YES 6.890000000000001
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_GE :: 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 (\key elt rest ->(key,elt) : rest) [] fm |
|
| | foldFM :: (c -> a -> b -> b) -> b -> FiniteMap c a -> b
| foldFM | k z EmptyFM | = | z |
| foldFM | k z (Branch key elt _ fm_l fm_r) | = | foldFM k (k key elt (foldFM k z fm_r)) fm_l |
|
| | foldFM_GE :: Ord c => (c -> a -> b -> b) -> b -> c -> FiniteMap c a -> b
| foldFM_GE | k z fr EmptyFM | = | z |
| foldFM_GE | k z fr (Branch key elt _ fm_l fm_r) | |
| | | key >= fr | = |
| foldFM_GE k (k key elt (foldFM_GE k z fr fm_r)) fr fm_l |
|
| | | otherwise | = |
|
|
|
| | sizeFM :: FiniteMap a b -> Int
| sizeFM | EmptyFM | = | 0 |
| sizeFM | (Branch _ _ size _ _) | = | size |
|
module Maybe where
| | import qualified FiniteMap
import qualified Prelude
|
Lambda Reductions:
The following Lambda expression
\keyeltrest→(key,elt) : rest
is transformed to
| fmToList0 | key elt rest | = (key,elt) : rest |
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
mainModule FiniteMap
|
| ((foldFM_GE :: 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 :: (b -> a -> c -> c) -> c -> FiniteMap b a -> c
| foldFM | k z EmptyFM | = | z |
| foldFM | k z (Branch key elt _ fm_l fm_r) | = | foldFM k (k key elt (foldFM k z fm_r)) fm_l |
|
| | foldFM_GE :: Ord a => (a -> c -> b -> b) -> b -> a -> FiniteMap a c -> b
| foldFM_GE | k z fr EmptyFM | = | z |
| foldFM_GE | k z fr (Branch key elt _ fm_l fm_r) | |
| | | key >= fr | = |
| foldFM_GE k (k key elt (foldFM_GE k z fr fm_r)) fr fm_l |
|
| | | otherwise | = |
|
|
|
| | sizeFM :: FiniteMap a b -> Int
| sizeFM | EmptyFM | = | 0 |
| sizeFM | (Branch _ _ size _ _) | = | size |
|
module Maybe where
| | import qualified FiniteMap
import qualified Prelude
|
Case Reductions:
The following Case expression
| case | compare x y of |
| | EQ | → o |
| | LT | → LT |
| | GT | → GT |
is transformed to
| primCompAux0 | o EQ | = o |
| primCompAux0 | o LT | = LT |
| primCompAux0 | o GT | = GT |
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
mainModule FiniteMap
|
| ((foldFM_GE :: Ord a => (Maybe a -> b -> c -> c) -> c -> Maybe a -> FiniteMap (Maybe a) b -> c) :: 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 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 :: (b -> c -> a -> a) -> a -> FiniteMap b c -> a
| foldFM | k z EmptyFM | = | z |
| foldFM | k z (Branch key elt _ fm_l fm_r) | = | foldFM k (k key elt (foldFM k z fm_r)) fm_l |
|
| | foldFM_GE :: Ord c => (c -> b -> a -> a) -> a -> c -> FiniteMap c b -> a
| foldFM_GE | k z fr EmptyFM | = | z |
| foldFM_GE | k z fr (Branch key elt _ fm_l fm_r) | |
| | | key >= fr | = |
| foldFM_GE k (k key elt (foldFM_GE k z fr fm_r)) fr fm_l |
|
| | | otherwise | = |
|
|
|
| | sizeFM :: FiniteMap b a -> Int
| sizeFM | EmptyFM | = | 0 |
| sizeFM | (Branch _ _ size _ _) | = | size |
|
module Maybe where
| | import qualified FiniteMap
import qualified Prelude
|
If Reductions:
The following If expression
if primGEqNatS x y then Succ (primDivNatS (primMinusNatS x y) (Succ y)) else Zero
is transformed to
| primDivNatS0 | x y True | = Succ (primDivNatS (primMinusNatS x y) (Succ y)) |
| primDivNatS0 | x y False | = Zero |
The following If expression
if primGEqNatS x y then primModNatS (primMinusNatS x y) (Succ y) else Succ x
is transformed to
| primModNatS0 | x y True | = primModNatS (primMinusNatS x y) (Succ y) |
| primModNatS0 | x y False | = Succ x |
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
mainModule FiniteMap
|
| ((foldFM_GE :: 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 :: (a -> c -> b -> b) -> b -> FiniteMap a c -> b
| foldFM | k z EmptyFM | = | z |
| foldFM | k z (Branch key elt _ fm_l fm_r) | = | foldFM k (k key elt (foldFM k z fm_r)) fm_l |
|
| | foldFM_GE :: Ord c => (c -> a -> b -> b) -> b -> c -> FiniteMap c a -> b
| foldFM_GE | k z fr EmptyFM | = | z |
| foldFM_GE | k z fr (Branch key elt _ fm_l fm_r) | |
| | | key >= fr | = |
| foldFM_GE k (k key elt (foldFM_GE k z fr fm_r)) fr fm_l |
|
| | | 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_GE :: 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 b a = EmptyFM | Branch b a Int (FiniteMap b a) (FiniteMap b a)
|
| | instance (Eq a, Eq b) => Eq (FiniteMap b a) where
|
|
|
| (==) | fm_1 fm_2 | = | sizeFM fm_1 == sizeFM fm_2 && fmToList fm_1 == fmToList fm_2 |
|
|
| | fmToList :: FiniteMap b a -> [(b,a)]
| fmToList | fm | = | foldFM fmToList0 [] fm |
|
| |
| fmToList0 | key elt rest | = | (key,elt) : rest |
|
| | foldFM :: (c -> b -> a -> a) -> a -> FiniteMap c b -> a
| foldFM | k z EmptyFM | = | z |
| foldFM | k z (Branch key elt vw fm_l fm_r) | = | foldFM k (k key elt (foldFM k z fm_r)) fm_l |
|
| | foldFM_GE :: Ord a => (a -> c -> b -> b) -> b -> a -> FiniteMap a c -> b
| foldFM_GE | k z fr EmptyFM | = | z |
| foldFM_GE | k z fr (Branch key elt wv fm_l fm_r) | |
| | | key >= fr | = |
| foldFM_GE k (k key elt (foldFM_GE k z fr fm_r)) fr fm_l |
|
| | | otherwise | = |
|
|
|
| | sizeFM :: FiniteMap b a -> Int
| sizeFM | EmptyFM | = | 0 |
| sizeFM | (Branch vx vy size vz wu) | = | size |
|
module Maybe where
| | import qualified FiniteMap
import qualified Prelude
|
Cond Reductions:
The following Function with conditions
| foldFM_GE | k z fr EmptyFM | = z |
| foldFM_GE | k z fr (Branch key elt wv fm_l fm_r) |
| | | key >= fr |
| = | foldFM_GE k (k key elt (foldFM_GE k z fr fm_r)) fr fm_l |
|
| | | otherwise | |
|
is transformed to
| foldFM_GE | k z fr EmptyFM | = foldFM_GE3 k z fr EmptyFM |
| foldFM_GE | k z fr (Branch key elt wv fm_l fm_r) | = foldFM_GE2 k z fr (Branch key elt wv fm_l fm_r) |
| foldFM_GE1 | k z fr key elt wv fm_l fm_r True | = foldFM_GE k (k key elt (foldFM_GE k z fr fm_r)) fr fm_l |
| foldFM_GE1 | k z fr key elt wv fm_l fm_r False | = foldFM_GE0 k z fr key elt wv fm_l fm_r otherwise |
| foldFM_GE0 | k z fr key elt wv fm_l fm_r True | = foldFM_GE k z fr fm_r |
| foldFM_GE2 | k z fr (Branch key elt wv fm_l fm_r) | = foldFM_GE1 k z fr key elt wv fm_l fm_r (key >= fr) |
| foldFM_GE3 | k z fr EmptyFM | = z |
| foldFM_GE3 | vvu vvv vvw vvx | = foldFM_GE2 vvu vvv vvw vvx |
The following Function with conditions
| compare | x y |
| | | x == y | |
| | | x <= y | |
| | | otherwise | |
|
is transformed to
| compare | x y | = compare3 x y |
| compare1 | x y True | = LT |
| compare1 | x y False | = compare0 x y otherwise |
| compare2 | x y True | = EQ |
| compare2 | x y False | = compare1 x y (x <= y) |
| compare3 | x y | = compare2 x y (x == y) |
The following Function with conditions
| gcd' | x 0 | = x |
| gcd' | x y | = gcd' y (x `rem` y) |
is transformed to
| gcd' | x vvy | = gcd'2 x vvy |
| gcd' | x y | = gcd'0 x y |
| gcd'0 | x y | = gcd' y (x `rem` y) |
| gcd'1 | True x vvy | = x |
| gcd'1 | vvz vwu vwv | = gcd'0 vwu vwv |
| gcd'2 | x vvy | = gcd'1 (vvy == 0) x vvy |
| gcd'2 | vww vwx | = gcd'0 vww vwx |
The following Function with conditions
| gcd | 0 0 | = error [] |
| gcd | x y | =
| gcd' (abs x) (abs y) |
| where |
| gcd' | x 0 | = x |
| gcd' | x y | = gcd' y (x `rem` y) |
|
|
is transformed to
| gcd | vwy vwz | = gcd3 vwy vwz |
| gcd | x y | = gcd0 x y |
| gcd0 | x y | =
| gcd' (abs x) (abs y) |
| where |
| gcd' | x vvy | = gcd'2 x vvy |
| gcd' | x y | = gcd'0 x y |
|
|
| gcd'0 | x y | = gcd' y (x `rem` y) |
|
|
| gcd'1 | True x vvy | = x |
| gcd'1 | vvz vwu vwv | = gcd'0 vwu vwv |
|
|
| gcd'2 | x vvy | = gcd'1 (vvy == 0) x vvy |
| gcd'2 | vww vwx | = gcd'0 vww vwx |
|
|
| gcd1 | True vwy vwz | = error [] |
| gcd1 | vxu vxv vxw | = gcd0 vxv vxw |
| gcd2 | True vwy vwz | = gcd1 (vwz == 0) vwy vwz |
| gcd2 | vxx vxy vxz | = gcd0 vxy vxz |
| gcd3 | vwy vwz | = gcd2 (vwy == 0) vwy vwz |
| gcd3 | vyu vyv | = gcd0 vyu vyv |
The following Function with conditions
is transformed to
| absReal1 | x True | = x |
| absReal1 | x False | = absReal0 x otherwise |
| absReal0 | x True | = `negate` x |
| absReal2 | x | = absReal1 x (x >= 0) |
The following Function with conditions
is transformed to
| undefined0 | True | = undefined |
| undefined1 | | = undefined0 False |
The following Function with conditions
| reduce | x y |
| | | y == 0 | |
| | | otherwise |
| = | x `quot` d :% (y `quot` d) |
|
|
| where | |
|
is transformed to
| reduce2 | x y | =
| reduce1 x y (y == 0) |
| where | |
|
| reduce0 | x y True | = x `quot` d :% (y `quot` d) |
|
|
| reduce1 | x y True | = error [] |
| reduce1 | x y False | = reduce0 x y otherwise |
|
|
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
mainModule FiniteMap
|
| ((foldFM_GE :: 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 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 :: (a -> b -> c -> c) -> c -> FiniteMap a b -> 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_GE :: Ord a => (a -> c -> b -> b) -> b -> a -> FiniteMap a c -> b
| foldFM_GE | k z fr EmptyFM | = | foldFM_GE3 k z fr EmptyFM |
| foldFM_GE | k z fr (Branch key elt wv fm_l fm_r) | = | foldFM_GE2 k z fr (Branch key elt wv fm_l fm_r) |
|
| |
| foldFM_GE0 | k z fr key elt wv fm_l fm_r True | = | foldFM_GE k z fr fm_r |
|
| |
| foldFM_GE1 | k z fr key elt wv fm_l fm_r True | = | foldFM_GE k (k key elt (foldFM_GE k z fr fm_r)) fr fm_l |
| foldFM_GE1 | k z fr key elt wv fm_l fm_r False | = | foldFM_GE0 k z fr key elt wv fm_l fm_r otherwise |
|
| |
| foldFM_GE2 | k z fr (Branch key elt wv fm_l fm_r) | = | foldFM_GE1 k z fr key elt wv fm_l fm_r (key >= fr) |
|
| |
| foldFM_GE3 | k z fr EmptyFM | = | z |
| foldFM_GE3 | vvu vvv vvw vvx | = | foldFM_GE2 vvu vvv vvw vvx |
|
| | sizeFM :: FiniteMap a b -> Int
| sizeFM | EmptyFM | = | 0 |
| sizeFM | (Branch vx vy size vz wu) | = | size |
|
module Maybe where
| | import qualified FiniteMap
import qualified Prelude
|
Let/Where Reductions:
The bindings of the following Let/Where expression
| reduce1 x y (y == 0) |
| where | |
|
| reduce0 | x y True | = x `quot` d :% (y `quot` d) |
|
|
| reduce1 | x y True | = error [] |
| reduce1 | x y False | = reduce0 x y otherwise |
|
are unpacked to the following functions on top level
| reduce2D | vyw vyx | = gcd vyw vyx |
| reduce2Reduce1 | vyw vyx x y True | = error [] |
| reduce2Reduce1 | vyw vyx x y False | = reduce2Reduce0 vyw vyx x y otherwise |
| reduce2Reduce0 | vyw vyx x y True | = x `quot` reduce2D vyw vyx :% (y `quot` reduce2D vyw vyx) |
The bindings of the following Let/Where expression
| gcd' (abs x) (abs y) |
| where |
| gcd' | x vvy | = gcd'2 x vvy |
| gcd' | x y | = gcd'0 x y |
|
|
| gcd'0 | x y | = gcd' y (x `rem` y) |
|
|
| gcd'1 | True x vvy | = x |
| gcd'1 | vvz vwu vwv | = gcd'0 vwu vwv |
|
|
| gcd'2 | x vvy | = gcd'1 (vvy == 0) x vvy |
| gcd'2 | vww vwx | = gcd'0 vww vwx |
|
are unpacked to the following functions on top level
| gcd0Gcd'0 | x y | = gcd0Gcd' y (x `rem` y) |
| gcd0Gcd' | x vvy | = gcd0Gcd'2 x vvy |
| gcd0Gcd' | x y | = gcd0Gcd'0 x y |
| gcd0Gcd'1 | True x vvy | = x |
| gcd0Gcd'1 | vvz vwu vwv | = gcd0Gcd'0 vwu vwv |
| gcd0Gcd'2 | x vvy | = gcd0Gcd'1 (vvy == 0) x vvy |
| gcd0Gcd'2 | vww vwx | = gcd0Gcd'0 vww vwx |
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
mainModule FiniteMap
|
| ((foldFM_GE :: Ord a => (Maybe a -> b -> c -> c) -> c -> Maybe a -> FiniteMap (Maybe a) b -> c) :: 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 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 :: (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_GE :: Ord c => (c -> a -> b -> b) -> b -> c -> FiniteMap c a -> b
| foldFM_GE | k z fr EmptyFM | = | foldFM_GE3 k z fr EmptyFM |
| foldFM_GE | k z fr (Branch key elt wv fm_l fm_r) | = | foldFM_GE2 k z fr (Branch key elt wv fm_l fm_r) |
|
| |
| foldFM_GE0 | k z fr key elt wv fm_l fm_r True | = | foldFM_GE k z fr fm_r |
|
| |
| foldFM_GE1 | k z fr key elt wv fm_l fm_r True | = | foldFM_GE k (k key elt (foldFM_GE k z fr fm_r)) fr fm_l |
| foldFM_GE1 | k z fr key elt wv fm_l fm_r False | = | foldFM_GE0 k z fr key elt wv fm_l fm_r otherwise |
|
| |
| foldFM_GE2 | k z fr (Branch key elt wv fm_l fm_r) | = | foldFM_GE1 k z fr key elt wv fm_l fm_r (key >= fr) |
|
| |
| foldFM_GE3 | k z fr EmptyFM | = | z |
| foldFM_GE3 | vvu vvv vvw vvx | = | foldFM_GE2 vvu vvv vvw vvx |
|
| | sizeFM :: FiniteMap a b -> Int
| sizeFM | EmptyFM | = | 0 |
| sizeFM | (Branch vx vy size vz wu) | = | 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_GE :: 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 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 :: (c -> a -> b -> b) -> b -> FiniteMap c a -> b
| foldFM | k z EmptyFM | = | z |
| foldFM | k z (Branch key elt vw fm_l fm_r) | = | foldFM k (k key elt (foldFM k z fm_r)) fm_l |
|
| | foldFM_GE :: Ord a => (a -> c -> b -> b) -> b -> a -> FiniteMap a c -> b
| foldFM_GE | k z fr EmptyFM | = | foldFM_GE3 k z fr EmptyFM |
| foldFM_GE | k z fr (Branch key elt wv fm_l fm_r) | = | foldFM_GE2 k z fr (Branch key elt wv fm_l fm_r) |
|
| |
| foldFM_GE0 | k z fr key elt wv fm_l fm_r True | = | foldFM_GE k z fr fm_r |
|
| |
| foldFM_GE1 | k z fr key elt wv fm_l fm_r True | = | foldFM_GE k (k key elt (foldFM_GE k z fr fm_r)) fr fm_l |
| foldFM_GE1 | k z fr key elt wv fm_l fm_r False | = | foldFM_GE0 k z fr key elt wv fm_l fm_r otherwise |
|
| |
| foldFM_GE2 | k z fr (Branch key elt wv fm_l fm_r) | = | foldFM_GE1 k z fr key elt wv fm_l fm_r (key >= fr) |
|
| |
| foldFM_GE3 | k z fr EmptyFM | = | z |
| foldFM_GE3 | vvu vvv vvw vvx | = | foldFM_GE2 vvu vvv vvw vvx |
|
| | sizeFM :: FiniteMap a b -> Int
| sizeFM | EmptyFM | = | Pos Zero |
| sizeFM | (Branch vx vy size vz wu) | = | 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
Q DP problem:
The TRS P consists of the following rules:
new_primCmpNat(Succ(vyy330000), Succ(vyy340000)) → new_primCmpNat(vyy330000, vyy340000)
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(vyy330000), Succ(vyy340000)) → new_primCmpNat(vyy330000, vyy340000)
The graph contains the following edges 1 > 1, 2 > 2
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDPSizeChangeProof
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_primPlusNat(Succ(vyy9900), Succ(vyy500000)) → new_primPlusNat(vyy9900, vyy500000)
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(vyy9900), Succ(vyy500000)) → new_primPlusNat(vyy9900, vyy500000)
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
↳ QDPSizeChangeProof
↳ QDP
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_primMulNat(Succ(vyy600000), Succ(vyy50000)) → new_primMulNat(vyy600000, Succ(vyy50000))
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(vyy600000), Succ(vyy50000)) → new_primMulNat(vyy600000, Succ(vyy50000))
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
Q DP problem:
The TRS P consists of the following rules:
new_primEqNat(Succ(vyy60000), Succ(vyy5000)) → new_primEqNat(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_primEqNat(Succ(vyy60000), Succ(vyy5000)) → new_primEqNat(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
↳ QDPSizeChangeProof
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_esEs(@2(vyy6000, vyy6001), @2(vyy500, vyy501), app(app(ty_@2, h), ba), bb) → new_esEs(vyy6000, vyy500, h, ba)
new_esEs2(@3(vyy6000, vyy6001, vyy6002), @3(vyy500, vyy501, vyy502), app(app(app(ty_@3, bac), bad), bae), hf, hg) → new_esEs2(vyy6000, vyy500, bac, bad, bae)
new_esEs1(:(vyy6000, vyy6001), :(vyy500, vyy501), app(app(ty_@2, gb), gc)) → new_esEs(vyy6000, vyy500, gb, gc)
new_esEs2(@3(vyy6000, vyy6001, vyy6002), @3(vyy500, vyy501, vyy502), bag, app(ty_Maybe, bbh), hg) → new_esEs3(vyy6001, vyy501, bbh)
new_esEs(@2(vyy6000, vyy6001), @2(vyy500, vyy501), app(ty_Maybe, ca), bb) → new_esEs3(vyy6000, vyy500, ca)
new_esEs(@2(vyy6000, vyy6001), @2(vyy500, vyy501), app(ty_[], be), bb) → new_esEs1(vyy6000, vyy500, be)
new_esEs3(Just(vyy6000), Just(vyy500), app(app(ty_Either, bdd), bde)) → new_esEs0(vyy6000, vyy500, bdd, bde)
new_esEs2(@3(vyy6000, vyy6001, vyy6002), @3(vyy500, vyy501, vyy502), bag, hf, app(ty_Maybe, bda)) → new_esEs3(vyy6002, vyy502, bda)
new_esEs2(@3(vyy6000, vyy6001, vyy6002), @3(vyy500, vyy501, vyy502), app(app(ty_Either, hh), baa), hf, hg) → new_esEs0(vyy6000, vyy500, hh, baa)
new_esEs1(:(vyy6000, vyy6001), :(vyy500, vyy501), hc) → new_esEs1(vyy6001, vyy501, hc)
new_esEs2(@3(vyy6000, vyy6001, vyy6002), @3(vyy500, vyy501, vyy502), bag, app(ty_[], bbd), hg) → new_esEs1(vyy6001, vyy501, bbd)
new_esEs0(Left(vyy6000), Left(vyy500), app(ty_Maybe, ef), dg) → new_esEs3(vyy6000, vyy500, ef)
new_esEs1(:(vyy6000, vyy6001), :(vyy500, vyy501), app(ty_[], gf)) → new_esEs1(vyy6000, vyy500, gf)
new_esEs(@2(vyy6000, vyy6001), @2(vyy500, vyy501), cb, app(app(ty_Either, ce), cf)) → new_esEs0(vyy6001, vyy501, ce, cf)
new_esEs0(Left(vyy6000), Left(vyy500), app(app(app(ty_@3, ec), ed), ee), dg) → new_esEs2(vyy6000, vyy500, ec, ed, ee)
new_esEs0(Left(vyy6000), Left(vyy500), app(app(ty_Either, dh), ea), dg) → new_esEs0(vyy6000, vyy500, dh, ea)
new_esEs0(Left(vyy6000), Left(vyy500), app(app(ty_@2, de), df), dg) → new_esEs(vyy6000, vyy500, de, df)
new_esEs(@2(vyy6000, vyy6001), @2(vyy500, vyy501), cb, app(ty_Maybe, dd)) → new_esEs3(vyy6001, vyy501, dd)
new_esEs(@2(vyy6000, vyy6001), @2(vyy500, vyy501), app(app(ty_Either, bc), bd), bb) → new_esEs0(vyy6000, vyy500, bc, bd)
new_esEs(@2(vyy6000, vyy6001), @2(vyy500, vyy501), cb, app(app(app(ty_@3, da), db), dc)) → new_esEs2(vyy6001, vyy501, da, db, dc)
new_esEs0(Right(vyy6000), Right(vyy500), eg, app(app(ty_Either, fb), fc)) → new_esEs0(vyy6000, vyy500, fb, fc)
new_esEs(@2(vyy6000, vyy6001), @2(vyy500, vyy501), cb, app(ty_[], cg)) → new_esEs1(vyy6001, vyy501, cg)
new_esEs1(:(vyy6000, vyy6001), :(vyy500, vyy501), app(app(ty_Either, gd), ge)) → new_esEs0(vyy6000, vyy500, gd, ge)
new_esEs0(Right(vyy6000), Right(vyy500), eg, app(ty_[], fd)) → new_esEs1(vyy6000, vyy500, fd)
new_esEs0(Left(vyy6000), Left(vyy500), app(ty_[], eb), dg) → new_esEs1(vyy6000, vyy500, eb)
new_esEs2(@3(vyy6000, vyy6001, vyy6002), @3(vyy500, vyy501, vyy502), bag, app(app(app(ty_@3, bbe), bbf), bbg), hg) → new_esEs2(vyy6001, vyy501, bbe, bbf, bbg)
new_esEs0(Right(vyy6000), Right(vyy500), eg, app(app(app(ty_@3, ff), fg), fh)) → new_esEs2(vyy6000, vyy500, ff, fg, fh)
new_esEs3(Just(vyy6000), Just(vyy500), app(app(app(ty_@3, bdg), bdh), bea)) → new_esEs2(vyy6000, vyy500, bdg, bdh, bea)
new_esEs3(Just(vyy6000), Just(vyy500), app(ty_Maybe, beb)) → new_esEs3(vyy6000, vyy500, beb)
new_esEs2(@3(vyy6000, vyy6001, vyy6002), @3(vyy500, vyy501, vyy502), app(ty_Maybe, baf), hf, hg) → new_esEs3(vyy6000, vyy500, baf)
new_esEs3(Just(vyy6000), Just(vyy500), app(app(ty_@2, bdb), bdc)) → new_esEs(vyy6000, vyy500, bdb, bdc)
new_esEs0(Right(vyy6000), Right(vyy500), eg, app(ty_Maybe, ga)) → new_esEs3(vyy6000, vyy500, ga)
new_esEs(@2(vyy6000, vyy6001), @2(vyy500, vyy501), cb, app(app(ty_@2, cc), cd)) → new_esEs(vyy6001, vyy501, cc, cd)
new_esEs(@2(vyy6000, vyy6001), @2(vyy500, vyy501), app(app(app(ty_@3, bf), bg), bh), bb) → new_esEs2(vyy6000, vyy500, bf, bg, bh)
new_esEs2(@3(vyy6000, vyy6001, vyy6002), @3(vyy500, vyy501, vyy502), bag, hf, app(ty_[], bce)) → new_esEs1(vyy6002, vyy502, bce)
new_esEs2(@3(vyy6000, vyy6001, vyy6002), @3(vyy500, vyy501, vyy502), bag, app(app(ty_@2, bah), bba), hg) → new_esEs(vyy6001, vyy501, bah, bba)
new_esEs3(Just(vyy6000), Just(vyy500), app(ty_[], bdf)) → new_esEs1(vyy6000, vyy500, bdf)
new_esEs2(@3(vyy6000, vyy6001, vyy6002), @3(vyy500, vyy501, vyy502), app(app(ty_@2, hd), he), hf, hg) → new_esEs(vyy6000, vyy500, hd, he)
new_esEs2(@3(vyy6000, vyy6001, vyy6002), @3(vyy500, vyy501, vyy502), bag, app(app(ty_Either, bbb), bbc), hg) → new_esEs0(vyy6001, vyy501, bbb, bbc)
new_esEs0(Right(vyy6000), Right(vyy500), eg, app(app(ty_@2, eh), fa)) → new_esEs(vyy6000, vyy500, eh, fa)
new_esEs2(@3(vyy6000, vyy6001, vyy6002), @3(vyy500, vyy501, vyy502), app(ty_[], bab), hf, hg) → new_esEs1(vyy6000, vyy500, bab)
new_esEs2(@3(vyy6000, vyy6001, vyy6002), @3(vyy500, vyy501, vyy502), bag, hf, app(app(ty_@2, bca), bcb)) → new_esEs(vyy6002, vyy502, bca, bcb)
new_esEs1(:(vyy6000, vyy6001), :(vyy500, vyy501), app(app(app(ty_@3, gg), gh), ha)) → new_esEs2(vyy6000, vyy500, gg, gh, ha)
new_esEs1(:(vyy6000, vyy6001), :(vyy500, vyy501), app(ty_Maybe, hb)) → new_esEs3(vyy6000, vyy500, hb)
new_esEs2(@3(vyy6000, vyy6001, vyy6002), @3(vyy500, vyy501, vyy502), bag, hf, app(app(ty_Either, bcc), bcd)) → new_esEs0(vyy6002, vyy502, bcc, bcd)
new_esEs2(@3(vyy6000, vyy6001, vyy6002), @3(vyy500, vyy501, vyy502), bag, hf, app(app(app(ty_@3, bcf), bcg), bch)) → new_esEs2(vyy6002, vyy502, bcf, bcg, bch)
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_esEs3(Just(vyy6000), Just(vyy500), app(app(ty_@2, bdb), bdc)) → new_esEs(vyy6000, vyy500, bdb, bdc)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
- new_esEs3(Just(vyy6000), Just(vyy500), app(app(app(ty_@3, bdg), bdh), bea)) → new_esEs2(vyy6000, vyy500, bdg, bdh, bea)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
- new_esEs3(Just(vyy6000), Just(vyy500), app(ty_[], bdf)) → new_esEs1(vyy6000, vyy500, bdf)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
- new_esEs1(:(vyy6000, vyy6001), :(vyy500, vyy501), app(app(ty_@2, gb), gc)) → new_esEs(vyy6000, vyy500, gb, gc)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
- new_esEs1(:(vyy6000, vyy6001), :(vyy500, vyy501), app(app(app(ty_@3, gg), gh), ha)) → new_esEs2(vyy6000, vyy500, gg, gh, ha)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
- new_esEs3(Just(vyy6000), Just(vyy500), app(ty_Maybe, beb)) → new_esEs3(vyy6000, vyy500, beb)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
- new_esEs3(Just(vyy6000), Just(vyy500), app(app(ty_Either, bdd), bde)) → new_esEs0(vyy6000, vyy500, bdd, bde)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
- new_esEs1(:(vyy6000, vyy6001), :(vyy500, vyy501), app(ty_Maybe, hb)) → new_esEs3(vyy6000, vyy500, hb)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
- new_esEs1(:(vyy6000, vyy6001), :(vyy500, vyy501), app(app(ty_Either, gd), ge)) → new_esEs0(vyy6000, vyy500, gd, ge)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
- new_esEs(@2(vyy6000, vyy6001), @2(vyy500, vyy501), app(app(ty_@2, h), ba), bb) → new_esEs(vyy6000, vyy500, h, ba)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
- new_esEs(@2(vyy6000, vyy6001), @2(vyy500, vyy501), cb, app(app(ty_@2, cc), cd)) → new_esEs(vyy6001, vyy501, cc, cd)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
- new_esEs(@2(vyy6000, vyy6001), @2(vyy500, vyy501), cb, app(app(app(ty_@3, da), db), dc)) → new_esEs2(vyy6001, vyy501, da, db, dc)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5
- new_esEs(@2(vyy6000, vyy6001), @2(vyy500, vyy501), app(app(app(ty_@3, bf), bg), bh), bb) → new_esEs2(vyy6000, vyy500, bf, bg, bh)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
- new_esEs(@2(vyy6000, vyy6001), @2(vyy500, vyy501), app(ty_[], be), bb) → new_esEs1(vyy6000, vyy500, be)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
- new_esEs(@2(vyy6000, vyy6001), @2(vyy500, vyy501), cb, app(ty_[], cg)) → new_esEs1(vyy6001, vyy501, cg)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
- new_esEs(@2(vyy6000, vyy6001), @2(vyy500, vyy501), app(ty_Maybe, ca), bb) → new_esEs3(vyy6000, vyy500, ca)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
- new_esEs(@2(vyy6000, vyy6001), @2(vyy500, vyy501), cb, app(ty_Maybe, dd)) → new_esEs3(vyy6001, vyy501, dd)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
- new_esEs(@2(vyy6000, vyy6001), @2(vyy500, vyy501), cb, app(app(ty_Either, ce), cf)) → new_esEs0(vyy6001, vyy501, ce, cf)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
- new_esEs(@2(vyy6000, vyy6001), @2(vyy500, vyy501), app(app(ty_Either, bc), bd), bb) → new_esEs0(vyy6000, vyy500, bc, bd)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
- new_esEs2(@3(vyy6000, vyy6001, vyy6002), @3(vyy500, vyy501, vyy502), bag, app(app(ty_@2, bah), bba), hg) → new_esEs(vyy6001, vyy501, bah, bba)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
- new_esEs2(@3(vyy6000, vyy6001, vyy6002), @3(vyy500, vyy501, vyy502), app(app(ty_@2, hd), he), hf, hg) → new_esEs(vyy6000, vyy500, hd, he)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
- new_esEs2(@3(vyy6000, vyy6001, vyy6002), @3(vyy500, vyy501, vyy502), bag, hf, app(app(ty_@2, bca), bcb)) → new_esEs(vyy6002, vyy502, bca, bcb)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4
- new_esEs0(Left(vyy6000), Left(vyy500), app(app(ty_@2, de), df), dg) → new_esEs(vyy6000, vyy500, de, df)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
- new_esEs0(Right(vyy6000), Right(vyy500), eg, app(app(ty_@2, eh), fa)) → new_esEs(vyy6000, vyy500, eh, fa)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
- new_esEs2(@3(vyy6000, vyy6001, vyy6002), @3(vyy500, vyy501, vyy502), app(app(app(ty_@3, bac), bad), bae), hf, hg) → new_esEs2(vyy6000, vyy500, bac, bad, bae)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
- new_esEs2(@3(vyy6000, vyy6001, vyy6002), @3(vyy500, vyy501, vyy502), bag, app(app(app(ty_@3, bbe), bbf), bbg), hg) → new_esEs2(vyy6001, vyy501, bbe, bbf, bbg)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5
- new_esEs2(@3(vyy6000, vyy6001, vyy6002), @3(vyy500, vyy501, vyy502), bag, hf, app(app(app(ty_@3, bcf), bcg), bch)) → new_esEs2(vyy6002, vyy502, bcf, bcg, bch)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4, 5 > 5
- new_esEs2(@3(vyy6000, vyy6001, vyy6002), @3(vyy500, vyy501, vyy502), bag, app(ty_[], bbd), hg) → new_esEs1(vyy6001, vyy501, bbd)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
- new_esEs2(@3(vyy6000, vyy6001, vyy6002), @3(vyy500, vyy501, vyy502), bag, hf, app(ty_[], bce)) → new_esEs1(vyy6002, vyy502, bce)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3
- new_esEs2(@3(vyy6000, vyy6001, vyy6002), @3(vyy500, vyy501, vyy502), app(ty_[], bab), hf, hg) → new_esEs1(vyy6000, vyy500, bab)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
- new_esEs2(@3(vyy6000, vyy6001, vyy6002), @3(vyy500, vyy501, vyy502), bag, app(ty_Maybe, bbh), hg) → new_esEs3(vyy6001, vyy501, bbh)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
- new_esEs2(@3(vyy6000, vyy6001, vyy6002), @3(vyy500, vyy501, vyy502), bag, hf, app(ty_Maybe, bda)) → new_esEs3(vyy6002, vyy502, bda)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3
- new_esEs2(@3(vyy6000, vyy6001, vyy6002), @3(vyy500, vyy501, vyy502), app(ty_Maybe, baf), hf, hg) → new_esEs3(vyy6000, vyy500, baf)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
- new_esEs2(@3(vyy6000, vyy6001, vyy6002), @3(vyy500, vyy501, vyy502), app(app(ty_Either, hh), baa), hf, hg) → new_esEs0(vyy6000, vyy500, hh, baa)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
- new_esEs2(@3(vyy6000, vyy6001, vyy6002), @3(vyy500, vyy501, vyy502), bag, app(app(ty_Either, bbb), bbc), hg) → new_esEs0(vyy6001, vyy501, bbb, bbc)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
- new_esEs2(@3(vyy6000, vyy6001, vyy6002), @3(vyy500, vyy501, vyy502), bag, hf, app(app(ty_Either, bcc), bcd)) → new_esEs0(vyy6002, vyy502, bcc, bcd)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4
- new_esEs0(Left(vyy6000), Left(vyy500), app(app(app(ty_@3, ec), ed), ee), dg) → new_esEs2(vyy6000, vyy500, ec, ed, ee)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
- new_esEs0(Right(vyy6000), Right(vyy500), eg, app(app(app(ty_@3, ff), fg), fh)) → new_esEs2(vyy6000, vyy500, ff, fg, fh)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5
- new_esEs1(:(vyy6000, vyy6001), :(vyy500, vyy501), hc) → new_esEs1(vyy6001, vyy501, hc)
The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3
- new_esEs1(:(vyy6000, vyy6001), :(vyy500, vyy501), app(ty_[], gf)) → new_esEs1(vyy6000, vyy500, gf)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
- new_esEs0(Right(vyy6000), Right(vyy500), eg, app(ty_[], fd)) → new_esEs1(vyy6000, vyy500, fd)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
- new_esEs0(Left(vyy6000), Left(vyy500), app(ty_[], eb), dg) → new_esEs1(vyy6000, vyy500, eb)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
- new_esEs0(Left(vyy6000), Left(vyy500), app(ty_Maybe, ef), dg) → new_esEs3(vyy6000, vyy500, ef)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
- new_esEs0(Right(vyy6000), Right(vyy500), eg, app(ty_Maybe, ga)) → new_esEs3(vyy6000, vyy500, ga)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
- new_esEs0(Left(vyy6000), Left(vyy500), app(app(ty_Either, dh), ea), dg) → new_esEs0(vyy6000, vyy500, dh, ea)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
- new_esEs0(Right(vyy6000), Right(vyy500), eg, app(app(ty_Either, fb), fc)) → new_esEs0(vyy6000, vyy500, fb, fc)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDPSizeChangeProof
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_ltEs1(@2(vyy33000, vyy33001), @2(vyy34000, vyy34001), de, app(app(ty_@2, dh), ea)) → new_ltEs1(vyy33001, vyy34001, dh, ea)
new_ltEs3(Left(vyy33000), Left(vyy34000), app(app(ty_Either, bcg), bch), bbh) → new_ltEs3(vyy33000, vyy34000, bcg, bch)
new_compare20(Just(@3(vyy33000, vyy33001, vyy33002)), Just(@3(vyy34000, vyy34001, vyy34002)), False, app(app(app(ty_@3, app(app(ty_@2, bah), bba)), gb), he)) → new_lt1(vyy33000, vyy34000, bah, bba)
new_ltEs1(@2(vyy33000, vyy33001), @2(vyy34000, vyy34001), app(ty_Maybe, cb), eg) → new_compare20(vyy33000, vyy34000, new_esEs4(vyy33000, vyy34000, cb), cb)
new_compare20(Just(@3(vyy33000, vyy33001, vyy33002)), Just(@3(vyy34000, vyy34001, vyy34002)), False, app(app(app(ty_@3, ga), gb), app(app(ty_Either, hb), hc))) → new_ltEs3(vyy33002, vyy34002, hb, hc)
new_compare20(Just(@3(vyy33000, vyy33001, vyy33002)), Just(@3(vyy34000, vyy34001, vyy34002)), False, app(app(app(ty_@3, app(app(ty_Either, bbe), bbf)), gb), he)) → new_lt3(vyy33000, vyy34000, bbe, bbf)
new_ltEs2(@3(vyy33000, vyy33001, vyy33002), @3(vyy34000, vyy34001, vyy34002), ga, gb, app(app(ty_Either, hb), hc)) → new_ltEs3(vyy33002, vyy34002, hb, hc)
new_compare20(Just(Left(vyy33000)), Just(Left(vyy34000)), False, app(app(ty_Either, app(ty_[], bca)), bbh)) → new_ltEs0(vyy33000, vyy34000, bca)
new_ltEs(Just(vyy33000), Just(vyy34000), app(ty_[], cd)) → new_ltEs0(vyy33000, vyy34000, cd)
new_compare20(Just(Right(vyy33000)), Just(Right(vyy34000)), False, app(app(ty_Either, bda), app(app(ty_Either, bea), beb))) → new_ltEs3(vyy33000, vyy34000, bea, beb)
new_compare20(Just(@3(vyy33000, vyy33001, vyy33002)), Just(@3(vyy34000, vyy34001, vyy34002)), False, app(app(app(ty_@3, ga), gb), app(ty_[], gd))) → new_ltEs0(vyy33002, vyy34002, gd)
new_ltEs3(Left(vyy33000), Left(vyy34000), app(ty_Maybe, bbg), bbh) → new_ltEs(vyy33000, vyy34000, bbg)
new_ltEs2(@3(vyy33000, vyy33001, vyy33002), @3(vyy34000, vyy34001, vyy34002), ga, app(app(app(ty_@3, baa), bab), bac), he) → new_lt2(vyy33001, vyy34001, baa, bab, bac)
new_compare20(Just(@2(vyy33000, vyy33001)), Just(@2(vyy34000, vyy34001)), False, app(app(ty_@2, app(ty_Maybe, cb)), eg)) → new_compare20(vyy33000, vyy34000, new_esEs4(vyy33000, vyy34000, cb), cb)
new_compare20(Just(@3(vyy33000, vyy33001, vyy33002)), Just(@3(vyy34000, vyy34001, vyy34002)), False, app(app(app(ty_@3, app(ty_[], bag)), gb), he)) → new_lt0(vyy33000, vyy34000, bag)
new_compare20(Just(@3(vyy33000, vyy33001, vyy33002)), Just(@3(vyy34000, vyy34001, vyy34002)), False, app(app(app(ty_@3, app(ty_Maybe, baf)), gb), he)) → new_lt(vyy33000, vyy34000, baf)
new_ltEs(Just(vyy33000), Just(vyy34000), app(app(ty_Either, dc), dd)) → new_ltEs3(vyy33000, vyy34000, dc, dd)
new_primCompAux(vyy33000, vyy34000, vyy98, app(ty_[], bb)) → new_compare(vyy33000, vyy34000, bb)
new_compare20(Just(Left(vyy33000)), Just(Left(vyy34000)), False, app(app(ty_Either, app(app(ty_Either, bcg), bch)), bbh)) → new_ltEs3(vyy33000, vyy34000, bcg, bch)
new_compare20(Just(@2(vyy33000, vyy33001)), Just(@2(vyy34000, vyy34001)), False, app(app(ty_@2, de), app(ty_[], dg))) → new_ltEs0(vyy33001, vyy34001, dg)
new_lt0(vyy33000, vyy34000, eh) → new_compare(vyy33000, vyy34000, eh)
new_ltEs2(@3(vyy33000, vyy33001, vyy33002), @3(vyy34000, vyy34001, vyy34002), ga, gb, app(ty_Maybe, gc)) → new_ltEs(vyy33002, vyy34002, gc)
new_compare20(Just(Right(vyy33000)), Just(Right(vyy34000)), False, app(app(ty_Either, bda), app(ty_Maybe, bdb))) → new_ltEs(vyy33000, vyy34000, bdb)
new_ltEs1(@2(vyy33000, vyy33001), @2(vyy34000, vyy34001), de, app(ty_Maybe, df)) → new_ltEs(vyy33001, vyy34001, df)
new_lt(vyy33000, vyy34000, cb) → new_compare20(vyy33000, vyy34000, new_esEs4(vyy33000, vyy34000, cb), cb)
new_ltEs3(Right(vyy33000), Right(vyy34000), bda, app(app(ty_Either, bea), beb)) → new_ltEs3(vyy33000, vyy34000, bea, beb)
new_ltEs1(@2(vyy33000, vyy33001), @2(vyy34000, vyy34001), app(ty_[], eh), eg) → new_compare(vyy33000, vyy34000, eh)
new_ltEs1(@2(vyy33000, vyy33001), @2(vyy34000, vyy34001), app(app(app(ty_@3, fc), fd), ff), eg) → new_compare22(vyy33000, vyy34000, new_esEs6(vyy33000, vyy34000, fc, fd, ff), fc, fd, ff)
new_compare20(Just(@3(vyy33000, vyy33001, vyy33002)), Just(@3(vyy34000, vyy34001, vyy34002)), False, app(app(app(ty_@3, ga), app(app(ty_Either, bad), bae)), he)) → new_lt3(vyy33001, vyy34001, bad, bae)
new_compare20(Just(@2(vyy33000, vyy33001)), Just(@2(vyy34000, vyy34001)), False, app(app(ty_@2, app(app(app(ty_@3, fc), fd), ff)), eg)) → new_compare22(vyy33000, vyy34000, new_esEs6(vyy33000, vyy34000, fc, fd, ff), fc, fd, ff)
new_compare20(Just(Just(vyy33000)), Just(Just(vyy34000)), False, app(ty_Maybe, app(app(ty_@2, ce), cf))) → new_ltEs1(vyy33000, vyy34000, ce, cf)
new_compare20(Just(Right(vyy33000)), Just(Right(vyy34000)), False, app(app(ty_Either, bda), app(app(app(ty_@3, bdf), bdg), bdh))) → new_ltEs2(vyy33000, vyy34000, bdf, bdg, bdh)
new_ltEs3(Right(vyy33000), Right(vyy34000), bda, app(ty_[], bdc)) → new_ltEs0(vyy33000, vyy34000, bdc)
new_ltEs2(@3(vyy33000, vyy33001, vyy33002), @3(vyy34000, vyy34001, vyy34002), ga, gb, app(app(ty_@2, ge), gf)) → new_ltEs1(vyy33002, vyy34002, ge, gf)
new_compare23(vyy33000, vyy34000, False, fg, fh) → new_ltEs3(vyy33000, vyy34000, fg, fh)
new_ltEs1(@2(vyy33000, vyy33001), @2(vyy34000, vyy34001), de, app(app(app(ty_@3, eb), ec), ed)) → new_ltEs2(vyy33001, vyy34001, eb, ec, ed)
new_ltEs(Just(vyy33000), Just(vyy34000), app(app(app(ty_@3, cg), da), db)) → new_ltEs2(vyy33000, vyy34000, cg, da, db)
new_compare20(Just(:(vyy33000, vyy33001)), Just(:(vyy34000, vyy34001)), False, app(ty_[], h)) → new_compare(vyy33001, vyy34001, h)
new_primCompAux(vyy33000, vyy34000, vyy98, app(ty_Maybe, ba)) → new_compare1(vyy33000, vyy34000, ba)
new_primCompAux(vyy33000, vyy34000, vyy98, app(app(app(ty_@3, be), bf), bg)) → new_compare3(vyy33000, vyy34000, be, bf, bg)
new_ltEs2(@3(vyy33000, vyy33001, vyy33002), @3(vyy34000, vyy34001, vyy34002), ga, app(ty_Maybe, hd), he) → new_lt(vyy33001, vyy34001, hd)
new_ltEs2(@3(vyy33000, vyy33001, vyy33002), @3(vyy34000, vyy34001, vyy34002), app(ty_[], bag), gb, he) → new_lt0(vyy33000, vyy34000, bag)
new_ltEs3(Left(vyy33000), Left(vyy34000), app(app(app(ty_@3, bcd), bce), bcf), bbh) → new_ltEs2(vyy33000, vyy34000, bcd, bce, bcf)
new_compare20(Just(@3(vyy33000, vyy33001, vyy33002)), Just(@3(vyy34000, vyy34001, vyy34002)), False, app(app(app(ty_@3, ga), app(ty_[], hf)), he)) → new_lt0(vyy33001, vyy34001, hf)
new_ltEs1(@2(vyy33000, vyy33001), @2(vyy34000, vyy34001), app(app(ty_Either, fg), fh), eg) → new_compare23(vyy33000, vyy34000, new_esEs7(vyy33000, vyy34000, fg, fh), fg, fh)
new_compare20(Just(@3(vyy33000, vyy33001, vyy33002)), Just(@3(vyy34000, vyy34001, vyy34002)), False, app(app(app(ty_@3, app(app(app(ty_@3, bbb), bbc), bbd)), gb), he)) → new_lt2(vyy33000, vyy34000, bbb, bbc, bbd)
new_ltEs2(@3(vyy33000, vyy33001, vyy33002), @3(vyy34000, vyy34001, vyy34002), ga, app(ty_[], hf), he) → new_lt0(vyy33001, vyy34001, hf)
new_compare20(Just(@2(vyy33000, vyy33001)), Just(@2(vyy34000, vyy34001)), False, app(app(ty_@2, de), app(ty_Maybe, df))) → new_ltEs(vyy33001, vyy34001, df)
new_compare20(Just(Just(vyy33000)), Just(Just(vyy34000)), False, app(ty_Maybe, app(ty_Maybe, cc))) → new_ltEs(vyy33000, vyy34000, cc)
new_ltEs3(Left(vyy33000), Left(vyy34000), app(app(ty_@2, bcb), bcc), bbh) → new_ltEs1(vyy33000, vyy34000, bcb, bcc)
new_compare22(vyy33000, vyy34000, False, fc, fd, ff) → new_ltEs2(vyy33000, vyy34000, fc, fd, ff)
new_compare20(Just(@2(vyy33000, vyy33001)), Just(@2(vyy34000, vyy34001)), False, app(app(ty_@2, de), app(app(app(ty_@3, eb), ec), ed))) → new_ltEs2(vyy33001, vyy34001, eb, ec, ed)
new_ltEs0(:(vyy33000, vyy33001), :(vyy34000, vyy34001), h) → new_compare(vyy33001, vyy34001, h)
new_compare20(Just(@2(vyy33000, vyy33001)), Just(@2(vyy34000, vyy34001)), False, app(app(ty_@2, app(app(ty_Either, fg), fh)), eg)) → new_compare23(vyy33000, vyy34000, new_esEs7(vyy33000, vyy34000, fg, fh), fg, fh)
new_ltEs3(Right(vyy33000), Right(vyy34000), bda, app(app(app(ty_@3, bdf), bdg), bdh)) → new_ltEs2(vyy33000, vyy34000, bdf, bdg, bdh)
new_compare20(Just(@2(vyy33000, vyy33001)), Just(@2(vyy34000, vyy34001)), False, app(app(ty_@2, app(ty_[], eh)), eg)) → new_compare(vyy33000, vyy34000, eh)
new_ltEs2(@3(vyy33000, vyy33001, vyy33002), @3(vyy34000, vyy34001, vyy34002), ga, gb, app(app(app(ty_@3, gg), gh), ha)) → new_ltEs2(vyy33002, vyy34002, gg, gh, ha)
new_ltEs2(@3(vyy33000, vyy33001, vyy33002), @3(vyy34000, vyy34001, vyy34002), app(app(ty_@2, bah), bba), gb, he) → new_lt1(vyy33000, vyy34000, bah, bba)
new_ltEs2(@3(vyy33000, vyy33001, vyy33002), @3(vyy34000, vyy34001, vyy34002), ga, gb, app(ty_[], gd)) → new_ltEs0(vyy33002, vyy34002, gd)
new_ltEs3(Left(vyy33000), Left(vyy34000), app(ty_[], bca), bbh) → new_ltEs0(vyy33000, vyy34000, bca)
new_compare2(vyy33000, vyy34000, fa, fb) → new_compare21(vyy33000, vyy34000, new_esEs5(vyy33000, vyy34000, fa, fb), fa, fb)
new_compare20(Just(@3(vyy33000, vyy33001, vyy33002)), Just(@3(vyy34000, vyy34001, vyy34002)), False, app(app(app(ty_@3, ga), gb), app(app(app(ty_@3, gg), gh), ha))) → new_ltEs2(vyy33002, vyy34002, gg, gh, ha)
new_compare20(Just(Left(vyy33000)), Just(Left(vyy34000)), False, app(app(ty_Either, app(app(ty_@2, bcb), bcc)), bbh)) → new_ltEs1(vyy33000, vyy34000, bcb, bcc)
new_ltEs2(@3(vyy33000, vyy33001, vyy33002), @3(vyy34000, vyy34001, vyy34002), app(app(ty_Either, bbe), bbf), gb, he) → new_lt3(vyy33000, vyy34000, bbe, bbf)
new_compare20(Just(@3(vyy33000, vyy33001, vyy33002)), Just(@3(vyy34000, vyy34001, vyy34002)), False, app(app(app(ty_@3, ga), gb), app(app(ty_@2, ge), gf))) → new_ltEs1(vyy33002, vyy34002, ge, gf)
new_ltEs(Just(vyy33000), Just(vyy34000), app(ty_Maybe, cc)) → new_ltEs(vyy33000, vyy34000, cc)
new_compare20(Just(@2(vyy33000, vyy33001)), Just(@2(vyy34000, vyy34001)), False, app(app(ty_@2, de), app(app(ty_Either, ee), ef))) → new_ltEs3(vyy33001, vyy34001, ee, ef)
new_compare3(vyy33000, vyy34000, fc, fd, ff) → new_compare22(vyy33000, vyy34000, new_esEs6(vyy33000, vyy34000, fc, fd, ff), fc, fd, ff)
new_compare20(Just(Left(vyy33000)), Just(Left(vyy34000)), False, app(app(ty_Either, app(ty_Maybe, bbg)), bbh)) → new_ltEs(vyy33000, vyy34000, bbg)
new_lt3(vyy33000, vyy34000, fg, fh) → new_compare23(vyy33000, vyy34000, new_esEs7(vyy33000, vyy34000, fg, fh), fg, fh)
new_compare20(Just(@3(vyy33000, vyy33001, vyy33002)), Just(@3(vyy34000, vyy34001, vyy34002)), False, app(app(app(ty_@3, ga), app(ty_Maybe, hd)), he)) → new_lt(vyy33001, vyy34001, hd)
new_compare20(Just(Left(vyy33000)), Just(Left(vyy34000)), False, app(app(ty_Either, app(app(app(ty_@3, bcd), bce), bcf)), bbh)) → new_ltEs2(vyy33000, vyy34000, bcd, bce, bcf)
new_compare21(vyy33000, vyy34000, False, fa, fb) → new_ltEs1(vyy33000, vyy34000, fa, fb)
new_compare20(Just(Just(vyy33000)), Just(Just(vyy34000)), False, app(ty_Maybe, app(app(app(ty_@3, cg), da), db))) → new_ltEs2(vyy33000, vyy34000, cg, da, db)
new_primCompAux(vyy33000, vyy34000, vyy98, app(app(ty_Either, bh), ca)) → new_compare4(vyy33000, vyy34000, bh, ca)
new_ltEs1(@2(vyy33000, vyy33001), @2(vyy34000, vyy34001), de, app(ty_[], dg)) → new_ltEs0(vyy33001, vyy34001, dg)
new_ltEs1(@2(vyy33000, vyy33001), @2(vyy34000, vyy34001), app(app(ty_@2, fa), fb), eg) → new_compare21(vyy33000, vyy34000, new_esEs5(vyy33000, vyy34000, fa, fb), fa, fb)
new_compare20(Just(@3(vyy33000, vyy33001, vyy33002)), Just(@3(vyy34000, vyy34001, vyy34002)), False, app(app(app(ty_@3, ga), gb), app(ty_Maybe, gc))) → new_ltEs(vyy33002, vyy34002, gc)
new_ltEs0(:(vyy33000, vyy33001), :(vyy34000, vyy34001), h) → new_primCompAux(vyy33000, vyy34000, new_compare0(vyy33001, vyy34001, h), h)
new_compare20(Just(:(vyy33000, vyy33001)), Just(:(vyy34000, vyy34001)), False, app(ty_[], h)) → new_primCompAux(vyy33000, vyy34000, new_compare0(vyy33001, vyy34001, h), h)
new_lt2(vyy33000, vyy34000, fc, fd, ff) → new_compare22(vyy33000, vyy34000, new_esEs6(vyy33000, vyy34000, fc, fd, ff), fc, fd, ff)
new_ltEs2(@3(vyy33000, vyy33001, vyy33002), @3(vyy34000, vyy34001, vyy34002), ga, app(app(ty_@2, hg), hh), he) → new_lt1(vyy33001, vyy34001, hg, hh)
new_compare20(Just(@2(vyy33000, vyy33001)), Just(@2(vyy34000, vyy34001)), False, app(app(ty_@2, app(app(ty_@2, fa), fb)), eg)) → new_compare21(vyy33000, vyy34000, new_esEs5(vyy33000, vyy34000, fa, fb), fa, fb)
new_ltEs(Just(vyy33000), Just(vyy34000), app(app(ty_@2, ce), cf)) → new_ltEs1(vyy33000, vyy34000, ce, cf)
new_primCompAux(vyy33000, vyy34000, vyy98, app(app(ty_@2, bc), bd)) → new_compare2(vyy33000, vyy34000, bc, bd)
new_compare(:(vyy33000, vyy33001), :(vyy34000, vyy34001), h) → new_compare(vyy33001, vyy34001, h)
new_ltEs2(@3(vyy33000, vyy33001, vyy33002), @3(vyy34000, vyy34001, vyy34002), app(ty_Maybe, baf), gb, he) → new_lt(vyy33000, vyy34000, baf)
new_compare20(Just(@3(vyy33000, vyy33001, vyy33002)), Just(@3(vyy34000, vyy34001, vyy34002)), False, app(app(app(ty_@3, ga), app(app(app(ty_@3, baa), bab), bac)), he)) → new_lt2(vyy33001, vyy34001, baa, bab, bac)
new_compare(:(vyy33000, vyy33001), :(vyy34000, vyy34001), h) → new_primCompAux(vyy33000, vyy34000, new_compare0(vyy33001, vyy34001, h), h)
new_compare20(Just(@2(vyy33000, vyy33001)), Just(@2(vyy34000, vyy34001)), False, app(app(ty_@2, de), app(app(ty_@2, dh), ea))) → new_ltEs1(vyy33001, vyy34001, dh, ea)
new_ltEs2(@3(vyy33000, vyy33001, vyy33002), @3(vyy34000, vyy34001, vyy34002), app(app(app(ty_@3, bbb), bbc), bbd), gb, he) → new_lt2(vyy33000, vyy34000, bbb, bbc, bbd)
new_compare1(vyy33000, vyy34000, cb) → new_compare20(vyy33000, vyy34000, new_esEs4(vyy33000, vyy34000, cb), cb)
new_ltEs1(@2(vyy33000, vyy33001), @2(vyy34000, vyy34001), de, app(app(ty_Either, ee), ef)) → new_ltEs3(vyy33001, vyy34001, ee, ef)
new_ltEs3(Right(vyy33000), Right(vyy34000), bda, app(app(ty_@2, bdd), bde)) → new_ltEs1(vyy33000, vyy34000, bdd, bde)
new_ltEs3(Right(vyy33000), Right(vyy34000), bda, app(ty_Maybe, bdb)) → new_ltEs(vyy33000, vyy34000, bdb)
new_compare20(Just(@3(vyy33000, vyy33001, vyy33002)), Just(@3(vyy34000, vyy34001, vyy34002)), False, app(app(app(ty_@3, ga), app(app(ty_@2, hg), hh)), he)) → new_lt1(vyy33001, vyy34001, hg, hh)
new_lt1(vyy33000, vyy34000, fa, fb) → new_compare21(vyy33000, vyy34000, new_esEs5(vyy33000, vyy34000, fa, fb), fa, fb)
new_ltEs2(@3(vyy33000, vyy33001, vyy33002), @3(vyy34000, vyy34001, vyy34002), ga, app(app(ty_Either, bad), bae), he) → new_lt3(vyy33001, vyy34001, bad, bae)
new_compare20(Just(Just(vyy33000)), Just(Just(vyy34000)), False, app(ty_Maybe, app(app(ty_Either, dc), dd))) → new_ltEs3(vyy33000, vyy34000, dc, dd)
new_compare20(Just(Right(vyy33000)), Just(Right(vyy34000)), False, app(app(ty_Either, bda), app(app(ty_@2, bdd), bde))) → new_ltEs1(vyy33000, vyy34000, bdd, bde)
new_compare20(Just(Right(vyy33000)), Just(Right(vyy34000)), False, app(app(ty_Either, bda), app(ty_[], bdc))) → new_ltEs0(vyy33000, vyy34000, bdc)
new_compare20(Just(Just(vyy33000)), Just(Just(vyy34000)), False, app(ty_Maybe, app(ty_[], cd))) → new_ltEs0(vyy33000, vyy34000, cd)
new_compare4(vyy33000, vyy34000, fg, fh) → new_compare23(vyy33000, vyy34000, new_esEs7(vyy33000, vyy34000, fg, fh), fg, fh)
The TRS R consists of the following rules:
new_esEs4(Just(vyy6000), Just(vyy500), app(ty_Maybe, ceh)) → new_esEs4(vyy6000, vyy500, ceh)
new_ltEs19(vyy3300, vyy3400, app(app(ty_@2, de), eg)) → new_ltEs5(vyy3300, vyy3400, de, eg)
new_esEs23(vyy33000, vyy34000, app(app(ty_Either, bbe), bbf)) → new_esEs7(vyy33000, vyy34000, bbe, bbf)
new_lt10(vyy33001, vyy34001, ty_Integer) → new_lt6(vyy33001, vyy34001)
new_lt4(vyy33000, vyy34000) → new_esEs8(new_compare5(vyy33000, vyy34000), LT)
new_esEs4(Just(vyy6000), Just(vyy500), ty_Ordering) → new_esEs8(vyy6000, vyy500)
new_esEs7(Left(vyy6000), Left(vyy500), app(app(ty_Either, bfa), bfb), bef) → new_esEs7(vyy6000, vyy500, bfa, bfb)
new_ltEs6(Left(vyy33000), Left(vyy34000), app(app(app(ty_@3, bcd), bce), bcf), bbh) → new_ltEs15(vyy33000, vyy34000, bcd, bce, bcf)
new_compare5(@0, @0) → EQ
new_esEs27(vyy6002, vyy502, app(ty_[], dbf)) → new_esEs16(vyy6002, vyy502, dbf)
new_lt10(vyy33001, vyy34001, ty_Char) → new_lt8(vyy33001, vyy34001)
new_esEs25(vyy6000, vyy500, ty_Integer) → new_esEs12(vyy6000, vyy500)
new_esEs25(vyy6000, vyy500, app(ty_[], chb)) → new_esEs16(vyy6000, vyy500, chb)
new_esEs7(Right(vyy6000), Right(vyy500), bfh, ty_Bool) → new_esEs15(vyy6000, vyy500)
new_esEs25(vyy6000, vyy500, ty_Bool) → new_esEs15(vyy6000, vyy500)
new_ltEs6(Right(vyy33000), Right(vyy34000), bda, ty_Char) → new_ltEs11(vyy33000, vyy34000)
new_esEs17(Char(vyy6000), Char(vyy500)) → new_primEqNat0(vyy6000, vyy500)
new_esEs7(Left(vyy6000), Left(vyy500), app(ty_Maybe, bfg), bef) → new_esEs4(vyy6000, vyy500, bfg)
new_esEs24(vyy33001, vyy34001, ty_Char) → new_esEs17(vyy33001, vyy34001)
new_ltEs6(Right(vyy33000), Right(vyy34000), bda, app(app(ty_@2, bdd), bde)) → new_ltEs5(vyy33000, vyy34000, bdd, bde)
new_esEs19(vyy6000, vyy500, ty_Bool) → new_esEs15(vyy6000, vyy500)
new_lt20(vyy33000, vyy34000, app(ty_Ratio, cfh)) → new_lt16(vyy33000, vyy34000, cfh)
new_lt10(vyy33001, vyy34001, app(ty_Ratio, cfd)) → new_lt16(vyy33001, vyy34001, cfd)
new_esEs19(vyy6000, vyy500, app(ty_[], cbf)) → new_esEs16(vyy6000, vyy500, cbf)
new_compare10(vyy33000, vyy34000, True, fa, fb) → LT
new_esEs26(vyy6001, vyy501, ty_Float) → new_esEs10(vyy6001, vyy501)
new_esEs26(vyy6001, vyy501, ty_Double) → new_esEs14(vyy6001, vyy501)
new_esEs24(vyy33001, vyy34001, app(ty_Maybe, hd)) → new_esEs4(vyy33001, vyy34001, hd)
new_esEs4(Nothing, Just(vyy500), cdf) → False
new_esEs4(Just(vyy6000), Nothing, cdf) → False
new_esEs4(Just(vyy6000), Just(vyy500), ty_Char) → new_esEs17(vyy6000, vyy500)
new_ltEs20(vyy33001, vyy34001, ty_@0) → new_ltEs8(vyy33001, vyy34001)
new_ltEs7(Just(vyy33000), Just(vyy34000), ty_Integer) → new_ltEs17(vyy33000, vyy34000)
new_esEs25(vyy6000, vyy500, ty_Char) → new_esEs17(vyy6000, vyy500)
new_primCompAux1(vyy33000, vyy34000, vyy98, h) → new_primCompAux0(vyy98, new_compare18(vyy33000, vyy34000, h))
new_ltEs18(vyy33002, vyy34002, app(ty_Ratio, cfe)) → new_ltEs12(vyy33002, vyy34002, cfe)
new_ltEs19(vyy3300, vyy3400, app(ty_Ratio, cfb)) → new_ltEs12(vyy3300, vyy3400, cfb)
new_compare18(vyy33000, vyy34000, ty_Double) → new_compare32(vyy33000, vyy34000)
new_compare18(vyy33000, vyy34000, ty_Float) → new_compare6(vyy33000, vyy34000)
new_ltEs6(Left(vyy33000), Left(vyy34000), ty_Char, bbh) → new_ltEs11(vyy33000, vyy34000)
new_compare29(vyy33000, vyy34000, False) → new_compare15(vyy33000, vyy34000, new_ltEs16(vyy33000, vyy34000))
new_primMulNat0(Zero, Zero) → Zero
new_ltEs8(vyy3300, vyy3400) → new_not(new_esEs8(new_compare5(vyy3300, vyy3400), GT))
new_esEs24(vyy33001, vyy34001, ty_@0) → new_esEs13(vyy33001, vyy34001)
new_esEs7(Right(vyy6000), Right(vyy500), bfh, ty_Double) → new_esEs14(vyy6000, vyy500)
new_ltEs4(vyy3300, vyy3400, h) → new_not(new_esEs8(new_compare0(vyy3300, vyy3400, h), GT))
new_esEs26(vyy6001, vyy501, app(ty_[], dad)) → new_esEs16(vyy6001, vyy501, dad)
new_esEs18(vyy6000, vyy500, app(ty_[], cab)) → new_esEs16(vyy6000, vyy500, cab)
new_compare29(vyy33000, vyy34000, True) → EQ
new_esEs4(Just(vyy6000), Just(vyy500), app(app(app(ty_@3, cee), cef), ceg)) → new_esEs6(vyy6000, vyy500, cee, cef, ceg)
new_esEs7(Left(vyy6000), Left(vyy500), ty_Double, bef) → new_esEs14(vyy6000, vyy500)
new_ltEs9(GT, LT) → False
new_esEs20(vyy6001, vyy501, app(ty_Maybe, cdd)) → new_esEs4(vyy6001, vyy501, cdd)
new_lt11(vyy33000, vyy34000, app(app(ty_@2, bah), bba)) → new_lt14(vyy33000, vyy34000, bah, bba)
new_ltEs16(False, True) → True
new_lt11(vyy33000, vyy34000, ty_Float) → new_lt5(vyy33000, vyy34000)
new_esEs7(Right(vyy6000), Right(vyy500), bfh, ty_Ordering) → new_esEs8(vyy6000, vyy500)
new_lt20(vyy33000, vyy34000, app(app(app(ty_@3, fc), fd), ff)) → new_lt18(vyy33000, vyy34000, fc, fd, ff)
new_esEs27(vyy6002, vyy502, ty_Integer) → new_esEs12(vyy6002, vyy502)
new_compare18(vyy33000, vyy34000, app(app(app(ty_@3, be), bf), bg)) → new_compare33(vyy33000, vyy34000, be, bf, bg)
new_ltEs16(True, False) → False
new_lt10(vyy33001, vyy34001, ty_@0) → new_lt4(vyy33001, vyy34001)
new_esEs23(vyy33000, vyy34000, app(ty_Maybe, baf)) → new_esEs4(vyy33000, vyy34000, baf)
new_ltEs19(vyy3300, vyy3400, ty_Bool) → new_ltEs16(vyy3300, vyy3400)
new_esEs27(vyy6002, vyy502, app(ty_Ratio, dba)) → new_esEs9(vyy6002, vyy502, dba)
new_compare30(vyy33000, vyy34000) → new_compare28(vyy33000, vyy34000, new_esEs8(vyy33000, vyy34000))
new_esEs23(vyy33000, vyy34000, ty_@0) → new_esEs13(vyy33000, vyy34000)
new_ltEs6(Left(vyy33000), Left(vyy34000), app(app(ty_Either, bcg), bch), bbh) → new_ltEs6(vyy33000, vyy34000, bcg, bch)
new_ltEs6(Left(vyy33000), Left(vyy34000), ty_Float, bbh) → new_ltEs10(vyy33000, vyy34000)
new_lt11(vyy33000, vyy34000, app(ty_[], bag)) → new_lt13(vyy33000, vyy34000, bag)
new_esEs24(vyy33001, vyy34001, app(app(ty_@2, hg), hh)) → new_esEs5(vyy33001, vyy34001, hg, hh)
new_esEs4(Just(vyy6000), Just(vyy500), ty_Float) → new_esEs10(vyy6000, vyy500)
new_esEs7(Right(vyy6000), Right(vyy500), bfh, app(ty_Ratio, bga)) → new_esEs9(vyy6000, vyy500, bga)
new_compare18(vyy33000, vyy34000, app(ty_Maybe, ba)) → new_compare7(vyy33000, vyy34000, ba)
new_esEs23(vyy33000, vyy34000, ty_Integer) → new_esEs12(vyy33000, vyy34000)
new_esEs25(vyy6000, vyy500, ty_Double) → new_esEs14(vyy6000, vyy500)
new_ltEs9(EQ, GT) → True
new_esEs28(vyy33000, vyy34000, ty_Double) → new_esEs14(vyy33000, vyy34000)
new_esEs12(Integer(vyy6000), Integer(vyy500)) → new_primEqInt(vyy6000, vyy500)
new_ltEs10(vyy3300, vyy3400) → new_not(new_esEs8(new_compare6(vyy3300, vyy3400), GT))
new_lt20(vyy33000, vyy34000, app(ty_[], eh)) → new_lt13(vyy33000, vyy34000, eh)
new_compare15(vyy33000, vyy34000, False) → GT
new_esEs26(vyy6001, vyy501, app(ty_Maybe, dah)) → new_esEs4(vyy6001, vyy501, dah)
new_ltEs6(Right(vyy33000), Right(vyy34000), bda, ty_Integer) → new_ltEs17(vyy33000, vyy34000)
new_esEs28(vyy33000, vyy34000, ty_Integer) → new_esEs12(vyy33000, vyy34000)
new_lt20(vyy33000, vyy34000, ty_Ordering) → new_lt15(vyy33000, vyy34000)
new_ltEs7(Just(vyy33000), Just(vyy34000), ty_Bool) → new_ltEs16(vyy33000, vyy34000)
new_esEs27(vyy6002, vyy502, ty_Double) → new_esEs14(vyy6002, vyy502)
new_ltEs16(True, True) → True
new_ltEs9(LT, EQ) → True
new_ltEs7(Just(vyy33000), Just(vyy34000), ty_Double) → new_ltEs14(vyy33000, vyy34000)
new_lt11(vyy33000, vyy34000, app(ty_Ratio, cfc)) → new_lt16(vyy33000, vyy34000, cfc)
new_pePe(False, vyy97) → vyy97
new_lt10(vyy33001, vyy34001, app(ty_[], hf)) → new_lt13(vyy33001, vyy34001, hf)
new_esEs7(Right(vyy6000), Left(vyy500), bfh, bef) → False
new_esEs7(Left(vyy6000), Right(vyy500), bfh, bef) → False
new_esEs15(True, False) → False
new_esEs15(False, True) → False
new_ltEs6(Left(vyy33000), Left(vyy34000), ty_Double, bbh) → new_ltEs14(vyy33000, vyy34000)
new_ltEs7(Just(vyy33000), Just(vyy34000), app(ty_Ratio, cga)) → new_ltEs12(vyy33000, vyy34000, cga)
new_ltEs19(vyy3300, vyy3400, ty_Float) → new_ltEs10(vyy3300, vyy3400)
new_esEs27(vyy6002, vyy502, app(app(ty_Either, dbd), dbe)) → new_esEs7(vyy6002, vyy502, dbd, dbe)
new_lt6(vyy33000, vyy34000) → new_esEs8(new_compare9(vyy33000, vyy34000), LT)
new_esEs28(vyy33000, vyy34000, ty_@0) → new_esEs13(vyy33000, vyy34000)
new_lt11(vyy33000, vyy34000, ty_Double) → new_lt17(vyy33000, vyy34000)
new_esEs26(vyy6001, vyy501, ty_@0) → new_esEs13(vyy6001, vyy501)
new_lt11(vyy33000, vyy34000, ty_Integer) → new_lt6(vyy33000, vyy34000)
new_esEs26(vyy6001, vyy501, ty_Int) → new_esEs11(vyy6001, vyy501)
new_compare15(vyy33000, vyy34000, True) → LT
new_esEs22(vyy6001, vyy501, ty_Int) → new_esEs11(vyy6001, vyy501)
new_esEs22(vyy6001, vyy501, ty_Integer) → new_esEs12(vyy6001, vyy501)
new_lt20(vyy33000, vyy34000, app(app(ty_@2, fa), fb)) → new_lt14(vyy33000, vyy34000, fa, fb)
new_ltEs9(EQ, EQ) → True
new_ltEs20(vyy33001, vyy34001, app(app(app(ty_@3, eb), ec), ed)) → new_ltEs15(vyy33001, vyy34001, eb, ec, ed)
new_esEs19(vyy6000, vyy500, app(app(ty_Either, cbd), cbe)) → new_esEs7(vyy6000, vyy500, cbd, cbe)
new_lt20(vyy33000, vyy34000, ty_Float) → new_lt5(vyy33000, vyy34000)
new_esEs20(vyy6001, vyy501, app(app(ty_@2, ccd), cce)) → new_esEs5(vyy6001, vyy501, ccd, cce)
new_ltEs18(vyy33002, vyy34002, ty_Int) → new_ltEs13(vyy33002, vyy34002)
new_lt20(vyy33000, vyy34000, app(app(ty_Either, fg), fh)) → new_lt7(vyy33000, vyy34000, fg, fh)
new_ltEs18(vyy33002, vyy34002, ty_Char) → new_ltEs11(vyy33002, vyy34002)
new_esEs23(vyy33000, vyy34000, ty_Double) → new_esEs14(vyy33000, vyy34000)
new_esEs7(Right(vyy6000), Right(vyy500), bfh, app(app(ty_@2, bgb), bgc)) → new_esEs5(vyy6000, vyy500, bgb, bgc)
new_ltEs6(Left(vyy33000), Left(vyy34000), ty_Ordering, bbh) → new_ltEs9(vyy33000, vyy34000)
new_primCmpNat0(Zero, Succ(vyy340000)) → LT
new_ltEs20(vyy33001, vyy34001, ty_Double) → new_ltEs14(vyy33001, vyy34001)
new_compare14(vyy33000, vyy34000, False) → GT
new_compare27(Nothing, Just(vyy3400), False, cff) → LT
new_esEs8(LT, LT) → True
new_esEs18(vyy6000, vyy500, ty_@0) → new_esEs13(vyy6000, vyy500)
new_lt10(vyy33001, vyy34001, ty_Ordering) → new_lt15(vyy33001, vyy34001)
new_esEs19(vyy6000, vyy500, app(ty_Maybe, ccb)) → new_esEs4(vyy6000, vyy500, ccb)
new_esEs7(Left(vyy6000), Left(vyy500), ty_Int, bef) → new_esEs11(vyy6000, vyy500)
new_esEs25(vyy6000, vyy500, ty_Ordering) → new_esEs8(vyy6000, vyy500)
new_esEs18(vyy6000, vyy500, app(ty_Ratio, bhe)) → new_esEs9(vyy6000, vyy500, bhe)
new_esEs24(vyy33001, vyy34001, app(app(ty_Either, bad), bae)) → new_esEs7(vyy33001, vyy34001, bad, bae)
new_esEs20(vyy6001, vyy501, app(app(app(ty_@3, cda), cdb), cdc)) → new_esEs6(vyy6001, vyy501, cda, cdb, cdc)
new_esEs28(vyy33000, vyy34000, ty_Float) → new_esEs10(vyy33000, vyy34000)
new_compare0([], [], h) → EQ
new_pePe(True, vyy97) → True
new_primEqNat0(Zero, Zero) → True
new_ltEs19(vyy3300, vyy3400, ty_Int) → new_ltEs13(vyy3300, vyy3400)
new_esEs20(vyy6001, vyy501, ty_Int) → new_esEs11(vyy6001, vyy501)
new_esEs26(vyy6001, vyy501, ty_Char) → new_esEs17(vyy6001, vyy501)
new_esEs7(Left(vyy6000), Left(vyy500), app(app(ty_@2, beg), beh), bef) → new_esEs5(vyy6000, vyy500, beg, beh)
new_ltEs18(vyy33002, vyy34002, ty_Float) → new_ltEs10(vyy33002, vyy34002)
new_primMulNat0(Succ(vyy600000), Succ(vyy50000)) → new_primPlusNat1(new_primMulNat0(vyy600000, Succ(vyy50000)), vyy50000)
new_esEs18(vyy6000, vyy500, ty_Bool) → new_esEs15(vyy6000, vyy500)
new_compare14(vyy33000, vyy34000, True) → LT
new_ltEs19(vyy3300, vyy3400, app(ty_[], h)) → new_ltEs4(vyy3300, vyy3400, h)
new_ltEs6(Right(vyy33000), Right(vyy34000), bda, app(app(app(ty_@3, bdf), bdg), bdh)) → new_ltEs15(vyy33000, vyy34000, bdf, bdg, bdh)
new_esEs7(Left(vyy6000), Left(vyy500), ty_Ordering, bef) → new_esEs8(vyy6000, vyy500)
new_esEs5(@2(vyy6000, vyy6001), @2(vyy500, vyy501), cag, cah) → new_asAs(new_esEs19(vyy6000, vyy500, cag), new_esEs20(vyy6001, vyy501, cah))
new_esEs26(vyy6001, vyy501, ty_Bool) → new_esEs15(vyy6001, vyy501)
new_ltEs9(EQ, LT) → False
new_ltEs13(vyy3300, vyy3400) → new_not(new_esEs8(new_compare16(vyy3300, vyy3400), GT))
new_ltEs7(Just(vyy33000), Just(vyy34000), ty_@0) → new_ltEs8(vyy33000, vyy34000)
new_esEs18(vyy6000, vyy500, app(app(ty_@2, bhf), bhg)) → new_esEs5(vyy6000, vyy500, bhf, bhg)
new_esEs7(Right(vyy6000), Right(vyy500), bfh, app(app(app(ty_@3, bgg), bgh), bha)) → new_esEs6(vyy6000, vyy500, bgg, bgh, bha)
new_sr(vyy6000, vyy500) → new_primMulInt(vyy6000, vyy500)
new_compare12(vyy33000, vyy34000, True, fc, fd, ff) → LT
new_ltEs7(Just(vyy33000), Just(vyy34000), ty_Int) → new_ltEs13(vyy33000, vyy34000)
new_esEs26(vyy6001, vyy501, ty_Ordering) → new_esEs8(vyy6001, vyy501)
new_esEs8(GT, GT) → True
new_ltEs12(vyy3300, vyy3400, cfb) → new_not(new_esEs8(new_compare31(vyy3300, vyy3400, cfb), GT))
new_esEs18(vyy6000, vyy500, app(app(app(ty_@3, cac), cad), cae)) → new_esEs6(vyy6000, vyy500, cac, cad, cae)
new_ltEs20(vyy33001, vyy34001, app(app(ty_Either, ee), ef)) → new_ltEs6(vyy33001, vyy34001, ee, ef)
new_ltEs7(Just(vyy33000), Just(vyy34000), app(app(app(ty_@3, cg), da), db)) → new_ltEs15(vyy33000, vyy34000, cg, da, db)
new_esEs7(Right(vyy6000), Right(vyy500), bfh, app(app(ty_Either, bgd), bge)) → new_esEs7(vyy6000, vyy500, bgd, bge)
new_lt20(vyy33000, vyy34000, ty_Double) → new_lt17(vyy33000, vyy34000)
new_esEs26(vyy6001, vyy501, app(app(app(ty_@3, dae), daf), dag)) → new_esEs6(vyy6001, vyy501, dae, daf, dag)
new_esEs8(GT, LT) → False
new_esEs8(LT, GT) → False
new_ltEs20(vyy33001, vyy34001, ty_Bool) → new_ltEs16(vyy33001, vyy34001)
new_ltEs19(vyy3300, vyy3400, app(app(app(ty_@3, ga), gb), he)) → new_ltEs15(vyy3300, vyy3400, ga, gb, he)
new_esEs26(vyy6001, vyy501, ty_Integer) → new_esEs12(vyy6001, vyy501)
new_ltEs6(Right(vyy33000), Right(vyy34000), bda, ty_Int) → new_ltEs13(vyy33000, vyy34000)
new_lt11(vyy33000, vyy34000, ty_@0) → new_lt4(vyy33000, vyy34000)
new_primEqInt(Neg(Succ(vyy60000)), Neg(Succ(vyy5000))) → new_primEqNat0(vyy60000, vyy5000)
new_esEs7(Right(vyy6000), Right(vyy500), bfh, ty_Char) → new_esEs17(vyy6000, vyy500)
new_esEs15(True, True) → True
new_esEs20(vyy6001, vyy501, ty_Ordering) → new_esEs8(vyy6001, vyy501)
new_esEs23(vyy33000, vyy34000, ty_Ordering) → new_esEs8(vyy33000, vyy34000)
new_compare27(Just(vyy3300), Nothing, False, cff) → GT
new_compare18(vyy33000, vyy34000, ty_Ordering) → new_compare30(vyy33000, vyy34000)
new_compare19(vyy33000, vyy34000, fa, fb) → new_compare24(vyy33000, vyy34000, new_esEs5(vyy33000, vyy34000, fa, fb), fa, fb)
new_esEs28(vyy33000, vyy34000, app(ty_Maybe, cb)) → new_esEs4(vyy33000, vyy34000, cb)
new_ltEs7(Just(vyy33000), Just(vyy34000), app(ty_[], cd)) → new_ltEs4(vyy33000, vyy34000, cd)
new_compare27(Nothing, Nothing, False, cff) → LT
new_compare18(vyy33000, vyy34000, app(ty_Ratio, cfa)) → new_compare31(vyy33000, vyy34000, cfa)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs24(vyy33001, vyy34001, app(app(app(ty_@3, baa), bab), bac)) → new_esEs6(vyy33001, vyy34001, baa, bab, bac)
new_esEs18(vyy6000, vyy500, ty_Float) → new_esEs10(vyy6000, vyy500)
new_ltEs6(Right(vyy33000), Right(vyy34000), bda, app(ty_Ratio, bed)) → new_ltEs12(vyy33000, vyy34000, bed)
new_esEs19(vyy6000, vyy500, ty_Integer) → new_esEs12(vyy6000, vyy500)
new_primEqInt(Neg(Zero), Neg(Succ(vyy5000))) → False
new_primEqInt(Neg(Succ(vyy60000)), Neg(Zero)) → False
new_ltEs20(vyy33001, vyy34001, app(ty_[], dg)) → new_ltEs4(vyy33001, vyy34001, dg)
new_primCompAux0(vyy103, GT) → GT
new_esEs8(EQ, EQ) → True
new_esEs20(vyy6001, vyy501, ty_Bool) → new_esEs15(vyy6001, vyy501)
new_esEs4(Just(vyy6000), Just(vyy500), ty_@0) → new_esEs13(vyy6000, vyy500)
new_primPlusNat1(Zero, vyy50000) → Succ(vyy50000)
new_compare24(vyy33000, vyy34000, True, fa, fb) → EQ
new_ltEs9(LT, LT) → True
new_compare32(Double(vyy33000, vyy33001), Double(vyy34000, vyy34001)) → new_compare16(new_sr(vyy33000, vyy34000), new_sr(vyy33001, vyy34001))
new_esEs26(vyy6001, vyy501, app(app(ty_Either, dab), dac)) → new_esEs7(vyy6001, vyy501, dab, dac)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_lt20(vyy33000, vyy34000, ty_Char) → new_lt8(vyy33000, vyy34000)
new_ltEs20(vyy33001, vyy34001, app(app(ty_@2, dh), ea)) → new_ltEs5(vyy33001, vyy34001, dh, ea)
new_compare31(:%(vyy33000, vyy33001), :%(vyy34000, vyy34001), ty_Integer) → new_compare9(new_sr0(vyy33000, vyy34001), new_sr0(vyy34000, vyy33001))
new_ltEs18(vyy33002, vyy34002, ty_@0) → new_ltEs8(vyy33002, vyy34002)
new_esEs4(Just(vyy6000), Just(vyy500), app(app(ty_Either, ceb), cec)) → new_esEs7(vyy6000, vyy500, ceb, cec)
new_primCmpNat0(Succ(vyy330000), Succ(vyy340000)) → new_primCmpNat0(vyy330000, vyy340000)
new_esEs23(vyy33000, vyy34000, ty_Float) → new_esEs10(vyy33000, vyy34000)
new_ltEs18(vyy33002, vyy34002, app(app(ty_Either, hb), hc)) → new_ltEs6(vyy33002, vyy34002, hb, hc)
new_esEs25(vyy6000, vyy500, app(ty_Maybe, chf)) → new_esEs4(vyy6000, vyy500, chf)
new_compare18(vyy33000, vyy34000, ty_@0) → new_compare5(vyy33000, vyy34000)
new_esEs18(vyy6000, vyy500, ty_Double) → new_esEs14(vyy6000, vyy500)
new_esEs4(Just(vyy6000), Just(vyy500), ty_Bool) → new_esEs15(vyy6000, vyy500)
new_primEqInt(Pos(Succ(vyy60000)), Pos(Succ(vyy5000))) → new_primEqNat0(vyy60000, vyy5000)
new_compare10(vyy33000, vyy34000, False, fa, fb) → GT
new_ltEs19(vyy3300, vyy3400, ty_Integer) → new_ltEs17(vyy3300, vyy3400)
new_ltEs5(@2(vyy33000, vyy33001), @2(vyy34000, vyy34001), de, eg) → new_pePe(new_lt20(vyy33000, vyy34000, de), new_asAs(new_esEs28(vyy33000, vyy34000, de), new_ltEs20(vyy33001, vyy34001, eg)))
new_esEs4(Just(vyy6000), Just(vyy500), app(app(ty_@2, cdh), cea)) → new_esEs5(vyy6000, vyy500, cdh, cea)
new_esEs28(vyy33000, vyy34000, ty_Char) → new_esEs17(vyy33000, vyy34000)
new_ltEs18(vyy33002, vyy34002, app(app(app(ty_@3, gg), gh), ha)) → new_ltEs15(vyy33002, vyy34002, gg, gh, ha)
new_lt10(vyy33001, vyy34001, app(ty_Maybe, hd)) → new_lt12(vyy33001, vyy34001, hd)
new_esEs23(vyy33000, vyy34000, ty_Char) → new_esEs17(vyy33000, vyy34000)
new_compare17(vyy33000, vyy34000, fg, fh) → new_compare25(vyy33000, vyy34000, new_esEs7(vyy33000, vyy34000, fg, fh), fg, fh)
new_ltEs7(Just(vyy33000), Just(vyy34000), ty_Float) → new_ltEs10(vyy33000, vyy34000)
new_ltEs7(Just(vyy33000), Just(vyy34000), app(app(ty_Either, dc), dd)) → new_ltEs6(vyy33000, vyy34000, dc, dd)
new_ltEs7(Nothing, Just(vyy34000), cfg) → True
new_primEqNat0(Succ(vyy60000), Succ(vyy5000)) → new_primEqNat0(vyy60000, vyy5000)
new_esEs27(vyy6002, vyy502, ty_Ordering) → new_esEs8(vyy6002, vyy502)
new_esEs7(Right(vyy6000), Right(vyy500), bfh, app(ty_[], bgf)) → new_esEs16(vyy6000, vyy500, bgf)
new_esEs19(vyy6000, vyy500, app(app(app(ty_@3, cbg), cbh), cca)) → new_esEs6(vyy6000, vyy500, cbg, cbh, cca)
new_esEs20(vyy6001, vyy501, ty_Double) → new_esEs14(vyy6001, vyy501)
new_ltEs19(vyy3300, vyy3400, ty_Double) → new_ltEs14(vyy3300, vyy3400)
new_compare25(vyy33000, vyy34000, False, fg, fh) → new_compare11(vyy33000, vyy34000, new_ltEs6(vyy33000, vyy34000, fg, fh), fg, fh)
new_esEs7(Right(vyy6000), Right(vyy500), bfh, ty_Float) → new_esEs10(vyy6000, vyy500)
new_esEs20(vyy6001, vyy501, ty_Float) → new_esEs10(vyy6001, vyy501)
new_esEs28(vyy33000, vyy34000, ty_Int) → new_esEs11(vyy33000, vyy34000)
new_lt20(vyy33000, vyy34000, ty_@0) → new_lt4(vyy33000, vyy34000)
new_primCmpInt(Neg(Succ(vyy330000)), Neg(vyy34000)) → new_primCmpNat0(vyy34000, Succ(vyy330000))
new_ltEs18(vyy33002, vyy34002, app(app(ty_@2, ge), gf)) → new_ltEs5(vyy33002, vyy34002, ge, gf)
new_esEs24(vyy33001, vyy34001, ty_Ordering) → new_esEs8(vyy33001, vyy34001)
new_esEs18(vyy6000, vyy500, ty_Char) → new_esEs17(vyy6000, vyy500)
new_lt19(vyy33000, vyy34000) → new_esEs8(new_compare34(vyy33000, vyy34000), LT)
new_esEs23(vyy33000, vyy34000, ty_Bool) → new_esEs15(vyy33000, vyy34000)
new_ltEs6(Left(vyy33000), Right(vyy34000), bda, bbh) → True
new_lt11(vyy33000, vyy34000, app(app(app(ty_@3, bbb), bbc), bbd)) → new_lt18(vyy33000, vyy34000, bbb, bbc, bbd)
new_esEs10(Float(vyy6000, vyy6001), Float(vyy500, vyy501)) → new_esEs11(new_sr(vyy6000, vyy500), new_sr(vyy6001, vyy501))
new_esEs21(vyy6000, vyy500, ty_Int) → new_esEs11(vyy6000, vyy500)
new_ltEs6(Right(vyy33000), Left(vyy34000), bda, bbh) → False
new_esEs28(vyy33000, vyy34000, ty_Ordering) → new_esEs8(vyy33000, vyy34000)
new_esEs8(EQ, LT) → False
new_esEs8(LT, EQ) → False
new_primEqInt(Pos(Succ(vyy60000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(vyy5000))) → False
new_lt10(vyy33001, vyy34001, app(app(ty_Either, bad), bae)) → new_lt7(vyy33001, vyy34001, bad, bae)
new_compare13(vyy83, vyy84, True, bhc) → LT
new_primPlusNat0(Zero, Succ(vyy500000)) → Succ(vyy500000)
new_primPlusNat0(Succ(vyy9900), Zero) → Succ(vyy9900)
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(vyy330000), Zero) → GT
new_ltEs19(vyy3300, vyy3400, ty_Ordering) → new_ltEs9(vyy3300, vyy3400)
new_esEs23(vyy33000, vyy34000, app(app(ty_@2, bah), bba)) → new_esEs5(vyy33000, vyy34000, bah, bba)
new_ltEs6(Left(vyy33000), Left(vyy34000), app(app(ty_@2, bcb), bcc), bbh) → new_ltEs5(vyy33000, vyy34000, bcb, bcc)
new_esEs19(vyy6000, vyy500, ty_@0) → new_esEs13(vyy6000, vyy500)
new_primCmpInt(Neg(Zero), Pos(Succ(vyy340000))) → LT
new_compare11(vyy33000, vyy34000, True, fg, fh) → LT
new_ltEs20(vyy33001, vyy34001, ty_Integer) → new_ltEs17(vyy33001, vyy34001)
new_sr0(Integer(vyy340000), Integer(vyy330010)) → Integer(new_primMulInt(vyy340000, vyy330010))
new_primEqInt(Neg(Succ(vyy60000)), Pos(vyy500)) → False
new_primEqInt(Pos(Succ(vyy60000)), Neg(vyy500)) → False
new_esEs6(@3(vyy6000, vyy6001, vyy6002), @3(vyy500, vyy501, vyy502), cgb, cgc, cgd) → new_asAs(new_esEs25(vyy6000, vyy500, cgb), new_asAs(new_esEs26(vyy6001, vyy501, cgc), new_esEs27(vyy6002, vyy502, cgd)))
new_esEs25(vyy6000, vyy500, ty_@0) → new_esEs13(vyy6000, vyy500)
new_esEs16(:(vyy6000, vyy6001), :(vyy500, vyy501), bhd) → new_asAs(new_esEs18(vyy6000, vyy500, bhd), new_esEs16(vyy6001, vyy501, bhd))
new_ltEs6(Left(vyy33000), Left(vyy34000), ty_Int, bbh) → new_ltEs13(vyy33000, vyy34000)
new_lt7(vyy33000, vyy34000, fg, fh) → new_esEs8(new_compare17(vyy33000, vyy34000, fg, fh), LT)
new_ltEs7(Just(vyy33000), Just(vyy34000), app(app(ty_@2, ce), cf)) → new_ltEs5(vyy33000, vyy34000, ce, cf)
new_primEqInt(Neg(Zero), Pos(Succ(vyy5000))) → False
new_primEqInt(Pos(Zero), Neg(Succ(vyy5000))) → False
new_esEs13(@0, @0) → True
new_lt11(vyy33000, vyy34000, app(ty_Maybe, baf)) → new_lt12(vyy33000, vyy34000, baf)
new_primCmpInt(Pos(Zero), Pos(Succ(vyy340000))) → new_primCmpNat0(Zero, Succ(vyy340000))
new_esEs28(vyy33000, vyy34000, app(app(ty_Either, fg), fh)) → new_esEs7(vyy33000, vyy34000, fg, fh)
new_esEs7(Right(vyy6000), Right(vyy500), bfh, ty_@0) → new_esEs13(vyy6000, vyy500)
new_esEs9(:%(vyy6000, vyy6001), :%(vyy500, vyy501), cde) → new_asAs(new_esEs21(vyy6000, vyy500, cde), new_esEs22(vyy6001, vyy501, cde))
new_esEs7(Right(vyy6000), Right(vyy500), bfh, app(ty_Maybe, bhb)) → new_esEs4(vyy6000, vyy500, bhb)
new_ltEs20(vyy33001, vyy34001, ty_Int) → new_ltEs13(vyy33001, vyy34001)
new_ltEs6(Right(vyy33000), Right(vyy34000), bda, app(ty_Maybe, bdb)) → new_ltEs7(vyy33000, vyy34000, bdb)
new_lt20(vyy33000, vyy34000, ty_Integer) → new_lt6(vyy33000, vyy34000)
new_esEs27(vyy6002, vyy502, ty_Float) → new_esEs10(vyy6002, vyy502)
new_esEs4(Just(vyy6000), Just(vyy500), ty_Integer) → new_esEs12(vyy6000, vyy500)
new_esEs8(GT, EQ) → False
new_esEs8(EQ, GT) → False
new_esEs4(Just(vyy6000), Just(vyy500), app(ty_Ratio, cdg)) → new_esEs9(vyy6000, vyy500, cdg)
new_lt11(vyy33000, vyy34000, app(app(ty_Either, bbe), bbf)) → new_lt7(vyy33000, vyy34000, bbe, bbf)
new_esEs26(vyy6001, vyy501, app(app(ty_@2, chh), daa)) → new_esEs5(vyy6001, vyy501, chh, daa)
new_primCompAux0(vyy103, LT) → LT
new_ltEs6(Left(vyy33000), Left(vyy34000), ty_Integer, bbh) → new_ltEs17(vyy33000, vyy34000)
new_lt20(vyy33000, vyy34000, ty_Bool) → new_lt19(vyy33000, vyy34000)
new_lt10(vyy33001, vyy34001, app(app(ty_@2, hg), hh)) → new_lt14(vyy33001, vyy34001, hg, hh)
new_esEs11(vyy600, vyy50) → new_primEqInt(vyy600, vyy50)
new_not(False) → True
new_ltEs15(@3(vyy33000, vyy33001, vyy33002), @3(vyy34000, vyy34001, vyy34002), ga, gb, he) → new_pePe(new_lt11(vyy33000, vyy34000, ga), new_asAs(new_esEs23(vyy33000, vyy34000, ga), new_pePe(new_lt10(vyy33001, vyy34001, gb), new_asAs(new_esEs24(vyy33001, vyy34001, gb), new_ltEs18(vyy33002, vyy34002, he)))))
new_compare18(vyy33000, vyy34000, app(app(ty_@2, bc), bd)) → new_compare19(vyy33000, vyy34000, bc, bd)
new_esEs14(Double(vyy6000, vyy6001), Double(vyy500, vyy501)) → new_esEs11(new_sr(vyy6000, vyy500), new_sr(vyy6001, vyy501))
new_esEs28(vyy33000, vyy34000, app(ty_[], eh)) → new_esEs16(vyy33000, vyy34000, eh)
new_primCmpInt(Pos(Succ(vyy330000)), Pos(vyy34000)) → new_primCmpNat0(Succ(vyy330000), vyy34000)
new_compare12(vyy33000, vyy34000, False, fc, fd, ff) → GT
new_esEs19(vyy6000, vyy500, ty_Int) → new_esEs11(vyy6000, vyy500)
new_esEs7(Left(vyy6000), Left(vyy500), ty_Integer, bef) → new_esEs12(vyy6000, vyy500)
new_esEs19(vyy6000, vyy500, ty_Char) → new_esEs17(vyy6000, vyy500)
new_ltEs9(LT, GT) → True
new_ltEs20(vyy33001, vyy34001, ty_Char) → new_ltEs11(vyy33001, vyy34001)
new_ltEs14(vyy3300, vyy3400) → new_not(new_esEs8(new_compare32(vyy3300, vyy3400), GT))
new_esEs25(vyy6000, vyy500, ty_Float) → new_esEs10(vyy6000, vyy500)
new_lt11(vyy33000, vyy34000, ty_Char) → new_lt8(vyy33000, vyy34000)
new_esEs24(vyy33001, vyy34001, ty_Integer) → new_esEs12(vyy33001, vyy34001)
new_esEs28(vyy33000, vyy34000, app(app(ty_@2, fa), fb)) → new_esEs5(vyy33000, vyy34000, fa, fb)
new_compare0(:(vyy33000, vyy33001), [], h) → GT
new_ltEs18(vyy33002, vyy34002, app(ty_Maybe, gc)) → new_ltEs7(vyy33002, vyy34002, gc)
new_esEs18(vyy6000, vyy500, app(ty_Maybe, caf)) → new_esEs4(vyy6000, vyy500, caf)
new_compare28(vyy33000, vyy34000, True) → EQ
new_esEs7(Left(vyy6000), Left(vyy500), app(ty_Ratio, bee), bef) → new_esEs9(vyy6000, vyy500, bee)
new_compare18(vyy33000, vyy34000, ty_Char) → new_compare8(vyy33000, vyy34000)
new_compare6(Float(vyy33000, vyy33001), Float(vyy34000, vyy34001)) → new_compare16(new_sr(vyy33000, vyy34000), new_sr(vyy33001, vyy34001))
new_esEs27(vyy6002, vyy502, ty_Int) → new_esEs11(vyy6002, vyy502)
new_compare11(vyy33000, vyy34000, False, fg, fh) → GT
new_lt11(vyy33000, vyy34000, ty_Bool) → new_lt19(vyy33000, vyy34000)
new_compare18(vyy33000, vyy34000, app(ty_[], bb)) → new_compare0(vyy33000, vyy34000, bb)
new_ltEs7(Just(vyy33000), Just(vyy34000), app(ty_Maybe, cc)) → new_ltEs7(vyy33000, vyy34000, cc)
new_primCmpInt(Pos(Succ(vyy330000)), Neg(vyy34000)) → GT
new_esEs18(vyy6000, vyy500, app(app(ty_Either, bhh), caa)) → new_esEs7(vyy6000, vyy500, bhh, caa)
new_lt15(vyy33000, vyy34000) → new_esEs8(new_compare30(vyy33000, vyy34000), LT)
new_primMulInt(Pos(vyy60000), Pos(vyy5000)) → Pos(new_primMulNat0(vyy60000, vyy5000))
new_ltEs6(Right(vyy33000), Right(vyy34000), bda, ty_@0) → new_ltEs8(vyy33000, vyy34000)
new_compare24(vyy33000, vyy34000, False, fa, fb) → new_compare10(vyy33000, vyy34000, new_ltEs5(vyy33000, vyy34000, fa, fb), fa, fb)
new_esEs27(vyy6002, vyy502, ty_Char) → new_esEs17(vyy6002, vyy502)
new_ltEs18(vyy33002, vyy34002, ty_Integer) → new_ltEs17(vyy33002, vyy34002)
new_primMulInt(Neg(vyy60000), Neg(vyy5000)) → Pos(new_primMulNat0(vyy60000, vyy5000))
new_esEs24(vyy33001, vyy34001, ty_Bool) → new_esEs15(vyy33001, vyy34001)
new_esEs28(vyy33000, vyy34000, app(ty_Ratio, cfh)) → new_esEs9(vyy33000, vyy34000, cfh)
new_primEqNat0(Zero, Succ(vyy5000)) → False
new_primEqNat0(Succ(vyy60000), Zero) → False
new_esEs7(Left(vyy6000), Left(vyy500), app(ty_[], bfc), bef) → new_esEs16(vyy6000, vyy500, bfc)
new_ltEs7(Just(vyy33000), Just(vyy34000), ty_Ordering) → new_ltEs9(vyy33000, vyy34000)
new_primPlusNat0(Zero, Zero) → Zero
new_ltEs6(Right(vyy33000), Right(vyy34000), bda, ty_Float) → new_ltEs10(vyy33000, vyy34000)
new_compare25(vyy33000, vyy34000, True, fg, fh) → EQ
new_lt13(vyy33000, vyy34000, eh) → new_esEs8(new_compare0(vyy33000, vyy34000, eh), LT)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs28(vyy33000, vyy34000, app(app(app(ty_@3, fc), fd), ff)) → new_esEs6(vyy33000, vyy34000, fc, fd, ff)
new_esEs4(Nothing, Nothing, cdf) → True
new_esEs7(Left(vyy6000), Left(vyy500), ty_Char, bef) → new_esEs17(vyy6000, vyy500)
new_esEs27(vyy6002, vyy502, app(app(app(ty_@3, dbg), dbh), dca)) → new_esEs6(vyy6002, vyy502, dbg, dbh, dca)
new_lt10(vyy33001, vyy34001, ty_Int) → new_lt9(vyy33001, vyy34001)
new_esEs27(vyy6002, vyy502, app(app(ty_@2, dbb), dbc)) → new_esEs5(vyy6002, vyy502, dbb, dbc)
new_esEs16(:(vyy6000, vyy6001), [], bhd) → False
new_esEs16([], :(vyy500, vyy501), bhd) → False
new_ltEs9(GT, GT) → True
new_esEs23(vyy33000, vyy34000, ty_Int) → new_esEs11(vyy33000, vyy34000)
new_ltEs7(Nothing, Nothing, cfg) → True
new_esEs27(vyy6002, vyy502, app(ty_Maybe, dcb)) → new_esEs4(vyy6002, vyy502, dcb)
new_primPlusNat1(Succ(vyy990), vyy50000) → Succ(Succ(new_primPlusNat0(vyy990, vyy50000)))
new_compare13(vyy83, vyy84, False, bhc) → GT
new_lt16(vyy33000, vyy34000, cfh) → new_esEs8(new_compare31(vyy33000, vyy34000, cfh), LT)
new_primCmpInt(Neg(Zero), Neg(Succ(vyy340000))) → new_primCmpNat0(Succ(vyy340000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(vyy340000))) → GT
new_ltEs6(Left(vyy33000), Left(vyy34000), app(ty_Ratio, bec), bbh) → new_ltEs12(vyy33000, vyy34000, bec)
new_compare0(:(vyy33000, vyy33001), :(vyy34000, vyy34001), h) → new_primCompAux1(vyy33000, vyy34000, new_compare0(vyy33001, vyy34001, h), h)
new_compare28(vyy33000, vyy34000, False) → new_compare14(vyy33000, vyy34000, new_ltEs9(vyy33000, vyy34000))
new_lt14(vyy33000, vyy34000, fa, fb) → new_esEs8(new_compare19(vyy33000, vyy34000, fa, fb), LT)
new_esEs4(Just(vyy6000), Just(vyy500), app(ty_[], ced)) → new_esEs16(vyy6000, vyy500, ced)
new_esEs19(vyy6000, vyy500, ty_Double) → new_esEs14(vyy6000, vyy500)
new_compare7(vyy33000, vyy34000, cb) → new_compare27(vyy33000, vyy34000, new_esEs4(vyy33000, vyy34000, cb), cb)
new_esEs24(vyy33001, vyy34001, ty_Int) → new_esEs11(vyy33001, vyy34001)
new_lt11(vyy33000, vyy34000, ty_Ordering) → new_lt15(vyy33000, vyy34000)
new_esEs18(vyy6000, vyy500, ty_Integer) → new_esEs12(vyy6000, vyy500)
new_esEs20(vyy6001, vyy501, app(app(ty_Either, ccf), ccg)) → new_esEs7(vyy6001, vyy501, ccf, ccg)
new_ltEs17(vyy3300, vyy3400) → new_not(new_esEs8(new_compare9(vyy3300, vyy3400), GT))
new_ltEs6(Right(vyy33000), Right(vyy34000), bda, app(app(ty_Either, bea), beb)) → new_ltEs6(vyy33000, vyy34000, bea, beb)
new_esEs19(vyy6000, vyy500, app(app(ty_@2, cbb), cbc)) → new_esEs5(vyy6000, vyy500, cbb, cbc)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_lt9(vyy33000, vyy34000) → new_esEs8(new_compare16(vyy33000, vyy34000), LT)
new_esEs4(Just(vyy6000), Just(vyy500), ty_Double) → new_esEs14(vyy6000, vyy500)
new_esEs20(vyy6001, vyy501, app(ty_[], cch)) → new_esEs16(vyy6001, vyy501, cch)
new_compare9(Integer(vyy33000), Integer(vyy34000)) → new_primCmpInt(vyy33000, vyy34000)
new_asAs(False, vyy90) → False
new_esEs25(vyy6000, vyy500, app(ty_Ratio, cge)) → new_esEs9(vyy6000, vyy500, cge)
new_ltEs6(Left(vyy33000), Left(vyy34000), app(ty_Maybe, bbg), bbh) → new_ltEs7(vyy33000, vyy34000, bbg)
new_esEs19(vyy6000, vyy500, ty_Float) → new_esEs10(vyy6000, vyy500)
new_compare34(vyy33000, vyy34000) → new_compare29(vyy33000, vyy34000, new_esEs15(vyy33000, vyy34000))
new_primMulInt(Pos(vyy60000), Neg(vyy5000)) → Neg(new_primMulNat0(vyy60000, vyy5000))
new_primMulInt(Neg(vyy60000), Pos(vyy5000)) → Neg(new_primMulNat0(vyy60000, vyy5000))
new_ltEs19(vyy3300, vyy3400, ty_Char) → new_ltEs11(vyy3300, vyy3400)
new_compare16(vyy3300, vyy3400) → new_primCmpInt(vyy3300, vyy3400)
new_primMulNat0(Zero, Succ(vyy50000)) → Zero
new_primMulNat0(Succ(vyy600000), Zero) → Zero
new_esEs7(Left(vyy6000), Left(vyy500), ty_Float, bef) → new_esEs10(vyy6000, vyy500)
new_esEs23(vyy33000, vyy34000, app(app(app(ty_@3, bbb), bbc), bbd)) → new_esEs6(vyy33000, vyy34000, bbb, bbc, bbd)
new_ltEs18(vyy33002, vyy34002, app(ty_[], gd)) → new_ltEs4(vyy33002, vyy34002, gd)
new_esEs24(vyy33001, vyy34001, ty_Float) → new_esEs10(vyy33001, vyy34001)
new_compare31(:%(vyy33000, vyy33001), :%(vyy34000, vyy34001), ty_Int) → new_compare16(new_sr(vyy33000, vyy34001), new_sr(vyy34000, vyy33001))
new_esEs24(vyy33001, vyy34001, app(ty_[], hf)) → new_esEs16(vyy33001, vyy34001, hf)
new_ltEs20(vyy33001, vyy34001, ty_Ordering) → new_ltEs9(vyy33001, vyy34001)
new_esEs26(vyy6001, vyy501, app(ty_Ratio, chg)) → new_esEs9(vyy6001, vyy501, chg)
new_esEs27(vyy6002, vyy502, ty_@0) → new_esEs13(vyy6002, vyy502)
new_esEs18(vyy6000, vyy500, ty_Ordering) → new_esEs8(vyy6000, vyy500)
new_ltEs11(vyy3300, vyy3400) → new_not(new_esEs8(new_compare8(vyy3300, vyy3400), GT))
new_ltEs20(vyy33001, vyy34001, app(ty_Ratio, dcc)) → new_ltEs12(vyy33001, vyy34001, dcc)
new_esEs25(vyy6000, vyy500, app(app(app(ty_@3, chc), chd), che)) → new_esEs6(vyy6000, vyy500, chc, chd, che)
new_ltEs9(GT, EQ) → False
new_esEs7(Left(vyy6000), Left(vyy500), app(app(app(ty_@3, bfd), bfe), bff), bef) → new_esEs6(vyy6000, vyy500, bfd, bfe, bff)
new_esEs20(vyy6001, vyy501, ty_Integer) → new_esEs12(vyy6001, vyy501)
new_lt10(vyy33001, vyy34001, ty_Float) → new_lt5(vyy33001, vyy34001)
new_ltEs19(vyy3300, vyy3400, ty_@0) → new_ltEs8(vyy3300, vyy3400)
new_esEs28(vyy33000, vyy34000, ty_Bool) → new_esEs15(vyy33000, vyy34000)
new_lt5(vyy33000, vyy34000) → new_esEs8(new_compare6(vyy33000, vyy34000), LT)
new_esEs18(vyy6000, vyy500, ty_Int) → new_esEs11(vyy6000, vyy500)
new_compare18(vyy33000, vyy34000, ty_Bool) → new_compare34(vyy33000, vyy34000)
new_ltEs20(vyy33001, vyy34001, ty_Float) → new_ltEs10(vyy33001, vyy34001)
new_esEs7(Right(vyy6000), Right(vyy500), bfh, ty_Int) → new_esEs11(vyy6000, vyy500)
new_ltEs7(Just(vyy33000), Nothing, cfg) → False
new_esEs4(Just(vyy6000), Just(vyy500), ty_Int) → new_esEs11(vyy6000, vyy500)
new_esEs7(Right(vyy6000), Right(vyy500), bfh, ty_Integer) → new_esEs12(vyy6000, vyy500)
new_ltEs7(Just(vyy33000), Just(vyy34000), ty_Char) → new_ltEs11(vyy33000, vyy34000)
new_esEs16([], [], bhd) → True
new_esEs20(vyy6001, vyy501, app(ty_Ratio, ccc)) → new_esEs9(vyy6001, vyy501, ccc)
new_lt11(vyy33000, vyy34000, ty_Int) → new_lt9(vyy33000, vyy34000)
new_esEs25(vyy6000, vyy500, app(app(ty_@2, cgf), cgg)) → new_esEs5(vyy6000, vyy500, cgf, cgg)
new_lt10(vyy33001, vyy34001, ty_Bool) → new_lt19(vyy33001, vyy34001)
new_ltEs6(Left(vyy33000), Left(vyy34000), app(ty_[], bca), bbh) → new_ltEs4(vyy33000, vyy34000, bca)
new_ltEs18(vyy33002, vyy34002, ty_Double) → new_ltEs14(vyy33002, vyy34002)
new_ltEs18(vyy33002, vyy34002, ty_Ordering) → new_ltEs9(vyy33002, vyy34002)
new_ltEs19(vyy3300, vyy3400, app(ty_Maybe, cfg)) → new_ltEs7(vyy3300, vyy3400, cfg)
new_esEs23(vyy33000, vyy34000, app(ty_Ratio, cfc)) → new_esEs9(vyy33000, vyy34000, cfc)
new_ltEs18(vyy33002, vyy34002, ty_Bool) → new_ltEs16(vyy33002, vyy34002)
new_lt18(vyy33000, vyy34000, fc, fd, ff) → new_esEs8(new_compare33(vyy33000, vyy34000, fc, fd, ff), LT)
new_lt10(vyy33001, vyy34001, app(app(app(ty_@3, baa), bab), bac)) → new_lt18(vyy33001, vyy34001, baa, bab, bac)
new_compare27(vyy330, vyy340, True, cff) → EQ
new_esEs19(vyy6000, vyy500, app(ty_Ratio, cba)) → new_esEs9(vyy6000, vyy500, cba)
new_ltEs6(Left(vyy33000), Left(vyy34000), ty_@0, bbh) → new_ltEs8(vyy33000, vyy34000)
new_esEs7(Left(vyy6000), Left(vyy500), ty_Bool, bef) → new_esEs15(vyy6000, vyy500)
new_ltEs6(Right(vyy33000), Right(vyy34000), bda, ty_Double) → new_ltEs14(vyy33000, vyy34000)
new_compare18(vyy33000, vyy34000, app(app(ty_Either, bh), ca)) → new_compare17(vyy33000, vyy34000, bh, ca)
new_ltEs6(Right(vyy33000), Right(vyy34000), bda, app(ty_[], bdc)) → new_ltEs4(vyy33000, vyy34000, bdc)
new_esEs20(vyy6001, vyy501, ty_Char) → new_esEs17(vyy6001, vyy501)
new_primPlusNat0(Succ(vyy9900), Succ(vyy500000)) → Succ(Succ(new_primPlusNat0(vyy9900, vyy500000)))
new_compare26(vyy33000, vyy34000, False, fc, fd, ff) → new_compare12(vyy33000, vyy34000, new_ltEs15(vyy33000, vyy34000, fc, fd, ff), fc, fd, ff)
new_compare26(vyy33000, vyy34000, True, fc, fd, ff) → EQ
new_esEs23(vyy33000, vyy34000, app(ty_[], bag)) → new_esEs16(vyy33000, vyy34000, bag)
new_compare0([], :(vyy34000, vyy34001), h) → LT
new_ltEs6(Right(vyy33000), Right(vyy34000), bda, ty_Bool) → new_ltEs16(vyy33000, vyy34000)
new_compare27(Just(vyy3300), Just(vyy3400), False, cff) → new_compare13(vyy3300, vyy3400, new_ltEs19(vyy3300, vyy3400, cff), cff)
new_ltEs6(Right(vyy33000), Right(vyy34000), bda, ty_Ordering) → new_ltEs9(vyy33000, vyy34000)
new_lt10(vyy33001, vyy34001, ty_Double) → new_lt17(vyy33001, vyy34001)
new_asAs(True, vyy90) → vyy90
new_esEs25(vyy6000, vyy500, ty_Int) → new_esEs11(vyy6000, vyy500)
new_lt8(vyy33000, vyy34000) → new_esEs8(new_compare8(vyy33000, vyy34000), LT)
new_ltEs16(False, False) → True
new_compare18(vyy33000, vyy34000, ty_Integer) → new_compare9(vyy33000, vyy34000)
new_esEs27(vyy6002, vyy502, ty_Bool) → new_esEs15(vyy6002, vyy502)
new_esEs7(Left(vyy6000), Left(vyy500), ty_@0, bef) → new_esEs13(vyy6000, vyy500)
new_esEs19(vyy6000, vyy500, ty_Ordering) → new_esEs8(vyy6000, vyy500)
new_lt20(vyy33000, vyy34000, ty_Int) → new_lt9(vyy33000, vyy34000)
new_ltEs6(Left(vyy33000), Left(vyy34000), ty_Bool, bbh) → new_ltEs16(vyy33000, vyy34000)
new_esEs21(vyy6000, vyy500, ty_Integer) → new_esEs12(vyy6000, vyy500)
new_lt17(vyy33000, vyy34000) → new_esEs8(new_compare32(vyy33000, vyy34000), LT)
new_lt12(vyy33000, vyy34000, cb) → new_esEs8(new_compare7(vyy33000, vyy34000, cb), LT)
new_compare18(vyy33000, vyy34000, ty_Int) → new_compare16(vyy33000, vyy34000)
new_ltEs20(vyy33001, vyy34001, app(ty_Maybe, df)) → new_ltEs7(vyy33001, vyy34001, df)
new_esEs25(vyy6000, vyy500, app(app(ty_Either, cgh), cha)) → new_esEs7(vyy6000, vyy500, cgh, cha)
new_compare8(Char(vyy33000), Char(vyy34000)) → new_primCmpNat0(vyy33000, vyy34000)
new_compare33(vyy33000, vyy34000, fc, fd, ff) → new_compare26(vyy33000, vyy34000, new_esEs6(vyy33000, vyy34000, fc, fd, ff), fc, fd, ff)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs24(vyy33001, vyy34001, app(ty_Ratio, cfd)) → new_esEs9(vyy33001, vyy34001, cfd)
new_primCompAux0(vyy103, EQ) → vyy103
new_esEs20(vyy6001, vyy501, ty_@0) → new_esEs13(vyy6001, vyy501)
new_ltEs19(vyy3300, vyy3400, app(app(ty_Either, bda), bbh)) → new_ltEs6(vyy3300, vyy3400, bda, bbh)
new_lt20(vyy33000, vyy34000, app(ty_Maybe, cb)) → new_lt12(vyy33000, vyy34000, cb)
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primCmpInt(Neg(Succ(vyy330000)), Pos(vyy34000)) → LT
new_esEs24(vyy33001, vyy34001, ty_Double) → new_esEs14(vyy33001, vyy34001)
new_not(True) → False
new_esEs15(False, False) → True
The set Q consists of the following terms:
new_compare19(x0, x1, x2, x3)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs7(Just(x0), Just(x1), ty_Ordering)
new_esEs13(@0, @0)
new_ltEs18(x0, x1, app(ty_Maybe, x2))
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_primPlusNat0(Succ(x0), Zero)
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, ty_@0)
new_ltEs16(True, True)
new_compare18(x0, x1, ty_Bool)
new_lt14(x0, x1, x2, x3)
new_esEs28(x0, x1, app(ty_[], x2))
new_esEs28(x0, x1, ty_Char)
new_compare27(Just(x0), Just(x1), False, x2)
new_esEs18(x0, x1, app(app(ty_@2, x2), x3))
new_compare33(x0, x1, x2, x3, x4)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_primEqNat0(Zero, Succ(x0))
new_lt5(x0, x1)
new_lt20(x0, x1, ty_Integer)
new_esEs25(x0, x1, ty_Integer)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs25(x0, x1, ty_Bool)
new_esEs24(x0, x1, ty_Float)
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_esEs25(x0, x1, ty_Char)
new_ltEs20(x0, x1, ty_Bool)
new_ltEs18(x0, x1, ty_Bool)
new_esEs22(x0, x1, ty_Integer)
new_asAs(True, x0)
new_esEs26(x0, x1, ty_Float)
new_lt11(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs18(x0, x1, app(ty_[], x2))
new_lt10(x0, x1, ty_Char)
new_ltEs12(x0, x1, x2)
new_compare0([], [], x0)
new_lt20(x0, x1, ty_Ordering)
new_esEs18(x0, x1, ty_Double)
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_lt10(x0, x1, ty_Float)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs27(x0, x1, ty_Bool)
new_esEs7(Right(x0), Right(x1), x2, ty_Bool)
new_esEs15(True, True)
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs25(x0, x1, ty_Float)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_esEs27(x0, x1, ty_Float)
new_lt20(x0, x1, ty_Double)
new_esEs23(x0, x1, ty_Integer)
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_ltEs6(Left(x0), Left(x1), ty_Integer, x2)
new_esEs25(x0, x1, ty_@0)
new_compare10(x0, x1, True, x2, x3)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_lt20(x0, x1, app(ty_[], x2))
new_esEs4(Just(x0), Just(x1), app(ty_Maybe, x2))
new_ltEs4(x0, x1, x2)
new_esEs24(x0, x1, ty_Double)
new_compare18(x0, x1, ty_Int)
new_lt11(x0, x1, ty_Bool)
new_primMulNat0(Zero, Succ(x0))
new_esEs7(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs28(x0, x1, ty_Ordering)
new_esEs15(False, False)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs18(x0, x1, ty_Float)
new_esEs8(GT, GT)
new_ltEs6(Left(x0), Left(x1), ty_Int, x2)
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs7(Just(x0), Nothing, x1)
new_sr0(Integer(x0), Integer(x1))
new_esEs24(x0, x1, ty_Integer)
new_compare7(x0, x1, x2)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_esEs20(x0, x1, ty_Integer)
new_esEs4(Just(x0), Just(x1), ty_Ordering)
new_ltEs18(x0, x1, app(app(ty_@2, x2), x3))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_lt10(x0, x1, ty_Double)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_compare14(x0, x1, False)
new_esEs27(x0, x1, ty_Integer)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_esEs6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs8(LT, LT)
new_primPlusNat0(Succ(x0), Succ(x1))
new_esEs26(x0, x1, ty_Char)
new_compare18(x0, x1, ty_Char)
new_ltEs6(Left(x0), Left(x1), ty_Bool, x2)
new_lt10(x0, x1, app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_lt10(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt11(x0, x1, app(ty_Ratio, x2))
new_esEs19(x0, x1, ty_Double)
new_lt11(x0, x1, app(ty_[], x2))
new_ltEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs18(x0, x1, ty_Int)
new_esEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt12(x0, x1, x2)
new_esEs25(x0, x1, app(ty_[], x2))
new_esEs7(Right(x0), Right(x1), x2, ty_@0)
new_esEs7(Left(x0), Left(x1), ty_Bool, x2)
new_ltEs10(x0, x1)
new_esEs24(x0, x1, ty_Int)
new_esEs11(x0, x1)
new_primPlusNat0(Zero, Succ(x0))
new_compare0(:(x0, x1), :(x2, x3), x4)
new_esEs26(x0, x1, app(ty_[], x2))
new_esEs7(Right(x0), Right(x1), x2, ty_Char)
new_esEs8(GT, LT)
new_esEs8(LT, GT)
new_esEs20(x0, x1, ty_Int)
new_compare6(Float(x0, x1), Float(x2, x3))
new_ltEs7(Nothing, Nothing, x0)
new_lt11(x0, x1, ty_@0)
new_esEs23(x0, x1, ty_Double)
new_ltEs9(EQ, EQ)
new_compare5(@0, @0)
new_esEs4(Just(x0), Just(x1), ty_Bool)
new_primCompAux0(x0, EQ)
new_compare0(:(x0, x1), [], x2)
new_lt10(x0, x1, ty_Int)
new_esEs7(Left(x0), Right(x1), x2, x3)
new_esEs7(Right(x0), Left(x1), x2, x3)
new_primEqNat0(Zero, Zero)
new_primCmpNat0(Succ(x0), Zero)
new_primEqNat0(Succ(x0), Zero)
new_ltEs7(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_esEs19(x0, x1, ty_Ordering)
new_compare17(x0, x1, x2, x3)
new_esEs7(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_ltEs19(x0, x1, ty_Int)
new_compare14(x0, x1, True)
new_esEs19(x0, x1, ty_Int)
new_ltEs7(Just(x0), Just(x1), ty_Char)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs6(Right(x0), Right(x1), x2, ty_Float)
new_esEs7(Left(x0), Left(x1), ty_Int, x2)
new_esEs27(x0, x1, ty_Char)
new_ltEs6(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_esEs4(Just(x0), Just(x1), ty_Float)
new_esEs26(x0, x1, ty_@0)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primMulNat0(Zero, Zero)
new_compare18(x0, x1, ty_Float)
new_esEs20(x0, x1, ty_@0)
new_ltEs7(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs18(x0, x1, ty_@0)
new_compare11(x0, x1, True, x2, x3)
new_esEs24(x0, x1, ty_Bool)
new_esEs7(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_compare24(x0, x1, True, x2, x3)
new_primMulNat0(Succ(x0), Zero)
new_esEs9(:%(x0, x1), :%(x2, x3), x4)
new_esEs18(x0, x1, app(ty_[], x2))
new_compare26(x0, x1, False, x2, x3, x4)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_esEs18(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_compare18(x0, x1, ty_Ordering)
new_ltEs6(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs4(Just(x0), Just(x1), ty_@0)
new_lt20(x0, x1, ty_Float)
new_lt4(x0, x1)
new_lt11(x0, x1, ty_Ordering)
new_ltEs6(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs4(Just(x0), Just(x1), app(ty_Ratio, x2))
new_lt19(x0, x1)
new_esEs28(x0, x1, ty_Double)
new_ltEs7(Nothing, Just(x0), x1)
new_compare15(x0, x1, True)
new_ltEs6(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs23(x0, x1, app(ty_[], x2))
new_esEs18(x0, x1, ty_Integer)
new_pePe(False, x0)
new_esEs19(x0, x1, ty_Bool)
new_ltEs18(x0, x1, ty_Float)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_esEs21(x0, x1, ty_Int)
new_ltEs19(x0, x1, app(ty_[], x2))
new_ltEs11(x0, x1)
new_esEs25(x0, x1, ty_Double)
new_lt10(x0, x1, app(ty_Ratio, x2))
new_lt10(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(Left(x0), Left(x1), ty_Char, x2)
new_esEs28(x0, x1, ty_Bool)
new_esEs7(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs16([], :(x0, x1), x2)
new_lt11(x0, x1, ty_Double)
new_ltEs9(GT, EQ)
new_ltEs9(EQ, GT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs7(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs6(Right(x0), Right(x1), x2, app(ty_[], x3))
new_primCmpNat0(Succ(x0), Succ(x1))
new_esEs7(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_ltEs7(Just(x0), Just(x1), app(ty_Maybe, x2))
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_compare15(x0, x1, False)
new_ltEs6(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs23(x0, x1, ty_Ordering)
new_primCmpNat0(Zero, Succ(x0))
new_ltEs20(x0, x1, ty_Int)
new_esEs27(x0, x1, ty_Int)
new_lt10(x0, x1, app(ty_[], x2))
new_asAs(False, x0)
new_compare27(Nothing, Nothing, False, x0)
new_ltEs6(Left(x0), Left(x1), ty_Double, x2)
new_ltEs18(x0, x1, app(ty_Ratio, x2))
new_ltEs5(@2(x0, x1), @2(x2, x3), x4, x5)
new_primPlusNat0(Zero, Zero)
new_lt20(x0, x1, ty_Int)
new_primCompAux0(x0, LT)
new_lt10(x0, x1, ty_Ordering)
new_ltEs6(Left(x0), Left(x1), ty_@0, x2)
new_ltEs19(x0, x1, ty_Char)
new_compare13(x0, x1, False, x2)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_compare29(x0, x1, True)
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, app(ty_[], x2))
new_compare24(x0, x1, False, x2, x3)
new_esEs25(x0, x1, ty_Int)
new_ltEs18(x0, x1, app(app(ty_Either, x2), x3))
new_primPlusNat1(Zero, x0)
new_ltEs6(Left(x0), Left(x1), ty_Ordering, x2)
new_compare16(x0, x1)
new_esEs23(x0, x1, ty_Bool)
new_ltEs6(Right(x0), Right(x1), x2, ty_Double)
new_compare9(Integer(x0), Integer(x1))
new_esEs7(Left(x0), Left(x1), ty_Integer, x2)
new_ltEs7(Just(x0), Just(x1), ty_Integer)
new_esEs16(:(x0, x1), [], x2)
new_ltEs6(Right(x0), Right(x1), x2, ty_Int)
new_lt11(x0, x1, ty_Integer)
new_ltEs9(EQ, LT)
new_ltEs9(LT, EQ)
new_esEs7(Left(x0), Left(x1), ty_@0, x2)
new_ltEs7(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_ltEs6(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs27(x0, x1, app(ty_[], x2))
new_sr(x0, x1)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs18(x0, x1, app(ty_Maybe, x2))
new_compare18(x0, x1, app(ty_Ratio, x2))
new_esEs12(Integer(x0), Integer(x1))
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_compare18(x0, x1, app(app(ty_@2, x2), x3))
new_lt11(x0, x1, ty_Int)
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Neg(Zero), Pos(Zero))
new_primEqInt(Pos(Zero), Neg(Zero))
new_lt16(x0, x1, x2)
new_esEs20(x0, x1, ty_Double)
new_esEs24(x0, x1, ty_@0)
new_esEs23(x0, x1, ty_Float)
new_compare18(x0, x1, app(ty_Maybe, x2))
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(Left(x0), Left(x1), ty_Float, x2)
new_compare8(Char(x0), Char(x1))
new_ltEs20(x0, x1, ty_@0)
new_esEs7(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_esEs18(x0, x1, ty_Char)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs15(True, False)
new_esEs15(False, True)
new_esEs8(EQ, EQ)
new_esEs14(Double(x0, x1), Double(x2, x3))
new_esEs18(x0, x1, ty_Ordering)
new_esEs19(x0, x1, app(ty_[], x2))
new_esEs17(Char(x0), Char(x1))
new_primEqInt(Neg(Zero), Neg(Zero))
new_ltEs7(Just(x0), Just(x1), ty_@0)
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs7(Just(x0), Just(x1), ty_Float)
new_esEs28(x0, x1, ty_Integer)
new_compare11(x0, x1, False, x2, x3)
new_lt18(x0, x1, x2, x3, x4)
new_esEs27(x0, x1, ty_@0)
new_ltEs6(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs22(x0, x1, ty_Int)
new_ltEs7(Just(x0), Just(x1), ty_Bool)
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_esEs24(x0, x1, app(ty_[], x2))
new_primCompAux1(x0, x1, x2, x3)
new_esEs24(x0, x1, ty_Char)
new_lt13(x0, x1, x2)
new_primCompAux0(x0, GT)
new_ltEs19(x0, x1, ty_Double)
new_ltEs6(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_lt10(x0, x1, ty_@0)
new_ltEs7(Just(x0), Just(x1), ty_Double)
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_ltEs19(x0, x1, ty_Ordering)
new_lt11(x0, x1, app(ty_Maybe, x2))
new_esEs28(x0, x1, ty_Float)
new_ltEs6(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs4(Just(x0), Just(x1), app(ty_[], x2))
new_esEs7(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_ltEs6(Right(x0), Right(x1), x2, ty_Integer)
new_compare13(x0, x1, True, x2)
new_ltEs18(x0, x1, ty_Ordering)
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_pePe(True, x0)
new_esEs26(x0, x1, ty_Ordering)
new_ltEs9(LT, LT)
new_esEs20(x0, x1, ty_Char)
new_ltEs6(Left(x0), Right(x1), x2, x3)
new_ltEs6(Right(x0), Left(x1), x2, x3)
new_ltEs18(x0, x1, ty_Integer)
new_ltEs16(False, True)
new_ltEs16(True, False)
new_esEs19(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs19(x0, x1, ty_Bool)
new_lt20(x0, x1, ty_Char)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_compare31(:%(x0, x1), :%(x2, x3), ty_Integer)
new_compare18(x0, x1, ty_@0)
new_esEs26(x0, x1, ty_Double)
new_esEs4(Just(x0), Just(x1), ty_Int)
new_esEs19(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, ty_Bool)
new_ltEs19(x0, x1, ty_@0)
new_ltEs14(x0, x1)
new_esEs20(x0, x1, ty_Ordering)
new_compare25(x0, x1, False, x2, x3)
new_esEs19(x0, x1, ty_Integer)
new_primCmpNat0(Zero, Zero)
new_esEs4(Nothing, Just(x0), x1)
new_compare27(Just(x0), Nothing, False, x1)
new_esEs7(Right(x0), Right(x1), x2, ty_Double)
new_primEqNat0(Succ(x0), Succ(x1))
new_ltEs20(x0, x1, ty_Ordering)
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_compare10(x0, x1, False, x2, x3)
new_compare29(x0, x1, False)
new_primMulNat0(Succ(x0), Succ(x1))
new_ltEs19(x0, x1, ty_Integer)
new_compare27(Nothing, Just(x0), False, x1)
new_lt10(x0, x1, app(ty_Maybe, x2))
new_compare28(x0, x1, False)
new_esEs7(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs27(x0, x1, ty_Ordering)
new_lt8(x0, x1)
new_compare26(x0, x1, True, x2, x3, x4)
new_ltEs20(x0, x1, ty_Integer)
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_compare12(x0, x1, False, x2, x3, x4)
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_esEs7(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_ltEs6(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_primPlusNat1(Succ(x0), x1)
new_esEs4(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_compare18(x0, x1, app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_esEs19(x0, x1, ty_Float)
new_esEs16(:(x0, x1), :(x2, x3), x4)
new_lt9(x0, x1)
new_ltEs6(Right(x0), Right(x1), x2, ty_@0)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs21(x0, x1, ty_Integer)
new_compare30(x0, x1)
new_ltEs20(x0, x1, ty_Char)
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_ltEs20(x0, x1, ty_Float)
new_ltEs9(GT, LT)
new_ltEs9(LT, GT)
new_esEs26(x0, x1, ty_Int)
new_lt10(x0, x1, ty_Bool)
new_esEs7(Right(x0), Right(x1), x2, ty_Int)
new_esEs24(x0, x1, ty_Ordering)
new_esEs23(x0, x1, ty_Int)
new_esEs4(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_not(True)
new_ltEs19(x0, x1, ty_Float)
new_compare31(:%(x0, x1), :%(x2, x3), ty_Int)
new_esEs20(x0, x1, ty_Float)
new_esEs18(x0, x1, ty_Bool)
new_esEs5(@2(x0, x1), @2(x2, x3), x4, x5)
new_lt11(x0, x1, ty_Float)
new_ltEs18(x0, x1, ty_Double)
new_esEs19(x0, x1, app(ty_Ratio, x2))
new_compare34(x0, x1)
new_esEs4(Just(x0), Just(x1), ty_Double)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_not(False)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs6(Right(x0), Right(x1), x2, ty_Char)
new_ltEs6(Left(x0), Left(x1), ty_Float, x2)
new_compare25(x0, x1, True, x2, x3)
new_ltEs7(Just(x0), Just(x1), ty_Int)
new_lt15(x0, x1)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_compare28(x0, x1, True)
new_ltEs8(x0, x1)
new_esEs26(x0, x1, ty_Integer)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_esEs4(Just(x0), Just(x1), ty_Integer)
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs13(x0, x1)
new_esEs23(x0, x1, ty_Char)
new_esEs7(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs4(Just(x0), Just(x1), ty_Char)
new_esEs19(x0, x1, ty_@0)
new_ltEs6(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs7(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs17(x0, x1)
new_esEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs19(x0, x1, app(app(ty_@2, x2), x3))
new_lt6(x0, x1)
new_lt11(x0, x1, app(app(ty_Either, x2), x3))
new_compare18(x0, x1, ty_Double)
new_esEs20(x0, x1, ty_Bool)
new_compare18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs7(Right(x0), Right(x1), x2, ty_Float)
new_lt20(x0, x1, ty_@0)
new_lt10(x0, x1, ty_Integer)
new_esEs7(Left(x0), Left(x1), ty_Double, x2)
new_esEs4(Nothing, Nothing, x0)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_primMulInt(Neg(x0), Neg(x1))
new_ltEs9(GT, GT)
new_esEs19(x0, x1, ty_Char)
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_compare18(x0, x1, ty_Integer)
new_ltEs18(x0, x1, ty_Char)
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs6(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_compare18(x0, x1, app(ty_[], x2))
new_lt17(x0, x1)
new_ltEs6(Right(x0), Right(x1), x2, ty_Bool)
new_compare12(x0, x1, True, x2, x3, x4)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs28(x0, x1, ty_Int)
new_esEs20(x0, x1, app(ty_[], x2))
new_esEs10(Float(x0, x1), Float(x2, x3))
new_ltEs7(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs4(Just(x0), Nothing, x1)
new_compare32(Double(x0, x1), Double(x2, x3))
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_ltEs6(Left(x0), Left(x1), ty_Char, x2)
new_ltEs20(x0, x1, ty_Double)
new_ltEs15(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs18(x0, x1, ty_@0)
new_esEs7(Right(x0), Right(x1), x2, ty_Integer)
new_primEqInt(Pos(Zero), Pos(Zero))
new_esEs25(x0, x1, ty_Ordering)
new_esEs18(x0, x1, app(ty_Ratio, x2))
new_lt7(x0, x1, x2, x3)
new_lt20(x0, x1, ty_Bool)
new_esEs18(x0, x1, ty_Int)
new_compare27(x0, x1, True, x2)
new_lt11(x0, x1, app(app(ty_@2, x2), x3))
new_compare0([], :(x0, x1), x2)
new_lt11(x0, x1, ty_Char)
new_ltEs7(Just(x0), Just(x1), app(ty_Ratio, x2))
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs28(x0, x1, ty_@0)
new_esEs4(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_primMulInt(Pos(x0), Pos(x1))
new_ltEs16(False, False)
new_esEs16([], [], x0)
new_esEs27(x0, x1, ty_Double)
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(@2(vyy33000, vyy33001), @2(vyy34000, vyy34001), de, app(app(ty_@2, dh), ea)) → new_ltEs1(vyy33001, vyy34001, dh, ea)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
- new_ltEs1(@2(vyy33000, vyy33001), @2(vyy34000, vyy34001), de, app(app(ty_Either, ee), ef)) → new_ltEs3(vyy33001, vyy34001, ee, ef)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
- new_ltEs1(@2(vyy33000, vyy33001), @2(vyy34000, vyy34001), app(ty_Maybe, cb), eg) → new_compare20(vyy33000, vyy34000, new_esEs4(vyy33000, vyy34000, cb), cb)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 4
- new_lt1(vyy33000, vyy34000, fa, fb) → new_compare21(vyy33000, vyy34000, new_esEs5(vyy33000, vyy34000, fa, fb), fa, fb)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 4, 4 >= 5
- new_compare20(Just(@2(vyy33000, vyy33001)), Just(@2(vyy34000, vyy34001)), False, app(app(ty_@2, app(ty_Maybe, cb)), eg)) → new_compare20(vyy33000, vyy34000, new_esEs4(vyy33000, vyy34000, cb), cb)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 4
- new_lt3(vyy33000, vyy34000, fg, fh) → new_compare23(vyy33000, vyy34000, new_esEs7(vyy33000, vyy34000, fg, fh), fg, fh)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 4, 4 >= 5
- new_ltEs1(@2(vyy33000, vyy33001), @2(vyy34000, vyy34001), de, app(app(app(ty_@3, eb), ec), ed)) → new_ltEs2(vyy33001, vyy34001, eb, ec, ed)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5
- new_ltEs1(@2(vyy33000, vyy33001), @2(vyy34000, vyy34001), de, app(ty_Maybe, df)) → new_ltEs(vyy33001, vyy34001, df)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
- new_lt2(vyy33000, vyy34000, fc, fd, ff) → new_compare22(vyy33000, vyy34000, new_esEs6(vyy33000, vyy34000, fc, fd, ff), fc, fd, ff)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 4, 4 >= 5, 5 >= 6
- new_ltEs(Just(vyy33000), Just(vyy34000), app(app(ty_@2, ce), cf)) → new_ltEs1(vyy33000, vyy34000, ce, cf)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
- new_ltEs(Just(vyy33000), Just(vyy34000), app(app(ty_Either, dc), dd)) → new_ltEs3(vyy33000, vyy34000, dc, dd)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
- new_ltEs(Just(vyy33000), Just(vyy34000), app(app(app(ty_@3, cg), da), db)) → new_ltEs2(vyy33000, vyy34000, cg, da, db)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
- new_ltEs(Just(vyy33000), Just(vyy34000), app(ty_Maybe, cc)) → new_ltEs(vyy33000, vyy34000, cc)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
- new_ltEs2(@3(vyy33000, vyy33001, vyy33002), @3(vyy34000, vyy34001, vyy34002), ga, gb, app(ty_Maybe, gc)) → new_ltEs(vyy33002, vyy34002, gc)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3
- new_ltEs(Just(vyy33000), Just(vyy34000), app(ty_[], cd)) → new_ltEs0(vyy33000, vyy34000, cd)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
- new_lt0(vyy33000, vyy34000, eh) → new_compare(vyy33000, vyy34000, eh)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3
- new_lt(vyy33000, vyy34000, cb) → new_compare20(vyy33000, vyy34000, new_esEs4(vyy33000, vyy34000, cb), cb)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 4
- new_compare1(vyy33000, vyy34000, cb) → new_compare20(vyy33000, vyy34000, new_esEs4(vyy33000, vyy34000, cb), cb)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 4
- new_compare20(Just(:(vyy33000, vyy33001)), Just(:(vyy34000, vyy34001)), False, app(ty_[], h)) → new_primCompAux(vyy33000, vyy34000, new_compare0(vyy33001, vyy34001, h), h)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 4
- new_ltEs0(:(vyy33000, vyy33001), :(vyy34000, vyy34001), h) → new_primCompAux(vyy33000, vyy34000, new_compare0(vyy33001, vyy34001, h), h)
The graph contains the following edges 1 > 1, 2 > 2, 3 >= 4
- new_ltEs0(:(vyy33000, vyy33001), :(vyy34000, vyy34001), h) → new_compare(vyy33001, vyy34001, h)
The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3
- new_compare(:(vyy33000, vyy33001), :(vyy34000, vyy34001), h) → new_primCompAux(vyy33000, vyy34000, new_compare0(vyy33001, vyy34001, h), h)
The graph contains the following edges 1 > 1, 2 > 2, 3 >= 4
- new_compare(:(vyy33000, vyy33001), :(vyy34000, vyy34001), h) → new_compare(vyy33001, vyy34001, h)
The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3
- new_compare22(vyy33000, vyy34000, False, fc, fd, ff) → new_ltEs2(vyy33000, vyy34000, fc, fd, ff)
The graph contains the following edges 1 >= 1, 2 >= 2, 4 >= 3, 5 >= 4, 6 >= 5
- new_ltEs2(@3(vyy33000, vyy33001, vyy33002), @3(vyy34000, vyy34001, vyy34002), ga, gb, app(app(app(ty_@3, gg), gh), ha)) → new_ltEs2(vyy33002, vyy34002, gg, gh, ha)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4, 5 > 5
- new_ltEs2(@3(vyy33000, vyy33001, vyy33002), @3(vyy34000, vyy34001, vyy34002), ga, gb, app(app(ty_@2, ge), gf)) → new_ltEs1(vyy33002, vyy34002, ge, gf)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4
- new_compare21(vyy33000, vyy34000, False, fa, fb) → new_ltEs1(vyy33000, vyy34000, fa, fb)
The graph contains the following edges 1 >= 1, 2 >= 2, 4 >= 3, 5 >= 4
- new_ltEs2(@3(vyy33000, vyy33001, vyy33002), @3(vyy34000, vyy34001, vyy34002), ga, gb, app(app(ty_Either, hb), hc)) → new_ltEs3(vyy33002, vyy34002, hb, hc)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4
- new_compare23(vyy33000, vyy34000, False, fg, fh) → new_ltEs3(vyy33000, vyy34000, fg, fh)
The graph contains the following edges 1 >= 1, 2 >= 2, 4 >= 3, 5 >= 4
- new_ltEs1(@2(vyy33000, vyy33001), @2(vyy34000, vyy34001), app(app(ty_Either, fg), fh), eg) → new_compare23(vyy33000, vyy34000, new_esEs7(vyy33000, vyy34000, fg, fh), fg, fh)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 4, 3 > 5
- new_compare20(Just(@2(vyy33000, vyy33001)), Just(@2(vyy34000, vyy34001)), False, app(app(ty_@2, app(app(ty_Either, fg), fh)), eg)) → new_compare23(vyy33000, vyy34000, new_esEs7(vyy33000, vyy34000, fg, fh), fg, fh)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 4, 4 > 5
- new_compare4(vyy33000, vyy34000, fg, fh) → new_compare23(vyy33000, vyy34000, new_esEs7(vyy33000, vyy34000, fg, fh), fg, fh)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 4, 4 >= 5
- new_compare3(vyy33000, vyy34000, fc, fd, ff) → new_compare22(vyy33000, vyy34000, new_esEs6(vyy33000, vyy34000, fc, fd, ff), fc, fd, ff)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 4, 4 >= 5, 5 >= 6
- new_ltEs1(@2(vyy33000, vyy33001), @2(vyy34000, vyy34001), app(app(app(ty_@3, fc), fd), ff), eg) → new_compare22(vyy33000, vyy34000, new_esEs6(vyy33000, vyy34000, fc, fd, ff), fc, fd, ff)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 4, 3 > 5, 3 > 6
- new_compare20(Just(@2(vyy33000, vyy33001)), Just(@2(vyy34000, vyy34001)), False, app(app(ty_@2, app(app(app(ty_@3, fc), fd), ff)), eg)) → new_compare22(vyy33000, vyy34000, new_esEs6(vyy33000, vyy34000, fc, fd, ff), fc, fd, ff)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 4, 4 > 5, 4 > 6
- new_ltEs1(@2(vyy33000, vyy33001), @2(vyy34000, vyy34001), de, app(ty_[], dg)) → new_ltEs0(vyy33001, vyy34001, dg)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
- new_ltEs2(@3(vyy33000, vyy33001, vyy33002), @3(vyy34000, vyy34001, vyy34002), ga, gb, app(ty_[], gd)) → new_ltEs0(vyy33002, vyy34002, gd)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3
- new_primCompAux(vyy33000, vyy34000, vyy98, app(app(ty_@2, bc), bd)) → new_compare2(vyy33000, vyy34000, bc, bd)
The graph contains the following edges 1 >= 1, 2 >= 2, 4 > 3, 4 > 4
- new_primCompAux(vyy33000, vyy34000, vyy98, app(app(app(ty_@3, be), bf), bg)) → new_compare3(vyy33000, vyy34000, be, bf, bg)
The graph contains the following edges 1 >= 1, 2 >= 2, 4 > 3, 4 > 4, 4 > 5
- new_ltEs1(@2(vyy33000, vyy33001), @2(vyy34000, vyy34001), app(app(ty_@2, fa), fb), eg) → new_compare21(vyy33000, vyy34000, new_esEs5(vyy33000, vyy34000, fa, fb), fa, fb)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 4, 3 > 5
- new_ltEs1(@2(vyy33000, vyy33001), @2(vyy34000, vyy34001), app(ty_[], eh), eg) → new_compare(vyy33000, vyy34000, eh)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
- new_compare20(Just(@2(vyy33000, vyy33001)), Just(@2(vyy34000, vyy34001)), False, app(app(ty_@2, app(app(ty_@2, fa), fb)), eg)) → new_compare21(vyy33000, vyy34000, new_esEs5(vyy33000, vyy34000, fa, fb), fa, fb)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 4, 4 > 5
- new_compare2(vyy33000, vyy34000, fa, fb) → new_compare21(vyy33000, vyy34000, new_esEs5(vyy33000, vyy34000, fa, fb), fa, fb)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 4, 4 >= 5
- new_primCompAux(vyy33000, vyy34000, vyy98, app(ty_[], bb)) → new_compare(vyy33000, vyy34000, bb)
The graph contains the following edges 1 >= 1, 2 >= 2, 4 > 3
- new_primCompAux(vyy33000, vyy34000, vyy98, app(ty_Maybe, ba)) → new_compare1(vyy33000, vyy34000, ba)
The graph contains the following edges 1 >= 1, 2 >= 2, 4 > 3
- new_primCompAux(vyy33000, vyy34000, vyy98, app(app(ty_Either, bh), ca)) → new_compare4(vyy33000, vyy34000, bh, ca)
The graph contains the following edges 1 >= 1, 2 >= 2, 4 > 3, 4 > 4
- new_ltEs3(Left(vyy33000), Left(vyy34000), app(app(ty_@2, bcb), bcc), bbh) → new_ltEs1(vyy33000, vyy34000, bcb, bcc)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
- new_ltEs3(Right(vyy33000), Right(vyy34000), bda, app(app(ty_@2, bdd), bde)) → new_ltEs1(vyy33000, vyy34000, bdd, bde)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
- new_compare20(Just(Just(vyy33000)), Just(Just(vyy34000)), False, app(ty_Maybe, app(app(ty_@2, ce), cf))) → new_ltEs1(vyy33000, vyy34000, ce, cf)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
- new_compare20(Just(Left(vyy33000)), Just(Left(vyy34000)), False, app(app(ty_Either, app(app(ty_@2, bcb), bcc)), bbh)) → new_ltEs1(vyy33000, vyy34000, bcb, bcc)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
- new_compare20(Just(@3(vyy33000, vyy33001, vyy33002)), Just(@3(vyy34000, vyy34001, vyy34002)), False, app(app(app(ty_@3, ga), gb), app(app(ty_@2, ge), gf))) → new_ltEs1(vyy33002, vyy34002, ge, gf)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
- new_compare20(Just(@2(vyy33000, vyy33001)), Just(@2(vyy34000, vyy34001)), False, app(app(ty_@2, de), app(app(ty_@2, dh), ea))) → new_ltEs1(vyy33001, vyy34001, dh, ea)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
- new_compare20(Just(Right(vyy33000)), Just(Right(vyy34000)), False, app(app(ty_Either, bda), app(app(ty_@2, bdd), bde))) → new_ltEs1(vyy33000, vyy34000, bdd, bde)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
- new_ltEs3(Left(vyy33000), Left(vyy34000), app(app(ty_Either, bcg), bch), bbh) → new_ltEs3(vyy33000, vyy34000, bcg, bch)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
- new_ltEs3(Right(vyy33000), Right(vyy34000), bda, app(app(ty_Either, bea), beb)) → new_ltEs3(vyy33000, vyy34000, bea, beb)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
- new_ltEs3(Left(vyy33000), Left(vyy34000), app(app(app(ty_@3, bcd), bce), bcf), bbh) → new_ltEs2(vyy33000, vyy34000, bcd, bce, bcf)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
- new_ltEs3(Right(vyy33000), Right(vyy34000), bda, app(app(app(ty_@3, bdf), bdg), bdh)) → new_ltEs2(vyy33000, vyy34000, bdf, bdg, bdh)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5
- new_ltEs3(Left(vyy33000), Left(vyy34000), app(ty_Maybe, bbg), bbh) → new_ltEs(vyy33000, vyy34000, bbg)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
- new_ltEs3(Right(vyy33000), Right(vyy34000), bda, app(ty_Maybe, bdb)) → new_ltEs(vyy33000, vyy34000, bdb)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
- new_ltEs3(Right(vyy33000), Right(vyy34000), bda, app(ty_[], bdc)) → new_ltEs0(vyy33000, vyy34000, bdc)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
- new_ltEs3(Left(vyy33000), Left(vyy34000), app(ty_[], bca), bbh) → new_ltEs0(vyy33000, vyy34000, bca)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
- new_compare20(Just(@3(vyy33000, vyy33001, vyy33002)), Just(@3(vyy34000, vyy34001, vyy34002)), False, app(app(app(ty_@3, ga), gb), app(app(ty_Either, hb), hc))) → new_ltEs3(vyy33002, vyy34002, hb, hc)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
- new_compare20(Just(Right(vyy33000)), Just(Right(vyy34000)), False, app(app(ty_Either, bda), app(app(ty_Either, bea), beb))) → new_ltEs3(vyy33000, vyy34000, bea, beb)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
- new_compare20(Just(Left(vyy33000)), Just(Left(vyy34000)), False, app(app(ty_Either, app(app(ty_Either, bcg), bch)), bbh)) → new_ltEs3(vyy33000, vyy34000, bcg, bch)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
- new_compare20(Just(@2(vyy33000, vyy33001)), Just(@2(vyy34000, vyy34001)), False, app(app(ty_@2, de), app(app(ty_Either, ee), ef))) → new_ltEs3(vyy33001, vyy34001, ee, ef)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
- new_compare20(Just(Just(vyy33000)), Just(Just(vyy34000)), False, app(ty_Maybe, app(app(ty_Either, dc), dd))) → new_ltEs3(vyy33000, vyy34000, dc, dd)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
- new_compare20(Just(Right(vyy33000)), Just(Right(vyy34000)), False, app(app(ty_Either, bda), app(app(app(ty_@3, bdf), bdg), bdh))) → new_ltEs2(vyy33000, vyy34000, bdf, bdg, bdh)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5
- new_compare20(Just(@2(vyy33000, vyy33001)), Just(@2(vyy34000, vyy34001)), False, app(app(ty_@2, de), app(app(app(ty_@3, eb), ec), ed))) → new_ltEs2(vyy33001, vyy34001, eb, ec, ed)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5
- new_compare20(Just(@3(vyy33000, vyy33001, vyy33002)), Just(@3(vyy34000, vyy34001, vyy34002)), False, app(app(app(ty_@3, ga), gb), app(app(app(ty_@3, gg), gh), ha))) → new_ltEs2(vyy33002, vyy34002, gg, gh, ha)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5
- new_compare20(Just(Left(vyy33000)), Just(Left(vyy34000)), False, app(app(ty_Either, app(app(app(ty_@3, bcd), bce), bcf)), bbh)) → new_ltEs2(vyy33000, vyy34000, bcd, bce, bcf)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5
- new_compare20(Just(Just(vyy33000)), Just(Just(vyy34000)), False, app(ty_Maybe, app(app(app(ty_@3, cg), da), db))) → new_ltEs2(vyy33000, vyy34000, cg, da, db)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5
- new_compare20(Just(Right(vyy33000)), Just(Right(vyy34000)), False, app(app(ty_Either, bda), app(ty_Maybe, bdb))) → new_ltEs(vyy33000, vyy34000, bdb)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
- new_compare20(Just(@2(vyy33000, vyy33001)), Just(@2(vyy34000, vyy34001)), False, app(app(ty_@2, de), app(ty_Maybe, df))) → new_ltEs(vyy33001, vyy34001, df)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
- new_compare20(Just(Just(vyy33000)), Just(Just(vyy34000)), False, app(ty_Maybe, app(ty_Maybe, cc))) → new_ltEs(vyy33000, vyy34000, cc)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
- new_compare20(Just(Left(vyy33000)), Just(Left(vyy34000)), False, app(app(ty_Either, app(ty_Maybe, bbg)), bbh)) → new_ltEs(vyy33000, vyy34000, bbg)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
- new_compare20(Just(@3(vyy33000, vyy33001, vyy33002)), Just(@3(vyy34000, vyy34001, vyy34002)), False, app(app(app(ty_@3, ga), gb), app(ty_Maybe, gc))) → new_ltEs(vyy33002, vyy34002, gc)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
- new_compare20(Just(@3(vyy33000, vyy33001, vyy33002)), Just(@3(vyy34000, vyy34001, vyy34002)), False, app(app(app(ty_@3, app(ty_[], bag)), gb), he)) → new_lt0(vyy33000, vyy34000, bag)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
- new_compare20(Just(@3(vyy33000, vyy33001, vyy33002)), Just(@3(vyy34000, vyy34001, vyy34002)), False, app(app(app(ty_@3, ga), app(ty_[], hf)), he)) → new_lt0(vyy33001, vyy34001, hf)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
- new_compare20(Just(@3(vyy33000, vyy33001, vyy33002)), Just(@3(vyy34000, vyy34001, vyy34002)), False, app(app(app(ty_@3, app(ty_Maybe, baf)), gb), he)) → new_lt(vyy33000, vyy34000, baf)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
- new_compare20(Just(@3(vyy33000, vyy33001, vyy33002)), Just(@3(vyy34000, vyy34001, vyy34002)), False, app(app(app(ty_@3, ga), app(ty_Maybe, hd)), he)) → new_lt(vyy33001, vyy34001, hd)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
- new_compare20(Just(Left(vyy33000)), Just(Left(vyy34000)), False, app(app(ty_Either, app(ty_[], bca)), bbh)) → new_ltEs0(vyy33000, vyy34000, bca)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
- new_compare20(Just(@3(vyy33000, vyy33001, vyy33002)), Just(@3(vyy34000, vyy34001, vyy34002)), False, app(app(app(ty_@3, ga), gb), app(ty_[], gd))) → new_ltEs0(vyy33002, vyy34002, gd)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
- new_compare20(Just(@2(vyy33000, vyy33001)), Just(@2(vyy34000, vyy34001)), False, app(app(ty_@2, de), app(ty_[], dg))) → new_ltEs0(vyy33001, vyy34001, dg)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
- new_compare20(Just(Right(vyy33000)), Just(Right(vyy34000)), False, app(app(ty_Either, bda), app(ty_[], bdc))) → new_ltEs0(vyy33000, vyy34000, bdc)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
- new_compare20(Just(Just(vyy33000)), Just(Just(vyy34000)), False, app(ty_Maybe, app(ty_[], cd))) → new_ltEs0(vyy33000, vyy34000, cd)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
- new_compare20(Just(@3(vyy33000, vyy33001, vyy33002)), Just(@3(vyy34000, vyy34001, vyy34002)), False, app(app(app(ty_@3, app(app(ty_Either, bbe), bbf)), gb), he)) → new_lt3(vyy33000, vyy34000, bbe, bbf)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
- new_compare20(Just(@3(vyy33000, vyy33001, vyy33002)), Just(@3(vyy34000, vyy34001, vyy34002)), False, app(app(app(ty_@3, ga), app(app(ty_Either, bad), bae)), he)) → new_lt3(vyy33001, vyy34001, bad, bae)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
- new_compare20(Just(@3(vyy33000, vyy33001, vyy33002)), Just(@3(vyy34000, vyy34001, vyy34002)), False, app(app(app(ty_@3, app(app(app(ty_@3, bbb), bbc), bbd)), gb), he)) → new_lt2(vyy33000, vyy34000, bbb, bbc, bbd)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5
- new_compare20(Just(@3(vyy33000, vyy33001, vyy33002)), Just(@3(vyy34000, vyy34001, vyy34002)), False, app(app(app(ty_@3, ga), app(app(app(ty_@3, baa), bab), bac)), he)) → new_lt2(vyy33001, vyy34001, baa, bab, bac)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5
- new_compare20(Just(:(vyy33000, vyy33001)), Just(:(vyy34000, vyy34001)), False, app(ty_[], h)) → new_compare(vyy33001, vyy34001, h)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
- new_compare20(Just(@2(vyy33000, vyy33001)), Just(@2(vyy34000, vyy34001)), False, app(app(ty_@2, app(ty_[], eh)), eg)) → new_compare(vyy33000, vyy34000, eh)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
- new_compare20(Just(@3(vyy33000, vyy33001, vyy33002)), Just(@3(vyy34000, vyy34001, vyy34002)), False, app(app(app(ty_@3, app(app(ty_@2, bah), bba)), gb), he)) → new_lt1(vyy33000, vyy34000, bah, bba)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
- new_compare20(Just(@3(vyy33000, vyy33001, vyy33002)), Just(@3(vyy34000, vyy34001, vyy34002)), False, app(app(app(ty_@3, ga), app(app(ty_@2, hg), hh)), he)) → new_lt1(vyy33001, vyy34001, hg, hh)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
- new_ltEs2(@3(vyy33000, vyy33001, vyy33002), @3(vyy34000, vyy34001, vyy34002), app(ty_[], bag), gb, he) → new_lt0(vyy33000, vyy34000, bag)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
- new_ltEs2(@3(vyy33000, vyy33001, vyy33002), @3(vyy34000, vyy34001, vyy34002), ga, app(ty_[], hf), he) → new_lt0(vyy33001, vyy34001, hf)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
- new_ltEs2(@3(vyy33000, vyy33001, vyy33002), @3(vyy34000, vyy34001, vyy34002), ga, app(ty_Maybe, hd), he) → new_lt(vyy33001, vyy34001, hd)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
- new_ltEs2(@3(vyy33000, vyy33001, vyy33002), @3(vyy34000, vyy34001, vyy34002), app(ty_Maybe, baf), gb, he) → new_lt(vyy33000, vyy34000, baf)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
- new_ltEs2(@3(vyy33000, vyy33001, vyy33002), @3(vyy34000, vyy34001, vyy34002), app(app(ty_Either, bbe), bbf), gb, he) → new_lt3(vyy33000, vyy34000, bbe, bbf)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
- new_ltEs2(@3(vyy33000, vyy33001, vyy33002), @3(vyy34000, vyy34001, vyy34002), ga, app(app(ty_Either, bad), bae), he) → new_lt3(vyy33001, vyy34001, bad, bae)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
- new_ltEs2(@3(vyy33000, vyy33001, vyy33002), @3(vyy34000, vyy34001, vyy34002), ga, app(app(app(ty_@3, baa), bab), bac), he) → new_lt2(vyy33001, vyy34001, baa, bab, bac)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5
- new_ltEs2(@3(vyy33000, vyy33001, vyy33002), @3(vyy34000, vyy34001, vyy34002), app(app(app(ty_@3, bbb), bbc), bbd), gb, he) → new_lt2(vyy33000, vyy34000, bbb, bbc, bbd)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
- new_ltEs2(@3(vyy33000, vyy33001, vyy33002), @3(vyy34000, vyy34001, vyy34002), app(app(ty_@2, bah), bba), gb, he) → new_lt1(vyy33000, vyy34000, bah, bba)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
- new_ltEs2(@3(vyy33000, vyy33001, vyy33002), @3(vyy34000, vyy34001, vyy34002), ga, app(app(ty_@2, hg), hh), he) → new_lt1(vyy33001, vyy34001, hg, hh)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ DependencyGraphProof
Q DP problem:
The TRS P consists of the following rules:
new_foldFM_GE11(vyy17, vyy19, vyy20, vyy21, vyy22, vyy23, vyy24, False, bc, bd, be) → new_foldFM_GE(vyy17, Just(vyy19), vyy24, bc, bd, be)
new_foldFM_GE10(vyy3, vyy600, vyy61, vyy62, vyy63, vyy64, False, h, ba, bb) → new_foldFM_GE(vyy3, Nothing, vyy64, h, ba, bb)
new_foldFM_GE(vyy3, Nothing, Branch(Nothing, vyy61, vyy62, vyy63, vyy64), h, ba, bb) → new_foldFM_GE(vyy3, Nothing, vyy63, h, ba, bb)
new_foldFM_GE1(vyy3, vyy50, vyy61, vyy62, vyy63, vyy64, True, h, ba, bb) → new_foldFM_GE(vyy3, Just(vyy50), vyy64, h, ba, bb)
new_foldFM_GE(vyy3, Nothing, Branch(Just(vyy600), vyy61, vyy62, vyy63, vyy64), h, ba, bb) → new_foldFM_GE10(vyy3, vyy600, vyy61, vyy62, vyy63, vyy64, new_esEs8(new_compare27(Just(vyy600), Nothing, False, ba), LT), h, ba, bb)
new_foldFM_GE11(vyy17, vyy19, vyy20, vyy21, vyy22, vyy23, vyy24, False, bc, bd, be) → new_foldFM_GE(vyy17, Just(vyy19), vyy23, bc, bd, be)
new_foldFM_GE(vyy3, Just(vyy50), Branch(Just(vyy600), vyy61, vyy62, vyy63, vyy64), h, ba, bb) → new_foldFM_GE11(vyy3, vyy50, vyy600, vyy61, vyy62, vyy63, vyy64, new_esEs8(new_compare27(Just(vyy600), Just(vyy50), new_esEs29(vyy600, vyy50, ba), ba), LT), h, ba, bb)
new_foldFM_GE1(vyy3, vyy50, vyy61, vyy62, vyy63, vyy64, False, h, ba, bb) → new_foldFM_GE(vyy3, Just(vyy50), vyy63, h, ba, bb)
new_foldFM_GE(vyy3, Nothing, Branch(Nothing, vyy61, vyy62, vyy63, vyy64), h, ba, bb) → new_foldFM_GE(vyy3, Nothing, vyy64, h, ba, bb)
new_foldFM_GE1(vyy3, vyy50, vyy61, vyy62, vyy63, vyy64, False, h, ba, bb) → new_foldFM_GE(vyy3, Just(vyy50), vyy64, h, ba, bb)
new_foldFM_GE(vyy3, Just(vyy50), Branch(Nothing, vyy61, vyy62, vyy63, vyy64), h, ba, bb) → new_foldFM_GE1(vyy3, vyy50, vyy61, vyy62, vyy63, vyy64, new_esEs8(new_compare27(Nothing, Just(vyy50), False, ba), LT), h, ba, bb)
new_foldFM_GE10(vyy3, vyy600, vyy61, vyy62, vyy63, vyy64, True, h, ba, bb) → new_foldFM_GE(vyy3, Nothing, vyy64, h, ba, bb)
new_foldFM_GE10(vyy3, vyy600, vyy61, vyy62, vyy63, vyy64, False, h, ba, bb) → new_foldFM_GE(vyy3, Nothing, vyy63, h, ba, bb)
new_foldFM_GE11(vyy17, vyy19, vyy20, vyy21, vyy22, vyy23, vyy24, True, bc, bd, be) → new_foldFM_GE(vyy17, Just(vyy19), vyy24, bc, bd, be)
The TRS R consists of the following rules:
new_esEs4(Just(vyy6000), Just(vyy500), app(ty_Maybe, bgb)) → new_esEs4(vyy6000, vyy500, bgb)
new_ltEs19(vyy3300, vyy3400, app(app(ty_@2, cea), ceb)) → new_ltEs5(vyy3300, vyy3400, cea, ceb)
new_esEs23(vyy33000, vyy34000, app(app(ty_Either, cba), cbb)) → new_esEs7(vyy33000, vyy34000, cba, cbb)
new_lt10(vyy33001, vyy34001, ty_Integer) → new_lt6(vyy33001, vyy34001)
new_lt4(vyy33000, vyy34000) → new_esEs8(new_compare5(vyy33000, vyy34000), LT)
new_esEs4(Just(vyy6000), Just(vyy500), ty_Ordering) → new_esEs8(vyy6000, vyy500)
new_esEs7(Left(vyy6000), Left(vyy500), app(app(ty_Either, fd), ff), fa) → new_esEs7(vyy6000, vyy500, fd, ff)
new_ltEs6(Left(vyy33000), Left(vyy34000), app(app(app(ty_@3, cg), da), db), cb) → new_ltEs15(vyy33000, vyy34000, cg, da, db)
new_compare5(@0, @0) → EQ
new_esEs27(vyy6002, vyy502, app(ty_[], dbb)) → new_esEs16(vyy6002, vyy502, dbb)
new_lt10(vyy33001, vyy34001, ty_Char) → new_lt8(vyy33001, vyy34001)
new_esEs25(vyy6000, vyy500, ty_Integer) → new_esEs12(vyy6000, vyy500)
new_esEs25(vyy6000, vyy500, app(ty_[], cgf)) → new_esEs16(vyy6000, vyy500, cgf)
new_esEs7(Right(vyy6000), Right(vyy500), gd, ty_Bool) → new_esEs15(vyy6000, vyy500)
new_esEs25(vyy6000, vyy500, ty_Bool) → new_esEs15(vyy6000, vyy500)
new_ltEs6(Right(vyy33000), Right(vyy34000), de, ty_Char) → new_ltEs11(vyy33000, vyy34000)
new_esEs17(Char(vyy6000), Char(vyy500)) → new_primEqNat0(vyy6000, vyy500)
new_esEs7(Left(vyy6000), Left(vyy500), app(ty_Maybe, gc), fa) → new_esEs4(vyy6000, vyy500, gc)
new_esEs24(vyy33001, vyy34001, ty_Char) → new_esEs17(vyy33001, vyy34001)
new_ltEs6(Right(vyy33000), Right(vyy34000), de, app(app(ty_@2, dh), ea)) → new_ltEs5(vyy33000, vyy34000, dh, ea)
new_esEs29(vyy600, vyy50, ty_@0) → new_esEs13(vyy600, vyy50)
new_esEs19(vyy6000, vyy500, ty_Bool) → new_esEs15(vyy6000, vyy500)
new_lt20(vyy33000, vyy34000, app(ty_Ratio, cec)) → new_lt16(vyy33000, vyy34000, cec)
new_lt10(vyy33001, vyy34001, app(ty_Ratio, cbg)) → new_lt16(vyy33001, vyy34001, cbg)
new_esEs19(vyy6000, vyy500, app(ty_[], bch)) → new_esEs16(vyy6000, vyy500, bch)
new_compare10(vyy33000, vyy34000, True, bg, bh) → LT
new_esEs29(vyy600, vyy50, ty_Double) → new_esEs14(vyy600, vyy50)
new_esEs26(vyy6001, vyy501, ty_Float) → new_esEs10(vyy6001, vyy501)
new_esEs26(vyy6001, vyy501, ty_Double) → new_esEs14(vyy6001, vyy501)
new_esEs24(vyy33001, vyy34001, app(ty_Maybe, cbc)) → new_esEs4(vyy33001, vyy34001, cbc)
new_esEs4(Nothing, Just(vyy500), beh) → False
new_esEs4(Just(vyy6000), Nothing, beh) → False
new_esEs4(Just(vyy6000), Just(vyy500), ty_Char) → new_esEs17(vyy6000, vyy500)
new_ltEs20(vyy33001, vyy34001, ty_@0) → new_ltEs8(vyy33001, vyy34001)
new_ltEs7(Just(vyy33000), Just(vyy34000), ty_Integer) → new_ltEs17(vyy33000, vyy34000)
new_esEs25(vyy6000, vyy500, ty_Char) → new_esEs17(vyy6000, vyy500)
new_primCompAux1(vyy33000, vyy34000, vyy98, bf) → new_primCompAux0(vyy98, new_compare18(vyy33000, vyy34000, bf))
new_ltEs18(vyy33002, vyy34002, app(ty_Ratio, cda)) → new_ltEs12(vyy33002, vyy34002, cda)
new_ltEs19(vyy3300, vyy3400, app(ty_Ratio, bhe)) → new_ltEs12(vyy3300, vyy3400, bhe)
new_compare18(vyy33000, vyy34000, ty_Double) → new_compare32(vyy33000, vyy34000)
new_compare18(vyy33000, vyy34000, ty_Float) → new_compare6(vyy33000, vyy34000)
new_ltEs6(Left(vyy33000), Left(vyy34000), ty_Char, cb) → new_ltEs11(vyy33000, vyy34000)
new_compare29(vyy33000, vyy34000, False) → new_compare15(vyy33000, vyy34000, new_ltEs16(vyy33000, vyy34000))
new_primMulNat0(Zero, Zero) → Zero
new_ltEs8(vyy3300, vyy3400) → new_not(new_esEs8(new_compare5(vyy3300, vyy3400), GT))
new_esEs24(vyy33001, vyy34001, ty_@0) → new_esEs13(vyy33001, vyy34001)
new_esEs7(Right(vyy6000), Right(vyy500), gd, ty_Double) → new_esEs14(vyy6000, vyy500)
new_ltEs4(vyy3300, vyy3400, bf) → new_not(new_esEs8(new_compare0(vyy3300, vyy3400, bf), GT))
new_esEs26(vyy6001, vyy501, app(ty_[], chh)) → new_esEs16(vyy6001, vyy501, chh)
new_esEs18(vyy6000, vyy500, app(ty_[], bbd)) → new_esEs16(vyy6000, vyy500, bbd)
new_compare29(vyy33000, vyy34000, True) → EQ
new_esEs4(Just(vyy6000), Just(vyy500), app(app(app(ty_@3, bfg), bfh), bga)) → new_esEs6(vyy6000, vyy500, bfg, bfh, bga)
new_esEs7(Left(vyy6000), Left(vyy500), ty_Double, fa) → new_esEs14(vyy6000, vyy500)
new_ltEs9(GT, LT) → False
new_esEs20(vyy6001, vyy501, app(ty_Maybe, bef)) → new_esEs4(vyy6001, vyy501, bef)
new_lt11(vyy33000, vyy34000, app(app(ty_@2, cac), cad)) → new_lt14(vyy33000, vyy34000, cac, cad)
new_ltEs16(False, True) → True
new_lt11(vyy33000, vyy34000, ty_Float) → new_lt5(vyy33000, vyy34000)
new_esEs7(Right(vyy6000), Right(vyy500), gd, ty_Ordering) → new_esEs8(vyy6000, vyy500)
new_lt20(vyy33000, vyy34000, app(app(app(ty_@3, baa), bab), bac)) → new_lt18(vyy33000, vyy34000, baa, bab, bac)
new_esEs27(vyy6002, vyy502, ty_Integer) → new_esEs12(vyy6002, vyy502)
new_compare18(vyy33000, vyy34000, app(app(app(ty_@3, bgh), bha), bhb)) → new_compare33(vyy33000, vyy34000, bgh, bha, bhb)
new_ltEs16(True, False) → False
new_lt10(vyy33001, vyy34001, ty_@0) → new_lt4(vyy33001, vyy34001)
new_esEs23(vyy33000, vyy34000, app(ty_Maybe, caa)) → new_esEs4(vyy33000, vyy34000, caa)
new_ltEs19(vyy3300, vyy3400, ty_Bool) → new_ltEs16(vyy3300, vyy3400)
new_esEs27(vyy6002, vyy502, app(ty_Ratio, dae)) → new_esEs9(vyy6002, vyy502, dae)
new_compare30(vyy33000, vyy34000) → new_compare28(vyy33000, vyy34000, new_esEs8(vyy33000, vyy34000))
new_esEs23(vyy33000, vyy34000, ty_@0) → new_esEs13(vyy33000, vyy34000)
new_ltEs6(Left(vyy33000), Left(vyy34000), app(app(ty_Either, dc), dd), cb) → new_ltEs6(vyy33000, vyy34000, dc, dd)
new_ltEs6(Left(vyy33000), Left(vyy34000), ty_Float, cb) → new_ltEs10(vyy33000, vyy34000)
new_lt11(vyy33000, vyy34000, app(ty_[], cab)) → new_lt13(vyy33000, vyy34000, cab)
new_esEs24(vyy33001, vyy34001, app(app(ty_@2, cbe), cbf)) → new_esEs5(vyy33001, vyy34001, cbe, cbf)
new_esEs4(Just(vyy6000), Just(vyy500), ty_Float) → new_esEs10(vyy6000, vyy500)
new_esEs7(Right(vyy6000), Right(vyy500), gd, app(ty_Ratio, ge)) → new_esEs9(vyy6000, vyy500, ge)
new_compare18(vyy33000, vyy34000, app(ty_Maybe, bgc)) → new_compare7(vyy33000, vyy34000, bgc)
new_esEs23(vyy33000, vyy34000, ty_Integer) → new_esEs12(vyy33000, vyy34000)
new_esEs25(vyy6000, vyy500, ty_Double) → new_esEs14(vyy6000, vyy500)
new_ltEs9(EQ, GT) → True
new_esEs28(vyy33000, vyy34000, ty_Double) → new_esEs14(vyy33000, vyy34000)
new_esEs12(Integer(vyy6000), Integer(vyy500)) → new_primEqInt(vyy6000, vyy500)
new_ltEs10(vyy3300, vyy3400) → new_not(new_esEs8(new_compare6(vyy3300, vyy3400), GT))
new_lt20(vyy33000, vyy34000, app(ty_[], dbg)) → new_lt13(vyy33000, vyy34000, dbg)
new_compare15(vyy33000, vyy34000, False) → GT
new_esEs26(vyy6001, vyy501, app(ty_Maybe, dad)) → new_esEs4(vyy6001, vyy501, dad)
new_ltEs6(Right(vyy33000), Right(vyy34000), de, ty_Integer) → new_ltEs17(vyy33000, vyy34000)
new_esEs28(vyy33000, vyy34000, ty_Integer) → new_esEs12(vyy33000, vyy34000)
new_lt20(vyy33000, vyy34000, ty_Ordering) → new_lt15(vyy33000, vyy34000)
new_ltEs7(Just(vyy33000), Just(vyy34000), ty_Bool) → new_ltEs16(vyy33000, vyy34000)
new_esEs27(vyy6002, vyy502, ty_Double) → new_esEs14(vyy6002, vyy502)
new_ltEs16(True, True) → True
new_ltEs9(LT, EQ) → True
new_ltEs7(Just(vyy33000), Just(vyy34000), ty_Double) → new_ltEs14(vyy33000, vyy34000)
new_lt11(vyy33000, vyy34000, app(ty_Ratio, cae)) → new_lt16(vyy33000, vyy34000, cae)
new_pePe(False, vyy97) → vyy97
new_lt10(vyy33001, vyy34001, app(ty_[], cbd)) → new_lt13(vyy33001, vyy34001, cbd)
new_esEs7(Right(vyy6000), Left(vyy500), gd, fa) → False
new_esEs7(Left(vyy6000), Right(vyy500), gd, fa) → False
new_esEs15(True, False) → False
new_esEs15(False, True) → False
new_ltEs6(Left(vyy33000), Left(vyy34000), ty_Double, cb) → new_ltEs14(vyy33000, vyy34000)
new_ltEs7(Just(vyy33000), Just(vyy34000), app(ty_Ratio, ceh)) → new_ltEs12(vyy33000, vyy34000, ceh)
new_ltEs19(vyy3300, vyy3400, ty_Float) → new_ltEs10(vyy3300, vyy3400)
new_esEs27(vyy6002, vyy502, app(app(ty_Either, dah), dba)) → new_esEs7(vyy6002, vyy502, dah, dba)
new_lt6(vyy33000, vyy34000) → new_esEs8(new_compare9(vyy33000, vyy34000), LT)
new_esEs28(vyy33000, vyy34000, ty_@0) → new_esEs13(vyy33000, vyy34000)
new_lt11(vyy33000, vyy34000, ty_Double) → new_lt17(vyy33000, vyy34000)
new_esEs26(vyy6001, vyy501, ty_@0) → new_esEs13(vyy6001, vyy501)
new_lt11(vyy33000, vyy34000, ty_Integer) → new_lt6(vyy33000, vyy34000)
new_esEs26(vyy6001, vyy501, ty_Int) → new_esEs11(vyy6001, vyy501)
new_compare15(vyy33000, vyy34000, True) → LT
new_esEs22(vyy6001, vyy501, ty_Int) → new_esEs11(vyy6001, vyy501)
new_esEs22(vyy6001, vyy501, ty_Integer) → new_esEs12(vyy6001, vyy501)
new_lt20(vyy33000, vyy34000, app(app(ty_@2, bg), bh)) → new_lt14(vyy33000, vyy34000, bg, bh)
new_ltEs9(EQ, EQ) → True
new_ltEs20(vyy33001, vyy34001, app(app(app(ty_@3, dce), dcf), dcg)) → new_ltEs15(vyy33001, vyy34001, dce, dcf, dcg)
new_esEs19(vyy6000, vyy500, app(app(ty_Either, bcf), bcg)) → new_esEs7(vyy6000, vyy500, bcf, bcg)
new_lt20(vyy33000, vyy34000, ty_Float) → new_lt5(vyy33000, vyy34000)
new_esEs20(vyy6001, vyy501, app(app(ty_@2, bdf), bdg)) → new_esEs5(vyy6001, vyy501, bdf, bdg)
new_ltEs18(vyy33002, vyy34002, ty_Int) → new_ltEs13(vyy33002, vyy34002)
new_lt20(vyy33000, vyy34000, app(app(ty_Either, hg), hh)) → new_lt7(vyy33000, vyy34000, hg, hh)
new_ltEs18(vyy33002, vyy34002, ty_Char) → new_ltEs11(vyy33002, vyy34002)
new_esEs23(vyy33000, vyy34000, ty_Double) → new_esEs14(vyy33000, vyy34000)
new_esEs7(Right(vyy6000), Right(vyy500), gd, app(app(ty_@2, gf), gg)) → new_esEs5(vyy6000, vyy500, gf, gg)
new_ltEs6(Left(vyy33000), Left(vyy34000), ty_Ordering, cb) → new_ltEs9(vyy33000, vyy34000)
new_primCmpNat0(Zero, Succ(vyy340000)) → LT
new_ltEs20(vyy33001, vyy34001, ty_Double) → new_ltEs14(vyy33001, vyy34001)
new_compare14(vyy33000, vyy34000, False) → GT
new_compare27(Nothing, Just(vyy3400), False, cdg) → LT
new_esEs8(LT, LT) → True
new_esEs18(vyy6000, vyy500, ty_@0) → new_esEs13(vyy6000, vyy500)
new_lt10(vyy33001, vyy34001, ty_Ordering) → new_lt15(vyy33001, vyy34001)
new_esEs19(vyy6000, vyy500, app(ty_Maybe, bdd)) → new_esEs4(vyy6000, vyy500, bdd)
new_esEs7(Left(vyy6000), Left(vyy500), ty_Int, fa) → new_esEs11(vyy6000, vyy500)
new_esEs25(vyy6000, vyy500, ty_Ordering) → new_esEs8(vyy6000, vyy500)
new_esEs18(vyy6000, vyy500, app(ty_Ratio, bag)) → new_esEs9(vyy6000, vyy500, bag)
new_esEs24(vyy33001, vyy34001, app(app(ty_Either, ccc), ccd)) → new_esEs7(vyy33001, vyy34001, ccc, ccd)
new_esEs20(vyy6001, vyy501, app(app(app(ty_@3, bec), bed), bee)) → new_esEs6(vyy6001, vyy501, bec, bed, bee)
new_esEs28(vyy33000, vyy34000, ty_Float) → new_esEs10(vyy33000, vyy34000)
new_compare0([], [], bf) → EQ
new_pePe(True, vyy97) → True
new_primEqNat0(Zero, Zero) → True
new_ltEs19(vyy3300, vyy3400, ty_Int) → new_ltEs13(vyy3300, vyy3400)
new_esEs20(vyy6001, vyy501, ty_Int) → new_esEs11(vyy6001, vyy501)
new_esEs26(vyy6001, vyy501, ty_Char) → new_esEs17(vyy6001, vyy501)
new_esEs7(Left(vyy6000), Left(vyy500), app(app(ty_@2, fb), fc), fa) → new_esEs5(vyy6000, vyy500, fb, fc)
new_ltEs18(vyy33002, vyy34002, ty_Float) → new_ltEs10(vyy33002, vyy34002)
new_primMulNat0(Succ(vyy600000), Succ(vyy50000)) → new_primPlusNat1(new_primMulNat0(vyy600000, Succ(vyy50000)), vyy50000)
new_esEs18(vyy6000, vyy500, ty_Bool) → new_esEs15(vyy6000, vyy500)
new_compare14(vyy33000, vyy34000, True) → LT
new_ltEs19(vyy3300, vyy3400, app(ty_[], bf)) → new_ltEs4(vyy3300, vyy3400, bf)
new_ltEs6(Right(vyy33000), Right(vyy34000), de, app(app(app(ty_@3, ec), ed), ee)) → new_ltEs15(vyy33000, vyy34000, ec, ed, ee)
new_esEs7(Left(vyy6000), Left(vyy500), ty_Ordering, fa) → new_esEs8(vyy6000, vyy500)
new_esEs5(@2(vyy6000, vyy6001), @2(vyy500, vyy501), bca, bcb) → new_asAs(new_esEs19(vyy6000, vyy500, bca), new_esEs20(vyy6001, vyy501, bcb))
new_esEs26(vyy6001, vyy501, ty_Bool) → new_esEs15(vyy6001, vyy501)
new_ltEs9(EQ, LT) → False
new_ltEs13(vyy3300, vyy3400) → new_not(new_esEs8(new_compare16(vyy3300, vyy3400), GT))
new_ltEs7(Just(vyy33000), Just(vyy34000), ty_@0) → new_ltEs8(vyy33000, vyy34000)
new_esEs18(vyy6000, vyy500, app(app(ty_@2, bah), bba)) → new_esEs5(vyy6000, vyy500, bah, bba)
new_esEs7(Right(vyy6000), Right(vyy500), gd, app(app(app(ty_@3, hc), hd), he)) → new_esEs6(vyy6000, vyy500, hc, hd, he)
new_sr(vyy6000, vyy500) → new_primMulInt(vyy6000, vyy500)
new_compare12(vyy33000, vyy34000, True, baa, bab, bac) → LT
new_ltEs7(Just(vyy33000), Just(vyy34000), ty_Int) → new_ltEs13(vyy33000, vyy34000)
new_esEs26(vyy6001, vyy501, ty_Ordering) → new_esEs8(vyy6001, vyy501)
new_esEs8(GT, GT) → True
new_ltEs12(vyy3300, vyy3400, bhe) → new_not(new_esEs8(new_compare31(vyy3300, vyy3400, bhe), GT))
new_esEs18(vyy6000, vyy500, app(app(app(ty_@3, bbe), bbf), bbg)) → new_esEs6(vyy6000, vyy500, bbe, bbf, bbg)
new_ltEs20(vyy33001, vyy34001, app(app(ty_Either, dch), dda)) → new_ltEs6(vyy33001, vyy34001, dch, dda)
new_ltEs7(Just(vyy33000), Just(vyy34000), app(app(app(ty_@3, cfa), cfb), cfc)) → new_ltEs15(vyy33000, vyy34000, cfa, cfb, cfc)
new_esEs7(Right(vyy6000), Right(vyy500), gd, app(app(ty_Either, gh), ha)) → new_esEs7(vyy6000, vyy500, gh, ha)
new_lt20(vyy33000, vyy34000, ty_Double) → new_lt17(vyy33000, vyy34000)
new_esEs26(vyy6001, vyy501, app(app(app(ty_@3, daa), dab), dac)) → new_esEs6(vyy6001, vyy501, daa, dab, dac)
new_esEs8(GT, LT) → False
new_esEs8(LT, GT) → False
new_ltEs20(vyy33001, vyy34001, ty_Bool) → new_ltEs16(vyy33001, vyy34001)
new_ltEs19(vyy3300, vyy3400, app(app(app(ty_@3, bhf), bhg), bhh)) → new_ltEs15(vyy3300, vyy3400, bhf, bhg, bhh)
new_esEs26(vyy6001, vyy501, ty_Integer) → new_esEs12(vyy6001, vyy501)
new_ltEs6(Right(vyy33000), Right(vyy34000), de, ty_Int) → new_ltEs13(vyy33000, vyy34000)
new_lt11(vyy33000, vyy34000, ty_@0) → new_lt4(vyy33000, vyy34000)
new_primEqInt(Neg(Succ(vyy60000)), Neg(Succ(vyy5000))) → new_primEqNat0(vyy60000, vyy5000)
new_esEs7(Right(vyy6000), Right(vyy500), gd, ty_Char) → new_esEs17(vyy6000, vyy500)
new_esEs15(True, True) → True
new_esEs20(vyy6001, vyy501, ty_Ordering) → new_esEs8(vyy6001, vyy501)
new_esEs23(vyy33000, vyy34000, ty_Ordering) → new_esEs8(vyy33000, vyy34000)
new_compare27(Just(vyy3300), Nothing, False, cdg) → GT
new_compare18(vyy33000, vyy34000, ty_Ordering) → new_compare30(vyy33000, vyy34000)
new_compare19(vyy33000, vyy34000, bg, bh) → new_compare24(vyy33000, vyy34000, new_esEs5(vyy33000, vyy34000, bg, bh), bg, bh)
new_esEs28(vyy33000, vyy34000, app(ty_Maybe, bad)) → new_esEs4(vyy33000, vyy34000, bad)
new_ltEs7(Just(vyy33000), Just(vyy34000), app(ty_[], cee)) → new_ltEs4(vyy33000, vyy34000, cee)
new_compare27(Nothing, Nothing, False, cdg) → LT
new_compare18(vyy33000, vyy34000, app(ty_Ratio, bgg)) → new_compare31(vyy33000, vyy34000, bgg)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs24(vyy33001, vyy34001, app(app(app(ty_@3, cbh), cca), ccb)) → new_esEs6(vyy33001, vyy34001, cbh, cca, ccb)
new_esEs18(vyy6000, vyy500, ty_Float) → new_esEs10(vyy6000, vyy500)
new_ltEs6(Right(vyy33000), Right(vyy34000), de, app(ty_Ratio, eb)) → new_ltEs12(vyy33000, vyy34000, eb)
new_esEs19(vyy6000, vyy500, ty_Integer) → new_esEs12(vyy6000, vyy500)
new_primEqInt(Neg(Zero), Neg(Succ(vyy5000))) → False
new_primEqInt(Neg(Succ(vyy60000)), Neg(Zero)) → False
new_ltEs20(vyy33001, vyy34001, app(ty_[], dca)) → new_ltEs4(vyy33001, vyy34001, dca)
new_primCompAux0(vyy103, GT) → GT
new_esEs8(EQ, EQ) → True
new_esEs20(vyy6001, vyy501, ty_Bool) → new_esEs15(vyy6001, vyy501)
new_esEs4(Just(vyy6000), Just(vyy500), ty_@0) → new_esEs13(vyy6000, vyy500)
new_primPlusNat1(Zero, vyy50000) → Succ(vyy50000)
new_compare24(vyy33000, vyy34000, True, bg, bh) → EQ
new_ltEs9(LT, LT) → True
new_esEs29(vyy600, vyy50, app(ty_[], baf)) → new_esEs16(vyy600, vyy50, baf)
new_compare32(Double(vyy33000, vyy33001), Double(vyy34000, vyy34001)) → new_compare16(new_sr(vyy33000, vyy34000), new_sr(vyy33001, vyy34001))
new_esEs26(vyy6001, vyy501, app(app(ty_Either, chf), chg)) → new_esEs7(vyy6001, vyy501, chf, chg)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_lt20(vyy33000, vyy34000, ty_Char) → new_lt8(vyy33000, vyy34000)
new_ltEs20(vyy33001, vyy34001, app(app(ty_@2, dcb), dcc)) → new_ltEs5(vyy33001, vyy34001, dcb, dcc)
new_compare31(:%(vyy33000, vyy33001), :%(vyy34000, vyy34001), ty_Integer) → new_compare9(new_sr0(vyy33000, vyy34001), new_sr0(vyy34000, vyy33001))
new_ltEs18(vyy33002, vyy34002, ty_@0) → new_ltEs8(vyy33002, vyy34002)
new_esEs4(Just(vyy6000), Just(vyy500), app(app(ty_Either, bfd), bfe)) → new_esEs7(vyy6000, vyy500, bfd, bfe)
new_primCmpNat0(Succ(vyy330000), Succ(vyy340000)) → new_primCmpNat0(vyy330000, vyy340000)
new_esEs23(vyy33000, vyy34000, ty_Float) → new_esEs10(vyy33000, vyy34000)
new_ltEs18(vyy33002, vyy34002, app(app(ty_Either, cde), cdf)) → new_ltEs6(vyy33002, vyy34002, cde, cdf)
new_esEs25(vyy6000, vyy500, app(ty_Maybe, chb)) → new_esEs4(vyy6000, vyy500, chb)
new_compare18(vyy33000, vyy34000, ty_@0) → new_compare5(vyy33000, vyy34000)
new_esEs18(vyy6000, vyy500, ty_Double) → new_esEs14(vyy6000, vyy500)
new_esEs4(Just(vyy6000), Just(vyy500), ty_Bool) → new_esEs15(vyy6000, vyy500)
new_primEqInt(Pos(Succ(vyy60000)), Pos(Succ(vyy5000))) → new_primEqNat0(vyy60000, vyy5000)
new_compare10(vyy33000, vyy34000, False, bg, bh) → GT
new_ltEs19(vyy3300, vyy3400, ty_Integer) → new_ltEs17(vyy3300, vyy3400)
new_ltEs5(@2(vyy33000, vyy33001), @2(vyy34000, vyy34001), cea, ceb) → new_pePe(new_lt20(vyy33000, vyy34000, cea), new_asAs(new_esEs28(vyy33000, vyy34000, cea), new_ltEs20(vyy33001, vyy34001, ceb)))
new_esEs4(Just(vyy6000), Just(vyy500), app(app(ty_@2, bfb), bfc)) → new_esEs5(vyy6000, vyy500, bfb, bfc)
new_esEs28(vyy33000, vyy34000, ty_Char) → new_esEs17(vyy33000, vyy34000)
new_ltEs18(vyy33002, vyy34002, app(app(app(ty_@3, cdb), cdc), cdd)) → new_ltEs15(vyy33002, vyy34002, cdb, cdc, cdd)
new_lt10(vyy33001, vyy34001, app(ty_Maybe, cbc)) → new_lt12(vyy33001, vyy34001, cbc)
new_esEs23(vyy33000, vyy34000, ty_Char) → new_esEs17(vyy33000, vyy34000)
new_compare17(vyy33000, vyy34000, hg, hh) → new_compare25(vyy33000, vyy34000, new_esEs7(vyy33000, vyy34000, hg, hh), hg, hh)
new_ltEs7(Just(vyy33000), Just(vyy34000), ty_Float) → new_ltEs10(vyy33000, vyy34000)
new_ltEs7(Just(vyy33000), Just(vyy34000), app(app(ty_Either, cfd), cfe)) → new_ltEs6(vyy33000, vyy34000, cfd, cfe)
new_ltEs7(Nothing, Just(vyy34000), cdh) → True
new_primEqNat0(Succ(vyy60000), Succ(vyy5000)) → new_primEqNat0(vyy60000, vyy5000)
new_esEs27(vyy6002, vyy502, ty_Ordering) → new_esEs8(vyy6002, vyy502)
new_esEs7(Right(vyy6000), Right(vyy500), gd, app(ty_[], hb)) → new_esEs16(vyy6000, vyy500, hb)
new_esEs19(vyy6000, vyy500, app(app(app(ty_@3, bda), bdb), bdc)) → new_esEs6(vyy6000, vyy500, bda, bdb, bdc)
new_esEs20(vyy6001, vyy501, ty_Double) → new_esEs14(vyy6001, vyy501)
new_ltEs19(vyy3300, vyy3400, ty_Double) → new_ltEs14(vyy3300, vyy3400)
new_compare25(vyy33000, vyy34000, False, hg, hh) → new_compare11(vyy33000, vyy34000, new_ltEs6(vyy33000, vyy34000, hg, hh), hg, hh)
new_esEs7(Right(vyy6000), Right(vyy500), gd, ty_Float) → new_esEs10(vyy6000, vyy500)
new_esEs20(vyy6001, vyy501, ty_Float) → new_esEs10(vyy6001, vyy501)
new_esEs28(vyy33000, vyy34000, ty_Int) → new_esEs11(vyy33000, vyy34000)
new_lt20(vyy33000, vyy34000, ty_@0) → new_lt4(vyy33000, vyy34000)
new_primCmpInt(Neg(Succ(vyy330000)), Neg(vyy34000)) → new_primCmpNat0(vyy34000, Succ(vyy330000))
new_ltEs18(vyy33002, vyy34002, app(app(ty_@2, ccg), cch)) → new_ltEs5(vyy33002, vyy34002, ccg, cch)
new_esEs24(vyy33001, vyy34001, ty_Ordering) → new_esEs8(vyy33001, vyy34001)
new_esEs18(vyy6000, vyy500, ty_Char) → new_esEs17(vyy6000, vyy500)
new_lt19(vyy33000, vyy34000) → new_esEs8(new_compare34(vyy33000, vyy34000), LT)
new_esEs23(vyy33000, vyy34000, ty_Bool) → new_esEs15(vyy33000, vyy34000)
new_ltEs6(Left(vyy33000), Right(vyy34000), de, cb) → True
new_lt11(vyy33000, vyy34000, app(app(app(ty_@3, caf), cag), cah)) → new_lt18(vyy33000, vyy34000, caf, cag, cah)
new_esEs10(Float(vyy6000, vyy6001), Float(vyy500, vyy501)) → new_esEs11(new_sr(vyy6000, vyy500), new_sr(vyy6001, vyy501))
new_esEs21(vyy6000, vyy500, ty_Int) → new_esEs11(vyy6000, vyy500)
new_ltEs6(Right(vyy33000), Left(vyy34000), de, cb) → False
new_esEs28(vyy33000, vyy34000, ty_Ordering) → new_esEs8(vyy33000, vyy34000)
new_esEs8(EQ, LT) → False
new_esEs8(LT, EQ) → False
new_primEqInt(Pos(Succ(vyy60000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(vyy5000))) → False
new_lt10(vyy33001, vyy34001, app(app(ty_Either, ccc), ccd)) → new_lt7(vyy33001, vyy34001, ccc, ccd)
new_compare13(vyy83, vyy84, True, bae) → LT
new_primPlusNat0(Zero, Succ(vyy500000)) → Succ(vyy500000)
new_primPlusNat0(Succ(vyy9900), Zero) → Succ(vyy9900)
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(vyy330000), Zero) → GT
new_ltEs19(vyy3300, vyy3400, ty_Ordering) → new_ltEs9(vyy3300, vyy3400)
new_esEs23(vyy33000, vyy34000, app(app(ty_@2, cac), cad)) → new_esEs5(vyy33000, vyy34000, cac, cad)
new_ltEs6(Left(vyy33000), Left(vyy34000), app(app(ty_@2, cd), ce), cb) → new_ltEs5(vyy33000, vyy34000, cd, ce)
new_esEs19(vyy6000, vyy500, ty_@0) → new_esEs13(vyy6000, vyy500)
new_primCmpInt(Neg(Zero), Pos(Succ(vyy340000))) → LT
new_compare11(vyy33000, vyy34000, True, hg, hh) → LT
new_ltEs20(vyy33001, vyy34001, ty_Integer) → new_ltEs17(vyy33001, vyy34001)
new_sr0(Integer(vyy340000), Integer(vyy330010)) → Integer(new_primMulInt(vyy340000, vyy330010))
new_primEqInt(Pos(Succ(vyy60000)), Neg(vyy500)) → False
new_primEqInt(Neg(Succ(vyy60000)), Pos(vyy500)) → False
new_esEs6(@3(vyy6000, vyy6001, vyy6002), @3(vyy500, vyy501, vyy502), cff, cfg, cfh) → new_asAs(new_esEs25(vyy6000, vyy500, cff), new_asAs(new_esEs26(vyy6001, vyy501, cfg), new_esEs27(vyy6002, vyy502, cfh)))
new_esEs25(vyy6000, vyy500, ty_@0) → new_esEs13(vyy6000, vyy500)
new_esEs29(vyy600, vyy50, app(app(ty_@2, bca), bcb)) → new_esEs5(vyy600, vyy50, bca, bcb)
new_esEs16(:(vyy6000, vyy6001), :(vyy500, vyy501), baf) → new_asAs(new_esEs18(vyy6000, vyy500, baf), new_esEs16(vyy6001, vyy501, baf))
new_ltEs6(Left(vyy33000), Left(vyy34000), ty_Int, cb) → new_ltEs13(vyy33000, vyy34000)
new_lt7(vyy33000, vyy34000, hg, hh) → new_esEs8(new_compare17(vyy33000, vyy34000, hg, hh), LT)
new_ltEs7(Just(vyy33000), Just(vyy34000), app(app(ty_@2, cef), ceg)) → new_ltEs5(vyy33000, vyy34000, cef, ceg)
new_primEqInt(Neg(Zero), Pos(Succ(vyy5000))) → False
new_primEqInt(Pos(Zero), Neg(Succ(vyy5000))) → False
new_esEs13(@0, @0) → True
new_lt11(vyy33000, vyy34000, app(ty_Maybe, caa)) → new_lt12(vyy33000, vyy34000, caa)
new_primCmpInt(Pos(Zero), Pos(Succ(vyy340000))) → new_primCmpNat0(Zero, Succ(vyy340000))
new_esEs28(vyy33000, vyy34000, app(app(ty_Either, hg), hh)) → new_esEs7(vyy33000, vyy34000, hg, hh)
new_esEs7(Right(vyy6000), Right(vyy500), gd, ty_@0) → new_esEs13(vyy6000, vyy500)
new_esEs9(:%(vyy6000, vyy6001), :%(vyy500, vyy501), beg) → new_asAs(new_esEs21(vyy6000, vyy500, beg), new_esEs22(vyy6001, vyy501, beg))
new_esEs7(Right(vyy6000), Right(vyy500), gd, app(ty_Maybe, hf)) → new_esEs4(vyy6000, vyy500, hf)
new_ltEs20(vyy33001, vyy34001, ty_Int) → new_ltEs13(vyy33001, vyy34001)
new_ltEs6(Right(vyy33000), Right(vyy34000), de, app(ty_Maybe, df)) → new_ltEs7(vyy33000, vyy34000, df)
new_lt20(vyy33000, vyy34000, ty_Integer) → new_lt6(vyy33000, vyy34000)
new_esEs27(vyy6002, vyy502, ty_Float) → new_esEs10(vyy6002, vyy502)
new_esEs4(Just(vyy6000), Just(vyy500), ty_Integer) → new_esEs12(vyy6000, vyy500)
new_esEs8(GT, EQ) → False
new_esEs8(EQ, GT) → False
new_esEs4(Just(vyy6000), Just(vyy500), app(ty_Ratio, bfa)) → new_esEs9(vyy6000, vyy500, bfa)
new_lt11(vyy33000, vyy34000, app(app(ty_Either, cba), cbb)) → new_lt7(vyy33000, vyy34000, cba, cbb)
new_esEs26(vyy6001, vyy501, app(app(ty_@2, chd), che)) → new_esEs5(vyy6001, vyy501, chd, che)
new_primCompAux0(vyy103, LT) → LT
new_ltEs6(Left(vyy33000), Left(vyy34000), ty_Integer, cb) → new_ltEs17(vyy33000, vyy34000)
new_lt20(vyy33000, vyy34000, ty_Bool) → new_lt19(vyy33000, vyy34000)
new_lt10(vyy33001, vyy34001, app(app(ty_@2, cbe), cbf)) → new_lt14(vyy33001, vyy34001, cbe, cbf)
new_esEs11(vyy600, vyy50) → new_primEqInt(vyy600, vyy50)
new_not(False) → True
new_ltEs15(@3(vyy33000, vyy33001, vyy33002), @3(vyy34000, vyy34001, vyy34002), bhf, bhg, bhh) → new_pePe(new_lt11(vyy33000, vyy34000, bhf), new_asAs(new_esEs23(vyy33000, vyy34000, bhf), new_pePe(new_lt10(vyy33001, vyy34001, bhg), new_asAs(new_esEs24(vyy33001, vyy34001, bhg), new_ltEs18(vyy33002, vyy34002, bhh)))))
new_compare18(vyy33000, vyy34000, app(app(ty_@2, bge), bgf)) → new_compare19(vyy33000, vyy34000, bge, bgf)
new_esEs14(Double(vyy6000, vyy6001), Double(vyy500, vyy501)) → new_esEs11(new_sr(vyy6000, vyy500), new_sr(vyy6001, vyy501))
new_esEs28(vyy33000, vyy34000, app(ty_[], dbg)) → new_esEs16(vyy33000, vyy34000, dbg)
new_primCmpInt(Pos(Succ(vyy330000)), Pos(vyy34000)) → new_primCmpNat0(Succ(vyy330000), vyy34000)
new_esEs29(vyy600, vyy50, ty_Integer) → new_esEs12(vyy600, vyy50)
new_compare12(vyy33000, vyy34000, False, baa, bab, bac) → GT
new_esEs19(vyy6000, vyy500, ty_Int) → new_esEs11(vyy6000, vyy500)
new_esEs7(Left(vyy6000), Left(vyy500), ty_Integer, fa) → new_esEs12(vyy6000, vyy500)
new_esEs19(vyy6000, vyy500, ty_Char) → new_esEs17(vyy6000, vyy500)
new_ltEs9(LT, GT) → True
new_ltEs20(vyy33001, vyy34001, ty_Char) → new_ltEs11(vyy33001, vyy34001)
new_ltEs14(vyy3300, vyy3400) → new_not(new_esEs8(new_compare32(vyy3300, vyy3400), GT))
new_esEs25(vyy6000, vyy500, ty_Float) → new_esEs10(vyy6000, vyy500)
new_lt11(vyy33000, vyy34000, ty_Char) → new_lt8(vyy33000, vyy34000)
new_esEs24(vyy33001, vyy34001, ty_Integer) → new_esEs12(vyy33001, vyy34001)
new_esEs28(vyy33000, vyy34000, app(app(ty_@2, bg), bh)) → new_esEs5(vyy33000, vyy34000, bg, bh)
new_compare0(:(vyy33000, vyy33001), [], bf) → GT
new_ltEs18(vyy33002, vyy34002, app(ty_Maybe, cce)) → new_ltEs7(vyy33002, vyy34002, cce)
new_esEs18(vyy6000, vyy500, app(ty_Maybe, bbh)) → new_esEs4(vyy6000, vyy500, bbh)
new_compare28(vyy33000, vyy34000, True) → EQ
new_esEs7(Left(vyy6000), Left(vyy500), app(ty_Ratio, eh), fa) → new_esEs9(vyy6000, vyy500, eh)
new_compare18(vyy33000, vyy34000, ty_Char) → new_compare8(vyy33000, vyy34000)
new_compare6(Float(vyy33000, vyy33001), Float(vyy34000, vyy34001)) → new_compare16(new_sr(vyy33000, vyy34000), new_sr(vyy33001, vyy34001))
new_esEs27(vyy6002, vyy502, ty_Int) → new_esEs11(vyy6002, vyy502)
new_compare11(vyy33000, vyy34000, False, hg, hh) → GT
new_lt11(vyy33000, vyy34000, ty_Bool) → new_lt19(vyy33000, vyy34000)
new_compare18(vyy33000, vyy34000, app(ty_[], bgd)) → new_compare0(vyy33000, vyy34000, bgd)
new_ltEs7(Just(vyy33000), Just(vyy34000), app(ty_Maybe, ced)) → new_ltEs7(vyy33000, vyy34000, ced)
new_primCmpInt(Pos(Succ(vyy330000)), Neg(vyy34000)) → GT
new_esEs18(vyy6000, vyy500, app(app(ty_Either, bbb), bbc)) → new_esEs7(vyy6000, vyy500, bbb, bbc)
new_lt15(vyy33000, vyy34000) → new_esEs8(new_compare30(vyy33000, vyy34000), LT)
new_primMulInt(Pos(vyy60000), Pos(vyy5000)) → Pos(new_primMulNat0(vyy60000, vyy5000))
new_ltEs6(Right(vyy33000), Right(vyy34000), de, ty_@0) → new_ltEs8(vyy33000, vyy34000)
new_compare24(vyy33000, vyy34000, False, bg, bh) → new_compare10(vyy33000, vyy34000, new_ltEs5(vyy33000, vyy34000, bg, bh), bg, bh)
new_esEs27(vyy6002, vyy502, ty_Char) → new_esEs17(vyy6002, vyy502)
new_ltEs18(vyy33002, vyy34002, ty_Integer) → new_ltEs17(vyy33002, vyy34002)
new_primMulInt(Neg(vyy60000), Neg(vyy5000)) → Pos(new_primMulNat0(vyy60000, vyy5000))
new_esEs24(vyy33001, vyy34001, ty_Bool) → new_esEs15(vyy33001, vyy34001)
new_esEs28(vyy33000, vyy34000, app(ty_Ratio, cec)) → new_esEs9(vyy33000, vyy34000, cec)
new_primEqNat0(Zero, Succ(vyy5000)) → False
new_primEqNat0(Succ(vyy60000), Zero) → False
new_esEs7(Left(vyy6000), Left(vyy500), app(ty_[], fg), fa) → new_esEs16(vyy6000, vyy500, fg)
new_ltEs7(Just(vyy33000), Just(vyy34000), ty_Ordering) → new_ltEs9(vyy33000, vyy34000)
new_primPlusNat0(Zero, Zero) → Zero
new_ltEs6(Right(vyy33000), Right(vyy34000), de, ty_Float) → new_ltEs10(vyy33000, vyy34000)
new_compare25(vyy33000, vyy34000, True, hg, hh) → EQ
new_lt13(vyy33000, vyy34000, dbg) → new_esEs8(new_compare0(vyy33000, vyy34000, dbg), LT)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs28(vyy33000, vyy34000, app(app(app(ty_@3, baa), bab), bac)) → new_esEs6(vyy33000, vyy34000, baa, bab, bac)
new_esEs4(Nothing, Nothing, beh) → True
new_esEs7(Left(vyy6000), Left(vyy500), ty_Char, fa) → new_esEs17(vyy6000, vyy500)
new_esEs27(vyy6002, vyy502, app(app(app(ty_@3, dbc), dbd), dbe)) → new_esEs6(vyy6002, vyy502, dbc, dbd, dbe)
new_lt10(vyy33001, vyy34001, ty_Int) → new_lt9(vyy33001, vyy34001)
new_esEs27(vyy6002, vyy502, app(app(ty_@2, daf), dag)) → new_esEs5(vyy6002, vyy502, daf, dag)
new_esEs16(:(vyy6000, vyy6001), [], baf) → False
new_esEs16([], :(vyy500, vyy501), baf) → False
new_ltEs9(GT, GT) → True
new_esEs23(vyy33000, vyy34000, ty_Int) → new_esEs11(vyy33000, vyy34000)
new_ltEs7(Nothing, Nothing, cdh) → True
new_esEs27(vyy6002, vyy502, app(ty_Maybe, dbf)) → new_esEs4(vyy6002, vyy502, dbf)
new_primPlusNat1(Succ(vyy990), vyy50000) → Succ(Succ(new_primPlusNat0(vyy990, vyy50000)))
new_compare13(vyy83, vyy84, False, bae) → GT
new_lt16(vyy33000, vyy34000, cec) → new_esEs8(new_compare31(vyy33000, vyy34000, cec), LT)
new_primCmpInt(Neg(Zero), Neg(Succ(vyy340000))) → new_primCmpNat0(Succ(vyy340000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(vyy340000))) → GT
new_ltEs6(Left(vyy33000), Left(vyy34000), app(ty_Ratio, cf), cb) → new_ltEs12(vyy33000, vyy34000, cf)
new_compare0(:(vyy33000, vyy33001), :(vyy34000, vyy34001), bf) → new_primCompAux1(vyy33000, vyy34000, new_compare0(vyy33001, vyy34001, bf), bf)
new_compare28(vyy33000, vyy34000, False) → new_compare14(vyy33000, vyy34000, new_ltEs9(vyy33000, vyy34000))
new_lt14(vyy33000, vyy34000, bg, bh) → new_esEs8(new_compare19(vyy33000, vyy34000, bg, bh), LT)
new_esEs4(Just(vyy6000), Just(vyy500), app(ty_[], bff)) → new_esEs16(vyy6000, vyy500, bff)
new_esEs19(vyy6000, vyy500, ty_Double) → new_esEs14(vyy6000, vyy500)
new_compare7(vyy33000, vyy34000, bad) → new_compare27(vyy33000, vyy34000, new_esEs4(vyy33000, vyy34000, bad), bad)
new_esEs24(vyy33001, vyy34001, ty_Int) → new_esEs11(vyy33001, vyy34001)
new_lt11(vyy33000, vyy34000, ty_Ordering) → new_lt15(vyy33000, vyy34000)
new_esEs18(vyy6000, vyy500, ty_Integer) → new_esEs12(vyy6000, vyy500)
new_esEs20(vyy6001, vyy501, app(app(ty_Either, bdh), bea)) → new_esEs7(vyy6001, vyy501, bdh, bea)
new_ltEs17(vyy3300, vyy3400) → new_not(new_esEs8(new_compare9(vyy3300, vyy3400), GT))
new_esEs29(vyy600, vyy50, app(ty_Ratio, beg)) → new_esEs9(vyy600, vyy50, beg)
new_ltEs6(Right(vyy33000), Right(vyy34000), de, app(app(ty_Either, ef), eg)) → new_ltEs6(vyy33000, vyy34000, ef, eg)
new_esEs19(vyy6000, vyy500, app(app(ty_@2, bcd), bce)) → new_esEs5(vyy6000, vyy500, bcd, bce)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_lt9(vyy33000, vyy34000) → new_esEs8(new_compare16(vyy33000, vyy34000), LT)
new_esEs4(Just(vyy6000), Just(vyy500), ty_Double) → new_esEs14(vyy6000, vyy500)
new_esEs20(vyy6001, vyy501, app(ty_[], beb)) → new_esEs16(vyy6001, vyy501, beb)
new_esEs29(vyy600, vyy50, ty_Bool) → new_esEs15(vyy600, vyy50)
new_compare9(Integer(vyy33000), Integer(vyy34000)) → new_primCmpInt(vyy33000, vyy34000)
new_asAs(False, vyy90) → False
new_esEs25(vyy6000, vyy500, app(ty_Ratio, cga)) → new_esEs9(vyy6000, vyy500, cga)
new_ltEs6(Left(vyy33000), Left(vyy34000), app(ty_Maybe, ca), cb) → new_ltEs7(vyy33000, vyy34000, ca)
new_esEs19(vyy6000, vyy500, ty_Float) → new_esEs10(vyy6000, vyy500)
new_compare34(vyy33000, vyy34000) → new_compare29(vyy33000, vyy34000, new_esEs15(vyy33000, vyy34000))
new_primMulInt(Pos(vyy60000), Neg(vyy5000)) → Neg(new_primMulNat0(vyy60000, vyy5000))
new_primMulInt(Neg(vyy60000), Pos(vyy5000)) → Neg(new_primMulNat0(vyy60000, vyy5000))
new_ltEs19(vyy3300, vyy3400, ty_Char) → new_ltEs11(vyy3300, vyy3400)
new_compare16(vyy3300, vyy3400) → new_primCmpInt(vyy3300, vyy3400)
new_primMulNat0(Zero, Succ(vyy50000)) → Zero
new_primMulNat0(Succ(vyy600000), Zero) → Zero
new_esEs7(Left(vyy6000), Left(vyy500), ty_Float, fa) → new_esEs10(vyy6000, vyy500)
new_esEs23(vyy33000, vyy34000, app(app(app(ty_@3, caf), cag), cah)) → new_esEs6(vyy33000, vyy34000, caf, cag, cah)
new_ltEs18(vyy33002, vyy34002, app(ty_[], ccf)) → new_ltEs4(vyy33002, vyy34002, ccf)
new_esEs24(vyy33001, vyy34001, ty_Float) → new_esEs10(vyy33001, vyy34001)
new_esEs29(vyy600, vyy50, ty_Int) → new_esEs11(vyy600, vyy50)
new_compare31(:%(vyy33000, vyy33001), :%(vyy34000, vyy34001), ty_Int) → new_compare16(new_sr(vyy33000, vyy34001), new_sr(vyy34000, vyy33001))
new_esEs24(vyy33001, vyy34001, app(ty_[], cbd)) → new_esEs16(vyy33001, vyy34001, cbd)
new_esEs29(vyy600, vyy50, ty_Char) → new_esEs17(vyy600, vyy50)
new_ltEs20(vyy33001, vyy34001, ty_Ordering) → new_ltEs9(vyy33001, vyy34001)
new_esEs26(vyy6001, vyy501, app(ty_Ratio, chc)) → new_esEs9(vyy6001, vyy501, chc)
new_esEs27(vyy6002, vyy502, ty_@0) → new_esEs13(vyy6002, vyy502)
new_esEs29(vyy600, vyy50, ty_Float) → new_esEs10(vyy600, vyy50)
new_esEs18(vyy6000, vyy500, ty_Ordering) → new_esEs8(vyy6000, vyy500)
new_ltEs11(vyy3300, vyy3400) → new_not(new_esEs8(new_compare8(vyy3300, vyy3400), GT))
new_ltEs20(vyy33001, vyy34001, app(ty_Ratio, dcd)) → new_ltEs12(vyy33001, vyy34001, dcd)
new_esEs25(vyy6000, vyy500, app(app(app(ty_@3, cgg), cgh), cha)) → new_esEs6(vyy6000, vyy500, cgg, cgh, cha)
new_ltEs9(GT, EQ) → False
new_esEs7(Left(vyy6000), Left(vyy500), app(app(app(ty_@3, fh), ga), gb), fa) → new_esEs6(vyy6000, vyy500, fh, ga, gb)
new_esEs20(vyy6001, vyy501, ty_Integer) → new_esEs12(vyy6001, vyy501)
new_lt10(vyy33001, vyy34001, ty_Float) → new_lt5(vyy33001, vyy34001)
new_ltEs19(vyy3300, vyy3400, ty_@0) → new_ltEs8(vyy3300, vyy3400)
new_esEs28(vyy33000, vyy34000, ty_Bool) → new_esEs15(vyy33000, vyy34000)
new_lt5(vyy33000, vyy34000) → new_esEs8(new_compare6(vyy33000, vyy34000), LT)
new_esEs18(vyy6000, vyy500, ty_Int) → new_esEs11(vyy6000, vyy500)
new_compare18(vyy33000, vyy34000, ty_Bool) → new_compare34(vyy33000, vyy34000)
new_ltEs20(vyy33001, vyy34001, ty_Float) → new_ltEs10(vyy33001, vyy34001)
new_esEs7(Right(vyy6000), Right(vyy500), gd, ty_Int) → new_esEs11(vyy6000, vyy500)
new_ltEs7(Just(vyy33000), Nothing, cdh) → False
new_esEs4(Just(vyy6000), Just(vyy500), ty_Int) → new_esEs11(vyy6000, vyy500)
new_esEs7(Right(vyy6000), Right(vyy500), gd, ty_Integer) → new_esEs12(vyy6000, vyy500)
new_ltEs7(Just(vyy33000), Just(vyy34000), ty_Char) → new_ltEs11(vyy33000, vyy34000)
new_esEs16([], [], baf) → True
new_esEs20(vyy6001, vyy501, app(ty_Ratio, bde)) → new_esEs9(vyy6001, vyy501, bde)
new_lt11(vyy33000, vyy34000, ty_Int) → new_lt9(vyy33000, vyy34000)
new_esEs25(vyy6000, vyy500, app(app(ty_@2, cgb), cgc)) → new_esEs5(vyy6000, vyy500, cgb, cgc)
new_lt10(vyy33001, vyy34001, ty_Bool) → new_lt19(vyy33001, vyy34001)
new_ltEs6(Left(vyy33000), Left(vyy34000), app(ty_[], cc), cb) → new_ltEs4(vyy33000, vyy34000, cc)
new_ltEs18(vyy33002, vyy34002, ty_Double) → new_ltEs14(vyy33002, vyy34002)
new_ltEs18(vyy33002, vyy34002, ty_Ordering) → new_ltEs9(vyy33002, vyy34002)
new_ltEs19(vyy3300, vyy3400, app(ty_Maybe, cdh)) → new_ltEs7(vyy3300, vyy3400, cdh)
new_esEs23(vyy33000, vyy34000, app(ty_Ratio, cae)) → new_esEs9(vyy33000, vyy34000, cae)
new_ltEs18(vyy33002, vyy34002, ty_Bool) → new_ltEs16(vyy33002, vyy34002)
new_esEs29(vyy600, vyy50, app(app(app(ty_@3, cff), cfg), cfh)) → new_esEs6(vyy600, vyy50, cff, cfg, cfh)
new_lt18(vyy33000, vyy34000, baa, bab, bac) → new_esEs8(new_compare33(vyy33000, vyy34000, baa, bab, bac), LT)
new_lt10(vyy33001, vyy34001, app(app(app(ty_@3, cbh), cca), ccb)) → new_lt18(vyy33001, vyy34001, cbh, cca, ccb)
new_esEs29(vyy600, vyy50, app(app(ty_Either, gd), fa)) → new_esEs7(vyy600, vyy50, gd, fa)
new_compare27(vyy330, vyy340, True, cdg) → EQ
new_esEs19(vyy6000, vyy500, app(ty_Ratio, bcc)) → new_esEs9(vyy6000, vyy500, bcc)
new_ltEs6(Left(vyy33000), Left(vyy34000), ty_@0, cb) → new_ltEs8(vyy33000, vyy34000)
new_esEs7(Left(vyy6000), Left(vyy500), ty_Bool, fa) → new_esEs15(vyy6000, vyy500)
new_ltEs6(Right(vyy33000), Right(vyy34000), de, ty_Double) → new_ltEs14(vyy33000, vyy34000)
new_compare18(vyy33000, vyy34000, app(app(ty_Either, bhc), bhd)) → new_compare17(vyy33000, vyy34000, bhc, bhd)
new_ltEs6(Right(vyy33000), Right(vyy34000), de, app(ty_[], dg)) → new_ltEs4(vyy33000, vyy34000, dg)
new_esEs20(vyy6001, vyy501, ty_Char) → new_esEs17(vyy6001, vyy501)
new_primPlusNat0(Succ(vyy9900), Succ(vyy500000)) → Succ(Succ(new_primPlusNat0(vyy9900, vyy500000)))
new_compare26(vyy33000, vyy34000, False, baa, bab, bac) → new_compare12(vyy33000, vyy34000, new_ltEs15(vyy33000, vyy34000, baa, bab, bac), baa, bab, bac)
new_compare26(vyy33000, vyy34000, True, baa, bab, bac) → EQ
new_esEs23(vyy33000, vyy34000, app(ty_[], cab)) → new_esEs16(vyy33000, vyy34000, cab)
new_compare0([], :(vyy34000, vyy34001), bf) → LT
new_ltEs6(Right(vyy33000), Right(vyy34000), de, ty_Bool) → new_ltEs16(vyy33000, vyy34000)
new_compare27(Just(vyy3300), Just(vyy3400), False, cdg) → new_compare13(vyy3300, vyy3400, new_ltEs19(vyy3300, vyy3400, cdg), cdg)
new_ltEs6(Right(vyy33000), Right(vyy34000), de, ty_Ordering) → new_ltEs9(vyy33000, vyy34000)
new_lt10(vyy33001, vyy34001, ty_Double) → new_lt17(vyy33001, vyy34001)
new_asAs(True, vyy90) → vyy90
new_esEs25(vyy6000, vyy500, ty_Int) → new_esEs11(vyy6000, vyy500)
new_lt8(vyy33000, vyy34000) → new_esEs8(new_compare8(vyy33000, vyy34000), LT)
new_ltEs16(False, False) → True
new_compare18(vyy33000, vyy34000, ty_Integer) → new_compare9(vyy33000, vyy34000)
new_esEs27(vyy6002, vyy502, ty_Bool) → new_esEs15(vyy6002, vyy502)
new_esEs7(Left(vyy6000), Left(vyy500), ty_@0, fa) → new_esEs13(vyy6000, vyy500)
new_esEs19(vyy6000, vyy500, ty_Ordering) → new_esEs8(vyy6000, vyy500)
new_lt20(vyy33000, vyy34000, ty_Int) → new_lt9(vyy33000, vyy34000)
new_ltEs6(Left(vyy33000), Left(vyy34000), ty_Bool, cb) → new_ltEs16(vyy33000, vyy34000)
new_esEs21(vyy6000, vyy500, ty_Integer) → new_esEs12(vyy6000, vyy500)
new_lt17(vyy33000, vyy34000) → new_esEs8(new_compare32(vyy33000, vyy34000), LT)
new_lt12(vyy33000, vyy34000, bad) → new_esEs8(new_compare7(vyy33000, vyy34000, bad), LT)
new_esEs29(vyy600, vyy50, app(ty_Maybe, beh)) → new_esEs4(vyy600, vyy50, beh)
new_compare18(vyy33000, vyy34000, ty_Int) → new_compare16(vyy33000, vyy34000)
new_ltEs20(vyy33001, vyy34001, app(ty_Maybe, dbh)) → new_ltEs7(vyy33001, vyy34001, dbh)
new_esEs25(vyy6000, vyy500, app(app(ty_Either, cgd), cge)) → new_esEs7(vyy6000, vyy500, cgd, cge)
new_compare8(Char(vyy33000), Char(vyy34000)) → new_primCmpNat0(vyy33000, vyy34000)
new_compare33(vyy33000, vyy34000, baa, bab, bac) → new_compare26(vyy33000, vyy34000, new_esEs6(vyy33000, vyy34000, baa, bab, bac), baa, bab, bac)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs24(vyy33001, vyy34001, app(ty_Ratio, cbg)) → new_esEs9(vyy33001, vyy34001, cbg)
new_primCompAux0(vyy103, EQ) → vyy103
new_esEs20(vyy6001, vyy501, ty_@0) → new_esEs13(vyy6001, vyy501)
new_esEs29(vyy600, vyy50, ty_Ordering) → new_esEs8(vyy600, vyy50)
new_ltEs19(vyy3300, vyy3400, app(app(ty_Either, de), cb)) → new_ltEs6(vyy3300, vyy3400, de, cb)
new_lt20(vyy33000, vyy34000, app(ty_Maybe, bad)) → new_lt12(vyy33000, vyy34000, bad)
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primCmpInt(Neg(Succ(vyy330000)), Pos(vyy34000)) → LT
new_esEs24(vyy33001, vyy34001, ty_Double) → new_esEs14(vyy33001, vyy34001)
new_not(True) → False
new_esEs15(False, False) → True
The set Q consists of the following terms:
new_ltEs7(Just(x0), Just(x1), ty_Ordering)
new_esEs13(@0, @0)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_primPlusNat0(Succ(x0), Zero)
new_esEs23(x0, x1, ty_@0)
new_ltEs16(True, True)
new_ltEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare18(x0, x1, ty_Bool)
new_esEs28(x0, x1, ty_Char)
new_ltEs6(Right(x0), Right(x1), x2, ty_Double)
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_primEqNat0(Zero, Succ(x0))
new_lt5(x0, x1)
new_lt20(x0, x1, ty_Integer)
new_esEs25(x0, x1, ty_Integer)
new_compare25(x0, x1, False, x2, x3)
new_esEs25(x0, x1, ty_Bool)
new_esEs24(x0, x1, ty_Float)
new_primCompAux1(x0, x1, x2, x3)
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_esEs7(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs25(x0, x1, ty_Char)
new_ltEs20(x0, x1, ty_Bool)
new_compare0([], [], x0)
new_lt10(x0, x1, app(ty_[], x2))
new_ltEs18(x0, x1, ty_Bool)
new_esEs22(x0, x1, ty_Integer)
new_asAs(True, x0)
new_esEs26(x0, x1, ty_Float)
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_lt10(x0, x1, ty_Char)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs6(Right(x0), Right(x1), x2, ty_Int)
new_lt20(x0, x1, ty_Ordering)
new_esEs18(x0, x1, ty_Double)
new_lt10(x0, x1, ty_Float)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_ltEs6(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs4(Just(x0), Just(x1), app(ty_[], x2))
new_esEs27(x0, x1, ty_Bool)
new_esEs15(True, True)
new_esEs29(x0, x1, ty_Double)
new_esEs25(x0, x1, ty_Float)
new_esEs27(x0, x1, ty_Float)
new_ltEs6(Right(x0), Right(x1), x2, ty_Float)
new_lt20(x0, x1, ty_Double)
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, ty_Integer)
new_esEs25(x0, x1, ty_@0)
new_ltEs18(x0, x1, app(ty_Maybe, x2))
new_esEs7(Right(x0), Right(x1), x2, ty_@0)
new_ltEs7(Just(x0), Just(x1), app(ty_[], x2))
new_esEs24(x0, x1, ty_Double)
new_compare18(x0, x1, ty_Int)
new_lt11(x0, x1, ty_Bool)
new_primMulNat0(Zero, Succ(x0))
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_esEs28(x0, x1, ty_Ordering)
new_esEs15(False, False)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs26(x0, x1, app(ty_[], x2))
new_esEs18(x0, x1, ty_Float)
new_ltEs6(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs8(GT, GT)
new_esEs7(Right(x0), Right(x1), x2, ty_Ordering)
new_sr0(Integer(x0), Integer(x1))
new_esEs24(x0, x1, ty_Integer)
new_esEs20(x0, x1, ty_Integer)
new_esEs18(x0, x1, app(ty_[], x2))
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs6(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs4(Just(x0), Just(x1), ty_Ordering)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_lt10(x0, x1, ty_Double)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_compare14(x0, x1, False)
new_esEs27(x0, x1, ty_Integer)
new_esEs8(LT, LT)
new_primPlusNat0(Succ(x0), Succ(x1))
new_esEs26(x0, x1, ty_Char)
new_esEs16([], [], x0)
new_compare18(x0, x1, ty_Char)
new_ltEs6(Left(x0), Left(x1), ty_Bool, x2)
new_ltEs6(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_compare10(x0, x1, False, x2, x3)
new_esEs19(x0, x1, ty_Double)
new_lt10(x0, x1, app(app(ty_Either, x2), x3))
new_lt18(x0, x1, x2, x3, x4)
new_ltEs18(x0, x1, ty_Int)
new_ltEs6(Right(x0), Right(x1), x2, ty_Char)
new_lt7(x0, x1, x2, x3)
new_ltEs10(x0, x1)
new_esEs7(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs24(x0, x1, ty_Int)
new_esEs11(x0, x1)
new_esEs7(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_primPlusNat0(Zero, Succ(x0))
new_compare11(x0, x1, True, x2, x3)
new_lt11(x0, x1, app(app(ty_@2, x2), x3))
new_esEs8(GT, LT)
new_esEs8(LT, GT)
new_esEs5(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs20(x0, x1, app(ty_[], x2))
new_esEs20(x0, x1, ty_Int)
new_compare6(Float(x0, x1), Float(x2, x3))
new_lt11(x0, x1, ty_@0)
new_esEs23(x0, x1, ty_Double)
new_ltEs9(EQ, EQ)
new_compare5(@0, @0)
new_esEs4(Just(x0), Just(x1), ty_Bool)
new_ltEs18(x0, x1, app(app(ty_Either, x2), x3))
new_primCompAux0(x0, EQ)
new_esEs7(Left(x0), Left(x1), ty_Float, x2)
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_compare18(x0, x1, app(app(ty_@2, x2), x3))
new_lt10(x0, x1, ty_Int)
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primEqNat0(Zero, Zero)
new_primCmpNat0(Succ(x0), Zero)
new_primEqNat0(Succ(x0), Zero)
new_ltEs6(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs19(x0, x1, ty_Ordering)
new_lt11(x0, x1, app(ty_[], x2))
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(Left(x0), Left(x1), ty_Char, x2)
new_ltEs19(x0, x1, ty_Int)
new_esEs27(x0, x1, app(ty_[], x2))
new_lt11(x0, x1, app(ty_Ratio, x2))
new_compare14(x0, x1, True)
new_esEs19(x0, x1, ty_Int)
new_compare7(x0, x1, x2)
new_ltEs7(Just(x0), Just(x1), ty_Char)
new_esEs4(Nothing, Nothing, x0)
new_esEs27(x0, x1, ty_Char)
new_esEs4(Just(x0), Just(x1), ty_Float)
new_esEs7(Right(x0), Right(x1), x2, ty_Integer)
new_ltEs6(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs26(x0, x1, ty_@0)
new_primMulNat0(Zero, Zero)
new_compare18(x0, x1, ty_Float)
new_esEs20(x0, x1, ty_@0)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_esEs16(:(x0, x1), [], x2)
new_ltEs18(x0, x1, ty_@0)
new_esEs7(Left(x0), Left(x1), ty_Integer, x2)
new_esEs24(x0, x1, ty_Bool)
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_esEs7(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs28(x0, x1, app(ty_[], x2))
new_primMulNat0(Succ(x0), Zero)
new_ltEs7(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_lt13(x0, x1, x2)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_esEs9(:%(x0, x1), :%(x2, x3), x4)
new_esEs18(x0, x1, app(ty_Ratio, x2))
new_compare18(x0, x1, ty_Ordering)
new_esEs4(Just(x0), Just(x1), ty_@0)
new_lt20(x0, x1, ty_Float)
new_lt4(x0, x1)
new_ltEs6(Right(x0), Right(x1), x2, app(ty_[], x3))
new_lt11(x0, x1, ty_Ordering)
new_lt19(x0, x1)
new_ltEs7(Just(x0), Just(x1), app(ty_Ratio, x2))
new_compare13(x0, x1, False, x2)
new_compare27(x0, x1, True, x2)
new_esEs28(x0, x1, ty_Double)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs7(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_compare15(x0, x1, True)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_esEs18(x0, x1, ty_Integer)
new_pePe(False, x0)
new_esEs19(x0, x1, ty_Bool)
new_ltEs6(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs4(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_ltEs18(x0, x1, ty_Float)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_esEs21(x0, x1, ty_Int)
new_ltEs11(x0, x1)
new_esEs29(x0, x1, ty_Int)
new_esEs25(x0, x1, ty_Double)
new_esEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, app(ty_Ratio, x2))
new_esEs28(x0, x1, ty_Bool)
new_esEs19(x0, x1, app(ty_Ratio, x2))
new_esEs4(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_lt11(x0, x1, ty_Double)
new_ltEs9(GT, EQ)
new_ltEs9(EQ, GT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpNat0(Succ(x0), Succ(x1))
new_ltEs6(Left(x0), Left(x1), ty_@0, x2)
new_compare18(x0, x1, app(ty_[], x2))
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_compare0([], :(x0, x1), x2)
new_esEs7(Right(x0), Left(x1), x2, x3)
new_compare15(x0, x1, False)
new_esEs7(Left(x0), Right(x1), x2, x3)
new_esEs23(x0, x1, ty_Ordering)
new_primCmpNat0(Zero, Succ(x0))
new_esEs7(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_ltEs6(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_ltEs20(x0, x1, ty_Int)
new_esEs27(x0, x1, ty_Int)
new_asAs(False, x0)
new_lt11(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primPlusNat0(Zero, Zero)
new_lt20(x0, x1, ty_Int)
new_primCompAux0(x0, LT)
new_esEs7(Left(x0), Left(x1), ty_Int, x2)
new_lt10(x0, x1, ty_Ordering)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, ty_Char)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_esEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare18(x0, x1, app(app(ty_Either, x2), x3))
new_lt10(x0, x1, app(app(ty_@2, x2), x3))
new_compare12(x0, x1, True, x2, x3, x4)
new_esEs7(Left(x0), Left(x1), app(ty_[], x2), x3)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_compare29(x0, x1, True)
new_compare27(Nothing, Just(x0), False, x1)
new_lt11(x0, x1, app(ty_Maybe, x2))
new_esEs7(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs25(x0, x1, ty_Int)
new_esEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs6(Left(x0), Left(x1), ty_Char, x2)
new_primPlusNat1(Zero, x0)
new_compare16(x0, x1)
new_esEs7(Right(x0), Right(x1), x2, ty_Double)
new_ltEs7(Just(x0), Nothing, x1)
new_esEs23(x0, x1, ty_Bool)
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_compare9(Integer(x0), Integer(x1))
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs7(Just(x0), Just(x1), ty_Integer)
new_esEs4(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_compare17(x0, x1, x2, x3)
new_lt11(x0, x1, ty_Integer)
new_compare18(x0, x1, app(ty_Maybe, x2))
new_ltEs9(EQ, LT)
new_ltEs9(LT, EQ)
new_compare26(x0, x1, True, x2, x3, x4)
new_esEs7(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs29(x0, x1, ty_@0)
new_sr(x0, x1)
new_esEs7(Left(x0), Left(x1), ty_Bool, x2)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs15(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs12(Integer(x0), Integer(x1))
new_compare25(x0, x1, True, x2, x3)
new_lt11(x0, x1, ty_Int)
new_primEqInt(Neg(Zero), Pos(Zero))
new_primEqInt(Pos(Zero), Neg(Zero))
new_compare0(:(x0, x1), :(x2, x3), x4)
new_compare0(:(x0, x1), [], x2)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs20(x0, x1, ty_Double)
new_ltEs4(x0, x1, x2)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_esEs7(Right(x0), Right(x1), x2, ty_Bool)
new_esEs24(x0, x1, ty_@0)
new_esEs23(x0, x1, ty_Float)
new_compare33(x0, x1, x2, x3, x4)
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_ltEs5(@2(x0, x1), @2(x2, x3), x4, x5)
new_compare8(Char(x0), Char(x1))
new_lt11(x0, x1, app(app(ty_Either, x2), x3))
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_ltEs20(x0, x1, ty_@0)
new_esEs18(x0, x1, ty_Char)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs15(True, False)
new_esEs15(False, True)
new_esEs8(EQ, EQ)
new_esEs14(Double(x0, x1), Double(x2, x3))
new_esEs18(x0, x1, ty_Ordering)
new_esEs17(Char(x0), Char(x1))
new_primEqInt(Neg(Zero), Neg(Zero))
new_ltEs7(Just(x0), Just(x1), ty_@0)
new_ltEs7(Just(x0), Just(x1), ty_Float)
new_esEs28(x0, x1, ty_Integer)
new_esEs6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs27(x0, x1, ty_@0)
new_compare27(Just(x0), Nothing, False, x1)
new_ltEs6(Left(x0), Left(x1), ty_Float, x2)
new_compare11(x0, x1, False, x2, x3)
new_esEs22(x0, x1, ty_Int)
new_ltEs7(Just(x0), Just(x1), ty_Bool)
new_ltEs6(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs24(x0, x1, ty_Char)
new_ltEs6(Left(x0), Left(x1), ty_Ordering, x2)
new_compare26(x0, x1, False, x2, x3, x4)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs4(Nothing, Just(x0), x1)
new_compare24(x0, x1, False, x2, x3)
new_ltEs18(x0, x1, app(ty_Ratio, x2))
new_primCompAux0(x0, GT)
new_ltEs19(x0, x1, ty_Double)
new_lt10(x0, x1, ty_@0)
new_ltEs7(Just(x0), Just(x1), ty_Double)
new_esEs18(x0, x1, app(ty_Maybe, x2))
new_ltEs19(x0, x1, ty_Ordering)
new_compare18(x0, x1, app(ty_Ratio, x2))
new_esEs28(x0, x1, ty_Float)
new_esEs7(Right(x0), Right(x1), x2, ty_Float)
new_ltEs20(x0, x1, app(ty_[], x2))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_lt10(x0, x1, app(ty_Maybe, x2))
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs18(x0, x1, ty_Ordering)
new_lt10(x0, x1, app(ty_Ratio, x2))
new_pePe(True, x0)
new_esEs26(x0, x1, ty_Ordering)
new_ltEs9(LT, LT)
new_esEs29(x0, x1, ty_Integer)
new_esEs20(x0, x1, ty_Char)
new_ltEs18(x0, x1, ty_Integer)
new_compare10(x0, x1, True, x2, x3)
new_esEs7(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_ltEs16(False, True)
new_ltEs16(True, False)
new_ltEs19(x0, x1, ty_Bool)
new_lt20(x0, x1, ty_Char)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_esEs29(x0, x1, app(ty_[], x2))
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_compare31(:%(x0, x1), :%(x2, x3), ty_Integer)
new_compare18(x0, x1, ty_@0)
new_esEs26(x0, x1, ty_Double)
new_ltEs18(x0, x1, app(ty_[], x2))
new_esEs4(Just(x0), Just(x1), ty_Int)
new_esEs26(x0, x1, ty_Bool)
new_ltEs6(Right(x0), Right(x1), x2, ty_@0)
new_ltEs19(x0, x1, ty_@0)
new_ltEs14(x0, x1)
new_ltEs6(Left(x0), Right(x1), x2, x3)
new_ltEs6(Right(x0), Left(x1), x2, x3)
new_esEs19(x0, x1, app(app(ty_Either, x2), x3))
new_compare19(x0, x1, x2, x3)
new_esEs20(x0, x1, ty_Ordering)
new_esEs19(x0, x1, ty_Integer)
new_primCmpNat0(Zero, Zero)
new_esEs19(x0, x1, app(ty_Maybe, x2))
new_primEqNat0(Succ(x0), Succ(x1))
new_compare27(Just(x0), Just(x1), False, x2)
new_ltEs20(x0, x1, ty_Ordering)
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare29(x0, x1, False)
new_primMulNat0(Succ(x0), Succ(x1))
new_ltEs19(x0, x1, ty_Integer)
new_ltEs7(Nothing, Just(x0), x1)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_compare28(x0, x1, False)
new_esEs29(x0, x1, ty_Float)
new_esEs27(x0, x1, ty_Ordering)
new_ltEs12(x0, x1, x2)
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs6(Left(x0), Left(x1), ty_Int, x2)
new_lt8(x0, x1)
new_ltEs20(x0, x1, ty_Integer)
new_esEs4(Just(x0), Nothing, x1)
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_esEs7(Left(x0), Left(x1), ty_Double, x2)
new_compare24(x0, x1, True, x2, x3)
new_primPlusNat1(Succ(x0), x1)
new_ltEs6(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_esEs19(x0, x1, ty_Float)
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs6(Right(x0), Right(x1), x2, ty_Integer)
new_lt9(x0, x1)
new_ltEs7(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_esEs21(x0, x1, ty_Integer)
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_compare30(x0, x1)
new_ltEs20(x0, x1, ty_Char)
new_ltEs20(x0, x1, ty_Float)
new_ltEs9(GT, LT)
new_ltEs9(LT, GT)
new_ltEs7(Nothing, Nothing, x0)
new_esEs26(x0, x1, ty_Int)
new_lt10(x0, x1, ty_Bool)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs16(:(x0, x1), :(x2, x3), x4)
new_compare27(Nothing, Nothing, False, x0)
new_esEs24(x0, x1, ty_Ordering)
new_esEs18(x0, x1, app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, ty_Int)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_not(True)
new_ltEs19(x0, x1, ty_Float)
new_compare31(:%(x0, x1), :%(x2, x3), ty_Int)
new_esEs19(x0, x1, app(ty_[], x2))
new_esEs20(x0, x1, ty_Float)
new_esEs18(x0, x1, ty_Bool)
new_esEs23(x0, x1, app(ty_[], x2))
new_esEs16([], :(x0, x1), x2)
new_lt11(x0, x1, ty_Float)
new_esEs29(x0, x1, ty_Ordering)
new_ltEs18(x0, x1, ty_Double)
new_esEs7(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_compare34(x0, x1)
new_esEs4(Just(x0), Just(x1), ty_Double)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_not(False)
new_esEs25(x0, x1, app(ty_[], x2))
new_esEs29(x0, x1, ty_Char)
new_ltEs7(Just(x0), Just(x1), ty_Int)
new_ltEs6(Left(x0), Left(x1), app(ty_[], x2), x3)
new_lt15(x0, x1)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_compare28(x0, x1, True)
new_ltEs8(x0, x1)
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_ltEs6(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs26(x0, x1, ty_Integer)
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_esEs4(Just(x0), Just(x1), ty_Integer)
new_ltEs13(x0, x1)
new_esEs23(x0, x1, ty_Char)
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs7(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs4(Just(x0), Just(x1), ty_Char)
new_esEs19(x0, x1, ty_@0)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_compare13(x0, x1, True, x2)
new_lt10(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_ltEs6(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs17(x0, x1)
new_esEs24(x0, x1, app(ty_[], x2))
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_lt6(x0, x1)
new_ltEs6(Left(x0), Left(x1), ty_Double, x2)
new_compare18(x0, x1, ty_Double)
new_esEs7(Left(x0), Left(x1), ty_@0, x2)
new_esEs20(x0, x1, ty_Bool)
new_lt20(x0, x1, ty_@0)
new_lt10(x0, x1, ty_Integer)
new_lt14(x0, x1, x2, x3)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_primMulInt(Neg(x0), Neg(x1))
new_ltEs9(GT, GT)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs19(x0, x1, ty_Char)
new_compare18(x0, x1, ty_Integer)
new_ltEs18(x0, x1, ty_Char)
new_lt17(x0, x1)
new_esEs7(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs28(x0, x1, ty_Int)
new_compare12(x0, x1, False, x2, x3, x4)
new_lt20(x0, x1, app(ty_[], x2))
new_esEs10(Float(x0, x1), Float(x2, x3))
new_compare32(Double(x0, x1), Double(x2, x3))
new_ltEs20(x0, x1, ty_Double)
new_esEs18(x0, x1, ty_@0)
new_esEs29(x0, x1, ty_Bool)
new_compare18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primEqInt(Pos(Zero), Pos(Zero))
new_esEs25(x0, x1, ty_Ordering)
new_lt20(x0, x1, ty_Bool)
new_lt12(x0, x1, x2)
new_esEs18(x0, x1, ty_Int)
new_ltEs6(Left(x0), Left(x1), ty_Integer, x2)
new_ltEs18(x0, x1, app(app(ty_@2, x2), x3))
new_lt16(x0, x1, x2)
new_esEs7(Right(x0), Right(x1), x2, ty_Char)
new_lt11(x0, x1, ty_Char)
new_esEs18(x0, x1, app(app(ty_@2, x2), x3))
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_esEs28(x0, x1, ty_@0)
new_esEs4(Just(x0), Just(x1), app(ty_Maybe, x2))
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_primMulInt(Pos(x0), Pos(x1))
new_esEs7(Right(x0), Right(x1), x2, ty_Int)
new_ltEs16(False, False)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs4(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs27(x0, x1, ty_Double)
new_ltEs19(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
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
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ UsableRulesProof
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_foldFM_GE10(vyy3, vyy600, vyy61, vyy62, vyy63, vyy64, False, h, ba, bb) → new_foldFM_GE(vyy3, Nothing, vyy64, h, ba, bb)
new_foldFM_GE(vyy3, Nothing, Branch(Nothing, vyy61, vyy62, vyy63, vyy64), h, ba, bb) → new_foldFM_GE(vyy3, Nothing, vyy63, h, ba, bb)
new_foldFM_GE(vyy3, Nothing, Branch(Nothing, vyy61, vyy62, vyy63, vyy64), h, ba, bb) → new_foldFM_GE(vyy3, Nothing, vyy64, h, ba, bb)
new_foldFM_GE(vyy3, Nothing, Branch(Just(vyy600), vyy61, vyy62, vyy63, vyy64), h, ba, bb) → new_foldFM_GE10(vyy3, vyy600, vyy61, vyy62, vyy63, vyy64, new_esEs8(new_compare27(Just(vyy600), Nothing, False, ba), LT), h, ba, bb)
new_foldFM_GE10(vyy3, vyy600, vyy61, vyy62, vyy63, vyy64, True, h, ba, bb) → new_foldFM_GE(vyy3, Nothing, vyy64, h, ba, bb)
new_foldFM_GE10(vyy3, vyy600, vyy61, vyy62, vyy63, vyy64, False, h, ba, bb) → new_foldFM_GE(vyy3, Nothing, vyy63, h, ba, bb)
The TRS R consists of the following rules:
new_esEs4(Just(vyy6000), Just(vyy500), app(ty_Maybe, bgb)) → new_esEs4(vyy6000, vyy500, bgb)
new_ltEs19(vyy3300, vyy3400, app(app(ty_@2, cea), ceb)) → new_ltEs5(vyy3300, vyy3400, cea, ceb)
new_esEs23(vyy33000, vyy34000, app(app(ty_Either, cba), cbb)) → new_esEs7(vyy33000, vyy34000, cba, cbb)
new_lt10(vyy33001, vyy34001, ty_Integer) → new_lt6(vyy33001, vyy34001)
new_lt4(vyy33000, vyy34000) → new_esEs8(new_compare5(vyy33000, vyy34000), LT)
new_esEs4(Just(vyy6000), Just(vyy500), ty_Ordering) → new_esEs8(vyy6000, vyy500)
new_esEs7(Left(vyy6000), Left(vyy500), app(app(ty_Either, fd), ff), fa) → new_esEs7(vyy6000, vyy500, fd, ff)
new_ltEs6(Left(vyy33000), Left(vyy34000), app(app(app(ty_@3, cg), da), db), cb) → new_ltEs15(vyy33000, vyy34000, cg, da, db)
new_compare5(@0, @0) → EQ
new_esEs27(vyy6002, vyy502, app(ty_[], dbb)) → new_esEs16(vyy6002, vyy502, dbb)
new_lt10(vyy33001, vyy34001, ty_Char) → new_lt8(vyy33001, vyy34001)
new_esEs25(vyy6000, vyy500, ty_Integer) → new_esEs12(vyy6000, vyy500)
new_esEs25(vyy6000, vyy500, app(ty_[], cgf)) → new_esEs16(vyy6000, vyy500, cgf)
new_esEs7(Right(vyy6000), Right(vyy500), gd, ty_Bool) → new_esEs15(vyy6000, vyy500)
new_esEs25(vyy6000, vyy500, ty_Bool) → new_esEs15(vyy6000, vyy500)
new_ltEs6(Right(vyy33000), Right(vyy34000), de, ty_Char) → new_ltEs11(vyy33000, vyy34000)
new_esEs17(Char(vyy6000), Char(vyy500)) → new_primEqNat0(vyy6000, vyy500)
new_esEs7(Left(vyy6000), Left(vyy500), app(ty_Maybe, gc), fa) → new_esEs4(vyy6000, vyy500, gc)
new_esEs24(vyy33001, vyy34001, ty_Char) → new_esEs17(vyy33001, vyy34001)
new_ltEs6(Right(vyy33000), Right(vyy34000), de, app(app(ty_@2, dh), ea)) → new_ltEs5(vyy33000, vyy34000, dh, ea)
new_esEs29(vyy600, vyy50, ty_@0) → new_esEs13(vyy600, vyy50)
new_esEs19(vyy6000, vyy500, ty_Bool) → new_esEs15(vyy6000, vyy500)
new_lt20(vyy33000, vyy34000, app(ty_Ratio, cec)) → new_lt16(vyy33000, vyy34000, cec)
new_lt10(vyy33001, vyy34001, app(ty_Ratio, cbg)) → new_lt16(vyy33001, vyy34001, cbg)
new_esEs19(vyy6000, vyy500, app(ty_[], bch)) → new_esEs16(vyy6000, vyy500, bch)
new_compare10(vyy33000, vyy34000, True, bg, bh) → LT
new_esEs29(vyy600, vyy50, ty_Double) → new_esEs14(vyy600, vyy50)
new_esEs26(vyy6001, vyy501, ty_Float) → new_esEs10(vyy6001, vyy501)
new_esEs26(vyy6001, vyy501, ty_Double) → new_esEs14(vyy6001, vyy501)
new_esEs24(vyy33001, vyy34001, app(ty_Maybe, cbc)) → new_esEs4(vyy33001, vyy34001, cbc)
new_esEs4(Nothing, Just(vyy500), beh) → False
new_esEs4(Just(vyy6000), Nothing, beh) → False
new_esEs4(Just(vyy6000), Just(vyy500), ty_Char) → new_esEs17(vyy6000, vyy500)
new_ltEs20(vyy33001, vyy34001, ty_@0) → new_ltEs8(vyy33001, vyy34001)
new_ltEs7(Just(vyy33000), Just(vyy34000), ty_Integer) → new_ltEs17(vyy33000, vyy34000)
new_esEs25(vyy6000, vyy500, ty_Char) → new_esEs17(vyy6000, vyy500)
new_primCompAux1(vyy33000, vyy34000, vyy98, bf) → new_primCompAux0(vyy98, new_compare18(vyy33000, vyy34000, bf))
new_ltEs18(vyy33002, vyy34002, app(ty_Ratio, cda)) → new_ltEs12(vyy33002, vyy34002, cda)
new_ltEs19(vyy3300, vyy3400, app(ty_Ratio, bhe)) → new_ltEs12(vyy3300, vyy3400, bhe)
new_compare18(vyy33000, vyy34000, ty_Double) → new_compare32(vyy33000, vyy34000)
new_compare18(vyy33000, vyy34000, ty_Float) → new_compare6(vyy33000, vyy34000)
new_ltEs6(Left(vyy33000), Left(vyy34000), ty_Char, cb) → new_ltEs11(vyy33000, vyy34000)
new_compare29(vyy33000, vyy34000, False) → new_compare15(vyy33000, vyy34000, new_ltEs16(vyy33000, vyy34000))
new_primMulNat0(Zero, Zero) → Zero
new_ltEs8(vyy3300, vyy3400) → new_not(new_esEs8(new_compare5(vyy3300, vyy3400), GT))
new_esEs24(vyy33001, vyy34001, ty_@0) → new_esEs13(vyy33001, vyy34001)
new_esEs7(Right(vyy6000), Right(vyy500), gd, ty_Double) → new_esEs14(vyy6000, vyy500)
new_ltEs4(vyy3300, vyy3400, bf) → new_not(new_esEs8(new_compare0(vyy3300, vyy3400, bf), GT))
new_esEs26(vyy6001, vyy501, app(ty_[], chh)) → new_esEs16(vyy6001, vyy501, chh)
new_esEs18(vyy6000, vyy500, app(ty_[], bbd)) → new_esEs16(vyy6000, vyy500, bbd)
new_compare29(vyy33000, vyy34000, True) → EQ
new_esEs4(Just(vyy6000), Just(vyy500), app(app(app(ty_@3, bfg), bfh), bga)) → new_esEs6(vyy6000, vyy500, bfg, bfh, bga)
new_esEs7(Left(vyy6000), Left(vyy500), ty_Double, fa) → new_esEs14(vyy6000, vyy500)
new_ltEs9(GT, LT) → False
new_esEs20(vyy6001, vyy501, app(ty_Maybe, bef)) → new_esEs4(vyy6001, vyy501, bef)
new_lt11(vyy33000, vyy34000, app(app(ty_@2, cac), cad)) → new_lt14(vyy33000, vyy34000, cac, cad)
new_ltEs16(False, True) → True
new_lt11(vyy33000, vyy34000, ty_Float) → new_lt5(vyy33000, vyy34000)
new_esEs7(Right(vyy6000), Right(vyy500), gd, ty_Ordering) → new_esEs8(vyy6000, vyy500)
new_lt20(vyy33000, vyy34000, app(app(app(ty_@3, baa), bab), bac)) → new_lt18(vyy33000, vyy34000, baa, bab, bac)
new_esEs27(vyy6002, vyy502, ty_Integer) → new_esEs12(vyy6002, vyy502)
new_compare18(vyy33000, vyy34000, app(app(app(ty_@3, bgh), bha), bhb)) → new_compare33(vyy33000, vyy34000, bgh, bha, bhb)
new_ltEs16(True, False) → False
new_lt10(vyy33001, vyy34001, ty_@0) → new_lt4(vyy33001, vyy34001)
new_esEs23(vyy33000, vyy34000, app(ty_Maybe, caa)) → new_esEs4(vyy33000, vyy34000, caa)
new_ltEs19(vyy3300, vyy3400, ty_Bool) → new_ltEs16(vyy3300, vyy3400)
new_esEs27(vyy6002, vyy502, app(ty_Ratio, dae)) → new_esEs9(vyy6002, vyy502, dae)
new_compare30(vyy33000, vyy34000) → new_compare28(vyy33000, vyy34000, new_esEs8(vyy33000, vyy34000))
new_esEs23(vyy33000, vyy34000, ty_@0) → new_esEs13(vyy33000, vyy34000)
new_ltEs6(Left(vyy33000), Left(vyy34000), app(app(ty_Either, dc), dd), cb) → new_ltEs6(vyy33000, vyy34000, dc, dd)
new_ltEs6(Left(vyy33000), Left(vyy34000), ty_Float, cb) → new_ltEs10(vyy33000, vyy34000)
new_lt11(vyy33000, vyy34000, app(ty_[], cab)) → new_lt13(vyy33000, vyy34000, cab)
new_esEs24(vyy33001, vyy34001, app(app(ty_@2, cbe), cbf)) → new_esEs5(vyy33001, vyy34001, cbe, cbf)
new_esEs4(Just(vyy6000), Just(vyy500), ty_Float) → new_esEs10(vyy6000, vyy500)
new_esEs7(Right(vyy6000), Right(vyy500), gd, app(ty_Ratio, ge)) → new_esEs9(vyy6000, vyy500, ge)
new_compare18(vyy33000, vyy34000, app(ty_Maybe, bgc)) → new_compare7(vyy33000, vyy34000, bgc)
new_esEs23(vyy33000, vyy34000, ty_Integer) → new_esEs12(vyy33000, vyy34000)
new_esEs25(vyy6000, vyy500, ty_Double) → new_esEs14(vyy6000, vyy500)
new_ltEs9(EQ, GT) → True
new_esEs28(vyy33000, vyy34000, ty_Double) → new_esEs14(vyy33000, vyy34000)
new_esEs12(Integer(vyy6000), Integer(vyy500)) → new_primEqInt(vyy6000, vyy500)
new_ltEs10(vyy3300, vyy3400) → new_not(new_esEs8(new_compare6(vyy3300, vyy3400), GT))
new_lt20(vyy33000, vyy34000, app(ty_[], dbg)) → new_lt13(vyy33000, vyy34000, dbg)
new_compare15(vyy33000, vyy34000, False) → GT
new_esEs26(vyy6001, vyy501, app(ty_Maybe, dad)) → new_esEs4(vyy6001, vyy501, dad)
new_ltEs6(Right(vyy33000), Right(vyy34000), de, ty_Integer) → new_ltEs17(vyy33000, vyy34000)
new_esEs28(vyy33000, vyy34000, ty_Integer) → new_esEs12(vyy33000, vyy34000)
new_lt20(vyy33000, vyy34000, ty_Ordering) → new_lt15(vyy33000, vyy34000)
new_ltEs7(Just(vyy33000), Just(vyy34000), ty_Bool) → new_ltEs16(vyy33000, vyy34000)
new_esEs27(vyy6002, vyy502, ty_Double) → new_esEs14(vyy6002, vyy502)
new_ltEs16(True, True) → True
new_ltEs9(LT, EQ) → True
new_ltEs7(Just(vyy33000), Just(vyy34000), ty_Double) → new_ltEs14(vyy33000, vyy34000)
new_lt11(vyy33000, vyy34000, app(ty_Ratio, cae)) → new_lt16(vyy33000, vyy34000, cae)
new_pePe(False, vyy97) → vyy97
new_lt10(vyy33001, vyy34001, app(ty_[], cbd)) → new_lt13(vyy33001, vyy34001, cbd)
new_esEs7(Right(vyy6000), Left(vyy500), gd, fa) → False
new_esEs7(Left(vyy6000), Right(vyy500), gd, fa) → False
new_esEs15(True, False) → False
new_esEs15(False, True) → False
new_ltEs6(Left(vyy33000), Left(vyy34000), ty_Double, cb) → new_ltEs14(vyy33000, vyy34000)
new_ltEs7(Just(vyy33000), Just(vyy34000), app(ty_Ratio, ceh)) → new_ltEs12(vyy33000, vyy34000, ceh)
new_ltEs19(vyy3300, vyy3400, ty_Float) → new_ltEs10(vyy3300, vyy3400)
new_esEs27(vyy6002, vyy502, app(app(ty_Either, dah), dba)) → new_esEs7(vyy6002, vyy502, dah, dba)
new_lt6(vyy33000, vyy34000) → new_esEs8(new_compare9(vyy33000, vyy34000), LT)
new_esEs28(vyy33000, vyy34000, ty_@0) → new_esEs13(vyy33000, vyy34000)
new_lt11(vyy33000, vyy34000, ty_Double) → new_lt17(vyy33000, vyy34000)
new_esEs26(vyy6001, vyy501, ty_@0) → new_esEs13(vyy6001, vyy501)
new_lt11(vyy33000, vyy34000, ty_Integer) → new_lt6(vyy33000, vyy34000)
new_esEs26(vyy6001, vyy501, ty_Int) → new_esEs11(vyy6001, vyy501)
new_compare15(vyy33000, vyy34000, True) → LT
new_esEs22(vyy6001, vyy501, ty_Int) → new_esEs11(vyy6001, vyy501)
new_esEs22(vyy6001, vyy501, ty_Integer) → new_esEs12(vyy6001, vyy501)
new_lt20(vyy33000, vyy34000, app(app(ty_@2, bg), bh)) → new_lt14(vyy33000, vyy34000, bg, bh)
new_ltEs9(EQ, EQ) → True
new_ltEs20(vyy33001, vyy34001, app(app(app(ty_@3, dce), dcf), dcg)) → new_ltEs15(vyy33001, vyy34001, dce, dcf, dcg)
new_esEs19(vyy6000, vyy500, app(app(ty_Either, bcf), bcg)) → new_esEs7(vyy6000, vyy500, bcf, bcg)
new_lt20(vyy33000, vyy34000, ty_Float) → new_lt5(vyy33000, vyy34000)
new_esEs20(vyy6001, vyy501, app(app(ty_@2, bdf), bdg)) → new_esEs5(vyy6001, vyy501, bdf, bdg)
new_ltEs18(vyy33002, vyy34002, ty_Int) → new_ltEs13(vyy33002, vyy34002)
new_lt20(vyy33000, vyy34000, app(app(ty_Either, hg), hh)) → new_lt7(vyy33000, vyy34000, hg, hh)
new_ltEs18(vyy33002, vyy34002, ty_Char) → new_ltEs11(vyy33002, vyy34002)
new_esEs23(vyy33000, vyy34000, ty_Double) → new_esEs14(vyy33000, vyy34000)
new_esEs7(Right(vyy6000), Right(vyy500), gd, app(app(ty_@2, gf), gg)) → new_esEs5(vyy6000, vyy500, gf, gg)
new_ltEs6(Left(vyy33000), Left(vyy34000), ty_Ordering, cb) → new_ltEs9(vyy33000, vyy34000)
new_primCmpNat0(Zero, Succ(vyy340000)) → LT
new_ltEs20(vyy33001, vyy34001, ty_Double) → new_ltEs14(vyy33001, vyy34001)
new_compare14(vyy33000, vyy34000, False) → GT
new_compare27(Nothing, Just(vyy3400), False, cdg) → LT
new_esEs8(LT, LT) → True
new_esEs18(vyy6000, vyy500, ty_@0) → new_esEs13(vyy6000, vyy500)
new_lt10(vyy33001, vyy34001, ty_Ordering) → new_lt15(vyy33001, vyy34001)
new_esEs19(vyy6000, vyy500, app(ty_Maybe, bdd)) → new_esEs4(vyy6000, vyy500, bdd)
new_esEs7(Left(vyy6000), Left(vyy500), ty_Int, fa) → new_esEs11(vyy6000, vyy500)
new_esEs25(vyy6000, vyy500, ty_Ordering) → new_esEs8(vyy6000, vyy500)
new_esEs18(vyy6000, vyy500, app(ty_Ratio, bag)) → new_esEs9(vyy6000, vyy500, bag)
new_esEs24(vyy33001, vyy34001, app(app(ty_Either, ccc), ccd)) → new_esEs7(vyy33001, vyy34001, ccc, ccd)
new_esEs20(vyy6001, vyy501, app(app(app(ty_@3, bec), bed), bee)) → new_esEs6(vyy6001, vyy501, bec, bed, bee)
new_esEs28(vyy33000, vyy34000, ty_Float) → new_esEs10(vyy33000, vyy34000)
new_compare0([], [], bf) → EQ
new_pePe(True, vyy97) → True
new_primEqNat0(Zero, Zero) → True
new_ltEs19(vyy3300, vyy3400, ty_Int) → new_ltEs13(vyy3300, vyy3400)
new_esEs20(vyy6001, vyy501, ty_Int) → new_esEs11(vyy6001, vyy501)
new_esEs26(vyy6001, vyy501, ty_Char) → new_esEs17(vyy6001, vyy501)
new_esEs7(Left(vyy6000), Left(vyy500), app(app(ty_@2, fb), fc), fa) → new_esEs5(vyy6000, vyy500, fb, fc)
new_ltEs18(vyy33002, vyy34002, ty_Float) → new_ltEs10(vyy33002, vyy34002)
new_primMulNat0(Succ(vyy600000), Succ(vyy50000)) → new_primPlusNat1(new_primMulNat0(vyy600000, Succ(vyy50000)), vyy50000)
new_esEs18(vyy6000, vyy500, ty_Bool) → new_esEs15(vyy6000, vyy500)
new_compare14(vyy33000, vyy34000, True) → LT
new_ltEs19(vyy3300, vyy3400, app(ty_[], bf)) → new_ltEs4(vyy3300, vyy3400, bf)
new_ltEs6(Right(vyy33000), Right(vyy34000), de, app(app(app(ty_@3, ec), ed), ee)) → new_ltEs15(vyy33000, vyy34000, ec, ed, ee)
new_esEs7(Left(vyy6000), Left(vyy500), ty_Ordering, fa) → new_esEs8(vyy6000, vyy500)
new_esEs5(@2(vyy6000, vyy6001), @2(vyy500, vyy501), bca, bcb) → new_asAs(new_esEs19(vyy6000, vyy500, bca), new_esEs20(vyy6001, vyy501, bcb))
new_esEs26(vyy6001, vyy501, ty_Bool) → new_esEs15(vyy6001, vyy501)
new_ltEs9(EQ, LT) → False
new_ltEs13(vyy3300, vyy3400) → new_not(new_esEs8(new_compare16(vyy3300, vyy3400), GT))
new_ltEs7(Just(vyy33000), Just(vyy34000), ty_@0) → new_ltEs8(vyy33000, vyy34000)
new_esEs18(vyy6000, vyy500, app(app(ty_@2, bah), bba)) → new_esEs5(vyy6000, vyy500, bah, bba)
new_esEs7(Right(vyy6000), Right(vyy500), gd, app(app(app(ty_@3, hc), hd), he)) → new_esEs6(vyy6000, vyy500, hc, hd, he)
new_sr(vyy6000, vyy500) → new_primMulInt(vyy6000, vyy500)
new_compare12(vyy33000, vyy34000, True, baa, bab, bac) → LT
new_ltEs7(Just(vyy33000), Just(vyy34000), ty_Int) → new_ltEs13(vyy33000, vyy34000)
new_esEs26(vyy6001, vyy501, ty_Ordering) → new_esEs8(vyy6001, vyy501)
new_esEs8(GT, GT) → True
new_ltEs12(vyy3300, vyy3400, bhe) → new_not(new_esEs8(new_compare31(vyy3300, vyy3400, bhe), GT))
new_esEs18(vyy6000, vyy500, app(app(app(ty_@3, bbe), bbf), bbg)) → new_esEs6(vyy6000, vyy500, bbe, bbf, bbg)
new_ltEs20(vyy33001, vyy34001, app(app(ty_Either, dch), dda)) → new_ltEs6(vyy33001, vyy34001, dch, dda)
new_ltEs7(Just(vyy33000), Just(vyy34000), app(app(app(ty_@3, cfa), cfb), cfc)) → new_ltEs15(vyy33000, vyy34000, cfa, cfb, cfc)
new_esEs7(Right(vyy6000), Right(vyy500), gd, app(app(ty_Either, gh), ha)) → new_esEs7(vyy6000, vyy500, gh, ha)
new_lt20(vyy33000, vyy34000, ty_Double) → new_lt17(vyy33000, vyy34000)
new_esEs26(vyy6001, vyy501, app(app(app(ty_@3, daa), dab), dac)) → new_esEs6(vyy6001, vyy501, daa, dab, dac)
new_esEs8(GT, LT) → False
new_esEs8(LT, GT) → False
new_ltEs20(vyy33001, vyy34001, ty_Bool) → new_ltEs16(vyy33001, vyy34001)
new_ltEs19(vyy3300, vyy3400, app(app(app(ty_@3, bhf), bhg), bhh)) → new_ltEs15(vyy3300, vyy3400, bhf, bhg, bhh)
new_esEs26(vyy6001, vyy501, ty_Integer) → new_esEs12(vyy6001, vyy501)
new_ltEs6(Right(vyy33000), Right(vyy34000), de, ty_Int) → new_ltEs13(vyy33000, vyy34000)
new_lt11(vyy33000, vyy34000, ty_@0) → new_lt4(vyy33000, vyy34000)
new_primEqInt(Neg(Succ(vyy60000)), Neg(Succ(vyy5000))) → new_primEqNat0(vyy60000, vyy5000)
new_esEs7(Right(vyy6000), Right(vyy500), gd, ty_Char) → new_esEs17(vyy6000, vyy500)
new_esEs15(True, True) → True
new_esEs20(vyy6001, vyy501, ty_Ordering) → new_esEs8(vyy6001, vyy501)
new_esEs23(vyy33000, vyy34000, ty_Ordering) → new_esEs8(vyy33000, vyy34000)
new_compare27(Just(vyy3300), Nothing, False, cdg) → GT
new_compare18(vyy33000, vyy34000, ty_Ordering) → new_compare30(vyy33000, vyy34000)
new_compare19(vyy33000, vyy34000, bg, bh) → new_compare24(vyy33000, vyy34000, new_esEs5(vyy33000, vyy34000, bg, bh), bg, bh)
new_esEs28(vyy33000, vyy34000, app(ty_Maybe, bad)) → new_esEs4(vyy33000, vyy34000, bad)
new_ltEs7(Just(vyy33000), Just(vyy34000), app(ty_[], cee)) → new_ltEs4(vyy33000, vyy34000, cee)
new_compare27(Nothing, Nothing, False, cdg) → LT
new_compare18(vyy33000, vyy34000, app(ty_Ratio, bgg)) → new_compare31(vyy33000, vyy34000, bgg)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs24(vyy33001, vyy34001, app(app(app(ty_@3, cbh), cca), ccb)) → new_esEs6(vyy33001, vyy34001, cbh, cca, ccb)
new_esEs18(vyy6000, vyy500, ty_Float) → new_esEs10(vyy6000, vyy500)
new_ltEs6(Right(vyy33000), Right(vyy34000), de, app(ty_Ratio, eb)) → new_ltEs12(vyy33000, vyy34000, eb)
new_esEs19(vyy6000, vyy500, ty_Integer) → new_esEs12(vyy6000, vyy500)
new_primEqInt(Neg(Zero), Neg(Succ(vyy5000))) → False
new_primEqInt(Neg(Succ(vyy60000)), Neg(Zero)) → False
new_ltEs20(vyy33001, vyy34001, app(ty_[], dca)) → new_ltEs4(vyy33001, vyy34001, dca)
new_primCompAux0(vyy103, GT) → GT
new_esEs8(EQ, EQ) → True
new_esEs20(vyy6001, vyy501, ty_Bool) → new_esEs15(vyy6001, vyy501)
new_esEs4(Just(vyy6000), Just(vyy500), ty_@0) → new_esEs13(vyy6000, vyy500)
new_primPlusNat1(Zero, vyy50000) → Succ(vyy50000)
new_compare24(vyy33000, vyy34000, True, bg, bh) → EQ
new_ltEs9(LT, LT) → True
new_esEs29(vyy600, vyy50, app(ty_[], baf)) → new_esEs16(vyy600, vyy50, baf)
new_compare32(Double(vyy33000, vyy33001), Double(vyy34000, vyy34001)) → new_compare16(new_sr(vyy33000, vyy34000), new_sr(vyy33001, vyy34001))
new_esEs26(vyy6001, vyy501, app(app(ty_Either, chf), chg)) → new_esEs7(vyy6001, vyy501, chf, chg)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_lt20(vyy33000, vyy34000, ty_Char) → new_lt8(vyy33000, vyy34000)
new_ltEs20(vyy33001, vyy34001, app(app(ty_@2, dcb), dcc)) → new_ltEs5(vyy33001, vyy34001, dcb, dcc)
new_compare31(:%(vyy33000, vyy33001), :%(vyy34000, vyy34001), ty_Integer) → new_compare9(new_sr0(vyy33000, vyy34001), new_sr0(vyy34000, vyy33001))
new_ltEs18(vyy33002, vyy34002, ty_@0) → new_ltEs8(vyy33002, vyy34002)
new_esEs4(Just(vyy6000), Just(vyy500), app(app(ty_Either, bfd), bfe)) → new_esEs7(vyy6000, vyy500, bfd, bfe)
new_primCmpNat0(Succ(vyy330000), Succ(vyy340000)) → new_primCmpNat0(vyy330000, vyy340000)
new_esEs23(vyy33000, vyy34000, ty_Float) → new_esEs10(vyy33000, vyy34000)
new_ltEs18(vyy33002, vyy34002, app(app(ty_Either, cde), cdf)) → new_ltEs6(vyy33002, vyy34002, cde, cdf)
new_esEs25(vyy6000, vyy500, app(ty_Maybe, chb)) → new_esEs4(vyy6000, vyy500, chb)
new_compare18(vyy33000, vyy34000, ty_@0) → new_compare5(vyy33000, vyy34000)
new_esEs18(vyy6000, vyy500, ty_Double) → new_esEs14(vyy6000, vyy500)
new_esEs4(Just(vyy6000), Just(vyy500), ty_Bool) → new_esEs15(vyy6000, vyy500)
new_primEqInt(Pos(Succ(vyy60000)), Pos(Succ(vyy5000))) → new_primEqNat0(vyy60000, vyy5000)
new_compare10(vyy33000, vyy34000, False, bg, bh) → GT
new_ltEs19(vyy3300, vyy3400, ty_Integer) → new_ltEs17(vyy3300, vyy3400)
new_ltEs5(@2(vyy33000, vyy33001), @2(vyy34000, vyy34001), cea, ceb) → new_pePe(new_lt20(vyy33000, vyy34000, cea), new_asAs(new_esEs28(vyy33000, vyy34000, cea), new_ltEs20(vyy33001, vyy34001, ceb)))
new_esEs4(Just(vyy6000), Just(vyy500), app(app(ty_@2, bfb), bfc)) → new_esEs5(vyy6000, vyy500, bfb, bfc)
new_esEs28(vyy33000, vyy34000, ty_Char) → new_esEs17(vyy33000, vyy34000)
new_ltEs18(vyy33002, vyy34002, app(app(app(ty_@3, cdb), cdc), cdd)) → new_ltEs15(vyy33002, vyy34002, cdb, cdc, cdd)
new_lt10(vyy33001, vyy34001, app(ty_Maybe, cbc)) → new_lt12(vyy33001, vyy34001, cbc)
new_esEs23(vyy33000, vyy34000, ty_Char) → new_esEs17(vyy33000, vyy34000)
new_compare17(vyy33000, vyy34000, hg, hh) → new_compare25(vyy33000, vyy34000, new_esEs7(vyy33000, vyy34000, hg, hh), hg, hh)
new_ltEs7(Just(vyy33000), Just(vyy34000), ty_Float) → new_ltEs10(vyy33000, vyy34000)
new_ltEs7(Just(vyy33000), Just(vyy34000), app(app(ty_Either, cfd), cfe)) → new_ltEs6(vyy33000, vyy34000, cfd, cfe)
new_ltEs7(Nothing, Just(vyy34000), cdh) → True
new_primEqNat0(Succ(vyy60000), Succ(vyy5000)) → new_primEqNat0(vyy60000, vyy5000)
new_esEs27(vyy6002, vyy502, ty_Ordering) → new_esEs8(vyy6002, vyy502)
new_esEs7(Right(vyy6000), Right(vyy500), gd, app(ty_[], hb)) → new_esEs16(vyy6000, vyy500, hb)
new_esEs19(vyy6000, vyy500, app(app(app(ty_@3, bda), bdb), bdc)) → new_esEs6(vyy6000, vyy500, bda, bdb, bdc)
new_esEs20(vyy6001, vyy501, ty_Double) → new_esEs14(vyy6001, vyy501)
new_ltEs19(vyy3300, vyy3400, ty_Double) → new_ltEs14(vyy3300, vyy3400)
new_compare25(vyy33000, vyy34000, False, hg, hh) → new_compare11(vyy33000, vyy34000, new_ltEs6(vyy33000, vyy34000, hg, hh), hg, hh)
new_esEs7(Right(vyy6000), Right(vyy500), gd, ty_Float) → new_esEs10(vyy6000, vyy500)
new_esEs20(vyy6001, vyy501, ty_Float) → new_esEs10(vyy6001, vyy501)
new_esEs28(vyy33000, vyy34000, ty_Int) → new_esEs11(vyy33000, vyy34000)
new_lt20(vyy33000, vyy34000, ty_@0) → new_lt4(vyy33000, vyy34000)
new_primCmpInt(Neg(Succ(vyy330000)), Neg(vyy34000)) → new_primCmpNat0(vyy34000, Succ(vyy330000))
new_ltEs18(vyy33002, vyy34002, app(app(ty_@2, ccg), cch)) → new_ltEs5(vyy33002, vyy34002, ccg, cch)
new_esEs24(vyy33001, vyy34001, ty_Ordering) → new_esEs8(vyy33001, vyy34001)
new_esEs18(vyy6000, vyy500, ty_Char) → new_esEs17(vyy6000, vyy500)
new_lt19(vyy33000, vyy34000) → new_esEs8(new_compare34(vyy33000, vyy34000), LT)
new_esEs23(vyy33000, vyy34000, ty_Bool) → new_esEs15(vyy33000, vyy34000)
new_ltEs6(Left(vyy33000), Right(vyy34000), de, cb) → True
new_lt11(vyy33000, vyy34000, app(app(app(ty_@3, caf), cag), cah)) → new_lt18(vyy33000, vyy34000, caf, cag, cah)
new_esEs10(Float(vyy6000, vyy6001), Float(vyy500, vyy501)) → new_esEs11(new_sr(vyy6000, vyy500), new_sr(vyy6001, vyy501))
new_esEs21(vyy6000, vyy500, ty_Int) → new_esEs11(vyy6000, vyy500)
new_ltEs6(Right(vyy33000), Left(vyy34000), de, cb) → False
new_esEs28(vyy33000, vyy34000, ty_Ordering) → new_esEs8(vyy33000, vyy34000)
new_esEs8(EQ, LT) → False
new_esEs8(LT, EQ) → False
new_primEqInt(Pos(Succ(vyy60000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(vyy5000))) → False
new_lt10(vyy33001, vyy34001, app(app(ty_Either, ccc), ccd)) → new_lt7(vyy33001, vyy34001, ccc, ccd)
new_compare13(vyy83, vyy84, True, bae) → LT
new_primPlusNat0(Zero, Succ(vyy500000)) → Succ(vyy500000)
new_primPlusNat0(Succ(vyy9900), Zero) → Succ(vyy9900)
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(vyy330000), Zero) → GT
new_ltEs19(vyy3300, vyy3400, ty_Ordering) → new_ltEs9(vyy3300, vyy3400)
new_esEs23(vyy33000, vyy34000, app(app(ty_@2, cac), cad)) → new_esEs5(vyy33000, vyy34000, cac, cad)
new_ltEs6(Left(vyy33000), Left(vyy34000), app(app(ty_@2, cd), ce), cb) → new_ltEs5(vyy33000, vyy34000, cd, ce)
new_esEs19(vyy6000, vyy500, ty_@0) → new_esEs13(vyy6000, vyy500)
new_primCmpInt(Neg(Zero), Pos(Succ(vyy340000))) → LT
new_compare11(vyy33000, vyy34000, True, hg, hh) → LT
new_ltEs20(vyy33001, vyy34001, ty_Integer) → new_ltEs17(vyy33001, vyy34001)
new_sr0(Integer(vyy340000), Integer(vyy330010)) → Integer(new_primMulInt(vyy340000, vyy330010))
new_primEqInt(Pos(Succ(vyy60000)), Neg(vyy500)) → False
new_primEqInt(Neg(Succ(vyy60000)), Pos(vyy500)) → False
new_esEs6(@3(vyy6000, vyy6001, vyy6002), @3(vyy500, vyy501, vyy502), cff, cfg, cfh) → new_asAs(new_esEs25(vyy6000, vyy500, cff), new_asAs(new_esEs26(vyy6001, vyy501, cfg), new_esEs27(vyy6002, vyy502, cfh)))
new_esEs25(vyy6000, vyy500, ty_@0) → new_esEs13(vyy6000, vyy500)
new_esEs29(vyy600, vyy50, app(app(ty_@2, bca), bcb)) → new_esEs5(vyy600, vyy50, bca, bcb)
new_esEs16(:(vyy6000, vyy6001), :(vyy500, vyy501), baf) → new_asAs(new_esEs18(vyy6000, vyy500, baf), new_esEs16(vyy6001, vyy501, baf))
new_ltEs6(Left(vyy33000), Left(vyy34000), ty_Int, cb) → new_ltEs13(vyy33000, vyy34000)
new_lt7(vyy33000, vyy34000, hg, hh) → new_esEs8(new_compare17(vyy33000, vyy34000, hg, hh), LT)
new_ltEs7(Just(vyy33000), Just(vyy34000), app(app(ty_@2, cef), ceg)) → new_ltEs5(vyy33000, vyy34000, cef, ceg)
new_primEqInt(Neg(Zero), Pos(Succ(vyy5000))) → False
new_primEqInt(Pos(Zero), Neg(Succ(vyy5000))) → False
new_esEs13(@0, @0) → True
new_lt11(vyy33000, vyy34000, app(ty_Maybe, caa)) → new_lt12(vyy33000, vyy34000, caa)
new_primCmpInt(Pos(Zero), Pos(Succ(vyy340000))) → new_primCmpNat0(Zero, Succ(vyy340000))
new_esEs28(vyy33000, vyy34000, app(app(ty_Either, hg), hh)) → new_esEs7(vyy33000, vyy34000, hg, hh)
new_esEs7(Right(vyy6000), Right(vyy500), gd, ty_@0) → new_esEs13(vyy6000, vyy500)
new_esEs9(:%(vyy6000, vyy6001), :%(vyy500, vyy501), beg) → new_asAs(new_esEs21(vyy6000, vyy500, beg), new_esEs22(vyy6001, vyy501, beg))
new_esEs7(Right(vyy6000), Right(vyy500), gd, app(ty_Maybe, hf)) → new_esEs4(vyy6000, vyy500, hf)
new_ltEs20(vyy33001, vyy34001, ty_Int) → new_ltEs13(vyy33001, vyy34001)
new_ltEs6(Right(vyy33000), Right(vyy34000), de, app(ty_Maybe, df)) → new_ltEs7(vyy33000, vyy34000, df)
new_lt20(vyy33000, vyy34000, ty_Integer) → new_lt6(vyy33000, vyy34000)
new_esEs27(vyy6002, vyy502, ty_Float) → new_esEs10(vyy6002, vyy502)
new_esEs4(Just(vyy6000), Just(vyy500), ty_Integer) → new_esEs12(vyy6000, vyy500)
new_esEs8(GT, EQ) → False
new_esEs8(EQ, GT) → False
new_esEs4(Just(vyy6000), Just(vyy500), app(ty_Ratio, bfa)) → new_esEs9(vyy6000, vyy500, bfa)
new_lt11(vyy33000, vyy34000, app(app(ty_Either, cba), cbb)) → new_lt7(vyy33000, vyy34000, cba, cbb)
new_esEs26(vyy6001, vyy501, app(app(ty_@2, chd), che)) → new_esEs5(vyy6001, vyy501, chd, che)
new_primCompAux0(vyy103, LT) → LT
new_ltEs6(Left(vyy33000), Left(vyy34000), ty_Integer, cb) → new_ltEs17(vyy33000, vyy34000)
new_lt20(vyy33000, vyy34000, ty_Bool) → new_lt19(vyy33000, vyy34000)
new_lt10(vyy33001, vyy34001, app(app(ty_@2, cbe), cbf)) → new_lt14(vyy33001, vyy34001, cbe, cbf)
new_esEs11(vyy600, vyy50) → new_primEqInt(vyy600, vyy50)
new_not(False) → True
new_ltEs15(@3(vyy33000, vyy33001, vyy33002), @3(vyy34000, vyy34001, vyy34002), bhf, bhg, bhh) → new_pePe(new_lt11(vyy33000, vyy34000, bhf), new_asAs(new_esEs23(vyy33000, vyy34000, bhf), new_pePe(new_lt10(vyy33001, vyy34001, bhg), new_asAs(new_esEs24(vyy33001, vyy34001, bhg), new_ltEs18(vyy33002, vyy34002, bhh)))))
new_compare18(vyy33000, vyy34000, app(app(ty_@2, bge), bgf)) → new_compare19(vyy33000, vyy34000, bge, bgf)
new_esEs14(Double(vyy6000, vyy6001), Double(vyy500, vyy501)) → new_esEs11(new_sr(vyy6000, vyy500), new_sr(vyy6001, vyy501))
new_esEs28(vyy33000, vyy34000, app(ty_[], dbg)) → new_esEs16(vyy33000, vyy34000, dbg)
new_primCmpInt(Pos(Succ(vyy330000)), Pos(vyy34000)) → new_primCmpNat0(Succ(vyy330000), vyy34000)
new_esEs29(vyy600, vyy50, ty_Integer) → new_esEs12(vyy600, vyy50)
new_compare12(vyy33000, vyy34000, False, baa, bab, bac) → GT
new_esEs19(vyy6000, vyy500, ty_Int) → new_esEs11(vyy6000, vyy500)
new_esEs7(Left(vyy6000), Left(vyy500), ty_Integer, fa) → new_esEs12(vyy6000, vyy500)
new_esEs19(vyy6000, vyy500, ty_Char) → new_esEs17(vyy6000, vyy500)
new_ltEs9(LT, GT) → True
new_ltEs20(vyy33001, vyy34001, ty_Char) → new_ltEs11(vyy33001, vyy34001)
new_ltEs14(vyy3300, vyy3400) → new_not(new_esEs8(new_compare32(vyy3300, vyy3400), GT))
new_esEs25(vyy6000, vyy500, ty_Float) → new_esEs10(vyy6000, vyy500)
new_lt11(vyy33000, vyy34000, ty_Char) → new_lt8(vyy33000, vyy34000)
new_esEs24(vyy33001, vyy34001, ty_Integer) → new_esEs12(vyy33001, vyy34001)
new_esEs28(vyy33000, vyy34000, app(app(ty_@2, bg), bh)) → new_esEs5(vyy33000, vyy34000, bg, bh)
new_compare0(:(vyy33000, vyy33001), [], bf) → GT
new_ltEs18(vyy33002, vyy34002, app(ty_Maybe, cce)) → new_ltEs7(vyy33002, vyy34002, cce)
new_esEs18(vyy6000, vyy500, app(ty_Maybe, bbh)) → new_esEs4(vyy6000, vyy500, bbh)
new_compare28(vyy33000, vyy34000, True) → EQ
new_esEs7(Left(vyy6000), Left(vyy500), app(ty_Ratio, eh), fa) → new_esEs9(vyy6000, vyy500, eh)
new_compare18(vyy33000, vyy34000, ty_Char) → new_compare8(vyy33000, vyy34000)
new_compare6(Float(vyy33000, vyy33001), Float(vyy34000, vyy34001)) → new_compare16(new_sr(vyy33000, vyy34000), new_sr(vyy33001, vyy34001))
new_esEs27(vyy6002, vyy502, ty_Int) → new_esEs11(vyy6002, vyy502)
new_compare11(vyy33000, vyy34000, False, hg, hh) → GT
new_lt11(vyy33000, vyy34000, ty_Bool) → new_lt19(vyy33000, vyy34000)
new_compare18(vyy33000, vyy34000, app(ty_[], bgd)) → new_compare0(vyy33000, vyy34000, bgd)
new_ltEs7(Just(vyy33000), Just(vyy34000), app(ty_Maybe, ced)) → new_ltEs7(vyy33000, vyy34000, ced)
new_primCmpInt(Pos(Succ(vyy330000)), Neg(vyy34000)) → GT
new_esEs18(vyy6000, vyy500, app(app(ty_Either, bbb), bbc)) → new_esEs7(vyy6000, vyy500, bbb, bbc)
new_lt15(vyy33000, vyy34000) → new_esEs8(new_compare30(vyy33000, vyy34000), LT)
new_primMulInt(Pos(vyy60000), Pos(vyy5000)) → Pos(new_primMulNat0(vyy60000, vyy5000))
new_ltEs6(Right(vyy33000), Right(vyy34000), de, ty_@0) → new_ltEs8(vyy33000, vyy34000)
new_compare24(vyy33000, vyy34000, False, bg, bh) → new_compare10(vyy33000, vyy34000, new_ltEs5(vyy33000, vyy34000, bg, bh), bg, bh)
new_esEs27(vyy6002, vyy502, ty_Char) → new_esEs17(vyy6002, vyy502)
new_ltEs18(vyy33002, vyy34002, ty_Integer) → new_ltEs17(vyy33002, vyy34002)
new_primMulInt(Neg(vyy60000), Neg(vyy5000)) → Pos(new_primMulNat0(vyy60000, vyy5000))
new_esEs24(vyy33001, vyy34001, ty_Bool) → new_esEs15(vyy33001, vyy34001)
new_esEs28(vyy33000, vyy34000, app(ty_Ratio, cec)) → new_esEs9(vyy33000, vyy34000, cec)
new_primEqNat0(Zero, Succ(vyy5000)) → False
new_primEqNat0(Succ(vyy60000), Zero) → False
new_esEs7(Left(vyy6000), Left(vyy500), app(ty_[], fg), fa) → new_esEs16(vyy6000, vyy500, fg)
new_ltEs7(Just(vyy33000), Just(vyy34000), ty_Ordering) → new_ltEs9(vyy33000, vyy34000)
new_primPlusNat0(Zero, Zero) → Zero
new_ltEs6(Right(vyy33000), Right(vyy34000), de, ty_Float) → new_ltEs10(vyy33000, vyy34000)
new_compare25(vyy33000, vyy34000, True, hg, hh) → EQ
new_lt13(vyy33000, vyy34000, dbg) → new_esEs8(new_compare0(vyy33000, vyy34000, dbg), LT)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs28(vyy33000, vyy34000, app(app(app(ty_@3, baa), bab), bac)) → new_esEs6(vyy33000, vyy34000, baa, bab, bac)
new_esEs4(Nothing, Nothing, beh) → True
new_esEs7(Left(vyy6000), Left(vyy500), ty_Char, fa) → new_esEs17(vyy6000, vyy500)
new_esEs27(vyy6002, vyy502, app(app(app(ty_@3, dbc), dbd), dbe)) → new_esEs6(vyy6002, vyy502, dbc, dbd, dbe)
new_lt10(vyy33001, vyy34001, ty_Int) → new_lt9(vyy33001, vyy34001)
new_esEs27(vyy6002, vyy502, app(app(ty_@2, daf), dag)) → new_esEs5(vyy6002, vyy502, daf, dag)
new_esEs16(:(vyy6000, vyy6001), [], baf) → False
new_esEs16([], :(vyy500, vyy501), baf) → False
new_ltEs9(GT, GT) → True
new_esEs23(vyy33000, vyy34000, ty_Int) → new_esEs11(vyy33000, vyy34000)
new_ltEs7(Nothing, Nothing, cdh) → True
new_esEs27(vyy6002, vyy502, app(ty_Maybe, dbf)) → new_esEs4(vyy6002, vyy502, dbf)
new_primPlusNat1(Succ(vyy990), vyy50000) → Succ(Succ(new_primPlusNat0(vyy990, vyy50000)))
new_compare13(vyy83, vyy84, False, bae) → GT
new_lt16(vyy33000, vyy34000, cec) → new_esEs8(new_compare31(vyy33000, vyy34000, cec), LT)
new_primCmpInt(Neg(Zero), Neg(Succ(vyy340000))) → new_primCmpNat0(Succ(vyy340000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(vyy340000))) → GT
new_ltEs6(Left(vyy33000), Left(vyy34000), app(ty_Ratio, cf), cb) → new_ltEs12(vyy33000, vyy34000, cf)
new_compare0(:(vyy33000, vyy33001), :(vyy34000, vyy34001), bf) → new_primCompAux1(vyy33000, vyy34000, new_compare0(vyy33001, vyy34001, bf), bf)
new_compare28(vyy33000, vyy34000, False) → new_compare14(vyy33000, vyy34000, new_ltEs9(vyy33000, vyy34000))
new_lt14(vyy33000, vyy34000, bg, bh) → new_esEs8(new_compare19(vyy33000, vyy34000, bg, bh), LT)
new_esEs4(Just(vyy6000), Just(vyy500), app(ty_[], bff)) → new_esEs16(vyy6000, vyy500, bff)
new_esEs19(vyy6000, vyy500, ty_Double) → new_esEs14(vyy6000, vyy500)
new_compare7(vyy33000, vyy34000, bad) → new_compare27(vyy33000, vyy34000, new_esEs4(vyy33000, vyy34000, bad), bad)
new_esEs24(vyy33001, vyy34001, ty_Int) → new_esEs11(vyy33001, vyy34001)
new_lt11(vyy33000, vyy34000, ty_Ordering) → new_lt15(vyy33000, vyy34000)
new_esEs18(vyy6000, vyy500, ty_Integer) → new_esEs12(vyy6000, vyy500)
new_esEs20(vyy6001, vyy501, app(app(ty_Either, bdh), bea)) → new_esEs7(vyy6001, vyy501, bdh, bea)
new_ltEs17(vyy3300, vyy3400) → new_not(new_esEs8(new_compare9(vyy3300, vyy3400), GT))
new_esEs29(vyy600, vyy50, app(ty_Ratio, beg)) → new_esEs9(vyy600, vyy50, beg)
new_ltEs6(Right(vyy33000), Right(vyy34000), de, app(app(ty_Either, ef), eg)) → new_ltEs6(vyy33000, vyy34000, ef, eg)
new_esEs19(vyy6000, vyy500, app(app(ty_@2, bcd), bce)) → new_esEs5(vyy6000, vyy500, bcd, bce)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_lt9(vyy33000, vyy34000) → new_esEs8(new_compare16(vyy33000, vyy34000), LT)
new_esEs4(Just(vyy6000), Just(vyy500), ty_Double) → new_esEs14(vyy6000, vyy500)
new_esEs20(vyy6001, vyy501, app(ty_[], beb)) → new_esEs16(vyy6001, vyy501, beb)
new_esEs29(vyy600, vyy50, ty_Bool) → new_esEs15(vyy600, vyy50)
new_compare9(Integer(vyy33000), Integer(vyy34000)) → new_primCmpInt(vyy33000, vyy34000)
new_asAs(False, vyy90) → False
new_esEs25(vyy6000, vyy500, app(ty_Ratio, cga)) → new_esEs9(vyy6000, vyy500, cga)
new_ltEs6(Left(vyy33000), Left(vyy34000), app(ty_Maybe, ca), cb) → new_ltEs7(vyy33000, vyy34000, ca)
new_esEs19(vyy6000, vyy500, ty_Float) → new_esEs10(vyy6000, vyy500)
new_compare34(vyy33000, vyy34000) → new_compare29(vyy33000, vyy34000, new_esEs15(vyy33000, vyy34000))
new_primMulInt(Pos(vyy60000), Neg(vyy5000)) → Neg(new_primMulNat0(vyy60000, vyy5000))
new_primMulInt(Neg(vyy60000), Pos(vyy5000)) → Neg(new_primMulNat0(vyy60000, vyy5000))
new_ltEs19(vyy3300, vyy3400, ty_Char) → new_ltEs11(vyy3300, vyy3400)
new_compare16(vyy3300, vyy3400) → new_primCmpInt(vyy3300, vyy3400)
new_primMulNat0(Zero, Succ(vyy50000)) → Zero
new_primMulNat0(Succ(vyy600000), Zero) → Zero
new_esEs7(Left(vyy6000), Left(vyy500), ty_Float, fa) → new_esEs10(vyy6000, vyy500)
new_esEs23(vyy33000, vyy34000, app(app(app(ty_@3, caf), cag), cah)) → new_esEs6(vyy33000, vyy34000, caf, cag, cah)
new_ltEs18(vyy33002, vyy34002, app(ty_[], ccf)) → new_ltEs4(vyy33002, vyy34002, ccf)
new_esEs24(vyy33001, vyy34001, ty_Float) → new_esEs10(vyy33001, vyy34001)
new_esEs29(vyy600, vyy50, ty_Int) → new_esEs11(vyy600, vyy50)
new_compare31(:%(vyy33000, vyy33001), :%(vyy34000, vyy34001), ty_Int) → new_compare16(new_sr(vyy33000, vyy34001), new_sr(vyy34000, vyy33001))
new_esEs24(vyy33001, vyy34001, app(ty_[], cbd)) → new_esEs16(vyy33001, vyy34001, cbd)
new_esEs29(vyy600, vyy50, ty_Char) → new_esEs17(vyy600, vyy50)
new_ltEs20(vyy33001, vyy34001, ty_Ordering) → new_ltEs9(vyy33001, vyy34001)
new_esEs26(vyy6001, vyy501, app(ty_Ratio, chc)) → new_esEs9(vyy6001, vyy501, chc)
new_esEs27(vyy6002, vyy502, ty_@0) → new_esEs13(vyy6002, vyy502)
new_esEs29(vyy600, vyy50, ty_Float) → new_esEs10(vyy600, vyy50)
new_esEs18(vyy6000, vyy500, ty_Ordering) → new_esEs8(vyy6000, vyy500)
new_ltEs11(vyy3300, vyy3400) → new_not(new_esEs8(new_compare8(vyy3300, vyy3400), GT))
new_ltEs20(vyy33001, vyy34001, app(ty_Ratio, dcd)) → new_ltEs12(vyy33001, vyy34001, dcd)
new_esEs25(vyy6000, vyy500, app(app(app(ty_@3, cgg), cgh), cha)) → new_esEs6(vyy6000, vyy500, cgg, cgh, cha)
new_ltEs9(GT, EQ) → False
new_esEs7(Left(vyy6000), Left(vyy500), app(app(app(ty_@3, fh), ga), gb), fa) → new_esEs6(vyy6000, vyy500, fh, ga, gb)
new_esEs20(vyy6001, vyy501, ty_Integer) → new_esEs12(vyy6001, vyy501)
new_lt10(vyy33001, vyy34001, ty_Float) → new_lt5(vyy33001, vyy34001)
new_ltEs19(vyy3300, vyy3400, ty_@0) → new_ltEs8(vyy3300, vyy3400)
new_esEs28(vyy33000, vyy34000, ty_Bool) → new_esEs15(vyy33000, vyy34000)
new_lt5(vyy33000, vyy34000) → new_esEs8(new_compare6(vyy33000, vyy34000), LT)
new_esEs18(vyy6000, vyy500, ty_Int) → new_esEs11(vyy6000, vyy500)
new_compare18(vyy33000, vyy34000, ty_Bool) → new_compare34(vyy33000, vyy34000)
new_ltEs20(vyy33001, vyy34001, ty_Float) → new_ltEs10(vyy33001, vyy34001)
new_esEs7(Right(vyy6000), Right(vyy500), gd, ty_Int) → new_esEs11(vyy6000, vyy500)
new_ltEs7(Just(vyy33000), Nothing, cdh) → False
new_esEs4(Just(vyy6000), Just(vyy500), ty_Int) → new_esEs11(vyy6000, vyy500)
new_esEs7(Right(vyy6000), Right(vyy500), gd, ty_Integer) → new_esEs12(vyy6000, vyy500)
new_ltEs7(Just(vyy33000), Just(vyy34000), ty_Char) → new_ltEs11(vyy33000, vyy34000)
new_esEs16([], [], baf) → True
new_esEs20(vyy6001, vyy501, app(ty_Ratio, bde)) → new_esEs9(vyy6001, vyy501, bde)
new_lt11(vyy33000, vyy34000, ty_Int) → new_lt9(vyy33000, vyy34000)
new_esEs25(vyy6000, vyy500, app(app(ty_@2, cgb), cgc)) → new_esEs5(vyy6000, vyy500, cgb, cgc)
new_lt10(vyy33001, vyy34001, ty_Bool) → new_lt19(vyy33001, vyy34001)
new_ltEs6(Left(vyy33000), Left(vyy34000), app(ty_[], cc), cb) → new_ltEs4(vyy33000, vyy34000, cc)
new_ltEs18(vyy33002, vyy34002, ty_Double) → new_ltEs14(vyy33002, vyy34002)
new_ltEs18(vyy33002, vyy34002, ty_Ordering) → new_ltEs9(vyy33002, vyy34002)
new_ltEs19(vyy3300, vyy3400, app(ty_Maybe, cdh)) → new_ltEs7(vyy3300, vyy3400, cdh)
new_esEs23(vyy33000, vyy34000, app(ty_Ratio, cae)) → new_esEs9(vyy33000, vyy34000, cae)
new_ltEs18(vyy33002, vyy34002, ty_Bool) → new_ltEs16(vyy33002, vyy34002)
new_esEs29(vyy600, vyy50, app(app(app(ty_@3, cff), cfg), cfh)) → new_esEs6(vyy600, vyy50, cff, cfg, cfh)
new_lt18(vyy33000, vyy34000, baa, bab, bac) → new_esEs8(new_compare33(vyy33000, vyy34000, baa, bab, bac), LT)
new_lt10(vyy33001, vyy34001, app(app(app(ty_@3, cbh), cca), ccb)) → new_lt18(vyy33001, vyy34001, cbh, cca, ccb)
new_esEs29(vyy600, vyy50, app(app(ty_Either, gd), fa)) → new_esEs7(vyy600, vyy50, gd, fa)
new_compare27(vyy330, vyy340, True, cdg) → EQ
new_esEs19(vyy6000, vyy500, app(ty_Ratio, bcc)) → new_esEs9(vyy6000, vyy500, bcc)
new_ltEs6(Left(vyy33000), Left(vyy34000), ty_@0, cb) → new_ltEs8(vyy33000, vyy34000)
new_esEs7(Left(vyy6000), Left(vyy500), ty_Bool, fa) → new_esEs15(vyy6000, vyy500)
new_ltEs6(Right(vyy33000), Right(vyy34000), de, ty_Double) → new_ltEs14(vyy33000, vyy34000)
new_compare18(vyy33000, vyy34000, app(app(ty_Either, bhc), bhd)) → new_compare17(vyy33000, vyy34000, bhc, bhd)
new_ltEs6(Right(vyy33000), Right(vyy34000), de, app(ty_[], dg)) → new_ltEs4(vyy33000, vyy34000, dg)
new_esEs20(vyy6001, vyy501, ty_Char) → new_esEs17(vyy6001, vyy501)
new_primPlusNat0(Succ(vyy9900), Succ(vyy500000)) → Succ(Succ(new_primPlusNat0(vyy9900, vyy500000)))
new_compare26(vyy33000, vyy34000, False, baa, bab, bac) → new_compare12(vyy33000, vyy34000, new_ltEs15(vyy33000, vyy34000, baa, bab, bac), baa, bab, bac)
new_compare26(vyy33000, vyy34000, True, baa, bab, bac) → EQ
new_esEs23(vyy33000, vyy34000, app(ty_[], cab)) → new_esEs16(vyy33000, vyy34000, cab)
new_compare0([], :(vyy34000, vyy34001), bf) → LT
new_ltEs6(Right(vyy33000), Right(vyy34000), de, ty_Bool) → new_ltEs16(vyy33000, vyy34000)
new_compare27(Just(vyy3300), Just(vyy3400), False, cdg) → new_compare13(vyy3300, vyy3400, new_ltEs19(vyy3300, vyy3400, cdg), cdg)
new_ltEs6(Right(vyy33000), Right(vyy34000), de, ty_Ordering) → new_ltEs9(vyy33000, vyy34000)
new_lt10(vyy33001, vyy34001, ty_Double) → new_lt17(vyy33001, vyy34001)
new_asAs(True, vyy90) → vyy90
new_esEs25(vyy6000, vyy500, ty_Int) → new_esEs11(vyy6000, vyy500)
new_lt8(vyy33000, vyy34000) → new_esEs8(new_compare8(vyy33000, vyy34000), LT)
new_ltEs16(False, False) → True
new_compare18(vyy33000, vyy34000, ty_Integer) → new_compare9(vyy33000, vyy34000)
new_esEs27(vyy6002, vyy502, ty_Bool) → new_esEs15(vyy6002, vyy502)
new_esEs7(Left(vyy6000), Left(vyy500), ty_@0, fa) → new_esEs13(vyy6000, vyy500)
new_esEs19(vyy6000, vyy500, ty_Ordering) → new_esEs8(vyy6000, vyy500)
new_lt20(vyy33000, vyy34000, ty_Int) → new_lt9(vyy33000, vyy34000)
new_ltEs6(Left(vyy33000), Left(vyy34000), ty_Bool, cb) → new_ltEs16(vyy33000, vyy34000)
new_esEs21(vyy6000, vyy500, ty_Integer) → new_esEs12(vyy6000, vyy500)
new_lt17(vyy33000, vyy34000) → new_esEs8(new_compare32(vyy33000, vyy34000), LT)
new_lt12(vyy33000, vyy34000, bad) → new_esEs8(new_compare7(vyy33000, vyy34000, bad), LT)
new_esEs29(vyy600, vyy50, app(ty_Maybe, beh)) → new_esEs4(vyy600, vyy50, beh)
new_compare18(vyy33000, vyy34000, ty_Int) → new_compare16(vyy33000, vyy34000)
new_ltEs20(vyy33001, vyy34001, app(ty_Maybe, dbh)) → new_ltEs7(vyy33001, vyy34001, dbh)
new_esEs25(vyy6000, vyy500, app(app(ty_Either, cgd), cge)) → new_esEs7(vyy6000, vyy500, cgd, cge)
new_compare8(Char(vyy33000), Char(vyy34000)) → new_primCmpNat0(vyy33000, vyy34000)
new_compare33(vyy33000, vyy34000, baa, bab, bac) → new_compare26(vyy33000, vyy34000, new_esEs6(vyy33000, vyy34000, baa, bab, bac), baa, bab, bac)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs24(vyy33001, vyy34001, app(ty_Ratio, cbg)) → new_esEs9(vyy33001, vyy34001, cbg)
new_primCompAux0(vyy103, EQ) → vyy103
new_esEs20(vyy6001, vyy501, ty_@0) → new_esEs13(vyy6001, vyy501)
new_esEs29(vyy600, vyy50, ty_Ordering) → new_esEs8(vyy600, vyy50)
new_ltEs19(vyy3300, vyy3400, app(app(ty_Either, de), cb)) → new_ltEs6(vyy3300, vyy3400, de, cb)
new_lt20(vyy33000, vyy34000, app(ty_Maybe, bad)) → new_lt12(vyy33000, vyy34000, bad)
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primCmpInt(Neg(Succ(vyy330000)), Pos(vyy34000)) → LT
new_esEs24(vyy33001, vyy34001, ty_Double) → new_esEs14(vyy33001, vyy34001)
new_not(True) → False
new_esEs15(False, False) → True
The set Q consists of the following terms:
new_ltEs7(Just(x0), Just(x1), ty_Ordering)
new_esEs13(@0, @0)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_primPlusNat0(Succ(x0), Zero)
new_esEs23(x0, x1, ty_@0)
new_ltEs16(True, True)
new_ltEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare18(x0, x1, ty_Bool)
new_esEs28(x0, x1, ty_Char)
new_ltEs6(Right(x0), Right(x1), x2, ty_Double)
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_primEqNat0(Zero, Succ(x0))
new_lt5(x0, x1)
new_lt20(x0, x1, ty_Integer)
new_esEs25(x0, x1, ty_Integer)
new_compare25(x0, x1, False, x2, x3)
new_esEs25(x0, x1, ty_Bool)
new_esEs24(x0, x1, ty_Float)
new_primCompAux1(x0, x1, x2, x3)
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_esEs7(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs25(x0, x1, ty_Char)
new_ltEs20(x0, x1, ty_Bool)
new_compare0([], [], x0)
new_lt10(x0, x1, app(ty_[], x2))
new_ltEs18(x0, x1, ty_Bool)
new_esEs22(x0, x1, ty_Integer)
new_asAs(True, x0)
new_esEs26(x0, x1, ty_Float)
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_lt10(x0, x1, ty_Char)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs6(Right(x0), Right(x1), x2, ty_Int)
new_lt20(x0, x1, ty_Ordering)
new_esEs18(x0, x1, ty_Double)
new_lt10(x0, x1, ty_Float)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_ltEs6(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs4(Just(x0), Just(x1), app(ty_[], x2))
new_esEs27(x0, x1, ty_Bool)
new_esEs15(True, True)
new_esEs29(x0, x1, ty_Double)
new_esEs25(x0, x1, ty_Float)
new_esEs27(x0, x1, ty_Float)
new_ltEs6(Right(x0), Right(x1), x2, ty_Float)
new_lt20(x0, x1, ty_Double)
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, ty_Integer)
new_esEs25(x0, x1, ty_@0)
new_ltEs18(x0, x1, app(ty_Maybe, x2))
new_esEs7(Right(x0), Right(x1), x2, ty_@0)
new_ltEs7(Just(x0), Just(x1), app(ty_[], x2))
new_esEs24(x0, x1, ty_Double)
new_compare18(x0, x1, ty_Int)
new_lt11(x0, x1, ty_Bool)
new_primMulNat0(Zero, Succ(x0))
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_esEs28(x0, x1, ty_Ordering)
new_esEs15(False, False)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs26(x0, x1, app(ty_[], x2))
new_esEs18(x0, x1, ty_Float)
new_ltEs6(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs8(GT, GT)
new_esEs7(Right(x0), Right(x1), x2, ty_Ordering)
new_sr0(Integer(x0), Integer(x1))
new_esEs24(x0, x1, ty_Integer)
new_esEs20(x0, x1, ty_Integer)
new_esEs18(x0, x1, app(ty_[], x2))
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs6(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs4(Just(x0), Just(x1), ty_Ordering)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_lt10(x0, x1, ty_Double)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_compare14(x0, x1, False)
new_esEs27(x0, x1, ty_Integer)
new_esEs8(LT, LT)
new_primPlusNat0(Succ(x0), Succ(x1))
new_esEs26(x0, x1, ty_Char)
new_esEs16([], [], x0)
new_compare18(x0, x1, ty_Char)
new_ltEs6(Left(x0), Left(x1), ty_Bool, x2)
new_ltEs6(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_compare10(x0, x1, False, x2, x3)
new_esEs19(x0, x1, ty_Double)
new_lt10(x0, x1, app(app(ty_Either, x2), x3))
new_lt18(x0, x1, x2, x3, x4)
new_ltEs18(x0, x1, ty_Int)
new_ltEs6(Right(x0), Right(x1), x2, ty_Char)
new_lt7(x0, x1, x2, x3)
new_ltEs10(x0, x1)
new_esEs7(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs24(x0, x1, ty_Int)
new_esEs11(x0, x1)
new_esEs7(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_primPlusNat0(Zero, Succ(x0))
new_compare11(x0, x1, True, x2, x3)
new_lt11(x0, x1, app(app(ty_@2, x2), x3))
new_esEs8(GT, LT)
new_esEs8(LT, GT)
new_esEs5(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs20(x0, x1, app(ty_[], x2))
new_esEs20(x0, x1, ty_Int)
new_compare6(Float(x0, x1), Float(x2, x3))
new_lt11(x0, x1, ty_@0)
new_esEs23(x0, x1, ty_Double)
new_ltEs9(EQ, EQ)
new_compare5(@0, @0)
new_esEs4(Just(x0), Just(x1), ty_Bool)
new_ltEs18(x0, x1, app(app(ty_Either, x2), x3))
new_primCompAux0(x0, EQ)
new_esEs7(Left(x0), Left(x1), ty_Float, x2)
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_compare18(x0, x1, app(app(ty_@2, x2), x3))
new_lt10(x0, x1, ty_Int)
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primEqNat0(Zero, Zero)
new_primCmpNat0(Succ(x0), Zero)
new_primEqNat0(Succ(x0), Zero)
new_ltEs6(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs19(x0, x1, ty_Ordering)
new_lt11(x0, x1, app(ty_[], x2))
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(Left(x0), Left(x1), ty_Char, x2)
new_ltEs19(x0, x1, ty_Int)
new_esEs27(x0, x1, app(ty_[], x2))
new_lt11(x0, x1, app(ty_Ratio, x2))
new_compare14(x0, x1, True)
new_esEs19(x0, x1, ty_Int)
new_compare7(x0, x1, x2)
new_ltEs7(Just(x0), Just(x1), ty_Char)
new_esEs4(Nothing, Nothing, x0)
new_esEs27(x0, x1, ty_Char)
new_esEs4(Just(x0), Just(x1), ty_Float)
new_esEs7(Right(x0), Right(x1), x2, ty_Integer)
new_ltEs6(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs26(x0, x1, ty_@0)
new_primMulNat0(Zero, Zero)
new_compare18(x0, x1, ty_Float)
new_esEs20(x0, x1, ty_@0)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_esEs16(:(x0, x1), [], x2)
new_ltEs18(x0, x1, ty_@0)
new_esEs7(Left(x0), Left(x1), ty_Integer, x2)
new_esEs24(x0, x1, ty_Bool)
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_esEs7(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs28(x0, x1, app(ty_[], x2))
new_primMulNat0(Succ(x0), Zero)
new_ltEs7(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_lt13(x0, x1, x2)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_esEs9(:%(x0, x1), :%(x2, x3), x4)
new_esEs18(x0, x1, app(ty_Ratio, x2))
new_compare18(x0, x1, ty_Ordering)
new_esEs4(Just(x0), Just(x1), ty_@0)
new_lt20(x0, x1, ty_Float)
new_lt4(x0, x1)
new_ltEs6(Right(x0), Right(x1), x2, app(ty_[], x3))
new_lt11(x0, x1, ty_Ordering)
new_lt19(x0, x1)
new_ltEs7(Just(x0), Just(x1), app(ty_Ratio, x2))
new_compare13(x0, x1, False, x2)
new_compare27(x0, x1, True, x2)
new_esEs28(x0, x1, ty_Double)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs7(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_compare15(x0, x1, True)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_esEs18(x0, x1, ty_Integer)
new_pePe(False, x0)
new_esEs19(x0, x1, ty_Bool)
new_ltEs6(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs4(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_ltEs18(x0, x1, ty_Float)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_esEs21(x0, x1, ty_Int)
new_ltEs11(x0, x1)
new_esEs29(x0, x1, ty_Int)
new_esEs25(x0, x1, ty_Double)
new_esEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, app(ty_Ratio, x2))
new_esEs28(x0, x1, ty_Bool)
new_esEs19(x0, x1, app(ty_Ratio, x2))
new_esEs4(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_lt11(x0, x1, ty_Double)
new_ltEs9(GT, EQ)
new_ltEs9(EQ, GT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpNat0(Succ(x0), Succ(x1))
new_ltEs6(Left(x0), Left(x1), ty_@0, x2)
new_compare18(x0, x1, app(ty_[], x2))
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_compare0([], :(x0, x1), x2)
new_esEs7(Right(x0), Left(x1), x2, x3)
new_compare15(x0, x1, False)
new_esEs7(Left(x0), Right(x1), x2, x3)
new_esEs23(x0, x1, ty_Ordering)
new_primCmpNat0(Zero, Succ(x0))
new_esEs7(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_ltEs6(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_ltEs20(x0, x1, ty_Int)
new_esEs27(x0, x1, ty_Int)
new_asAs(False, x0)
new_lt11(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primPlusNat0(Zero, Zero)
new_lt20(x0, x1, ty_Int)
new_primCompAux0(x0, LT)
new_esEs7(Left(x0), Left(x1), ty_Int, x2)
new_lt10(x0, x1, ty_Ordering)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, ty_Char)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_esEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare18(x0, x1, app(app(ty_Either, x2), x3))
new_lt10(x0, x1, app(app(ty_@2, x2), x3))
new_compare12(x0, x1, True, x2, x3, x4)
new_esEs7(Left(x0), Left(x1), app(ty_[], x2), x3)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_compare29(x0, x1, True)
new_compare27(Nothing, Just(x0), False, x1)
new_lt11(x0, x1, app(ty_Maybe, x2))
new_esEs7(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs25(x0, x1, ty_Int)
new_esEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs6(Left(x0), Left(x1), ty_Char, x2)
new_primPlusNat1(Zero, x0)
new_compare16(x0, x1)
new_esEs7(Right(x0), Right(x1), x2, ty_Double)
new_ltEs7(Just(x0), Nothing, x1)
new_esEs23(x0, x1, ty_Bool)
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_compare9(Integer(x0), Integer(x1))
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs7(Just(x0), Just(x1), ty_Integer)
new_esEs4(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_compare17(x0, x1, x2, x3)
new_lt11(x0, x1, ty_Integer)
new_compare18(x0, x1, app(ty_Maybe, x2))
new_ltEs9(EQ, LT)
new_ltEs9(LT, EQ)
new_compare26(x0, x1, True, x2, x3, x4)
new_esEs7(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs29(x0, x1, ty_@0)
new_sr(x0, x1)
new_esEs7(Left(x0), Left(x1), ty_Bool, x2)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs15(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs12(Integer(x0), Integer(x1))
new_compare25(x0, x1, True, x2, x3)
new_lt11(x0, x1, ty_Int)
new_primEqInt(Neg(Zero), Pos(Zero))
new_primEqInt(Pos(Zero), Neg(Zero))
new_compare0(:(x0, x1), :(x2, x3), x4)
new_compare0(:(x0, x1), [], x2)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs20(x0, x1, ty_Double)
new_ltEs4(x0, x1, x2)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_esEs7(Right(x0), Right(x1), x2, ty_Bool)
new_esEs24(x0, x1, ty_@0)
new_esEs23(x0, x1, ty_Float)
new_compare33(x0, x1, x2, x3, x4)
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_ltEs5(@2(x0, x1), @2(x2, x3), x4, x5)
new_compare8(Char(x0), Char(x1))
new_lt11(x0, x1, app(app(ty_Either, x2), x3))
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_ltEs20(x0, x1, ty_@0)
new_esEs18(x0, x1, ty_Char)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs15(True, False)
new_esEs15(False, True)
new_esEs8(EQ, EQ)
new_esEs14(Double(x0, x1), Double(x2, x3))
new_esEs18(x0, x1, ty_Ordering)
new_esEs17(Char(x0), Char(x1))
new_primEqInt(Neg(Zero), Neg(Zero))
new_ltEs7(Just(x0), Just(x1), ty_@0)
new_ltEs7(Just(x0), Just(x1), ty_Float)
new_esEs28(x0, x1, ty_Integer)
new_esEs6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs27(x0, x1, ty_@0)
new_compare27(Just(x0), Nothing, False, x1)
new_ltEs6(Left(x0), Left(x1), ty_Float, x2)
new_compare11(x0, x1, False, x2, x3)
new_esEs22(x0, x1, ty_Int)
new_ltEs7(Just(x0), Just(x1), ty_Bool)
new_ltEs6(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs24(x0, x1, ty_Char)
new_ltEs6(Left(x0), Left(x1), ty_Ordering, x2)
new_compare26(x0, x1, False, x2, x3, x4)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs4(Nothing, Just(x0), x1)
new_compare24(x0, x1, False, x2, x3)
new_ltEs18(x0, x1, app(ty_Ratio, x2))
new_primCompAux0(x0, GT)
new_ltEs19(x0, x1, ty_Double)
new_lt10(x0, x1, ty_@0)
new_ltEs7(Just(x0), Just(x1), ty_Double)
new_esEs18(x0, x1, app(ty_Maybe, x2))
new_ltEs19(x0, x1, ty_Ordering)
new_compare18(x0, x1, app(ty_Ratio, x2))
new_esEs28(x0, x1, ty_Float)
new_esEs7(Right(x0), Right(x1), x2, ty_Float)
new_ltEs20(x0, x1, app(ty_[], x2))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_lt10(x0, x1, app(ty_Maybe, x2))
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs18(x0, x1, ty_Ordering)
new_lt10(x0, x1, app(ty_Ratio, x2))
new_pePe(True, x0)
new_esEs26(x0, x1, ty_Ordering)
new_ltEs9(LT, LT)
new_esEs29(x0, x1, ty_Integer)
new_esEs20(x0, x1, ty_Char)
new_ltEs18(x0, x1, ty_Integer)
new_compare10(x0, x1, True, x2, x3)
new_esEs7(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_ltEs16(False, True)
new_ltEs16(True, False)
new_ltEs19(x0, x1, ty_Bool)
new_lt20(x0, x1, ty_Char)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_esEs29(x0, x1, app(ty_[], x2))
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_compare31(:%(x0, x1), :%(x2, x3), ty_Integer)
new_compare18(x0, x1, ty_@0)
new_esEs26(x0, x1, ty_Double)
new_ltEs18(x0, x1, app(ty_[], x2))
new_esEs4(Just(x0), Just(x1), ty_Int)
new_esEs26(x0, x1, ty_Bool)
new_ltEs6(Right(x0), Right(x1), x2, ty_@0)
new_ltEs19(x0, x1, ty_@0)
new_ltEs14(x0, x1)
new_ltEs6(Left(x0), Right(x1), x2, x3)
new_ltEs6(Right(x0), Left(x1), x2, x3)
new_esEs19(x0, x1, app(app(ty_Either, x2), x3))
new_compare19(x0, x1, x2, x3)
new_esEs20(x0, x1, ty_Ordering)
new_esEs19(x0, x1, ty_Integer)
new_primCmpNat0(Zero, Zero)
new_esEs19(x0, x1, app(ty_Maybe, x2))
new_primEqNat0(Succ(x0), Succ(x1))
new_compare27(Just(x0), Just(x1), False, x2)
new_ltEs20(x0, x1, ty_Ordering)
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare29(x0, x1, False)
new_primMulNat0(Succ(x0), Succ(x1))
new_ltEs19(x0, x1, ty_Integer)
new_ltEs7(Nothing, Just(x0), x1)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_compare28(x0, x1, False)
new_esEs29(x0, x1, ty_Float)
new_esEs27(x0, x1, ty_Ordering)
new_ltEs12(x0, x1, x2)
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs6(Left(x0), Left(x1), ty_Int, x2)
new_lt8(x0, x1)
new_ltEs20(x0, x1, ty_Integer)
new_esEs4(Just(x0), Nothing, x1)
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_esEs7(Left(x0), Left(x1), ty_Double, x2)
new_compare24(x0, x1, True, x2, x3)
new_primPlusNat1(Succ(x0), x1)
new_ltEs6(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_esEs19(x0, x1, ty_Float)
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs6(Right(x0), Right(x1), x2, ty_Integer)
new_lt9(x0, x1)
new_ltEs7(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_esEs21(x0, x1, ty_Integer)
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_compare30(x0, x1)
new_ltEs20(x0, x1, ty_Char)
new_ltEs20(x0, x1, ty_Float)
new_ltEs9(GT, LT)
new_ltEs9(LT, GT)
new_ltEs7(Nothing, Nothing, x0)
new_esEs26(x0, x1, ty_Int)
new_lt10(x0, x1, ty_Bool)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs16(:(x0, x1), :(x2, x3), x4)
new_compare27(Nothing, Nothing, False, x0)
new_esEs24(x0, x1, ty_Ordering)
new_esEs18(x0, x1, app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, ty_Int)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_not(True)
new_ltEs19(x0, x1, ty_Float)
new_compare31(:%(x0, x1), :%(x2, x3), ty_Int)
new_esEs19(x0, x1, app(ty_[], x2))
new_esEs20(x0, x1, ty_Float)
new_esEs18(x0, x1, ty_Bool)
new_esEs23(x0, x1, app(ty_[], x2))
new_esEs16([], :(x0, x1), x2)
new_lt11(x0, x1, ty_Float)
new_esEs29(x0, x1, ty_Ordering)
new_ltEs18(x0, x1, ty_Double)
new_esEs7(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_compare34(x0, x1)
new_esEs4(Just(x0), Just(x1), ty_Double)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_not(False)
new_esEs25(x0, x1, app(ty_[], x2))
new_esEs29(x0, x1, ty_Char)
new_ltEs7(Just(x0), Just(x1), ty_Int)
new_ltEs6(Left(x0), Left(x1), app(ty_[], x2), x3)
new_lt15(x0, x1)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_compare28(x0, x1, True)
new_ltEs8(x0, x1)
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_ltEs6(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs26(x0, x1, ty_Integer)
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_esEs4(Just(x0), Just(x1), ty_Integer)
new_ltEs13(x0, x1)
new_esEs23(x0, x1, ty_Char)
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs7(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs4(Just(x0), Just(x1), ty_Char)
new_esEs19(x0, x1, ty_@0)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_compare13(x0, x1, True, x2)
new_lt10(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_ltEs6(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs17(x0, x1)
new_esEs24(x0, x1, app(ty_[], x2))
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_lt6(x0, x1)
new_ltEs6(Left(x0), Left(x1), ty_Double, x2)
new_compare18(x0, x1, ty_Double)
new_esEs7(Left(x0), Left(x1), ty_@0, x2)
new_esEs20(x0, x1, ty_Bool)
new_lt20(x0, x1, ty_@0)
new_lt10(x0, x1, ty_Integer)
new_lt14(x0, x1, x2, x3)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_primMulInt(Neg(x0), Neg(x1))
new_ltEs9(GT, GT)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs19(x0, x1, ty_Char)
new_compare18(x0, x1, ty_Integer)
new_ltEs18(x0, x1, ty_Char)
new_lt17(x0, x1)
new_esEs7(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs28(x0, x1, ty_Int)
new_compare12(x0, x1, False, x2, x3, x4)
new_lt20(x0, x1, app(ty_[], x2))
new_esEs10(Float(x0, x1), Float(x2, x3))
new_compare32(Double(x0, x1), Double(x2, x3))
new_ltEs20(x0, x1, ty_Double)
new_esEs18(x0, x1, ty_@0)
new_esEs29(x0, x1, ty_Bool)
new_compare18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primEqInt(Pos(Zero), Pos(Zero))
new_esEs25(x0, x1, ty_Ordering)
new_lt20(x0, x1, ty_Bool)
new_lt12(x0, x1, x2)
new_esEs18(x0, x1, ty_Int)
new_ltEs6(Left(x0), Left(x1), ty_Integer, x2)
new_ltEs18(x0, x1, app(app(ty_@2, x2), x3))
new_lt16(x0, x1, x2)
new_esEs7(Right(x0), Right(x1), x2, ty_Char)
new_lt11(x0, x1, ty_Char)
new_esEs18(x0, x1, app(app(ty_@2, x2), x3))
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_esEs28(x0, x1, ty_@0)
new_esEs4(Just(x0), Just(x1), app(ty_Maybe, x2))
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_primMulInt(Pos(x0), Pos(x1))
new_esEs7(Right(x0), Right(x1), x2, ty_Int)
new_ltEs16(False, False)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs4(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs27(x0, x1, ty_Double)
new_ltEs19(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
We have to consider all minimal (P,Q,R)-chains.
As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [15] we can delete all non-usable rules [17] from R.
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QReductionProof
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_foldFM_GE10(vyy3, vyy600, vyy61, vyy62, vyy63, vyy64, False, h, ba, bb) → new_foldFM_GE(vyy3, Nothing, vyy64, h, ba, bb)
new_foldFM_GE(vyy3, Nothing, Branch(Nothing, vyy61, vyy62, vyy63, vyy64), h, ba, bb) → new_foldFM_GE(vyy3, Nothing, vyy63, h, ba, bb)
new_foldFM_GE(vyy3, Nothing, Branch(Nothing, vyy61, vyy62, vyy63, vyy64), h, ba, bb) → new_foldFM_GE(vyy3, Nothing, vyy64, h, ba, bb)
new_foldFM_GE(vyy3, Nothing, Branch(Just(vyy600), vyy61, vyy62, vyy63, vyy64), h, ba, bb) → new_foldFM_GE10(vyy3, vyy600, vyy61, vyy62, vyy63, vyy64, new_esEs8(new_compare27(Just(vyy600), Nothing, False, ba), LT), h, ba, bb)
new_foldFM_GE10(vyy3, vyy600, vyy61, vyy62, vyy63, vyy64, True, h, ba, bb) → new_foldFM_GE(vyy3, Nothing, vyy64, h, ba, bb)
new_foldFM_GE10(vyy3, vyy600, vyy61, vyy62, vyy63, vyy64, False, h, ba, bb) → new_foldFM_GE(vyy3, Nothing, vyy63, h, ba, bb)
The TRS R consists of the following rules:
new_compare27(Just(vyy3300), Nothing, False, cdg) → GT
new_esEs8(LT, LT) → True
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
The set Q consists of the following terms:
new_ltEs7(Just(x0), Just(x1), ty_Ordering)
new_esEs13(@0, @0)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_primPlusNat0(Succ(x0), Zero)
new_esEs23(x0, x1, ty_@0)
new_ltEs16(True, True)
new_ltEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare18(x0, x1, ty_Bool)
new_esEs28(x0, x1, ty_Char)
new_ltEs6(Right(x0), Right(x1), x2, ty_Double)
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_primEqNat0(Zero, Succ(x0))
new_lt5(x0, x1)
new_lt20(x0, x1, ty_Integer)
new_esEs25(x0, x1, ty_Integer)
new_compare25(x0, x1, False, x2, x3)
new_esEs25(x0, x1, ty_Bool)
new_esEs24(x0, x1, ty_Float)
new_primCompAux1(x0, x1, x2, x3)
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_esEs7(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs25(x0, x1, ty_Char)
new_ltEs20(x0, x1, ty_Bool)
new_compare0([], [], x0)
new_lt10(x0, x1, app(ty_[], x2))
new_ltEs18(x0, x1, ty_Bool)
new_esEs22(x0, x1, ty_Integer)
new_asAs(True, x0)
new_esEs26(x0, x1, ty_Float)
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_lt10(x0, x1, ty_Char)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs6(Right(x0), Right(x1), x2, ty_Int)
new_lt20(x0, x1, ty_Ordering)
new_esEs18(x0, x1, ty_Double)
new_lt10(x0, x1, ty_Float)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_ltEs6(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs4(Just(x0), Just(x1), app(ty_[], x2))
new_esEs27(x0, x1, ty_Bool)
new_esEs15(True, True)
new_esEs29(x0, x1, ty_Double)
new_esEs25(x0, x1, ty_Float)
new_esEs27(x0, x1, ty_Float)
new_ltEs6(Right(x0), Right(x1), x2, ty_Float)
new_lt20(x0, x1, ty_Double)
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, ty_Integer)
new_esEs25(x0, x1, ty_@0)
new_ltEs18(x0, x1, app(ty_Maybe, x2))
new_esEs7(Right(x0), Right(x1), x2, ty_@0)
new_ltEs7(Just(x0), Just(x1), app(ty_[], x2))
new_esEs24(x0, x1, ty_Double)
new_compare18(x0, x1, ty_Int)
new_lt11(x0, x1, ty_Bool)
new_primMulNat0(Zero, Succ(x0))
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_esEs28(x0, x1, ty_Ordering)
new_esEs15(False, False)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs26(x0, x1, app(ty_[], x2))
new_esEs18(x0, x1, ty_Float)
new_ltEs6(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs8(GT, GT)
new_esEs7(Right(x0), Right(x1), x2, ty_Ordering)
new_sr0(Integer(x0), Integer(x1))
new_esEs24(x0, x1, ty_Integer)
new_esEs20(x0, x1, ty_Integer)
new_esEs18(x0, x1, app(ty_[], x2))
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs6(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs4(Just(x0), Just(x1), ty_Ordering)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_lt10(x0, x1, ty_Double)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_compare14(x0, x1, False)
new_esEs27(x0, x1, ty_Integer)
new_esEs8(LT, LT)
new_primPlusNat0(Succ(x0), Succ(x1))
new_esEs26(x0, x1, ty_Char)
new_esEs16([], [], x0)
new_compare18(x0, x1, ty_Char)
new_ltEs6(Left(x0), Left(x1), ty_Bool, x2)
new_ltEs6(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_compare10(x0, x1, False, x2, x3)
new_esEs19(x0, x1, ty_Double)
new_lt10(x0, x1, app(app(ty_Either, x2), x3))
new_lt18(x0, x1, x2, x3, x4)
new_ltEs18(x0, x1, ty_Int)
new_ltEs6(Right(x0), Right(x1), x2, ty_Char)
new_lt7(x0, x1, x2, x3)
new_ltEs10(x0, x1)
new_esEs7(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs24(x0, x1, ty_Int)
new_esEs11(x0, x1)
new_esEs7(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_primPlusNat0(Zero, Succ(x0))
new_compare11(x0, x1, True, x2, x3)
new_lt11(x0, x1, app(app(ty_@2, x2), x3))
new_esEs8(GT, LT)
new_esEs8(LT, GT)
new_esEs5(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs20(x0, x1, app(ty_[], x2))
new_esEs20(x0, x1, ty_Int)
new_compare6(Float(x0, x1), Float(x2, x3))
new_lt11(x0, x1, ty_@0)
new_esEs23(x0, x1, ty_Double)
new_ltEs9(EQ, EQ)
new_compare5(@0, @0)
new_esEs4(Just(x0), Just(x1), ty_Bool)
new_ltEs18(x0, x1, app(app(ty_Either, x2), x3))
new_primCompAux0(x0, EQ)
new_esEs7(Left(x0), Left(x1), ty_Float, x2)
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_compare18(x0, x1, app(app(ty_@2, x2), x3))
new_lt10(x0, x1, ty_Int)
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primEqNat0(Zero, Zero)
new_primCmpNat0(Succ(x0), Zero)
new_primEqNat0(Succ(x0), Zero)
new_ltEs6(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs19(x0, x1, ty_Ordering)
new_lt11(x0, x1, app(ty_[], x2))
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(Left(x0), Left(x1), ty_Char, x2)
new_ltEs19(x0, x1, ty_Int)
new_esEs27(x0, x1, app(ty_[], x2))
new_lt11(x0, x1, app(ty_Ratio, x2))
new_compare14(x0, x1, True)
new_esEs19(x0, x1, ty_Int)
new_compare7(x0, x1, x2)
new_ltEs7(Just(x0), Just(x1), ty_Char)
new_esEs4(Nothing, Nothing, x0)
new_esEs27(x0, x1, ty_Char)
new_esEs4(Just(x0), Just(x1), ty_Float)
new_esEs7(Right(x0), Right(x1), x2, ty_Integer)
new_ltEs6(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs26(x0, x1, ty_@0)
new_primMulNat0(Zero, Zero)
new_compare18(x0, x1, ty_Float)
new_esEs20(x0, x1, ty_@0)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_esEs16(:(x0, x1), [], x2)
new_ltEs18(x0, x1, ty_@0)
new_esEs7(Left(x0), Left(x1), ty_Integer, x2)
new_esEs24(x0, x1, ty_Bool)
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_esEs7(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs28(x0, x1, app(ty_[], x2))
new_primMulNat0(Succ(x0), Zero)
new_ltEs7(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_lt13(x0, x1, x2)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_esEs9(:%(x0, x1), :%(x2, x3), x4)
new_esEs18(x0, x1, app(ty_Ratio, x2))
new_compare18(x0, x1, ty_Ordering)
new_esEs4(Just(x0), Just(x1), ty_@0)
new_lt20(x0, x1, ty_Float)
new_lt4(x0, x1)
new_ltEs6(Right(x0), Right(x1), x2, app(ty_[], x3))
new_lt11(x0, x1, ty_Ordering)
new_lt19(x0, x1)
new_ltEs7(Just(x0), Just(x1), app(ty_Ratio, x2))
new_compare13(x0, x1, False, x2)
new_compare27(x0, x1, True, x2)
new_esEs28(x0, x1, ty_Double)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs7(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_compare15(x0, x1, True)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_esEs18(x0, x1, ty_Integer)
new_pePe(False, x0)
new_esEs19(x0, x1, ty_Bool)
new_ltEs6(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs4(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_ltEs18(x0, x1, ty_Float)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_esEs21(x0, x1, ty_Int)
new_ltEs11(x0, x1)
new_esEs29(x0, x1, ty_Int)
new_esEs25(x0, x1, ty_Double)
new_esEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, app(ty_Ratio, x2))
new_esEs28(x0, x1, ty_Bool)
new_esEs19(x0, x1, app(ty_Ratio, x2))
new_esEs4(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_lt11(x0, x1, ty_Double)
new_ltEs9(GT, EQ)
new_ltEs9(EQ, GT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpNat0(Succ(x0), Succ(x1))
new_ltEs6(Left(x0), Left(x1), ty_@0, x2)
new_compare18(x0, x1, app(ty_[], x2))
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_compare0([], :(x0, x1), x2)
new_esEs7(Right(x0), Left(x1), x2, x3)
new_compare15(x0, x1, False)
new_esEs7(Left(x0), Right(x1), x2, x3)
new_esEs23(x0, x1, ty_Ordering)
new_primCmpNat0(Zero, Succ(x0))
new_esEs7(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_ltEs6(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_ltEs20(x0, x1, ty_Int)
new_esEs27(x0, x1, ty_Int)
new_asAs(False, x0)
new_lt11(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primPlusNat0(Zero, Zero)
new_lt20(x0, x1, ty_Int)
new_primCompAux0(x0, LT)
new_esEs7(Left(x0), Left(x1), ty_Int, x2)
new_lt10(x0, x1, ty_Ordering)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, ty_Char)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_esEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare18(x0, x1, app(app(ty_Either, x2), x3))
new_lt10(x0, x1, app(app(ty_@2, x2), x3))
new_compare12(x0, x1, True, x2, x3, x4)
new_esEs7(Left(x0), Left(x1), app(ty_[], x2), x3)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_compare29(x0, x1, True)
new_compare27(Nothing, Just(x0), False, x1)
new_lt11(x0, x1, app(ty_Maybe, x2))
new_esEs7(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs25(x0, x1, ty_Int)
new_esEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs6(Left(x0), Left(x1), ty_Char, x2)
new_primPlusNat1(Zero, x0)
new_compare16(x0, x1)
new_esEs7(Right(x0), Right(x1), x2, ty_Double)
new_ltEs7(Just(x0), Nothing, x1)
new_esEs23(x0, x1, ty_Bool)
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_compare9(Integer(x0), Integer(x1))
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs7(Just(x0), Just(x1), ty_Integer)
new_esEs4(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_compare17(x0, x1, x2, x3)
new_lt11(x0, x1, ty_Integer)
new_compare18(x0, x1, app(ty_Maybe, x2))
new_ltEs9(EQ, LT)
new_ltEs9(LT, EQ)
new_compare26(x0, x1, True, x2, x3, x4)
new_esEs7(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs29(x0, x1, ty_@0)
new_sr(x0, x1)
new_esEs7(Left(x0), Left(x1), ty_Bool, x2)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs15(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs12(Integer(x0), Integer(x1))
new_compare25(x0, x1, True, x2, x3)
new_lt11(x0, x1, ty_Int)
new_primEqInt(Neg(Zero), Pos(Zero))
new_primEqInt(Pos(Zero), Neg(Zero))
new_compare0(:(x0, x1), :(x2, x3), x4)
new_compare0(:(x0, x1), [], x2)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs20(x0, x1, ty_Double)
new_ltEs4(x0, x1, x2)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_esEs7(Right(x0), Right(x1), x2, ty_Bool)
new_esEs24(x0, x1, ty_@0)
new_esEs23(x0, x1, ty_Float)
new_compare33(x0, x1, x2, x3, x4)
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_ltEs5(@2(x0, x1), @2(x2, x3), x4, x5)
new_compare8(Char(x0), Char(x1))
new_lt11(x0, x1, app(app(ty_Either, x2), x3))
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_ltEs20(x0, x1, ty_@0)
new_esEs18(x0, x1, ty_Char)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs15(True, False)
new_esEs15(False, True)
new_esEs8(EQ, EQ)
new_esEs14(Double(x0, x1), Double(x2, x3))
new_esEs18(x0, x1, ty_Ordering)
new_esEs17(Char(x0), Char(x1))
new_primEqInt(Neg(Zero), Neg(Zero))
new_ltEs7(Just(x0), Just(x1), ty_@0)
new_ltEs7(Just(x0), Just(x1), ty_Float)
new_esEs28(x0, x1, ty_Integer)
new_esEs6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs27(x0, x1, ty_@0)
new_compare27(Just(x0), Nothing, False, x1)
new_ltEs6(Left(x0), Left(x1), ty_Float, x2)
new_compare11(x0, x1, False, x2, x3)
new_esEs22(x0, x1, ty_Int)
new_ltEs7(Just(x0), Just(x1), ty_Bool)
new_ltEs6(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs24(x0, x1, ty_Char)
new_ltEs6(Left(x0), Left(x1), ty_Ordering, x2)
new_compare26(x0, x1, False, x2, x3, x4)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs4(Nothing, Just(x0), x1)
new_compare24(x0, x1, False, x2, x3)
new_ltEs18(x0, x1, app(ty_Ratio, x2))
new_primCompAux0(x0, GT)
new_ltEs19(x0, x1, ty_Double)
new_lt10(x0, x1, ty_@0)
new_ltEs7(Just(x0), Just(x1), ty_Double)
new_esEs18(x0, x1, app(ty_Maybe, x2))
new_ltEs19(x0, x1, ty_Ordering)
new_compare18(x0, x1, app(ty_Ratio, x2))
new_esEs28(x0, x1, ty_Float)
new_esEs7(Right(x0), Right(x1), x2, ty_Float)
new_ltEs20(x0, x1, app(ty_[], x2))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_lt10(x0, x1, app(ty_Maybe, x2))
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs18(x0, x1, ty_Ordering)
new_lt10(x0, x1, app(ty_Ratio, x2))
new_pePe(True, x0)
new_esEs26(x0, x1, ty_Ordering)
new_ltEs9(LT, LT)
new_esEs29(x0, x1, ty_Integer)
new_esEs20(x0, x1, ty_Char)
new_ltEs18(x0, x1, ty_Integer)
new_compare10(x0, x1, True, x2, x3)
new_esEs7(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_ltEs16(False, True)
new_ltEs16(True, False)
new_ltEs19(x0, x1, ty_Bool)
new_lt20(x0, x1, ty_Char)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_esEs29(x0, x1, app(ty_[], x2))
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_compare31(:%(x0, x1), :%(x2, x3), ty_Integer)
new_compare18(x0, x1, ty_@0)
new_esEs26(x0, x1, ty_Double)
new_ltEs18(x0, x1, app(ty_[], x2))
new_esEs4(Just(x0), Just(x1), ty_Int)
new_esEs26(x0, x1, ty_Bool)
new_ltEs6(Right(x0), Right(x1), x2, ty_@0)
new_ltEs19(x0, x1, ty_@0)
new_ltEs14(x0, x1)
new_ltEs6(Left(x0), Right(x1), x2, x3)
new_ltEs6(Right(x0), Left(x1), x2, x3)
new_esEs19(x0, x1, app(app(ty_Either, x2), x3))
new_compare19(x0, x1, x2, x3)
new_esEs20(x0, x1, ty_Ordering)
new_esEs19(x0, x1, ty_Integer)
new_primCmpNat0(Zero, Zero)
new_esEs19(x0, x1, app(ty_Maybe, x2))
new_primEqNat0(Succ(x0), Succ(x1))
new_compare27(Just(x0), Just(x1), False, x2)
new_ltEs20(x0, x1, ty_Ordering)
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare29(x0, x1, False)
new_primMulNat0(Succ(x0), Succ(x1))
new_ltEs19(x0, x1, ty_Integer)
new_ltEs7(Nothing, Just(x0), x1)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_compare28(x0, x1, False)
new_esEs29(x0, x1, ty_Float)
new_esEs27(x0, x1, ty_Ordering)
new_ltEs12(x0, x1, x2)
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs6(Left(x0), Left(x1), ty_Int, x2)
new_lt8(x0, x1)
new_ltEs20(x0, x1, ty_Integer)
new_esEs4(Just(x0), Nothing, x1)
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_esEs7(Left(x0), Left(x1), ty_Double, x2)
new_compare24(x0, x1, True, x2, x3)
new_primPlusNat1(Succ(x0), x1)
new_ltEs6(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_esEs19(x0, x1, ty_Float)
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs6(Right(x0), Right(x1), x2, ty_Integer)
new_lt9(x0, x1)
new_ltEs7(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_esEs21(x0, x1, ty_Integer)
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_compare30(x0, x1)
new_ltEs20(x0, x1, ty_Char)
new_ltEs20(x0, x1, ty_Float)
new_ltEs9(GT, LT)
new_ltEs9(LT, GT)
new_ltEs7(Nothing, Nothing, x0)
new_esEs26(x0, x1, ty_Int)
new_lt10(x0, x1, ty_Bool)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs16(:(x0, x1), :(x2, x3), x4)
new_compare27(Nothing, Nothing, False, x0)
new_esEs24(x0, x1, ty_Ordering)
new_esEs18(x0, x1, app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, ty_Int)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_not(True)
new_ltEs19(x0, x1, ty_Float)
new_compare31(:%(x0, x1), :%(x2, x3), ty_Int)
new_esEs19(x0, x1, app(ty_[], x2))
new_esEs20(x0, x1, ty_Float)
new_esEs18(x0, x1, ty_Bool)
new_esEs23(x0, x1, app(ty_[], x2))
new_esEs16([], :(x0, x1), x2)
new_lt11(x0, x1, ty_Float)
new_esEs29(x0, x1, ty_Ordering)
new_ltEs18(x0, x1, ty_Double)
new_esEs7(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_compare34(x0, x1)
new_esEs4(Just(x0), Just(x1), ty_Double)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_not(False)
new_esEs25(x0, x1, app(ty_[], x2))
new_esEs29(x0, x1, ty_Char)
new_ltEs7(Just(x0), Just(x1), ty_Int)
new_ltEs6(Left(x0), Left(x1), app(ty_[], x2), x3)
new_lt15(x0, x1)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_compare28(x0, x1, True)
new_ltEs8(x0, x1)
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_ltEs6(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs26(x0, x1, ty_Integer)
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_esEs4(Just(x0), Just(x1), ty_Integer)
new_ltEs13(x0, x1)
new_esEs23(x0, x1, ty_Char)
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs7(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs4(Just(x0), Just(x1), ty_Char)
new_esEs19(x0, x1, ty_@0)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_compare13(x0, x1, True, x2)
new_lt10(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_ltEs6(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs17(x0, x1)
new_esEs24(x0, x1, app(ty_[], x2))
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_lt6(x0, x1)
new_ltEs6(Left(x0), Left(x1), ty_Double, x2)
new_compare18(x0, x1, ty_Double)
new_esEs7(Left(x0), Left(x1), ty_@0, x2)
new_esEs20(x0, x1, ty_Bool)
new_lt20(x0, x1, ty_@0)
new_lt10(x0, x1, ty_Integer)
new_lt14(x0, x1, x2, x3)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_primMulInt(Neg(x0), Neg(x1))
new_ltEs9(GT, GT)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs19(x0, x1, ty_Char)
new_compare18(x0, x1, ty_Integer)
new_ltEs18(x0, x1, ty_Char)
new_lt17(x0, x1)
new_esEs7(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs28(x0, x1, ty_Int)
new_compare12(x0, x1, False, x2, x3, x4)
new_lt20(x0, x1, app(ty_[], x2))
new_esEs10(Float(x0, x1), Float(x2, x3))
new_compare32(Double(x0, x1), Double(x2, x3))
new_ltEs20(x0, x1, ty_Double)
new_esEs18(x0, x1, ty_@0)
new_esEs29(x0, x1, ty_Bool)
new_compare18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primEqInt(Pos(Zero), Pos(Zero))
new_esEs25(x0, x1, ty_Ordering)
new_lt20(x0, x1, ty_Bool)
new_lt12(x0, x1, x2)
new_esEs18(x0, x1, ty_Int)
new_ltEs6(Left(x0), Left(x1), ty_Integer, x2)
new_ltEs18(x0, x1, app(app(ty_@2, x2), x3))
new_lt16(x0, x1, x2)
new_esEs7(Right(x0), Right(x1), x2, ty_Char)
new_lt11(x0, x1, ty_Char)
new_esEs18(x0, x1, app(app(ty_@2, x2), x3))
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_esEs28(x0, x1, ty_@0)
new_esEs4(Just(x0), Just(x1), app(ty_Maybe, x2))
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_primMulInt(Pos(x0), Pos(x1))
new_esEs7(Right(x0), Right(x1), x2, ty_Int)
new_ltEs16(False, False)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs4(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs27(x0, x1, ty_Double)
new_ltEs19(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, app(app(app(ty_@3, x2), 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_ltEs7(Just(x0), Just(x1), ty_Ordering)
new_esEs13(@0, @0)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_primPlusNat0(Succ(x0), Zero)
new_esEs23(x0, x1, ty_@0)
new_ltEs16(True, True)
new_ltEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare18(x0, x1, ty_Bool)
new_esEs28(x0, x1, ty_Char)
new_ltEs6(Right(x0), Right(x1), x2, ty_Double)
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_primEqNat0(Zero, Succ(x0))
new_lt5(x0, x1)
new_lt20(x0, x1, ty_Integer)
new_esEs25(x0, x1, ty_Integer)
new_compare25(x0, x1, False, x2, x3)
new_esEs25(x0, x1, ty_Bool)
new_esEs24(x0, x1, ty_Float)
new_primCompAux1(x0, x1, x2, x3)
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_esEs7(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs25(x0, x1, ty_Char)
new_ltEs20(x0, x1, ty_Bool)
new_compare0([], [], x0)
new_lt10(x0, x1, app(ty_[], x2))
new_ltEs18(x0, x1, ty_Bool)
new_esEs22(x0, x1, ty_Integer)
new_asAs(True, x0)
new_esEs26(x0, x1, ty_Float)
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_lt10(x0, x1, ty_Char)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs6(Right(x0), Right(x1), x2, ty_Int)
new_lt20(x0, x1, ty_Ordering)
new_esEs18(x0, x1, ty_Double)
new_lt10(x0, x1, ty_Float)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_ltEs6(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs4(Just(x0), Just(x1), app(ty_[], x2))
new_esEs27(x0, x1, ty_Bool)
new_esEs15(True, True)
new_esEs29(x0, x1, ty_Double)
new_esEs25(x0, x1, ty_Float)
new_esEs27(x0, x1, ty_Float)
new_ltEs6(Right(x0), Right(x1), x2, ty_Float)
new_lt20(x0, x1, ty_Double)
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, ty_Integer)
new_esEs25(x0, x1, ty_@0)
new_ltEs18(x0, x1, app(ty_Maybe, x2))
new_esEs7(Right(x0), Right(x1), x2, ty_@0)
new_ltEs7(Just(x0), Just(x1), app(ty_[], x2))
new_esEs24(x0, x1, ty_Double)
new_compare18(x0, x1, ty_Int)
new_lt11(x0, x1, ty_Bool)
new_primMulNat0(Zero, Succ(x0))
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_esEs28(x0, x1, ty_Ordering)
new_esEs15(False, False)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs26(x0, x1, app(ty_[], x2))
new_esEs18(x0, x1, ty_Float)
new_ltEs6(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs7(Right(x0), Right(x1), x2, ty_Ordering)
new_sr0(Integer(x0), Integer(x1))
new_esEs24(x0, x1, ty_Integer)
new_esEs20(x0, x1, ty_Integer)
new_esEs18(x0, x1, app(ty_[], x2))
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs6(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs4(Just(x0), Just(x1), ty_Ordering)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_lt10(x0, x1, ty_Double)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_compare14(x0, x1, False)
new_esEs27(x0, x1, ty_Integer)
new_primPlusNat0(Succ(x0), Succ(x1))
new_esEs26(x0, x1, ty_Char)
new_esEs16([], [], x0)
new_compare18(x0, x1, ty_Char)
new_ltEs6(Left(x0), Left(x1), ty_Bool, x2)
new_ltEs6(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_compare10(x0, x1, False, x2, x3)
new_esEs19(x0, x1, ty_Double)
new_lt10(x0, x1, app(app(ty_Either, x2), x3))
new_lt18(x0, x1, x2, x3, x4)
new_ltEs18(x0, x1, ty_Int)
new_ltEs6(Right(x0), Right(x1), x2, ty_Char)
new_lt7(x0, x1, x2, x3)
new_ltEs10(x0, x1)
new_esEs7(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs24(x0, x1, ty_Int)
new_esEs11(x0, x1)
new_esEs7(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_primPlusNat0(Zero, Succ(x0))
new_compare11(x0, x1, True, x2, x3)
new_lt11(x0, x1, app(app(ty_@2, x2), x3))
new_esEs5(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs20(x0, x1, app(ty_[], x2))
new_esEs20(x0, x1, ty_Int)
new_compare6(Float(x0, x1), Float(x2, x3))
new_lt11(x0, x1, ty_@0)
new_esEs23(x0, x1, ty_Double)
new_ltEs9(EQ, EQ)
new_compare5(@0, @0)
new_esEs4(Just(x0), Just(x1), ty_Bool)
new_ltEs18(x0, x1, app(app(ty_Either, x2), x3))
new_primCompAux0(x0, EQ)
new_esEs7(Left(x0), Left(x1), ty_Float, x2)
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_compare18(x0, x1, app(app(ty_@2, x2), x3))
new_lt10(x0, x1, ty_Int)
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primEqNat0(Zero, Zero)
new_primCmpNat0(Succ(x0), Zero)
new_primEqNat0(Succ(x0), Zero)
new_ltEs6(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs19(x0, x1, ty_Ordering)
new_lt11(x0, x1, app(ty_[], x2))
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(Left(x0), Left(x1), ty_Char, x2)
new_ltEs19(x0, x1, ty_Int)
new_esEs27(x0, x1, app(ty_[], x2))
new_lt11(x0, x1, app(ty_Ratio, x2))
new_compare14(x0, x1, True)
new_esEs19(x0, x1, ty_Int)
new_compare7(x0, x1, x2)
new_ltEs7(Just(x0), Just(x1), ty_Char)
new_esEs4(Nothing, Nothing, x0)
new_esEs27(x0, x1, ty_Char)
new_esEs4(Just(x0), Just(x1), ty_Float)
new_esEs7(Right(x0), Right(x1), x2, ty_Integer)
new_ltEs6(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs26(x0, x1, ty_@0)
new_primMulNat0(Zero, Zero)
new_compare18(x0, x1, ty_Float)
new_esEs20(x0, x1, ty_@0)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_esEs16(:(x0, x1), [], x2)
new_ltEs18(x0, x1, ty_@0)
new_esEs7(Left(x0), Left(x1), ty_Integer, x2)
new_esEs24(x0, x1, ty_Bool)
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_esEs7(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs28(x0, x1, app(ty_[], x2))
new_primMulNat0(Succ(x0), Zero)
new_ltEs7(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_lt13(x0, x1, x2)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_esEs9(:%(x0, x1), :%(x2, x3), x4)
new_esEs18(x0, x1, app(ty_Ratio, x2))
new_compare18(x0, x1, ty_Ordering)
new_esEs4(Just(x0), Just(x1), ty_@0)
new_lt20(x0, x1, ty_Float)
new_lt4(x0, x1)
new_ltEs6(Right(x0), Right(x1), x2, app(ty_[], x3))
new_lt11(x0, x1, ty_Ordering)
new_lt19(x0, x1)
new_ltEs7(Just(x0), Just(x1), app(ty_Ratio, x2))
new_compare13(x0, x1, False, x2)
new_esEs28(x0, x1, ty_Double)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs7(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_compare15(x0, x1, True)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_esEs18(x0, x1, ty_Integer)
new_pePe(False, x0)
new_esEs19(x0, x1, ty_Bool)
new_ltEs6(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs4(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_ltEs18(x0, x1, ty_Float)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_esEs21(x0, x1, ty_Int)
new_ltEs11(x0, x1)
new_esEs29(x0, x1, ty_Int)
new_esEs25(x0, x1, ty_Double)
new_esEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, app(ty_Ratio, x2))
new_esEs28(x0, x1, ty_Bool)
new_esEs19(x0, x1, app(ty_Ratio, x2))
new_esEs4(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_lt11(x0, x1, ty_Double)
new_ltEs9(GT, EQ)
new_ltEs9(EQ, GT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpNat0(Succ(x0), Succ(x1))
new_ltEs6(Left(x0), Left(x1), ty_@0, x2)
new_compare18(x0, x1, app(ty_[], x2))
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_compare0([], :(x0, x1), x2)
new_esEs7(Right(x0), Left(x1), x2, x3)
new_compare15(x0, x1, False)
new_esEs7(Left(x0), Right(x1), x2, x3)
new_esEs23(x0, x1, ty_Ordering)
new_primCmpNat0(Zero, Succ(x0))
new_esEs7(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_ltEs6(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_ltEs20(x0, x1, ty_Int)
new_esEs27(x0, x1, ty_Int)
new_asAs(False, x0)
new_lt11(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primPlusNat0(Zero, Zero)
new_lt20(x0, x1, ty_Int)
new_primCompAux0(x0, LT)
new_esEs7(Left(x0), Left(x1), ty_Int, x2)
new_lt10(x0, x1, ty_Ordering)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, ty_Char)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_esEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare18(x0, x1, app(app(ty_Either, x2), x3))
new_lt10(x0, x1, app(app(ty_@2, x2), x3))
new_compare12(x0, x1, True, x2, x3, x4)
new_esEs7(Left(x0), Left(x1), app(ty_[], x2), x3)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_compare29(x0, x1, True)
new_lt11(x0, x1, app(ty_Maybe, x2))
new_esEs7(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs25(x0, x1, ty_Int)
new_esEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs6(Left(x0), Left(x1), ty_Char, x2)
new_primPlusNat1(Zero, x0)
new_compare16(x0, x1)
new_esEs7(Right(x0), Right(x1), x2, ty_Double)
new_ltEs7(Just(x0), Nothing, x1)
new_esEs23(x0, x1, ty_Bool)
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_compare9(Integer(x0), Integer(x1))
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs7(Just(x0), Just(x1), ty_Integer)
new_esEs4(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_compare17(x0, x1, x2, x3)
new_lt11(x0, x1, ty_Integer)
new_compare18(x0, x1, app(ty_Maybe, x2))
new_ltEs9(EQ, LT)
new_ltEs9(LT, EQ)
new_compare26(x0, x1, True, x2, x3, x4)
new_esEs7(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs29(x0, x1, ty_@0)
new_sr(x0, x1)
new_esEs7(Left(x0), Left(x1), ty_Bool, x2)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs15(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs12(Integer(x0), Integer(x1))
new_compare25(x0, x1, True, x2, x3)
new_lt11(x0, x1, ty_Int)
new_primEqInt(Neg(Zero), Pos(Zero))
new_primEqInt(Pos(Zero), Neg(Zero))
new_compare0(:(x0, x1), :(x2, x3), x4)
new_compare0(:(x0, x1), [], x2)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs20(x0, x1, ty_Double)
new_ltEs4(x0, x1, x2)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_esEs7(Right(x0), Right(x1), x2, ty_Bool)
new_esEs24(x0, x1, ty_@0)
new_esEs23(x0, x1, ty_Float)
new_compare33(x0, x1, x2, x3, x4)
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_ltEs5(@2(x0, x1), @2(x2, x3), x4, x5)
new_compare8(Char(x0), Char(x1))
new_lt11(x0, x1, app(app(ty_Either, x2), x3))
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_ltEs20(x0, x1, ty_@0)
new_esEs18(x0, x1, ty_Char)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs15(True, False)
new_esEs15(False, True)
new_esEs14(Double(x0, x1), Double(x2, x3))
new_esEs18(x0, x1, ty_Ordering)
new_esEs17(Char(x0), Char(x1))
new_primEqInt(Neg(Zero), Neg(Zero))
new_ltEs7(Just(x0), Just(x1), ty_@0)
new_ltEs7(Just(x0), Just(x1), ty_Float)
new_esEs28(x0, x1, ty_Integer)
new_esEs6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs27(x0, x1, ty_@0)
new_ltEs6(Left(x0), Left(x1), ty_Float, x2)
new_compare11(x0, x1, False, x2, x3)
new_esEs22(x0, x1, ty_Int)
new_ltEs7(Just(x0), Just(x1), ty_Bool)
new_ltEs6(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs24(x0, x1, ty_Char)
new_ltEs6(Left(x0), Left(x1), ty_Ordering, x2)
new_compare26(x0, x1, False, x2, x3, x4)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs4(Nothing, Just(x0), x1)
new_compare24(x0, x1, False, x2, x3)
new_ltEs18(x0, x1, app(ty_Ratio, x2))
new_primCompAux0(x0, GT)
new_ltEs19(x0, x1, ty_Double)
new_lt10(x0, x1, ty_@0)
new_ltEs7(Just(x0), Just(x1), ty_Double)
new_esEs18(x0, x1, app(ty_Maybe, x2))
new_ltEs19(x0, x1, ty_Ordering)
new_compare18(x0, x1, app(ty_Ratio, x2))
new_esEs28(x0, x1, ty_Float)
new_esEs7(Right(x0), Right(x1), x2, ty_Float)
new_ltEs20(x0, x1, app(ty_[], x2))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_lt10(x0, x1, app(ty_Maybe, x2))
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs18(x0, x1, ty_Ordering)
new_lt10(x0, x1, app(ty_Ratio, x2))
new_pePe(True, x0)
new_esEs26(x0, x1, ty_Ordering)
new_ltEs9(LT, LT)
new_esEs29(x0, x1, ty_Integer)
new_esEs20(x0, x1, ty_Char)
new_ltEs18(x0, x1, ty_Integer)
new_compare10(x0, x1, True, x2, x3)
new_esEs7(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_ltEs16(False, True)
new_ltEs16(True, False)
new_ltEs19(x0, x1, ty_Bool)
new_lt20(x0, x1, ty_Char)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_esEs29(x0, x1, app(ty_[], x2))
new_compare31(:%(x0, x1), :%(x2, x3), ty_Integer)
new_compare18(x0, x1, ty_@0)
new_esEs26(x0, x1, ty_Double)
new_ltEs18(x0, x1, app(ty_[], x2))
new_esEs4(Just(x0), Just(x1), ty_Int)
new_esEs26(x0, x1, ty_Bool)
new_ltEs6(Right(x0), Right(x1), x2, ty_@0)
new_ltEs19(x0, x1, ty_@0)
new_ltEs14(x0, x1)
new_ltEs6(Left(x0), Right(x1), x2, x3)
new_ltEs6(Right(x0), Left(x1), x2, x3)
new_esEs19(x0, x1, app(app(ty_Either, x2), x3))
new_compare19(x0, x1, x2, x3)
new_esEs20(x0, x1, ty_Ordering)
new_esEs19(x0, x1, ty_Integer)
new_primCmpNat0(Zero, Zero)
new_esEs19(x0, x1, app(ty_Maybe, x2))
new_primEqNat0(Succ(x0), Succ(x1))
new_ltEs20(x0, x1, ty_Ordering)
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare29(x0, x1, False)
new_primMulNat0(Succ(x0), Succ(x1))
new_ltEs19(x0, x1, ty_Integer)
new_ltEs7(Nothing, Just(x0), x1)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_compare28(x0, x1, False)
new_esEs29(x0, x1, ty_Float)
new_esEs27(x0, x1, ty_Ordering)
new_ltEs12(x0, x1, x2)
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs6(Left(x0), Left(x1), ty_Int, x2)
new_lt8(x0, x1)
new_ltEs20(x0, x1, ty_Integer)
new_esEs4(Just(x0), Nothing, x1)
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_esEs7(Left(x0), Left(x1), ty_Double, x2)
new_compare24(x0, x1, True, x2, x3)
new_primPlusNat1(Succ(x0), x1)
new_ltEs6(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_esEs19(x0, x1, ty_Float)
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs6(Right(x0), Right(x1), x2, ty_Integer)
new_lt9(x0, x1)
new_ltEs7(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_esEs21(x0, x1, ty_Integer)
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_compare30(x0, x1)
new_ltEs20(x0, x1, ty_Char)
new_ltEs20(x0, x1, ty_Float)
new_ltEs9(GT, LT)
new_ltEs9(LT, GT)
new_ltEs7(Nothing, Nothing, x0)
new_esEs26(x0, x1, ty_Int)
new_lt10(x0, x1, ty_Bool)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs16(:(x0, x1), :(x2, x3), x4)
new_esEs24(x0, x1, ty_Ordering)
new_esEs18(x0, x1, app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, ty_Int)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_not(True)
new_ltEs19(x0, x1, ty_Float)
new_compare31(:%(x0, x1), :%(x2, x3), ty_Int)
new_esEs19(x0, x1, app(ty_[], x2))
new_esEs20(x0, x1, ty_Float)
new_esEs18(x0, x1, ty_Bool)
new_esEs23(x0, x1, app(ty_[], x2))
new_esEs16([], :(x0, x1), x2)
new_lt11(x0, x1, ty_Float)
new_esEs29(x0, x1, ty_Ordering)
new_ltEs18(x0, x1, ty_Double)
new_esEs7(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_compare34(x0, x1)
new_esEs4(Just(x0), Just(x1), ty_Double)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_not(False)
new_esEs25(x0, x1, app(ty_[], x2))
new_esEs29(x0, x1, ty_Char)
new_ltEs7(Just(x0), Just(x1), ty_Int)
new_ltEs6(Left(x0), Left(x1), app(ty_[], x2), x3)
new_lt15(x0, x1)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_compare28(x0, x1, True)
new_ltEs8(x0, x1)
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_ltEs6(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs26(x0, x1, ty_Integer)
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_esEs4(Just(x0), Just(x1), ty_Integer)
new_ltEs13(x0, x1)
new_esEs23(x0, x1, ty_Char)
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs7(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs4(Just(x0), Just(x1), ty_Char)
new_esEs19(x0, x1, ty_@0)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_compare13(x0, x1, True, x2)
new_lt10(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs6(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs17(x0, x1)
new_esEs24(x0, x1, app(ty_[], x2))
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_lt6(x0, x1)
new_ltEs6(Left(x0), Left(x1), ty_Double, x2)
new_compare18(x0, x1, ty_Double)
new_esEs7(Left(x0), Left(x1), ty_@0, x2)
new_esEs20(x0, x1, ty_Bool)
new_lt20(x0, x1, ty_@0)
new_lt10(x0, x1, ty_Integer)
new_lt14(x0, x1, x2, x3)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_primMulInt(Neg(x0), Neg(x1))
new_ltEs9(GT, GT)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs19(x0, x1, ty_Char)
new_compare18(x0, x1, ty_Integer)
new_ltEs18(x0, x1, ty_Char)
new_lt17(x0, x1)
new_esEs7(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs28(x0, x1, ty_Int)
new_compare12(x0, x1, False, x2, x3, x4)
new_lt20(x0, x1, app(ty_[], x2))
new_esEs10(Float(x0, x1), Float(x2, x3))
new_compare32(Double(x0, x1), Double(x2, x3))
new_ltEs20(x0, x1, ty_Double)
new_esEs18(x0, x1, ty_@0)
new_esEs29(x0, x1, ty_Bool)
new_compare18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primEqInt(Pos(Zero), Pos(Zero))
new_esEs25(x0, x1, ty_Ordering)
new_lt20(x0, x1, ty_Bool)
new_lt12(x0, x1, x2)
new_esEs18(x0, x1, ty_Int)
new_ltEs6(Left(x0), Left(x1), ty_Integer, x2)
new_ltEs18(x0, x1, app(app(ty_@2, x2), x3))
new_lt16(x0, x1, x2)
new_esEs7(Right(x0), Right(x1), x2, ty_Char)
new_lt11(x0, x1, ty_Char)
new_esEs18(x0, x1, app(app(ty_@2, x2), x3))
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_esEs28(x0, x1, ty_@0)
new_esEs4(Just(x0), Just(x1), app(ty_Maybe, x2))
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_primMulInt(Pos(x0), Pos(x1))
new_esEs7(Right(x0), Right(x1), x2, ty_Int)
new_ltEs16(False, False)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs4(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs27(x0, x1, ty_Double)
new_ltEs19(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QReductionProof
↳ QDP
↳ QDPSizeChangeProof
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_foldFM_GE10(vyy3, vyy600, vyy61, vyy62, vyy63, vyy64, False, h, ba, bb) → new_foldFM_GE(vyy3, Nothing, vyy64, h, ba, bb)
new_foldFM_GE(vyy3, Nothing, Branch(Nothing, vyy61, vyy62, vyy63, vyy64), h, ba, bb) → new_foldFM_GE(vyy3, Nothing, vyy63, h, ba, bb)
new_foldFM_GE(vyy3, Nothing, Branch(Nothing, vyy61, vyy62, vyy63, vyy64), h, ba, bb) → new_foldFM_GE(vyy3, Nothing, vyy64, h, ba, bb)
new_foldFM_GE(vyy3, Nothing, Branch(Just(vyy600), vyy61, vyy62, vyy63, vyy64), h, ba, bb) → new_foldFM_GE10(vyy3, vyy600, vyy61, vyy62, vyy63, vyy64, new_esEs8(new_compare27(Just(vyy600), Nothing, False, ba), LT), h, ba, bb)
new_foldFM_GE10(vyy3, vyy600, vyy61, vyy62, vyy63, vyy64, True, h, ba, bb) → new_foldFM_GE(vyy3, Nothing, vyy64, h, ba, bb)
new_foldFM_GE10(vyy3, vyy600, vyy61, vyy62, vyy63, vyy64, False, h, ba, bb) → new_foldFM_GE(vyy3, Nothing, vyy63, h, ba, bb)
The TRS R consists of the following rules:
new_compare27(Just(vyy3300), Nothing, False, cdg) → GT
new_esEs8(LT, LT) → True
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
The set Q consists of the following terms:
new_esEs8(GT, GT)
new_esEs8(LT, LT)
new_esEs8(GT, LT)
new_esEs8(LT, GT)
new_compare27(x0, x1, True, x2)
new_compare27(Nothing, Just(x0), False, x1)
new_esEs8(EQ, EQ)
new_compare27(Just(x0), Nothing, False, x1)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_compare27(Just(x0), Just(x1), False, x2)
new_compare27(Nothing, Nothing, False, x0)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
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_GE(vyy3, Nothing, Branch(Just(vyy600), vyy61, vyy62, vyy63, vyy64), h, ba, bb) → new_foldFM_GE10(vyy3, vyy600, vyy61, vyy62, vyy63, vyy64, new_esEs8(new_compare27(Just(vyy600), Nothing, False, ba), LT), h, ba, bb)
The graph contains the following edges 1 >= 1, 3 > 2, 3 > 3, 3 > 4, 3 > 5, 3 > 6, 4 >= 8, 5 >= 9, 6 >= 10
- new_foldFM_GE(vyy3, Nothing, Branch(Nothing, vyy61, vyy62, vyy63, vyy64), h, ba, bb) → new_foldFM_GE(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
- new_foldFM_GE(vyy3, Nothing, Branch(Nothing, vyy61, vyy62, vyy63, vyy64), h, ba, bb) → new_foldFM_GE(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_GE10(vyy3, vyy600, vyy61, vyy62, vyy63, vyy64, False, h, ba, bb) → new_foldFM_GE(vyy3, Nothing, vyy64, h, ba, bb)
The graph contains the following edges 1 >= 1, 6 >= 3, 8 >= 4, 9 >= 5, 10 >= 6
- new_foldFM_GE10(vyy3, vyy600, vyy61, vyy62, vyy63, vyy64, True, h, ba, bb) → new_foldFM_GE(vyy3, Nothing, vyy64, h, ba, bb)
The graph contains the following edges 1 >= 1, 6 >= 3, 8 >= 4, 9 >= 5, 10 >= 6
- new_foldFM_GE10(vyy3, vyy600, vyy61, vyy62, vyy63, vyy64, False, h, ba, bb) → new_foldFM_GE(vyy3, Nothing, vyy63, h, ba, bb)
The graph contains the following edges 1 >= 1, 5 >= 3, 8 >= 4, 9 >= 5, 10 >= 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
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPSizeChangeProof
Q DP problem:
The TRS P consists of the following rules:
new_foldFM_GE1(vyy3, vyy50, vyy61, vyy62, vyy63, vyy64, False, h, ba, bb) → new_foldFM_GE(vyy3, Just(vyy50), vyy63, h, ba, bb)
new_foldFM_GE11(vyy17, vyy19, vyy20, vyy21, vyy22, vyy23, vyy24, False, bc, bd, be) → new_foldFM_GE(vyy17, Just(vyy19), vyy24, bc, bd, be)
new_foldFM_GE1(vyy3, vyy50, vyy61, vyy62, vyy63, vyy64, True, h, ba, bb) → new_foldFM_GE(vyy3, Just(vyy50), vyy64, h, ba, bb)
new_foldFM_GE1(vyy3, vyy50, vyy61, vyy62, vyy63, vyy64, False, h, ba, bb) → new_foldFM_GE(vyy3, Just(vyy50), vyy64, h, ba, bb)
new_foldFM_GE(vyy3, Just(vyy50), Branch(Nothing, vyy61, vyy62, vyy63, vyy64), h, ba, bb) → new_foldFM_GE1(vyy3, vyy50, vyy61, vyy62, vyy63, vyy64, new_esEs8(new_compare27(Nothing, Just(vyy50), False, ba), LT), h, ba, bb)
new_foldFM_GE11(vyy17, vyy19, vyy20, vyy21, vyy22, vyy23, vyy24, False, bc, bd, be) → new_foldFM_GE(vyy17, Just(vyy19), vyy23, bc, bd, be)
new_foldFM_GE(vyy3, Just(vyy50), Branch(Just(vyy600), vyy61, vyy62, vyy63, vyy64), h, ba, bb) → new_foldFM_GE11(vyy3, vyy50, vyy600, vyy61, vyy62, vyy63, vyy64, new_esEs8(new_compare27(Just(vyy600), Just(vyy50), new_esEs29(vyy600, vyy50, ba), ba), LT), h, ba, bb)
new_foldFM_GE11(vyy17, vyy19, vyy20, vyy21, vyy22, vyy23, vyy24, True, bc, bd, be) → new_foldFM_GE(vyy17, Just(vyy19), vyy24, bc, bd, be)
The TRS R consists of the following rules:
new_esEs4(Just(vyy6000), Just(vyy500), app(ty_Maybe, bgb)) → new_esEs4(vyy6000, vyy500, bgb)
new_ltEs19(vyy3300, vyy3400, app(app(ty_@2, cea), ceb)) → new_ltEs5(vyy3300, vyy3400, cea, ceb)
new_esEs23(vyy33000, vyy34000, app(app(ty_Either, cba), cbb)) → new_esEs7(vyy33000, vyy34000, cba, cbb)
new_lt10(vyy33001, vyy34001, ty_Integer) → new_lt6(vyy33001, vyy34001)
new_lt4(vyy33000, vyy34000) → new_esEs8(new_compare5(vyy33000, vyy34000), LT)
new_esEs4(Just(vyy6000), Just(vyy500), ty_Ordering) → new_esEs8(vyy6000, vyy500)
new_esEs7(Left(vyy6000), Left(vyy500), app(app(ty_Either, fd), ff), fa) → new_esEs7(vyy6000, vyy500, fd, ff)
new_ltEs6(Left(vyy33000), Left(vyy34000), app(app(app(ty_@3, cg), da), db), cb) → new_ltEs15(vyy33000, vyy34000, cg, da, db)
new_compare5(@0, @0) → EQ
new_esEs27(vyy6002, vyy502, app(ty_[], dbb)) → new_esEs16(vyy6002, vyy502, dbb)
new_lt10(vyy33001, vyy34001, ty_Char) → new_lt8(vyy33001, vyy34001)
new_esEs25(vyy6000, vyy500, ty_Integer) → new_esEs12(vyy6000, vyy500)
new_esEs25(vyy6000, vyy500, app(ty_[], cgf)) → new_esEs16(vyy6000, vyy500, cgf)
new_esEs7(Right(vyy6000), Right(vyy500), gd, ty_Bool) → new_esEs15(vyy6000, vyy500)
new_esEs25(vyy6000, vyy500, ty_Bool) → new_esEs15(vyy6000, vyy500)
new_ltEs6(Right(vyy33000), Right(vyy34000), de, ty_Char) → new_ltEs11(vyy33000, vyy34000)
new_esEs17(Char(vyy6000), Char(vyy500)) → new_primEqNat0(vyy6000, vyy500)
new_esEs7(Left(vyy6000), Left(vyy500), app(ty_Maybe, gc), fa) → new_esEs4(vyy6000, vyy500, gc)
new_esEs24(vyy33001, vyy34001, ty_Char) → new_esEs17(vyy33001, vyy34001)
new_ltEs6(Right(vyy33000), Right(vyy34000), de, app(app(ty_@2, dh), ea)) → new_ltEs5(vyy33000, vyy34000, dh, ea)
new_esEs29(vyy600, vyy50, ty_@0) → new_esEs13(vyy600, vyy50)
new_esEs19(vyy6000, vyy500, ty_Bool) → new_esEs15(vyy6000, vyy500)
new_lt20(vyy33000, vyy34000, app(ty_Ratio, cec)) → new_lt16(vyy33000, vyy34000, cec)
new_lt10(vyy33001, vyy34001, app(ty_Ratio, cbg)) → new_lt16(vyy33001, vyy34001, cbg)
new_esEs19(vyy6000, vyy500, app(ty_[], bch)) → new_esEs16(vyy6000, vyy500, bch)
new_compare10(vyy33000, vyy34000, True, bg, bh) → LT
new_esEs29(vyy600, vyy50, ty_Double) → new_esEs14(vyy600, vyy50)
new_esEs26(vyy6001, vyy501, ty_Float) → new_esEs10(vyy6001, vyy501)
new_esEs26(vyy6001, vyy501, ty_Double) → new_esEs14(vyy6001, vyy501)
new_esEs24(vyy33001, vyy34001, app(ty_Maybe, cbc)) → new_esEs4(vyy33001, vyy34001, cbc)
new_esEs4(Nothing, Just(vyy500), beh) → False
new_esEs4(Just(vyy6000), Nothing, beh) → False
new_esEs4(Just(vyy6000), Just(vyy500), ty_Char) → new_esEs17(vyy6000, vyy500)
new_ltEs20(vyy33001, vyy34001, ty_@0) → new_ltEs8(vyy33001, vyy34001)
new_ltEs7(Just(vyy33000), Just(vyy34000), ty_Integer) → new_ltEs17(vyy33000, vyy34000)
new_esEs25(vyy6000, vyy500, ty_Char) → new_esEs17(vyy6000, vyy500)
new_primCompAux1(vyy33000, vyy34000, vyy98, bf) → new_primCompAux0(vyy98, new_compare18(vyy33000, vyy34000, bf))
new_ltEs18(vyy33002, vyy34002, app(ty_Ratio, cda)) → new_ltEs12(vyy33002, vyy34002, cda)
new_ltEs19(vyy3300, vyy3400, app(ty_Ratio, bhe)) → new_ltEs12(vyy3300, vyy3400, bhe)
new_compare18(vyy33000, vyy34000, ty_Double) → new_compare32(vyy33000, vyy34000)
new_compare18(vyy33000, vyy34000, ty_Float) → new_compare6(vyy33000, vyy34000)
new_ltEs6(Left(vyy33000), Left(vyy34000), ty_Char, cb) → new_ltEs11(vyy33000, vyy34000)
new_compare29(vyy33000, vyy34000, False) → new_compare15(vyy33000, vyy34000, new_ltEs16(vyy33000, vyy34000))
new_primMulNat0(Zero, Zero) → Zero
new_ltEs8(vyy3300, vyy3400) → new_not(new_esEs8(new_compare5(vyy3300, vyy3400), GT))
new_esEs24(vyy33001, vyy34001, ty_@0) → new_esEs13(vyy33001, vyy34001)
new_esEs7(Right(vyy6000), Right(vyy500), gd, ty_Double) → new_esEs14(vyy6000, vyy500)
new_ltEs4(vyy3300, vyy3400, bf) → new_not(new_esEs8(new_compare0(vyy3300, vyy3400, bf), GT))
new_esEs26(vyy6001, vyy501, app(ty_[], chh)) → new_esEs16(vyy6001, vyy501, chh)
new_esEs18(vyy6000, vyy500, app(ty_[], bbd)) → new_esEs16(vyy6000, vyy500, bbd)
new_compare29(vyy33000, vyy34000, True) → EQ
new_esEs4(Just(vyy6000), Just(vyy500), app(app(app(ty_@3, bfg), bfh), bga)) → new_esEs6(vyy6000, vyy500, bfg, bfh, bga)
new_esEs7(Left(vyy6000), Left(vyy500), ty_Double, fa) → new_esEs14(vyy6000, vyy500)
new_ltEs9(GT, LT) → False
new_esEs20(vyy6001, vyy501, app(ty_Maybe, bef)) → new_esEs4(vyy6001, vyy501, bef)
new_lt11(vyy33000, vyy34000, app(app(ty_@2, cac), cad)) → new_lt14(vyy33000, vyy34000, cac, cad)
new_ltEs16(False, True) → True
new_lt11(vyy33000, vyy34000, ty_Float) → new_lt5(vyy33000, vyy34000)
new_esEs7(Right(vyy6000), Right(vyy500), gd, ty_Ordering) → new_esEs8(vyy6000, vyy500)
new_lt20(vyy33000, vyy34000, app(app(app(ty_@3, baa), bab), bac)) → new_lt18(vyy33000, vyy34000, baa, bab, bac)
new_esEs27(vyy6002, vyy502, ty_Integer) → new_esEs12(vyy6002, vyy502)
new_compare18(vyy33000, vyy34000, app(app(app(ty_@3, bgh), bha), bhb)) → new_compare33(vyy33000, vyy34000, bgh, bha, bhb)
new_ltEs16(True, False) → False
new_lt10(vyy33001, vyy34001, ty_@0) → new_lt4(vyy33001, vyy34001)
new_esEs23(vyy33000, vyy34000, app(ty_Maybe, caa)) → new_esEs4(vyy33000, vyy34000, caa)
new_ltEs19(vyy3300, vyy3400, ty_Bool) → new_ltEs16(vyy3300, vyy3400)
new_esEs27(vyy6002, vyy502, app(ty_Ratio, dae)) → new_esEs9(vyy6002, vyy502, dae)
new_compare30(vyy33000, vyy34000) → new_compare28(vyy33000, vyy34000, new_esEs8(vyy33000, vyy34000))
new_esEs23(vyy33000, vyy34000, ty_@0) → new_esEs13(vyy33000, vyy34000)
new_ltEs6(Left(vyy33000), Left(vyy34000), app(app(ty_Either, dc), dd), cb) → new_ltEs6(vyy33000, vyy34000, dc, dd)
new_ltEs6(Left(vyy33000), Left(vyy34000), ty_Float, cb) → new_ltEs10(vyy33000, vyy34000)
new_lt11(vyy33000, vyy34000, app(ty_[], cab)) → new_lt13(vyy33000, vyy34000, cab)
new_esEs24(vyy33001, vyy34001, app(app(ty_@2, cbe), cbf)) → new_esEs5(vyy33001, vyy34001, cbe, cbf)
new_esEs4(Just(vyy6000), Just(vyy500), ty_Float) → new_esEs10(vyy6000, vyy500)
new_esEs7(Right(vyy6000), Right(vyy500), gd, app(ty_Ratio, ge)) → new_esEs9(vyy6000, vyy500, ge)
new_compare18(vyy33000, vyy34000, app(ty_Maybe, bgc)) → new_compare7(vyy33000, vyy34000, bgc)
new_esEs23(vyy33000, vyy34000, ty_Integer) → new_esEs12(vyy33000, vyy34000)
new_esEs25(vyy6000, vyy500, ty_Double) → new_esEs14(vyy6000, vyy500)
new_ltEs9(EQ, GT) → True
new_esEs28(vyy33000, vyy34000, ty_Double) → new_esEs14(vyy33000, vyy34000)
new_esEs12(Integer(vyy6000), Integer(vyy500)) → new_primEqInt(vyy6000, vyy500)
new_ltEs10(vyy3300, vyy3400) → new_not(new_esEs8(new_compare6(vyy3300, vyy3400), GT))
new_lt20(vyy33000, vyy34000, app(ty_[], dbg)) → new_lt13(vyy33000, vyy34000, dbg)
new_compare15(vyy33000, vyy34000, False) → GT
new_esEs26(vyy6001, vyy501, app(ty_Maybe, dad)) → new_esEs4(vyy6001, vyy501, dad)
new_ltEs6(Right(vyy33000), Right(vyy34000), de, ty_Integer) → new_ltEs17(vyy33000, vyy34000)
new_esEs28(vyy33000, vyy34000, ty_Integer) → new_esEs12(vyy33000, vyy34000)
new_lt20(vyy33000, vyy34000, ty_Ordering) → new_lt15(vyy33000, vyy34000)
new_ltEs7(Just(vyy33000), Just(vyy34000), ty_Bool) → new_ltEs16(vyy33000, vyy34000)
new_esEs27(vyy6002, vyy502, ty_Double) → new_esEs14(vyy6002, vyy502)
new_ltEs16(True, True) → True
new_ltEs9(LT, EQ) → True
new_ltEs7(Just(vyy33000), Just(vyy34000), ty_Double) → new_ltEs14(vyy33000, vyy34000)
new_lt11(vyy33000, vyy34000, app(ty_Ratio, cae)) → new_lt16(vyy33000, vyy34000, cae)
new_pePe(False, vyy97) → vyy97
new_lt10(vyy33001, vyy34001, app(ty_[], cbd)) → new_lt13(vyy33001, vyy34001, cbd)
new_esEs7(Right(vyy6000), Left(vyy500), gd, fa) → False
new_esEs7(Left(vyy6000), Right(vyy500), gd, fa) → False
new_esEs15(True, False) → False
new_esEs15(False, True) → False
new_ltEs6(Left(vyy33000), Left(vyy34000), ty_Double, cb) → new_ltEs14(vyy33000, vyy34000)
new_ltEs7(Just(vyy33000), Just(vyy34000), app(ty_Ratio, ceh)) → new_ltEs12(vyy33000, vyy34000, ceh)
new_ltEs19(vyy3300, vyy3400, ty_Float) → new_ltEs10(vyy3300, vyy3400)
new_esEs27(vyy6002, vyy502, app(app(ty_Either, dah), dba)) → new_esEs7(vyy6002, vyy502, dah, dba)
new_lt6(vyy33000, vyy34000) → new_esEs8(new_compare9(vyy33000, vyy34000), LT)
new_esEs28(vyy33000, vyy34000, ty_@0) → new_esEs13(vyy33000, vyy34000)
new_lt11(vyy33000, vyy34000, ty_Double) → new_lt17(vyy33000, vyy34000)
new_esEs26(vyy6001, vyy501, ty_@0) → new_esEs13(vyy6001, vyy501)
new_lt11(vyy33000, vyy34000, ty_Integer) → new_lt6(vyy33000, vyy34000)
new_esEs26(vyy6001, vyy501, ty_Int) → new_esEs11(vyy6001, vyy501)
new_compare15(vyy33000, vyy34000, True) → LT
new_esEs22(vyy6001, vyy501, ty_Int) → new_esEs11(vyy6001, vyy501)
new_esEs22(vyy6001, vyy501, ty_Integer) → new_esEs12(vyy6001, vyy501)
new_lt20(vyy33000, vyy34000, app(app(ty_@2, bg), bh)) → new_lt14(vyy33000, vyy34000, bg, bh)
new_ltEs9(EQ, EQ) → True
new_ltEs20(vyy33001, vyy34001, app(app(app(ty_@3, dce), dcf), dcg)) → new_ltEs15(vyy33001, vyy34001, dce, dcf, dcg)
new_esEs19(vyy6000, vyy500, app(app(ty_Either, bcf), bcg)) → new_esEs7(vyy6000, vyy500, bcf, bcg)
new_lt20(vyy33000, vyy34000, ty_Float) → new_lt5(vyy33000, vyy34000)
new_esEs20(vyy6001, vyy501, app(app(ty_@2, bdf), bdg)) → new_esEs5(vyy6001, vyy501, bdf, bdg)
new_ltEs18(vyy33002, vyy34002, ty_Int) → new_ltEs13(vyy33002, vyy34002)
new_lt20(vyy33000, vyy34000, app(app(ty_Either, hg), hh)) → new_lt7(vyy33000, vyy34000, hg, hh)
new_ltEs18(vyy33002, vyy34002, ty_Char) → new_ltEs11(vyy33002, vyy34002)
new_esEs23(vyy33000, vyy34000, ty_Double) → new_esEs14(vyy33000, vyy34000)
new_esEs7(Right(vyy6000), Right(vyy500), gd, app(app(ty_@2, gf), gg)) → new_esEs5(vyy6000, vyy500, gf, gg)
new_ltEs6(Left(vyy33000), Left(vyy34000), ty_Ordering, cb) → new_ltEs9(vyy33000, vyy34000)
new_primCmpNat0(Zero, Succ(vyy340000)) → LT
new_ltEs20(vyy33001, vyy34001, ty_Double) → new_ltEs14(vyy33001, vyy34001)
new_compare14(vyy33000, vyy34000, False) → GT
new_compare27(Nothing, Just(vyy3400), False, cdg) → LT
new_esEs8(LT, LT) → True
new_esEs18(vyy6000, vyy500, ty_@0) → new_esEs13(vyy6000, vyy500)
new_lt10(vyy33001, vyy34001, ty_Ordering) → new_lt15(vyy33001, vyy34001)
new_esEs19(vyy6000, vyy500, app(ty_Maybe, bdd)) → new_esEs4(vyy6000, vyy500, bdd)
new_esEs7(Left(vyy6000), Left(vyy500), ty_Int, fa) → new_esEs11(vyy6000, vyy500)
new_esEs25(vyy6000, vyy500, ty_Ordering) → new_esEs8(vyy6000, vyy500)
new_esEs18(vyy6000, vyy500, app(ty_Ratio, bag)) → new_esEs9(vyy6000, vyy500, bag)
new_esEs24(vyy33001, vyy34001, app(app(ty_Either, ccc), ccd)) → new_esEs7(vyy33001, vyy34001, ccc, ccd)
new_esEs20(vyy6001, vyy501, app(app(app(ty_@3, bec), bed), bee)) → new_esEs6(vyy6001, vyy501, bec, bed, bee)
new_esEs28(vyy33000, vyy34000, ty_Float) → new_esEs10(vyy33000, vyy34000)
new_compare0([], [], bf) → EQ
new_pePe(True, vyy97) → True
new_primEqNat0(Zero, Zero) → True
new_ltEs19(vyy3300, vyy3400, ty_Int) → new_ltEs13(vyy3300, vyy3400)
new_esEs20(vyy6001, vyy501, ty_Int) → new_esEs11(vyy6001, vyy501)
new_esEs26(vyy6001, vyy501, ty_Char) → new_esEs17(vyy6001, vyy501)
new_esEs7(Left(vyy6000), Left(vyy500), app(app(ty_@2, fb), fc), fa) → new_esEs5(vyy6000, vyy500, fb, fc)
new_ltEs18(vyy33002, vyy34002, ty_Float) → new_ltEs10(vyy33002, vyy34002)
new_primMulNat0(Succ(vyy600000), Succ(vyy50000)) → new_primPlusNat1(new_primMulNat0(vyy600000, Succ(vyy50000)), vyy50000)
new_esEs18(vyy6000, vyy500, ty_Bool) → new_esEs15(vyy6000, vyy500)
new_compare14(vyy33000, vyy34000, True) → LT
new_ltEs19(vyy3300, vyy3400, app(ty_[], bf)) → new_ltEs4(vyy3300, vyy3400, bf)
new_ltEs6(Right(vyy33000), Right(vyy34000), de, app(app(app(ty_@3, ec), ed), ee)) → new_ltEs15(vyy33000, vyy34000, ec, ed, ee)
new_esEs7(Left(vyy6000), Left(vyy500), ty_Ordering, fa) → new_esEs8(vyy6000, vyy500)
new_esEs5(@2(vyy6000, vyy6001), @2(vyy500, vyy501), bca, bcb) → new_asAs(new_esEs19(vyy6000, vyy500, bca), new_esEs20(vyy6001, vyy501, bcb))
new_esEs26(vyy6001, vyy501, ty_Bool) → new_esEs15(vyy6001, vyy501)
new_ltEs9(EQ, LT) → False
new_ltEs13(vyy3300, vyy3400) → new_not(new_esEs8(new_compare16(vyy3300, vyy3400), GT))
new_ltEs7(Just(vyy33000), Just(vyy34000), ty_@0) → new_ltEs8(vyy33000, vyy34000)
new_esEs18(vyy6000, vyy500, app(app(ty_@2, bah), bba)) → new_esEs5(vyy6000, vyy500, bah, bba)
new_esEs7(Right(vyy6000), Right(vyy500), gd, app(app(app(ty_@3, hc), hd), he)) → new_esEs6(vyy6000, vyy500, hc, hd, he)
new_sr(vyy6000, vyy500) → new_primMulInt(vyy6000, vyy500)
new_compare12(vyy33000, vyy34000, True, baa, bab, bac) → LT
new_ltEs7(Just(vyy33000), Just(vyy34000), ty_Int) → new_ltEs13(vyy33000, vyy34000)
new_esEs26(vyy6001, vyy501, ty_Ordering) → new_esEs8(vyy6001, vyy501)
new_esEs8(GT, GT) → True
new_ltEs12(vyy3300, vyy3400, bhe) → new_not(new_esEs8(new_compare31(vyy3300, vyy3400, bhe), GT))
new_esEs18(vyy6000, vyy500, app(app(app(ty_@3, bbe), bbf), bbg)) → new_esEs6(vyy6000, vyy500, bbe, bbf, bbg)
new_ltEs20(vyy33001, vyy34001, app(app(ty_Either, dch), dda)) → new_ltEs6(vyy33001, vyy34001, dch, dda)
new_ltEs7(Just(vyy33000), Just(vyy34000), app(app(app(ty_@3, cfa), cfb), cfc)) → new_ltEs15(vyy33000, vyy34000, cfa, cfb, cfc)
new_esEs7(Right(vyy6000), Right(vyy500), gd, app(app(ty_Either, gh), ha)) → new_esEs7(vyy6000, vyy500, gh, ha)
new_lt20(vyy33000, vyy34000, ty_Double) → new_lt17(vyy33000, vyy34000)
new_esEs26(vyy6001, vyy501, app(app(app(ty_@3, daa), dab), dac)) → new_esEs6(vyy6001, vyy501, daa, dab, dac)
new_esEs8(GT, LT) → False
new_esEs8(LT, GT) → False
new_ltEs20(vyy33001, vyy34001, ty_Bool) → new_ltEs16(vyy33001, vyy34001)
new_ltEs19(vyy3300, vyy3400, app(app(app(ty_@3, bhf), bhg), bhh)) → new_ltEs15(vyy3300, vyy3400, bhf, bhg, bhh)
new_esEs26(vyy6001, vyy501, ty_Integer) → new_esEs12(vyy6001, vyy501)
new_ltEs6(Right(vyy33000), Right(vyy34000), de, ty_Int) → new_ltEs13(vyy33000, vyy34000)
new_lt11(vyy33000, vyy34000, ty_@0) → new_lt4(vyy33000, vyy34000)
new_primEqInt(Neg(Succ(vyy60000)), Neg(Succ(vyy5000))) → new_primEqNat0(vyy60000, vyy5000)
new_esEs7(Right(vyy6000), Right(vyy500), gd, ty_Char) → new_esEs17(vyy6000, vyy500)
new_esEs15(True, True) → True
new_esEs20(vyy6001, vyy501, ty_Ordering) → new_esEs8(vyy6001, vyy501)
new_esEs23(vyy33000, vyy34000, ty_Ordering) → new_esEs8(vyy33000, vyy34000)
new_compare27(Just(vyy3300), Nothing, False, cdg) → GT
new_compare18(vyy33000, vyy34000, ty_Ordering) → new_compare30(vyy33000, vyy34000)
new_compare19(vyy33000, vyy34000, bg, bh) → new_compare24(vyy33000, vyy34000, new_esEs5(vyy33000, vyy34000, bg, bh), bg, bh)
new_esEs28(vyy33000, vyy34000, app(ty_Maybe, bad)) → new_esEs4(vyy33000, vyy34000, bad)
new_ltEs7(Just(vyy33000), Just(vyy34000), app(ty_[], cee)) → new_ltEs4(vyy33000, vyy34000, cee)
new_compare27(Nothing, Nothing, False, cdg) → LT
new_compare18(vyy33000, vyy34000, app(ty_Ratio, bgg)) → new_compare31(vyy33000, vyy34000, bgg)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs24(vyy33001, vyy34001, app(app(app(ty_@3, cbh), cca), ccb)) → new_esEs6(vyy33001, vyy34001, cbh, cca, ccb)
new_esEs18(vyy6000, vyy500, ty_Float) → new_esEs10(vyy6000, vyy500)
new_ltEs6(Right(vyy33000), Right(vyy34000), de, app(ty_Ratio, eb)) → new_ltEs12(vyy33000, vyy34000, eb)
new_esEs19(vyy6000, vyy500, ty_Integer) → new_esEs12(vyy6000, vyy500)
new_primEqInt(Neg(Zero), Neg(Succ(vyy5000))) → False
new_primEqInt(Neg(Succ(vyy60000)), Neg(Zero)) → False
new_ltEs20(vyy33001, vyy34001, app(ty_[], dca)) → new_ltEs4(vyy33001, vyy34001, dca)
new_primCompAux0(vyy103, GT) → GT
new_esEs8(EQ, EQ) → True
new_esEs20(vyy6001, vyy501, ty_Bool) → new_esEs15(vyy6001, vyy501)
new_esEs4(Just(vyy6000), Just(vyy500), ty_@0) → new_esEs13(vyy6000, vyy500)
new_primPlusNat1(Zero, vyy50000) → Succ(vyy50000)
new_compare24(vyy33000, vyy34000, True, bg, bh) → EQ
new_ltEs9(LT, LT) → True
new_esEs29(vyy600, vyy50, app(ty_[], baf)) → new_esEs16(vyy600, vyy50, baf)
new_compare32(Double(vyy33000, vyy33001), Double(vyy34000, vyy34001)) → new_compare16(new_sr(vyy33000, vyy34000), new_sr(vyy33001, vyy34001))
new_esEs26(vyy6001, vyy501, app(app(ty_Either, chf), chg)) → new_esEs7(vyy6001, vyy501, chf, chg)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_lt20(vyy33000, vyy34000, ty_Char) → new_lt8(vyy33000, vyy34000)
new_ltEs20(vyy33001, vyy34001, app(app(ty_@2, dcb), dcc)) → new_ltEs5(vyy33001, vyy34001, dcb, dcc)
new_compare31(:%(vyy33000, vyy33001), :%(vyy34000, vyy34001), ty_Integer) → new_compare9(new_sr0(vyy33000, vyy34001), new_sr0(vyy34000, vyy33001))
new_ltEs18(vyy33002, vyy34002, ty_@0) → new_ltEs8(vyy33002, vyy34002)
new_esEs4(Just(vyy6000), Just(vyy500), app(app(ty_Either, bfd), bfe)) → new_esEs7(vyy6000, vyy500, bfd, bfe)
new_primCmpNat0(Succ(vyy330000), Succ(vyy340000)) → new_primCmpNat0(vyy330000, vyy340000)
new_esEs23(vyy33000, vyy34000, ty_Float) → new_esEs10(vyy33000, vyy34000)
new_ltEs18(vyy33002, vyy34002, app(app(ty_Either, cde), cdf)) → new_ltEs6(vyy33002, vyy34002, cde, cdf)
new_esEs25(vyy6000, vyy500, app(ty_Maybe, chb)) → new_esEs4(vyy6000, vyy500, chb)
new_compare18(vyy33000, vyy34000, ty_@0) → new_compare5(vyy33000, vyy34000)
new_esEs18(vyy6000, vyy500, ty_Double) → new_esEs14(vyy6000, vyy500)
new_esEs4(Just(vyy6000), Just(vyy500), ty_Bool) → new_esEs15(vyy6000, vyy500)
new_primEqInt(Pos(Succ(vyy60000)), Pos(Succ(vyy5000))) → new_primEqNat0(vyy60000, vyy5000)
new_compare10(vyy33000, vyy34000, False, bg, bh) → GT
new_ltEs19(vyy3300, vyy3400, ty_Integer) → new_ltEs17(vyy3300, vyy3400)
new_ltEs5(@2(vyy33000, vyy33001), @2(vyy34000, vyy34001), cea, ceb) → new_pePe(new_lt20(vyy33000, vyy34000, cea), new_asAs(new_esEs28(vyy33000, vyy34000, cea), new_ltEs20(vyy33001, vyy34001, ceb)))
new_esEs4(Just(vyy6000), Just(vyy500), app(app(ty_@2, bfb), bfc)) → new_esEs5(vyy6000, vyy500, bfb, bfc)
new_esEs28(vyy33000, vyy34000, ty_Char) → new_esEs17(vyy33000, vyy34000)
new_ltEs18(vyy33002, vyy34002, app(app(app(ty_@3, cdb), cdc), cdd)) → new_ltEs15(vyy33002, vyy34002, cdb, cdc, cdd)
new_lt10(vyy33001, vyy34001, app(ty_Maybe, cbc)) → new_lt12(vyy33001, vyy34001, cbc)
new_esEs23(vyy33000, vyy34000, ty_Char) → new_esEs17(vyy33000, vyy34000)
new_compare17(vyy33000, vyy34000, hg, hh) → new_compare25(vyy33000, vyy34000, new_esEs7(vyy33000, vyy34000, hg, hh), hg, hh)
new_ltEs7(Just(vyy33000), Just(vyy34000), ty_Float) → new_ltEs10(vyy33000, vyy34000)
new_ltEs7(Just(vyy33000), Just(vyy34000), app(app(ty_Either, cfd), cfe)) → new_ltEs6(vyy33000, vyy34000, cfd, cfe)
new_ltEs7(Nothing, Just(vyy34000), cdh) → True
new_primEqNat0(Succ(vyy60000), Succ(vyy5000)) → new_primEqNat0(vyy60000, vyy5000)
new_esEs27(vyy6002, vyy502, ty_Ordering) → new_esEs8(vyy6002, vyy502)
new_esEs7(Right(vyy6000), Right(vyy500), gd, app(ty_[], hb)) → new_esEs16(vyy6000, vyy500, hb)
new_esEs19(vyy6000, vyy500, app(app(app(ty_@3, bda), bdb), bdc)) → new_esEs6(vyy6000, vyy500, bda, bdb, bdc)
new_esEs20(vyy6001, vyy501, ty_Double) → new_esEs14(vyy6001, vyy501)
new_ltEs19(vyy3300, vyy3400, ty_Double) → new_ltEs14(vyy3300, vyy3400)
new_compare25(vyy33000, vyy34000, False, hg, hh) → new_compare11(vyy33000, vyy34000, new_ltEs6(vyy33000, vyy34000, hg, hh), hg, hh)
new_esEs7(Right(vyy6000), Right(vyy500), gd, ty_Float) → new_esEs10(vyy6000, vyy500)
new_esEs20(vyy6001, vyy501, ty_Float) → new_esEs10(vyy6001, vyy501)
new_esEs28(vyy33000, vyy34000, ty_Int) → new_esEs11(vyy33000, vyy34000)
new_lt20(vyy33000, vyy34000, ty_@0) → new_lt4(vyy33000, vyy34000)
new_primCmpInt(Neg(Succ(vyy330000)), Neg(vyy34000)) → new_primCmpNat0(vyy34000, Succ(vyy330000))
new_ltEs18(vyy33002, vyy34002, app(app(ty_@2, ccg), cch)) → new_ltEs5(vyy33002, vyy34002, ccg, cch)
new_esEs24(vyy33001, vyy34001, ty_Ordering) → new_esEs8(vyy33001, vyy34001)
new_esEs18(vyy6000, vyy500, ty_Char) → new_esEs17(vyy6000, vyy500)
new_lt19(vyy33000, vyy34000) → new_esEs8(new_compare34(vyy33000, vyy34000), LT)
new_esEs23(vyy33000, vyy34000, ty_Bool) → new_esEs15(vyy33000, vyy34000)
new_ltEs6(Left(vyy33000), Right(vyy34000), de, cb) → True
new_lt11(vyy33000, vyy34000, app(app(app(ty_@3, caf), cag), cah)) → new_lt18(vyy33000, vyy34000, caf, cag, cah)
new_esEs10(Float(vyy6000, vyy6001), Float(vyy500, vyy501)) → new_esEs11(new_sr(vyy6000, vyy500), new_sr(vyy6001, vyy501))
new_esEs21(vyy6000, vyy500, ty_Int) → new_esEs11(vyy6000, vyy500)
new_ltEs6(Right(vyy33000), Left(vyy34000), de, cb) → False
new_esEs28(vyy33000, vyy34000, ty_Ordering) → new_esEs8(vyy33000, vyy34000)
new_esEs8(EQ, LT) → False
new_esEs8(LT, EQ) → False
new_primEqInt(Pos(Succ(vyy60000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(vyy5000))) → False
new_lt10(vyy33001, vyy34001, app(app(ty_Either, ccc), ccd)) → new_lt7(vyy33001, vyy34001, ccc, ccd)
new_compare13(vyy83, vyy84, True, bae) → LT
new_primPlusNat0(Zero, Succ(vyy500000)) → Succ(vyy500000)
new_primPlusNat0(Succ(vyy9900), Zero) → Succ(vyy9900)
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(vyy330000), Zero) → GT
new_ltEs19(vyy3300, vyy3400, ty_Ordering) → new_ltEs9(vyy3300, vyy3400)
new_esEs23(vyy33000, vyy34000, app(app(ty_@2, cac), cad)) → new_esEs5(vyy33000, vyy34000, cac, cad)
new_ltEs6(Left(vyy33000), Left(vyy34000), app(app(ty_@2, cd), ce), cb) → new_ltEs5(vyy33000, vyy34000, cd, ce)
new_esEs19(vyy6000, vyy500, ty_@0) → new_esEs13(vyy6000, vyy500)
new_primCmpInt(Neg(Zero), Pos(Succ(vyy340000))) → LT
new_compare11(vyy33000, vyy34000, True, hg, hh) → LT
new_ltEs20(vyy33001, vyy34001, ty_Integer) → new_ltEs17(vyy33001, vyy34001)
new_sr0(Integer(vyy340000), Integer(vyy330010)) → Integer(new_primMulInt(vyy340000, vyy330010))
new_primEqInt(Pos(Succ(vyy60000)), Neg(vyy500)) → False
new_primEqInt(Neg(Succ(vyy60000)), Pos(vyy500)) → False
new_esEs6(@3(vyy6000, vyy6001, vyy6002), @3(vyy500, vyy501, vyy502), cff, cfg, cfh) → new_asAs(new_esEs25(vyy6000, vyy500, cff), new_asAs(new_esEs26(vyy6001, vyy501, cfg), new_esEs27(vyy6002, vyy502, cfh)))
new_esEs25(vyy6000, vyy500, ty_@0) → new_esEs13(vyy6000, vyy500)
new_esEs29(vyy600, vyy50, app(app(ty_@2, bca), bcb)) → new_esEs5(vyy600, vyy50, bca, bcb)
new_esEs16(:(vyy6000, vyy6001), :(vyy500, vyy501), baf) → new_asAs(new_esEs18(vyy6000, vyy500, baf), new_esEs16(vyy6001, vyy501, baf))
new_ltEs6(Left(vyy33000), Left(vyy34000), ty_Int, cb) → new_ltEs13(vyy33000, vyy34000)
new_lt7(vyy33000, vyy34000, hg, hh) → new_esEs8(new_compare17(vyy33000, vyy34000, hg, hh), LT)
new_ltEs7(Just(vyy33000), Just(vyy34000), app(app(ty_@2, cef), ceg)) → new_ltEs5(vyy33000, vyy34000, cef, ceg)
new_primEqInt(Neg(Zero), Pos(Succ(vyy5000))) → False
new_primEqInt(Pos(Zero), Neg(Succ(vyy5000))) → False
new_esEs13(@0, @0) → True
new_lt11(vyy33000, vyy34000, app(ty_Maybe, caa)) → new_lt12(vyy33000, vyy34000, caa)
new_primCmpInt(Pos(Zero), Pos(Succ(vyy340000))) → new_primCmpNat0(Zero, Succ(vyy340000))
new_esEs28(vyy33000, vyy34000, app(app(ty_Either, hg), hh)) → new_esEs7(vyy33000, vyy34000, hg, hh)
new_esEs7(Right(vyy6000), Right(vyy500), gd, ty_@0) → new_esEs13(vyy6000, vyy500)
new_esEs9(:%(vyy6000, vyy6001), :%(vyy500, vyy501), beg) → new_asAs(new_esEs21(vyy6000, vyy500, beg), new_esEs22(vyy6001, vyy501, beg))
new_esEs7(Right(vyy6000), Right(vyy500), gd, app(ty_Maybe, hf)) → new_esEs4(vyy6000, vyy500, hf)
new_ltEs20(vyy33001, vyy34001, ty_Int) → new_ltEs13(vyy33001, vyy34001)
new_ltEs6(Right(vyy33000), Right(vyy34000), de, app(ty_Maybe, df)) → new_ltEs7(vyy33000, vyy34000, df)
new_lt20(vyy33000, vyy34000, ty_Integer) → new_lt6(vyy33000, vyy34000)
new_esEs27(vyy6002, vyy502, ty_Float) → new_esEs10(vyy6002, vyy502)
new_esEs4(Just(vyy6000), Just(vyy500), ty_Integer) → new_esEs12(vyy6000, vyy500)
new_esEs8(GT, EQ) → False
new_esEs8(EQ, GT) → False
new_esEs4(Just(vyy6000), Just(vyy500), app(ty_Ratio, bfa)) → new_esEs9(vyy6000, vyy500, bfa)
new_lt11(vyy33000, vyy34000, app(app(ty_Either, cba), cbb)) → new_lt7(vyy33000, vyy34000, cba, cbb)
new_esEs26(vyy6001, vyy501, app(app(ty_@2, chd), che)) → new_esEs5(vyy6001, vyy501, chd, che)
new_primCompAux0(vyy103, LT) → LT
new_ltEs6(Left(vyy33000), Left(vyy34000), ty_Integer, cb) → new_ltEs17(vyy33000, vyy34000)
new_lt20(vyy33000, vyy34000, ty_Bool) → new_lt19(vyy33000, vyy34000)
new_lt10(vyy33001, vyy34001, app(app(ty_@2, cbe), cbf)) → new_lt14(vyy33001, vyy34001, cbe, cbf)
new_esEs11(vyy600, vyy50) → new_primEqInt(vyy600, vyy50)
new_not(False) → True
new_ltEs15(@3(vyy33000, vyy33001, vyy33002), @3(vyy34000, vyy34001, vyy34002), bhf, bhg, bhh) → new_pePe(new_lt11(vyy33000, vyy34000, bhf), new_asAs(new_esEs23(vyy33000, vyy34000, bhf), new_pePe(new_lt10(vyy33001, vyy34001, bhg), new_asAs(new_esEs24(vyy33001, vyy34001, bhg), new_ltEs18(vyy33002, vyy34002, bhh)))))
new_compare18(vyy33000, vyy34000, app(app(ty_@2, bge), bgf)) → new_compare19(vyy33000, vyy34000, bge, bgf)
new_esEs14(Double(vyy6000, vyy6001), Double(vyy500, vyy501)) → new_esEs11(new_sr(vyy6000, vyy500), new_sr(vyy6001, vyy501))
new_esEs28(vyy33000, vyy34000, app(ty_[], dbg)) → new_esEs16(vyy33000, vyy34000, dbg)
new_primCmpInt(Pos(Succ(vyy330000)), Pos(vyy34000)) → new_primCmpNat0(Succ(vyy330000), vyy34000)
new_esEs29(vyy600, vyy50, ty_Integer) → new_esEs12(vyy600, vyy50)
new_compare12(vyy33000, vyy34000, False, baa, bab, bac) → GT
new_esEs19(vyy6000, vyy500, ty_Int) → new_esEs11(vyy6000, vyy500)
new_esEs7(Left(vyy6000), Left(vyy500), ty_Integer, fa) → new_esEs12(vyy6000, vyy500)
new_esEs19(vyy6000, vyy500, ty_Char) → new_esEs17(vyy6000, vyy500)
new_ltEs9(LT, GT) → True
new_ltEs20(vyy33001, vyy34001, ty_Char) → new_ltEs11(vyy33001, vyy34001)
new_ltEs14(vyy3300, vyy3400) → new_not(new_esEs8(new_compare32(vyy3300, vyy3400), GT))
new_esEs25(vyy6000, vyy500, ty_Float) → new_esEs10(vyy6000, vyy500)
new_lt11(vyy33000, vyy34000, ty_Char) → new_lt8(vyy33000, vyy34000)
new_esEs24(vyy33001, vyy34001, ty_Integer) → new_esEs12(vyy33001, vyy34001)
new_esEs28(vyy33000, vyy34000, app(app(ty_@2, bg), bh)) → new_esEs5(vyy33000, vyy34000, bg, bh)
new_compare0(:(vyy33000, vyy33001), [], bf) → GT
new_ltEs18(vyy33002, vyy34002, app(ty_Maybe, cce)) → new_ltEs7(vyy33002, vyy34002, cce)
new_esEs18(vyy6000, vyy500, app(ty_Maybe, bbh)) → new_esEs4(vyy6000, vyy500, bbh)
new_compare28(vyy33000, vyy34000, True) → EQ
new_esEs7(Left(vyy6000), Left(vyy500), app(ty_Ratio, eh), fa) → new_esEs9(vyy6000, vyy500, eh)
new_compare18(vyy33000, vyy34000, ty_Char) → new_compare8(vyy33000, vyy34000)
new_compare6(Float(vyy33000, vyy33001), Float(vyy34000, vyy34001)) → new_compare16(new_sr(vyy33000, vyy34000), new_sr(vyy33001, vyy34001))
new_esEs27(vyy6002, vyy502, ty_Int) → new_esEs11(vyy6002, vyy502)
new_compare11(vyy33000, vyy34000, False, hg, hh) → GT
new_lt11(vyy33000, vyy34000, ty_Bool) → new_lt19(vyy33000, vyy34000)
new_compare18(vyy33000, vyy34000, app(ty_[], bgd)) → new_compare0(vyy33000, vyy34000, bgd)
new_ltEs7(Just(vyy33000), Just(vyy34000), app(ty_Maybe, ced)) → new_ltEs7(vyy33000, vyy34000, ced)
new_primCmpInt(Pos(Succ(vyy330000)), Neg(vyy34000)) → GT
new_esEs18(vyy6000, vyy500, app(app(ty_Either, bbb), bbc)) → new_esEs7(vyy6000, vyy500, bbb, bbc)
new_lt15(vyy33000, vyy34000) → new_esEs8(new_compare30(vyy33000, vyy34000), LT)
new_primMulInt(Pos(vyy60000), Pos(vyy5000)) → Pos(new_primMulNat0(vyy60000, vyy5000))
new_ltEs6(Right(vyy33000), Right(vyy34000), de, ty_@0) → new_ltEs8(vyy33000, vyy34000)
new_compare24(vyy33000, vyy34000, False, bg, bh) → new_compare10(vyy33000, vyy34000, new_ltEs5(vyy33000, vyy34000, bg, bh), bg, bh)
new_esEs27(vyy6002, vyy502, ty_Char) → new_esEs17(vyy6002, vyy502)
new_ltEs18(vyy33002, vyy34002, ty_Integer) → new_ltEs17(vyy33002, vyy34002)
new_primMulInt(Neg(vyy60000), Neg(vyy5000)) → Pos(new_primMulNat0(vyy60000, vyy5000))
new_esEs24(vyy33001, vyy34001, ty_Bool) → new_esEs15(vyy33001, vyy34001)
new_esEs28(vyy33000, vyy34000, app(ty_Ratio, cec)) → new_esEs9(vyy33000, vyy34000, cec)
new_primEqNat0(Zero, Succ(vyy5000)) → False
new_primEqNat0(Succ(vyy60000), Zero) → False
new_esEs7(Left(vyy6000), Left(vyy500), app(ty_[], fg), fa) → new_esEs16(vyy6000, vyy500, fg)
new_ltEs7(Just(vyy33000), Just(vyy34000), ty_Ordering) → new_ltEs9(vyy33000, vyy34000)
new_primPlusNat0(Zero, Zero) → Zero
new_ltEs6(Right(vyy33000), Right(vyy34000), de, ty_Float) → new_ltEs10(vyy33000, vyy34000)
new_compare25(vyy33000, vyy34000, True, hg, hh) → EQ
new_lt13(vyy33000, vyy34000, dbg) → new_esEs8(new_compare0(vyy33000, vyy34000, dbg), LT)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs28(vyy33000, vyy34000, app(app(app(ty_@3, baa), bab), bac)) → new_esEs6(vyy33000, vyy34000, baa, bab, bac)
new_esEs4(Nothing, Nothing, beh) → True
new_esEs7(Left(vyy6000), Left(vyy500), ty_Char, fa) → new_esEs17(vyy6000, vyy500)
new_esEs27(vyy6002, vyy502, app(app(app(ty_@3, dbc), dbd), dbe)) → new_esEs6(vyy6002, vyy502, dbc, dbd, dbe)
new_lt10(vyy33001, vyy34001, ty_Int) → new_lt9(vyy33001, vyy34001)
new_esEs27(vyy6002, vyy502, app(app(ty_@2, daf), dag)) → new_esEs5(vyy6002, vyy502, daf, dag)
new_esEs16(:(vyy6000, vyy6001), [], baf) → False
new_esEs16([], :(vyy500, vyy501), baf) → False
new_ltEs9(GT, GT) → True
new_esEs23(vyy33000, vyy34000, ty_Int) → new_esEs11(vyy33000, vyy34000)
new_ltEs7(Nothing, Nothing, cdh) → True
new_esEs27(vyy6002, vyy502, app(ty_Maybe, dbf)) → new_esEs4(vyy6002, vyy502, dbf)
new_primPlusNat1(Succ(vyy990), vyy50000) → Succ(Succ(new_primPlusNat0(vyy990, vyy50000)))
new_compare13(vyy83, vyy84, False, bae) → GT
new_lt16(vyy33000, vyy34000, cec) → new_esEs8(new_compare31(vyy33000, vyy34000, cec), LT)
new_primCmpInt(Neg(Zero), Neg(Succ(vyy340000))) → new_primCmpNat0(Succ(vyy340000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(vyy340000))) → GT
new_ltEs6(Left(vyy33000), Left(vyy34000), app(ty_Ratio, cf), cb) → new_ltEs12(vyy33000, vyy34000, cf)
new_compare0(:(vyy33000, vyy33001), :(vyy34000, vyy34001), bf) → new_primCompAux1(vyy33000, vyy34000, new_compare0(vyy33001, vyy34001, bf), bf)
new_compare28(vyy33000, vyy34000, False) → new_compare14(vyy33000, vyy34000, new_ltEs9(vyy33000, vyy34000))
new_lt14(vyy33000, vyy34000, bg, bh) → new_esEs8(new_compare19(vyy33000, vyy34000, bg, bh), LT)
new_esEs4(Just(vyy6000), Just(vyy500), app(ty_[], bff)) → new_esEs16(vyy6000, vyy500, bff)
new_esEs19(vyy6000, vyy500, ty_Double) → new_esEs14(vyy6000, vyy500)
new_compare7(vyy33000, vyy34000, bad) → new_compare27(vyy33000, vyy34000, new_esEs4(vyy33000, vyy34000, bad), bad)
new_esEs24(vyy33001, vyy34001, ty_Int) → new_esEs11(vyy33001, vyy34001)
new_lt11(vyy33000, vyy34000, ty_Ordering) → new_lt15(vyy33000, vyy34000)
new_esEs18(vyy6000, vyy500, ty_Integer) → new_esEs12(vyy6000, vyy500)
new_esEs20(vyy6001, vyy501, app(app(ty_Either, bdh), bea)) → new_esEs7(vyy6001, vyy501, bdh, bea)
new_ltEs17(vyy3300, vyy3400) → new_not(new_esEs8(new_compare9(vyy3300, vyy3400), GT))
new_esEs29(vyy600, vyy50, app(ty_Ratio, beg)) → new_esEs9(vyy600, vyy50, beg)
new_ltEs6(Right(vyy33000), Right(vyy34000), de, app(app(ty_Either, ef), eg)) → new_ltEs6(vyy33000, vyy34000, ef, eg)
new_esEs19(vyy6000, vyy500, app(app(ty_@2, bcd), bce)) → new_esEs5(vyy6000, vyy500, bcd, bce)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_lt9(vyy33000, vyy34000) → new_esEs8(new_compare16(vyy33000, vyy34000), LT)
new_esEs4(Just(vyy6000), Just(vyy500), ty_Double) → new_esEs14(vyy6000, vyy500)
new_esEs20(vyy6001, vyy501, app(ty_[], beb)) → new_esEs16(vyy6001, vyy501, beb)
new_esEs29(vyy600, vyy50, ty_Bool) → new_esEs15(vyy600, vyy50)
new_compare9(Integer(vyy33000), Integer(vyy34000)) → new_primCmpInt(vyy33000, vyy34000)
new_asAs(False, vyy90) → False
new_esEs25(vyy6000, vyy500, app(ty_Ratio, cga)) → new_esEs9(vyy6000, vyy500, cga)
new_ltEs6(Left(vyy33000), Left(vyy34000), app(ty_Maybe, ca), cb) → new_ltEs7(vyy33000, vyy34000, ca)
new_esEs19(vyy6000, vyy500, ty_Float) → new_esEs10(vyy6000, vyy500)
new_compare34(vyy33000, vyy34000) → new_compare29(vyy33000, vyy34000, new_esEs15(vyy33000, vyy34000))
new_primMulInt(Pos(vyy60000), Neg(vyy5000)) → Neg(new_primMulNat0(vyy60000, vyy5000))
new_primMulInt(Neg(vyy60000), Pos(vyy5000)) → Neg(new_primMulNat0(vyy60000, vyy5000))
new_ltEs19(vyy3300, vyy3400, ty_Char) → new_ltEs11(vyy3300, vyy3400)
new_compare16(vyy3300, vyy3400) → new_primCmpInt(vyy3300, vyy3400)
new_primMulNat0(Zero, Succ(vyy50000)) → Zero
new_primMulNat0(Succ(vyy600000), Zero) → Zero
new_esEs7(Left(vyy6000), Left(vyy500), ty_Float, fa) → new_esEs10(vyy6000, vyy500)
new_esEs23(vyy33000, vyy34000, app(app(app(ty_@3, caf), cag), cah)) → new_esEs6(vyy33000, vyy34000, caf, cag, cah)
new_ltEs18(vyy33002, vyy34002, app(ty_[], ccf)) → new_ltEs4(vyy33002, vyy34002, ccf)
new_esEs24(vyy33001, vyy34001, ty_Float) → new_esEs10(vyy33001, vyy34001)
new_esEs29(vyy600, vyy50, ty_Int) → new_esEs11(vyy600, vyy50)
new_compare31(:%(vyy33000, vyy33001), :%(vyy34000, vyy34001), ty_Int) → new_compare16(new_sr(vyy33000, vyy34001), new_sr(vyy34000, vyy33001))
new_esEs24(vyy33001, vyy34001, app(ty_[], cbd)) → new_esEs16(vyy33001, vyy34001, cbd)
new_esEs29(vyy600, vyy50, ty_Char) → new_esEs17(vyy600, vyy50)
new_ltEs20(vyy33001, vyy34001, ty_Ordering) → new_ltEs9(vyy33001, vyy34001)
new_esEs26(vyy6001, vyy501, app(ty_Ratio, chc)) → new_esEs9(vyy6001, vyy501, chc)
new_esEs27(vyy6002, vyy502, ty_@0) → new_esEs13(vyy6002, vyy502)
new_esEs29(vyy600, vyy50, ty_Float) → new_esEs10(vyy600, vyy50)
new_esEs18(vyy6000, vyy500, ty_Ordering) → new_esEs8(vyy6000, vyy500)
new_ltEs11(vyy3300, vyy3400) → new_not(new_esEs8(new_compare8(vyy3300, vyy3400), GT))
new_ltEs20(vyy33001, vyy34001, app(ty_Ratio, dcd)) → new_ltEs12(vyy33001, vyy34001, dcd)
new_esEs25(vyy6000, vyy500, app(app(app(ty_@3, cgg), cgh), cha)) → new_esEs6(vyy6000, vyy500, cgg, cgh, cha)
new_ltEs9(GT, EQ) → False
new_esEs7(Left(vyy6000), Left(vyy500), app(app(app(ty_@3, fh), ga), gb), fa) → new_esEs6(vyy6000, vyy500, fh, ga, gb)
new_esEs20(vyy6001, vyy501, ty_Integer) → new_esEs12(vyy6001, vyy501)
new_lt10(vyy33001, vyy34001, ty_Float) → new_lt5(vyy33001, vyy34001)
new_ltEs19(vyy3300, vyy3400, ty_@0) → new_ltEs8(vyy3300, vyy3400)
new_esEs28(vyy33000, vyy34000, ty_Bool) → new_esEs15(vyy33000, vyy34000)
new_lt5(vyy33000, vyy34000) → new_esEs8(new_compare6(vyy33000, vyy34000), LT)
new_esEs18(vyy6000, vyy500, ty_Int) → new_esEs11(vyy6000, vyy500)
new_compare18(vyy33000, vyy34000, ty_Bool) → new_compare34(vyy33000, vyy34000)
new_ltEs20(vyy33001, vyy34001, ty_Float) → new_ltEs10(vyy33001, vyy34001)
new_esEs7(Right(vyy6000), Right(vyy500), gd, ty_Int) → new_esEs11(vyy6000, vyy500)
new_ltEs7(Just(vyy33000), Nothing, cdh) → False
new_esEs4(Just(vyy6000), Just(vyy500), ty_Int) → new_esEs11(vyy6000, vyy500)
new_esEs7(Right(vyy6000), Right(vyy500), gd, ty_Integer) → new_esEs12(vyy6000, vyy500)
new_ltEs7(Just(vyy33000), Just(vyy34000), ty_Char) → new_ltEs11(vyy33000, vyy34000)
new_esEs16([], [], baf) → True
new_esEs20(vyy6001, vyy501, app(ty_Ratio, bde)) → new_esEs9(vyy6001, vyy501, bde)
new_lt11(vyy33000, vyy34000, ty_Int) → new_lt9(vyy33000, vyy34000)
new_esEs25(vyy6000, vyy500, app(app(ty_@2, cgb), cgc)) → new_esEs5(vyy6000, vyy500, cgb, cgc)
new_lt10(vyy33001, vyy34001, ty_Bool) → new_lt19(vyy33001, vyy34001)
new_ltEs6(Left(vyy33000), Left(vyy34000), app(ty_[], cc), cb) → new_ltEs4(vyy33000, vyy34000, cc)
new_ltEs18(vyy33002, vyy34002, ty_Double) → new_ltEs14(vyy33002, vyy34002)
new_ltEs18(vyy33002, vyy34002, ty_Ordering) → new_ltEs9(vyy33002, vyy34002)
new_ltEs19(vyy3300, vyy3400, app(ty_Maybe, cdh)) → new_ltEs7(vyy3300, vyy3400, cdh)
new_esEs23(vyy33000, vyy34000, app(ty_Ratio, cae)) → new_esEs9(vyy33000, vyy34000, cae)
new_ltEs18(vyy33002, vyy34002, ty_Bool) → new_ltEs16(vyy33002, vyy34002)
new_esEs29(vyy600, vyy50, app(app(app(ty_@3, cff), cfg), cfh)) → new_esEs6(vyy600, vyy50, cff, cfg, cfh)
new_lt18(vyy33000, vyy34000, baa, bab, bac) → new_esEs8(new_compare33(vyy33000, vyy34000, baa, bab, bac), LT)
new_lt10(vyy33001, vyy34001, app(app(app(ty_@3, cbh), cca), ccb)) → new_lt18(vyy33001, vyy34001, cbh, cca, ccb)
new_esEs29(vyy600, vyy50, app(app(ty_Either, gd), fa)) → new_esEs7(vyy600, vyy50, gd, fa)
new_compare27(vyy330, vyy340, True, cdg) → EQ
new_esEs19(vyy6000, vyy500, app(ty_Ratio, bcc)) → new_esEs9(vyy6000, vyy500, bcc)
new_ltEs6(Left(vyy33000), Left(vyy34000), ty_@0, cb) → new_ltEs8(vyy33000, vyy34000)
new_esEs7(Left(vyy6000), Left(vyy500), ty_Bool, fa) → new_esEs15(vyy6000, vyy500)
new_ltEs6(Right(vyy33000), Right(vyy34000), de, ty_Double) → new_ltEs14(vyy33000, vyy34000)
new_compare18(vyy33000, vyy34000, app(app(ty_Either, bhc), bhd)) → new_compare17(vyy33000, vyy34000, bhc, bhd)
new_ltEs6(Right(vyy33000), Right(vyy34000), de, app(ty_[], dg)) → new_ltEs4(vyy33000, vyy34000, dg)
new_esEs20(vyy6001, vyy501, ty_Char) → new_esEs17(vyy6001, vyy501)
new_primPlusNat0(Succ(vyy9900), Succ(vyy500000)) → Succ(Succ(new_primPlusNat0(vyy9900, vyy500000)))
new_compare26(vyy33000, vyy34000, False, baa, bab, bac) → new_compare12(vyy33000, vyy34000, new_ltEs15(vyy33000, vyy34000, baa, bab, bac), baa, bab, bac)
new_compare26(vyy33000, vyy34000, True, baa, bab, bac) → EQ
new_esEs23(vyy33000, vyy34000, app(ty_[], cab)) → new_esEs16(vyy33000, vyy34000, cab)
new_compare0([], :(vyy34000, vyy34001), bf) → LT
new_ltEs6(Right(vyy33000), Right(vyy34000), de, ty_Bool) → new_ltEs16(vyy33000, vyy34000)
new_compare27(Just(vyy3300), Just(vyy3400), False, cdg) → new_compare13(vyy3300, vyy3400, new_ltEs19(vyy3300, vyy3400, cdg), cdg)
new_ltEs6(Right(vyy33000), Right(vyy34000), de, ty_Ordering) → new_ltEs9(vyy33000, vyy34000)
new_lt10(vyy33001, vyy34001, ty_Double) → new_lt17(vyy33001, vyy34001)
new_asAs(True, vyy90) → vyy90
new_esEs25(vyy6000, vyy500, ty_Int) → new_esEs11(vyy6000, vyy500)
new_lt8(vyy33000, vyy34000) → new_esEs8(new_compare8(vyy33000, vyy34000), LT)
new_ltEs16(False, False) → True
new_compare18(vyy33000, vyy34000, ty_Integer) → new_compare9(vyy33000, vyy34000)
new_esEs27(vyy6002, vyy502, ty_Bool) → new_esEs15(vyy6002, vyy502)
new_esEs7(Left(vyy6000), Left(vyy500), ty_@0, fa) → new_esEs13(vyy6000, vyy500)
new_esEs19(vyy6000, vyy500, ty_Ordering) → new_esEs8(vyy6000, vyy500)
new_lt20(vyy33000, vyy34000, ty_Int) → new_lt9(vyy33000, vyy34000)
new_ltEs6(Left(vyy33000), Left(vyy34000), ty_Bool, cb) → new_ltEs16(vyy33000, vyy34000)
new_esEs21(vyy6000, vyy500, ty_Integer) → new_esEs12(vyy6000, vyy500)
new_lt17(vyy33000, vyy34000) → new_esEs8(new_compare32(vyy33000, vyy34000), LT)
new_lt12(vyy33000, vyy34000, bad) → new_esEs8(new_compare7(vyy33000, vyy34000, bad), LT)
new_esEs29(vyy600, vyy50, app(ty_Maybe, beh)) → new_esEs4(vyy600, vyy50, beh)
new_compare18(vyy33000, vyy34000, ty_Int) → new_compare16(vyy33000, vyy34000)
new_ltEs20(vyy33001, vyy34001, app(ty_Maybe, dbh)) → new_ltEs7(vyy33001, vyy34001, dbh)
new_esEs25(vyy6000, vyy500, app(app(ty_Either, cgd), cge)) → new_esEs7(vyy6000, vyy500, cgd, cge)
new_compare8(Char(vyy33000), Char(vyy34000)) → new_primCmpNat0(vyy33000, vyy34000)
new_compare33(vyy33000, vyy34000, baa, bab, bac) → new_compare26(vyy33000, vyy34000, new_esEs6(vyy33000, vyy34000, baa, bab, bac), baa, bab, bac)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs24(vyy33001, vyy34001, app(ty_Ratio, cbg)) → new_esEs9(vyy33001, vyy34001, cbg)
new_primCompAux0(vyy103, EQ) → vyy103
new_esEs20(vyy6001, vyy501, ty_@0) → new_esEs13(vyy6001, vyy501)
new_esEs29(vyy600, vyy50, ty_Ordering) → new_esEs8(vyy600, vyy50)
new_ltEs19(vyy3300, vyy3400, app(app(ty_Either, de), cb)) → new_ltEs6(vyy3300, vyy3400, de, cb)
new_lt20(vyy33000, vyy34000, app(ty_Maybe, bad)) → new_lt12(vyy33000, vyy34000, bad)
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primCmpInt(Neg(Succ(vyy330000)), Pos(vyy34000)) → LT
new_esEs24(vyy33001, vyy34001, ty_Double) → new_esEs14(vyy33001, vyy34001)
new_not(True) → False
new_esEs15(False, False) → True
The set Q consists of the following terms:
new_ltEs7(Just(x0), Just(x1), ty_Ordering)
new_esEs13(@0, @0)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_primPlusNat0(Succ(x0), Zero)
new_esEs23(x0, x1, ty_@0)
new_ltEs16(True, True)
new_ltEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare18(x0, x1, ty_Bool)
new_esEs28(x0, x1, ty_Char)
new_ltEs6(Right(x0), Right(x1), x2, ty_Double)
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_primEqNat0(Zero, Succ(x0))
new_lt5(x0, x1)
new_lt20(x0, x1, ty_Integer)
new_esEs25(x0, x1, ty_Integer)
new_compare25(x0, x1, False, x2, x3)
new_esEs25(x0, x1, ty_Bool)
new_esEs24(x0, x1, ty_Float)
new_primCompAux1(x0, x1, x2, x3)
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_esEs7(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs25(x0, x1, ty_Char)
new_ltEs20(x0, x1, ty_Bool)
new_compare0([], [], x0)
new_lt10(x0, x1, app(ty_[], x2))
new_ltEs18(x0, x1, ty_Bool)
new_esEs22(x0, x1, ty_Integer)
new_asAs(True, x0)
new_esEs26(x0, x1, ty_Float)
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_lt10(x0, x1, ty_Char)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs6(Right(x0), Right(x1), x2, ty_Int)
new_lt20(x0, x1, ty_Ordering)
new_esEs18(x0, x1, ty_Double)
new_lt10(x0, x1, ty_Float)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_ltEs6(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs4(Just(x0), Just(x1), app(ty_[], x2))
new_esEs27(x0, x1, ty_Bool)
new_esEs15(True, True)
new_esEs29(x0, x1, ty_Double)
new_esEs25(x0, x1, ty_Float)
new_esEs27(x0, x1, ty_Float)
new_ltEs6(Right(x0), Right(x1), x2, ty_Float)
new_lt20(x0, x1, ty_Double)
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, ty_Integer)
new_esEs25(x0, x1, ty_@0)
new_ltEs18(x0, x1, app(ty_Maybe, x2))
new_esEs7(Right(x0), Right(x1), x2, ty_@0)
new_ltEs7(Just(x0), Just(x1), app(ty_[], x2))
new_esEs24(x0, x1, ty_Double)
new_compare18(x0, x1, ty_Int)
new_lt11(x0, x1, ty_Bool)
new_primMulNat0(Zero, Succ(x0))
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_esEs28(x0, x1, ty_Ordering)
new_esEs15(False, False)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs26(x0, x1, app(ty_[], x2))
new_esEs18(x0, x1, ty_Float)
new_ltEs6(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs8(GT, GT)
new_esEs7(Right(x0), Right(x1), x2, ty_Ordering)
new_sr0(Integer(x0), Integer(x1))
new_esEs24(x0, x1, ty_Integer)
new_esEs20(x0, x1, ty_Integer)
new_esEs18(x0, x1, app(ty_[], x2))
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs6(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs4(Just(x0), Just(x1), ty_Ordering)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_lt10(x0, x1, ty_Double)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_compare14(x0, x1, False)
new_esEs27(x0, x1, ty_Integer)
new_esEs8(LT, LT)
new_primPlusNat0(Succ(x0), Succ(x1))
new_esEs26(x0, x1, ty_Char)
new_esEs16([], [], x0)
new_compare18(x0, x1, ty_Char)
new_ltEs6(Left(x0), Left(x1), ty_Bool, x2)
new_ltEs6(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_compare10(x0, x1, False, x2, x3)
new_esEs19(x0, x1, ty_Double)
new_lt10(x0, x1, app(app(ty_Either, x2), x3))
new_lt18(x0, x1, x2, x3, x4)
new_ltEs18(x0, x1, ty_Int)
new_ltEs6(Right(x0), Right(x1), x2, ty_Char)
new_lt7(x0, x1, x2, x3)
new_ltEs10(x0, x1)
new_esEs7(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs24(x0, x1, ty_Int)
new_esEs11(x0, x1)
new_esEs7(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_primPlusNat0(Zero, Succ(x0))
new_compare11(x0, x1, True, x2, x3)
new_lt11(x0, x1, app(app(ty_@2, x2), x3))
new_esEs8(GT, LT)
new_esEs8(LT, GT)
new_esEs5(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs20(x0, x1, app(ty_[], x2))
new_esEs20(x0, x1, ty_Int)
new_compare6(Float(x0, x1), Float(x2, x3))
new_lt11(x0, x1, ty_@0)
new_esEs23(x0, x1, ty_Double)
new_ltEs9(EQ, EQ)
new_compare5(@0, @0)
new_esEs4(Just(x0), Just(x1), ty_Bool)
new_ltEs18(x0, x1, app(app(ty_Either, x2), x3))
new_primCompAux0(x0, EQ)
new_esEs7(Left(x0), Left(x1), ty_Float, x2)
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_compare18(x0, x1, app(app(ty_@2, x2), x3))
new_lt10(x0, x1, ty_Int)
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primEqNat0(Zero, Zero)
new_primCmpNat0(Succ(x0), Zero)
new_primEqNat0(Succ(x0), Zero)
new_ltEs6(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs19(x0, x1, ty_Ordering)
new_lt11(x0, x1, app(ty_[], x2))
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(Left(x0), Left(x1), ty_Char, x2)
new_ltEs19(x0, x1, ty_Int)
new_esEs27(x0, x1, app(ty_[], x2))
new_lt11(x0, x1, app(ty_Ratio, x2))
new_compare14(x0, x1, True)
new_esEs19(x0, x1, ty_Int)
new_compare7(x0, x1, x2)
new_ltEs7(Just(x0), Just(x1), ty_Char)
new_esEs4(Nothing, Nothing, x0)
new_esEs27(x0, x1, ty_Char)
new_esEs4(Just(x0), Just(x1), ty_Float)
new_esEs7(Right(x0), Right(x1), x2, ty_Integer)
new_ltEs6(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs26(x0, x1, ty_@0)
new_primMulNat0(Zero, Zero)
new_compare18(x0, x1, ty_Float)
new_esEs20(x0, x1, ty_@0)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_esEs16(:(x0, x1), [], x2)
new_ltEs18(x0, x1, ty_@0)
new_esEs7(Left(x0), Left(x1), ty_Integer, x2)
new_esEs24(x0, x1, ty_Bool)
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_esEs7(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs28(x0, x1, app(ty_[], x2))
new_primMulNat0(Succ(x0), Zero)
new_ltEs7(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_lt13(x0, x1, x2)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_esEs9(:%(x0, x1), :%(x2, x3), x4)
new_esEs18(x0, x1, app(ty_Ratio, x2))
new_compare18(x0, x1, ty_Ordering)
new_esEs4(Just(x0), Just(x1), ty_@0)
new_lt20(x0, x1, ty_Float)
new_lt4(x0, x1)
new_ltEs6(Right(x0), Right(x1), x2, app(ty_[], x3))
new_lt11(x0, x1, ty_Ordering)
new_lt19(x0, x1)
new_ltEs7(Just(x0), Just(x1), app(ty_Ratio, x2))
new_compare13(x0, x1, False, x2)
new_compare27(x0, x1, True, x2)
new_esEs28(x0, x1, ty_Double)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs7(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_compare15(x0, x1, True)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_esEs18(x0, x1, ty_Integer)
new_pePe(False, x0)
new_esEs19(x0, x1, ty_Bool)
new_ltEs6(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs4(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_ltEs18(x0, x1, ty_Float)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_esEs21(x0, x1, ty_Int)
new_ltEs11(x0, x1)
new_esEs29(x0, x1, ty_Int)
new_esEs25(x0, x1, ty_Double)
new_esEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, app(ty_Ratio, x2))
new_esEs28(x0, x1, ty_Bool)
new_esEs19(x0, x1, app(ty_Ratio, x2))
new_esEs4(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_lt11(x0, x1, ty_Double)
new_ltEs9(GT, EQ)
new_ltEs9(EQ, GT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpNat0(Succ(x0), Succ(x1))
new_ltEs6(Left(x0), Left(x1), ty_@0, x2)
new_compare18(x0, x1, app(ty_[], x2))
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_compare0([], :(x0, x1), x2)
new_esEs7(Right(x0), Left(x1), x2, x3)
new_compare15(x0, x1, False)
new_esEs7(Left(x0), Right(x1), x2, x3)
new_esEs23(x0, x1, ty_Ordering)
new_primCmpNat0(Zero, Succ(x0))
new_esEs7(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_ltEs6(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_ltEs20(x0, x1, ty_Int)
new_esEs27(x0, x1, ty_Int)
new_asAs(False, x0)
new_lt11(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primPlusNat0(Zero, Zero)
new_lt20(x0, x1, ty_Int)
new_primCompAux0(x0, LT)
new_esEs7(Left(x0), Left(x1), ty_Int, x2)
new_lt10(x0, x1, ty_Ordering)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, ty_Char)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_esEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare18(x0, x1, app(app(ty_Either, x2), x3))
new_lt10(x0, x1, app(app(ty_@2, x2), x3))
new_compare12(x0, x1, True, x2, x3, x4)
new_esEs7(Left(x0), Left(x1), app(ty_[], x2), x3)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_compare29(x0, x1, True)
new_compare27(Nothing, Just(x0), False, x1)
new_lt11(x0, x1, app(ty_Maybe, x2))
new_esEs7(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs25(x0, x1, ty_Int)
new_esEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs6(Left(x0), Left(x1), ty_Char, x2)
new_primPlusNat1(Zero, x0)
new_compare16(x0, x1)
new_esEs7(Right(x0), Right(x1), x2, ty_Double)
new_ltEs7(Just(x0), Nothing, x1)
new_esEs23(x0, x1, ty_Bool)
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_compare9(Integer(x0), Integer(x1))
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs7(Just(x0), Just(x1), ty_Integer)
new_esEs4(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_compare17(x0, x1, x2, x3)
new_lt11(x0, x1, ty_Integer)
new_compare18(x0, x1, app(ty_Maybe, x2))
new_ltEs9(EQ, LT)
new_ltEs9(LT, EQ)
new_compare26(x0, x1, True, x2, x3, x4)
new_esEs7(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs29(x0, x1, ty_@0)
new_sr(x0, x1)
new_esEs7(Left(x0), Left(x1), ty_Bool, x2)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs15(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs12(Integer(x0), Integer(x1))
new_compare25(x0, x1, True, x2, x3)
new_lt11(x0, x1, ty_Int)
new_primEqInt(Neg(Zero), Pos(Zero))
new_primEqInt(Pos(Zero), Neg(Zero))
new_compare0(:(x0, x1), :(x2, x3), x4)
new_compare0(:(x0, x1), [], x2)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs20(x0, x1, ty_Double)
new_ltEs4(x0, x1, x2)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_esEs7(Right(x0), Right(x1), x2, ty_Bool)
new_esEs24(x0, x1, ty_@0)
new_esEs23(x0, x1, ty_Float)
new_compare33(x0, x1, x2, x3, x4)
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_ltEs5(@2(x0, x1), @2(x2, x3), x4, x5)
new_compare8(Char(x0), Char(x1))
new_lt11(x0, x1, app(app(ty_Either, x2), x3))
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_ltEs20(x0, x1, ty_@0)
new_esEs18(x0, x1, ty_Char)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs15(True, False)
new_esEs15(False, True)
new_esEs8(EQ, EQ)
new_esEs14(Double(x0, x1), Double(x2, x3))
new_esEs18(x0, x1, ty_Ordering)
new_esEs17(Char(x0), Char(x1))
new_primEqInt(Neg(Zero), Neg(Zero))
new_ltEs7(Just(x0), Just(x1), ty_@0)
new_ltEs7(Just(x0), Just(x1), ty_Float)
new_esEs28(x0, x1, ty_Integer)
new_esEs6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs27(x0, x1, ty_@0)
new_compare27(Just(x0), Nothing, False, x1)
new_ltEs6(Left(x0), Left(x1), ty_Float, x2)
new_compare11(x0, x1, False, x2, x3)
new_esEs22(x0, x1, ty_Int)
new_ltEs7(Just(x0), Just(x1), ty_Bool)
new_ltEs6(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs24(x0, x1, ty_Char)
new_ltEs6(Left(x0), Left(x1), ty_Ordering, x2)
new_compare26(x0, x1, False, x2, x3, x4)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs4(Nothing, Just(x0), x1)
new_compare24(x0, x1, False, x2, x3)
new_ltEs18(x0, x1, app(ty_Ratio, x2))
new_primCompAux0(x0, GT)
new_ltEs19(x0, x1, ty_Double)
new_lt10(x0, x1, ty_@0)
new_ltEs7(Just(x0), Just(x1), ty_Double)
new_esEs18(x0, x1, app(ty_Maybe, x2))
new_ltEs19(x0, x1, ty_Ordering)
new_compare18(x0, x1, app(ty_Ratio, x2))
new_esEs28(x0, x1, ty_Float)
new_esEs7(Right(x0), Right(x1), x2, ty_Float)
new_ltEs20(x0, x1, app(ty_[], x2))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_lt10(x0, x1, app(ty_Maybe, x2))
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs18(x0, x1, ty_Ordering)
new_lt10(x0, x1, app(ty_Ratio, x2))
new_pePe(True, x0)
new_esEs26(x0, x1, ty_Ordering)
new_ltEs9(LT, LT)
new_esEs29(x0, x1, ty_Integer)
new_esEs20(x0, x1, ty_Char)
new_ltEs18(x0, x1, ty_Integer)
new_compare10(x0, x1, True, x2, x3)
new_esEs7(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_ltEs16(False, True)
new_ltEs16(True, False)
new_ltEs19(x0, x1, ty_Bool)
new_lt20(x0, x1, ty_Char)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_esEs29(x0, x1, app(ty_[], x2))
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_compare31(:%(x0, x1), :%(x2, x3), ty_Integer)
new_compare18(x0, x1, ty_@0)
new_esEs26(x0, x1, ty_Double)
new_ltEs18(x0, x1, app(ty_[], x2))
new_esEs4(Just(x0), Just(x1), ty_Int)
new_esEs26(x0, x1, ty_Bool)
new_ltEs6(Right(x0), Right(x1), x2, ty_@0)
new_ltEs19(x0, x1, ty_@0)
new_ltEs14(x0, x1)
new_ltEs6(Left(x0), Right(x1), x2, x3)
new_ltEs6(Right(x0), Left(x1), x2, x3)
new_esEs19(x0, x1, app(app(ty_Either, x2), x3))
new_compare19(x0, x1, x2, x3)
new_esEs20(x0, x1, ty_Ordering)
new_esEs19(x0, x1, ty_Integer)
new_primCmpNat0(Zero, Zero)
new_esEs19(x0, x1, app(ty_Maybe, x2))
new_primEqNat0(Succ(x0), Succ(x1))
new_compare27(Just(x0), Just(x1), False, x2)
new_ltEs20(x0, x1, ty_Ordering)
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare29(x0, x1, False)
new_primMulNat0(Succ(x0), Succ(x1))
new_ltEs19(x0, x1, ty_Integer)
new_ltEs7(Nothing, Just(x0), x1)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_compare28(x0, x1, False)
new_esEs29(x0, x1, ty_Float)
new_esEs27(x0, x1, ty_Ordering)
new_ltEs12(x0, x1, x2)
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs6(Left(x0), Left(x1), ty_Int, x2)
new_lt8(x0, x1)
new_ltEs20(x0, x1, ty_Integer)
new_esEs4(Just(x0), Nothing, x1)
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_esEs7(Left(x0), Left(x1), ty_Double, x2)
new_compare24(x0, x1, True, x2, x3)
new_primPlusNat1(Succ(x0), x1)
new_ltEs6(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_esEs19(x0, x1, ty_Float)
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs6(Right(x0), Right(x1), x2, ty_Integer)
new_lt9(x0, x1)
new_ltEs7(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_esEs21(x0, x1, ty_Integer)
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_compare30(x0, x1)
new_ltEs20(x0, x1, ty_Char)
new_ltEs20(x0, x1, ty_Float)
new_ltEs9(GT, LT)
new_ltEs9(LT, GT)
new_ltEs7(Nothing, Nothing, x0)
new_esEs26(x0, x1, ty_Int)
new_lt10(x0, x1, ty_Bool)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs16(:(x0, x1), :(x2, x3), x4)
new_compare27(Nothing, Nothing, False, x0)
new_esEs24(x0, x1, ty_Ordering)
new_esEs18(x0, x1, app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, ty_Int)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_not(True)
new_ltEs19(x0, x1, ty_Float)
new_compare31(:%(x0, x1), :%(x2, x3), ty_Int)
new_esEs19(x0, x1, app(ty_[], x2))
new_esEs20(x0, x1, ty_Float)
new_esEs18(x0, x1, ty_Bool)
new_esEs23(x0, x1, app(ty_[], x2))
new_esEs16([], :(x0, x1), x2)
new_lt11(x0, x1, ty_Float)
new_esEs29(x0, x1, ty_Ordering)
new_ltEs18(x0, x1, ty_Double)
new_esEs7(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_compare34(x0, x1)
new_esEs4(Just(x0), Just(x1), ty_Double)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_not(False)
new_esEs25(x0, x1, app(ty_[], x2))
new_esEs29(x0, x1, ty_Char)
new_ltEs7(Just(x0), Just(x1), ty_Int)
new_ltEs6(Left(x0), Left(x1), app(ty_[], x2), x3)
new_lt15(x0, x1)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_compare28(x0, x1, True)
new_ltEs8(x0, x1)
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_ltEs6(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs26(x0, x1, ty_Integer)
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_esEs4(Just(x0), Just(x1), ty_Integer)
new_ltEs13(x0, x1)
new_esEs23(x0, x1, ty_Char)
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs7(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs4(Just(x0), Just(x1), ty_Char)
new_esEs19(x0, x1, ty_@0)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_compare13(x0, x1, True, x2)
new_lt10(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_ltEs6(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs17(x0, x1)
new_esEs24(x0, x1, app(ty_[], x2))
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_lt6(x0, x1)
new_ltEs6(Left(x0), Left(x1), ty_Double, x2)
new_compare18(x0, x1, ty_Double)
new_esEs7(Left(x0), Left(x1), ty_@0, x2)
new_esEs20(x0, x1, ty_Bool)
new_lt20(x0, x1, ty_@0)
new_lt10(x0, x1, ty_Integer)
new_lt14(x0, x1, x2, x3)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_primMulInt(Neg(x0), Neg(x1))
new_ltEs9(GT, GT)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs19(x0, x1, ty_Char)
new_compare18(x0, x1, ty_Integer)
new_ltEs18(x0, x1, ty_Char)
new_lt17(x0, x1)
new_esEs7(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs28(x0, x1, ty_Int)
new_compare12(x0, x1, False, x2, x3, x4)
new_lt20(x0, x1, app(ty_[], x2))
new_esEs10(Float(x0, x1), Float(x2, x3))
new_compare32(Double(x0, x1), Double(x2, x3))
new_ltEs20(x0, x1, ty_Double)
new_esEs18(x0, x1, ty_@0)
new_esEs29(x0, x1, ty_Bool)
new_compare18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primEqInt(Pos(Zero), Pos(Zero))
new_esEs25(x0, x1, ty_Ordering)
new_lt20(x0, x1, ty_Bool)
new_lt12(x0, x1, x2)
new_esEs18(x0, x1, ty_Int)
new_ltEs6(Left(x0), Left(x1), ty_Integer, x2)
new_ltEs18(x0, x1, app(app(ty_@2, x2), x3))
new_lt16(x0, x1, x2)
new_esEs7(Right(x0), Right(x1), x2, ty_Char)
new_lt11(x0, x1, ty_Char)
new_esEs18(x0, x1, app(app(ty_@2, x2), x3))
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_esEs28(x0, x1, ty_@0)
new_esEs4(Just(x0), Just(x1), app(ty_Maybe, x2))
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_primMulInt(Pos(x0), Pos(x1))
new_esEs7(Right(x0), Right(x1), x2, ty_Int)
new_ltEs16(False, False)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs4(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs27(x0, x1, ty_Double)
new_ltEs19(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
We have to consider all minimal (P,Q,R)-chains.
By using the subterm criterion [20] together with the size-change analysis [32] we have proven that there are no infinite chains for this DP problem. From the DPs we obtained the following set of size-change graphs:
- new_foldFM_GE(vyy3, Just(vyy50), Branch(Just(vyy600), vyy61, vyy62, vyy63, vyy64), h, ba, bb) → new_foldFM_GE11(vyy3, vyy50, vyy600, vyy61, vyy62, vyy63, vyy64, new_esEs8(new_compare27(Just(vyy600), Just(vyy50), new_esEs29(vyy600, vyy50, ba), ba), LT), 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_GE(vyy3, Just(vyy50), Branch(Nothing, vyy61, vyy62, vyy63, vyy64), h, ba, bb) → new_foldFM_GE1(vyy3, vyy50, vyy61, vyy62, vyy63, vyy64, new_esEs8(new_compare27(Nothing, Just(vyy50), False, ba), LT), h, ba, bb)
The graph contains the following edges 1 >= 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5, 3 > 6, 4 >= 8, 5 >= 9, 6 >= 10
- new_foldFM_GE11(vyy17, vyy19, vyy20, vyy21, vyy22, vyy23, vyy24, False, bc, bd, be) → new_foldFM_GE(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_GE11(vyy17, vyy19, vyy20, vyy21, vyy22, vyy23, vyy24, False, bc, bd, be) → new_foldFM_GE(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_GE11(vyy17, vyy19, vyy20, vyy21, vyy22, vyy23, vyy24, True, bc, bd, be) → new_foldFM_GE(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_GE1(vyy3, vyy50, vyy61, vyy62, vyy63, vyy64, True, h, ba, bb) → new_foldFM_GE(vyy3, Just(vyy50), vyy64, h, ba, bb)
The graph contains the following edges 1 >= 1, 6 >= 3, 8 >= 4, 9 >= 5, 10 >= 6
- new_foldFM_GE1(vyy3, vyy50, vyy61, vyy62, vyy63, vyy64, False, h, ba, bb) → new_foldFM_GE(vyy3, Just(vyy50), vyy63, h, ba, bb)
The graph contains the following edges 1 >= 1, 5 >= 3, 8 >= 4, 9 >= 5, 10 >= 6
- new_foldFM_GE1(vyy3, vyy50, vyy61, vyy62, vyy63, vyy64, False, h, ba, bb) → new_foldFM_GE(vyy3, Just(vyy50), vyy64, h, ba, bb)
The graph contains the following edges 1 >= 1, 6 >= 3, 8 >= 4, 9 >= 5, 10 >= 6