YES 8.513
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
|
| ((foldFM_LE :: Ord b => (Maybe b -> a -> c -> c) -> c -> Maybe b -> FiniteMap (Maybe b) a -> c) :: Ord b => (Maybe b -> a -> c -> c) -> c -> Maybe b -> FiniteMap (Maybe b) a -> c) |
module FiniteMap where
| | import qualified Maybe
import qualified Prelude
|
| | data FiniteMap b a = EmptyFM | Branch b a Int (FiniteMap b a) (FiniteMap b a)
|
| | instance (Eq a, Eq b) => Eq (FiniteMap 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 |
|
| | 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 -> 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
|
Lambda Reductions:
The following Lambda expression
\keyeltrest→(key,elt) : rest
is transformed to
| fmToList0 | key elt rest | = (key,elt) : rest |
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
mainModule FiniteMap
|
| ((foldFM_LE :: Ord c => (Maybe c -> a -> b -> b) -> b -> Maybe c -> FiniteMap (Maybe c) a -> b) :: Ord c => (Maybe c -> a -> b -> b) -> b -> Maybe c -> FiniteMap (Maybe c) 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 |
|
| | 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 c => (c -> b -> a -> a) -> a -> c -> FiniteMap c b -> a
| foldFM_LE | k z fr EmptyFM | = | z |
| foldFM_LE | k z fr (Branch key elt _ fm_l fm_r) | |
| | | key <= fr | = |
| foldFM_LE k (k key elt (foldFM_LE k z fr fm_l)) fr fm_r |
|
| | | otherwise | = |
|
|
|
| | sizeFM :: FiniteMap 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
|
| ((foldFM_LE :: Ord b => (Maybe b -> c -> a -> a) -> a -> Maybe b -> FiniteMap (Maybe b) c -> a) :: Ord b => (Maybe b -> c -> a -> a) -> a -> Maybe b -> FiniteMap (Maybe b) c -> 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 a b -> [(a,b)]
| fmToList | fm | = | foldFM fmToList0 [] fm |
|
| |
| fmToList0 | key elt rest | = | (key,elt) : rest |
|
| | foldFM :: (c -> b -> a -> a) -> a -> FiniteMap c b -> a
| foldFM | k z EmptyFM | = | z |
| foldFM | k z (Branch key elt _ fm_l fm_r) | = | foldFM k (k key elt (foldFM k z fm_r)) fm_l |
|
| | foldFM_LE :: Ord c => (c -> b -> a -> a) -> a -> c -> FiniteMap c b -> a
| foldFM_LE | k z fr EmptyFM | = | z |
| foldFM_LE | k z fr (Branch key elt _ fm_l fm_r) | |
| | | key <= fr | = |
| foldFM_LE k (k key elt (foldFM_LE k z fr fm_l)) fr fm_r |
|
| | | otherwise | = |
|
|
|
| | sizeFM :: FiniteMap a b -> Int
| sizeFM | EmptyFM | = | 0 |
| sizeFM | (Branch _ _ size _ _) | = | size |
|
module Maybe where
| | import qualified FiniteMap
import qualified Prelude
|
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
|
| ((foldFM_LE :: Ord c => (Maybe c -> a -> b -> b) -> b -> Maybe c -> FiniteMap (Maybe c) a -> b) :: Ord c => (Maybe c -> a -> b -> b) -> b -> Maybe c -> FiniteMap (Maybe c) a -> b) |
module FiniteMap where
| | import qualified Maybe
import qualified Prelude
|
| | data FiniteMap a b = EmptyFM | Branch a b Int (FiniteMap a b) (FiniteMap a b)
|
| | instance (Eq a, Eq b) => Eq (FiniteMap b a) where
|
|
|
| (==) | fm_1 fm_2 | = | sizeFM fm_1 == sizeFM fm_2 && fmToList fm_1 == fmToList fm_2 |
|
|
| | fmToList :: FiniteMap a b -> [(a,b)]
| fmToList | fm | = | foldFM fmToList0 [] fm |
|
| |
| fmToList0 | key elt rest | = | (key,elt) : rest |
|
| | foldFM :: (a -> b -> c -> c) -> c -> FiniteMap a b -> c
| foldFM | k z EmptyFM | = | z |
| foldFM | k z (Branch key elt _ fm_l fm_r) | = | foldFM k (k key elt (foldFM k z fm_r)) fm_l |
|
| | foldFM_LE :: Ord 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 _ fm_l fm_r) | |
| | | key <= fr | = |
| foldFM_LE k (k key elt (foldFM_LE k z fr fm_l)) fr fm_r |
|
| | | otherwise | = |
|
|
|
| | sizeFM :: FiniteMap b a -> Int
| sizeFM | EmptyFM | = | 0 |
| sizeFM | (Branch _ _ size _ _) | = | size |
|
module Maybe where
| | import qualified FiniteMap
import qualified Prelude
|
Replaced joker patterns by fresh variables and removed binding patterns.
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
mainModule FiniteMap
|
| ((foldFM_LE :: Ord b => (Maybe b -> a -> c -> c) -> c -> Maybe b -> FiniteMap (Maybe b) a -> c) :: Ord b => (Maybe b -> a -> c -> c) -> c -> Maybe b -> FiniteMap (Maybe b) a -> c) |
module FiniteMap where
| | import qualified Maybe
import qualified Prelude
|
| | data FiniteMap b a = EmptyFM | Branch b a Int (FiniteMap b a) (FiniteMap b a)
|
| | instance (Eq a, Eq b) => Eq (FiniteMap 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 |
|
| | foldFM :: (a -> c -> b -> b) -> b -> FiniteMap a c -> b
| foldFM | k z EmptyFM | = | z |
| foldFM | k z (Branch key elt vw fm_l fm_r) | = | foldFM k (k key elt (foldFM k z fm_r)) fm_l |
|
| | foldFM_LE :: Ord c => (c -> b -> a -> a) -> a -> c -> FiniteMap c b -> a
| 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
| absReal0 | x True | = `negate` x |
| absReal1 | x True | = x |
| absReal1 | x False | = absReal0 x otherwise |
| absReal2 | x | = absReal1 x (x >= 0) |
The following Function with conditions
is transformed to
| undefined0 | True | = undefined |
| undefined1 | | = undefined0 False |
The following Function with conditions
| reduce | x y |
| | | y == 0 | |
| | | otherwise |
| = | x `quot` d :% (y `quot` d) |
|
|
| where | |
|
is transformed to
| reduce2 | x y | =
| reduce1 x y (y == 0) |
| where | |
|
| reduce0 | x y True | = x `quot` d :% (y `quot` d) |
|
|
| reduce1 | x y True | = error [] |
| reduce1 | x y False | = reduce0 x y otherwise |
|
|
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
mainModule FiniteMap
|
| ((foldFM_LE :: Ord b => (Maybe b -> c -> a -> a) -> a -> Maybe b -> FiniteMap (Maybe b) c -> a) :: Ord b => (Maybe b -> c -> a -> a) -> a -> Maybe b -> FiniteMap (Maybe b) c -> a) |
module FiniteMap where
| | import qualified Maybe
import qualified Prelude
|
| | data FiniteMap a b = EmptyFM | Branch a b Int (FiniteMap a b) (FiniteMap a b)
|
| | instance (Eq a, Eq b) => Eq (FiniteMap a b) where
|
|
|
| (==) | fm_1 fm_2 | = | sizeFM fm_1 == sizeFM fm_2 && fmToList fm_1 == fmToList fm_2 |
|
|
| | fmToList :: FiniteMap a b -> [(a,b)]
| fmToList | fm | = | foldFM fmToList0 [] fm |
|
| |
| fmToList0 | 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 b => (b -> c -> a -> a) -> a -> b -> FiniteMap b c -> a
| foldFM_LE | k z fr EmptyFM | = | foldFM_LE3 k z fr EmptyFM |
| foldFM_LE | k z fr (Branch key elt vx fm_l fm_r) | = | foldFM_LE2 k z fr (Branch key elt vx fm_l fm_r) |
|
| |
| foldFM_LE0 | k z fr key elt vx fm_l fm_r True | = | foldFM_LE k z fr fm_l |
|
| |
| foldFM_LE1 | k z fr key elt vx fm_l fm_r True | = | foldFM_LE k (k key elt (foldFM_LE k z fr fm_l)) fr fm_r |
| foldFM_LE1 | k z fr key elt vx fm_l fm_r False | = | foldFM_LE0 k z fr key elt vx fm_l fm_r otherwise |
|
| |
| foldFM_LE2 | k z fr (Branch key elt vx fm_l fm_r) | = | foldFM_LE1 k z fr key elt vx fm_l fm_r (key <= fr) |
|
| |
| foldFM_LE3 | k z fr EmptyFM | = | z |
| foldFM_LE3 | vvu vvv vvw vvx | = | foldFM_LE2 vvu vvv vvw vvx |
|
| | sizeFM :: FiniteMap b a -> Int
| sizeFM | EmptyFM | = | 0 |
| sizeFM | (Branch vy vz size wu wv) | = | size |
|
module Maybe where
| | import qualified FiniteMap
import qualified Prelude
|
Let/Where Reductions:
The bindings of the following Let/Where expression
| reduce1 x y (y == 0) |
| where | |
|
| reduce0 | x y True | = x `quot` d :% (y `quot` d) |
|
|
| reduce1 | x y True | = error [] |
| reduce1 | x y False | = reduce0 x y otherwise |
|
are unpacked to the following functions on top level
| reduce2Reduce0 | vyw vyx x y True | = x `quot` reduce2D vyw vyx :% (y `quot` reduce2D vyw vyx) |
| reduce2D | vyw vyx | = gcd vyw vyx |
| reduce2Reduce1 | vyw vyx x y True | = error [] |
| reduce2Reduce1 | vyw vyx x y False | = reduce2Reduce0 vyw vyx x y otherwise |
The bindings of the following Let/Where expression
| gcd' (abs x) (abs y) |
| where |
| gcd' | x vvy | = gcd'2 x vvy |
| gcd' | x y | = gcd'0 x y |
|
|
| gcd'0 | x y | = gcd' y (x `rem` y) |
|
|
| gcd'1 | True x vvy | = x |
| gcd'1 | vvz vwu vwv | = gcd'0 vwu vwv |
|
|
| gcd'2 | x vvy | = gcd'1 (vvy == 0) x vvy |
| gcd'2 | vww vwx | = gcd'0 vww vwx |
|
are unpacked to the following functions on top level
| gcd0Gcd'2 | x vvy | = gcd0Gcd'1 (vvy == 0) x vvy |
| gcd0Gcd'2 | vww vwx | = gcd0Gcd'0 vww vwx |
| gcd0Gcd' | x vvy | = gcd0Gcd'2 x vvy |
| gcd0Gcd' | x y | = gcd0Gcd'0 x y |
| gcd0Gcd'0 | x y | = gcd0Gcd' y (x `rem` y) |
| gcd0Gcd'1 | True x vvy | = x |
| gcd0Gcd'1 | vvz vwu vwv | = gcd0Gcd'0 vwu vwv |
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
mainModule FiniteMap
|
| ((foldFM_LE :: Ord c => (Maybe c -> b -> a -> a) -> a -> Maybe c -> FiniteMap (Maybe c) b -> a) :: Ord c => (Maybe c -> b -> a -> a) -> a -> Maybe c -> FiniteMap (Maybe c) 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 b a) where
|
|
|
| (==) | fm_1 fm_2 | = | sizeFM fm_1 == sizeFM fm_2 && fmToList fm_1 == fmToList fm_2 |
|
|
| | fmToList :: FiniteMap b a -> [(b,a)]
| fmToList | fm | = | foldFM fmToList0 [] fm |
|
| |
| fmToList0 | key elt rest | = | (key,elt) : rest |
|
| | 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 -> a -> b -> b) -> b -> c -> FiniteMap c a -> b
| foldFM_LE | k z fr EmptyFM | = | foldFM_LE3 k z fr EmptyFM |
| foldFM_LE | k z fr (Branch key elt vx fm_l fm_r) | = | foldFM_LE2 k z fr (Branch key elt vx fm_l fm_r) |
|
| |
| foldFM_LE0 | k z fr key elt vx fm_l fm_r True | = | foldFM_LE k z fr fm_l |
|
| |
| foldFM_LE1 | k z fr key elt vx fm_l fm_r True | = | foldFM_LE k (k key elt (foldFM_LE k z fr fm_l)) fr fm_r |
| foldFM_LE1 | k z fr key elt vx fm_l fm_r False | = | foldFM_LE0 k z fr key elt vx fm_l fm_r otherwise |
|
| |
| foldFM_LE2 | k z fr (Branch key elt vx fm_l fm_r) | = | foldFM_LE1 k z fr key elt vx fm_l fm_r (key <= fr) |
|
| |
| foldFM_LE3 | k z fr EmptyFM | = | z |
| foldFM_LE3 | vvu vvv vvw vvx | = | foldFM_LE2 vvu vvv vvw vvx |
|
| | sizeFM :: FiniteMap b a -> Int
| sizeFM | EmptyFM | = | 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
|
| (foldFM_LE :: Ord a => (Maybe a -> b -> c -> c) -> c -> Maybe a -> FiniteMap (Maybe a) b -> c) |
module FiniteMap where
| | import qualified Maybe
import qualified Prelude
|
| | data FiniteMap a b = EmptyFM | Branch a b Int (FiniteMap a b) (FiniteMap a b)
|
| | instance (Eq a, Eq b) => Eq (FiniteMap 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 |
|
| | 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
Q DP problem:
The TRS P consists of the following rules:
new_foldFM(vyy360, vyy361, vyy80, Branch(vyy3630, vyy3631, vyy3632, vyy3633, vyy3634), h, ba) → new_foldFM(vyy3630, vyy3631, new_foldFM0(vyy360, vyy361, vyy80, vyy3634, h, ba), vyy3633, h, ba)
new_foldFM(vyy360, vyy361, vyy80, Branch(vyy3630, vyy3631, vyy3632, vyy3633, vyy3634), h, ba) → new_foldFM(vyy360, vyy361, vyy80, vyy3634, h, ba)
The TRS R consists of the following rules:
new_foldFM0(vyy360, vyy361, vyy80, EmptyFM, h, ba) → :(@2(vyy360, vyy361), vyy80)
new_foldFM0(vyy360, vyy361, vyy80, Branch(vyy3630, vyy3631, vyy3632, vyy3633, vyy3634), h, ba) → new_foldFM0(vyy3630, vyy3631, new_foldFM0(vyy360, vyy361, vyy80, vyy3634, h, ba), vyy3633, h, ba)
The set Q consists of the following terms:
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
We have to consider all minimal (P,Q,R)-chains.
By using the subterm criterion [20] together with the size-change analysis [32] we have proven that there are no infinite chains for this DP problem. From the DPs we obtained the following set of size-change graphs:
- new_foldFM(vyy360, vyy361, vyy80, Branch(vyy3630, vyy3631, vyy3632, vyy3633, vyy3634), h, ba) → new_foldFM(vyy3630, vyy3631, new_foldFM0(vyy360, vyy361, vyy80, vyy3634, h, ba), vyy3633, h, ba)
The graph contains the following edges 4 > 1, 4 > 2, 4 > 4, 5 >= 5, 6 >= 6
- new_foldFM(vyy360, vyy361, vyy80, Branch(vyy3630, vyy3631, vyy3632, vyy3633, vyy3634), h, ba) → new_foldFM(vyy360, vyy361, vyy80, vyy3634, h, ba)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 > 4, 5 >= 5, 6 >= 6
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDPSizeChangeProof
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_foldFM1(Branch(vyy360, vyy361, vyy362, vyy363, vyy364), h, ba) → new_foldFM1(vyy364, 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(vyy360, vyy361, vyy362, vyy363, vyy364), h, ba) → new_foldFM1(vyy364, h, ba)
The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDPSizeChangeProof
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_primEqNat(Succ(vyy3500), Succ(vyy3600)) → new_primEqNat(vyy3500, vyy3600)
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(vyy3500), Succ(vyy3600)) → new_primEqNat(vyy3500, vyy3600)
The graph contains the following edges 1 > 1, 2 > 2
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDPSizeChangeProof
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_primPlusNat(Succ(vyy8100), Succ(vyy6001000)) → new_primPlusNat(vyy8100, vyy6001000)
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(vyy8100), Succ(vyy6001000)) → new_primPlusNat(vyy8100, vyy6001000)
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
Q DP problem:
The TRS P consists of the following rules:
new_primMulNat(Succ(vyy50000), Succ(vyy600100)) → new_primMulNat(vyy50000, Succ(vyy600100))
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(vyy50000), Succ(vyy600100)) → new_primMulNat(vyy50000, Succ(vyy600100))
The graph contains the following edges 1 > 1, 2 >= 2
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ Rewriting
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_esEs(Right(vyy350), Right(vyy360), cd, app(app(ty_@2, dg), dh)) → new_esEs4(vyy350, vyy360, dg, dh)
new_esEs4(@2(vyy350, vyy351), @2(vyy360, vyy361), app(app(ty_Either, bfc), bfd), bfe) → new_esEs(vyy350, vyy360, bfc, bfd)
new_esEs4(@2(vyy350, vyy351), @2(vyy360, vyy361), app(app(app(ty_@3, bff), bfg), bfh), bfe) → new_esEs0(vyy350, vyy360, bff, bfg, bfh)
new_esEs1(Just(vyy350), Just(vyy360), app(app(ty_Either, baf), bag)) → new_esEs(vyy350, vyy360, baf, bag)
new_esEs3(:(vyy350, vyy351), :(vyy360, vyy361), app(ty_[], bdd)) → new_esEs3(vyy350, vyy360, bdd)
new_esEs3(:(vyy350, vyy351), :(vyy360, vyy361), app(app(ty_@2, bde), bdf)) → new_esEs4(vyy350, vyy360, bde, bdf)
new_esEs1(Just(vyy350), Just(vyy360), app(app(app(ty_@3, bah), bba), bbb)) → new_esEs0(vyy350, vyy360, bah, bba, bbb)
new_esEs0(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), ea, eb, app(app(ty_Either, ec), ed)) → new_esEs(vyy352, vyy362, ec, ed)
new_esEs0(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), app(ty_[], bac), eb, ga) → new_esEs3(vyy350, vyy360, bac)
new_esEs4(@2(vyy350, vyy351), @2(vyy360, vyy361), app(ty_Maybe, bga), bfe) → new_esEs1(vyy350, vyy360, bga)
new_esEs1(Just(vyy350), Just(vyy360), app(ty_[], bbf)) → new_esEs3(vyy350, vyy360, bbf)
new_esEs3(:(vyy350, vyy351), :(vyy360, vyy361), app(app(app(ty_@3, bcf), bcg), bch)) → new_esEs0(vyy350, vyy360, bcf, bcg, bch)
new_esEs4(@2(vyy350, vyy351), @2(vyy360, vyy361), app(ty_[], bgd), bfe) → new_esEs3(vyy350, vyy360, bgd)
new_esEs4(@2(vyy350, vyy351), @2(vyy360, vyy361), bdg, app(app(ty_Either, bdh), bea)) → new_esEs(vyy351, vyy361, bdh, bea)
new_esEs0(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), app(app(ty_@2, bad), bae), eb, ga) → new_esEs4(vyy350, vyy360, bad, bae)
new_esEs(Left(vyy350), Left(vyy360), app(app(app(ty_@3, bc), bd), be), bb) → new_esEs0(vyy350, vyy360, bc, bd, be)
new_esEs(Right(vyy350), Right(vyy360), cd, app(app(ty_FiniteMap, dd), de)) → new_esEs2(vyy350, vyy360, dd, de)
new_esEs4(@2(vyy350, vyy351), @2(vyy360, vyy361), bdg, app(app(app(ty_@3, beb), bec), bed)) → new_esEs0(vyy351, vyy361, beb, bec, bed)
new_esEs3(:(vyy350, vyy351), :(vyy360, vyy361), bcc) → new_esEs3(vyy351, vyy361, bcc)
new_esEs(Left(vyy350), Left(vyy360), app(ty_[], ca), bb) → new_esEs3(vyy350, vyy360, ca)
new_esEs0(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), ea, app(ty_[], gh), ga) → new_esEs3(vyy351, vyy361, gh)
new_esEs4(@2(vyy350, vyy351), @2(vyy360, vyy361), bdg, app(app(ty_FiniteMap, bef), beg)) → new_esEs2(vyy351, vyy361, bef, beg)
new_esEs(Left(vyy350), Left(vyy360), app(ty_Maybe, bf), bb) → new_esEs1(vyy350, vyy360, bf)
new_esEs1(Just(vyy350), Just(vyy360), app(ty_Maybe, bbc)) → new_esEs1(vyy350, vyy360, bbc)
new_esEs4(@2(vyy350, vyy351), @2(vyy360, vyy361), bdg, app(ty_[], beh)) → new_esEs3(vyy351, vyy361, beh)
new_esEs(Left(vyy350), Left(vyy360), app(app(ty_@2, cb), cc), bb) → new_esEs4(vyy350, vyy360, cb, cc)
new_esEs1(Just(vyy350), Just(vyy360), app(app(ty_FiniteMap, bbd), bbe)) → new_esEs2(vyy350, vyy360, bbd, bbe)
new_esEs4(@2(vyy350, vyy351), @2(vyy360, vyy361), bdg, app(app(ty_@2, bfa), bfb)) → new_esEs4(vyy351, vyy361, bfa, bfb)
new_esEs(Right(vyy350), Right(vyy360), cd, app(ty_Maybe, dc)) → new_esEs1(vyy350, vyy360, dc)
new_esEs(Left(vyy350), Left(vyy360), app(app(ty_Either, h), ba), bb) → new_esEs(vyy350, vyy360, h, ba)
new_esEs(Left(vyy350), Left(vyy360), app(app(ty_FiniteMap, bg), bh), bb) → new_esEs2(vyy350, vyy360, bg, bh)
new_esEs3(:(vyy350, vyy351), :(vyy360, vyy361), app(app(ty_Either, bcd), bce)) → new_esEs(vyy350, vyy360, bcd, bce)
new_esEs0(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), ea, app(ty_Maybe, ge), ga) → new_esEs1(vyy351, vyy361, ge)
new_esEs3(:(vyy350, vyy351), :(vyy360, vyy361), app(ty_Maybe, bda)) → new_esEs1(vyy350, vyy360, bda)
new_esEs0(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), app(app(ty_Either, hc), hd), eb, ga) → new_esEs(vyy350, vyy360, hc, hd)
new_esEs0(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), ea, app(app(ty_FiniteMap, gf), gg), ga) → new_esEs2(vyy351, vyy361, gf, gg)
new_esEs1(Just(vyy350), Just(vyy360), app(app(ty_@2, bbg), bbh)) → new_esEs4(vyy350, vyy360, bbg, bbh)
new_esEs0(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), ea, eb, app(ty_[], fc)) → new_esEs3(vyy352, vyy362, fc)
new_esEs4(@2(vyy350, vyy351), @2(vyy360, vyy361), app(app(ty_@2, bge), bgf), bfe) → new_esEs4(vyy350, vyy360, bge, bgf)
new_esEs(Right(vyy350), Right(vyy360), cd, app(app(app(ty_@3, cg), da), db)) → new_esEs0(vyy350, vyy360, cg, da, db)
new_esEs0(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), ea, app(app(ty_@2, ha), hb), ga) → new_esEs4(vyy351, vyy361, ha, hb)
new_esEs0(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), ea, app(app(app(ty_@3, gb), gc), gd), ga) → new_esEs0(vyy351, vyy361, gb, gc, gd)
new_esEs4(@2(vyy350, vyy351), @2(vyy360, vyy361), bdg, app(ty_Maybe, bee)) → new_esEs1(vyy351, vyy361, bee)
new_esEs4(@2(vyy350, vyy351), @2(vyy360, vyy361), app(app(ty_FiniteMap, bgb), bgc), bfe) → new_esEs2(vyy350, vyy360, bgb, bgc)
new_esEs3(:(vyy350, vyy351), :(vyy360, vyy361), app(app(ty_FiniteMap, bdb), bdc)) → new_esEs2(vyy350, vyy360, bdb, bdc)
new_esEs(Right(vyy350), Right(vyy360), cd, app(app(ty_Either, ce), cf)) → new_esEs(vyy350, vyy360, ce, cf)
new_esEs0(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), app(app(ty_FiniteMap, baa), bab), eb, ga) → new_esEs2(vyy350, vyy360, baa, bab)
new_esEs(Right(vyy350), Right(vyy360), cd, app(ty_[], df)) → new_esEs3(vyy350, vyy360, df)
new_esEs0(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), ea, eb, app(app(app(ty_@3, ee), ef), eg)) → new_esEs0(vyy352, vyy362, ee, ef, eg)
new_esEs0(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), ea, eb, app(ty_Maybe, eh)) → new_esEs1(vyy352, vyy362, eh)
new_esEs0(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), ea, eb, app(app(ty_FiniteMap, fa), fb)) → new_esEs2(vyy352, vyy362, fa, fb)
new_esEs2(vyy35, vyy36, bca, bcb) → new_esEs3(new_fmToList(vyy35, bca, bcb), new_fmToList(vyy36, bca, bcb), app(app(ty_@2, bca), bcb))
new_esEs0(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), ea, app(app(ty_Either, fg), fh), ga) → new_esEs(vyy351, vyy361, fg, fh)
new_esEs0(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), app(ty_Maybe, hh), eb, ga) → new_esEs1(vyy350, vyy360, hh)
new_esEs0(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), app(app(app(ty_@3, he), hf), hg), eb, ga) → new_esEs0(vyy350, vyy360, he, hf, hg)
new_esEs0(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), ea, eb, app(app(ty_@2, fd), ff)) → new_esEs4(vyy352, vyy362, fd, ff)
The TRS R consists of the following rules:
new_foldFM0(vyy360, vyy361, vyy80, EmptyFM, bca, bcb) → :(@2(vyy360, vyy361), vyy80)
new_foldFM0(vyy360, vyy361, vyy80, Branch(vyy3630, vyy3631, vyy3632, vyy3633, vyy3634), bca, bcb) → new_foldFM0(vyy3630, vyy3631, new_foldFM0(vyy360, vyy361, vyy80, vyy3634, bca, bcb), vyy3633, bca, bcb)
new_fmToList(vyy36, bca, bcb) → new_foldFM2(vyy36, bca, bcb)
new_foldFM2(Branch(vyy360, vyy361, vyy362, vyy363, vyy364), bca, bcb) → new_foldFM0(vyy360, vyy361, new_foldFM2(vyy364, bca, bcb), vyy363, bca, bcb)
new_foldFM2(EmptyFM, bca, bcb) → []
The set Q consists of the following terms:
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
new_foldFM2(EmptyFM, x0, x1)
new_fmToList(x0, x1, x2)
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_esEs2(vyy35, vyy36, bca, bcb) → new_esEs3(new_fmToList(vyy35, bca, bcb), new_fmToList(vyy36, bca, bcb), app(app(ty_@2, bca), bcb)) at position [0] we obtained the following new rules:
new_esEs2(vyy35, vyy36, bca, bcb) → new_esEs3(new_foldFM2(vyy35, bca, bcb), new_fmToList(vyy36, bca, bcb), app(app(ty_@2, bca), bcb))
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ Rewriting
↳ QDP
↳ Rewriting
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_esEs(Right(vyy350), Right(vyy360), cd, app(app(ty_@2, dg), dh)) → new_esEs4(vyy350, vyy360, dg, dh)
new_esEs4(@2(vyy350, vyy351), @2(vyy360, vyy361), app(app(ty_Either, bfc), bfd), bfe) → new_esEs(vyy350, vyy360, bfc, bfd)
new_esEs3(:(vyy350, vyy351), :(vyy360, vyy361), app(app(ty_@2, bde), bdf)) → new_esEs4(vyy350, vyy360, bde, bdf)
new_esEs3(:(vyy350, vyy351), :(vyy360, vyy361), app(ty_[], bdd)) → new_esEs3(vyy350, vyy360, bdd)
new_esEs1(Just(vyy350), Just(vyy360), app(app(ty_Either, baf), bag)) → new_esEs(vyy350, vyy360, baf, bag)
new_esEs4(@2(vyy350, vyy351), @2(vyy360, vyy361), app(app(app(ty_@3, bff), bfg), bfh), bfe) → new_esEs0(vyy350, vyy360, bff, bfg, bfh)
new_esEs1(Just(vyy350), Just(vyy360), app(app(app(ty_@3, bah), bba), bbb)) → new_esEs0(vyy350, vyy360, bah, bba, bbb)
new_esEs0(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), app(ty_[], bac), eb, ga) → new_esEs3(vyy350, vyy360, bac)
new_esEs0(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), ea, eb, app(app(ty_Either, ec), ed)) → new_esEs(vyy352, vyy362, ec, ed)
new_esEs3(:(vyy350, vyy351), :(vyy360, vyy361), app(app(app(ty_@3, bcf), bcg), bch)) → new_esEs0(vyy350, vyy360, bcf, bcg, bch)
new_esEs1(Just(vyy350), Just(vyy360), app(ty_[], bbf)) → new_esEs3(vyy350, vyy360, bbf)
new_esEs4(@2(vyy350, vyy351), @2(vyy360, vyy361), app(ty_Maybe, bga), bfe) → new_esEs1(vyy350, vyy360, bga)
new_esEs4(@2(vyy350, vyy351), @2(vyy360, vyy361), app(ty_[], bgd), bfe) → new_esEs3(vyy350, vyy360, bgd)
new_esEs4(@2(vyy350, vyy351), @2(vyy360, vyy361), bdg, app(app(ty_Either, bdh), bea)) → new_esEs(vyy351, vyy361, bdh, bea)
new_esEs0(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), app(app(ty_@2, bad), bae), eb, ga) → new_esEs4(vyy350, vyy360, bad, bae)
new_esEs(Left(vyy350), Left(vyy360), app(app(app(ty_@3, bc), bd), be), bb) → new_esEs0(vyy350, vyy360, bc, bd, be)
new_esEs(Right(vyy350), Right(vyy360), cd, app(app(ty_FiniteMap, dd), de)) → new_esEs2(vyy350, vyy360, dd, de)
new_esEs4(@2(vyy350, vyy351), @2(vyy360, vyy361), bdg, app(app(app(ty_@3, beb), bec), bed)) → new_esEs0(vyy351, vyy361, beb, bec, bed)
new_esEs(Left(vyy350), Left(vyy360), app(ty_[], ca), bb) → new_esEs3(vyy350, vyy360, ca)
new_esEs3(:(vyy350, vyy351), :(vyy360, vyy361), bcc) → new_esEs3(vyy351, vyy361, bcc)
new_esEs0(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), ea, app(ty_[], gh), ga) → new_esEs3(vyy351, vyy361, gh)
new_esEs4(@2(vyy350, vyy351), @2(vyy360, vyy361), bdg, app(app(ty_FiniteMap, bef), beg)) → new_esEs2(vyy351, vyy361, bef, beg)
new_esEs(Left(vyy350), Left(vyy360), app(ty_Maybe, bf), bb) → new_esEs1(vyy350, vyy360, bf)
new_esEs1(Just(vyy350), Just(vyy360), app(ty_Maybe, bbc)) → new_esEs1(vyy350, vyy360, bbc)
new_esEs4(@2(vyy350, vyy351), @2(vyy360, vyy361), bdg, app(ty_[], beh)) → new_esEs3(vyy351, vyy361, beh)
new_esEs(Left(vyy350), Left(vyy360), app(app(ty_@2, cb), cc), bb) → new_esEs4(vyy350, vyy360, cb, cc)
new_esEs1(Just(vyy350), Just(vyy360), app(app(ty_FiniteMap, bbd), bbe)) → new_esEs2(vyy350, vyy360, bbd, bbe)
new_esEs4(@2(vyy350, vyy351), @2(vyy360, vyy361), bdg, app(app(ty_@2, bfa), bfb)) → new_esEs4(vyy351, vyy361, bfa, bfb)
new_esEs(Right(vyy350), Right(vyy360), cd, app(ty_Maybe, dc)) → new_esEs1(vyy350, vyy360, dc)
new_esEs(Left(vyy350), Left(vyy360), app(app(ty_Either, h), ba), bb) → new_esEs(vyy350, vyy360, h, ba)
new_esEs3(:(vyy350, vyy351), :(vyy360, vyy361), app(app(ty_Either, bcd), bce)) → new_esEs(vyy350, vyy360, bcd, bce)
new_esEs(Left(vyy350), Left(vyy360), app(app(ty_FiniteMap, bg), bh), bb) → new_esEs2(vyy350, vyy360, bg, bh)
new_esEs0(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), ea, app(ty_Maybe, ge), ga) → new_esEs1(vyy351, vyy361, ge)
new_esEs3(:(vyy350, vyy351), :(vyy360, vyy361), app(ty_Maybe, bda)) → new_esEs1(vyy350, vyy360, bda)
new_esEs1(Just(vyy350), Just(vyy360), app(app(ty_@2, bbg), bbh)) → new_esEs4(vyy350, vyy360, bbg, bbh)
new_esEs0(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), ea, app(app(ty_FiniteMap, gf), gg), ga) → new_esEs2(vyy351, vyy361, gf, gg)
new_esEs0(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), app(app(ty_Either, hc), hd), eb, ga) → new_esEs(vyy350, vyy360, hc, hd)
new_esEs0(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), ea, eb, app(ty_[], fc)) → new_esEs3(vyy352, vyy362, fc)
new_esEs(Right(vyy350), Right(vyy360), cd, app(app(app(ty_@3, cg), da), db)) → new_esEs0(vyy350, vyy360, cg, da, db)
new_esEs4(@2(vyy350, vyy351), @2(vyy360, vyy361), app(app(ty_@2, bge), bgf), bfe) → new_esEs4(vyy350, vyy360, bge, bgf)
new_esEs0(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), ea, app(app(ty_@2, ha), hb), ga) → new_esEs4(vyy351, vyy361, ha, hb)
new_esEs0(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), ea, app(app(app(ty_@3, gb), gc), gd), ga) → new_esEs0(vyy351, vyy361, gb, gc, gd)
new_esEs4(@2(vyy350, vyy351), @2(vyy360, vyy361), bdg, app(ty_Maybe, bee)) → new_esEs1(vyy351, vyy361, bee)
new_esEs3(:(vyy350, vyy351), :(vyy360, vyy361), app(app(ty_FiniteMap, bdb), bdc)) → new_esEs2(vyy350, vyy360, bdb, bdc)
new_esEs4(@2(vyy350, vyy351), @2(vyy360, vyy361), app(app(ty_FiniteMap, bgb), bgc), bfe) → new_esEs2(vyy350, vyy360, bgb, bgc)
new_esEs2(vyy35, vyy36, bca, bcb) → new_esEs3(new_foldFM2(vyy35, bca, bcb), new_fmToList(vyy36, bca, bcb), app(app(ty_@2, bca), bcb))
new_esEs(Right(vyy350), Right(vyy360), cd, app(app(ty_Either, ce), cf)) → new_esEs(vyy350, vyy360, ce, cf)
new_esEs0(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), app(app(ty_FiniteMap, baa), bab), eb, ga) → new_esEs2(vyy350, vyy360, baa, bab)
new_esEs(Right(vyy350), Right(vyy360), cd, app(ty_[], df)) → new_esEs3(vyy350, vyy360, df)
new_esEs0(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), ea, eb, app(ty_Maybe, eh)) → new_esEs1(vyy352, vyy362, eh)
new_esEs0(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), ea, eb, app(app(app(ty_@3, ee), ef), eg)) → new_esEs0(vyy352, vyy362, ee, ef, eg)
new_esEs0(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), ea, eb, app(app(ty_FiniteMap, fa), fb)) → new_esEs2(vyy352, vyy362, fa, fb)
new_esEs0(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), ea, app(app(ty_Either, fg), fh), ga) → new_esEs(vyy351, vyy361, fg, fh)
new_esEs0(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), app(ty_Maybe, hh), eb, ga) → new_esEs1(vyy350, vyy360, hh)
new_esEs0(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), ea, eb, app(app(ty_@2, fd), ff)) → new_esEs4(vyy352, vyy362, fd, ff)
new_esEs0(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), app(app(app(ty_@3, he), hf), hg), eb, ga) → new_esEs0(vyy350, vyy360, he, hf, hg)
The TRS R consists of the following rules:
new_foldFM0(vyy360, vyy361, vyy80, EmptyFM, bca, bcb) → :(@2(vyy360, vyy361), vyy80)
new_foldFM0(vyy360, vyy361, vyy80, Branch(vyy3630, vyy3631, vyy3632, vyy3633, vyy3634), bca, bcb) → new_foldFM0(vyy3630, vyy3631, new_foldFM0(vyy360, vyy361, vyy80, vyy3634, bca, bcb), vyy3633, bca, bcb)
new_fmToList(vyy36, bca, bcb) → new_foldFM2(vyy36, bca, bcb)
new_foldFM2(Branch(vyy360, vyy361, vyy362, vyy363, vyy364), bca, bcb) → new_foldFM0(vyy360, vyy361, new_foldFM2(vyy364, bca, bcb), vyy363, bca, bcb)
new_foldFM2(EmptyFM, bca, bcb) → []
The set Q consists of the following terms:
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
new_foldFM2(EmptyFM, x0, x1)
new_fmToList(x0, x1, x2)
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_esEs2(vyy35, vyy36, bca, bcb) → new_esEs3(new_foldFM2(vyy35, bca, bcb), new_fmToList(vyy36, bca, bcb), app(app(ty_@2, bca), bcb)) at position [1] we obtained the following new rules:
new_esEs2(vyy35, vyy36, bca, bcb) → new_esEs3(new_foldFM2(vyy35, bca, bcb), new_foldFM2(vyy36, bca, bcb), app(app(ty_@2, bca), bcb))
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ Rewriting
↳ QDP
↳ Rewriting
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_esEs(Right(vyy350), Right(vyy360), cd, app(app(ty_@2, dg), dh)) → new_esEs4(vyy350, vyy360, dg, dh)
new_esEs4(@2(vyy350, vyy351), @2(vyy360, vyy361), app(app(ty_Either, bfc), bfd), bfe) → new_esEs(vyy350, vyy360, bfc, bfd)
new_esEs4(@2(vyy350, vyy351), @2(vyy360, vyy361), app(app(app(ty_@3, bff), bfg), bfh), bfe) → new_esEs0(vyy350, vyy360, bff, bfg, bfh)
new_esEs1(Just(vyy350), Just(vyy360), app(app(ty_Either, baf), bag)) → new_esEs(vyy350, vyy360, baf, bag)
new_esEs3(:(vyy350, vyy351), :(vyy360, vyy361), app(ty_[], bdd)) → new_esEs3(vyy350, vyy360, bdd)
new_esEs3(:(vyy350, vyy351), :(vyy360, vyy361), app(app(ty_@2, bde), bdf)) → new_esEs4(vyy350, vyy360, bde, bdf)
new_esEs1(Just(vyy350), Just(vyy360), app(app(app(ty_@3, bah), bba), bbb)) → new_esEs0(vyy350, vyy360, bah, bba, bbb)
new_esEs0(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), ea, eb, app(app(ty_Either, ec), ed)) → new_esEs(vyy352, vyy362, ec, ed)
new_esEs0(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), app(ty_[], bac), eb, ga) → new_esEs3(vyy350, vyy360, bac)
new_esEs4(@2(vyy350, vyy351), @2(vyy360, vyy361), app(ty_Maybe, bga), bfe) → new_esEs1(vyy350, vyy360, bga)
new_esEs1(Just(vyy350), Just(vyy360), app(ty_[], bbf)) → new_esEs3(vyy350, vyy360, bbf)
new_esEs3(:(vyy350, vyy351), :(vyy360, vyy361), app(app(app(ty_@3, bcf), bcg), bch)) → new_esEs0(vyy350, vyy360, bcf, bcg, bch)
new_esEs4(@2(vyy350, vyy351), @2(vyy360, vyy361), app(ty_[], bgd), bfe) → new_esEs3(vyy350, vyy360, bgd)
new_esEs4(@2(vyy350, vyy351), @2(vyy360, vyy361), bdg, app(app(ty_Either, bdh), bea)) → new_esEs(vyy351, vyy361, bdh, bea)
new_esEs0(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), app(app(ty_@2, bad), bae), eb, ga) → new_esEs4(vyy350, vyy360, bad, bae)
new_esEs(Left(vyy350), Left(vyy360), app(app(app(ty_@3, bc), bd), be), bb) → new_esEs0(vyy350, vyy360, bc, bd, be)
new_esEs(Right(vyy350), Right(vyy360), cd, app(app(ty_FiniteMap, dd), de)) → new_esEs2(vyy350, vyy360, dd, de)
new_esEs4(@2(vyy350, vyy351), @2(vyy360, vyy361), bdg, app(app(app(ty_@3, beb), bec), bed)) → new_esEs0(vyy351, vyy361, beb, bec, bed)
new_esEs3(:(vyy350, vyy351), :(vyy360, vyy361), bcc) → new_esEs3(vyy351, vyy361, bcc)
new_esEs(Left(vyy350), Left(vyy360), app(ty_[], ca), bb) → new_esEs3(vyy350, vyy360, ca)
new_esEs0(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), ea, app(ty_[], gh), ga) → new_esEs3(vyy351, vyy361, gh)
new_esEs4(@2(vyy350, vyy351), @2(vyy360, vyy361), bdg, app(app(ty_FiniteMap, bef), beg)) → new_esEs2(vyy351, vyy361, bef, beg)
new_esEs(Left(vyy350), Left(vyy360), app(ty_Maybe, bf), bb) → new_esEs1(vyy350, vyy360, bf)
new_esEs1(Just(vyy350), Just(vyy360), app(ty_Maybe, bbc)) → new_esEs1(vyy350, vyy360, bbc)
new_esEs4(@2(vyy350, vyy351), @2(vyy360, vyy361), bdg, app(ty_[], beh)) → new_esEs3(vyy351, vyy361, beh)
new_esEs(Left(vyy350), Left(vyy360), app(app(ty_@2, cb), cc), bb) → new_esEs4(vyy350, vyy360, cb, cc)
new_esEs1(Just(vyy350), Just(vyy360), app(app(ty_FiniteMap, bbd), bbe)) → new_esEs2(vyy350, vyy360, bbd, bbe)
new_esEs4(@2(vyy350, vyy351), @2(vyy360, vyy361), bdg, app(app(ty_@2, bfa), bfb)) → new_esEs4(vyy351, vyy361, bfa, bfb)
new_esEs(Right(vyy350), Right(vyy360), cd, app(ty_Maybe, dc)) → new_esEs1(vyy350, vyy360, dc)
new_esEs(Left(vyy350), Left(vyy360), app(app(ty_Either, h), ba), bb) → new_esEs(vyy350, vyy360, h, ba)
new_esEs2(vyy35, vyy36, bca, bcb) → new_esEs3(new_foldFM2(vyy35, bca, bcb), new_foldFM2(vyy36, bca, bcb), app(app(ty_@2, bca), bcb))
new_esEs(Left(vyy350), Left(vyy360), app(app(ty_FiniteMap, bg), bh), bb) → new_esEs2(vyy350, vyy360, bg, bh)
new_esEs3(:(vyy350, vyy351), :(vyy360, vyy361), app(app(ty_Either, bcd), bce)) → new_esEs(vyy350, vyy360, bcd, bce)
new_esEs0(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), ea, app(ty_Maybe, ge), ga) → new_esEs1(vyy351, vyy361, ge)
new_esEs3(:(vyy350, vyy351), :(vyy360, vyy361), app(ty_Maybe, bda)) → new_esEs1(vyy350, vyy360, bda)
new_esEs0(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), app(app(ty_Either, hc), hd), eb, ga) → new_esEs(vyy350, vyy360, hc, hd)
new_esEs0(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), ea, app(app(ty_FiniteMap, gf), gg), ga) → new_esEs2(vyy351, vyy361, gf, gg)
new_esEs1(Just(vyy350), Just(vyy360), app(app(ty_@2, bbg), bbh)) → new_esEs4(vyy350, vyy360, bbg, bbh)
new_esEs0(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), ea, eb, app(ty_[], fc)) → new_esEs3(vyy352, vyy362, fc)
new_esEs4(@2(vyy350, vyy351), @2(vyy360, vyy361), app(app(ty_@2, bge), bgf), bfe) → new_esEs4(vyy350, vyy360, bge, bgf)
new_esEs(Right(vyy350), Right(vyy360), cd, app(app(app(ty_@3, cg), da), db)) → new_esEs0(vyy350, vyy360, cg, da, db)
new_esEs0(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), ea, app(app(ty_@2, ha), hb), ga) → new_esEs4(vyy351, vyy361, ha, hb)
new_esEs0(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), ea, app(app(app(ty_@3, gb), gc), gd), ga) → new_esEs0(vyy351, vyy361, gb, gc, gd)
new_esEs4(@2(vyy350, vyy351), @2(vyy360, vyy361), bdg, app(ty_Maybe, bee)) → new_esEs1(vyy351, vyy361, bee)
new_esEs4(@2(vyy350, vyy351), @2(vyy360, vyy361), app(app(ty_FiniteMap, bgb), bgc), bfe) → new_esEs2(vyy350, vyy360, bgb, bgc)
new_esEs3(:(vyy350, vyy351), :(vyy360, vyy361), app(app(ty_FiniteMap, bdb), bdc)) → new_esEs2(vyy350, vyy360, bdb, bdc)
new_esEs(Right(vyy350), Right(vyy360), cd, app(app(ty_Either, ce), cf)) → new_esEs(vyy350, vyy360, ce, cf)
new_esEs0(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), app(app(ty_FiniteMap, baa), bab), eb, ga) → new_esEs2(vyy350, vyy360, baa, bab)
new_esEs(Right(vyy350), Right(vyy360), cd, app(ty_[], df)) → new_esEs3(vyy350, vyy360, df)
new_esEs0(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), ea, eb, app(app(app(ty_@3, ee), ef), eg)) → new_esEs0(vyy352, vyy362, ee, ef, eg)
new_esEs0(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), ea, eb, app(ty_Maybe, eh)) → new_esEs1(vyy352, vyy362, eh)
new_esEs0(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), ea, eb, app(app(ty_FiniteMap, fa), fb)) → new_esEs2(vyy352, vyy362, fa, fb)
new_esEs0(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), ea, app(app(ty_Either, fg), fh), ga) → new_esEs(vyy351, vyy361, fg, fh)
new_esEs0(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), app(ty_Maybe, hh), eb, ga) → new_esEs1(vyy350, vyy360, hh)
new_esEs0(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), app(app(app(ty_@3, he), hf), hg), eb, ga) → new_esEs0(vyy350, vyy360, he, hf, hg)
new_esEs0(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), ea, eb, app(app(ty_@2, fd), ff)) → new_esEs4(vyy352, vyy362, fd, ff)
The TRS R consists of the following rules:
new_foldFM0(vyy360, vyy361, vyy80, EmptyFM, bca, bcb) → :(@2(vyy360, vyy361), vyy80)
new_foldFM0(vyy360, vyy361, vyy80, Branch(vyy3630, vyy3631, vyy3632, vyy3633, vyy3634), bca, bcb) → new_foldFM0(vyy3630, vyy3631, new_foldFM0(vyy360, vyy361, vyy80, vyy3634, bca, bcb), vyy3633, bca, bcb)
new_fmToList(vyy36, bca, bcb) → new_foldFM2(vyy36, bca, bcb)
new_foldFM2(Branch(vyy360, vyy361, vyy362, vyy363, vyy364), bca, bcb) → new_foldFM0(vyy360, vyy361, new_foldFM2(vyy364, bca, bcb), vyy363, bca, bcb)
new_foldFM2(EmptyFM, bca, bcb) → []
The set Q consists of the following terms:
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
new_foldFM2(EmptyFM, x0, x1)
new_fmToList(x0, x1, x2)
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
We have to consider all minimal (P,Q,R)-chains.
As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [15] we can delete all non-usable rules [17] from R.
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ Rewriting
↳ QDP
↳ Rewriting
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QReductionProof
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_esEs(Right(vyy350), Right(vyy360), cd, app(app(ty_@2, dg), dh)) → new_esEs4(vyy350, vyy360, dg, dh)
new_esEs4(@2(vyy350, vyy351), @2(vyy360, vyy361), app(app(ty_Either, bfc), bfd), bfe) → new_esEs(vyy350, vyy360, bfc, bfd)
new_esEs4(@2(vyy350, vyy351), @2(vyy360, vyy361), app(app(app(ty_@3, bff), bfg), bfh), bfe) → new_esEs0(vyy350, vyy360, bff, bfg, bfh)
new_esEs1(Just(vyy350), Just(vyy360), app(app(ty_Either, baf), bag)) → new_esEs(vyy350, vyy360, baf, bag)
new_esEs3(:(vyy350, vyy351), :(vyy360, vyy361), app(ty_[], bdd)) → new_esEs3(vyy350, vyy360, bdd)
new_esEs3(:(vyy350, vyy351), :(vyy360, vyy361), app(app(ty_@2, bde), bdf)) → new_esEs4(vyy350, vyy360, bde, bdf)
new_esEs1(Just(vyy350), Just(vyy360), app(app(app(ty_@3, bah), bba), bbb)) → new_esEs0(vyy350, vyy360, bah, bba, bbb)
new_esEs0(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), ea, eb, app(app(ty_Either, ec), ed)) → new_esEs(vyy352, vyy362, ec, ed)
new_esEs0(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), app(ty_[], bac), eb, ga) → new_esEs3(vyy350, vyy360, bac)
new_esEs4(@2(vyy350, vyy351), @2(vyy360, vyy361), app(ty_Maybe, bga), bfe) → new_esEs1(vyy350, vyy360, bga)
new_esEs1(Just(vyy350), Just(vyy360), app(ty_[], bbf)) → new_esEs3(vyy350, vyy360, bbf)
new_esEs3(:(vyy350, vyy351), :(vyy360, vyy361), app(app(app(ty_@3, bcf), bcg), bch)) → new_esEs0(vyy350, vyy360, bcf, bcg, bch)
new_esEs4(@2(vyy350, vyy351), @2(vyy360, vyy361), app(ty_[], bgd), bfe) → new_esEs3(vyy350, vyy360, bgd)
new_esEs4(@2(vyy350, vyy351), @2(vyy360, vyy361), bdg, app(app(ty_Either, bdh), bea)) → new_esEs(vyy351, vyy361, bdh, bea)
new_esEs0(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), app(app(ty_@2, bad), bae), eb, ga) → new_esEs4(vyy350, vyy360, bad, bae)
new_esEs(Left(vyy350), Left(vyy360), app(app(app(ty_@3, bc), bd), be), bb) → new_esEs0(vyy350, vyy360, bc, bd, be)
new_esEs(Right(vyy350), Right(vyy360), cd, app(app(ty_FiniteMap, dd), de)) → new_esEs2(vyy350, vyy360, dd, de)
new_esEs4(@2(vyy350, vyy351), @2(vyy360, vyy361), bdg, app(app(app(ty_@3, beb), bec), bed)) → new_esEs0(vyy351, vyy361, beb, bec, bed)
new_esEs3(:(vyy350, vyy351), :(vyy360, vyy361), bcc) → new_esEs3(vyy351, vyy361, bcc)
new_esEs(Left(vyy350), Left(vyy360), app(ty_[], ca), bb) → new_esEs3(vyy350, vyy360, ca)
new_esEs0(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), ea, app(ty_[], gh), ga) → new_esEs3(vyy351, vyy361, gh)
new_esEs4(@2(vyy350, vyy351), @2(vyy360, vyy361), bdg, app(app(ty_FiniteMap, bef), beg)) → new_esEs2(vyy351, vyy361, bef, beg)
new_esEs(Left(vyy350), Left(vyy360), app(ty_Maybe, bf), bb) → new_esEs1(vyy350, vyy360, bf)
new_esEs1(Just(vyy350), Just(vyy360), app(ty_Maybe, bbc)) → new_esEs1(vyy350, vyy360, bbc)
new_esEs4(@2(vyy350, vyy351), @2(vyy360, vyy361), bdg, app(ty_[], beh)) → new_esEs3(vyy351, vyy361, beh)
new_esEs(Left(vyy350), Left(vyy360), app(app(ty_@2, cb), cc), bb) → new_esEs4(vyy350, vyy360, cb, cc)
new_esEs1(Just(vyy350), Just(vyy360), app(app(ty_FiniteMap, bbd), bbe)) → new_esEs2(vyy350, vyy360, bbd, bbe)
new_esEs4(@2(vyy350, vyy351), @2(vyy360, vyy361), bdg, app(app(ty_@2, bfa), bfb)) → new_esEs4(vyy351, vyy361, bfa, bfb)
new_esEs(Right(vyy350), Right(vyy360), cd, app(ty_Maybe, dc)) → new_esEs1(vyy350, vyy360, dc)
new_esEs(Left(vyy350), Left(vyy360), app(app(ty_Either, h), ba), bb) → new_esEs(vyy350, vyy360, h, ba)
new_esEs2(vyy35, vyy36, bca, bcb) → new_esEs3(new_foldFM2(vyy35, bca, bcb), new_foldFM2(vyy36, bca, bcb), app(app(ty_@2, bca), bcb))
new_esEs(Left(vyy350), Left(vyy360), app(app(ty_FiniteMap, bg), bh), bb) → new_esEs2(vyy350, vyy360, bg, bh)
new_esEs3(:(vyy350, vyy351), :(vyy360, vyy361), app(app(ty_Either, bcd), bce)) → new_esEs(vyy350, vyy360, bcd, bce)
new_esEs0(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), ea, app(ty_Maybe, ge), ga) → new_esEs1(vyy351, vyy361, ge)
new_esEs3(:(vyy350, vyy351), :(vyy360, vyy361), app(ty_Maybe, bda)) → new_esEs1(vyy350, vyy360, bda)
new_esEs0(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), app(app(ty_Either, hc), hd), eb, ga) → new_esEs(vyy350, vyy360, hc, hd)
new_esEs0(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), ea, app(app(ty_FiniteMap, gf), gg), ga) → new_esEs2(vyy351, vyy361, gf, gg)
new_esEs1(Just(vyy350), Just(vyy360), app(app(ty_@2, bbg), bbh)) → new_esEs4(vyy350, vyy360, bbg, bbh)
new_esEs0(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), ea, eb, app(ty_[], fc)) → new_esEs3(vyy352, vyy362, fc)
new_esEs4(@2(vyy350, vyy351), @2(vyy360, vyy361), app(app(ty_@2, bge), bgf), bfe) → new_esEs4(vyy350, vyy360, bge, bgf)
new_esEs(Right(vyy350), Right(vyy360), cd, app(app(app(ty_@3, cg), da), db)) → new_esEs0(vyy350, vyy360, cg, da, db)
new_esEs0(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), ea, app(app(ty_@2, ha), hb), ga) → new_esEs4(vyy351, vyy361, ha, hb)
new_esEs0(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), ea, app(app(app(ty_@3, gb), gc), gd), ga) → new_esEs0(vyy351, vyy361, gb, gc, gd)
new_esEs4(@2(vyy350, vyy351), @2(vyy360, vyy361), bdg, app(ty_Maybe, bee)) → new_esEs1(vyy351, vyy361, bee)
new_esEs4(@2(vyy350, vyy351), @2(vyy360, vyy361), app(app(ty_FiniteMap, bgb), bgc), bfe) → new_esEs2(vyy350, vyy360, bgb, bgc)
new_esEs3(:(vyy350, vyy351), :(vyy360, vyy361), app(app(ty_FiniteMap, bdb), bdc)) → new_esEs2(vyy350, vyy360, bdb, bdc)
new_esEs(Right(vyy350), Right(vyy360), cd, app(app(ty_Either, ce), cf)) → new_esEs(vyy350, vyy360, ce, cf)
new_esEs0(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), app(app(ty_FiniteMap, baa), bab), eb, ga) → new_esEs2(vyy350, vyy360, baa, bab)
new_esEs(Right(vyy350), Right(vyy360), cd, app(ty_[], df)) → new_esEs3(vyy350, vyy360, df)
new_esEs0(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), ea, eb, app(app(app(ty_@3, ee), ef), eg)) → new_esEs0(vyy352, vyy362, ee, ef, eg)
new_esEs0(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), ea, eb, app(ty_Maybe, eh)) → new_esEs1(vyy352, vyy362, eh)
new_esEs0(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), ea, eb, app(app(ty_FiniteMap, fa), fb)) → new_esEs2(vyy352, vyy362, fa, fb)
new_esEs0(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), ea, app(app(ty_Either, fg), fh), ga) → new_esEs(vyy351, vyy361, fg, fh)
new_esEs0(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), app(ty_Maybe, hh), eb, ga) → new_esEs1(vyy350, vyy360, hh)
new_esEs0(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), app(app(app(ty_@3, he), hf), hg), eb, ga) → new_esEs0(vyy350, vyy360, he, hf, hg)
new_esEs0(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), ea, eb, app(app(ty_@2, fd), ff)) → new_esEs4(vyy352, vyy362, fd, ff)
The TRS R consists of the following rules:
new_foldFM2(Branch(vyy360, vyy361, vyy362, vyy363, vyy364), bca, bcb) → new_foldFM0(vyy360, vyy361, new_foldFM2(vyy364, bca, bcb), vyy363, bca, bcb)
new_foldFM2(EmptyFM, bca, bcb) → []
new_foldFM0(vyy360, vyy361, vyy80, EmptyFM, bca, bcb) → :(@2(vyy360, vyy361), vyy80)
new_foldFM0(vyy360, vyy361, vyy80, Branch(vyy3630, vyy3631, vyy3632, vyy3633, vyy3634), bca, bcb) → new_foldFM0(vyy3630, vyy3631, new_foldFM0(vyy360, vyy361, vyy80, vyy3634, bca, bcb), vyy3633, bca, bcb)
The set Q consists of the following terms:
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
new_foldFM2(EmptyFM, x0, x1)
new_fmToList(x0, x1, x2)
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
We have to consider all minimal (P,Q,R)-chains.
We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.
new_fmToList(x0, x1, x2)
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ Rewriting
↳ QDP
↳ Rewriting
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QReductionProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_esEs(Right(vyy350), Right(vyy360), cd, app(app(ty_@2, dg), dh)) → new_esEs4(vyy350, vyy360, dg, dh)
new_esEs4(@2(vyy350, vyy351), @2(vyy360, vyy361), app(app(ty_Either, bfc), bfd), bfe) → new_esEs(vyy350, vyy360, bfc, bfd)
new_esEs4(@2(vyy350, vyy351), @2(vyy360, vyy361), app(app(app(ty_@3, bff), bfg), bfh), bfe) → new_esEs0(vyy350, vyy360, bff, bfg, bfh)
new_esEs1(Just(vyy350), Just(vyy360), app(app(ty_Either, baf), bag)) → new_esEs(vyy350, vyy360, baf, bag)
new_esEs3(:(vyy350, vyy351), :(vyy360, vyy361), app(ty_[], bdd)) → new_esEs3(vyy350, vyy360, bdd)
new_esEs3(:(vyy350, vyy351), :(vyy360, vyy361), app(app(ty_@2, bde), bdf)) → new_esEs4(vyy350, vyy360, bde, bdf)
new_esEs1(Just(vyy350), Just(vyy360), app(app(app(ty_@3, bah), bba), bbb)) → new_esEs0(vyy350, vyy360, bah, bba, bbb)
new_esEs0(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), ea, eb, app(app(ty_Either, ec), ed)) → new_esEs(vyy352, vyy362, ec, ed)
new_esEs0(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), app(ty_[], bac), eb, ga) → new_esEs3(vyy350, vyy360, bac)
new_esEs4(@2(vyy350, vyy351), @2(vyy360, vyy361), app(ty_Maybe, bga), bfe) → new_esEs1(vyy350, vyy360, bga)
new_esEs1(Just(vyy350), Just(vyy360), app(ty_[], bbf)) → new_esEs3(vyy350, vyy360, bbf)
new_esEs3(:(vyy350, vyy351), :(vyy360, vyy361), app(app(app(ty_@3, bcf), bcg), bch)) → new_esEs0(vyy350, vyy360, bcf, bcg, bch)
new_esEs4(@2(vyy350, vyy351), @2(vyy360, vyy361), app(ty_[], bgd), bfe) → new_esEs3(vyy350, vyy360, bgd)
new_esEs4(@2(vyy350, vyy351), @2(vyy360, vyy361), bdg, app(app(ty_Either, bdh), bea)) → new_esEs(vyy351, vyy361, bdh, bea)
new_esEs0(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), app(app(ty_@2, bad), bae), eb, ga) → new_esEs4(vyy350, vyy360, bad, bae)
new_esEs(Left(vyy350), Left(vyy360), app(app(app(ty_@3, bc), bd), be), bb) → new_esEs0(vyy350, vyy360, bc, bd, be)
new_esEs(Right(vyy350), Right(vyy360), cd, app(app(ty_FiniteMap, dd), de)) → new_esEs2(vyy350, vyy360, dd, de)
new_esEs4(@2(vyy350, vyy351), @2(vyy360, vyy361), bdg, app(app(app(ty_@3, beb), bec), bed)) → new_esEs0(vyy351, vyy361, beb, bec, bed)
new_esEs(Left(vyy350), Left(vyy360), app(ty_[], ca), bb) → new_esEs3(vyy350, vyy360, ca)
new_esEs3(:(vyy350, vyy351), :(vyy360, vyy361), bcc) → new_esEs3(vyy351, vyy361, bcc)
new_esEs0(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), ea, app(ty_[], gh), ga) → new_esEs3(vyy351, vyy361, gh)
new_esEs4(@2(vyy350, vyy351), @2(vyy360, vyy361), bdg, app(app(ty_FiniteMap, bef), beg)) → new_esEs2(vyy351, vyy361, bef, beg)
new_esEs(Left(vyy350), Left(vyy360), app(ty_Maybe, bf), bb) → new_esEs1(vyy350, vyy360, bf)
new_esEs1(Just(vyy350), Just(vyy360), app(ty_Maybe, bbc)) → new_esEs1(vyy350, vyy360, bbc)
new_esEs4(@2(vyy350, vyy351), @2(vyy360, vyy361), bdg, app(ty_[], beh)) → new_esEs3(vyy351, vyy361, beh)
new_esEs(Left(vyy350), Left(vyy360), app(app(ty_@2, cb), cc), bb) → new_esEs4(vyy350, vyy360, cb, cc)
new_esEs1(Just(vyy350), Just(vyy360), app(app(ty_FiniteMap, bbd), bbe)) → new_esEs2(vyy350, vyy360, bbd, bbe)
new_esEs4(@2(vyy350, vyy351), @2(vyy360, vyy361), bdg, app(app(ty_@2, bfa), bfb)) → new_esEs4(vyy351, vyy361, bfa, bfb)
new_esEs(Right(vyy350), Right(vyy360), cd, app(ty_Maybe, dc)) → new_esEs1(vyy350, vyy360, dc)
new_esEs(Left(vyy350), Left(vyy360), app(app(ty_Either, h), ba), bb) → new_esEs(vyy350, vyy360, h, ba)
new_esEs2(vyy35, vyy36, bca, bcb) → new_esEs3(new_foldFM2(vyy35, bca, bcb), new_foldFM2(vyy36, bca, bcb), app(app(ty_@2, bca), bcb))
new_esEs(Left(vyy350), Left(vyy360), app(app(ty_FiniteMap, bg), bh), bb) → new_esEs2(vyy350, vyy360, bg, bh)
new_esEs3(:(vyy350, vyy351), :(vyy360, vyy361), app(app(ty_Either, bcd), bce)) → new_esEs(vyy350, vyy360, bcd, bce)
new_esEs0(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), ea, app(ty_Maybe, ge), ga) → new_esEs1(vyy351, vyy361, ge)
new_esEs3(:(vyy350, vyy351), :(vyy360, vyy361), app(ty_Maybe, bda)) → new_esEs1(vyy350, vyy360, bda)
new_esEs0(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), app(app(ty_Either, hc), hd), eb, ga) → new_esEs(vyy350, vyy360, hc, hd)
new_esEs0(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), ea, app(app(ty_FiniteMap, gf), gg), ga) → new_esEs2(vyy351, vyy361, gf, gg)
new_esEs1(Just(vyy350), Just(vyy360), app(app(ty_@2, bbg), bbh)) → new_esEs4(vyy350, vyy360, bbg, bbh)
new_esEs0(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), ea, eb, app(ty_[], fc)) → new_esEs3(vyy352, vyy362, fc)
new_esEs4(@2(vyy350, vyy351), @2(vyy360, vyy361), app(app(ty_@2, bge), bgf), bfe) → new_esEs4(vyy350, vyy360, bge, bgf)
new_esEs(Right(vyy350), Right(vyy360), cd, app(app(app(ty_@3, cg), da), db)) → new_esEs0(vyy350, vyy360, cg, da, db)
new_esEs0(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), ea, app(app(ty_@2, ha), hb), ga) → new_esEs4(vyy351, vyy361, ha, hb)
new_esEs0(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), ea, app(app(app(ty_@3, gb), gc), gd), ga) → new_esEs0(vyy351, vyy361, gb, gc, gd)
new_esEs4(@2(vyy350, vyy351), @2(vyy360, vyy361), bdg, app(ty_Maybe, bee)) → new_esEs1(vyy351, vyy361, bee)
new_esEs4(@2(vyy350, vyy351), @2(vyy360, vyy361), app(app(ty_FiniteMap, bgb), bgc), bfe) → new_esEs2(vyy350, vyy360, bgb, bgc)
new_esEs3(:(vyy350, vyy351), :(vyy360, vyy361), app(app(ty_FiniteMap, bdb), bdc)) → new_esEs2(vyy350, vyy360, bdb, bdc)
new_esEs(Right(vyy350), Right(vyy360), cd, app(app(ty_Either, ce), cf)) → new_esEs(vyy350, vyy360, ce, cf)
new_esEs0(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), app(app(ty_FiniteMap, baa), bab), eb, ga) → new_esEs2(vyy350, vyy360, baa, bab)
new_esEs(Right(vyy350), Right(vyy360), cd, app(ty_[], df)) → new_esEs3(vyy350, vyy360, df)
new_esEs0(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), ea, eb, app(ty_Maybe, eh)) → new_esEs1(vyy352, vyy362, eh)
new_esEs0(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), ea, eb, app(app(app(ty_@3, ee), ef), eg)) → new_esEs0(vyy352, vyy362, ee, ef, eg)
new_esEs0(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), ea, eb, app(app(ty_FiniteMap, fa), fb)) → new_esEs2(vyy352, vyy362, fa, fb)
new_esEs0(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), ea, app(app(ty_Either, fg), fh), ga) → new_esEs(vyy351, vyy361, fg, fh)
new_esEs0(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), app(ty_Maybe, hh), eb, ga) → new_esEs1(vyy350, vyy360, hh)
new_esEs0(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), ea, eb, app(app(ty_@2, fd), ff)) → new_esEs4(vyy352, vyy362, fd, ff)
new_esEs0(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), app(app(app(ty_@3, he), hf), hg), eb, ga) → new_esEs0(vyy350, vyy360, he, hf, hg)
The TRS R consists of the following rules:
new_foldFM2(Branch(vyy360, vyy361, vyy362, vyy363, vyy364), bca, bcb) → new_foldFM0(vyy360, vyy361, new_foldFM2(vyy364, bca, bcb), vyy363, bca, bcb)
new_foldFM2(EmptyFM, bca, bcb) → []
new_foldFM0(vyy360, vyy361, vyy80, EmptyFM, bca, bcb) → :(@2(vyy360, vyy361), vyy80)
new_foldFM0(vyy360, vyy361, vyy80, Branch(vyy3630, vyy3631, vyy3632, vyy3633, vyy3634), bca, bcb) → new_foldFM0(vyy3630, vyy3631, new_foldFM0(vyy360, vyy361, vyy80, vyy3634, bca, bcb), vyy3633, bca, bcb)
The set Q consists of the following terms:
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
new_foldFM2(EmptyFM, x0, x1)
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_esEs4(@2(vyy350, vyy351), @2(vyy360, vyy361), app(app(ty_Either, bfc), bfd), bfe) → new_esEs(vyy350, vyy360, bfc, bfd)
new_esEs4(@2(vyy350, vyy351), @2(vyy360, vyy361), app(app(app(ty_@3, bff), bfg), bfh), bfe) → new_esEs0(vyy350, vyy360, bff, bfg, bfh)
new_esEs1(Just(vyy350), Just(vyy360), app(app(ty_Either, baf), bag)) → new_esEs(vyy350, vyy360, baf, bag)
new_esEs3(:(vyy350, vyy351), :(vyy360, vyy361), app(ty_[], bdd)) → new_esEs3(vyy350, vyy360, bdd)
new_esEs1(Just(vyy350), Just(vyy360), app(app(app(ty_@3, bah), bba), bbb)) → new_esEs0(vyy350, vyy360, bah, bba, bbb)
new_esEs0(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), ea, eb, app(app(ty_Either, ec), ed)) → new_esEs(vyy352, vyy362, ec, ed)
new_esEs0(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), app(ty_[], bac), eb, ga) → new_esEs3(vyy350, vyy360, bac)
new_esEs4(@2(vyy350, vyy351), @2(vyy360, vyy361), app(ty_Maybe, bga), bfe) → new_esEs1(vyy350, vyy360, bga)
new_esEs1(Just(vyy350), Just(vyy360), app(ty_[], bbf)) → new_esEs3(vyy350, vyy360, bbf)
new_esEs3(:(vyy350, vyy351), :(vyy360, vyy361), app(app(app(ty_@3, bcf), bcg), bch)) → new_esEs0(vyy350, vyy360, bcf, bcg, bch)
new_esEs4(@2(vyy350, vyy351), @2(vyy360, vyy361), app(ty_[], bgd), bfe) → new_esEs3(vyy350, vyy360, bgd)
new_esEs4(@2(vyy350, vyy351), @2(vyy360, vyy361), bdg, app(app(ty_Either, bdh), bea)) → new_esEs(vyy351, vyy361, bdh, bea)
new_esEs(Left(vyy350), Left(vyy360), app(app(app(ty_@3, bc), bd), be), bb) → new_esEs0(vyy350, vyy360, bc, bd, be)
new_esEs4(@2(vyy350, vyy351), @2(vyy360, vyy361), bdg, app(app(app(ty_@3, beb), bec), bed)) → new_esEs0(vyy351, vyy361, beb, bec, bed)
new_esEs(Left(vyy350), Left(vyy360), app(ty_[], ca), bb) → new_esEs3(vyy350, vyy360, ca)
new_esEs3(:(vyy350, vyy351), :(vyy360, vyy361), bcc) → new_esEs3(vyy351, vyy361, bcc)
new_esEs0(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), ea, app(ty_[], gh), ga) → new_esEs3(vyy351, vyy361, gh)
new_esEs4(@2(vyy350, vyy351), @2(vyy360, vyy361), bdg, app(app(ty_FiniteMap, bef), beg)) → new_esEs2(vyy351, vyy361, bef, beg)
new_esEs(Left(vyy350), Left(vyy360), app(ty_Maybe, bf), bb) → new_esEs1(vyy350, vyy360, bf)
new_esEs1(Just(vyy350), Just(vyy360), app(ty_Maybe, bbc)) → new_esEs1(vyy350, vyy360, bbc)
new_esEs4(@2(vyy350, vyy351), @2(vyy360, vyy361), bdg, app(ty_[], beh)) → new_esEs3(vyy351, vyy361, beh)
new_esEs4(@2(vyy350, vyy351), @2(vyy360, vyy361), bdg, app(app(ty_@2, bfa), bfb)) → new_esEs4(vyy351, vyy361, bfa, bfb)
new_esEs(Right(vyy350), Right(vyy360), cd, app(ty_Maybe, dc)) → new_esEs1(vyy350, vyy360, dc)
new_esEs(Left(vyy350), Left(vyy360), app(app(ty_Either, h), ba), bb) → new_esEs(vyy350, vyy360, h, ba)
new_esEs2(vyy35, vyy36, bca, bcb) → new_esEs3(new_foldFM2(vyy35, bca, bcb), new_foldFM2(vyy36, bca, bcb), app(app(ty_@2, bca), bcb))
new_esEs3(:(vyy350, vyy351), :(vyy360, vyy361), app(app(ty_Either, bcd), bce)) → new_esEs(vyy350, vyy360, bcd, bce)
new_esEs0(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), ea, app(ty_Maybe, ge), ga) → new_esEs1(vyy351, vyy361, ge)
new_esEs3(:(vyy350, vyy351), :(vyy360, vyy361), app(ty_Maybe, bda)) → new_esEs1(vyy350, vyy360, bda)
new_esEs0(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), app(app(ty_Either, hc), hd), eb, ga) → new_esEs(vyy350, vyy360, hc, hd)
new_esEs0(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), ea, eb, app(ty_[], fc)) → new_esEs3(vyy352, vyy362, fc)
new_esEs4(@2(vyy350, vyy351), @2(vyy360, vyy361), app(app(ty_@2, bge), bgf), bfe) → new_esEs4(vyy350, vyy360, bge, bgf)
new_esEs(Right(vyy350), Right(vyy360), cd, app(app(app(ty_@3, cg), da), db)) → new_esEs0(vyy350, vyy360, cg, da, db)
new_esEs0(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), ea, app(app(app(ty_@3, gb), gc), gd), ga) → new_esEs0(vyy351, vyy361, gb, gc, gd)
new_esEs4(@2(vyy350, vyy351), @2(vyy360, vyy361), bdg, app(ty_Maybe, bee)) → new_esEs1(vyy351, vyy361, bee)
new_esEs4(@2(vyy350, vyy351), @2(vyy360, vyy361), app(app(ty_FiniteMap, bgb), bgc), bfe) → new_esEs2(vyy350, vyy360, bgb, bgc)
new_esEs(Right(vyy350), Right(vyy360), cd, app(app(ty_Either, ce), cf)) → new_esEs(vyy350, vyy360, ce, cf)
new_esEs(Right(vyy350), Right(vyy360), cd, app(ty_[], df)) → new_esEs3(vyy350, vyy360, df)
new_esEs0(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), ea, eb, app(ty_Maybe, eh)) → new_esEs1(vyy352, vyy362, eh)
new_esEs0(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), ea, eb, app(app(app(ty_@3, ee), ef), eg)) → new_esEs0(vyy352, vyy362, ee, ef, eg)
new_esEs0(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), ea, app(app(ty_Either, fg), fh), ga) → new_esEs(vyy351, vyy361, fg, fh)
new_esEs0(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), app(ty_Maybe, hh), eb, ga) → new_esEs1(vyy350, vyy360, hh)
new_esEs0(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), app(app(app(ty_@3, he), hf), hg), eb, ga) → new_esEs0(vyy350, vyy360, he, hf, hg)
The remaining pairs can at least be oriented weakly.
new_esEs(Right(vyy350), Right(vyy360), cd, app(app(ty_@2, dg), dh)) → new_esEs4(vyy350, vyy360, dg, dh)
new_esEs3(:(vyy350, vyy351), :(vyy360, vyy361), app(app(ty_@2, bde), bdf)) → new_esEs4(vyy350, vyy360, bde, bdf)
new_esEs0(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), app(app(ty_@2, bad), bae), eb, ga) → new_esEs4(vyy350, vyy360, bad, bae)
new_esEs(Right(vyy350), Right(vyy360), cd, app(app(ty_FiniteMap, dd), de)) → new_esEs2(vyy350, vyy360, dd, de)
new_esEs(Left(vyy350), Left(vyy360), app(app(ty_@2, cb), cc), bb) → new_esEs4(vyy350, vyy360, cb, cc)
new_esEs1(Just(vyy350), Just(vyy360), app(app(ty_FiniteMap, bbd), bbe)) → new_esEs2(vyy350, vyy360, bbd, bbe)
new_esEs(Left(vyy350), Left(vyy360), app(app(ty_FiniteMap, bg), bh), bb) → new_esEs2(vyy350, vyy360, bg, bh)
new_esEs0(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), ea, app(app(ty_FiniteMap, gf), gg), ga) → new_esEs2(vyy351, vyy361, gf, gg)
new_esEs1(Just(vyy350), Just(vyy360), app(app(ty_@2, bbg), bbh)) → new_esEs4(vyy350, vyy360, bbg, bbh)
new_esEs0(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), ea, app(app(ty_@2, ha), hb), ga) → new_esEs4(vyy351, vyy361, ha, hb)
new_esEs3(:(vyy350, vyy351), :(vyy360, vyy361), app(app(ty_FiniteMap, bdb), bdc)) → new_esEs2(vyy350, vyy360, bdb, bdc)
new_esEs0(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), app(app(ty_FiniteMap, baa), bab), eb, ga) → new_esEs2(vyy350, vyy360, baa, bab)
new_esEs0(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), ea, eb, app(app(ty_FiniteMap, fa), fb)) → new_esEs2(vyy352, vyy362, fa, fb)
new_esEs0(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), ea, eb, app(app(ty_@2, fd), ff)) → new_esEs4(vyy352, vyy362, fd, ff)
Used ordering: Polynomial interpretation [25]:
POL(:(x1, x2)) = 1 + x1 + x2
POL(@2(x1, x2)) = 1 + x1 + x2
POL(@3(x1, x2, x3)) = 1 + x1 + x2 + x3
POL(Branch(x1, x2, x3, x4, x5)) = 1 + x1 + x2 + x4 + x5
POL(EmptyFM) = 1
POL(Just(x1)) = 1 + x1
POL(Left(x1)) = 1 + x1
POL(Right(x1)) = 1 + x1
POL([]) = 0
POL(app(x1, x2)) = 0
POL(new_esEs(x1, x2, x3, x4)) = x2
POL(new_esEs0(x1, x2, x3, x4, x5)) = x2
POL(new_esEs1(x1, x2, x3)) = x2
POL(new_esEs2(x1, x2, x3, x4)) = 1 + x2
POL(new_esEs3(x1, x2, x3)) = x2
POL(new_esEs4(x1, x2, x3, x4)) = 1 + x2
POL(new_foldFM0(x1, x2, x3, x4, x5, x6)) = 1 + x1 + x2 + x3 + x4
POL(new_foldFM2(x1, x2, x3)) = x1
POL(ty_@2) = 0
POL(ty_@3) = 0
POL(ty_Either) = 0
POL(ty_FiniteMap) = 0
POL(ty_Maybe) = 0
POL(ty_[]) = 0
The following usable rules [17] were oriented:
new_foldFM0(vyy360, vyy361, vyy80, EmptyFM, bca, bcb) → :(@2(vyy360, vyy361), vyy80)
new_foldFM0(vyy360, vyy361, vyy80, Branch(vyy3630, vyy3631, vyy3632, vyy3633, vyy3634), bca, bcb) → new_foldFM0(vyy3630, vyy3631, new_foldFM0(vyy360, vyy361, vyy80, vyy3634, bca, bcb), vyy3633, bca, bcb)
new_foldFM2(Branch(vyy360, vyy361, vyy362, vyy363, vyy364), bca, bcb) → new_foldFM0(vyy360, vyy361, new_foldFM2(vyy364, bca, bcb), vyy363, bca, bcb)
new_foldFM2(EmptyFM, bca, bcb) → []
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ Rewriting
↳ QDP
↳ Rewriting
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QReductionProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_esEs(Left(vyy350), Left(vyy360), app(app(ty_FiniteMap, bg), bh), bb) → new_esEs2(vyy350, vyy360, bg, bh)
new_esEs0(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), app(app(ty_FiniteMap, baa), bab), eb, ga) → new_esEs2(vyy350, vyy360, baa, bab)
new_esEs(Right(vyy350), Right(vyy360), cd, app(app(ty_@2, dg), dh)) → new_esEs4(vyy350, vyy360, dg, dh)
new_esEs0(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), ea, app(app(ty_FiniteMap, gf), gg), ga) → new_esEs2(vyy351, vyy361, gf, gg)
new_esEs1(Just(vyy350), Just(vyy360), app(app(ty_@2, bbg), bbh)) → new_esEs4(vyy350, vyy360, bbg, bbh)
new_esEs3(:(vyy350, vyy351), :(vyy360, vyy361), app(app(ty_@2, bde), bdf)) → new_esEs4(vyy350, vyy360, bde, bdf)
new_esEs0(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), ea, eb, app(app(ty_FiniteMap, fa), fb)) → new_esEs2(vyy352, vyy362, fa, fb)
new_esEs(Left(vyy350), Left(vyy360), app(app(ty_@2, cb), cc), bb) → new_esEs4(vyy350, vyy360, cb, cc)
new_esEs0(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), ea, app(app(ty_@2, ha), hb), ga) → new_esEs4(vyy351, vyy361, ha, hb)
new_esEs0(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), app(app(ty_@2, bad), bae), eb, ga) → new_esEs4(vyy350, vyy360, bad, bae)
new_esEs1(Just(vyy350), Just(vyy360), app(app(ty_FiniteMap, bbd), bbe)) → new_esEs2(vyy350, vyy360, bbd, bbe)
new_esEs(Right(vyy350), Right(vyy360), cd, app(app(ty_FiniteMap, dd), de)) → new_esEs2(vyy350, vyy360, dd, de)
new_esEs3(:(vyy350, vyy351), :(vyy360, vyy361), app(app(ty_FiniteMap, bdb), bdc)) → new_esEs2(vyy350, vyy360, bdb, bdc)
new_esEs0(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), ea, eb, app(app(ty_@2, fd), ff)) → new_esEs4(vyy352, vyy362, fd, ff)
The TRS R consists of the following rules:
new_foldFM2(Branch(vyy360, vyy361, vyy362, vyy363, vyy364), bca, bcb) → new_foldFM0(vyy360, vyy361, new_foldFM2(vyy364, bca, bcb), vyy363, bca, bcb)
new_foldFM2(EmptyFM, bca, bcb) → []
new_foldFM0(vyy360, vyy361, vyy80, EmptyFM, bca, bcb) → :(@2(vyy360, vyy361), vyy80)
new_foldFM0(vyy360, vyy361, vyy80, Branch(vyy3630, vyy3631, vyy3632, vyy3633, vyy3634), bca, bcb) → new_foldFM0(vyy3630, vyy3631, new_foldFM0(vyy360, vyy361, vyy80, vyy3634, bca, bcb), vyy3633, bca, bcb)
The set Q consists of the following terms:
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
new_foldFM2(EmptyFM, x0, x1)
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 0 SCCs with 14 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
↳ QDPSizeChangeProof
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_primCmpNat(Succ(vyy60000), Succ(vyy5000)) → new_primCmpNat(vyy60000, vyy5000)
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(vyy60000), Succ(vyy5000)) → new_primCmpNat(vyy60000, vyy5000)
The graph contains the following edges 1 > 1, 2 > 2
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDPSizeChangeProof
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_ltEs(Right(vyy6000), Right(vyy500), cb, app(ty_[], cf)) → new_ltEs1(vyy6000, vyy500, cf)
new_compare0(:(vyy6000, vyy6001), :(vyy500, vyy501), ef) → new_primCompAux(vyy6000, vyy500, new_compare(vyy6001, vyy501, ef), ef)
new_ltEs2(@3(vyy6000, vyy6001, vyy6002), @3(vyy500, vyy501, vyy502), gg, gh, app(app(app(ty_@3, he), hf), hg)) → new_ltEs2(vyy6002, vyy502, he, hf, hg)
new_ltEs(Left(vyy6000), Left(vyy500), app(app(ty_Either, h), ba), bb) → new_ltEs(vyy6000, vyy500, h, ba)
new_ltEs(Right(vyy6000), Right(vyy500), cb, app(app(ty_Either, cc), cd)) → new_ltEs(vyy6000, vyy500, cc, cd)
new_compare0(:(vyy6000, vyy6001), :(vyy500, vyy501), ef) → new_compare0(vyy6001, vyy501, ef)
new_ltEs0(Just(vyy6000), Just(vyy500), app(app(ty_@2, ed), ee)) → new_ltEs3(vyy6000, vyy500, ed, ee)
new_compare3(vyy6000, vyy500, gd, ge, gf) → new_compare22(vyy6000, vyy500, new_esEs7(vyy6000, vyy500, gd, ge, gf), gd, ge, gf)
new_ltEs3(@2(vyy6000, vyy6001), @2(vyy500, vyy501), bbg, app(ty_Maybe, bcb)) → new_ltEs0(vyy6001, vyy501, bcb)
new_ltEs2(@3(vyy6000, vyy6001, vyy6002), @3(vyy500, vyy501, vyy502), app(ty_Maybe, gc), gh, bad) → new_compare21(vyy6000, vyy500, new_esEs6(vyy6000, vyy500, gc), gc)
new_compare21(vyy6000, vyy500, False, gc) → new_ltEs0(vyy6000, vyy500, gc)
new_ltEs2(@3(vyy6000, vyy6001, vyy6002), @3(vyy500, vyy501, vyy502), gg, app(app(app(ty_@3, bag), bah), bba), bad) → new_lt2(vyy6001, vyy501, bag, bah, bba)
new_lt0(vyy6000, vyy500, gc) → new_compare21(vyy6000, vyy500, new_esEs6(vyy6000, vyy500, gc), gc)
new_ltEs0(Just(vyy6000), Just(vyy500), app(ty_Maybe, dg)) → new_ltEs0(vyy6000, vyy500, dg)
new_ltEs0(Just(vyy6000), Just(vyy500), app(app(app(ty_@3, ea), eb), ec)) → new_ltEs2(vyy6000, vyy500, ea, eb, ec)
new_ltEs2(@3(vyy6000, vyy6001, vyy6002), @3(vyy500, vyy501, vyy502), app(app(app(ty_@3, gd), ge), gf), gh, bad) → new_compare22(vyy6000, vyy500, new_esEs7(vyy6000, vyy500, gd, ge, gf), gd, ge, gf)
new_primCompAux(vyy6000, vyy500, vyy62, app(ty_[], fb)) → new_compare0(vyy6000, vyy500, fb)
new_ltEs(Left(vyy6000), Left(vyy500), app(app(ty_@2, bh), ca), bb) → new_ltEs3(vyy6000, vyy500, bh, ca)
new_lt(vyy6000, vyy500, ga, gb) → new_compare20(vyy6000, vyy500, new_esEs5(vyy6000, vyy500, ga, gb), ga, gb)
new_primCompAux(vyy6000, vyy500, vyy62, app(ty_Maybe, fa)) → new_compare2(vyy6000, vyy500, fa)
new_ltEs3(@2(vyy6000, vyy6001), @2(vyy500, vyy501), bbg, app(app(ty_@2, bcg), bch)) → new_ltEs3(vyy6001, vyy501, bcg, bch)
new_ltEs1(:(vyy6000, vyy6001), :(vyy500, vyy501), ef) → new_primCompAux(vyy6000, vyy500, new_compare(vyy6001, vyy501, ef), ef)
new_ltEs2(@3(vyy6000, vyy6001, vyy6002), @3(vyy500, vyy501, vyy502), gg, gh, app(app(ty_@2, hh), baa)) → new_ltEs3(vyy6002, vyy502, hh, baa)
new_ltEs2(@3(vyy6000, vyy6001, vyy6002), @3(vyy500, vyy501, vyy502), gg, gh, app(ty_[], hd)) → new_ltEs1(vyy6002, vyy502, hd)
new_primCompAux(vyy6000, vyy500, vyy62, app(app(ty_Either, eg), eh)) → new_compare1(vyy6000, vyy500, eg, eh)
new_ltEs2(@3(vyy6000, vyy6001, vyy6002), @3(vyy500, vyy501, vyy502), app(ty_[], bbd), gh, bad) → new_compare0(vyy6000, vyy500, bbd)
new_compare2(vyy6000, vyy500, gc) → new_compare21(vyy6000, vyy500, new_esEs6(vyy6000, vyy500, gc), gc)
new_ltEs(Left(vyy6000), Left(vyy500), app(app(app(ty_@3, be), bf), bg), bb) → new_ltEs2(vyy6000, vyy500, be, bf, bg)
new_compare20(vyy6000, vyy500, False, ga, gb) → new_ltEs(vyy6000, vyy500, ga, gb)
new_ltEs3(@2(vyy6000, vyy6001), @2(vyy500, vyy501), app(ty_Maybe, bdd), bdc) → new_lt0(vyy6000, vyy500, bdd)
new_ltEs(Right(vyy6000), Right(vyy500), cb, app(app(ty_@2, dc), dd)) → new_ltEs3(vyy6000, vyy500, dc, dd)
new_ltEs3(@2(vyy6000, vyy6001), @2(vyy500, vyy501), bbg, app(app(app(ty_@3, bcd), bce), bcf)) → new_ltEs2(vyy6001, vyy501, bcd, bce, bcf)
new_lt1(vyy6000, vyy500, bbd) → new_compare0(vyy6000, vyy500, bbd)
new_ltEs2(@3(vyy6000, vyy6001, vyy6002), @3(vyy500, vyy501, vyy502), gg, gh, app(app(ty_Either, ha), hb)) → new_ltEs(vyy6002, vyy502, ha, hb)
new_ltEs2(@3(vyy6000, vyy6001, vyy6002), @3(vyy500, vyy501, vyy502), gg, gh, app(ty_Maybe, hc)) → new_ltEs0(vyy6002, vyy502, hc)
new_compare23(vyy6000, vyy500, False, bbe, bbf) → new_ltEs3(vyy6000, vyy500, bbe, bbf)
new_ltEs3(@2(vyy6000, vyy6001), @2(vyy500, vyy501), bbg, app(app(ty_Either, bbh), bca)) → new_ltEs(vyy6001, vyy501, bbh, bca)
new_ltEs3(@2(vyy6000, vyy6001), @2(vyy500, vyy501), app(app(ty_@2, bea), beb), bdc) → new_lt3(vyy6000, vyy500, bea, beb)
new_ltEs3(@2(vyy6000, vyy6001), @2(vyy500, vyy501), app(app(app(ty_@3, bdf), bdg), bdh), bdc) → new_lt2(vyy6000, vyy500, bdf, bdg, bdh)
new_ltEs2(@3(vyy6000, vyy6001, vyy6002), @3(vyy500, vyy501, vyy502), app(app(ty_Either, ga), gb), gh, bad) → new_compare20(vyy6000, vyy500, new_esEs5(vyy6000, vyy500, ga, gb), ga, gb)
new_lt3(vyy6000, vyy500, bbe, bbf) → new_compare23(vyy6000, vyy500, new_esEs8(vyy6000, vyy500, bbe, bbf), bbe, bbf)
new_primCompAux(vyy6000, vyy500, vyy62, app(app(app(ty_@3, fc), fd), ff)) → new_compare3(vyy6000, vyy500, fc, fd, ff)
new_compare4(vyy6000, vyy500, bbe, bbf) → new_compare23(vyy6000, vyy500, new_esEs8(vyy6000, vyy500, bbe, bbf), bbe, bbf)
new_ltEs(Left(vyy6000), Left(vyy500), app(ty_Maybe, bc), bb) → new_ltEs0(vyy6000, vyy500, bc)
new_primCompAux(vyy6000, vyy500, vyy62, app(app(ty_@2, fg), fh)) → new_compare4(vyy6000, vyy500, fg, fh)
new_ltEs(Right(vyy6000), Right(vyy500), cb, app(app(app(ty_@3, cg), da), db)) → new_ltEs2(vyy6000, vyy500, cg, da, db)
new_ltEs0(Just(vyy6000), Just(vyy500), app(ty_[], dh)) → new_ltEs1(vyy6000, vyy500, dh)
new_ltEs1(:(vyy6000, vyy6001), :(vyy500, vyy501), ef) → new_compare0(vyy6001, vyy501, ef)
new_ltEs2(@3(vyy6000, vyy6001, vyy6002), @3(vyy500, vyy501, vyy502), gg, app(ty_Maybe, bae), bad) → new_lt0(vyy6001, vyy501, bae)
new_ltEs(Left(vyy6000), Left(vyy500), app(ty_[], bd), bb) → new_ltEs1(vyy6000, vyy500, bd)
new_ltEs3(@2(vyy6000, vyy6001), @2(vyy500, vyy501), app(app(ty_Either, bda), bdb), bdc) → new_lt(vyy6000, vyy500, bda, bdb)
new_compare1(vyy6000, vyy500, ga, gb) → new_compare20(vyy6000, vyy500, new_esEs5(vyy6000, vyy500, ga, gb), ga, gb)
new_ltEs2(@3(vyy6000, vyy6001, vyy6002), @3(vyy500, vyy501, vyy502), gg, app(app(ty_Either, bab), bac), bad) → new_lt(vyy6001, vyy501, bab, bac)
new_lt2(vyy6000, vyy500, gd, ge, gf) → new_compare22(vyy6000, vyy500, new_esEs7(vyy6000, vyy500, gd, ge, gf), gd, ge, gf)
new_ltEs(Right(vyy6000), Right(vyy500), cb, app(ty_Maybe, ce)) → new_ltEs0(vyy6000, vyy500, ce)
new_ltEs2(@3(vyy6000, vyy6001, vyy6002), @3(vyy500, vyy501, vyy502), gg, app(app(ty_@2, bbb), bbc), bad) → new_lt3(vyy6001, vyy501, bbb, bbc)
new_compare22(vyy6000, vyy500, False, gd, ge, gf) → new_ltEs2(vyy6000, vyy500, gd, ge, gf)
new_ltEs2(@3(vyy6000, vyy6001, vyy6002), @3(vyy500, vyy501, vyy502), gg, app(ty_[], baf), bad) → new_lt1(vyy6001, vyy501, baf)
new_ltEs3(@2(vyy6000, vyy6001), @2(vyy500, vyy501), app(ty_[], bde), bdc) → new_lt1(vyy6000, vyy500, bde)
new_ltEs2(@3(vyy6000, vyy6001, vyy6002), @3(vyy500, vyy501, vyy502), app(app(ty_@2, bbe), bbf), gh, bad) → new_compare23(vyy6000, vyy500, new_esEs8(vyy6000, vyy500, bbe, bbf), bbe, bbf)
new_ltEs0(Just(vyy6000), Just(vyy500), app(app(ty_Either, de), df)) → new_ltEs(vyy6000, vyy500, de, df)
new_ltEs3(@2(vyy6000, vyy6001), @2(vyy500, vyy501), bbg, app(ty_[], bcc)) → new_ltEs1(vyy6001, vyy501, bcc)
The TRS R consists of the following rules:
new_esEs22(vyy352, vyy362, ty_Double) → new_esEs17(vyy352, vyy362)
new_esEs11(Float(vyy350, vyy351), Float(vyy360, vyy361)) → new_esEs14(new_sr(vyy350, vyy360), new_sr(vyy351, vyy361))
new_ltEs4(Right(vyy6000), Right(vyy500), cb, ty_Integer) → new_ltEs17(vyy6000, vyy500)
new_esEs24(vyy350, vyy360, app(app(ty_Either, chb), chc)) → new_esEs5(vyy350, vyy360, chb, chc)
new_compare5(@0, @0) → EQ
new_ltEs19(vyy6001, vyy501, ty_Ordering) → new_ltEs16(vyy6001, vyy501)
new_ltEs16(GT, GT) → True
new_ltEs8(False, True) → True
new_ltEs4(Right(vyy6000), Right(vyy500), cb, app(ty_[], cf)) → new_ltEs11(vyy6000, vyy500, cf)
new_ltEs4(Right(vyy6000), Right(vyy500), cb, ty_Char) → new_ltEs15(vyy6000, vyy500)
new_compare15(vyy6000, vyy500, True, bbe, bbf) → LT
new_lt7(vyy6000, vyy500) → new_esEs10(new_compare13(vyy6000, vyy500))
new_ltEs19(vyy6001, vyy501, ty_Char) → new_ltEs15(vyy6001, vyy501)
new_ltEs4(Left(vyy6000), Left(vyy500), app(ty_[], bd), bb) → new_ltEs11(vyy6000, vyy500, bd)
new_esEs10(GT) → False
new_esEs23(vyy351, vyy361, app(app(ty_Either, cff), cfg)) → new_esEs5(vyy351, vyy361, cff, cfg)
new_lt16(vyy6000, vyy500, bbe, bbf) → new_esEs10(new_compare9(vyy6000, vyy500, bbe, bbf))
new_lt8(vyy6001, vyy501, app(ty_Ratio, bhf)) → new_lt13(vyy6001, vyy501, bhf)
new_compare([], :(vyy500, vyy501), ef) → LT
new_compare10(vyy6000, vyy500, True, ga, gb) → LT
new_esEs6(Just(vyy350), Just(vyy360), ty_Char) → new_esEs20(vyy350, vyy360)
new_lt8(vyy6001, vyy501, ty_Int) → new_lt19(vyy6001, vyy501)
new_lt8(vyy6001, vyy501, app(app(app(ty_@3, bag), bah), bba)) → new_lt15(vyy6001, vyy501, bag, bah, bba)
new_lt9(vyy6000, vyy500, ty_Float) → new_lt5(vyy6000, vyy500)
new_ltEs16(LT, GT) → True
new_ltEs7(Just(vyy6000), Just(vyy500), ty_Integer) → new_ltEs17(vyy6000, vyy500)
new_lt8(vyy6001, vyy501, ty_Ordering) → new_lt7(vyy6001, vyy501)
new_esEs5(Left(vyy350), Left(vyy360), ty_@0, bec) → new_esEs16(vyy350, vyy360)
new_esEs28(vyy350, vyy360, ty_Int) → new_esEs14(vyy350, vyy360)
new_ltEs6(vyy6002, vyy502, app(ty_Ratio, bhe)) → new_ltEs9(vyy6002, vyy502, bhe)
new_esEs21(vyy350, vyy360, ty_Int) → new_esEs14(vyy350, vyy360)
new_esEs20(Char(vyy350), Char(vyy360)) → new_primEqNat0(vyy350, vyy360)
new_esEs6(Just(vyy350), Just(vyy360), ty_@0) → new_esEs16(vyy350, vyy360)
new_ltEs4(Left(vyy6000), Left(vyy500), ty_Int, bb) → new_ltEs18(vyy6000, vyy500)
new_primMulNat0(Zero, Zero) → Zero
new_esEs25(vyy351, vyy361, ty_Char) → new_esEs20(vyy351, vyy361)
new_esEs6(Just(vyy350), Just(vyy360), app(ty_Ratio, cch)) → new_esEs13(vyy350, vyy360, cch)
new_compare(:(vyy6000, vyy6001), [], ef) → GT
new_esEs23(vyy351, vyy361, app(ty_Ratio, cgc)) → new_esEs13(vyy351, vyy361, cgc)
new_esEs6(Just(vyy350), Just(vyy360), ty_Bool) → new_esEs19(vyy350, vyy360)
new_ltEs6(vyy6002, vyy502, app(app(app(ty_@3, he), hf), hg)) → new_ltEs5(vyy6002, vyy502, he, hf, hg)
new_lt20(vyy6000, vyy500, ty_Integer) → new_lt18(vyy6000, vyy500)
new_esEs6(Just(vyy350), Just(vyy360), ty_Float) → new_esEs11(vyy350, vyy360)
new_lt9(vyy6000, vyy500, ty_Double) → new_lt6(vyy6000, vyy500)
new_lt9(vyy6000, vyy500, app(app(ty_@2, bbe), bbf)) → new_lt16(vyy6000, vyy500, bbe, bbf)
new_not(GT) → False
new_compare17(vyy6000, vyy500, ty_Char) → new_compare14(vyy6000, vyy500)
new_ltEs7(Just(vyy6000), Just(vyy500), ty_Double) → new_ltEs10(vyy6000, vyy500)
new_esEs10(EQ) → False
new_compare17(vyy6000, vyy500, ty_Double) → new_compare8(vyy6000, vyy500)
new_esEs12(GT, LT) → False
new_esEs12(LT, GT) → False
new_esEs5(Right(vyy350), Right(vyy360), bfh, ty_Integer) → new_esEs9(vyy350, vyy360)
new_esEs23(vyy351, vyy361, app(app(ty_FiniteMap, cge), cgf)) → new_esEs15(vyy351, vyy361, cge, cgf)
new_lt8(vyy6001, vyy501, app(app(ty_@2, bbb), bbc)) → new_lt16(vyy6001, vyy501, bbb, bbc)
new_esEs22(vyy352, vyy362, app(ty_Maybe, ceh)) → new_esEs6(vyy352, vyy362, ceh)
new_esEs21(vyy350, vyy360, app(app(app(ty_@3, cad), cae), caf)) → new_esEs7(vyy350, vyy360, cad, cae, caf)
new_esEs22(vyy352, vyy362, ty_Integer) → new_esEs9(vyy352, vyy362)
new_compare28(:%(vyy6000, vyy6001), :%(vyy500, vyy501), ty_Integer) → new_compare16(new_sr0(vyy6000, vyy501), new_sr0(vyy500, vyy6001))
new_lt9(vyy6000, vyy500, ty_Char) → new_lt17(vyy6000, vyy500)
new_esEs29(vyy35, vyy36, app(app(app(ty_@3, cdg), cdh), cea)) → new_esEs7(vyy35, vyy36, cdg, cdh, cea)
new_lt8(vyy6001, vyy501, app(app(ty_Either, bab), bac)) → new_lt10(vyy6001, vyy501, bab, bac)
new_pePe(False, vyy35, vyy36, vyy52, def) → new_asAs(new_esEs29(vyy35, vyy36, def), vyy52)
new_compare26(vyy6000, vyy500, False, bbe, bbf) → new_compare15(vyy6000, vyy500, new_ltEs13(vyy6000, vyy500, bbe, bbf), bbe, bbf)
new_ltEs18(vyy600, vyy50) → new_not(new_compare11(vyy600, vyy50))
new_foldFM0(vyy360, vyy361, vyy80, EmptyFM, cbf, cbg) → :(@2(vyy360, vyy361), vyy80)
new_esEs21(vyy350, vyy360, app(app(ty_@2, cbd), cbe)) → new_esEs8(vyy350, vyy360, cbd, cbe)
new_esEs22(vyy352, vyy362, ty_Ordering) → new_esEs12(vyy352, vyy362)
new_esEs5(Left(vyy350), Left(vyy360), app(ty_Maybe, bfb), bec) → new_esEs6(vyy350, vyy360, bfb)
new_ltEs19(vyy6001, vyy501, app(app(ty_Either, bbh), bca)) → new_ltEs4(vyy6001, vyy501, bbh, bca)
new_ltEs17(vyy600, vyy50) → new_not(new_compare16(vyy600, vyy50))
new_lt9(vyy6000, vyy500, app(app(ty_Either, ga), gb)) → new_lt10(vyy6000, vyy500, ga, gb)
new_esEs26(vyy350, vyy360, app(app(ty_@2, ddh), dea)) → new_esEs8(vyy350, vyy360, ddh, dea)
new_esEs18(:(vyy350, vyy351), [], caa) → False
new_esEs18([], :(vyy360, vyy361), caa) → False
new_ltEs14(vyy600, vyy50) → new_not(new_compare5(vyy600, vyy50))
new_esEs26(vyy350, vyy360, app(app(ty_FiniteMap, dde), ddf)) → new_esEs15(vyy350, vyy360, dde, ddf)
new_lt5(vyy6000, vyy500) → new_esEs10(new_compare6(vyy6000, vyy500))
new_ltEs19(vyy6001, vyy501, app(ty_[], bcc)) → new_ltEs11(vyy6001, vyy501, bcc)
new_esEs6(Just(vyy350), Just(vyy360), app(app(ty_FiniteMap, cdb), cdc)) → new_esEs15(vyy350, vyy360, cdb, cdc)
new_ltEs16(EQ, GT) → True
new_ltEs4(Right(vyy6000), Right(vyy500), cb, app(app(ty_Either, cc), cd)) → new_ltEs4(vyy6000, vyy500, cc, cd)
new_lt20(vyy6000, vyy500, ty_Float) → new_lt5(vyy6000, vyy500)
new_esEs29(vyy35, vyy36, app(ty_Ratio, dec)) → new_esEs13(vyy35, vyy36, dec)
new_lt8(vyy6001, vyy501, app(ty_[], baf)) → new_lt14(vyy6001, vyy501, baf)
new_ltEs4(Left(vyy6000), Right(vyy500), cb, bb) → True
new_esEs25(vyy351, vyy361, app(app(ty_FiniteMap, dca), dcb)) → new_esEs15(vyy351, vyy361, dca, dcb)
new_esEs23(vyy351, vyy361, app(app(app(ty_@3, cfh), cga), cgb)) → new_esEs7(vyy351, vyy361, cfh, cga, cgb)
new_primCmpNat0(Zero, Succ(vyy5000)) → LT
new_compare211(vyy6000, vyy500, False) → new_compare110(vyy6000, vyy500, new_ltEs16(vyy6000, vyy500))
new_esEs5(Left(vyy350), Left(vyy360), ty_Float, bec) → new_esEs11(vyy350, vyy360)
new_esEs26(vyy350, vyy360, ty_Double) → new_esEs17(vyy350, vyy360)
new_compare29(vyy6000, vyy500, False, gc) → new_compare111(vyy6000, vyy500, new_ltEs7(vyy6000, vyy500, gc), gc)
new_compare17(vyy6000, vyy500, ty_Bool) → new_compare27(vyy6000, vyy500)
new_esEs25(vyy351, vyy361, app(app(ty_Either, dbb), dbc)) → new_esEs5(vyy351, vyy361, dbb, dbc)
new_esEs6(Just(vyy350), Just(vyy360), ty_Ordering) → new_esEs12(vyy350, vyy360)
new_lt11(vyy6000, vyy500, gc) → new_esEs10(new_compare19(vyy6000, vyy500, gc))
new_compare25(vyy6000, vyy500, True, gd, ge, gf) → EQ
new_esEs21(vyy350, vyy360, app(ty_Ratio, cag)) → new_esEs13(vyy350, vyy360, cag)
new_esEs25(vyy351, vyy361, ty_Double) → new_esEs17(vyy351, vyy361)
new_ltEs4(Left(vyy6000), Left(vyy500), app(ty_Ratio, ded), bb) → new_ltEs9(vyy6000, vyy500, ded)
new_esEs12(LT, LT) → True
new_esEs25(vyy351, vyy361, app(ty_Ratio, dbg)) → new_esEs13(vyy351, vyy361, dbg)
new_esEs23(vyy351, vyy361, ty_Int) → new_esEs14(vyy351, vyy361)
new_esEs5(Right(vyy350), Right(vyy360), bfh, app(app(ty_@2, bhc), bhd)) → new_esEs8(vyy350, vyy360, bhc, bhd)
new_compare27(vyy6000, vyy500) → new_compare210(vyy6000, vyy500, new_esEs19(vyy6000, vyy500))
new_esEs23(vyy351, vyy361, ty_@0) → new_esEs16(vyy351, vyy361)
new_primEqNat0(Zero, Zero) → True
new_esEs6(Just(vyy350), Just(vyy360), app(app(app(ty_@3, cce), ccf), ccg)) → new_esEs7(vyy350, vyy360, cce, ccf, ccg)
new_lt9(vyy6000, vyy500, app(ty_[], bbd)) → new_lt14(vyy6000, vyy500, bbd)
new_esEs29(vyy35, vyy36, app(ty_Maybe, ccb)) → new_esEs6(vyy35, vyy36, ccb)
new_ltEs6(vyy6002, vyy502, ty_Ordering) → new_ltEs16(vyy6002, vyy502)
new_esEs26(vyy350, vyy360, app(ty_Maybe, ddd)) → new_esEs6(vyy350, vyy360, ddd)
new_esEs25(vyy351, vyy361, app(ty_[], dcc)) → new_esEs18(vyy351, vyy361, dcc)
new_primMulNat0(Succ(vyy50000), Succ(vyy600100)) → new_primPlusNat1(new_primMulNat0(vyy50000, Succ(vyy600100)), vyy600100)
new_lt8(vyy6001, vyy501, ty_@0) → new_lt4(vyy6001, vyy501)
new_esEs29(vyy35, vyy36, ty_Int) → new_esEs14(vyy35, vyy36)
new_esEs23(vyy351, vyy361, ty_Integer) → new_esEs9(vyy351, vyy361)
new_esEs26(vyy350, vyy360, app(ty_Ratio, ddc)) → new_esEs13(vyy350, vyy360, ddc)
new_esEs6(Just(vyy350), Just(vyy360), ty_Int) → new_esEs14(vyy350, vyy360)
new_esEs24(vyy350, vyy360, app(ty_[], dac)) → new_esEs18(vyy350, vyy360, dac)
new_esEs26(vyy350, vyy360, ty_@0) → new_esEs16(vyy350, vyy360)
new_ltEs7(Just(vyy6000), Just(vyy500), ty_Float) → new_ltEs12(vyy6000, vyy500)
new_esEs19(True, True) → True
new_ltEs16(EQ, LT) → False
new_ltEs16(GT, EQ) → False
new_sr(vyy500, vyy6001) → new_primMulInt(vyy500, vyy6001)
new_compare12(vyy6000, vyy500, True, gd, ge, gf) → LT
new_ltEs6(vyy6002, vyy502, ty_Integer) → new_ltEs17(vyy6002, vyy502)
new_lt8(vyy6001, vyy501, ty_Char) → new_lt17(vyy6001, vyy501)
new_lt20(vyy6000, vyy500, app(ty_Maybe, bdd)) → new_lt11(vyy6000, vyy500, bdd)
new_compare9(vyy6000, vyy500, bbe, bbf) → new_compare26(vyy6000, vyy500, new_esEs8(vyy6000, vyy500, bbe, bbf), bbe, bbf)
new_esEs5(Right(vyy350), Right(vyy360), bfh, app(ty_[], bhb)) → new_esEs18(vyy350, vyy360, bhb)
new_esEs26(vyy350, vyy360, ty_Float) → new_esEs11(vyy350, vyy360)
new_ltEs19(vyy6001, vyy501, ty_Double) → new_ltEs10(vyy6001, vyy501)
new_esEs22(vyy352, vyy362, app(ty_[], cfc)) → new_esEs18(vyy352, vyy362, cfc)
new_lt20(vyy6000, vyy500, ty_Char) → new_lt17(vyy6000, vyy500)
new_lt19(vyy6000, vyy500) → new_esEs10(new_compare11(vyy6000, vyy500))
new_ltEs6(vyy6002, vyy502, ty_Double) → new_ltEs10(vyy6002, vyy502)
new_esEs5(Left(vyy350), Left(vyy360), app(ty_Ratio, bfa), bec) → new_esEs13(vyy350, vyy360, bfa)
new_esEs25(vyy351, vyy361, ty_Ordering) → new_esEs12(vyy351, vyy361)
new_primEqInt(Neg(Succ(vyy3500)), Neg(Succ(vyy3600))) → new_primEqNat0(vyy3500, vyy3600)
new_esEs25(vyy351, vyy361, app(app(ty_@2, dcd), dce)) → new_esEs8(vyy351, vyy361, dcd, dce)
new_ltEs16(LT, EQ) → True
new_compare7(vyy6000, vyy500, gd, ge, gf) → new_compare25(vyy6000, vyy500, new_esEs7(vyy6000, vyy500, gd, ge, gf), gd, ge, gf)
new_ltEs6(vyy6002, vyy502, ty_Float) → new_ltEs12(vyy6002, vyy502)
new_esEs24(vyy350, vyy360, ty_Bool) → new_esEs19(vyy350, vyy360)
new_esEs21(vyy350, vyy360, ty_@0) → new_esEs16(vyy350, vyy360)
new_compare17(vyy6000, vyy500, ty_Float) → new_compare6(vyy6000, vyy500)
new_esEs29(vyy35, vyy36, app(app(ty_Either, bfh), bec)) → new_esEs5(vyy35, vyy36, bfh, bec)
new_ltEs8(True, True) → True
new_esEs26(vyy350, vyy360, app(app(app(ty_@3, dch), dda), ddb)) → new_esEs7(vyy350, vyy360, dch, dda, ddb)
new_ltEs4(Left(vyy6000), Left(vyy500), ty_Char, bb) → new_ltEs15(vyy6000, vyy500)
new_ltEs4(Left(vyy6000), Left(vyy500), ty_Float, bb) → new_ltEs12(vyy6000, vyy500)
new_ltEs19(vyy6001, vyy501, app(ty_Ratio, daf)) → new_ltEs9(vyy6001, vyy501, daf)
new_esEs12(LT, EQ) → False
new_esEs12(EQ, LT) → False
new_ltEs15(vyy600, vyy50) → new_not(new_compare14(vyy600, vyy50))
new_esEs21(vyy350, vyy360, app(ty_[], cbc)) → new_esEs18(vyy350, vyy360, cbc)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs5(Left(vyy350), Left(vyy360), app(app(app(ty_@3, bef), beg), beh), bec) → new_esEs7(vyy350, vyy360, bef, beg, beh)
new_compare17(vyy6000, vyy500, app(ty_Ratio, bhh)) → new_compare28(vyy6000, vyy500, bhh)
new_esEs19(False, False) → True
new_lt20(vyy6000, vyy500, ty_Ordering) → new_lt7(vyy6000, vyy500)
new_compare17(vyy6000, vyy500, ty_Int) → new_compare11(vyy6000, vyy500)
new_primEqInt(Neg(Zero), Neg(Succ(vyy3600))) → False
new_primEqInt(Neg(Succ(vyy3500)), Neg(Zero)) → False
new_ltEs4(Left(vyy6000), Left(vyy500), app(app(ty_Either, h), ba), bb) → new_ltEs4(vyy6000, vyy500, h, ba)
new_ltEs9(vyy600, vyy50, deb) → new_not(new_compare28(vyy600, vyy50, deb))
new_compare26(vyy6000, vyy500, True, bbe, bbf) → EQ
new_primPlusNat1(Zero, vyy600100) → Succ(vyy600100)
new_compare111(vyy6000, vyy500, True, gc) → LT
new_esEs24(vyy350, vyy360, ty_Integer) → new_esEs9(vyy350, vyy360)
new_compare24(vyy6000, vyy500, True, ga, gb) → EQ
new_esEs6(Just(vyy350), Just(vyy360), ty_Double) → new_esEs17(vyy350, vyy360)
new_esEs26(vyy350, vyy360, app(ty_[], ddg)) → new_esEs18(vyy350, vyy360, ddg)
new_compare([], [], ef) → EQ
new_foldFM0(vyy360, vyy361, vyy80, Branch(vyy3630, vyy3631, vyy3632, vyy3633, vyy3634), cbf, cbg) → new_foldFM0(vyy3630, vyy3631, new_foldFM0(vyy360, vyy361, vyy80, vyy3634, cbf, cbg), vyy3633, cbf, cbg)
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_ltEs7(Just(vyy6000), Just(vyy500), ty_Int) → new_ltEs18(vyy6000, vyy500)
new_ltEs4(Right(vyy6000), Right(vyy500), cb, app(ty_Maybe, ce)) → new_ltEs7(vyy6000, vyy500, ce)
new_compare14(Char(vyy6000), Char(vyy500)) → new_primCmpNat0(vyy6000, vyy500)
new_lt9(vyy6000, vyy500, app(ty_Ratio, bhg)) → new_lt13(vyy6000, vyy500, bhg)
new_ltEs16(GT, LT) → False
new_lt9(vyy6000, vyy500, ty_Ordering) → new_lt7(vyy6000, vyy500)
new_primCmpNat0(Succ(vyy60000), Succ(vyy5000)) → new_primCmpNat0(vyy60000, vyy5000)
new_esEs22(vyy352, vyy362, ty_Char) → new_esEs20(vyy352, vyy362)
new_esEs9(Integer(vyy350), Integer(vyy360)) → new_primEqInt(vyy350, vyy360)
new_sizeFM(EmptyFM, cbf, cbg) → Pos(Zero)
new_esEs6(Nothing, Nothing, ccb) → True
new_compare112(vyy6000, vyy500, True) → LT
new_primEqInt(Pos(Succ(vyy3500)), Pos(Succ(vyy3600))) → new_primEqNat0(vyy3500, vyy3600)
new_compare10(vyy6000, vyy500, False, ga, gb) → GT
new_ltEs19(vyy6001, vyy501, ty_Integer) → new_ltEs17(vyy6001, vyy501)
new_esEs21(vyy350, vyy360, app(ty_Maybe, cah)) → new_esEs6(vyy350, vyy360, cah)
new_esEs26(vyy350, vyy360, ty_Bool) → new_esEs19(vyy350, vyy360)
new_ltEs7(Nothing, Just(vyy500), cbh) → True
new_ltEs6(vyy6002, vyy502, ty_Int) → new_ltEs18(vyy6002, vyy502)
new_esEs5(Right(vyy350), Right(vyy360), bfh, app(app(ty_Either, bga), bgb)) → new_esEs5(vyy350, vyy360, bga, bgb)
new_lt9(vyy6000, vyy500, ty_Int) → new_lt19(vyy6000, vyy500)
new_esEs6(Just(vyy350), Nothing, ccb) → False
new_esEs6(Nothing, Just(vyy360), ccb) → False
new_esEs15(vyy35, vyy36, cbf, cbg) → new_asAs(new_esEs14(new_sizeFM(vyy35, cbf, cbg), new_sizeFM(vyy36, cbf, cbg)), new_esEs18(new_fmToList(vyy35, cbf, cbg), new_fmToList(vyy36, cbf, cbg), app(app(ty_@2, cbf), cbg)))
new_primEqNat0(Succ(vyy3500), Succ(vyy3600)) → new_primEqNat0(vyy3500, vyy3600)
new_esEs24(vyy350, vyy360, ty_@0) → new_esEs16(vyy350, vyy360)
new_compare17(vyy6000, vyy500, ty_Integer) → new_compare16(vyy6000, vyy500)
new_esEs26(vyy350, vyy360, ty_Ordering) → new_esEs12(vyy350, vyy360)
new_lt9(vyy6000, vyy500, ty_Bool) → new_lt12(vyy6000, vyy500)
new_lt8(vyy6001, vyy501, app(ty_Maybe, bae)) → new_lt11(vyy6001, vyy501, bae)
new_primCompAux00(vyy66, LT) → LT
new_ltEs5(@3(vyy6000, vyy6001, vyy6002), @3(vyy500, vyy501, vyy502), gg, gh, bad) → new_pePe(new_lt9(vyy6000, vyy500, gg), vyy6000, vyy500, new_pePe(new_lt8(vyy6001, vyy501, gh), vyy6001, vyy501, new_ltEs6(vyy6002, vyy502, bad), gh), gg)
new_lt4(vyy6000, vyy500) → new_esEs10(new_compare5(vyy6000, vyy500))
new_ltEs4(Right(vyy6000), Right(vyy500), cb, ty_Float) → new_ltEs12(vyy6000, vyy500)
new_lt20(vyy6000, vyy500, ty_@0) → new_lt4(vyy6000, vyy500)
new_primCmpInt(Neg(Succ(vyy60000)), Neg(vyy500)) → new_primCmpNat0(vyy500, Succ(vyy60000))
new_compare17(vyy6000, vyy500, app(app(ty_@2, fg), fh)) → new_compare9(vyy6000, vyy500, fg, fh)
new_esEs12(EQ, EQ) → True
new_ltEs19(vyy6001, vyy501, ty_Bool) → new_ltEs8(vyy6001, vyy501)
new_esEs5(Right(vyy350), Right(vyy360), bfh, ty_@0) → new_esEs16(vyy350, vyy360)
new_esEs22(vyy352, vyy362, app(app(ty_FiniteMap, cfa), cfb)) → new_esEs15(vyy352, vyy362, cfa, cfb)
new_compare24(vyy6000, vyy500, False, ga, gb) → new_compare10(vyy6000, vyy500, new_ltEs4(vyy6000, vyy500, ga, gb), ga, gb)
new_ltEs6(vyy6002, vyy502, app(ty_Maybe, hc)) → new_ltEs7(vyy6002, vyy502, hc)
new_esEs5(Left(vyy350), Left(vyy360), ty_Int, bec) → new_esEs14(vyy350, vyy360)
new_primEqInt(Pos(Succ(vyy3500)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(vyy3600))) → False
new_ltEs13(@2(vyy6000, vyy6001), @2(vyy500, vyy501), bbg, bdc) → new_pePe(new_lt20(vyy6000, vyy500, bbg), vyy6000, vyy500, new_ltEs19(vyy6001, vyy501, bdc), bbg)
new_primPlusNat0(Succ(vyy8100), Zero) → Succ(vyy8100)
new_primPlusNat0(Zero, Succ(vyy6001000)) → Succ(vyy6001000)
new_lt9(vyy6000, vyy500, ty_@0) → new_lt4(vyy6000, vyy500)
new_esEs21(vyy350, vyy360, ty_Bool) → new_esEs19(vyy350, vyy360)
new_lt15(vyy6000, vyy500, gd, ge, gf) → new_esEs10(new_compare7(vyy6000, vyy500, gd, ge, gf))
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(vyy60000), Zero) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(vyy5000))) → LT
new_esEs19(False, True) → False
new_esEs19(True, False) → False
new_esEs5(Right(vyy350), Right(vyy360), bfh, ty_Bool) → new_esEs19(vyy350, vyy360)
new_lt10(vyy6000, vyy500, ga, gb) → new_esEs10(new_compare18(vyy6000, vyy500, ga, gb))
new_esEs22(vyy352, vyy362, app(ty_Ratio, ceg)) → new_esEs13(vyy352, vyy362, ceg)
new_compare17(vyy6000, vyy500, app(ty_[], fb)) → new_compare(vyy6000, vyy500, fb)
new_esEs27(vyy351, vyy361, ty_Integer) → new_esEs9(vyy351, vyy361)
new_sr0(Integer(vyy5000), Integer(vyy60010)) → Integer(new_primMulInt(vyy5000, vyy60010))
new_esEs21(vyy350, vyy360, ty_Double) → new_esEs17(vyy350, vyy360)
new_primEqInt(Pos(Succ(vyy3500)), Neg(vyy360)) → False
new_primEqInt(Neg(Succ(vyy3500)), Pos(vyy360)) → False
new_esEs25(vyy351, vyy361, ty_Bool) → new_esEs19(vyy351, vyy361)
new_esEs24(vyy350, vyy360, app(ty_Ratio, chg)) → new_esEs13(vyy350, vyy360, chg)
new_compare(:(vyy6000, vyy6001), :(vyy500, vyy501), ef) → new_primCompAux0(vyy6000, vyy500, new_compare(vyy6001, vyy501, ef), ef)
new_foldFM2(EmptyFM, cbf, cbg) → []
new_esEs24(vyy350, vyy360, ty_Int) → new_esEs14(vyy350, vyy360)
new_esEs21(vyy350, vyy360, ty_Ordering) → new_esEs12(vyy350, vyy360)
new_lt8(vyy6001, vyy501, ty_Float) → new_lt5(vyy6001, vyy501)
new_primEqInt(Neg(Zero), Pos(Succ(vyy3600))) → False
new_primEqInt(Pos(Zero), Neg(Succ(vyy3600))) → False
new_esEs24(vyy350, vyy360, ty_Ordering) → new_esEs12(vyy350, vyy360)
new_primCmpInt(Pos(Zero), Pos(Succ(vyy5000))) → new_primCmpNat0(Zero, Succ(vyy5000))
new_primCompAux00(vyy66, EQ) → vyy66
new_esEs23(vyy351, vyy361, ty_Double) → new_esEs17(vyy351, vyy361)
new_ltEs16(EQ, EQ) → True
new_esEs23(vyy351, vyy361, ty_Bool) → new_esEs19(vyy351, vyy361)
new_compare17(vyy6000, vyy500, app(app(ty_Either, eg), eh)) → new_compare18(vyy6000, vyy500, eg, eh)
new_esEs22(vyy352, vyy362, ty_Bool) → new_esEs19(vyy352, vyy362)
new_esEs6(Just(vyy350), Just(vyy360), app(app(ty_@2, cde), cdf)) → new_esEs8(vyy350, vyy360, cde, cdf)
new_esEs22(vyy352, vyy362, ty_@0) → new_esEs16(vyy352, vyy362)
new_esEs5(Left(vyy350), Left(vyy360), ty_Double, bec) → new_esEs17(vyy350, vyy360)
new_esEs7(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), cdg, cdh, cea) → new_asAs(new_esEs24(vyy350, vyy360, cdg), new_asAs(new_esEs23(vyy351, vyy361, cdh), new_esEs22(vyy352, vyy362, cea)))
new_esEs29(vyy35, vyy36, app(app(ty_FiniteMap, cbf), cbg)) → new_esEs15(vyy35, vyy36, cbf, cbg)
new_ltEs19(vyy6001, vyy501, app(app(ty_@2, bcg), bch)) → new_ltEs13(vyy6001, vyy501, bcg, bch)
new_esEs23(vyy351, vyy361, ty_Float) → new_esEs11(vyy351, vyy361)
new_ltEs8(True, False) → False
new_esEs5(Left(vyy350), Left(vyy360), app(app(ty_@2, bff), bfg), bec) → new_esEs8(vyy350, vyy360, bff, bfg)
new_ltEs4(Right(vyy6000), Left(vyy500), cb, bb) → False
new_compare16(Integer(vyy6000), Integer(vyy500)) → new_primCmpInt(vyy6000, vyy500)
new_primCmpInt(Pos(Succ(vyy60000)), Pos(vyy500)) → new_primCmpNat0(Succ(vyy60000), vyy500)
new_esEs22(vyy352, vyy362, ty_Float) → new_esEs11(vyy352, vyy362)
new_esEs12(GT, EQ) → False
new_esEs12(EQ, GT) → False
new_compare12(vyy6000, vyy500, False, gd, ge, gf) → GT
new_lt8(vyy6001, vyy501, ty_Integer) → new_lt18(vyy6001, vyy501)
new_esEs6(Just(vyy350), Just(vyy360), app(ty_[], cdd)) → new_esEs18(vyy350, vyy360, cdd)
new_esEs29(vyy35, vyy36, app(app(ty_@2, dah), dba)) → new_esEs8(vyy35, vyy36, dah, dba)
new_ltEs4(Right(vyy6000), Right(vyy500), cb, ty_Ordering) → new_ltEs16(vyy6000, vyy500)
new_lt20(vyy6000, vyy500, app(app(app(ty_@3, bdf), bdg), bdh)) → new_lt15(vyy6000, vyy500, bdf, bdg, bdh)
new_ltEs19(vyy6001, vyy501, ty_Int) → new_ltEs18(vyy6001, vyy501)
new_lt9(vyy6000, vyy500, ty_Integer) → new_lt18(vyy6000, vyy500)
new_not0 → True
new_esEs5(Right(vyy350), Right(vyy360), bfh, ty_Int) → new_esEs14(vyy350, vyy360)
new_esEs5(Right(vyy350), Right(vyy360), bfh, ty_Double) → new_esEs17(vyy350, vyy360)
new_compare17(vyy6000, vyy500, app(ty_Maybe, fa)) → new_compare19(vyy6000, vyy500, fa)
new_ltEs6(vyy6002, vyy502, app(ty_[], hd)) → new_ltEs11(vyy6002, vyy502, hd)
new_lt20(vyy6000, vyy500, ty_Double) → new_lt6(vyy6000, vyy500)
new_esEs26(vyy350, vyy360, app(app(ty_Either, dcf), dcg)) → new_esEs5(vyy350, vyy360, dcf, dcg)
new_primCompAux0(vyy6000, vyy500, vyy62, ef) → new_primCompAux00(vyy62, new_compare17(vyy6000, vyy500, ef))
new_esEs5(Left(vyy350), Left(vyy360), ty_Bool, bec) → new_esEs19(vyy350, vyy360)
new_esEs5(Right(vyy350), Right(vyy360), bfh, app(app(ty_FiniteMap, bgh), bha)) → new_esEs15(vyy350, vyy360, bgh, bha)
new_ltEs4(Right(vyy6000), Right(vyy500), cb, app(ty_Ratio, dee)) → new_ltEs9(vyy6000, vyy500, dee)
new_esEs22(vyy352, vyy362, app(app(app(ty_@3, ced), cee), cef)) → new_esEs7(vyy352, vyy362, ced, cee, cef)
new_primCmpInt(Pos(Succ(vyy60000)), Neg(vyy500)) → GT
new_lt6(vyy6000, vyy500) → new_esEs10(new_compare8(vyy6000, vyy500))
new_ltEs7(Just(vyy6000), Just(vyy500), app(ty_Maybe, dg)) → new_ltEs7(vyy6000, vyy500, dg)
new_ltEs4(Right(vyy6000), Right(vyy500), cb, ty_Bool) → new_ltEs8(vyy6000, vyy500)
new_esEs29(vyy35, vyy36, ty_@0) → new_esEs16(vyy35, vyy36)
new_esEs29(vyy35, vyy36, ty_Integer) → new_esEs9(vyy35, vyy36)
new_primMulInt(Pos(vyy5000), Pos(vyy60010)) → Pos(new_primMulNat0(vyy5000, vyy60010))
new_compare13(vyy6000, vyy500) → new_compare211(vyy6000, vyy500, new_esEs12(vyy6000, vyy500))
new_ltEs4(Left(vyy6000), Left(vyy500), app(app(ty_@2, bh), ca), bb) → new_ltEs13(vyy6000, vyy500, bh, ca)
new_ltEs4(Left(vyy6000), Left(vyy500), ty_@0, bb) → new_ltEs14(vyy6000, vyy500)
new_ltEs4(Left(vyy6000), Left(vyy500), ty_Integer, bb) → new_ltEs17(vyy6000, vyy500)
new_esEs24(vyy350, vyy360, app(app(ty_FiniteMap, daa), dab)) → new_esEs15(vyy350, vyy360, daa, dab)
new_ltEs6(vyy6002, vyy502, app(app(ty_Either, ha), hb)) → new_ltEs4(vyy6002, vyy502, ha, hb)
new_lt20(vyy6000, vyy500, app(app(ty_Either, bda), bdb)) → new_lt10(vyy6000, vyy500, bda, bdb)
new_esEs5(Right(vyy350), Left(vyy360), bfh, bec) → False
new_esEs5(Left(vyy350), Right(vyy360), bfh, bec) → False
new_primMulInt(Neg(vyy5000), Neg(vyy60010)) → Pos(new_primMulNat0(vyy5000, vyy60010))
new_compare110(vyy6000, vyy500, True) → LT
new_ltEs4(Right(vyy6000), Right(vyy500), cb, app(app(ty_@2, dc), dd)) → new_ltEs13(vyy6000, vyy500, dc, dd)
new_primEqNat0(Succ(vyy3500), Zero) → False
new_primEqNat0(Zero, Succ(vyy3600)) → False
new_ltEs8(False, False) → True
new_primPlusNat0(Zero, Zero) → Zero
new_esEs25(vyy351, vyy361, app(ty_Maybe, dbh)) → new_esEs6(vyy351, vyy361, dbh)
new_compare110(vyy6000, vyy500, False) → GT
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs5(Left(vyy350), Left(vyy360), app(ty_[], bfe), bec) → new_esEs18(vyy350, vyy360, bfe)
new_compare210(vyy6000, vyy500, True) → EQ
new_sizeFM(Branch(vyy360, vyy361, vyy362, vyy363, vyy364), cbf, cbg) → vyy362
new_ltEs4(Right(vyy6000), Right(vyy500), cb, ty_Double) → new_ltEs10(vyy6000, vyy500)
new_ltEs7(Nothing, Nothing, cbh) → True
new_pePe(True, vyy35, vyy36, vyy52, def) → True
new_primPlusNat1(Succ(vyy810), vyy600100) → Succ(Succ(new_primPlusNat0(vyy810, vyy600100)))
new_foldFM2(Branch(vyy360, vyy361, vyy362, vyy363, vyy364), cbf, cbg) → new_foldFM0(vyy360, vyy361, new_foldFM2(vyy364, cbf, cbg), vyy363, cbf, cbg)
new_esEs5(Left(vyy350), Left(vyy360), app(app(ty_FiniteMap, bfc), bfd), bec) → new_esEs15(vyy350, vyy360, bfc, bfd)
new_ltEs7(Just(vyy6000), Just(vyy500), app(app(app(ty_@3, ea), eb), ec)) → new_ltEs5(vyy6000, vyy500, ea, eb, ec)
new_lt9(vyy6000, vyy500, app(app(app(ty_@3, gd), ge), gf)) → new_lt15(vyy6000, vyy500, gd, ge, gf)
new_ltEs7(Just(vyy6000), Just(vyy500), ty_Ordering) → new_ltEs16(vyy6000, vyy500)
new_primCmpInt(Neg(Zero), Neg(Succ(vyy5000))) → new_primCmpNat0(Succ(vyy5000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(vyy5000))) → GT
new_esEs29(vyy35, vyy36, ty_Bool) → new_esEs19(vyy35, vyy36)
new_esEs23(vyy351, vyy361, app(app(ty_@2, cgh), cha)) → new_esEs8(vyy351, vyy361, cgh, cha)
new_ltEs6(vyy6002, vyy502, app(app(ty_@2, hh), baa)) → new_ltEs13(vyy6002, vyy502, hh, baa)
new_esEs5(Right(vyy350), Right(vyy360), bfh, app(app(app(ty_@3, bgc), bgd), bge)) → new_esEs7(vyy350, vyy360, bgc, bgd, bge)
new_compare15(vyy6000, vyy500, False, bbe, bbf) → GT
new_ltEs7(Just(vyy6000), Just(vyy500), ty_Char) → new_ltEs15(vyy6000, vyy500)
new_esEs25(vyy351, vyy361, ty_Int) → new_esEs14(vyy351, vyy361)
new_esEs6(Just(vyy350), Just(vyy360), app(app(ty_Either, ccc), ccd)) → new_esEs5(vyy350, vyy360, ccc, ccd)
new_lt14(vyy6000, vyy500, bbd) → new_esEs10(new_compare(vyy6000, vyy500, bbd))
new_esEs10(LT) → True
new_esEs5(Right(vyy350), Right(vyy360), bfh, ty_Float) → new_esEs11(vyy350, vyy360)
new_ltEs6(vyy6002, vyy502, ty_@0) → new_ltEs14(vyy6002, vyy502)
new_esEs27(vyy351, vyy361, ty_Int) → new_esEs14(vyy351, vyy361)
new_esEs28(vyy350, vyy360, ty_Integer) → new_esEs9(vyy350, vyy360)
new_esEs26(vyy350, vyy360, ty_Char) → new_esEs20(vyy350, vyy360)
new_esEs24(vyy350, vyy360, app(app(app(ty_@3, chd), che), chf)) → new_esEs7(vyy350, vyy360, chd, che, chf)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_compare29(vyy6000, vyy500, True, gc) → EQ
new_lt8(vyy6001, vyy501, ty_Double) → new_lt6(vyy6001, vyy501)
new_compare17(vyy6000, vyy500, ty_Ordering) → new_compare13(vyy6000, vyy500)
new_esEs26(vyy350, vyy360, ty_Int) → new_esEs14(vyy350, vyy360)
new_esEs13(:%(vyy350, vyy351), :%(vyy360, vyy361), dec) → new_asAs(new_esEs28(vyy350, vyy360, dec), new_esEs27(vyy351, vyy361, dec))
new_esEs6(Just(vyy350), Just(vyy360), ty_Integer) → new_esEs9(vyy350, vyy360)
new_asAs(False, vyy61) → False
new_compare18(vyy6000, vyy500, ga, gb) → new_compare24(vyy6000, vyy500, new_esEs5(vyy6000, vyy500, ga, gb), ga, gb)
new_primMulInt(Pos(vyy5000), Neg(vyy60010)) → Neg(new_primMulNat0(vyy5000, vyy60010))
new_primMulInt(Neg(vyy5000), Pos(vyy60010)) → Neg(new_primMulNat0(vyy5000, vyy60010))
new_lt12(vyy6000, vyy500) → new_esEs10(new_compare27(vyy6000, vyy500))
new_primMulNat0(Zero, Succ(vyy600100)) → Zero
new_primMulNat0(Succ(vyy50000), Zero) → Zero
new_compare8(Double(vyy6000, vyy6001), Double(vyy500, vyy501)) → new_compare11(new_sr(vyy6000, vyy500), new_sr(vyy6001, vyy501))
new_esEs18([], [], caa) → True
new_esEs21(vyy350, vyy360, app(app(ty_Either, cab), cac)) → new_esEs5(vyy350, vyy360, cab, cac)
new_esEs29(vyy35, vyy36, ty_Char) → new_esEs20(vyy35, vyy36)
new_esEs6(Just(vyy350), Just(vyy360), app(ty_Maybe, cda)) → new_esEs6(vyy350, vyy360, cda)
new_esEs21(vyy350, vyy360, app(app(ty_FiniteMap, cba), cbb)) → new_esEs15(vyy350, vyy360, cba, cbb)
new_esEs25(vyy351, vyy361, ty_@0) → new_esEs16(vyy351, vyy361)
new_lt20(vyy6000, vyy500, app(ty_[], bde)) → new_lt14(vyy6000, vyy500, bde)
new_esEs29(vyy35, vyy36, ty_Float) → new_esEs11(vyy35, vyy36)
new_ltEs4(Right(vyy6000), Right(vyy500), cb, ty_@0) → new_ltEs14(vyy6000, vyy500)
new_esEs23(vyy351, vyy361, ty_Ordering) → new_esEs12(vyy351, vyy361)
new_esEs29(vyy35, vyy36, ty_Double) → new_esEs17(vyy35, vyy36)
new_ltEs11(vyy600, vyy50, ef) → new_not(new_compare(vyy600, vyy50, ef))
new_esEs24(vyy350, vyy360, ty_Float) → new_esEs11(vyy350, vyy360)
new_not(EQ) → new_not0
new_esEs23(vyy351, vyy361, app(ty_Maybe, cgd)) → new_esEs6(vyy351, vyy361, cgd)
new_lt20(vyy6000, vyy500, app(app(ty_@2, bea), beb)) → new_lt16(vyy6000, vyy500, bea, beb)
new_esEs21(vyy350, vyy360, ty_Integer) → new_esEs9(vyy350, vyy360)
new_esEs24(vyy350, vyy360, ty_Char) → new_esEs20(vyy350, vyy360)
new_esEs26(vyy350, vyy360, ty_Integer) → new_esEs9(vyy350, vyy360)
new_ltEs7(Just(vyy6000), Just(vyy500), app(ty_[], dh)) → new_ltEs11(vyy6000, vyy500, dh)
new_esEs16(@0, @0) → True
new_lt9(vyy6000, vyy500, app(ty_Maybe, gc)) → new_lt11(vyy6000, vyy500, gc)
new_ltEs19(vyy6001, vyy501, ty_@0) → new_ltEs14(vyy6001, vyy501)
new_compare111(vyy6000, vyy500, False, gc) → GT
new_ltEs6(vyy6002, vyy502, ty_Bool) → new_ltEs8(vyy6002, vyy502)
new_esEs5(Left(vyy350), Left(vyy360), ty_Char, bec) → new_esEs20(vyy350, vyy360)
new_esEs24(vyy350, vyy360, ty_Double) → new_esEs17(vyy350, vyy360)
new_esEs5(Right(vyy350), Right(vyy360), bfh, app(ty_Maybe, bgg)) → new_esEs6(vyy350, vyy360, bgg)
new_ltEs7(Just(vyy6000), Just(vyy500), ty_Bool) → new_ltEs8(vyy6000, vyy500)
new_ltEs7(Just(vyy6000), Just(vyy500), ty_@0) → new_ltEs14(vyy6000, vyy500)
new_compare11(vyy600, vyy50) → new_primCmpInt(vyy600, vyy50)
new_esEs14(vyy35, vyy36) → new_primEqInt(vyy35, vyy36)
new_ltEs19(vyy6001, vyy501, app(app(app(ty_@3, bcd), bce), bcf)) → new_ltEs5(vyy6001, vyy501, bcd, bce, bcf)
new_esEs25(vyy351, vyy361, app(app(app(ty_@3, dbd), dbe), dbf)) → new_esEs7(vyy351, vyy361, dbd, dbe, dbf)
new_esEs8(@2(vyy350, vyy351), @2(vyy360, vyy361), dah, dba) → new_asAs(new_esEs26(vyy350, vyy360, dah), new_esEs25(vyy351, vyy361, dba))
new_ltEs6(vyy6002, vyy502, ty_Char) → new_ltEs15(vyy6002, vyy502)
new_compare17(vyy6000, vyy500, app(app(app(ty_@3, fc), fd), ff)) → new_compare7(vyy6000, vyy500, fc, fd, ff)
new_esEs21(vyy350, vyy360, ty_Char) → new_esEs20(vyy350, vyy360)
new_ltEs7(Just(vyy6000), Nothing, cbh) → False
new_lt20(vyy6000, vyy500, ty_Int) → new_lt19(vyy6000, vyy500)
new_lt13(vyy6000, vyy500, bhg) → new_esEs10(new_compare28(vyy6000, vyy500, bhg))
new_not(LT) → new_not0
new_lt18(vyy6000, vyy500) → new_esEs10(new_compare16(vyy6000, vyy500))
new_ltEs19(vyy6001, vyy501, app(ty_Maybe, bcb)) → new_ltEs7(vyy6001, vyy501, bcb)
new_esEs5(Left(vyy350), Left(vyy360), app(app(ty_Either, bed), bee), bec) → new_esEs5(vyy350, vyy360, bed, bee)
new_ltEs7(Just(vyy6000), Just(vyy500), app(app(ty_@2, ed), ee)) → new_ltEs13(vyy6000, vyy500, ed, ee)
new_lt20(vyy6000, vyy500, ty_Bool) → new_lt12(vyy6000, vyy500)
new_ltEs4(Left(vyy6000), Left(vyy500), ty_Ordering, bb) → new_ltEs16(vyy6000, vyy500)
new_compare112(vyy6000, vyy500, False) → GT
new_ltEs4(Left(vyy6000), Left(vyy500), app(ty_Maybe, bc), bb) → new_ltEs7(vyy6000, vyy500, bc)
new_ltEs12(vyy600, vyy50) → new_not(new_compare6(vyy600, vyy50))
new_compare210(vyy6000, vyy500, False) → new_compare112(vyy6000, vyy500, new_ltEs8(vyy6000, vyy500))
new_esEs12(GT, GT) → True
new_compare25(vyy6000, vyy500, False, gd, ge, gf) → new_compare12(vyy6000, vyy500, new_ltEs5(vyy6000, vyy500, gd, ge, gf), gd, ge, gf)
new_esEs23(vyy351, vyy361, ty_Char) → new_esEs20(vyy351, vyy361)
new_esEs21(vyy350, vyy360, ty_Float) → new_esEs11(vyy350, vyy360)
new_esEs22(vyy352, vyy362, ty_Int) → new_esEs14(vyy352, vyy362)
new_compare19(vyy6000, vyy500, gc) → new_compare29(vyy6000, vyy500, new_esEs6(vyy6000, vyy500, gc), gc)
new_primPlusNat0(Succ(vyy8100), Succ(vyy6001000)) → Succ(Succ(new_primPlusNat0(vyy8100, vyy6001000)))
new_esEs29(vyy35, vyy36, ty_Ordering) → new_esEs12(vyy35, vyy36)
new_esEs29(vyy35, vyy36, app(ty_[], caa)) → new_esEs18(vyy35, vyy36, caa)
new_esEs5(Right(vyy350), Right(vyy360), bfh, ty_Ordering) → new_esEs12(vyy350, vyy360)
new_ltEs4(Left(vyy6000), Left(vyy500), ty_Double, bb) → new_ltEs10(vyy6000, vyy500)
new_esEs18(:(vyy350, vyy351), :(vyy360, vyy361), caa) → new_asAs(new_esEs21(vyy350, vyy360, caa), new_esEs18(vyy351, vyy361, caa))
new_asAs(True, vyy61) → vyy61
new_compare28(:%(vyy6000, vyy6001), :%(vyy500, vyy501), ty_Int) → new_compare11(new_sr(vyy6000, vyy501), new_sr(vyy500, vyy6001))
new_esEs22(vyy352, vyy362, app(app(ty_@2, cfd), cfe)) → new_esEs8(vyy352, vyy362, cfd, cfe)
new_esEs17(Double(vyy350, vyy351), Double(vyy360, vyy361)) → new_esEs14(new_sr(vyy350, vyy360), new_sr(vyy351, vyy361))
new_ltEs19(vyy6001, vyy501, ty_Float) → new_ltEs12(vyy6001, vyy501)
new_esEs25(vyy351, vyy361, ty_Float) → new_esEs11(vyy351, vyy361)
new_esEs5(Left(vyy350), Left(vyy360), ty_Ordering, bec) → new_esEs12(vyy350, vyy360)
new_ltEs16(LT, LT) → True
new_compare211(vyy6000, vyy500, True) → EQ
new_fmToList(vyy36, cbf, cbg) → new_foldFM2(vyy36, cbf, cbg)
new_lt17(vyy6000, vyy500) → new_esEs10(new_compare14(vyy6000, vyy500))
new_compare6(Float(vyy6000, vyy6001), Float(vyy500, vyy501)) → new_compare11(new_sr(vyy6000, vyy500), new_sr(vyy6001, vyy501))
new_esEs24(vyy350, vyy360, app(app(ty_@2, dad), dae)) → new_esEs8(vyy350, vyy360, dad, dae)
new_ltEs4(Left(vyy6000), Left(vyy500), ty_Bool, bb) → new_ltEs8(vyy6000, vyy500)
new_esEs24(vyy350, vyy360, app(ty_Maybe, chh)) → new_esEs6(vyy350, vyy360, chh)
new_esEs5(Right(vyy350), Right(vyy360), bfh, ty_Char) → new_esEs20(vyy350, vyy360)
new_ltEs4(Right(vyy6000), Right(vyy500), cb, ty_Int) → new_ltEs18(vyy6000, vyy500)
new_lt20(vyy6000, vyy500, app(ty_Ratio, dag)) → new_lt13(vyy6000, vyy500, dag)
new_esEs23(vyy351, vyy361, app(ty_[], cgg)) → new_esEs18(vyy351, vyy361, cgg)
new_esEs5(Left(vyy350), Left(vyy360), ty_Integer, bec) → new_esEs9(vyy350, vyy360)
new_esEs22(vyy352, vyy362, app(app(ty_Either, ceb), cec)) → new_esEs5(vyy352, vyy362, ceb, cec)
new_primCompAux00(vyy66, GT) → GT
new_compare17(vyy6000, vyy500, ty_@0) → new_compare5(vyy6000, vyy500)
new_ltEs7(Just(vyy6000), Just(vyy500), app(ty_Ratio, cca)) → new_ltEs9(vyy6000, vyy500, cca)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_lt8(vyy6001, vyy501, ty_Bool) → new_lt12(vyy6001, vyy501)
new_ltEs4(Left(vyy6000), Left(vyy500), app(app(app(ty_@3, be), bf), bg), bb) → new_ltEs5(vyy6000, vyy500, be, bf, bg)
new_esEs5(Right(vyy350), Right(vyy360), bfh, app(ty_Ratio, bgf)) → new_esEs13(vyy350, vyy360, bgf)
new_ltEs7(Just(vyy6000), Just(vyy500), app(app(ty_Either, de), df)) → new_ltEs4(vyy6000, vyy500, de, df)
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primCmpInt(Neg(Succ(vyy60000)), Pos(vyy500)) → LT
new_esEs25(vyy351, vyy361, ty_Integer) → new_esEs9(vyy351, vyy361)
new_ltEs10(vyy600, vyy50) → new_not(new_compare8(vyy600, vyy50))
new_ltEs4(Right(vyy6000), Right(vyy500), cb, app(app(app(ty_@3, cg), da), db)) → new_ltEs5(vyy6000, vyy500, cg, da, db)
The set Q consists of the following terms:
new_esEs22(x0, x1, ty_Integer)
new_esEs25(x0, x1, ty_Int)
new_esEs6(Just(x0), Nothing, x1)
new_ltEs6(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs4(Left(x0), Left(x1), ty_@0, x2)
new_esEs5(Left(x0), Left(x1), ty_Integer, x2)
new_ltEs11(x0, x1, x2)
new_ltEs7(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_compare(:(x0, x1), [], x2)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs13(:%(x0, x1), :%(x2, x3), x4)
new_ltEs6(x0, x1, ty_Float)
new_lt8(x0, x1, ty_Int)
new_esEs5(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs24(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_lt9(x0, x1, ty_@0)
new_lt8(x0, x1, app(ty_Ratio, x2))
new_pePe(False, x0, x1, x2, x3)
new_foldFM2(EmptyFM, x0, x1)
new_ltEs4(Left(x0), Left(x1), app(ty_[], x2), x3)
new_lt8(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs7(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_compare(:(x0, x1), :(x2, x3), x4)
new_esEs22(x0, x1, ty_@0)
new_fmToList(x0, x1, x2)
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs22(x0, x1, app(ty_[], x2))
new_ltEs19(x0, x1, ty_Integer)
new_compare([], [], x0)
new_compare9(x0, x1, x2, x3)
new_esEs22(x0, x1, ty_Char)
new_esEs18([], [], x0)
new_esEs6(Nothing, Nothing, x0)
new_esEs23(x0, x1, ty_Integer)
new_compare110(x0, x1, True)
new_esEs23(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_esEs21(x0, x1, ty_Double)
new_ltEs6(x0, x1, app(app(ty_Either, x2), x3))
new_primMulNat0(Succ(x0), Zero)
new_esEs26(x0, x1, ty_Char)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_compare29(x0, x1, True, x2)
new_compare110(x0, x1, False)
new_esEs12(EQ, GT)
new_esEs12(GT, EQ)
new_ltEs6(x0, x1, ty_Char)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs29(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs10(GT)
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
new_lt20(x0, x1, ty_Int)
new_esEs23(x0, x1, ty_Int)
new_esEs28(x0, x1, ty_Integer)
new_esEs6(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_ltEs8(True, True)
new_ltEs6(x0, x1, app(ty_[], x2))
new_esEs12(GT, GT)
new_esEs23(x0, x1, ty_Ordering)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs23(x0, x1, ty_Char)
new_lt13(x0, x1, x2)
new_ltEs7(Just(x0), Just(x1), ty_@0)
new_esEs16(@0, @0)
new_esEs6(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs5(Right(x0), Right(x1), x2, ty_Char)
new_esEs22(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs5(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs6(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_compare17(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, ty_Int)
new_ltEs4(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs8(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs23(x0, x1, ty_Bool)
new_compare15(x0, x1, False, x2, x3)
new_ltEs19(x0, x1, ty_Float)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs5(Left(x0), Left(x1), app(app(ty_FiniteMap, x2), x3), x4)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_compare112(x0, x1, True)
new_esEs19(True, True)
new_esEs29(x0, x1, ty_Integer)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_compare11(x0, x1)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_lt8(x0, x1, ty_Char)
new_compare5(@0, @0)
new_esEs21(x0, x1, ty_Int)
new_ltEs4(Left(x0), Left(x1), ty_Bool, x2)
new_lt20(x0, x1, ty_Ordering)
new_ltEs4(Left(x0), Right(x1), x2, x3)
new_ltEs4(Right(x0), Left(x1), x2, x3)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_compare17(x0, x1, ty_Double)
new_ltEs4(Right(x0), Right(x1), x2, ty_Double)
new_primEqNat0(Zero, Zero)
new_lt8(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs4(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs5(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs25(x0, x1, app(ty_[], x2))
new_primPlusNat0(Zero, Succ(x0))
new_esEs6(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_lt20(x0, x1, ty_Double)
new_ltEs6(x0, x1, ty_Ordering)
new_esEs9(Integer(x0), Integer(x1))
new_esEs6(Just(x0), Just(x1), ty_Float)
new_lt8(x0, x1, ty_Float)
new_compare10(x0, x1, False, x2, x3)
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_compare26(x0, x1, True, x2, x3)
new_esEs17(Double(x0, x1), Double(x2, x3))
new_lt9(x0, x1, app(ty_Ratio, x2))
new_primMulNat0(Zero, Zero)
new_esEs29(x0, x1, ty_Char)
new_esEs29(x0, x1, ty_Float)
new_ltEs4(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_compare6(Float(x0, x1), Float(x2, x3))
new_ltEs17(x0, x1)
new_esEs25(x0, x1, ty_Integer)
new_ltEs6(x0, x1, app(ty_Maybe, x2))
new_esEs5(Right(x0), Right(x1), x2, ty_Ordering)
new_ltEs5(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_ltEs7(Just(x0), Just(x1), ty_Bool)
new_esEs25(x0, x1, ty_Double)
new_ltEs6(x0, x1, ty_Double)
new_ltEs4(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_compare17(x0, x1, ty_Int)
new_esEs7(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_lt4(x0, x1)
new_compare25(x0, x1, True, x2, x3, x4)
new_esEs5(Right(x0), Right(x1), x2, ty_Integer)
new_ltEs7(Just(x0), Just(x1), app(ty_[], x2))
new_esEs26(x0, x1, ty_Ordering)
new_compare112(x0, x1, False)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs23(x0, x1, ty_Float)
new_primMulNat0(Succ(x0), Succ(x1))
new_esEs24(x0, x1, ty_Float)
new_esEs5(Left(x0), Left(x1), ty_@0, x2)
new_ltEs19(x0, x1, ty_Ordering)
new_ltEs4(Right(x0), Right(x1), x2, ty_Float)
new_ltEs19(x0, x1, ty_Bool)
new_esEs5(Right(x0), Right(x1), x2, ty_Int)
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
new_esEs21(x0, x1, ty_Bool)
new_esEs27(x0, x1, ty_Int)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_esEs5(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_compare17(x0, x1, app(ty_Maybe, x2))
new_primCmpNat0(Succ(x0), Succ(x1))
new_compare17(x0, x1, ty_Integer)
new_ltEs4(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs25(x0, x1, ty_Ordering)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Just(x0), Just(x1), app(app(ty_FiniteMap, x2), x3))
new_esEs24(x0, x1, ty_@0)
new_lt9(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_esEs24(x0, x1, ty_Double)
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_ltEs4(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs6(Just(x0), Just(x1), ty_Integer)
new_compare210(x0, x1, True)
new_esEs26(x0, x1, app(ty_[], x2))
new_esEs24(x0, x1, ty_Bool)
new_lt20(x0, x1, ty_Char)
new_ltEs7(Nothing, Nothing, x0)
new_primEqNat0(Zero, Succ(x0))
new_esEs14(x0, x1)
new_lt20(x0, x1, ty_Integer)
new_lt9(x0, x1, ty_Float)
new_esEs19(True, False)
new_esEs19(False, True)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_esEs12(LT, EQ)
new_esEs12(EQ, LT)
new_esEs5(Right(x0), Right(x1), x2, ty_Bool)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_compare14(Char(x0), Char(x1))
new_esEs27(x0, x1, ty_Integer)
new_esEs25(x0, x1, ty_Char)
new_esEs5(Left(x0), Left(x1), ty_Bool, x2)
new_ltEs7(Just(x0), Just(x1), ty_Double)
new_esEs25(x0, x1, ty_Float)
new_sr(x0, x1)
new_compare17(x0, x1, ty_@0)
new_ltEs18(x0, x1)
new_ltEs7(Just(x0), Just(x1), ty_Ordering)
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_not0
new_compare15(x0, x1, True, x2, x3)
new_esEs29(x0, x1, ty_@0)
new_ltEs19(x0, x1, ty_Char)
new_lt9(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare24(x0, x1, False, x2, x3)
new_esEs12(EQ, EQ)
new_primPlusNat0(Zero, Zero)
new_ltEs16(EQ, EQ)
new_compare210(x0, x1, False)
new_esEs5(Left(x0), Left(x1), app(ty_[], x2), x3)
new_ltEs4(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_lt14(x0, x1, x2)
new_lt8(x0, x1, app(app(ty_@2, x2), x3))
new_esEs24(x0, x1, ty_Ordering)
new_esEs22(x0, x1, ty_Bool)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_primPlusNat0(Succ(x0), Succ(x1))
new_esEs5(Left(x0), Left(x1), ty_Float, x2)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_ltEs7(Nothing, Just(x0), x1)
new_esEs18(:(x0, x1), [], x2)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_esEs28(x0, x1, ty_Int)
new_esEs6(Just(x0), Just(x1), ty_Ordering)
new_ltEs16(LT, LT)
new_compare211(x0, x1, True)
new_esEs5(Right(x0), Right(x1), x2, ty_@0)
new_primMulInt(Pos(x0), Pos(x1))
new_ltEs7(Just(x0), Just(x1), ty_Float)
new_lt9(x0, x1, ty_Double)
new_ltEs9(x0, x1, x2)
new_lt8(x0, x1, app(ty_[], x2))
new_ltEs13(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs5(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_lt12(x0, x1)
new_lt8(x0, x1, ty_Integer)
new_lt8(x0, x1, ty_Ordering)
new_esEs25(x0, x1, ty_Bool)
new_compare17(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_lt9(x0, x1, ty_Char)
new_ltEs4(Right(x0), Right(x1), x2, ty_Ordering)
new_ltEs4(Right(x0), Right(x1), x2, ty_Char)
new_lt10(x0, x1, x2, x3)
new_sizeFM(EmptyFM, x0, x1)
new_lt6(x0, x1)
new_ltEs16(GT, LT)
new_ltEs16(LT, GT)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs4(Right(x0), Right(x1), x2, ty_Integer)
new_esEs21(x0, x1, ty_Float)
new_not(GT)
new_ltEs4(Left(x0), Left(x1), ty_Integer, x2)
new_ltEs8(False, False)
new_asAs(False, x0)
new_esEs26(x0, x1, ty_Float)
new_primEqNat0(Succ(x0), Zero)
new_compare19(x0, x1, x2)
new_lt20(x0, x1, ty_Float)
new_asAs(True, x0)
new_lt15(x0, x1, x2, x3, x4)
new_primEqInt(Neg(Zero), Pos(Zero))
new_primEqInt(Pos(Zero), Neg(Zero))
new_ltEs10(x0, x1)
new_ltEs8(False, True)
new_ltEs8(True, False)
new_ltEs7(Just(x0), Just(x1), app(ty_Maybe, x2))
new_ltEs14(x0, x1)
new_primCmpNat0(Succ(x0), Zero)
new_esEs26(x0, x1, ty_Double)
new_esEs5(Left(x0), Right(x1), x2, x3)
new_esEs5(Right(x0), Left(x1), x2, x3)
new_esEs18(:(x0, x1), :(x2, x3), x4)
new_lt9(x0, x1, app(app(ty_@2, x2), x3))
new_esEs19(False, False)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_lt19(x0, x1)
new_esEs6(Just(x0), Just(x1), ty_Int)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_esEs5(Right(x0), Right(x1), x2, ty_Float)
new_ltEs6(x0, x1, ty_@0)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs24(x0, x1, ty_Integer)
new_primEqInt(Neg(Zero), Neg(Zero))
new_esEs5(Left(x0), Left(x1), ty_Char, x2)
new_esEs6(Just(x0), Just(x1), app(ty_[], x2))
new_compare17(x0, x1, ty_Float)
new_compare17(x0, x1, app(app(ty_@2, x2), x3))
new_lt8(x0, x1, ty_Double)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_lt9(x0, x1, app(ty_[], x2))
new_lt8(x0, x1, app(ty_Maybe, x2))
new_ltEs4(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs7(Just(x0), Just(x1), ty_Char)
new_esEs26(x0, x1, ty_Integer)
new_esEs24(x0, x1, ty_Int)
new_compare17(x0, x1, ty_Ordering)
new_compare28(:%(x0, x1), :%(x2, x3), ty_Integer)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primCompAux0(x0, x1, x2, x3)
new_ltEs4(Left(x0), Left(x1), ty_Int, x2)
new_compare12(x0, x1, False, x2, x3, x4)
new_ltEs4(Right(x0), Right(x1), x2, ty_@0)
new_ltEs16(GT, GT)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_esEs5(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs21(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, app(ty_[], x2))
new_compare28(:%(x0, x1), :%(x2, x3), ty_Int)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_lt9(x0, x1, app(ty_Maybe, x2))
new_ltEs4(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs29(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_compare10(x0, x1, True, x2, x3)
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_primEqNat0(Succ(x0), Succ(x1))
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_ltEs4(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs29(x0, x1, ty_Ordering)
new_ltEs6(x0, x1, ty_Bool)
new_esEs29(x0, x1, ty_Int)
new_compare13(x0, x1)
new_esEs5(Left(x0), Left(x1), ty_Ordering, x2)
new_ltEs19(x0, x1, app(ty_[], x2))
new_esEs6(Just(x0), Just(x1), ty_@0)
new_esEs26(x0, x1, ty_@0)
new_lt11(x0, x1, x2)
new_esEs10(EQ)
new_ltEs4(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs12(x0, x1)
new_compare17(x0, x1, ty_Char)
new_esEs5(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_lt9(x0, x1, ty_Ordering)
new_esEs6(Nothing, Just(x0), x1)
new_primCmpNat0(Zero, Zero)
new_ltEs7(Just(x0), Just(x1), ty_Integer)
new_esEs21(x0, x1, ty_Char)
new_esEs29(x0, x1, ty_Bool)
new_ltEs7(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs5(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs6(Just(x0), Just(x1), ty_Double)
new_primPlusNat0(Succ(x0), Zero)
new_esEs26(x0, x1, ty_Bool)
new_primCompAux00(x0, EQ)
new_sr0(Integer(x0), Integer(x1))
new_compare27(x0, x1)
new_compare7(x0, x1, x2, x3, x4)
new_esEs22(x0, x1, ty_Ordering)
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_compare([], :(x0, x1), x2)
new_esEs5(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_esEs5(Right(x0), Right(x1), x2, ty_Double)
new_primMulNat0(Zero, Succ(x0))
new_ltEs4(Left(x0), Left(x1), ty_Float, x2)
new_ltEs6(x0, x1, ty_Int)
new_ltEs4(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_ltEs4(Left(x0), Left(x1), ty_Char, x2)
new_ltEs6(x0, x1, app(ty_Ratio, x2))
new_primCmpNat0(Zero, Succ(x0))
new_pePe(True, x0, x1, x2, x3)
new_primCompAux00(x0, GT)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs24(x0, x1, ty_Char)
new_esEs10(LT)
new_esEs6(Just(x0), Just(x1), ty_Bool)
new_esEs21(x0, x1, ty_Integer)
new_lt17(x0, x1)
new_ltEs6(x0, x1, ty_Integer)
new_esEs25(x0, x1, ty_@0)
new_lt20(x0, x1, ty_Bool)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_esEs5(Left(x0), Left(x1), ty_Int, x2)
new_primCompAux00(x0, LT)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_esEs11(Float(x0, x1), Float(x2, x3))
new_not(EQ)
new_esEs18([], :(x0, x1), x2)
new_ltEs16(GT, EQ)
new_ltEs16(EQ, GT)
new_esEs5(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_primPlusNat1(Zero, x0)
new_esEs15(x0, x1, x2, x3)
new_lt9(x0, x1, ty_Bool)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_ltEs16(LT, EQ)
new_ltEs16(EQ, LT)
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_esEs26(x0, x1, ty_Int)
new_compare17(x0, x1, app(ty_[], x2))
new_lt5(x0, x1)
new_esEs6(Just(x0), Just(x1), app(ty_Maybe, x2))
new_compare111(x0, x1, False, x2)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare17(x0, x1, ty_Bool)
new_esEs21(x0, x1, ty_Ordering)
new_compare8(Double(x0, x1), Double(x2, x3))
new_esEs20(Char(x0), Char(x1))
new_esEs21(x0, x1, ty_@0)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_esEs23(x0, x1, ty_@0)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs23(x0, x1, app(ty_[], x2))
new_ltEs19(x0, x1, ty_@0)
new_lt7(x0, x1)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_esEs6(Just(x0), Just(x1), ty_Char)
new_lt8(x0, x1, ty_@0)
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt16(x0, x1, x2, x3)
new_lt9(x0, x1, ty_Integer)
new_compare26(x0, x1, False, x2, x3)
new_lt9(x0, x1, ty_Int)
new_compare12(x0, x1, True, x2, x3, x4)
new_compare111(x0, x1, True, x2)
new_ltEs19(x0, x1, ty_Double)
new_lt8(x0, x1, ty_Bool)
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare16(Integer(x0), Integer(x1))
new_ltEs4(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_compare17(x0, x1, app(ty_Ratio, x2))
new_ltEs6(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs19(x0, x1, ty_Int)
new_compare25(x0, x1, False, x2, x3, x4)
new_esEs23(x0, x1, ty_Double)
new_esEs25(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs22(x0, x1, ty_Double)
new_primEqInt(Pos(Zero), Pos(Zero))
new_compare24(x0, x1, True, x2, x3)
new_lt18(x0, x1)
new_esEs5(Right(x0), Right(x1), x2, app(app(ty_FiniteMap, x3), x4))
new_ltEs4(Left(x0), Left(x1), ty_Double, x2)
new_esEs5(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_lt20(x0, x1, ty_@0)
new_esEs26(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs5(Left(x0), Left(x1), ty_Double, x2)
new_ltEs4(Right(x0), Right(x1), x2, ty_Int)
new_ltEs7(Just(x0), Just(x1), app(ty_Ratio, x2))
new_primPlusNat1(Succ(x0), x1)
new_esEs29(x0, x1, ty_Double)
new_ltEs7(Just(x0), Just(x1), ty_Int)
new_esEs24(x0, x1, app(ty_[], x2))
new_esEs12(LT, LT)
new_ltEs7(Just(x0), Nothing, x1)
new_not(LT)
new_esEs22(x0, x1, ty_Float)
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_compare29(x0, x1, False, x2)
new_compare18(x0, x1, x2, x3)
new_ltEs15(x0, x1)
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_compare211(x0, x1, False)
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_ltEs1(:(vyy6000, vyy6001), :(vyy500, vyy501), ef) → new_compare0(vyy6001, vyy501, ef)
The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3
- new_ltEs1(:(vyy6000, vyy6001), :(vyy500, vyy501), ef) → new_primCompAux(vyy6000, vyy500, new_compare(vyy6001, vyy501, ef), ef)
The graph contains the following edges 1 > 1, 2 > 2, 3 >= 4
- new_primCompAux(vyy6000, vyy500, vyy62, app(ty_[], fb)) → new_compare0(vyy6000, vyy500, fb)
The graph contains the following edges 1 >= 1, 2 >= 2, 4 > 3
- new_ltEs2(@3(vyy6000, vyy6001, vyy6002), @3(vyy500, vyy501, vyy502), gg, gh, app(app(ty_Either, ha), hb)) → new_ltEs(vyy6002, vyy502, ha, hb)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4
- new_ltEs2(@3(vyy6000, vyy6001, vyy6002), @3(vyy500, vyy501, vyy502), app(ty_[], bbd), gh, bad) → new_compare0(vyy6000, vyy500, bbd)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
- new_ltEs2(@3(vyy6000, vyy6001, vyy6002), @3(vyy500, vyy501, vyy502), gg, gh, app(app(app(ty_@3, he), hf), hg)) → new_ltEs2(vyy6002, vyy502, he, hf, hg)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4, 5 > 5
- new_compare0(:(vyy6000, vyy6001), :(vyy500, vyy501), ef) → new_compare0(vyy6001, vyy501, ef)
The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3
- new_lt1(vyy6000, vyy500, bbd) → new_compare0(vyy6000, vyy500, bbd)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3
- new_compare0(:(vyy6000, vyy6001), :(vyy500, vyy501), ef) → new_primCompAux(vyy6000, vyy500, new_compare(vyy6001, vyy501, ef), ef)
The graph contains the following edges 1 > 1, 2 > 2, 3 >= 4
- new_ltEs3(@2(vyy6000, vyy6001), @2(vyy500, vyy501), bbg, app(app(ty_Either, bbh), bca)) → new_ltEs(vyy6001, vyy501, bbh, bca)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
- new_ltEs2(@3(vyy6000, vyy6001, vyy6002), @3(vyy500, vyy501, vyy502), gg, gh, app(ty_Maybe, hc)) → new_ltEs0(vyy6002, vyy502, hc)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3
- new_ltEs3(@2(vyy6000, vyy6001), @2(vyy500, vyy501), bbg, app(app(app(ty_@3, bcd), bce), bcf)) → new_ltEs2(vyy6001, vyy501, bcd, bce, bcf)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5
- new_ltEs3(@2(vyy6000, vyy6001), @2(vyy500, vyy501), bbg, app(ty_Maybe, bcb)) → new_ltEs0(vyy6001, vyy501, bcb)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
- new_primCompAux(vyy6000, vyy500, vyy62, app(app(app(ty_@3, fc), fd), ff)) → new_compare3(vyy6000, vyy500, fc, fd, ff)
The graph contains the following edges 1 >= 1, 2 >= 2, 4 > 3, 4 > 4, 4 > 5
- new_compare22(vyy6000, vyy500, False, gd, ge, gf) → new_ltEs2(vyy6000, vyy500, gd, ge, gf)
The graph contains the following edges 1 >= 1, 2 >= 2, 4 >= 3, 5 >= 4, 6 >= 5
- new_ltEs0(Just(vyy6000), Just(vyy500), app(app(app(ty_@3, ea), eb), ec)) → new_ltEs2(vyy6000, vyy500, ea, eb, ec)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
- new_ltEs0(Just(vyy6000), Just(vyy500), app(app(ty_Either, de), df)) → new_ltEs(vyy6000, vyy500, de, df)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
- new_compare20(vyy6000, vyy500, False, ga, gb) → new_ltEs(vyy6000, vyy500, ga, gb)
The graph contains the following edges 1 >= 1, 2 >= 2, 4 >= 3, 5 >= 4
- new_ltEs2(@3(vyy6000, vyy6001, vyy6002), @3(vyy500, vyy501, vyy502), gg, gh, app(app(ty_@2, hh), baa)) → new_ltEs3(vyy6002, vyy502, hh, baa)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4
- new_ltEs3(@2(vyy6000, vyy6001), @2(vyy500, vyy501), bbg, app(app(ty_@2, bcg), bch)) → new_ltEs3(vyy6001, vyy501, bcg, bch)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
- new_ltEs0(Just(vyy6000), Just(vyy500), app(ty_Maybe, dg)) → new_ltEs0(vyy6000, vyy500, dg)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
- new_compare21(vyy6000, vyy500, False, gc) → new_ltEs0(vyy6000, vyy500, gc)
The graph contains the following edges 1 >= 1, 2 >= 2, 4 >= 3
- new_ltEs0(Just(vyy6000), Just(vyy500), app(app(ty_@2, ed), ee)) → new_ltEs3(vyy6000, vyy500, ed, ee)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
- new_ltEs0(Just(vyy6000), Just(vyy500), app(ty_[], dh)) → new_ltEs1(vyy6000, vyy500, dh)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
- new_compare23(vyy6000, vyy500, False, bbe, bbf) → new_ltEs3(vyy6000, vyy500, bbe, bbf)
The graph contains the following edges 1 >= 1, 2 >= 2, 4 >= 3, 5 >= 4
- new_ltEs2(@3(vyy6000, vyy6001, vyy6002), @3(vyy500, vyy501, vyy502), app(ty_Maybe, gc), gh, bad) → new_compare21(vyy6000, vyy500, new_esEs6(vyy6000, vyy500, gc), gc)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 4
- new_lt2(vyy6000, vyy500, gd, ge, gf) → new_compare22(vyy6000, vyy500, new_esEs7(vyy6000, vyy500, gd, ge, gf), gd, ge, gf)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 4, 4 >= 5, 5 >= 6
- new_ltEs2(@3(vyy6000, vyy6001, vyy6002), @3(vyy500, vyy501, vyy502), gg, app(ty_Maybe, bae), bad) → new_lt0(vyy6001, vyy501, bae)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
- new_ltEs3(@2(vyy6000, vyy6001), @2(vyy500, vyy501), app(ty_Maybe, bdd), bdc) → new_lt0(vyy6000, vyy500, bdd)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
- new_ltEs2(@3(vyy6000, vyy6001, vyy6002), @3(vyy500, vyy501, vyy502), gg, app(app(ty_Either, bab), bac), bad) → new_lt(vyy6001, vyy501, bab, bac)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
- new_ltEs3(@2(vyy6000, vyy6001), @2(vyy500, vyy501), app(app(ty_Either, bda), bdb), bdc) → new_lt(vyy6000, vyy500, bda, bdb)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
- new_compare2(vyy6000, vyy500, gc) → new_compare21(vyy6000, vyy500, new_esEs6(vyy6000, vyy500, gc), gc)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 4
- new_lt0(vyy6000, vyy500, gc) → new_compare21(vyy6000, vyy500, new_esEs6(vyy6000, vyy500, gc), gc)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 4
- new_ltEs2(@3(vyy6000, vyy6001, vyy6002), @3(vyy500, vyy501, vyy502), gg, gh, app(ty_[], hd)) → new_ltEs1(vyy6002, vyy502, hd)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3
- new_ltEs3(@2(vyy6000, vyy6001), @2(vyy500, vyy501), bbg, app(ty_[], bcc)) → new_ltEs1(vyy6001, vyy501, bcc)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
- new_compare1(vyy6000, vyy500, ga, gb) → new_compare20(vyy6000, vyy500, new_esEs5(vyy6000, vyy500, ga, gb), ga, gb)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 4, 4 >= 5
- new_primCompAux(vyy6000, vyy500, vyy62, app(ty_Maybe, fa)) → new_compare2(vyy6000, vyy500, fa)
The graph contains the following edges 1 >= 1, 2 >= 2, 4 > 3
- new_ltEs2(@3(vyy6000, vyy6001, vyy6002), @3(vyy500, vyy501, vyy502), app(app(ty_Either, ga), gb), gh, bad) → new_compare20(vyy6000, vyy500, new_esEs5(vyy6000, vyy500, ga, gb), ga, gb)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 4, 3 > 5
- new_lt(vyy6000, vyy500, ga, gb) → new_compare20(vyy6000, vyy500, new_esEs5(vyy6000, vyy500, ga, gb), ga, gb)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 4, 4 >= 5
- new_ltEs2(@3(vyy6000, vyy6001, vyy6002), @3(vyy500, vyy501, vyy502), gg, app(ty_[], baf), bad) → new_lt1(vyy6001, vyy501, baf)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
- new_ltEs3(@2(vyy6000, vyy6001), @2(vyy500, vyy501), app(ty_[], bde), bdc) → new_lt1(vyy6000, vyy500, bde)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
- new_ltEs2(@3(vyy6000, vyy6001, vyy6002), @3(vyy500, vyy501, vyy502), app(app(ty_@2, bbe), bbf), gh, bad) → new_compare23(vyy6000, vyy500, new_esEs8(vyy6000, vyy500, bbe, bbf), bbe, bbf)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 4, 3 > 5
- new_compare3(vyy6000, vyy500, gd, ge, gf) → new_compare22(vyy6000, vyy500, new_esEs7(vyy6000, vyy500, gd, ge, gf), gd, ge, gf)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 4, 4 >= 5, 5 >= 6
- new_lt3(vyy6000, vyy500, bbe, bbf) → new_compare23(vyy6000, vyy500, new_esEs8(vyy6000, vyy500, bbe, bbf), bbe, bbf)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 4, 4 >= 5
- new_compare4(vyy6000, vyy500, bbe, bbf) → new_compare23(vyy6000, vyy500, new_esEs8(vyy6000, vyy500, bbe, bbf), bbe, bbf)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 4, 4 >= 5
- new_ltEs2(@3(vyy6000, vyy6001, vyy6002), @3(vyy500, vyy501, vyy502), gg, app(app(ty_@2, bbb), bbc), bad) → new_lt3(vyy6001, vyy501, bbb, bbc)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
- new_ltEs3(@2(vyy6000, vyy6001), @2(vyy500, vyy501), app(app(ty_@2, bea), beb), bdc) → new_lt3(vyy6000, vyy500, bea, beb)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
- new_ltEs3(@2(vyy6000, vyy6001), @2(vyy500, vyy501), app(app(app(ty_@3, bdf), bdg), bdh), bdc) → new_lt2(vyy6000, vyy500, bdf, bdg, bdh)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
- new_primCompAux(vyy6000, vyy500, vyy62, app(app(ty_@2, fg), fh)) → new_compare4(vyy6000, vyy500, fg, fh)
The graph contains the following edges 1 >= 1, 2 >= 2, 4 > 3, 4 > 4
- new_primCompAux(vyy6000, vyy500, vyy62, app(app(ty_Either, eg), eh)) → new_compare1(vyy6000, vyy500, eg, eh)
The graph contains the following edges 1 >= 1, 2 >= 2, 4 > 3, 4 > 4
- new_ltEs2(@3(vyy6000, vyy6001, vyy6002), @3(vyy500, vyy501, vyy502), gg, app(app(app(ty_@3, bag), bah), bba), bad) → new_lt2(vyy6001, vyy501, bag, bah, bba)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5
- new_ltEs2(@3(vyy6000, vyy6001, vyy6002), @3(vyy500, vyy501, vyy502), app(app(app(ty_@3, gd), ge), gf), gh, bad) → new_compare22(vyy6000, vyy500, new_esEs7(vyy6000, vyy500, gd, ge, gf), gd, ge, gf)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 4, 3 > 5, 3 > 6
- new_ltEs(Left(vyy6000), Left(vyy500), app(app(ty_Either, h), ba), bb) → new_ltEs(vyy6000, vyy500, h, ba)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
- new_ltEs(Right(vyy6000), Right(vyy500), cb, app(app(ty_Either, cc), cd)) → new_ltEs(vyy6000, vyy500, cc, cd)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
- new_ltEs(Left(vyy6000), Left(vyy500), app(app(app(ty_@3, be), bf), bg), bb) → new_ltEs2(vyy6000, vyy500, be, bf, bg)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
- new_ltEs(Right(vyy6000), Right(vyy500), cb, app(app(app(ty_@3, cg), da), db)) → new_ltEs2(vyy6000, vyy500, cg, da, db)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5
- new_ltEs(Left(vyy6000), Left(vyy500), app(ty_Maybe, bc), bb) → new_ltEs0(vyy6000, vyy500, bc)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
- new_ltEs(Right(vyy6000), Right(vyy500), cb, app(ty_Maybe, ce)) → new_ltEs0(vyy6000, vyy500, ce)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
- new_ltEs(Left(vyy6000), Left(vyy500), app(app(ty_@2, bh), ca), bb) → new_ltEs3(vyy6000, vyy500, bh, ca)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
- new_ltEs(Right(vyy6000), Right(vyy500), cb, app(app(ty_@2, dc), dd)) → new_ltEs3(vyy6000, vyy500, dc, dd)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
- new_ltEs(Right(vyy6000), Right(vyy500), cb, app(ty_[], cf)) → new_ltEs1(vyy6000, vyy500, cf)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
- new_ltEs(Left(vyy6000), Left(vyy500), app(ty_[], bd), bb) → new_ltEs1(vyy6000, vyy500, bd)
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
↳ DependencyGraphProof
Q DP problem:
The TRS P consists of the following rules:
new_foldFM_LE(vyy3, Nothing, Branch(Just(vyy600), vyy61, vyy62, vyy63, vyy64), h, ba, bb) → new_foldFM_LE(vyy3, Nothing, vyy63, h, ba, bb)
new_foldFM_LE1(vyy17, vyy19, vyy20, vyy21, vyy22, vyy23, vyy24, False, bc, bd, be) → new_foldFM_LE(vyy17, Just(vyy19), vyy23, bc, bd, be)
new_foldFM_LE(vyy3, Nothing, Branch(Nothing, vyy61, vyy62, vyy63, vyy64), h, ba, bb) → new_foldFM_LE(vyy3, Nothing, vyy64, h, ba, bb)
new_foldFM_LE(vyy3, Just(vyy50), Branch(Just(vyy600), vyy61, vyy62, vyy63, vyy64), h, ba, bb) → new_foldFM_LE1(vyy3, vyy50, vyy600, vyy61, vyy62, vyy63, vyy64, new_ltEs20(vyy600, vyy50, ba), h, ba, bb)
new_foldFM_LE(vyy3, Nothing, Branch(Nothing, vyy61, vyy62, vyy63, vyy64), h, ba, bb) → new_foldFM_LE(vyy3, Nothing, vyy63, h, ba, bb)
new_foldFM_LE1(vyy17, vyy19, vyy20, vyy21, vyy22, vyy23, vyy24, True, bc, bd, be) → new_foldFM_LE(vyy17, Just(vyy19), vyy24, bc, bd, be)
new_foldFM_LE1(vyy17, vyy19, vyy20, vyy21, vyy22, vyy23, vyy24, True, bc, bd, be) → new_foldFM_LE(vyy17, Just(vyy19), vyy23, bc, bd, be)
new_foldFM_LE(vyy3, Just(vyy50), Branch(Nothing, vyy61, vyy62, vyy63, vyy64), h, ba, bb) → new_foldFM_LE(vyy3, Just(vyy50), vyy64, h, ba, bb)
new_foldFM_LE(vyy3, Just(vyy50), Branch(Nothing, vyy61, vyy62, vyy63, vyy64), h, ba, bb) → new_foldFM_LE(vyy3, Just(vyy50), vyy63, h, ba, bb)
The TRS R consists of the following rules:
new_esEs22(vyy352, vyy362, ty_Double) → new_esEs17(vyy352, vyy362)
new_esEs11(Float(vyy350, vyy351), Float(vyy360, vyy361)) → new_esEs14(new_sr(vyy350, vyy360), new_sr(vyy351, vyy361))
new_ltEs4(Right(vyy6000), Right(vyy500), dea, ty_Integer) → new_ltEs17(vyy6000, vyy500)
new_esEs24(vyy350, vyy360, app(app(ty_Either, cch), cda)) → new_esEs5(vyy350, vyy360, cch, cda)
new_compare5(@0, @0) → EQ
new_ltEs19(vyy6001, vyy501, ty_Ordering) → new_ltEs16(vyy6001, vyy501)
new_ltEs16(GT, GT) → True
new_ltEs8(False, True) → True
new_ltEs4(Right(vyy6000), Right(vyy500), dea, app(ty_[], def)) → new_ltEs11(vyy6000, vyy500, def)
new_ltEs4(Right(vyy6000), Right(vyy500), dea, ty_Char) → new_ltEs15(vyy6000, vyy500)
new_ltEs20(vyy600, vyy50, app(ty_Ratio, dcd)) → new_ltEs9(vyy600, vyy50, dcd)
new_compare15(vyy6000, vyy500, True, fg, fh) → LT
new_lt7(vyy6000, vyy500) → new_esEs10(new_compare13(vyy6000, vyy500))
new_ltEs19(vyy6001, vyy501, ty_Char) → new_ltEs15(vyy6001, vyy501)
new_ltEs4(Left(vyy6000), Left(vyy500), app(ty_[], ddc), dch) → new_ltEs11(vyy6000, vyy500, ddc)
new_esEs10(GT) → False
new_esEs23(vyy351, vyy361, app(app(ty_Either, cbd), cbe)) → new_esEs5(vyy351, vyy361, cbd, cbe)
new_lt16(vyy6000, vyy500, fg, fh) → new_esEs10(new_compare9(vyy6000, vyy500, fg, fh))
new_lt8(vyy6001, vyy501, app(ty_Ratio, baa)) → new_lt13(vyy6001, vyy501, baa)
new_compare([], :(vyy500, vyy501), bbc) → LT
new_compare10(vyy6000, vyy500, True, bf, bg) → LT
new_esEs6(Just(vyy350), Just(vyy360), ty_Char) → new_esEs20(vyy350, vyy360)
new_lt8(vyy6001, vyy501, ty_Int) → new_lt19(vyy6001, vyy501)
new_lt8(vyy6001, vyy501, app(app(app(ty_@3, bac), bad), bae)) → new_lt15(vyy6001, vyy501, bac, bad, bae)
new_lt9(vyy6000, vyy500, ty_Float) → new_lt5(vyy6000, vyy500)
new_ltEs16(LT, GT) → True
new_ltEs7(Just(vyy6000), Just(vyy500), ty_Integer) → new_ltEs17(vyy6000, vyy500)
new_lt8(vyy6001, vyy501, ty_Ordering) → new_lt7(vyy6001, vyy501)
new_esEs5(Left(vyy350), Left(vyy360), ty_@0, bh) → new_esEs16(vyy350, vyy360)
new_esEs28(vyy350, vyy360, ty_Int) → new_esEs14(vyy350, vyy360)
new_ltEs6(vyy6002, vyy502, app(ty_Ratio, gg)) → new_ltEs9(vyy6002, vyy502, gg)
new_esEs21(vyy350, vyy360, ty_Int) → new_esEs14(vyy350, vyy360)
new_esEs20(Char(vyy350), Char(vyy360)) → new_primEqNat0(vyy350, vyy360)
new_esEs6(Just(vyy350), Just(vyy360), ty_@0) → new_esEs16(vyy350, vyy360)
new_ltEs4(Left(vyy6000), Left(vyy500), ty_Int, dch) → new_ltEs18(vyy6000, vyy500)
new_primMulNat0(Zero, Zero) → Zero
new_esEs25(vyy351, vyy361, ty_Char) → new_esEs20(vyy351, vyy361)
new_esEs6(Just(vyy350), Just(vyy360), app(ty_Ratio, bgf)) → new_esEs13(vyy350, vyy360, bgf)
new_compare(:(vyy6000, vyy6001), [], bbc) → GT
new_esEs23(vyy351, vyy361, app(ty_Ratio, cca)) → new_esEs13(vyy351, vyy361, cca)
new_ltEs20(vyy600, vyy50, ty_Float) → new_ltEs12(vyy600, vyy50)
new_esEs6(Just(vyy350), Just(vyy360), ty_Bool) → new_esEs19(vyy350, vyy360)
new_ltEs6(vyy6002, vyy502, app(app(app(ty_@3, ha), hb), hc)) → new_ltEs5(vyy6002, vyy502, ha, hb, hc)
new_lt20(vyy6000, vyy500, ty_Integer) → new_lt18(vyy6000, vyy500)
new_esEs6(Just(vyy350), Just(vyy360), ty_Float) → new_esEs11(vyy350, vyy360)
new_lt9(vyy6000, vyy500, ty_Double) → new_lt6(vyy6000, vyy500)
new_lt9(vyy6000, vyy500, app(app(ty_@2, fg), fh)) → new_lt16(vyy6000, vyy500, fg, fh)
new_not(GT) → False
new_compare17(vyy6000, vyy500, ty_Char) → new_compare14(vyy6000, vyy500)
new_ltEs7(Just(vyy6000), Just(vyy500), ty_Double) → new_ltEs10(vyy6000, vyy500)
new_esEs10(EQ) → False
new_compare17(vyy6000, vyy500, ty_Double) → new_compare8(vyy6000, vyy500)
new_esEs12(GT, LT) → False
new_esEs12(LT, GT) → False
new_esEs5(Right(vyy350), Right(vyy360), df, ty_Integer) → new_esEs9(vyy350, vyy360)
new_esEs23(vyy351, vyy361, app(app(ty_FiniteMap, ccc), ccd)) → new_esEs15(vyy351, vyy361, ccc, ccd)
new_lt8(vyy6001, vyy501, app(app(ty_@2, baf), bag)) → new_lt16(vyy6001, vyy501, baf, bag)
new_esEs22(vyy352, vyy362, app(ty_Maybe, caf)) → new_esEs6(vyy352, vyy362, caf)
new_esEs21(vyy350, vyy360, app(app(app(ty_@3, bda), bdb), bdc)) → new_esEs7(vyy350, vyy360, bda, bdb, bdc)
new_esEs22(vyy352, vyy362, ty_Integer) → new_esEs9(vyy352, vyy362)
new_compare28(:%(vyy6000, vyy6001), :%(vyy500, vyy501), ty_Integer) → new_compare16(new_sr0(vyy6000, vyy501), new_sr0(vyy500, vyy6001))
new_lt9(vyy6000, vyy500, ty_Char) → new_lt17(vyy6000, vyy500)
new_esEs29(vyy35, vyy36, app(app(app(ty_@3, bhe), bhf), bhg)) → new_esEs7(vyy35, vyy36, bhe, bhf, bhg)
new_lt8(vyy6001, vyy501, app(app(ty_Either, hf), hg)) → new_lt10(vyy6001, vyy501, hf, hg)
new_pePe(False, vyy35, vyy36, vyy52, dfd) → new_asAs(new_esEs29(vyy35, vyy36, dfd), vyy52)
new_compare26(vyy6000, vyy500, False, fg, fh) → new_compare15(vyy6000, vyy500, new_ltEs13(vyy6000, vyy500, fg, fh), fg, fh)
new_ltEs18(vyy600, vyy50) → new_not(new_compare11(vyy600, vyy50))
new_foldFM0(vyy360, vyy361, vyy80, EmptyFM, bec, bed) → :(@2(vyy360, vyy361), vyy80)
new_esEs21(vyy350, vyy360, app(app(ty_@2, bea), beb)) → new_esEs8(vyy350, vyy360, bea, beb)
new_esEs22(vyy352, vyy362, ty_Ordering) → new_esEs12(vyy352, vyy362)
new_esEs5(Left(vyy350), Left(vyy360), app(ty_Maybe, cg), bh) → new_esEs6(vyy350, vyy360, cg)
new_ltEs19(vyy6001, vyy501, app(app(ty_Either, cef), ceg)) → new_ltEs4(vyy6001, vyy501, cef, ceg)
new_ltEs17(vyy600, vyy50) → new_not(new_compare16(vyy600, vyy50))
new_lt9(vyy6000, vyy500, app(app(ty_Either, bf), bg)) → new_lt10(vyy6000, vyy500, bf, bg)
new_esEs26(vyy350, vyy360, app(app(ty_@2, dcb), dcc)) → new_esEs8(vyy350, vyy360, dcb, dcc)
new_esEs18(:(vyy350, vyy351), [], bcf) → False
new_esEs18([], :(vyy360, vyy361), bcf) → False
new_ltEs14(vyy600, vyy50) → new_not(new_compare5(vyy600, vyy50))
new_esEs26(vyy350, vyy360, app(app(ty_FiniteMap, dbg), dbh)) → new_esEs15(vyy350, vyy360, dbg, dbh)
new_lt5(vyy6000, vyy500) → new_esEs10(new_compare6(vyy6000, vyy500))
new_ltEs19(vyy6001, vyy501, app(ty_[], cfb)) → new_ltEs11(vyy6001, vyy501, cfb)
new_esEs6(Just(vyy350), Just(vyy360), app(app(ty_FiniteMap, bgh), bha)) → new_esEs15(vyy350, vyy360, bgh, bha)
new_ltEs16(EQ, GT) → True
new_ltEs20(vyy600, vyy50, app(app(ty_Either, dea), dch)) → new_ltEs4(vyy600, vyy50, dea, dch)
new_ltEs4(Right(vyy6000), Right(vyy500), dea, app(app(ty_Either, deb), dec)) → new_ltEs4(vyy6000, vyy500, deb, dec)
new_lt20(vyy6000, vyy500, ty_Float) → new_lt5(vyy6000, vyy500)
new_esEs29(vyy35, vyy36, app(ty_Ratio, dce)) → new_esEs13(vyy35, vyy36, dce)
new_lt8(vyy6001, vyy501, app(ty_[], bab)) → new_lt14(vyy6001, vyy501, bab)
new_ltEs4(Left(vyy6000), Right(vyy500), dea, dch) → True
new_esEs25(vyy351, vyy361, app(app(ty_FiniteMap, dac), dad)) → new_esEs15(vyy351, vyy361, dac, dad)
new_esEs23(vyy351, vyy361, app(app(app(ty_@3, cbf), cbg), cbh)) → new_esEs7(vyy351, vyy361, cbf, cbg, cbh)
new_primCmpNat0(Zero, Succ(vyy5000)) → LT
new_compare211(vyy6000, vyy500, False) → new_compare110(vyy6000, vyy500, new_ltEs16(vyy6000, vyy500))
new_esEs5(Left(vyy350), Left(vyy360), ty_Float, bh) → new_esEs11(vyy350, vyy360)
new_esEs26(vyy350, vyy360, ty_Double) → new_esEs17(vyy350, vyy360)
new_compare29(vyy6000, vyy500, False, bah) → new_compare111(vyy6000, vyy500, new_ltEs7(vyy6000, vyy500, bah), bah)
new_ltEs20(vyy600, vyy50, ty_Bool) → new_ltEs8(vyy600, vyy50)
new_compare17(vyy6000, vyy500, ty_Bool) → new_compare27(vyy6000, vyy500)
new_esEs25(vyy351, vyy361, app(app(ty_Either, chd), che)) → new_esEs5(vyy351, vyy361, chd, che)
new_esEs6(Just(vyy350), Just(vyy360), ty_Ordering) → new_esEs12(vyy350, vyy360)
new_lt11(vyy6000, vyy500, bah) → new_esEs10(new_compare19(vyy6000, vyy500, bah))
new_compare25(vyy6000, vyy500, True, fc, fd, ff) → EQ
new_esEs21(vyy350, vyy360, app(ty_Ratio, bdd)) → new_esEs13(vyy350, vyy360, bdd)
new_esEs25(vyy351, vyy361, ty_Double) → new_esEs17(vyy351, vyy361)
new_ltEs4(Left(vyy6000), Left(vyy500), app(ty_Ratio, ddb), dch) → new_ltEs9(vyy6000, vyy500, ddb)
new_esEs12(LT, LT) → True
new_esEs25(vyy351, vyy361, app(ty_Ratio, daa)) → new_esEs13(vyy351, vyy361, daa)
new_esEs23(vyy351, vyy361, ty_Int) → new_esEs14(vyy351, vyy361)
new_esEs5(Right(vyy350), Right(vyy360), df, app(app(ty_@2, fa), fb)) → new_esEs8(vyy350, vyy360, fa, fb)
new_compare27(vyy6000, vyy500) → new_compare210(vyy6000, vyy500, new_esEs19(vyy6000, vyy500))
new_esEs23(vyy351, vyy361, ty_@0) → new_esEs16(vyy351, vyy361)
new_primEqNat0(Zero, Zero) → True
new_esEs6(Just(vyy350), Just(vyy360), app(app(app(ty_@3, bgc), bgd), bge)) → new_esEs7(vyy350, vyy360, bgc, bgd, bge)
new_lt9(vyy6000, vyy500, app(ty_[], bbb)) → new_lt14(vyy6000, vyy500, bbb)
new_esEs29(vyy35, vyy36, app(ty_Maybe, bfh)) → new_esEs6(vyy35, vyy36, bfh)
new_ltEs6(vyy6002, vyy502, ty_Ordering) → new_ltEs16(vyy6002, vyy502)
new_esEs26(vyy350, vyy360, app(ty_Maybe, dbf)) → new_esEs6(vyy350, vyy360, dbf)
new_esEs25(vyy351, vyy361, app(ty_[], dae)) → new_esEs18(vyy351, vyy361, dae)
new_primMulNat0(Succ(vyy50000), Succ(vyy600100)) → new_primPlusNat1(new_primMulNat0(vyy50000, Succ(vyy600100)), vyy600100)
new_lt8(vyy6001, vyy501, ty_@0) → new_lt4(vyy6001, vyy501)
new_esEs29(vyy35, vyy36, ty_Int) → new_esEs14(vyy35, vyy36)
new_esEs23(vyy351, vyy361, ty_Integer) → new_esEs9(vyy351, vyy361)
new_esEs26(vyy350, vyy360, app(ty_Ratio, dbe)) → new_esEs13(vyy350, vyy360, dbe)
new_esEs6(Just(vyy350), Just(vyy360), ty_Int) → new_esEs14(vyy350, vyy360)
new_esEs24(vyy350, vyy360, app(ty_[], cea)) → new_esEs18(vyy350, vyy360, cea)
new_esEs26(vyy350, vyy360, ty_@0) → new_esEs16(vyy350, vyy360)
new_ltEs7(Just(vyy6000), Just(vyy500), ty_Float) → new_ltEs12(vyy6000, vyy500)
new_esEs19(True, True) → True
new_ltEs16(EQ, LT) → False
new_ltEs16(GT, EQ) → False
new_sr(vyy500, vyy6001) → new_primMulInt(vyy500, vyy6001)
new_compare12(vyy6000, vyy500, True, fc, fd, ff) → LT
new_ltEs6(vyy6002, vyy502, ty_Integer) → new_ltEs17(vyy6002, vyy502)
new_lt8(vyy6001, vyy501, ty_Char) → new_lt17(vyy6001, vyy501)
new_lt20(vyy6000, vyy500, app(ty_Maybe, cgb)) → new_lt11(vyy6000, vyy500, cgb)
new_compare9(vyy6000, vyy500, fg, fh) → new_compare26(vyy6000, vyy500, new_esEs8(vyy6000, vyy500, fg, fh), fg, fh)
new_esEs5(Right(vyy350), Right(vyy360), df, app(ty_[], eh)) → new_esEs18(vyy350, vyy360, eh)
new_esEs26(vyy350, vyy360, ty_Float) → new_esEs11(vyy350, vyy360)
new_ltEs19(vyy6001, vyy501, ty_Double) → new_ltEs10(vyy6001, vyy501)
new_esEs22(vyy352, vyy362, app(ty_[], cba)) → new_esEs18(vyy352, vyy362, cba)
new_lt20(vyy6000, vyy500, ty_Char) → new_lt17(vyy6000, vyy500)
new_lt19(vyy6000, vyy500) → new_esEs10(new_compare11(vyy6000, vyy500))
new_ltEs6(vyy6002, vyy502, ty_Double) → new_ltEs10(vyy6002, vyy502)
new_esEs5(Left(vyy350), Left(vyy360), app(ty_Ratio, cf), bh) → new_esEs13(vyy350, vyy360, cf)
new_esEs25(vyy351, vyy361, ty_Ordering) → new_esEs12(vyy351, vyy361)
new_ltEs20(vyy600, vyy50, app(app(app(ty_@3, ga), gb), gc)) → new_ltEs5(vyy600, vyy50, ga, gb, gc)
new_primEqInt(Neg(Succ(vyy3500)), Neg(Succ(vyy3600))) → new_primEqNat0(vyy3500, vyy3600)
new_esEs25(vyy351, vyy361, app(app(ty_@2, daf), dag)) → new_esEs8(vyy351, vyy361, daf, dag)
new_ltEs16(LT, EQ) → True
new_compare7(vyy6000, vyy500, fc, fd, ff) → new_compare25(vyy6000, vyy500, new_esEs7(vyy6000, vyy500, fc, fd, ff), fc, fd, ff)
new_ltEs6(vyy6002, vyy502, ty_Float) → new_ltEs12(vyy6002, vyy502)
new_esEs24(vyy350, vyy360, ty_Bool) → new_esEs19(vyy350, vyy360)
new_esEs21(vyy350, vyy360, ty_@0) → new_esEs16(vyy350, vyy360)
new_compare17(vyy6000, vyy500, ty_Float) → new_compare6(vyy6000, vyy500)
new_esEs29(vyy35, vyy36, app(app(ty_Either, df), bh)) → new_esEs5(vyy35, vyy36, df, bh)
new_ltEs8(True, True) → True
new_esEs26(vyy350, vyy360, app(app(app(ty_@3, dbb), dbc), dbd)) → new_esEs7(vyy350, vyy360, dbb, dbc, dbd)
new_ltEs4(Left(vyy6000), Left(vyy500), ty_Char, dch) → new_ltEs15(vyy6000, vyy500)
new_ltEs4(Left(vyy6000), Left(vyy500), ty_Float, dch) → new_ltEs12(vyy6000, vyy500)
new_ltEs19(vyy6001, vyy501, app(ty_Ratio, cfa)) → new_ltEs9(vyy6001, vyy501, cfa)
new_esEs12(LT, EQ) → False
new_esEs12(EQ, LT) → False
new_ltEs15(vyy600, vyy50) → new_not(new_compare14(vyy600, vyy50))
new_esEs21(vyy350, vyy360, app(ty_[], bdh)) → new_esEs18(vyy350, vyy360, bdh)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs5(Left(vyy350), Left(vyy360), app(app(app(ty_@3, cc), cd), ce), bh) → new_esEs7(vyy350, vyy360, cc, cd, ce)
new_compare17(vyy6000, vyy500, app(ty_Ratio, bbg)) → new_compare28(vyy6000, vyy500, bbg)
new_esEs19(False, False) → True
new_lt20(vyy6000, vyy500, ty_Ordering) → new_lt7(vyy6000, vyy500)
new_compare17(vyy6000, vyy500, ty_Int) → new_compare11(vyy6000, vyy500)
new_primEqInt(Neg(Zero), Neg(Succ(vyy3600))) → False
new_primEqInt(Neg(Succ(vyy3500)), Neg(Zero)) → False
new_ltEs4(Left(vyy6000), Left(vyy500), app(app(ty_Either, dcf), dcg), dch) → new_ltEs4(vyy6000, vyy500, dcf, dcg)
new_ltEs9(vyy600, vyy50, dcd) → new_not(new_compare28(vyy600, vyy50, dcd))
new_compare26(vyy6000, vyy500, True, fg, fh) → EQ
new_primPlusNat1(Zero, vyy600100) → Succ(vyy600100)
new_compare111(vyy6000, vyy500, True, bah) → LT
new_esEs24(vyy350, vyy360, ty_Integer) → new_esEs9(vyy350, vyy360)
new_compare24(vyy6000, vyy500, True, bf, bg) → EQ
new_esEs6(Just(vyy350), Just(vyy360), ty_Double) → new_esEs17(vyy350, vyy360)
new_esEs26(vyy350, vyy360, app(ty_[], dca)) → new_esEs18(vyy350, vyy360, dca)
new_compare([], [], bbc) → EQ
new_foldFM0(vyy360, vyy361, vyy80, Branch(vyy3630, vyy3631, vyy3632, vyy3633, vyy3634), bec, bed) → new_foldFM0(vyy3630, vyy3631, new_foldFM0(vyy360, vyy361, vyy80, vyy3634, bec, bed), vyy3633, bec, bed)
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_ltEs7(Just(vyy6000), Just(vyy500), ty_Int) → new_ltEs18(vyy6000, vyy500)
new_ltEs4(Right(vyy6000), Right(vyy500), dea, app(ty_Maybe, ded)) → new_ltEs7(vyy6000, vyy500, ded)
new_compare14(Char(vyy6000), Char(vyy500)) → new_primCmpNat0(vyy6000, vyy500)
new_lt9(vyy6000, vyy500, app(ty_Ratio, bba)) → new_lt13(vyy6000, vyy500, bba)
new_ltEs16(GT, LT) → False
new_lt9(vyy6000, vyy500, ty_Ordering) → new_lt7(vyy6000, vyy500)
new_primCmpNat0(Succ(vyy60000), Succ(vyy5000)) → new_primCmpNat0(vyy60000, vyy5000)
new_esEs22(vyy352, vyy362, ty_Char) → new_esEs20(vyy352, vyy362)
new_esEs9(Integer(vyy350), Integer(vyy360)) → new_primEqInt(vyy350, vyy360)
new_sizeFM(EmptyFM, bec, bed) → Pos(Zero)
new_esEs6(Nothing, Nothing, bfh) → True
new_compare112(vyy6000, vyy500, True) → LT
new_primEqInt(Pos(Succ(vyy3500)), Pos(Succ(vyy3600))) → new_primEqNat0(vyy3500, vyy3600)
new_compare10(vyy6000, vyy500, False, bf, bg) → GT
new_ltEs19(vyy6001, vyy501, ty_Integer) → new_ltEs17(vyy6001, vyy501)
new_esEs21(vyy350, vyy360, app(ty_Maybe, bde)) → new_esEs6(vyy350, vyy360, bde)
new_esEs26(vyy350, vyy360, ty_Bool) → new_esEs19(vyy350, vyy360)
new_ltEs7(Nothing, Just(vyy500), bee) → True
new_ltEs6(vyy6002, vyy502, ty_Int) → new_ltEs18(vyy6002, vyy502)
new_esEs5(Right(vyy350), Right(vyy360), df, app(app(ty_Either, dg), dh)) → new_esEs5(vyy350, vyy360, dg, dh)
new_lt9(vyy6000, vyy500, ty_Int) → new_lt19(vyy6000, vyy500)
new_esEs6(Just(vyy350), Nothing, bfh) → False
new_esEs6(Nothing, Just(vyy360), bfh) → False
new_esEs15(vyy35, vyy36, bec, bed) → new_asAs(new_esEs14(new_sizeFM(vyy35, bec, bed), new_sizeFM(vyy36, bec, bed)), new_esEs18(new_fmToList(vyy35, bec, bed), new_fmToList(vyy36, bec, bed), app(app(ty_@2, bec), bed)))
new_primEqNat0(Succ(vyy3500), Succ(vyy3600)) → new_primEqNat0(vyy3500, vyy3600)
new_esEs24(vyy350, vyy360, ty_@0) → new_esEs16(vyy350, vyy360)
new_compare17(vyy6000, vyy500, ty_Integer) → new_compare16(vyy6000, vyy500)
new_esEs26(vyy350, vyy360, ty_Ordering) → new_esEs12(vyy350, vyy360)
new_lt9(vyy6000, vyy500, ty_Bool) → new_lt12(vyy6000, vyy500)
new_lt8(vyy6001, vyy501, app(ty_Maybe, hh)) → new_lt11(vyy6001, vyy501, hh)
new_primCompAux00(vyy66, LT) → LT
new_ltEs5(@3(vyy6000, vyy6001, vyy6002), @3(vyy500, vyy501, vyy502), ga, gb, gc) → new_pePe(new_lt9(vyy6000, vyy500, ga), vyy6000, vyy500, new_pePe(new_lt8(vyy6001, vyy501, gb), vyy6001, vyy501, new_ltEs6(vyy6002, vyy502, gc), gb), ga)
new_lt4(vyy6000, vyy500) → new_esEs10(new_compare5(vyy6000, vyy500))
new_ltEs4(Right(vyy6000), Right(vyy500), dea, ty_Float) → new_ltEs12(vyy6000, vyy500)
new_lt20(vyy6000, vyy500, ty_@0) → new_lt4(vyy6000, vyy500)
new_primCmpInt(Neg(Succ(vyy60000)), Neg(vyy500)) → new_primCmpNat0(vyy500, Succ(vyy60000))
new_compare17(vyy6000, vyy500, app(app(ty_@2, bcd), bce)) → new_compare9(vyy6000, vyy500, bcd, bce)
new_esEs12(EQ, EQ) → True
new_ltEs19(vyy6001, vyy501, ty_Bool) → new_ltEs8(vyy6001, vyy501)
new_esEs5(Right(vyy350), Right(vyy360), df, ty_@0) → new_esEs16(vyy350, vyy360)
new_esEs22(vyy352, vyy362, app(app(ty_FiniteMap, cag), cah)) → new_esEs15(vyy352, vyy362, cag, cah)
new_compare24(vyy6000, vyy500, False, bf, bg) → new_compare10(vyy6000, vyy500, new_ltEs4(vyy6000, vyy500, bf, bg), bf, bg)
new_ltEs6(vyy6002, vyy502, app(ty_Maybe, gf)) → new_ltEs7(vyy6002, vyy502, gf)
new_esEs5(Left(vyy350), Left(vyy360), ty_Int, bh) → new_esEs14(vyy350, vyy360)
new_primEqInt(Pos(Succ(vyy3500)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(vyy3600))) → False
new_ltEs13(@2(vyy6000, vyy6001), @2(vyy500, vyy501), ced, cee) → new_pePe(new_lt20(vyy6000, vyy500, ced), vyy6000, vyy500, new_ltEs19(vyy6001, vyy501, cee), ced)
new_primPlusNat0(Succ(vyy8100), Zero) → Succ(vyy8100)
new_primPlusNat0(Zero, Succ(vyy6001000)) → Succ(vyy6001000)
new_lt9(vyy6000, vyy500, ty_@0) → new_lt4(vyy6000, vyy500)
new_esEs21(vyy350, vyy360, ty_Bool) → new_esEs19(vyy350, vyy360)
new_lt15(vyy6000, vyy500, fc, fd, ff) → new_esEs10(new_compare7(vyy6000, vyy500, fc, fd, ff))
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(vyy60000), Zero) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(vyy5000))) → LT
new_ltEs20(vyy600, vyy50, ty_@0) → new_ltEs14(vyy600, vyy50)
new_esEs19(False, True) → False
new_esEs19(True, False) → False
new_esEs5(Right(vyy350), Right(vyy360), df, ty_Bool) → new_esEs19(vyy350, vyy360)
new_lt10(vyy6000, vyy500, bf, bg) → new_esEs10(new_compare18(vyy6000, vyy500, bf, bg))
new_esEs22(vyy352, vyy362, app(ty_Ratio, cae)) → new_esEs13(vyy352, vyy362, cae)
new_compare17(vyy6000, vyy500, app(ty_[], bbh)) → new_compare(vyy6000, vyy500, bbh)
new_esEs27(vyy351, vyy361, ty_Integer) → new_esEs9(vyy351, vyy361)
new_ltEs20(vyy600, vyy50, ty_Integer) → new_ltEs17(vyy600, vyy50)
new_sr0(Integer(vyy5000), Integer(vyy60010)) → Integer(new_primMulInt(vyy5000, vyy60010))
new_esEs21(vyy350, vyy360, ty_Double) → new_esEs17(vyy350, vyy360)
new_primEqInt(Pos(Succ(vyy3500)), Neg(vyy360)) → False
new_primEqInt(Neg(Succ(vyy3500)), Pos(vyy360)) → False
new_esEs25(vyy351, vyy361, ty_Bool) → new_esEs19(vyy351, vyy361)
new_esEs24(vyy350, vyy360, app(ty_Ratio, cde)) → new_esEs13(vyy350, vyy360, cde)
new_compare(:(vyy6000, vyy6001), :(vyy500, vyy501), bbc) → new_primCompAux0(vyy6000, vyy500, new_compare(vyy6001, vyy501, bbc), bbc)
new_foldFM2(EmptyFM, bec, bed) → []
new_esEs24(vyy350, vyy360, ty_Int) → new_esEs14(vyy350, vyy360)
new_ltEs20(vyy600, vyy50, ty_Double) → new_ltEs10(vyy600, vyy50)
new_esEs21(vyy350, vyy360, ty_Ordering) → new_esEs12(vyy350, vyy360)
new_lt8(vyy6001, vyy501, ty_Float) → new_lt5(vyy6001, vyy501)
new_primEqInt(Neg(Zero), Pos(Succ(vyy3600))) → False
new_primEqInt(Pos(Zero), Neg(Succ(vyy3600))) → False
new_esEs24(vyy350, vyy360, ty_Ordering) → new_esEs12(vyy350, vyy360)
new_primCmpInt(Pos(Zero), Pos(Succ(vyy5000))) → new_primCmpNat0(Zero, Succ(vyy5000))
new_primCompAux00(vyy66, EQ) → vyy66
new_esEs23(vyy351, vyy361, ty_Double) → new_esEs17(vyy351, vyy361)
new_ltEs16(EQ, EQ) → True
new_esEs23(vyy351, vyy361, ty_Bool) → new_esEs19(vyy351, vyy361)
new_compare17(vyy6000, vyy500, app(app(ty_Either, bbd), bbe)) → new_compare18(vyy6000, vyy500, bbd, bbe)
new_esEs22(vyy352, vyy362, ty_Bool) → new_esEs19(vyy352, vyy362)
new_esEs6(Just(vyy350), Just(vyy360), app(app(ty_@2, bhc), bhd)) → new_esEs8(vyy350, vyy360, bhc, bhd)
new_esEs22(vyy352, vyy362, ty_@0) → new_esEs16(vyy352, vyy362)
new_esEs5(Left(vyy350), Left(vyy360), ty_Double, bh) → new_esEs17(vyy350, vyy360)
new_esEs7(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), bhe, bhf, bhg) → new_asAs(new_esEs24(vyy350, vyy360, bhe), new_asAs(new_esEs23(vyy351, vyy361, bhf), new_esEs22(vyy352, vyy362, bhg)))
new_esEs29(vyy35, vyy36, app(app(ty_FiniteMap, bec), bed)) → new_esEs15(vyy35, vyy36, bec, bed)
new_ltEs19(vyy6001, vyy501, app(app(ty_@2, cff), cfg)) → new_ltEs13(vyy6001, vyy501, cff, cfg)
new_esEs23(vyy351, vyy361, ty_Float) → new_esEs11(vyy351, vyy361)
new_ltEs8(True, False) → False
new_esEs5(Left(vyy350), Left(vyy360), app(app(ty_@2, dd), de), bh) → new_esEs8(vyy350, vyy360, dd, de)
new_ltEs4(Right(vyy6000), Left(vyy500), dea, dch) → False
new_compare16(Integer(vyy6000), Integer(vyy500)) → new_primCmpInt(vyy6000, vyy500)
new_primCmpInt(Pos(Succ(vyy60000)), Pos(vyy500)) → new_primCmpNat0(Succ(vyy60000), vyy500)
new_esEs22(vyy352, vyy362, ty_Float) → new_esEs11(vyy352, vyy362)
new_esEs12(GT, EQ) → False
new_esEs12(EQ, GT) → False
new_compare12(vyy6000, vyy500, False, fc, fd, ff) → GT
new_lt8(vyy6001, vyy501, ty_Integer) → new_lt18(vyy6001, vyy501)
new_esEs6(Just(vyy350), Just(vyy360), app(ty_[], bhb)) → new_esEs18(vyy350, vyy360, bhb)
new_esEs29(vyy35, vyy36, app(app(ty_@2, chb), chc)) → new_esEs8(vyy35, vyy36, chb, chc)
new_ltEs4(Right(vyy6000), Right(vyy500), dea, ty_Ordering) → new_ltEs16(vyy6000, vyy500)
new_lt20(vyy6000, vyy500, app(app(app(ty_@3, cge), cgf), cgg)) → new_lt15(vyy6000, vyy500, cge, cgf, cgg)
new_ltEs19(vyy6001, vyy501, ty_Int) → new_ltEs18(vyy6001, vyy501)
new_lt9(vyy6000, vyy500, ty_Integer) → new_lt18(vyy6000, vyy500)
new_not0 → True
new_esEs5(Right(vyy350), Right(vyy360), df, ty_Int) → new_esEs14(vyy350, vyy360)
new_esEs5(Right(vyy350), Right(vyy360), df, ty_Double) → new_esEs17(vyy350, vyy360)
new_compare17(vyy6000, vyy500, app(ty_Maybe, bbf)) → new_compare19(vyy6000, vyy500, bbf)
new_ltEs6(vyy6002, vyy502, app(ty_[], gh)) → new_ltEs11(vyy6002, vyy502, gh)
new_lt20(vyy6000, vyy500, ty_Double) → new_lt6(vyy6000, vyy500)
new_esEs26(vyy350, vyy360, app(app(ty_Either, dah), dba)) → new_esEs5(vyy350, vyy360, dah, dba)
new_primCompAux0(vyy6000, vyy500, vyy62, bbc) → new_primCompAux00(vyy62, new_compare17(vyy6000, vyy500, bbc))
new_esEs5(Left(vyy350), Left(vyy360), ty_Bool, bh) → new_esEs19(vyy350, vyy360)
new_esEs5(Right(vyy350), Right(vyy360), df, app(app(ty_FiniteMap, ef), eg)) → new_esEs15(vyy350, vyy360, ef, eg)
new_ltEs4(Right(vyy6000), Right(vyy500), dea, app(ty_Ratio, dee)) → new_ltEs9(vyy6000, vyy500, dee)
new_esEs22(vyy352, vyy362, app(app(app(ty_@3, cab), cac), cad)) → new_esEs7(vyy352, vyy362, cab, cac, cad)
new_primCmpInt(Pos(Succ(vyy60000)), Neg(vyy500)) → GT
new_lt6(vyy6000, vyy500) → new_esEs10(new_compare8(vyy6000, vyy500))
new_ltEs7(Just(vyy6000), Just(vyy500), app(ty_Maybe, beh)) → new_ltEs7(vyy6000, vyy500, beh)
new_ltEs4(Right(vyy6000), Right(vyy500), dea, ty_Bool) → new_ltEs8(vyy6000, vyy500)
new_esEs29(vyy35, vyy36, ty_@0) → new_esEs16(vyy35, vyy36)
new_esEs29(vyy35, vyy36, ty_Integer) → new_esEs9(vyy35, vyy36)
new_primMulInt(Pos(vyy5000), Pos(vyy60010)) → Pos(new_primMulNat0(vyy5000, vyy60010))
new_compare13(vyy6000, vyy500) → new_compare211(vyy6000, vyy500, new_esEs12(vyy6000, vyy500))
new_ltEs4(Left(vyy6000), Left(vyy500), app(app(ty_@2, ddg), ddh), dch) → new_ltEs13(vyy6000, vyy500, ddg, ddh)
new_ltEs4(Left(vyy6000), Left(vyy500), ty_@0, dch) → new_ltEs14(vyy6000, vyy500)
new_ltEs4(Left(vyy6000), Left(vyy500), ty_Integer, dch) → new_ltEs17(vyy6000, vyy500)
new_esEs24(vyy350, vyy360, app(app(ty_FiniteMap, cdg), cdh)) → new_esEs15(vyy350, vyy360, cdg, cdh)
new_ltEs6(vyy6002, vyy502, app(app(ty_Either, gd), ge)) → new_ltEs4(vyy6002, vyy502, gd, ge)
new_lt20(vyy6000, vyy500, app(app(ty_Either, cfh), cga)) → new_lt10(vyy6000, vyy500, cfh, cga)
new_esEs5(Right(vyy350), Left(vyy360), df, bh) → False
new_esEs5(Left(vyy350), Right(vyy360), df, bh) → False
new_primMulInt(Neg(vyy5000), Neg(vyy60010)) → Pos(new_primMulNat0(vyy5000, vyy60010))
new_compare110(vyy6000, vyy500, True) → LT
new_ltEs4(Right(vyy6000), Right(vyy500), dea, app(app(ty_@2, dfb), dfc)) → new_ltEs13(vyy6000, vyy500, dfb, dfc)
new_primEqNat0(Succ(vyy3500), Zero) → False
new_primEqNat0(Zero, Succ(vyy3600)) → False
new_ltEs20(vyy600, vyy50, ty_Int) → new_ltEs18(vyy600, vyy50)
new_ltEs8(False, False) → True
new_primPlusNat0(Zero, Zero) → Zero
new_ltEs20(vyy600, vyy50, ty_Char) → new_ltEs15(vyy600, vyy50)
new_esEs25(vyy351, vyy361, app(ty_Maybe, dab)) → new_esEs6(vyy351, vyy361, dab)
new_compare110(vyy6000, vyy500, False) → GT
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs5(Left(vyy350), Left(vyy360), app(ty_[], dc), bh) → new_esEs18(vyy350, vyy360, dc)
new_compare210(vyy6000, vyy500, True) → EQ
new_sizeFM(Branch(vyy360, vyy361, vyy362, vyy363, vyy364), bec, bed) → vyy362
new_ltEs4(Right(vyy6000), Right(vyy500), dea, ty_Double) → new_ltEs10(vyy6000, vyy500)
new_ltEs20(vyy600, vyy50, ty_Ordering) → new_ltEs16(vyy600, vyy50)
new_ltEs7(Nothing, Nothing, bee) → True
new_pePe(True, vyy35, vyy36, vyy52, dfd) → True
new_primPlusNat1(Succ(vyy810), vyy600100) → Succ(Succ(new_primPlusNat0(vyy810, vyy600100)))
new_foldFM2(Branch(vyy360, vyy361, vyy362, vyy363, vyy364), bec, bed) → new_foldFM0(vyy360, vyy361, new_foldFM2(vyy364, bec, bed), vyy363, bec, bed)
new_esEs5(Left(vyy350), Left(vyy360), app(app(ty_FiniteMap, da), db), bh) → new_esEs15(vyy350, vyy360, da, db)
new_ltEs7(Just(vyy6000), Just(vyy500), app(app(app(ty_@3, bfc), bfd), bfe)) → new_ltEs5(vyy6000, vyy500, bfc, bfd, bfe)
new_lt9(vyy6000, vyy500, app(app(app(ty_@3, fc), fd), ff)) → new_lt15(vyy6000, vyy500, fc, fd, ff)
new_ltEs7(Just(vyy6000), Just(vyy500), ty_Ordering) → new_ltEs16(vyy6000, vyy500)
new_primCmpInt(Neg(Zero), Neg(Succ(vyy5000))) → new_primCmpNat0(Succ(vyy5000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(vyy5000))) → GT
new_esEs29(vyy35, vyy36, ty_Bool) → new_esEs19(vyy35, vyy36)
new_esEs23(vyy351, vyy361, app(app(ty_@2, ccf), ccg)) → new_esEs8(vyy351, vyy361, ccf, ccg)
new_ltEs6(vyy6002, vyy502, app(app(ty_@2, hd), he)) → new_ltEs13(vyy6002, vyy502, hd, he)
new_esEs5(Right(vyy350), Right(vyy360), df, app(app(app(ty_@3, ea), eb), ec)) → new_esEs7(vyy350, vyy360, ea, eb, ec)
new_compare15(vyy6000, vyy500, False, fg, fh) → GT
new_ltEs7(Just(vyy6000), Just(vyy500), ty_Char) → new_ltEs15(vyy6000, vyy500)
new_esEs25(vyy351, vyy361, ty_Int) → new_esEs14(vyy351, vyy361)
new_esEs6(Just(vyy350), Just(vyy360), app(app(ty_Either, bga), bgb)) → new_esEs5(vyy350, vyy360, bga, bgb)
new_lt14(vyy6000, vyy500, bbb) → new_esEs10(new_compare(vyy6000, vyy500, bbb))
new_esEs10(LT) → True
new_esEs5(Right(vyy350), Right(vyy360), df, ty_Float) → new_esEs11(vyy350, vyy360)
new_ltEs6(vyy6002, vyy502, ty_@0) → new_ltEs14(vyy6002, vyy502)
new_esEs27(vyy351, vyy361, ty_Int) → new_esEs14(vyy351, vyy361)
new_esEs28(vyy350, vyy360, ty_Integer) → new_esEs9(vyy350, vyy360)
new_esEs26(vyy350, vyy360, ty_Char) → new_esEs20(vyy350, vyy360)
new_esEs24(vyy350, vyy360, app(app(app(ty_@3, cdb), cdc), cdd)) → new_esEs7(vyy350, vyy360, cdb, cdc, cdd)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_compare29(vyy6000, vyy500, True, bah) → EQ
new_lt8(vyy6001, vyy501, ty_Double) → new_lt6(vyy6001, vyy501)
new_compare17(vyy6000, vyy500, ty_Ordering) → new_compare13(vyy6000, vyy500)
new_esEs26(vyy350, vyy360, ty_Int) → new_esEs14(vyy350, vyy360)
new_esEs13(:%(vyy350, vyy351), :%(vyy360, vyy361), dce) → new_asAs(new_esEs28(vyy350, vyy360, dce), new_esEs27(vyy351, vyy361, dce))
new_esEs6(Just(vyy350), Just(vyy360), ty_Integer) → new_esEs9(vyy350, vyy360)
new_asAs(False, vyy61) → False
new_compare18(vyy6000, vyy500, bf, bg) → new_compare24(vyy6000, vyy500, new_esEs5(vyy6000, vyy500, bf, bg), bf, bg)
new_primMulInt(Pos(vyy5000), Neg(vyy60010)) → Neg(new_primMulNat0(vyy5000, vyy60010))
new_primMulInt(Neg(vyy5000), Pos(vyy60010)) → Neg(new_primMulNat0(vyy5000, vyy60010))
new_lt12(vyy6000, vyy500) → new_esEs10(new_compare27(vyy6000, vyy500))
new_ltEs20(vyy600, vyy50, app(ty_[], bbc)) → new_ltEs11(vyy600, vyy50, bbc)
new_primMulNat0(Zero, Succ(vyy600100)) → Zero
new_primMulNat0(Succ(vyy50000), Zero) → Zero
new_compare8(Double(vyy6000, vyy6001), Double(vyy500, vyy501)) → new_compare11(new_sr(vyy6000, vyy500), new_sr(vyy6001, vyy501))
new_esEs18([], [], bcf) → True
new_esEs21(vyy350, vyy360, app(app(ty_Either, bcg), bch)) → new_esEs5(vyy350, vyy360, bcg, bch)
new_esEs29(vyy35, vyy36, ty_Char) → new_esEs20(vyy35, vyy36)
new_esEs6(Just(vyy350), Just(vyy360), app(ty_Maybe, bgg)) → new_esEs6(vyy350, vyy360, bgg)
new_esEs21(vyy350, vyy360, app(app(ty_FiniteMap, bdf), bdg)) → new_esEs15(vyy350, vyy360, bdf, bdg)
new_esEs25(vyy351, vyy361, ty_@0) → new_esEs16(vyy351, vyy361)
new_lt20(vyy6000, vyy500, app(ty_[], cgd)) → new_lt14(vyy6000, vyy500, cgd)
new_esEs29(vyy35, vyy36, ty_Float) → new_esEs11(vyy35, vyy36)
new_ltEs4(Right(vyy6000), Right(vyy500), dea, ty_@0) → new_ltEs14(vyy6000, vyy500)
new_esEs23(vyy351, vyy361, ty_Ordering) → new_esEs12(vyy351, vyy361)
new_esEs29(vyy35, vyy36, ty_Double) → new_esEs17(vyy35, vyy36)
new_ltEs11(vyy600, vyy50, bbc) → new_not(new_compare(vyy600, vyy50, bbc))
new_esEs24(vyy350, vyy360, ty_Float) → new_esEs11(vyy350, vyy360)
new_not(EQ) → new_not0
new_esEs23(vyy351, vyy361, app(ty_Maybe, ccb)) → new_esEs6(vyy351, vyy361, ccb)
new_lt20(vyy6000, vyy500, app(app(ty_@2, cgh), cha)) → new_lt16(vyy6000, vyy500, cgh, cha)
new_esEs21(vyy350, vyy360, ty_Integer) → new_esEs9(vyy350, vyy360)
new_esEs24(vyy350, vyy360, ty_Char) → new_esEs20(vyy350, vyy360)
new_esEs26(vyy350, vyy360, ty_Integer) → new_esEs9(vyy350, vyy360)
new_ltEs7(Just(vyy6000), Just(vyy500), app(ty_[], bfb)) → new_ltEs11(vyy6000, vyy500, bfb)
new_esEs16(@0, @0) → True
new_lt9(vyy6000, vyy500, app(ty_Maybe, bah)) → new_lt11(vyy6000, vyy500, bah)
new_ltEs19(vyy6001, vyy501, ty_@0) → new_ltEs14(vyy6001, vyy501)
new_compare111(vyy6000, vyy500, False, bah) → GT
new_ltEs6(vyy6002, vyy502, ty_Bool) → new_ltEs8(vyy6002, vyy502)
new_esEs5(Left(vyy350), Left(vyy360), ty_Char, bh) → new_esEs20(vyy350, vyy360)
new_esEs24(vyy350, vyy360, ty_Double) → new_esEs17(vyy350, vyy360)
new_esEs5(Right(vyy350), Right(vyy360), df, app(ty_Maybe, ee)) → new_esEs6(vyy350, vyy360, ee)
new_ltEs7(Just(vyy6000), Just(vyy500), ty_Bool) → new_ltEs8(vyy6000, vyy500)
new_ltEs7(Just(vyy6000), Just(vyy500), ty_@0) → new_ltEs14(vyy6000, vyy500)
new_compare11(vyy600, vyy50) → new_primCmpInt(vyy600, vyy50)
new_esEs14(vyy35, vyy36) → new_primEqInt(vyy35, vyy36)
new_ltEs19(vyy6001, vyy501, app(app(app(ty_@3, cfc), cfd), cfe)) → new_ltEs5(vyy6001, vyy501, cfc, cfd, cfe)
new_esEs25(vyy351, vyy361, app(app(app(ty_@3, chf), chg), chh)) → new_esEs7(vyy351, vyy361, chf, chg, chh)
new_esEs8(@2(vyy350, vyy351), @2(vyy360, vyy361), chb, chc) → new_asAs(new_esEs26(vyy350, vyy360, chb), new_esEs25(vyy351, vyy361, chc))
new_ltEs6(vyy6002, vyy502, ty_Char) → new_ltEs15(vyy6002, vyy502)
new_compare17(vyy6000, vyy500, app(app(app(ty_@3, bca), bcb), bcc)) → new_compare7(vyy6000, vyy500, bca, bcb, bcc)
new_esEs21(vyy350, vyy360, ty_Char) → new_esEs20(vyy350, vyy360)
new_ltEs7(Just(vyy6000), Nothing, bee) → False
new_lt20(vyy6000, vyy500, ty_Int) → new_lt19(vyy6000, vyy500)
new_lt13(vyy6000, vyy500, bba) → new_esEs10(new_compare28(vyy6000, vyy500, bba))
new_not(LT) → new_not0
new_lt18(vyy6000, vyy500) → new_esEs10(new_compare16(vyy6000, vyy500))
new_ltEs19(vyy6001, vyy501, app(ty_Maybe, ceh)) → new_ltEs7(vyy6001, vyy501, ceh)
new_esEs5(Left(vyy350), Left(vyy360), app(app(ty_Either, ca), cb), bh) → new_esEs5(vyy350, vyy360, ca, cb)
new_ltEs7(Just(vyy6000), Just(vyy500), app(app(ty_@2, bff), bfg)) → new_ltEs13(vyy6000, vyy500, bff, bfg)
new_lt20(vyy6000, vyy500, ty_Bool) → new_lt12(vyy6000, vyy500)
new_ltEs4(Left(vyy6000), Left(vyy500), ty_Ordering, dch) → new_ltEs16(vyy6000, vyy500)
new_compare112(vyy6000, vyy500, False) → GT
new_ltEs4(Left(vyy6000), Left(vyy500), app(ty_Maybe, dda), dch) → new_ltEs7(vyy6000, vyy500, dda)
new_ltEs12(vyy600, vyy50) → new_not(new_compare6(vyy600, vyy50))
new_compare210(vyy6000, vyy500, False) → new_compare112(vyy6000, vyy500, new_ltEs8(vyy6000, vyy500))
new_esEs12(GT, GT) → True
new_compare25(vyy6000, vyy500, False, fc, fd, ff) → new_compare12(vyy6000, vyy500, new_ltEs5(vyy6000, vyy500, fc, fd, ff), fc, fd, ff)
new_esEs23(vyy351, vyy361, ty_Char) → new_esEs20(vyy351, vyy361)
new_esEs21(vyy350, vyy360, ty_Float) → new_esEs11(vyy350, vyy360)
new_esEs22(vyy352, vyy362, ty_Int) → new_esEs14(vyy352, vyy362)
new_compare19(vyy6000, vyy500, bah) → new_compare29(vyy6000, vyy500, new_esEs6(vyy6000, vyy500, bah), bah)
new_primPlusNat0(Succ(vyy8100), Succ(vyy6001000)) → Succ(Succ(new_primPlusNat0(vyy8100, vyy6001000)))
new_esEs29(vyy35, vyy36, ty_Ordering) → new_esEs12(vyy35, vyy36)
new_esEs29(vyy35, vyy36, app(ty_[], bcf)) → new_esEs18(vyy35, vyy36, bcf)
new_esEs5(Right(vyy350), Right(vyy360), df, ty_Ordering) → new_esEs12(vyy350, vyy360)
new_ltEs4(Left(vyy6000), Left(vyy500), ty_Double, dch) → new_ltEs10(vyy6000, vyy500)
new_esEs18(:(vyy350, vyy351), :(vyy360, vyy361), bcf) → new_asAs(new_esEs21(vyy350, vyy360, bcf), new_esEs18(vyy351, vyy361, bcf))
new_asAs(True, vyy61) → vyy61
new_compare28(:%(vyy6000, vyy6001), :%(vyy500, vyy501), ty_Int) → new_compare11(new_sr(vyy6000, vyy501), new_sr(vyy500, vyy6001))
new_esEs22(vyy352, vyy362, app(app(ty_@2, cbb), cbc)) → new_esEs8(vyy352, vyy362, cbb, cbc)
new_esEs17(Double(vyy350, vyy351), Double(vyy360, vyy361)) → new_esEs14(new_sr(vyy350, vyy360), new_sr(vyy351, vyy361))
new_ltEs19(vyy6001, vyy501, ty_Float) → new_ltEs12(vyy6001, vyy501)
new_esEs25(vyy351, vyy361, ty_Float) → new_esEs11(vyy351, vyy361)
new_esEs5(Left(vyy350), Left(vyy360), ty_Ordering, bh) → new_esEs12(vyy350, vyy360)
new_ltEs16(LT, LT) → True
new_compare211(vyy6000, vyy500, True) → EQ
new_fmToList(vyy36, bec, bed) → new_foldFM2(vyy36, bec, bed)
new_lt17(vyy6000, vyy500) → new_esEs10(new_compare14(vyy6000, vyy500))
new_compare6(Float(vyy6000, vyy6001), Float(vyy500, vyy501)) → new_compare11(new_sr(vyy6000, vyy500), new_sr(vyy6001, vyy501))
new_esEs24(vyy350, vyy360, app(app(ty_@2, ceb), cec)) → new_esEs8(vyy350, vyy360, ceb, cec)
new_ltEs20(vyy600, vyy50, app(app(ty_@2, ced), cee)) → new_ltEs13(vyy600, vyy50, ced, cee)
new_ltEs4(Left(vyy6000), Left(vyy500), ty_Bool, dch) → new_ltEs8(vyy6000, vyy500)
new_esEs24(vyy350, vyy360, app(ty_Maybe, cdf)) → new_esEs6(vyy350, vyy360, cdf)
new_ltEs20(vyy600, vyy50, app(ty_Maybe, bee)) → new_ltEs7(vyy600, vyy50, bee)
new_esEs5(Right(vyy350), Right(vyy360), df, ty_Char) → new_esEs20(vyy350, vyy360)
new_ltEs4(Right(vyy6000), Right(vyy500), dea, ty_Int) → new_ltEs18(vyy6000, vyy500)
new_lt20(vyy6000, vyy500, app(ty_Ratio, cgc)) → new_lt13(vyy6000, vyy500, cgc)
new_esEs23(vyy351, vyy361, app(ty_[], cce)) → new_esEs18(vyy351, vyy361, cce)
new_esEs5(Left(vyy350), Left(vyy360), ty_Integer, bh) → new_esEs9(vyy350, vyy360)
new_esEs22(vyy352, vyy362, app(app(ty_Either, bhh), caa)) → new_esEs5(vyy352, vyy362, bhh, caa)
new_primCompAux00(vyy66, GT) → GT
new_compare17(vyy6000, vyy500, ty_@0) → new_compare5(vyy6000, vyy500)
new_ltEs7(Just(vyy6000), Just(vyy500), app(ty_Ratio, bfa)) → new_ltEs9(vyy6000, vyy500, bfa)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_lt8(vyy6001, vyy501, ty_Bool) → new_lt12(vyy6001, vyy501)
new_ltEs4(Left(vyy6000), Left(vyy500), app(app(app(ty_@3, ddd), dde), ddf), dch) → new_ltEs5(vyy6000, vyy500, ddd, dde, ddf)
new_esEs5(Right(vyy350), Right(vyy360), df, app(ty_Ratio, ed)) → new_esEs13(vyy350, vyy360, ed)
new_ltEs7(Just(vyy6000), Just(vyy500), app(app(ty_Either, bef), beg)) → new_ltEs4(vyy6000, vyy500, bef, beg)
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primCmpInt(Neg(Succ(vyy60000)), Pos(vyy500)) → LT
new_esEs25(vyy351, vyy361, ty_Integer) → new_esEs9(vyy351, vyy361)
new_ltEs10(vyy600, vyy50) → new_not(new_compare8(vyy600, vyy50))
new_ltEs4(Right(vyy6000), Right(vyy500), dea, app(app(app(ty_@3, deg), deh), dfa)) → new_ltEs5(vyy6000, vyy500, deg, deh, dfa)
The set Q consists of the following terms:
new_lt8(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, ty_Integer)
new_esEs5(Left(x0), Left(x1), ty_Integer, x2)
new_esEs25(x0, x1, ty_Int)
new_esEs26(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs5(Left(x0), Left(x1), ty_Int, x2)
new_ltEs4(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_ltEs20(x0, x1, ty_Integer)
new_ltEs4(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_ltEs6(x0, x1, ty_Float)
new_lt8(x0, x1, ty_Int)
new_esEs25(x0, x1, app(ty_[], x2))
new_lt16(x0, x1, x2, x3)
new_lt9(x0, x1, ty_@0)
new_compare24(x0, x1, False, x2, x3)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs6(Nothing, Just(x0), x1)
new_compare111(x0, x1, False, x2)
new_compare12(x0, x1, True, x2, x3, x4)
new_esEs22(x0, x1, ty_@0)
new_lt9(x0, x1, app(app(ty_@2, x2), x3))
new_pePe(False, x0, x1, x2, x3)
new_ltEs4(Left(x0), Left(x1), ty_Double, x2)
new_ltEs4(Left(x0), Left(x1), ty_Char, x2)
new_ltEs6(x0, x1, app(ty_[], x2))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs5(Left(x0), Left(x1), ty_Bool, x2)
new_ltEs19(x0, x1, ty_Integer)
new_esEs5(Right(x0), Right(x1), x2, ty_@0)
new_esEs22(x0, x1, ty_Char)
new_esEs5(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs7(Nothing, Just(x0), x1)
new_esEs23(x0, x1, ty_Integer)
new_compare110(x0, x1, True)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs21(x0, x1, ty_Double)
new_esEs5(Right(x0), Right(x1), x2, ty_Int)
new_esEs23(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_ltEs19(x0, x1, app(ty_[], x2))
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_primMulNat0(Succ(x0), Zero)
new_esEs26(x0, x1, app(ty_[], x2))
new_esEs26(x0, x1, ty_Char)
new_ltEs7(Just(x0), Just(x1), app(ty_[], x2))
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare110(x0, x1, False)
new_esEs12(EQ, GT)
new_esEs12(GT, EQ)
new_lt10(x0, x1, x2, x3)
new_ltEs6(x0, x1, ty_Char)
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_lt8(x0, x1, app(ty_Maybe, x2))
new_ltEs4(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs10(GT)
new_lt9(x0, x1, app(ty_Ratio, x2))
new_esEs5(Left(x0), Right(x1), x2, x3)
new_esEs5(Right(x0), Left(x1), x2, x3)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_lt20(x0, x1, ty_Int)
new_esEs23(x0, x1, ty_Int)
new_esEs28(x0, x1, ty_Integer)
new_ltEs8(True, True)
new_esEs6(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs5(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs4(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs6(Nothing, Nothing, x0)
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs6(x0, x1, app(ty_Maybe, x2))
new_esEs12(GT, GT)
new_esEs23(x0, x1, ty_Ordering)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_lt8(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs23(x0, x1, ty_Char)
new_ltEs7(Just(x0), Just(x1), ty_@0)
new_esEs16(@0, @0)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs9(x0, x1, x2)
new_esEs5(Right(x0), Right(x1), x2, ty_Double)
new_esEs22(x0, x1, ty_Int)
new_ltEs20(x0, x1, ty_@0)
new_ltEs4(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_compare24(x0, x1, True, x2, x3)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, ty_Ordering)
new_esEs23(x0, x1, ty_Bool)
new_esEs6(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs19(x0, x1, ty_Float)
new_lt14(x0, x1, x2)
new_ltEs7(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs7(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs19(True, True)
new_compare25(x0, x1, True, x2, x3, x4)
new_compare112(x0, x1, True)
new_esEs29(x0, x1, ty_Integer)
new_esEs5(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_compare11(x0, x1)
new_lt8(x0, x1, app(ty_[], x2))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_ltEs4(Left(x0), Left(x1), ty_Bool, x2)
new_esEs5(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs5(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt8(x0, x1, ty_Char)
new_compare5(@0, @0)
new_esEs21(x0, x1, ty_Int)
new_esEs5(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_lt20(x0, x1, ty_Ordering)
new_esEs29(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_compare17(x0, x1, ty_Double)
new_primEqNat0(Zero, Zero)
new_compare9(x0, x1, x2, x3)
new_esEs18(:(x0, x1), :(x2, x3), x4)
new_primPlusNat0(Zero, Succ(x0))
new_ltEs4(Right(x0), Right(x1), x2, ty_Float)
new_lt20(x0, x1, ty_Double)
new_ltEs6(x0, x1, app(ty_Ratio, x2))
new_ltEs6(x0, x1, ty_Ordering)
new_esEs9(Integer(x0), Integer(x1))
new_ltEs4(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs6(Just(x0), Just(x1), ty_Float)
new_esEs29(x0, x1, app(ty_[], x2))
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_lt8(x0, x1, ty_Float)
new_esEs17(Double(x0, x1), Double(x2, x3))
new_esEs29(x0, x1, ty_Float)
new_primMulNat0(Zero, Zero)
new_esEs18([], :(x0, x1), x2)
new_esEs29(x0, x1, ty_Char)
new_esEs6(Just(x0), Just(x1), app(app(ty_FiniteMap, x2), x3))
new_esEs5(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs7(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_compare17(x0, x1, app(ty_[], x2))
new_compare6(Float(x0, x1), Float(x2, x3))
new_ltEs17(x0, x1)
new_esEs25(x0, x1, ty_Integer)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_lt9(x0, x1, app(ty_Maybe, x2))
new_ltEs4(Left(x0), Left(x1), app(ty_[], x2), x3)
new_ltEs7(Just(x0), Just(x1), ty_Bool)
new_esEs25(x0, x1, ty_Double)
new_ltEs6(x0, x1, ty_Double)
new_compare17(x0, x1, ty_Int)
new_compare10(x0, x1, True, x2, x3)
new_lt4(x0, x1)
new_esEs26(x0, x1, ty_Ordering)
new_compare112(x0, x1, False)
new_lt11(x0, x1, x2)
new_esEs23(x0, x1, ty_Float)
new_primMulNat0(Succ(x0), Succ(x1))
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
new_esEs24(x0, x1, ty_Float)
new_ltEs19(x0, x1, ty_Ordering)
new_compare29(x0, x1, True, x2)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs19(x0, x1, ty_Bool)
new_foldFM2(EmptyFM, x0, x1)
new_esEs21(x0, x1, ty_Bool)
new_ltEs6(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, app(ty_[], x2))
new_esEs27(x0, x1, ty_Int)
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, app(ty_[], x2))
new_primCmpNat0(Succ(x0), Succ(x1))
new_compare17(x0, x1, ty_Integer)
new_esEs25(x0, x1, ty_Ordering)
new_compare111(x0, x1, True, x2)
new_ltEs20(x0, x1, ty_Bool)
new_esEs24(x0, x1, ty_@0)
new_esEs24(x0, x1, ty_Double)
new_compare17(x0, x1, app(ty_Ratio, x2))
new_esEs5(Right(x0), Right(x1), x2, app(app(ty_FiniteMap, x3), x4))
new_ltEs13(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs5(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_ltEs4(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs6(Just(x0), Just(x1), ty_Integer)
new_compare210(x0, x1, True)
new_esEs24(x0, x1, ty_Bool)
new_lt20(x0, x1, ty_Char)
new_compare([], :(x0, x1), x2)
new_primEqNat0(Zero, Succ(x0))
new_esEs14(x0, x1)
new_ltEs4(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_lt20(x0, x1, ty_Integer)
new_lt9(x0, x1, ty_Float)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs6(Just(x0), Nothing, x1)
new_esEs19(True, False)
new_esEs19(False, True)
new_ltEs20(x0, x1, ty_Char)
new_esEs12(LT, EQ)
new_esEs12(EQ, LT)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs5(Right(x0), Right(x1), x2, ty_Char)
new_compare14(Char(x0), Char(x1))
new_esEs27(x0, x1, ty_Integer)
new_esEs25(x0, x1, ty_Char)
new_ltEs7(Just(x0), Just(x1), ty_Double)
new_esEs25(x0, x1, ty_Float)
new_sr(x0, x1)
new_compare17(x0, x1, ty_@0)
new_esEs5(Left(x0), Left(x1), app(app(ty_FiniteMap, x2), x3), x4)
new_ltEs18(x0, x1)
new_ltEs7(Just(x0), Just(x1), ty_Ordering)
new_not0
new_esEs29(x0, x1, ty_@0)
new_ltEs19(x0, x1, ty_Char)
new_esEs12(EQ, EQ)
new_ltEs4(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_primPlusNat0(Zero, Zero)
new_ltEs16(EQ, EQ)
new_compare15(x0, x1, False, x2, x3)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_compare210(x0, x1, False)
new_esEs24(x0, x1, ty_Ordering)
new_esEs22(x0, x1, ty_Bool)
new_esEs5(Right(x0), Right(x1), x2, ty_Bool)
new_primPlusNat0(Succ(x0), Succ(x1))
new_esEs6(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_esEs28(x0, x1, ty_Int)
new_esEs6(Just(x0), Just(x1), ty_Ordering)
new_ltEs16(LT, LT)
new_compare211(x0, x1, True)
new_primMulInt(Pos(x0), Pos(x1))
new_ltEs7(Just(x0), Just(x1), ty_Float)
new_lt9(x0, x1, ty_Double)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_lt12(x0, x1)
new_lt8(x0, x1, ty_Integer)
new_esEs5(Left(x0), Left(x1), app(ty_[], x2), x3)
new_lt8(x0, x1, ty_Ordering)
new_esEs25(x0, x1, ty_Bool)
new_ltEs20(x0, x1, app(ty_[], x2))
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_lt9(x0, x1, ty_Char)
new_lt8(x0, x1, app(ty_Ratio, x2))
new_ltEs4(Left(x0), Left(x1), ty_Ordering, x2)
new_lt20(x0, x1, app(ty_[], x2))
new_lt6(x0, x1)
new_ltEs4(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs16(GT, LT)
new_ltEs16(LT, GT)
new_ltEs7(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_ltEs6(x0, x1, app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_esEs21(x0, x1, ty_Float)
new_not(GT)
new_ltEs4(Right(x0), Right(x1), x2, ty_@0)
new_ltEs8(False, False)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare17(x0, x1, app(ty_Maybe, x2))
new_ltEs4(Left(x0), Left(x1), ty_Float, x2)
new_asAs(False, x0)
new_esEs26(x0, x1, ty_Float)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_primEqNat0(Succ(x0), Zero)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_lt20(x0, x1, ty_Float)
new_asAs(True, x0)
new_primEqInt(Neg(Zero), Pos(Zero))
new_primEqInt(Pos(Zero), Neg(Zero))
new_ltEs10(x0, x1)
new_ltEs8(False, True)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs8(True, False)
new_lt15(x0, x1, x2, x3, x4)
new_compare17(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs5(Right(x0), Right(x1), x2, ty_Integer)
new_esEs25(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs5(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_pePe(True, x0, x1, x2, x3)
new_ltEs14(x0, x1)
new_primCmpNat0(Succ(x0), Zero)
new_esEs26(x0, x1, ty_Double)
new_compare26(x0, x1, False, x2, x3)
new_compare12(x0, x1, False, x2, x3, x4)
new_ltEs4(Left(x0), Right(x1), x2, x3)
new_ltEs4(Right(x0), Left(x1), x2, x3)
new_esEs19(False, False)
new_compare15(x0, x1, True, x2, x3)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_lt19(x0, x1)
new_esEs6(Just(x0), Just(x1), ty_Int)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_lt20(x0, x1, app(ty_Ratio, x2))
new_ltEs6(x0, x1, ty_@0)
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs24(x0, x1, ty_Integer)
new_primEqInt(Neg(Zero), Neg(Zero))
new_ltEs20(x0, x1, ty_Float)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_compare17(x0, x1, ty_Float)
new_lt8(x0, x1, ty_Double)
new_primCompAux0(x0, x1, x2, x3)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_compare26(x0, x1, True, x2, x3)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_ltEs4(Left(x0), Left(x1), ty_@0, x2)
new_fmToList(x0, x1, x2)
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs7(Just(x0), Just(x1), ty_Char)
new_esEs26(x0, x1, ty_Integer)
new_esEs24(x0, x1, ty_Int)
new_compare17(x0, x1, ty_Ordering)
new_compare28(:%(x0, x1), :%(x2, x3), ty_Integer)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_ltEs16(GT, GT)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_esEs5(Left(x0), Left(x1), ty_Char, x2)
new_esEs18(:(x0, x1), [], x2)
new_ltEs7(Just(x0), Nothing, x1)
new_esEs5(Left(x0), Left(x1), ty_@0, x2)
new_compare29(x0, x1, False, x2)
new_compare28(:%(x0, x1), :%(x2, x3), ty_Int)
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs29(x0, x1, ty_Ordering)
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_esEs24(x0, x1, app(ty_[], x2))
new_ltEs6(x0, x1, ty_Bool)
new_esEs29(x0, x1, ty_Int)
new_compare13(x0, x1)
new_ltEs4(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs6(Just(x0), Just(x1), ty_@0)
new_esEs26(x0, x1, ty_@0)
new_esEs10(EQ)
new_ltEs12(x0, x1)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_compare17(x0, x1, ty_Char)
new_lt9(x0, x1, ty_Ordering)
new_primCmpNat0(Zero, Zero)
new_esEs5(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_ltEs7(Just(x0), Just(x1), ty_Integer)
new_esEs21(x0, x1, ty_Char)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_esEs29(x0, x1, ty_Bool)
new_esEs6(Just(x0), Just(x1), ty_Double)
new_primPlusNat0(Succ(x0), Zero)
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, ty_Bool)
new_primCompAux00(x0, EQ)
new_ltEs4(Right(x0), Right(x1), x2, ty_Int)
new_esEs8(@2(x0, x1), @2(x2, x3), x4, x5)
new_lt9(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_sr0(Integer(x0), Integer(x1))
new_esEs24(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_compare27(x0, x1)
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, ty_Ordering)
new_primMulNat0(Zero, Succ(x0))
new_compare25(x0, x1, False, x2, x3, x4)
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs6(x0, x1, ty_Int)
new_compare18(x0, x1, x2, x3)
new_compare([], [], x0)
new_primCmpNat0(Zero, Succ(x0))
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_primCompAux00(x0, GT)
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_lt9(x0, x1, app(app(ty_Either, x2), x3))
new_compare17(x0, x1, app(app(ty_@2, x2), x3))
new_esEs24(x0, x1, ty_Char)
new_esEs5(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs10(LT)
new_esEs6(Just(x0), Just(x1), ty_Bool)
new_ltEs11(x0, x1, x2)
new_lt8(x0, x1, app(app(ty_@2, x2), x3))
new_esEs21(x0, x1, ty_Integer)
new_lt17(x0, x1)
new_ltEs6(x0, x1, ty_Integer)
new_ltEs7(Nothing, Nothing, x0)
new_esEs25(x0, x1, ty_@0)
new_lt20(x0, x1, ty_Bool)
new_ltEs7(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs21(x0, x1, app(ty_[], x2))
new_primCompAux00(x0, LT)
new_not(EQ)
new_esEs11(Float(x0, x1), Float(x2, x3))
new_ltEs4(Right(x0), Right(x1), x2, ty_Double)
new_ltEs16(GT, EQ)
new_ltEs16(EQ, GT)
new_ltEs20(x0, x1, ty_Double)
new_compare(:(x0, x1), :(x2, x3), x4)
new_esEs5(Right(x0), Right(x1), x2, ty_Float)
new_primPlusNat1(Zero, x0)
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt9(x0, x1, ty_Bool)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_esEs22(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_ltEs6(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs5(Right(x0), Right(x1), x2, ty_Ordering)
new_ltEs16(LT, EQ)
new_ltEs16(EQ, LT)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_esEs5(Left(x0), Left(x1), ty_Float, x2)
new_ltEs4(Left(x0), Left(x1), ty_Integer, x2)
new_compare(:(x0, x1), [], x2)
new_esEs5(Left(x0), Left(x1), ty_Double, x2)
new_esEs26(x0, x1, ty_Int)
new_ltEs4(Right(x0), Right(x1), x2, ty_Integer)
new_lt5(x0, x1)
new_sizeFM(EmptyFM, x0, x1)
new_compare17(x0, x1, ty_Bool)
new_esEs21(x0, x1, ty_Ordering)
new_compare10(x0, x1, False, x2, x3)
new_compare8(Double(x0, x1), Double(x2, x3))
new_ltEs4(Left(x0), Left(x1), ty_Int, x2)
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs20(Char(x0), Char(x1))
new_esEs21(x0, x1, ty_@0)
new_esEs6(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs7(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs23(x0, x1, ty_@0)
new_esEs5(Left(x0), Left(x1), ty_Ordering, x2)
new_ltEs4(Right(x0), Right(x1), x2, ty_Char)
new_ltEs5(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_ltEs19(x0, x1, ty_@0)
new_lt7(x0, x1)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_esEs6(Just(x0), Just(x1), ty_Char)
new_lt8(x0, x1, ty_@0)
new_lt9(x0, x1, ty_Integer)
new_esEs18([], [], x0)
new_compare7(x0, x1, x2, x3, x4)
new_lt9(x0, x1, ty_Int)
new_ltEs19(x0, x1, ty_Double)
new_lt8(x0, x1, ty_Bool)
new_lt9(x0, x1, app(ty_[], x2))
new_esEs15(x0, x1, x2, x3)
new_esEs13(:%(x0, x1), :%(x2, x3), x4)
new_compare16(Integer(x0), Integer(x1))
new_esEs6(Just(x0), Just(x1), app(ty_Maybe, x2))
new_ltEs19(x0, x1, ty_Int)
new_lt13(x0, x1, x2)
new_esEs23(x0, x1, ty_Double)
new_esEs22(x0, x1, ty_Double)
new_primEqInt(Pos(Zero), Pos(Zero))
new_ltEs4(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_lt18(x0, x1)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_compare17(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs4(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs20(x0, x1, ty_Int)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, ty_@0)
new_compare19(x0, x1, x2)
new_esEs29(x0, x1, ty_Double)
new_primPlusNat1(Succ(x0), x1)
new_ltEs7(Just(x0), Just(x1), ty_Int)
new_esEs12(LT, LT)
new_not(LT)
new_esEs22(x0, x1, ty_Float)
new_ltEs15(x0, x1)
new_compare211(x0, x1, False)
We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph [15,17,22] contains 2 SCCs.
↳ 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
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPSizeChangeProof
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_foldFM_LE1(vyy17, vyy19, vyy20, vyy21, vyy22, vyy23, vyy24, False, bc, bd, be) → new_foldFM_LE(vyy17, Just(vyy19), vyy23, bc, bd, be)
new_foldFM_LE(vyy3, Just(vyy50), Branch(Just(vyy600), vyy61, vyy62, vyy63, vyy64), h, ba, bb) → new_foldFM_LE1(vyy3, vyy50, vyy600, vyy61, vyy62, vyy63, vyy64, new_ltEs20(vyy600, vyy50, ba), h, ba, bb)
new_foldFM_LE1(vyy17, vyy19, vyy20, vyy21, vyy22, vyy23, vyy24, True, bc, bd, be) → new_foldFM_LE(vyy17, Just(vyy19), vyy24, bc, bd, be)
new_foldFM_LE1(vyy17, vyy19, vyy20, vyy21, vyy22, vyy23, vyy24, True, bc, bd, be) → new_foldFM_LE(vyy17, Just(vyy19), vyy23, bc, bd, be)
new_foldFM_LE(vyy3, Just(vyy50), Branch(Nothing, vyy61, vyy62, vyy63, vyy64), h, ba, bb) → new_foldFM_LE(vyy3, Just(vyy50), vyy64, h, ba, bb)
new_foldFM_LE(vyy3, Just(vyy50), Branch(Nothing, vyy61, vyy62, vyy63, vyy64), h, ba, bb) → new_foldFM_LE(vyy3, Just(vyy50), vyy63, h, ba, bb)
The TRS R consists of the following rules:
new_esEs22(vyy352, vyy362, ty_Double) → new_esEs17(vyy352, vyy362)
new_esEs11(Float(vyy350, vyy351), Float(vyy360, vyy361)) → new_esEs14(new_sr(vyy350, vyy360), new_sr(vyy351, vyy361))
new_ltEs4(Right(vyy6000), Right(vyy500), dea, ty_Integer) → new_ltEs17(vyy6000, vyy500)
new_esEs24(vyy350, vyy360, app(app(ty_Either, cch), cda)) → new_esEs5(vyy350, vyy360, cch, cda)
new_compare5(@0, @0) → EQ
new_ltEs19(vyy6001, vyy501, ty_Ordering) → new_ltEs16(vyy6001, vyy501)
new_ltEs16(GT, GT) → True
new_ltEs8(False, True) → True
new_ltEs4(Right(vyy6000), Right(vyy500), dea, app(ty_[], def)) → new_ltEs11(vyy6000, vyy500, def)
new_ltEs4(Right(vyy6000), Right(vyy500), dea, ty_Char) → new_ltEs15(vyy6000, vyy500)
new_ltEs20(vyy600, vyy50, app(ty_Ratio, dcd)) → new_ltEs9(vyy600, vyy50, dcd)
new_compare15(vyy6000, vyy500, True, fg, fh) → LT
new_lt7(vyy6000, vyy500) → new_esEs10(new_compare13(vyy6000, vyy500))
new_ltEs19(vyy6001, vyy501, ty_Char) → new_ltEs15(vyy6001, vyy501)
new_ltEs4(Left(vyy6000), Left(vyy500), app(ty_[], ddc), dch) → new_ltEs11(vyy6000, vyy500, ddc)
new_esEs10(GT) → False
new_esEs23(vyy351, vyy361, app(app(ty_Either, cbd), cbe)) → new_esEs5(vyy351, vyy361, cbd, cbe)
new_lt16(vyy6000, vyy500, fg, fh) → new_esEs10(new_compare9(vyy6000, vyy500, fg, fh))
new_lt8(vyy6001, vyy501, app(ty_Ratio, baa)) → new_lt13(vyy6001, vyy501, baa)
new_compare([], :(vyy500, vyy501), bbc) → LT
new_compare10(vyy6000, vyy500, True, bf, bg) → LT
new_esEs6(Just(vyy350), Just(vyy360), ty_Char) → new_esEs20(vyy350, vyy360)
new_lt8(vyy6001, vyy501, ty_Int) → new_lt19(vyy6001, vyy501)
new_lt8(vyy6001, vyy501, app(app(app(ty_@3, bac), bad), bae)) → new_lt15(vyy6001, vyy501, bac, bad, bae)
new_lt9(vyy6000, vyy500, ty_Float) → new_lt5(vyy6000, vyy500)
new_ltEs16(LT, GT) → True
new_ltEs7(Just(vyy6000), Just(vyy500), ty_Integer) → new_ltEs17(vyy6000, vyy500)
new_lt8(vyy6001, vyy501, ty_Ordering) → new_lt7(vyy6001, vyy501)
new_esEs5(Left(vyy350), Left(vyy360), ty_@0, bh) → new_esEs16(vyy350, vyy360)
new_esEs28(vyy350, vyy360, ty_Int) → new_esEs14(vyy350, vyy360)
new_ltEs6(vyy6002, vyy502, app(ty_Ratio, gg)) → new_ltEs9(vyy6002, vyy502, gg)
new_esEs21(vyy350, vyy360, ty_Int) → new_esEs14(vyy350, vyy360)
new_esEs20(Char(vyy350), Char(vyy360)) → new_primEqNat0(vyy350, vyy360)
new_esEs6(Just(vyy350), Just(vyy360), ty_@0) → new_esEs16(vyy350, vyy360)
new_ltEs4(Left(vyy6000), Left(vyy500), ty_Int, dch) → new_ltEs18(vyy6000, vyy500)
new_primMulNat0(Zero, Zero) → Zero
new_esEs25(vyy351, vyy361, ty_Char) → new_esEs20(vyy351, vyy361)
new_esEs6(Just(vyy350), Just(vyy360), app(ty_Ratio, bgf)) → new_esEs13(vyy350, vyy360, bgf)
new_compare(:(vyy6000, vyy6001), [], bbc) → GT
new_esEs23(vyy351, vyy361, app(ty_Ratio, cca)) → new_esEs13(vyy351, vyy361, cca)
new_ltEs20(vyy600, vyy50, ty_Float) → new_ltEs12(vyy600, vyy50)
new_esEs6(Just(vyy350), Just(vyy360), ty_Bool) → new_esEs19(vyy350, vyy360)
new_ltEs6(vyy6002, vyy502, app(app(app(ty_@3, ha), hb), hc)) → new_ltEs5(vyy6002, vyy502, ha, hb, hc)
new_lt20(vyy6000, vyy500, ty_Integer) → new_lt18(vyy6000, vyy500)
new_esEs6(Just(vyy350), Just(vyy360), ty_Float) → new_esEs11(vyy350, vyy360)
new_lt9(vyy6000, vyy500, ty_Double) → new_lt6(vyy6000, vyy500)
new_lt9(vyy6000, vyy500, app(app(ty_@2, fg), fh)) → new_lt16(vyy6000, vyy500, fg, fh)
new_not(GT) → False
new_compare17(vyy6000, vyy500, ty_Char) → new_compare14(vyy6000, vyy500)
new_ltEs7(Just(vyy6000), Just(vyy500), ty_Double) → new_ltEs10(vyy6000, vyy500)
new_esEs10(EQ) → False
new_compare17(vyy6000, vyy500, ty_Double) → new_compare8(vyy6000, vyy500)
new_esEs12(GT, LT) → False
new_esEs12(LT, GT) → False
new_esEs5(Right(vyy350), Right(vyy360), df, ty_Integer) → new_esEs9(vyy350, vyy360)
new_esEs23(vyy351, vyy361, app(app(ty_FiniteMap, ccc), ccd)) → new_esEs15(vyy351, vyy361, ccc, ccd)
new_lt8(vyy6001, vyy501, app(app(ty_@2, baf), bag)) → new_lt16(vyy6001, vyy501, baf, bag)
new_esEs22(vyy352, vyy362, app(ty_Maybe, caf)) → new_esEs6(vyy352, vyy362, caf)
new_esEs21(vyy350, vyy360, app(app(app(ty_@3, bda), bdb), bdc)) → new_esEs7(vyy350, vyy360, bda, bdb, bdc)
new_esEs22(vyy352, vyy362, ty_Integer) → new_esEs9(vyy352, vyy362)
new_compare28(:%(vyy6000, vyy6001), :%(vyy500, vyy501), ty_Integer) → new_compare16(new_sr0(vyy6000, vyy501), new_sr0(vyy500, vyy6001))
new_lt9(vyy6000, vyy500, ty_Char) → new_lt17(vyy6000, vyy500)
new_esEs29(vyy35, vyy36, app(app(app(ty_@3, bhe), bhf), bhg)) → new_esEs7(vyy35, vyy36, bhe, bhf, bhg)
new_lt8(vyy6001, vyy501, app(app(ty_Either, hf), hg)) → new_lt10(vyy6001, vyy501, hf, hg)
new_pePe(False, vyy35, vyy36, vyy52, dfd) → new_asAs(new_esEs29(vyy35, vyy36, dfd), vyy52)
new_compare26(vyy6000, vyy500, False, fg, fh) → new_compare15(vyy6000, vyy500, new_ltEs13(vyy6000, vyy500, fg, fh), fg, fh)
new_ltEs18(vyy600, vyy50) → new_not(new_compare11(vyy600, vyy50))
new_foldFM0(vyy360, vyy361, vyy80, EmptyFM, bec, bed) → :(@2(vyy360, vyy361), vyy80)
new_esEs21(vyy350, vyy360, app(app(ty_@2, bea), beb)) → new_esEs8(vyy350, vyy360, bea, beb)
new_esEs22(vyy352, vyy362, ty_Ordering) → new_esEs12(vyy352, vyy362)
new_esEs5(Left(vyy350), Left(vyy360), app(ty_Maybe, cg), bh) → new_esEs6(vyy350, vyy360, cg)
new_ltEs19(vyy6001, vyy501, app(app(ty_Either, cef), ceg)) → new_ltEs4(vyy6001, vyy501, cef, ceg)
new_ltEs17(vyy600, vyy50) → new_not(new_compare16(vyy600, vyy50))
new_lt9(vyy6000, vyy500, app(app(ty_Either, bf), bg)) → new_lt10(vyy6000, vyy500, bf, bg)
new_esEs26(vyy350, vyy360, app(app(ty_@2, dcb), dcc)) → new_esEs8(vyy350, vyy360, dcb, dcc)
new_esEs18(:(vyy350, vyy351), [], bcf) → False
new_esEs18([], :(vyy360, vyy361), bcf) → False
new_ltEs14(vyy600, vyy50) → new_not(new_compare5(vyy600, vyy50))
new_esEs26(vyy350, vyy360, app(app(ty_FiniteMap, dbg), dbh)) → new_esEs15(vyy350, vyy360, dbg, dbh)
new_lt5(vyy6000, vyy500) → new_esEs10(new_compare6(vyy6000, vyy500))
new_ltEs19(vyy6001, vyy501, app(ty_[], cfb)) → new_ltEs11(vyy6001, vyy501, cfb)
new_esEs6(Just(vyy350), Just(vyy360), app(app(ty_FiniteMap, bgh), bha)) → new_esEs15(vyy350, vyy360, bgh, bha)
new_ltEs16(EQ, GT) → True
new_ltEs20(vyy600, vyy50, app(app(ty_Either, dea), dch)) → new_ltEs4(vyy600, vyy50, dea, dch)
new_ltEs4(Right(vyy6000), Right(vyy500), dea, app(app(ty_Either, deb), dec)) → new_ltEs4(vyy6000, vyy500, deb, dec)
new_lt20(vyy6000, vyy500, ty_Float) → new_lt5(vyy6000, vyy500)
new_esEs29(vyy35, vyy36, app(ty_Ratio, dce)) → new_esEs13(vyy35, vyy36, dce)
new_lt8(vyy6001, vyy501, app(ty_[], bab)) → new_lt14(vyy6001, vyy501, bab)
new_ltEs4(Left(vyy6000), Right(vyy500), dea, dch) → True
new_esEs25(vyy351, vyy361, app(app(ty_FiniteMap, dac), dad)) → new_esEs15(vyy351, vyy361, dac, dad)
new_esEs23(vyy351, vyy361, app(app(app(ty_@3, cbf), cbg), cbh)) → new_esEs7(vyy351, vyy361, cbf, cbg, cbh)
new_primCmpNat0(Zero, Succ(vyy5000)) → LT
new_compare211(vyy6000, vyy500, False) → new_compare110(vyy6000, vyy500, new_ltEs16(vyy6000, vyy500))
new_esEs5(Left(vyy350), Left(vyy360), ty_Float, bh) → new_esEs11(vyy350, vyy360)
new_esEs26(vyy350, vyy360, ty_Double) → new_esEs17(vyy350, vyy360)
new_compare29(vyy6000, vyy500, False, bah) → new_compare111(vyy6000, vyy500, new_ltEs7(vyy6000, vyy500, bah), bah)
new_ltEs20(vyy600, vyy50, ty_Bool) → new_ltEs8(vyy600, vyy50)
new_compare17(vyy6000, vyy500, ty_Bool) → new_compare27(vyy6000, vyy500)
new_esEs25(vyy351, vyy361, app(app(ty_Either, chd), che)) → new_esEs5(vyy351, vyy361, chd, che)
new_esEs6(Just(vyy350), Just(vyy360), ty_Ordering) → new_esEs12(vyy350, vyy360)
new_lt11(vyy6000, vyy500, bah) → new_esEs10(new_compare19(vyy6000, vyy500, bah))
new_compare25(vyy6000, vyy500, True, fc, fd, ff) → EQ
new_esEs21(vyy350, vyy360, app(ty_Ratio, bdd)) → new_esEs13(vyy350, vyy360, bdd)
new_esEs25(vyy351, vyy361, ty_Double) → new_esEs17(vyy351, vyy361)
new_ltEs4(Left(vyy6000), Left(vyy500), app(ty_Ratio, ddb), dch) → new_ltEs9(vyy6000, vyy500, ddb)
new_esEs12(LT, LT) → True
new_esEs25(vyy351, vyy361, app(ty_Ratio, daa)) → new_esEs13(vyy351, vyy361, daa)
new_esEs23(vyy351, vyy361, ty_Int) → new_esEs14(vyy351, vyy361)
new_esEs5(Right(vyy350), Right(vyy360), df, app(app(ty_@2, fa), fb)) → new_esEs8(vyy350, vyy360, fa, fb)
new_compare27(vyy6000, vyy500) → new_compare210(vyy6000, vyy500, new_esEs19(vyy6000, vyy500))
new_esEs23(vyy351, vyy361, ty_@0) → new_esEs16(vyy351, vyy361)
new_primEqNat0(Zero, Zero) → True
new_esEs6(Just(vyy350), Just(vyy360), app(app(app(ty_@3, bgc), bgd), bge)) → new_esEs7(vyy350, vyy360, bgc, bgd, bge)
new_lt9(vyy6000, vyy500, app(ty_[], bbb)) → new_lt14(vyy6000, vyy500, bbb)
new_esEs29(vyy35, vyy36, app(ty_Maybe, bfh)) → new_esEs6(vyy35, vyy36, bfh)
new_ltEs6(vyy6002, vyy502, ty_Ordering) → new_ltEs16(vyy6002, vyy502)
new_esEs26(vyy350, vyy360, app(ty_Maybe, dbf)) → new_esEs6(vyy350, vyy360, dbf)
new_esEs25(vyy351, vyy361, app(ty_[], dae)) → new_esEs18(vyy351, vyy361, dae)
new_primMulNat0(Succ(vyy50000), Succ(vyy600100)) → new_primPlusNat1(new_primMulNat0(vyy50000, Succ(vyy600100)), vyy600100)
new_lt8(vyy6001, vyy501, ty_@0) → new_lt4(vyy6001, vyy501)
new_esEs29(vyy35, vyy36, ty_Int) → new_esEs14(vyy35, vyy36)
new_esEs23(vyy351, vyy361, ty_Integer) → new_esEs9(vyy351, vyy361)
new_esEs26(vyy350, vyy360, app(ty_Ratio, dbe)) → new_esEs13(vyy350, vyy360, dbe)
new_esEs6(Just(vyy350), Just(vyy360), ty_Int) → new_esEs14(vyy350, vyy360)
new_esEs24(vyy350, vyy360, app(ty_[], cea)) → new_esEs18(vyy350, vyy360, cea)
new_esEs26(vyy350, vyy360, ty_@0) → new_esEs16(vyy350, vyy360)
new_ltEs7(Just(vyy6000), Just(vyy500), ty_Float) → new_ltEs12(vyy6000, vyy500)
new_esEs19(True, True) → True
new_ltEs16(EQ, LT) → False
new_ltEs16(GT, EQ) → False
new_sr(vyy500, vyy6001) → new_primMulInt(vyy500, vyy6001)
new_compare12(vyy6000, vyy500, True, fc, fd, ff) → LT
new_ltEs6(vyy6002, vyy502, ty_Integer) → new_ltEs17(vyy6002, vyy502)
new_lt8(vyy6001, vyy501, ty_Char) → new_lt17(vyy6001, vyy501)
new_lt20(vyy6000, vyy500, app(ty_Maybe, cgb)) → new_lt11(vyy6000, vyy500, cgb)
new_compare9(vyy6000, vyy500, fg, fh) → new_compare26(vyy6000, vyy500, new_esEs8(vyy6000, vyy500, fg, fh), fg, fh)
new_esEs5(Right(vyy350), Right(vyy360), df, app(ty_[], eh)) → new_esEs18(vyy350, vyy360, eh)
new_esEs26(vyy350, vyy360, ty_Float) → new_esEs11(vyy350, vyy360)
new_ltEs19(vyy6001, vyy501, ty_Double) → new_ltEs10(vyy6001, vyy501)
new_esEs22(vyy352, vyy362, app(ty_[], cba)) → new_esEs18(vyy352, vyy362, cba)
new_lt20(vyy6000, vyy500, ty_Char) → new_lt17(vyy6000, vyy500)
new_lt19(vyy6000, vyy500) → new_esEs10(new_compare11(vyy6000, vyy500))
new_ltEs6(vyy6002, vyy502, ty_Double) → new_ltEs10(vyy6002, vyy502)
new_esEs5(Left(vyy350), Left(vyy360), app(ty_Ratio, cf), bh) → new_esEs13(vyy350, vyy360, cf)
new_esEs25(vyy351, vyy361, ty_Ordering) → new_esEs12(vyy351, vyy361)
new_ltEs20(vyy600, vyy50, app(app(app(ty_@3, ga), gb), gc)) → new_ltEs5(vyy600, vyy50, ga, gb, gc)
new_primEqInt(Neg(Succ(vyy3500)), Neg(Succ(vyy3600))) → new_primEqNat0(vyy3500, vyy3600)
new_esEs25(vyy351, vyy361, app(app(ty_@2, daf), dag)) → new_esEs8(vyy351, vyy361, daf, dag)
new_ltEs16(LT, EQ) → True
new_compare7(vyy6000, vyy500, fc, fd, ff) → new_compare25(vyy6000, vyy500, new_esEs7(vyy6000, vyy500, fc, fd, ff), fc, fd, ff)
new_ltEs6(vyy6002, vyy502, ty_Float) → new_ltEs12(vyy6002, vyy502)
new_esEs24(vyy350, vyy360, ty_Bool) → new_esEs19(vyy350, vyy360)
new_esEs21(vyy350, vyy360, ty_@0) → new_esEs16(vyy350, vyy360)
new_compare17(vyy6000, vyy500, ty_Float) → new_compare6(vyy6000, vyy500)
new_esEs29(vyy35, vyy36, app(app(ty_Either, df), bh)) → new_esEs5(vyy35, vyy36, df, bh)
new_ltEs8(True, True) → True
new_esEs26(vyy350, vyy360, app(app(app(ty_@3, dbb), dbc), dbd)) → new_esEs7(vyy350, vyy360, dbb, dbc, dbd)
new_ltEs4(Left(vyy6000), Left(vyy500), ty_Char, dch) → new_ltEs15(vyy6000, vyy500)
new_ltEs4(Left(vyy6000), Left(vyy500), ty_Float, dch) → new_ltEs12(vyy6000, vyy500)
new_ltEs19(vyy6001, vyy501, app(ty_Ratio, cfa)) → new_ltEs9(vyy6001, vyy501, cfa)
new_esEs12(LT, EQ) → False
new_esEs12(EQ, LT) → False
new_ltEs15(vyy600, vyy50) → new_not(new_compare14(vyy600, vyy50))
new_esEs21(vyy350, vyy360, app(ty_[], bdh)) → new_esEs18(vyy350, vyy360, bdh)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs5(Left(vyy350), Left(vyy360), app(app(app(ty_@3, cc), cd), ce), bh) → new_esEs7(vyy350, vyy360, cc, cd, ce)
new_compare17(vyy6000, vyy500, app(ty_Ratio, bbg)) → new_compare28(vyy6000, vyy500, bbg)
new_esEs19(False, False) → True
new_lt20(vyy6000, vyy500, ty_Ordering) → new_lt7(vyy6000, vyy500)
new_compare17(vyy6000, vyy500, ty_Int) → new_compare11(vyy6000, vyy500)
new_primEqInt(Neg(Zero), Neg(Succ(vyy3600))) → False
new_primEqInt(Neg(Succ(vyy3500)), Neg(Zero)) → False
new_ltEs4(Left(vyy6000), Left(vyy500), app(app(ty_Either, dcf), dcg), dch) → new_ltEs4(vyy6000, vyy500, dcf, dcg)
new_ltEs9(vyy600, vyy50, dcd) → new_not(new_compare28(vyy600, vyy50, dcd))
new_compare26(vyy6000, vyy500, True, fg, fh) → EQ
new_primPlusNat1(Zero, vyy600100) → Succ(vyy600100)
new_compare111(vyy6000, vyy500, True, bah) → LT
new_esEs24(vyy350, vyy360, ty_Integer) → new_esEs9(vyy350, vyy360)
new_compare24(vyy6000, vyy500, True, bf, bg) → EQ
new_esEs6(Just(vyy350), Just(vyy360), ty_Double) → new_esEs17(vyy350, vyy360)
new_esEs26(vyy350, vyy360, app(ty_[], dca)) → new_esEs18(vyy350, vyy360, dca)
new_compare([], [], bbc) → EQ
new_foldFM0(vyy360, vyy361, vyy80, Branch(vyy3630, vyy3631, vyy3632, vyy3633, vyy3634), bec, bed) → new_foldFM0(vyy3630, vyy3631, new_foldFM0(vyy360, vyy361, vyy80, vyy3634, bec, bed), vyy3633, bec, bed)
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_ltEs7(Just(vyy6000), Just(vyy500), ty_Int) → new_ltEs18(vyy6000, vyy500)
new_ltEs4(Right(vyy6000), Right(vyy500), dea, app(ty_Maybe, ded)) → new_ltEs7(vyy6000, vyy500, ded)
new_compare14(Char(vyy6000), Char(vyy500)) → new_primCmpNat0(vyy6000, vyy500)
new_lt9(vyy6000, vyy500, app(ty_Ratio, bba)) → new_lt13(vyy6000, vyy500, bba)
new_ltEs16(GT, LT) → False
new_lt9(vyy6000, vyy500, ty_Ordering) → new_lt7(vyy6000, vyy500)
new_primCmpNat0(Succ(vyy60000), Succ(vyy5000)) → new_primCmpNat0(vyy60000, vyy5000)
new_esEs22(vyy352, vyy362, ty_Char) → new_esEs20(vyy352, vyy362)
new_esEs9(Integer(vyy350), Integer(vyy360)) → new_primEqInt(vyy350, vyy360)
new_sizeFM(EmptyFM, bec, bed) → Pos(Zero)
new_esEs6(Nothing, Nothing, bfh) → True
new_compare112(vyy6000, vyy500, True) → LT
new_primEqInt(Pos(Succ(vyy3500)), Pos(Succ(vyy3600))) → new_primEqNat0(vyy3500, vyy3600)
new_compare10(vyy6000, vyy500, False, bf, bg) → GT
new_ltEs19(vyy6001, vyy501, ty_Integer) → new_ltEs17(vyy6001, vyy501)
new_esEs21(vyy350, vyy360, app(ty_Maybe, bde)) → new_esEs6(vyy350, vyy360, bde)
new_esEs26(vyy350, vyy360, ty_Bool) → new_esEs19(vyy350, vyy360)
new_ltEs7(Nothing, Just(vyy500), bee) → True
new_ltEs6(vyy6002, vyy502, ty_Int) → new_ltEs18(vyy6002, vyy502)
new_esEs5(Right(vyy350), Right(vyy360), df, app(app(ty_Either, dg), dh)) → new_esEs5(vyy350, vyy360, dg, dh)
new_lt9(vyy6000, vyy500, ty_Int) → new_lt19(vyy6000, vyy500)
new_esEs6(Just(vyy350), Nothing, bfh) → False
new_esEs6(Nothing, Just(vyy360), bfh) → False
new_esEs15(vyy35, vyy36, bec, bed) → new_asAs(new_esEs14(new_sizeFM(vyy35, bec, bed), new_sizeFM(vyy36, bec, bed)), new_esEs18(new_fmToList(vyy35, bec, bed), new_fmToList(vyy36, bec, bed), app(app(ty_@2, bec), bed)))
new_primEqNat0(Succ(vyy3500), Succ(vyy3600)) → new_primEqNat0(vyy3500, vyy3600)
new_esEs24(vyy350, vyy360, ty_@0) → new_esEs16(vyy350, vyy360)
new_compare17(vyy6000, vyy500, ty_Integer) → new_compare16(vyy6000, vyy500)
new_esEs26(vyy350, vyy360, ty_Ordering) → new_esEs12(vyy350, vyy360)
new_lt9(vyy6000, vyy500, ty_Bool) → new_lt12(vyy6000, vyy500)
new_lt8(vyy6001, vyy501, app(ty_Maybe, hh)) → new_lt11(vyy6001, vyy501, hh)
new_primCompAux00(vyy66, LT) → LT
new_ltEs5(@3(vyy6000, vyy6001, vyy6002), @3(vyy500, vyy501, vyy502), ga, gb, gc) → new_pePe(new_lt9(vyy6000, vyy500, ga), vyy6000, vyy500, new_pePe(new_lt8(vyy6001, vyy501, gb), vyy6001, vyy501, new_ltEs6(vyy6002, vyy502, gc), gb), ga)
new_lt4(vyy6000, vyy500) → new_esEs10(new_compare5(vyy6000, vyy500))
new_ltEs4(Right(vyy6000), Right(vyy500), dea, ty_Float) → new_ltEs12(vyy6000, vyy500)
new_lt20(vyy6000, vyy500, ty_@0) → new_lt4(vyy6000, vyy500)
new_primCmpInt(Neg(Succ(vyy60000)), Neg(vyy500)) → new_primCmpNat0(vyy500, Succ(vyy60000))
new_compare17(vyy6000, vyy500, app(app(ty_@2, bcd), bce)) → new_compare9(vyy6000, vyy500, bcd, bce)
new_esEs12(EQ, EQ) → True
new_ltEs19(vyy6001, vyy501, ty_Bool) → new_ltEs8(vyy6001, vyy501)
new_esEs5(Right(vyy350), Right(vyy360), df, ty_@0) → new_esEs16(vyy350, vyy360)
new_esEs22(vyy352, vyy362, app(app(ty_FiniteMap, cag), cah)) → new_esEs15(vyy352, vyy362, cag, cah)
new_compare24(vyy6000, vyy500, False, bf, bg) → new_compare10(vyy6000, vyy500, new_ltEs4(vyy6000, vyy500, bf, bg), bf, bg)
new_ltEs6(vyy6002, vyy502, app(ty_Maybe, gf)) → new_ltEs7(vyy6002, vyy502, gf)
new_esEs5(Left(vyy350), Left(vyy360), ty_Int, bh) → new_esEs14(vyy350, vyy360)
new_primEqInt(Pos(Succ(vyy3500)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(vyy3600))) → False
new_ltEs13(@2(vyy6000, vyy6001), @2(vyy500, vyy501), ced, cee) → new_pePe(new_lt20(vyy6000, vyy500, ced), vyy6000, vyy500, new_ltEs19(vyy6001, vyy501, cee), ced)
new_primPlusNat0(Succ(vyy8100), Zero) → Succ(vyy8100)
new_primPlusNat0(Zero, Succ(vyy6001000)) → Succ(vyy6001000)
new_lt9(vyy6000, vyy500, ty_@0) → new_lt4(vyy6000, vyy500)
new_esEs21(vyy350, vyy360, ty_Bool) → new_esEs19(vyy350, vyy360)
new_lt15(vyy6000, vyy500, fc, fd, ff) → new_esEs10(new_compare7(vyy6000, vyy500, fc, fd, ff))
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(vyy60000), Zero) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(vyy5000))) → LT
new_ltEs20(vyy600, vyy50, ty_@0) → new_ltEs14(vyy600, vyy50)
new_esEs19(False, True) → False
new_esEs19(True, False) → False
new_esEs5(Right(vyy350), Right(vyy360), df, ty_Bool) → new_esEs19(vyy350, vyy360)
new_lt10(vyy6000, vyy500, bf, bg) → new_esEs10(new_compare18(vyy6000, vyy500, bf, bg))
new_esEs22(vyy352, vyy362, app(ty_Ratio, cae)) → new_esEs13(vyy352, vyy362, cae)
new_compare17(vyy6000, vyy500, app(ty_[], bbh)) → new_compare(vyy6000, vyy500, bbh)
new_esEs27(vyy351, vyy361, ty_Integer) → new_esEs9(vyy351, vyy361)
new_ltEs20(vyy600, vyy50, ty_Integer) → new_ltEs17(vyy600, vyy50)
new_sr0(Integer(vyy5000), Integer(vyy60010)) → Integer(new_primMulInt(vyy5000, vyy60010))
new_esEs21(vyy350, vyy360, ty_Double) → new_esEs17(vyy350, vyy360)
new_primEqInt(Pos(Succ(vyy3500)), Neg(vyy360)) → False
new_primEqInt(Neg(Succ(vyy3500)), Pos(vyy360)) → False
new_esEs25(vyy351, vyy361, ty_Bool) → new_esEs19(vyy351, vyy361)
new_esEs24(vyy350, vyy360, app(ty_Ratio, cde)) → new_esEs13(vyy350, vyy360, cde)
new_compare(:(vyy6000, vyy6001), :(vyy500, vyy501), bbc) → new_primCompAux0(vyy6000, vyy500, new_compare(vyy6001, vyy501, bbc), bbc)
new_foldFM2(EmptyFM, bec, bed) → []
new_esEs24(vyy350, vyy360, ty_Int) → new_esEs14(vyy350, vyy360)
new_ltEs20(vyy600, vyy50, ty_Double) → new_ltEs10(vyy600, vyy50)
new_esEs21(vyy350, vyy360, ty_Ordering) → new_esEs12(vyy350, vyy360)
new_lt8(vyy6001, vyy501, ty_Float) → new_lt5(vyy6001, vyy501)
new_primEqInt(Neg(Zero), Pos(Succ(vyy3600))) → False
new_primEqInt(Pos(Zero), Neg(Succ(vyy3600))) → False
new_esEs24(vyy350, vyy360, ty_Ordering) → new_esEs12(vyy350, vyy360)
new_primCmpInt(Pos(Zero), Pos(Succ(vyy5000))) → new_primCmpNat0(Zero, Succ(vyy5000))
new_primCompAux00(vyy66, EQ) → vyy66
new_esEs23(vyy351, vyy361, ty_Double) → new_esEs17(vyy351, vyy361)
new_ltEs16(EQ, EQ) → True
new_esEs23(vyy351, vyy361, ty_Bool) → new_esEs19(vyy351, vyy361)
new_compare17(vyy6000, vyy500, app(app(ty_Either, bbd), bbe)) → new_compare18(vyy6000, vyy500, bbd, bbe)
new_esEs22(vyy352, vyy362, ty_Bool) → new_esEs19(vyy352, vyy362)
new_esEs6(Just(vyy350), Just(vyy360), app(app(ty_@2, bhc), bhd)) → new_esEs8(vyy350, vyy360, bhc, bhd)
new_esEs22(vyy352, vyy362, ty_@0) → new_esEs16(vyy352, vyy362)
new_esEs5(Left(vyy350), Left(vyy360), ty_Double, bh) → new_esEs17(vyy350, vyy360)
new_esEs7(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), bhe, bhf, bhg) → new_asAs(new_esEs24(vyy350, vyy360, bhe), new_asAs(new_esEs23(vyy351, vyy361, bhf), new_esEs22(vyy352, vyy362, bhg)))
new_esEs29(vyy35, vyy36, app(app(ty_FiniteMap, bec), bed)) → new_esEs15(vyy35, vyy36, bec, bed)
new_ltEs19(vyy6001, vyy501, app(app(ty_@2, cff), cfg)) → new_ltEs13(vyy6001, vyy501, cff, cfg)
new_esEs23(vyy351, vyy361, ty_Float) → new_esEs11(vyy351, vyy361)
new_ltEs8(True, False) → False
new_esEs5(Left(vyy350), Left(vyy360), app(app(ty_@2, dd), de), bh) → new_esEs8(vyy350, vyy360, dd, de)
new_ltEs4(Right(vyy6000), Left(vyy500), dea, dch) → False
new_compare16(Integer(vyy6000), Integer(vyy500)) → new_primCmpInt(vyy6000, vyy500)
new_primCmpInt(Pos(Succ(vyy60000)), Pos(vyy500)) → new_primCmpNat0(Succ(vyy60000), vyy500)
new_esEs22(vyy352, vyy362, ty_Float) → new_esEs11(vyy352, vyy362)
new_esEs12(GT, EQ) → False
new_esEs12(EQ, GT) → False
new_compare12(vyy6000, vyy500, False, fc, fd, ff) → GT
new_lt8(vyy6001, vyy501, ty_Integer) → new_lt18(vyy6001, vyy501)
new_esEs6(Just(vyy350), Just(vyy360), app(ty_[], bhb)) → new_esEs18(vyy350, vyy360, bhb)
new_esEs29(vyy35, vyy36, app(app(ty_@2, chb), chc)) → new_esEs8(vyy35, vyy36, chb, chc)
new_ltEs4(Right(vyy6000), Right(vyy500), dea, ty_Ordering) → new_ltEs16(vyy6000, vyy500)
new_lt20(vyy6000, vyy500, app(app(app(ty_@3, cge), cgf), cgg)) → new_lt15(vyy6000, vyy500, cge, cgf, cgg)
new_ltEs19(vyy6001, vyy501, ty_Int) → new_ltEs18(vyy6001, vyy501)
new_lt9(vyy6000, vyy500, ty_Integer) → new_lt18(vyy6000, vyy500)
new_not0 → True
new_esEs5(Right(vyy350), Right(vyy360), df, ty_Int) → new_esEs14(vyy350, vyy360)
new_esEs5(Right(vyy350), Right(vyy360), df, ty_Double) → new_esEs17(vyy350, vyy360)
new_compare17(vyy6000, vyy500, app(ty_Maybe, bbf)) → new_compare19(vyy6000, vyy500, bbf)
new_ltEs6(vyy6002, vyy502, app(ty_[], gh)) → new_ltEs11(vyy6002, vyy502, gh)
new_lt20(vyy6000, vyy500, ty_Double) → new_lt6(vyy6000, vyy500)
new_esEs26(vyy350, vyy360, app(app(ty_Either, dah), dba)) → new_esEs5(vyy350, vyy360, dah, dba)
new_primCompAux0(vyy6000, vyy500, vyy62, bbc) → new_primCompAux00(vyy62, new_compare17(vyy6000, vyy500, bbc))
new_esEs5(Left(vyy350), Left(vyy360), ty_Bool, bh) → new_esEs19(vyy350, vyy360)
new_esEs5(Right(vyy350), Right(vyy360), df, app(app(ty_FiniteMap, ef), eg)) → new_esEs15(vyy350, vyy360, ef, eg)
new_ltEs4(Right(vyy6000), Right(vyy500), dea, app(ty_Ratio, dee)) → new_ltEs9(vyy6000, vyy500, dee)
new_esEs22(vyy352, vyy362, app(app(app(ty_@3, cab), cac), cad)) → new_esEs7(vyy352, vyy362, cab, cac, cad)
new_primCmpInt(Pos(Succ(vyy60000)), Neg(vyy500)) → GT
new_lt6(vyy6000, vyy500) → new_esEs10(new_compare8(vyy6000, vyy500))
new_ltEs7(Just(vyy6000), Just(vyy500), app(ty_Maybe, beh)) → new_ltEs7(vyy6000, vyy500, beh)
new_ltEs4(Right(vyy6000), Right(vyy500), dea, ty_Bool) → new_ltEs8(vyy6000, vyy500)
new_esEs29(vyy35, vyy36, ty_@0) → new_esEs16(vyy35, vyy36)
new_esEs29(vyy35, vyy36, ty_Integer) → new_esEs9(vyy35, vyy36)
new_primMulInt(Pos(vyy5000), Pos(vyy60010)) → Pos(new_primMulNat0(vyy5000, vyy60010))
new_compare13(vyy6000, vyy500) → new_compare211(vyy6000, vyy500, new_esEs12(vyy6000, vyy500))
new_ltEs4(Left(vyy6000), Left(vyy500), app(app(ty_@2, ddg), ddh), dch) → new_ltEs13(vyy6000, vyy500, ddg, ddh)
new_ltEs4(Left(vyy6000), Left(vyy500), ty_@0, dch) → new_ltEs14(vyy6000, vyy500)
new_ltEs4(Left(vyy6000), Left(vyy500), ty_Integer, dch) → new_ltEs17(vyy6000, vyy500)
new_esEs24(vyy350, vyy360, app(app(ty_FiniteMap, cdg), cdh)) → new_esEs15(vyy350, vyy360, cdg, cdh)
new_ltEs6(vyy6002, vyy502, app(app(ty_Either, gd), ge)) → new_ltEs4(vyy6002, vyy502, gd, ge)
new_lt20(vyy6000, vyy500, app(app(ty_Either, cfh), cga)) → new_lt10(vyy6000, vyy500, cfh, cga)
new_esEs5(Right(vyy350), Left(vyy360), df, bh) → False
new_esEs5(Left(vyy350), Right(vyy360), df, bh) → False
new_primMulInt(Neg(vyy5000), Neg(vyy60010)) → Pos(new_primMulNat0(vyy5000, vyy60010))
new_compare110(vyy6000, vyy500, True) → LT
new_ltEs4(Right(vyy6000), Right(vyy500), dea, app(app(ty_@2, dfb), dfc)) → new_ltEs13(vyy6000, vyy500, dfb, dfc)
new_primEqNat0(Succ(vyy3500), Zero) → False
new_primEqNat0(Zero, Succ(vyy3600)) → False
new_ltEs20(vyy600, vyy50, ty_Int) → new_ltEs18(vyy600, vyy50)
new_ltEs8(False, False) → True
new_primPlusNat0(Zero, Zero) → Zero
new_ltEs20(vyy600, vyy50, ty_Char) → new_ltEs15(vyy600, vyy50)
new_esEs25(vyy351, vyy361, app(ty_Maybe, dab)) → new_esEs6(vyy351, vyy361, dab)
new_compare110(vyy6000, vyy500, False) → GT
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs5(Left(vyy350), Left(vyy360), app(ty_[], dc), bh) → new_esEs18(vyy350, vyy360, dc)
new_compare210(vyy6000, vyy500, True) → EQ
new_sizeFM(Branch(vyy360, vyy361, vyy362, vyy363, vyy364), bec, bed) → vyy362
new_ltEs4(Right(vyy6000), Right(vyy500), dea, ty_Double) → new_ltEs10(vyy6000, vyy500)
new_ltEs20(vyy600, vyy50, ty_Ordering) → new_ltEs16(vyy600, vyy50)
new_ltEs7(Nothing, Nothing, bee) → True
new_pePe(True, vyy35, vyy36, vyy52, dfd) → True
new_primPlusNat1(Succ(vyy810), vyy600100) → Succ(Succ(new_primPlusNat0(vyy810, vyy600100)))
new_foldFM2(Branch(vyy360, vyy361, vyy362, vyy363, vyy364), bec, bed) → new_foldFM0(vyy360, vyy361, new_foldFM2(vyy364, bec, bed), vyy363, bec, bed)
new_esEs5(Left(vyy350), Left(vyy360), app(app(ty_FiniteMap, da), db), bh) → new_esEs15(vyy350, vyy360, da, db)
new_ltEs7(Just(vyy6000), Just(vyy500), app(app(app(ty_@3, bfc), bfd), bfe)) → new_ltEs5(vyy6000, vyy500, bfc, bfd, bfe)
new_lt9(vyy6000, vyy500, app(app(app(ty_@3, fc), fd), ff)) → new_lt15(vyy6000, vyy500, fc, fd, ff)
new_ltEs7(Just(vyy6000), Just(vyy500), ty_Ordering) → new_ltEs16(vyy6000, vyy500)
new_primCmpInt(Neg(Zero), Neg(Succ(vyy5000))) → new_primCmpNat0(Succ(vyy5000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(vyy5000))) → GT
new_esEs29(vyy35, vyy36, ty_Bool) → new_esEs19(vyy35, vyy36)
new_esEs23(vyy351, vyy361, app(app(ty_@2, ccf), ccg)) → new_esEs8(vyy351, vyy361, ccf, ccg)
new_ltEs6(vyy6002, vyy502, app(app(ty_@2, hd), he)) → new_ltEs13(vyy6002, vyy502, hd, he)
new_esEs5(Right(vyy350), Right(vyy360), df, app(app(app(ty_@3, ea), eb), ec)) → new_esEs7(vyy350, vyy360, ea, eb, ec)
new_compare15(vyy6000, vyy500, False, fg, fh) → GT
new_ltEs7(Just(vyy6000), Just(vyy500), ty_Char) → new_ltEs15(vyy6000, vyy500)
new_esEs25(vyy351, vyy361, ty_Int) → new_esEs14(vyy351, vyy361)
new_esEs6(Just(vyy350), Just(vyy360), app(app(ty_Either, bga), bgb)) → new_esEs5(vyy350, vyy360, bga, bgb)
new_lt14(vyy6000, vyy500, bbb) → new_esEs10(new_compare(vyy6000, vyy500, bbb))
new_esEs10(LT) → True
new_esEs5(Right(vyy350), Right(vyy360), df, ty_Float) → new_esEs11(vyy350, vyy360)
new_ltEs6(vyy6002, vyy502, ty_@0) → new_ltEs14(vyy6002, vyy502)
new_esEs27(vyy351, vyy361, ty_Int) → new_esEs14(vyy351, vyy361)
new_esEs28(vyy350, vyy360, ty_Integer) → new_esEs9(vyy350, vyy360)
new_esEs26(vyy350, vyy360, ty_Char) → new_esEs20(vyy350, vyy360)
new_esEs24(vyy350, vyy360, app(app(app(ty_@3, cdb), cdc), cdd)) → new_esEs7(vyy350, vyy360, cdb, cdc, cdd)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_compare29(vyy6000, vyy500, True, bah) → EQ
new_lt8(vyy6001, vyy501, ty_Double) → new_lt6(vyy6001, vyy501)
new_compare17(vyy6000, vyy500, ty_Ordering) → new_compare13(vyy6000, vyy500)
new_esEs26(vyy350, vyy360, ty_Int) → new_esEs14(vyy350, vyy360)
new_esEs13(:%(vyy350, vyy351), :%(vyy360, vyy361), dce) → new_asAs(new_esEs28(vyy350, vyy360, dce), new_esEs27(vyy351, vyy361, dce))
new_esEs6(Just(vyy350), Just(vyy360), ty_Integer) → new_esEs9(vyy350, vyy360)
new_asAs(False, vyy61) → False
new_compare18(vyy6000, vyy500, bf, bg) → new_compare24(vyy6000, vyy500, new_esEs5(vyy6000, vyy500, bf, bg), bf, bg)
new_primMulInt(Pos(vyy5000), Neg(vyy60010)) → Neg(new_primMulNat0(vyy5000, vyy60010))
new_primMulInt(Neg(vyy5000), Pos(vyy60010)) → Neg(new_primMulNat0(vyy5000, vyy60010))
new_lt12(vyy6000, vyy500) → new_esEs10(new_compare27(vyy6000, vyy500))
new_ltEs20(vyy600, vyy50, app(ty_[], bbc)) → new_ltEs11(vyy600, vyy50, bbc)
new_primMulNat0(Zero, Succ(vyy600100)) → Zero
new_primMulNat0(Succ(vyy50000), Zero) → Zero
new_compare8(Double(vyy6000, vyy6001), Double(vyy500, vyy501)) → new_compare11(new_sr(vyy6000, vyy500), new_sr(vyy6001, vyy501))
new_esEs18([], [], bcf) → True
new_esEs21(vyy350, vyy360, app(app(ty_Either, bcg), bch)) → new_esEs5(vyy350, vyy360, bcg, bch)
new_esEs29(vyy35, vyy36, ty_Char) → new_esEs20(vyy35, vyy36)
new_esEs6(Just(vyy350), Just(vyy360), app(ty_Maybe, bgg)) → new_esEs6(vyy350, vyy360, bgg)
new_esEs21(vyy350, vyy360, app(app(ty_FiniteMap, bdf), bdg)) → new_esEs15(vyy350, vyy360, bdf, bdg)
new_esEs25(vyy351, vyy361, ty_@0) → new_esEs16(vyy351, vyy361)
new_lt20(vyy6000, vyy500, app(ty_[], cgd)) → new_lt14(vyy6000, vyy500, cgd)
new_esEs29(vyy35, vyy36, ty_Float) → new_esEs11(vyy35, vyy36)
new_ltEs4(Right(vyy6000), Right(vyy500), dea, ty_@0) → new_ltEs14(vyy6000, vyy500)
new_esEs23(vyy351, vyy361, ty_Ordering) → new_esEs12(vyy351, vyy361)
new_esEs29(vyy35, vyy36, ty_Double) → new_esEs17(vyy35, vyy36)
new_ltEs11(vyy600, vyy50, bbc) → new_not(new_compare(vyy600, vyy50, bbc))
new_esEs24(vyy350, vyy360, ty_Float) → new_esEs11(vyy350, vyy360)
new_not(EQ) → new_not0
new_esEs23(vyy351, vyy361, app(ty_Maybe, ccb)) → new_esEs6(vyy351, vyy361, ccb)
new_lt20(vyy6000, vyy500, app(app(ty_@2, cgh), cha)) → new_lt16(vyy6000, vyy500, cgh, cha)
new_esEs21(vyy350, vyy360, ty_Integer) → new_esEs9(vyy350, vyy360)
new_esEs24(vyy350, vyy360, ty_Char) → new_esEs20(vyy350, vyy360)
new_esEs26(vyy350, vyy360, ty_Integer) → new_esEs9(vyy350, vyy360)
new_ltEs7(Just(vyy6000), Just(vyy500), app(ty_[], bfb)) → new_ltEs11(vyy6000, vyy500, bfb)
new_esEs16(@0, @0) → True
new_lt9(vyy6000, vyy500, app(ty_Maybe, bah)) → new_lt11(vyy6000, vyy500, bah)
new_ltEs19(vyy6001, vyy501, ty_@0) → new_ltEs14(vyy6001, vyy501)
new_compare111(vyy6000, vyy500, False, bah) → GT
new_ltEs6(vyy6002, vyy502, ty_Bool) → new_ltEs8(vyy6002, vyy502)
new_esEs5(Left(vyy350), Left(vyy360), ty_Char, bh) → new_esEs20(vyy350, vyy360)
new_esEs24(vyy350, vyy360, ty_Double) → new_esEs17(vyy350, vyy360)
new_esEs5(Right(vyy350), Right(vyy360), df, app(ty_Maybe, ee)) → new_esEs6(vyy350, vyy360, ee)
new_ltEs7(Just(vyy6000), Just(vyy500), ty_Bool) → new_ltEs8(vyy6000, vyy500)
new_ltEs7(Just(vyy6000), Just(vyy500), ty_@0) → new_ltEs14(vyy6000, vyy500)
new_compare11(vyy600, vyy50) → new_primCmpInt(vyy600, vyy50)
new_esEs14(vyy35, vyy36) → new_primEqInt(vyy35, vyy36)
new_ltEs19(vyy6001, vyy501, app(app(app(ty_@3, cfc), cfd), cfe)) → new_ltEs5(vyy6001, vyy501, cfc, cfd, cfe)
new_esEs25(vyy351, vyy361, app(app(app(ty_@3, chf), chg), chh)) → new_esEs7(vyy351, vyy361, chf, chg, chh)
new_esEs8(@2(vyy350, vyy351), @2(vyy360, vyy361), chb, chc) → new_asAs(new_esEs26(vyy350, vyy360, chb), new_esEs25(vyy351, vyy361, chc))
new_ltEs6(vyy6002, vyy502, ty_Char) → new_ltEs15(vyy6002, vyy502)
new_compare17(vyy6000, vyy500, app(app(app(ty_@3, bca), bcb), bcc)) → new_compare7(vyy6000, vyy500, bca, bcb, bcc)
new_esEs21(vyy350, vyy360, ty_Char) → new_esEs20(vyy350, vyy360)
new_ltEs7(Just(vyy6000), Nothing, bee) → False
new_lt20(vyy6000, vyy500, ty_Int) → new_lt19(vyy6000, vyy500)
new_lt13(vyy6000, vyy500, bba) → new_esEs10(new_compare28(vyy6000, vyy500, bba))
new_not(LT) → new_not0
new_lt18(vyy6000, vyy500) → new_esEs10(new_compare16(vyy6000, vyy500))
new_ltEs19(vyy6001, vyy501, app(ty_Maybe, ceh)) → new_ltEs7(vyy6001, vyy501, ceh)
new_esEs5(Left(vyy350), Left(vyy360), app(app(ty_Either, ca), cb), bh) → new_esEs5(vyy350, vyy360, ca, cb)
new_ltEs7(Just(vyy6000), Just(vyy500), app(app(ty_@2, bff), bfg)) → new_ltEs13(vyy6000, vyy500, bff, bfg)
new_lt20(vyy6000, vyy500, ty_Bool) → new_lt12(vyy6000, vyy500)
new_ltEs4(Left(vyy6000), Left(vyy500), ty_Ordering, dch) → new_ltEs16(vyy6000, vyy500)
new_compare112(vyy6000, vyy500, False) → GT
new_ltEs4(Left(vyy6000), Left(vyy500), app(ty_Maybe, dda), dch) → new_ltEs7(vyy6000, vyy500, dda)
new_ltEs12(vyy600, vyy50) → new_not(new_compare6(vyy600, vyy50))
new_compare210(vyy6000, vyy500, False) → new_compare112(vyy6000, vyy500, new_ltEs8(vyy6000, vyy500))
new_esEs12(GT, GT) → True
new_compare25(vyy6000, vyy500, False, fc, fd, ff) → new_compare12(vyy6000, vyy500, new_ltEs5(vyy6000, vyy500, fc, fd, ff), fc, fd, ff)
new_esEs23(vyy351, vyy361, ty_Char) → new_esEs20(vyy351, vyy361)
new_esEs21(vyy350, vyy360, ty_Float) → new_esEs11(vyy350, vyy360)
new_esEs22(vyy352, vyy362, ty_Int) → new_esEs14(vyy352, vyy362)
new_compare19(vyy6000, vyy500, bah) → new_compare29(vyy6000, vyy500, new_esEs6(vyy6000, vyy500, bah), bah)
new_primPlusNat0(Succ(vyy8100), Succ(vyy6001000)) → Succ(Succ(new_primPlusNat0(vyy8100, vyy6001000)))
new_esEs29(vyy35, vyy36, ty_Ordering) → new_esEs12(vyy35, vyy36)
new_esEs29(vyy35, vyy36, app(ty_[], bcf)) → new_esEs18(vyy35, vyy36, bcf)
new_esEs5(Right(vyy350), Right(vyy360), df, ty_Ordering) → new_esEs12(vyy350, vyy360)
new_ltEs4(Left(vyy6000), Left(vyy500), ty_Double, dch) → new_ltEs10(vyy6000, vyy500)
new_esEs18(:(vyy350, vyy351), :(vyy360, vyy361), bcf) → new_asAs(new_esEs21(vyy350, vyy360, bcf), new_esEs18(vyy351, vyy361, bcf))
new_asAs(True, vyy61) → vyy61
new_compare28(:%(vyy6000, vyy6001), :%(vyy500, vyy501), ty_Int) → new_compare11(new_sr(vyy6000, vyy501), new_sr(vyy500, vyy6001))
new_esEs22(vyy352, vyy362, app(app(ty_@2, cbb), cbc)) → new_esEs8(vyy352, vyy362, cbb, cbc)
new_esEs17(Double(vyy350, vyy351), Double(vyy360, vyy361)) → new_esEs14(new_sr(vyy350, vyy360), new_sr(vyy351, vyy361))
new_ltEs19(vyy6001, vyy501, ty_Float) → new_ltEs12(vyy6001, vyy501)
new_esEs25(vyy351, vyy361, ty_Float) → new_esEs11(vyy351, vyy361)
new_esEs5(Left(vyy350), Left(vyy360), ty_Ordering, bh) → new_esEs12(vyy350, vyy360)
new_ltEs16(LT, LT) → True
new_compare211(vyy6000, vyy500, True) → EQ
new_fmToList(vyy36, bec, bed) → new_foldFM2(vyy36, bec, bed)
new_lt17(vyy6000, vyy500) → new_esEs10(new_compare14(vyy6000, vyy500))
new_compare6(Float(vyy6000, vyy6001), Float(vyy500, vyy501)) → new_compare11(new_sr(vyy6000, vyy500), new_sr(vyy6001, vyy501))
new_esEs24(vyy350, vyy360, app(app(ty_@2, ceb), cec)) → new_esEs8(vyy350, vyy360, ceb, cec)
new_ltEs20(vyy600, vyy50, app(app(ty_@2, ced), cee)) → new_ltEs13(vyy600, vyy50, ced, cee)
new_ltEs4(Left(vyy6000), Left(vyy500), ty_Bool, dch) → new_ltEs8(vyy6000, vyy500)
new_esEs24(vyy350, vyy360, app(ty_Maybe, cdf)) → new_esEs6(vyy350, vyy360, cdf)
new_ltEs20(vyy600, vyy50, app(ty_Maybe, bee)) → new_ltEs7(vyy600, vyy50, bee)
new_esEs5(Right(vyy350), Right(vyy360), df, ty_Char) → new_esEs20(vyy350, vyy360)
new_ltEs4(Right(vyy6000), Right(vyy500), dea, ty_Int) → new_ltEs18(vyy6000, vyy500)
new_lt20(vyy6000, vyy500, app(ty_Ratio, cgc)) → new_lt13(vyy6000, vyy500, cgc)
new_esEs23(vyy351, vyy361, app(ty_[], cce)) → new_esEs18(vyy351, vyy361, cce)
new_esEs5(Left(vyy350), Left(vyy360), ty_Integer, bh) → new_esEs9(vyy350, vyy360)
new_esEs22(vyy352, vyy362, app(app(ty_Either, bhh), caa)) → new_esEs5(vyy352, vyy362, bhh, caa)
new_primCompAux00(vyy66, GT) → GT
new_compare17(vyy6000, vyy500, ty_@0) → new_compare5(vyy6000, vyy500)
new_ltEs7(Just(vyy6000), Just(vyy500), app(ty_Ratio, bfa)) → new_ltEs9(vyy6000, vyy500, bfa)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_lt8(vyy6001, vyy501, ty_Bool) → new_lt12(vyy6001, vyy501)
new_ltEs4(Left(vyy6000), Left(vyy500), app(app(app(ty_@3, ddd), dde), ddf), dch) → new_ltEs5(vyy6000, vyy500, ddd, dde, ddf)
new_esEs5(Right(vyy350), Right(vyy360), df, app(ty_Ratio, ed)) → new_esEs13(vyy350, vyy360, ed)
new_ltEs7(Just(vyy6000), Just(vyy500), app(app(ty_Either, bef), beg)) → new_ltEs4(vyy6000, vyy500, bef, beg)
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primCmpInt(Neg(Succ(vyy60000)), Pos(vyy500)) → LT
new_esEs25(vyy351, vyy361, ty_Integer) → new_esEs9(vyy351, vyy361)
new_ltEs10(vyy600, vyy50) → new_not(new_compare8(vyy600, vyy50))
new_ltEs4(Right(vyy6000), Right(vyy500), dea, app(app(app(ty_@3, deg), deh), dfa)) → new_ltEs5(vyy6000, vyy500, deg, deh, dfa)
The set Q consists of the following terms:
new_lt8(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, ty_Integer)
new_esEs5(Left(x0), Left(x1), ty_Integer, x2)
new_esEs25(x0, x1, ty_Int)
new_esEs26(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs5(Left(x0), Left(x1), ty_Int, x2)
new_ltEs4(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_ltEs20(x0, x1, ty_Integer)
new_ltEs4(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_ltEs6(x0, x1, ty_Float)
new_lt8(x0, x1, ty_Int)
new_esEs25(x0, x1, app(ty_[], x2))
new_lt16(x0, x1, x2, x3)
new_lt9(x0, x1, ty_@0)
new_compare24(x0, x1, False, x2, x3)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs6(Nothing, Just(x0), x1)
new_compare111(x0, x1, False, x2)
new_compare12(x0, x1, True, x2, x3, x4)
new_esEs22(x0, x1, ty_@0)
new_lt9(x0, x1, app(app(ty_@2, x2), x3))
new_pePe(False, x0, x1, x2, x3)
new_ltEs4(Left(x0), Left(x1), ty_Double, x2)
new_ltEs4(Left(x0), Left(x1), ty_Char, x2)
new_ltEs6(x0, x1, app(ty_[], x2))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs5(Left(x0), Left(x1), ty_Bool, x2)
new_ltEs19(x0, x1, ty_Integer)
new_esEs5(Right(x0), Right(x1), x2, ty_@0)
new_esEs22(x0, x1, ty_Char)
new_esEs5(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs7(Nothing, Just(x0), x1)
new_esEs23(x0, x1, ty_Integer)
new_compare110(x0, x1, True)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs21(x0, x1, ty_Double)
new_esEs5(Right(x0), Right(x1), x2, ty_Int)
new_esEs23(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_ltEs19(x0, x1, app(ty_[], x2))
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_primMulNat0(Succ(x0), Zero)
new_esEs26(x0, x1, app(ty_[], x2))
new_esEs26(x0, x1, ty_Char)
new_ltEs7(Just(x0), Just(x1), app(ty_[], x2))
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare110(x0, x1, False)
new_esEs12(EQ, GT)
new_esEs12(GT, EQ)
new_lt10(x0, x1, x2, x3)
new_ltEs6(x0, x1, ty_Char)
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_lt8(x0, x1, app(ty_Maybe, x2))
new_ltEs4(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs10(GT)
new_lt9(x0, x1, app(ty_Ratio, x2))
new_esEs5(Left(x0), Right(x1), x2, x3)
new_esEs5(Right(x0), Left(x1), x2, x3)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_lt20(x0, x1, ty_Int)
new_esEs23(x0, x1, ty_Int)
new_esEs28(x0, x1, ty_Integer)
new_ltEs8(True, True)
new_esEs6(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs5(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs4(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs6(Nothing, Nothing, x0)
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs6(x0, x1, app(ty_Maybe, x2))
new_esEs12(GT, GT)
new_esEs23(x0, x1, ty_Ordering)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_lt8(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs23(x0, x1, ty_Char)
new_ltEs7(Just(x0), Just(x1), ty_@0)
new_esEs16(@0, @0)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs9(x0, x1, x2)
new_esEs5(Right(x0), Right(x1), x2, ty_Double)
new_esEs22(x0, x1, ty_Int)
new_ltEs20(x0, x1, ty_@0)
new_ltEs4(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_compare24(x0, x1, True, x2, x3)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, ty_Ordering)
new_esEs23(x0, x1, ty_Bool)
new_esEs6(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs19(x0, x1, ty_Float)
new_lt14(x0, x1, x2)
new_ltEs7(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs7(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs19(True, True)
new_compare25(x0, x1, True, x2, x3, x4)
new_compare112(x0, x1, True)
new_esEs29(x0, x1, ty_Integer)
new_esEs5(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_compare11(x0, x1)
new_lt8(x0, x1, app(ty_[], x2))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_ltEs4(Left(x0), Left(x1), ty_Bool, x2)
new_esEs5(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs5(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt8(x0, x1, ty_Char)
new_compare5(@0, @0)
new_esEs21(x0, x1, ty_Int)
new_esEs5(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_lt20(x0, x1, ty_Ordering)
new_esEs29(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_compare17(x0, x1, ty_Double)
new_primEqNat0(Zero, Zero)
new_compare9(x0, x1, x2, x3)
new_esEs18(:(x0, x1), :(x2, x3), x4)
new_primPlusNat0(Zero, Succ(x0))
new_ltEs4(Right(x0), Right(x1), x2, ty_Float)
new_lt20(x0, x1, ty_Double)
new_ltEs6(x0, x1, app(ty_Ratio, x2))
new_ltEs6(x0, x1, ty_Ordering)
new_esEs9(Integer(x0), Integer(x1))
new_ltEs4(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs6(Just(x0), Just(x1), ty_Float)
new_esEs29(x0, x1, app(ty_[], x2))
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_lt8(x0, x1, ty_Float)
new_esEs17(Double(x0, x1), Double(x2, x3))
new_esEs29(x0, x1, ty_Float)
new_primMulNat0(Zero, Zero)
new_esEs18([], :(x0, x1), x2)
new_esEs29(x0, x1, ty_Char)
new_esEs6(Just(x0), Just(x1), app(app(ty_FiniteMap, x2), x3))
new_esEs5(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs7(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_compare17(x0, x1, app(ty_[], x2))
new_compare6(Float(x0, x1), Float(x2, x3))
new_ltEs17(x0, x1)
new_esEs25(x0, x1, ty_Integer)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_lt9(x0, x1, app(ty_Maybe, x2))
new_ltEs4(Left(x0), Left(x1), app(ty_[], x2), x3)
new_ltEs7(Just(x0), Just(x1), ty_Bool)
new_esEs25(x0, x1, ty_Double)
new_ltEs6(x0, x1, ty_Double)
new_compare17(x0, x1, ty_Int)
new_compare10(x0, x1, True, x2, x3)
new_lt4(x0, x1)
new_esEs26(x0, x1, ty_Ordering)
new_compare112(x0, x1, False)
new_lt11(x0, x1, x2)
new_esEs23(x0, x1, ty_Float)
new_primMulNat0(Succ(x0), Succ(x1))
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
new_esEs24(x0, x1, ty_Float)
new_ltEs19(x0, x1, ty_Ordering)
new_compare29(x0, x1, True, x2)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs19(x0, x1, ty_Bool)
new_foldFM2(EmptyFM, x0, x1)
new_esEs21(x0, x1, ty_Bool)
new_ltEs6(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, app(ty_[], x2))
new_esEs27(x0, x1, ty_Int)
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, app(ty_[], x2))
new_primCmpNat0(Succ(x0), Succ(x1))
new_compare17(x0, x1, ty_Integer)
new_esEs25(x0, x1, ty_Ordering)
new_compare111(x0, x1, True, x2)
new_ltEs20(x0, x1, ty_Bool)
new_esEs24(x0, x1, ty_@0)
new_esEs24(x0, x1, ty_Double)
new_compare17(x0, x1, app(ty_Ratio, x2))
new_esEs5(Right(x0), Right(x1), x2, app(app(ty_FiniteMap, x3), x4))
new_ltEs13(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs5(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_ltEs4(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs6(Just(x0), Just(x1), ty_Integer)
new_compare210(x0, x1, True)
new_esEs24(x0, x1, ty_Bool)
new_lt20(x0, x1, ty_Char)
new_compare([], :(x0, x1), x2)
new_primEqNat0(Zero, Succ(x0))
new_esEs14(x0, x1)
new_ltEs4(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_lt20(x0, x1, ty_Integer)
new_lt9(x0, x1, ty_Float)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs6(Just(x0), Nothing, x1)
new_esEs19(True, False)
new_esEs19(False, True)
new_ltEs20(x0, x1, ty_Char)
new_esEs12(LT, EQ)
new_esEs12(EQ, LT)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs5(Right(x0), Right(x1), x2, ty_Char)
new_compare14(Char(x0), Char(x1))
new_esEs27(x0, x1, ty_Integer)
new_esEs25(x0, x1, ty_Char)
new_ltEs7(Just(x0), Just(x1), ty_Double)
new_esEs25(x0, x1, ty_Float)
new_sr(x0, x1)
new_compare17(x0, x1, ty_@0)
new_esEs5(Left(x0), Left(x1), app(app(ty_FiniteMap, x2), x3), x4)
new_ltEs18(x0, x1)
new_ltEs7(Just(x0), Just(x1), ty_Ordering)
new_not0
new_esEs29(x0, x1, ty_@0)
new_ltEs19(x0, x1, ty_Char)
new_esEs12(EQ, EQ)
new_ltEs4(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_primPlusNat0(Zero, Zero)
new_ltEs16(EQ, EQ)
new_compare15(x0, x1, False, x2, x3)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_compare210(x0, x1, False)
new_esEs24(x0, x1, ty_Ordering)
new_esEs22(x0, x1, ty_Bool)
new_esEs5(Right(x0), Right(x1), x2, ty_Bool)
new_primPlusNat0(Succ(x0), Succ(x1))
new_esEs6(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_esEs28(x0, x1, ty_Int)
new_esEs6(Just(x0), Just(x1), ty_Ordering)
new_ltEs16(LT, LT)
new_compare211(x0, x1, True)
new_primMulInt(Pos(x0), Pos(x1))
new_ltEs7(Just(x0), Just(x1), ty_Float)
new_lt9(x0, x1, ty_Double)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_lt12(x0, x1)
new_lt8(x0, x1, ty_Integer)
new_esEs5(Left(x0), Left(x1), app(ty_[], x2), x3)
new_lt8(x0, x1, ty_Ordering)
new_esEs25(x0, x1, ty_Bool)
new_ltEs20(x0, x1, app(ty_[], x2))
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_lt9(x0, x1, ty_Char)
new_lt8(x0, x1, app(ty_Ratio, x2))
new_ltEs4(Left(x0), Left(x1), ty_Ordering, x2)
new_lt20(x0, x1, app(ty_[], x2))
new_lt6(x0, x1)
new_ltEs4(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs16(GT, LT)
new_ltEs16(LT, GT)
new_ltEs7(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_ltEs6(x0, x1, app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_esEs21(x0, x1, ty_Float)
new_not(GT)
new_ltEs4(Right(x0), Right(x1), x2, ty_@0)
new_ltEs8(False, False)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare17(x0, x1, app(ty_Maybe, x2))
new_ltEs4(Left(x0), Left(x1), ty_Float, x2)
new_asAs(False, x0)
new_esEs26(x0, x1, ty_Float)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_primEqNat0(Succ(x0), Zero)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_lt20(x0, x1, ty_Float)
new_asAs(True, x0)
new_primEqInt(Neg(Zero), Pos(Zero))
new_primEqInt(Pos(Zero), Neg(Zero))
new_ltEs10(x0, x1)
new_ltEs8(False, True)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs8(True, False)
new_lt15(x0, x1, x2, x3, x4)
new_compare17(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs5(Right(x0), Right(x1), x2, ty_Integer)
new_esEs25(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs5(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_pePe(True, x0, x1, x2, x3)
new_ltEs14(x0, x1)
new_primCmpNat0(Succ(x0), Zero)
new_esEs26(x0, x1, ty_Double)
new_compare26(x0, x1, False, x2, x3)
new_compare12(x0, x1, False, x2, x3, x4)
new_ltEs4(Left(x0), Right(x1), x2, x3)
new_ltEs4(Right(x0), Left(x1), x2, x3)
new_esEs19(False, False)
new_compare15(x0, x1, True, x2, x3)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_lt19(x0, x1)
new_esEs6(Just(x0), Just(x1), ty_Int)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_lt20(x0, x1, app(ty_Ratio, x2))
new_ltEs6(x0, x1, ty_@0)
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs24(x0, x1, ty_Integer)
new_primEqInt(Neg(Zero), Neg(Zero))
new_ltEs20(x0, x1, ty_Float)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_compare17(x0, x1, ty_Float)
new_lt8(x0, x1, ty_Double)
new_primCompAux0(x0, x1, x2, x3)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_compare26(x0, x1, True, x2, x3)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_ltEs4(Left(x0), Left(x1), ty_@0, x2)
new_fmToList(x0, x1, x2)
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs7(Just(x0), Just(x1), ty_Char)
new_esEs26(x0, x1, ty_Integer)
new_esEs24(x0, x1, ty_Int)
new_compare17(x0, x1, ty_Ordering)
new_compare28(:%(x0, x1), :%(x2, x3), ty_Integer)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_ltEs16(GT, GT)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_esEs5(Left(x0), Left(x1), ty_Char, x2)
new_esEs18(:(x0, x1), [], x2)
new_ltEs7(Just(x0), Nothing, x1)
new_esEs5(Left(x0), Left(x1), ty_@0, x2)
new_compare29(x0, x1, False, x2)
new_compare28(:%(x0, x1), :%(x2, x3), ty_Int)
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs29(x0, x1, ty_Ordering)
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_esEs24(x0, x1, app(ty_[], x2))
new_ltEs6(x0, x1, ty_Bool)
new_esEs29(x0, x1, ty_Int)
new_compare13(x0, x1)
new_ltEs4(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs6(Just(x0), Just(x1), ty_@0)
new_esEs26(x0, x1, ty_@0)
new_esEs10(EQ)
new_ltEs12(x0, x1)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_compare17(x0, x1, ty_Char)
new_lt9(x0, x1, ty_Ordering)
new_primCmpNat0(Zero, Zero)
new_esEs5(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_ltEs7(Just(x0), Just(x1), ty_Integer)
new_esEs21(x0, x1, ty_Char)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_esEs29(x0, x1, ty_Bool)
new_esEs6(Just(x0), Just(x1), ty_Double)
new_primPlusNat0(Succ(x0), Zero)
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, ty_Bool)
new_primCompAux00(x0, EQ)
new_ltEs4(Right(x0), Right(x1), x2, ty_Int)
new_esEs8(@2(x0, x1), @2(x2, x3), x4, x5)
new_lt9(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_sr0(Integer(x0), Integer(x1))
new_esEs24(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_compare27(x0, x1)
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, ty_Ordering)
new_primMulNat0(Zero, Succ(x0))
new_compare25(x0, x1, False, x2, x3, x4)
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs6(x0, x1, ty_Int)
new_compare18(x0, x1, x2, x3)
new_compare([], [], x0)
new_primCmpNat0(Zero, Succ(x0))
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_primCompAux00(x0, GT)
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_lt9(x0, x1, app(app(ty_Either, x2), x3))
new_compare17(x0, x1, app(app(ty_@2, x2), x3))
new_esEs24(x0, x1, ty_Char)
new_esEs5(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs10(LT)
new_esEs6(Just(x0), Just(x1), ty_Bool)
new_ltEs11(x0, x1, x2)
new_lt8(x0, x1, app(app(ty_@2, x2), x3))
new_esEs21(x0, x1, ty_Integer)
new_lt17(x0, x1)
new_ltEs6(x0, x1, ty_Integer)
new_ltEs7(Nothing, Nothing, x0)
new_esEs25(x0, x1, ty_@0)
new_lt20(x0, x1, ty_Bool)
new_ltEs7(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs21(x0, x1, app(ty_[], x2))
new_primCompAux00(x0, LT)
new_not(EQ)
new_esEs11(Float(x0, x1), Float(x2, x3))
new_ltEs4(Right(x0), Right(x1), x2, ty_Double)
new_ltEs16(GT, EQ)
new_ltEs16(EQ, GT)
new_ltEs20(x0, x1, ty_Double)
new_compare(:(x0, x1), :(x2, x3), x4)
new_esEs5(Right(x0), Right(x1), x2, ty_Float)
new_primPlusNat1(Zero, x0)
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt9(x0, x1, ty_Bool)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_esEs22(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_ltEs6(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs5(Right(x0), Right(x1), x2, ty_Ordering)
new_ltEs16(LT, EQ)
new_ltEs16(EQ, LT)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_esEs5(Left(x0), Left(x1), ty_Float, x2)
new_ltEs4(Left(x0), Left(x1), ty_Integer, x2)
new_compare(:(x0, x1), [], x2)
new_esEs5(Left(x0), Left(x1), ty_Double, x2)
new_esEs26(x0, x1, ty_Int)
new_ltEs4(Right(x0), Right(x1), x2, ty_Integer)
new_lt5(x0, x1)
new_sizeFM(EmptyFM, x0, x1)
new_compare17(x0, x1, ty_Bool)
new_esEs21(x0, x1, ty_Ordering)
new_compare10(x0, x1, False, x2, x3)
new_compare8(Double(x0, x1), Double(x2, x3))
new_ltEs4(Left(x0), Left(x1), ty_Int, x2)
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs20(Char(x0), Char(x1))
new_esEs21(x0, x1, ty_@0)
new_esEs6(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs7(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs23(x0, x1, ty_@0)
new_esEs5(Left(x0), Left(x1), ty_Ordering, x2)
new_ltEs4(Right(x0), Right(x1), x2, ty_Char)
new_ltEs5(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_ltEs19(x0, x1, ty_@0)
new_lt7(x0, x1)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_esEs6(Just(x0), Just(x1), ty_Char)
new_lt8(x0, x1, ty_@0)
new_lt9(x0, x1, ty_Integer)
new_esEs18([], [], x0)
new_compare7(x0, x1, x2, x3, x4)
new_lt9(x0, x1, ty_Int)
new_ltEs19(x0, x1, ty_Double)
new_lt8(x0, x1, ty_Bool)
new_lt9(x0, x1, app(ty_[], x2))
new_esEs15(x0, x1, x2, x3)
new_esEs13(:%(x0, x1), :%(x2, x3), x4)
new_compare16(Integer(x0), Integer(x1))
new_esEs6(Just(x0), Just(x1), app(ty_Maybe, x2))
new_ltEs19(x0, x1, ty_Int)
new_lt13(x0, x1, x2)
new_esEs23(x0, x1, ty_Double)
new_esEs22(x0, x1, ty_Double)
new_primEqInt(Pos(Zero), Pos(Zero))
new_ltEs4(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_lt18(x0, x1)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_compare17(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs4(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs20(x0, x1, ty_Int)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, ty_@0)
new_compare19(x0, x1, x2)
new_esEs29(x0, x1, ty_Double)
new_primPlusNat1(Succ(x0), x1)
new_ltEs7(Just(x0), Just(x1), ty_Int)
new_esEs12(LT, LT)
new_not(LT)
new_esEs22(x0, x1, ty_Float)
new_ltEs15(x0, x1)
new_compare211(x0, x1, False)
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(vyy3, Just(vyy50), Branch(Just(vyy600), vyy61, vyy62, vyy63, vyy64), h, ba, bb) → new_foldFM_LE1(vyy3, vyy50, vyy600, vyy61, vyy62, vyy63, vyy64, new_ltEs20(vyy600, vyy50, ba), h, ba, bb)
The graph contains the following edges 1 >= 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5, 3 > 6, 3 > 7, 4 >= 9, 5 >= 10, 6 >= 11
- new_foldFM_LE1(vyy17, vyy19, vyy20, vyy21, vyy22, vyy23, vyy24, False, bc, bd, be) → new_foldFM_LE(vyy17, Just(vyy19), vyy23, bc, bd, be)
The graph contains the following edges 1 >= 1, 6 >= 3, 9 >= 4, 10 >= 5, 11 >= 6
- new_foldFM_LE1(vyy17, vyy19, vyy20, vyy21, vyy22, vyy23, vyy24, True, bc, bd, be) → new_foldFM_LE(vyy17, Just(vyy19), vyy23, bc, bd, be)
The graph contains the following edges 1 >= 1, 6 >= 3, 9 >= 4, 10 >= 5, 11 >= 6
- new_foldFM_LE1(vyy17, vyy19, vyy20, vyy21, vyy22, vyy23, vyy24, True, bc, bd, be) → new_foldFM_LE(vyy17, Just(vyy19), vyy24, bc, bd, be)
The graph contains the following edges 1 >= 1, 7 >= 3, 9 >= 4, 10 >= 5, 11 >= 6
- new_foldFM_LE(vyy3, Just(vyy50), Branch(Nothing, vyy61, vyy62, vyy63, vyy64), h, ba, bb) → new_foldFM_LE(vyy3, Just(vyy50), vyy64, h, ba, bb)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 >= 4, 5 >= 5, 6 >= 6
- new_foldFM_LE(vyy3, Just(vyy50), Branch(Nothing, vyy61, vyy62, vyy63, vyy64), h, ba, bb) → new_foldFM_LE(vyy3, Just(vyy50), vyy63, h, ba, bb)
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
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ UsableRulesProof
Q DP problem:
The TRS P consists of the following rules:
new_foldFM_LE(vyy3, Nothing, Branch(Just(vyy600), vyy61, vyy62, vyy63, vyy64), h, ba, bb) → new_foldFM_LE(vyy3, Nothing, vyy63, h, ba, bb)
new_foldFM_LE(vyy3, Nothing, Branch(Nothing, vyy61, vyy62, vyy63, vyy64), h, ba, bb) → new_foldFM_LE(vyy3, Nothing, vyy64, h, ba, bb)
new_foldFM_LE(vyy3, Nothing, Branch(Nothing, vyy61, vyy62, vyy63, vyy64), h, ba, bb) → new_foldFM_LE(vyy3, Nothing, vyy63, h, ba, bb)
The TRS R consists of the following rules:
new_esEs22(vyy352, vyy362, ty_Double) → new_esEs17(vyy352, vyy362)
new_esEs11(Float(vyy350, vyy351), Float(vyy360, vyy361)) → new_esEs14(new_sr(vyy350, vyy360), new_sr(vyy351, vyy361))
new_ltEs4(Right(vyy6000), Right(vyy500), dea, ty_Integer) → new_ltEs17(vyy6000, vyy500)
new_esEs24(vyy350, vyy360, app(app(ty_Either, cch), cda)) → new_esEs5(vyy350, vyy360, cch, cda)
new_compare5(@0, @0) → EQ
new_ltEs19(vyy6001, vyy501, ty_Ordering) → new_ltEs16(vyy6001, vyy501)
new_ltEs16(GT, GT) → True
new_ltEs8(False, True) → True
new_ltEs4(Right(vyy6000), Right(vyy500), dea, app(ty_[], def)) → new_ltEs11(vyy6000, vyy500, def)
new_ltEs4(Right(vyy6000), Right(vyy500), dea, ty_Char) → new_ltEs15(vyy6000, vyy500)
new_ltEs20(vyy600, vyy50, app(ty_Ratio, dcd)) → new_ltEs9(vyy600, vyy50, dcd)
new_compare15(vyy6000, vyy500, True, fg, fh) → LT
new_lt7(vyy6000, vyy500) → new_esEs10(new_compare13(vyy6000, vyy500))
new_ltEs19(vyy6001, vyy501, ty_Char) → new_ltEs15(vyy6001, vyy501)
new_ltEs4(Left(vyy6000), Left(vyy500), app(ty_[], ddc), dch) → new_ltEs11(vyy6000, vyy500, ddc)
new_esEs10(GT) → False
new_esEs23(vyy351, vyy361, app(app(ty_Either, cbd), cbe)) → new_esEs5(vyy351, vyy361, cbd, cbe)
new_lt16(vyy6000, vyy500, fg, fh) → new_esEs10(new_compare9(vyy6000, vyy500, fg, fh))
new_lt8(vyy6001, vyy501, app(ty_Ratio, baa)) → new_lt13(vyy6001, vyy501, baa)
new_compare([], :(vyy500, vyy501), bbc) → LT
new_compare10(vyy6000, vyy500, True, bf, bg) → LT
new_esEs6(Just(vyy350), Just(vyy360), ty_Char) → new_esEs20(vyy350, vyy360)
new_lt8(vyy6001, vyy501, ty_Int) → new_lt19(vyy6001, vyy501)
new_lt8(vyy6001, vyy501, app(app(app(ty_@3, bac), bad), bae)) → new_lt15(vyy6001, vyy501, bac, bad, bae)
new_lt9(vyy6000, vyy500, ty_Float) → new_lt5(vyy6000, vyy500)
new_ltEs16(LT, GT) → True
new_ltEs7(Just(vyy6000), Just(vyy500), ty_Integer) → new_ltEs17(vyy6000, vyy500)
new_lt8(vyy6001, vyy501, ty_Ordering) → new_lt7(vyy6001, vyy501)
new_esEs5(Left(vyy350), Left(vyy360), ty_@0, bh) → new_esEs16(vyy350, vyy360)
new_esEs28(vyy350, vyy360, ty_Int) → new_esEs14(vyy350, vyy360)
new_ltEs6(vyy6002, vyy502, app(ty_Ratio, gg)) → new_ltEs9(vyy6002, vyy502, gg)
new_esEs21(vyy350, vyy360, ty_Int) → new_esEs14(vyy350, vyy360)
new_esEs20(Char(vyy350), Char(vyy360)) → new_primEqNat0(vyy350, vyy360)
new_esEs6(Just(vyy350), Just(vyy360), ty_@0) → new_esEs16(vyy350, vyy360)
new_ltEs4(Left(vyy6000), Left(vyy500), ty_Int, dch) → new_ltEs18(vyy6000, vyy500)
new_primMulNat0(Zero, Zero) → Zero
new_esEs25(vyy351, vyy361, ty_Char) → new_esEs20(vyy351, vyy361)
new_esEs6(Just(vyy350), Just(vyy360), app(ty_Ratio, bgf)) → new_esEs13(vyy350, vyy360, bgf)
new_compare(:(vyy6000, vyy6001), [], bbc) → GT
new_esEs23(vyy351, vyy361, app(ty_Ratio, cca)) → new_esEs13(vyy351, vyy361, cca)
new_ltEs20(vyy600, vyy50, ty_Float) → new_ltEs12(vyy600, vyy50)
new_esEs6(Just(vyy350), Just(vyy360), ty_Bool) → new_esEs19(vyy350, vyy360)
new_ltEs6(vyy6002, vyy502, app(app(app(ty_@3, ha), hb), hc)) → new_ltEs5(vyy6002, vyy502, ha, hb, hc)
new_lt20(vyy6000, vyy500, ty_Integer) → new_lt18(vyy6000, vyy500)
new_esEs6(Just(vyy350), Just(vyy360), ty_Float) → new_esEs11(vyy350, vyy360)
new_lt9(vyy6000, vyy500, ty_Double) → new_lt6(vyy6000, vyy500)
new_lt9(vyy6000, vyy500, app(app(ty_@2, fg), fh)) → new_lt16(vyy6000, vyy500, fg, fh)
new_not(GT) → False
new_compare17(vyy6000, vyy500, ty_Char) → new_compare14(vyy6000, vyy500)
new_ltEs7(Just(vyy6000), Just(vyy500), ty_Double) → new_ltEs10(vyy6000, vyy500)
new_esEs10(EQ) → False
new_compare17(vyy6000, vyy500, ty_Double) → new_compare8(vyy6000, vyy500)
new_esEs12(GT, LT) → False
new_esEs12(LT, GT) → False
new_esEs5(Right(vyy350), Right(vyy360), df, ty_Integer) → new_esEs9(vyy350, vyy360)
new_esEs23(vyy351, vyy361, app(app(ty_FiniteMap, ccc), ccd)) → new_esEs15(vyy351, vyy361, ccc, ccd)
new_lt8(vyy6001, vyy501, app(app(ty_@2, baf), bag)) → new_lt16(vyy6001, vyy501, baf, bag)
new_esEs22(vyy352, vyy362, app(ty_Maybe, caf)) → new_esEs6(vyy352, vyy362, caf)
new_esEs21(vyy350, vyy360, app(app(app(ty_@3, bda), bdb), bdc)) → new_esEs7(vyy350, vyy360, bda, bdb, bdc)
new_esEs22(vyy352, vyy362, ty_Integer) → new_esEs9(vyy352, vyy362)
new_compare28(:%(vyy6000, vyy6001), :%(vyy500, vyy501), ty_Integer) → new_compare16(new_sr0(vyy6000, vyy501), new_sr0(vyy500, vyy6001))
new_lt9(vyy6000, vyy500, ty_Char) → new_lt17(vyy6000, vyy500)
new_esEs29(vyy35, vyy36, app(app(app(ty_@3, bhe), bhf), bhg)) → new_esEs7(vyy35, vyy36, bhe, bhf, bhg)
new_lt8(vyy6001, vyy501, app(app(ty_Either, hf), hg)) → new_lt10(vyy6001, vyy501, hf, hg)
new_pePe(False, vyy35, vyy36, vyy52, dfd) → new_asAs(new_esEs29(vyy35, vyy36, dfd), vyy52)
new_compare26(vyy6000, vyy500, False, fg, fh) → new_compare15(vyy6000, vyy500, new_ltEs13(vyy6000, vyy500, fg, fh), fg, fh)
new_ltEs18(vyy600, vyy50) → new_not(new_compare11(vyy600, vyy50))
new_foldFM0(vyy360, vyy361, vyy80, EmptyFM, bec, bed) → :(@2(vyy360, vyy361), vyy80)
new_esEs21(vyy350, vyy360, app(app(ty_@2, bea), beb)) → new_esEs8(vyy350, vyy360, bea, beb)
new_esEs22(vyy352, vyy362, ty_Ordering) → new_esEs12(vyy352, vyy362)
new_esEs5(Left(vyy350), Left(vyy360), app(ty_Maybe, cg), bh) → new_esEs6(vyy350, vyy360, cg)
new_ltEs19(vyy6001, vyy501, app(app(ty_Either, cef), ceg)) → new_ltEs4(vyy6001, vyy501, cef, ceg)
new_ltEs17(vyy600, vyy50) → new_not(new_compare16(vyy600, vyy50))
new_lt9(vyy6000, vyy500, app(app(ty_Either, bf), bg)) → new_lt10(vyy6000, vyy500, bf, bg)
new_esEs26(vyy350, vyy360, app(app(ty_@2, dcb), dcc)) → new_esEs8(vyy350, vyy360, dcb, dcc)
new_esEs18(:(vyy350, vyy351), [], bcf) → False
new_esEs18([], :(vyy360, vyy361), bcf) → False
new_ltEs14(vyy600, vyy50) → new_not(new_compare5(vyy600, vyy50))
new_esEs26(vyy350, vyy360, app(app(ty_FiniteMap, dbg), dbh)) → new_esEs15(vyy350, vyy360, dbg, dbh)
new_lt5(vyy6000, vyy500) → new_esEs10(new_compare6(vyy6000, vyy500))
new_ltEs19(vyy6001, vyy501, app(ty_[], cfb)) → new_ltEs11(vyy6001, vyy501, cfb)
new_esEs6(Just(vyy350), Just(vyy360), app(app(ty_FiniteMap, bgh), bha)) → new_esEs15(vyy350, vyy360, bgh, bha)
new_ltEs16(EQ, GT) → True
new_ltEs20(vyy600, vyy50, app(app(ty_Either, dea), dch)) → new_ltEs4(vyy600, vyy50, dea, dch)
new_ltEs4(Right(vyy6000), Right(vyy500), dea, app(app(ty_Either, deb), dec)) → new_ltEs4(vyy6000, vyy500, deb, dec)
new_lt20(vyy6000, vyy500, ty_Float) → new_lt5(vyy6000, vyy500)
new_esEs29(vyy35, vyy36, app(ty_Ratio, dce)) → new_esEs13(vyy35, vyy36, dce)
new_lt8(vyy6001, vyy501, app(ty_[], bab)) → new_lt14(vyy6001, vyy501, bab)
new_ltEs4(Left(vyy6000), Right(vyy500), dea, dch) → True
new_esEs25(vyy351, vyy361, app(app(ty_FiniteMap, dac), dad)) → new_esEs15(vyy351, vyy361, dac, dad)
new_esEs23(vyy351, vyy361, app(app(app(ty_@3, cbf), cbg), cbh)) → new_esEs7(vyy351, vyy361, cbf, cbg, cbh)
new_primCmpNat0(Zero, Succ(vyy5000)) → LT
new_compare211(vyy6000, vyy500, False) → new_compare110(vyy6000, vyy500, new_ltEs16(vyy6000, vyy500))
new_esEs5(Left(vyy350), Left(vyy360), ty_Float, bh) → new_esEs11(vyy350, vyy360)
new_esEs26(vyy350, vyy360, ty_Double) → new_esEs17(vyy350, vyy360)
new_compare29(vyy6000, vyy500, False, bah) → new_compare111(vyy6000, vyy500, new_ltEs7(vyy6000, vyy500, bah), bah)
new_ltEs20(vyy600, vyy50, ty_Bool) → new_ltEs8(vyy600, vyy50)
new_compare17(vyy6000, vyy500, ty_Bool) → new_compare27(vyy6000, vyy500)
new_esEs25(vyy351, vyy361, app(app(ty_Either, chd), che)) → new_esEs5(vyy351, vyy361, chd, che)
new_esEs6(Just(vyy350), Just(vyy360), ty_Ordering) → new_esEs12(vyy350, vyy360)
new_lt11(vyy6000, vyy500, bah) → new_esEs10(new_compare19(vyy6000, vyy500, bah))
new_compare25(vyy6000, vyy500, True, fc, fd, ff) → EQ
new_esEs21(vyy350, vyy360, app(ty_Ratio, bdd)) → new_esEs13(vyy350, vyy360, bdd)
new_esEs25(vyy351, vyy361, ty_Double) → new_esEs17(vyy351, vyy361)
new_ltEs4(Left(vyy6000), Left(vyy500), app(ty_Ratio, ddb), dch) → new_ltEs9(vyy6000, vyy500, ddb)
new_esEs12(LT, LT) → True
new_esEs25(vyy351, vyy361, app(ty_Ratio, daa)) → new_esEs13(vyy351, vyy361, daa)
new_esEs23(vyy351, vyy361, ty_Int) → new_esEs14(vyy351, vyy361)
new_esEs5(Right(vyy350), Right(vyy360), df, app(app(ty_@2, fa), fb)) → new_esEs8(vyy350, vyy360, fa, fb)
new_compare27(vyy6000, vyy500) → new_compare210(vyy6000, vyy500, new_esEs19(vyy6000, vyy500))
new_esEs23(vyy351, vyy361, ty_@0) → new_esEs16(vyy351, vyy361)
new_primEqNat0(Zero, Zero) → True
new_esEs6(Just(vyy350), Just(vyy360), app(app(app(ty_@3, bgc), bgd), bge)) → new_esEs7(vyy350, vyy360, bgc, bgd, bge)
new_lt9(vyy6000, vyy500, app(ty_[], bbb)) → new_lt14(vyy6000, vyy500, bbb)
new_esEs29(vyy35, vyy36, app(ty_Maybe, bfh)) → new_esEs6(vyy35, vyy36, bfh)
new_ltEs6(vyy6002, vyy502, ty_Ordering) → new_ltEs16(vyy6002, vyy502)
new_esEs26(vyy350, vyy360, app(ty_Maybe, dbf)) → new_esEs6(vyy350, vyy360, dbf)
new_esEs25(vyy351, vyy361, app(ty_[], dae)) → new_esEs18(vyy351, vyy361, dae)
new_primMulNat0(Succ(vyy50000), Succ(vyy600100)) → new_primPlusNat1(new_primMulNat0(vyy50000, Succ(vyy600100)), vyy600100)
new_lt8(vyy6001, vyy501, ty_@0) → new_lt4(vyy6001, vyy501)
new_esEs29(vyy35, vyy36, ty_Int) → new_esEs14(vyy35, vyy36)
new_esEs23(vyy351, vyy361, ty_Integer) → new_esEs9(vyy351, vyy361)
new_esEs26(vyy350, vyy360, app(ty_Ratio, dbe)) → new_esEs13(vyy350, vyy360, dbe)
new_esEs6(Just(vyy350), Just(vyy360), ty_Int) → new_esEs14(vyy350, vyy360)
new_esEs24(vyy350, vyy360, app(ty_[], cea)) → new_esEs18(vyy350, vyy360, cea)
new_esEs26(vyy350, vyy360, ty_@0) → new_esEs16(vyy350, vyy360)
new_ltEs7(Just(vyy6000), Just(vyy500), ty_Float) → new_ltEs12(vyy6000, vyy500)
new_esEs19(True, True) → True
new_ltEs16(EQ, LT) → False
new_ltEs16(GT, EQ) → False
new_sr(vyy500, vyy6001) → new_primMulInt(vyy500, vyy6001)
new_compare12(vyy6000, vyy500, True, fc, fd, ff) → LT
new_ltEs6(vyy6002, vyy502, ty_Integer) → new_ltEs17(vyy6002, vyy502)
new_lt8(vyy6001, vyy501, ty_Char) → new_lt17(vyy6001, vyy501)
new_lt20(vyy6000, vyy500, app(ty_Maybe, cgb)) → new_lt11(vyy6000, vyy500, cgb)
new_compare9(vyy6000, vyy500, fg, fh) → new_compare26(vyy6000, vyy500, new_esEs8(vyy6000, vyy500, fg, fh), fg, fh)
new_esEs5(Right(vyy350), Right(vyy360), df, app(ty_[], eh)) → new_esEs18(vyy350, vyy360, eh)
new_esEs26(vyy350, vyy360, ty_Float) → new_esEs11(vyy350, vyy360)
new_ltEs19(vyy6001, vyy501, ty_Double) → new_ltEs10(vyy6001, vyy501)
new_esEs22(vyy352, vyy362, app(ty_[], cba)) → new_esEs18(vyy352, vyy362, cba)
new_lt20(vyy6000, vyy500, ty_Char) → new_lt17(vyy6000, vyy500)
new_lt19(vyy6000, vyy500) → new_esEs10(new_compare11(vyy6000, vyy500))
new_ltEs6(vyy6002, vyy502, ty_Double) → new_ltEs10(vyy6002, vyy502)
new_esEs5(Left(vyy350), Left(vyy360), app(ty_Ratio, cf), bh) → new_esEs13(vyy350, vyy360, cf)
new_esEs25(vyy351, vyy361, ty_Ordering) → new_esEs12(vyy351, vyy361)
new_ltEs20(vyy600, vyy50, app(app(app(ty_@3, ga), gb), gc)) → new_ltEs5(vyy600, vyy50, ga, gb, gc)
new_primEqInt(Neg(Succ(vyy3500)), Neg(Succ(vyy3600))) → new_primEqNat0(vyy3500, vyy3600)
new_esEs25(vyy351, vyy361, app(app(ty_@2, daf), dag)) → new_esEs8(vyy351, vyy361, daf, dag)
new_ltEs16(LT, EQ) → True
new_compare7(vyy6000, vyy500, fc, fd, ff) → new_compare25(vyy6000, vyy500, new_esEs7(vyy6000, vyy500, fc, fd, ff), fc, fd, ff)
new_ltEs6(vyy6002, vyy502, ty_Float) → new_ltEs12(vyy6002, vyy502)
new_esEs24(vyy350, vyy360, ty_Bool) → new_esEs19(vyy350, vyy360)
new_esEs21(vyy350, vyy360, ty_@0) → new_esEs16(vyy350, vyy360)
new_compare17(vyy6000, vyy500, ty_Float) → new_compare6(vyy6000, vyy500)
new_esEs29(vyy35, vyy36, app(app(ty_Either, df), bh)) → new_esEs5(vyy35, vyy36, df, bh)
new_ltEs8(True, True) → True
new_esEs26(vyy350, vyy360, app(app(app(ty_@3, dbb), dbc), dbd)) → new_esEs7(vyy350, vyy360, dbb, dbc, dbd)
new_ltEs4(Left(vyy6000), Left(vyy500), ty_Char, dch) → new_ltEs15(vyy6000, vyy500)
new_ltEs4(Left(vyy6000), Left(vyy500), ty_Float, dch) → new_ltEs12(vyy6000, vyy500)
new_ltEs19(vyy6001, vyy501, app(ty_Ratio, cfa)) → new_ltEs9(vyy6001, vyy501, cfa)
new_esEs12(LT, EQ) → False
new_esEs12(EQ, LT) → False
new_ltEs15(vyy600, vyy50) → new_not(new_compare14(vyy600, vyy50))
new_esEs21(vyy350, vyy360, app(ty_[], bdh)) → new_esEs18(vyy350, vyy360, bdh)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs5(Left(vyy350), Left(vyy360), app(app(app(ty_@3, cc), cd), ce), bh) → new_esEs7(vyy350, vyy360, cc, cd, ce)
new_compare17(vyy6000, vyy500, app(ty_Ratio, bbg)) → new_compare28(vyy6000, vyy500, bbg)
new_esEs19(False, False) → True
new_lt20(vyy6000, vyy500, ty_Ordering) → new_lt7(vyy6000, vyy500)
new_compare17(vyy6000, vyy500, ty_Int) → new_compare11(vyy6000, vyy500)
new_primEqInt(Neg(Zero), Neg(Succ(vyy3600))) → False
new_primEqInt(Neg(Succ(vyy3500)), Neg(Zero)) → False
new_ltEs4(Left(vyy6000), Left(vyy500), app(app(ty_Either, dcf), dcg), dch) → new_ltEs4(vyy6000, vyy500, dcf, dcg)
new_ltEs9(vyy600, vyy50, dcd) → new_not(new_compare28(vyy600, vyy50, dcd))
new_compare26(vyy6000, vyy500, True, fg, fh) → EQ
new_primPlusNat1(Zero, vyy600100) → Succ(vyy600100)
new_compare111(vyy6000, vyy500, True, bah) → LT
new_esEs24(vyy350, vyy360, ty_Integer) → new_esEs9(vyy350, vyy360)
new_compare24(vyy6000, vyy500, True, bf, bg) → EQ
new_esEs6(Just(vyy350), Just(vyy360), ty_Double) → new_esEs17(vyy350, vyy360)
new_esEs26(vyy350, vyy360, app(ty_[], dca)) → new_esEs18(vyy350, vyy360, dca)
new_compare([], [], bbc) → EQ
new_foldFM0(vyy360, vyy361, vyy80, Branch(vyy3630, vyy3631, vyy3632, vyy3633, vyy3634), bec, bed) → new_foldFM0(vyy3630, vyy3631, new_foldFM0(vyy360, vyy361, vyy80, vyy3634, bec, bed), vyy3633, bec, bed)
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_ltEs7(Just(vyy6000), Just(vyy500), ty_Int) → new_ltEs18(vyy6000, vyy500)
new_ltEs4(Right(vyy6000), Right(vyy500), dea, app(ty_Maybe, ded)) → new_ltEs7(vyy6000, vyy500, ded)
new_compare14(Char(vyy6000), Char(vyy500)) → new_primCmpNat0(vyy6000, vyy500)
new_lt9(vyy6000, vyy500, app(ty_Ratio, bba)) → new_lt13(vyy6000, vyy500, bba)
new_ltEs16(GT, LT) → False
new_lt9(vyy6000, vyy500, ty_Ordering) → new_lt7(vyy6000, vyy500)
new_primCmpNat0(Succ(vyy60000), Succ(vyy5000)) → new_primCmpNat0(vyy60000, vyy5000)
new_esEs22(vyy352, vyy362, ty_Char) → new_esEs20(vyy352, vyy362)
new_esEs9(Integer(vyy350), Integer(vyy360)) → new_primEqInt(vyy350, vyy360)
new_sizeFM(EmptyFM, bec, bed) → Pos(Zero)
new_esEs6(Nothing, Nothing, bfh) → True
new_compare112(vyy6000, vyy500, True) → LT
new_primEqInt(Pos(Succ(vyy3500)), Pos(Succ(vyy3600))) → new_primEqNat0(vyy3500, vyy3600)
new_compare10(vyy6000, vyy500, False, bf, bg) → GT
new_ltEs19(vyy6001, vyy501, ty_Integer) → new_ltEs17(vyy6001, vyy501)
new_esEs21(vyy350, vyy360, app(ty_Maybe, bde)) → new_esEs6(vyy350, vyy360, bde)
new_esEs26(vyy350, vyy360, ty_Bool) → new_esEs19(vyy350, vyy360)
new_ltEs7(Nothing, Just(vyy500), bee) → True
new_ltEs6(vyy6002, vyy502, ty_Int) → new_ltEs18(vyy6002, vyy502)
new_esEs5(Right(vyy350), Right(vyy360), df, app(app(ty_Either, dg), dh)) → new_esEs5(vyy350, vyy360, dg, dh)
new_lt9(vyy6000, vyy500, ty_Int) → new_lt19(vyy6000, vyy500)
new_esEs6(Just(vyy350), Nothing, bfh) → False
new_esEs6(Nothing, Just(vyy360), bfh) → False
new_esEs15(vyy35, vyy36, bec, bed) → new_asAs(new_esEs14(new_sizeFM(vyy35, bec, bed), new_sizeFM(vyy36, bec, bed)), new_esEs18(new_fmToList(vyy35, bec, bed), new_fmToList(vyy36, bec, bed), app(app(ty_@2, bec), bed)))
new_primEqNat0(Succ(vyy3500), Succ(vyy3600)) → new_primEqNat0(vyy3500, vyy3600)
new_esEs24(vyy350, vyy360, ty_@0) → new_esEs16(vyy350, vyy360)
new_compare17(vyy6000, vyy500, ty_Integer) → new_compare16(vyy6000, vyy500)
new_esEs26(vyy350, vyy360, ty_Ordering) → new_esEs12(vyy350, vyy360)
new_lt9(vyy6000, vyy500, ty_Bool) → new_lt12(vyy6000, vyy500)
new_lt8(vyy6001, vyy501, app(ty_Maybe, hh)) → new_lt11(vyy6001, vyy501, hh)
new_primCompAux00(vyy66, LT) → LT
new_ltEs5(@3(vyy6000, vyy6001, vyy6002), @3(vyy500, vyy501, vyy502), ga, gb, gc) → new_pePe(new_lt9(vyy6000, vyy500, ga), vyy6000, vyy500, new_pePe(new_lt8(vyy6001, vyy501, gb), vyy6001, vyy501, new_ltEs6(vyy6002, vyy502, gc), gb), ga)
new_lt4(vyy6000, vyy500) → new_esEs10(new_compare5(vyy6000, vyy500))
new_ltEs4(Right(vyy6000), Right(vyy500), dea, ty_Float) → new_ltEs12(vyy6000, vyy500)
new_lt20(vyy6000, vyy500, ty_@0) → new_lt4(vyy6000, vyy500)
new_primCmpInt(Neg(Succ(vyy60000)), Neg(vyy500)) → new_primCmpNat0(vyy500, Succ(vyy60000))
new_compare17(vyy6000, vyy500, app(app(ty_@2, bcd), bce)) → new_compare9(vyy6000, vyy500, bcd, bce)
new_esEs12(EQ, EQ) → True
new_ltEs19(vyy6001, vyy501, ty_Bool) → new_ltEs8(vyy6001, vyy501)
new_esEs5(Right(vyy350), Right(vyy360), df, ty_@0) → new_esEs16(vyy350, vyy360)
new_esEs22(vyy352, vyy362, app(app(ty_FiniteMap, cag), cah)) → new_esEs15(vyy352, vyy362, cag, cah)
new_compare24(vyy6000, vyy500, False, bf, bg) → new_compare10(vyy6000, vyy500, new_ltEs4(vyy6000, vyy500, bf, bg), bf, bg)
new_ltEs6(vyy6002, vyy502, app(ty_Maybe, gf)) → new_ltEs7(vyy6002, vyy502, gf)
new_esEs5(Left(vyy350), Left(vyy360), ty_Int, bh) → new_esEs14(vyy350, vyy360)
new_primEqInt(Pos(Succ(vyy3500)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(vyy3600))) → False
new_ltEs13(@2(vyy6000, vyy6001), @2(vyy500, vyy501), ced, cee) → new_pePe(new_lt20(vyy6000, vyy500, ced), vyy6000, vyy500, new_ltEs19(vyy6001, vyy501, cee), ced)
new_primPlusNat0(Succ(vyy8100), Zero) → Succ(vyy8100)
new_primPlusNat0(Zero, Succ(vyy6001000)) → Succ(vyy6001000)
new_lt9(vyy6000, vyy500, ty_@0) → new_lt4(vyy6000, vyy500)
new_esEs21(vyy350, vyy360, ty_Bool) → new_esEs19(vyy350, vyy360)
new_lt15(vyy6000, vyy500, fc, fd, ff) → new_esEs10(new_compare7(vyy6000, vyy500, fc, fd, ff))
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(vyy60000), Zero) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(vyy5000))) → LT
new_ltEs20(vyy600, vyy50, ty_@0) → new_ltEs14(vyy600, vyy50)
new_esEs19(False, True) → False
new_esEs19(True, False) → False
new_esEs5(Right(vyy350), Right(vyy360), df, ty_Bool) → new_esEs19(vyy350, vyy360)
new_lt10(vyy6000, vyy500, bf, bg) → new_esEs10(new_compare18(vyy6000, vyy500, bf, bg))
new_esEs22(vyy352, vyy362, app(ty_Ratio, cae)) → new_esEs13(vyy352, vyy362, cae)
new_compare17(vyy6000, vyy500, app(ty_[], bbh)) → new_compare(vyy6000, vyy500, bbh)
new_esEs27(vyy351, vyy361, ty_Integer) → new_esEs9(vyy351, vyy361)
new_ltEs20(vyy600, vyy50, ty_Integer) → new_ltEs17(vyy600, vyy50)
new_sr0(Integer(vyy5000), Integer(vyy60010)) → Integer(new_primMulInt(vyy5000, vyy60010))
new_esEs21(vyy350, vyy360, ty_Double) → new_esEs17(vyy350, vyy360)
new_primEqInt(Pos(Succ(vyy3500)), Neg(vyy360)) → False
new_primEqInt(Neg(Succ(vyy3500)), Pos(vyy360)) → False
new_esEs25(vyy351, vyy361, ty_Bool) → new_esEs19(vyy351, vyy361)
new_esEs24(vyy350, vyy360, app(ty_Ratio, cde)) → new_esEs13(vyy350, vyy360, cde)
new_compare(:(vyy6000, vyy6001), :(vyy500, vyy501), bbc) → new_primCompAux0(vyy6000, vyy500, new_compare(vyy6001, vyy501, bbc), bbc)
new_foldFM2(EmptyFM, bec, bed) → []
new_esEs24(vyy350, vyy360, ty_Int) → new_esEs14(vyy350, vyy360)
new_ltEs20(vyy600, vyy50, ty_Double) → new_ltEs10(vyy600, vyy50)
new_esEs21(vyy350, vyy360, ty_Ordering) → new_esEs12(vyy350, vyy360)
new_lt8(vyy6001, vyy501, ty_Float) → new_lt5(vyy6001, vyy501)
new_primEqInt(Neg(Zero), Pos(Succ(vyy3600))) → False
new_primEqInt(Pos(Zero), Neg(Succ(vyy3600))) → False
new_esEs24(vyy350, vyy360, ty_Ordering) → new_esEs12(vyy350, vyy360)
new_primCmpInt(Pos(Zero), Pos(Succ(vyy5000))) → new_primCmpNat0(Zero, Succ(vyy5000))
new_primCompAux00(vyy66, EQ) → vyy66
new_esEs23(vyy351, vyy361, ty_Double) → new_esEs17(vyy351, vyy361)
new_ltEs16(EQ, EQ) → True
new_esEs23(vyy351, vyy361, ty_Bool) → new_esEs19(vyy351, vyy361)
new_compare17(vyy6000, vyy500, app(app(ty_Either, bbd), bbe)) → new_compare18(vyy6000, vyy500, bbd, bbe)
new_esEs22(vyy352, vyy362, ty_Bool) → new_esEs19(vyy352, vyy362)
new_esEs6(Just(vyy350), Just(vyy360), app(app(ty_@2, bhc), bhd)) → new_esEs8(vyy350, vyy360, bhc, bhd)
new_esEs22(vyy352, vyy362, ty_@0) → new_esEs16(vyy352, vyy362)
new_esEs5(Left(vyy350), Left(vyy360), ty_Double, bh) → new_esEs17(vyy350, vyy360)
new_esEs7(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), bhe, bhf, bhg) → new_asAs(new_esEs24(vyy350, vyy360, bhe), new_asAs(new_esEs23(vyy351, vyy361, bhf), new_esEs22(vyy352, vyy362, bhg)))
new_esEs29(vyy35, vyy36, app(app(ty_FiniteMap, bec), bed)) → new_esEs15(vyy35, vyy36, bec, bed)
new_ltEs19(vyy6001, vyy501, app(app(ty_@2, cff), cfg)) → new_ltEs13(vyy6001, vyy501, cff, cfg)
new_esEs23(vyy351, vyy361, ty_Float) → new_esEs11(vyy351, vyy361)
new_ltEs8(True, False) → False
new_esEs5(Left(vyy350), Left(vyy360), app(app(ty_@2, dd), de), bh) → new_esEs8(vyy350, vyy360, dd, de)
new_ltEs4(Right(vyy6000), Left(vyy500), dea, dch) → False
new_compare16(Integer(vyy6000), Integer(vyy500)) → new_primCmpInt(vyy6000, vyy500)
new_primCmpInt(Pos(Succ(vyy60000)), Pos(vyy500)) → new_primCmpNat0(Succ(vyy60000), vyy500)
new_esEs22(vyy352, vyy362, ty_Float) → new_esEs11(vyy352, vyy362)
new_esEs12(GT, EQ) → False
new_esEs12(EQ, GT) → False
new_compare12(vyy6000, vyy500, False, fc, fd, ff) → GT
new_lt8(vyy6001, vyy501, ty_Integer) → new_lt18(vyy6001, vyy501)
new_esEs6(Just(vyy350), Just(vyy360), app(ty_[], bhb)) → new_esEs18(vyy350, vyy360, bhb)
new_esEs29(vyy35, vyy36, app(app(ty_@2, chb), chc)) → new_esEs8(vyy35, vyy36, chb, chc)
new_ltEs4(Right(vyy6000), Right(vyy500), dea, ty_Ordering) → new_ltEs16(vyy6000, vyy500)
new_lt20(vyy6000, vyy500, app(app(app(ty_@3, cge), cgf), cgg)) → new_lt15(vyy6000, vyy500, cge, cgf, cgg)
new_ltEs19(vyy6001, vyy501, ty_Int) → new_ltEs18(vyy6001, vyy501)
new_lt9(vyy6000, vyy500, ty_Integer) → new_lt18(vyy6000, vyy500)
new_not0 → True
new_esEs5(Right(vyy350), Right(vyy360), df, ty_Int) → new_esEs14(vyy350, vyy360)
new_esEs5(Right(vyy350), Right(vyy360), df, ty_Double) → new_esEs17(vyy350, vyy360)
new_compare17(vyy6000, vyy500, app(ty_Maybe, bbf)) → new_compare19(vyy6000, vyy500, bbf)
new_ltEs6(vyy6002, vyy502, app(ty_[], gh)) → new_ltEs11(vyy6002, vyy502, gh)
new_lt20(vyy6000, vyy500, ty_Double) → new_lt6(vyy6000, vyy500)
new_esEs26(vyy350, vyy360, app(app(ty_Either, dah), dba)) → new_esEs5(vyy350, vyy360, dah, dba)
new_primCompAux0(vyy6000, vyy500, vyy62, bbc) → new_primCompAux00(vyy62, new_compare17(vyy6000, vyy500, bbc))
new_esEs5(Left(vyy350), Left(vyy360), ty_Bool, bh) → new_esEs19(vyy350, vyy360)
new_esEs5(Right(vyy350), Right(vyy360), df, app(app(ty_FiniteMap, ef), eg)) → new_esEs15(vyy350, vyy360, ef, eg)
new_ltEs4(Right(vyy6000), Right(vyy500), dea, app(ty_Ratio, dee)) → new_ltEs9(vyy6000, vyy500, dee)
new_esEs22(vyy352, vyy362, app(app(app(ty_@3, cab), cac), cad)) → new_esEs7(vyy352, vyy362, cab, cac, cad)
new_primCmpInt(Pos(Succ(vyy60000)), Neg(vyy500)) → GT
new_lt6(vyy6000, vyy500) → new_esEs10(new_compare8(vyy6000, vyy500))
new_ltEs7(Just(vyy6000), Just(vyy500), app(ty_Maybe, beh)) → new_ltEs7(vyy6000, vyy500, beh)
new_ltEs4(Right(vyy6000), Right(vyy500), dea, ty_Bool) → new_ltEs8(vyy6000, vyy500)
new_esEs29(vyy35, vyy36, ty_@0) → new_esEs16(vyy35, vyy36)
new_esEs29(vyy35, vyy36, ty_Integer) → new_esEs9(vyy35, vyy36)
new_primMulInt(Pos(vyy5000), Pos(vyy60010)) → Pos(new_primMulNat0(vyy5000, vyy60010))
new_compare13(vyy6000, vyy500) → new_compare211(vyy6000, vyy500, new_esEs12(vyy6000, vyy500))
new_ltEs4(Left(vyy6000), Left(vyy500), app(app(ty_@2, ddg), ddh), dch) → new_ltEs13(vyy6000, vyy500, ddg, ddh)
new_ltEs4(Left(vyy6000), Left(vyy500), ty_@0, dch) → new_ltEs14(vyy6000, vyy500)
new_ltEs4(Left(vyy6000), Left(vyy500), ty_Integer, dch) → new_ltEs17(vyy6000, vyy500)
new_esEs24(vyy350, vyy360, app(app(ty_FiniteMap, cdg), cdh)) → new_esEs15(vyy350, vyy360, cdg, cdh)
new_ltEs6(vyy6002, vyy502, app(app(ty_Either, gd), ge)) → new_ltEs4(vyy6002, vyy502, gd, ge)
new_lt20(vyy6000, vyy500, app(app(ty_Either, cfh), cga)) → new_lt10(vyy6000, vyy500, cfh, cga)
new_esEs5(Right(vyy350), Left(vyy360), df, bh) → False
new_esEs5(Left(vyy350), Right(vyy360), df, bh) → False
new_primMulInt(Neg(vyy5000), Neg(vyy60010)) → Pos(new_primMulNat0(vyy5000, vyy60010))
new_compare110(vyy6000, vyy500, True) → LT
new_ltEs4(Right(vyy6000), Right(vyy500), dea, app(app(ty_@2, dfb), dfc)) → new_ltEs13(vyy6000, vyy500, dfb, dfc)
new_primEqNat0(Succ(vyy3500), Zero) → False
new_primEqNat0(Zero, Succ(vyy3600)) → False
new_ltEs20(vyy600, vyy50, ty_Int) → new_ltEs18(vyy600, vyy50)
new_ltEs8(False, False) → True
new_primPlusNat0(Zero, Zero) → Zero
new_ltEs20(vyy600, vyy50, ty_Char) → new_ltEs15(vyy600, vyy50)
new_esEs25(vyy351, vyy361, app(ty_Maybe, dab)) → new_esEs6(vyy351, vyy361, dab)
new_compare110(vyy6000, vyy500, False) → GT
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs5(Left(vyy350), Left(vyy360), app(ty_[], dc), bh) → new_esEs18(vyy350, vyy360, dc)
new_compare210(vyy6000, vyy500, True) → EQ
new_sizeFM(Branch(vyy360, vyy361, vyy362, vyy363, vyy364), bec, bed) → vyy362
new_ltEs4(Right(vyy6000), Right(vyy500), dea, ty_Double) → new_ltEs10(vyy6000, vyy500)
new_ltEs20(vyy600, vyy50, ty_Ordering) → new_ltEs16(vyy600, vyy50)
new_ltEs7(Nothing, Nothing, bee) → True
new_pePe(True, vyy35, vyy36, vyy52, dfd) → True
new_primPlusNat1(Succ(vyy810), vyy600100) → Succ(Succ(new_primPlusNat0(vyy810, vyy600100)))
new_foldFM2(Branch(vyy360, vyy361, vyy362, vyy363, vyy364), bec, bed) → new_foldFM0(vyy360, vyy361, new_foldFM2(vyy364, bec, bed), vyy363, bec, bed)
new_esEs5(Left(vyy350), Left(vyy360), app(app(ty_FiniteMap, da), db), bh) → new_esEs15(vyy350, vyy360, da, db)
new_ltEs7(Just(vyy6000), Just(vyy500), app(app(app(ty_@3, bfc), bfd), bfe)) → new_ltEs5(vyy6000, vyy500, bfc, bfd, bfe)
new_lt9(vyy6000, vyy500, app(app(app(ty_@3, fc), fd), ff)) → new_lt15(vyy6000, vyy500, fc, fd, ff)
new_ltEs7(Just(vyy6000), Just(vyy500), ty_Ordering) → new_ltEs16(vyy6000, vyy500)
new_primCmpInt(Neg(Zero), Neg(Succ(vyy5000))) → new_primCmpNat0(Succ(vyy5000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(vyy5000))) → GT
new_esEs29(vyy35, vyy36, ty_Bool) → new_esEs19(vyy35, vyy36)
new_esEs23(vyy351, vyy361, app(app(ty_@2, ccf), ccg)) → new_esEs8(vyy351, vyy361, ccf, ccg)
new_ltEs6(vyy6002, vyy502, app(app(ty_@2, hd), he)) → new_ltEs13(vyy6002, vyy502, hd, he)
new_esEs5(Right(vyy350), Right(vyy360), df, app(app(app(ty_@3, ea), eb), ec)) → new_esEs7(vyy350, vyy360, ea, eb, ec)
new_compare15(vyy6000, vyy500, False, fg, fh) → GT
new_ltEs7(Just(vyy6000), Just(vyy500), ty_Char) → new_ltEs15(vyy6000, vyy500)
new_esEs25(vyy351, vyy361, ty_Int) → new_esEs14(vyy351, vyy361)
new_esEs6(Just(vyy350), Just(vyy360), app(app(ty_Either, bga), bgb)) → new_esEs5(vyy350, vyy360, bga, bgb)
new_lt14(vyy6000, vyy500, bbb) → new_esEs10(new_compare(vyy6000, vyy500, bbb))
new_esEs10(LT) → True
new_esEs5(Right(vyy350), Right(vyy360), df, ty_Float) → new_esEs11(vyy350, vyy360)
new_ltEs6(vyy6002, vyy502, ty_@0) → new_ltEs14(vyy6002, vyy502)
new_esEs27(vyy351, vyy361, ty_Int) → new_esEs14(vyy351, vyy361)
new_esEs28(vyy350, vyy360, ty_Integer) → new_esEs9(vyy350, vyy360)
new_esEs26(vyy350, vyy360, ty_Char) → new_esEs20(vyy350, vyy360)
new_esEs24(vyy350, vyy360, app(app(app(ty_@3, cdb), cdc), cdd)) → new_esEs7(vyy350, vyy360, cdb, cdc, cdd)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_compare29(vyy6000, vyy500, True, bah) → EQ
new_lt8(vyy6001, vyy501, ty_Double) → new_lt6(vyy6001, vyy501)
new_compare17(vyy6000, vyy500, ty_Ordering) → new_compare13(vyy6000, vyy500)
new_esEs26(vyy350, vyy360, ty_Int) → new_esEs14(vyy350, vyy360)
new_esEs13(:%(vyy350, vyy351), :%(vyy360, vyy361), dce) → new_asAs(new_esEs28(vyy350, vyy360, dce), new_esEs27(vyy351, vyy361, dce))
new_esEs6(Just(vyy350), Just(vyy360), ty_Integer) → new_esEs9(vyy350, vyy360)
new_asAs(False, vyy61) → False
new_compare18(vyy6000, vyy500, bf, bg) → new_compare24(vyy6000, vyy500, new_esEs5(vyy6000, vyy500, bf, bg), bf, bg)
new_primMulInt(Pos(vyy5000), Neg(vyy60010)) → Neg(new_primMulNat0(vyy5000, vyy60010))
new_primMulInt(Neg(vyy5000), Pos(vyy60010)) → Neg(new_primMulNat0(vyy5000, vyy60010))
new_lt12(vyy6000, vyy500) → new_esEs10(new_compare27(vyy6000, vyy500))
new_ltEs20(vyy600, vyy50, app(ty_[], bbc)) → new_ltEs11(vyy600, vyy50, bbc)
new_primMulNat0(Zero, Succ(vyy600100)) → Zero
new_primMulNat0(Succ(vyy50000), Zero) → Zero
new_compare8(Double(vyy6000, vyy6001), Double(vyy500, vyy501)) → new_compare11(new_sr(vyy6000, vyy500), new_sr(vyy6001, vyy501))
new_esEs18([], [], bcf) → True
new_esEs21(vyy350, vyy360, app(app(ty_Either, bcg), bch)) → new_esEs5(vyy350, vyy360, bcg, bch)
new_esEs29(vyy35, vyy36, ty_Char) → new_esEs20(vyy35, vyy36)
new_esEs6(Just(vyy350), Just(vyy360), app(ty_Maybe, bgg)) → new_esEs6(vyy350, vyy360, bgg)
new_esEs21(vyy350, vyy360, app(app(ty_FiniteMap, bdf), bdg)) → new_esEs15(vyy350, vyy360, bdf, bdg)
new_esEs25(vyy351, vyy361, ty_@0) → new_esEs16(vyy351, vyy361)
new_lt20(vyy6000, vyy500, app(ty_[], cgd)) → new_lt14(vyy6000, vyy500, cgd)
new_esEs29(vyy35, vyy36, ty_Float) → new_esEs11(vyy35, vyy36)
new_ltEs4(Right(vyy6000), Right(vyy500), dea, ty_@0) → new_ltEs14(vyy6000, vyy500)
new_esEs23(vyy351, vyy361, ty_Ordering) → new_esEs12(vyy351, vyy361)
new_esEs29(vyy35, vyy36, ty_Double) → new_esEs17(vyy35, vyy36)
new_ltEs11(vyy600, vyy50, bbc) → new_not(new_compare(vyy600, vyy50, bbc))
new_esEs24(vyy350, vyy360, ty_Float) → new_esEs11(vyy350, vyy360)
new_not(EQ) → new_not0
new_esEs23(vyy351, vyy361, app(ty_Maybe, ccb)) → new_esEs6(vyy351, vyy361, ccb)
new_lt20(vyy6000, vyy500, app(app(ty_@2, cgh), cha)) → new_lt16(vyy6000, vyy500, cgh, cha)
new_esEs21(vyy350, vyy360, ty_Integer) → new_esEs9(vyy350, vyy360)
new_esEs24(vyy350, vyy360, ty_Char) → new_esEs20(vyy350, vyy360)
new_esEs26(vyy350, vyy360, ty_Integer) → new_esEs9(vyy350, vyy360)
new_ltEs7(Just(vyy6000), Just(vyy500), app(ty_[], bfb)) → new_ltEs11(vyy6000, vyy500, bfb)
new_esEs16(@0, @0) → True
new_lt9(vyy6000, vyy500, app(ty_Maybe, bah)) → new_lt11(vyy6000, vyy500, bah)
new_ltEs19(vyy6001, vyy501, ty_@0) → new_ltEs14(vyy6001, vyy501)
new_compare111(vyy6000, vyy500, False, bah) → GT
new_ltEs6(vyy6002, vyy502, ty_Bool) → new_ltEs8(vyy6002, vyy502)
new_esEs5(Left(vyy350), Left(vyy360), ty_Char, bh) → new_esEs20(vyy350, vyy360)
new_esEs24(vyy350, vyy360, ty_Double) → new_esEs17(vyy350, vyy360)
new_esEs5(Right(vyy350), Right(vyy360), df, app(ty_Maybe, ee)) → new_esEs6(vyy350, vyy360, ee)
new_ltEs7(Just(vyy6000), Just(vyy500), ty_Bool) → new_ltEs8(vyy6000, vyy500)
new_ltEs7(Just(vyy6000), Just(vyy500), ty_@0) → new_ltEs14(vyy6000, vyy500)
new_compare11(vyy600, vyy50) → new_primCmpInt(vyy600, vyy50)
new_esEs14(vyy35, vyy36) → new_primEqInt(vyy35, vyy36)
new_ltEs19(vyy6001, vyy501, app(app(app(ty_@3, cfc), cfd), cfe)) → new_ltEs5(vyy6001, vyy501, cfc, cfd, cfe)
new_esEs25(vyy351, vyy361, app(app(app(ty_@3, chf), chg), chh)) → new_esEs7(vyy351, vyy361, chf, chg, chh)
new_esEs8(@2(vyy350, vyy351), @2(vyy360, vyy361), chb, chc) → new_asAs(new_esEs26(vyy350, vyy360, chb), new_esEs25(vyy351, vyy361, chc))
new_ltEs6(vyy6002, vyy502, ty_Char) → new_ltEs15(vyy6002, vyy502)
new_compare17(vyy6000, vyy500, app(app(app(ty_@3, bca), bcb), bcc)) → new_compare7(vyy6000, vyy500, bca, bcb, bcc)
new_esEs21(vyy350, vyy360, ty_Char) → new_esEs20(vyy350, vyy360)
new_ltEs7(Just(vyy6000), Nothing, bee) → False
new_lt20(vyy6000, vyy500, ty_Int) → new_lt19(vyy6000, vyy500)
new_lt13(vyy6000, vyy500, bba) → new_esEs10(new_compare28(vyy6000, vyy500, bba))
new_not(LT) → new_not0
new_lt18(vyy6000, vyy500) → new_esEs10(new_compare16(vyy6000, vyy500))
new_ltEs19(vyy6001, vyy501, app(ty_Maybe, ceh)) → new_ltEs7(vyy6001, vyy501, ceh)
new_esEs5(Left(vyy350), Left(vyy360), app(app(ty_Either, ca), cb), bh) → new_esEs5(vyy350, vyy360, ca, cb)
new_ltEs7(Just(vyy6000), Just(vyy500), app(app(ty_@2, bff), bfg)) → new_ltEs13(vyy6000, vyy500, bff, bfg)
new_lt20(vyy6000, vyy500, ty_Bool) → new_lt12(vyy6000, vyy500)
new_ltEs4(Left(vyy6000), Left(vyy500), ty_Ordering, dch) → new_ltEs16(vyy6000, vyy500)
new_compare112(vyy6000, vyy500, False) → GT
new_ltEs4(Left(vyy6000), Left(vyy500), app(ty_Maybe, dda), dch) → new_ltEs7(vyy6000, vyy500, dda)
new_ltEs12(vyy600, vyy50) → new_not(new_compare6(vyy600, vyy50))
new_compare210(vyy6000, vyy500, False) → new_compare112(vyy6000, vyy500, new_ltEs8(vyy6000, vyy500))
new_esEs12(GT, GT) → True
new_compare25(vyy6000, vyy500, False, fc, fd, ff) → new_compare12(vyy6000, vyy500, new_ltEs5(vyy6000, vyy500, fc, fd, ff), fc, fd, ff)
new_esEs23(vyy351, vyy361, ty_Char) → new_esEs20(vyy351, vyy361)
new_esEs21(vyy350, vyy360, ty_Float) → new_esEs11(vyy350, vyy360)
new_esEs22(vyy352, vyy362, ty_Int) → new_esEs14(vyy352, vyy362)
new_compare19(vyy6000, vyy500, bah) → new_compare29(vyy6000, vyy500, new_esEs6(vyy6000, vyy500, bah), bah)
new_primPlusNat0(Succ(vyy8100), Succ(vyy6001000)) → Succ(Succ(new_primPlusNat0(vyy8100, vyy6001000)))
new_esEs29(vyy35, vyy36, ty_Ordering) → new_esEs12(vyy35, vyy36)
new_esEs29(vyy35, vyy36, app(ty_[], bcf)) → new_esEs18(vyy35, vyy36, bcf)
new_esEs5(Right(vyy350), Right(vyy360), df, ty_Ordering) → new_esEs12(vyy350, vyy360)
new_ltEs4(Left(vyy6000), Left(vyy500), ty_Double, dch) → new_ltEs10(vyy6000, vyy500)
new_esEs18(:(vyy350, vyy351), :(vyy360, vyy361), bcf) → new_asAs(new_esEs21(vyy350, vyy360, bcf), new_esEs18(vyy351, vyy361, bcf))
new_asAs(True, vyy61) → vyy61
new_compare28(:%(vyy6000, vyy6001), :%(vyy500, vyy501), ty_Int) → new_compare11(new_sr(vyy6000, vyy501), new_sr(vyy500, vyy6001))
new_esEs22(vyy352, vyy362, app(app(ty_@2, cbb), cbc)) → new_esEs8(vyy352, vyy362, cbb, cbc)
new_esEs17(Double(vyy350, vyy351), Double(vyy360, vyy361)) → new_esEs14(new_sr(vyy350, vyy360), new_sr(vyy351, vyy361))
new_ltEs19(vyy6001, vyy501, ty_Float) → new_ltEs12(vyy6001, vyy501)
new_esEs25(vyy351, vyy361, ty_Float) → new_esEs11(vyy351, vyy361)
new_esEs5(Left(vyy350), Left(vyy360), ty_Ordering, bh) → new_esEs12(vyy350, vyy360)
new_ltEs16(LT, LT) → True
new_compare211(vyy6000, vyy500, True) → EQ
new_fmToList(vyy36, bec, bed) → new_foldFM2(vyy36, bec, bed)
new_lt17(vyy6000, vyy500) → new_esEs10(new_compare14(vyy6000, vyy500))
new_compare6(Float(vyy6000, vyy6001), Float(vyy500, vyy501)) → new_compare11(new_sr(vyy6000, vyy500), new_sr(vyy6001, vyy501))
new_esEs24(vyy350, vyy360, app(app(ty_@2, ceb), cec)) → new_esEs8(vyy350, vyy360, ceb, cec)
new_ltEs20(vyy600, vyy50, app(app(ty_@2, ced), cee)) → new_ltEs13(vyy600, vyy50, ced, cee)
new_ltEs4(Left(vyy6000), Left(vyy500), ty_Bool, dch) → new_ltEs8(vyy6000, vyy500)
new_esEs24(vyy350, vyy360, app(ty_Maybe, cdf)) → new_esEs6(vyy350, vyy360, cdf)
new_ltEs20(vyy600, vyy50, app(ty_Maybe, bee)) → new_ltEs7(vyy600, vyy50, bee)
new_esEs5(Right(vyy350), Right(vyy360), df, ty_Char) → new_esEs20(vyy350, vyy360)
new_ltEs4(Right(vyy6000), Right(vyy500), dea, ty_Int) → new_ltEs18(vyy6000, vyy500)
new_lt20(vyy6000, vyy500, app(ty_Ratio, cgc)) → new_lt13(vyy6000, vyy500, cgc)
new_esEs23(vyy351, vyy361, app(ty_[], cce)) → new_esEs18(vyy351, vyy361, cce)
new_esEs5(Left(vyy350), Left(vyy360), ty_Integer, bh) → new_esEs9(vyy350, vyy360)
new_esEs22(vyy352, vyy362, app(app(ty_Either, bhh), caa)) → new_esEs5(vyy352, vyy362, bhh, caa)
new_primCompAux00(vyy66, GT) → GT
new_compare17(vyy6000, vyy500, ty_@0) → new_compare5(vyy6000, vyy500)
new_ltEs7(Just(vyy6000), Just(vyy500), app(ty_Ratio, bfa)) → new_ltEs9(vyy6000, vyy500, bfa)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_lt8(vyy6001, vyy501, ty_Bool) → new_lt12(vyy6001, vyy501)
new_ltEs4(Left(vyy6000), Left(vyy500), app(app(app(ty_@3, ddd), dde), ddf), dch) → new_ltEs5(vyy6000, vyy500, ddd, dde, ddf)
new_esEs5(Right(vyy350), Right(vyy360), df, app(ty_Ratio, ed)) → new_esEs13(vyy350, vyy360, ed)
new_ltEs7(Just(vyy6000), Just(vyy500), app(app(ty_Either, bef), beg)) → new_ltEs4(vyy6000, vyy500, bef, beg)
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primCmpInt(Neg(Succ(vyy60000)), Pos(vyy500)) → LT
new_esEs25(vyy351, vyy361, ty_Integer) → new_esEs9(vyy351, vyy361)
new_ltEs10(vyy600, vyy50) → new_not(new_compare8(vyy600, vyy50))
new_ltEs4(Right(vyy6000), Right(vyy500), dea, app(app(app(ty_@3, deg), deh), dfa)) → new_ltEs5(vyy6000, vyy500, deg, deh, dfa)
The set Q consists of the following terms:
new_lt8(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, ty_Integer)
new_esEs5(Left(x0), Left(x1), ty_Integer, x2)
new_esEs25(x0, x1, ty_Int)
new_esEs26(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs5(Left(x0), Left(x1), ty_Int, x2)
new_ltEs4(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_ltEs20(x0, x1, ty_Integer)
new_ltEs4(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_ltEs6(x0, x1, ty_Float)
new_lt8(x0, x1, ty_Int)
new_esEs25(x0, x1, app(ty_[], x2))
new_lt16(x0, x1, x2, x3)
new_lt9(x0, x1, ty_@0)
new_compare24(x0, x1, False, x2, x3)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs6(Nothing, Just(x0), x1)
new_compare111(x0, x1, False, x2)
new_compare12(x0, x1, True, x2, x3, x4)
new_esEs22(x0, x1, ty_@0)
new_lt9(x0, x1, app(app(ty_@2, x2), x3))
new_pePe(False, x0, x1, x2, x3)
new_ltEs4(Left(x0), Left(x1), ty_Double, x2)
new_ltEs4(Left(x0), Left(x1), ty_Char, x2)
new_ltEs6(x0, x1, app(ty_[], x2))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs5(Left(x0), Left(x1), ty_Bool, x2)
new_ltEs19(x0, x1, ty_Integer)
new_esEs5(Right(x0), Right(x1), x2, ty_@0)
new_esEs22(x0, x1, ty_Char)
new_esEs5(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs7(Nothing, Just(x0), x1)
new_esEs23(x0, x1, ty_Integer)
new_compare110(x0, x1, True)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs21(x0, x1, ty_Double)
new_esEs5(Right(x0), Right(x1), x2, ty_Int)
new_esEs23(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_ltEs19(x0, x1, app(ty_[], x2))
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_primMulNat0(Succ(x0), Zero)
new_esEs26(x0, x1, app(ty_[], x2))
new_esEs26(x0, x1, ty_Char)
new_ltEs7(Just(x0), Just(x1), app(ty_[], x2))
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare110(x0, x1, False)
new_esEs12(EQ, GT)
new_esEs12(GT, EQ)
new_lt10(x0, x1, x2, x3)
new_ltEs6(x0, x1, ty_Char)
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_lt8(x0, x1, app(ty_Maybe, x2))
new_ltEs4(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs10(GT)
new_lt9(x0, x1, app(ty_Ratio, x2))
new_esEs5(Left(x0), Right(x1), x2, x3)
new_esEs5(Right(x0), Left(x1), x2, x3)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_lt20(x0, x1, ty_Int)
new_esEs23(x0, x1, ty_Int)
new_esEs28(x0, x1, ty_Integer)
new_ltEs8(True, True)
new_esEs6(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs5(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs4(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs6(Nothing, Nothing, x0)
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs6(x0, x1, app(ty_Maybe, x2))
new_esEs12(GT, GT)
new_esEs23(x0, x1, ty_Ordering)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_lt8(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs23(x0, x1, ty_Char)
new_ltEs7(Just(x0), Just(x1), ty_@0)
new_esEs16(@0, @0)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs9(x0, x1, x2)
new_esEs5(Right(x0), Right(x1), x2, ty_Double)
new_esEs22(x0, x1, ty_Int)
new_ltEs20(x0, x1, ty_@0)
new_ltEs4(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_compare24(x0, x1, True, x2, x3)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, ty_Ordering)
new_esEs23(x0, x1, ty_Bool)
new_esEs6(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs19(x0, x1, ty_Float)
new_lt14(x0, x1, x2)
new_ltEs7(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs7(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs19(True, True)
new_compare25(x0, x1, True, x2, x3, x4)
new_compare112(x0, x1, True)
new_esEs29(x0, x1, ty_Integer)
new_esEs5(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_compare11(x0, x1)
new_lt8(x0, x1, app(ty_[], x2))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_ltEs4(Left(x0), Left(x1), ty_Bool, x2)
new_esEs5(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs5(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt8(x0, x1, ty_Char)
new_compare5(@0, @0)
new_esEs21(x0, x1, ty_Int)
new_esEs5(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_lt20(x0, x1, ty_Ordering)
new_esEs29(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_compare17(x0, x1, ty_Double)
new_primEqNat0(Zero, Zero)
new_compare9(x0, x1, x2, x3)
new_esEs18(:(x0, x1), :(x2, x3), x4)
new_primPlusNat0(Zero, Succ(x0))
new_ltEs4(Right(x0), Right(x1), x2, ty_Float)
new_lt20(x0, x1, ty_Double)
new_ltEs6(x0, x1, app(ty_Ratio, x2))
new_ltEs6(x0, x1, ty_Ordering)
new_esEs9(Integer(x0), Integer(x1))
new_ltEs4(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs6(Just(x0), Just(x1), ty_Float)
new_esEs29(x0, x1, app(ty_[], x2))
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_lt8(x0, x1, ty_Float)
new_esEs17(Double(x0, x1), Double(x2, x3))
new_esEs29(x0, x1, ty_Float)
new_primMulNat0(Zero, Zero)
new_esEs18([], :(x0, x1), x2)
new_esEs29(x0, x1, ty_Char)
new_esEs6(Just(x0), Just(x1), app(app(ty_FiniteMap, x2), x3))
new_esEs5(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs7(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_compare17(x0, x1, app(ty_[], x2))
new_compare6(Float(x0, x1), Float(x2, x3))
new_ltEs17(x0, x1)
new_esEs25(x0, x1, ty_Integer)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_lt9(x0, x1, app(ty_Maybe, x2))
new_ltEs4(Left(x0), Left(x1), app(ty_[], x2), x3)
new_ltEs7(Just(x0), Just(x1), ty_Bool)
new_esEs25(x0, x1, ty_Double)
new_ltEs6(x0, x1, ty_Double)
new_compare17(x0, x1, ty_Int)
new_compare10(x0, x1, True, x2, x3)
new_lt4(x0, x1)
new_esEs26(x0, x1, ty_Ordering)
new_compare112(x0, x1, False)
new_lt11(x0, x1, x2)
new_esEs23(x0, x1, ty_Float)
new_primMulNat0(Succ(x0), Succ(x1))
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
new_esEs24(x0, x1, ty_Float)
new_ltEs19(x0, x1, ty_Ordering)
new_compare29(x0, x1, True, x2)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs19(x0, x1, ty_Bool)
new_foldFM2(EmptyFM, x0, x1)
new_esEs21(x0, x1, ty_Bool)
new_ltEs6(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, app(ty_[], x2))
new_esEs27(x0, x1, ty_Int)
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, app(ty_[], x2))
new_primCmpNat0(Succ(x0), Succ(x1))
new_compare17(x0, x1, ty_Integer)
new_esEs25(x0, x1, ty_Ordering)
new_compare111(x0, x1, True, x2)
new_ltEs20(x0, x1, ty_Bool)
new_esEs24(x0, x1, ty_@0)
new_esEs24(x0, x1, ty_Double)
new_compare17(x0, x1, app(ty_Ratio, x2))
new_esEs5(Right(x0), Right(x1), x2, app(app(ty_FiniteMap, x3), x4))
new_ltEs13(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs5(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_ltEs4(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs6(Just(x0), Just(x1), ty_Integer)
new_compare210(x0, x1, True)
new_esEs24(x0, x1, ty_Bool)
new_lt20(x0, x1, ty_Char)
new_compare([], :(x0, x1), x2)
new_primEqNat0(Zero, Succ(x0))
new_esEs14(x0, x1)
new_ltEs4(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_lt20(x0, x1, ty_Integer)
new_lt9(x0, x1, ty_Float)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs6(Just(x0), Nothing, x1)
new_esEs19(True, False)
new_esEs19(False, True)
new_ltEs20(x0, x1, ty_Char)
new_esEs12(LT, EQ)
new_esEs12(EQ, LT)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs5(Right(x0), Right(x1), x2, ty_Char)
new_compare14(Char(x0), Char(x1))
new_esEs27(x0, x1, ty_Integer)
new_esEs25(x0, x1, ty_Char)
new_ltEs7(Just(x0), Just(x1), ty_Double)
new_esEs25(x0, x1, ty_Float)
new_sr(x0, x1)
new_compare17(x0, x1, ty_@0)
new_esEs5(Left(x0), Left(x1), app(app(ty_FiniteMap, x2), x3), x4)
new_ltEs18(x0, x1)
new_ltEs7(Just(x0), Just(x1), ty_Ordering)
new_not0
new_esEs29(x0, x1, ty_@0)
new_ltEs19(x0, x1, ty_Char)
new_esEs12(EQ, EQ)
new_ltEs4(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_primPlusNat0(Zero, Zero)
new_ltEs16(EQ, EQ)
new_compare15(x0, x1, False, x2, x3)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_compare210(x0, x1, False)
new_esEs24(x0, x1, ty_Ordering)
new_esEs22(x0, x1, ty_Bool)
new_esEs5(Right(x0), Right(x1), x2, ty_Bool)
new_primPlusNat0(Succ(x0), Succ(x1))
new_esEs6(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_esEs28(x0, x1, ty_Int)
new_esEs6(Just(x0), Just(x1), ty_Ordering)
new_ltEs16(LT, LT)
new_compare211(x0, x1, True)
new_primMulInt(Pos(x0), Pos(x1))
new_ltEs7(Just(x0), Just(x1), ty_Float)
new_lt9(x0, x1, ty_Double)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_lt12(x0, x1)
new_lt8(x0, x1, ty_Integer)
new_esEs5(Left(x0), Left(x1), app(ty_[], x2), x3)
new_lt8(x0, x1, ty_Ordering)
new_esEs25(x0, x1, ty_Bool)
new_ltEs20(x0, x1, app(ty_[], x2))
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_lt9(x0, x1, ty_Char)
new_lt8(x0, x1, app(ty_Ratio, x2))
new_ltEs4(Left(x0), Left(x1), ty_Ordering, x2)
new_lt20(x0, x1, app(ty_[], x2))
new_lt6(x0, x1)
new_ltEs4(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs16(GT, LT)
new_ltEs16(LT, GT)
new_ltEs7(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_ltEs6(x0, x1, app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_esEs21(x0, x1, ty_Float)
new_not(GT)
new_ltEs4(Right(x0), Right(x1), x2, ty_@0)
new_ltEs8(False, False)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare17(x0, x1, app(ty_Maybe, x2))
new_ltEs4(Left(x0), Left(x1), ty_Float, x2)
new_asAs(False, x0)
new_esEs26(x0, x1, ty_Float)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_primEqNat0(Succ(x0), Zero)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_lt20(x0, x1, ty_Float)
new_asAs(True, x0)
new_primEqInt(Neg(Zero), Pos(Zero))
new_primEqInt(Pos(Zero), Neg(Zero))
new_ltEs10(x0, x1)
new_ltEs8(False, True)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs8(True, False)
new_lt15(x0, x1, x2, x3, x4)
new_compare17(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs5(Right(x0), Right(x1), x2, ty_Integer)
new_esEs25(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs5(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_pePe(True, x0, x1, x2, x3)
new_ltEs14(x0, x1)
new_primCmpNat0(Succ(x0), Zero)
new_esEs26(x0, x1, ty_Double)
new_compare26(x0, x1, False, x2, x3)
new_compare12(x0, x1, False, x2, x3, x4)
new_ltEs4(Left(x0), Right(x1), x2, x3)
new_ltEs4(Right(x0), Left(x1), x2, x3)
new_esEs19(False, False)
new_compare15(x0, x1, True, x2, x3)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_lt19(x0, x1)
new_esEs6(Just(x0), Just(x1), ty_Int)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_lt20(x0, x1, app(ty_Ratio, x2))
new_ltEs6(x0, x1, ty_@0)
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs24(x0, x1, ty_Integer)
new_primEqInt(Neg(Zero), Neg(Zero))
new_ltEs20(x0, x1, ty_Float)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_compare17(x0, x1, ty_Float)
new_lt8(x0, x1, ty_Double)
new_primCompAux0(x0, x1, x2, x3)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_compare26(x0, x1, True, x2, x3)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_ltEs4(Left(x0), Left(x1), ty_@0, x2)
new_fmToList(x0, x1, x2)
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs7(Just(x0), Just(x1), ty_Char)
new_esEs26(x0, x1, ty_Integer)
new_esEs24(x0, x1, ty_Int)
new_compare17(x0, x1, ty_Ordering)
new_compare28(:%(x0, x1), :%(x2, x3), ty_Integer)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_ltEs16(GT, GT)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_esEs5(Left(x0), Left(x1), ty_Char, x2)
new_esEs18(:(x0, x1), [], x2)
new_ltEs7(Just(x0), Nothing, x1)
new_esEs5(Left(x0), Left(x1), ty_@0, x2)
new_compare29(x0, x1, False, x2)
new_compare28(:%(x0, x1), :%(x2, x3), ty_Int)
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs29(x0, x1, ty_Ordering)
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_esEs24(x0, x1, app(ty_[], x2))
new_ltEs6(x0, x1, ty_Bool)
new_esEs29(x0, x1, ty_Int)
new_compare13(x0, x1)
new_ltEs4(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs6(Just(x0), Just(x1), ty_@0)
new_esEs26(x0, x1, ty_@0)
new_esEs10(EQ)
new_ltEs12(x0, x1)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_compare17(x0, x1, ty_Char)
new_lt9(x0, x1, ty_Ordering)
new_primCmpNat0(Zero, Zero)
new_esEs5(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_ltEs7(Just(x0), Just(x1), ty_Integer)
new_esEs21(x0, x1, ty_Char)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_esEs29(x0, x1, ty_Bool)
new_esEs6(Just(x0), Just(x1), ty_Double)
new_primPlusNat0(Succ(x0), Zero)
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, ty_Bool)
new_primCompAux00(x0, EQ)
new_ltEs4(Right(x0), Right(x1), x2, ty_Int)
new_esEs8(@2(x0, x1), @2(x2, x3), x4, x5)
new_lt9(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_sr0(Integer(x0), Integer(x1))
new_esEs24(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_compare27(x0, x1)
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, ty_Ordering)
new_primMulNat0(Zero, Succ(x0))
new_compare25(x0, x1, False, x2, x3, x4)
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs6(x0, x1, ty_Int)
new_compare18(x0, x1, x2, x3)
new_compare([], [], x0)
new_primCmpNat0(Zero, Succ(x0))
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_primCompAux00(x0, GT)
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_lt9(x0, x1, app(app(ty_Either, x2), x3))
new_compare17(x0, x1, app(app(ty_@2, x2), x3))
new_esEs24(x0, x1, ty_Char)
new_esEs5(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs10(LT)
new_esEs6(Just(x0), Just(x1), ty_Bool)
new_ltEs11(x0, x1, x2)
new_lt8(x0, x1, app(app(ty_@2, x2), x3))
new_esEs21(x0, x1, ty_Integer)
new_lt17(x0, x1)
new_ltEs6(x0, x1, ty_Integer)
new_ltEs7(Nothing, Nothing, x0)
new_esEs25(x0, x1, ty_@0)
new_lt20(x0, x1, ty_Bool)
new_ltEs7(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs21(x0, x1, app(ty_[], x2))
new_primCompAux00(x0, LT)
new_not(EQ)
new_esEs11(Float(x0, x1), Float(x2, x3))
new_ltEs4(Right(x0), Right(x1), x2, ty_Double)
new_ltEs16(GT, EQ)
new_ltEs16(EQ, GT)
new_ltEs20(x0, x1, ty_Double)
new_compare(:(x0, x1), :(x2, x3), x4)
new_esEs5(Right(x0), Right(x1), x2, ty_Float)
new_primPlusNat1(Zero, x0)
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt9(x0, x1, ty_Bool)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_esEs22(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_ltEs6(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs5(Right(x0), Right(x1), x2, ty_Ordering)
new_ltEs16(LT, EQ)
new_ltEs16(EQ, LT)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_esEs5(Left(x0), Left(x1), ty_Float, x2)
new_ltEs4(Left(x0), Left(x1), ty_Integer, x2)
new_compare(:(x0, x1), [], x2)
new_esEs5(Left(x0), Left(x1), ty_Double, x2)
new_esEs26(x0, x1, ty_Int)
new_ltEs4(Right(x0), Right(x1), x2, ty_Integer)
new_lt5(x0, x1)
new_sizeFM(EmptyFM, x0, x1)
new_compare17(x0, x1, ty_Bool)
new_esEs21(x0, x1, ty_Ordering)
new_compare10(x0, x1, False, x2, x3)
new_compare8(Double(x0, x1), Double(x2, x3))
new_ltEs4(Left(x0), Left(x1), ty_Int, x2)
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs20(Char(x0), Char(x1))
new_esEs21(x0, x1, ty_@0)
new_esEs6(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs7(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs23(x0, x1, ty_@0)
new_esEs5(Left(x0), Left(x1), ty_Ordering, x2)
new_ltEs4(Right(x0), Right(x1), x2, ty_Char)
new_ltEs5(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_ltEs19(x0, x1, ty_@0)
new_lt7(x0, x1)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_esEs6(Just(x0), Just(x1), ty_Char)
new_lt8(x0, x1, ty_@0)
new_lt9(x0, x1, ty_Integer)
new_esEs18([], [], x0)
new_compare7(x0, x1, x2, x3, x4)
new_lt9(x0, x1, ty_Int)
new_ltEs19(x0, x1, ty_Double)
new_lt8(x0, x1, ty_Bool)
new_lt9(x0, x1, app(ty_[], x2))
new_esEs15(x0, x1, x2, x3)
new_esEs13(:%(x0, x1), :%(x2, x3), x4)
new_compare16(Integer(x0), Integer(x1))
new_esEs6(Just(x0), Just(x1), app(ty_Maybe, x2))
new_ltEs19(x0, x1, ty_Int)
new_lt13(x0, x1, x2)
new_esEs23(x0, x1, ty_Double)
new_esEs22(x0, x1, ty_Double)
new_primEqInt(Pos(Zero), Pos(Zero))
new_ltEs4(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_lt18(x0, x1)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_compare17(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs4(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs20(x0, x1, ty_Int)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, ty_@0)
new_compare19(x0, x1, x2)
new_esEs29(x0, x1, ty_Double)
new_primPlusNat1(Succ(x0), x1)
new_ltEs7(Just(x0), Just(x1), ty_Int)
new_esEs12(LT, LT)
new_not(LT)
new_esEs22(x0, x1, ty_Float)
new_ltEs15(x0, x1)
new_compare211(x0, x1, False)
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
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QReductionProof
Q DP problem:
The TRS P consists of the following rules:
new_foldFM_LE(vyy3, Nothing, Branch(Just(vyy600), vyy61, vyy62, vyy63, vyy64), h, ba, bb) → new_foldFM_LE(vyy3, Nothing, vyy63, h, ba, bb)
new_foldFM_LE(vyy3, Nothing, Branch(Nothing, vyy61, vyy62, vyy63, vyy64), h, ba, bb) → new_foldFM_LE(vyy3, Nothing, vyy64, h, ba, bb)
new_foldFM_LE(vyy3, Nothing, Branch(Nothing, vyy61, vyy62, vyy63, vyy64), h, ba, bb) → new_foldFM_LE(vyy3, Nothing, vyy63, h, ba, bb)
R is empty.
The set Q consists of the following terms:
new_lt8(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, ty_Integer)
new_esEs5(Left(x0), Left(x1), ty_Integer, x2)
new_esEs25(x0, x1, ty_Int)
new_esEs26(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs5(Left(x0), Left(x1), ty_Int, x2)
new_ltEs4(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_ltEs20(x0, x1, ty_Integer)
new_ltEs4(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_ltEs6(x0, x1, ty_Float)
new_lt8(x0, x1, ty_Int)
new_esEs25(x0, x1, app(ty_[], x2))
new_lt16(x0, x1, x2, x3)
new_lt9(x0, x1, ty_@0)
new_compare24(x0, x1, False, x2, x3)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs6(Nothing, Just(x0), x1)
new_compare111(x0, x1, False, x2)
new_compare12(x0, x1, True, x2, x3, x4)
new_esEs22(x0, x1, ty_@0)
new_lt9(x0, x1, app(app(ty_@2, x2), x3))
new_pePe(False, x0, x1, x2, x3)
new_ltEs4(Left(x0), Left(x1), ty_Double, x2)
new_ltEs4(Left(x0), Left(x1), ty_Char, x2)
new_ltEs6(x0, x1, app(ty_[], x2))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs5(Left(x0), Left(x1), ty_Bool, x2)
new_ltEs19(x0, x1, ty_Integer)
new_esEs5(Right(x0), Right(x1), x2, ty_@0)
new_esEs22(x0, x1, ty_Char)
new_esEs5(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs7(Nothing, Just(x0), x1)
new_esEs23(x0, x1, ty_Integer)
new_compare110(x0, x1, True)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs21(x0, x1, ty_Double)
new_esEs5(Right(x0), Right(x1), x2, ty_Int)
new_esEs23(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_ltEs19(x0, x1, app(ty_[], x2))
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_primMulNat0(Succ(x0), Zero)
new_esEs26(x0, x1, app(ty_[], x2))
new_esEs26(x0, x1, ty_Char)
new_ltEs7(Just(x0), Just(x1), app(ty_[], x2))
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare110(x0, x1, False)
new_esEs12(EQ, GT)
new_esEs12(GT, EQ)
new_lt10(x0, x1, x2, x3)
new_ltEs6(x0, x1, ty_Char)
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_lt8(x0, x1, app(ty_Maybe, x2))
new_ltEs4(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs10(GT)
new_lt9(x0, x1, app(ty_Ratio, x2))
new_esEs5(Left(x0), Right(x1), x2, x3)
new_esEs5(Right(x0), Left(x1), x2, x3)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_lt20(x0, x1, ty_Int)
new_esEs23(x0, x1, ty_Int)
new_esEs28(x0, x1, ty_Integer)
new_ltEs8(True, True)
new_esEs6(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs5(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs4(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs6(Nothing, Nothing, x0)
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs6(x0, x1, app(ty_Maybe, x2))
new_esEs12(GT, GT)
new_esEs23(x0, x1, ty_Ordering)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_lt8(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs23(x0, x1, ty_Char)
new_ltEs7(Just(x0), Just(x1), ty_@0)
new_esEs16(@0, @0)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs9(x0, x1, x2)
new_esEs5(Right(x0), Right(x1), x2, ty_Double)
new_esEs22(x0, x1, ty_Int)
new_ltEs20(x0, x1, ty_@0)
new_ltEs4(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_compare24(x0, x1, True, x2, x3)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, ty_Ordering)
new_esEs23(x0, x1, ty_Bool)
new_esEs6(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs19(x0, x1, ty_Float)
new_lt14(x0, x1, x2)
new_ltEs7(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs7(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs19(True, True)
new_compare25(x0, x1, True, x2, x3, x4)
new_compare112(x0, x1, True)
new_esEs29(x0, x1, ty_Integer)
new_esEs5(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_compare11(x0, x1)
new_lt8(x0, x1, app(ty_[], x2))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_ltEs4(Left(x0), Left(x1), ty_Bool, x2)
new_esEs5(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs5(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt8(x0, x1, ty_Char)
new_compare5(@0, @0)
new_esEs21(x0, x1, ty_Int)
new_esEs5(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_lt20(x0, x1, ty_Ordering)
new_esEs29(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_compare17(x0, x1, ty_Double)
new_primEqNat0(Zero, Zero)
new_compare9(x0, x1, x2, x3)
new_esEs18(:(x0, x1), :(x2, x3), x4)
new_primPlusNat0(Zero, Succ(x0))
new_ltEs4(Right(x0), Right(x1), x2, ty_Float)
new_lt20(x0, x1, ty_Double)
new_ltEs6(x0, x1, app(ty_Ratio, x2))
new_ltEs6(x0, x1, ty_Ordering)
new_esEs9(Integer(x0), Integer(x1))
new_ltEs4(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs6(Just(x0), Just(x1), ty_Float)
new_esEs29(x0, x1, app(ty_[], x2))
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_lt8(x0, x1, ty_Float)
new_esEs17(Double(x0, x1), Double(x2, x3))
new_esEs29(x0, x1, ty_Float)
new_primMulNat0(Zero, Zero)
new_esEs18([], :(x0, x1), x2)
new_esEs29(x0, x1, ty_Char)
new_esEs6(Just(x0), Just(x1), app(app(ty_FiniteMap, x2), x3))
new_esEs5(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs7(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_compare17(x0, x1, app(ty_[], x2))
new_compare6(Float(x0, x1), Float(x2, x3))
new_ltEs17(x0, x1)
new_esEs25(x0, x1, ty_Integer)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_lt9(x0, x1, app(ty_Maybe, x2))
new_ltEs4(Left(x0), Left(x1), app(ty_[], x2), x3)
new_ltEs7(Just(x0), Just(x1), ty_Bool)
new_esEs25(x0, x1, ty_Double)
new_ltEs6(x0, x1, ty_Double)
new_compare17(x0, x1, ty_Int)
new_compare10(x0, x1, True, x2, x3)
new_lt4(x0, x1)
new_esEs26(x0, x1, ty_Ordering)
new_compare112(x0, x1, False)
new_lt11(x0, x1, x2)
new_esEs23(x0, x1, ty_Float)
new_primMulNat0(Succ(x0), Succ(x1))
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
new_esEs24(x0, x1, ty_Float)
new_ltEs19(x0, x1, ty_Ordering)
new_compare29(x0, x1, True, x2)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs19(x0, x1, ty_Bool)
new_foldFM2(EmptyFM, x0, x1)
new_esEs21(x0, x1, ty_Bool)
new_ltEs6(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, app(ty_[], x2))
new_esEs27(x0, x1, ty_Int)
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, app(ty_[], x2))
new_primCmpNat0(Succ(x0), Succ(x1))
new_compare17(x0, x1, ty_Integer)
new_esEs25(x0, x1, ty_Ordering)
new_compare111(x0, x1, True, x2)
new_ltEs20(x0, x1, ty_Bool)
new_esEs24(x0, x1, ty_@0)
new_esEs24(x0, x1, ty_Double)
new_compare17(x0, x1, app(ty_Ratio, x2))
new_esEs5(Right(x0), Right(x1), x2, app(app(ty_FiniteMap, x3), x4))
new_ltEs13(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs5(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_ltEs4(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs6(Just(x0), Just(x1), ty_Integer)
new_compare210(x0, x1, True)
new_esEs24(x0, x1, ty_Bool)
new_lt20(x0, x1, ty_Char)
new_compare([], :(x0, x1), x2)
new_primEqNat0(Zero, Succ(x0))
new_esEs14(x0, x1)
new_ltEs4(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_lt20(x0, x1, ty_Integer)
new_lt9(x0, x1, ty_Float)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs6(Just(x0), Nothing, x1)
new_esEs19(True, False)
new_esEs19(False, True)
new_ltEs20(x0, x1, ty_Char)
new_esEs12(LT, EQ)
new_esEs12(EQ, LT)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs5(Right(x0), Right(x1), x2, ty_Char)
new_compare14(Char(x0), Char(x1))
new_esEs27(x0, x1, ty_Integer)
new_esEs25(x0, x1, ty_Char)
new_ltEs7(Just(x0), Just(x1), ty_Double)
new_esEs25(x0, x1, ty_Float)
new_sr(x0, x1)
new_compare17(x0, x1, ty_@0)
new_esEs5(Left(x0), Left(x1), app(app(ty_FiniteMap, x2), x3), x4)
new_ltEs18(x0, x1)
new_ltEs7(Just(x0), Just(x1), ty_Ordering)
new_not0
new_esEs29(x0, x1, ty_@0)
new_ltEs19(x0, x1, ty_Char)
new_esEs12(EQ, EQ)
new_ltEs4(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_primPlusNat0(Zero, Zero)
new_ltEs16(EQ, EQ)
new_compare15(x0, x1, False, x2, x3)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_compare210(x0, x1, False)
new_esEs24(x0, x1, ty_Ordering)
new_esEs22(x0, x1, ty_Bool)
new_esEs5(Right(x0), Right(x1), x2, ty_Bool)
new_primPlusNat0(Succ(x0), Succ(x1))
new_esEs6(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_esEs28(x0, x1, ty_Int)
new_esEs6(Just(x0), Just(x1), ty_Ordering)
new_ltEs16(LT, LT)
new_compare211(x0, x1, True)
new_primMulInt(Pos(x0), Pos(x1))
new_ltEs7(Just(x0), Just(x1), ty_Float)
new_lt9(x0, x1, ty_Double)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_lt12(x0, x1)
new_lt8(x0, x1, ty_Integer)
new_esEs5(Left(x0), Left(x1), app(ty_[], x2), x3)
new_lt8(x0, x1, ty_Ordering)
new_esEs25(x0, x1, ty_Bool)
new_ltEs20(x0, x1, app(ty_[], x2))
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_lt9(x0, x1, ty_Char)
new_lt8(x0, x1, app(ty_Ratio, x2))
new_ltEs4(Left(x0), Left(x1), ty_Ordering, x2)
new_lt20(x0, x1, app(ty_[], x2))
new_lt6(x0, x1)
new_ltEs4(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs16(GT, LT)
new_ltEs16(LT, GT)
new_ltEs7(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_ltEs6(x0, x1, app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_esEs21(x0, x1, ty_Float)
new_not(GT)
new_ltEs4(Right(x0), Right(x1), x2, ty_@0)
new_ltEs8(False, False)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare17(x0, x1, app(ty_Maybe, x2))
new_ltEs4(Left(x0), Left(x1), ty_Float, x2)
new_asAs(False, x0)
new_esEs26(x0, x1, ty_Float)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_primEqNat0(Succ(x0), Zero)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_lt20(x0, x1, ty_Float)
new_asAs(True, x0)
new_primEqInt(Neg(Zero), Pos(Zero))
new_primEqInt(Pos(Zero), Neg(Zero))
new_ltEs10(x0, x1)
new_ltEs8(False, True)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs8(True, False)
new_lt15(x0, x1, x2, x3, x4)
new_compare17(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs5(Right(x0), Right(x1), x2, ty_Integer)
new_esEs25(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs5(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_pePe(True, x0, x1, x2, x3)
new_ltEs14(x0, x1)
new_primCmpNat0(Succ(x0), Zero)
new_esEs26(x0, x1, ty_Double)
new_compare26(x0, x1, False, x2, x3)
new_compare12(x0, x1, False, x2, x3, x4)
new_ltEs4(Left(x0), Right(x1), x2, x3)
new_ltEs4(Right(x0), Left(x1), x2, x3)
new_esEs19(False, False)
new_compare15(x0, x1, True, x2, x3)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_lt19(x0, x1)
new_esEs6(Just(x0), Just(x1), ty_Int)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_lt20(x0, x1, app(ty_Ratio, x2))
new_ltEs6(x0, x1, ty_@0)
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs24(x0, x1, ty_Integer)
new_primEqInt(Neg(Zero), Neg(Zero))
new_ltEs20(x0, x1, ty_Float)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_compare17(x0, x1, ty_Float)
new_lt8(x0, x1, ty_Double)
new_primCompAux0(x0, x1, x2, x3)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_compare26(x0, x1, True, x2, x3)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_ltEs4(Left(x0), Left(x1), ty_@0, x2)
new_fmToList(x0, x1, x2)
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs7(Just(x0), Just(x1), ty_Char)
new_esEs26(x0, x1, ty_Integer)
new_esEs24(x0, x1, ty_Int)
new_compare17(x0, x1, ty_Ordering)
new_compare28(:%(x0, x1), :%(x2, x3), ty_Integer)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_ltEs16(GT, GT)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_esEs5(Left(x0), Left(x1), ty_Char, x2)
new_esEs18(:(x0, x1), [], x2)
new_ltEs7(Just(x0), Nothing, x1)
new_esEs5(Left(x0), Left(x1), ty_@0, x2)
new_compare29(x0, x1, False, x2)
new_compare28(:%(x0, x1), :%(x2, x3), ty_Int)
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs29(x0, x1, ty_Ordering)
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_esEs24(x0, x1, app(ty_[], x2))
new_ltEs6(x0, x1, ty_Bool)
new_esEs29(x0, x1, ty_Int)
new_compare13(x0, x1)
new_ltEs4(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs6(Just(x0), Just(x1), ty_@0)
new_esEs26(x0, x1, ty_@0)
new_esEs10(EQ)
new_ltEs12(x0, x1)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_compare17(x0, x1, ty_Char)
new_lt9(x0, x1, ty_Ordering)
new_primCmpNat0(Zero, Zero)
new_esEs5(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_ltEs7(Just(x0), Just(x1), ty_Integer)
new_esEs21(x0, x1, ty_Char)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_esEs29(x0, x1, ty_Bool)
new_esEs6(Just(x0), Just(x1), ty_Double)
new_primPlusNat0(Succ(x0), Zero)
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, ty_Bool)
new_primCompAux00(x0, EQ)
new_ltEs4(Right(x0), Right(x1), x2, ty_Int)
new_esEs8(@2(x0, x1), @2(x2, x3), x4, x5)
new_lt9(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_sr0(Integer(x0), Integer(x1))
new_esEs24(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_compare27(x0, x1)
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, ty_Ordering)
new_primMulNat0(Zero, Succ(x0))
new_compare25(x0, x1, False, x2, x3, x4)
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs6(x0, x1, ty_Int)
new_compare18(x0, x1, x2, x3)
new_compare([], [], x0)
new_primCmpNat0(Zero, Succ(x0))
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_primCompAux00(x0, GT)
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_lt9(x0, x1, app(app(ty_Either, x2), x3))
new_compare17(x0, x1, app(app(ty_@2, x2), x3))
new_esEs24(x0, x1, ty_Char)
new_esEs5(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs10(LT)
new_esEs6(Just(x0), Just(x1), ty_Bool)
new_ltEs11(x0, x1, x2)
new_lt8(x0, x1, app(app(ty_@2, x2), x3))
new_esEs21(x0, x1, ty_Integer)
new_lt17(x0, x1)
new_ltEs6(x0, x1, ty_Integer)
new_ltEs7(Nothing, Nothing, x0)
new_esEs25(x0, x1, ty_@0)
new_lt20(x0, x1, ty_Bool)
new_ltEs7(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs21(x0, x1, app(ty_[], x2))
new_primCompAux00(x0, LT)
new_not(EQ)
new_esEs11(Float(x0, x1), Float(x2, x3))
new_ltEs4(Right(x0), Right(x1), x2, ty_Double)
new_ltEs16(GT, EQ)
new_ltEs16(EQ, GT)
new_ltEs20(x0, x1, ty_Double)
new_compare(:(x0, x1), :(x2, x3), x4)
new_esEs5(Right(x0), Right(x1), x2, ty_Float)
new_primPlusNat1(Zero, x0)
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt9(x0, x1, ty_Bool)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_esEs22(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_ltEs6(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs5(Right(x0), Right(x1), x2, ty_Ordering)
new_ltEs16(LT, EQ)
new_ltEs16(EQ, LT)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_esEs5(Left(x0), Left(x1), ty_Float, x2)
new_ltEs4(Left(x0), Left(x1), ty_Integer, x2)
new_compare(:(x0, x1), [], x2)
new_esEs5(Left(x0), Left(x1), ty_Double, x2)
new_esEs26(x0, x1, ty_Int)
new_ltEs4(Right(x0), Right(x1), x2, ty_Integer)
new_lt5(x0, x1)
new_sizeFM(EmptyFM, x0, x1)
new_compare17(x0, x1, ty_Bool)
new_esEs21(x0, x1, ty_Ordering)
new_compare10(x0, x1, False, x2, x3)
new_compare8(Double(x0, x1), Double(x2, x3))
new_ltEs4(Left(x0), Left(x1), ty_Int, x2)
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs20(Char(x0), Char(x1))
new_esEs21(x0, x1, ty_@0)
new_esEs6(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs7(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs23(x0, x1, ty_@0)
new_esEs5(Left(x0), Left(x1), ty_Ordering, x2)
new_ltEs4(Right(x0), Right(x1), x2, ty_Char)
new_ltEs5(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_ltEs19(x0, x1, ty_@0)
new_lt7(x0, x1)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_esEs6(Just(x0), Just(x1), ty_Char)
new_lt8(x0, x1, ty_@0)
new_lt9(x0, x1, ty_Integer)
new_esEs18([], [], x0)
new_compare7(x0, x1, x2, x3, x4)
new_lt9(x0, x1, ty_Int)
new_ltEs19(x0, x1, ty_Double)
new_lt8(x0, x1, ty_Bool)
new_lt9(x0, x1, app(ty_[], x2))
new_esEs15(x0, x1, x2, x3)
new_esEs13(:%(x0, x1), :%(x2, x3), x4)
new_compare16(Integer(x0), Integer(x1))
new_esEs6(Just(x0), Just(x1), app(ty_Maybe, x2))
new_ltEs19(x0, x1, ty_Int)
new_lt13(x0, x1, x2)
new_esEs23(x0, x1, ty_Double)
new_esEs22(x0, x1, ty_Double)
new_primEqInt(Pos(Zero), Pos(Zero))
new_ltEs4(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_lt18(x0, x1)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_compare17(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs4(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs20(x0, x1, ty_Int)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, ty_@0)
new_compare19(x0, x1, x2)
new_esEs29(x0, x1, ty_Double)
new_primPlusNat1(Succ(x0), x1)
new_ltEs7(Just(x0), Just(x1), ty_Int)
new_esEs12(LT, LT)
new_not(LT)
new_esEs22(x0, x1, ty_Float)
new_ltEs15(x0, x1)
new_compare211(x0, x1, False)
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_lt8(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, ty_Integer)
new_esEs5(Left(x0), Left(x1), ty_Integer, x2)
new_esEs25(x0, x1, ty_Int)
new_esEs26(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs5(Left(x0), Left(x1), ty_Int, x2)
new_ltEs4(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_ltEs20(x0, x1, ty_Integer)
new_ltEs4(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_ltEs6(x0, x1, ty_Float)
new_lt8(x0, x1, ty_Int)
new_esEs25(x0, x1, app(ty_[], x2))
new_lt16(x0, x1, x2, x3)
new_lt9(x0, x1, ty_@0)
new_compare24(x0, x1, False, x2, x3)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs6(Nothing, Just(x0), x1)
new_compare111(x0, x1, False, x2)
new_compare12(x0, x1, True, x2, x3, x4)
new_esEs22(x0, x1, ty_@0)
new_lt9(x0, x1, app(app(ty_@2, x2), x3))
new_pePe(False, x0, x1, x2, x3)
new_ltEs4(Left(x0), Left(x1), ty_Double, x2)
new_ltEs4(Left(x0), Left(x1), ty_Char, x2)
new_ltEs6(x0, x1, app(ty_[], x2))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs5(Left(x0), Left(x1), ty_Bool, x2)
new_ltEs19(x0, x1, ty_Integer)
new_esEs5(Right(x0), Right(x1), x2, ty_@0)
new_esEs22(x0, x1, ty_Char)
new_esEs5(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs7(Nothing, Just(x0), x1)
new_esEs23(x0, x1, ty_Integer)
new_compare110(x0, x1, True)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs21(x0, x1, ty_Double)
new_esEs5(Right(x0), Right(x1), x2, ty_Int)
new_esEs23(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_ltEs19(x0, x1, app(ty_[], x2))
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_primMulNat0(Succ(x0), Zero)
new_esEs26(x0, x1, app(ty_[], x2))
new_esEs26(x0, x1, ty_Char)
new_ltEs7(Just(x0), Just(x1), app(ty_[], x2))
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare110(x0, x1, False)
new_esEs12(EQ, GT)
new_esEs12(GT, EQ)
new_lt10(x0, x1, x2, x3)
new_ltEs6(x0, x1, ty_Char)
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_lt8(x0, x1, app(ty_Maybe, x2))
new_ltEs4(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs10(GT)
new_lt9(x0, x1, app(ty_Ratio, x2))
new_esEs5(Left(x0), Right(x1), x2, x3)
new_esEs5(Right(x0), Left(x1), x2, x3)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_lt20(x0, x1, ty_Int)
new_esEs23(x0, x1, ty_Int)
new_esEs28(x0, x1, ty_Integer)
new_ltEs8(True, True)
new_esEs6(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs5(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs4(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs6(Nothing, Nothing, x0)
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs6(x0, x1, app(ty_Maybe, x2))
new_esEs12(GT, GT)
new_esEs23(x0, x1, ty_Ordering)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_lt8(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs23(x0, x1, ty_Char)
new_ltEs7(Just(x0), Just(x1), ty_@0)
new_esEs16(@0, @0)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs9(x0, x1, x2)
new_esEs5(Right(x0), Right(x1), x2, ty_Double)
new_esEs22(x0, x1, ty_Int)
new_ltEs20(x0, x1, ty_@0)
new_ltEs4(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_compare24(x0, x1, True, x2, x3)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, ty_Ordering)
new_esEs23(x0, x1, ty_Bool)
new_esEs6(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs19(x0, x1, ty_Float)
new_lt14(x0, x1, x2)
new_ltEs7(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs7(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs19(True, True)
new_compare25(x0, x1, True, x2, x3, x4)
new_compare112(x0, x1, True)
new_esEs29(x0, x1, ty_Integer)
new_esEs5(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_compare11(x0, x1)
new_lt8(x0, x1, app(ty_[], x2))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_ltEs4(Left(x0), Left(x1), ty_Bool, x2)
new_esEs5(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs5(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt8(x0, x1, ty_Char)
new_compare5(@0, @0)
new_esEs21(x0, x1, ty_Int)
new_esEs5(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_lt20(x0, x1, ty_Ordering)
new_esEs29(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_compare17(x0, x1, ty_Double)
new_primEqNat0(Zero, Zero)
new_compare9(x0, x1, x2, x3)
new_esEs18(:(x0, x1), :(x2, x3), x4)
new_primPlusNat0(Zero, Succ(x0))
new_ltEs4(Right(x0), Right(x1), x2, ty_Float)
new_lt20(x0, x1, ty_Double)
new_ltEs6(x0, x1, app(ty_Ratio, x2))
new_ltEs6(x0, x1, ty_Ordering)
new_esEs9(Integer(x0), Integer(x1))
new_ltEs4(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs6(Just(x0), Just(x1), ty_Float)
new_esEs29(x0, x1, app(ty_[], x2))
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_lt8(x0, x1, ty_Float)
new_esEs17(Double(x0, x1), Double(x2, x3))
new_esEs29(x0, x1, ty_Float)
new_primMulNat0(Zero, Zero)
new_esEs18([], :(x0, x1), x2)
new_esEs29(x0, x1, ty_Char)
new_esEs6(Just(x0), Just(x1), app(app(ty_FiniteMap, x2), x3))
new_esEs5(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs7(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_compare17(x0, x1, app(ty_[], x2))
new_compare6(Float(x0, x1), Float(x2, x3))
new_ltEs17(x0, x1)
new_esEs25(x0, x1, ty_Integer)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_lt9(x0, x1, app(ty_Maybe, x2))
new_ltEs4(Left(x0), Left(x1), app(ty_[], x2), x3)
new_ltEs7(Just(x0), Just(x1), ty_Bool)
new_esEs25(x0, x1, ty_Double)
new_ltEs6(x0, x1, ty_Double)
new_compare17(x0, x1, ty_Int)
new_compare10(x0, x1, True, x2, x3)
new_lt4(x0, x1)
new_esEs26(x0, x1, ty_Ordering)
new_compare112(x0, x1, False)
new_lt11(x0, x1, x2)
new_esEs23(x0, x1, ty_Float)
new_primMulNat0(Succ(x0), Succ(x1))
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
new_esEs24(x0, x1, ty_Float)
new_ltEs19(x0, x1, ty_Ordering)
new_compare29(x0, x1, True, x2)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs19(x0, x1, ty_Bool)
new_foldFM2(EmptyFM, x0, x1)
new_esEs21(x0, x1, ty_Bool)
new_ltEs6(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, app(ty_[], x2))
new_esEs27(x0, x1, ty_Int)
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, app(ty_[], x2))
new_primCmpNat0(Succ(x0), Succ(x1))
new_compare17(x0, x1, ty_Integer)
new_esEs25(x0, x1, ty_Ordering)
new_compare111(x0, x1, True, x2)
new_ltEs20(x0, x1, ty_Bool)
new_esEs24(x0, x1, ty_@0)
new_esEs24(x0, x1, ty_Double)
new_compare17(x0, x1, app(ty_Ratio, x2))
new_esEs5(Right(x0), Right(x1), x2, app(app(ty_FiniteMap, x3), x4))
new_ltEs13(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs5(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_ltEs4(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs6(Just(x0), Just(x1), ty_Integer)
new_compare210(x0, x1, True)
new_esEs24(x0, x1, ty_Bool)
new_lt20(x0, x1, ty_Char)
new_compare([], :(x0, x1), x2)
new_primEqNat0(Zero, Succ(x0))
new_esEs14(x0, x1)
new_ltEs4(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_lt20(x0, x1, ty_Integer)
new_lt9(x0, x1, ty_Float)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs6(Just(x0), Nothing, x1)
new_esEs19(True, False)
new_esEs19(False, True)
new_ltEs20(x0, x1, ty_Char)
new_esEs12(LT, EQ)
new_esEs12(EQ, LT)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs5(Right(x0), Right(x1), x2, ty_Char)
new_compare14(Char(x0), Char(x1))
new_esEs27(x0, x1, ty_Integer)
new_esEs25(x0, x1, ty_Char)
new_ltEs7(Just(x0), Just(x1), ty_Double)
new_esEs25(x0, x1, ty_Float)
new_sr(x0, x1)
new_compare17(x0, x1, ty_@0)
new_esEs5(Left(x0), Left(x1), app(app(ty_FiniteMap, x2), x3), x4)
new_ltEs18(x0, x1)
new_ltEs7(Just(x0), Just(x1), ty_Ordering)
new_not0
new_esEs29(x0, x1, ty_@0)
new_ltEs19(x0, x1, ty_Char)
new_esEs12(EQ, EQ)
new_ltEs4(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_primPlusNat0(Zero, Zero)
new_ltEs16(EQ, EQ)
new_compare15(x0, x1, False, x2, x3)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_compare210(x0, x1, False)
new_esEs24(x0, x1, ty_Ordering)
new_esEs22(x0, x1, ty_Bool)
new_esEs5(Right(x0), Right(x1), x2, ty_Bool)
new_primPlusNat0(Succ(x0), Succ(x1))
new_esEs6(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_esEs28(x0, x1, ty_Int)
new_esEs6(Just(x0), Just(x1), ty_Ordering)
new_ltEs16(LT, LT)
new_compare211(x0, x1, True)
new_primMulInt(Pos(x0), Pos(x1))
new_ltEs7(Just(x0), Just(x1), ty_Float)
new_lt9(x0, x1, ty_Double)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_lt12(x0, x1)
new_lt8(x0, x1, ty_Integer)
new_esEs5(Left(x0), Left(x1), app(ty_[], x2), x3)
new_lt8(x0, x1, ty_Ordering)
new_esEs25(x0, x1, ty_Bool)
new_ltEs20(x0, x1, app(ty_[], x2))
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_lt9(x0, x1, ty_Char)
new_lt8(x0, x1, app(ty_Ratio, x2))
new_ltEs4(Left(x0), Left(x1), ty_Ordering, x2)
new_lt20(x0, x1, app(ty_[], x2))
new_lt6(x0, x1)
new_ltEs4(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs16(GT, LT)
new_ltEs16(LT, GT)
new_ltEs7(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_ltEs6(x0, x1, app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_esEs21(x0, x1, ty_Float)
new_not(GT)
new_ltEs4(Right(x0), Right(x1), x2, ty_@0)
new_ltEs8(False, False)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare17(x0, x1, app(ty_Maybe, x2))
new_ltEs4(Left(x0), Left(x1), ty_Float, x2)
new_asAs(False, x0)
new_esEs26(x0, x1, ty_Float)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_primEqNat0(Succ(x0), Zero)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_lt20(x0, x1, ty_Float)
new_asAs(True, x0)
new_primEqInt(Neg(Zero), Pos(Zero))
new_primEqInt(Pos(Zero), Neg(Zero))
new_ltEs10(x0, x1)
new_ltEs8(False, True)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs8(True, False)
new_lt15(x0, x1, x2, x3, x4)
new_compare17(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs5(Right(x0), Right(x1), x2, ty_Integer)
new_esEs25(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs5(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_pePe(True, x0, x1, x2, x3)
new_ltEs14(x0, x1)
new_primCmpNat0(Succ(x0), Zero)
new_esEs26(x0, x1, ty_Double)
new_compare26(x0, x1, False, x2, x3)
new_compare12(x0, x1, False, x2, x3, x4)
new_ltEs4(Left(x0), Right(x1), x2, x3)
new_ltEs4(Right(x0), Left(x1), x2, x3)
new_esEs19(False, False)
new_compare15(x0, x1, True, x2, x3)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_lt19(x0, x1)
new_esEs6(Just(x0), Just(x1), ty_Int)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_lt20(x0, x1, app(ty_Ratio, x2))
new_ltEs6(x0, x1, ty_@0)
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs24(x0, x1, ty_Integer)
new_primEqInt(Neg(Zero), Neg(Zero))
new_ltEs20(x0, x1, ty_Float)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_compare17(x0, x1, ty_Float)
new_lt8(x0, x1, ty_Double)
new_primCompAux0(x0, x1, x2, x3)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_compare26(x0, x1, True, x2, x3)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_ltEs4(Left(x0), Left(x1), ty_@0, x2)
new_fmToList(x0, x1, x2)
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs7(Just(x0), Just(x1), ty_Char)
new_esEs26(x0, x1, ty_Integer)
new_esEs24(x0, x1, ty_Int)
new_compare17(x0, x1, ty_Ordering)
new_compare28(:%(x0, x1), :%(x2, x3), ty_Integer)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_ltEs16(GT, GT)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_esEs5(Left(x0), Left(x1), ty_Char, x2)
new_esEs18(:(x0, x1), [], x2)
new_ltEs7(Just(x0), Nothing, x1)
new_esEs5(Left(x0), Left(x1), ty_@0, x2)
new_compare29(x0, x1, False, x2)
new_compare28(:%(x0, x1), :%(x2, x3), ty_Int)
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs29(x0, x1, ty_Ordering)
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_esEs24(x0, x1, app(ty_[], x2))
new_ltEs6(x0, x1, ty_Bool)
new_esEs29(x0, x1, ty_Int)
new_compare13(x0, x1)
new_ltEs4(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs6(Just(x0), Just(x1), ty_@0)
new_esEs26(x0, x1, ty_@0)
new_esEs10(EQ)
new_ltEs12(x0, x1)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_compare17(x0, x1, ty_Char)
new_lt9(x0, x1, ty_Ordering)
new_primCmpNat0(Zero, Zero)
new_esEs5(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_ltEs7(Just(x0), Just(x1), ty_Integer)
new_esEs21(x0, x1, ty_Char)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_esEs29(x0, x1, ty_Bool)
new_esEs6(Just(x0), Just(x1), ty_Double)
new_primPlusNat0(Succ(x0), Zero)
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, ty_Bool)
new_primCompAux00(x0, EQ)
new_ltEs4(Right(x0), Right(x1), x2, ty_Int)
new_esEs8(@2(x0, x1), @2(x2, x3), x4, x5)
new_lt9(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_sr0(Integer(x0), Integer(x1))
new_esEs24(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_compare27(x0, x1)
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, ty_Ordering)
new_primMulNat0(Zero, Succ(x0))
new_compare25(x0, x1, False, x2, x3, x4)
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs6(x0, x1, ty_Int)
new_compare18(x0, x1, x2, x3)
new_compare([], [], x0)
new_primCmpNat0(Zero, Succ(x0))
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_primCompAux00(x0, GT)
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_lt9(x0, x1, app(app(ty_Either, x2), x3))
new_compare17(x0, x1, app(app(ty_@2, x2), x3))
new_esEs24(x0, x1, ty_Char)
new_esEs5(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs10(LT)
new_esEs6(Just(x0), Just(x1), ty_Bool)
new_ltEs11(x0, x1, x2)
new_lt8(x0, x1, app(app(ty_@2, x2), x3))
new_esEs21(x0, x1, ty_Integer)
new_lt17(x0, x1)
new_ltEs6(x0, x1, ty_Integer)
new_ltEs7(Nothing, Nothing, x0)
new_esEs25(x0, x1, ty_@0)
new_lt20(x0, x1, ty_Bool)
new_ltEs7(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs21(x0, x1, app(ty_[], x2))
new_primCompAux00(x0, LT)
new_not(EQ)
new_esEs11(Float(x0, x1), Float(x2, x3))
new_ltEs4(Right(x0), Right(x1), x2, ty_Double)
new_ltEs16(GT, EQ)
new_ltEs16(EQ, GT)
new_ltEs20(x0, x1, ty_Double)
new_compare(:(x0, x1), :(x2, x3), x4)
new_esEs5(Right(x0), Right(x1), x2, ty_Float)
new_primPlusNat1(Zero, x0)
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt9(x0, x1, ty_Bool)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_esEs22(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_ltEs6(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs5(Right(x0), Right(x1), x2, ty_Ordering)
new_ltEs16(LT, EQ)
new_ltEs16(EQ, LT)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_esEs5(Left(x0), Left(x1), ty_Float, x2)
new_ltEs4(Left(x0), Left(x1), ty_Integer, x2)
new_compare(:(x0, x1), [], x2)
new_esEs5(Left(x0), Left(x1), ty_Double, x2)
new_esEs26(x0, x1, ty_Int)
new_ltEs4(Right(x0), Right(x1), x2, ty_Integer)
new_lt5(x0, x1)
new_sizeFM(EmptyFM, x0, x1)
new_compare17(x0, x1, ty_Bool)
new_esEs21(x0, x1, ty_Ordering)
new_compare10(x0, x1, False, x2, x3)
new_compare8(Double(x0, x1), Double(x2, x3))
new_ltEs4(Left(x0), Left(x1), ty_Int, x2)
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs20(Char(x0), Char(x1))
new_esEs21(x0, x1, ty_@0)
new_esEs6(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs7(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs23(x0, x1, ty_@0)
new_esEs5(Left(x0), Left(x1), ty_Ordering, x2)
new_ltEs4(Right(x0), Right(x1), x2, ty_Char)
new_ltEs5(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_ltEs19(x0, x1, ty_@0)
new_lt7(x0, x1)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_esEs6(Just(x0), Just(x1), ty_Char)
new_lt8(x0, x1, ty_@0)
new_lt9(x0, x1, ty_Integer)
new_esEs18([], [], x0)
new_compare7(x0, x1, x2, x3, x4)
new_lt9(x0, x1, ty_Int)
new_ltEs19(x0, x1, ty_Double)
new_lt8(x0, x1, ty_Bool)
new_lt9(x0, x1, app(ty_[], x2))
new_esEs15(x0, x1, x2, x3)
new_esEs13(:%(x0, x1), :%(x2, x3), x4)
new_compare16(Integer(x0), Integer(x1))
new_esEs6(Just(x0), Just(x1), app(ty_Maybe, x2))
new_ltEs19(x0, x1, ty_Int)
new_lt13(x0, x1, x2)
new_esEs23(x0, x1, ty_Double)
new_esEs22(x0, x1, ty_Double)
new_primEqInt(Pos(Zero), Pos(Zero))
new_ltEs4(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_lt18(x0, x1)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_compare17(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs4(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs20(x0, x1, ty_Int)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, ty_@0)
new_compare19(x0, x1, x2)
new_esEs29(x0, x1, ty_Double)
new_primPlusNat1(Succ(x0), x1)
new_ltEs7(Just(x0), Just(x1), ty_Int)
new_esEs12(LT, LT)
new_not(LT)
new_esEs22(x0, x1, ty_Float)
new_ltEs15(x0, x1)
new_compare211(x0, x1, False)
↳ 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
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QReductionProof
↳ QDP
↳ QDPSizeChangeProof
Q DP problem:
The TRS P consists of the following rules:
new_foldFM_LE(vyy3, Nothing, Branch(Just(vyy600), vyy61, vyy62, vyy63, vyy64), h, ba, bb) → new_foldFM_LE(vyy3, Nothing, vyy63, h, ba, bb)
new_foldFM_LE(vyy3, Nothing, Branch(Nothing, vyy61, vyy62, vyy63, vyy64), h, ba, bb) → new_foldFM_LE(vyy3, Nothing, vyy64, h, ba, bb)
new_foldFM_LE(vyy3, Nothing, Branch(Nothing, vyy61, vyy62, vyy63, vyy64), h, ba, bb) → new_foldFM_LE(vyy3, Nothing, vyy63, h, ba, bb)
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_foldFM_LE(vyy3, Nothing, Branch(Just(vyy600), vyy61, vyy62, vyy63, vyy64), h, ba, bb) → new_foldFM_LE(vyy3, Nothing, vyy63, h, ba, bb)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 >= 4, 5 >= 5, 6 >= 6
- new_foldFM_LE(vyy3, Nothing, Branch(Nothing, vyy61, vyy62, vyy63, vyy64), h, ba, bb) → new_foldFM_LE(vyy3, Nothing, vyy64, h, ba, bb)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 2, 3 > 3, 4 >= 4, 5 >= 5, 6 >= 6
- new_foldFM_LE(vyy3, Nothing, Branch(Nothing, vyy61, vyy62, vyy63, vyy64), h, ba, bb) → new_foldFM_LE(vyy3, Nothing, vyy63, h, ba, bb)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 2, 3 > 3, 4 >= 4, 5 >= 5, 6 >= 6