm criterion [20] together with the size-change analysis [32] we have proven that there are no infinite chains for this DP problem. From the DPs we obtained the following set of size-change graphs:
- new_primMulNat(Succ(vyy300100), Succ(vyy40100)) → new_primMulNat(vyy300100, Succ(vyy40100))
The graph contains the following edges 1 > 1, 2 >= 2
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDPSizeChangeProof
↳ QDP
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_primEqNat(Succ(vyy4000), Succ(vyy4100)) → new_primEqNat(vyy4000, vyy4100)
R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By using the subterm criterion [20] together with the size-change analysis [32] we have proven that there are no infinite chains for this DP problem. From the DPs we obtained the following set of size-change graphs:
- new_primEqNat(Succ(vyy4000), Succ(vyy4100)) → new_primEqNat(vyy4000, vyy4100)
The graph contains the following edges 1 > 1, 2 > 2
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ Rewriting
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_esEs(@2(vyy400, vyy401), @2(vyy410, vyy411), app(app(ty_@2, cd), ce), cf) → new_esEs(vyy400, vyy410, cd, ce)
new_esEs(@2(vyy400, vyy401), @2(vyy410, vyy411), app(ty_[], cg), cf) → new_esEs0(vyy400, vyy410, cg)
new_esEs2(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ha, app(ty_Maybe, bbb), bah) → new_esEs1(vyy401, vyy411, bbb)
new_esEs2(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), app(ty_Maybe, bce), hb, bah) → new_esEs1(vyy400, vyy410, bce)
new_esEs2(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ha, hb, app(ty_[], he)) → new_esEs0(vyy402, vyy412, he)
new_esEs(@2(vyy400, vyy401), @2(vyy410, vyy411), app(app(ty_FiniteMap, dg), dh), cf) → new_esEs4(vyy400, vyy410, dg, dh)
new_esEs2(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ha, app(app(ty_Either, bbf), bbg), bah) → new_esEs3(vyy401, vyy411, bbf, bbg)
new_esEs3(Right(vyy400), Right(vyy410), bfa, app(app(ty_Either, bga), bgb)) → new_esEs3(vyy400, vyy410, bga, bgb)
new_esEs3(Left(vyy400), Left(vyy410), app(app(ty_Either, bee), bef), bdg) → new_esEs3(vyy400, vyy410, bee, bef)
new_esEs1(Just(vyy400), Just(vyy410), app(app(ty_Either, ge), gf)) → new_esEs3(vyy400, vyy410, ge, gf)
new_esEs(@2(vyy400, vyy401), @2(vyy410, vyy411), app(app(ty_Either, de), df), cf) → new_esEs3(vyy400, vyy410, de, df)
new_esEs0(:(vyy400, vyy401), :(vyy410, vyy411), app(ty_Maybe, ee)) → new_esEs1(vyy400, vyy410, ee)
new_esEs3(Left(vyy400), Left(vyy410), app(ty_[], bdh), bdg) → new_esEs0(vyy400, vyy410, bdh)
new_esEs(@2(vyy400, vyy401), @2(vyy410, vyy411), h, app(app(ty_Either, bh), ca)) → new_esEs3(vyy401, vyy411, bh, ca)
new_esEs3(Right(vyy400), Right(vyy410), bfa, app(ty_[], bfd)) → new_esEs0(vyy400, vyy410, bfd)
new_esEs(@2(vyy400, vyy401), @2(vyy410, vyy411), h, app(ty_[], bc)) → new_esEs0(vyy401, vyy411, bc)
new_esEs1(Just(vyy400), Just(vyy410), app(ty_Maybe, ga)) → new_esEs1(vyy400, vyy410, ga)
new_esEs2(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ha, hb, app(ty_Maybe, hf)) → new_esEs1(vyy402, vyy412, hf)
new_esEs(@2(vyy400, vyy401), @2(vyy410, vyy411), h, app(app(ty_@2, ba), bb)) → new_esEs(vyy401, vyy411, ba, bb)
new_esEs1(Just(vyy400), Just(vyy410), app(app(app(ty_@3, gb), gc), gd)) → new_esEs2(vyy400, vyy410, gb, gc, gd)
new_esEs(@2(vyy400, vyy401), @2(vyy410, vyy411), app(app(app(ty_@3, db), dc), dd), cf) → new_esEs2(vyy400, vyy410, db, dc, dd)
new_esEs3(Right(vyy400), Right(vyy410), bfa, app(app(ty_FiniteMap, bgc), bgd)) → new_esEs4(vyy400, vyy410, bgc, bgd)
new_esEs2(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), app(app(ty_@2, bcb), bcc), hb, bah) → new_esEs(vyy400, vyy410, bcb, bcc)
new_esEs2(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), app(ty_[], bcd), hb, bah) → new_esEs0(vyy400, vyy410, bcd)
new_esEs0(:(vyy400, vyy401), :(vyy410, vyy411), app(app(ty_FiniteMap, fc), fd)) → new_esEs4(vyy400, vyy410, fc, fd)
new_esEs2(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ha, app(ty_[], bba), bah) → new_esEs0(vyy401, vyy411, bba)
new_esEs0(:(vyy400, vyy401), :(vyy410, vyy411), ea) → new_esEs0(vyy401, vyy411, ea)
new_esEs2(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ha, hb, app(app(app(ty_@3, hg), hh), baa)) → new_esEs2(vyy402, vyy412, hg, hh, baa)
new_esEs2(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), app(app(app(ty_@3, bcf), bcg), bch), hb, bah) → new_esEs2(vyy400, vyy410, bcf, bcg, bch)
new_esEs3(Left(vyy400), Left(vyy410), app(ty_Maybe, bea), bdg) → new_esEs1(vyy400, vyy410, bea)
new_esEs0(:(vyy400, vyy401), :(vyy410, vyy411), app(app(app(ty_@3, ef), eg), eh)) → new_esEs2(vyy400, vyy410, ef, eg, eh)
new_esEs1(Just(vyy400), Just(vyy410), app(app(ty_@2, ff), fg)) → new_esEs(vyy400, vyy410, ff, fg)
new_esEs(@2(vyy400, vyy401), @2(vyy410, vyy411), h, app(ty_Maybe, bd)) → new_esEs1(vyy401, vyy411, bd)
new_esEs4(vyy40, vyy41, bge, bgf) → new_esEs0(new_fmToList(vyy40, bge, bgf), new_fmToList(vyy41, bge, bgf), app(app(ty_@2, bge), bgf))
new_esEs1(Just(vyy400), Just(vyy410), app(ty_[], fh)) → new_esEs0(vyy400, vyy410, fh)
new_esEs0(:(vyy400, vyy401), :(vyy410, vyy411), app(app(ty_Either, fa), fb)) → new_esEs3(vyy400, vyy410, fa, fb)
new_esEs3(Left(vyy400), Left(vyy410), app(app(ty_@2, bde), bdf), bdg) → new_esEs(vyy400, vyy410, bde, bdf)
new_esEs3(Left(vyy400), Left(vyy410), app(app(ty_FiniteMap, beg), beh), bdg) → new_esEs4(vyy400, vyy410, beg, beh)
new_esEs(@2(vyy400, vyy401), @2(vyy410, vyy411), h, app(app(app(ty_@3, be), bf), bg)) → new_esEs2(vyy401, vyy411, be, bf, bg)
new_esEs2(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ha, app(app(ty_FiniteMap, bbh), bca), bah) → new_esEs4(vyy401, vyy411, bbh, bca)
new_esEs2(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), app(app(ty_Either, bda), bdb), hb, bah) → new_esEs3(vyy400, vyy410, bda, bdb)
new_esEs3(Right(vyy400), Right(vyy410), bfa, app(ty_Maybe, bfe)) → new_esEs1(vyy400, vyy410, bfe)
new_esEs2(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ha, app(app(app(ty_@3, bbc), bbd), bbe), bah) → new_esEs2(vyy401, vyy411, bbc, bbd, bbe)
new_esEs3(Right(vyy400), Right(vyy410), bfa, app(app(app(ty_@3, bff), bfg), bfh)) → new_esEs2(vyy400, vyy410, bff, bfg, bfh)
new_esEs1(Just(vyy400), Just(vyy410), app(app(ty_FiniteMap, gg), gh)) → new_esEs4(vyy400, vyy410, gg, gh)
new_esEs2(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), app(app(ty_FiniteMap, bdc), bdd), hb, bah) → new_esEs4(vyy400, vyy410, bdc, bdd)
new_esEs0(:(vyy400, vyy401), :(vyy410, vyy411), app(app(ty_@2, eb), ec)) → new_esEs(vyy400, vyy410, eb, ec)
new_esEs2(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ha, app(app(ty_@2, baf), bag), bah) → new_esEs(vyy401, vyy411, baf, bag)
new_esEs2(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ha, hb, app(app(ty_FiniteMap, bad), bae)) → new_esEs4(vyy402, vyy412, bad, bae)
new_esEs0(:(vyy400, vyy401), :(vyy410, vyy411), app(ty_[], ed)) → new_esEs0(vyy400, vyy410, ed)
new_esEs3(Left(vyy400), Left(vyy410), app(app(app(ty_@3, beb), bec), bed), bdg) → new_esEs2(vyy400, vyy410, beb, bec, bed)
new_esEs2(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ha, hb, app(app(ty_Either, bab), bac)) → new_esEs3(vyy402, vyy412, bab, bac)
new_esEs2(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ha, hb, app(app(ty_@2, hc), hd)) → new_esEs(vyy402, vyy412, hc, hd)
new_esEs(@2(vyy400, vyy401), @2(vyy410, vyy411), h, app(app(ty_FiniteMap, cb), cc)) → new_esEs4(vyy401, vyy411, cb, cc)
new_esEs3(Right(vyy400), Right(vyy410), bfa, app(app(ty_@2, bfb), bfc)) → new_esEs(vyy400, vyy410, bfb, bfc)
new_esEs(@2(vyy400, vyy401), @2(vyy410, vyy411), app(ty_Maybe, da), cf) → new_esEs1(vyy400, vyy410, da)
The TRS R consists of the following rules:
new_foldFM0(vyy410, vyy411, vyy85, EmptyFM, bge, bgf) → :(@2(vyy410, vyy411), vyy85)
new_foldFM0(vyy410, vyy411, vyy85, Branch(vyy4130, vyy4131, vyy4132, vyy4133, vyy4134), bge, bgf) → new_foldFM0(vyy4130, vyy4131, new_foldFM0(vyy410, vyy411, vyy85, vyy4134, bge, bgf), vyy4133, bge, bgf)
new_fmToList(vyy41, bge, bgf) → new_foldFM2(vyy41, bge, bgf)
new_foldFM2(Branch(vyy410, vyy411, vyy412, vyy413, vyy414), bge, bgf) → new_foldFM0(vyy410, vyy411, new_foldFM2(vyy414, bge, bgf), vyy413, bge, bgf)
new_foldFM2(EmptyFM, bge, bgf) → []
The set Q consists of the following terms:
new_fmToList(x0, x1, x2)
new_foldFM2(EmptyFM, x0, x1)
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
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 rewriting [15] the rule new_esEs4(vyy40, vyy41, bge, bgf) → new_esEs0(new_fmToList(vyy40, bge, bgf), new_fmToList(vyy41, bge, bgf), app(app(ty_@2, bge), bgf)) at position [0] we obtained the following new rules:
new_esEs4(vyy40, vyy41, bge, bgf) → new_esEs0(new_foldFM2(vyy40, bge, bgf), new_fmToList(vyy41, bge, bgf), app(app(ty_@2, bge), bgf))
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ Rewriting
↳ QDP
↳ Rewriting
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_esEs(@2(vyy400, vyy401), @2(vyy410, vyy411), app(ty_[], cg), cf) → new_esEs0(vyy400, vyy410, cg)
new_esEs(@2(vyy400, vyy401), @2(vyy410, vyy411), app(app(ty_@2, cd), ce), cf) → new_esEs(vyy400, vyy410, cd, ce)
new_esEs2(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), app(ty_Maybe, bce), hb, bah) → new_esEs1(vyy400, vyy410, bce)
new_esEs2(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ha, app(ty_Maybe, bbb), bah) → new_esEs1(vyy401, vyy411, bbb)
new_esEs2(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ha, hb, app(ty_[], he)) → new_esEs0(vyy402, vyy412, he)
new_esEs2(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ha, app(app(ty_Either, bbf), bbg), bah) → new_esEs3(vyy401, vyy411, bbf, bbg)
new_esEs(@2(vyy400, vyy401), @2(vyy410, vyy411), app(app(ty_FiniteMap, dg), dh), cf) → new_esEs4(vyy400, vyy410, dg, dh)
new_esEs3(Right(vyy400), Right(vyy410), bfa, app(app(ty_Either, bga), bgb)) → new_esEs3(vyy400, vyy410, bga, bgb)
new_esEs3(Left(vyy400), Left(vyy410), app(app(ty_Either, bee), bef), bdg) → new_esEs3(vyy400, vyy410, bee, bef)
new_esEs1(Just(vyy400), Just(vyy410), app(app(ty_Either, ge), gf)) → new_esEs3(vyy400, vyy410, ge, gf)
new_esEs(@2(vyy400, vyy401), @2(vyy410, vyy411), app(app(ty_Either, de), df), cf) → new_esEs3(vyy400, vyy410, de, df)
new_esEs0(:(vyy400, vyy401), :(vyy410, vyy411), app(ty_Maybe, ee)) → new_esEs1(vyy400, vyy410, ee)
new_esEs3(Left(vyy400), Left(vyy410), app(ty_[], bdh), bdg) → new_esEs0(vyy400, vyy410, bdh)
new_esEs(@2(vyy400, vyy401), @2(vyy410, vyy411), h, app(app(ty_Either, bh), ca)) → new_esEs3(vyy401, vyy411, bh, ca)
new_esEs3(Right(vyy400), Right(vyy410), bfa, app(ty_[], bfd)) → new_esEs0(vyy400, vyy410, bfd)
new_esEs(@2(vyy400, vyy401), @2(vyy410, vyy411), h, app(ty_[], bc)) → new_esEs0(vyy401, vyy411, bc)
new_esEs1(Just(vyy400), Just(vyy410), app(ty_Maybe, ga)) → new_esEs1(vyy400, vyy410, ga)
new_esEs4(vyy40, vyy41, bge, bgf) → new_esEs0(new_foldFM2(vyy40, bge, bgf), new_fmToList(vyy41, bge, bgf), app(app(ty_@2, bge), bgf))
new_esEs(@2(vyy400, vyy401), @2(vyy410, vyy411), h, app(app(ty_@2, ba), bb)) → new_esEs(vyy401, vyy411, ba, bb)
new_esEs2(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ha, hb, app(ty_Maybe, hf)) → new_esEs1(vyy402, vyy412, hf)
new_esEs1(Just(vyy400), Just(vyy410), app(app(app(ty_@3, gb), gc), gd)) → new_esEs2(vyy400, vyy410, gb, gc, gd)
new_esEs(@2(vyy400, vyy401), @2(vyy410, vyy411), app(app(app(ty_@3, db), dc), dd), cf) → new_esEs2(vyy400, vyy410, db, dc, dd)
new_esEs3(Right(vyy400), Right(vyy410), bfa, app(app(ty_FiniteMap, bgc), bgd)) → new_esEs4(vyy400, vyy410, bgc, bgd)
new_esEs2(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), app(app(ty_@2, bcb), bcc), hb, bah) → new_esEs(vyy400, vyy410, bcb, bcc)
new_esEs2(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), app(ty_[], bcd), hb, bah) → new_esEs0(vyy400, vyy410, bcd)
new_esEs2(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ha, app(ty_[], bba), bah) → new_esEs0(vyy401, vyy411, bba)
new_esEs0(:(vyy400, vyy401), :(vyy410, vyy411), app(app(ty_FiniteMap, fc), fd)) → new_esEs4(vyy400, vyy410, fc, fd)
new_esEs2(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ha, hb, app(app(app(ty_@3, hg), hh), baa)) → new_esEs2(vyy402, vyy412, hg, hh, baa)
new_esEs0(:(vyy400, vyy401), :(vyy410, vyy411), ea) → new_esEs0(vyy401, vyy411, ea)
new_esEs2(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), app(app(app(ty_@3, bcf), bcg), bch), hb, bah) → new_esEs2(vyy400, vyy410, bcf, bcg, bch)
new_esEs3(Left(vyy400), Left(vyy410), app(ty_Maybe, bea), bdg) → new_esEs1(vyy400, vyy410, bea)
new_esEs0(:(vyy400, vyy401), :(vyy410, vyy411), app(app(app(ty_@3, ef), eg), eh)) → new_esEs2(vyy400, vyy410, ef, eg, eh)
new_esEs1(Just(vyy400), Just(vyy410), app(app(ty_@2, ff), fg)) → new_esEs(vyy400, vyy410, ff, fg)
new_esEs(@2(vyy400, vyy401), @2(vyy410, vyy411), h, app(ty_Maybe, bd)) → new_esEs1(vyy401, vyy411, bd)
new_esEs1(Just(vyy400), Just(vyy410), app(ty_[], fh)) → new_esEs0(vyy400, vyy410, fh)
new_esEs3(Left(vyy400), Left(vyy410), app(app(ty_@2, bde), bdf), bdg) → new_esEs(vyy400, vyy410, bde, bdf)
new_esEs0(:(vyy400, vyy401), :(vyy410, vyy411), app(app(ty_Either, fa), fb)) → new_esEs3(vyy400, vyy410, fa, fb)
new_esEs3(Left(vyy400), Left(vyy410), app(app(ty_FiniteMap, beg), beh), bdg) → new_esEs4(vyy400, vyy410, beg, beh)
new_esEs(@2(vyy400, vyy401), @2(vyy410, vyy411), h, app(app(app(ty_@3, be), bf), bg)) → new_esEs2(vyy401, vyy411, be, bf, bg)
new_esEs2(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ha, app(app(ty_FiniteMap, bbh), bca), bah) → new_esEs4(vyy401, vyy411, bbh, bca)
new_esEs2(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), app(app(ty_Either, bda), bdb), hb, bah) → new_esEs3(vyy400, vyy410, bda, bdb)
new_esEs3(Right(vyy400), Right(vyy410), bfa, app(ty_Maybe, bfe)) → new_esEs1(vyy400, vyy410, bfe)
new_esEs2(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ha, app(app(app(ty_@3, bbc), bbd), bbe), bah) → new_esEs2(vyy401, vyy411, bbc, bbd, bbe)
new_esEs3(Right(vyy400), Right(vyy410), bfa, app(app(app(ty_@3, bff), bfg), bfh)) → new_esEs2(vyy400, vyy410, bff, bfg, bfh)
new_esEs1(Just(vyy400), Just(vyy410), app(app(ty_FiniteMap, gg), gh)) → new_esEs4(vyy400, vyy410, gg, gh)
new_esEs2(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), app(app(ty_FiniteMap, bdc), bdd), hb, bah) → new_esEs4(vyy400, vyy410, bdc, bdd)
new_esEs0(:(vyy400, vyy401), :(vyy410, vyy411), app(app(ty_@2, eb), ec)) → new_esEs(vyy400, vyy410, eb, ec)
new_esEs2(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ha, app(app(ty_@2, baf), bag), bah) → new_esEs(vyy401, vyy411, baf, bag)
new_esEs0(:(vyy400, vyy401), :(vyy410, vyy411), app(ty_[], ed)) → new_esEs0(vyy400, vyy410, ed)
new_esEs2(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ha, hb, app(app(ty_FiniteMap, bad), bae)) → new_esEs4(vyy402, vyy412, bad, bae)
new_esEs3(Left(vyy400), Left(vyy410), app(app(app(ty_@3, beb), bec), bed), bdg) → new_esEs2(vyy400, vyy410, beb, bec, bed)
new_esEs2(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ha, hb, app(app(ty_Either, bab), bac)) → new_esEs3(vyy402, vyy412, bab, bac)
new_esEs2(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ha, hb, app(app(ty_@2, hc), hd)) → new_esEs(vyy402, vyy412, hc, hd)
new_esEs(@2(vyy400, vyy401), @2(vyy410, vyy411), h, app(app(ty_FiniteMap, cb), cc)) → new_esEs4(vyy401, vyy411, cb, cc)
new_esEs3(Right(vyy400), Right(vyy410), bfa, app(app(ty_@2, bfb), bfc)) → new_esEs(vyy400, vyy410, bfb, bfc)
new_esEs(@2(vyy400, vyy401), @2(vyy410, vyy411), app(ty_Maybe, da), cf) → new_esEs1(vyy400, vyy410, da)
The TRS R consists of the following rules:
new_foldFM0(vyy410, vyy411, vyy85, EmptyFM, bge, bgf) → :(@2(vyy410, vyy411), vyy85)
new_foldFM0(vyy410, vyy411, vyy85, Branch(vyy4130, vyy4131, vyy4132, vyy4133, vyy4134), bge, bgf) → new_foldFM0(vyy4130, vyy4131, new_foldFM0(vyy410, vyy411, vyy85, vyy4134, bge, bgf), vyy4133, bge, bgf)
new_fmToList(vyy41, bge, bgf) → new_foldFM2(vyy41, bge, bgf)
new_foldFM2(Branch(vyy410, vyy411, vyy412, vyy413, vyy414), bge, bgf) → new_foldFM0(vyy410, vyy411, new_foldFM2(vyy414, bge, bgf), vyy413, bge, bgf)
new_foldFM2(EmptyFM, bge, bgf) → []
The set Q consists of the following terms:
new_fmToList(x0, x1, x2)
new_foldFM2(EmptyFM, x0, x1)
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
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 rewriting [15] the rule new_esEs4(vyy40, vyy41, bge, bgf) → new_esEs0(new_foldFM2(vyy40, bge, bgf), new_fmToList(vyy41, bge, bgf), app(app(ty_@2, bge), bgf)) at position [1] we obtained the following new rules:
new_esEs4(vyy40, vyy41, bge, bgf) → new_esEs0(new_foldFM2(vyy40, bge, bgf), new_foldFM2(vyy41, bge, bgf), app(app(ty_@2, bge), bgf))
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ Rewriting
↳ QDP
↳ Rewriting
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_esEs(@2(vyy400, vyy401), @2(vyy410, vyy411), app(app(ty_@2, cd), ce), cf) → new_esEs(vyy400, vyy410, cd, ce)
new_esEs(@2(vyy400, vyy401), @2(vyy410, vyy411), app(ty_[], cg), cf) → new_esEs0(vyy400, vyy410, cg)
new_esEs2(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ha, app(ty_Maybe, bbb), bah) → new_esEs1(vyy401, vyy411, bbb)
new_esEs2(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), app(ty_Maybe, bce), hb, bah) → new_esEs1(vyy400, vyy410, bce)
new_esEs2(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ha, hb, app(ty_[], he)) → new_esEs0(vyy402, vyy412, he)
new_esEs(@2(vyy400, vyy401), @2(vyy410, vyy411), app(app(ty_FiniteMap, dg), dh), cf) → new_esEs4(vyy400, vyy410, dg, dh)
new_esEs2(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ha, app(app(ty_Either, bbf), bbg), bah) → new_esEs3(vyy401, vyy411, bbf, bbg)
new_esEs3(Right(vyy400), Right(vyy410), bfa, app(app(ty_Either, bga), bgb)) → new_esEs3(vyy400, vyy410, bga, bgb)
new_esEs3(Left(vyy400), Left(vyy410), app(app(ty_Either, bee), bef), bdg) → new_esEs3(vyy400, vyy410, bee, bef)
new_esEs1(Just(vyy400), Just(vyy410), app(app(ty_Either, ge), gf)) → new_esEs3(vyy400, vyy410, ge, gf)
new_esEs(@2(vyy400, vyy401), @2(vyy410, vyy411), app(app(ty_Either, de), df), cf) → new_esEs3(vyy400, vyy410, de, df)
new_esEs0(:(vyy400, vyy401), :(vyy410, vyy411), app(ty_Maybe, ee)) → new_esEs1(vyy400, vyy410, ee)
new_esEs3(Left(vyy400), Left(vyy410), app(ty_[], bdh), bdg) → new_esEs0(vyy400, vyy410, bdh)
new_esEs(@2(vyy400, vyy401), @2(vyy410, vyy411), h, app(app(ty_Either, bh), ca)) → new_esEs3(vyy401, vyy411, bh, ca)
new_esEs3(Right(vyy400), Right(vyy410), bfa, app(ty_[], bfd)) → new_esEs0(vyy400, vyy410, bfd)
new_esEs(@2(vyy400, vyy401), @2(vyy410, vyy411), h, app(ty_[], bc)) → new_esEs0(vyy401, vyy411, bc)
new_esEs1(Just(vyy400), Just(vyy410), app(ty_Maybe, ga)) → new_esEs1(vyy400, vyy410, ga)
new_esEs2(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ha, hb, app(ty_Maybe, hf)) → new_esEs1(vyy402, vyy412, hf)
new_esEs(@2(vyy400, vyy401), @2(vyy410, vyy411), h, app(app(ty_@2, ba), bb)) → new_esEs(vyy401, vyy411, ba, bb)
new_esEs1(Just(vyy400), Just(vyy410), app(app(app(ty_@3, gb), gc), gd)) → new_esEs2(vyy400, vyy410, gb, gc, gd)
new_esEs(@2(vyy400, vyy401), @2(vyy410, vyy411), app(app(app(ty_@3, db), dc), dd), cf) → new_esEs2(vyy400, vyy410, db, dc, dd)
new_esEs3(Right(vyy400), Right(vyy410), bfa, app(app(ty_FiniteMap, bgc), bgd)) → new_esEs4(vyy400, vyy410, bgc, bgd)
new_esEs2(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), app(app(ty_@2, bcb), bcc), hb, bah) → new_esEs(vyy400, vyy410, bcb, bcc)
new_esEs2(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), app(ty_[], bcd), hb, bah) → new_esEs0(vyy400, vyy410, bcd)
new_esEs0(:(vyy400, vyy401), :(vyy410, vyy411), app(app(ty_FiniteMap, fc), fd)) → new_esEs4(vyy400, vyy410, fc, fd)
new_esEs2(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ha, app(ty_[], bba), bah) → new_esEs0(vyy401, vyy411, bba)
new_esEs4(vyy40, vyy41, bge, bgf) → new_esEs0(new_foldFM2(vyy40, bge, bgf), new_foldFM2(vyy41, bge, bgf), app(app(ty_@2, bge), bgf))
new_esEs0(:(vyy400, vyy401), :(vyy410, vyy411), ea) → new_esEs0(vyy401, vyy411, ea)
new_esEs2(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ha, hb, app(app(app(ty_@3, hg), hh), baa)) → new_esEs2(vyy402, vyy412, hg, hh, baa)
new_esEs2(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), app(app(app(ty_@3, bcf), bcg), bch), hb, bah) → new_esEs2(vyy400, vyy410, bcf, bcg, bch)
new_esEs3(Left(vyy400), Left(vyy410), app(ty_Maybe, bea), bdg) → new_esEs1(vyy400, vyy410, bea)
new_esEs0(:(vyy400, vyy401), :(vyy410, vyy411), app(app(app(ty_@3, ef), eg), eh)) → new_esEs2(vyy400, vyy410, ef, eg, eh)
new_esEs1(Just(vyy400), Just(vyy410), app(app(ty_@2, ff), fg)) → new_esEs(vyy400, vyy410, ff, fg)
new_esEs(@2(vyy400, vyy401), @2(vyy410, vyy411), h, app(ty_Maybe, bd)) → new_esEs1(vyy401, vyy411, bd)
new_esEs1(Just(vyy400), Just(vyy410), app(ty_[], fh)) → new_esEs0(vyy400, vyy410, fh)
new_esEs0(:(vyy400, vyy401), :(vyy410, vyy411), app(app(ty_Either, fa), fb)) → new_esEs3(vyy400, vyy410, fa, fb)
new_esEs3(Left(vyy400), Left(vyy410), app(app(ty_@2, bde), bdf), bdg) → new_esEs(vyy400, vyy410, bde, bdf)
new_esEs3(Left(vyy400), Left(vyy410), app(app(ty_FiniteMap, beg), beh), bdg) → new_esEs4(vyy400, vyy410, beg, beh)
new_esEs(@2(vyy400, vyy401), @2(vyy410, vyy411), h, app(app(app(ty_@3, be), bf), bg)) → new_esEs2(vyy401, vyy411, be, bf, bg)
new_esEs2(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ha, app(app(ty_FiniteMap, bbh), bca), bah) → new_esEs4(vyy401, vyy411, bbh, bca)
new_esEs2(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), app(app(ty_Either, bda), bdb), hb, bah) → new_esEs3(vyy400, vyy410, bda, bdb)
new_esEs3(Right(vyy400), Right(vyy410), bfa, app(ty_Maybe, bfe)) → new_esEs1(vyy400, vyy410, bfe)
new_esEs2(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ha, app(app(app(ty_@3, bbc), bbd), bbe), bah) → new_esEs2(vyy401, vyy411, bbc, bbd, bbe)
new_esEs3(Right(vyy400), Right(vyy410), bfa, app(app(app(ty_@3, bff), bfg), bfh)) → new_esEs2(vyy400, vyy410, bff, bfg, bfh)
new_esEs1(Just(vyy400), Just(vyy410), app(app(ty_FiniteMap, gg), gh)) → new_esEs4(vyy400, vyy410, gg, gh)
new_esEs2(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), app(app(ty_FiniteMap, bdc), bdd), hb, bah) → new_esEs4(vyy400, vyy410, bdc, bdd)
new_esEs0(:(vyy400, vyy401), :(vyy410, vyy411), app(app(ty_@2, eb), ec)) → new_esEs(vyy400, vyy410, eb, ec)
new_esEs2(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ha, app(app(ty_@2, baf), bag), bah) → new_esEs(vyy401, vyy411, baf, bag)
new_esEs2(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ha, hb, app(app(ty_FiniteMap, bad), bae)) → new_esEs4(vyy402, vyy412, bad, bae)
new_esEs0(:(vyy400, vyy401), :(vyy410, vyy411), app(ty_[], ed)) → new_esEs0(vyy400, vyy410, ed)
new_esEs3(Left(vyy400), Left(vyy410), app(app(app(ty_@3, beb), bec), bed), bdg) → new_esEs2(vyy400, vyy410, beb, bec, bed)
new_esEs2(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ha, hb, app(app(ty_Either, bab), bac)) → new_esEs3(vyy402, vyy412, bab, bac)
new_esEs2(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ha, hb, app(app(ty_@2, hc), hd)) → new_esEs(vyy402, vyy412, hc, hd)
new_esEs(@2(vyy400, vyy401), @2(vyy410, vyy411), h, app(app(ty_FiniteMap, cb), cc)) → new_esEs4(vyy401, vyy411, cb, cc)
new_esEs3(Right(vyy400), Right(vyy410), bfa, app(app(ty_@2, bfb), bfc)) → new_esEs(vyy400, vyy410, bfb, bfc)
new_esEs(@2(vyy400, vyy401), @2(vyy410, vyy411), app(ty_Maybe, da), cf) → new_esEs1(vyy400, vyy410, da)
The TRS R consists of the following rules:
new_foldFM0(vyy410, vyy411, vyy85, EmptyFM, bge, bgf) → :(@2(vyy410, vyy411), vyy85)
new_foldFM0(vyy410, vyy411, vyy85, Branch(vyy4130, vyy4131, vyy4132, vyy4133, vyy4134), bge, bgf) → new_foldFM0(vyy4130, vyy4131, new_foldFM0(vyy410, vyy411, vyy85, vyy4134, bge, bgf), vyy4133, bge, bgf)
new_fmToList(vyy41, bge, bgf) → new_foldFM2(vyy41, bge, bgf)
new_foldFM2(Branch(vyy410, vyy411, vyy412, vyy413, vyy414), bge, bgf) → new_foldFM0(vyy410, vyy411, new_foldFM2(vyy414, bge, bgf), vyy413, bge, bgf)
new_foldFM2(EmptyFM, bge, bgf) → []
The set Q consists of the following terms:
new_fmToList(x0, x1, x2)
new_foldFM2(EmptyFM, x0, x1)
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
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.
As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [15] we can delete all non-usable rules [17] from R.
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ Rewriting
↳ QDP
↳ Rewriting
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QReductionProof
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_esEs(@2(vyy400, vyy401), @2(vyy410, vyy411), app(app(ty_@2, cd), ce), cf) → new_esEs(vyy400, vyy410, cd, ce)
new_esEs(@2(vyy400, vyy401), @2(vyy410, vyy411), app(ty_[], cg), cf) → new_esEs0(vyy400, vyy410, cg)
new_esEs2(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ha, app(ty_Maybe, bbb), bah) → new_esEs1(vyy401, vyy411, bbb)
new_esEs2(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), app(ty_Maybe, bce), hb, bah) → new_esEs1(vyy400, vyy410, bce)
new_esEs2(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ha, hb, app(ty_[], he)) → new_esEs0(vyy402, vyy412, he)
new_esEs(@2(vyy400, vyy401), @2(vyy410, vyy411), app(app(ty_FiniteMap, dg), dh), cf) → new_esEs4(vyy400, vyy410, dg, dh)
new_esEs2(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ha, app(app(ty_Either, bbf), bbg), bah) → new_esEs3(vyy401, vyy411, bbf, bbg)
new_esEs3(Right(vyy400), Right(vyy410), bfa, app(app(ty_Either, bga), bgb)) → new_esEs3(vyy400, vyy410, bga, bgb)
new_esEs3(Left(vyy400), Left(vyy410), app(app(ty_Either, bee), bef), bdg) → new_esEs3(vyy400, vyy410, bee, bef)
new_esEs1(Just(vyy400), Just(vyy410), app(app(ty_Either, ge), gf)) → new_esEs3(vyy400, vyy410, ge, gf)
new_esEs(@2(vyy400, vyy401), @2(vyy410, vyy411), app(app(ty_Either, de), df), cf) → new_esEs3(vyy400, vyy410, de, df)
new_esEs0(:(vyy400, vyy401), :(vyy410, vyy411), app(ty_Maybe, ee)) → new_esEs1(vyy400, vyy410, ee)
new_esEs3(Left(vyy400), Left(vyy410), app(ty_[], bdh), bdg) → new_esEs0(vyy400, vyy410, bdh)
new_esEs(@2(vyy400, vyy401), @2(vyy410, vyy411), h, app(app(ty_Either, bh), ca)) → new_esEs3(vyy401, vyy411, bh, ca)
new_esEs3(Right(vyy400), Right(vyy410), bfa, app(ty_[], bfd)) → new_esEs0(vyy400, vyy410, bfd)
new_esEs(@2(vyy400, vyy401), @2(vyy410, vyy411), h, app(ty_[], bc)) → new_esEs0(vyy401, vyy411, bc)
new_esEs1(Just(vyy400), Just(vyy410), app(ty_Maybe, ga)) → new_esEs1(vyy400, vyy410, ga)
new_esEs2(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ha, hb, app(ty_Maybe, hf)) → new_esEs1(vyy402, vyy412, hf)
new_esEs(@2(vyy400, vyy401), @2(vyy410, vyy411), h, app(app(ty_@2, ba), bb)) → new_esEs(vyy401, vyy411, ba, bb)
new_esEs1(Just(vyy400), Just(vyy410), app(app(app(ty_@3, gb), gc), gd)) → new_esEs2(vyy400, vyy410, gb, gc, gd)
new_esEs(@2(vyy400, vyy401), @2(vyy410, vyy411), app(app(app(ty_@3, db), dc), dd), cf) → new_esEs2(vyy400, vyy410, db, dc, dd)
new_esEs3(Right(vyy400), Right(vyy410), bfa, app(app(ty_FiniteMap, bgc), bgd)) → new_esEs4(vyy400, vyy410, bgc, bgd)
new_esEs2(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), app(app(ty_@2, bcb), bcc), hb, bah) → new_esEs(vyy400, vyy410, bcb, bcc)
new_esEs2(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), app(ty_[], bcd), hb, bah) → new_esEs0(vyy400, vyy410, bcd)
new_esEs0(:(vyy400, vyy401), :(vyy410, vyy411), app(app(ty_FiniteMap, fc), fd)) → new_esEs4(vyy400, vyy410, fc, fd)
new_esEs2(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ha, app(ty_[], bba), bah) → new_esEs0(vyy401, vyy411, bba)
new_esEs4(vyy40, vyy41, bge, bgf) → new_esEs0(new_foldFM2(vyy40, bge, bgf), new_foldFM2(vyy41, bge, bgf), app(app(ty_@2, bge), bgf))
new_esEs0(:(vyy400, vyy401), :(vyy410, vyy411), ea) → new_esEs0(vyy401, vyy411, ea)
new_esEs2(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ha, hb, app(app(app(ty_@3, hg), hh), baa)) → new_esEs2(vyy402, vyy412, hg, hh, baa)
new_esEs2(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), app(app(app(ty_@3, bcf), bcg), bch), hb, bah) → new_esEs2(vyy400, vyy410, bcf, bcg, bch)
new_esEs3(Left(vyy400), Left(vyy410), app(ty_Maybe, bea), bdg) → new_esEs1(vyy400, vyy410, bea)
new_esEs0(:(vyy400, vyy401), :(vyy410, vyy411), app(app(app(ty_@3, ef), eg), eh)) → new_esEs2(vyy400, vyy410, ef, eg, eh)
new_esEs1(Just(vyy400), Just(vyy410), app(app(ty_@2, ff), fg)) → new_esEs(vyy400, vyy410, ff, fg)
new_esEs(@2(vyy400, vyy401), @2(vyy410, vyy411), h, app(ty_Maybe, bd)) → new_esEs1(vyy401, vyy411, bd)
new_esEs1(Just(vyy400), Just(vyy410), app(ty_[], fh)) → new_esEs0(vyy400, vyy410, fh)
new_esEs0(:(vyy400, vyy401), :(vyy410, vyy411), app(app(ty_Either, fa), fb)) → new_esEs3(vyy400, vyy410, fa, fb)
new_esEs3(Left(vyy400), Left(vyy410), app(app(ty_@2, bde), bdf), bdg) → new_esEs(vyy400, vyy410, bde, bdf)
new_esEs3(Left(vyy400), Left(vyy410), app(app(ty_FiniteMap, beg), beh), bdg) → new_esEs4(vyy400, vyy410, beg, beh)
new_esEs(@2(vyy400, vyy401), @2(vyy410, vyy411), h, app(app(app(ty_@3, be), bf), bg)) → new_esEs2(vyy401, vyy411, be, bf, bg)
new_esEs2(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ha, app(app(ty_FiniteMap, bbh), bca), bah) → new_esEs4(vyy401, vyy411, bbh, bca)
new_esEs2(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), app(app(ty_Either, bda), bdb), hb, bah) → new_esEs3(vyy400, vyy410, bda, bdb)
new_esEs3(Right(vyy400), Right(vyy410), bfa, app(ty_Maybe, bfe)) → new_esEs1(vyy400, vyy410, bfe)
new_esEs2(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ha, app(app(app(ty_@3, bbc), bbd), bbe), bah) → new_esEs2(vyy401, vyy411, bbc, bbd, bbe)
new_esEs3(Right(vyy400), Right(vyy410), bfa, app(app(app(ty_@3, bff), bfg), bfh)) → new_esEs2(vyy400, vyy410, bff, bfg, bfh)
new_esEs1(Just(vyy400), Just(vyy410), app(app(ty_FiniteMap, gg), gh)) → new_esEs4(vyy400, vyy410, gg, gh)
new_esEs2(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), app(app(ty_FiniteMap, bdc), bdd), hb, bah) → new_esEs4(vyy400, vyy410, bdc, bdd)
new_esEs0(:(vyy400, vyy401), :(vyy410, vyy411), app(app(ty_@2, eb), ec)) → new_esEs(vyy400, vyy410, eb, ec)
new_esEs2(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ha, app(app(ty_@2, baf), bag), bah) → new_esEs(vyy401, vyy411, baf, bag)
new_esEs0(:(vyy400, vyy401), :(vyy410, vyy411), app(ty_[], ed)) → new_esEs0(vyy400, vyy410, ed)
new_esEs2(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ha, hb, app(app(ty_FiniteMap, bad), bae)) → new_esEs4(vyy402, vyy412, bad, bae)
new_esEs3(Left(vyy400), Left(vyy410), app(app(app(ty_@3, beb), bec), bed), bdg) → new_esEs2(vyy400, vyy410, beb, bec, bed)
new_esEs2(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ha, hb, app(app(ty_Either, bab), bac)) → new_esEs3(vyy402, vyy412, bab, bac)
new_esEs2(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ha, hb, app(app(ty_@2, hc), hd)) → new_esEs(vyy402, vyy412, hc, hd)
new_esEs(@2(vyy400, vyy401), @2(vyy410, vyy411), h, app(app(ty_FiniteMap, cb), cc)) → new_esEs4(vyy401, vyy411, cb, cc)
new_esEs3(Right(vyy400), Right(vyy410), bfa, app(app(ty_@2, bfb), bfc)) → new_esEs(vyy400, vyy410, bfb, bfc)
new_esEs(@2(vyy400, vyy401), @2(vyy410, vyy411), app(ty_Maybe, da), cf) → new_esEs1(vyy400, vyy410, da)
The TRS R consists of the following rules:
new_foldFM2(Branch(vyy410, vyy411, vyy412, vyy413, vyy414), bge, bgf) → new_foldFM0(vyy410, vyy411, new_foldFM2(vyy414, bge, bgf), vyy413, bge, bgf)
new_foldFM2(EmptyFM, bge, bgf) → []
new_foldFM0(vyy410, vyy411, vyy85, EmptyFM, bge, bgf) → :(@2(vyy410, vyy411), vyy85)
new_foldFM0(vyy410, vyy411, vyy85, Branch(vyy4130, vyy4131, vyy4132, vyy4133, vyy4134), bge, bgf) → new_foldFM0(vyy4130, vyy4131, new_foldFM0(vyy410, vyy411, vyy85, vyy4134, bge, bgf), vyy4133, bge, bgf)
The set Q consists of the following terms:
new_fmToList(x0, x1, x2)
new_foldFM2(EmptyFM, x0, x1)
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
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.
We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.
new_fmToList(x0, x1, x2)
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ Rewriting
↳ QDP
↳ Rewriting
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QReductionProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_esEs(@2(vyy400, vyy401), @2(vyy410, vyy411), app(app(ty_@2, cd), ce), cf) → new_esEs(vyy400, vyy410, cd, ce)
new_esEs(@2(vyy400, vyy401), @2(vyy410, vyy411), app(ty_[], cg), cf) → new_esEs0(vyy400, vyy410, cg)
new_esEs2(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ha, app(ty_Maybe, bbb), bah) → new_esEs1(vyy401, vyy411, bbb)
new_esEs2(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), app(ty_Maybe, bce), hb, bah) → new_esEs1(vyy400, vyy410, bce)
new_esEs2(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ha, hb, app(ty_[], he)) → new_esEs0(vyy402, vyy412, he)
new_esEs(@2(vyy400, vyy401), @2(vyy410, vyy411), app(app(ty_FiniteMap, dg), dh), cf) → new_esEs4(vyy400, vyy410, dg, dh)
new_esEs2(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ha, app(app(ty_Either, bbf), bbg), bah) → new_esEs3(vyy401, vyy411, bbf, bbg)
new_esEs3(Right(vyy400), Right(vyy410), bfa, app(app(ty_Either, bga), bgb)) → new_esEs3(vyy400, vyy410, bga, bgb)
new_esEs3(Left(vyy400), Left(vyy410), app(app(ty_Either, bee), bef), bdg) → new_esEs3(vyy400, vyy410, bee, bef)
new_esEs1(Just(vyy400), Just(vyy410), app(app(ty_Either, ge), gf)) → new_esEs3(vyy400, vyy410, ge, gf)
new_esEs(@2(vyy400, vyy401), @2(vyy410, vyy411), app(app(ty_Either, de), df), cf) → new_esEs3(vyy400, vyy410, de, df)
new_esEs0(:(vyy400, vyy401), :(vyy410, vyy411), app(ty_Maybe, ee)) → new_esEs1(vyy400, vyy410, ee)
new_esEs3(Left(vyy400), Left(vyy410), app(ty_[], bdh), bdg) → new_esEs0(vyy400, vyy410, bdh)
new_esEs(@2(vyy400, vyy401), @2(vyy410, vyy411), h, app(app(ty_Either, bh), ca)) → new_esEs3(vyy401, vyy411, bh, ca)
new_esEs3(Right(vyy400), Right(vyy410), bfa, app(ty_[], bfd)) → new_esEs0(vyy400, vyy410, bfd)
new_esEs(@2(vyy400, vyy401), @2(vyy410, vyy411), h, app(ty_[], bc)) → new_esEs0(vyy401, vyy411, bc)
new_esEs1(Just(vyy400), Just(vyy410), app(ty_Maybe, ga)) → new_esEs1(vyy400, vyy410, ga)
new_esEs(@2(vyy400, vyy401), @2(vyy410, vyy411), h, app(app(ty_@2, ba), bb)) → new_esEs(vyy401, vyy411, ba, bb)
new_esEs2(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ha, hb, app(ty_Maybe, hf)) → new_esEs1(vyy402, vyy412, hf)
new_esEs1(Just(vyy400), Just(vyy410), app(app(app(ty_@3, gb), gc), gd)) → new_esEs2(vyy400, vyy410, gb, gc, gd)
new_esEs(@2(vyy400, vyy401), @2(vyy410, vyy411), app(app(app(ty_@3, db), dc), dd), cf) → new_esEs2(vyy400, vyy410, db, dc, dd)
new_esEs3(Right(vyy400), Right(vyy410), bfa, app(app(ty_FiniteMap, bgc), bgd)) → new_esEs4(vyy400, vyy410, bgc, bgd)
new_esEs2(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), app(app(ty_@2, bcb), bcc), hb, bah) → new_esEs(vyy400, vyy410, bcb, bcc)
new_esEs2(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), app(ty_[], bcd), hb, bah) → new_esEs0(vyy400, vyy410, bcd)
new_esEs0(:(vyy400, vyy401), :(vyy410, vyy411), app(app(ty_FiniteMap, fc), fd)) → new_esEs4(vyy400, vyy410, fc, fd)
new_esEs2(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ha, app(ty_[], bba), bah) → new_esEs0(vyy401, vyy411, bba)
new_esEs4(vyy40, vyy41, bge, bgf) → new_esEs0(new_foldFM2(vyy40, bge, bgf), new_foldFM2(vyy41, bge, bgf), app(app(ty_@2, bge), bgf))
new_esEs0(:(vyy400, vyy401), :(vyy410, vyy411), ea) → new_esEs0(vyy401, vyy411, ea)
new_esEs2(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ha, hb, app(app(app(ty_@3, hg), hh), baa)) → new_esEs2(vyy402, vyy412, hg, hh, baa)
new_esEs2(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), app(app(app(ty_@3, bcf), bcg), bch), hb, bah) → new_esEs2(vyy400, vyy410, bcf, bcg, bch)
new_esEs3(Left(vyy400), Left(vyy410), app(ty_Maybe, bea), bdg) → new_esEs1(vyy400, vyy410, bea)
new_esEs0(:(vyy400, vyy401), :(vyy410, vyy411), app(app(app(ty_@3, ef), eg), eh)) → new_esEs2(vyy400, vyy410, ef, eg, eh)
new_esEs1(Just(vyy400), Just(vyy410), app(app(ty_@2, ff), fg)) → new_esEs(vyy400, vyy410, ff, fg)
new_esEs(@2(vyy400, vyy401), @2(vyy410, vyy411), h, app(ty_Maybe, bd)) → new_esEs1(vyy401, vyy411, bd)
new_esEs1(Just(vyy400), Just(vyy410), app(ty_[], fh)) → new_esEs0(vyy400, vyy410, fh)
new_esEs0(:(vyy400, vyy401), :(vyy410, vyy411), app(app(ty_Either, fa), fb)) → new_esEs3(vyy400, vyy410, fa, fb)
new_esEs3(Left(vyy400), Left(vyy410), app(app(ty_@2, bde), bdf), bdg) → new_esEs(vyy400, vyy410, bde, bdf)
new_esEs3(Left(vyy400), Left(vyy410), app(app(ty_FiniteMap, beg), beh), bdg) → new_esEs4(vyy400, vyy410, beg, beh)
new_esEs(@2(vyy400, vyy401), @2(vyy410, vyy411), h, app(app(app(ty_@3, be), bf), bg)) → new_esEs2(vyy401, vyy411, be, bf, bg)
new_esEs2(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ha, app(app(ty_FiniteMap, bbh), bca), bah) → new_esEs4(vyy401, vyy411, bbh, bca)
new_esEs2(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), app(app(ty_Either, bda), bdb), hb, bah) → new_esEs3(vyy400, vyy410, bda, bdb)
new_esEs3(Right(vyy400), Right(vyy410), bfa, app(ty_Maybe, bfe)) → new_esEs1(vyy400, vyy410, bfe)
new_esEs2(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ha, app(app(app(ty_@3, bbc), bbd), bbe), bah) → new_esEs2(vyy401, vyy411, bbc, bbd, bbe)
new_esEs3(Right(vyy400), Right(vyy410), bfa, app(app(app(ty_@3, bff), bfg), bfh)) → new_esEs2(vyy400, vyy410, bff, bfg, bfh)
new_esEs1(Just(vyy400), Just(vyy410), app(app(ty_FiniteMap, gg), gh)) → new_esEs4(vyy400, vyy410, gg, gh)
new_esEs2(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), app(app(ty_FiniteMap, bdc), bdd), hb, bah) → new_esEs4(vyy400, vyy410, bdc, bdd)
new_esEs0(:(vyy400, vyy401), :(vyy410, vyy411), app(app(ty_@2, eb), ec)) → new_esEs(vyy400, vyy410, eb, ec)
new_esEs2(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ha, app(app(ty_@2, baf), bag), bah) → new_esEs(vyy401, vyy411, baf, bag)
new_esEs2(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ha, hb, app(app(ty_FiniteMap, bad), bae)) → new_esEs4(vyy402, vyy412, bad, bae)
new_esEs0(:(vyy400, vyy401), :(vyy410, vyy411), app(ty_[], ed)) → new_esEs0(vyy400, vyy410, ed)
new_esEs3(Left(vyy400), Left(vyy410), app(app(app(ty_@3, beb), bec), bed), bdg) → new_esEs2(vyy400, vyy410, beb, bec, bed)
new_esEs2(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ha, hb, app(app(ty_Either, bab), bac)) → new_esEs3(vyy402, vyy412, bab, bac)
new_esEs2(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ha, hb, app(app(ty_@2, hc), hd)) → new_esEs(vyy402, vyy412, hc, hd)
new_esEs(@2(vyy400, vyy401), @2(vyy410, vyy411), h, app(app(ty_FiniteMap, cb), cc)) → new_esEs4(vyy401, vyy411, cb, cc)
new_esEs3(Right(vyy400), Right(vyy410), bfa, app(app(ty_@2, bfb), bfc)) → new_esEs(vyy400, vyy410, bfb, bfc)
new_esEs(@2(vyy400, vyy401), @2(vyy410, vyy411), app(ty_Maybe, da), cf) → new_esEs1(vyy400, vyy410, da)
The TRS R consists of the following rules:
new_foldFM2(Branch(vyy410, vyy411, vyy412, vyy413, vyy414), bge, bgf) → new_foldFM0(vyy410, vyy411, new_foldFM2(vyy414, bge, bgf), vyy413, bge, bgf)
new_foldFM2(EmptyFM, bge, bgf) → []
new_foldFM0(vyy410, vyy411, vyy85, EmptyFM, bge, bgf) → :(@2(vyy410, vyy411), vyy85)
new_foldFM0(vyy410, vyy411, vyy85, Branch(vyy4130, vyy4131, vyy4132, vyy4133, vyy4134), bge, bgf) → new_foldFM0(vyy4130, vyy4131, new_foldFM0(vyy410, vyy411, vyy85, vyy4134, bge, bgf), vyy4133, bge, bgf)
The set Q consists of the following terms:
new_foldFM2(EmptyFM, x0, x1)
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
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.
We use the reduction pair processor [15].
The following pairs can be oriented strictly and are deleted.
new_esEs(@2(vyy400, vyy401), @2(vyy410, vyy411), app(app(ty_@2, cd), ce), cf) → new_esEs(vyy400, vyy410, cd, ce)
new_esEs(@2(vyy400, vyy401), @2(vyy410, vyy411), app(ty_[], cg), cf) → new_esEs0(vyy400, vyy410, cg)
new_esEs2(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ha, app(ty_Maybe, bbb), bah) → new_esEs1(vyy401, vyy411, bbb)
new_esEs2(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), app(ty_Maybe, bce), hb, bah) → new_esEs1(vyy400, vyy410, bce)
new_esEs2(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ha, hb, app(ty_[], he)) → new_esEs0(vyy402, vyy412, he)
new_esEs(@2(vyy400, vyy401), @2(vyy410, vyy411), app(app(ty_FiniteMap, dg), dh), cf) → new_esEs4(vyy400, vyy410, dg, dh)
new_esEs2(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ha, app(app(ty_Either, bbf), bbg), bah) → new_esEs3(vyy401, vyy411, bbf, bbg)
new_esEs3(Right(vyy400), Right(vyy410), bfa, app(app(ty_Either, bga), bgb)) → new_esEs3(vyy400, vyy410, bga, bgb)
new_esEs3(Left(vyy400), Left(vyy410), app(app(ty_Either, bee), bef), bdg) → new_esEs3(vyy400, vyy410, bee, bef)
new_esEs1(Just(vyy400), Just(vyy410), app(app(ty_Either, ge), gf)) → new_esEs3(vyy400, vyy410, ge, gf)
new_esEs(@2(vyy400, vyy401), @2(vyy410, vyy411), app(app(ty_Either, de), df), cf) → new_esEs3(vyy400, vyy410, de, df)
new_esEs3(Left(vyy400), Left(vyy410), app(ty_[], bdh), bdg) → new_esEs0(vyy400, vyy410, bdh)
new_esEs(@2(vyy400, vyy401), @2(vyy410, vyy411), h, app(app(ty_Either, bh), ca)) → new_esEs3(vyy401, vyy411, bh, ca)
new_esEs3(Right(vyy400), Right(vyy410), bfa, app(ty_[], bfd)) → new_esEs0(vyy400, vyy410, bfd)
new_esEs(@2(vyy400, vyy401), @2(vyy410, vyy411), h, app(ty_[], bc)) → new_esEs0(vyy401, vyy411, bc)
new_esEs1(Just(vyy400), Just(vyy410), app(ty_Maybe, ga)) → new_esEs1(vyy400, vyy410, ga)
new_esEs(@2(vyy400, vyy401), @2(vyy410, vyy411), h, app(app(ty_@2, ba), bb)) → new_esEs(vyy401, vyy411, ba, bb)
new_esEs2(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ha, hb, app(ty_Maybe, hf)) → new_esEs1(vyy402, vyy412, hf)
new_esEs1(Just(vyy400), Just(vyy410), app(app(app(ty_@3, gb), gc), gd)) → new_esEs2(vyy400, vyy410, gb, gc, gd)
new_esEs(@2(vyy400, vyy401), @2(vyy410, vyy411), app(app(app(ty_@3, db), dc), dd), cf) → new_esEs2(vyy400, vyy410, db, dc, dd)
new_esEs3(Right(vyy400), Right(vyy410), bfa, app(app(ty_FiniteMap, bgc), bgd)) → new_esEs4(vyy400, vyy410, bgc, bgd)
new_esEs2(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), app(app(ty_@2, bcb), bcc), hb, bah) → new_esEs(vyy400, vyy410, bcb, bcc)
new_esEs2(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), app(ty_[], bcd), hb, bah) → new_esEs0(vyy400, vyy410, bcd)
new_esEs2(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ha, app(ty_[], bba), bah) → new_esEs0(vyy401, vyy411, bba)
new_esEs2(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ha, hb, app(app(app(ty_@3, hg), hh), baa)) → new_esEs2(vyy402, vyy412, hg, hh, baa)
new_esEs2(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), app(app(app(ty_@3, bcf), bcg), bch), hb, bah) → new_esEs2(vyy400, vyy410, bcf, bcg, bch)
new_esEs3(Left(vyy400), Left(vyy410), app(ty_Maybe, bea), bdg) → new_esEs1(vyy400, vyy410, bea)
new_esEs1(Just(vyy400), Just(vyy410), app(app(ty_@2, ff), fg)) → new_esEs(vyy400, vyy410, ff, fg)
new_esEs(@2(vyy400, vyy401), @2(vyy410, vyy411), h, app(ty_Maybe, bd)) → new_esEs1(vyy401, vyy411, bd)
new_esEs1(Just(vyy400), Just(vyy410), app(ty_[], fh)) → new_esEs0(vyy400, vyy410, fh)
new_esEs3(Left(vyy400), Left(vyy410), app(app(ty_@2, bde), bdf), bdg) → new_esEs(vyy400, vyy410, bde, bdf)
new_esEs3(Left(vyy400), Left(vyy410), app(app(ty_FiniteMap, beg), beh), bdg) → new_esEs4(vyy400, vyy410, beg, beh)
new_esEs(@2(vyy400, vyy401), @2(vyy410, vyy411), h, app(app(app(ty_@3, be), bf), bg)) → new_esEs2(vyy401, vyy411, be, bf, bg)
new_esEs2(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ha, app(app(ty_FiniteMap, bbh), bca), bah) → new_esEs4(vyy401, vyy411, bbh, bca)
new_esEs2(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), app(app(ty_Either, bda), bdb), hb, bah) → new_esEs3(vyy400, vyy410, bda, bdb)
new_esEs3(Right(vyy400), Right(vyy410), bfa, app(ty_Maybe, bfe)) → new_esEs1(vyy400, vyy410, bfe)
new_esEs2(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ha, app(app(app(ty_@3, bbc), bbd), bbe), bah) → new_esEs2(vyy401, vyy411, bbc, bbd, bbe)
new_esEs3(Right(vyy400), Right(vyy410), bfa, app(app(app(ty_@3, bff), bfg), bfh)) → new_esEs2(vyy400, vyy410, bff, bfg, bfh)
new_esEs1(Just(vyy400), Just(vyy410), app(app(ty_FiniteMap, gg), gh)) → new_esEs4(vyy400, vyy410, gg, gh)
new_esEs2(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), app(app(ty_FiniteMap, bdc), bdd), hb, bah) → new_esEs4(vyy400, vyy410, bdc, bdd)
new_esEs2(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ha, app(app(ty_@2, baf), bag), bah) → new_esEs(vyy401, vyy411, baf, bag)
new_esEs2(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ha, hb, app(app(ty_FiniteMap, bad), bae)) → new_esEs4(vyy402, vyy412, bad, bae)
new_esEs0(:(vyy400, vyy401), :(vyy410, vyy411), app(ty_[], ed)) → new_esEs0(vyy400, vyy410, ed)
new_esEs3(Left(vyy400), Left(vyy410), app(app(app(ty_@3, beb), bec), bed), bdg) → new_esEs2(vyy400, vyy410, beb, bec, bed)
new_esEs2(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ha, hb, app(app(ty_Either, bab), bac)) → new_esEs3(vyy402, vyy412, bab, bac)
new_esEs2(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), ha, hb, app(app(ty_@2, hc), hd)) → new_esEs(vyy402, vyy412, hc, hd)
new_esEs(@2(vyy400, vyy401), @2(vyy410, vyy411), h, app(app(ty_FiniteMap, cb), cc)) → new_esEs4(vyy401, vyy411, cb, cc)
new_esEs3(Right(vyy400), Right(vyy410), bfa, app(app(ty_@2, bfb), bfc)) → new_esEs(vyy400, vyy410, bfb, bfc)
new_esEs(@2(vyy400, vyy401), @2(vyy410, vyy411), app(ty_Maybe, da), cf) → new_esEs1(vyy400, vyy410, da)
The remaining pairs can at least be oriented weakly.
new_esEs0(:(vyy400, vyy401), :(vyy410, vyy411), app(ty_Maybe, ee)) → new_esEs1(vyy400, vyy410, ee)
new_esEs0(:(vyy400, vyy401), :(vyy410, vyy411), app(app(ty_FiniteMap, fc), fd)) → new_esEs4(vyy400, vyy410, fc, fd)
new_esEs4(vyy40, vyy41, bge, bgf) → new_esEs0(new_foldFM2(vyy40, bge, bgf), new_foldFM2(vyy41, bge, bgf), app(app(ty_@2, bge), bgf))
new_esEs0(:(vyy400, vyy401), :(vyy410, vyy411), ea) → new_esEs0(vyy401, vyy411, ea)
new_esEs0(:(vyy400, vyy401), :(vyy410, vyy411), app(app(app(ty_@3, ef), eg), eh)) → new_esEs2(vyy400, vyy410, ef, eg, eh)
new_esEs0(:(vyy400, vyy401), :(vyy410, vyy411), app(app(ty_Either, fa), fb)) → new_esEs3(vyy400, vyy410, fa, fb)
new_esEs0(:(vyy400, vyy401), :(vyy410, vyy411), app(app(ty_@2, eb), ec)) → new_esEs(vyy400, vyy410, eb, ec)
Used ordering: Polynomial interpretation [25]:
POL(:(x1, x2)) = 0
POL(@2(x1, x2)) = 0
POL(@3(x1, x2, x3)) = 0
POL(Branch(x1, x2, x3, x4, x5)) = 0
POL(EmptyFM) = 0
POL(Just(x1)) = 0
POL(Left(x1)) = 0
POL(Right(x1)) = 0
POL([]) = 0
POL(app(x1, x2)) = x1 + x2
POL(new_esEs(x1, x2, x3, x4)) = 1 + x3 + x4
POL(new_esEs0(x1, x2, x3)) = x3
POL(new_esEs1(x1, x2, x3)) = 1 + x3
POL(new_esEs2(x1, x2, x3, x4, x5)) = 1 + x3 + x4 + x5
POL(new_esEs3(x1, x2, x3, x4)) = 1 + x3 + x4
POL(new_esEs4(x1, x2, x3, x4)) = 1 + x3 + x4
POL(new_foldFM0(x1, x2, x3, x4, x5, x6)) = 0
POL(new_foldFM2(x1, x2, x3)) = 0
POL(ty_@2) = 1
POL(ty_@3) = 1
POL(ty_Either) = 1
POL(ty_FiniteMap) = 1
POL(ty_Maybe) = 1
POL(ty_[]) = 1
The following usable rules [17] were oriented:
none
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ Rewriting
↳ QDP
↳ Rewriting
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QReductionProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_esEs0(:(vyy400, vyy401), :(vyy410, vyy411), app(ty_Maybe, ee)) → new_esEs1(vyy400, vyy410, ee)
new_esEs0(:(vyy400, vyy401), :(vyy410, vyy411), app(app(ty_@2, eb), ec)) → new_esEs(vyy400, vyy410, eb, ec)
new_esEs0(:(vyy400, vyy401), :(vyy410, vyy411), app(app(ty_Either, fa), fb)) → new_esEs3(vyy400, vyy410, fa, fb)
new_esEs0(:(vyy400, vyy401), :(vyy410, vyy411), app(app(ty_FiniteMap, fc), fd)) → new_esEs4(vyy400, vyy410, fc, fd)
new_esEs4(vyy40, vyy41, bge, bgf) → new_esEs0(new_foldFM2(vyy40, bge, bgf), new_foldFM2(vyy41, bge, bgf), app(app(ty_@2, bge), bgf))
new_esEs0(:(vyy400, vyy401), :(vyy410, vyy411), app(app(app(ty_@3, ef), eg), eh)) → new_esEs2(vyy400, vyy410, ef, eg, eh)
new_esEs0(:(vyy400, vyy401), :(vyy410, vyy411), ea) → new_esEs0(vyy401, vyy411, ea)
The TRS R consists of the following rules:
new_foldFM2(Branch(vyy410, vyy411, vyy412, vyy413, vyy414), bge, bgf) → new_foldFM0(vyy410, vyy411, new_foldFM2(vyy414, bge, bgf), vyy413, bge, bgf)
new_foldFM2(EmptyFM, bge, bgf) → []
new_foldFM0(vyy410, vyy411, vyy85, EmptyFM, bge, bgf) → :(@2(vyy410, vyy411), vyy85)
new_foldFM0(vyy410, vyy411, vyy85, Branch(vyy4130, vyy4131, vyy4132, vyy4133, vyy4134), bge, bgf) → new_foldFM0(vyy4130, vyy4131, new_foldFM0(vyy410, vyy411, vyy85, vyy4134, bge, bgf), vyy4133, bge, bgf)
The set Q consists of the following terms:
new_foldFM2(EmptyFM, x0, x1)
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
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.
The approximation of the Dependency Graph [15,17,22] contains 1 SCC with 4 less nodes.
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ Rewriting
↳ QDP
↳ Rewriting
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QReductionProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_esEs0(:(vyy400, vyy401), :(vyy410, vyy411), app(app(ty_FiniteMap, fc), fd)) → new_esEs4(vyy400, vyy410, fc, fd)
new_esEs4(vyy40, vyy41, bge, bgf) → new_esEs0(new_foldFM2(vyy40, bge, bgf), new_foldFM2(vyy41, bge, bgf), app(app(ty_@2, bge), bgf))
new_esEs0(:(vyy400, vyy401), :(vyy410, vyy411), ea) → new_esEs0(vyy401, vyy411, ea)
The TRS R consists of the following rules:
new_foldFM2(Branch(vyy410, vyy411, vyy412, vyy413, vyy414), bge, bgf) → new_foldFM0(vyy410, vyy411, new_foldFM2(vyy414, bge, bgf), vyy413, bge, bgf)
new_foldFM2(EmptyFM, bge, bgf) → []
new_foldFM0(vyy410, vyy411, vyy85, EmptyFM, bge, bgf) → :(@2(vyy410, vyy411), vyy85)
new_foldFM0(vyy410, vyy411, vyy85, Branch(vyy4130, vyy4131, vyy4132, vyy4133, vyy4134), bge, bgf) → new_foldFM0(vyy4130, vyy4131, new_foldFM0(vyy410, vyy411, vyy85, vyy4134, bge, bgf), vyy4133, bge, bgf)
The set Q consists of the following terms:
new_foldFM2(EmptyFM, x0, x1)
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
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.
We use the reduction pair processor [15].
The following pairs can be oriented strictly and are deleted.
new_esEs0(:(vyy400, vyy401), :(vyy410, vyy411), app(app(ty_FiniteMap, fc), fd)) → new_esEs4(vyy400, vyy410, fc, fd)
The remaining pairs can at least be oriented weakly.
new_esEs4(vyy40, vyy41, bge, bgf) → new_esEs0(new_foldFM2(vyy40, bge, bgf), new_foldFM2(vyy41, bge, bgf), app(app(ty_@2, bge), bgf))
new_esEs0(:(vyy400, vyy401), :(vyy410, vyy411), ea) → new_esEs0(vyy401, vyy411, ea)
Used ordering: Polynomial interpretation [25]:
POL(:(x1, x2)) = 0
POL(@2(x1, x2)) = 0
POL(Branch(x1, x2, x3, x4, x5)) = 0
POL(EmptyFM) = 0
POL([]) = 0
POL(app(x1, x2)) = x1
POL(new_esEs0(x1, x2, x3)) = x3
POL(new_esEs4(x1, x2, x3, x4)) = 0
POL(new_foldFM0(x1, x2, x3, x4, x5, x6)) = 0
POL(new_foldFM2(x1, x2, x3)) = 0
POL(ty_@2) = 0
POL(ty_FiniteMap) = 1
The following usable rules [17] were oriented:
none
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ Rewriting
↳ QDP
↳ Rewriting
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QReductionProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_esEs4(vyy40, vyy41, bge, bgf) → new_esEs0(new_foldFM2(vyy40, bge, bgf), new_foldFM2(vyy41, bge, bgf), app(app(ty_@2, bge), bgf))
new_esEs0(:(vyy400, vyy401), :(vyy410, vyy411), ea) → new_esEs0(vyy401, vyy411, ea)
The TRS R consists of the following rules:
new_foldFM2(Branch(vyy410, vyy411, vyy412, vyy413, vyy414), bge, bgf) → new_foldFM0(vyy410, vyy411, new_foldFM2(vyy414, bge, bgf), vyy413, bge, bgf)
new_foldFM2(EmptyFM, bge, bgf) → []
new_foldFM0(vyy410, vyy411, vyy85, EmptyFM, bge, bgf) → :(@2(vyy410, vyy411), vyy85)
new_foldFM0(vyy410, vyy411, vyy85, Branch(vyy4130, vyy4131, vyy4132, vyy4133, vyy4134), bge, bgf) → new_foldFM0(vyy4130, vyy4131, new_foldFM0(vyy410, vyy411, vyy85, vyy4134, bge, bgf), vyy4133, bge, bgf)
The set Q consists of the following terms:
new_foldFM2(EmptyFM, x0, x1)
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
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.
The approximation of the Dependency Graph [15,17,22] contains 1 SCC with 1 less node.
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ Rewriting
↳ QDP
↳ Rewriting
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QReductionProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_esEs0(:(vyy400, vyy401), :(vyy410, vyy411), ea) → new_esEs0(vyy401, vyy411, ea)
The TRS R consists of the following rules:
new_foldFM2(Branch(vyy410, vyy411, vyy412, vyy413, vyy414), bge, bgf) → new_foldFM0(vyy410, vyy411, new_foldFM2(vyy414, bge, bgf), vyy413, bge, bgf)
new_foldFM2(EmptyFM, bge, bgf) → []
new_foldFM0(vyy410, vyy411, vyy85, EmptyFM, bge, bgf) → :(@2(vyy410, vyy411), vyy85)
new_foldFM0(vyy410, vyy411, vyy85, Branch(vyy4130, vyy4131, vyy4132, vyy4133, vyy4134), bge, bgf) → new_foldFM0(vyy4130, vyy4131, new_foldFM0(vyy410, vyy411, vyy85, vyy4134, bge, bgf), vyy4133, bge, bgf)
The set Q consists of the following terms:
new_foldFM2(EmptyFM, x0, x1)
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
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.
As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [15] we can delete all non-usable rules [17] from R.
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ Rewriting
↳ QDP
↳ Rewriting
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QReductionProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QReductionProof
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_esEs0(:(vyy400, vyy401), :(vyy410, vyy411), ea) → new_esEs0(vyy401, vyy411, ea)
R is empty.
The set Q consists of the following terms:
new_foldFM2(EmptyFM, x0, x1)
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
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.
We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.
new_foldFM2(EmptyFM, x0, x1)
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
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
↳ QDP
↳ Rewriting
↳ QDP
↳ Rewriting
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QReductionProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QReductionProof
↳ QDP
↳ QDPSizeChangeProof
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_esEs0(:(vyy400, vyy401), :(vyy410, vyy411), ea) → new_esEs0(vyy401, vyy411, ea)
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_esEs0(:(vyy400, vyy401), :(vyy410, vyy411), ea) → new_esEs0(vyy401, vyy411, ea)
The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDPSizeChangeProof
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_compare(:(vyy3000, vyy3001), :(vyy400, vyy401), bda) → new_primCompAux(vyy3000, vyy400, new_compare4(vyy3001, vyy401, bda), bda)
new_ltEs0(@2(vyy3000, vyy3001), @2(vyy400, vyy401), app(app(ty_@2, fc), fd), fb) → new_lt0(vyy3000, vyy400, fc, fd)
new_ltEs1(Left(vyy3000), Left(vyy400), app(ty_Maybe, bad), hg) → new_ltEs2(vyy3000, vyy400, bad)
new_ltEs0(@2(vyy3000, vyy3001), @2(vyy400, vyy401), app(app(ty_Either, ff), fg), fb) → new_lt1(vyy3000, vyy400, ff, fg)
new_ltEs(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), cc, bc, app(ty_Maybe, ee)) → new_ltEs2(vyy3002, vyy402, ee)
new_ltEs1(Left(vyy3000), Left(vyy400), app(app(ty_Either, bab), bac), hg) → new_ltEs1(vyy3000, vyy400, bab, bac)
new_ltEs1(Right(vyy3000), Right(vyy400), baf, app(ty_Maybe, bbf)) → new_ltEs2(vyy3000, vyy400, bbf)
new_ltEs(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), cc, app(app(ty_@2, cg), da), bd) → new_lt0(vyy3001, vyy401, cg, da)
new_lt(vyy3000, vyy400, h, ba, bb) → new_compare2(vyy3000, vyy400, new_esEs5(vyy3000, vyy400, h, ba, bb), h, ba, bb)
new_primCompAux(vyy3000, vyy400, vyy67, app(app(app(ty_@3, bdb), bdc), bdd)) → new_compare0(vyy3000, vyy400, bdb, bdc, bdd)
new_ltEs2(Just(vyy3000), Just(vyy400), app(ty_[], bch)) → new_ltEs3(vyy3000, vyy400, bch)
new_compare5(vyy3000, vyy400, ca) → new_compare22(vyy3000, vyy400, new_esEs8(vyy3000, vyy400, ca), ca)
new_ltEs(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), app(ty_Maybe, ca), bc, bd) → new_compare22(vyy3000, vyy400, new_esEs8(vyy3000, vyy400, ca), ca)
new_ltEs1(Left(vyy3000), Left(vyy400), app(app(app(ty_@3, hd), he), hf), hg) → new_ltEs(vyy3000, vyy400, hd, he, hf)
new_ltEs0(@2(vyy3000, vyy3001), @2(vyy400, vyy401), gb, app(app(app(ty_@3, gc), gd), ge)) → new_ltEs(vyy3001, vyy401, gc, gd, ge)
new_ltEs3(:(vyy3000, vyy3001), :(vyy400, vyy401), bda) → new_compare(vyy3001, vyy401, bda)
new_primCompAux(vyy3000, vyy400, vyy67, app(ty_[], beb)) → new_compare(vyy3000, vyy400, beb)
new_compare0(vyy3000, vyy400, h, ba, bb) → new_compare2(vyy3000, vyy400, new_esEs5(vyy3000, vyy400, h, ba, bb), h, ba, bb)
new_compare3(vyy3000, vyy400, bg, bh) → new_compare21(vyy3000, vyy400, new_esEs7(vyy3000, vyy400, bg, bh), bg, bh)
new_ltEs0(@2(vyy3000, vyy3001), @2(vyy400, vyy401), gb, app(ty_Maybe, hb)) → new_ltEs2(vyy3001, vyy401, hb)
new_ltEs1(Right(vyy3000), Right(vyy400), baf, app(ty_[], bbg)) → new_ltEs3(vyy3000, vyy400, bbg)
new_compare20(vyy3000, vyy400, False, be, bf) → new_ltEs0(vyy3000, vyy400, be, bf)
new_lt2(vyy3000, vyy400, ca) → new_compare22(vyy3000, vyy400, new_esEs8(vyy3000, vyy400, ca), ca)
new_compare21(vyy3000, vyy400, False, bg, bh) → new_ltEs1(vyy3000, vyy400, bg, bh)
new_ltEs0(@2(vyy3000, vyy3001), @2(vyy400, vyy401), app(ty_[], ga), fb) → new_lt3(vyy3000, vyy400, ga)
new_ltEs2(Just(vyy3000), Just(vyy400), app(app(ty_Either, bce), bcf)) → new_ltEs1(vyy3000, vyy400, bce, bcf)
new_ltEs(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), app(app(ty_Either, bg), bh), bc, bd) → new_compare21(vyy3000, vyy400, new_esEs7(vyy3000, vyy400, bg, bh), bg, bh)
new_ltEs1(Right(vyy3000), Right(vyy400), baf, app(app(app(ty_@3, bag), bah), bba)) → new_ltEs(vyy3000, vyy400, bag, bah, bba)
new_ltEs0(@2(vyy3000, vyy3001), @2(vyy400, vyy401), gb, app(app(ty_@2, gf), gg)) → new_ltEs0(vyy3001, vyy401, gf, gg)
new_ltEs(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), app(app(app(ty_@3, h), ba), bb), bc, bd) → new_compare2(vyy3000, vyy400, new_esEs5(vyy3000, vyy400, h, ba, bb), h, ba, bb)
new_compare22(vyy3000, vyy400, False, ca) → new_ltEs2(vyy3000, vyy400, ca)
new_ltEs(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), cc, app(app(app(ty_@3, cd), ce), cf), bd) → new_lt(vyy3001, vyy401, cd, ce, cf)
new_ltEs3(:(vyy3000, vyy3001), :(vyy400, vyy401), bda) → new_primCompAux(vyy3000, vyy400, new_compare4(vyy3001, vyy401, bda), bda)
new_ltEs(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), cc, bc, app(ty_[], ef)) → new_ltEs3(vyy3002, vyy402, ef)
new_ltEs2(Just(vyy3000), Just(vyy400), app(ty_Maybe, bcg)) → new_ltEs2(vyy3000, vyy400, bcg)
new_compare(:(vyy3000, vyy3001), :(vyy400, vyy401), bda) → new_compare(vyy3001, vyy401, bda)
new_ltEs(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), cc, app(ty_[], de), bd) → new_lt3(vyy3001, vyy401, de)
new_lt3(vyy3000, vyy400, cb) → new_compare(vyy3000, vyy400, cb)
new_primCompAux(vyy3000, vyy400, vyy67, app(app(ty_Either, bdg), bdh)) → new_compare3(vyy3000, vyy400, bdg, bdh)
new_lt0(vyy3000, vyy400, be, bf) → new_compare20(vyy3000, vyy400, new_esEs6(vyy3000, vyy400, be, bf), be, bf)
new_compare2(vyy3000, vyy400, False, h, ba, bb) → new_ltEs(vyy3000, vyy400, h, ba, bb)
new_ltEs1(Left(vyy3000), Left(vyy400), app(ty_[], bae), hg) → new_ltEs3(vyy3000, vyy400, bae)
new_ltEs2(Just(vyy3000), Just(vyy400), app(app(app(ty_@3, bbh), bca), bcb)) → new_ltEs(vyy3000, vyy400, bbh, bca, bcb)
new_ltEs(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), app(app(ty_@2, be), bf), bc, bd) → new_compare20(vyy3000, vyy400, new_esEs6(vyy3000, vyy400, be, bf), be, bf)
new_ltEs1(Right(vyy3000), Right(vyy400), baf, app(app(ty_Either, bbd), bbe)) → new_ltEs1(vyy3000, vyy400, bbd, bbe)
new_primCompAux(vyy3000, vyy400, vyy67, app(ty_Maybe, bea)) → new_compare5(vyy3000, vyy400, bea)
new_ltEs0(@2(vyy3000, vyy3001), @2(vyy400, vyy401), app(app(app(ty_@3, eg), eh), fa), fb) → new_lt(vyy3000, vyy400, eg, eh, fa)
new_ltEs(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), app(ty_[], cb), bc, bd) → new_compare(vyy3000, vyy400, cb)
new_ltEs0(@2(vyy3000, vyy3001), @2(vyy400, vyy401), gb, app(ty_[], hc)) → new_ltEs3(vyy3001, vyy401, hc)
new_ltEs0(@2(vyy3000, vyy3001), @2(vyy400, vyy401), gb, app(app(ty_Either, gh), ha)) → new_ltEs1(vyy3001, vyy401, gh, ha)
new_ltEs(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), cc, bc, app(app(app(ty_@3, df), dg), dh)) → new_ltEs(vyy3002, vyy402, df, dg, dh)
new_lt1(vyy3000, vyy400, bg, bh) → new_compare21(vyy3000, vyy400, new_esEs7(vyy3000, vyy400, bg, bh), bg, bh)
new_ltEs0(@2(vyy3000, vyy3001), @2(vyy400, vyy401), app(ty_Maybe, fh), fb) → new_lt2(vyy3000, vyy400, fh)
new_primCompAux(vyy3000, vyy400, vyy67, app(app(ty_@2, bde), bdf)) → new_compare1(vyy3000, vyy400, bde, bdf)
new_ltEs(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), cc, app(ty_Maybe, dd), bd) → new_lt2(vyy3001, vyy401, dd)
new_ltEs2(Just(vyy3000), Just(vyy400), app(app(ty_@2, bcc), bcd)) → new_ltEs0(vyy3000, vyy400, bcc, bcd)
new_ltEs(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), cc, bc, app(app(ty_Either, ec), ed)) → new_ltEs1(vyy3002, vyy402, ec, ed)
new_compare1(vyy3000, vyy400, be, bf) → new_compare20(vyy3000, vyy400, new_esEs6(vyy3000, vyy400, be, bf), be, bf)
new_ltEs1(Left(vyy3000), Left(vyy400), app(app(ty_@2, hh), baa), hg) → new_ltEs0(vyy3000, vyy400, hh, baa)
new_ltEs1(Right(vyy3000), Right(vyy400), baf, app(app(ty_@2, bbb), bbc)) → new_ltEs0(vyy3000, vyy400, bbb, bbc)
new_ltEs(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), cc, bc, app(app(ty_@2, ea), eb)) → new_ltEs0(vyy3002, vyy402, ea, eb)
new_ltEs(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), cc, app(app(ty_Either, db), dc), bd) → new_lt1(vyy3001, vyy401, db, dc)
The TRS R consists of the following rules:
new_esEs23(vyy401, vyy411, app(app(ty_Either, ccd), cce)) → new_esEs7(vyy401, vyy411, ccd, cce)
new_esEs23(vyy401, vyy411, ty_Ordering) → new_esEs18(vyy401, vyy411)
new_esEs25(vyy401, vyy411, ty_Int) → new_esEs19(vyy401, vyy411)
new_esEs7(Left(vyy400), Left(vyy410), app(app(ty_Either, cfd), cfe), bhg) → new_esEs7(vyy400, vyy410, cfd, cfe)
new_esEs24(vyy400, vyy410, ty_Float) → new_esEs12(vyy400, vyy410)
new_esEs8(Just(vyy400), Just(vyy410), app(app(ty_@2, bee), bef)) → new_esEs6(vyy400, vyy410, bee, bef)
new_esEs21(vyy40, vyy41, app(app(ty_@2, bgg), bgh)) → new_esEs6(vyy40, vyy41, bgg, bgh)
new_esEs18(LT, LT) → True
new_esEs24(vyy400, vyy410, app(app(app(ty_@3, cdd), cde), cdf)) → new_esEs5(vyy400, vyy410, cdd, cde, cdf)
new_ltEs13(Right(vyy3000), Right(vyy400), baf, ty_Integer) → new_ltEs17(vyy3000, vyy400)
new_ltEs14(GT, GT) → True
new_ltEs18(Just(vyy3000), Just(vyy400), app(ty_Maybe, bcg)) → new_ltEs18(vyy3000, vyy400, bcg)
new_esEs18(LT, EQ) → False
new_esEs18(EQ, LT) → False
new_lt20(vyy3001, vyy401, ty_Float) → new_lt14(vyy3001, vyy401)
new_esEs28(vyy401, vyy411, ty_Char) → new_esEs16(vyy401, vyy411)
new_ltEs13(Left(vyy3000), Left(vyy400), app(ty_[], bae), hg) → new_ltEs4(vyy3000, vyy400, bae)
new_lt19(vyy3000, vyy400, app(app(ty_@2, be), bf)) → new_lt10(vyy3000, vyy400, be, bf)
new_lt19(vyy3000, vyy400, ty_@0) → new_lt8(vyy3000, vyy400)
new_ltEs11(vyy3001, vyy401, app(ty_Ratio, bgb)) → new_ltEs5(vyy3001, vyy401, bgb)
new_ltEs19(vyy3002, vyy402, app(ty_Ratio, def)) → new_ltEs5(vyy3002, vyy402, def)
new_esEs27(vyy402, vyy412, ty_Bool) → new_esEs17(vyy402, vyy412)
new_primMulNat0(Zero, Zero) → Zero
new_esEs7(Left(vyy400), Left(vyy410), app(app(app(ty_@3, ceh), cfa), cfb), bhg) → new_esEs5(vyy400, vyy410, ceh, cfa, cfb)
new_lt20(vyy3001, vyy401, ty_Int) → new_lt13(vyy3001, vyy401)
new_ltEs13(Left(vyy3000), Left(vyy400), app(app(ty_@2, hh), baa), hg) → new_ltEs10(vyy3000, vyy400, hh, baa)
new_ltEs13(Left(vyy3000), Left(vyy400), app(ty_Maybe, bad), hg) → new_ltEs18(vyy3000, vyy400, bad)
new_compare18(vyy3000, vyy400, True, h, ba, bb) → LT
new_lt20(vyy3001, vyy401, ty_@0) → new_lt8(vyy3001, vyy401)
new_esEs21(vyy40, vyy41, ty_Bool) → new_esEs17(vyy40, vyy41)
new_compare25(vyy3000, vyy400, True, ca) → EQ
new_esEs23(vyy401, vyy411, ty_Float) → new_esEs12(vyy401, vyy411)
new_esEs29(vyy400, vyy410, ty_Ordering) → new_esEs18(vyy400, vyy410)
new_esEs27(vyy402, vyy412, app(app(ty_FiniteMap, dbc), dbd)) → new_esEs20(vyy402, vyy412, dbc, dbd)
new_esEs9(LT) → True
new_esEs24(vyy400, vyy410, ty_Integer) → new_esEs15(vyy400, vyy410)
new_esEs8(Just(vyy400), Just(vyy410), ty_Integer) → new_esEs15(vyy400, vyy410)
new_lt19(vyy3000, vyy400, ty_Ordering) → new_lt6(vyy3000, vyy400)
new_ltEs9(True, False) → False
new_ltEs11(vyy3001, vyy401, ty_Int) → new_ltEs15(vyy3001, vyy401)
new_esEs29(vyy400, vyy410, app(app(ty_FiniteMap, dec), ded)) → new_esEs20(vyy400, vyy410, dec, ded)
new_esEs8(Just(vyy400), Just(vyy410), ty_Ordering) → new_esEs18(vyy400, vyy410)
new_not(GT) → False
new_esEs20(vyy40, vyy41, bgd, bge) → new_asAs(new_esEs19(new_sizeFM(vyy40, bgd, bge), new_sizeFM(vyy41, bgd, bge)), new_esEs11(new_fmToList(vyy40, bgd, bge), new_fmToList(vyy41, bgd, bge), app(app(ty_@2, bgd), bge)))
new_lt19(vyy3000, vyy400, app(app(app(ty_@3, h), ba), bb)) → new_lt9(vyy3000, vyy400, h, ba, bb)
new_lt7(vyy3000, vyy400, ty_Char) → new_lt12(vyy3000, vyy400)
new_ltEs13(Right(vyy3000), Right(vyy400), baf, app(ty_Maybe, bbf)) → new_ltEs18(vyy3000, vyy400, bbf)
new_esEs17(True, True) → True
new_esEs7(Right(vyy400), Right(vyy410), bhf, app(app(app(ty_@3, cgd), cge), cgf)) → new_esEs5(vyy400, vyy410, cgd, cge, cgf)
new_lt19(vyy3000, vyy400, ty_Int) → new_lt13(vyy3000, vyy400)
new_lt13(vyy3000, vyy400) → new_esEs9(new_compare6(vyy3000, vyy400))
new_esEs8(Just(vyy400), Just(vyy410), ty_Float) → new_esEs12(vyy400, vyy410)
new_esEs11([], [], bha) → True
new_esEs22(vyy400, vyy410, app(ty_Ratio, cag)) → new_esEs14(vyy400, vyy410, cag)
new_esEs21(vyy40, vyy41, app(ty_Ratio, bhe)) → new_esEs14(vyy40, vyy41, bhe)
new_esEs23(vyy401, vyy411, ty_Double) → new_esEs13(vyy401, vyy411)
new_esEs15(Integer(vyy400), Integer(vyy410)) → new_primEqInt(vyy400, vyy410)
new_esEs18(LT, GT) → False
new_esEs18(GT, LT) → False
new_esEs6(@2(vyy400, vyy401), @2(vyy410, vyy411), bgg, bgh) → new_asAs(new_esEs24(vyy400, vyy410, bgg), new_esEs23(vyy401, vyy411, bgh))
new_compare15(vyy3000, vyy400, False, ca) → GT
new_esEs28(vyy401, vyy411, app(app(app(ty_@3, dca), dcb), dcc)) → new_esEs5(vyy401, vyy411, dca, dcb, dcc)
new_ltEs19(vyy3002, vyy402, ty_Bool) → new_ltEs9(vyy3002, vyy402)
new_ltEs18(Just(vyy3000), Just(vyy400), ty_Double) → new_ltEs16(vyy3000, vyy400)
new_esEs29(vyy400, vyy410, ty_Integer) → new_esEs15(vyy400, vyy410)
new_ltEs13(Left(vyy3000), Left(vyy400), app(ty_Ratio, chd), hg) → new_ltEs5(vyy3000, vyy400, chd)
new_esEs22(vyy400, vyy410, app(app(ty_Either, cah), cba)) → new_esEs7(vyy400, vyy410, cah, cba)
new_foldFM0(vyy410, vyy411, vyy85, EmptyFM, bgd, bge) → :(@2(vyy410, vyy411), vyy85)
new_ltEs11(vyy3001, vyy401, ty_Float) → new_ltEs7(vyy3001, vyy401)
new_ltEs13(Left(vyy3000), Left(vyy400), ty_Char, hg) → new_ltEs8(vyy3000, vyy400)
new_esEs24(vyy400, vyy410, app(ty_Ratio, cdg)) → new_esEs14(vyy400, vyy410, cdg)
new_esEs7(Right(vyy400), Left(vyy410), bhf, bhg) → False
new_esEs7(Left(vyy400), Right(vyy410), bhf, bhg) → False
new_esEs14(:%(vyy400, vyy401), :%(vyy410, vyy411), bhe) → new_asAs(new_esEs26(vyy400, vyy410, bhe), new_esEs25(vyy401, vyy411, bhe))
new_ltEs15(vyy300, vyy40) → new_not(new_compare6(vyy300, vyy40))
new_esEs27(vyy402, vyy412, app(app(ty_Either, dba), dbb)) → new_esEs7(vyy402, vyy412, dba, dbb)
new_ltEs14(GT, EQ) → False
new_ltEs18(Just(vyy3000), Just(vyy400), ty_Integer) → new_ltEs17(vyy3000, vyy400)
new_esEs7(Right(vyy400), Right(vyy410), bhf, ty_Char) → new_esEs16(vyy400, vyy410)
new_ltEs11(vyy3001, vyy401, app(app(ty_Either, gh), ha)) → new_ltEs13(vyy3001, vyy401, gh, ha)
new_esEs5(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), bhb, bhc, bhd) → new_asAs(new_esEs29(vyy400, vyy410, bhb), new_asAs(new_esEs28(vyy401, vyy411, bhc), new_esEs27(vyy402, vyy412, bhd)))
new_compare23(vyy3000, vyy400, False, be, bf) → new_compare112(vyy3000, vyy400, new_ltEs10(vyy3000, vyy400, be, bf), be, bf)
new_ltEs18(Just(vyy3000), Just(vyy400), app(ty_Ratio, chg)) → new_ltEs5(vyy3000, vyy400, chg)
new_primCompAux1(vyy3000, vyy400, vyy67, bda) → new_primCompAux0(vyy67, new_compare30(vyy3000, vyy400, bda))
new_lt7(vyy3000, vyy400, app(app(ty_@2, fc), fd)) → new_lt10(vyy3000, vyy400, fc, fd)
new_compare30(vyy3000, vyy400, app(ty_Ratio, chh)) → new_compare7(vyy3000, vyy400, chh)
new_ltEs13(Right(vyy3000), Right(vyy400), baf, ty_Char) → new_ltEs8(vyy3000, vyy400)
new_esEs24(vyy400, vyy410, app(ty_[], cdb)) → new_esEs11(vyy400, vyy410, cdb)
new_esEs29(vyy400, vyy410, app(ty_Maybe, ddd)) → new_esEs8(vyy400, vyy410, ddd)
new_esEs29(vyy400, vyy410, app(ty_[], ddc)) → new_esEs11(vyy400, vyy410, ddc)
new_compare30(vyy3000, vyy400, ty_Float) → new_compare12(vyy3000, vyy400)
new_esEs27(vyy402, vyy412, ty_Int) → new_esEs19(vyy402, vyy412)
new_compare31(vyy3000, vyy400, bg, bh) → new_compare29(vyy3000, vyy400, new_esEs7(vyy3000, vyy400, bg, bh), bg, bh)
new_ltEs11(vyy3001, vyy401, app(app(ty_@2, gf), gg)) → new_ltEs10(vyy3001, vyy401, gf, gg)
new_primCmpNat0(Zero, Succ(vyy4000)) → LT
new_esEs22(vyy400, vyy410, app(app(ty_FiniteMap, cbb), cbc)) → new_esEs20(vyy400, vyy410, cbb, cbc)
new_esEs7(Left(vyy400), Left(vyy410), ty_Double, bhg) → new_esEs13(vyy400, vyy410)
new_ltEs18(Just(vyy3000), Just(vyy400), app(app(ty_@2, bcc), bcd)) → new_ltEs10(vyy3000, vyy400, bcc, bcd)
new_lt18(vyy3000, vyy400, ca) → new_esEs9(new_compare28(vyy3000, vyy400, ca))
new_lt20(vyy3001, vyy401, ty_Ordering) → new_lt6(vyy3001, vyy401)
new_esEs27(vyy402, vyy412, ty_@0) → new_esEs10(vyy402, vyy412)
new_esEs24(vyy400, vyy410, app(app(ty_FiniteMap, ceb), cec)) → new_esEs20(vyy400, vyy410, ceb, cec)
new_esEs28(vyy401, vyy411, app(ty_[], dbg)) → new_esEs11(vyy401, vyy411, dbg)
new_esEs24(vyy400, vyy410, app(app(ty_Either, cdh), cea)) → new_esEs7(vyy400, vyy410, cdh, cea)
new_esEs24(vyy400, vyy410, app(app(ty_@2, cch), cda)) → new_esEs6(vyy400, vyy410, cch, cda)
new_esEs27(vyy402, vyy412, ty_Ordering) → new_esEs18(vyy402, vyy412)
new_primEqNat0(Zero, Zero) → True
new_compare26(vyy3000, vyy400, True) → EQ
new_ltEs13(Left(vyy3000), Left(vyy400), ty_Integer, hg) → new_ltEs17(vyy3000, vyy400)
new_esEs22(vyy400, vyy410, app(ty_Maybe, cac)) → new_esEs8(vyy400, vyy410, cac)
new_esEs23(vyy401, vyy411, app(app(ty_FiniteMap, ccf), ccg)) → new_esEs20(vyy401, vyy411, ccf, ccg)
new_ltEs18(Just(vyy3000), Just(vyy400), ty_Char) → new_ltEs8(vyy3000, vyy400)
new_ltEs13(Left(vyy3000), Left(vyy400), ty_Int, hg) → new_ltEs15(vyy3000, vyy400)
new_compare29(vyy3000, vyy400, True, bg, bh) → EQ
new_compare111(vyy3000, vyy400, False, bg, bh) → GT
new_esEs8(Just(vyy400), Just(vyy410), ty_Int) → new_esEs19(vyy400, vyy410)
new_lt20(vyy3001, vyy401, app(app(ty_@2, cg), da)) → new_lt10(vyy3001, vyy401, cg, da)
new_ltEs13(Left(vyy3000), Left(vyy400), ty_@0, hg) → new_ltEs6(vyy3000, vyy400)
new_ltEs19(vyy3002, vyy402, app(ty_[], ef)) → new_ltEs4(vyy3002, vyy402, ef)
new_ltEs11(vyy3001, vyy401, app(app(app(ty_@3, gc), gd), ge)) → new_ltEs12(vyy3001, vyy401, gc, gd, ge)
new_esEs17(False, False) → True
new_esEs17(False, True) → False
new_esEs17(True, False) → False
new_compare12(Float(vyy3000, vyy3001), Float(vyy400, vyy401)) → new_compare6(new_sr(vyy3000, vyy400), new_sr(vyy3001, vyy401))
new_compare30(vyy3000, vyy400, app(ty_Maybe, bea)) → new_compare28(vyy3000, vyy400, bea)
new_esEs7(Right(vyy400), Right(vyy410), bhf, ty_Ordering) → new_esEs18(vyy400, vyy410)
new_esEs21(vyy40, vyy41, app(ty_Maybe, bed)) → new_esEs8(vyy40, vyy41, bed)
new_sr(vyy3001, vyy401) → new_primMulInt(vyy3001, vyy401)
new_ltEs14(EQ, LT) → False
new_esEs24(vyy400, vyy410, ty_Bool) → new_esEs17(vyy400, vyy410)
new_lt14(vyy3000, vyy400) → new_esEs9(new_compare12(vyy3000, vyy400))
new_ltEs19(vyy3002, vyy402, app(app(app(ty_@3, df), dg), dh)) → new_ltEs12(vyy3002, vyy402, df, dg, dh)
new_esEs11(:(vyy400, vyy401), :(vyy410, vyy411), bha) → new_asAs(new_esEs22(vyy400, vyy410, bha), new_esEs11(vyy401, vyy411, bha))
new_primPlusNat0(Succ(vyy860), vyy40100) → Succ(Succ(new_primPlusNat1(vyy860, vyy40100)))
new_compare4([], [], bda) → EQ
new_esEs7(Right(vyy400), Right(vyy410), bhf, app(app(ty_Either, cgh), cha)) → new_esEs7(vyy400, vyy410, cgh, cha)
new_esEs22(vyy400, vyy410, ty_Char) → new_esEs16(vyy400, vyy410)
new_esEs18(EQ, GT) → False
new_esEs18(GT, EQ) → False
new_compare30(vyy3000, vyy400, app(ty_[], beb)) → new_compare4(vyy3000, vyy400, beb)
new_esEs16(Char(vyy400), Char(vyy410)) → new_primEqNat0(vyy400, vyy410)
new_compare30(vyy3000, vyy400, ty_Char) → new_compare13(vyy3000, vyy400)
new_esEs8(Just(vyy400), Nothing, bed) → False
new_esEs8(Nothing, Just(vyy410), bed) → False
new_ltEs19(vyy3002, vyy402, ty_Float) → new_ltEs7(vyy3002, vyy402)
new_compare24(vyy3000, vyy400, True, h, ba, bb) → EQ
new_primEqInt(Neg(Succ(vyy4000)), Neg(Succ(vyy4100))) → new_primEqNat0(vyy4000, vyy4100)
new_compare30(vyy3000, vyy400, ty_Int) → new_compare6(vyy3000, vyy400)
new_ltEs19(vyy3002, vyy402, app(app(ty_@2, ea), eb)) → new_ltEs10(vyy3002, vyy402, ea, eb)
new_esEs9(GT) → False
new_primPlusNat1(Zero, Succ(vyy401000)) → Succ(vyy401000)
new_primPlusNat1(Succ(vyy8600), Zero) → Succ(vyy8600)
new_compare26(vyy3000, vyy400, False) → new_compare110(vyy3000, vyy400, new_ltEs14(vyy3000, vyy400))
new_esEs9(EQ) → False
new_esEs28(vyy401, vyy411, app(ty_Maybe, dbh)) → new_esEs8(vyy401, vyy411, dbh)
new_compare16(vyy3000, vyy400, True) → LT
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs7(Left(vyy400), Left(vyy410), ty_Integer, bhg) → new_esEs15(vyy400, vyy410)
new_lt20(vyy3001, vyy401, app(ty_Maybe, dd)) → new_lt18(vyy3001, vyy401, dd)
new_esEs7(Left(vyy400), Left(vyy410), app(app(ty_@2, ced), cee), bhg) → new_esEs6(vyy400, vyy410, ced, cee)
new_esEs28(vyy401, vyy411, ty_Double) → new_esEs13(vyy401, vyy411)
new_compare112(vyy3000, vyy400, False, be, bf) → GT
new_lt19(vyy3000, vyy400, ty_Double) → new_lt16(vyy3000, vyy400)
new_primEqInt(Neg(Zero), Neg(Succ(vyy4100))) → False
new_primEqInt(Neg(Succ(vyy4000)), Neg(Zero)) → False
new_lt19(vyy3000, vyy400, ty_Char) → new_lt12(vyy3000, vyy400)
new_primCompAux0(vyy71, GT) → GT
new_ltEs6(vyy300, vyy40) → new_not(new_compare8(vyy300, vyy40))
new_ltEs10(@2(vyy3000, vyy3001), @2(vyy400, vyy401), gb, fb) → new_pePe(new_lt7(vyy3000, vyy400, gb), vyy3000, vyy400, new_ltEs11(vyy3001, vyy401, fb), gb)
new_ltEs13(Right(vyy3000), Right(vyy400), baf, app(ty_Ratio, che)) → new_ltEs5(vyy3000, vyy400, che)
new_lt7(vyy3000, vyy400, ty_Integer) → new_lt17(vyy3000, vyy400)
new_compare11(Double(vyy3000, vyy3001), Double(vyy400, vyy401)) → new_compare6(new_sr(vyy3000, vyy400), new_sr(vyy3001, vyy401))
new_esEs22(vyy400, vyy410, app(app(app(ty_@3, cad), cae), caf)) → new_esEs5(vyy400, vyy410, cad, cae, caf)
new_compare30(vyy3000, vyy400, ty_Bool) → new_compare10(vyy3000, vyy400)
new_ltEs13(Left(vyy3000), Left(vyy400), ty_Double, hg) → new_ltEs16(vyy3000, vyy400)
new_foldFM0(vyy410, vyy411, vyy85, Branch(vyy4130, vyy4131, vyy4132, vyy4133, vyy4134), bgd, bge) → new_foldFM0(vyy4130, vyy4131, new_foldFM0(vyy410, vyy411, vyy85, vyy4134, bgd, bge), vyy4133, bgd, bge)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_esEs24(vyy400, vyy410, ty_Ordering) → new_esEs18(vyy400, vyy410)
new_compare6(vyy300, vyy40) → new_primCmpInt(vyy300, vyy40)
new_esEs28(vyy401, vyy411, ty_Int) → new_esEs19(vyy401, vyy411)
new_esEs7(Right(vyy400), Right(vyy410), bhf, app(ty_[], cgb)) → new_esEs11(vyy400, vyy410, cgb)
new_esEs7(Left(vyy400), Left(vyy410), ty_Int, bhg) → new_esEs19(vyy400, vyy410)
new_esEs23(vyy401, vyy411, ty_Char) → new_esEs16(vyy401, vyy411)
new_ltEs13(Right(vyy3000), Right(vyy400), baf, ty_Float) → new_ltEs7(vyy3000, vyy400)
new_primCmpNat0(Succ(vyy30000), Succ(vyy4000)) → new_primCmpNat0(vyy30000, vyy4000)
new_esEs7(Right(vyy400), Right(vyy410), bhf, app(app(ty_@2, cfh), cga)) → new_esEs6(vyy400, vyy410, cfh, cga)
new_sizeFM(EmptyFM, bgd, bge) → Pos(Zero)
new_esEs7(Left(vyy400), Left(vyy410), app(app(ty_FiniteMap, cff), cfg), bhg) → new_esEs20(vyy400, vyy410, cff, cfg)
new_primEqInt(Pos(Succ(vyy4000)), Pos(Succ(vyy4100))) → new_primEqNat0(vyy4000, vyy4100)
new_ltEs19(vyy3002, vyy402, ty_Integer) → new_ltEs17(vyy3002, vyy402)
new_ltEs17(vyy300, vyy40) → new_not(new_compare17(vyy300, vyy40))
new_esEs21(vyy40, vyy41, ty_Int) → new_esEs19(vyy40, vyy41)
new_esEs28(vyy401, vyy411, app(app(ty_FiniteMap, dcg), dch)) → new_esEs20(vyy401, vyy411, dcg, dch)
new_esEs13(Double(vyy400, vyy401), Double(vyy410, vyy411)) → new_esEs19(new_sr(vyy400, vyy410), new_sr(vyy401, vyy411))
new_esEs26(vyy400, vyy410, ty_Integer) → new_esEs15(vyy400, vyy410)
new_esEs7(Left(vyy400), Left(vyy410), app(ty_[], cef), bhg) → new_esEs11(vyy400, vyy410, cef)
new_lt7(vyy3000, vyy400, app(ty_Maybe, fh)) → new_lt18(vyy3000, vyy400, fh)
new_ltEs7(vyy300, vyy40) → new_not(new_compare12(vyy300, vyy40))
new_primEqNat0(Succ(vyy4000), Succ(vyy4100)) → new_primEqNat0(vyy4000, vyy4100)
new_esEs23(vyy401, vyy411, app(ty_Ratio, ccc)) → new_esEs14(vyy401, vyy411, ccc)
new_lt7(vyy3000, vyy400, app(ty_Ratio, bga)) → new_lt15(vyy3000, vyy400, bga)
new_ltEs19(vyy3002, vyy402, app(app(ty_Either, ec), ed)) → new_ltEs13(vyy3002, vyy402, ec, ed)
new_esEs7(Left(vyy400), Left(vyy410), ty_Ordering, bhg) → new_esEs18(vyy400, vyy410)
new_esEs27(vyy402, vyy412, ty_Char) → new_esEs16(vyy402, vyy412)
new_esEs27(vyy402, vyy412, ty_Float) → new_esEs12(vyy402, vyy412)
new_ltEs18(Just(vyy3000), Just(vyy400), ty_Ordering) → new_ltEs14(vyy3000, vyy400)
new_lt20(vyy3001, vyy401, ty_Integer) → new_lt17(vyy3001, vyy401)
new_compare19(vyy3000, vyy400, h, ba, bb) → new_compare24(vyy3000, vyy400, new_esEs5(vyy3000, vyy400, h, ba, bb), h, ba, bb)
new_lt17(vyy3000, vyy400) → new_esEs9(new_compare17(vyy3000, vyy400))
new_primCmpInt(Neg(Succ(vyy30000)), Neg(vyy400)) → new_primCmpNat0(vyy400, Succ(vyy30000))
new_esEs7(Right(vyy400), Right(vyy410), bhf, app(ty_Ratio, cgg)) → new_esEs14(vyy400, vyy410, cgg)
new_esEs27(vyy402, vyy412, app(app(app(ty_@3, dae), daf), dag)) → new_esEs5(vyy402, vyy412, dae, daf, dag)
new_ltEs13(Right(vyy3000), Right(vyy400), baf, app(ty_[], bbg)) → new_ltEs4(vyy3000, vyy400, bbg)
new_lt6(vyy3000, vyy400) → new_esEs9(new_compare14(vyy3000, vyy400))
new_ltEs18(Just(vyy3000), Just(vyy400), ty_Bool) → new_ltEs9(vyy3000, vyy400)
new_primEqInt(Pos(Zero), Pos(Succ(vyy4100))) → False
new_primEqInt(Pos(Succ(vyy4000)), Pos(Zero)) → False
new_esEs24(vyy400, vyy410, ty_@0) → new_esEs10(vyy400, vyy410)
new_primCmpNat0(Zero, Zero) → EQ
new_ltEs18(Nothing, Nothing, chf) → True
new_primCmpNat0(Succ(vyy30000), Zero) → GT
new_ltEs5(vyy300, vyy40, bec) → new_not(new_compare7(vyy300, vyy40, bec))
new_lt20(vyy3001, vyy401, ty_Bool) → new_lt5(vyy3001, vyy401)
new_primCmpInt(Neg(Zero), Pos(Succ(vyy4000))) → LT
new_esEs21(vyy40, vyy41, ty_Char) → new_esEs16(vyy40, vyy41)
new_esEs8(Just(vyy400), Just(vyy410), ty_Char) → new_esEs16(vyy400, vyy410)
new_compare30(vyy3000, vyy400, ty_Ordering) → new_compare14(vyy3000, vyy400)
new_esEs21(vyy40, vyy41, ty_Double) → new_esEs13(vyy40, vyy41)
new_ltEs11(vyy3001, vyy401, ty_Integer) → new_ltEs17(vyy3001, vyy401)
new_sr0(Integer(vyy4000), Integer(vyy30010)) → Integer(new_primMulInt(vyy4000, vyy30010))
new_lt11(vyy3000, vyy400, bg, bh) → new_esEs9(new_compare31(vyy3000, vyy400, bg, bh))
new_primPlusNat1(Succ(vyy8600), Succ(vyy401000)) → Succ(Succ(new_primPlusNat1(vyy8600, vyy401000)))
new_esEs7(Right(vyy400), Right(vyy410), bhf, app(ty_Maybe, cgc)) → new_esEs8(vyy400, vyy410, cgc)
new_primEqInt(Neg(Succ(vyy4000)), Pos(vyy410)) → False
new_primEqInt(Pos(Succ(vyy4000)), Neg(vyy410)) → False
new_ltEs19(vyy3002, vyy402, ty_Double) → new_ltEs16(vyy3002, vyy402)
new_lt19(vyy3000, vyy400, app(ty_Ratio, bgc)) → new_lt15(vyy3000, vyy400, bgc)
new_compare27(vyy3000, vyy400, False) → new_compare16(vyy3000, vyy400, new_ltEs9(vyy3000, vyy400))
new_esEs7(Left(vyy400), Left(vyy410), ty_@0, bhg) → new_esEs10(vyy400, vyy410)
new_foldFM2(EmptyFM, bgd, bge) → []
new_compare7(:%(vyy3000, vyy3001), :%(vyy400, vyy401), ty_Integer) → new_compare17(new_sr0(vyy3000, vyy401), new_sr0(vyy400, vyy3001))
new_lt19(vyy3000, vyy400, ty_Bool) → new_lt5(vyy3000, vyy400)
new_esEs11(:(vyy400, vyy401), [], bha) → False
new_esEs11([], :(vyy410, vyy411), bha) → False
new_esEs22(vyy400, vyy410, app(app(ty_@2, bhh), caa)) → new_esEs6(vyy400, vyy410, bhh, caa)
new_ltEs11(vyy3001, vyy401, app(ty_Maybe, hb)) → new_ltEs18(vyy3001, vyy401, hb)
new_primEqInt(Neg(Zero), Pos(Succ(vyy4100))) → False
new_primEqInt(Pos(Zero), Neg(Succ(vyy4100))) → False
new_lt7(vyy3000, vyy400, app(app(app(ty_@3, eg), eh), fa)) → new_lt9(vyy3000, vyy400, eg, eh, fa)
new_esEs21(vyy40, vyy41, ty_Integer) → new_esEs15(vyy40, vyy41)
new_esEs22(vyy400, vyy410, app(ty_[], cab)) → new_esEs11(vyy400, vyy410, cab)
new_primCmpInt(Pos(Zero), Pos(Succ(vyy4000))) → new_primCmpNat0(Zero, Succ(vyy4000))
new_esEs28(vyy401, vyy411, app(app(ty_Either, dce), dcf)) → new_esEs7(vyy401, vyy411, dce, dcf)
new_esEs7(Right(vyy400), Right(vyy410), bhf, ty_Float) → new_esEs12(vyy400, vyy410)
new_esEs7(Right(vyy400), Right(vyy410), bhf, ty_Double) → new_esEs13(vyy400, vyy410)
new_lt20(vyy3001, vyy401, app(app(app(ty_@3, cd), ce), cf)) → new_lt9(vyy3001, vyy401, cd, ce, cf)
new_esEs21(vyy40, vyy41, ty_Ordering) → new_esEs18(vyy40, vyy41)
new_ltEs11(vyy3001, vyy401, ty_Bool) → new_ltEs9(vyy3001, vyy401)
new_esEs8(Just(vyy400), Just(vyy410), app(ty_[], beg)) → new_esEs11(vyy400, vyy410, beg)
new_esEs28(vyy401, vyy411, ty_Float) → new_esEs12(vyy401, vyy411)
new_esEs27(vyy402, vyy412, app(ty_Maybe, dad)) → new_esEs8(vyy402, vyy412, dad)
new_ltEs13(Left(vyy3000), Left(vyy400), ty_Float, hg) → new_ltEs7(vyy3000, vyy400)
new_esEs28(vyy401, vyy411, app(ty_Ratio, dcd)) → new_esEs14(vyy401, vyy411, dcd)
new_ltEs18(Just(vyy3000), Just(vyy400), ty_Float) → new_ltEs7(vyy3000, vyy400)
new_primCompAux0(vyy71, LT) → LT
new_ltEs19(vyy3002, vyy402, ty_Char) → new_ltEs8(vyy3002, vyy402)
new_esEs23(vyy401, vyy411, ty_Int) → new_esEs19(vyy401, vyy411)
new_lt19(vyy3000, vyy400, app(ty_Maybe, ca)) → new_lt18(vyy3000, vyy400, ca)
new_esEs8(Just(vyy400), Just(vyy410), ty_@0) → new_esEs10(vyy400, vyy410)
new_ltEs18(Just(vyy3000), Nothing, chf) → False
new_compare30(vyy3000, vyy400, app(app(ty_@2, bde), bdf)) → new_compare9(vyy3000, vyy400, bde, bdf)
new_primCmpInt(Pos(Succ(vyy30000)), Pos(vyy400)) → new_primCmpNat0(Succ(vyy30000), vyy400)
new_primPlusNat0(Zero, vyy40100) → Succ(vyy40100)
new_esEs7(Right(vyy400), Right(vyy410), bhf, ty_Bool) → new_esEs17(vyy400, vyy410)
new_esEs23(vyy401, vyy411, app(app(ty_@2, cbd), cbe)) → new_esEs6(vyy401, vyy411, cbd, cbe)
new_ltEs13(Right(vyy3000), Right(vyy400), baf, ty_Ordering) → new_ltEs14(vyy3000, vyy400)
new_esEs22(vyy400, vyy410, ty_Bool) → new_esEs17(vyy400, vyy410)
new_lt19(vyy3000, vyy400, ty_Integer) → new_lt17(vyy3000, vyy400)
new_esEs25(vyy401, vyy411, ty_Integer) → new_esEs15(vyy401, vyy411)
new_compare30(vyy3000, vyy400, ty_Double) → new_compare11(vyy3000, vyy400)
new_ltEs14(LT, LT) → True
new_esEs8(Just(vyy400), Just(vyy410), app(ty_Ratio, bfd)) → new_esEs14(vyy400, vyy410, bfd)
new_esEs8(Just(vyy400), Just(vyy410), ty_Double) → new_esEs13(vyy400, vyy410)
new_not0 → True
new_esEs23(vyy401, vyy411, app(ty_Maybe, cbg)) → new_esEs8(vyy401, vyy411, cbg)
new_compare30(vyy3000, vyy400, app(app(ty_Either, bdg), bdh)) → new_compare31(vyy3000, vyy400, bdg, bdh)
new_esEs23(vyy401, vyy411, ty_@0) → new_esEs10(vyy401, vyy411)
new_lt19(vyy3000, vyy400, ty_Float) → new_lt14(vyy3000, vyy400)
new_lt19(vyy3000, vyy400, app(ty_[], cb)) → new_lt4(vyy3000, vyy400, cb)
new_esEs18(GT, GT) → True
new_primCmpInt(Pos(Succ(vyy30000)), Neg(vyy400)) → GT
new_esEs21(vyy40, vyy41, app(app(app(ty_@3, bhb), bhc), bhd)) → new_esEs5(vyy40, vyy41, bhb, bhc, bhd)
new_esEs8(Just(vyy400), Just(vyy410), app(app(ty_Either, bfe), bff)) → new_esEs7(vyy400, vyy410, bfe, bff)
new_esEs7(Left(vyy400), Left(vyy410), app(ty_Ratio, cfc), bhg) → new_esEs14(vyy400, vyy410, cfc)
new_esEs21(vyy40, vyy41, app(app(ty_FiniteMap, bgd), bge)) → new_esEs20(vyy40, vyy41, bgd, bge)
new_primMulInt(Pos(vyy30010), Pos(vyy4010)) → Pos(new_primMulNat0(vyy30010, vyy4010))
new_lt15(vyy3000, vyy400, bgc) → new_esEs9(new_compare7(vyy3000, vyy400, bgc))
new_esEs22(vyy400, vyy410, ty_Double) → new_esEs13(vyy400, vyy410)
new_ltEs12(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), cc, bc, bd) → new_pePe(new_lt19(vyy3000, vyy400, cc), vyy3000, vyy400, new_pePe(new_lt20(vyy3001, vyy401, bc), vyy3001, vyy401, new_ltEs19(vyy3002, vyy402, bd), bc), cc)
new_ltEs9(True, True) → True
new_esEs27(vyy402, vyy412, app(app(ty_@2, daa), dab)) → new_esEs6(vyy402, vyy412, daa, dab)
new_primMulInt(Neg(vyy30010), Neg(vyy4010)) → Pos(new_primMulNat0(vyy30010, vyy4010))
new_ltEs13(Right(vyy3000), Right(vyy400), baf, ty_Bool) → new_ltEs9(vyy3000, vyy400)
new_compare110(vyy3000, vyy400, True) → LT
new_ltEs18(Just(vyy3000), Just(vyy400), app(app(ty_Either, bce), bcf)) → new_ltEs13(vyy3000, vyy400, bce, bcf)
new_esEs29(vyy400, vyy410, app(app(ty_@2, dda), ddb)) → new_esEs6(vyy400, vyy410, dda, ddb)
new_lt7(vyy3000, vyy400, ty_Double) → new_lt16(vyy3000, vyy400)
new_primEqNat0(Succ(vyy4000), Zero) → False
new_primEqNat0(Zero, Succ(vyy4100)) → False
new_esEs21(vyy40, vyy41, ty_@0) → new_esEs10(vyy40, vyy41)
new_esEs24(vyy400, vyy410, ty_Char) → new_esEs16(vyy400, vyy410)
new_ltEs19(vyy3002, vyy402, ty_@0) → new_ltEs6(vyy3002, vyy402)
new_lt20(vyy3001, vyy401, app(ty_Ratio, dee)) → new_lt15(vyy3001, vyy401, dee)
new_esEs22(vyy400, vyy410, ty_Ordering) → new_esEs18(vyy400, vyy410)
new_lt19(vyy3000, vyy400, app(app(ty_Either, bg), bh)) → new_lt11(vyy3000, vyy400, bg, bh)
new_compare9(vyy3000, vyy400, be, bf) → new_compare23(vyy3000, vyy400, new_esEs6(vyy3000, vyy400, be, bf), be, bf)
new_compare110(vyy3000, vyy400, False) → GT
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_ltEs18(Just(vyy3000), Just(vyy400), ty_Int) → new_ltEs15(vyy3000, vyy400)
new_ltEs9(False, False) → True
new_compare30(vyy3000, vyy400, ty_@0) → new_compare8(vyy3000, vyy400)
new_ltEs11(vyy3001, vyy401, ty_Char) → new_ltEs8(vyy3001, vyy401)
new_compare4(:(vyy3000, vyy3001), [], bda) → GT
new_sizeFM(Branch(vyy410, vyy411, vyy412, vyy413, vyy414), bgd, bge) → vyy412
new_lt7(vyy3000, vyy400, ty_@0) → new_lt8(vyy3000, vyy400)
new_esEs21(vyy40, vyy41, app(app(ty_Either, bhf), bhg)) → new_esEs7(vyy40, vyy41, bhf, bhg)
new_pePe(True, vyy40, vyy41, vyy57, bgf) → True
new_esEs22(vyy400, vyy410, ty_@0) → new_esEs10(vyy400, vyy410)
new_foldFM2(Branch(vyy410, vyy411, vyy412, vyy413, vyy414), bgd, bge) → new_foldFM0(vyy410, vyy411, new_foldFM2(vyy414, bgd, bge), vyy413, bgd, bge)
new_lt20(vyy3001, vyy401, app(app(ty_Either, db), dc)) → new_lt11(vyy3001, vyy401, db, dc)
new_esEs29(vyy400, vyy410, app(app(app(ty_@3, dde), ddf), ddg)) → new_esEs5(vyy400, vyy410, dde, ddf, ddg)
new_esEs7(Left(vyy400), Left(vyy410), app(ty_Maybe, ceg), bhg) → new_esEs8(vyy400, vyy410, ceg)
new_compare23(vyy3000, vyy400, True, be, bf) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(vyy4000))) → new_primCmpNat0(Succ(vyy4000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(vyy4000))) → GT
new_esEs23(vyy401, vyy411, ty_Bool) → new_esEs17(vyy401, vyy411)
new_compare13(Char(vyy3000), Char(vyy400)) → new_primCmpNat0(vyy3000, vyy400)
new_lt7(vyy3000, vyy400, ty_Ordering) → new_lt6(vyy3000, vyy400)
new_compare4([], :(vyy400, vyy401), bda) → LT
new_compare30(vyy3000, vyy400, app(app(app(ty_@3, bdb), bdc), bdd)) → new_compare19(vyy3000, vyy400, bdb, bdc, bdd)
new_lt7(vyy3000, vyy400, ty_Bool) → new_lt5(vyy3000, vyy400)
new_esEs23(vyy401, vyy411, app(ty_[], cbf)) → new_esEs11(vyy401, vyy411, cbf)
new_lt16(vyy3000, vyy400) → new_esEs9(new_compare11(vyy3000, vyy400))
new_esEs29(vyy400, vyy410, ty_Int) → new_esEs19(vyy400, vyy410)
new_esEs28(vyy401, vyy411, app(app(ty_@2, dbe), dbf)) → new_esEs6(vyy401, vyy411, dbe, dbf)
new_esEs21(vyy40, vyy41, ty_Float) → new_esEs12(vyy40, vyy41)
new_ltEs19(vyy3002, vyy402, ty_Ordering) → new_ltEs14(vyy3002, vyy402)
new_ltEs13(Left(vyy3000), Left(vyy400), app(app(ty_Either, bab), bac), hg) → new_ltEs13(vyy3000, vyy400, bab, bac)
new_esEs8(Just(vyy400), Just(vyy410), ty_Bool) → new_esEs17(vyy400, vyy410)
new_compare24(vyy3000, vyy400, False, h, ba, bb) → new_compare18(vyy3000, vyy400, new_ltEs12(vyy3000, vyy400, h, ba, bb), h, ba, bb)
new_lt20(vyy3001, vyy401, ty_Double) → new_lt16(vyy3001, vyy401)
new_ltEs13(Right(vyy3000), Right(vyy400), baf, app(app(ty_Either, bbd), bbe)) → new_ltEs13(vyy3000, vyy400, bbd, bbe)
new_ltEs18(Just(vyy3000), Just(vyy400), app(ty_[], bch)) → new_ltEs4(vyy3000, vyy400, bch)
new_ltEs18(Just(vyy3000), Just(vyy400), ty_@0) → new_ltEs6(vyy3000, vyy400)
new_esEs19(vyy40, vyy41) → new_primEqInt(vyy40, vyy41)
new_ltEs13(Left(vyy3000), Left(vyy400), app(app(app(ty_@3, hd), he), hf), hg) → new_ltEs12(vyy3000, vyy400, hd, he, hf)
new_esEs8(Nothing, Nothing, bed) → True
new_esEs10(@0, @0) → True
new_esEs27(vyy402, vyy412, app(ty_Ratio, dah)) → new_esEs14(vyy402, vyy412, dah)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs29(vyy400, vyy410, ty_Bool) → new_esEs17(vyy400, vyy410)
new_ltEs13(Left(vyy3000), Left(vyy400), ty_Ordering, hg) → new_ltEs14(vyy3000, vyy400)
new_ltEs16(vyy300, vyy40) → new_not(new_compare11(vyy300, vyy40))
new_esEs28(vyy401, vyy411, ty_@0) → new_esEs10(vyy401, vyy411)
new_asAs(False, vyy66) → False
new_lt9(vyy3000, vyy400, h, ba, bb) → new_esEs9(new_compare19(vyy3000, vyy400, h, ba, bb))
new_primMulInt(Neg(vyy30010), Pos(vyy4010)) → Neg(new_primMulNat0(vyy30010, vyy4010))
new_primMulInt(Pos(vyy30010), Neg(vyy4010)) → Neg(new_primMulNat0(vyy30010, vyy4010))
new_esEs22(vyy400, vyy410, ty_Float) → new_esEs12(vyy400, vyy410)
new_esEs27(vyy402, vyy412, ty_Double) → new_esEs13(vyy402, vyy412)
new_ltEs13(Left(vyy3000), Right(vyy400), baf, hg) → True
new_primMulNat0(Succ(vyy300100), Zero) → Zero
new_primMulNat0(Zero, Succ(vyy40100)) → Zero
new_esEs24(vyy400, vyy410, ty_Double) → new_esEs13(vyy400, vyy410)
new_compare30(vyy3000, vyy400, ty_Integer) → new_compare17(vyy3000, vyy400)
new_esEs7(Right(vyy400), Right(vyy410), bhf, ty_Integer) → new_esEs15(vyy400, vyy410)
new_lt7(vyy3000, vyy400, app(ty_[], ga)) → new_lt4(vyy3000, vyy400, ga)
new_ltEs13(Right(vyy3000), Right(vyy400), baf, ty_Int) → new_ltEs15(vyy3000, vyy400)
new_ltEs8(vyy300, vyy40) → new_not(new_compare13(vyy300, vyy40))
new_pePe(False, vyy40, vyy41, vyy57, bgf) → new_asAs(new_esEs21(vyy40, vyy41, bgf), vyy57)
new_ltEs11(vyy3001, vyy401, ty_@0) → new_ltEs6(vyy3001, vyy401)
new_compare17(Integer(vyy3000), Integer(vyy400)) → new_primCmpInt(vyy3000, vyy400)
new_ltEs11(vyy3001, vyy401, ty_Ordering) → new_ltEs14(vyy3001, vyy401)
new_esEs29(vyy400, vyy410, ty_Double) → new_esEs13(vyy400, vyy410)
new_ltEs18(Nothing, Just(vyy400), chf) → True
new_ltEs14(GT, LT) → False
new_lt20(vyy3001, vyy401, app(ty_[], de)) → new_lt4(vyy3001, vyy401, de)
new_not(EQ) → new_not0
new_esEs8(Just(vyy400), Just(vyy410), app(app(app(ty_@3, bfa), bfb), bfc)) → new_esEs5(vyy400, vyy410, bfa, bfb, bfc)
new_compare29(vyy3000, vyy400, False, bg, bh) → new_compare111(vyy3000, vyy400, new_ltEs13(vyy3000, vyy400, bg, bh), bg, bh)
new_lt10(vyy3000, vyy400, be, bf) → new_esEs9(new_compare9(vyy3000, vyy400, be, bf))
new_esEs28(vyy401, vyy411, ty_Integer) → new_esEs15(vyy401, vyy411)
new_lt5(vyy3000, vyy400) → new_esEs9(new_compare10(vyy3000, vyy400))
new_compare18(vyy3000, vyy400, False, h, ba, bb) → GT
new_esEs7(Right(vyy400), Right(vyy410), bhf, ty_Int) → new_esEs19(vyy400, vyy410)
new_ltEs9(False, True) → True
new_ltEs13(Right(vyy3000), Right(vyy400), baf, app(app(ty_@2, bbb), bbc)) → new_ltEs10(vyy3000, vyy400, bbb, bbc)
new_esEs23(vyy401, vyy411, ty_Integer) → new_esEs15(vyy401, vyy411)
new_compare25(vyy3000, vyy400, False, ca) → new_compare15(vyy3000, vyy400, new_ltEs18(vyy3000, vyy400, ca), ca)
new_compare27(vyy3000, vyy400, True) → EQ
new_ltEs13(Right(vyy3000), Left(vyy400), baf, hg) → False
new_lt4(vyy3000, vyy400, cb) → new_esEs9(new_compare4(vyy3000, vyy400, cb))
new_esEs28(vyy401, vyy411, ty_Bool) → new_esEs17(vyy401, vyy411)
new_compare14(vyy3000, vyy400) → new_compare26(vyy3000, vyy400, new_esEs18(vyy3000, vyy400))
new_esEs27(vyy402, vyy412, app(ty_[], dac)) → new_esEs11(vyy402, vyy412, dac)
new_lt7(vyy3000, vyy400, ty_Int) → new_lt13(vyy3000, vyy400)
new_esEs22(vyy400, vyy410, ty_Int) → new_esEs19(vyy400, vyy410)
new_ltEs19(vyy3002, vyy402, ty_Int) → new_ltEs15(vyy3002, vyy402)
new_ltEs14(LT, GT) → True
new_esEs24(vyy400, vyy410, app(ty_Maybe, cdc)) → new_esEs8(vyy400, vyy410, cdc)
new_not(LT) → new_not0
new_ltEs14(LT, EQ) → True
new_lt12(vyy3000, vyy400) → new_esEs9(new_compare13(vyy3000, vyy400))
new_esEs26(vyy400, vyy410, ty_Int) → new_esEs19(vyy400, vyy410)
new_compare4(:(vyy3000, vyy3001), :(vyy400, vyy401), bda) → new_primCompAux1(vyy3000, vyy400, new_compare4(vyy3001, vyy401, bda), bda)
new_compare28(vyy3000, vyy400, ca) → new_compare25(vyy3000, vyy400, new_esEs8(vyy3000, vyy400, ca), ca)
new_esEs29(vyy400, vyy410, app(app(ty_Either, dea), deb)) → new_esEs7(vyy400, vyy410, dea, deb)
new_esEs21(vyy40, vyy41, app(ty_[], bha)) → new_esEs11(vyy40, vyy41, bha)
new_esEs7(Left(vyy400), Left(vyy410), ty_Bool, bhg) → new_esEs17(vyy400, vyy410)
new_lt20(vyy3001, vyy401, ty_Char) → new_lt12(vyy3001, vyy401)
new_esEs29(vyy400, vyy410, ty_Char) → new_esEs16(vyy400, vyy410)
new_esEs12(Float(vyy400, vyy401), Float(vyy410, vyy411)) → new_esEs19(new_sr(vyy400, vyy410), new_sr(vyy401, vyy411))
new_esEs28(vyy401, vyy411, ty_Ordering) → new_esEs18(vyy401, vyy411)
new_ltEs11(vyy3001, vyy401, app(ty_[], hc)) → new_ltEs4(vyy3001, vyy401, hc)
new_esEs29(vyy400, vyy410, ty_@0) → new_esEs10(vyy400, vyy410)
new_esEs22(vyy400, vyy410, ty_Integer) → new_esEs15(vyy400, vyy410)
new_primPlusNat1(Zero, Zero) → Zero
new_compare111(vyy3000, vyy400, True, bg, bh) → LT
new_compare15(vyy3000, vyy400, True, ca) → LT
new_asAs(True, vyy66) → vyy66
new_ltEs14(EQ, EQ) → True
new_compare112(vyy3000, vyy400, True, be, bf) → LT
new_primMulNat0(Succ(vyy300100), Succ(vyy40100)) → new_primPlusNat0(new_primMulNat0(vyy300100, Succ(vyy40100)), vyy40100)
new_esEs29(vyy400, vyy410, ty_Float) → new_esEs12(vyy400, vyy410)
new_esEs8(Just(vyy400), Just(vyy410), app(ty_Maybe, beh)) → new_esEs8(vyy400, vyy410, beh)
new_esEs24(vyy400, vyy410, ty_Int) → new_esEs19(vyy400, vyy410)
new_compare8(@0, @0) → EQ
new_esEs7(Left(vyy400), Left(vyy410), ty_Char, bhg) → new_esEs16(vyy400, vyy410)
new_fmToList(vyy41, bgd, bge) → new_foldFM2(vyy41, bgd, bge)
new_ltEs13(Left(vyy3000), Left(vyy400), ty_Bool, hg) → new_ltEs9(vyy3000, vyy400)
new_esEs23(vyy401, vyy411, app(app(app(ty_@3, cbh), cca), ccb)) → new_esEs5(vyy401, vyy411, cbh, cca, ccb)
new_esEs29(vyy400, vyy410, app(ty_Ratio, ddh)) → new_esEs14(vyy400, vyy410, ddh)
new_ltEs4(vyy300, vyy40, bda) → new_not(new_compare4(vyy300, vyy40, bda))
new_compare10(vyy3000, vyy400) → new_compare27(vyy3000, vyy400, new_esEs17(vyy3000, vyy400))
new_lt8(vyy3000, vyy400) → new_esEs9(new_compare8(vyy3000, vyy400))
new_ltEs13(Right(vyy3000), Right(vyy400), baf, app(app(app(ty_@3, bag), bah), bba)) → new_ltEs12(vyy3000, vyy400, bag, bah, bba)
new_esEs7(Left(vyy400), Left(vyy410), ty_Float, bhg) → new_esEs12(vyy400, vyy410)
new_ltEs11(vyy3001, vyy401, ty_Double) → new_ltEs16(vyy3001, vyy401)
new_lt7(vyy3000, vyy400, app(app(ty_Either, ff), fg)) → new_lt11(vyy3000, vyy400, ff, fg)
new_ltEs13(Right(vyy3000), Right(vyy400), baf, ty_@0) → new_ltEs6(vyy3000, vyy400)
new_ltEs13(Right(vyy3000), Right(vyy400), baf, ty_Double) → new_ltEs16(vyy3000, vyy400)
new_lt7(vyy3000, vyy400, ty_Float) → new_lt14(vyy3000, vyy400)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_ltEs14(EQ, GT) → True
new_esEs7(Right(vyy400), Right(vyy410), bhf, ty_@0) → new_esEs10(vyy400, vyy410)
new_primCompAux0(vyy71, EQ) → vyy71
new_compare7(:%(vyy3000, vyy3001), :%(vyy400, vyy401), ty_Int) → new_compare6(new_sr(vyy3000, vyy401), new_sr(vyy400, vyy3001))
new_esEs8(Just(vyy400), Just(vyy410), app(app(ty_FiniteMap, bfg), bfh)) → new_esEs20(vyy400, vyy410, bfg, bfh)
new_ltEs18(Just(vyy3000), Just(vyy400), app(app(app(ty_@3, bbh), bca), bcb)) → new_ltEs12(vyy3000, vyy400, bbh, bca, bcb)
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_ltEs19(vyy3002, vyy402, app(ty_Maybe, ee)) → new_ltEs18(vyy3002, vyy402, ee)
new_esEs27(vyy402, vyy412, ty_Integer) → new_esEs15(vyy402, vyy412)
new_esEs18(EQ, EQ) → True
new_esEs7(Right(vyy400), Right(vyy410), bhf, app(app(ty_FiniteMap, chb), chc)) → new_esEs20(vyy400, vyy410, chb, chc)
new_primCmpInt(Neg(Succ(vyy30000)), Pos(vyy400)) → LT
new_compare16(vyy3000, vyy400, False) → GT
The set Q consists of the following terms:
new_compare29(x0, x1, True, x2, x3)
new_ltEs18(Just(x0), Just(x1), ty_Double)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_compare30(x0, x1, ty_Int)
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_compare9(x0, x1, x2, x3)
new_esEs8(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, ty_Char)
new_lt16(x0, x1)
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_esEs7(Left(x0), Left(x1), ty_Integer, x2)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs18(LT, LT)
new_pePe(False, x0, x1, x2, x3)
new_ltEs11(x0, x1, ty_Integer)
new_ltEs13(Left(x0), Left(x1), ty_@0, x2)
new_esEs23(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_compare110(x0, x1, False)
new_ltEs13(Right(x0), Right(x1), x2, ty_Bool)
new_esEs9(EQ)
new_ltEs18(Just(x0), Just(x1), app(ty_Ratio, x2))
new_compare26(x0, x1, True)
new_ltEs18(Just(x0), Just(x1), app(ty_Maybe, x2))
new_lt19(x0, x1, app(ty_Ratio, x2))
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_ltEs18(Just(x0), Just(x1), ty_Ordering)
new_compare30(x0, x1, ty_Bool)
new_compare4([], [], x0)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_compare19(x0, x1, x2, x3, x4)
new_compare30(x0, x1, ty_@0)
new_ltEs13(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_primMulNat0(Zero, Succ(x0))
new_esEs29(x0, x1, ty_Ordering)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpNat0(Zero, Succ(x0))
new_primCmpNat0(Succ(x0), Zero)
new_esEs8(Just(x0), Just(x1), ty_@0)
new_esEs28(x0, x1, ty_Integer)
new_compare6(x0, x1)
new_ltEs8(x0, x1)
new_compare25(x0, x1, False, x2)
new_ltEs19(x0, x1, ty_Float)
new_compare7(:%(x0, x1), :%(x2, x3), ty_Int)
new_esEs7(Right(x0), Right(x1), x2, ty_Float)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs22(x0, x1, app(ty_[], x2))
new_compare4(:(x0, x1), :(x2, x3), x4)
new_esEs7(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_lt20(x0, x1, ty_Double)
new_compare30(x0, x1, app(ty_Maybe, x2))
new_esEs11([], :(x0, x1), x2)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_lt19(x0, x1, ty_Integer)
new_esEs7(Right(x0), Right(x1), x2, ty_Bool)
new_lt20(x0, x1, app(ty_[], x2))
new_ltEs13(Left(x0), Left(x1), app(ty_[], x2), x3)
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs11([], [], x0)
new_compare30(x0, x1, ty_Double)
new_asAs(False, x0)
new_esEs27(x0, x1, ty_Bool)
new_ltEs13(Left(x0), Left(x1), ty_Bool, x2)
new_esEs18(EQ, GT)
new_esEs18(GT, EQ)
new_esEs27(x0, x1, ty_Int)
new_esEs8(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs17(False, False)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs11(x0, x1, ty_Char)
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_compare24(x0, x1, True, x2, x3, x4)
new_sr(x0, x1)
new_compare8(@0, @0)
new_esEs25(x0, x1, ty_Int)
new_ltEs13(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_compare23(x0, x1, True, x2, x3)
new_esEs18(EQ, EQ)
new_esEs7(Left(x0), Left(x1), ty_Double, x2)
new_esEs7(Right(x0), Right(x1), x2, ty_Int)
new_esEs8(Just(x0), Just(x1), ty_Float)
new_ltEs4(x0, x1, x2)
new_compare27(x0, x1, True)
new_esEs7(Left(x0), Left(x1), ty_Int, x2)
new_ltEs5(x0, x1, x2)
new_esEs7(Left(x0), Left(x1), ty_Float, x2)
new_ltEs13(Left(x0), Left(x1), ty_Float, x2)
new_esEs28(x0, x1, ty_Char)
new_esEs8(Just(x0), Just(x1), ty_Ordering)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_ltEs13(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_lt19(x0, x1, app(ty_[], x2))
new_esEs21(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs29(x0, x1, ty_Char)
new_esEs22(x0, x1, ty_Char)
new_esEs7(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_ltEs18(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs14(EQ, EQ)
new_primEqNat0(Zero, Zero)
new_primCmpNat0(Succ(x0), Succ(x1))
new_compare30(x0, x1, app(ty_Ratio, x2))
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs18(Just(x0), Nothing, x1)
new_esEs25(x0, x1, ty_Integer)
new_esEs7(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_esEs29(x0, x1, ty_Int)
new_lt20(x0, x1, ty_@0)
new_lt7(x0, x1, ty_Double)
new_ltEs9(False, False)
new_ltEs19(x0, x1, ty_Int)
new_esEs24(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_lt20(x0, x1, ty_Char)
new_esEs23(x0, x1, ty_Integer)
new_primPlusNat1(Zero, Succ(x0))
new_primMulNat0(Zero, Zero)
new_primMulInt(Pos(x0), Pos(x1))
new_ltEs13(Right(x0), Right(x1), x2, ty_Char)
new_lt7(x0, x1, ty_Char)
new_esEs21(x0, x1, ty_Float)
new_esEs23(x0, x1, ty_@0)
new_esEs7(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_compare25(x0, x1, True, x2)
new_lt4(x0, x1, x2)
new_compare24(x0, x1, False, x2, x3, x4)
new_esEs24(x0, x1, ty_Bool)
new_esEs8(Just(x0), Just(x1), ty_Integer)
new_esEs7(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_primPlusNat1(Succ(x0), Zero)
new_lt7(x0, x1, ty_Ordering)
new_primMulNat0(Succ(x0), Succ(x1))
new_esEs21(x0, x1, ty_@0)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_esEs28(x0, x1, ty_Bool)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
new_ltEs16(x0, x1)
new_esEs23(x0, x1, ty_Double)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, ty_Int)
new_lt9(x0, x1, x2, x3, x4)
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_lt14(x0, x1)
new_esEs27(x0, x1, ty_@0)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_lt19(x0, x1, ty_Ordering)
new_lt7(x0, x1, app(ty_[], x2))
new_esEs21(x0, x1, ty_Char)
new_lt10(x0, x1, x2, x3)
new_esEs8(Just(x0), Just(x1), ty_Char)
new_esEs7(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_ltEs6(x0, x1)
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
new_ltEs13(Left(x0), Left(x1), ty_Integer, x2)
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs11(x0, x1, app(ty_Ratio, x2))
new_lt20(x0, x1, ty_Bool)
new_ltEs11(x0, x1, ty_Float)
new_esEs28(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_lt7(x0, x1, ty_Int)
new_lt11(x0, x1, x2, x3)
new_primPlusNat0(Succ(x0), x1)
new_esEs27(x0, x1, ty_Integer)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_compare27(x0, x1, False)
new_primPlusNat1(Zero, Zero)
new_not0
new_esEs29(x0, x1, ty_@0)
new_lt18(x0, x1, x2)
new_lt7(x0, x1, app(ty_Ratio, x2))
new_primMulNat0(Succ(x0), Zero)
new_esEs21(x0, x1, ty_Bool)
new_esEs27(x0, x1, ty_Ordering)
new_compare13(Char(x0), Char(x1))
new_esEs9(GT)
new_ltEs14(LT, LT)
new_ltEs13(Right(x0), Right(x1), x2, ty_Float)
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_compare30(x0, x1, app(ty_[], x2))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs19(x0, x1)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_lt7(x0, x1, ty_Integer)
new_esEs29(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs24(x0, x1, ty_@0)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs8(Just(x0), Just(x1), app(app(ty_FiniteMap, x2), x3))
new_ltEs11(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs7(x0, x1)
new_compare110(x0, x1, True)
new_compare18(x0, x1, True, x2, x3, x4)
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_esEs18(GT, GT)
new_esEs7(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_lt15(x0, x1, x2)
new_ltEs13(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs11(x0, x1, ty_Double)
new_ltEs9(False, True)
new_ltEs9(True, False)
new_lt7(x0, x1, app(app(ty_@2, x2), x3))
new_lt5(x0, x1)
new_compare12(Float(x0, x1), Float(x2, x3))
new_esEs22(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_lt7(x0, x1, app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, app(ty_[], x2))
new_esEs11(:(x0, x1), :(x2, x3), x4)
new_compare30(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs9(True, True)
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_esEs10(@0, @0)
new_not(GT)
new_esEs27(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs11(:(x0, x1), [], x2)
new_ltEs18(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs8(Just(x0), Just(x1), ty_Double)
new_ltEs13(Left(x0), Left(x1), ty_Int, x2)
new_ltEs18(Nothing, Just(x0), x1)
new_ltEs13(Right(x0), Left(x1), x2, x3)
new_ltEs13(Left(x0), Right(x1), x2, x3)
new_compare111(x0, x1, True, x2, x3)
new_esEs24(x0, x1, ty_Ordering)
new_esEs16(Char(x0), Char(x1))
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_lt7(x0, x1, ty_Bool)
new_primEqInt(Neg(Zero), Pos(Zero))
new_primEqInt(Pos(Zero), Neg(Zero))
new_ltEs14(LT, EQ)
new_ltEs14(EQ, LT)
new_compare16(x0, x1, False)
new_ltEs13(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_compare14(x0, x1)
new_esEs7(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs24(x0, x1, ty_Integer)
new_ltEs11(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs18(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs18(Just(x0), Just(x1), ty_Bool)
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_lt19(x0, x1, app(ty_Maybe, x2))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs29(x0, x1, ty_Float)
new_ltEs13(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs10(@2(x0, x1), @2(x2, x3), x4, x5)
new_primPlusNat1(Succ(x0), Succ(x1))
new_lt19(x0, x1, ty_Int)
new_esEs28(x0, x1, app(ty_[], x2))
new_primEqInt(Neg(Zero), Neg(Zero))
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_compare7(:%(x0, x1), :%(x2, x3), ty_Integer)
new_compare16(x0, x1, True)
new_esEs6(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs28(x0, x1, ty_Ordering)
new_primCompAux0(x0, EQ)
new_ltEs13(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_ltEs18(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_ltEs19(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, ty_Float)
new_compare10(x0, x1)
new_lt7(x0, x1, ty_Float)
new_compare11(Double(x0, x1), Double(x2, x3))
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs28(x0, x1, ty_Double)
new_primCompAux0(x0, LT)
new_compare15(x0, x1, True, x2)
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt17(x0, x1)
new_ltEs11(x0, x1, ty_Bool)
new_ltEs13(Right(x0), Right(x1), x2, ty_Double)
new_pePe(True, x0, x1, x2, x3)
new_esEs23(x0, x1, app(ty_[], x2))
new_foldFM2(EmptyFM, x0, x1)
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs18(Just(x0), Just(x1), ty_Float)
new_compare17(Integer(x0), Integer(x1))
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, app(ty_[], x2))
new_esEs27(x0, x1, ty_Char)
new_compare15(x0, x1, False, x2)
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs11(x0, x1, app(ty_Maybe, x2))
new_lt8(x0, x1)
new_primEqNat0(Succ(x0), Zero)
new_esEs7(Right(x0), Right(x1), x2, ty_Integer)
new_esEs9(LT)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt7(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs24(x0, x1, ty_Int)
new_ltEs11(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primEqNat0(Zero, Succ(x0))
new_esEs22(x0, x1, ty_Double)
new_esEs24(x0, x1, ty_Float)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_esEs8(Just(x0), Nothing, x1)
new_esEs22(x0, x1, ty_Int)
new_ltEs18(Just(x0), Just(x1), ty_Char)
new_esEs14(:%(x0, x1), :%(x2, x3), x4)
new_esEs7(Right(x0), Right(x1), x2, ty_Char)
new_compare18(x0, x1, False, x2, x3, x4)
new_primPlusNat0(Zero, x0)
new_ltEs14(EQ, GT)
new_ltEs14(GT, EQ)
new_esEs22(x0, x1, ty_Bool)
new_esEs22(x0, x1, ty_Ordering)
new_compare111(x0, x1, False, x2, x3)
new_lt19(x0, x1, ty_Double)
new_esEs8(Nothing, Just(x0), x1)
new_ltEs13(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_compare31(x0, x1, x2, x3)
new_primCmpNat0(Zero, Zero)
new_esEs8(Just(x0), Just(x1), ty_Int)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs8(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_compare26(x0, x1, False)
new_ltEs11(x0, x1, ty_Int)
new_lt7(x0, x1, app(ty_Maybe, x2))
new_esEs12(Float(x0, x1), Float(x2, x3))
new_primCompAux0(x0, GT)
new_esEs28(x0, x1, ty_Int)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_esEs7(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_primCompAux1(x0, x1, x2, x3)
new_esEs29(x0, x1, ty_Integer)
new_lt13(x0, x1)
new_esEs28(x0, x1, ty_@0)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_lt19(x0, x1, ty_@0)
new_esEs23(x0, x1, ty_Ordering)
new_lt12(x0, x1)
new_ltEs13(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs13(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_ltEs18(Nothing, Nothing, x0)
new_ltEs19(x0, x1, ty_Double)
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs18(Just(x0), Just(x1), ty_Int)
new_esEs8(Just(x0), Just(x1), app(ty_[], x2))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_lt7(x0, x1, ty_@0)
new_compare28(x0, x1, x2)
new_esEs26(x0, x1, ty_Int)
new_esEs18(LT, EQ)
new_esEs18(EQ, LT)
new_ltEs13(Left(x0), Left(x1), ty_Double, x2)
new_ltEs19(x0, x1, ty_Bool)
new_esEs24(x0, x1, app(ty_[], x2))
new_ltEs14(LT, GT)
new_ltEs14(GT, LT)
new_esEs23(x0, x1, ty_Float)
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_esEs7(Left(x0), Left(x1), ty_@0, x2)
new_esEs5(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs7(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs29(x0, x1, ty_Bool)
new_esEs21(x0, x1, ty_Integer)
new_compare30(x0, x1, ty_Float)
new_ltEs11(x0, x1, app(app(ty_Either, x2), x3))
new_esEs7(Right(x0), Right(x1), x2, ty_@0)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_esEs8(Just(x0), Just(x1), ty_Bool)
new_lt19(x0, x1, ty_Char)
new_compare112(x0, x1, False, x2, x3)
new_sizeFM(EmptyFM, x0, x1)
new_esEs7(Left(x0), Right(x1), x2, x3)
new_esEs7(Right(x0), Left(x1), x2, x3)
new_esEs22(x0, x1, ty_@0)
new_ltEs12(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs23(x0, x1, ty_Char)
new_ltEs14(GT, GT)
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_FiniteMap, x3), x4))
new_compare112(x0, x1, True, x2, x3)
new_esEs27(x0, x1, ty_Double)
new_esEs27(x0, x1, ty_Float)
new_ltEs18(Just(x0), Just(x1), ty_@0)
new_esEs24(x0, x1, ty_Char)
new_not(EQ)
new_esEs7(Left(x0), Left(x1), app(ty_[], x2), x3)
new_ltEs13(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_ltEs13(Right(x0), Right(x1), x2, ty_Integer)
new_esEs15(Integer(x0), Integer(x1))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_lt6(x0, x1)
new_esEs23(x0, x1, ty_Bool)
new_esEs29(x0, x1, ty_Double)
new_compare30(x0, x1, app(app(ty_Either, x2), x3))
new_lt19(x0, x1, ty_Bool)
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_esEs7(Left(x0), Left(x1), ty_Char, x2)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_esEs21(x0, x1, ty_Double)
new_esEs8(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs7(Left(x0), Left(x1), ty_Bool, x2)
new_compare4([], :(x0, x1), x2)
new_esEs22(x0, x1, ty_Integer)
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs15(x0, x1)
new_lt20(x0, x1, ty_Integer)
new_fmToList(x0, x1, x2)
new_ltEs19(x0, x1, ty_Ordering)
new_esEs18(GT, LT)
new_esEs18(LT, GT)
new_lt20(x0, x1, ty_Ordering)
new_esEs26(x0, x1, ty_Integer)
new_lt20(x0, x1, ty_Int)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_lt19(x0, x1, ty_Float)
new_compare29(x0, x1, False, x2, x3)
new_esEs17(False, True)
new_esEs17(True, False)
new_ltEs13(Right(x0), Right(x1), x2, ty_Int)
new_ltEs13(Left(x0), Left(x1), ty_Char, x2)
new_esEs20(x0, x1, x2, x3)
new_compare30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs11(x0, x1, ty_Ordering)
new_esEs7(Left(x0), Left(x1), ty_Ordering, x2)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sr0(Integer(x0), Integer(x1))
new_esEs23(x0, x1, ty_Int)
new_compare4(:(x0, x1), [], x2)
new_esEs22(x0, x1, ty_Float)
new_compare23(x0, x1, False, x2, x3)
new_esEs21(x0, x1, ty_Ordering)
new_ltEs17(x0, x1)
new_esEs28(x0, x1, ty_Float)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_primEqInt(Pos(Zero), Pos(Zero))
new_esEs17(True, True)
new_esEs8(Just(x0), Just(x1), app(ty_Ratio, x2))
new_ltEs11(x0, x1, ty_@0)
new_ltEs13(Right(x0), Right(x1), x2, ty_@0)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_ltEs18(Just(x0), Just(x1), ty_Integer)
new_ltEs19(x0, x1, ty_@0)
new_esEs29(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, app(ty_Ratio, x2))
new_esEs7(Right(x0), Right(x1), x2, ty_Double)
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_asAs(True, x0)
new_esEs7(Left(x0), Left(x1), app(app(ty_FiniteMap, x2), x3), x4)
new_compare30(x0, x1, ty_Char)
new_esEs8(Nothing, Nothing, x0)
new_esEs13(Double(x0, x1), Double(x2, x3))
new_primMulInt(Neg(x0), Neg(x1))
new_ltEs13(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs24(x0, x1, ty_Double)
new_ltEs13(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_compare30(x0, x1, ty_Integer)
new_not(LT)
new_ltEs19(x0, x1, ty_Integer)
new_compare30(x0, x1, ty_Ordering)
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_primCompAux(vyy3000, vyy400, vyy67, app(ty_[], beb)) → new_compare(vyy3000, vyy400, beb)
The graph contains the following edges 1 >= 1, 2 >= 2, 4 > 3
- new_lt0(vyy3000, vyy400, be, bf) → new_compare20(vyy3000, vyy400, new_esEs6(vyy3000, vyy400, be, bf), be, bf)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 4, 4 >= 5
- new_ltEs2(Just(vyy3000), Just(vyy400), app(app(ty_@2, bcc), bcd)) → new_ltEs0(vyy3000, vyy400, bcc, bcd)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
- new_ltEs2(Just(vyy3000), Just(vyy400), app(app(ty_Either, bce), bcf)) → new_ltEs1(vyy3000, vyy400, bce, bcf)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
- new_lt1(vyy3000, vyy400, bg, bh) → new_compare21(vyy3000, vyy400, new_esEs7(vyy3000, vyy400, bg, bh), bg, bh)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 4, 4 >= 5
- new_ltEs2(Just(vyy3000), Just(vyy400), app(app(app(ty_@3, bbh), bca), bcb)) → new_ltEs(vyy3000, vyy400, bbh, bca, bcb)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
- new_compare2(vyy3000, vyy400, False, h, ba, bb) → new_ltEs(vyy3000, vyy400, h, ba, bb)
The graph contains the following edges 1 >= 1, 2 >= 2, 4 >= 3, 5 >= 4, 6 >= 5
- new_compare0(vyy3000, vyy400, h, ba, bb) → new_compare2(vyy3000, vyy400, new_esEs5(vyy3000, vyy400, h, ba, bb), h, ba, bb)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 4, 4 >= 5, 5 >= 6
- new_ltEs3(:(vyy3000, vyy3001), :(vyy400, vyy401), bda) → new_compare(vyy3001, vyy401, bda)
The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3
- new_ltEs2(Just(vyy3000), Just(vyy400), app(ty_Maybe, bcg)) → new_ltEs2(vyy3000, vyy400, bcg)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
- new_ltEs2(Just(vyy3000), Just(vyy400), app(ty_[], bch)) → new_ltEs3(vyy3000, vyy400, bch)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
- new_ltEs3(:(vyy3000, vyy3001), :(vyy400, vyy401), bda) → new_primCompAux(vyy3000, vyy400, new_compare4(vyy3001, vyy401, bda), bda)
The graph contains the following edges 1 > 1, 2 > 2, 3 >= 4
- new_compare(:(vyy3000, vyy3001), :(vyy400, vyy401), bda) → new_primCompAux(vyy3000, vyy400, new_compare4(vyy3001, vyy401, bda), bda)
The graph contains the following edges 1 > 1, 2 > 2, 3 >= 4
- new_primCompAux(vyy3000, vyy400, vyy67, app(ty_Maybe, bea)) → new_compare5(vyy3000, vyy400, bea)
The graph contains the following edges 1 >= 1, 2 >= 2, 4 > 3
- new_compare22(vyy3000, vyy400, False, ca) → new_ltEs2(vyy3000, vyy400, ca)
The graph contains the following edges 1 >= 1, 2 >= 2, 4 >= 3
- new_ltEs(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), app(ty_[], cb), bc, bd) → new_compare(vyy3000, vyy400, cb)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
- new_ltEs(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), cc, bc, app(app(ty_@2, ea), eb)) → new_ltEs0(vyy3002, vyy402, ea, eb)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4
- new_ltEs(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), cc, bc, app(app(ty_Either, ec), ed)) → new_ltEs1(vyy3002, vyy402, ec, ed)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4
- new_ltEs(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), cc, bc, app(app(app(ty_@3, df), dg), dh)) → new_ltEs(vyy3002, vyy402, df, dg, dh)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4, 5 > 5
- new_ltEs0(@2(vyy3000, vyy3001), @2(vyy400, vyy401), gb, app(app(app(ty_@3, gc), gd), ge)) → new_ltEs(vyy3001, vyy401, gc, gd, ge)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5
- new_ltEs(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), cc, app(app(app(ty_@3, cd), ce), cf), bd) → new_lt(vyy3001, vyy401, cd, ce, cf)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5
- new_ltEs0(@2(vyy3000, vyy3001), @2(vyy400, vyy401), app(app(app(ty_@3, eg), eh), fa), fb) → new_lt(vyy3000, vyy400, eg, eh, fa)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
- new_ltEs(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), cc, bc, app(ty_Maybe, ee)) → new_ltEs2(vyy3002, vyy402, ee)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3
- new_ltEs0(@2(vyy3000, vyy3001), @2(vyy400, vyy401), gb, app(ty_Maybe, hb)) → new_ltEs2(vyy3001, vyy401, hb)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
- new_compare(:(vyy3000, vyy3001), :(vyy400, vyy401), bda) → new_compare(vyy3001, vyy401, bda)
The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3
- new_lt3(vyy3000, vyy400, cb) → new_compare(vyy3000, vyy400, cb)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3
- new_ltEs(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), cc, bc, app(ty_[], ef)) → new_ltEs3(vyy3002, vyy402, ef)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3
- new_ltEs0(@2(vyy3000, vyy3001), @2(vyy400, vyy401), gb, app(ty_[], hc)) → new_ltEs3(vyy3001, vyy401, hc)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
- new_primCompAux(vyy3000, vyy400, vyy67, app(app(app(ty_@3, bdb), bdc), bdd)) → new_compare0(vyy3000, vyy400, bdb, bdc, bdd)
The graph contains the following edges 1 >= 1, 2 >= 2, 4 > 3, 4 > 4, 4 > 5
- new_primCompAux(vyy3000, vyy400, vyy67, app(app(ty_Either, bdg), bdh)) → new_compare3(vyy3000, vyy400, bdg, bdh)
The graph contains the following edges 1 >= 1, 2 >= 2, 4 > 3, 4 > 4
- new_primCompAux(vyy3000, vyy400, vyy67, app(app(ty_@2, bde), bdf)) → new_compare1(vyy3000, vyy400, bde, bdf)
The graph contains the following edges 1 >= 1, 2 >= 2, 4 > 3, 4 > 4
- new_compare21(vyy3000, vyy400, False, bg, bh) → new_ltEs1(vyy3000, vyy400, bg, bh)
The graph contains the following edges 1 >= 1, 2 >= 2, 4 >= 3, 5 >= 4
- new_ltEs0(@2(vyy3000, vyy3001), @2(vyy400, vyy401), gb, app(app(ty_Either, gh), ha)) → new_ltEs1(vyy3001, vyy401, gh, ha)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
- new_ltEs0(@2(vyy3000, vyy3001), @2(vyy400, vyy401), gb, app(app(ty_@2, gf), gg)) → new_ltEs0(vyy3001, vyy401, gf, gg)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
- new_compare20(vyy3000, vyy400, False, be, bf) → new_ltEs0(vyy3000, vyy400, be, bf)
The graph contains the following edges 1 >= 1, 2 >= 2, 4 >= 3, 5 >= 4
- new_ltEs(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), app(app(ty_@2, be), bf), bc, bd) → new_compare20(vyy3000, vyy400, new_esEs6(vyy3000, vyy400, be, bf), be, bf)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 4, 3 > 5
- new_compare1(vyy3000, vyy400, be, bf) → new_compare20(vyy3000, vyy400, new_esEs6(vyy3000, vyy400, be, bf), be, bf)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 4, 4 >= 5
- new_ltEs(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), cc, app(ty_Maybe, dd), bd) → new_lt2(vyy3001, vyy401, dd)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
- new_ltEs0(@2(vyy3000, vyy3001), @2(vyy400, vyy401), app(ty_Maybe, fh), fb) → new_lt2(vyy3000, vyy400, fh)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
- new_ltEs(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), app(app(ty_Either, bg), bh), bc, bd) → new_compare21(vyy3000, vyy400, new_esEs7(vyy3000, vyy400, bg, bh), bg, bh)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 4, 3 > 5
- new_compare3(vyy3000, vyy400, bg, bh) → new_compare21(vyy3000, vyy400, new_esEs7(vyy3000, vyy400, bg, bh), bg, bh)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 4, 4 >= 5
- new_ltEs(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), app(ty_Maybe, ca), bc, bd) → new_compare22(vyy3000, vyy400, new_esEs8(vyy3000, vyy400, ca), ca)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 4
- new_lt(vyy3000, vyy400, h, ba, bb) → new_compare2(vyy3000, vyy400, new_esEs5(vyy3000, vyy400, h, ba, bb), h, ba, bb)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 4, 4 >= 5, 5 >= 6
- new_ltEs(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), cc, app(ty_[], de), bd) → new_lt3(vyy3001, vyy401, de)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
- new_ltEs0(@2(vyy3000, vyy3001), @2(vyy400, vyy401), app(ty_[], ga), fb) → new_lt3(vyy3000, vyy400, ga)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
- new_ltEs(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), cc, app(app(ty_@2, cg), da), bd) → new_lt0(vyy3001, vyy401, cg, da)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
- new_ltEs0(@2(vyy3000, vyy3001), @2(vyy400, vyy401), app(app(ty_@2, fc), fd), fb) → new_lt0(vyy3000, vyy400, fc, fd)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
- new_ltEs0(@2(vyy3000, vyy3001), @2(vyy400, vyy401), app(app(ty_Either, ff), fg), fb) → new_lt1(vyy3000, vyy400, ff, fg)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
- new_ltEs(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), app(app(app(ty_@3, h), ba), bb), bc, bd) → new_compare2(vyy3000, vyy400, new_esEs5(vyy3000, vyy400, h, ba, bb), h, ba, bb)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 4, 3 > 5, 3 > 6
- new_ltEs(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), cc, app(app(ty_Either, db), dc), bd) → new_lt1(vyy3001, vyy401, db, dc)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
- new_compare5(vyy3000, vyy400, ca) → new_compare22(vyy3000, vyy400, new_esEs8(vyy3000, vyy400, ca), ca)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 4
- new_lt2(vyy3000, vyy400, ca) → new_compare22(vyy3000, vyy400, new_esEs8(vyy3000, vyy400, ca), ca)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 4
- new_ltEs1(Left(vyy3000), Left(vyy400), app(app(ty_@2, hh), baa), hg) → new_ltEs0(vyy3000, vyy400, hh, baa)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
- new_ltEs1(Right(vyy3000), Right(vyy400), baf, app(app(ty_@2, bbb), bbc)) → new_ltEs0(vyy3000, vyy400, bbb, bbc)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
- new_ltEs1(Left(vyy3000), Left(vyy400), app(app(ty_Either, bab), bac), hg) → new_ltEs1(vyy3000, vyy400, bab, bac)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
- new_ltEs1(Right(vyy3000), Right(vyy400), baf, app(app(ty_Either, bbd), bbe)) → new_ltEs1(vyy3000, vyy400, bbd, bbe)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
- new_ltEs1(Left(vyy3000), Left(vyy400), app(app(app(ty_@3, hd), he), hf), hg) → new_ltEs(vyy3000, vyy400, hd, he, hf)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
- new_ltEs1(Right(vyy3000), Right(vyy400), baf, app(app(app(ty_@3, bag), bah), bba)) → new_ltEs(vyy3000, vyy400, bag, bah, bba)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5
- new_ltEs1(Left(vyy3000), Left(vyy400), app(ty_Maybe, bad), hg) → new_ltEs2(vyy3000, vyy400, bad)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
- new_ltEs1(Right(vyy3000), Right(vyy400), baf, app(ty_Maybe, bbf)) → new_ltEs2(vyy3000, vyy400, bbf)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
- new_ltEs1(Right(vyy3000), Right(vyy400), baf, app(ty_[], bbg)) → new_ltEs3(vyy3000, vyy400, bbg)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
- new_ltEs1(Left(vyy3000), Left(vyy400), app(ty_[], bae), hg) → new_ltEs3(vyy3000, vyy400, bae)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDPSizeChangeProof
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_foldFM_LE1(vyy26, vyy40, vyy340, vyy341, vyy342, vyy343, EmptyFM, True, h, ba) → new_foldFM_LE(vyy26, vyy40, vyy343, h, ba)
new_foldFM_LE2(vyy340, vyy341, vyy30, vyy40, vyy3440, vyy3441, vyy3442, vyy3443, vyy3444, h, ba) → new_foldFM_LE1(new_fmToList_LE0(vyy340, vyy341, vyy30, h, ba), vyy40, vyy3440, vyy3441, vyy3442, vyy3443, vyy3444, new_ltEs18(vyy3440, Just(vyy40), h), h, ba)
new_foldFM_LE1(vyy26, vyy40, vyy340, vyy341, vyy342, vyy343, Branch(vyy3440, vyy3441, vyy3442, vyy3443, vyy3444), True, h, ba) → new_foldFM_LE2(vyy340, vyy341, new_foldFM_LE0(vyy26, vyy40, vyy343, h, ba), vyy40, vyy3440, vyy3441, vyy3442, vyy3443, vyy3444, h, ba)
new_foldFM_LE1(vyy26, vyy40, vyy340, vyy341, vyy342, Branch(vyy3430, vyy3431, vyy3432, vyy3433, vyy3434), vyy344, False, h, ba) → new_foldFM_LE1(vyy26, vyy40, vyy3430, vyy3431, vyy3432, vyy3433, vyy3434, new_ltEs18(vyy3430, Just(vyy40), h), h, ba)
new_foldFM_LE1(vyy26, vyy40, vyy340, vyy341, vyy342, vyy343, Branch(vyy3440, vyy3441, vyy3442, vyy3443, vyy3444), True, h, ba) → new_foldFM_LE(vyy26, vyy40, vyy343, h, ba)
new_foldFM_LE(vyy26, vyy40, Branch(vyy3430, vyy3431, vyy3432, vyy3433, vyy3434), h, ba) → new_foldFM_LE1(vyy26, vyy40, vyy3430, vyy3431, vyy3432, vyy3433, vyy3434, new_ltEs18(vyy3430, Just(vyy40), h), h, ba)
The TRS R consists of the following rules:
new_esEs23(vyy401, vyy411, app(app(ty_Either, bda), bdb)) → new_esEs7(vyy401, vyy411, bda, bdb)
new_esEs23(vyy401, vyy411, ty_Ordering) → new_esEs18(vyy401, vyy411)
new_esEs25(vyy401, vyy411, ty_Int) → new_esEs19(vyy401, vyy411)
new_esEs7(Left(vyy400), Left(vyy410), app(app(ty_Either, bga), bgb), baa) → new_esEs7(vyy400, vyy410, bga, bgb)
new_esEs24(vyy400, vyy410, ty_Float) → new_esEs12(vyy400, vyy410)
new_esEs8(Just(vyy400), Just(vyy410), app(app(ty_@2, bh), ca)) → new_esEs6(vyy400, vyy410, bh, ca)
new_esEs21(vyy40, vyy41, app(app(ty_@2, ha), hb)) → new_esEs6(vyy40, vyy41, ha, hb)
new_esEs18(LT, LT) → True
new_esEs24(vyy400, vyy410, app(app(app(ty_@3, bea), beb), bec)) → new_esEs5(vyy400, vyy410, bea, beb, bec)
new_ltEs13(Right(vyy3000), Right(vyy400), cbf, ty_Integer) → new_ltEs17(vyy3000, vyy400)
new_ltEs14(GT, GT) → True
new_ltEs18(Just(vyy3000), Just(vyy400), app(ty_Maybe, ceb)) → new_ltEs18(vyy3000, vyy400, ceb)
new_esEs18(LT, EQ) → False
new_esEs18(EQ, LT) → False
new_lt20(vyy3001, vyy401, ty_Float) → new_lt14(vyy3001, vyy401)
new_esEs28(vyy401, vyy411, ty_Char) → new_esEs16(vyy401, vyy411)
new_ltEs13(Left(vyy3000), Left(vyy400), app(ty_[], cbe), cac) → new_ltEs4(vyy3000, vyy400, cbe)
new_lt19(vyy3000, vyy400, app(app(ty_@2, bd), be)) → new_lt10(vyy3000, vyy400, bd, be)
new_lt19(vyy3000, vyy400, ty_@0) → new_lt8(vyy3000, vyy400)
new_ltEs11(vyy3001, vyy401, app(ty_Ratio, ga)) → new_ltEs5(vyy3001, vyy401, ga)
new_ltEs19(vyy3002, vyy402, app(ty_Ratio, def)) → new_ltEs5(vyy3002, vyy402, def)
new_esEs27(vyy402, vyy412, ty_Bool) → new_esEs17(vyy402, vyy412)
new_primMulNat0(Zero, Zero) → Zero
new_esEs7(Left(vyy400), Left(vyy410), app(app(app(ty_@3, bfe), bff), bfg), baa) → new_esEs5(vyy400, vyy410, bfe, bff, bfg)
new_lt20(vyy3001, vyy401, ty_Int) → new_lt13(vyy3001, vyy401)
new_ltEs13(Left(vyy3000), Left(vyy400), app(app(ty_@2, cag), cah), cac) → new_ltEs10(vyy3000, vyy400, cag, cah)
new_ltEs13(Left(vyy3000), Left(vyy400), app(ty_Maybe, cbd), cac) → new_ltEs18(vyy3000, vyy400, cbd)
new_compare18(vyy3000, vyy400, True, bab, bac, bad) → LT
new_lt20(vyy3001, vyy401, ty_@0) → new_lt8(vyy3001, vyy401)
new_esEs21(vyy40, vyy41, ty_Bool) → new_esEs17(vyy40, vyy41)
new_compare25(vyy3000, vyy400, True, ge) → EQ
new_esEs23(vyy401, vyy411, ty_Float) → new_esEs12(vyy401, vyy411)
new_esEs29(vyy400, vyy410, ty_Ordering) → new_esEs18(vyy400, vyy410)
new_esEs27(vyy402, vyy412, app(app(ty_FiniteMap, cgh), cha)) → new_esEs20(vyy402, vyy412, cgh, cha)
new_esEs9(LT) → True
new_esEs24(vyy400, vyy410, ty_Integer) → new_esEs15(vyy400, vyy410)
new_esEs8(Just(vyy400), Just(vyy410), ty_Integer) → new_esEs15(vyy400, vyy410)
new_lt19(vyy3000, vyy400, ty_Ordering) → new_lt6(vyy3000, vyy400)
new_ltEs9(True, False) → False
new_ltEs11(vyy3001, vyy401, ty_Int) → new_ltEs15(vyy3001, vyy401)
new_esEs29(vyy400, vyy410, app(app(ty_FiniteMap, dbh), dca)) → new_esEs20(vyy400, vyy410, dbh, dca)
new_esEs8(Just(vyy400), Just(vyy410), ty_Ordering) → new_esEs18(vyy400, vyy410)
new_not(GT) → False
new_esEs20(vyy40, vyy41, gf, gg) → new_asAs(new_esEs19(new_sizeFM(vyy40, gf, gg), new_sizeFM(vyy41, gf, gg)), new_esEs11(new_fmToList(vyy40, gf, gg), new_fmToList(vyy41, gf, gg), app(app(ty_@2, gf), gg)))
new_lt19(vyy3000, vyy400, app(app(app(ty_@3, bab), bac), bad)) → new_lt9(vyy3000, vyy400, bab, bac, bad)
new_lt7(vyy3000, vyy400, ty_Char) → new_lt12(vyy3000, vyy400)
new_ltEs13(Right(vyy3000), Right(vyy400), cbf, app(ty_Maybe, ccg)) → new_ltEs18(vyy3000, vyy400, ccg)
new_esEs17(True, True) → True
new_esEs7(Right(vyy400), Right(vyy410), hh, app(app(app(ty_@3, bha), bhb), bhc)) → new_esEs5(vyy400, vyy410, bha, bhb, bhc)
new_lt19(vyy3000, vyy400, ty_Int) → new_lt13(vyy3000, vyy400)
new_lt13(vyy3000, vyy400) → new_esEs9(new_compare6(vyy3000, vyy400))
new_esEs8(Just(vyy400), Just(vyy410), ty_Float) → new_esEs12(vyy400, vyy410)
new_esEs11([], [], hc) → True
new_esEs22(vyy400, vyy410, app(ty_Ratio, bbd)) → new_esEs14(vyy400, vyy410, bbd)
new_esEs21(vyy40, vyy41, app(ty_Ratio, hg)) → new_esEs14(vyy40, vyy41, hg)
new_esEs23(vyy401, vyy411, ty_Double) → new_esEs13(vyy401, vyy411)
new_esEs15(Integer(vyy400), Integer(vyy410)) → new_primEqInt(vyy400, vyy410)
new_esEs18(LT, GT) → False
new_esEs18(GT, LT) → False
new_esEs6(@2(vyy400, vyy401), @2(vyy410, vyy411), ha, hb) → new_asAs(new_esEs24(vyy400, vyy410, ha), new_esEs23(vyy401, vyy411, hb))
new_compare15(vyy3000, vyy400, False, ge) → GT
new_esEs28(vyy401, vyy411, app(app(app(ty_@3, chf), chg), chh)) → new_esEs5(vyy401, vyy411, chf, chg, chh)
new_ltEs19(vyy3002, vyy402, ty_Bool) → new_ltEs9(vyy3002, vyy402)
new_ltEs18(Just(vyy3000), Just(vyy400), ty_Double) → new_ltEs16(vyy3000, vyy400)
new_ltEs13(Left(vyy3000), Left(vyy400), app(ty_Ratio, cbc), cac) → new_ltEs5(vyy3000, vyy400, cbc)
new_esEs22(vyy400, vyy410, app(app(ty_Either, bbe), bbf)) → new_esEs7(vyy400, vyy410, bbe, bbf)
new_esEs29(vyy400, vyy410, ty_Integer) → new_esEs15(vyy400, vyy410)
new_foldFM0(vyy410, vyy411, vyy85, EmptyFM, gf, gg) → :(@2(vyy410, vyy411), vyy85)
new_ltEs11(vyy3001, vyy401, ty_Float) → new_ltEs7(vyy3001, vyy401)
new_ltEs13(Left(vyy3000), Left(vyy400), ty_Char, cac) → new_ltEs8(vyy3000, vyy400)
new_esEs24(vyy400, vyy410, app(ty_Ratio, bed)) → new_esEs14(vyy400, vyy410, bed)
new_esEs7(Right(vyy400), Left(vyy410), hh, baa) → False
new_esEs7(Left(vyy400), Right(vyy410), hh, baa) → False
new_esEs14(:%(vyy400, vyy401), :%(vyy410, vyy411), hg) → new_asAs(new_esEs26(vyy400, vyy410, hg), new_esEs25(vyy401, vyy411, hg))
new_ltEs15(vyy300, vyy40) → new_not(new_compare6(vyy300, vyy40))
new_esEs27(vyy402, vyy412, app(app(ty_Either, cgf), cgg)) → new_esEs7(vyy402, vyy412, cgf, cgg)
new_ltEs14(GT, EQ) → False
new_ltEs18(Just(vyy3000), Just(vyy400), ty_Integer) → new_ltEs17(vyy3000, vyy400)
new_esEs7(Right(vyy400), Right(vyy410), hh, ty_Char) → new_esEs16(vyy400, vyy410)
new_ltEs11(vyy3001, vyy401, app(app(ty_Either, fg), fh)) → new_ltEs13(vyy3001, vyy401, fg, fh)
new_esEs5(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), hd, he, hf) → new_asAs(new_esEs29(vyy400, vyy410, hd), new_asAs(new_esEs28(vyy401, vyy411, he), new_esEs27(vyy402, vyy412, hf)))
new_compare23(vyy3000, vyy400, False, bd, be) → new_compare112(vyy3000, vyy400, new_ltEs10(vyy3000, vyy400, bd, be), bd, be)
new_ltEs18(Just(vyy3000), Just(vyy400), app(ty_Ratio, cea)) → new_ltEs5(vyy3000, vyy400, cea)
new_primCompAux1(vyy3000, vyy400, vyy67, bb) → new_primCompAux0(vyy67, new_compare30(vyy3000, vyy400, bb))
new_lt7(vyy3000, vyy400, app(app(ty_@2, eb), ec)) → new_lt10(vyy3000, vyy400, eb, ec)
new_compare30(vyy3000, vyy400, app(ty_Ratio, cfc)) → new_compare7(vyy3000, vyy400, cfc)
new_ltEs13(Right(vyy3000), Right(vyy400), cbf, ty_Char) → new_ltEs8(vyy3000, vyy400)
new_esEs24(vyy400, vyy410, app(ty_[], bdg)) → new_esEs11(vyy400, vyy410, bdg)
new_esEs29(vyy400, vyy410, app(ty_Maybe, dba)) → new_esEs8(vyy400, vyy410, dba)
new_esEs29(vyy400, vyy410, app(ty_[], dah)) → new_esEs11(vyy400, vyy410, dah)
new_compare30(vyy3000, vyy400, ty_Float) → new_compare12(vyy3000, vyy400)
new_esEs27(vyy402, vyy412, ty_Int) → new_esEs19(vyy402, vyy412)
new_compare31(vyy3000, vyy400, caa, cab) → new_compare29(vyy3000, vyy400, new_esEs7(vyy3000, vyy400, caa, cab), caa, cab)
new_ltEs11(vyy3001, vyy401, app(app(ty_@2, fd), ff)) → new_ltEs10(vyy3001, vyy401, fd, ff)
new_primCmpNat0(Zero, Succ(vyy4000)) → LT
new_esEs22(vyy400, vyy410, app(app(ty_FiniteMap, bbg), bbh)) → new_esEs20(vyy400, vyy410, bbg, bbh)
new_esEs7(Left(vyy400), Left(vyy410), ty_Double, baa) → new_esEs13(vyy400, vyy410)
new_ltEs18(Just(vyy3000), Just(vyy400), app(app(ty_@2, cde), cdf)) → new_ltEs10(vyy3000, vyy400, cde, cdf)
new_lt18(vyy3000, vyy400, ge) → new_esEs9(new_compare28(vyy3000, vyy400, ge))
new_lt20(vyy3001, vyy401, ty_Ordering) → new_lt6(vyy3001, vyy401)
new_esEs27(vyy402, vyy412, ty_@0) → new_esEs10(vyy402, vyy412)
new_esEs24(vyy400, vyy410, app(app(ty_FiniteMap, beg), beh)) → new_esEs20(vyy400, vyy410, beg, beh)
new_esEs28(vyy401, vyy411, app(ty_[], chd)) → new_esEs11(vyy401, vyy411, chd)
new_esEs24(vyy400, vyy410, app(app(ty_Either, bee), bef)) → new_esEs7(vyy400, vyy410, bee, bef)
new_esEs24(vyy400, vyy410, app(app(ty_@2, bde), bdf)) → new_esEs6(vyy400, vyy410, bde, bdf)
new_esEs27(vyy402, vyy412, ty_Ordering) → new_esEs18(vyy402, vyy412)
new_primEqNat0(Zero, Zero) → True
new_compare26(vyy3000, vyy400, True) → EQ
new_ltEs13(Left(vyy3000), Left(vyy400), ty_Integer, cac) → new_ltEs17(vyy3000, vyy400)
new_esEs22(vyy400, vyy410, app(ty_Maybe, bah)) → new_esEs8(vyy400, vyy410, bah)
new_esEs23(vyy401, vyy411, app(app(ty_FiniteMap, bdc), bdd)) → new_esEs20(vyy401, vyy411, bdc, bdd)
new_ltEs18(Just(vyy3000), Just(vyy400), ty_Char) → new_ltEs8(vyy3000, vyy400)
new_ltEs13(Left(vyy3000), Left(vyy400), ty_Int, cac) → new_ltEs15(vyy3000, vyy400)
new_compare29(vyy3000, vyy400, True, caa, cab) → EQ
new_compare111(vyy3000, vyy400, False, caa, cab) → GT
new_esEs8(Just(vyy400), Just(vyy410), ty_Int) → new_esEs19(vyy400, vyy410)
new_lt20(vyy3001, vyy401, app(app(ty_@2, dch), dda)) → new_lt10(vyy3001, vyy401, dch, dda)
new_ltEs13(Left(vyy3000), Left(vyy400), ty_@0, cac) → new_ltEs6(vyy3000, vyy400)
new_ltEs19(vyy3002, vyy402, app(ty_[], deh)) → new_ltEs4(vyy3002, vyy402, deh)
new_ltEs11(vyy3001, vyy401, app(app(app(ty_@3, fa), fb), fc)) → new_ltEs12(vyy3001, vyy401, fa, fb, fc)
new_esEs17(False, False) → True
new_esEs17(False, True) → False
new_esEs17(True, False) → False
new_compare12(Float(vyy3000, vyy3001), Float(vyy400, vyy401)) → new_compare6(new_sr(vyy3000, vyy400), new_sr(vyy3001, vyy401))
new_compare30(vyy3000, vyy400, app(ty_Maybe, cfd)) → new_compare28(vyy3000, vyy400, cfd)
new_esEs7(Right(vyy400), Right(vyy410), hh, ty_Ordering) → new_esEs18(vyy400, vyy410)
new_esEs21(vyy40, vyy41, app(ty_Maybe, bg)) → new_esEs8(vyy40, vyy41, bg)
new_sr(vyy3001, vyy401) → new_primMulInt(vyy3001, vyy401)
new_ltEs14(EQ, LT) → False
new_esEs24(vyy400, vyy410, ty_Bool) → new_esEs17(vyy400, vyy410)
new_lt14(vyy3000, vyy400) → new_esEs9(new_compare12(vyy3000, vyy400))
new_foldFM_LE20(vyy340, vyy341, vyy30, vyy40, vyy3440, vyy3441, vyy3442, vyy3443, vyy3444, h, ba) → new_foldFM_LE10(new_fmToList_LE0(vyy340, vyy341, vyy30, h, ba), vyy40, vyy3440, vyy3441, vyy3442, vyy3443, vyy3444, new_ltEs18(vyy3440, Just(vyy40), h), h, ba)
new_ltEs19(vyy3002, vyy402, app(app(app(ty_@3, ddg), ddh), dea)) → new_ltEs12(vyy3002, vyy402, ddg, ddh, dea)
new_esEs11(:(vyy400, vyy401), :(vyy410, vyy411), hc) → new_asAs(new_esEs22(vyy400, vyy410, hc), new_esEs11(vyy401, vyy411, hc))
new_primPlusNat0(Succ(vyy860), vyy40100) → Succ(Succ(new_primPlusNat1(vyy860, vyy40100)))
new_compare4([], [], bb) → EQ
new_esEs7(Right(vyy400), Right(vyy410), hh, app(app(ty_Either, bhe), bhf)) → new_esEs7(vyy400, vyy410, bhe, bhf)
new_esEs22(vyy400, vyy410, ty_Char) → new_esEs16(vyy400, vyy410)
new_esEs18(EQ, GT) → False
new_esEs18(GT, EQ) → False
new_compare30(vyy3000, vyy400, app(ty_[], cfe)) → new_compare4(vyy3000, vyy400, cfe)
new_esEs16(Char(vyy400), Char(vyy410)) → new_primEqNat0(vyy400, vyy410)
new_compare30(vyy3000, vyy400, ty_Char) → new_compare13(vyy3000, vyy400)
new_esEs8(Just(vyy400), Nothing, bg) → False
new_esEs8(Nothing, Just(vyy410), bg) → False
new_ltEs19(vyy3002, vyy402, ty_Float) → new_ltEs7(vyy3002, vyy402)
new_compare24(vyy3000, vyy400, True, bab, bac, bad) → EQ
new_primEqInt(Neg(Succ(vyy4000)), Neg(Succ(vyy4100))) → new_primEqNat0(vyy4000, vyy4100)
new_compare30(vyy3000, vyy400, ty_Int) → new_compare6(vyy3000, vyy400)
new_ltEs19(vyy3002, vyy402, app(app(ty_@2, deb), dec)) → new_ltEs10(vyy3002, vyy402, deb, dec)
new_esEs9(GT) → False
new_primPlusNat1(Zero, Succ(vyy401000)) → Succ(vyy401000)
new_primPlusNat1(Succ(vyy8600), Zero) → Succ(vyy8600)
new_compare26(vyy3000, vyy400, False) → new_compare110(vyy3000, vyy400, new_ltEs14(vyy3000, vyy400))
new_esEs9(EQ) → False
new_esEs28(vyy401, vyy411, app(ty_Maybe, che)) → new_esEs8(vyy401, vyy411, che)
new_compare16(vyy3000, vyy400, True) → LT
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs7(Left(vyy400), Left(vyy410), ty_Integer, baa) → new_esEs15(vyy400, vyy410)
new_lt20(vyy3001, vyy401, app(ty_Maybe, dde)) → new_lt18(vyy3001, vyy401, dde)
new_esEs7(Left(vyy400), Left(vyy410), app(app(ty_@2, bfa), bfb), baa) → new_esEs6(vyy400, vyy410, bfa, bfb)
new_esEs28(vyy401, vyy411, ty_Double) → new_esEs13(vyy401, vyy411)
new_compare112(vyy3000, vyy400, False, bd, be) → GT
new_lt19(vyy3000, vyy400, ty_Double) → new_lt16(vyy3000, vyy400)
new_primEqInt(Neg(Zero), Neg(Succ(vyy4100))) → False
new_primEqInt(Neg(Succ(vyy4000)), Neg(Zero)) → False
new_lt19(vyy3000, vyy400, ty_Char) → new_lt12(vyy3000, vyy400)
new_primCompAux0(vyy71, GT) → GT
new_ltEs6(vyy300, vyy40) → new_not(new_compare8(vyy300, vyy40))
new_ltEs10(@2(vyy3000, vyy3001), @2(vyy400, vyy401), de, df) → new_pePe(new_lt7(vyy3000, vyy400, de), vyy3000, vyy400, new_ltEs11(vyy3001, vyy401, df), de)
new_ltEs13(Right(vyy3000), Right(vyy400), cbf, app(ty_Ratio, ccf)) → new_ltEs5(vyy3000, vyy400, ccf)
new_lt7(vyy3000, vyy400, ty_Integer) → new_lt17(vyy3000, vyy400)
new_compare11(Double(vyy3000, vyy3001), Double(vyy400, vyy401)) → new_compare6(new_sr(vyy3000, vyy400), new_sr(vyy3001, vyy401))
new_esEs22(vyy400, vyy410, app(app(app(ty_@3, bba), bbb), bbc)) → new_esEs5(vyy400, vyy410, bba, bbb, bbc)
new_compare30(vyy3000, vyy400, ty_Bool) → new_compare10(vyy3000, vyy400)
new_ltEs13(Left(vyy3000), Left(vyy400), ty_Double, cac) → new_ltEs16(vyy3000, vyy400)
new_foldFM0(vyy410, vyy411, vyy85, Branch(vyy4130, vyy4131, vyy4132, vyy4133, vyy4134), gf, gg) → new_foldFM0(vyy4130, vyy4131, new_foldFM0(vyy410, vyy411, vyy85, vyy4134, gf, gg), vyy4133, gf, gg)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_esEs24(vyy400, vyy410, ty_Ordering) → new_esEs18(vyy400, vyy410)
new_compare6(vyy300, vyy40) → new_primCmpInt(vyy300, vyy40)
new_esEs28(vyy401, vyy411, ty_Int) → new_esEs19(vyy401, vyy411)
new_esEs7(Right(vyy400), Right(vyy410), hh, app(ty_[], bgg)) → new_esEs11(vyy400, vyy410, bgg)
new_esEs7(Left(vyy400), Left(vyy410), ty_Int, baa) → new_esEs19(vyy400, vyy410)
new_esEs23(vyy401, vyy411, ty_Char) → new_esEs16(vyy401, vyy411)
new_ltEs13(Right(vyy3000), Right(vyy400), cbf, ty_Float) → new_ltEs7(vyy3000, vyy400)
new_primCmpNat0(Succ(vyy30000), Succ(vyy4000)) → new_primCmpNat0(vyy30000, vyy4000)
new_esEs7(Right(vyy400), Right(vyy410), hh, app(app(ty_@2, bge), bgf)) → new_esEs6(vyy400, vyy410, bge, bgf)
new_sizeFM(EmptyFM, gf, gg) → Pos(Zero)
new_esEs7(Left(vyy400), Left(vyy410), app(app(ty_FiniteMap, bgc), bgd), baa) → new_esEs20(vyy400, vyy410, bgc, bgd)
new_primEqInt(Pos(Succ(vyy4000)), Pos(Succ(vyy4100))) → new_primEqNat0(vyy4000, vyy4100)
new_ltEs19(vyy3002, vyy402, ty_Integer) → new_ltEs17(vyy3002, vyy402)
new_ltEs17(vyy300, vyy40) → new_not(new_compare17(vyy300, vyy40))
new_esEs21(vyy40, vyy41, ty_Int) → new_esEs19(vyy40, vyy41)
new_esEs28(vyy401, vyy411, app(app(ty_FiniteMap, dad), dae)) → new_esEs20(vyy401, vyy411, dad, dae)
new_esEs13(Double(vyy400, vyy401), Double(vyy410, vyy411)) → new_esEs19(new_sr(vyy400, vyy410), new_sr(vyy401, vyy411))
new_esEs26(vyy400, vyy410, ty_Integer) → new_esEs15(vyy400, vyy410)
new_esEs7(Left(vyy400), Left(vyy410), app(ty_[], bfc), baa) → new_esEs11(vyy400, vyy410, bfc)
new_lt7(vyy3000, vyy400, app(ty_Maybe, eg)) → new_lt18(vyy3000, vyy400, eg)
new_ltEs7(vyy300, vyy40) → new_not(new_compare12(vyy300, vyy40))
new_primEqNat0(Succ(vyy4000), Succ(vyy4100)) → new_primEqNat0(vyy4000, vyy4100)
new_esEs23(vyy401, vyy411, app(ty_Ratio, bch)) → new_esEs14(vyy401, vyy411, bch)
new_lt7(vyy3000, vyy400, app(ty_Ratio, ef)) → new_lt15(vyy3000, vyy400, ef)
new_ltEs19(vyy3002, vyy402, app(app(ty_Either, ded), dee)) → new_ltEs13(vyy3002, vyy402, ded, dee)
new_esEs7(Left(vyy400), Left(vyy410), ty_Ordering, baa) → new_esEs18(vyy400, vyy410)
new_esEs27(vyy402, vyy412, ty_Char) → new_esEs16(vyy402, vyy412)
new_esEs27(vyy402, vyy412, ty_Float) → new_esEs12(vyy402, vyy412)
new_ltEs18(Just(vyy3000), Just(vyy400), ty_Ordering) → new_ltEs14(vyy3000, vyy400)
new_lt20(vyy3001, vyy401, ty_Integer) → new_lt17(vyy3001, vyy401)
new_compare19(vyy3000, vyy400, bab, bac, bad) → new_compare24(vyy3000, vyy400, new_esEs5(vyy3000, vyy400, bab, bac, bad), bab, bac, bad)
new_lt17(vyy3000, vyy400) → new_esEs9(new_compare17(vyy3000, vyy400))
new_primCmpInt(Neg(Succ(vyy30000)), Neg(vyy400)) → new_primCmpNat0(vyy400, Succ(vyy30000))
new_esEs7(Right(vyy400), Right(vyy410), hh, app(ty_Ratio, bhd)) → new_esEs14(vyy400, vyy410, bhd)
new_esEs27(vyy402, vyy412, app(app(app(ty_@3, cgb), cgc), cgd)) → new_esEs5(vyy402, vyy412, cgb, cgc, cgd)
new_ltEs13(Right(vyy3000), Right(vyy400), cbf, app(ty_[], cch)) → new_ltEs4(vyy3000, vyy400, cch)
new_lt6(vyy3000, vyy400) → new_esEs9(new_compare14(vyy3000, vyy400))
new_ltEs18(Just(vyy3000), Just(vyy400), ty_Bool) → new_ltEs9(vyy3000, vyy400)
new_primEqInt(Pos(Zero), Pos(Succ(vyy4100))) → False
new_primEqInt(Pos(Succ(vyy4000)), Pos(Zero)) → False
new_esEs24(vyy400, vyy410, ty_@0) → new_esEs10(vyy400, vyy410)
new_primCmpNat0(Zero, Zero) → EQ
new_ltEs18(Nothing, Nothing, cda) → True
new_primCmpNat0(Succ(vyy30000), Zero) → GT
new_ltEs5(vyy300, vyy40, bc) → new_not(new_compare7(vyy300, vyy40, bc))
new_lt20(vyy3001, vyy401, ty_Bool) → new_lt5(vyy3001, vyy401)
new_primCmpInt(Neg(Zero), Pos(Succ(vyy4000))) → LT
new_esEs21(vyy40, vyy41, ty_Char) → new_esEs16(vyy40, vyy41)
new_esEs8(Just(vyy400), Just(vyy410), ty_Char) → new_esEs16(vyy400, vyy410)
new_compare30(vyy3000, vyy400, ty_Ordering) → new_compare14(vyy3000, vyy400)
new_esEs21(vyy40, vyy41, ty_Double) → new_esEs13(vyy40, vyy41)
new_ltEs11(vyy3001, vyy401, ty_Integer) → new_ltEs17(vyy3001, vyy401)
new_sr0(Integer(vyy4000), Integer(vyy30010)) → Integer(new_primMulInt(vyy4000, vyy30010))
new_lt11(vyy3000, vyy400, caa, cab) → new_esEs9(new_compare31(vyy3000, vyy400, caa, cab))
new_primPlusNat1(Succ(vyy8600), Succ(vyy401000)) → Succ(Succ(new_primPlusNat1(vyy8600, vyy401000)))
new_esEs7(Right(vyy400), Right(vyy410), hh, app(ty_Maybe, bgh)) → new_esEs8(vyy400, vyy410, bgh)
new_primEqInt(Neg(Succ(vyy4000)), Pos(vyy410)) → False
new_primEqInt(Pos(Succ(vyy4000)), Neg(vyy410)) → False
new_ltEs19(vyy3002, vyy402, ty_Double) → new_ltEs16(vyy3002, vyy402)
new_lt19(vyy3000, vyy400, app(ty_Ratio, gd)) → new_lt15(vyy3000, vyy400, gd)
new_compare27(vyy3000, vyy400, False) → new_compare16(vyy3000, vyy400, new_ltEs9(vyy3000, vyy400))
new_esEs7(Left(vyy400), Left(vyy410), ty_@0, baa) → new_esEs10(vyy400, vyy410)
new_foldFM2(EmptyFM, gf, gg) → []
new_compare7(:%(vyy3000, vyy3001), :%(vyy400, vyy401), ty_Integer) → new_compare17(new_sr0(vyy3000, vyy401), new_sr0(vyy400, vyy3001))
new_lt19(vyy3000, vyy400, ty_Bool) → new_lt5(vyy3000, vyy400)
new_foldFM_LE10(vyy26, vyy40, vyy340, vyy341, vyy342, vyy343, vyy344, False, h, ba) → new_foldFM_LE0(vyy26, vyy40, vyy343, h, ba)
new_esEs11(:(vyy400, vyy401), [], hc) → False
new_esEs11([], :(vyy410, vyy411), hc) → False
new_esEs22(vyy400, vyy410, app(app(ty_@2, bae), baf)) → new_esEs6(vyy400, vyy410, bae, baf)
new_ltEs11(vyy3001, vyy401, app(ty_Maybe, gb)) → new_ltEs18(vyy3001, vyy401, gb)
new_primEqInt(Neg(Zero), Pos(Succ(vyy4100))) → False
new_primEqInt(Pos(Zero), Neg(Succ(vyy4100))) → False
new_lt7(vyy3000, vyy400, app(app(app(ty_@3, dg), dh), ea)) → new_lt9(vyy3000, vyy400, dg, dh, ea)
new_esEs21(vyy40, vyy41, ty_Integer) → new_esEs15(vyy40, vyy41)
new_esEs22(vyy400, vyy410, app(ty_[], bag)) → new_esEs11(vyy400, vyy410, bag)
new_primCmpInt(Pos(Zero), Pos(Succ(vyy4000))) → new_primCmpNat0(Zero, Succ(vyy4000))
new_esEs28(vyy401, vyy411, app(app(ty_Either, dab), dac)) → new_esEs7(vyy401, vyy411, dab, dac)
new_esEs7(Right(vyy400), Right(vyy410), hh, ty_Float) → new_esEs12(vyy400, vyy410)
new_esEs7(Right(vyy400), Right(vyy410), hh, ty_Double) → new_esEs13(vyy400, vyy410)
new_lt20(vyy3001, vyy401, app(app(app(ty_@3, dce), dcf), dcg)) → new_lt9(vyy3001, vyy401, dce, dcf, dcg)
new_esEs21(vyy40, vyy41, ty_Ordering) → new_esEs18(vyy40, vyy41)
new_ltEs11(vyy3001, vyy401, ty_Bool) → new_ltEs9(vyy3001, vyy401)
new_esEs8(Just(vyy400), Just(vyy410), app(ty_[], cb)) → new_esEs11(vyy400, vyy410, cb)
new_esEs28(vyy401, vyy411, ty_Float) → new_esEs12(vyy401, vyy411)
new_esEs27(vyy402, vyy412, app(ty_Maybe, cga)) → new_esEs8(vyy402, vyy412, cga)
new_ltEs13(Left(vyy3000), Left(vyy400), ty_Float, cac) → new_ltEs7(vyy3000, vyy400)
new_esEs28(vyy401, vyy411, app(ty_Ratio, daa)) → new_esEs14(vyy401, vyy411, daa)
new_ltEs18(Just(vyy3000), Just(vyy400), ty_Float) → new_ltEs7(vyy3000, vyy400)
new_primCompAux0(vyy71, LT) → LT
new_ltEs19(vyy3002, vyy402, ty_Char) → new_ltEs8(vyy3002, vyy402)
new_esEs23(vyy401, vyy411, ty_Int) → new_esEs19(vyy401, vyy411)
new_lt19(vyy3000, vyy400, app(ty_Maybe, ge)) → new_lt18(vyy3000, vyy400, ge)
new_esEs8(Just(vyy400), Just(vyy410), ty_@0) → new_esEs10(vyy400, vyy410)
new_ltEs18(Just(vyy3000), Nothing, cda) → False
new_compare30(vyy3000, vyy400, app(app(ty_@2, ceg), ceh)) → new_compare9(vyy3000, vyy400, ceg, ceh)
new_primCmpInt(Pos(Succ(vyy30000)), Pos(vyy400)) → new_primCmpNat0(Succ(vyy30000), vyy400)
new_primPlusNat0(Zero, vyy40100) → Succ(vyy40100)
new_esEs7(Right(vyy400), Right(vyy410), hh, ty_Bool) → new_esEs17(vyy400, vyy410)
new_esEs23(vyy401, vyy411, app(app(ty_@2, bca), bcb)) → new_esEs6(vyy401, vyy411, bca, bcb)
new_ltEs13(Right(vyy3000), Right(vyy400), cbf, ty_Ordering) → new_ltEs14(vyy3000, vyy400)
new_esEs22(vyy400, vyy410, ty_Bool) → new_esEs17(vyy400, vyy410)
new_lt19(vyy3000, vyy400, ty_Integer) → new_lt17(vyy3000, vyy400)
new_esEs25(vyy401, vyy411, ty_Integer) → new_esEs15(vyy401, vyy411)
new_compare30(vyy3000, vyy400, ty_Double) → new_compare11(vyy3000, vyy400)
new_ltEs14(LT, LT) → True
new_esEs8(Just(vyy400), Just(vyy410), app(ty_Ratio, cg)) → new_esEs14(vyy400, vyy410, cg)
new_esEs8(Just(vyy400), Just(vyy410), ty_Double) → new_esEs13(vyy400, vyy410)
new_not0 → True
new_esEs23(vyy401, vyy411, app(ty_Maybe, bcd)) → new_esEs8(vyy401, vyy411, bcd)
new_compare30(vyy3000, vyy400, app(app(ty_Either, cfa), cfb)) → new_compare31(vyy3000, vyy400, cfa, cfb)
new_esEs23(vyy401, vyy411, ty_@0) → new_esEs10(vyy401, vyy411)
new_lt19(vyy3000, vyy400, ty_Float) → new_lt14(vyy3000, vyy400)
new_lt19(vyy3000, vyy400, app(ty_[], bf)) → new_lt4(vyy3000, vyy400, bf)
new_esEs18(GT, GT) → True
new_primCmpInt(Pos(Succ(vyy30000)), Neg(vyy400)) → GT
new_esEs21(vyy40, vyy41, app(app(app(ty_@3, hd), he), hf)) → new_esEs5(vyy40, vyy41, hd, he, hf)
new_esEs8(Just(vyy400), Just(vyy410), app(app(ty_Either, da), db)) → new_esEs7(vyy400, vyy410, da, db)
new_esEs7(Left(vyy400), Left(vyy410), app(ty_Ratio, bfh), baa) → new_esEs14(vyy400, vyy410, bfh)
new_esEs21(vyy40, vyy41, app(app(ty_FiniteMap, gf), gg)) → new_esEs20(vyy40, vyy41, gf, gg)
new_primMulInt(Pos(vyy30010), Pos(vyy4010)) → Pos(new_primMulNat0(vyy30010, vyy4010))
new_lt15(vyy3000, vyy400, gd) → new_esEs9(new_compare7(vyy3000, vyy400, gd))
new_esEs22(vyy400, vyy410, ty_Double) → new_esEs13(vyy400, vyy410)
new_ltEs12(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), dcb, dcc, dcd) → new_pePe(new_lt19(vyy3000, vyy400, dcb), vyy3000, vyy400, new_pePe(new_lt20(vyy3001, vyy401, dcc), vyy3001, vyy401, new_ltEs19(vyy3002, vyy402, dcd), dcc), dcb)
new_ltEs9(True, True) → True
new_esEs27(vyy402, vyy412, app(app(ty_@2, cff), cfg)) → new_esEs6(vyy402, vyy412, cff, cfg)
new_primMulInt(Neg(vyy30010), Neg(vyy4010)) → Pos(new_primMulNat0(vyy30010, vyy4010))
new_ltEs13(Right(vyy3000), Right(vyy400), cbf, ty_Bool) → new_ltEs9(vyy3000, vyy400)
new_compare110(vyy3000, vyy400, True) → LT
new_ltEs18(Just(vyy3000), Just(vyy400), app(app(ty_Either, cdg), cdh)) → new_ltEs13(vyy3000, vyy400, cdg, cdh)
new_esEs29(vyy400, vyy410, app(app(ty_@2, daf), dag)) → new_esEs6(vyy400, vyy410, daf, dag)
new_lt7(vyy3000, vyy400, ty_Double) → new_lt16(vyy3000, vyy400)
new_primEqNat0(Succ(vyy4000), Zero) → False
new_primEqNat0(Zero, Succ(vyy4100)) → False
new_esEs21(vyy40, vyy41, ty_@0) → new_esEs10(vyy40, vyy41)
new_esEs24(vyy400, vyy410, ty_Char) → new_esEs16(vyy400, vyy410)
new_ltEs19(vyy3002, vyy402, ty_@0) → new_ltEs6(vyy3002, vyy402)
new_lt20(vyy3001, vyy401, app(ty_Ratio, ddd)) → new_lt15(vyy3001, vyy401, ddd)
new_esEs22(vyy400, vyy410, ty_Ordering) → new_esEs18(vyy400, vyy410)
new_lt19(vyy3000, vyy400, app(app(ty_Either, caa), cab)) → new_lt11(vyy3000, vyy400, caa, cab)
new_compare9(vyy3000, vyy400, bd, be) → new_compare23(vyy3000, vyy400, new_esEs6(vyy3000, vyy400, bd, be), bd, be)
new_compare110(vyy3000, vyy400, False) → GT
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_ltEs18(Just(vyy3000), Just(vyy400), ty_Int) → new_ltEs15(vyy3000, vyy400)
new_ltEs9(False, False) → True
new_compare30(vyy3000, vyy400, ty_@0) → new_compare8(vyy3000, vyy400)
new_ltEs11(vyy3001, vyy401, ty_Char) → new_ltEs8(vyy3001, vyy401)
new_compare4(:(vyy3000, vyy3001), [], bb) → GT
new_sizeFM(Branch(vyy410, vyy411, vyy412, vyy413, vyy414), gf, gg) → vyy412
new_lt7(vyy3000, vyy400, ty_@0) → new_lt8(vyy3000, vyy400)
new_foldFM_LE10(vyy26, vyy40, vyy340, vyy341, vyy342, vyy343, EmptyFM, True, h, ba) → new_foldFM_LE3(vyy340, vyy341, new_foldFM_LE0(vyy26, vyy40, vyy343, h, ba), vyy40, h, ba)
new_esEs21(vyy40, vyy41, app(app(ty_Either, hh), baa)) → new_esEs7(vyy40, vyy41, hh, baa)
new_pePe(True, vyy40, vyy41, vyy57, gh) → True
new_esEs22(vyy400, vyy410, ty_@0) → new_esEs10(vyy400, vyy410)
new_foldFM2(Branch(vyy410, vyy411, vyy412, vyy413, vyy414), gf, gg) → new_foldFM0(vyy410, vyy411, new_foldFM2(vyy414, gf, gg), vyy413, gf, gg)
new_lt20(vyy3001, vyy401, app(app(ty_Either, ddb), ddc)) → new_lt11(vyy3001, vyy401, ddb, ddc)
new_esEs29(vyy400, vyy410, app(app(app(ty_@3, dbb), dbc), dbd)) → new_esEs5(vyy400, vyy410, dbb, dbc, dbd)
new_esEs7(Left(vyy400), Left(vyy410), app(ty_Maybe, bfd), baa) → new_esEs8(vyy400, vyy410, bfd)
new_compare23(vyy3000, vyy400, True, bd, be) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(vyy4000))) → new_primCmpNat0(Succ(vyy4000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(vyy4000))) → GT
new_esEs23(vyy401, vyy411, ty_Bool) → new_esEs17(vyy401, vyy411)
new_compare13(Char(vyy3000), Char(vyy400)) → new_primCmpNat0(vyy3000, vyy400)
new_lt7(vyy3000, vyy400, ty_Ordering) → new_lt6(vyy3000, vyy400)
new_foldFM_LE3(vyy340, vyy341, vyy29, vyy40, h, ba) → new_fmToList_LE0(vyy340, vyy341, vyy29, h, ba)
new_compare4([], :(vyy400, vyy401), bb) → LT
new_foldFM_LE0(vyy26, vyy40, Branch(vyy3430, vyy3431, vyy3432, vyy3433, vyy3434), h, ba) → new_foldFM_LE10(vyy26, vyy40, vyy3430, vyy3431, vyy3432, vyy3433, vyy3434, new_ltEs18(vyy3430, Just(vyy40), h), h, ba)
new_compare30(vyy3000, vyy400, app(app(app(ty_@3, ced), cee), cef)) → new_compare19(vyy3000, vyy400, ced, cee, cef)
new_lt7(vyy3000, vyy400, ty_Bool) → new_lt5(vyy3000, vyy400)
new_esEs23(vyy401, vyy411, app(ty_[], bcc)) → new_esEs11(vyy401, vyy411, bcc)
new_lt16(vyy3000, vyy400) → new_esEs9(new_compare11(vyy3000, vyy400))
new_esEs28(vyy401, vyy411, app(app(ty_@2, chb), chc)) → new_esEs6(vyy401, vyy411, chb, chc)
new_esEs21(vyy40, vyy41, ty_Float) → new_esEs12(vyy40, vyy41)
new_esEs29(vyy400, vyy410, ty_Int) → new_esEs19(vyy400, vyy410)
new_ltEs19(vyy3002, vyy402, ty_Ordering) → new_ltEs14(vyy3002, vyy402)
new_ltEs13(Left(vyy3000), Left(vyy400), app(app(ty_Either, cba), cbb), cac) → new_ltEs13(vyy3000, vyy400, cba, cbb)
new_esEs8(Just(vyy400), Just(vyy410), ty_Bool) → new_esEs17(vyy400, vyy410)
new_compare24(vyy3000, vyy400, False, bab, bac, bad) → new_compare18(vyy3000, vyy400, new_ltEs12(vyy3000, vyy400, bab, bac, bad), bab, bac, bad)
new_lt20(vyy3001, vyy401, ty_Double) → new_lt16(vyy3001, vyy401)
new_ltEs13(Right(vyy3000), Right(vyy400), cbf, app(app(ty_Either, ccd), cce)) → new_ltEs13(vyy3000, vyy400, ccd, cce)
new_ltEs18(Just(vyy3000), Just(vyy400), app(ty_[], cec)) → new_ltEs4(vyy3000, vyy400, cec)
new_ltEs18(Just(vyy3000), Just(vyy400), ty_@0) → new_ltEs6(vyy3000, vyy400)
new_esEs19(vyy40, vyy41) → new_primEqInt(vyy40, vyy41)
new_ltEs13(Left(vyy3000), Left(vyy400), app(app(app(ty_@3, cad), cae), caf), cac) → new_ltEs12(vyy3000, vyy400, cad, cae, caf)
new_esEs8(Nothing, Nothing, bg) → True
new_esEs10(@0, @0) → True
new_esEs27(vyy402, vyy412, app(ty_Ratio, cge)) → new_esEs14(vyy402, vyy412, cge)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs29(vyy400, vyy410, ty_Bool) → new_esEs17(vyy400, vyy410)
new_ltEs13(Left(vyy3000), Left(vyy400), ty_Ordering, cac) → new_ltEs14(vyy3000, vyy400)
new_ltEs16(vyy300, vyy40) → new_not(new_compare11(vyy300, vyy40))
new_esEs28(vyy401, vyy411, ty_@0) → new_esEs10(vyy401, vyy411)
new_asAs(False, vyy66) → False
new_lt9(vyy3000, vyy400, bab, bac, bad) → new_esEs9(new_compare19(vyy3000, vyy400, bab, bac, bad))
new_primMulInt(Neg(vyy30010), Pos(vyy4010)) → Neg(new_primMulNat0(vyy30010, vyy4010))
new_primMulInt(Pos(vyy30010), Neg(vyy4010)) → Neg(new_primMulNat0(vyy30010, vyy4010))
new_esEs22(vyy400, vyy410, ty_Float) → new_esEs12(vyy400, vyy410)
new_esEs27(vyy402, vyy412, ty_Double) → new_esEs13(vyy402, vyy412)
new_ltEs13(Left(vyy3000), Right(vyy400), cbf, cac) → True
new_primMulNat0(Succ(vyy300100), Zero) → Zero
new_primMulNat0(Zero, Succ(vyy40100)) → Zero
new_esEs24(vyy400, vyy410, ty_Double) → new_esEs13(vyy400, vyy410)
new_compare30(vyy3000, vyy400, ty_Integer) → new_compare17(vyy3000, vyy400)
new_esEs7(Right(vyy400), Right(vyy410), hh, ty_Integer) → new_esEs15(vyy400, vyy410)
new_lt7(vyy3000, vyy400, app(ty_[], eh)) → new_lt4(vyy3000, vyy400, eh)
new_ltEs13(Right(vyy3000), Right(vyy400), cbf, ty_Int) → new_ltEs15(vyy3000, vyy400)
new_ltEs8(vyy300, vyy40) → new_not(new_compare13(vyy300, vyy40))
new_pePe(False, vyy40, vyy41, vyy57, gh) → new_asAs(new_esEs21(vyy40, vyy41, gh), vyy57)
new_ltEs11(vyy3001, vyy401, ty_@0) → new_ltEs6(vyy3001, vyy401)
new_compare17(Integer(vyy3000), Integer(vyy400)) → new_primCmpInt(vyy3000, vyy400)
new_ltEs11(vyy3001, vyy401, ty_Ordering) → new_ltEs14(vyy3001, vyy401)
new_esEs29(vyy400, vyy410, ty_Double) → new_esEs13(vyy400, vyy410)
new_ltEs18(Nothing, Just(vyy400), cda) → True
new_ltEs14(GT, LT) → False
new_lt20(vyy3001, vyy401, app(ty_[], ddf)) → new_lt4(vyy3001, vyy401, ddf)
new_not(EQ) → new_not0
new_esEs8(Just(vyy400), Just(vyy410), app(app(app(ty_@3, cd), ce), cf)) → new_esEs5(vyy400, vyy410, cd, ce, cf)
new_compare29(vyy3000, vyy400, False, caa, cab) → new_compare111(vyy3000, vyy400, new_ltEs13(vyy3000, vyy400, caa, cab), caa, cab)
new_lt10(vyy3000, vyy400, bd, be) → new_esEs9(new_compare9(vyy3000, vyy400, bd, be))
new_esEs28(vyy401, vyy411, ty_Integer) → new_esEs15(vyy401, vyy411)
new_lt5(vyy3000, vyy400) → new_esEs9(new_compare10(vyy3000, vyy400))
new_compare18(vyy3000, vyy400, False, bab, bac, bad) → GT
new_esEs7(Right(vyy400), Right(vyy410), hh, ty_Int) → new_esEs19(vyy400, vyy410)
new_ltEs9(False, True) → True
new_foldFM_LE10(vyy26, vyy40, vyy340, vyy341, vyy342, vyy343, Branch(vyy3440, vyy3441, vyy3442, vyy3443, vyy3444), True, h, ba) → new_foldFM_LE20(vyy340, vyy341, new_foldFM_LE0(vyy26, vyy40, vyy343, h, ba), vyy40, vyy3440, vyy3441, vyy3442, vyy3443, vyy3444, h, ba)
new_ltEs13(Right(vyy3000), Right(vyy400), cbf, app(app(ty_@2, ccb), ccc)) → new_ltEs10(vyy3000, vyy400, ccb, ccc)
new_esEs23(vyy401, vyy411, ty_Integer) → new_esEs15(vyy401, vyy411)
new_compare25(vyy3000, vyy400, False, ge) → new_compare15(vyy3000, vyy400, new_ltEs18(vyy3000, vyy400, ge), ge)
new_compare27(vyy3000, vyy400, True) → EQ
new_ltEs13(Right(vyy3000), Left(vyy400), cbf, cac) → False
new_lt4(vyy3000, vyy400, bf) → new_esEs9(new_compare4(vyy3000, vyy400, bf))
new_esEs28(vyy401, vyy411, ty_Bool) → new_esEs17(vyy401, vyy411)
new_compare14(vyy3000, vyy400) → new_compare26(vyy3000, vyy400, new_esEs18(vyy3000, vyy400))
new_esEs27(vyy402, vyy412, app(ty_[], cfh)) → new_esEs11(vyy402, vyy412, cfh)
new_lt7(vyy3000, vyy400, ty_Int) → new_lt13(vyy3000, vyy400)
new_esEs22(vyy400, vyy410, ty_Int) → new_esEs19(vyy400, vyy410)
new_ltEs19(vyy3002, vyy402, ty_Int) → new_ltEs15(vyy3002, vyy402)
new_ltEs14(LT, GT) → True
new_esEs24(vyy400, vyy410, app(ty_Maybe, bdh)) → new_esEs8(vyy400, vyy410, bdh)
new_not(LT) → new_not0
new_ltEs14(LT, EQ) → True
new_lt12(vyy3000, vyy400) → new_esEs9(new_compare13(vyy3000, vyy400))
new_esEs26(vyy400, vyy410, ty_Int) → new_esEs19(vyy400, vyy410)
new_compare4(:(vyy3000, vyy3001), :(vyy400, vyy401), bb) → new_primCompAux1(vyy3000, vyy400, new_compare4(vyy3001, vyy401, bb), bb)
new_compare28(vyy3000, vyy400, ge) → new_compare25(vyy3000, vyy400, new_esEs8(vyy3000, vyy400, ge), ge)
new_esEs21(vyy40, vyy41, app(ty_[], hc)) → new_esEs11(vyy40, vyy41, hc)
new_esEs29(vyy400, vyy410, app(app(ty_Either, dbf), dbg)) → new_esEs7(vyy400, vyy410, dbf, dbg)
new_esEs7(Left(vyy400), Left(vyy410), ty_Bool, baa) → new_esEs17(vyy400, vyy410)
new_lt20(vyy3001, vyy401, ty_Char) → new_lt12(vyy3001, vyy401)
new_esEs29(vyy400, vyy410, ty_Char) → new_esEs16(vyy400, vyy410)
new_esEs12(Float(vyy400, vyy401), Float(vyy410, vyy411)) → new_esEs19(new_sr(vyy400, vyy410), new_sr(vyy401, vyy411))
new_esEs28(vyy401, vyy411, ty_Ordering) → new_esEs18(vyy401, vyy411)
new_ltEs11(vyy3001, vyy401, app(ty_[], gc)) → new_ltEs4(vyy3001, vyy401, gc)
new_esEs29(vyy400, vyy410, ty_@0) → new_esEs10(vyy400, vyy410)
new_esEs22(vyy400, vyy410, ty_Integer) → new_esEs15(vyy400, vyy410)
new_primPlusNat1(Zero, Zero) → Zero
new_compare111(vyy3000, vyy400, True, caa, cab) → LT
new_compare15(vyy3000, vyy400, True, ge) → LT
new_asAs(True, vyy66) → vyy66
new_ltEs14(EQ, EQ) → True
new_compare112(vyy3000, vyy400, True, bd, be) → LT
new_primMulNat0(Succ(vyy300100), Succ(vyy40100)) → new_primPlusNat0(new_primMulNat0(vyy300100, Succ(vyy40100)), vyy40100)
new_esEs29(vyy400, vyy410, ty_Float) → new_esEs12(vyy400, vyy410)
new_esEs8(Just(vyy400), Just(vyy410), app(ty_Maybe, cc)) → new_esEs8(vyy400, vyy410, cc)
new_esEs24(vyy400, vyy410, ty_Int) → new_esEs19(vyy400, vyy410)
new_compare8(@0, @0) → EQ
new_esEs7(Left(vyy400), Left(vyy410), ty_Char, baa) → new_esEs16(vyy400, vyy410)
new_fmToList(vyy41, gf, gg) → new_foldFM2(vyy41, gf, gg)
new_ltEs13(Left(vyy3000), Left(vyy400), ty_Bool, cac) → new_ltEs9(vyy3000, vyy400)
new_esEs23(vyy401, vyy411, app(app(app(ty_@3, bce), bcf), bcg)) → new_esEs5(vyy401, vyy411, bce, bcf, bcg)
new_esEs29(vyy400, vyy410, app(ty_Ratio, dbe)) → new_esEs14(vyy400, vyy410, dbe)
new_fmToList_LE0(vyy340, vyy341, vyy27, h, ba) → :(@2(vyy340, vyy341), vyy27)
new_ltEs4(vyy300, vyy40, bb) → new_not(new_compare4(vyy300, vyy40, bb))
new_compare10(vyy3000, vyy400) → new_compare27(vyy3000, vyy400, new_esEs17(vyy3000, vyy400))
new_lt8(vyy3000, vyy400) → new_esEs9(new_compare8(vyy3000, vyy400))
new_ltEs13(Right(vyy3000), Right(vyy400), cbf, app(app(app(ty_@3, cbg), cbh), cca)) → new_ltEs12(vyy3000, vyy400, cbg, cbh, cca)
new_esEs7(Left(vyy400), Left(vyy410), ty_Float, baa) → new_esEs12(vyy400, vyy410)
new_ltEs11(vyy3001, vyy401, ty_Double) → new_ltEs16(vyy3001, vyy401)
new_lt7(vyy3000, vyy400, app(app(ty_Either, ed), ee)) → new_lt11(vyy3000, vyy400, ed, ee)
new_ltEs13(Right(vyy3000), Right(vyy400), cbf, ty_@0) → new_ltEs6(vyy3000, vyy400)
new_ltEs13(Right(vyy3000), Right(vyy400), cbf, ty_Double) → new_ltEs16(vyy3000, vyy400)
new_lt7(vyy3000, vyy400, ty_Float) → new_lt14(vyy3000, vyy400)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_ltEs14(EQ, GT) → True
new_esEs7(Right(vyy400), Right(vyy410), hh, ty_@0) → new_esEs10(vyy400, vyy410)
new_primCompAux0(vyy71, EQ) → vyy71
new_compare7(:%(vyy3000, vyy3001), :%(vyy400, vyy401), ty_Int) → new_compare6(new_sr(vyy3000, vyy401), new_sr(vyy400, vyy3001))
new_esEs8(Just(vyy400), Just(vyy410), app(app(ty_FiniteMap, dc), dd)) → new_esEs20(vyy400, vyy410, dc, dd)
new_ltEs18(Just(vyy3000), Just(vyy400), app(app(app(ty_@3, cdb), cdc), cdd)) → new_ltEs12(vyy3000, vyy400, cdb, cdc, cdd)
new_foldFM_LE0(vyy26, vyy40, EmptyFM, h, ba) → vyy26
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_ltEs19(vyy3002, vyy402, app(ty_Maybe, deg)) → new_ltEs18(vyy3002, vyy402, deg)
new_esEs27(vyy402, vyy412, ty_Integer) → new_esEs15(vyy402, vyy412)
new_esEs18(EQ, EQ) → True
new_esEs7(Right(vyy400), Right(vyy410), hh, app(app(ty_FiniteMap, bhg), bhh)) → new_esEs20(vyy400, vyy410, bhg, bhh)
new_primCmpInt(Neg(Succ(vyy30000)), Pos(vyy400)) → LT
new_compare16(vyy3000, vyy400, False) → GT
The set Q consists of the following terms:
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs18(Just(x0), Just(x1), ty_Double)
new_compare30(x0, x1, ty_Int)
new_compare111(x0, x1, True, x2, x3)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs7(Left(x0), Right(x1), x2, x3)
new_esEs7(Right(x0), Left(x1), x2, x3)
new_foldFM2(EmptyFM, x0, x1)
new_ltEs19(x0, x1, ty_Char)
new_lt16(x0, x1)
new_compare4(:(x0, x1), [], x2)
new_ltEs13(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_primEqNat0(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_compare18(x0, x1, True, x2, x3, x4)
new_ltEs13(Left(x0), Left(x1), ty_Integer, x2)
new_esEs18(LT, LT)
new_ltEs5(x0, x1, x2)
new_ltEs11(x0, x1, ty_Integer)
new_compare110(x0, x1, False)
new_lt7(x0, x1, app(ty_[], x2))
new_ltEs13(Left(x0), Left(x1), ty_Char, x2)
new_foldFM_LE10(x0, x1, x2, x3, x4, x5, EmptyFM, True, x6, x7)
new_esEs9(EQ)
new_compare26(x0, x1, True)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_ltEs18(Just(x0), Just(x1), ty_Ordering)
new_compare30(x0, x1, ty_Bool)
new_compare30(x0, x1, ty_@0)
new_primMulNat0(Zero, Succ(x0))
new_esEs29(x0, x1, ty_Ordering)
new_esEs8(Just(x0), Just(x1), app(app(ty_FiniteMap, x2), x3))
new_primCmpNat0(Zero, Succ(x0))
new_primCmpNat0(Succ(x0), Zero)
new_esEs8(Just(x0), Just(x1), ty_@0)
new_esEs7(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs28(x0, x1, ty_Integer)
new_compare6(x0, x1)
new_esEs7(Left(x0), Left(x1), ty_Double, x2)
new_ltEs8(x0, x1)
new_ltEs19(x0, x1, ty_Float)
new_compare7(:%(x0, x1), :%(x2, x3), ty_Int)
new_lt19(x0, x1, app(ty_Maybe, x2))
new_compare9(x0, x1, x2, x3)
new_compare15(x0, x1, True, x2)
new_ltEs13(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_ltEs11(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs29(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, ty_Double)
new_compare29(x0, x1, True, x2, x3)
new_esEs7(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs7(Left(x0), Left(x1), ty_Char, x2)
new_lt19(x0, x1, ty_Integer)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_lt20(x0, x1, app(ty_[], x2))
new_esEs7(Right(x0), Right(x1), x2, ty_Int)
new_compare30(x0, x1, ty_Double)
new_asAs(False, x0)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs27(x0, x1, ty_Bool)
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_primCompAux1(x0, x1, x2, x3)
new_ltEs4(x0, x1, x2)
new_esEs7(Left(x0), Left(x1), ty_Int, x2)
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_esEs18(EQ, GT)
new_esEs18(GT, EQ)
new_esEs27(x0, x1, ty_Int)
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs7(Right(x0), Right(x1), x2, ty_@0)
new_esEs17(False, False)
new_ltEs18(Just(x0), Just(x1), app(ty_Maybe, x2))
new_foldFM_LE10(x0, x1, x2, x3, x4, x5, x6, False, x7, x8)
new_ltEs11(x0, x1, ty_Char)
new_esEs8(Nothing, Just(x0), x1)
new_sr(x0, x1)
new_compare8(@0, @0)
new_esEs25(x0, x1, ty_Int)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs18(EQ, EQ)
new_compare28(x0, x1, x2)
new_esEs8(Just(x0), Just(x1), ty_Float)
new_compare27(x0, x1, True)
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_FiniteMap, x3), x4))
new_ltEs18(Just(x0), Just(x1), app(ty_Ratio, x2))
new_compare29(x0, x1, False, x2, x3)
new_esEs28(x0, x1, ty_Char)
new_esEs8(Just(x0), Just(x1), ty_Ordering)
new_compare112(x0, x1, False, x2, x3)
new_ltEs11(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs18(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs29(x0, x1, ty_Char)
new_esEs22(x0, x1, ty_Char)
new_compare25(x0, x1, True, x2)
new_ltEs14(EQ, EQ)
new_primEqNat0(Zero, Zero)
new_ltEs11(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpNat0(Succ(x0), Succ(x1))
new_ltEs18(Nothing, Nothing, x0)
new_lt19(x0, x1, app(ty_[], x2))
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_esEs25(x0, x1, ty_Integer)
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs13(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs29(x0, x1, ty_Int)
new_lt20(x0, x1, ty_@0)
new_lt7(x0, x1, ty_Double)
new_fmToList(x0, x1, x2)
new_lt7(x0, x1, app(ty_Maybe, x2))
new_ltEs9(False, False)
new_ltEs19(x0, x1, ty_Int)
new_esEs22(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_compare112(x0, x1, True, x2, x3)
new_lt20(x0, x1, ty_Char)
new_esEs23(x0, x1, ty_Integer)
new_foldFM_LE20(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Zero, Succ(x0))
new_primMulNat0(Zero, Zero)
new_primMulInt(Pos(x0), Pos(x1))
new_lt7(x0, x1, ty_Char)
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, ty_Float)
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, ty_@0)
new_compare4([], :(x0, x1), x2)
new_lt7(x0, x1, app(app(ty_Either, x2), x3))
new_foldFM_LE0(x0, x1, EmptyFM, x2, x3)
new_esEs6(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs24(x0, x1, ty_Bool)
new_compare30(x0, x1, app(app(ty_Either, x2), x3))
new_esEs7(Left(x0), Left(x1), ty_Float, x2)
new_esEs8(Just(x0), Just(x1), ty_Integer)
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare4(:(x0, x1), :(x2, x3), x4)
new_primPlusNat1(Succ(x0), Zero)
new_lt7(x0, x1, ty_Ordering)
new_ltEs18(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs22(x0, x1, app(ty_[], x2))
new_ltEs13(Left(x0), Left(x1), ty_Bool, x2)
new_primMulNat0(Succ(x0), Succ(x1))
new_esEs21(x0, x1, ty_@0)
new_esEs28(x0, x1, ty_Bool)
new_compare30(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs13(Right(x0), Right(x1), x2, ty_Int)
new_ltEs16(x0, x1)
new_esEs29(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs23(x0, x1, ty_Double)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs11(x0, x1, app(ty_Maybe, x2))
new_esEs21(x0, x1, ty_Int)
new_esEs11(:(x0, x1), :(x2, x3), x4)
new_lt11(x0, x1, x2, x3)
new_lt14(x0, x1)
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_sizeFM(EmptyFM, x0, x1)
new_esEs27(x0, x1, ty_@0)
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
new_esEs11([], [], x0)
new_lt19(x0, x1, app(ty_Ratio, x2))
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_lt19(x0, x1, ty_Ordering)
new_esEs21(x0, x1, ty_Char)
new_compare23(x0, x1, True, x2, x3)
new_esEs7(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs8(Just(x0), Just(x1), ty_Char)
new_ltEs6(x0, x1)
new_compare4([], [], x0)
new_esEs23(x0, x1, app(ty_[], x2))
new_lt9(x0, x1, x2, x3, x4)
new_lt20(x0, x1, ty_Bool)
new_ltEs11(x0, x1, ty_Float)
new_compare31(x0, x1, x2, x3)
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_lt7(x0, x1, ty_Int)
new_lt4(x0, x1, x2)
new_primPlusNat0(Succ(x0), x1)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, ty_Integer)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs7(Left(x0), Left(x1), app(app(ty_FiniteMap, x2), x3), x4)
new_esEs20(x0, x1, x2, x3)
new_compare27(x0, x1, False)
new_primPlusNat1(Zero, Zero)
new_esEs8(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_not0
new_esEs29(x0, x1, ty_@0)
new_primMulNat0(Succ(x0), Zero)
new_esEs21(x0, x1, ty_Bool)
new_esEs27(x0, x1, ty_Ordering)
new_compare13(Char(x0), Char(x1))
new_esEs9(GT)
new_ltEs14(LT, LT)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs19(x0, x1)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_lt7(x0, x1, ty_Integer)
new_esEs14(:%(x0, x1), :%(x2, x3), x4)
new_esEs24(x0, x1, ty_@0)
new_ltEs7(x0, x1)
new_compare110(x0, x1, True)
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs13(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs7(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs18(GT, GT)
new_esEs11([], :(x0, x1), x2)
new_esEs7(Right(x0), Right(x1), x2, ty_Float)
new_esEs24(x0, x1, app(ty_[], x2))
new_ltEs11(x0, x1, ty_Double)
new_ltEs13(Left(x0), Left(x1), ty_@0, x2)
new_ltEs13(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs9(False, True)
new_ltEs9(True, False)
new_lt5(x0, x1)
new_compare12(Float(x0, x1), Float(x2, x3))
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_ltEs9(True, True)
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_ltEs18(Nothing, Just(x0), x1)
new_esEs10(@0, @0)
new_esEs28(x0, x1, app(ty_[], x2))
new_not(GT)
new_fmToList_LE0(x0, x1, x2, x3, x4)
new_ltEs13(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_ltEs13(Left(x0), Left(x1), ty_Double, x2)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_esEs8(Just(x0), Just(x1), ty_Double)
new_esEs8(Nothing, Nothing, x0)
new_foldFM_LE3(x0, x1, x2, x3, x4, x5)
new_esEs24(x0, x1, ty_Ordering)
new_esEs16(Char(x0), Char(x1))
new_lt7(x0, x1, ty_Bool)
new_primEqInt(Neg(Zero), Pos(Zero))
new_primEqInt(Pos(Zero), Neg(Zero))
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
new_ltEs14(LT, EQ)
new_ltEs14(EQ, LT)
new_compare16(x0, x1, False)
new_compare14(x0, x1)
new_esEs24(x0, x1, ty_Integer)
new_ltEs18(Just(x0), Just(x1), ty_Bool)
new_esEs27(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs27(x0, x1, app(ty_[], x2))
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_lt20(x0, x1, app(ty_Ratio, x2))
new_foldFM_LE10(x0, x1, x2, x3, x4, x5, Branch(x6, x7, x8, x9, x10), True, x11, x12)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs29(x0, x1, ty_Float)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs7(Left(x0), Left(x1), ty_Bool, x2)
new_lt19(x0, x1, ty_Int)
new_primEqInt(Neg(Zero), Neg(Zero))
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_compare7(:%(x0, x1), :%(x2, x3), ty_Integer)
new_esEs8(Just(x0), Just(x1), app(ty_Ratio, x2))
new_compare16(x0, x1, True)
new_esEs28(x0, x1, ty_Ordering)
new_primCompAux0(x0, EQ)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_esEs8(Just(x0), Nothing, x1)
new_ltEs13(Left(x0), Left(x1), app(ty_[], x2), x3)
new_lt20(x0, x1, ty_Float)
new_compare10(x0, x1)
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_lt7(x0, x1, ty_Float)
new_esEs8(Just(x0), Just(x1), app(ty_[], x2))
new_esEs7(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_compare11(Double(x0, x1), Double(x2, x3))
new_esEs28(x0, x1, ty_Double)
new_primCompAux0(x0, LT)
new_ltEs11(x0, x1, app(ty_[], x2))
new_lt17(x0, x1)
new_ltEs11(x0, x1, ty_Bool)
new_ltEs18(Just(x0), Nothing, x1)
new_ltEs13(Left(x0), Left(x1), ty_Ordering, x2)
new_compare24(x0, x1, True, x2, x3, x4)
new_esEs7(Right(x0), Right(x1), x2, ty_Char)
new_ltEs18(Just(x0), Just(x1), ty_Float)
new_compare17(Integer(x0), Integer(x1))
new_ltEs18(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, ty_Char)
new_lt8(x0, x1)
new_primEqNat0(Succ(x0), Zero)
new_esEs28(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs9(LT)
new_lt15(x0, x1, x2)
new_esEs7(Left(x0), Left(x1), ty_@0, x2)
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_esEs24(x0, x1, ty_Int)
new_primEqNat0(Zero, Succ(x0))
new_esEs22(x0, x1, ty_Double)
new_esEs7(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs24(x0, x1, ty_Float)
new_esEs22(x0, x1, ty_Int)
new_esEs7(Left(x0), Left(x1), ty_Integer, x2)
new_ltEs18(Just(x0), Just(x1), ty_Char)
new_primPlusNat0(Zero, x0)
new_ltEs18(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs14(EQ, GT)
new_ltEs14(GT, EQ)
new_esEs22(x0, x1, ty_Bool)
new_esEs22(x0, x1, ty_Ordering)
new_lt19(x0, x1, ty_Double)
new_lt7(x0, x1, app(app(ty_@2, x2), x3))
new_primCmpNat0(Zero, Zero)
new_lt10(x0, x1, x2, x3)
new_esEs8(Just(x0), Just(x1), ty_Int)
new_esEs7(Right(x0), Right(x1), x2, app(ty_[], x3))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_compare26(x0, x1, False)
new_ltEs11(x0, x1, ty_Int)
new_esEs12(Float(x0, x1), Float(x2, x3))
new_primCompAux0(x0, GT)
new_esEs28(x0, x1, ty_Int)
new_ltEs13(Left(x0), Left(x1), ty_Float, x2)
new_esEs29(x0, x1, ty_Integer)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_compare111(x0, x1, False, x2, x3)
new_lt13(x0, x1)
new_esEs28(x0, x1, ty_@0)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_lt19(x0, x1, ty_@0)
new_esEs24(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs23(x0, x1, ty_Ordering)
new_lt12(x0, x1)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs19(x0, x1, ty_Double)
new_lt7(x0, x1, app(ty_Ratio, x2))
new_ltEs18(Just(x0), Just(x1), ty_Int)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_lt7(x0, x1, ty_@0)
new_esEs26(x0, x1, ty_Int)
new_esEs18(LT, EQ)
new_esEs18(EQ, LT)
new_ltEs19(x0, x1, app(ty_[], x2))
new_ltEs19(x0, x1, ty_Bool)
new_ltEs14(LT, GT)
new_ltEs14(GT, LT)
new_esEs23(x0, x1, ty_Float)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs7(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs29(x0, x1, ty_Bool)
new_esEs21(x0, x1, ty_Integer)
new_compare30(x0, x1, ty_Float)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_esEs8(Just(x0), Just(x1), ty_Bool)
new_lt19(x0, x1, ty_Char)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_compare18(x0, x1, False, x2, x3, x4)
new_ltEs13(Right(x0), Right(x1), x2, ty_Float)
new_esEs8(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs7(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs22(x0, x1, ty_@0)
new_esEs5(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs23(x0, x1, ty_Char)
new_ltEs14(GT, GT)
new_compare30(x0, x1, app(ty_Maybe, x2))
new_esEs27(x0, x1, ty_Double)
new_esEs27(x0, x1, ty_Float)
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs18(Just(x0), Just(x1), ty_@0)
new_esEs24(x0, x1, ty_Char)
new_foldFM_LE0(x0, x1, Branch(x2, x3, x4, x5, x6), x7, x8)
new_not(EQ)
new_esEs8(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_ltEs13(Right(x0), Left(x1), x2, x3)
new_compare30(x0, x1, app(ty_Ratio, x2))
new_ltEs13(Left(x0), Right(x1), x2, x3)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_ltEs11(x0, x1, app(ty_Ratio, x2))
new_esEs15(Integer(x0), Integer(x1))
new_esEs7(Right(x0), Right(x1), x2, ty_Bool)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_lt6(x0, x1)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, ty_Bool)
new_esEs29(x0, x1, ty_Double)
new_compare19(x0, x1, x2, x3, x4)
new_lt19(x0, x1, ty_Bool)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_esEs7(Right(x0), Right(x1), x2, ty_Double)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_esEs21(x0, x1, ty_Double)
new_ltEs13(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs7(Right(x0), Right(x1), x2, ty_Integer)
new_lt7(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs13(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_compare25(x0, x1, False, x2)
new_esEs22(x0, x1, ty_Integer)
new_ltEs13(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_ltEs15(x0, x1)
new_esEs7(Left(x0), Left(x1), ty_Ordering, x2)
new_lt20(x0, x1, ty_Integer)
new_ltEs12(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_ltEs10(@2(x0, x1), @2(x2, x3), x4, x5)
new_ltEs19(x0, x1, ty_Ordering)
new_esEs18(GT, LT)
new_esEs18(LT, GT)
new_ltEs13(Right(x0), Right(x1), x2, ty_Integer)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, ty_Ordering)
new_esEs26(x0, x1, ty_Integer)
new_lt20(x0, x1, ty_Int)
new_esEs11(:(x0, x1), [], x2)
new_lt19(x0, x1, ty_Float)
new_ltEs13(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs13(Right(x0), Right(x1), x2, ty_Char)
new_esEs17(False, True)
new_esEs17(True, False)
new_ltEs13(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs21(x0, x1, app(ty_[], x2))
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs11(x0, x1, ty_Ordering)
new_ltEs13(Left(x0), Left(x1), ty_Int, x2)
new_ltEs13(Right(x0), Right(x1), x2, ty_Ordering)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sr0(Integer(x0), Integer(x1))
new_esEs23(x0, x1, ty_Int)
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs22(x0, x1, ty_Float)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, ty_Ordering)
new_ltEs13(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs17(x0, x1)
new_esEs28(x0, x1, ty_Float)
new_esEs7(Right(x0), Right(x1), x2, ty_Ordering)
new_lt18(x0, x1, x2)
new_primEqInt(Pos(Zero), Pos(Zero))
new_esEs17(True, True)
new_ltEs11(x0, x1, ty_@0)
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare15(x0, x1, False, x2)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_ltEs18(Just(x0), Just(x1), ty_Integer)
new_ltEs19(x0, x1, ty_@0)
new_ltEs13(Right(x0), Right(x1), x2, ty_@0)
new_compare23(x0, x1, False, x2, x3)
new_pePe(True, x0, x1, x2, x3)
new_asAs(True, x0)
new_ltEs13(Right(x0), Right(x1), x2, ty_Double)
new_compare30(x0, x1, ty_Char)
new_esEs13(Double(x0, x1), Double(x2, x3))
new_esEs7(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs8(Just(x0), Just(x1), app(ty_Maybe, x2))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs21(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs24(x0, x1, ty_Double)
new_compare30(x0, x1, app(ty_[], x2))
new_compare30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_pePe(False, x0, x1, x2, x3)
new_compare30(x0, x1, ty_Integer)
new_not(LT)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, ty_Integer)
new_compare30(x0, x1, ty_Ordering)
new_compare24(x0, x1, False, x2, x3, x4)
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
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_foldFM_LE(vyy26, vyy40, Branch(vyy3430, vyy3431, vyy3432, vyy3433, vyy3434), h, ba) → new_foldFM_LE1(vyy26, vyy40, vyy3430, vyy3431, vyy3432, vyy3433, vyy3434, new_ltEs18(vyy3430, Just(vyy40), h), h, ba)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 3 > 4, 3 > 5, 3 > 6, 3 > 7, 4 >= 9, 5 >= 10
- new_foldFM_LE1(vyy26, vyy40, vyy340, vyy341, vyy342, Branch(vyy3430, vyy3431, vyy3432, vyy3433, vyy3434), vyy344, False, h, ba) → new_foldFM_LE1(vyy26, vyy40, vyy3430, vyy3431, vyy3432, vyy3433, vyy3434, new_ltEs18(vyy3430, Just(vyy40), h), h, ba)
The graph contains the following edges 1 >= 1, 2 >= 2, 6 > 3, 6 > 4, 6 > 5, 6 > 6, 6 > 7, 9 >= 9, 10 >= 10
- new_foldFM_LE2(vyy340, vyy341, vyy30, vyy40, vyy3440, vyy3441, vyy3442, vyy3443, vyy3444, h, ba) → new_foldFM_LE1(new_fmToList_LE0(vyy340, vyy341, vyy30, h, ba), vyy40, vyy3440, vyy3441, vyy3442, vyy3443, vyy3444, new_ltEs18(vyy3440, Just(vyy40), h), h, ba)
The graph contains the following edges 4 >= 2, 5 >= 3, 6 >= 4, 7 >= 5, 8 >= 6, 9 >= 7, 10 >= 9, 11 >= 10
- new_foldFM_LE1(vyy26, vyy40, vyy340, vyy341, vyy342, vyy343, Branch(vyy3440, vyy3441, vyy3442, vyy3443, vyy3444), True, h, ba) → new_foldFM_LE2(vyy340, vyy341, new_foldFM_LE0(vyy26, vyy40, vyy343, h, ba), vyy40, vyy3440, vyy3441, vyy3442, vyy3443, vyy3444, h, ba)
The graph contains the following edges 3 >= 1, 4 >= 2, 2 >= 4, 7 > 5, 7 > 6, 7 > 7, 7 > 8, 7 > 9, 9 >= 10, 10 >= 11
- new_foldFM_LE1(vyy26, vyy40, vyy340, vyy341, vyy342, vyy343, EmptyFM, True, h, ba) → new_foldFM_LE(vyy26, vyy40, vyy343, h, ba)
The graph contains the following edges 1 >= 1, 2 >= 2, 6 >= 3, 9 >= 4, 10 >= 5
- new_foldFM_LE1(vyy26, vyy40, vyy340, vyy341, vyy342, vyy343, Branch(vyy3440, vyy3441, vyy3442, vyy3443, vyy3444), True, h, ba) → new_foldFM_LE(vyy26, vyy40, vyy343, h, ba)
The graph contains the following edges 1 >= 1, 2 >= 2, 6 >= 3, 9 >= 4, 10 >= 5
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ UsableRulesProof
Q DP problem:
The TRS P consists of the following rules:
new_foldFM_LE11(vyy24, vyy340, vyy341, vyy342, vyy343, Branch(vyy3440, vyy3441, vyy3442, vyy3443, vyy3444), True, h, ba) → new_foldFM_LE4(vyy24, vyy343, h, ba)
new_foldFM_LE11(vyy24, vyy340, vyy341, vyy342, Branch(vyy3430, vyy3431, vyy3432, vyy3433, vyy3434), vyy344, False, h, ba) → new_foldFM_LE11(vyy24, vyy3430, vyy3431, vyy3432, vyy3433, vyy3434, new_ltEs18(vyy3430, Nothing, h), h, ba)
new_foldFM_LE21(vyy340, vyy341, vyy28, vyy3440, vyy3441, vyy3442, vyy3443, vyy3444, h, ba) → new_foldFM_LE11(new_fmToList_LE0(vyy340, vyy341, vyy28, h, ba), vyy3440, vyy3441, vyy3442, vyy3443, vyy3444, new_ltEs18(vyy3440, Nothing, h), h, ba)
new_foldFM_LE4(vyy24, Branch(vyy3430, vyy3431, vyy3432, vyy3433, vyy3434), h, ba) → new_foldFM_LE11(vyy24, vyy3430, vyy3431, vyy3432, vyy3433, vyy3434, new_ltEs18(vyy3430, Nothing, h), h, ba)
new_foldFM_LE11(vyy24, vyy340, vyy341, vyy342, vyy343, Branch(vyy3440, vyy3441, vyy3442, vyy3443, vyy3444), True, h, ba) → new_foldFM_LE21(vyy340, vyy341, new_foldFM_LE5(vyy24, vyy343, h, ba), vyy3440, vyy3441, vyy3442, vyy3443, vyy3444, h, ba)
new_foldFM_LE11(vyy24, vyy340, vyy341, vyy342, vyy343, EmptyFM, True, h, ba) → new_foldFM_LE4(vyy24, vyy343, h, ba)
The TRS R consists of the following rules:
new_esEs23(vyy401, vyy411, app(app(ty_Either, bda), bdb)) → new_esEs7(vyy401, vyy411, bda, bdb)
new_esEs23(vyy401, vyy411, ty_Ordering) → new_esEs18(vyy401, vyy411)
new_esEs25(vyy401, vyy411, ty_Int) → new_esEs19(vyy401, vyy411)
new_esEs7(Left(vyy400), Left(vyy410), app(app(ty_Either, bga), bgb), baa) → new_esEs7(vyy400, vyy410, bga, bgb)
new_esEs24(vyy400, vyy410, ty_Float) → new_esEs12(vyy400, vyy410)
new_esEs8(Just(vyy400), Just(vyy410), app(app(ty_@2, bh), ca)) → new_esEs6(vyy400, vyy410, bh, ca)
new_esEs21(vyy40, vyy41, app(app(ty_@2, ha), hb)) → new_esEs6(vyy40, vyy41, ha, hb)
new_esEs18(LT, LT) → True
new_esEs24(vyy400, vyy410, app(app(app(ty_@3, bea), beb), bec)) → new_esEs5(vyy400, vyy410, bea, beb, bec)
new_ltEs13(Right(vyy3000), Right(vyy400), cbf, ty_Integer) → new_ltEs17(vyy3000, vyy400)
new_ltEs14(GT, GT) → True
new_ltEs18(Just(vyy3000), Just(vyy400), app(ty_Maybe, ceb)) → new_ltEs18(vyy3000, vyy400, ceb)
new_esEs18(LT, EQ) → False
new_esEs18(EQ, LT) → False
new_lt20(vyy3001, vyy401, ty_Float) → new_lt14(vyy3001, vyy401)
new_esEs28(vyy401, vyy411, ty_Char) → new_esEs16(vyy401, vyy411)
new_ltEs13(Left(vyy3000), Left(vyy400), app(ty_[], cbe), cac) → new_ltEs4(vyy3000, vyy400, cbe)
new_lt19(vyy3000, vyy400, app(app(ty_@2, bd), be)) → new_lt10(vyy3000, vyy400, bd, be)
new_lt19(vyy3000, vyy400, ty_@0) → new_lt8(vyy3000, vyy400)
new_ltEs11(vyy3001, vyy401, app(ty_Ratio, ga)) → new_ltEs5(vyy3001, vyy401, ga)
new_ltEs19(vyy3002, vyy402, app(ty_Ratio, def)) → new_ltEs5(vyy3002, vyy402, def)
new_esEs27(vyy402, vyy412, ty_Bool) → new_esEs17(vyy402, vyy412)
new_foldFM_LE5(vyy24, Branch(vyy3430, vyy3431, vyy3432, vyy3433, vyy3434), h, ba) → new_foldFM_LE12(vyy24, vyy3430, vyy3431, vyy3432, vyy3433, vyy3434, new_ltEs18(vyy3430, Nothing, h), h, ba)
new_primMulNat0(Zero, Zero) → Zero
new_esEs7(Left(vyy400), Left(vyy410), app(app(app(ty_@3, bfe), bff), bfg), baa) → new_esEs5(vyy400, vyy410, bfe, bff, bfg)
new_lt20(vyy3001, vyy401, ty_Int) → new_lt13(vyy3001, vyy401)
new_ltEs13(Left(vyy3000), Left(vyy400), app(app(ty_@2, cag), cah), cac) → new_ltEs10(vyy3000, vyy400, cag, cah)
new_ltEs13(Left(vyy3000), Left(vyy400), app(ty_Maybe, cbd), cac) → new_ltEs18(vyy3000, vyy400, cbd)
new_compare18(vyy3000, vyy400, True, bab, bac, bad) → LT
new_lt20(vyy3001, vyy401, ty_@0) → new_lt8(vyy3001, vyy401)
new_esEs21(vyy40, vyy41, ty_Bool) → new_esEs17(vyy40, vyy41)
new_compare25(vyy3000, vyy400, True, ge) → EQ
new_esEs23(vyy401, vyy411, ty_Float) → new_esEs12(vyy401, vyy411)
new_esEs29(vyy400, vyy410, ty_Ordering) → new_esEs18(vyy400, vyy410)
new_esEs27(vyy402, vyy412, app(app(ty_FiniteMap, cgh), cha)) → new_esEs20(vyy402, vyy412, cgh, cha)
new_esEs9(LT) → True
new_esEs24(vyy400, vyy410, ty_Integer) → new_esEs15(vyy400, vyy410)
new_esEs8(Just(vyy400), Just(vyy410), ty_Integer) → new_esEs15(vyy400, vyy410)
new_lt19(vyy3000, vyy400, ty_Ordering) → new_lt6(vyy3000, vyy400)
new_ltEs9(True, False) → False
new_ltEs11(vyy3001, vyy401, ty_Int) → new_ltEs15(vyy3001, vyy401)
new_esEs29(vyy400, vyy410, app(app(ty_FiniteMap, dbh), dca)) → new_esEs20(vyy400, vyy410, dbh, dca)
new_esEs8(Just(vyy400), Just(vyy410), ty_Ordering) → new_esEs18(vyy400, vyy410)
new_not(GT) → False
new_esEs20(vyy40, vyy41, gf, gg) → new_asAs(new_esEs19(new_sizeFM(vyy40, gf, gg), new_sizeFM(vyy41, gf, gg)), new_esEs11(new_fmToList(vyy40, gf, gg), new_fmToList(vyy41, gf, gg), app(app(ty_@2, gf), gg)))
new_lt19(vyy3000, vyy400, app(app(app(ty_@3, bab), bac), bad)) → new_lt9(vyy3000, vyy400, bab, bac, bad)
new_lt7(vyy3000, vyy400, ty_Char) → new_lt12(vyy3000, vyy400)
new_foldFM_LE12(vyy24, vyy340, vyy341, vyy342, vyy343, EmptyFM, True, h, ba) → new_foldFM_LE30(vyy340, vyy341, new_foldFM_LE5(vyy24, vyy343, h, ba), h, ba)
new_ltEs13(Right(vyy3000), Right(vyy400), cbf, app(ty_Maybe, ccg)) → new_ltEs18(vyy3000, vyy400, ccg)
new_esEs17(True, True) → True
new_esEs7(Right(vyy400), Right(vyy410), hh, app(app(app(ty_@3, bha), bhb), bhc)) → new_esEs5(vyy400, vyy410, bha, bhb, bhc)
new_lt19(vyy3000, vyy400, ty_Int) → new_lt13(vyy3000, vyy400)
new_lt13(vyy3000, vyy400) → new_esEs9(new_compare6(vyy3000, vyy400))
new_esEs8(Just(vyy400), Just(vyy410), ty_Float) → new_esEs12(vyy400, vyy410)
new_esEs11([], [], hc) → True
new_foldFM_LE12(vyy24, vyy340, vyy341, vyy342, vyy343, Branch(vyy3440, vyy3441, vyy3442, vyy3443, vyy3444), True, h, ba) → new_foldFM_LE22(vyy340, vyy341, new_foldFM_LE5(vyy24, vyy343, h, ba), vyy3440, vyy3441, vyy3442, vyy3443, vyy3444, h, ba)
new_esEs22(vyy400, vyy410, app(ty_Ratio, bbd)) → new_esEs14(vyy400, vyy410, bbd)
new_esEs21(vyy40, vyy41, app(ty_Ratio, hg)) → new_esEs14(vyy40, vyy41, hg)
new_esEs23(vyy401, vyy411, ty_Double) → new_esEs13(vyy401, vyy411)
new_esEs15(Integer(vyy400), Integer(vyy410)) → new_primEqInt(vyy400, vyy410)
new_esEs18(LT, GT) → False
new_esEs18(GT, LT) → False
new_esEs6(@2(vyy400, vyy401), @2(vyy410, vyy411), ha, hb) → new_asAs(new_esEs24(vyy400, vyy410, ha), new_esEs23(vyy401, vyy411, hb))
new_compare15(vyy3000, vyy400, False, ge) → GT
new_esEs28(vyy401, vyy411, app(app(app(ty_@3, chf), chg), chh)) → new_esEs5(vyy401, vyy411, chf, chg, chh)
new_ltEs19(vyy3002, vyy402, ty_Bool) → new_ltEs9(vyy3002, vyy402)
new_ltEs18(Just(vyy3000), Just(vyy400), ty_Double) → new_ltEs16(vyy3000, vyy400)
new_esEs29(vyy400, vyy410, ty_Integer) → new_esEs15(vyy400, vyy410)
new_ltEs13(Left(vyy3000), Left(vyy400), app(ty_Ratio, cbc), cac) → new_ltEs5(vyy3000, vyy400, cbc)
new_esEs22(vyy400, vyy410, app(app(ty_Either, bbe), bbf)) → new_esEs7(vyy400, vyy410, bbe, bbf)
new_foldFM0(vyy410, vyy411, vyy85, EmptyFM, gf, gg) → :(@2(vyy410, vyy411), vyy85)
new_ltEs11(vyy3001, vyy401, ty_Float) → new_ltEs7(vyy3001, vyy401)
new_ltEs13(Left(vyy3000), Left(vyy400), ty_Char, cac) → new_ltEs8(vyy3000, vyy400)
new_esEs24(vyy400, vyy410, app(ty_Ratio, bed)) → new_esEs14(vyy400, vyy410, bed)
new_esEs7(Right(vyy400), Left(vyy410), hh, baa) → False
new_esEs7(Left(vyy400), Right(vyy410), hh, baa) → False
new_esEs14(:%(vyy400, vyy401), :%(vyy410, vyy411), hg) → new_asAs(new_esEs26(vyy400, vyy410, hg), new_esEs25(vyy401, vyy411, hg))
new_ltEs15(vyy300, vyy40) → new_not(new_compare6(vyy300, vyy40))
new_esEs27(vyy402, vyy412, app(app(ty_Either, cgf), cgg)) → new_esEs7(vyy402, vyy412, cgf, cgg)
new_ltEs14(GT, EQ) → False
new_ltEs18(Just(vyy3000), Just(vyy400), ty_Integer) → new_ltEs17(vyy3000, vyy400)
new_esEs7(Right(vyy400), Right(vyy410), hh, ty_Char) → new_esEs16(vyy400, vyy410)
new_ltEs11(vyy3001, vyy401, app(app(ty_Either, fg), fh)) → new_ltEs13(vyy3001, vyy401, fg, fh)
new_esEs5(@3(vyy400, vyy401, vyy402), @3(vyy410, vyy411, vyy412), hd, he, hf) → new_asAs(new_esEs29(vyy400, vyy410, hd), new_asAs(new_esEs28(vyy401, vyy411, he), new_esEs27(vyy402, vyy412, hf)))
new_compare23(vyy3000, vyy400, False, bd, be) → new_compare112(vyy3000, vyy400, new_ltEs10(vyy3000, vyy400, bd, be), bd, be)
new_ltEs18(Just(vyy3000), Just(vyy400), app(ty_Ratio, cea)) → new_ltEs5(vyy3000, vyy400, cea)
new_primCompAux1(vyy3000, vyy400, vyy67, bb) → new_primCompAux0(vyy67, new_compare30(vyy3000, vyy400, bb))
new_lt7(vyy3000, vyy400, app(app(ty_@2, eb), ec)) → new_lt10(vyy3000, vyy400, eb, ec)
new_compare30(vyy3000, vyy400, app(ty_Ratio, cfc)) → new_compare7(vyy3000, vyy400, cfc)
new_ltEs13(Right(vyy3000), Right(vyy400), cbf, ty_Char) → new_ltEs8(vyy3000, vyy400)
new_esEs24(vyy400, vyy410, app(ty_[], bdg)) → new_esEs11(vyy400, vyy410, bdg)
new_esEs29(vyy400, vyy410, app(ty_Maybe, dba)) → new_esEs8(vyy400, vyy410, dba)
new_esEs29(vyy400, vyy410, app(ty_[], dah)) → new_esEs11(vyy400, vyy410, dah)
new_compare30(vyy3000, vyy400, ty_Float) → new_compare12(vyy3000, vyy400)
new_esEs27(vyy402, vyy412, ty_Int) → new_esEs19(vyy402, vyy412)
new_compare31(vyy3000, vyy400, caa, cab) → new_compare29(vyy3000, vyy400, new_esEs7(vyy3000, vyy400, caa, cab), caa, cab)
new_ltEs11(vyy3001, vyy401, app(app(ty_@2, fd), ff)) → new_ltEs10(vyy3001, vyy401, fd, ff)
new_primCmpNat0(Zero, Succ(vyy4000)) → LT
new_esEs22(vyy400, vyy410, app(app(ty_FiniteMap, bbg), bbh)) → new_esEs20(vyy400, vyy410, bbg, bbh)
new_esEs7(Left(vyy400), Left(vyy410), ty_Double, baa) → new_esEs13(vyy400, vyy410)
new_ltEs18(Just(vyy3000), Just(vyy400), app(app(ty_@2, cde), cdf)) → new_ltEs10(vyy3000, vyy400, cde, cdf)
new_lt18(vyy3000, vyy400, ge) → new_esEs9(new_compare28(vyy3000, vyy400, ge))
new_lt20(vyy3001, vyy401, ty_Ordering) → new_lt6(vyy3001, vyy401)
new_esEs27(vyy402, vyy412, ty_@0) → new_esEs10(vyy402, vyy412)
new_esEs24(vyy400, vyy410, app(app(ty_FiniteMap, beg), beh)) → new_esEs20(vyy400, vyy410, beg, beh)
new_esEs28(vyy401, vyy411, app(ty_[], chd)) → new_esEs11(vyy401, vyy411, chd)
new_esEs24(vyy400, vyy410, app(app(ty_Either, bee), bef)) → new_esEs7(vyy400, vyy410, bee, bef)
new_esEs24(vyy400, vyy410, app(app(ty_@2, bde), bdf)) → new_esEs6(vyy400, vyy410, bde, bdf)
new_esEs27(vyy402, vyy412, ty_Ordering) → new_esEs18(vyy402, vyy412)
new_primEqNat0(Zero, Zero) → True
new_compare26(vyy3000, vyy400, True) → EQ
new_ltEs13(Left(vyy3000), Left(vyy400), ty_Integer, cac) → new_ltEs17(vyy3000, vyy400)
new_esEs22(vyy400, vyy410, app(ty_Maybe, bah)) → new_esEs8(vyy400, vyy410, bah)
new_esEs23(vyy401, vyy411, app(app(ty_FiniteMap, bdc), bdd)) → new_esEs20(vyy401, vyy411, bdc, bdd)
new_ltEs18(Just(vyy3000), Just(vyy400), ty_Char) → new_ltEs8(vyy3000, vyy400)
new_ltEs13(Left(vyy3000), Left(vyy400), ty_Int, cac) → new_ltEs15(vyy3000, vyy400)
new_compare29(vyy3000, vyy400, True, caa, cab) → EQ
new_compare111(vyy3000, vyy400, False, caa, cab) → GT
new_esEs8(Just(vyy400), Just(vyy410), ty_Int) → new_esEs19(vyy400, vyy410)
new_lt20(vyy3001, vyy401, app(app(ty_@2, dch), dda)) → new_lt10(vyy3001, vyy401, dch, dda)
new_foldFM_LE5(vyy24, EmptyFM, h, ba) → vyy24
new_ltEs13(Left(vyy3000), Left(vyy400), ty_@0, cac) → new_ltEs6(vyy3000, vyy400)
new_ltEs19(vyy3002, vyy402, app(ty_[], deh)) → new_ltEs4(vyy3002, vyy402, deh)
new_ltEs11(vyy3001, vyy401, app(app(app(ty_@3, fa), fb), fc)) → new_ltEs12(vyy3001, vyy401, fa, fb, fc)
new_foldFM_LE30(vyy340, vyy341, vyy27, h, ba) → new_fmToList_LE0(vyy340, vyy341, vyy27, h, ba)
new_esEs17(False, False) → True
new_esEs17(False, True) → False
new_esEs17(True, False) → False
new_compare12(Float(vyy3000, vyy3001), Float(vyy400, vyy401)) → new_compare6(new_sr(vyy3000, vyy400), new_sr(vyy3001, vyy401))
new_compare30(vyy3000, vyy400, app(ty_Maybe, cfd)) → new_compare28(vyy3000, vyy400, cfd)
new_esEs7(Right(vyy400), Right(vyy410), hh, ty_Ordering) → new_esEs18(vyy400, vyy410)
new_esEs21(vyy40, vyy41, app(ty_Maybe, bg)) → new_esEs8(vyy40, vyy41, bg)
new_sr(vyy3001, vyy401) → new_primMulInt(vyy3001, vyy401)
new_ltEs14(EQ, LT) → False
new_lt14(vyy3000, vyy400) → new_esEs9(new_compare12(vyy3000, vyy400))
new_esEs24(vyy400, vyy410, ty_Bool) → new_esEs17(vyy400, vyy410)
new_ltEs19(vyy3002, vyy402, app(app(app(ty_@3, ddg), ddh), dea)) → new_ltEs12(vyy3002, vyy402, ddg, ddh, dea)
new_esEs11(:(vyy400, vyy401), :(vyy410, vyy411), hc) → new_asAs(new_esEs22(vyy400, vyy410, hc), new_esEs11(vyy401, vyy411, hc))
new_primPlusNat0(Succ(vyy860), vyy40100) → Succ(Succ(new_primPlusNat1(vyy860, vyy40100)))
new_compare4([], [], bb) → EQ
new_esEs7(Right(vyy400), Right(vyy410), hh, app(app(ty_Either, bhe), bhf)) → new_esEs7(vyy400, vyy410, bhe, bhf)
new_esEs22(vyy400, vyy410, ty_Char) → new_esEs16(vyy400, vyy410)
new_esEs18(EQ, GT) → False
new_esEs18(GT, EQ) → False
new_compare30(vyy3000, vyy400, app(ty_[], cfe)) → new_compare4(vyy3000, vyy400, cfe)
new_esEs16(Char(vyy400), Char(vyy410)) → new_primEqNat0(vyy400, vyy410)
new_compare30(vyy3000, vyy400, ty_Char) → new_compare13(vyy3000, vyy400)
new_esEs8(Just(vyy400), Nothing, bg) → False
new_esEs8(Nothing, Just(vyy410), bg) → False
new_ltEs19(vyy3002, vyy402, ty_Float) → new_ltEs7(vyy3002, vyy402)
new_compare24(vyy3000, vyy400, True, bab, bac, bad) → EQ
new_primEqInt(Neg(Succ(vyy4000)), Neg(Succ(vyy4100))) → new_primEqNat0(vyy4000, vyy4100)
new_compare30(vyy3000, vyy400, ty_Int) → new_compare6(vyy3000, vyy400)
new_ltEs19(vyy3002, vyy402, app(app(ty_@2, deb), dec)) → new_ltEs10(vyy3002, vyy402, deb, dec)
new_esEs9(GT) → False
new_primPlusNat1(Zero, Succ(vyy401000)) → Succ(vyy401000)
new_primPlusNat1(Succ(vyy8600), Zero) → Succ(vyy8600)
new_compare26(vyy3000, vyy400, False) → new_compare110(vyy3000, vyy400, new_ltEs14(vyy3000, vyy400))
new_esEs9(EQ) → False
new_esEs28(vyy401, vyy411, app(ty_Maybe, che)) → new_esEs8(vyy401, vyy411, che)
new_compare16(vyy3000, vyy400, True) → LT
new_foldFM_LE12(vyy24, vyy340, vyy341, vyy342, vyy343, vyy344, False, h, ba) → new_foldFM_LE5(vyy24, vyy343, h, ba)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs7(Left(vyy400), Left(vyy410), ty_Integer, baa) → new_esEs15(vyy400, vyy410)
new_lt20(vyy3001, vyy401, app(ty_Maybe, dde)) → new_lt18(vyy3001, vyy401, dde)
new_esEs7(Left(vyy400), Left(vyy410), app(app(ty_@2, bfa), bfb), baa) → new_esEs6(vyy400, vyy410, bfa, bfb)
new_esEs28(vyy401, vyy411, ty_Double) → new_esEs13(vyy401, vyy411)
new_compare112(vyy3000, vyy400, False, bd, be) → GT
new_lt19(vyy3000, vyy400, ty_Double) → new_lt16(vyy3000, vyy400)
new_primEqInt(Neg(Zero), Neg(Succ(vyy4100))) → False
new_primEqInt(Neg(Succ(vyy4000)), Neg(Zero)) → False
new_lt19(vyy3000, vyy400, ty_Char) → new_lt12(vyy3000, vyy400)
new_primCompAux0(vyy71, GT) → GT
new_ltEs6(vyy300, vyy40) → new_not(new_compare8(vyy300, vyy40))
new_ltEs10(@2(vyy3000, vyy3001), @2(vyy400, vyy401), de, df) → new_pePe(new_lt7(vyy3000, vyy400, de), vyy3000, vyy400, new_ltEs11(vyy3001, vyy401, df), de)
new_ltEs13(Right(vyy3000), Right(vyy400), cbf, app(ty_Ratio, ccf)) → new_ltEs5(vyy3000, vyy400, ccf)
new_lt7(vyy3000, vyy400, ty_Integer) → new_lt17(vyy3000, vyy400)
new_compare11(Double(vyy3000, vyy3001), Double(vyy400, vyy401)) → new_compare6(new_sr(vyy3000, vyy400), new_sr(vyy3001, vyy401))
new_esEs22(vyy400, vyy410, app(app(app(ty_@3, bba), bbb), bbc)) → new_esEs5(vyy400, vyy410, bba, bbb, bbc)
new_compare30(vyy3000, vyy400, ty_Bool) → new_compare10(vyy3000, vyy400)
new_ltEs13(Left(vyy3000), Left(vyy400), ty_Double, cac) → new_ltEs16(vyy3000, vyy400)
new_foldFM0(vyy410, vyy411, vyy85, Branch(vyy4130, vyy4131, vyy4132, vyy4133, vyy4134), gf, gg) → new_foldFM0(vyy4130, vyy4131, new_foldFM0(vyy410, vyy411, vyy85, vyy4134, gf, gg), vyy4133, gf, gg)
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_esEs24(vyy400, vyy410, ty_Ordering) → new_esEs18(vyy400, vyy410)
new_compare6(vyy300, vyy40) → new_primCmpInt(vyy300, vyy40)
new_esEs28(vyy401, vyy411, ty_Int) → new_esEs19(vyy401, vyy411)
new_esEs7(Right(vyy400), Right(vyy410), hh, app(ty_[], bgg)) → new_esEs11(vyy400, vyy410, bgg)
new_esEs7(Left(vyy400), Left(vyy410), ty_Int, baa) → new_esEs19(vyy400, vyy410)
new_esEs23(vyy401, vyy411, ty_Char) → new_esEs16(vyy401, vyy411)
new_ltEs13(Right(vyy3000), Right(vyy400), cbf, ty_Float) → new_ltEs7(vyy3000, vyy400)
new_primCmpNat0(Succ(vyy30000), Succ(vyy4000)) → new_primCmpNat0(vyy30000, vyy4000)
new_esEs7(Right(vyy400), Right(vyy410), hh, app(app(ty_@2, bge), bgf)) → new_esEs6(vyy400, vyy410, bge, bgf)
new_sizeFM(EmptyFM, gf, gg) → Pos(Zero)
new_esEs7(Left(vyy400), Left(vyy410), app(app(ty_FiniteMap, bgc), bgd), baa) → new_esEs20(vyy400, vyy410, bgc, bgd)
new_primEqInt(Pos(Succ(vyy4000)), Pos(Succ(vyy4100))) → new_primEqNat0(vyy4000, vyy4100)
new_ltEs19(vyy3002, vyy402, ty_Integer) → new_ltEs17(vyy3002, vyy402)
new_ltEs17(vyy300, vyy40) → new_not(new_compare17(vyy300, vyy40))
new_esEs21(vyy40, vyy41, ty_Int) → new_esEs19(vyy40, vyy41)
new_esEs28(vyy401, vyy411, app(app(ty_FiniteMap, dad), dae)) → new_esEs20(vyy401, vyy411, dad, dae)
new_esEs13(Double(vyy400, vyy401), Double(vyy410, vyy411)) → new_esEs19(new_sr(vyy400, vyy410), new_sr(vyy401, vyy411))
new_esEs26(vyy400, vyy410, ty_Integer) → new_esEs15(vyy400, vyy410)
new_esEs7(Left(vyy400), Left(vyy410), app(ty_[], bfc), baa) → new_esEs11(vyy400, vyy410, bfc)
new_lt7(vyy3000, vyy400, app(ty_Maybe, eg)) → new_lt18(vyy3000, vyy400, eg)
new_ltEs7(vyy300, vyy40) → new_not(new_compare12(vyy300, vyy40))
new_primEqNat0(Succ(vyy4000), Succ(vyy4100)) → new_primEqNat0(vyy4000, vyy4100)
new_esEs23(vyy401, vyy411, app(ty_Ratio, bch)) → new_esEs14(vyy401, vyy411, bch)
new_lt7(vyy3000, vyy400, app(ty_Ratio, ef)) → new_lt15(vyy3000, vyy400, ef)
new_ltEs19(vyy3002, vyy402, app(app(ty_Either, ded), dee)) → new_ltEs13(vyy3002, vyy402, ded, dee)
new_esEs7(Left(vyy400), Left(vyy410), ty_Ordering, baa) → new_esEs18(vyy400, vyy410)
new_esEs27(vyy402, vyy412, ty_Char) → new_esEs16(vyy402, vyy412)
new_esEs27(vyy402, vyy412, ty_Float) → new_esEs12(vyy402, vyy412)
new_ltEs18(Just(vyy3000), Just(vyy400), ty_Ordering) → new_ltEs14(vyy3000, vyy400)
new_lt20(vyy3001, vyy401, ty_Integer) → new_lt17(vyy3001, vyy401)
new_compare19(vyy3000, vyy400, bab, bac, bad) → new_compare24(vyy3000, vyy400, new_esEs5(vyy3000, vyy400, bab, bac, bad), bab, bac, bad)
new_lt17(vyy3000, vyy400) → new_esEs9(new_compare17(vyy3000, vyy400))
new_primCmpInt(Neg(Succ(vyy30000)), Neg(vyy400)) → new_primCmpNat0(vyy400, Succ(vyy30000))
new_esEs7(Right(vyy400), Right(vyy410), hh, app(ty_Ratio, bhd)) → new_esEs14(vyy400, vyy410, bhd)
new_esEs27(vyy402, vyy412, app(app(app(ty_@3, cgb), cgc), cgd)) → new_esEs5(vyy402, vyy412, cgb, cgc, cgd)
new_ltEs13(Right(vyy3000), Right(vyy400), cbf, app(ty_[], cch)) → new_ltEs4(vyy3000, vyy400, cch)
new_lt6(vyy3000, vyy400) → new_esEs9(new_compare14(vyy3000, vyy400))
new_ltEs18(Just(vyy3000), Just(vyy400), ty_Bool) → new_ltEs9(vyy3000, vyy400)
new_primEqInt(Pos(Zero), Pos(Succ(vyy4100))) → False
new_primEqInt(Pos(Succ(vyy4000)), Pos(Zero)) → False
new_esEs24(vyy400, vyy410, ty_@0) → new_esEs10(vyy400, vyy410)
new_primCmpNat0(Zero, Zero) → EQ
new_ltEs18(Nothing, Nothing, cda) → True
new_primCmpNat0(Succ(vyy30000), Zero) → GT
new_ltEs5(vyy300, vyy40, bc) → new_not(new_compare7(vyy300, vyy40, bc))
new_lt20(vyy3001, vyy401, ty_Bool) → new_lt5(vyy3001, vyy401)
new_primCmpInt(Neg(Zero), Pos(Succ(vyy4000))) → LT
new_esEs21(vyy40, vyy41, ty_Char) → new_esEs16(vyy40, vyy41)
new_esEs8(Just(vyy400), Just(vyy410), ty_Char) → new_esEs16(vyy400, vyy410)
new_compare30(vyy3000, vyy400, ty_Ordering) → new_compare14(vyy3000, vyy400)
new_esEs21(vyy40, vyy41, ty_Double) → new_esEs13(vyy40, vyy41)
new_ltEs11(vyy3001, vyy401, ty_Integer) → new_ltEs17(vyy3001, vyy401)
new_sr0(Integer(vyy4000), Integer(vyy30010)) → Integer(new_primMulInt(vyy4000, vyy30010))
new_lt11(vyy3000, vyy400, caa, cab) → new_esEs9(new_compare31(vyy3000, vyy400, caa, cab))
new_primPlusNat1(Succ(vyy8600), Succ(vyy401000)) → Succ(Succ(new_primPlusNat1(vyy8600, vyy401000)))
new_esEs7(Right(vyy400), Right(vyy410), hh, app(ty_Maybe, bgh)) → new_esEs8(vyy400, vyy410, bgh)
new_primEqInt(Neg(Succ(vyy4000)), Pos(vyy410)) → False
new_primEqInt(Pos(Succ(vyy4000)), Neg(vyy410)) → False
new_ltEs19(vyy3002, vyy402, ty_Double) → new_ltEs16(vyy3002, vyy402)
new_lt19(vyy3000, vyy400, app(ty_Ratio, gd)) → new_lt15(vyy3000, vyy400, gd)
new_compare27(vyy3000, vyy400, False) → new_compare16(vyy3000, vyy400, new_ltEs9(vyy3000, vyy400))
new_esEs7(Left(vyy400), Left(vyy410), ty_@0, baa) → new_esEs10(vyy400, vyy410)
new_foldFM2(EmptyFM, gf, gg) → []
new_compare7(:%(vyy3000, vyy3001), :%(vyy400, vyy401), ty_Integer) → new_compare17(new_sr0(vyy3000, vyy401), new_sr0(vyy400, vyy3001))
new_lt19(vyy3000, vyy400, ty_Bool) → new_lt5(vyy3000, vyy400)
new_esEs11(:(vyy400, vyy401), [], hc) → False
new_esEs11([], :(vyy410, vyy411), hc) → False
new_esEs22(vyy400, vyy410, app(app(ty_@2, bae), baf)) → new_esEs6(vyy400, vyy410, bae, baf)
new_ltEs11(vyy3001, vyy401, app(ty_Maybe, gb)) → new_ltEs18(vyy3001, vyy401, gb)
new_primEqInt(Neg(Zero), Pos(Succ(vyy4100))) → False
new_primEqInt(Pos(Zero), Neg(Succ(vyy4100))) → False
new_lt7(vyy3000, vyy400, app(app(app(ty_@3, dg), dh), ea)) → new_lt9(vyy3000, vyy400, dg, dh, ea)
new_esEs21(vyy40, vyy41, ty_Integer) → new_esEs15(vyy40, vyy41)
new_esEs22(vyy400, vyy410, app(ty_[], bag)) → new_esEs11(vyy400, vyy410, bag)
new_primCmpInt(Pos(Zero), Pos(Succ(vyy4000))) → new_primCmpNat0(Zero, Succ(vyy4000))
new_esEs28(vyy401, vyy411, app(app(ty_Either, dab), dac)) → new_esEs7(vyy401, vyy411, dab, dac)
new_esEs7(Right(vyy400), Right(vyy410), hh, ty_Float) → new_esEs12(vyy400, vyy410)
new_esEs7(Right(vyy400), Right(vyy410), hh, ty_Double) → new_esEs13(vyy400, vyy410)
new_lt20(vyy3001, vyy401, app(app(app(ty_@3, dce), dcf), dcg)) → new_lt9(vyy3001, vyy401, dce, dcf, dcg)
new_esEs21(vyy40, vyy41, ty_Ordering) → new_esEs18(vyy40, vyy41)
new_ltEs11(vyy3001, vyy401, ty_Bool) → new_ltEs9(vyy3001, vyy401)
new_esEs8(Just(vyy400), Just(vyy410), app(ty_[], cb)) → new_esEs11(vyy400, vyy410, cb)
new_esEs28(vyy401, vyy411, ty_Float) → new_esEs12(vyy401, vyy411)
new_esEs27(vyy402, vyy412, app(ty_Maybe, cga)) → new_esEs8(vyy402, vyy412, cga)
new_ltEs13(Left(vyy3000), Left(vyy400), ty_Float, cac) → new_ltEs7(vyy3000, vyy400)
new_esEs28(vyy401, vyy411, app(ty_Ratio, daa)) → new_esEs14(vyy401, vyy411, daa)
new_ltEs18(Just(vyy3000), Just(vyy400), ty_Float) → new_ltEs7(vyy3000, vyy400)
new_primCompAux0(vyy71, LT) → LT
new_ltEs19(vyy3002, vyy402, ty_Char) → new_ltEs8(vyy3002, vyy402)
new_esEs23(vyy401, vyy411, ty_Int) → new_esEs19(vyy401, vyy411)
new_lt19(vyy3000, vyy400, app(ty_Maybe, ge)) → new_lt18(vyy3000, vyy400, ge)
new_esEs8(Just(vyy400), Just(vyy410), ty_@0) → new_esEs10(vyy400, vyy410)
new_ltEs18(Just(vyy3000), Nothing, cda) → False
new_compare30(vyy3000, vyy400, app(app(ty_@2, ceg), ceh)) → new_compare9(vyy3000, vyy400, ceg, ceh)
new_primCmpInt(Pos(Succ(vyy30000)), Pos(vyy400)) → new_primCmpNat0(Succ(vyy30000), vyy400)
new_primPlusNat0(Zero, vyy40100) → Succ(vyy40100)
new_esEs7(Right(vyy400), Right(vyy410), hh, ty_Bool) → new_esEs17(vyy400, vyy410)
new_esEs23(vyy401, vyy411, app(app(ty_@2, bca), bcb)) → new_esEs6(vyy401, vyy411, bca, bcb)
new_ltEs13(Right(vyy3000), Right(vyy400), cbf, ty_Ordering) → new_ltEs14(vyy3000, vyy400)
new_esEs22(vyy400, vyy410, ty_Bool) → new_esEs17(vyy400, vyy410)
new_lt19(vyy3000, vyy400, ty_Integer) → new_lt17(vyy3000, vyy400)
new_esEs25(vyy401, vyy411, ty_Integer) → new_esEs15(vyy401, vyy411)
new_compare30(vyy3000, vyy400, ty_Double) → new_compare11(vyy3000, vyy400)
new_ltEs14(LT, LT) → True
new_esEs8(Just(vyy400), Just(vyy410), app(ty_Ratio, cg)) → new_esEs14(vyy400, vyy410, cg)
new_esEs8(Just(vyy400), Just(vyy410), ty_Double) → new_esEs13(vyy400, vyy410)
new_not0 → True
new_esEs23(vyy401, vyy411, app(ty_Maybe, bcd)) → new_esEs8(vyy401, vyy411, bcd)
new_compare30(vyy3000, vyy400, app(app(ty_Either, cfa), cfb)) → new_compare31(vyy3000, vyy400, cfa, cfb)
new_esEs23(vyy401, vyy411, ty_@0) → new_esEs10(vyy401, vyy411)
new_lt19(vyy3000, vyy400, ty_Float) → new_lt14(vyy3000, vyy400)
new_lt19(vyy3000, vyy400, app(ty_[], bf)) → new_lt4(vyy3000, vyy400, bf)
new_esEs18(GT, GT) → True
new_primCmpInt(Pos(Succ(vyy30000)), Neg(vyy400)) → GT
new_esEs21(vyy40, vyy41, app(app(app(ty_@3, hd), he), hf)) → new_esEs5(vyy40, vyy41, hd, he, hf)
new_esEs8(Just(vyy400), Just(vyy410), app(app(ty_Either, da), db)) → new_esEs7(vyy400, vyy410, da, db)
new_esEs7(Left(vyy400), Left(vyy410), app(ty_Ratio, bfh), baa) → new_esEs14(vyy400, vyy410, bfh)
new_esEs21(vyy40, vyy41, app(app(ty_FiniteMap, gf), gg)) → new_esEs20(vyy40, vyy41, gf, gg)
new_primMulInt(Pos(vyy30010), Pos(vyy4010)) → Pos(new_primMulNat0(vyy30010, vyy4010))
new_lt15(vyy3000, vyy400, gd) → new_esEs9(new_compare7(vyy3000, vyy400, gd))
new_esEs22(vyy400, vyy410, ty_Double) → new_esEs13(vyy400, vyy410)
new_ltEs12(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), dcb, dcc, dcd) → new_pePe(new_lt19(vyy3000, vyy400, dcb), vyy3000, vyy400, new_pePe(new_lt20(vyy3001, vyy401, dcc), vyy3001, vyy401, new_ltEs19(vyy3002, vyy402, dcd), dcc), dcb)
new_ltEs9(True, True) → True
new_esEs27(vyy402, vyy412, app(app(ty_@2, cff), cfg)) → new_esEs6(vyy402, vyy412, cff, cfg)
new_primMulInt(Neg(vyy30010), Neg(vyy4010)) → Pos(new_primMulNat0(vyy30010, vyy4010))
new_ltEs13(Right(vyy3000), Right(vyy400), cbf, ty_Bool) → new_ltEs9(vyy3000, vyy400)
new_compare110(vyy3000, vyy400, True) → LT
new_ltEs18(Just(vyy3000), Just(vyy400), app(app(ty_Either, cdg), cdh)) → new_ltEs13(vyy3000, vyy400, cdg, cdh)
new_esEs29(vyy400, vyy410, app(app(ty_@2, daf), dag)) → new_esEs6(vyy400, vyy410, daf, dag)
new_lt7(vyy3000, vyy400, ty_Double) → new_lt16(vyy3000, vyy400)
new_primEqNat0(Succ(vyy4000), Zero) → False
new_primEqNat0(Zero, Succ(vyy4100)) → False
new_esEs21(vyy40, vyy41, ty_@0) → new_esEs10(vyy40, vyy41)
new_esEs24(vyy400, vyy410, ty_Char) → new_esEs16(vyy400, vyy410)
new_ltEs19(vyy3002, vyy402, ty_@0) → new_ltEs6(vyy3002, vyy402)
new_lt20(vyy3001, vyy401, app(ty_Ratio, ddd)) → new_lt15(vyy3001, vyy401, ddd)
new_esEs22(vyy400, vyy410, ty_Ordering) → new_esEs18(vyy400, vyy410)
new_lt19(vyy3000, vyy400, app(app(ty_Either, caa), cab)) → new_lt11(vyy3000, vyy400, caa, cab)
new_compare110(vyy3000, vyy400, False) → GT
new_compare9(vyy3000, vyy400, bd, be) → new_compare23(vyy3000, vyy400, new_esEs6(vyy3000, vyy400, bd, be), bd, be)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_ltEs18(Just(vyy3000), Just(vyy400), ty_Int) → new_ltEs15(vyy3000, vyy400)
new_ltEs9(False, False) → True
new_compare30(vyy3000, vyy400, ty_@0) → new_compare8(vyy3000, vyy400)
new_ltEs11(vyy3001, vyy401, ty_Char) → new_ltEs8(vyy3001, vyy401)
new_compare4(:(vyy3000, vyy3001), [], bb) → GT
new_sizeFM(Branch(vyy410, vyy411, vyy412, vyy413, vyy414), gf, gg) → vyy412
new_lt7(vyy3000, vyy400, ty_@0) → new_lt8(vyy3000, vyy400)
new_esEs21(vyy40, vyy41, app(app(ty_Either, hh), baa)) → new_esEs7(vyy40, vyy41, hh, baa)
new_pePe(True, vyy40, vyy41, vyy57, gh) → True
new_esEs22(vyy400, vyy410, ty_@0) → new_esEs10(vyy400, vyy410)
new_foldFM2(Branch(vyy410, vyy411, vyy412, vyy413, vyy414), gf, gg) → new_foldFM0(vyy410, vyy411, new_foldFM2(vyy414, gf, gg), vyy413, gf, gg)
new_lt20(vyy3001, vyy401, app(app(ty_Either, ddb), ddc)) → new_lt11(vyy3001, vyy401, ddb, ddc)
new_esEs29(vyy400, vyy410, app(app(app(ty_@3, dbb), dbc), dbd)) → new_esEs5(vyy400, vyy410, dbb, dbc, dbd)
new_esEs7(Left(vyy400), Left(vyy410), app(ty_Maybe, bfd), baa) → new_esEs8(vyy400, vyy410, bfd)
new_compare23(vyy3000, vyy400, True, bd, be) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(vyy4000))) → new_primCmpNat0(Succ(vyy4000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(vyy4000))) → GT
new_esEs23(vyy401, vyy411, ty_Bool) → new_esEs17(vyy401, vyy411)
new_compare13(Char(vyy3000), Char(vyy400)) → new_primCmpNat0(vyy3000, vyy400)
new_lt7(vyy3000, vyy400, ty_Ordering) → new_lt6(vyy3000, vyy400)
new_compare4([], :(vyy400, vyy401), bb) → LT
new_compare30(vyy3000, vyy400, app(app(app(ty_@3, ced), cee), cef)) → new_compare19(vyy3000, vyy400, ced, cee, cef)
new_lt7(vyy3000, vyy400, ty_Bool) → new_lt5(vyy3000, vyy400)
new_esEs23(vyy401, vyy411, app(ty_[], bcc)) → new_esEs11(vyy401, vyy411, bcc)
new_lt16(vyy3000, vyy400) → new_esEs9(new_compare11(vyy3000, vyy400))
new_esEs28(vyy401, vyy411, app(app(ty_@2, chb), chc)) → new_esEs6(vyy401, vyy411, chb, chc)
new_esEs21(vyy40, vyy41, ty_Float) → new_esEs12(vyy40, vyy41)
new_esEs29(vyy400, vyy410, ty_Int) → new_esEs19(vyy400, vyy410)
new_ltEs19(vyy3002, vyy402, ty_Ordering) → new_ltEs14(vyy3002, vyy402)
new_ltEs13(Left(vyy3000), Left(vyy400), app(app(ty_Either, cba), cbb), cac) → new_ltEs13(vyy3000, vyy400, cba, cbb)
new_esEs8(Just(vyy400), Just(vyy410), ty_Bool) → new_esEs17(vyy400, vyy410)
new_compare24(vyy3000, vyy400, False, bab, bac, bad) → new_compare18(vyy3000, vyy400, new_ltEs12(vyy3000, vyy400, bab, bac, bad), bab, bac, bad)
new_lt20(vyy3001, vyy401, ty_Double) → new_lt16(vyy3001, vyy401)
new_ltEs13(Right(vyy3000), Right(vyy400), cbf, app(app(ty_Either, ccd), cce)) → new_ltEs13(vyy3000, vyy400, ccd, cce)
new_ltEs18(Just(vyy3000), Just(vyy400), app(ty_[], cec)) → new_ltEs4(vyy3000, vyy400, cec)
new_ltEs18(Just(vyy3000), Just(vyy400), ty_@0) → new_ltEs6(vyy3000, vyy400)
new_esEs19(vyy40, vyy41) → new_primEqInt(vyy40, vyy41)
new_ltEs13(Left(vyy3000), Left(vyy400), app(app(app(ty_@3, cad), cae), caf), cac) → new_ltEs12(vyy3000, vyy400, cad, cae, caf)
new_esEs8(Nothing, Nothing, bg) → True
new_esEs10(@0, @0) → True
new_esEs27(vyy402, vyy412, app(ty_Ratio, cge)) → new_esEs14(vyy402, vyy412, cge)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs29(vyy400, vyy410, ty_Bool) → new_esEs17(vyy400, vyy410)
new_ltEs13(Left(vyy3000), Left(vyy400), ty_Ordering, cac) → new_ltEs14(vyy3000, vyy400)
new_ltEs16(vyy300, vyy40) → new_not(new_compare11(vyy300, vyy40))
new_esEs28(vyy401, vyy411, ty_@0) → new_esEs10(vyy401, vyy411)
new_asAs(False, vyy66) → False
new_lt9(vyy3000, vyy400, bab, bac, bad) → new_esEs9(new_compare19(vyy3000, vyy400, bab, bac, bad))
new_primMulInt(Neg(vyy30010), Pos(vyy4010)) → Neg(new_primMulNat0(vyy30010, vyy4010))
new_primMulInt(Pos(vyy30010), Neg(vyy4010)) → Neg(new_primMulNat0(vyy30010, vyy4010))
new_esEs22(vyy400, vyy410, ty_Float) → new_esEs12(vyy400, vyy410)
new_esEs27(vyy402, vyy412, ty_Double) → new_esEs13(vyy402, vyy412)
new_ltEs13(Left(vyy3000), Right(vyy400), cbf, cac) → True
new_primMulNat0(Succ(vyy300100), Zero) → Zero
new_primMulNat0(Zero, Succ(vyy40100)) → Zero
new_esEs24(vyy400, vyy410, ty_Double) → new_esEs13(vyy400, vyy410)
new_compare30(vyy3000, vyy400, ty_Integer) → new_compare17(vyy3000, vyy400)
new_esEs7(Right(vyy400), Right(vyy410), hh, ty_Integer) → new_esEs15(vyy400, vyy410)
new_lt7(vyy3000, vyy400, app(ty_[], eh)) → new_lt4(vyy3000, vyy400, eh)
new_ltEs13(Right(vyy3000), Right(vyy400), cbf, ty_Int) → new_ltEs15(vyy3000, vyy400)
new_ltEs8(vyy300, vyy40) → new_not(new_compare13(vyy300, vyy40))
new_pePe(False, vyy40, vyy41, vyy57, gh) → new_asAs(new_esEs21(vyy40, vyy41, gh), vyy57)
new_ltEs11(vyy3001, vyy401, ty_@0) → new_ltEs6(vyy3001, vyy401)
new_compare17(Integer(vyy3000), Integer(vyy400)) → new_primCmpInt(vyy3000, vyy400)
new_ltEs11(vyy3001, vyy401, ty_Ordering) → new_ltEs14(vyy3001, vyy401)
new_esEs29(vyy400, vyy410, ty_Double) → new_esEs13(vyy400, vyy410)
new_ltEs18(Nothing, Just(vyy400), cda) → True
new_ltEs14(GT, LT) → False
new_lt20(vyy3001, vyy401, app(ty_[], ddf)) → new_lt4(vyy3001, vyy401, ddf)
new_not(EQ) → new_not0
new_esEs8(Just(vyy400), Just(vyy410), app(app(app(ty_@3, cd), ce), cf)) → new_esEs5(vyy400, vyy410, cd, ce, cf)
new_compare29(vyy3000, vyy400, False, caa, cab) → new_compare111(vyy3000, vyy400, new_ltEs13(vyy3000, vyy400, caa, cab), caa, cab)
new_lt10(vyy3000, vyy400, bd, be) → new_esEs9(new_compare9(vyy3000, vyy400, bd, be))
new_esEs28(vyy401, vyy411, ty_Integer) → new_esEs15(vyy401, vyy411)
new_lt5(vyy3000, vyy400) → new_esEs9(new_compare10(vyy3000, vyy400))
new_compare18(vyy3000, vyy400, False, bab, bac, bad) → GT
new_esEs7(Right(vyy400), Right(vyy410), hh, ty_Int) → new_esEs19(vyy400, vyy410)
new_ltEs9(False, True) → True
new_ltEs13(Right(vyy3000), Right(vyy400), cbf, app(app(ty_@2, ccb), ccc)) → new_ltEs10(vyy3000, vyy400, ccb, ccc)
new_esEs23(vyy401, vyy411, ty_Integer) → new_esEs15(vyy401, vyy411)
new_compare25(vyy3000, vyy400, False, ge) → new_compare15(vyy3000, vyy400, new_ltEs18(vyy3000, vyy400, ge), ge)
new_compare27(vyy3000, vyy400, True) → EQ
new_ltEs13(Right(vyy3000), Left(vyy400), cbf, cac) → False
new_lt4(vyy3000, vyy400, bf) → new_esEs9(new_compare4(vyy3000, vyy400, bf))
new_esEs28(vyy401, vyy411, ty_Bool) → new_esEs17(vyy401, vyy411)
new_compare14(vyy3000, vyy400) → new_compare26(vyy3000, vyy400, new_esEs18(vyy3000, vyy400))
new_esEs27(vyy402, vyy412, app(ty_[], cfh)) → new_esEs11(vyy402, vyy412, cfh)
new_lt7(vyy3000, vyy400, ty_Int) → new_lt13(vyy3000, vyy400)
new_esEs22(vyy400, vyy410, ty_Int) → new_esEs19(vyy400, vyy410)
new_ltEs19(vyy3002, vyy402, ty_Int) → new_ltEs15(vyy3002, vyy402)
new_ltEs14(LT, GT) → True
new_esEs24(vyy400, vyy410, app(ty_Maybe, bdh)) → new_esEs8(vyy400, vyy410, bdh)
new_not(LT) → new_not0
new_ltEs14(LT, EQ) → True
new_lt12(vyy3000, vyy400) → new_esEs9(new_compare13(vyy3000, vyy400))
new_esEs26(vyy400, vyy410, ty_Int) → new_esEs19(vyy400, vyy410)
new_compare4(:(vyy3000, vyy3001), :(vyy400, vyy401), bb) → new_primCompAux1(vyy3000, vyy400, new_compare4(vyy3001, vyy401, bb), bb)
new_compare28(vyy3000, vyy400, ge) → new_compare25(vyy3000, vyy400, new_esEs8(vyy3000, vyy400, ge), ge)
new_esEs21(vyy40, vyy41, app(ty_[], hc)) → new_esEs11(vyy40, vyy41, hc)
new_esEs29(vyy400, vyy410, app(app(ty_Either, dbf), dbg)) → new_esEs7(vyy400, vyy410, dbf, dbg)
new_esEs7(Left(vyy400), Left(vyy410), ty_Bool, baa) → new_esEs17(vyy400, vyy410)
new_lt20(vyy3001, vyy401, ty_Char) → new_lt12(vyy3001, vyy401)
new_esEs29(vyy400, vyy410, ty_Char) → new_esEs16(vyy400, vyy410)
new_esEs12(Float(vyy400, vyy401), Float(vyy410, vyy411)) → new_esEs19(new_sr(vyy400, vyy410), new_sr(vyy401, vyy411))
new_esEs28(vyy401, vyy411, ty_Ordering) → new_esEs18(vyy401, vyy411)
new_ltEs11(vyy3001, vyy401, app(ty_[], gc)) → new_ltEs4(vyy3001, vyy401, gc)
new_esEs29(vyy400, vyy410, ty_@0) → new_esEs10(vyy400, vyy410)
new_esEs22(vyy400, vyy410, ty_Integer) → new_esEs15(vyy400, vyy410)
new_primPlusNat1(Zero, Zero) → Zero
new_compare111(vyy3000, vyy400, True, caa, cab) → LT
new_compare15(vyy3000, vyy400, True, ge) → LT
new_asAs(True, vyy66) → vyy66
new_ltEs14(EQ, EQ) → True
new_compare112(vyy3000, vyy400, True, bd, be) → LT
new_primMulNat0(Succ(vyy300100), Succ(vyy40100)) → new_primPlusNat0(new_primMulNat0(vyy300100, Succ(vyy40100)), vyy40100)
new_foldFM_LE22(vyy340, vyy341, vyy28, vyy3440, vyy3441, vyy3442, vyy3443, vyy3444, h, ba) → new_foldFM_LE12(new_fmToList_LE0(vyy340, vyy341, vyy28, h, ba), vyy3440, vyy3441, vyy3442, vyy3443, vyy3444, new_ltEs18(vyy3440, Nothing, h), h, ba)
new_esEs29(vyy400, vyy410, ty_Float) → new_esEs12(vyy400, vyy410)
new_esEs8(Just(vyy400), Just(vyy410), app(ty_Maybe, cc)) → new_esEs8(vyy400, vyy410, cc)
new_esEs24(vyy400, vyy410, ty_Int) → new_esEs19(vyy400, vyy410)
new_compare8(@0, @0) → EQ
new_esEs7(Left(vyy400), Left(vyy410), ty_Char, baa) → new_esEs16(vyy400, vyy410)
new_fmToList(vyy41, gf, gg) → new_foldFM2(vyy41, gf, gg)
new_ltEs13(Left(vyy3000), Left(vyy400), ty_Bool, cac) → new_ltEs9(vyy3000, vyy400)
new_esEs23(vyy401, vyy411, app(app(app(ty_@3, bce), bcf), bcg)) → new_esEs5(vyy401, vyy411, bce, bcf, bcg)
new_esEs29(vyy400, vyy410, app(ty_Ratio, dbe)) → new_esEs14(vyy400, vyy410, dbe)
new_fmToList_LE0(vyy340, vyy341, vyy27, h, ba) → :(@2(vyy340, vyy341), vyy27)
new_ltEs4(vyy300, vyy40, bb) → new_not(new_compare4(vyy300, vyy40, bb))
new_compare10(vyy3000, vyy400) → new_compare27(vyy3000, vyy400, new_esEs17(vyy3000, vyy400))
new_lt8(vyy3000, vyy400) → new_esEs9(new_compare8(vyy3000, vyy400))
new_ltEs13(Right(vyy3000), Right(vyy400), cbf, app(app(app(ty_@3, cbg), cbh), cca)) → new_ltEs12(vyy3000, vyy400, cbg, cbh, cca)
new_esEs7(Left(vyy400), Left(vyy410), ty_Float, baa) → new_esEs12(vyy400, vyy410)
new_ltEs11(vyy3001, vyy401, ty_Double) → new_ltEs16(vyy3001, vyy401)
new_lt7(vyy3000, vyy400, app(app(ty_Either, ed), ee)) → new_lt11(vyy3000, vyy400, ed, ee)
new_ltEs13(Right(vyy3000), Right(vyy400), cbf, ty_@0) → new_ltEs6(vyy3000, vyy400)
new_ltEs13(Right(vyy3000), Right(vyy400), cbf, ty_Double) → new_ltEs16(vyy3000, vyy400)
new_lt7(vyy3000, vyy400, ty_Float) → new_lt14(vyy3000, vyy400)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_ltEs14(EQ, GT) → True
new_esEs7(Right(vyy400), Right(vyy410), hh, ty_@0) → new_esEs10(vyy400, vyy410)
new_primCompAux0(vyy71, EQ) → vyy71
new_compare7(:%(vyy3000, vyy3001), :%(vyy400, vyy401), ty_Int) → new_compare6(new_sr(vyy3000, vyy401), new_sr(vyy400, vyy3001))
new_esEs8(Just(vyy400), Just(vyy410), app(app(ty_FiniteMap, dc), dd)) → new_esEs20(vyy400, vyy410, dc, dd)
new_ltEs18(Just(vyy3000), Just(vyy400), app(app(app(ty_@3, cdb), cdc), cdd)) → new_ltEs12(vyy3000, vyy400, cdb, cdc, cdd)
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_ltEs19(vyy3002, vyy402, app(ty_Maybe, deg)) → new_ltEs18(vyy3002, vyy402, deg)
new_esEs27(vyy402, vyy412, ty_Integer) → new_esEs15(vyy402, vyy412)
new_esEs18(EQ, EQ) → True
new_esEs7(Right(vyy400), Right(vyy410), hh, app(app(ty_FiniteMap, bhg), bhh)) → new_esEs20(vyy400, vyy410, bhg, bhh)
new_primCmpInt(Neg(Succ(vyy30000)), Pos(vyy400)) → LT
new_compare16(vyy3000, vyy400, False) → GT
The set Q consists of the following terms:
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs18(Just(x0), Just(x1), ty_Double)
new_compare30(x0, x1, ty_Int)
new_compare111(x0, x1, True, x2, x3)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs7(Left(x0), Right(x1), x2, x3)
new_esEs7(Right(x0), Left(x1), x2, x3)
new_foldFM2(EmptyFM, x0, x1)
new_ltEs19(x0, x1, ty_Char)
new_lt16(x0, x1)
new_compare4(:(x0, x1), [], x2)
new_ltEs13(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_primEqNat0(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_compare18(x0, x1, True, x2, x3, x4)
new_ltEs13(Left(x0), Left(x1), ty_Integer, x2)
new_esEs18(LT, LT)
new_ltEs5(x0, x1, x2)
new_ltEs11(x0, x1, ty_Integer)
new_compare110(x0, x1, False)
new_lt7(x0, x1, app(ty_[], x2))
new_ltEs13(Left(x0), Left(x1), ty_Char, x2)
new_esEs9(EQ)
new_compare26(x0, x1, True)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_ltEs18(Just(x0), Just(x1), ty_Ordering)
new_compare30(x0, x1, ty_Bool)
new_compare30(x0, x1, ty_@0)
new_primMulNat0(Zero, Succ(x0))
new_esEs29(x0, x1, ty_Ordering)
new_foldFM_LE22(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9)
new_esEs8(Just(x0), Just(x1), app(app(ty_FiniteMap, x2), x3))
new_primCmpNat0(Zero, Succ(x0))
new_primCmpNat0(Succ(x0), Zero)
new_esEs8(Just(x0), Just(x1), ty_@0)
new_esEs7(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs28(x0, x1, ty_Integer)
new_compare6(x0, x1)
new_esEs7(Left(x0), Left(x1), ty_Double, x2)
new_ltEs8(x0, x1)
new_ltEs19(x0, x1, ty_Float)
new_compare7(:%(x0, x1), :%(x2, x3), ty_Int)
new_lt19(x0, x1, app(ty_Maybe, x2))
new_compare9(x0, x1, x2, x3)
new_compare15(x0, x1, True, x2)
new_ltEs13(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_ltEs11(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs29(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, ty_Double)
new_compare29(x0, x1, True, x2, x3)
new_esEs7(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs7(Left(x0), Left(x1), ty_Char, x2)
new_lt19(x0, x1, ty_Integer)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_lt20(x0, x1, app(ty_[], x2))
new_esEs7(Right(x0), Right(x1), x2, ty_Int)
new_compare30(x0, x1, ty_Double)
new_asAs(False, x0)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs27(x0, x1, ty_Bool)
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_primCompAux1(x0, x1, x2, x3)
new_ltEs4(x0, x1, x2)
new_esEs7(Left(x0), Left(x1), ty_Int, x2)
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_esEs18(EQ, GT)
new_esEs18(GT, EQ)
new_esEs27(x0, x1, ty_Int)
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs7(Right(x0), Right(x1), x2, ty_@0)
new_esEs17(False, False)
new_ltEs18(Just(x0), Just(x1), app(ty_Maybe, x2))
new_ltEs11(x0, x1, ty_Char)
new_esEs8(Nothing, Just(x0), x1)
new_sr(x0, x1)
new_compare8(@0, @0)
new_esEs25(x0, x1, ty_Int)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs18(EQ, EQ)
new_compare28(x0, x1, x2)
new_esEs8(Just(x0), Just(x1), ty_Float)
new_compare27(x0, x1, True)
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_FiniteMap, x3), x4))
new_ltEs18(Just(x0), Just(x1), app(ty_Ratio, x2))
new_compare29(x0, x1, False, x2, x3)
new_esEs28(x0, x1, ty_Char)
new_esEs8(Just(x0), Just(x1), ty_Ordering)
new_compare112(x0, x1, False, x2, x3)
new_ltEs11(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs18(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs29(x0, x1, ty_Char)
new_esEs22(x0, x1, ty_Char)
new_compare25(x0, x1, True, x2)
new_ltEs14(EQ, EQ)
new_primEqNat0(Zero, Zero)
new_ltEs11(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpNat0(Succ(x0), Succ(x1))
new_ltEs18(Nothing, Nothing, x0)
new_lt19(x0, x1, app(ty_[], x2))
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_esEs25(x0, x1, ty_Integer)
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs13(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs29(x0, x1, ty_Int)
new_lt20(x0, x1, ty_@0)
new_lt7(x0, x1, ty_Double)
new_fmToList(x0, x1, x2)
new_lt7(x0, x1, app(ty_Maybe, x2))
new_ltEs9(False, False)
new_ltEs19(x0, x1, ty_Int)
new_esEs22(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_compare112(x0, x1, True, x2, x3)
new_lt20(x0, x1, ty_Char)
new_esEs23(x0, x1, ty_Integer)
new_primPlusNat1(Zero, Succ(x0))
new_primMulNat0(Zero, Zero)
new_primMulInt(Pos(x0), Pos(x1))
new_lt7(x0, x1, ty_Char)
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, ty_Float)
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, ty_@0)
new_compare4([], :(x0, x1), x2)
new_lt7(x0, x1, app(app(ty_Either, x2), x3))
new_esEs6(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs24(x0, x1, ty_Bool)
new_compare30(x0, x1, app(app(ty_Either, x2), x3))
new_esEs7(Left(x0), Left(x1), ty_Float, x2)
new_esEs8(Just(x0), Just(x1), ty_Integer)
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare4(:(x0, x1), :(x2, x3), x4)
new_primPlusNat1(Succ(x0), Zero)
new_lt7(x0, x1, ty_Ordering)
new_ltEs18(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs22(x0, x1, app(ty_[], x2))
new_ltEs13(Left(x0), Left(x1), ty_Bool, x2)
new_primMulNat0(Succ(x0), Succ(x1))
new_esEs21(x0, x1, ty_@0)
new_esEs28(x0, x1, ty_Bool)
new_compare30(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs13(Right(x0), Right(x1), x2, ty_Int)
new_ltEs16(x0, x1)
new_esEs29(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs23(x0, x1, ty_Double)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs11(x0, x1, app(ty_Maybe, x2))
new_esEs21(x0, x1, ty_Int)
new_esEs11(:(x0, x1), :(x2, x3), x4)
new_lt11(x0, x1, x2, x3)
new_lt14(x0, x1)
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_sizeFM(EmptyFM, x0, x1)
new_esEs27(x0, x1, ty_@0)
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
new_esEs11([], [], x0)
new_lt19(x0, x1, app(ty_Ratio, x2))
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_lt19(x0, x1, ty_Ordering)
new_esEs21(x0, x1, ty_Char)
new_compare23(x0, x1, True, x2, x3)
new_esEs7(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs8(Just(x0), Just(x1), ty_Char)
new_ltEs6(x0, x1)
new_foldFM_LE5(x0, EmptyFM, x1, x2)
new_compare4([], [], x0)
new_esEs23(x0, x1, app(ty_[], x2))
new_lt9(x0, x1, x2, x3, x4)
new_lt20(x0, x1, ty_Bool)
new_ltEs11(x0, x1, ty_Float)
new_compare31(x0, x1, x2, x3)
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_lt7(x0, x1, ty_Int)
new_lt4(x0, x1, x2)
new_primPlusNat0(Succ(x0), x1)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, ty_Integer)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs7(Left(x0), Left(x1), app(app(ty_FiniteMap, x2), x3), x4)
new_esEs20(x0, x1, x2, x3)
new_compare27(x0, x1, False)
new_primPlusNat1(Zero, Zero)
new_esEs8(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_not0
new_esEs29(x0, x1, ty_@0)
new_primMulNat0(Succ(x0), Zero)
new_esEs21(x0, x1, ty_Bool)
new_foldFM_LE12(x0, x1, x2, x3, x4, EmptyFM, True, x5, x6)
new_esEs27(x0, x1, ty_Ordering)
new_compare13(Char(x0), Char(x1))
new_esEs9(GT)
new_ltEs14(LT, LT)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs19(x0, x1)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_lt7(x0, x1, ty_Integer)
new_esEs14(:%(x0, x1), :%(x2, x3), x4)
new_esEs24(x0, x1, ty_@0)
new_ltEs7(x0, x1)
new_compare110(x0, x1, True)
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs13(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs7(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs18(GT, GT)
new_esEs11([], :(x0, x1), x2)
new_esEs7(Right(x0), Right(x1), x2, ty_Float)
new_esEs24(x0, x1, app(ty_[], x2))
new_ltEs11(x0, x1, ty_Double)
new_ltEs13(Left(x0), Left(x1), ty_@0, x2)
new_ltEs13(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs9(False, True)
new_ltEs9(True, False)
new_lt5(x0, x1)
new_compare12(Float(x0, x1), Float(x2, x3))
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_ltEs9(True, True)
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_ltEs18(Nothing, Just(x0), x1)
new_esEs10(@0, @0)
new_esEs28(x0, x1, app(ty_[], x2))
new_not(GT)
new_fmToList_LE0(x0, x1, x2, x3, x4)
new_ltEs13(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_ltEs13(Left(x0), Left(x1), ty_Double, x2)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_esEs8(Just(x0), Just(x1), ty_Double)
new_esEs8(Nothing, Nothing, x0)
new_esEs24(x0, x1, ty_Ordering)
new_esEs16(Char(x0), Char(x1))
new_lt7(x0, x1, ty_Bool)
new_primEqInt(Neg(Zero), Pos(Zero))
new_primEqInt(Pos(Zero), Neg(Zero))
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
new_ltEs14(LT, EQ)
new_ltEs14(EQ, LT)
new_compare16(x0, x1, False)
new_compare14(x0, x1)
new_esEs24(x0, x1, ty_Integer)
new_ltEs18(Just(x0), Just(x1), ty_Bool)
new_esEs27(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs27(x0, x1, app(ty_[], x2))
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_lt20(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs29(x0, x1, ty_Float)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs7(Left(x0), Left(x1), ty_Bool, x2)
new_lt19(x0, x1, ty_Int)
new_primEqInt(Neg(Zero), Neg(Zero))
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_compare7(:%(x0, x1), :%(x2, x3), ty_Integer)
new_esEs8(Just(x0), Just(x1), app(ty_Ratio, x2))
new_compare16(x0, x1, True)
new_esEs28(x0, x1, ty_Ordering)
new_primCompAux0(x0, EQ)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_foldFM_LE12(x0, x1, x2, x3, x4, x5, False, x6, x7)
new_esEs8(Just(x0), Nothing, x1)
new_ltEs13(Left(x0), Left(x1), app(ty_[], x2), x3)
new_lt20(x0, x1, ty_Float)
new_compare10(x0, x1)
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_lt7(x0, x1, ty_Float)
new_esEs8(Just(x0), Just(x1), app(ty_[], x2))
new_esEs7(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_compare11(Double(x0, x1), Double(x2, x3))
new_esEs28(x0, x1, ty_Double)
new_primCompAux0(x0, LT)
new_ltEs11(x0, x1, app(ty_[], x2))
new_lt17(x0, x1)
new_ltEs11(x0, x1, ty_Bool)
new_ltEs18(Just(x0), Nothing, x1)
new_ltEs13(Left(x0), Left(x1), ty_Ordering, x2)
new_compare24(x0, x1, True, x2, x3, x4)
new_esEs7(Right(x0), Right(x1), x2, ty_Char)
new_ltEs18(Just(x0), Just(x1), ty_Float)
new_compare17(Integer(x0), Integer(x1))
new_ltEs18(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, ty_Char)
new_lt8(x0, x1)
new_primEqNat0(Succ(x0), Zero)
new_esEs28(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs9(LT)
new_lt15(x0, x1, x2)
new_esEs7(Left(x0), Left(x1), ty_@0, x2)
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_esEs24(x0, x1, ty_Int)
new_primEqNat0(Zero, Succ(x0))
new_esEs22(x0, x1, ty_Double)
new_esEs7(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs24(x0, x1, ty_Float)
new_esEs22(x0, x1, ty_Int)
new_esEs7(Left(x0), Left(x1), ty_Integer, x2)
new_ltEs18(Just(x0), Just(x1), ty_Char)
new_primPlusNat0(Zero, x0)
new_ltEs18(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs14(EQ, GT)
new_ltEs14(GT, EQ)
new_esEs22(x0, x1, ty_Bool)
new_esEs22(x0, x1, ty_Ordering)
new_lt19(x0, x1, ty_Double)
new_lt7(x0, x1, app(app(ty_@2, x2), x3))
new_primCmpNat0(Zero, Zero)
new_lt10(x0, x1, x2, x3)
new_esEs8(Just(x0), Just(x1), ty_Int)
new_esEs7(Right(x0), Right(x1), x2, app(ty_[], x3))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_compare26(x0, x1, False)
new_ltEs11(x0, x1, ty_Int)
new_esEs12(Float(x0, x1), Float(x2, x3))
new_primCompAux0(x0, GT)
new_esEs28(x0, x1, ty_Int)
new_ltEs13(Left(x0), Left(x1), ty_Float, x2)
new_esEs29(x0, x1, ty_Integer)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_compare111(x0, x1, False, x2, x3)
new_lt13(x0, x1)
new_esEs28(x0, x1, ty_@0)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_lt19(x0, x1, ty_@0)
new_foldFM_LE12(x0, x1, x2, x3, x4, Branch(x5, x6, x7, x8, x9), True, x10, x11)
new_esEs24(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs23(x0, x1, ty_Ordering)
new_lt12(x0, x1)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs19(x0, x1, ty_Double)
new_lt7(x0, x1, app(ty_Ratio, x2))
new_ltEs18(Just(x0), Just(x1), ty_Int)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_lt7(x0, x1, ty_@0)
new_esEs26(x0, x1, ty_Int)
new_esEs18(LT, EQ)
new_esEs18(EQ, LT)
new_ltEs19(x0, x1, app(ty_[], x2))
new_ltEs19(x0, x1, ty_Bool)
new_ltEs14(LT, GT)
new_ltEs14(GT, LT)
new_esEs23(x0, x1, ty_Float)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs7(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs29(x0, x1, ty_Bool)
new_esEs21(x0, x1, ty_Integer)
new_compare30(x0, x1, ty_Float)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_esEs8(Just(x0), Just(x1), ty_Bool)
new_lt19(x0, x1, ty_Char)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_compare18(x0, x1, False, x2, x3, x4)
new_ltEs13(Right(x0), Right(x1), x2, ty_Float)
new_esEs8(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs7(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs22(x0, x1, ty_@0)
new_esEs5(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs23(x0, x1, ty_Char)
new_ltEs14(GT, GT)
new_compare30(x0, x1, app(ty_Maybe, x2))
new_esEs27(x0, x1, ty_Double)
new_esEs27(x0, x1, ty_Float)
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs18(Just(x0), Just(x1), ty_@0)
new_esEs24(x0, x1, ty_Char)
new_not(EQ)
new_esEs8(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_foldFM_LE5(x0, Branch(x1, x2, x3, x4, x5), x6, x7)
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_ltEs13(Right(x0), Left(x1), x2, x3)
new_compare30(x0, x1, app(ty_Ratio, x2))
new_ltEs13(Left(x0), Right(x1), x2, x3)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_ltEs11(x0, x1, app(ty_Ratio, x2))
new_esEs15(Integer(x0), Integer(x1))
new_esEs7(Right(x0), Right(x1), x2, ty_Bool)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_lt6(x0, x1)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, ty_Bool)
new_esEs29(x0, x1, ty_Double)
new_compare19(x0, x1, x2, x3, x4)
new_lt19(x0, x1, ty_Bool)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_esEs7(Right(x0), Right(x1), x2, ty_Double)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_esEs21(x0, x1, ty_Double)
new_ltEs13(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs7(Right(x0), Right(x1), x2, ty_Integer)
new_lt7(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs13(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_compare25(x0, x1, False, x2)
new_esEs22(x0, x1, ty_Integer)
new_ltEs13(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_ltEs15(x0, x1)
new_esEs7(Left(x0), Left(x1), ty_Ordering, x2)
new_lt20(x0, x1, ty_Integer)
new_ltEs12(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_ltEs10(@2(x0, x1), @2(x2, x3), x4, x5)
new_ltEs19(x0, x1, ty_Ordering)
new_esEs18(GT, LT)
new_esEs18(LT, GT)
new_ltEs13(Right(x0), Right(x1), x2, ty_Integer)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, ty_Ordering)
new_esEs26(x0, x1, ty_Integer)
new_lt20(x0, x1, ty_Int)
new_esEs11(:(x0, x1), [], x2)
new_lt19(x0, x1, ty_Float)
new_ltEs13(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs13(Right(x0), Right(x1), x2, ty_Char)
new_esEs17(False, True)
new_esEs17(True, False)
new_ltEs13(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs21(x0, x1, app(ty_[], x2))
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs11(x0, x1, ty_Ordering)
new_ltEs13(Left(x0), Left(x1), ty_Int, x2)
new_ltEs13(Right(x0), Right(x1), x2, ty_Ordering)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sr0(Integer(x0), Integer(x1))
new_esEs23(x0, x1, ty_Int)
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs22(x0, x1, ty_Float)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, ty_Ordering)
new_ltEs13(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs17(x0, x1)
new_esEs28(x0, x1, ty_Float)
new_esEs7(Right(x0), Right(x1), x2, ty_Ordering)
new_lt18(x0, x1, x2)
new_primEqInt(Pos(Zero), Pos(Zero))
new_esEs17(True, True)
new_ltEs11(x0, x1, ty_@0)
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare15(x0, x1, False, x2)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_ltEs18(Just(x0), Just(x1), ty_Integer)
new_ltEs19(x0, x1, ty_@0)
new_ltEs13(Right(x0), Right(x1), x2, ty_@0)
new_compare23(x0, x1, False, x2, x3)
new_pePe(True, x0, x1, x2, x3)
new_asAs(True, x0)
new_ltEs13(Right(x0), Right(x1), x2, ty_Double)
new_compare30(x0, x1, ty_Char)
new_esEs13(Double(x0, x1), Double(x2, x3))
new_esEs7(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs8(Just(x0), Just(x1), app(ty_Maybe, x2))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs21(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs24(x0, x1, ty_Double)
new_compare30(x0, x1, app(ty_[], x2))
new_compare30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_pePe(False, x0, x1, x2, x3)
new_compare30(x0, x1, ty_Integer)
new_not(LT)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, ty_Integer)
new_compare30(x0, x1, ty_Ordering)
new_foldFM_LE30(x0, x1, x2, x3, x4)
new_compare24(x0, x1, False, x2, x3, x4)
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
We have to consider all minimal (P,Q,R)-chains.
As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [15] we can delete all non-usable rules [17] from R.
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QReductionProof
Q DP problem:
The TRS P consists of the following rules:
new_foldFM_LE11(vyy24, vyy340, vyy341, vyy342, vyy343, Branch(vyy3440, vyy3441, vyy3442, vyy3443, vyy3444), True, h, ba) → new_foldFM_LE4(vyy24, vyy343, h, ba)
new_foldFM_LE11(vyy24, vyy340, vyy341, vyy342, Branch(vyy3430, vyy3431, vyy3432, vyy3433, vyy3434), vyy344, False, h, ba) → new_foldFM_LE11(vyy24, vyy3430, vyy3431, vyy3432, vyy3433, vyy3434, new_ltEs18(vyy3430, Nothing, h), h, ba)
new_foldFM_LE21(vyy340, vyy341, vyy28, vyy3440, vyy3441, vyy3442, vyy3443, vyy3444, h, ba) → new_foldFM_LE11(new_fmToList_LE0(vyy340, vyy341, vyy28, h, ba), vyy3440, vyy3441, vyy3442, vyy3443, vyy3444, new_ltEs18(vyy3440, Nothing, h), h, ba)
new_foldFM_LE4(vyy24, Branch(vyy3430, vyy3431, vyy3432, vyy3433, vyy3434), h, ba) → new_foldFM_LE11(vyy24, vyy3430, vyy3431, vyy3432, vyy3433, vyy3434, new_ltEs18(vyy3430, Nothing, h), h, ba)
new_foldFM_LE11(vyy24, vyy340, vyy341, vyy342, vyy343, Branch(vyy3440, vyy3441, vyy3442, vyy3443, vyy3444), True, h, ba) → new_foldFM_LE21(vyy340, vyy341, new_foldFM_LE5(vyy24, vyy343, h, ba), vyy3440, vyy3441, vyy3442, vyy3443, vyy3444, h, ba)
new_foldFM_LE11(vyy24, vyy340, vyy341, vyy342, vyy343, EmptyFM, True, h, ba) → new_foldFM_LE4(vyy24, vyy343, h, ba)
The TRS R consists of the following rules:
new_ltEs18(Nothing, Nothing, cda) → True
new_ltEs18(Just(vyy3000), Nothing, cda) → False
new_foldFM_LE22(vyy340, vyy341, vyy28, vyy3440, vyy3441, vyy3442, vyy3443, vyy3444, h, ba) → new_foldFM_LE12(new_fmToList_LE0(vyy340, vyy341, vyy28, h, ba), vyy3440, vyy3441, vyy3442, vyy3443, vyy3444, new_ltEs18(vyy3440, Nothing, h), h, ba)
new_foldFM_LE12(vyy24, vyy340, vyy341, vyy342, vyy343, Branch(vyy3440, vyy3441, vyy3442, vyy3443, vyy3444), True, h, ba) → new_foldFM_LE22(vyy340, vyy341, new_foldFM_LE5(vyy24, vyy343, h, ba), vyy3440, vyy3441, vyy3442, vyy3443, vyy3444, h, ba)
new_foldFM_LE12(vyy24, vyy340, vyy341, vyy342, vyy343, vyy344, False, h, ba) → new_foldFM_LE5(vyy24, vyy343, h, ba)
new_foldFM_LE5(vyy24, Branch(vyy3430, vyy3431, vyy3432, vyy3433, vyy3434), h, ba) → new_foldFM_LE12(vyy24, vyy3430, vyy3431, vyy3432, vyy3433, vyy3434, new_ltEs18(vyy3430, Nothing, h), h, ba)
new_foldFM_LE5(vyy24, EmptyFM, h, ba) → vyy24
new_fmToList_LE0(vyy340, vyy341, vyy27, h, ba) → :(@2(vyy340, vyy341), vyy27)
new_foldFM_LE12(vyy24, vyy340, vyy341, vyy342, vyy343, EmptyFM, True, h, ba) → new_foldFM_LE30(vyy340, vyy341, new_foldFM_LE5(vyy24, vyy343, h, ba), h, ba)
new_foldFM_LE30(vyy340, vyy341, vyy27, h, ba) → new_fmToList_LE0(vyy340, vyy341, vyy27, h, ba)
The set Q consists of the following terms:
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs18(Just(x0), Just(x1), ty_Double)
new_compare30(x0, x1, ty_Int)
new_compare111(x0, x1, True, x2, x3)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs7(Left(x0), Right(x1), x2, x3)
new_esEs7(Right(x0), Left(x1), x2, x3)
new_foldFM2(EmptyFM, x0, x1)
new_ltEs19(x0, x1, ty_Char)
new_lt16(x0, x1)
new_compare4(:(x0, x1), [], x2)
new_ltEs13(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_primEqNat0(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_compare18(x0, x1, True, x2, x3, x4)
new_ltEs13(Left(x0), Left(x1), ty_Integer, x2)
new_esEs18(LT, LT)
new_ltEs5(x0, x1, x2)
new_ltEs11(x0, x1, ty_Integer)
new_compare110(x0, x1, False)
new_lt7(x0, x1, app(ty_[], x2))
new_ltEs13(Left(x0), Left(x1), ty_Char, x2)
new_esEs9(EQ)
new_compare26(x0, x1, True)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_ltEs18(Just(x0), Just(x1), ty_Ordering)
new_compare30(x0, x1, ty_Bool)
new_compare30(x0, x1, ty_@0)
new_primMulNat0(Zero, Succ(x0))
new_esEs29(x0, x1, ty_Ordering)
new_foldFM_LE22(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9)
new_esEs8(Just(x0), Just(x1), app(app(ty_FiniteMap, x2), x3))
new_primCmpNat0(Zero, Succ(x0))
new_primCmpNat0(Succ(x0), Zero)
new_esEs8(Just(x0), Just(x1), ty_@0)
new_esEs7(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs28(x0, x1, ty_Integer)
new_compare6(x0, x1)
new_esEs7(Left(x0), Left(x1), ty_Double, x2)
new_ltEs8(x0, x1)
new_ltEs19(x0, x1, ty_Float)
new_compare7(:%(x0, x1), :%(x2, x3), ty_Int)
new_lt19(x0, x1, app(ty_Maybe, x2))
new_compare9(x0, x1, x2, x3)
new_compare15(x0, x1, True, x2)
new_ltEs13(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_ltEs11(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs29(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, ty_Double)
new_compare29(x0, x1, True, x2, x3)
new_esEs7(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs7(Left(x0), Left(x1), ty_Char, x2)
new_lt19(x0, x1, ty_Integer)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_lt20(x0, x1, app(ty_[], x2))
new_esEs7(Right(x0), Right(x1), x2, ty_Int)
new_compare30(x0, x1, ty_Double)
new_asAs(False, x0)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs27(x0, x1, ty_Bool)
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_primCompAux1(x0, x1, x2, x3)
new_ltEs4(x0, x1, x2)
new_esEs7(Left(x0), Left(x1), ty_Int, x2)
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_esEs18(EQ, GT)
new_esEs18(GT, EQ)
new_esEs27(x0, x1, ty_Int)
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs7(Right(x0), Right(x1), x2, ty_@0)
new_esEs17(False, False)
new_ltEs18(Just(x0), Just(x1), app(ty_Maybe, x2))
new_ltEs11(x0, x1, ty_Char)
new_esEs8(Nothing, Just(x0), x1)
new_sr(x0, x1)
new_compare8(@0, @0)
new_esEs25(x0, x1, ty_Int)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs18(EQ, EQ)
new_compare28(x0, x1, x2)
new_esEs8(Just(x0), Just(x1), ty_Float)
new_compare27(x0, x1, True)
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_FiniteMap, x3), x4))
new_ltEs18(Just(x0), Just(x1), app(ty_Ratio, x2))
new_compare29(x0, x1, False, x2, x3)
new_esEs28(x0, x1, ty_Char)
new_esEs8(Just(x0), Just(x1), ty_Ordering)
new_compare112(x0, x1, False, x2, x3)
new_ltEs11(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs18(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs29(x0, x1, ty_Char)
new_esEs22(x0, x1, ty_Char)
new_compare25(x0, x1, True, x2)
new_ltEs14(EQ, EQ)
new_primEqNat0(Zero, Zero)
new_ltEs11(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpNat0(Succ(x0), Succ(x1))
new_ltEs18(Nothing, Nothing, x0)
new_lt19(x0, x1, app(ty_[], x2))
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_esEs25(x0, x1, ty_Integer)
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs13(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs29(x0, x1, ty_Int)
new_lt20(x0, x1, ty_@0)
new_lt7(x0, x1, ty_Double)
new_fmToList(x0, x1, x2)
new_lt7(x0, x1, app(ty_Maybe, x2))
new_ltEs9(False, False)
new_ltEs19(x0, x1, ty_Int)
new_esEs22(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_compare112(x0, x1, True, x2, x3)
new_lt20(x0, x1, ty_Char)
new_esEs23(x0, x1, ty_Integer)
new_primPlusNat1(Zero, Succ(x0))
new_primMulNat0(Zero, Zero)
new_primMulInt(Pos(x0), Pos(x1))
new_lt7(x0, x1, ty_Char)
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, ty_Float)
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, ty_@0)
new_compare4([], :(x0, x1), x2)
new_lt7(x0, x1, app(app(ty_Either, x2), x3))
new_esEs6(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs24(x0, x1, ty_Bool)
new_compare30(x0, x1, app(app(ty_Either, x2), x3))
new_esEs7(Left(x0), Left(x1), ty_Float, x2)
new_esEs8(Just(x0), Just(x1), ty_Integer)
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare4(:(x0, x1), :(x2, x3), x4)
new_primPlusNat1(Succ(x0), Zero)
new_lt7(x0, x1, ty_Ordering)
new_ltEs18(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs22(x0, x1, app(ty_[], x2))
new_ltEs13(Left(x0), Left(x1), ty_Bool, x2)
new_primMulNat0(Succ(x0), Succ(x1))
new_esEs21(x0, x1, ty_@0)
new_esEs28(x0, x1, ty_Bool)
new_compare30(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs13(Right(x0), Right(x1), x2, ty_Int)
new_ltEs16(x0, x1)
new_esEs29(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs23(x0, x1, ty_Double)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs11(x0, x1, app(ty_Maybe, x2))
new_esEs21(x0, x1, ty_Int)
new_esEs11(:(x0, x1), :(x2, x3), x4)
new_lt11(x0, x1, x2, x3)
new_lt14(x0, x1)
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_sizeFM(EmptyFM, x0, x1)
new_esEs27(x0, x1, ty_@0)
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
new_esEs11([], [], x0)
new_lt19(x0, x1, app(ty_Ratio, x2))
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_lt19(x0, x1, ty_Ordering)
new_esEs21(x0, x1, ty_Char)
new_compare23(x0, x1, True, x2, x3)
new_esEs7(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs8(Just(x0), Just(x1), ty_Char)
new_ltEs6(x0, x1)
new_foldFM_LE5(x0, EmptyFM, x1, x2)
new_compare4([], [], x0)
new_esEs23(x0, x1, app(ty_[], x2))
new_lt9(x0, x1, x2, x3, x4)
new_lt20(x0, x1, ty_Bool)
new_ltEs11(x0, x1, ty_Float)
new_compare31(x0, x1, x2, x3)
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_lt7(x0, x1, ty_Int)
new_lt4(x0, x1, x2)
new_primPlusNat0(Succ(x0), x1)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, ty_Integer)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs7(Left(x0), Left(x1), app(app(ty_FiniteMap, x2), x3), x4)
new_esEs20(x0, x1, x2, x3)
new_compare27(x0, x1, False)
new_primPlusNat1(Zero, Zero)
new_esEs8(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_not0
new_esEs29(x0, x1, ty_@0)
new_primMulNat0(Succ(x0), Zero)
new_esEs21(x0, x1, ty_Bool)
new_foldFM_LE12(x0, x1, x2, x3, x4, EmptyFM, True, x5, x6)
new_esEs27(x0, x1, ty_Ordering)
new_compare13(Char(x0), Char(x1))
new_esEs9(GT)
new_ltEs14(LT, LT)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs19(x0, x1)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_lt7(x0, x1, ty_Integer)
new_esEs14(:%(x0, x1), :%(x2, x3), x4)
new_esEs24(x0, x1, ty_@0)
new_ltEs7(x0, x1)
new_compare110(x0, x1, True)
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs13(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs7(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs18(GT, GT)
new_esEs11([], :(x0, x1), x2)
new_esEs7(Right(x0), Right(x1), x2, ty_Float)
new_esEs24(x0, x1, app(ty_[], x2))
new_ltEs11(x0, x1, ty_Double)
new_ltEs13(Left(x0), Left(x1), ty_@0, x2)
new_ltEs13(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs9(False, True)
new_ltEs9(True, False)
new_lt5(x0, x1)
new_compare12(Float(x0, x1), Float(x2, x3))
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_ltEs9(True, True)
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_ltEs18(Nothing, Just(x0), x1)
new_esEs10(@0, @0)
new_esEs28(x0, x1, app(ty_[], x2))
new_not(GT)
new_fmToList_LE0(x0, x1, x2, x3, x4)
new_ltEs13(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_ltEs13(Left(x0), Left(x1), ty_Double, x2)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_esEs8(Just(x0), Just(x1), ty_Double)
new_esEs8(Nothing, Nothing, x0)
new_esEs24(x0, x1, ty_Ordering)
new_esEs16(Char(x0), Char(x1))
new_lt7(x0, x1, ty_Bool)
new_primEqInt(Neg(Zero), Pos(Zero))
new_primEqInt(Pos(Zero), Neg(Zero))
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
new_ltEs14(LT, EQ)
new_ltEs14(EQ, LT)
new_compare16(x0, x1, False)
new_compare14(x0, x1)
new_esEs24(x0, x1, ty_Integer)
new_ltEs18(Just(x0), Just(x1), ty_Bool)
new_esEs27(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs27(x0, x1, app(ty_[], x2))
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_lt20(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs29(x0, x1, ty_Float)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs7(Left(x0), Left(x1), ty_Bool, x2)
new_lt19(x0, x1, ty_Int)
new_primEqInt(Neg(Zero), Neg(Zero))
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_compare7(:%(x0, x1), :%(x2, x3), ty_Integer)
new_esEs8(Just(x0), Just(x1), app(ty_Ratio, x2))
new_compare16(x0, x1, True)
new_esEs28(x0, x1, ty_Ordering)
new_primCompAux0(x0, EQ)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_foldFM_LE12(x0, x1, x2, x3, x4, x5, False, x6, x7)
new_esEs8(Just(x0), Nothing, x1)
new_ltEs13(Left(x0), Left(x1), app(ty_[], x2), x3)
new_lt20(x0, x1, ty_Float)
new_compare10(x0, x1)
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_lt7(x0, x1, ty_Float)
new_esEs8(Just(x0), Just(x1), app(ty_[], x2))
new_esEs7(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_compare11(Double(x0, x1), Double(x2, x3))
new_esEs28(x0, x1, ty_Double)
new_primCompAux0(x0, LT)
new_ltEs11(x0, x1, app(ty_[], x2))
new_lt17(x0, x1)
new_ltEs11(x0, x1, ty_Bool)
new_ltEs18(Just(x0), Nothing, x1)
new_ltEs13(Left(x0), Left(x1), ty_Ordering, x2)
new_compare24(x0, x1, True, x2, x3, x4)
new_esEs7(Right(x0), Right(x1), x2, ty_Char)
new_ltEs18(Just(x0), Just(x1), ty_Float)
new_compare17(Integer(x0), Integer(x1))
new_ltEs18(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, ty_Char)
new_lt8(x0, x1)
new_primEqNat0(Succ(x0), Zero)
new_esEs28(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs9(LT)
new_lt15(x0, x1, x2)
new_esEs7(Left(x0), Left(x1), ty_@0, x2)
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_esEs24(x0, x1, ty_Int)
new_primEqNat0(Zero, Succ(x0))
new_esEs22(x0, x1, ty_Double)
new_esEs7(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs24(x0, x1, ty_Float)
new_esEs22(x0, x1, ty_Int)
new_esEs7(Left(x0), Left(x1), ty_Integer, x2)
new_ltEs18(Just(x0), Just(x1), ty_Char)
new_primPlusNat0(Zero, x0)
new_ltEs18(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs14(EQ, GT)
new_ltEs14(GT, EQ)
new_esEs22(x0, x1, ty_Bool)
new_esEs22(x0, x1, ty_Ordering)
new_lt19(x0, x1, ty_Double)
new_lt7(x0, x1, app(app(ty_@2, x2), x3))
new_primCmpNat0(Zero, Zero)
new_lt10(x0, x1, x2, x3)
new_esEs8(Just(x0), Just(x1), ty_Int)
new_esEs7(Right(x0), Right(x1), x2, app(ty_[], x3))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_compare26(x0, x1, False)
new_ltEs11(x0, x1, ty_Int)
new_esEs12(Float(x0, x1), Float(x2, x3))
new_primCompAux0(x0, GT)
new_esEs28(x0, x1, ty_Int)
new_ltEs13(Left(x0), Left(x1), ty_Float, x2)
new_esEs29(x0, x1, ty_Integer)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_compare111(x0, x1, False, x2, x3)
new_lt13(x0, x1)
new_esEs28(x0, x1, ty_@0)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_lt19(x0, x1, ty_@0)
new_foldFM_LE12(x0, x1, x2, x3, x4, Branch(x5, x6, x7, x8, x9), True, x10, x11)
new_esEs24(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs23(x0, x1, ty_Ordering)
new_lt12(x0, x1)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs19(x0, x1, ty_Double)
new_lt7(x0, x1, app(ty_Ratio, x2))
new_ltEs18(Just(x0), Just(x1), ty_Int)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_lt7(x0, x1, ty_@0)
new_esEs26(x0, x1, ty_Int)
new_esEs18(LT, EQ)
new_esEs18(EQ, LT)
new_ltEs19(x0, x1, app(ty_[], x2))
new_ltEs19(x0, x1, ty_Bool)
new_ltEs14(LT, GT)
new_ltEs14(GT, LT)
new_esEs23(x0, x1, ty_Float)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs7(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs29(x0, x1, ty_Bool)
new_esEs21(x0, x1, ty_Integer)
new_compare30(x0, x1, ty_Float)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_esEs8(Just(x0), Just(x1), ty_Bool)
new_lt19(x0, x1, ty_Char)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_compare18(x0, x1, False, x2, x3, x4)
new_ltEs13(Right(x0), Right(x1), x2, ty_Float)
new_esEs8(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs7(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs22(x0, x1, ty_@0)
new_esEs5(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs23(x0, x1, ty_Char)
new_ltEs14(GT, GT)
new_compare30(x0, x1, app(ty_Maybe, x2))
new_esEs27(x0, x1, ty_Double)
new_esEs27(x0, x1, ty_Float)
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs18(Just(x0), Just(x1), ty_@0)
new_esEs24(x0, x1, ty_Char)
new_not(EQ)
new_esEs8(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_foldFM_LE5(x0, Branch(x1, x2, x3, x4, x5), x6, x7)
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_ltEs13(Right(x0), Left(x1), x2, x3)
new_compare30(x0, x1, app(ty_Ratio, x2))
new_ltEs13(Left(x0), Right(x1), x2, x3)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_ltEs11(x0, x1, app(ty_Ratio, x2))
new_esEs15(Integer(x0), Integer(x1))
new_esEs7(Right(x0), Right(x1), x2, ty_Bool)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_lt6(x0, x1)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, ty_Bool)
new_esEs29(x0, x1, ty_Double)
new_compare19(x0, x1, x2, x3, x4)
new_lt19(x0, x1, ty_Bool)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_esEs7(Right(x0), Right(x1), x2, ty_Double)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_esEs21(x0, x1, ty_Double)
new_ltEs13(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs7(Right(x0), Right(x1), x2, ty_Integer)
new_lt7(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs13(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_compare25(x0, x1, False, x2)
new_esEs22(x0, x1, ty_Integer)
new_ltEs13(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_ltEs15(x0, x1)
new_esEs7(Left(x0), Left(x1), ty_Ordering, x2)
new_lt20(x0, x1, ty_Integer)
new_ltEs12(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_ltEs10(@2(x0, x1), @2(x2, x3), x4, x5)
new_ltEs19(x0, x1, ty_Ordering)
new_esEs18(GT, LT)
new_esEs18(LT, GT)
new_ltEs13(Right(x0), Right(x1), x2, ty_Integer)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, ty_Ordering)
new_esEs26(x0, x1, ty_Integer)
new_lt20(x0, x1, ty_Int)
new_esEs11(:(x0, x1), [], x2)
new_lt19(x0, x1, ty_Float)
new_ltEs13(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs13(Right(x0), Right(x1), x2, ty_Char)
new_esEs17(False, True)
new_esEs17(True, False)
new_ltEs13(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs21(x0, x1, app(ty_[], x2))
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs11(x0, x1, ty_Ordering)
new_ltEs13(Left(x0), Left(x1), ty_Int, x2)
new_ltEs13(Right(x0), Right(x1), x2, ty_Ordering)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sr0(Integer(x0), Integer(x1))
new_esEs23(x0, x1, ty_Int)
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs22(x0, x1, ty_Float)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, ty_Ordering)
new_ltEs13(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs17(x0, x1)
new_esEs28(x0, x1, ty_Float)
new_esEs7(Right(x0), Right(x1), x2, ty_Ordering)
new_lt18(x0, x1, x2)
new_primEqInt(Pos(Zero), Pos(Zero))
new_esEs17(True, True)
new_ltEs11(x0, x1, ty_@0)
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare15(x0, x1, False, x2)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_ltEs18(Just(x0), Just(x1), ty_Integer)
new_ltEs19(x0, x1, ty_@0)
new_ltEs13(Right(x0), Right(x1), x2, ty_@0)
new_compare23(x0, x1, False, x2, x3)
new_pePe(True, x0, x1, x2, x3)
new_asAs(True, x0)
new_ltEs13(Right(x0), Right(x1), x2, ty_Double)
new_compare30(x0, x1, ty_Char)
new_esEs13(Double(x0, x1), Double(x2, x3))
new_esEs7(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs8(Just(x0), Just(x1), app(ty_Maybe, x2))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs21(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs24(x0, x1, ty_Double)
new_compare30(x0, x1, app(ty_[], x2))
new_compare30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_pePe(False, x0, x1, x2, x3)
new_compare30(x0, x1, ty_Integer)
new_not(LT)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, ty_Integer)
new_compare30(x0, x1, ty_Ordering)
new_foldFM_LE30(x0, x1, x2, x3, x4)
new_compare24(x0, x1, False, x2, x3, x4)
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
We have to consider all minimal (P,Q,R)-chains.
We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_compare30(x0, x1, ty_Int)
new_compare111(x0, x1, True, x2, x3)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs7(Left(x0), Right(x1), x2, x3)
new_esEs7(Right(x0), Left(x1), x2, x3)
new_foldFM2(EmptyFM, x0, x1)
new_ltEs19(x0, x1, ty_Char)
new_lt16(x0, x1)
new_compare4(:(x0, x1), [], x2)
new_ltEs13(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_primEqNat0(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_compare18(x0, x1, True, x2, x3, x4)
new_ltEs13(Left(x0), Left(x1), ty_Integer, x2)
new_esEs18(LT, LT)
new_ltEs5(x0, x1, x2)
new_ltEs11(x0, x1, ty_Integer)
new_compare110(x0, x1, False)
new_lt7(x0, x1, app(ty_[], x2))
new_ltEs13(Left(x0), Left(x1), ty_Char, x2)
new_esEs9(EQ)
new_compare26(x0, x1, True)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_compare30(x0, x1, ty_Bool)
new_compare30(x0, x1, ty_@0)
new_primMulNat0(Zero, Succ(x0))
new_esEs29(x0, x1, ty_Ordering)
new_esEs8(Just(x0), Just(x1), app(app(ty_FiniteMap, x2), x3))
new_primCmpNat0(Zero, Succ(x0))
new_primCmpNat0(Succ(x0), Zero)
new_esEs8(Just(x0), Just(x1), ty_@0)
new_esEs7(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs28(x0, x1, ty_Integer)
new_compare6(x0, x1)
new_esEs7(Left(x0), Left(x1), ty_Double, x2)
new_ltEs8(x0, x1)
new_ltEs19(x0, x1, ty_Float)
new_compare7(:%(x0, x1), :%(x2, x3), ty_Int)
new_lt19(x0, x1, app(ty_Maybe, x2))
new_compare9(x0, x1, x2, x3)
new_compare15(x0, x1, True, x2)
new_ltEs13(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_ltEs11(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs29(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, ty_Double)
new_compare29(x0, x1, True, x2, x3)
new_esEs7(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs7(Left(x0), Left(x1), ty_Char, x2)
new_lt19(x0, x1, ty_Integer)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_lt20(x0, x1, app(ty_[], x2))
new_esEs7(Right(x0), Right(x1), x2, ty_Int)
new_compare30(x0, x1, ty_Double)
new_asAs(False, x0)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs27(x0, x1, ty_Bool)
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_primCompAux1(x0, x1, x2, x3)
new_ltEs4(x0, x1, x2)
new_esEs7(Left(x0), Left(x1), ty_Int, x2)
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_esEs18(EQ, GT)
new_esEs18(GT, EQ)
new_esEs27(x0, x1, ty_Int)
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs7(Right(x0), Right(x1), x2, ty_@0)
new_esEs17(False, False)
new_ltEs11(x0, x1, ty_Char)
new_esEs8(Nothing, Just(x0), x1)
new_sr(x0, x1)
new_compare8(@0, @0)
new_esEs25(x0, x1, ty_Int)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs18(EQ, EQ)
new_compare28(x0, x1, x2)
new_esEs8(Just(x0), Just(x1), ty_Float)
new_compare27(x0, x1, True)
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_FiniteMap, x3), x4))
new_compare29(x0, x1, False, x2, x3)
new_esEs28(x0, x1, ty_Char)
new_esEs8(Just(x0), Just(x1), ty_Ordering)
new_compare112(x0, x1, False, x2, x3)
new_ltEs11(x0, x1, app(app(ty_@2, x2), x3))
new_esEs29(x0, x1, ty_Char)
new_esEs22(x0, x1, ty_Char)
new_compare25(x0, x1, True, x2)
new_ltEs14(EQ, EQ)
new_primEqNat0(Zero, Zero)
new_ltEs11(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpNat0(Succ(x0), Succ(x1))
new_lt19(x0, x1, app(ty_[], x2))
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_esEs25(x0, x1, ty_Integer)
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs13(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs29(x0, x1, ty_Int)
new_lt20(x0, x1, ty_@0)
new_lt7(x0, x1, ty_Double)
new_fmToList(x0, x1, x2)
new_lt7(x0, x1, app(ty_Maybe, x2))
new_ltEs9(False, False)
new_ltEs19(x0, x1, ty_Int)
new_esEs22(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_compare112(x0, x1, True, x2, x3)
new_lt20(x0, x1, ty_Char)
new_esEs23(x0, x1, ty_Integer)
new_primPlusNat1(Zero, Succ(x0))
new_primMulNat0(Zero, Zero)
new_primMulInt(Pos(x0), Pos(x1))
new_lt7(x0, x1, ty_Char)
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, ty_Float)
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, ty_@0)
new_compare4([], :(x0, x1), x2)
new_lt7(x0, x1, app(app(ty_Either, x2), x3))
new_esEs6(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs24(x0, x1, ty_Bool)
new_compare30(x0, x1, app(app(ty_Either, x2), x3))
new_esEs7(Left(x0), Left(x1), ty_Float, x2)
new_esEs8(Just(x0), Just(x1), ty_Integer)
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare4(:(x0, x1), :(x2, x3), x4)
new_primPlusNat1(Succ(x0), Zero)
new_lt7(x0, x1, ty_Ordering)
new_esEs22(x0, x1, app(ty_[], x2))
new_ltEs13(Left(x0), Left(x1), ty_Bool, x2)
new_primMulNat0(Succ(x0), Succ(x1))
new_esEs21(x0, x1, ty_@0)
new_esEs28(x0, x1, ty_Bool)
new_compare30(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs13(Right(x0), Right(x1), x2, ty_Int)
new_ltEs16(x0, x1)
new_esEs29(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs23(x0, x1, ty_Double)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs11(x0, x1, app(ty_Maybe, x2))
new_esEs21(x0, x1, ty_Int)
new_esEs11(:(x0, x1), :(x2, x3), x4)
new_lt11(x0, x1, x2, x3)
new_lt14(x0, x1)
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_sizeFM(EmptyFM, x0, x1)
new_esEs27(x0, x1, ty_@0)
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
new_esEs11([], [], x0)
new_lt19(x0, x1, app(ty_Ratio, x2))
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_lt19(x0, x1, ty_Ordering)
new_esEs21(x0, x1, ty_Char)
new_compare23(x0, x1, True, x2, x3)
new_esEs7(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs8(Just(x0), Just(x1), ty_Char)
new_ltEs6(x0, x1)
new_compare4([], [], x0)
new_esEs23(x0, x1, app(ty_[], x2))
new_lt9(x0, x1, x2, x3, x4)
new_lt20(x0, x1, ty_Bool)
new_ltEs11(x0, x1, ty_Float)
new_compare31(x0, x1, x2, x3)
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_lt7(x0, x1, ty_Int)
new_lt4(x0, x1, x2)
new_primPlusNat0(Succ(x0), x1)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, ty_Integer)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs7(Left(x0), Left(x1), app(app(ty_FiniteMap, x2), x3), x4)
new_esEs20(x0, x1, x2, x3)
new_compare27(x0, x1, False)
new_primPlusNat1(Zero, Zero)
new_esEs8(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_not0
new_esEs29(x0, x1, ty_@0)
new_primMulNat0(Succ(x0), Zero)
new_esEs21(x0, x1, ty_Bool)
new_esEs27(x0, x1, ty_Ordering)
new_compare13(Char(x0), Char(x1))
new_esEs9(GT)
new_ltEs14(LT, LT)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs19(x0, x1)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_lt7(x0, x1, ty_Integer)
new_esEs14(:%(x0, x1), :%(x2, x3), x4)
new_esEs24(x0, x1, ty_@0)
new_ltEs7(x0, x1)
new_compare110(x0, x1, True)
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs13(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs7(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs18(GT, GT)
new_esEs11([], :(x0, x1), x2)
new_esEs7(Right(x0), Right(x1), x2, ty_Float)
new_esEs24(x0, x1, app(ty_[], x2))
new_ltEs11(x0, x1, ty_Double)
new_ltEs13(Left(x0), Left(x1), ty_@0, x2)
new_ltEs13(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs9(False, True)
new_ltEs9(True, False)
new_lt5(x0, x1)
new_compare12(Float(x0, x1), Float(x2, x3))
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_ltEs9(True, True)
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_esEs10(@0, @0)
new_esEs28(x0, x1, app(ty_[], x2))
new_not(GT)
new_ltEs13(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_ltEs13(Left(x0), Left(x1), ty_Double, x2)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_esEs8(Just(x0), Just(x1), ty_Double)
new_esEs8(Nothing, Nothing, x0)
new_esEs24(x0, x1, ty_Ordering)
new_esEs16(Char(x0), Char(x1))
new_lt7(x0, x1, ty_Bool)
new_primEqInt(Neg(Zero), Pos(Zero))
new_primEqInt(Pos(Zero), Neg(Zero))
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
new_ltEs14(LT, EQ)
new_ltEs14(EQ, LT)
new_compare16(x0, x1, False)
new_compare14(x0, x1)
new_esEs24(x0, x1, ty_Integer)
new_esEs27(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs27(x0, x1, app(ty_[], x2))
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_lt20(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs29(x0, x1, ty_Float)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs7(Left(x0), Left(x1), ty_Bool, x2)
new_lt19(x0, x1, ty_Int)
new_primEqInt(Neg(Zero), Neg(Zero))
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_compare7(:%(x0, x1), :%(x2, x3), ty_Integer)
new_esEs8(Just(x0), Just(x1), app(ty_Ratio, x2))
new_compare16(x0, x1, True)
new_esEs28(x0, x1, ty_Ordering)
new_primCompAux0(x0, EQ)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_esEs8(Just(x0), Nothing, x1)
new_ltEs13(Left(x0), Left(x1), app(ty_[], x2), x3)
new_lt20(x0, x1, ty_Float)
new_compare10(x0, x1)
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_lt7(x0, x1, ty_Float)
new_esEs8(Just(x0), Just(x1), app(ty_[], x2))
new_esEs7(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_compare11(Double(x0, x1), Double(x2, x3))
new_esEs28(x0, x1, ty_Double)
new_primCompAux0(x0, LT)
new_ltEs11(x0, x1, app(ty_[], x2))
new_lt17(x0, x1)
new_ltEs11(x0, x1, ty_Bool)
new_ltEs13(Left(x0), Left(x1), ty_Ordering, x2)
new_compare24(x0, x1, True, x2, x3, x4)
new_esEs7(Right(x0), Right(x1), x2, ty_Char)
new_compare17(Integer(x0), Integer(x1))
new_esEs27(x0, x1, ty_Char)
new_lt8(x0, x1)
new_primEqNat0(Succ(x0), Zero)
new_esEs28(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs9(LT)
new_lt15(x0, x1, x2)
new_esEs7(Left(x0), Left(x1), ty_@0, x2)
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_esEs24(x0, x1, ty_Int)
new_primEqNat0(Zero, Succ(x0))
new_esEs22(x0, x1, ty_Double)
new_esEs7(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs24(x0, x1, ty_Float)
new_esEs22(x0, x1, ty_Int)
new_esEs7(Left(x0), Left(x1), ty_Integer, x2)
new_primPlusNat0(Zero, x0)
new_ltEs14(EQ, GT)
new_ltEs14(GT, EQ)
new_esEs22(x0, x1, ty_Bool)
new_esEs22(x0, x1, ty_Ordering)
new_lt19(x0, x1, ty_Double)
new_lt7(x0, x1, app(app(ty_@2, x2), x3))
new_primCmpNat0(Zero, Zero)
new_lt10(x0, x1, x2, x3)
new_esEs8(Just(x0), Just(x1), ty_Int)
new_esEs7(Right(x0), Right(x1), x2, app(ty_[], x3))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_compare26(x0, x1, False)
new_ltEs11(x0, x1, ty_Int)
new_esEs12(Float(x0, x1), Float(x2, x3))
new_primCompAux0(x0, GT)
new_esEs28(x0, x1, ty_Int)
new_ltEs13(Left(x0), Left(x1), ty_Float, x2)
new_esEs29(x0, x1, ty_Integer)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_compare111(x0, x1, False, x2, x3)
new_lt13(x0, x1)
new_esEs28(x0, x1, ty_@0)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_lt19(x0, x1, ty_@0)
new_esEs24(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs23(x0, x1, ty_Ordering)
new_lt12(x0, x1)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs19(x0, x1, ty_Double)
new_lt7(x0, x1, app(ty_Ratio, x2))
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_lt7(x0, x1, ty_@0)
new_esEs26(x0, x1, ty_Int)
new_esEs18(LT, EQ)
new_esEs18(EQ, LT)
new_ltEs19(x0, x1, app(ty_[], x2))
new_ltEs19(x0, x1, ty_Bool)
new_ltEs14(LT, GT)
new_ltEs14(GT, LT)
new_esEs23(x0, x1, ty_Float)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs7(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs29(x0, x1, ty_Bool)
new_esEs21(x0, x1, ty_Integer)
new_compare30(x0, x1, ty_Float)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_esEs8(Just(x0), Just(x1), ty_Bool)
new_lt19(x0, x1, ty_Char)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_compare18(x0, x1, False, x2, x3, x4)
new_ltEs13(Right(x0), Right(x1), x2, ty_Float)
new_esEs8(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs7(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs22(x0, x1, ty_@0)
new_esEs5(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs23(x0, x1, ty_Char)
new_ltEs14(GT, GT)
new_compare30(x0, x1, app(ty_Maybe, x2))
new_esEs27(x0, x1, ty_Double)
new_esEs27(x0, x1, ty_Float)
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs24(x0, x1, ty_Char)
new_not(EQ)
new_esEs8(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_ltEs13(Right(x0), Left(x1), x2, x3)
new_compare30(x0, x1, app(ty_Ratio, x2))
new_ltEs13(Left(x0), Right(x1), x2, x3)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_ltEs11(x0, x1, app(ty_Ratio, x2))
new_esEs15(Integer(x0), Integer(x1))
new_esEs7(Right(x0), Right(x1), x2, ty_Bool)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_lt6(x0, x1)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, ty_Bool)
new_esEs29(x0, x1, ty_Double)
new_compare19(x0, x1, x2, x3, x4)
new_lt19(x0, x1, ty_Bool)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_esEs7(Right(x0), Right(x1), x2, ty_Double)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_esEs21(x0, x1, ty_Double)
new_ltEs13(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs7(Right(x0), Right(x1), x2, ty_Integer)
new_lt7(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs13(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_compare25(x0, x1, False, x2)
new_esEs22(x0, x1, ty_Integer)
new_ltEs13(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_ltEs15(x0, x1)
new_esEs7(Left(x0), Left(x1), ty_Ordering, x2)
new_lt20(x0, x1, ty_Integer)
new_ltEs12(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_ltEs10(@2(x0, x1), @2(x2, x3), x4, x5)
new_ltEs19(x0, x1, ty_Ordering)
new_esEs18(GT, LT)
new_esEs18(LT, GT)
new_ltEs13(Right(x0), Right(x1), x2, ty_Integer)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, ty_Ordering)
new_esEs26(x0, x1, ty_Integer)
new_lt20(x0, x1, ty_Int)
new_esEs11(:(x0, x1), [], x2)
new_lt19(x0, x1, ty_Float)
new_ltEs13(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs13(Right(x0), Right(x1), x2, ty_Char)
new_esEs17(False, True)
new_esEs17(True, False)
new_ltEs13(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs21(x0, x1, app(ty_[], x2))
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs11(x0, x1, ty_Ordering)
new_ltEs13(Left(x0), Left(x1), ty_Int, x2)
new_ltEs13(Right(x0), Right(x1), x2, ty_Ordering)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sr0(Integer(x0), Integer(x1))
new_esEs23(x0, x1, ty_Int)
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs22(x0, x1, ty_Float)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, ty_Ordering)
new_ltEs13(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs17(x0, x1)
new_esEs28(x0, x1, ty_Float)
new_esEs7(Right(x0), Right(x1), x2, ty_Ordering)
new_lt18(x0, x1, x2)
new_primEqInt(Pos(Zero), Pos(Zero))
new_esEs17(True, True)
new_ltEs11(x0, x1, ty_@0)
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare15(x0, x1, False, x2)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_ltEs19(x0, x1, ty_@0)
new_ltEs13(Right(x0), Right(x1), x2, ty_@0)
new_compare23(x0, x1, False, x2, x3)
new_pePe(True, x0, x1, x2, x3)
new_asAs(True, x0)
new_ltEs13(Right(x0), Right(x1), x2, ty_Double)
new_compare30(x0, x1, ty_Char)
new_esEs13(Double(x0, x1), Double(x2, x3))
new_esEs7(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs8(Just(x0), Just(x1), app(ty_Maybe, x2))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs21(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs24(x0, x1, ty_Double)
new_compare30(x0, x1, app(ty_[], x2))
new_compare30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_pePe(False, x0, x1, x2, x3)
new_compare30(x0, x1, ty_Integer)
new_not(LT)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, ty_Integer)
new_compare30(x0, x1, ty_Ordering)
new_compare24(x0, x1, False, x2, x3, x4)
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QReductionProof
↳ QDP
↳ QDPSizeChangeProof
Q DP problem:
The TRS P consists of the following rules:
new_foldFM_LE11(vyy24, vyy340, vyy341, vyy342, vyy343, Branch(vyy3440, vyy3441, vyy3442, vyy3443, vyy3444), True, h, ba) → new_foldFM_LE4(vyy24, vyy343, h, ba)
new_foldFM_LE11(vyy24, vyy340, vyy341, vyy342, Branch(vyy3430, vyy3431, vyy3432, vyy3433, vyy3434), vyy344, False, h, ba) → new_foldFM_LE11(vyy24, vyy3430, vyy3431, vyy3432, vyy3433, vyy3434, new_ltEs18(vyy3430, Nothing, h), h, ba)
new_foldFM_LE21(vyy340, vyy341, vyy28, vyy3440, vyy3441, vyy3442, vyy3443, vyy3444, h, ba) → new_foldFM_LE11(new_fmToList_LE0(vyy340, vyy341, vyy28, h, ba), vyy3440, vyy3441, vyy3442, vyy3443, vyy3444, new_ltEs18(vyy3440, Nothing, h), h, ba)
new_foldFM_LE11(vyy24, vyy340, vyy341, vyy342, vyy343, Branch(vyy3440, vyy3441, vyy3442, vyy3443, vyy3444), True, h, ba) → new_foldFM_LE21(vyy340, vyy341, new_foldFM_LE5(vyy24, vyy343, h, ba), vyy3440, vyy3441, vyy3442, vyy3443, vyy3444, h, ba)
new_foldFM_LE4(vyy24, Branch(vyy3430, vyy3431, vyy3432, vyy3433, vyy3434), h, ba) → new_foldFM_LE11(vyy24, vyy3430, vyy3431, vyy3432, vyy3433, vyy3434, new_ltEs18(vyy3430, Nothing, h), h, ba)
new_foldFM_LE11(vyy24, vyy340, vyy341, vyy342, vyy343, EmptyFM, True, h, ba) → new_foldFM_LE4(vyy24, vyy343, h, ba)
The TRS R consists of the following rules:
new_ltEs18(Nothing, Nothing, cda) → True
new_ltEs18(Just(vyy3000), Nothing, cda) → False
new_foldFM_LE22(vyy340, vyy341, vyy28, vyy3440, vyy3441, vyy3442, vyy3443, vyy3444, h, ba) → new_foldFM_LE12(new_fmToList_LE0(vyy340, vyy341, vyy28, h, ba), vyy3440, vyy3441, vyy3442, vyy3443, vyy3444, new_ltEs18(vyy3440, Nothing, h), h, ba)
new_foldFM_LE12(vyy24, vyy340, vyy341, vyy342, vyy343, Branch(vyy3440, vyy3441, vyy3442, vyy3443, vyy3444), True, h, ba) → new_foldFM_LE22(vyy340, vyy341, new_foldFM_LE5(vyy24, vyy343, h, ba), vyy3440, vyy3441, vyy3442, vyy3443, vyy3444, h, ba)
new_foldFM_LE12(vyy24, vyy340, vyy341, vyy342, vyy343, vyy344, False, h, ba) → new_foldFM_LE5(vyy24, vyy343, h, ba)
new_foldFM_LE5(vyy24, Branch(vyy3430, vyy3431, vyy3432, vyy3433, vyy3434), h, ba) → new_foldFM_LE12(vyy24, vyy3430, vyy3431, vyy3432, vyy3433, vyy3434, new_ltEs18(vyy3430, Nothing, h), h, ba)
new_foldFM_LE5(vyy24, EmptyFM, h, ba) → vyy24
new_fmToList_LE0(vyy340, vyy341, vyy27, h, ba) → :(@2(vyy340, vyy341), vyy27)
new_foldFM_LE12(vyy24, vyy340, vyy341, vyy342, vyy343, EmptyFM, True, h, ba) → new_foldFM_LE30(vyy340, vyy341, new_foldFM_LE5(vyy24, vyy343, h, ba), h, ba)
new_foldFM_LE30(vyy340, vyy341, vyy27, h, ba) → new_fmToList_LE0(vyy340, vyy341, vyy27, h, ba)
The set Q consists of the following terms:
new_ltEs18(Just(x0), Just(x1), ty_Double)
new_ltEs18(Just(x0), Just(x1), ty_Ordering)
new_foldFM_LE22(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9)
new_ltEs18(Just(x0), Just(x1), app(ty_Maybe, x2))
new_ltEs18(Just(x0), Just(x1), app(ty_Ratio, x2))
new_ltEs18(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs18(Nothing, Nothing, x0)
new_ltEs18(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_foldFM_LE5(x0, EmptyFM, x1, x2)
new_foldFM_LE12(x0, x1, x2, x3, x4, EmptyFM, True, x5, x6)
new_ltEs18(Nothing, Just(x0), x1)
new_fmToList_LE0(x0, x1, x2, x3, x4)
new_ltEs18(Just(x0), Just(x1), ty_Bool)
new_foldFM_LE12(x0, x1, x2, x3, x4, x5, False, x6, x7)
new_ltEs18(Just(x0), Nothing, x1)
new_ltEs18(Just(x0), Just(x1), ty_Float)
new_ltEs18(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_ltEs18(Just(x0), Just(x1), ty_Char)
new_ltEs18(Just(x0), Just(x1), app(ty_[], x2))
new_foldFM_LE12(x0, x1, x2, x3, x4, Branch(x5, x6, x7, x8, x9), True, x10, x11)
new_ltEs18(Just(x0), Just(x1), ty_Int)
new_ltEs18(Just(x0), Just(x1), ty_@0)
new_foldFM_LE5(x0, Branch(x1, x2, x3, x4, x5), x6, x7)
new_ltEs18(Just(x0), Just(x1), ty_Integer)
new_foldFM_LE30(x0, x1, x2, x3, x4)
We have to consider all minimal (P,Q,R)-chains.
By using the subterm criterion [20] together with the size-change analysis [32] we have proven that there are no infinite chains for this DP problem. From the DPs we obtained the following set of size-change graphs:
- new_foldFM_LE4(vyy24, Branch(vyy3430, vyy3431, vyy3432, vyy3433, vyy3434), h, ba) → new_foldFM_LE11(vyy24, vyy3430, vyy3431, vyy3432, vyy3433, vyy3434, new_ltEs18(vyy3430, Nothing, h), h, ba)
The graph contains the following edges 1 >= 1, 2 > 2, 2 > 3, 2 > 4, 2 > 5, 2 > 6, 3 >= 8, 4 >= 9
- new_foldFM_LE11(vyy24, vyy340, vyy341, vyy342, Branch(vyy3430, vyy3431, vyy3432, vyy3433, vyy3434), vyy344, False, h, ba) → new_foldFM_LE11(vyy24, vyy3430, vyy3431, vyy3432, vyy3433, vyy3434, new_ltEs18(vyy3430, Nothing, h), h, ba)
The graph contains the following edges 1 >= 1, 5 > 2, 5 > 3, 5 > 4, 5 > 5, 5 > 6, 8 >= 8, 9 >= 9
- new_foldFM_LE21(vyy340, vyy341, vyy28, vyy3440, vyy3441, vyy3442, vyy3443, vyy3444, h, ba) → new_foldFM_LE11(new_fmToList_LE0(vyy340, vyy341, vyy28, h, ba), vyy3440, vyy3441, vyy3442, vyy3443, vyy3444, new_ltEs18(vyy3440, Nothing, h), h, ba)
The graph contains the following edges 4 >= 2, 5 >= 3, 6 >= 4, 7 >= 5, 8 >= 6, 9 >= 8, 10 >= 9
- new_foldFM_LE11(vyy24, vyy340, vyy341, vyy342, vyy343, Branch(vyy3440, vyy3441, vyy3442, vyy3443, vyy3444), True, h, ba) → new_foldFM_LE21(vyy340, vyy341, new_foldFM_LE5(vyy24, vyy343, h, ba), vyy3440, vyy3441, vyy3442, vyy3443, vyy3444, h, ba)
The graph contains the following edges 2 >= 1, 3 >= 2, 6 > 4, 6 > 5, 6 > 6, 6 > 7, 6 > 8, 8 >= 9, 9 >= 10
- new_foldFM_LE11(vyy24, vyy340, vyy341, vyy342, vyy343, Branch(vyy3440, vyy3441, vyy3442, vyy3443, vyy3444), True, h, ba) → new_foldFM_LE4(vyy24, vyy343, h, ba)
The graph contains the following edges 1 >= 1, 5 >= 2, 8 >= 3, 9 >= 4
- new_foldFM_LE11(vyy24, vyy340, vyy341, vyy342, vyy343, EmptyFM, True, h, ba) → new_foldFM_LE4(vyy24, vyy343, h, ba)
The graph contains the following edges 1 >= 1, 5 >= 2, 8 >= 3, 9 >= 4