YES
H-Termination proof of ../tpdb/FP/full_haskell/FiniteMap_foldFM_LE_9.hs
H-Termination of the given Haskell-Program with start terms could successfully be proven:
↳ HASKELL
↳ LR
mainModule Main
|
| ((FiniteMap.foldFM_LE :: Ord a => (Maybe a -> c -> b -> b) -> b -> Maybe a -> FiniteMap.FiniteMap (Maybe a) c -> b) :: Ord a => (Maybe a -> c -> b -> b) -> b -> Maybe a -> FiniteMap.FiniteMap (Maybe a) c -> b) |
module FiniteMap where
| | import qualified Main
import qualified Maybe
import qualified Prelude
|
| | data FiniteMap a b = EmptyFM | Branch a b Int (FiniteMap a b) (FiniteMap a b)
|
| | instance (Eq a, Eq b) => Eq (FiniteMap a b) where
|
|
|
| (==) | fm_1 fm_2 | = | sizeFM fm_1 == sizeFM fm_2 && fmToList fm_1 == fmToList fm_2 |
|
|
| | fmToList :: FiniteMap a b -> [(a,b)]
| fmToList | fm | = | foldFM (\key elt rest ->(key,elt) : rest) [] fm |
|
| | foldFM :: (c -> a -> b -> b) -> b -> FiniteMap c a -> b
| foldFM | k z EmptyFM | = | z |
| foldFM | k z (Branch key elt _ fm_l fm_r) | = | foldFM k (k key elt (foldFM k z fm_r)) fm_l |
|
| | foldFM_LE :: Ord c => (c -> a -> b -> b) -> b -> c -> FiniteMap c a -> b
| foldFM_LE | k z fr EmptyFM | = | z |
| foldFM_LE | k z fr (Branch key elt _ fm_l fm_r) | |
| | | key <= fr | = |
| foldFM_LE k (k key elt (foldFM_LE k z fr fm_l)) fr fm_r |
|
| | | otherwise | = |
|
|
|
| | sizeFM :: FiniteMap b a -> Int
| sizeFM | EmptyFM | = | 0 |
| sizeFM | (Branch _ _ size _ _) | = | size |
|
module Main where
| | import qualified FiniteMap
import qualified Maybe
import qualified Prelude
|
module Maybe where
| | import qualified FiniteMap
import qualified Main
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 Main
|
| ((FiniteMap.foldFM_LE :: Ord c => (Maybe c -> a -> b -> b) -> b -> Maybe c -> FiniteMap.FiniteMap (Maybe c) a -> b) :: Ord c => (Maybe c -> a -> b -> b) -> b -> Maybe c -> FiniteMap.FiniteMap (Maybe c) a -> b) |
module FiniteMap where
| | import qualified Main
import qualified Maybe
import qualified Prelude
|
| | data FiniteMap a b = EmptyFM | Branch a b Int (FiniteMap a b) (FiniteMap a b)
|
| | instance (Eq a, Eq b) => Eq (FiniteMap a b) where
|
|
|
| (==) | fm_1 fm_2 | = | sizeFM fm_1 == sizeFM fm_2 && fmToList fm_1 == fmToList fm_2 |
|
|
| | fmToList :: FiniteMap b a -> [(b,a)]
| fmToList | fm | = | foldFM fmToList0 [] fm |
|
| |
| fmToList0 | key elt rest | = | (key,elt) : rest |
|
| | foldFM :: (c -> a -> b -> b) -> b -> FiniteMap c a -> b
| foldFM | k z EmptyFM | = | z |
| foldFM | k z (Branch key elt _ fm_l fm_r) | = | foldFM k (k key elt (foldFM k z fm_r)) fm_l |
|
| | foldFM_LE :: Ord b => (b -> a -> c -> c) -> c -> b -> FiniteMap b a -> c
| foldFM_LE | k z fr EmptyFM | = | z |
| foldFM_LE | k z fr (Branch key elt _ fm_l fm_r) | |
| | | key <= fr | = |
| foldFM_LE k (k key elt (foldFM_LE k z fr fm_l)) fr fm_r |
|
| | | otherwise | = |
|
|
|
| | sizeFM :: FiniteMap b a -> Int
| sizeFM | EmptyFM | = | 0 |
| sizeFM | (Branch _ _ size _ _) | = | size |
|
module Main where
| | import qualified FiniteMap
import qualified Maybe
import qualified Prelude
|
module Maybe where
| | import qualified FiniteMap
import qualified Main
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 Main
|
| ((FiniteMap.foldFM_LE :: Ord c => (Maybe c -> b -> a -> a) -> a -> Maybe c -> FiniteMap.FiniteMap (Maybe c) b -> a) :: Ord c => (Maybe c -> b -> a -> a) -> a -> Maybe c -> FiniteMap.FiniteMap (Maybe c) b -> a) |
module FiniteMap where
| | import qualified Main
import qualified Maybe
import qualified Prelude
|
| | data FiniteMap a b = EmptyFM | Branch a b Int (FiniteMap a b) (FiniteMap a b)
|
| | instance (Eq a, Eq b) => Eq (FiniteMap a b) where
|
|
|
| (==) | fm_1 fm_2 | = | sizeFM fm_1 == sizeFM fm_2 && fmToList fm_1 == fmToList fm_2 |
|
|
| | fmToList :: FiniteMap a b -> [(a,b)]
| fmToList | fm | = | foldFM fmToList0 [] fm |
|
| |
| fmToList0 | key elt rest | = | (key,elt) : rest |
|
| | foldFM :: (b -> a -> c -> c) -> c -> FiniteMap b a -> c
| foldFM | k z EmptyFM | = | z |
| foldFM | k z (Branch key elt _ fm_l fm_r) | = | foldFM k (k key elt (foldFM k z fm_r)) fm_l |
|
| | foldFM_LE :: Ord c => (c -> b -> a -> a) -> a -> c -> FiniteMap c b -> a
| foldFM_LE | k z fr EmptyFM | = | z |
| foldFM_LE | k z fr (Branch key elt _ fm_l fm_r) | |
| | | key <= fr | = |
| foldFM_LE k (k key elt (foldFM_LE k z fr fm_l)) fr fm_r |
|
| | | otherwise | = |
|
|
|
| | sizeFM :: FiniteMap a b -> Int
| sizeFM | EmptyFM | = | 0 |
| sizeFM | (Branch _ _ size _ _) | = | size |
|
module Main where
| | import qualified FiniteMap
import qualified Maybe
import qualified Prelude
|
module Maybe where
| | import qualified FiniteMap
import qualified Main
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 Main
|
| ((FiniteMap.foldFM_LE :: Ord a => (Maybe a -> c -> b -> b) -> b -> Maybe a -> FiniteMap.FiniteMap (Maybe a) c -> b) :: Ord a => (Maybe a -> c -> b -> b) -> b -> Maybe a -> FiniteMap.FiniteMap (Maybe a) c -> b) |
module FiniteMap where
| | import qualified Main
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 :: (a -> b -> c -> c) -> c -> FiniteMap a b -> c
| foldFM | k z EmptyFM | = | z |
| foldFM | k z (Branch key elt _ fm_l fm_r) | = | foldFM k (k key elt (foldFM k z fm_r)) fm_l |
|
| | foldFM_LE :: Ord a => (a -> b -> c -> c) -> c -> a -> FiniteMap a b -> c
| foldFM_LE | k z fr EmptyFM | = | z |
| foldFM_LE | k z fr (Branch key elt _ fm_l fm_r) | |
| | | key <= fr | = |
| foldFM_LE k (k key elt (foldFM_LE k z fr fm_l)) fr fm_r |
|
| | | otherwise | = |
|
|
|
| | sizeFM :: FiniteMap b a -> Int
| sizeFM | EmptyFM | = | 0 |
| sizeFM | (Branch _ _ size _ _) | = | size |
|
module Main where
| | import qualified FiniteMap
import qualified Maybe
import qualified Prelude
|
module Maybe where
| | import qualified FiniteMap
import qualified Main
import qualified Prelude
|
Replaced joker patterns by fresh variables and removed binding patterns.
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
mainModule Main
|
| ((FiniteMap.foldFM_LE :: Ord c => (Maybe c -> a -> b -> b) -> b -> Maybe c -> FiniteMap.FiniteMap (Maybe c) a -> b) :: Ord c => (Maybe c -> a -> b -> b) -> b -> Maybe c -> FiniteMap.FiniteMap (Maybe c) a -> b) |
module FiniteMap where
| | import qualified Main
import qualified Maybe
import qualified Prelude
|
| | data FiniteMap b a = EmptyFM | Branch b a Int (FiniteMap b a) (FiniteMap b a)
|
| | instance (Eq a, Eq b) => Eq (FiniteMap a b) where
|
|
|
| (==) | fm_1 fm_2 | = | sizeFM fm_1 == sizeFM fm_2 && fmToList fm_1 == fmToList fm_2 |
|
|
| | fmToList :: FiniteMap b a -> [(b,a)]
| fmToList | fm | = | foldFM fmToList0 [] fm |
|
| |
| fmToList0 | key elt rest | = | (key,elt) : rest |
|
| | foldFM :: (a -> 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_LE :: Ord c => (c -> b -> a -> a) -> a -> c -> FiniteMap c b -> a
| foldFM_LE | k z fr EmptyFM | = | z |
| foldFM_LE | k z fr (Branch key elt vx fm_l fm_r) | |
| | | key <= fr | = |
| foldFM_LE k (k key elt (foldFM_LE k z fr fm_l)) fr fm_r |
|
| | | otherwise | = |
|
|
|
| | sizeFM :: FiniteMap a b -> Int
| sizeFM | EmptyFM | = | 0 |
| sizeFM | (Branch vy vz size wu wv) | = | size |
|
module Main where
| | import qualified FiniteMap
import qualified Maybe
import qualified Prelude
|
module Maybe where
| | import qualified FiniteMap
import qualified Main
import qualified Prelude
|
Cond Reductions:
The following Function with conditions
| foldFM_LE | k z fr EmptyFM | = z |
| foldFM_LE | k z fr (Branch key elt vx fm_l fm_r) |
| | | key <= fr |
| = | foldFM_LE k (k key elt (foldFM_LE k z fr fm_l)) fr fm_r |
|
| | | otherwise | |
|
is transformed to
| foldFM_LE | k z fr EmptyFM | = foldFM_LE3 k z fr EmptyFM |
| foldFM_LE | k z fr (Branch key elt vx fm_l fm_r) | = foldFM_LE2 k z fr (Branch key elt vx fm_l fm_r) |
| foldFM_LE1 | k z fr key elt vx fm_l fm_r True | = foldFM_LE k (k key elt (foldFM_LE k z fr fm_l)) fr fm_r |
| foldFM_LE1 | k z fr key elt vx fm_l fm_r False | = foldFM_LE0 k z fr key elt vx fm_l fm_r otherwise |
| foldFM_LE0 | k z fr key elt vx fm_l fm_r True | = foldFM_LE k z fr fm_l |
| foldFM_LE2 | k z fr (Branch key elt vx fm_l fm_r) | = foldFM_LE1 k z fr key elt vx fm_l fm_r (key <= fr) |
| foldFM_LE3 | k z fr EmptyFM | = z |
| foldFM_LE3 | vvu vvv vvw vvx | = foldFM_LE2 vvu vvv vvw vvx |
The following Function with conditions
| 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 |
|
|
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) |
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
mainModule Main
|
| ((FiniteMap.foldFM_LE :: Ord a => (Maybe a -> b -> c -> c) -> c -> Maybe a -> FiniteMap.FiniteMap (Maybe a) b -> c) :: Ord a => (Maybe a -> b -> c -> c) -> c -> Maybe a -> FiniteMap.FiniteMap (Maybe a) b -> c) |
module FiniteMap where
| | import qualified Main
import qualified Maybe
import qualified Prelude
|
| | data FiniteMap a b = EmptyFM | Branch a b Int (FiniteMap a b) (FiniteMap a b)
|
| | instance (Eq a, Eq b) => Eq (FiniteMap a b) where
|
|
|
| (==) | fm_1 fm_2 | = | sizeFM fm_1 == sizeFM fm_2 && fmToList fm_1 == fmToList fm_2 |
|
|
| | fmToList :: FiniteMap a b -> [(a,b)]
| fmToList | fm | = | foldFM fmToList0 [] fm |
|
| |
| fmToList0 | key elt rest | = | (key,elt) : rest |
|
| | foldFM :: (c -> b -> a -> a) -> a -> FiniteMap c b -> a
| foldFM | k z EmptyFM | = | z |
| foldFM | k z (Branch key elt vw fm_l fm_r) | = | foldFM k (k key elt (foldFM k z fm_r)) fm_l |
|
| | foldFM_LE :: Ord b => (b -> a -> c -> c) -> c -> b -> FiniteMap b a -> c
| foldFM_LE | k z fr EmptyFM | = | foldFM_LE3 k z fr EmptyFM |
| foldFM_LE | k z fr (Branch key elt vx fm_l fm_r) | = | foldFM_LE2 k z fr (Branch key elt vx fm_l fm_r) |
|
| |
| foldFM_LE0 | k z fr key elt vx fm_l fm_r True | = | foldFM_LE k z fr fm_l |
|
| |
| foldFM_LE1 | k z fr key elt vx fm_l fm_r True | = | foldFM_LE k (k key elt (foldFM_LE k z fr fm_l)) fr fm_r |
| foldFM_LE1 | k z fr key elt vx fm_l fm_r False | = | foldFM_LE0 k z fr key elt vx fm_l fm_r otherwise |
|
| |
| foldFM_LE2 | k z fr (Branch key elt vx fm_l fm_r) | = | foldFM_LE1 k z fr key elt vx fm_l fm_r (key <= fr) |
|
| |
| foldFM_LE3 | k z fr EmptyFM | = | z |
| foldFM_LE3 | vvu vvv vvw vvx | = | foldFM_LE2 vvu vvv vvw vvx |
|
| | sizeFM :: FiniteMap a b -> Int
| sizeFM | EmptyFM | = | 0 |
| sizeFM | (Branch vy vz size wu wv) | = | size |
|
module Main where
| | import qualified FiniteMap
import qualified Maybe
import qualified Prelude
|
module Maybe where
| | import qualified FiniteMap
import qualified Main
import qualified Prelude
|
Let/Where Reductions:
The bindings of the following Let/Where expression
| reduce1 x y (y == 0) |
| where | |
|
| reduce0 | x y True | = x `quot` d :% (y `quot` d) |
|
|
| reduce1 | x y True | = error [] |
| reduce1 | x y False | = reduce0 x y otherwise |
|
are unpacked to the following functions on top level
| reduce2Reduce0 | vyw vyx x y True | = x `quot` reduce2D vyw vyx :% (y `quot` reduce2D vyw vyx) |
| reduce2Reduce1 | vyw vyx x y True | = error [] |
| reduce2Reduce1 | vyw vyx x y False | = reduce2Reduce0 vyw vyx x y otherwise |
| reduce2D | vyw vyx | = gcd vyw vyx |
The bindings of the following Let/Where expression
| gcd' (abs x) (abs y) |
| where |
| gcd' | x vvy | = gcd'2 x vvy |
| gcd' | x y | = gcd'0 x y |
|
|
| gcd'0 | x y | = gcd' y (x `rem` y) |
|
|
| gcd'1 | True x vvy | = x |
| gcd'1 | vvz vwu vwv | = gcd'0 vwu vwv |
|
|
| gcd'2 | x vvy | = gcd'1 (vvy == 0) x vvy |
| gcd'2 | vww vwx | = gcd'0 vww vwx |
|
are unpacked to the following functions on top level
| gcd0Gcd'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 Main
|
| ((FiniteMap.foldFM_LE :: Ord a => (Maybe a -> b -> c -> c) -> c -> Maybe a -> FiniteMap.FiniteMap (Maybe a) b -> c) :: Ord a => (Maybe a -> b -> c -> c) -> c -> Maybe a -> FiniteMap.FiniteMap (Maybe a) b -> c) |
module FiniteMap where
| | import qualified Main
import qualified Maybe
import qualified Prelude
|
| | data FiniteMap b a = EmptyFM | Branch b a Int (FiniteMap b a) (FiniteMap b a)
|
| | instance (Eq a, Eq b) => Eq (FiniteMap a b) where
|
|
|
| (==) | fm_1 fm_2 | = | sizeFM fm_1 == sizeFM fm_2 && fmToList fm_1 == fmToList fm_2 |
|
|
| | fmToList :: FiniteMap b a -> [(b,a)]
| fmToList | fm | = | foldFM fmToList0 [] fm |
|
| |
| fmToList0 | key elt rest | = | (key,elt) : rest |
|
| | foldFM :: (a -> 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_LE :: Ord b => (b -> a -> c -> c) -> c -> b -> FiniteMap b a -> c
| foldFM_LE | k z fr EmptyFM | = | foldFM_LE3 k z fr EmptyFM |
| foldFM_LE | k z fr (Branch key elt vx fm_l fm_r) | = | foldFM_LE2 k z fr (Branch key elt vx fm_l fm_r) |
|
| |
| foldFM_LE0 | k z fr key elt vx fm_l fm_r True | = | foldFM_LE k z fr fm_l |
|
| |
| foldFM_LE1 | k z fr key elt vx fm_l fm_r True | = | foldFM_LE k (k key elt (foldFM_LE k z fr fm_l)) fr fm_r |
| foldFM_LE1 | k z fr key elt vx fm_l fm_r False | = | foldFM_LE0 k z fr key elt vx fm_l fm_r otherwise |
|
| |
| foldFM_LE2 | k z fr (Branch key elt vx fm_l fm_r) | = | foldFM_LE1 k z fr key elt vx fm_l fm_r (key <= fr) |
|
| |
| foldFM_LE3 | k z fr EmptyFM | = | z |
| foldFM_LE3 | vvu vvv vvw vvx | = | foldFM_LE2 vvu vvv vvw vvx |
|
| | sizeFM :: FiniteMap b a -> Int
| sizeFM | EmptyFM | = | 0 |
| sizeFM | (Branch vy vz size wu wv) | = | size |
|
module Main where
| | import qualified FiniteMap
import qualified Maybe
import qualified Prelude
|
module Maybe where
| | import qualified FiniteMap
import qualified Main
import qualified Prelude
|
Num Reduction:All numbers are transformed to thier corresponding representation with Succ, Pred and Zero.
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
mainModule Main
|
| (FiniteMap.foldFM_LE :: Ord a => (Maybe a -> b -> c -> c) -> c -> Maybe a -> FiniteMap.FiniteMap (Maybe a) b -> c) |
module FiniteMap where
| | import qualified Main
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 :: (c -> b -> a -> a) -> a -> FiniteMap c b -> a
| foldFM | k z EmptyFM | = | z |
| foldFM | k z (Branch key elt vw fm_l fm_r) | = | foldFM k (k key elt (foldFM k z fm_r)) fm_l |
|
| | foldFM_LE :: Ord a => (a -> c -> b -> b) -> b -> a -> FiniteMap a c -> b
| foldFM_LE | k z fr EmptyFM | = | foldFM_LE3 k z fr EmptyFM |
| foldFM_LE | k z fr (Branch key elt vx fm_l fm_r) | = | foldFM_LE2 k z fr (Branch key elt vx fm_l fm_r) |
|
| |
| foldFM_LE0 | k z fr key elt vx fm_l fm_r True | = | foldFM_LE k z fr fm_l |
|
| |
| foldFM_LE1 | k z fr key elt vx fm_l fm_r True | = | foldFM_LE k (k key elt (foldFM_LE k z fr fm_l)) fr fm_r |
| foldFM_LE1 | k z fr key elt vx fm_l fm_r False | = | foldFM_LE0 k z fr key elt vx fm_l fm_r otherwise |
|
| |
| foldFM_LE2 | k z fr (Branch key elt vx fm_l fm_r) | = | foldFM_LE1 k z fr key elt vx fm_l fm_r (key <= fr) |
|
| |
| foldFM_LE3 | k z fr EmptyFM | = | z |
| foldFM_LE3 | vvu vvv vvw vvx | = | foldFM_LE2 vvu vvv vvw vvx |
|
| | sizeFM :: FiniteMap b a -> Int
| sizeFM | EmptyFM | = | Pos Zero |
| sizeFM | (Branch vy vz size wu wv) | = | size |
|
module Main where
| | import qualified FiniteMap
import qualified Maybe
import qualified Prelude
|
module Maybe where
| | import qualified FiniteMap
import qualified Main
import qualified Prelude
|
Haskell To QDPs
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ Rewriting
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_esEs0(Just(vyy440), Just(vyy450), app(app(ty_FiniteMap, fb), fc)) → new_esEs4(vyy440, vyy450, fb, fc)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), hb, app(app(app(ty_@3, hf), hg), hh), fh) → new_esEs1(vyy441, vyy451, hf, hg, hh)
new_esEs3(@2(vyy440, vyy441), @2(vyy450, vyy451), app(app(ty_FiniteMap, beg), beh), bdg) → new_esEs4(vyy440, vyy450, beg, beh)
new_esEs(Right(vyy440), Right(vyy450), cd, app(app(ty_FiniteMap, dg), dh)) → new_esEs4(vyy440, vyy450, dg, dh)
new_esEs0(Just(vyy440), Just(vyy450), app(ty_Maybe, ec)) → new_esEs0(vyy440, vyy450, ec)
new_esEs(Left(vyy440), Left(vyy450), app(ty_[], bg), bb) → new_esEs2(vyy440, vyy450, bg)
new_esEs(Right(vyy440), Right(vyy450), cd, app(app(ty_@2, de), df)) → new_esEs3(vyy440, vyy450, de, df)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), hb, fg, app(app(app(ty_@3, bba), bbb), bbc)) → new_esEs1(vyy442, vyy452, bba, bbb, bbc)
new_esEs3(@2(vyy440, vyy441), @2(vyy450, vyy451), bfa, app(app(ty_FiniteMap, bgc), bgd)) → new_esEs4(vyy441, vyy451, bgc, bgd)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), hb, fg, app(app(ty_FiniteMap, bbg), bbh)) → new_esEs4(vyy442, vyy452, bbg, bbh)
new_esEs3(@2(vyy440, vyy441), @2(vyy450, vyy451), app(ty_[], bed), bdg) → new_esEs2(vyy440, vyy450, bed)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), hb, fg, app(ty_Maybe, bah)) → new_esEs0(vyy442, vyy452, bah)
new_esEs(Left(vyy440), Left(vyy450), app(ty_Maybe, bc), bb) → new_esEs0(vyy440, vyy450, bc)
new_esEs2(:(vyy440, vyy441), :(vyy450, vyy451), app(ty_Maybe, bcc)) → new_esEs0(vyy440, vyy450, bcc)
new_esEs0(Just(vyy440), Just(vyy450), app(app(ty_Either, ea), eb)) → new_esEs(vyy440, vyy450, ea, eb)
new_esEs(Right(vyy440), Right(vyy450), cd, app(ty_[], dd)) → new_esEs2(vyy440, vyy450, dd)
new_esEs(Right(vyy440), Right(vyy450), cd, app(app(app(ty_@3, da), db), dc)) → new_esEs1(vyy440, vyy450, da, db, dc)
new_esEs(Left(vyy440), Left(vyy450), app(app(ty_@2, bh), ca), bb) → new_esEs3(vyy440, vyy450, bh, ca)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), hb, fg, app(app(ty_Either, baf), bag)) → new_esEs(vyy442, vyy452, baf, bag)
new_esEs3(@2(vyy440, vyy441), @2(vyy450, vyy451), app(app(ty_@2, bee), bef), bdg) → new_esEs3(vyy440, vyy450, bee, bef)
new_esEs3(@2(vyy440, vyy441), @2(vyy450, vyy451), bfa, app(ty_Maybe, bfd)) → new_esEs0(vyy441, vyy451, bfd)
new_esEs2(:(vyy440, vyy441), :(vyy450, vyy451), app(ty_[], bcg)) → new_esEs2(vyy440, vyy450, bcg)
new_esEs(Right(vyy440), Right(vyy450), cd, app(ty_Maybe, cg)) → new_esEs0(vyy440, vyy450, cg)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), app(ty_[], ge), fg, fh) → new_esEs2(vyy440, vyy450, ge)
new_esEs3(@2(vyy440, vyy441), @2(vyy450, vyy451), bfa, app(app(app(ty_@3, bfe), bff), bfg)) → new_esEs1(vyy441, vyy451, bfe, bff, bfg)
new_esEs(Left(vyy440), Left(vyy450), app(app(ty_FiniteMap, cb), cc), bb) → new_esEs4(vyy440, vyy450, cb, cc)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), hb, fg, app(app(ty_@2, bbe), bbf)) → new_esEs3(vyy442, vyy452, bbe, bbf)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), hb, app(app(ty_FiniteMap, bad), bae), fh) → new_esEs4(vyy441, vyy451, bad, bae)
new_esEs0(Just(vyy440), Just(vyy450), app(ty_[], eg)) → new_esEs2(vyy440, vyy450, eg)
new_esEs(Left(vyy440), Left(vyy450), app(app(ty_Either, h), ba), bb) → new_esEs(vyy440, vyy450, h, ba)
new_esEs2(:(vyy440, vyy441), :(vyy450, vyy451), app(app(ty_FiniteMap, bdb), bdc)) → new_esEs4(vyy440, vyy450, bdb, bdc)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), hb, app(app(ty_@2, bab), bac), fh) → new_esEs3(vyy441, vyy451, bab, bac)
new_esEs3(@2(vyy440, vyy441), @2(vyy450, vyy451), bfa, app(ty_[], bfh)) → new_esEs2(vyy441, vyy451, bfh)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), app(app(ty_FiniteMap, gh), ha), fg, fh) → new_esEs4(vyy440, vyy450, gh, ha)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), hb, app(ty_Maybe, he), fh) → new_esEs0(vyy441, vyy451, he)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), hb, fg, app(ty_[], bbd)) → new_esEs2(vyy442, vyy452, bbd)
new_esEs3(@2(vyy440, vyy441), @2(vyy450, vyy451), app(app(app(ty_@3, bea), beb), bec), bdg) → new_esEs1(vyy440, vyy450, bea, beb, bec)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), hb, app(ty_[], baa), fh) → new_esEs2(vyy441, vyy451, baa)
new_esEs3(@2(vyy440, vyy441), @2(vyy450, vyy451), bfa, app(app(ty_@2, bga), bgb)) → new_esEs3(vyy441, vyy451, bga, bgb)
new_esEs2(:(vyy440, vyy441), :(vyy450, vyy451), app(app(ty_Either, bca), bcb)) → new_esEs(vyy440, vyy450, bca, bcb)
new_esEs2(:(vyy440, vyy441), :(vyy450, vyy451), app(app(app(ty_@3, bcd), bce), bcf)) → new_esEs1(vyy440, vyy450, bcd, bce, bcf)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), app(app(app(ty_@3, gb), gc), gd), fg, fh) → new_esEs1(vyy440, vyy450, gb, gc, gd)
new_esEs(Right(vyy440), Right(vyy450), cd, app(app(ty_Either, ce), cf)) → new_esEs(vyy440, vyy450, ce, cf)
new_esEs3(@2(vyy440, vyy441), @2(vyy450, vyy451), app(ty_Maybe, bdh), bdg) → new_esEs0(vyy440, vyy450, bdh)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), app(app(ty_@2, gf), gg), fg, fh) → new_esEs3(vyy440, vyy450, gf, gg)
new_esEs2(:(vyy440, vyy441), :(vyy450, vyy451), app(app(ty_@2, bch), bda)) → new_esEs3(vyy440, vyy450, bch, bda)
new_esEs2(:(vyy440, vyy441), :(vyy450, vyy451), bdd) → new_esEs2(vyy441, vyy451, bdd)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), hb, app(app(ty_Either, hc), hd), fh) → new_esEs(vyy441, vyy451, hc, hd)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), app(app(ty_Either, fd), ff), fg, fh) → new_esEs(vyy440, vyy450, fd, ff)
new_esEs3(@2(vyy440, vyy441), @2(vyy450, vyy451), bfa, app(app(ty_Either, bfb), bfc)) → new_esEs(vyy441, vyy451, bfb, bfc)
new_esEs(Left(vyy440), Left(vyy450), app(app(app(ty_@3, bd), be), bf), bb) → new_esEs1(vyy440, vyy450, bd, be, bf)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), app(ty_Maybe, ga), fg, fh) → new_esEs0(vyy440, vyy450, ga)
new_esEs3(@2(vyy440, vyy441), @2(vyy450, vyy451), app(app(ty_Either, bde), bdf), bdg) → new_esEs(vyy440, vyy450, bde, bdf)
new_esEs0(Just(vyy440), Just(vyy450), app(app(ty_@2, eh), fa)) → new_esEs3(vyy440, vyy450, eh, fa)
new_esEs0(Just(vyy440), Just(vyy450), app(app(app(ty_@3, ed), ee), ef)) → new_esEs1(vyy440, vyy450, ed, ee, ef)
new_esEs4(vyy44, vyy45, bge, bgf) → new_esEs2(new_fmToList(vyy44, bge, bgf), new_fmToList(vyy45, bge, bgf), app(app(ty_@2, bge), bgf))
The TRS R consists of the following rules:
new_foldFM0(vyy450, vyy451, vyy74, EmptyFM, bge, bgf) → :(@2(vyy450, vyy451), vyy74)
new_foldFM0(vyy450, vyy451, vyy74, Branch(vyy4530, vyy4531, vyy4532, vyy4533, vyy4534), bge, bgf) → new_foldFM0(vyy4530, vyy4531, new_foldFM0(vyy450, vyy451, vyy74, vyy4534, bge, bgf), vyy4533, bge, bgf)
new_fmToList(vyy45, bge, bgf) → new_foldFM2(vyy45, bge, bgf)
new_foldFM2(Branch(vyy450, vyy451, vyy452, vyy453, vyy454), bge, bgf) → new_foldFM0(vyy450, vyy451, new_foldFM2(vyy454, bge, bgf), vyy453, bge, bgf)
new_foldFM2(EmptyFM, bge, bgf) → []
The set Q consists of the following terms:
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
new_fmToList(x0, x1, x2)
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_foldFM2(EmptyFM, x0, x1)
We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_esEs4(vyy44, vyy45, bge, bgf) → new_esEs2(new_fmToList(vyy44, bge, bgf), new_fmToList(vyy45, bge, bgf), app(app(ty_@2, bge), bgf)) at position [0] we obtained the following new rules:
new_esEs4(vyy44, vyy45, bge, bgf) → new_esEs2(new_foldFM2(vyy44, bge, bgf), new_fmToList(vyy45, bge, bgf), app(app(ty_@2, bge), bgf))
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ Rewriting
↳ QDP
↳ Rewriting
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_esEs0(Just(vyy440), Just(vyy450), app(app(ty_FiniteMap, fb), fc)) → new_esEs4(vyy440, vyy450, fb, fc)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), hb, app(app(app(ty_@3, hf), hg), hh), fh) → new_esEs1(vyy441, vyy451, hf, hg, hh)
new_esEs3(@2(vyy440, vyy441), @2(vyy450, vyy451), app(app(ty_FiniteMap, beg), beh), bdg) → new_esEs4(vyy440, vyy450, beg, beh)
new_esEs(Right(vyy440), Right(vyy450), cd, app(app(ty_FiniteMap, dg), dh)) → new_esEs4(vyy440, vyy450, dg, dh)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), hb, fg, app(app(app(ty_@3, bba), bbb), bbc)) → new_esEs1(vyy442, vyy452, bba, bbb, bbc)
new_esEs(Right(vyy440), Right(vyy450), cd, app(app(ty_@2, de), df)) → new_esEs3(vyy440, vyy450, de, df)
new_esEs(Left(vyy440), Left(vyy450), app(ty_[], bg), bb) → new_esEs2(vyy440, vyy450, bg)
new_esEs0(Just(vyy440), Just(vyy450), app(ty_Maybe, ec)) → new_esEs0(vyy440, vyy450, ec)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), hb, fg, app(app(ty_FiniteMap, bbg), bbh)) → new_esEs4(vyy442, vyy452, bbg, bbh)
new_esEs3(@2(vyy440, vyy441), @2(vyy450, vyy451), bfa, app(app(ty_FiniteMap, bgc), bgd)) → new_esEs4(vyy441, vyy451, bgc, bgd)
new_esEs3(@2(vyy440, vyy441), @2(vyy450, vyy451), app(ty_[], bed), bdg) → new_esEs2(vyy440, vyy450, bed)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), hb, fg, app(ty_Maybe, bah)) → new_esEs0(vyy442, vyy452, bah)
new_esEs(Left(vyy440), Left(vyy450), app(ty_Maybe, bc), bb) → new_esEs0(vyy440, vyy450, bc)
new_esEs4(vyy44, vyy45, bge, bgf) → new_esEs2(new_foldFM2(vyy44, bge, bgf), new_fmToList(vyy45, bge, bgf), app(app(ty_@2, bge), bgf))
new_esEs2(:(vyy440, vyy441), :(vyy450, vyy451), app(ty_Maybe, bcc)) → new_esEs0(vyy440, vyy450, bcc)
new_esEs0(Just(vyy440), Just(vyy450), app(app(ty_Either, ea), eb)) → new_esEs(vyy440, vyy450, ea, eb)
new_esEs(Right(vyy440), Right(vyy450), cd, app(app(app(ty_@3, da), db), dc)) → new_esEs1(vyy440, vyy450, da, db, dc)
new_esEs(Right(vyy440), Right(vyy450), cd, app(ty_[], dd)) → new_esEs2(vyy440, vyy450, dd)
new_esEs(Left(vyy440), Left(vyy450), app(app(ty_@2, bh), ca), bb) → new_esEs3(vyy440, vyy450, bh, ca)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), hb, fg, app(app(ty_Either, baf), bag)) → new_esEs(vyy442, vyy452, baf, bag)
new_esEs3(@2(vyy440, vyy441), @2(vyy450, vyy451), app(app(ty_@2, bee), bef), bdg) → new_esEs3(vyy440, vyy450, bee, bef)
new_esEs3(@2(vyy440, vyy441), @2(vyy450, vyy451), bfa, app(ty_Maybe, bfd)) → new_esEs0(vyy441, vyy451, bfd)
new_esEs(Right(vyy440), Right(vyy450), cd, app(ty_Maybe, cg)) → new_esEs0(vyy440, vyy450, cg)
new_esEs2(:(vyy440, vyy441), :(vyy450, vyy451), app(ty_[], bcg)) → new_esEs2(vyy440, vyy450, bcg)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), app(ty_[], ge), fg, fh) → new_esEs2(vyy440, vyy450, ge)
new_esEs(Left(vyy440), Left(vyy450), app(app(ty_FiniteMap, cb), cc), bb) → new_esEs4(vyy440, vyy450, cb, cc)
new_esEs3(@2(vyy440, vyy441), @2(vyy450, vyy451), bfa, app(app(app(ty_@3, bfe), bff), bfg)) → new_esEs1(vyy441, vyy451, bfe, bff, bfg)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), hb, fg, app(app(ty_@2, bbe), bbf)) → new_esEs3(vyy442, vyy452, bbe, bbf)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), hb, app(app(ty_FiniteMap, bad), bae), fh) → new_esEs4(vyy441, vyy451, bad, bae)
new_esEs(Left(vyy440), Left(vyy450), app(app(ty_Either, h), ba), bb) → new_esEs(vyy440, vyy450, h, ba)
new_esEs0(Just(vyy440), Just(vyy450), app(ty_[], eg)) → new_esEs2(vyy440, vyy450, eg)
new_esEs2(:(vyy440, vyy441), :(vyy450, vyy451), app(app(ty_FiniteMap, bdb), bdc)) → new_esEs4(vyy440, vyy450, bdb, bdc)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), hb, app(app(ty_@2, bab), bac), fh) → new_esEs3(vyy441, vyy451, bab, bac)
new_esEs3(@2(vyy440, vyy441), @2(vyy450, vyy451), bfa, app(ty_[], bfh)) → new_esEs2(vyy441, vyy451, bfh)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), app(app(ty_FiniteMap, gh), ha), fg, fh) → new_esEs4(vyy440, vyy450, gh, ha)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), hb, app(ty_Maybe, he), fh) → new_esEs0(vyy441, vyy451, he)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), hb, fg, app(ty_[], bbd)) → new_esEs2(vyy442, vyy452, bbd)
new_esEs3(@2(vyy440, vyy441), @2(vyy450, vyy451), app(app(app(ty_@3, bea), beb), bec), bdg) → new_esEs1(vyy440, vyy450, bea, beb, bec)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), hb, app(ty_[], baa), fh) → new_esEs2(vyy441, vyy451, baa)
new_esEs3(@2(vyy440, vyy441), @2(vyy450, vyy451), bfa, app(app(ty_@2, bga), bgb)) → new_esEs3(vyy441, vyy451, bga, bgb)
new_esEs2(:(vyy440, vyy441), :(vyy450, vyy451), app(app(app(ty_@3, bcd), bce), bcf)) → new_esEs1(vyy440, vyy450, bcd, bce, bcf)
new_esEs2(:(vyy440, vyy441), :(vyy450, vyy451), app(app(ty_Either, bca), bcb)) → new_esEs(vyy440, vyy450, bca, bcb)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), app(app(app(ty_@3, gb), gc), gd), fg, fh) → new_esEs1(vyy440, vyy450, gb, gc, gd)
new_esEs(Right(vyy440), Right(vyy450), cd, app(app(ty_Either, ce), cf)) → new_esEs(vyy440, vyy450, ce, cf)
new_esEs3(@2(vyy440, vyy441), @2(vyy450, vyy451), app(ty_Maybe, bdh), bdg) → new_esEs0(vyy440, vyy450, bdh)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), app(app(ty_@2, gf), gg), fg, fh) → new_esEs3(vyy440, vyy450, gf, gg)
new_esEs2(:(vyy440, vyy441), :(vyy450, vyy451), app(app(ty_@2, bch), bda)) → new_esEs3(vyy440, vyy450, bch, bda)
new_esEs2(:(vyy440, vyy441), :(vyy450, vyy451), bdd) → new_esEs2(vyy441, vyy451, bdd)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), hb, app(app(ty_Either, hc), hd), fh) → new_esEs(vyy441, vyy451, hc, hd)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), app(app(ty_Either, fd), ff), fg, fh) → new_esEs(vyy440, vyy450, fd, ff)
new_esEs3(@2(vyy440, vyy441), @2(vyy450, vyy451), bfa, app(app(ty_Either, bfb), bfc)) → new_esEs(vyy441, vyy451, bfb, bfc)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), app(ty_Maybe, ga), fg, fh) → new_esEs0(vyy440, vyy450, ga)
new_esEs(Left(vyy440), Left(vyy450), app(app(app(ty_@3, bd), be), bf), bb) → new_esEs1(vyy440, vyy450, bd, be, bf)
new_esEs3(@2(vyy440, vyy441), @2(vyy450, vyy451), app(app(ty_Either, bde), bdf), bdg) → new_esEs(vyy440, vyy450, bde, bdf)
new_esEs0(Just(vyy440), Just(vyy450), app(app(ty_@2, eh), fa)) → new_esEs3(vyy440, vyy450, eh, fa)
new_esEs0(Just(vyy440), Just(vyy450), app(app(app(ty_@3, ed), ee), ef)) → new_esEs1(vyy440, vyy450, ed, ee, ef)
The TRS R consists of the following rules:
new_foldFM0(vyy450, vyy451, vyy74, EmptyFM, bge, bgf) → :(@2(vyy450, vyy451), vyy74)
new_foldFM0(vyy450, vyy451, vyy74, Branch(vyy4530, vyy4531, vyy4532, vyy4533, vyy4534), bge, bgf) → new_foldFM0(vyy4530, vyy4531, new_foldFM0(vyy450, vyy451, vyy74, vyy4534, bge, bgf), vyy4533, bge, bgf)
new_fmToList(vyy45, bge, bgf) → new_foldFM2(vyy45, bge, bgf)
new_foldFM2(Branch(vyy450, vyy451, vyy452, vyy453, vyy454), bge, bgf) → new_foldFM0(vyy450, vyy451, new_foldFM2(vyy454, bge, bgf), vyy453, bge, bgf)
new_foldFM2(EmptyFM, bge, bgf) → []
The set Q consists of the following terms:
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
new_fmToList(x0, x1, x2)
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_foldFM2(EmptyFM, x0, x1)
We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_esEs4(vyy44, vyy45, bge, bgf) → new_esEs2(new_foldFM2(vyy44, bge, bgf), new_fmToList(vyy45, bge, bgf), app(app(ty_@2, bge), bgf)) at position [1] we obtained the following new rules:
new_esEs4(vyy44, vyy45, bge, bgf) → new_esEs2(new_foldFM2(vyy44, bge, bgf), new_foldFM2(vyy45, bge, bgf), app(app(ty_@2, bge), bgf))
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ Rewriting
↳ QDP
↳ Rewriting
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_esEs0(Just(vyy440), Just(vyy450), app(app(ty_FiniteMap, fb), fc)) → new_esEs4(vyy440, vyy450, fb, fc)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), hb, app(app(app(ty_@3, hf), hg), hh), fh) → new_esEs1(vyy441, vyy451, hf, hg, hh)
new_esEs3(@2(vyy440, vyy441), @2(vyy450, vyy451), app(app(ty_FiniteMap, beg), beh), bdg) → new_esEs4(vyy440, vyy450, beg, beh)
new_esEs(Right(vyy440), Right(vyy450), cd, app(app(ty_FiniteMap, dg), dh)) → new_esEs4(vyy440, vyy450, dg, dh)
new_esEs0(Just(vyy440), Just(vyy450), app(ty_Maybe, ec)) → new_esEs0(vyy440, vyy450, ec)
new_esEs(Left(vyy440), Left(vyy450), app(ty_[], bg), bb) → new_esEs2(vyy440, vyy450, bg)
new_esEs(Right(vyy440), Right(vyy450), cd, app(app(ty_@2, de), df)) → new_esEs3(vyy440, vyy450, de, df)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), hb, fg, app(app(app(ty_@3, bba), bbb), bbc)) → new_esEs1(vyy442, vyy452, bba, bbb, bbc)
new_esEs3(@2(vyy440, vyy441), @2(vyy450, vyy451), bfa, app(app(ty_FiniteMap, bgc), bgd)) → new_esEs4(vyy441, vyy451, bgc, bgd)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), hb, fg, app(app(ty_FiniteMap, bbg), bbh)) → new_esEs4(vyy442, vyy452, bbg, bbh)
new_esEs3(@2(vyy440, vyy441), @2(vyy450, vyy451), app(ty_[], bed), bdg) → new_esEs2(vyy440, vyy450, bed)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), hb, fg, app(ty_Maybe, bah)) → new_esEs0(vyy442, vyy452, bah)
new_esEs(Left(vyy440), Left(vyy450), app(ty_Maybe, bc), bb) → new_esEs0(vyy440, vyy450, bc)
new_esEs2(:(vyy440, vyy441), :(vyy450, vyy451), app(ty_Maybe, bcc)) → new_esEs0(vyy440, vyy450, bcc)
new_esEs0(Just(vyy440), Just(vyy450), app(app(ty_Either, ea), eb)) → new_esEs(vyy440, vyy450, ea, eb)
new_esEs(Right(vyy440), Right(vyy450), cd, app(ty_[], dd)) → new_esEs2(vyy440, vyy450, dd)
new_esEs(Right(vyy440), Right(vyy450), cd, app(app(app(ty_@3, da), db), dc)) → new_esEs1(vyy440, vyy450, da, db, dc)
new_esEs(Left(vyy440), Left(vyy450), app(app(ty_@2, bh), ca), bb) → new_esEs3(vyy440, vyy450, bh, ca)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), hb, fg, app(app(ty_Either, baf), bag)) → new_esEs(vyy442, vyy452, baf, bag)
new_esEs3(@2(vyy440, vyy441), @2(vyy450, vyy451), app(app(ty_@2, bee), bef), bdg) → new_esEs3(vyy440, vyy450, bee, bef)
new_esEs3(@2(vyy440, vyy441), @2(vyy450, vyy451), bfa, app(ty_Maybe, bfd)) → new_esEs0(vyy441, vyy451, bfd)
new_esEs2(:(vyy440, vyy441), :(vyy450, vyy451), app(ty_[], bcg)) → new_esEs2(vyy440, vyy450, bcg)
new_esEs(Right(vyy440), Right(vyy450), cd, app(ty_Maybe, cg)) → new_esEs0(vyy440, vyy450, cg)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), app(ty_[], ge), fg, fh) → new_esEs2(vyy440, vyy450, ge)
new_esEs3(@2(vyy440, vyy441), @2(vyy450, vyy451), bfa, app(app(app(ty_@3, bfe), bff), bfg)) → new_esEs1(vyy441, vyy451, bfe, bff, bfg)
new_esEs(Left(vyy440), Left(vyy450), app(app(ty_FiniteMap, cb), cc), bb) → new_esEs4(vyy440, vyy450, cb, cc)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), hb, fg, app(app(ty_@2, bbe), bbf)) → new_esEs3(vyy442, vyy452, bbe, bbf)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), hb, app(app(ty_FiniteMap, bad), bae), fh) → new_esEs4(vyy441, vyy451, bad, bae)
new_esEs0(Just(vyy440), Just(vyy450), app(ty_[], eg)) → new_esEs2(vyy440, vyy450, eg)
new_esEs(Left(vyy440), Left(vyy450), app(app(ty_Either, h), ba), bb) → new_esEs(vyy440, vyy450, h, ba)
new_esEs2(:(vyy440, vyy441), :(vyy450, vyy451), app(app(ty_FiniteMap, bdb), bdc)) → new_esEs4(vyy440, vyy450, bdb, bdc)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), hb, app(app(ty_@2, bab), bac), fh) → new_esEs3(vyy441, vyy451, bab, bac)
new_esEs3(@2(vyy440, vyy441), @2(vyy450, vyy451), bfa, app(ty_[], bfh)) → new_esEs2(vyy441, vyy451, bfh)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), app(app(ty_FiniteMap, gh), ha), fg, fh) → new_esEs4(vyy440, vyy450, gh, ha)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), hb, app(ty_Maybe, he), fh) → new_esEs0(vyy441, vyy451, he)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), hb, fg, app(ty_[], bbd)) → new_esEs2(vyy442, vyy452, bbd)
new_esEs4(vyy44, vyy45, bge, bgf) → new_esEs2(new_foldFM2(vyy44, bge, bgf), new_foldFM2(vyy45, bge, bgf), app(app(ty_@2, bge), bgf))
new_esEs3(@2(vyy440, vyy441), @2(vyy450, vyy451), app(app(app(ty_@3, bea), beb), bec), bdg) → new_esEs1(vyy440, vyy450, bea, beb, bec)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), hb, app(ty_[], baa), fh) → new_esEs2(vyy441, vyy451, baa)
new_esEs3(@2(vyy440, vyy441), @2(vyy450, vyy451), bfa, app(app(ty_@2, bga), bgb)) → new_esEs3(vyy441, vyy451, bga, bgb)
new_esEs2(:(vyy440, vyy441), :(vyy450, vyy451), app(app(ty_Either, bca), bcb)) → new_esEs(vyy440, vyy450, bca, bcb)
new_esEs2(:(vyy440, vyy441), :(vyy450, vyy451), app(app(app(ty_@3, bcd), bce), bcf)) → new_esEs1(vyy440, vyy450, bcd, bce, bcf)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), app(app(app(ty_@3, gb), gc), gd), fg, fh) → new_esEs1(vyy440, vyy450, gb, gc, gd)
new_esEs(Right(vyy440), Right(vyy450), cd, app(app(ty_Either, ce), cf)) → new_esEs(vyy440, vyy450, ce, cf)
new_esEs3(@2(vyy440, vyy441), @2(vyy450, vyy451), app(ty_Maybe, bdh), bdg) → new_esEs0(vyy440, vyy450, bdh)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), app(app(ty_@2, gf), gg), fg, fh) → new_esEs3(vyy440, vyy450, gf, gg)
new_esEs2(:(vyy440, vyy441), :(vyy450, vyy451), app(app(ty_@2, bch), bda)) → new_esEs3(vyy440, vyy450, bch, bda)
new_esEs2(:(vyy440, vyy441), :(vyy450, vyy451), bdd) → new_esEs2(vyy441, vyy451, bdd)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), hb, app(app(ty_Either, hc), hd), fh) → new_esEs(vyy441, vyy451, hc, hd)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), app(app(ty_Either, fd), ff), fg, fh) → new_esEs(vyy440, vyy450, fd, ff)
new_esEs3(@2(vyy440, vyy441), @2(vyy450, vyy451), bfa, app(app(ty_Either, bfb), bfc)) → new_esEs(vyy441, vyy451, bfb, bfc)
new_esEs(Left(vyy440), Left(vyy450), app(app(app(ty_@3, bd), be), bf), bb) → new_esEs1(vyy440, vyy450, bd, be, bf)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), app(ty_Maybe, ga), fg, fh) → new_esEs0(vyy440, vyy450, ga)
new_esEs3(@2(vyy440, vyy441), @2(vyy450, vyy451), app(app(ty_Either, bde), bdf), bdg) → new_esEs(vyy440, vyy450, bde, bdf)
new_esEs0(Just(vyy440), Just(vyy450), app(app(ty_@2, eh), fa)) → new_esEs3(vyy440, vyy450, eh, fa)
new_esEs0(Just(vyy440), Just(vyy450), app(app(app(ty_@3, ed), ee), ef)) → new_esEs1(vyy440, vyy450, ed, ee, ef)
The TRS R consists of the following rules:
new_foldFM0(vyy450, vyy451, vyy74, EmptyFM, bge, bgf) → :(@2(vyy450, vyy451), vyy74)
new_foldFM0(vyy450, vyy451, vyy74, Branch(vyy4530, vyy4531, vyy4532, vyy4533, vyy4534), bge, bgf) → new_foldFM0(vyy4530, vyy4531, new_foldFM0(vyy450, vyy451, vyy74, vyy4534, bge, bgf), vyy4533, bge, bgf)
new_fmToList(vyy45, bge, bgf) → new_foldFM2(vyy45, bge, bgf)
new_foldFM2(Branch(vyy450, vyy451, vyy452, vyy453, vyy454), bge, bgf) → new_foldFM0(vyy450, vyy451, new_foldFM2(vyy454, bge, bgf), vyy453, bge, bgf)
new_foldFM2(EmptyFM, bge, bgf) → []
The set Q consists of the following terms:
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
new_fmToList(x0, x1, x2)
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_foldFM2(EmptyFM, x0, x1)
We have to consider all minimal (P,Q,R)-chains.
As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [15] we can delete all non-usable rules [17] from R.
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ Rewriting
↳ QDP
↳ Rewriting
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QReductionProof
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_esEs0(Just(vyy440), Just(vyy450), app(app(ty_FiniteMap, fb), fc)) → new_esEs4(vyy440, vyy450, fb, fc)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), hb, app(app(app(ty_@3, hf), hg), hh), fh) → new_esEs1(vyy441, vyy451, hf, hg, hh)
new_esEs3(@2(vyy440, vyy441), @2(vyy450, vyy451), app(app(ty_FiniteMap, beg), beh), bdg) → new_esEs4(vyy440, vyy450, beg, beh)
new_esEs(Right(vyy440), Right(vyy450), cd, app(app(ty_FiniteMap, dg), dh)) → new_esEs4(vyy440, vyy450, dg, dh)
new_esEs0(Just(vyy440), Just(vyy450), app(ty_Maybe, ec)) → new_esEs0(vyy440, vyy450, ec)
new_esEs(Left(vyy440), Left(vyy450), app(ty_[], bg), bb) → new_esEs2(vyy440, vyy450, bg)
new_esEs(Right(vyy440), Right(vyy450), cd, app(app(ty_@2, de), df)) → new_esEs3(vyy440, vyy450, de, df)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), hb, fg, app(app(app(ty_@3, bba), bbb), bbc)) → new_esEs1(vyy442, vyy452, bba, bbb, bbc)
new_esEs3(@2(vyy440, vyy441), @2(vyy450, vyy451), bfa, app(app(ty_FiniteMap, bgc), bgd)) → new_esEs4(vyy441, vyy451, bgc, bgd)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), hb, fg, app(app(ty_FiniteMap, bbg), bbh)) → new_esEs4(vyy442, vyy452, bbg, bbh)
new_esEs3(@2(vyy440, vyy441), @2(vyy450, vyy451), app(ty_[], bed), bdg) → new_esEs2(vyy440, vyy450, bed)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), hb, fg, app(ty_Maybe, bah)) → new_esEs0(vyy442, vyy452, bah)
new_esEs(Left(vyy440), Left(vyy450), app(ty_Maybe, bc), bb) → new_esEs0(vyy440, vyy450, bc)
new_esEs2(:(vyy440, vyy441), :(vyy450, vyy451), app(ty_Maybe, bcc)) → new_esEs0(vyy440, vyy450, bcc)
new_esEs0(Just(vyy440), Just(vyy450), app(app(ty_Either, ea), eb)) → new_esEs(vyy440, vyy450, ea, eb)
new_esEs(Right(vyy440), Right(vyy450), cd, app(ty_[], dd)) → new_esEs2(vyy440, vyy450, dd)
new_esEs(Right(vyy440), Right(vyy450), cd, app(app(app(ty_@3, da), db), dc)) → new_esEs1(vyy440, vyy450, da, db, dc)
new_esEs(Left(vyy440), Left(vyy450), app(app(ty_@2, bh), ca), bb) → new_esEs3(vyy440, vyy450, bh, ca)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), hb, fg, app(app(ty_Either, baf), bag)) → new_esEs(vyy442, vyy452, baf, bag)
new_esEs3(@2(vyy440, vyy441), @2(vyy450, vyy451), app(app(ty_@2, bee), bef), bdg) → new_esEs3(vyy440, vyy450, bee, bef)
new_esEs3(@2(vyy440, vyy441), @2(vyy450, vyy451), bfa, app(ty_Maybe, bfd)) → new_esEs0(vyy441, vyy451, bfd)
new_esEs2(:(vyy440, vyy441), :(vyy450, vyy451), app(ty_[], bcg)) → new_esEs2(vyy440, vyy450, bcg)
new_esEs(Right(vyy440), Right(vyy450), cd, app(ty_Maybe, cg)) → new_esEs0(vyy440, vyy450, cg)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), app(ty_[], ge), fg, fh) → new_esEs2(vyy440, vyy450, ge)
new_esEs3(@2(vyy440, vyy441), @2(vyy450, vyy451), bfa, app(app(app(ty_@3, bfe), bff), bfg)) → new_esEs1(vyy441, vyy451, bfe, bff, bfg)
new_esEs(Left(vyy440), Left(vyy450), app(app(ty_FiniteMap, cb), cc), bb) → new_esEs4(vyy440, vyy450, cb, cc)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), hb, fg, app(app(ty_@2, bbe), bbf)) → new_esEs3(vyy442, vyy452, bbe, bbf)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), hb, app(app(ty_FiniteMap, bad), bae), fh) → new_esEs4(vyy441, vyy451, bad, bae)
new_esEs0(Just(vyy440), Just(vyy450), app(ty_[], eg)) → new_esEs2(vyy440, vyy450, eg)
new_esEs(Left(vyy440), Left(vyy450), app(app(ty_Either, h), ba), bb) → new_esEs(vyy440, vyy450, h, ba)
new_esEs2(:(vyy440, vyy441), :(vyy450, vyy451), app(app(ty_FiniteMap, bdb), bdc)) → new_esEs4(vyy440, vyy450, bdb, bdc)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), hb, app(app(ty_@2, bab), bac), fh) → new_esEs3(vyy441, vyy451, bab, bac)
new_esEs3(@2(vyy440, vyy441), @2(vyy450, vyy451), bfa, app(ty_[], bfh)) → new_esEs2(vyy441, vyy451, bfh)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), app(app(ty_FiniteMap, gh), ha), fg, fh) → new_esEs4(vyy440, vyy450, gh, ha)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), hb, app(ty_Maybe, he), fh) → new_esEs0(vyy441, vyy451, he)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), hb, fg, app(ty_[], bbd)) → new_esEs2(vyy442, vyy452, bbd)
new_esEs4(vyy44, vyy45, bge, bgf) → new_esEs2(new_foldFM2(vyy44, bge, bgf), new_foldFM2(vyy45, bge, bgf), app(app(ty_@2, bge), bgf))
new_esEs3(@2(vyy440, vyy441), @2(vyy450, vyy451), app(app(app(ty_@3, bea), beb), bec), bdg) → new_esEs1(vyy440, vyy450, bea, beb, bec)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), hb, app(ty_[], baa), fh) → new_esEs2(vyy441, vyy451, baa)
new_esEs3(@2(vyy440, vyy441), @2(vyy450, vyy451), bfa, app(app(ty_@2, bga), bgb)) → new_esEs3(vyy441, vyy451, bga, bgb)
new_esEs2(:(vyy440, vyy441), :(vyy450, vyy451), app(app(ty_Either, bca), bcb)) → new_esEs(vyy440, vyy450, bca, bcb)
new_esEs2(:(vyy440, vyy441), :(vyy450, vyy451), app(app(app(ty_@3, bcd), bce), bcf)) → new_esEs1(vyy440, vyy450, bcd, bce, bcf)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), app(app(app(ty_@3, gb), gc), gd), fg, fh) → new_esEs1(vyy440, vyy450, gb, gc, gd)
new_esEs(Right(vyy440), Right(vyy450), cd, app(app(ty_Either, ce), cf)) → new_esEs(vyy440, vyy450, ce, cf)
new_esEs3(@2(vyy440, vyy441), @2(vyy450, vyy451), app(ty_Maybe, bdh), bdg) → new_esEs0(vyy440, vyy450, bdh)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), app(app(ty_@2, gf), gg), fg, fh) → new_esEs3(vyy440, vyy450, gf, gg)
new_esEs2(:(vyy440, vyy441), :(vyy450, vyy451), app(app(ty_@2, bch), bda)) → new_esEs3(vyy440, vyy450, bch, bda)
new_esEs2(:(vyy440, vyy441), :(vyy450, vyy451), bdd) → new_esEs2(vyy441, vyy451, bdd)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), hb, app(app(ty_Either, hc), hd), fh) → new_esEs(vyy441, vyy451, hc, hd)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), app(app(ty_Either, fd), ff), fg, fh) → new_esEs(vyy440, vyy450, fd, ff)
new_esEs3(@2(vyy440, vyy441), @2(vyy450, vyy451), bfa, app(app(ty_Either, bfb), bfc)) → new_esEs(vyy441, vyy451, bfb, bfc)
new_esEs(Left(vyy440), Left(vyy450), app(app(app(ty_@3, bd), be), bf), bb) → new_esEs1(vyy440, vyy450, bd, be, bf)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), app(ty_Maybe, ga), fg, fh) → new_esEs0(vyy440, vyy450, ga)
new_esEs3(@2(vyy440, vyy441), @2(vyy450, vyy451), app(app(ty_Either, bde), bdf), bdg) → new_esEs(vyy440, vyy450, bde, bdf)
new_esEs0(Just(vyy440), Just(vyy450), app(app(ty_@2, eh), fa)) → new_esEs3(vyy440, vyy450, eh, fa)
new_esEs0(Just(vyy440), Just(vyy450), app(app(app(ty_@3, ed), ee), ef)) → new_esEs1(vyy440, vyy450, ed, ee, ef)
The TRS R consists of the following rules:
new_foldFM2(Branch(vyy450, vyy451, vyy452, vyy453, vyy454), bge, bgf) → new_foldFM0(vyy450, vyy451, new_foldFM2(vyy454, bge, bgf), vyy453, bge, bgf)
new_foldFM2(EmptyFM, bge, bgf) → []
new_foldFM0(vyy450, vyy451, vyy74, EmptyFM, bge, bgf) → :(@2(vyy450, vyy451), vyy74)
new_foldFM0(vyy450, vyy451, vyy74, Branch(vyy4530, vyy4531, vyy4532, vyy4533, vyy4534), bge, bgf) → new_foldFM0(vyy4530, vyy4531, new_foldFM0(vyy450, vyy451, vyy74, vyy4534, bge, bgf), vyy4533, bge, bgf)
The set Q consists of the following terms:
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
new_fmToList(x0, x1, x2)
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_foldFM2(EmptyFM, x0, x1)
We have to consider all minimal (P,Q,R)-chains.
We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.
new_fmToList(x0, x1, x2)
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ Rewriting
↳ QDP
↳ Rewriting
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QReductionProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_esEs0(Just(vyy440), Just(vyy450), app(app(ty_FiniteMap, fb), fc)) → new_esEs4(vyy440, vyy450, fb, fc)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), hb, app(app(app(ty_@3, hf), hg), hh), fh) → new_esEs1(vyy441, vyy451, hf, hg, hh)
new_esEs3(@2(vyy440, vyy441), @2(vyy450, vyy451), app(app(ty_FiniteMap, beg), beh), bdg) → new_esEs4(vyy440, vyy450, beg, beh)
new_esEs(Right(vyy440), Right(vyy450), cd, app(app(ty_FiniteMap, dg), dh)) → new_esEs4(vyy440, vyy450, dg, dh)
new_esEs0(Just(vyy440), Just(vyy450), app(ty_Maybe, ec)) → new_esEs0(vyy440, vyy450, ec)
new_esEs(Left(vyy440), Left(vyy450), app(ty_[], bg), bb) → new_esEs2(vyy440, vyy450, bg)
new_esEs(Right(vyy440), Right(vyy450), cd, app(app(ty_@2, de), df)) → new_esEs3(vyy440, vyy450, de, df)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), hb, fg, app(app(app(ty_@3, bba), bbb), bbc)) → new_esEs1(vyy442, vyy452, bba, bbb, bbc)
new_esEs3(@2(vyy440, vyy441), @2(vyy450, vyy451), bfa, app(app(ty_FiniteMap, bgc), bgd)) → new_esEs4(vyy441, vyy451, bgc, bgd)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), hb, fg, app(app(ty_FiniteMap, bbg), bbh)) → new_esEs4(vyy442, vyy452, bbg, bbh)
new_esEs3(@2(vyy440, vyy441), @2(vyy450, vyy451), app(ty_[], bed), bdg) → new_esEs2(vyy440, vyy450, bed)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), hb, fg, app(ty_Maybe, bah)) → new_esEs0(vyy442, vyy452, bah)
new_esEs(Left(vyy440), Left(vyy450), app(ty_Maybe, bc), bb) → new_esEs0(vyy440, vyy450, bc)
new_esEs2(:(vyy440, vyy441), :(vyy450, vyy451), app(ty_Maybe, bcc)) → new_esEs0(vyy440, vyy450, bcc)
new_esEs0(Just(vyy440), Just(vyy450), app(app(ty_Either, ea), eb)) → new_esEs(vyy440, vyy450, ea, eb)
new_esEs(Right(vyy440), Right(vyy450), cd, app(app(app(ty_@3, da), db), dc)) → new_esEs1(vyy440, vyy450, da, db, dc)
new_esEs(Right(vyy440), Right(vyy450), cd, app(ty_[], dd)) → new_esEs2(vyy440, vyy450, dd)
new_esEs(Left(vyy440), Left(vyy450), app(app(ty_@2, bh), ca), bb) → new_esEs3(vyy440, vyy450, bh, ca)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), hb, fg, app(app(ty_Either, baf), bag)) → new_esEs(vyy442, vyy452, baf, bag)
new_esEs3(@2(vyy440, vyy441), @2(vyy450, vyy451), app(app(ty_@2, bee), bef), bdg) → new_esEs3(vyy440, vyy450, bee, bef)
new_esEs3(@2(vyy440, vyy441), @2(vyy450, vyy451), bfa, app(ty_Maybe, bfd)) → new_esEs0(vyy441, vyy451, bfd)
new_esEs(Right(vyy440), Right(vyy450), cd, app(ty_Maybe, cg)) → new_esEs0(vyy440, vyy450, cg)
new_esEs2(:(vyy440, vyy441), :(vyy450, vyy451), app(ty_[], bcg)) → new_esEs2(vyy440, vyy450, bcg)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), app(ty_[], ge), fg, fh) → new_esEs2(vyy440, vyy450, ge)
new_esEs3(@2(vyy440, vyy441), @2(vyy450, vyy451), bfa, app(app(app(ty_@3, bfe), bff), bfg)) → new_esEs1(vyy441, vyy451, bfe, bff, bfg)
new_esEs(Left(vyy440), Left(vyy450), app(app(ty_FiniteMap, cb), cc), bb) → new_esEs4(vyy440, vyy450, cb, cc)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), hb, fg, app(app(ty_@2, bbe), bbf)) → new_esEs3(vyy442, vyy452, bbe, bbf)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), hb, app(app(ty_FiniteMap, bad), bae), fh) → new_esEs4(vyy441, vyy451, bad, bae)
new_esEs0(Just(vyy440), Just(vyy450), app(ty_[], eg)) → new_esEs2(vyy440, vyy450, eg)
new_esEs(Left(vyy440), Left(vyy450), app(app(ty_Either, h), ba), bb) → new_esEs(vyy440, vyy450, h, ba)
new_esEs2(:(vyy440, vyy441), :(vyy450, vyy451), app(app(ty_FiniteMap, bdb), bdc)) → new_esEs4(vyy440, vyy450, bdb, bdc)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), hb, app(app(ty_@2, bab), bac), fh) → new_esEs3(vyy441, vyy451, bab, bac)
new_esEs3(@2(vyy440, vyy441), @2(vyy450, vyy451), bfa, app(ty_[], bfh)) → new_esEs2(vyy441, vyy451, bfh)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), app(app(ty_FiniteMap, gh), ha), fg, fh) → new_esEs4(vyy440, vyy450, gh, ha)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), hb, app(ty_Maybe, he), fh) → new_esEs0(vyy441, vyy451, he)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), hb, fg, app(ty_[], bbd)) → new_esEs2(vyy442, vyy452, bbd)
new_esEs4(vyy44, vyy45, bge, bgf) → new_esEs2(new_foldFM2(vyy44, bge, bgf), new_foldFM2(vyy45, bge, bgf), app(app(ty_@2, bge), bgf))
new_esEs3(@2(vyy440, vyy441), @2(vyy450, vyy451), app(app(app(ty_@3, bea), beb), bec), bdg) → new_esEs1(vyy440, vyy450, bea, beb, bec)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), hb, app(ty_[], baa), fh) → new_esEs2(vyy441, vyy451, baa)
new_esEs3(@2(vyy440, vyy441), @2(vyy450, vyy451), bfa, app(app(ty_@2, bga), bgb)) → new_esEs3(vyy441, vyy451, bga, bgb)
new_esEs2(:(vyy440, vyy441), :(vyy450, vyy451), app(app(ty_Either, bca), bcb)) → new_esEs(vyy440, vyy450, bca, bcb)
new_esEs2(:(vyy440, vyy441), :(vyy450, vyy451), app(app(app(ty_@3, bcd), bce), bcf)) → new_esEs1(vyy440, vyy450, bcd, bce, bcf)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), app(app(app(ty_@3, gb), gc), gd), fg, fh) → new_esEs1(vyy440, vyy450, gb, gc, gd)
new_esEs(Right(vyy440), Right(vyy450), cd, app(app(ty_Either, ce), cf)) → new_esEs(vyy440, vyy450, ce, cf)
new_esEs3(@2(vyy440, vyy441), @2(vyy450, vyy451), app(ty_Maybe, bdh), bdg) → new_esEs0(vyy440, vyy450, bdh)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), app(app(ty_@2, gf), gg), fg, fh) → new_esEs3(vyy440, vyy450, gf, gg)
new_esEs2(:(vyy440, vyy441), :(vyy450, vyy451), app(app(ty_@2, bch), bda)) → new_esEs3(vyy440, vyy450, bch, bda)
new_esEs2(:(vyy440, vyy441), :(vyy450, vyy451), bdd) → new_esEs2(vyy441, vyy451, bdd)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), hb, app(app(ty_Either, hc), hd), fh) → new_esEs(vyy441, vyy451, hc, hd)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), app(app(ty_Either, fd), ff), fg, fh) → new_esEs(vyy440, vyy450, fd, ff)
new_esEs3(@2(vyy440, vyy441), @2(vyy450, vyy451), bfa, app(app(ty_Either, bfb), bfc)) → new_esEs(vyy441, vyy451, bfb, bfc)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), app(ty_Maybe, ga), fg, fh) → new_esEs0(vyy440, vyy450, ga)
new_esEs(Left(vyy440), Left(vyy450), app(app(app(ty_@3, bd), be), bf), bb) → new_esEs1(vyy440, vyy450, bd, be, bf)
new_esEs3(@2(vyy440, vyy441), @2(vyy450, vyy451), app(app(ty_Either, bde), bdf), bdg) → new_esEs(vyy440, vyy450, bde, bdf)
new_esEs0(Just(vyy440), Just(vyy450), app(app(ty_@2, eh), fa)) → new_esEs3(vyy440, vyy450, eh, fa)
new_esEs0(Just(vyy440), Just(vyy450), app(app(app(ty_@3, ed), ee), ef)) → new_esEs1(vyy440, vyy450, ed, ee, ef)
The TRS R consists of the following rules:
new_foldFM2(Branch(vyy450, vyy451, vyy452, vyy453, vyy454), bge, bgf) → new_foldFM0(vyy450, vyy451, new_foldFM2(vyy454, bge, bgf), vyy453, bge, bgf)
new_foldFM2(EmptyFM, bge, bgf) → []
new_foldFM0(vyy450, vyy451, vyy74, EmptyFM, bge, bgf) → :(@2(vyy450, vyy451), vyy74)
new_foldFM0(vyy450, vyy451, vyy74, Branch(vyy4530, vyy4531, vyy4532, vyy4533, vyy4534), bge, bgf) → new_foldFM0(vyy4530, vyy4531, new_foldFM0(vyy450, vyy451, vyy74, vyy4534, bge, bgf), vyy4533, bge, bgf)
The set Q consists of the following terms:
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_foldFM2(EmptyFM, x0, x1)
We have to consider all minimal (P,Q,R)-chains.
We use the reduction pair processor [15].
The following pairs can be oriented strictly and are deleted.
new_esEs0(Just(vyy440), Just(vyy450), app(app(ty_FiniteMap, fb), fc)) → new_esEs4(vyy440, vyy450, fb, fc)
new_esEs(Right(vyy440), Right(vyy450), cd, app(app(ty_FiniteMap, dg), dh)) → new_esEs4(vyy440, vyy450, dg, dh)
new_esEs0(Just(vyy440), Just(vyy450), app(ty_Maybe, ec)) → new_esEs0(vyy440, vyy450, ec)
new_esEs(Left(vyy440), Left(vyy450), app(ty_[], bg), bb) → new_esEs2(vyy440, vyy450, bg)
new_esEs(Right(vyy440), Right(vyy450), cd, app(app(ty_@2, de), df)) → new_esEs3(vyy440, vyy450, de, df)
new_esEs(Left(vyy440), Left(vyy450), app(ty_Maybe, bc), bb) → new_esEs0(vyy440, vyy450, bc)
new_esEs2(:(vyy440, vyy441), :(vyy450, vyy451), app(ty_Maybe, bcc)) → new_esEs0(vyy440, vyy450, bcc)
new_esEs0(Just(vyy440), Just(vyy450), app(app(ty_Either, ea), eb)) → new_esEs(vyy440, vyy450, ea, eb)
new_esEs(Right(vyy440), Right(vyy450), cd, app(app(app(ty_@3, da), db), dc)) → new_esEs1(vyy440, vyy450, da, db, dc)
new_esEs(Right(vyy440), Right(vyy450), cd, app(ty_[], dd)) → new_esEs2(vyy440, vyy450, dd)
new_esEs(Left(vyy440), Left(vyy450), app(app(ty_@2, bh), ca), bb) → new_esEs3(vyy440, vyy450, bh, ca)
new_esEs(Right(vyy440), Right(vyy450), cd, app(ty_Maybe, cg)) → new_esEs0(vyy440, vyy450, cg)
new_esEs2(:(vyy440, vyy441), :(vyy450, vyy451), app(ty_[], bcg)) → new_esEs2(vyy440, vyy450, bcg)
new_esEs(Left(vyy440), Left(vyy450), app(app(ty_FiniteMap, cb), cc), bb) → new_esEs4(vyy440, vyy450, cb, cc)
new_esEs0(Just(vyy440), Just(vyy450), app(ty_[], eg)) → new_esEs2(vyy440, vyy450, eg)
new_esEs(Left(vyy440), Left(vyy450), app(app(ty_Either, h), ba), bb) → new_esEs(vyy440, vyy450, h, ba)
new_esEs2(:(vyy440, vyy441), :(vyy450, vyy451), app(app(ty_FiniteMap, bdb), bdc)) → new_esEs4(vyy440, vyy450, bdb, bdc)
new_esEs2(:(vyy440, vyy441), :(vyy450, vyy451), app(app(ty_Either, bca), bcb)) → new_esEs(vyy440, vyy450, bca, bcb)
new_esEs2(:(vyy440, vyy441), :(vyy450, vyy451), app(app(app(ty_@3, bcd), bce), bcf)) → new_esEs1(vyy440, vyy450, bcd, bce, bcf)
new_esEs(Right(vyy440), Right(vyy450), cd, app(app(ty_Either, ce), cf)) → new_esEs(vyy440, vyy450, ce, cf)
new_esEs2(:(vyy440, vyy441), :(vyy450, vyy451), app(app(ty_@2, bch), bda)) → new_esEs3(vyy440, vyy450, bch, bda)
new_esEs(Left(vyy440), Left(vyy450), app(app(app(ty_@3, bd), be), bf), bb) → new_esEs1(vyy440, vyy450, bd, be, bf)
new_esEs0(Just(vyy440), Just(vyy450), app(app(ty_@2, eh), fa)) → new_esEs3(vyy440, vyy450, eh, fa)
new_esEs0(Just(vyy440), Just(vyy450), app(app(app(ty_@3, ed), ee), ef)) → new_esEs1(vyy440, vyy450, ed, ee, ef)
The remaining pairs can at least be oriented weakly.
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), hb, app(app(app(ty_@3, hf), hg), hh), fh) → new_esEs1(vyy441, vyy451, hf, hg, hh)
new_esEs3(@2(vyy440, vyy441), @2(vyy450, vyy451), app(app(ty_FiniteMap, beg), beh), bdg) → new_esEs4(vyy440, vyy450, beg, beh)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), hb, fg, app(app(app(ty_@3, bba), bbb), bbc)) → new_esEs1(vyy442, vyy452, bba, bbb, bbc)
new_esEs3(@2(vyy440, vyy441), @2(vyy450, vyy451), bfa, app(app(ty_FiniteMap, bgc), bgd)) → new_esEs4(vyy441, vyy451, bgc, bgd)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), hb, fg, app(app(ty_FiniteMap, bbg), bbh)) → new_esEs4(vyy442, vyy452, bbg, bbh)
new_esEs3(@2(vyy440, vyy441), @2(vyy450, vyy451), app(ty_[], bed), bdg) → new_esEs2(vyy440, vyy450, bed)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), hb, fg, app(ty_Maybe, bah)) → new_esEs0(vyy442, vyy452, bah)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), hb, fg, app(app(ty_Either, baf), bag)) → new_esEs(vyy442, vyy452, baf, bag)
new_esEs3(@2(vyy440, vyy441), @2(vyy450, vyy451), app(app(ty_@2, bee), bef), bdg) → new_esEs3(vyy440, vyy450, bee, bef)
new_esEs3(@2(vyy440, vyy441), @2(vyy450, vyy451), bfa, app(ty_Maybe, bfd)) → new_esEs0(vyy441, vyy451, bfd)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), app(ty_[], ge), fg, fh) → new_esEs2(vyy440, vyy450, ge)
new_esEs3(@2(vyy440, vyy441), @2(vyy450, vyy451), bfa, app(app(app(ty_@3, bfe), bff), bfg)) → new_esEs1(vyy441, vyy451, bfe, bff, bfg)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), hb, fg, app(app(ty_@2, bbe), bbf)) → new_esEs3(vyy442, vyy452, bbe, bbf)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), hb, app(app(ty_FiniteMap, bad), bae), fh) → new_esEs4(vyy441, vyy451, bad, bae)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), hb, app(app(ty_@2, bab), bac), fh) → new_esEs3(vyy441, vyy451, bab, bac)
new_esEs3(@2(vyy440, vyy441), @2(vyy450, vyy451), bfa, app(ty_[], bfh)) → new_esEs2(vyy441, vyy451, bfh)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), app(app(ty_FiniteMap, gh), ha), fg, fh) → new_esEs4(vyy440, vyy450, gh, ha)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), hb, app(ty_Maybe, he), fh) → new_esEs0(vyy441, vyy451, he)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), hb, fg, app(ty_[], bbd)) → new_esEs2(vyy442, vyy452, bbd)
new_esEs4(vyy44, vyy45, bge, bgf) → new_esEs2(new_foldFM2(vyy44, bge, bgf), new_foldFM2(vyy45, bge, bgf), app(app(ty_@2, bge), bgf))
new_esEs3(@2(vyy440, vyy441), @2(vyy450, vyy451), app(app(app(ty_@3, bea), beb), bec), bdg) → new_esEs1(vyy440, vyy450, bea, beb, bec)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), hb, app(ty_[], baa), fh) → new_esEs2(vyy441, vyy451, baa)
new_esEs3(@2(vyy440, vyy441), @2(vyy450, vyy451), bfa, app(app(ty_@2, bga), bgb)) → new_esEs3(vyy441, vyy451, bga, bgb)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), app(app(app(ty_@3, gb), gc), gd), fg, fh) → new_esEs1(vyy440, vyy450, gb, gc, gd)
new_esEs3(@2(vyy440, vyy441), @2(vyy450, vyy451), app(ty_Maybe, bdh), bdg) → new_esEs0(vyy440, vyy450, bdh)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), app(app(ty_@2, gf), gg), fg, fh) → new_esEs3(vyy440, vyy450, gf, gg)
new_esEs2(:(vyy440, vyy441), :(vyy450, vyy451), bdd) → new_esEs2(vyy441, vyy451, bdd)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), hb, app(app(ty_Either, hc), hd), fh) → new_esEs(vyy441, vyy451, hc, hd)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), app(app(ty_Either, fd), ff), fg, fh) → new_esEs(vyy440, vyy450, fd, ff)
new_esEs3(@2(vyy440, vyy441), @2(vyy450, vyy451), bfa, app(app(ty_Either, bfb), bfc)) → new_esEs(vyy441, vyy451, bfb, bfc)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), app(ty_Maybe, ga), fg, fh) → new_esEs0(vyy440, vyy450, ga)
new_esEs3(@2(vyy440, vyy441), @2(vyy450, vyy451), app(app(ty_Either, bde), bdf), bdg) → new_esEs(vyy440, vyy450, bde, bdf)
Used ordering: Polynomial interpretation [25]:
POL(:(x1, x2)) = 0
POL(@2(x1, x2)) = 0
POL(@3(x1, x2, x3)) = 0
POL(Branch(x1, x2, x3, x4, x5)) = 0
POL(EmptyFM) = 0
POL(Just(x1)) = 0
POL(Left(x1)) = 0
POL(Right(x1)) = 0
POL([]) = 0
POL(app(x1, x2)) = x1 + x2
POL(new_esEs(x1, x2, x3, x4)) = 1 + x3 + x4
POL(new_esEs0(x1, x2, x3)) = 1 + x3
POL(new_esEs1(x1, x2, x3, x4, x5)) = x3 + x4 + x5
POL(new_esEs2(x1, x2, x3)) = 1 + x3
POL(new_esEs3(x1, x2, x3, x4)) = x3 + x4
POL(new_esEs4(x1, x2, x3, x4)) = 1 + x3 + x4
POL(new_foldFM0(x1, x2, x3, x4, x5, x6)) = 0
POL(new_foldFM2(x1, x2, x3)) = 0
POL(ty_@2) = 0
POL(ty_@3) = 0
POL(ty_Either) = 1
POL(ty_FiniteMap) = 1
POL(ty_Maybe) = 1
POL(ty_[]) = 1
The following usable rules [17] were oriented:
none
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ Rewriting
↳ QDP
↳ Rewriting
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QReductionProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), hb, app(app(ty_@2, bab), bac), fh) → new_esEs3(vyy441, vyy451, bab, bac)
new_esEs3(@2(vyy440, vyy441), @2(vyy450, vyy451), bfa, app(ty_[], bfh)) → new_esEs2(vyy441, vyy451, bfh)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), hb, app(app(app(ty_@3, hf), hg), hh), fh) → new_esEs1(vyy441, vyy451, hf, hg, hh)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), app(app(ty_FiniteMap, gh), ha), fg, fh) → new_esEs4(vyy440, vyy450, gh, ha)
new_esEs3(@2(vyy440, vyy441), @2(vyy450, vyy451), app(app(ty_FiniteMap, beg), beh), bdg) → new_esEs4(vyy440, vyy450, beg, beh)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), hb, fg, app(app(app(ty_@3, bba), bbb), bbc)) → new_esEs1(vyy442, vyy452, bba, bbb, bbc)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), hb, app(ty_Maybe, he), fh) → new_esEs0(vyy441, vyy451, he)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), hb, fg, app(app(ty_FiniteMap, bbg), bbh)) → new_esEs4(vyy442, vyy452, bbg, bbh)
new_esEs3(@2(vyy440, vyy441), @2(vyy450, vyy451), bfa, app(app(ty_FiniteMap, bgc), bgd)) → new_esEs4(vyy441, vyy451, bgc, bgd)
new_esEs3(@2(vyy440, vyy441), @2(vyy450, vyy451), app(ty_[], bed), bdg) → new_esEs2(vyy440, vyy450, bed)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), hb, fg, app(ty_[], bbd)) → new_esEs2(vyy442, vyy452, bbd)
new_esEs4(vyy44, vyy45, bge, bgf) → new_esEs2(new_foldFM2(vyy44, bge, bgf), new_foldFM2(vyy45, bge, bgf), app(app(ty_@2, bge), bgf))
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), hb, fg, app(ty_Maybe, bah)) → new_esEs0(vyy442, vyy452, bah)
new_esEs3(@2(vyy440, vyy441), @2(vyy450, vyy451), app(app(app(ty_@3, bea), beb), bec), bdg) → new_esEs1(vyy440, vyy450, bea, beb, bec)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), hb, app(ty_[], baa), fh) → new_esEs2(vyy441, vyy451, baa)
new_esEs3(@2(vyy440, vyy441), @2(vyy450, vyy451), bfa, app(app(ty_@2, bga), bgb)) → new_esEs3(vyy441, vyy451, bga, bgb)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), app(app(app(ty_@3, gb), gc), gd), fg, fh) → new_esEs1(vyy440, vyy450, gb, gc, gd)
new_esEs3(@2(vyy440, vyy441), @2(vyy450, vyy451), app(ty_Maybe, bdh), bdg) → new_esEs0(vyy440, vyy450, bdh)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), app(app(ty_@2, gf), gg), fg, fh) → new_esEs3(vyy440, vyy450, gf, gg)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), hb, fg, app(app(ty_Either, baf), bag)) → new_esEs(vyy442, vyy452, baf, bag)
new_esEs2(:(vyy440, vyy441), :(vyy450, vyy451), bdd) → new_esEs2(vyy441, vyy451, bdd)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), hb, app(app(ty_Either, hc), hd), fh) → new_esEs(vyy441, vyy451, hc, hd)
new_esEs3(@2(vyy440, vyy441), @2(vyy450, vyy451), app(app(ty_@2, bee), bef), bdg) → new_esEs3(vyy440, vyy450, bee, bef)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), app(app(ty_Either, fd), ff), fg, fh) → new_esEs(vyy440, vyy450, fd, ff)
new_esEs3(@2(vyy440, vyy441), @2(vyy450, vyy451), bfa, app(ty_Maybe, bfd)) → new_esEs0(vyy441, vyy451, bfd)
new_esEs3(@2(vyy440, vyy441), @2(vyy450, vyy451), bfa, app(app(ty_Either, bfb), bfc)) → new_esEs(vyy441, vyy451, bfb, bfc)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), app(ty_Maybe, ga), fg, fh) → new_esEs0(vyy440, vyy450, ga)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), app(ty_[], ge), fg, fh) → new_esEs2(vyy440, vyy450, ge)
new_esEs3(@2(vyy440, vyy441), @2(vyy450, vyy451), app(app(ty_Either, bde), bdf), bdg) → new_esEs(vyy440, vyy450, bde, bdf)
new_esEs3(@2(vyy440, vyy441), @2(vyy450, vyy451), bfa, app(app(app(ty_@3, bfe), bff), bfg)) → new_esEs1(vyy441, vyy451, bfe, bff, bfg)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), hb, fg, app(app(ty_@2, bbe), bbf)) → new_esEs3(vyy442, vyy452, bbe, bbf)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), hb, app(app(ty_FiniteMap, bad), bae), fh) → new_esEs4(vyy441, vyy451, bad, bae)
The TRS R consists of the following rules:
new_foldFM2(Branch(vyy450, vyy451, vyy452, vyy453, vyy454), bge, bgf) → new_foldFM0(vyy450, vyy451, new_foldFM2(vyy454, bge, bgf), vyy453, bge, bgf)
new_foldFM2(EmptyFM, bge, bgf) → []
new_foldFM0(vyy450, vyy451, vyy74, EmptyFM, bge, bgf) → :(@2(vyy450, vyy451), vyy74)
new_foldFM0(vyy450, vyy451, vyy74, Branch(vyy4530, vyy4531, vyy4532, vyy4533, vyy4534), bge, bgf) → new_foldFM0(vyy4530, vyy4531, new_foldFM0(vyy450, vyy451, vyy74, vyy4534, bge, bgf), vyy4533, bge, bgf)
The set Q consists of the following terms:
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_foldFM2(EmptyFM, x0, x1)
We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph [15,17,22] contains 2 SCCs with 21 less nodes.
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ Rewriting
↳ QDP
↳ Rewriting
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QReductionProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_esEs2(:(vyy440, vyy441), :(vyy450, vyy451), bdd) → new_esEs2(vyy441, vyy451, bdd)
The TRS R consists of the following rules:
new_foldFM2(Branch(vyy450, vyy451, vyy452, vyy453, vyy454), bge, bgf) → new_foldFM0(vyy450, vyy451, new_foldFM2(vyy454, bge, bgf), vyy453, bge, bgf)
new_foldFM2(EmptyFM, bge, bgf) → []
new_foldFM0(vyy450, vyy451, vyy74, EmptyFM, bge, bgf) → :(@2(vyy450, vyy451), vyy74)
new_foldFM0(vyy450, vyy451, vyy74, Branch(vyy4530, vyy4531, vyy4532, vyy4533, vyy4534), bge, bgf) → new_foldFM0(vyy4530, vyy4531, new_foldFM0(vyy450, vyy451, vyy74, vyy4534, bge, bgf), vyy4533, bge, bgf)
The set Q consists of the following terms:
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_foldFM2(EmptyFM, x0, x1)
We have to consider all minimal (P,Q,R)-chains.
As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [15] we can delete all non-usable rules [17] from R.
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ Rewriting
↳ QDP
↳ Rewriting
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QReductionProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QReductionProof
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_esEs2(:(vyy440, vyy441), :(vyy450, vyy451), bdd) → new_esEs2(vyy441, vyy451, bdd)
R is empty.
The set Q consists of the following terms:
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_foldFM2(EmptyFM, x0, x1)
We have to consider all minimal (P,Q,R)-chains.
We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_foldFM2(EmptyFM, x0, x1)
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ Rewriting
↳ QDP
↳ Rewriting
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QReductionProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QReductionProof
↳ QDP
↳ QDPSizeChangeProof
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_esEs2(:(vyy440, vyy441), :(vyy450, vyy451), bdd) → new_esEs2(vyy441, vyy451, bdd)
R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By using the subterm criterion [20] together with the size-change analysis [32] we have proven that there are no infinite chains for this DP problem. From the DPs we obtained the following set of size-change graphs:
- new_esEs2(:(vyy440, vyy441), :(vyy450, vyy451), bdd) → new_esEs2(vyy441, vyy451, bdd)
The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ Rewriting
↳ QDP
↳ Rewriting
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QReductionProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), hb, fg, app(app(app(ty_@3, bba), bbb), bbc)) → new_esEs1(vyy442, vyy452, bba, bbb, bbc)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), hb, app(app(ty_@2, bab), bac), fh) → new_esEs3(vyy441, vyy451, bab, bac)
new_esEs3(@2(vyy440, vyy441), @2(vyy450, vyy451), bfa, app(app(app(ty_@3, bfe), bff), bfg)) → new_esEs1(vyy441, vyy451, bfe, bff, bfg)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), app(app(ty_@2, gf), gg), fg, fh) → new_esEs3(vyy440, vyy450, gf, gg)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), hb, fg, app(app(ty_@2, bbe), bbf)) → new_esEs3(vyy442, vyy452, bbe, bbf)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), hb, app(app(app(ty_@3, hf), hg), hh), fh) → new_esEs1(vyy441, vyy451, hf, hg, hh)
new_esEs3(@2(vyy440, vyy441), @2(vyy450, vyy451), app(app(app(ty_@3, bea), beb), bec), bdg) → new_esEs1(vyy440, vyy450, bea, beb, bec)
new_esEs3(@2(vyy440, vyy441), @2(vyy450, vyy451), app(app(ty_@2, bee), bef), bdg) → new_esEs3(vyy440, vyy450, bee, bef)
new_esEs3(@2(vyy440, vyy441), @2(vyy450, vyy451), bfa, app(app(ty_@2, bga), bgb)) → new_esEs3(vyy441, vyy451, bga, bgb)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), app(app(app(ty_@3, gb), gc), gd), fg, fh) → new_esEs1(vyy440, vyy450, gb, gc, gd)
The TRS R consists of the following rules:
new_foldFM2(Branch(vyy450, vyy451, vyy452, vyy453, vyy454), bge, bgf) → new_foldFM0(vyy450, vyy451, new_foldFM2(vyy454, bge, bgf), vyy453, bge, bgf)
new_foldFM2(EmptyFM, bge, bgf) → []
new_foldFM0(vyy450, vyy451, vyy74, EmptyFM, bge, bgf) → :(@2(vyy450, vyy451), vyy74)
new_foldFM0(vyy450, vyy451, vyy74, Branch(vyy4530, vyy4531, vyy4532, vyy4533, vyy4534), bge, bgf) → new_foldFM0(vyy4530, vyy4531, new_foldFM0(vyy450, vyy451, vyy74, vyy4534, bge, bgf), vyy4533, bge, bgf)
The set Q consists of the following terms:
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_foldFM2(EmptyFM, x0, x1)
We have to consider all minimal (P,Q,R)-chains.
As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [15] we can delete all non-usable rules [17] from R.
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ Rewriting
↳ QDP
↳ Rewriting
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QReductionProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QReductionProof
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), hb, fg, app(app(app(ty_@3, bba), bbb), bbc)) → new_esEs1(vyy442, vyy452, bba, bbb, bbc)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), hb, app(app(ty_@2, bab), bac), fh) → new_esEs3(vyy441, vyy451, bab, bac)
new_esEs3(@2(vyy440, vyy441), @2(vyy450, vyy451), bfa, app(app(app(ty_@3, bfe), bff), bfg)) → new_esEs1(vyy441, vyy451, bfe, bff, bfg)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), app(app(ty_@2, gf), gg), fg, fh) → new_esEs3(vyy440, vyy450, gf, gg)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), hb, fg, app(app(ty_@2, bbe), bbf)) → new_esEs3(vyy442, vyy452, bbe, bbf)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), hb, app(app(app(ty_@3, hf), hg), hh), fh) → new_esEs1(vyy441, vyy451, hf, hg, hh)
new_esEs3(@2(vyy440, vyy441), @2(vyy450, vyy451), app(app(app(ty_@3, bea), beb), bec), bdg) → new_esEs1(vyy440, vyy450, bea, beb, bec)
new_esEs3(@2(vyy440, vyy441), @2(vyy450, vyy451), app(app(ty_@2, bee), bef), bdg) → new_esEs3(vyy440, vyy450, bee, bef)
new_esEs3(@2(vyy440, vyy441), @2(vyy450, vyy451), bfa, app(app(ty_@2, bga), bgb)) → new_esEs3(vyy441, vyy451, bga, bgb)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), app(app(app(ty_@3, gb), gc), gd), fg, fh) → new_esEs1(vyy440, vyy450, gb, gc, gd)
R is empty.
The set Q consists of the following terms:
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_foldFM2(EmptyFM, x0, x1)
We have to consider all minimal (P,Q,R)-chains.
We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_foldFM2(EmptyFM, x0, x1)
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ Rewriting
↳ QDP
↳ Rewriting
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QReductionProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QReductionProof
↳ QDP
↳ QDPSizeChangeProof
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), hb, fg, app(app(app(ty_@3, bba), bbb), bbc)) → new_esEs1(vyy442, vyy452, bba, bbb, bbc)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), hb, app(app(ty_@2, bab), bac), fh) → new_esEs3(vyy441, vyy451, bab, bac)
new_esEs3(@2(vyy440, vyy441), @2(vyy450, vyy451), bfa, app(app(app(ty_@3, bfe), bff), bfg)) → new_esEs1(vyy441, vyy451, bfe, bff, bfg)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), app(app(ty_@2, gf), gg), fg, fh) → new_esEs3(vyy440, vyy450, gf, gg)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), hb, app(app(app(ty_@3, hf), hg), hh), fh) → new_esEs1(vyy441, vyy451, hf, hg, hh)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), hb, fg, app(app(ty_@2, bbe), bbf)) → new_esEs3(vyy442, vyy452, bbe, bbf)
new_esEs3(@2(vyy440, vyy441), @2(vyy450, vyy451), app(app(app(ty_@3, bea), beb), bec), bdg) → new_esEs1(vyy440, vyy450, bea, beb, bec)
new_esEs3(@2(vyy440, vyy441), @2(vyy450, vyy451), app(app(ty_@2, bee), bef), bdg) → new_esEs3(vyy440, vyy450, bee, bef)
new_esEs3(@2(vyy440, vyy441), @2(vyy450, vyy451), bfa, app(app(ty_@2, bga), bgb)) → new_esEs3(vyy441, vyy451, bga, bgb)
new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), app(app(app(ty_@3, gb), gc), gd), fg, fh) → new_esEs1(vyy440, vyy450, gb, gc, gd)
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_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), hb, fg, app(app(app(ty_@3, bba), bbb), bbc)) → new_esEs1(vyy442, vyy452, bba, bbb, bbc)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4, 5 > 5
- new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), hb, app(app(app(ty_@3, hf), hg), hh), fh) → new_esEs1(vyy441, vyy451, hf, hg, hh)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5
- new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), app(app(app(ty_@3, gb), gc), gd), fg, fh) → new_esEs1(vyy440, vyy450, gb, gc, gd)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
- new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), hb, app(app(ty_@2, bab), bac), fh) → new_esEs3(vyy441, vyy451, bab, bac)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
- new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), app(app(ty_@2, gf), gg), fg, fh) → new_esEs3(vyy440, vyy450, gf, gg)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
- new_esEs1(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), hb, fg, app(app(ty_@2, bbe), bbf)) → new_esEs3(vyy442, vyy452, bbe, bbf)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4
- new_esEs3(@2(vyy440, vyy441), @2(vyy450, vyy451), bfa, app(app(app(ty_@3, bfe), bff), bfg)) → new_esEs1(vyy441, vyy451, bfe, bff, bfg)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5
- new_esEs3(@2(vyy440, vyy441), @2(vyy450, vyy451), app(app(app(ty_@3, bea), beb), bec), bdg) → new_esEs1(vyy440, vyy450, bea, beb, bec)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
- new_esEs3(@2(vyy440, vyy441), @2(vyy450, vyy451), app(app(ty_@2, bee), bef), bdg) → new_esEs3(vyy440, vyy450, bee, bef)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
- new_esEs3(@2(vyy440, vyy441), @2(vyy450, vyy451), bfa, app(app(ty_@2, bga), bgb)) → new_esEs3(vyy441, vyy451, bga, bgb)
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
↳ QDPSizeChangeProof
↳ QDP
↳ QDP
↳ QDP
↳ 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
↳ QDPSizeChangeProof
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_primPlusNat(Succ(vyy7500), Succ(vyy500000)) → new_primPlusNat(vyy7500, 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(vyy7500), Succ(vyy500000)) → new_primPlusNat(vyy7500, 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
↳ QDP
↳ QDPSizeChangeProof
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_primCmpNat(Succ(vyy600000), Succ(vyy50000)) → new_primCmpNat(vyy600000, 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_primCmpNat(Succ(vyy600000), Succ(vyy50000)) → new_primCmpNat(vyy600000, 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
↳ QDP
↳ QDPSizeChangeProof
↳ QDP
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_primEqNat(Succ(vyy44000), Succ(vyy45000)) → new_primEqNat(vyy44000, vyy45000)
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(vyy44000), Succ(vyy45000)) → new_primEqNat(vyy44000, vyy45000)
The graph contains the following edges 1 > 1, 2 > 2
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDPSizeChangeProof
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_foldFM1(Branch(vyy450, vyy451, vyy452, vyy453, vyy454), h, ba) → new_foldFM1(vyy454, h, ba)
R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By using the subterm criterion [20] together with the size-change analysis [32] we have proven that there are no infinite chains for this DP problem. From the DPs we obtained the following set of size-change graphs:
- new_foldFM1(Branch(vyy450, vyy451, vyy452, vyy453, vyy454), h, ba) → new_foldFM1(vyy454, h, ba)
The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_foldFM_LE(vyy3, Nothing, Branch(Just(vyy600), vyy61, vyy62, vyy63, vyy64), h, ba, bb) → new_foldFM_LE(vyy3, Nothing, vyy63, h, ba, bb)
new_foldFM_LE1(vyy17, vyy19, vyy20, vyy21, vyy22, vyy23, vyy24, False, bc, bd, be) → new_foldFM_LE(vyy17, Just(vyy19), vyy23, bc, bd, be)
new_foldFM_LE(vyy3, Nothing, Branch(Nothing, vyy61, vyy62, vyy63, vyy64), h, ba, bb) → new_foldFM_LE(vyy3, Nothing, vyy64, h, ba, bb)
new_foldFM_LE(vyy3, Just(vyy50), Branch(Just(vyy600), vyy61, vyy62, vyy63, vyy64), h, ba, bb) → new_foldFM_LE1(vyy3, vyy50, vyy600, vyy61, vyy62, vyy63, vyy64, new_ltEs20(vyy600, vyy50, ba), h, ba, bb)
new_foldFM_LE(vyy3, Nothing, Branch(Nothing, vyy61, vyy62, vyy63, vyy64), h, ba, bb) → new_foldFM_LE(vyy3, Nothing, vyy63, h, ba, bb)
new_foldFM_LE1(vyy17, vyy19, vyy20, vyy21, vyy22, vyy23, vyy24, True, bc, bd, be) → new_foldFM_LE(vyy17, Just(vyy19), vyy24, bc, bd, be)
new_foldFM_LE1(vyy17, vyy19, vyy20, vyy21, vyy22, vyy23, vyy24, True, bc, bd, be) → new_foldFM_LE(vyy17, Just(vyy19), vyy23, bc, bd, be)
new_foldFM_LE(vyy3, Just(vyy50), Branch(Nothing, vyy61, vyy62, vyy63, vyy64), h, ba, bb) → new_foldFM_LE(vyy3, Just(vyy50), vyy64, h, ba, bb)
new_foldFM_LE(vyy3, Just(vyy50), Branch(Nothing, vyy61, vyy62, vyy63, vyy64), h, ba, bb) → new_foldFM_LE(vyy3, Just(vyy50), vyy63, h, ba, bb)
The TRS R consists of the following rules:
new_compare34(vyy6000, vyy500, app(app(ty_Either, dfc), dfd)) → new_compare32(vyy6000, vyy500, dfc, dfd)
new_esEs7(Just(vyy440), Just(vyy450), app(ty_Maybe, ca)) → new_esEs7(vyy440, vyy450, ca)
new_ltEs20(vyy600, vyy50, app(ty_Maybe, baa)) → new_ltEs18(vyy600, vyy50, baa)
new_esEs20(vyy440, vyy450, app(ty_Maybe, bbh)) → new_esEs7(vyy440, vyy450, bbh)
new_esEs23(vyy440, vyy450, ty_Ordering) → new_esEs18(vyy440, vyy450)
new_compare3(:(vyy6000, vyy6001), :(vyy500, vyy501), bhd) → new_primCompAux0(vyy6000, vyy500, new_compare3(vyy6001, vyy501, bhd), bhd)
new_lt20(vyy6000, vyy500, ty_Int) → new_lt16(vyy6000, vyy500)
new_primCmpNat2(Zero, vyy60000) → LT
new_ltEs9(@2(vyy6000, vyy6001), @2(vyy500, vyy501), cee, cef) → new_pePe(new_lt20(vyy6000, vyy500, cee), vyy6000, vyy500, new_ltEs19(vyy6001, vyy501, cef), cee)
new_esEs18(LT, LT) → True
new_esEs20(vyy440, vyy450, ty_Double) → new_esEs19(vyy440, vyy450)
new_lt4(vyy6000, vyy500, ty_Int) → new_lt16(vyy6000, vyy500)
new_lt20(vyy6000, vyy500, app(app(ty_Either, dd), de)) → new_lt19(vyy6000, vyy500, dd, de)
new_ltEs4(Left(vyy6000), Left(vyy500), app(ty_Maybe, dbb), ceh) → new_ltEs18(vyy6000, vyy500, dbb)
new_esEs25(vyy441, vyy451, ty_Ordering) → new_esEs18(vyy441, vyy451)
new_ltEs14(GT, GT) → True
new_primCmpNat1(Zero, Succ(vyy50000)) → LT
new_ltEs18(Just(vyy6000), Just(vyy500), ty_Float) → new_ltEs8(vyy6000, vyy500)
new_compare10(vyy6000, vyy500, True, dd, de) → LT
new_primCompAux0(vyy6000, vyy500, vyy56, bhd) → new_primCompAux00(vyy56, new_compare34(vyy6000, vyy500, bhd))
new_ltEs18(Just(vyy6000), Just(vyy500), app(ty_Maybe, bba)) → new_ltEs18(vyy6000, vyy500, bba)
new_esEs18(LT, EQ) → False
new_esEs18(EQ, LT) → False
new_esEs27(vyy44, vyy45, app(ty_Maybe, bf)) → new_esEs7(vyy44, vyy45, bf)
new_esEs20(vyy440, vyy450, ty_Float) → new_esEs9(vyy440, vyy450)
new_esEs23(vyy440, vyy450, ty_Bool) → new_esEs14(vyy440, vyy450)
new_ltEs18(Just(vyy6000), Just(vyy500), ty_@0) → new_ltEs17(vyy6000, vyy500)
new_ltEs4(Left(vyy6000), Left(vyy500), app(app(app(ty_@3, dae), daf), dag), ceh) → new_ltEs6(vyy6000, vyy500, dae, daf, dag)
new_esEs8(Left(vyy440), Left(vyy450), ty_Integer, cfc) → new_esEs15(vyy440, vyy450)
new_compare14(vyy6000, vyy500, True, bfd, bfe, bff) → LT
new_ltEs19(vyy6001, vyy501, app(ty_Ratio, ddd)) → new_ltEs5(vyy6001, vyy501, ddd)
new_esEs7(Just(vyy440), Just(vyy450), ty_Double) → new_esEs19(vyy440, vyy450)
new_primMulNat0(Zero, Zero) → Zero
new_lt4(vyy6000, vyy500, ty_Double) → new_lt8(vyy6000, vyy500)
new_compare32(vyy6000, vyy500, dd, de) → new_compare23(vyy6000, vyy500, new_esEs8(vyy6000, vyy500, dd, de), dd, de)
new_esEs8(Left(vyy440), Left(vyy450), app(app(ty_FiniteMap, cgd), cge), cfc) → new_esEs16(vyy440, vyy450, cgd, cge)
new_sr(Integer(vyy60000), Integer(vyy5010)) → Integer(new_primMulInt(vyy60000, vyy5010))
new_esEs21(vyy441, vyy451, app(app(ty_Either, bdb), bdc)) → new_esEs8(vyy441, vyy451, bdb, bdc)
new_ltEs4(Right(vyy6000), Right(vyy500), ceg, ty_Integer) → new_ltEs12(vyy6000, vyy500)
new_esEs21(vyy441, vyy451, app(ty_[], bdh)) → new_esEs10(vyy441, vyy451, bdh)
new_lt20(vyy6000, vyy500, ty_Float) → new_lt6(vyy6000, vyy500)
new_ltEs4(Left(vyy6000), Left(vyy500), app(app(ty_@2, dac), dad), ceh) → new_ltEs9(vyy6000, vyy500, dac, dad)
new_ltEs4(Right(vyy6000), Right(vyy500), ceg, app(app(app(ty_@3, dbg), dbh), dca)) → new_ltEs6(vyy6000, vyy500, dbg, dbh, dca)
new_esEs24(vyy440, vyy450, ty_Integer) → new_esEs15(vyy440, vyy450)
new_esEs16(vyy44, vyy45, beh, bfa) → new_asAs(new_esEs17(new_sizeFM(vyy44, beh, bfa), new_sizeFM(vyy45, beh, bfa)), new_esEs10(new_fmToList(vyy44, beh, bfa), new_fmToList(vyy45, beh, bfa), app(app(ty_@2, beh), bfa)))
new_esEs21(vyy441, vyy451, app(app(ty_FiniteMap, bed), bee)) → new_esEs16(vyy441, vyy451, bed, bee)
new_not(GT) → False
new_lt5(vyy6001, vyy501, ty_Ordering) → new_lt13(vyy6001, vyy501)
new_esEs8(Right(vyy440), Right(vyy450), cgf, app(app(ty_FiniteMap, daa), dab)) → new_esEs16(vyy440, vyy450, daa, dab)
new_esEs26(vyy442, vyy452, ty_Float) → new_esEs9(vyy442, vyy452)
new_ltEs4(Right(vyy6000), Right(vyy500), ceg, app(ty_Maybe, dcd)) → new_ltEs18(vyy6000, vyy500, dcd)
new_lt4(vyy6000, vyy500, app(ty_[], eh)) → new_lt15(vyy6000, vyy500, eh)
new_ltEs4(Left(vyy6000), Left(vyy500), ty_Float, ceh) → new_ltEs8(vyy6000, vyy500)
new_esEs26(vyy442, vyy452, app(ty_[], cdf)) → new_esEs10(vyy442, vyy452, cdf)
new_lt4(vyy6000, vyy500, app(ty_Maybe, fa)) → new_lt18(vyy6000, vyy500, fa)
new_ltEs4(Right(vyy6000), Right(vyy500), ceg, app(ty_Ratio, dcb)) → new_ltEs5(vyy6000, vyy500, dcb)
new_esEs8(Left(vyy440), Left(vyy450), ty_Bool, cfc) → new_esEs14(vyy440, vyy450)
new_esEs24(vyy440, vyy450, app(app(ty_@2, cag), cah)) → new_esEs5(vyy440, vyy450, cag, cah)
new_esEs8(Left(vyy440), Left(vyy450), app(app(ty_@2, cga), cgb), cfc) → new_esEs5(vyy440, vyy450, cga, cgb)
new_primCmpNat1(Succ(vyy600000), Succ(vyy50000)) → new_primCmpNat1(vyy600000, vyy50000)
new_esEs9(Float(vyy440, vyy441), Float(vyy450, vyy451)) → new_esEs17(new_sr0(vyy440, vyy450), new_sr0(vyy441, vyy451))
new_ltEs4(Left(vyy6000), Left(vyy500), ty_Int, ceh) → new_ltEs16(vyy6000, vyy500)
new_esEs15(Integer(vyy440), Integer(vyy450)) → new_primEqInt(vyy440, vyy450)
new_esEs18(LT, GT) → False
new_esEs18(GT, LT) → False
new_ltEs7(vyy6002, vyy502, app(ty_Maybe, hf)) → new_ltEs18(vyy6002, vyy502, hf)
new_compare34(vyy6000, vyy500, app(app(app(ty_@3, dee), def), deg)) → new_compare33(vyy6000, vyy500, dee, def, deg)
new_esEs26(vyy442, vyy452, ty_Char) → new_esEs13(vyy442, vyy452)
new_esEs21(vyy441, vyy451, ty_Int) → new_esEs17(vyy441, vyy451)
new_ltEs7(vyy6002, vyy502, app(app(ty_@2, gg), gh)) → new_ltEs9(vyy6002, vyy502, gg, gh)
new_foldFM0(vyy450, vyy451, vyy74, EmptyFM, beh, bfa) → :(@2(vyy450, vyy451), vyy74)
new_esEs29(vyy441, vyy451, ty_Integer) → new_esEs15(vyy441, vyy451)
new_esEs25(vyy441, vyy451, app(ty_[], ccb)) → new_esEs10(vyy441, vyy451, ccb)
new_ltEs19(vyy6001, vyy501, app(app(ty_Either, ddg), ddh)) → new_ltEs4(vyy6001, vyy501, ddg, ddh)
new_compare34(vyy6000, vyy500, app(ty_[], dfa)) → new_compare3(vyy6000, vyy500, dfa)
new_compare27(vyy6000, vyy500, False) → new_compare18(vyy6000, vyy500, new_ltEs14(vyy6000, vyy500))
new_compare34(vyy6000, vyy500, ty_Integer) → new_compare12(vyy6000, vyy500)
new_esEs25(vyy441, vyy451, ty_Bool) → new_esEs14(vyy441, vyy451)
new_lt5(vyy6001, vyy501, ty_@0) → new_lt17(vyy6001, vyy501)
new_ltEs7(vyy6002, vyy502, ty_Double) → new_ltEs10(vyy6002, vyy502)
new_ltEs14(GT, EQ) → False
new_esEs22(EQ) → False
new_esEs23(vyy440, vyy450, app(app(ty_Either, bfh), bga)) → new_esEs8(vyy440, vyy450, bfh, bga)
new_esEs20(vyy440, vyy450, app(ty_Ratio, bcg)) → new_esEs12(vyy440, vyy450, bcg)
new_esEs26(vyy442, vyy452, app(app(ty_Either, cch), cda)) → new_esEs8(vyy442, vyy452, cch, cda)
new_esEs27(vyy44, vyy45, app(app(ty_FiniteMap, beh), bfa)) → new_esEs16(vyy44, vyy45, beh, bfa)
new_esEs24(vyy440, vyy450, app(ty_Maybe, cab)) → new_esEs7(vyy440, vyy450, cab)
new_compare34(vyy6000, vyy500, app(app(ty_@2, dec), ded)) → new_compare31(vyy6000, vyy500, dec, ded)
new_esEs24(vyy440, vyy450, ty_@0) → new_esEs11(vyy440, vyy450)
new_ltEs20(vyy600, vyy50, app(app(ty_Either, ceg), ceh)) → new_ltEs4(vyy600, vyy50, ceg, ceh)
new_lt20(vyy6000, vyy500, app(app(app(ty_@3, bfd), bfe), bff)) → new_lt10(vyy6000, vyy500, bfd, bfe, bff)
new_esEs23(vyy440, vyy450, app(ty_Maybe, bgb)) → new_esEs7(vyy440, vyy450, bgb)
new_ltEs7(vyy6002, vyy502, app(ty_[], he)) → new_ltEs15(vyy6002, vyy502, he)
new_lt5(vyy6001, vyy501, app(app(app(ty_@3, fg), fh), ga)) → new_lt10(vyy6001, vyy501, fg, fh, ga)
new_ltEs4(Right(vyy6000), Right(vyy500), ceg, app(app(ty_Either, dce), dcf)) → new_ltEs4(vyy6000, vyy500, dce, dcf)
new_ltEs20(vyy600, vyy50, ty_Integer) → new_ltEs12(vyy600, vyy50)
new_compare13(vyy6000, vyy500, False, bfb, bfc) → GT
new_ltEs18(Just(vyy6000), Just(vyy500), app(ty_Ratio, bag)) → new_ltEs5(vyy6000, vyy500, bag)
new_ltEs11(False, True) → True
new_esEs20(vyy440, vyy450, app(app(ty_@2, bce), bcf)) → new_esEs5(vyy440, vyy450, bce, bcf)
new_compare19(vyy6000, vyy500, True) → LT
new_lt20(vyy6000, vyy500, app(app(ty_@2, bfb), bfc)) → new_lt7(vyy6000, vyy500, bfb, bfc)
new_ltEs4(Left(vyy6000), Right(vyy500), ceg, ceh) → True
new_esEs21(vyy441, vyy451, ty_Bool) → new_esEs14(vyy441, vyy451)
new_lt4(vyy6000, vyy500, app(app(ty_Either, fb), fc)) → new_lt19(vyy6000, vyy500, fb, fc)
new_esEs21(vyy441, vyy451, ty_Char) → new_esEs13(vyy441, vyy451)
new_compare24(vyy6000, vyy500, False, beg) → new_compare11(vyy6000, vyy500, new_ltEs18(vyy6000, vyy500, beg), beg)
new_ltEs15(vyy600, vyy50, bhd) → new_not(new_compare3(vyy600, vyy50, bhd))
new_esEs7(Just(vyy440), Just(vyy450), ty_Int) → new_esEs17(vyy440, vyy450)
new_esEs21(vyy441, vyy451, ty_Double) → new_esEs19(vyy441, vyy451)
new_lt14(vyy6000, vyy500, bef) → new_esEs22(new_compare6(vyy6000, vyy500, bef))
new_esEs20(vyy440, vyy450, ty_Ordering) → new_esEs18(vyy440, vyy450)
new_esEs20(vyy440, vyy450, ty_@0) → new_esEs11(vyy440, vyy450)
new_esEs23(vyy440, vyy450, ty_Double) → new_esEs19(vyy440, vyy450)
new_compare34(vyy6000, vyy500, ty_@0) → new_compare7(vyy6000, vyy500)
new_esEs20(vyy440, vyy450, app(app(app(ty_@3, bca), bcb), bcc)) → new_esEs6(vyy440, vyy450, bca, bcb, bcc)
new_lt4(vyy6000, vyy500, app(app(ty_@2, eb), ec)) → new_lt7(vyy6000, vyy500, eb, ec)
new_esEs8(Left(vyy440), Left(vyy450), ty_Char, cfc) → new_esEs13(vyy440, vyy450)
new_ltEs18(Just(vyy6000), Just(vyy500), app(app(app(ty_@3, bad), bae), baf)) → new_ltEs6(vyy6000, vyy500, bad, bae, baf)
new_primEqNat0(Zero, Zero) → True
new_esEs27(vyy44, vyy45, ty_Ordering) → new_esEs18(vyy44, vyy45)
new_esEs23(vyy440, vyy450, ty_@0) → new_esEs11(vyy440, vyy450)
new_esEs8(Right(vyy440), Right(vyy450), cgf, ty_Double) → new_esEs19(vyy440, vyy450)
new_lt15(vyy6000, vyy500, ced) → new_esEs22(new_compare3(vyy6000, vyy500, ced))
new_ltEs4(Right(vyy6000), Right(vyy500), ceg, ty_Ordering) → new_ltEs14(vyy6000, vyy500)
new_compare11(vyy6000, vyy500, True, beg) → LT
new_esEs8(Right(vyy440), Right(vyy450), cgf, ty_@0) → new_esEs11(vyy440, vyy450)
new_ltEs4(Right(vyy6000), Right(vyy500), ceg, app(app(ty_@2, dbe), dbf)) → new_ltEs9(vyy6000, vyy500, dbe, dbf)
new_ltEs20(vyy600, vyy50, ty_Float) → new_ltEs8(vyy600, vyy50)
new_esEs27(vyy44, vyy45, ty_Char) → new_esEs13(vyy44, vyy45)
new_ltEs19(vyy6001, vyy501, ty_Float) → new_ltEs8(vyy6001, vyy501)
new_compare17(Double(vyy6000, vyy6001), Double(vyy500, vyy501)) → new_compare16(new_sr0(vyy6000, vyy500), new_sr0(vyy6001, vyy501))
new_ltEs18(Just(vyy6000), Just(vyy500), ty_Int) → new_ltEs16(vyy6000, vyy500)
new_esEs7(Just(vyy440), Just(vyy450), app(app(ty_FiniteMap, db), dc)) → new_esEs16(vyy440, vyy450, db, dc)
new_esEs13(Char(vyy440), Char(vyy450)) → new_primEqInt(vyy440, vyy450)
new_ltEs20(vyy600, vyy50, app(app(ty_@2, cee), cef)) → new_ltEs9(vyy600, vyy50, cee, cef)
new_ltEs18(Just(vyy6000), Just(vyy500), ty_Double) → new_ltEs10(vyy6000, vyy500)
new_ltEs14(EQ, LT) → False
new_primCmpNat1(Zero, Zero) → EQ
new_esEs25(vyy441, vyy451, ty_Int) → new_esEs17(vyy441, vyy451)
new_primCmpInt(Neg(Zero), Neg(Succ(vyy5000))) → new_primCmpNat0(vyy5000, Zero)
new_esEs8(Left(vyy440), Left(vyy450), ty_Double, cfc) → new_esEs19(vyy440, vyy450)
new_esEs8(Right(vyy440), Right(vyy450), cgf, ty_Char) → new_esEs13(vyy440, vyy450)
new_primPlusNat0(Succ(vyy750), vyy50000) → Succ(Succ(new_primPlusNat1(vyy750, vyy50000)))
new_esEs21(vyy441, vyy451, ty_Float) → new_esEs9(vyy441, vyy451)
new_esEs7(Just(vyy440), Just(vyy450), app(ty_[], ce)) → new_esEs10(vyy440, vyy450, ce)
new_esEs23(vyy440, vyy450, ty_Float) → new_esEs9(vyy440, vyy450)
new_esEs26(vyy442, vyy452, app(app(app(ty_@3, cdc), cdd), cde)) → new_esEs6(vyy442, vyy452, cdc, cdd, cde)
new_ltEs7(vyy6002, vyy502, ty_Ordering) → new_ltEs14(vyy6002, vyy502)
new_ltEs19(vyy6001, vyy501, ty_Double) → new_ltEs10(vyy6001, vyy501)
new_esEs18(EQ, GT) → False
new_esEs18(GT, EQ) → False
new_lt20(vyy6000, vyy500, ty_Bool) → new_lt9(vyy6000, vyy500)
new_primCmpNat1(Succ(vyy600000), Zero) → GT
new_ltEs20(vyy600, vyy50, ty_Int) → new_ltEs16(vyy600, vyy50)
new_primEqInt(Neg(Succ(vyy4400)), Neg(Succ(vyy4500))) → new_primEqNat0(vyy4400, vyy4500)
new_compare25(vyy6000, vyy500, True) → EQ
new_ltEs4(Right(vyy6000), Right(vyy500), ceg, ty_Float) → new_ltEs8(vyy6000, vyy500)
new_compare13(vyy6000, vyy500, True, bfb, bfc) → LT
new_esEs25(vyy441, vyy451, app(app(ty_FiniteMap, ccf), ccg)) → new_esEs16(vyy441, vyy451, ccf, ccg)
new_esEs24(vyy440, vyy450, ty_Bool) → new_esEs14(vyy440, vyy450)
new_primPlusNat1(Succ(vyy7500), Zero) → Succ(vyy7500)
new_primPlusNat1(Zero, Succ(vyy500000)) → Succ(vyy500000)
new_ltEs4(Left(vyy6000), Left(vyy500), ty_Bool, ceh) → new_ltEs11(vyy6000, vyy500)
new_esEs8(Right(vyy440), Right(vyy450), cgf, app(app(ty_Either, cgg), cgh)) → new_esEs8(vyy440, vyy450, cgg, cgh)
new_esEs8(Right(vyy440), Left(vyy450), cgf, cfc) → False
new_esEs8(Left(vyy440), Right(vyy450), cgf, cfc) → False
new_lt4(vyy6000, vyy500, ty_Char) → new_lt12(vyy6000, vyy500)
new_compare3([], :(vyy500, vyy501), bhd) → LT
new_esEs20(vyy440, vyy450, app(app(ty_Either, bbf), bbg)) → new_esEs8(vyy440, vyy450, bbf, bbg)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_lt20(vyy6000, vyy500, app(ty_Maybe, beg)) → new_lt18(vyy6000, vyy500, beg)
new_ltEs20(vyy600, vyy50, ty_Bool) → new_ltEs11(vyy600, vyy50)
new_esEs24(vyy440, vyy450, app(app(app(ty_@3, cac), cad), cae)) → new_esEs6(vyy440, vyy450, cac, cad, cae)
new_compare3(:(vyy6000, vyy6001), [], bhd) → GT
new_lt5(vyy6001, vyy501, ty_Integer) → new_lt11(vyy6001, vyy501)
new_lt5(vyy6001, vyy501, app(app(ty_@2, fd), ff)) → new_lt7(vyy6001, vyy501, fd, ff)
new_compare18(vyy6000, vyy500, False) → GT
new_lt5(vyy6001, vyy501, ty_Int) → new_lt16(vyy6001, vyy501)
new_esEs29(vyy441, vyy451, ty_Int) → new_esEs17(vyy441, vyy451)
new_ltEs4(Left(vyy6000), Left(vyy500), app(app(ty_Either, dbc), dbd), ceh) → new_ltEs4(vyy6000, vyy500, dbc, dbd)
new_primEqInt(Neg(Succ(vyy4400)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(vyy4500))) → False
new_lt20(vyy6000, vyy500, ty_Integer) → new_lt11(vyy6000, vyy500)
new_esEs26(vyy442, vyy452, app(app(ty_FiniteMap, ceb), cec)) → new_esEs16(vyy442, vyy452, ceb, cec)
new_ltEs7(vyy6002, vyy502, app(ty_Ratio, hd)) → new_ltEs5(vyy6002, vyy502, hd)
new_lt20(vyy6000, vyy500, ty_Ordering) → new_lt13(vyy6000, vyy500)
new_esEs8(Left(vyy440), Left(vyy450), app(ty_[], cfh), cfc) → new_esEs10(vyy440, vyy450, cfh)
new_esEs27(vyy44, vyy45, app(app(ty_Either, cgf), cfc)) → new_esEs8(vyy44, vyy45, cgf, cfc)
new_esEs12(:%(vyy440, vyy441), :%(vyy450, vyy451), deb) → new_asAs(new_esEs28(vyy440, vyy450, deb), new_esEs29(vyy441, vyy451, deb))
new_compare34(vyy6000, vyy500, ty_Char) → new_compare29(vyy6000, vyy500)
new_foldFM0(vyy450, vyy451, vyy74, Branch(vyy4530, vyy4531, vyy4532, vyy4533, vyy4534), beh, bfa) → new_foldFM0(vyy4530, vyy4531, new_foldFM0(vyy450, vyy451, vyy74, vyy4534, beh, bfa), vyy4533, beh, bfa)
new_ltEs20(vyy600, vyy50, app(ty_Ratio, df)) → new_ltEs5(vyy600, vyy50, df)
new_compare34(vyy6000, vyy500, ty_Double) → new_compare17(vyy6000, vyy500)
new_esEs26(vyy442, vyy452, ty_@0) → new_esEs11(vyy442, vyy452)
new_compare25(vyy6000, vyy500, False) → new_compare19(vyy6000, vyy500, new_ltEs11(vyy6000, vyy500))
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_esEs24(vyy440, vyy450, ty_Ordering) → new_esEs18(vyy440, vyy450)
new_esEs10(:(vyy440, vyy441), [], bfg) → False
new_esEs10([], :(vyy450, vyy451), bfg) → False
new_lt20(vyy6000, vyy500, ty_Double) → new_lt8(vyy6000, vyy500)
new_sizeFM(EmptyFM, beh, bfa) → Pos(Zero)
new_compare11(vyy6000, vyy500, False, beg) → GT
new_compare6(:%(vyy6000, vyy6001), :%(vyy500, vyy501), ty_Integer) → new_compare12(new_sr(vyy6000, vyy501), new_sr(vyy500, vyy6001))
new_primEqInt(Pos(Succ(vyy4400)), Pos(Succ(vyy4500))) → new_primEqNat0(vyy4400, vyy4500)
new_compare10(vyy6000, vyy500, False, dd, de) → GT
new_esEs24(vyy440, vyy450, app(app(ty_FiniteMap, cbb), cbc)) → new_esEs16(vyy440, vyy450, cbb, cbc)
new_esEs24(vyy440, vyy450, app(app(ty_Either, bhh), caa)) → new_esEs8(vyy440, vyy450, bhh, caa)
new_esEs8(Left(vyy440), Left(vyy450), app(ty_Maybe, cfd), cfc) → new_esEs7(vyy440, vyy450, cfd)
new_esEs7(Just(vyy440), Just(vyy450), ty_Float) → new_esEs9(vyy440, vyy450)
new_esEs14(True, False) → False
new_esEs14(False, True) → False
new_ltEs4(Right(vyy6000), Right(vyy500), ceg, app(ty_[], dcc)) → new_ltEs15(vyy6000, vyy500, dcc)
new_esEs26(vyy442, vyy452, ty_Integer) → new_esEs15(vyy442, vyy452)
new_ltEs11(True, False) → False
new_ltEs18(Just(vyy6000), Just(vyy500), app(app(ty_Either, bbb), bbc)) → new_ltEs4(vyy6000, vyy500, bbb, bbc)
new_esEs8(Left(vyy440), Left(vyy450), app(app(app(ty_@3, cfe), cff), cfg), cfc) → new_esEs6(vyy440, vyy450, cfe, cff, cfg)
new_esEs10([], [], bfg) → True
new_esEs24(vyy440, vyy450, ty_Int) → new_esEs17(vyy440, vyy450)
new_primEqNat0(Succ(vyy44000), Succ(vyy45000)) → new_primEqNat0(vyy44000, vyy45000)
new_compare7(@0, @0) → EQ
new_esEs21(vyy441, vyy451, app(ty_Ratio, bec)) → new_esEs12(vyy441, vyy451, bec)
new_compare34(vyy6000, vyy500, ty_Float) → new_compare30(vyy6000, vyy500)
new_ltEs18(Just(vyy6000), Just(vyy500), ty_Ordering) → new_ltEs14(vyy6000, vyy500)
new_primCompAux00(vyy60, LT) → LT
new_ltEs4(Left(vyy6000), Left(vyy500), ty_Char, ceh) → new_ltEs13(vyy6000, vyy500)
new_esEs24(vyy440, vyy450, app(ty_Ratio, cba)) → new_esEs12(vyy440, vyy450, cba)
new_esEs24(vyy440, vyy450, ty_Float) → new_esEs9(vyy440, vyy450)
new_esEs23(vyy440, vyy450, app(app(ty_FiniteMap, bhb), bhc)) → new_esEs16(vyy440, vyy450, bhb, bhc)
new_ltEs20(vyy600, vyy50, ty_Ordering) → new_ltEs14(vyy600, vyy50)
new_esEs5(@2(vyy440, vyy441), @2(vyy450, vyy451), bbd, bbe) → new_asAs(new_esEs20(vyy440, vyy450, bbd), new_esEs21(vyy441, vyy451, bbe))
new_esEs7(Nothing, Nothing, bf) → True
new_esEs8(Right(vyy440), Right(vyy450), cgf, ty_Float) → new_esEs9(vyy440, vyy450)
new_primEqInt(Pos(Succ(vyy4400)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(vyy4500))) → False
new_ltEs12(vyy600, vyy50) → new_not(new_compare12(vyy600, vyy50))
new_esEs23(vyy440, vyy450, ty_Char) → new_esEs13(vyy440, vyy450)
new_compare34(vyy6000, vyy500, ty_Int) → new_compare16(vyy6000, vyy500)
new_esEs8(Right(vyy440), Right(vyy450), cgf, ty_Bool) → new_esEs14(vyy440, vyy450)
new_lt10(vyy6000, vyy500, bfd, bfe, bff) → new_esEs22(new_compare33(vyy6000, vyy500, bfd, bfe, bff))
new_ltEs4(Right(vyy6000), Right(vyy500), ceg, ty_@0) → new_ltEs17(vyy6000, vyy500)
new_ltEs18(Nothing, Nothing, baa) → True
new_compare18(vyy6000, vyy500, True) → LT
new_esEs23(vyy440, vyy450, app(app(ty_@2, bgg), bgh)) → new_esEs5(vyy440, vyy450, bgg, bgh)
new_esEs6(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), bhe, bhf, bhg) → new_asAs(new_esEs24(vyy440, vyy450, bhe), new_asAs(new_esEs25(vyy441, vyy451, bhf), new_esEs26(vyy442, vyy452, bhg)))
new_primCmpInt(Neg(Zero), Pos(Succ(vyy5000))) → LT
new_esEs8(Right(vyy440), Right(vyy450), cgf, ty_Ordering) → new_esEs18(vyy440, vyy450)
new_compare19(vyy6000, vyy500, False) → GT
new_ltEs7(vyy6002, vyy502, ty_Int) → new_ltEs16(vyy6002, vyy502)
new_lt4(vyy6000, vyy500, ty_Float) → new_lt6(vyy6000, vyy500)
new_compare14(vyy6000, vyy500, False, bfd, bfe, bff) → GT
new_compare28(vyy6000, vyy500, False, bfb, bfc) → new_compare13(vyy6000, vyy500, new_ltEs9(vyy6000, vyy500, bfb, bfc), bfb, bfc)
new_ltEs7(vyy6002, vyy502, ty_Bool) → new_ltEs11(vyy6002, vyy502)
new_compare26(vyy6000, vyy500, False, bfd, bfe, bff) → new_compare14(vyy6000, vyy500, new_ltEs6(vyy6000, vyy500, bfd, bfe, bff), bfd, bfe, bff)
new_primPlusNat1(Succ(vyy7500), Succ(vyy500000)) → Succ(Succ(new_primPlusNat1(vyy7500, vyy500000)))
new_ltEs20(vyy600, vyy50, ty_Char) → new_ltEs13(vyy600, vyy50)
new_compare28(vyy6000, vyy500, True, bfb, bfc) → EQ
new_esEs7(Just(vyy440), Just(vyy450), ty_Integer) → new_esEs15(vyy440, vyy450)
new_primEqInt(Pos(Succ(vyy4400)), Neg(vyy450)) → False
new_primEqInt(Neg(Succ(vyy4400)), Pos(vyy450)) → False
new_esEs7(Nothing, Just(vyy450), bf) → False
new_esEs7(Just(vyy440), Nothing, bf) → False
new_esEs20(vyy440, vyy450, ty_Char) → new_esEs13(vyy440, vyy450)
new_foldFM2(EmptyFM, beh, bfa) → []
new_compare34(vyy6000, vyy500, ty_Ordering) → new_compare15(vyy6000, vyy500)
new_compare34(vyy6000, vyy500, ty_Bool) → new_compare9(vyy6000, vyy500)
new_lt17(vyy6000, vyy500) → new_esEs22(new_compare7(vyy6000, vyy500))
new_ltEs20(vyy600, vyy50, ty_Double) → new_ltEs10(vyy600, vyy50)
new_compare31(vyy6000, vyy500, bfb, bfc) → new_compare28(vyy6000, vyy500, new_esEs5(vyy6000, vyy500, bfb, bfc), bfb, bfc)
new_esEs7(Just(vyy440), Just(vyy450), app(app(ty_Either, bg), bh)) → new_esEs8(vyy440, vyy450, bg, bh)
new_lt5(vyy6001, vyy501, ty_Bool) → new_lt9(vyy6001, vyy501)
new_esEs23(vyy440, vyy450, app(ty_Ratio, bha)) → new_esEs12(vyy440, vyy450, bha)
new_esEs26(vyy442, vyy452, ty_Int) → new_esEs17(vyy442, vyy452)
new_primEqInt(Pos(Zero), Neg(Succ(vyy4500))) → False
new_primEqInt(Neg(Zero), Pos(Succ(vyy4500))) → False
new_ltEs19(vyy6001, vyy501, app(app(ty_@2, dcg), dch)) → new_ltEs9(vyy6001, vyy501, dcg, dch)
new_primCmpNat2(Succ(vyy5000), vyy60000) → new_primCmpNat1(vyy5000, vyy60000)
new_esEs21(vyy441, vyy451, ty_Integer) → new_esEs15(vyy441, vyy451)
new_primCompAux00(vyy60, EQ) → vyy60
new_pePe(False, vyy44, vyy45, vyy46, dea) → new_asAs(new_esEs27(vyy44, vyy45, dea), vyy46)
new_esEs8(Left(vyy440), Left(vyy450), app(ty_Ratio, cgc), cfc) → new_esEs12(vyy440, vyy450, cgc)
new_esEs26(vyy442, vyy452, ty_Ordering) → new_esEs18(vyy442, vyy452)
new_esEs8(Left(vyy440), Left(vyy450), ty_@0, cfc) → new_esEs11(vyy440, vyy450)
new_esEs21(vyy441, vyy451, ty_Ordering) → new_esEs18(vyy441, vyy451)
new_ltEs4(Left(vyy6000), Left(vyy500), app(ty_[], dba), ceh) → new_ltEs15(vyy6000, vyy500, dba)
new_esEs8(Left(vyy440), Left(vyy450), ty_Int, cfc) → new_esEs17(vyy440, vyy450)
new_esEs26(vyy442, vyy452, app(app(ty_@2, cdg), cdh)) → new_esEs5(vyy442, vyy452, cdg, cdh)
new_esEs20(vyy440, vyy450, app(app(ty_FiniteMap, bch), bda)) → new_esEs16(vyy440, vyy450, bch, bda)
new_esEs24(vyy440, vyy450, ty_Char) → new_esEs13(vyy440, vyy450)
new_esEs21(vyy441, vyy451, app(app(ty_@2, bea), beb)) → new_esEs5(vyy441, vyy451, bea, beb)
new_ltEs20(vyy600, vyy50, app(app(app(ty_@3, dg), dh), ea)) → new_ltEs6(vyy600, vyy50, dg, dh, ea)
new_ltEs4(Right(vyy6000), Left(vyy500), ceg, ceh) → False
new_ltEs5(vyy600, vyy50, df) → new_not(new_compare6(vyy600, vyy50, df))
new_compare24(vyy6000, vyy500, True, beg) → EQ
new_ltEs18(Just(vyy6000), Nothing, baa) → False
new_primPlusNat0(Zero, vyy50000) → Succ(vyy50000)
new_ltEs17(vyy600, vyy50) → new_not(new_compare7(vyy600, vyy50))
new_compare15(vyy6000, vyy500) → new_compare27(vyy6000, vyy500, new_esEs18(vyy6000, vyy500))
new_ltEs18(Just(vyy6000), Just(vyy500), app(ty_[], bah)) → new_ltEs15(vyy6000, vyy500, bah)
new_esEs25(vyy441, vyy451, ty_Integer) → new_esEs15(vyy441, vyy451)
new_ltEs14(LT, LT) → True
new_esEs26(vyy442, vyy452, ty_Bool) → new_esEs14(vyy442, vyy452)
new_ltEs7(vyy6002, vyy502, app(app(app(ty_@3, ha), hb), hc)) → new_ltEs6(vyy6002, vyy502, ha, hb, hc)
new_ltEs4(Left(vyy6000), Left(vyy500), ty_Integer, ceh) → new_ltEs12(vyy6000, vyy500)
new_lt20(vyy6000, vyy500, app(ty_Ratio, bef)) → new_lt14(vyy6000, vyy500, bef)
new_not0 → True
new_ltEs19(vyy6001, vyy501, app(app(app(ty_@3, dda), ddb), ddc)) → new_ltEs6(vyy6001, vyy501, dda, ddb, ddc)
new_esEs23(vyy440, vyy450, app(ty_[], bgf)) → new_esEs10(vyy440, vyy450, bgf)
new_lt12(vyy6000, vyy500) → new_esEs22(new_compare29(vyy6000, vyy500))
new_ltEs11(False, False) → True
new_esEs19(Double(vyy440, vyy441), Double(vyy450, vyy451)) → new_esEs17(new_sr0(vyy440, vyy450), new_sr0(vyy441, vyy451))
new_compare12(Integer(vyy6000), Integer(vyy500)) → new_primCmpInt(vyy6000, vyy500)
new_ltEs7(vyy6002, vyy502, ty_Float) → new_ltEs8(vyy6002, vyy502)
new_esEs18(GT, GT) → True
new_ltEs19(vyy6001, vyy501, app(ty_[], dde)) → new_ltEs15(vyy6001, vyy501, dde)
new_ltEs20(vyy600, vyy50, ty_@0) → new_ltEs17(vyy600, vyy50)
new_lt4(vyy6000, vyy500, ty_Integer) → new_lt11(vyy6000, vyy500)
new_ltEs19(vyy6001, vyy501, ty_Integer) → new_ltEs12(vyy6001, vyy501)
new_primCmpInt(Pos(Succ(vyy60000)), Neg(vyy500)) → GT
new_esEs21(vyy441, vyy451, app(ty_Maybe, bdd)) → new_esEs7(vyy441, vyy451, bdd)
new_primMulInt(Pos(vyy60000), Pos(vyy5000)) → Pos(new_primMulNat0(vyy60000, vyy5000))
new_ltEs4(Left(vyy6000), Left(vyy500), app(ty_Ratio, dah), ceh) → new_ltEs5(vyy6000, vyy500, dah)
new_esEs8(Right(vyy440), Right(vyy450), cgf, app(app(app(ty_@3, chb), chc), chd)) → new_esEs6(vyy440, vyy450, chb, chc, chd)
new_primMulInt(Neg(vyy60000), Neg(vyy5000)) → Pos(new_primMulNat0(vyy60000, vyy5000))
new_esEs20(vyy440, vyy450, ty_Integer) → new_esEs15(vyy440, vyy450)
new_primEqNat0(Zero, Succ(vyy45000)) → False
new_primEqNat0(Succ(vyy44000), Zero) → False
new_esEs7(Just(vyy440), Just(vyy450), ty_Char) → new_esEs13(vyy440, vyy450)
new_lt5(vyy6001, vyy501, app(ty_[], gc)) → new_lt15(vyy6001, vyy501, gc)
new_esEs8(Right(vyy440), Right(vyy450), cgf, app(ty_Ratio, chh)) → new_esEs12(vyy440, vyy450, chh)
new_esEs17(vyy44, vyy45) → new_primEqInt(vyy44, vyy45)
new_esEs27(vyy44, vyy45, ty_@0) → new_esEs11(vyy44, vyy45)
new_ltEs7(vyy6002, vyy502, ty_Integer) → new_ltEs12(vyy6002, vyy502)
new_esEs20(vyy440, vyy450, ty_Bool) → new_esEs14(vyy440, vyy450)
new_lt20(vyy6000, vyy500, ty_@0) → new_lt17(vyy6000, vyy500)
new_esEs20(vyy440, vyy450, app(ty_[], bcd)) → new_esEs10(vyy440, vyy450, bcd)
new_compare23(vyy6000, vyy500, False, dd, de) → new_compare10(vyy6000, vyy500, new_ltEs4(vyy6000, vyy500, dd, de), dd, de)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_primCmpInt(Pos(Succ(vyy60000)), Pos(vyy500)) → new_primCmpNat0(vyy60000, vyy500)
new_esEs27(vyy44, vyy45, app(app(app(ty_@3, bhe), bhf), bhg)) → new_esEs6(vyy44, vyy45, bhe, bhf, bhg)
new_ltEs7(vyy6002, vyy502, app(app(ty_Either, hg), hh)) → new_ltEs4(vyy6002, vyy502, hg, hh)
new_esEs11(@0, @0) → True
new_esEs25(vyy441, vyy451, ty_@0) → new_esEs11(vyy441, vyy451)
new_esEs27(vyy44, vyy45, app(app(ty_@2, bbd), bbe)) → new_esEs5(vyy44, vyy45, bbd, bbe)
new_primCmpNat0(vyy60000, Zero) → GT
new_ltEs19(vyy6001, vyy501, ty_Char) → new_ltEs13(vyy6001, vyy501)
new_esEs27(vyy44, vyy45, ty_Int) → new_esEs17(vyy44, vyy45)
new_sizeFM(Branch(vyy450, vyy451, vyy452, vyy453, vyy454), beh, bfa) → vyy452
new_compare30(Float(vyy6000, vyy6001), Float(vyy500, vyy501)) → new_compare16(new_sr0(vyy6000, vyy500), new_sr0(vyy6001, vyy501))
new_ltEs4(Right(vyy6000), Right(vyy500), ceg, ty_Double) → new_ltEs10(vyy6000, vyy500)
new_ltEs19(vyy6001, vyy501, ty_@0) → new_ltEs17(vyy6001, vyy501)
new_esEs23(vyy440, vyy450, ty_Int) → new_esEs17(vyy440, vyy450)
new_pePe(True, vyy44, vyy45, vyy46, dea) → True
new_esEs24(vyy440, vyy450, ty_Double) → new_esEs19(vyy440, vyy450)
new_foldFM2(Branch(vyy450, vyy451, vyy452, vyy453, vyy454), beh, bfa) → new_foldFM0(vyy450, vyy451, new_foldFM2(vyy454, beh, bfa), vyy453, beh, bfa)
new_compare23(vyy6000, vyy500, True, dd, de) → EQ
new_lt5(vyy6001, vyy501, ty_Float) → new_lt6(vyy6001, vyy501)
new_primCmpInt(Pos(Zero), Neg(Succ(vyy5000))) → GT
new_compare8(vyy6000, vyy500, beg) → new_compare24(vyy6000, vyy500, new_esEs7(vyy6000, vyy500, beg), beg)
new_sr0(vyy6000, vyy500) → new_primMulInt(vyy6000, vyy500)
new_esEs10(:(vyy440, vyy441), :(vyy450, vyy451), bfg) → new_asAs(new_esEs23(vyy440, vyy450, bfg), new_esEs10(vyy441, vyy451, bfg))
new_esEs27(vyy44, vyy45, app(ty_Ratio, deb)) → new_esEs12(vyy44, vyy45, deb)
new_ltEs19(vyy6001, vyy501, ty_Ordering) → new_ltEs14(vyy6001, vyy501)
new_esEs8(Left(vyy440), Left(vyy450), app(app(ty_Either, cfa), cfb), cfc) → new_esEs8(vyy440, vyy450, cfa, cfb)
new_esEs25(vyy441, vyy451, app(ty_Maybe, cbf)) → new_esEs7(vyy441, vyy451, cbf)
new_esEs7(Just(vyy440), Just(vyy450), app(app(app(ty_@3, cb), cc), cd)) → new_esEs6(vyy440, vyy450, cb, cc, cd)
new_esEs24(vyy440, vyy450, app(ty_[], caf)) → new_esEs10(vyy440, vyy450, caf)
new_lt4(vyy6000, vyy500, ty_Ordering) → new_lt13(vyy6000, vyy500)
new_lt6(vyy6000, vyy500) → new_esEs22(new_compare30(vyy6000, vyy500))
new_lt9(vyy6000, vyy500) → new_esEs22(new_compare9(vyy6000, vyy500))
new_lt20(vyy6000, vyy500, app(ty_[], ced)) → new_lt15(vyy6000, vyy500, ced)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_compare29(Char(vyy6000), Char(vyy500)) → new_primCmpInt(vyy6000, vyy500)
new_esEs7(Just(vyy440), Just(vyy450), ty_@0) → new_esEs11(vyy440, vyy450)
new_ltEs18(Just(vyy6000), Just(vyy500), app(app(ty_@2, bab), bac)) → new_ltEs9(vyy6000, vyy500, bab, bac)
new_ltEs10(vyy600, vyy50) → new_not(new_compare17(vyy600, vyy50))
new_compare34(vyy6000, vyy500, app(ty_Maybe, dfb)) → new_compare8(vyy6000, vyy500, dfb)
new_lt18(vyy6000, vyy500, beg) → new_esEs22(new_compare8(vyy6000, vyy500, beg))
new_esEs28(vyy440, vyy450, ty_Int) → new_esEs17(vyy440, vyy450)
new_asAs(False, vyy55) → False
new_ltEs11(True, True) → True
new_compare3([], [], bhd) → EQ
new_primMulInt(Pos(vyy60000), Neg(vyy5000)) → Neg(new_primMulNat0(vyy60000, vyy5000))
new_primMulInt(Neg(vyy60000), Pos(vyy5000)) → Neg(new_primMulNat0(vyy60000, vyy5000))
new_primCmpInt(Neg(Succ(vyy60000)), Neg(vyy500)) → new_primCmpNat2(vyy500, vyy60000)
new_compare16(vyy600, vyy50) → new_primCmpInt(vyy600, vyy50)
new_primMulNat0(Succ(vyy600000), Zero) → Zero
new_primMulNat0(Zero, Succ(vyy50000)) → Zero
new_esEs23(vyy440, vyy450, app(app(app(ty_@3, bgc), bgd), bge)) → new_esEs6(vyy440, vyy450, bgc, bgd, bge)
new_lt4(vyy6000, vyy500, app(app(app(ty_@3, ed), ee), ef)) → new_lt10(vyy6000, vyy500, ed, ee, ef)
new_ltEs16(vyy600, vyy50) → new_not(new_compare16(vyy600, vyy50))
new_ltEs4(Right(vyy6000), Right(vyy500), ceg, ty_Int) → new_ltEs16(vyy6000, vyy500)
new_esEs8(Right(vyy440), Right(vyy450), cgf, ty_Int) → new_esEs17(vyy440, vyy450)
new_esEs26(vyy442, vyy452, app(ty_Maybe, cdb)) → new_esEs7(vyy442, vyy452, cdb)
new_ltEs18(Nothing, Just(vyy500), baa) → True
new_ltEs14(GT, LT) → False
new_not(EQ) → new_not0
new_esEs28(vyy440, vyy450, ty_Integer) → new_esEs15(vyy440, vyy450)
new_primCmpInt(Pos(Zero), Pos(Succ(vyy5000))) → new_primCmpNat2(Zero, vyy5000)
new_esEs25(vyy441, vyy451, app(app(app(ty_@3, cbg), cbh), cca)) → new_esEs6(vyy441, vyy451, cbg, cbh, cca)
new_lt8(vyy6000, vyy500) → new_esEs22(new_compare17(vyy6000, vyy500))
new_esEs23(vyy440, vyy450, ty_Integer) → new_esEs15(vyy440, vyy450)
new_esEs27(vyy44, vyy45, app(ty_[], bfg)) → new_esEs10(vyy44, vyy45, bfg)
new_compare27(vyy6000, vyy500, True) → EQ
new_esEs14(True, True) → True
new_ltEs19(vyy6001, vyy501, ty_Int) → new_ltEs16(vyy6001, vyy501)
new_ltEs4(Left(vyy6000), Left(vyy500), ty_Ordering, ceh) → new_ltEs14(vyy6000, vyy500)
new_ltEs18(Just(vyy6000), Just(vyy500), ty_Integer) → new_ltEs12(vyy6000, vyy500)
new_ltEs6(@3(vyy6000, vyy6001, vyy6002), @3(vyy500, vyy501, vyy502), dg, dh, ea) → new_pePe(new_lt4(vyy6000, vyy500, dg), vyy6000, vyy500, new_pePe(new_lt5(vyy6001, vyy501, dh), vyy6001, vyy501, new_ltEs7(vyy6002, vyy502, ea), dh), dg)
new_esEs27(vyy44, vyy45, ty_Bool) → new_esEs14(vyy44, vyy45)
new_esEs26(vyy442, vyy452, ty_Double) → new_esEs19(vyy442, vyy452)
new_lt19(vyy6000, vyy500, dd, de) → new_esEs22(new_compare32(vyy6000, vyy500, dd, de))
new_esEs26(vyy442, vyy452, app(ty_Ratio, cea)) → new_esEs12(vyy442, vyy452, cea)
new_ltEs18(Just(vyy6000), Just(vyy500), ty_Bool) → new_ltEs11(vyy6000, vyy500)
new_ltEs7(vyy6002, vyy502, ty_@0) → new_ltEs17(vyy6002, vyy502)
new_lt5(vyy6001, vyy501, app(app(ty_Either, ge), gf)) → new_lt19(vyy6001, vyy501, ge, gf)
new_ltEs20(vyy600, vyy50, app(ty_[], bhd)) → new_ltEs15(vyy600, vyy50, bhd)
new_ltEs4(Right(vyy6000), Right(vyy500), ceg, ty_Char) → new_ltEs13(vyy6000, vyy500)
new_esEs20(vyy440, vyy450, ty_Int) → new_esEs17(vyy440, vyy450)
new_esEs25(vyy441, vyy451, app(app(ty_@2, ccc), ccd)) → new_esEs5(vyy441, vyy451, ccc, ccd)
new_ltEs14(LT, GT) → True
new_esEs27(vyy44, vyy45, ty_Float) → new_esEs9(vyy44, vyy45)
new_not(LT) → new_not0
new_esEs8(Right(vyy440), Right(vyy450), cgf, ty_Integer) → new_esEs15(vyy440, vyy450)
new_lt5(vyy6001, vyy501, app(ty_Maybe, gd)) → new_lt18(vyy6001, vyy501, gd)
new_ltEs14(LT, EQ) → True
new_compare9(vyy6000, vyy500) → new_compare25(vyy6000, vyy500, new_esEs14(vyy6000, vyy500))
new_lt16(vyy6000, vyy500) → new_esEs22(new_compare16(vyy6000, vyy500))
new_lt13(vyy6000, vyy500) → new_esEs22(new_compare15(vyy6000, vyy500))
new_ltEs4(Right(vyy6000), Right(vyy500), ceg, ty_Bool) → new_ltEs11(vyy6000, vyy500)
new_lt4(vyy6000, vyy500, ty_Bool) → new_lt9(vyy6000, vyy500)
new_esEs14(False, False) → True
new_esEs8(Left(vyy440), Left(vyy450), ty_Float, cfc) → new_esEs9(vyy440, vyy450)
new_esEs7(Just(vyy440), Just(vyy450), app(app(ty_@2, cf), cg)) → new_esEs5(vyy440, vyy450, cf, cg)
new_lt20(vyy6000, vyy500, ty_Char) → new_lt12(vyy6000, vyy500)
new_ltEs7(vyy6002, vyy502, ty_Char) → new_ltEs13(vyy6002, vyy502)
new_esEs22(GT) → False
new_lt5(vyy6001, vyy501, ty_Double) → new_lt8(vyy6001, vyy501)
new_esEs25(vyy441, vyy451, ty_Double) → new_esEs19(vyy441, vyy451)
new_compare26(vyy6000, vyy500, True, bfd, bfe, bff) → EQ
new_esEs21(vyy441, vyy451, ty_@0) → new_esEs11(vyy441, vyy451)
new_ltEs4(Left(vyy6000), Left(vyy500), ty_Double, ceh) → new_ltEs10(vyy6000, vyy500)
new_primPlusNat1(Zero, Zero) → Zero
new_esEs21(vyy441, vyy451, app(app(app(ty_@3, bde), bdf), bdg)) → new_esEs6(vyy441, vyy451, bde, bdf, bdg)
new_asAs(True, vyy55) → vyy55
new_ltEs14(EQ, EQ) → True
new_primMulNat0(Succ(vyy600000), Succ(vyy50000)) → new_primPlusNat0(new_primMulNat0(vyy600000, Succ(vyy50000)), vyy50000)
new_lt5(vyy6001, vyy501, app(ty_Ratio, gb)) → new_lt14(vyy6001, vyy501, gb)
new_ltEs8(vyy600, vyy50) → new_not(new_compare30(vyy600, vyy50))
new_esEs7(Just(vyy440), Just(vyy450), ty_Bool) → new_esEs14(vyy440, vyy450)
new_compare6(:%(vyy6000, vyy6001), :%(vyy500, vyy501), ty_Int) → new_compare16(new_sr0(vyy6000, vyy501), new_sr0(vyy500, vyy6001))
new_fmToList(vyy45, beh, bfa) → new_foldFM2(vyy45, beh, bfa)
new_esEs8(Right(vyy440), Right(vyy450), cgf, app(app(ty_@2, chf), chg)) → new_esEs5(vyy440, vyy450, chf, chg)
new_ltEs13(vyy600, vyy50) → new_not(new_compare29(vyy600, vyy50))
new_esEs8(Left(vyy440), Left(vyy450), ty_Ordering, cfc) → new_esEs18(vyy440, vyy450)
new_lt11(vyy6000, vyy500) → new_esEs22(new_compare12(vyy6000, vyy500))
new_primCompAux00(vyy60, GT) → GT
new_ltEs18(Just(vyy6000), Just(vyy500), ty_Char) → new_ltEs13(vyy6000, vyy500)
new_esEs8(Right(vyy440), Right(vyy450), cgf, app(ty_[], che)) → new_esEs10(vyy440, vyy450, che)
new_compare33(vyy6000, vyy500, bfd, bfe, bff) → new_compare26(vyy6000, vyy500, new_esEs6(vyy6000, vyy500, bfd, bfe, bff), bfd, bfe, bff)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_ltEs14(EQ, GT) → True
new_esEs7(Just(vyy440), Just(vyy450), ty_Ordering) → new_esEs18(vyy440, vyy450)
new_lt4(vyy6000, vyy500, ty_@0) → new_lt17(vyy6000, vyy500)
new_ltEs4(Left(vyy6000), Left(vyy500), ty_@0, ceh) → new_ltEs17(vyy6000, vyy500)
new_lt5(vyy6001, vyy501, ty_Char) → new_lt12(vyy6001, vyy501)
new_esEs22(LT) → True
new_lt7(vyy6000, vyy500, bfb, bfc) → new_esEs22(new_compare31(vyy6000, vyy500, bfb, bfc))
new_lt4(vyy6000, vyy500, app(ty_Ratio, eg)) → new_lt14(vyy6000, vyy500, eg)
new_compare34(vyy6000, vyy500, app(ty_Ratio, deh)) → new_compare6(vyy6000, vyy500, deh)
new_esEs25(vyy441, vyy451, ty_Float) → new_esEs9(vyy441, vyy451)
new_esEs25(vyy441, vyy451, app(ty_Ratio, cce)) → new_esEs12(vyy441, vyy451, cce)
new_esEs7(Just(vyy440), Just(vyy450), app(ty_Ratio, da)) → new_esEs12(vyy440, vyy450, da)
new_primCmpNat0(vyy60000, Succ(vyy5000)) → new_primCmpNat1(vyy60000, vyy5000)
new_ltEs19(vyy6001, vyy501, app(ty_Maybe, ddf)) → new_ltEs18(vyy6001, vyy501, ddf)
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_esEs8(Right(vyy440), Right(vyy450), cgf, app(ty_Maybe, cha)) → new_esEs7(vyy440, vyy450, cha)
new_esEs25(vyy441, vyy451, app(app(ty_Either, cbd), cbe)) → new_esEs8(vyy441, vyy451, cbd, cbe)
new_esEs27(vyy44, vyy45, ty_Integer) → new_esEs15(vyy44, vyy45)
new_ltEs19(vyy6001, vyy501, ty_Bool) → new_ltEs11(vyy6001, vyy501)
new_esEs18(EQ, EQ) → True
new_esEs25(vyy441, vyy451, ty_Char) → new_esEs13(vyy441, vyy451)
new_primCmpInt(Neg(Succ(vyy60000)), Pos(vyy500)) → LT
new_esEs27(vyy44, vyy45, ty_Double) → new_esEs19(vyy44, vyy45)
The set Q consists of the following terms:
new_esEs21(x0, x1, ty_Int)
new_ltEs7(x0, x1, app(ty_Maybe, x2))
new_esEs8(Left(x0), Left(x1), ty_Integer, x2)
new_ltEs20(x0, x1, ty_Integer)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_esEs24(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_primPlusNat1(Succ(x0), Succ(x1))
new_ltEs7(x0, x1, ty_Int)
new_compare11(x0, x1, False, x2)
new_asAs(False, x0)
new_lt5(x0, x1, ty_Int)
new_lt8(x0, x1)
new_esEs8(Left(x0), Left(x1), ty_Bool, x2)
new_compare3(:(x0, x1), [], x2)
new_esEs7(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_esEs18(LT, LT)
new_esEs20(x0, x1, ty_Bool)
new_esEs7(Just(x0), Just(x1), ty_Char)
new_esEs24(x0, x1, ty_Ordering)
new_esEs21(x0, x1, ty_Bool)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs8(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_esEs8(Right(x0), Right(x1), x2, ty_Double)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_compare34(x0, x1, ty_Double)
new_esEs8(Right(x0), Right(x1), x2, ty_Ordering)
new_compare14(x0, x1, True, x2, x3, x4)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_esEs23(x0, x1, ty_Ordering)
new_esEs8(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs21(x0, x1, ty_@0)
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs26(x0, x1, ty_Char)
new_ltEs19(x0, x1, ty_Integer)
new_lt4(x0, x1, ty_Integer)
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs24(x0, x1, ty_Integer)
new_ltEs18(Nothing, Nothing, x0)
new_esEs20(x0, x1, ty_Float)
new_lt4(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare27(x0, x1, True)
new_esEs8(Right(x0), Right(x1), x2, app(ty_[], x3))
new_primMulNat0(Zero, Succ(x0))
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs7(Just(x0), Just(x1), ty_Bool)
new_esEs24(x0, x1, ty_Double)
new_ltEs4(Left(x0), Left(x1), ty_Bool, x2)
new_esEs23(x0, x1, ty_Char)
new_esEs11(@0, @0)
new_esEs22(LT)
new_compare13(x0, x1, True, x2, x3)
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_esEs29(x0, x1, ty_Integer)
new_ltEs4(Right(x0), Right(x1), x2, ty_Integer)
new_compare27(x0, x1, False)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_esEs8(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs21(x0, x1, ty_Integer)
new_esEs24(x0, x1, app(ty_[], x2))
new_ltEs4(Right(x0), Right(x1), x2, ty_Ordering)
new_compare10(x0, x1, True, x2, x3)
new_ltEs19(x0, x1, app(ty_[], x2))
new_compare19(x0, x1, False)
new_ltEs9(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_lt20(x0, x1, ty_Int)
new_esEs7(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_lt13(x0, x1)
new_primEqNat0(Zero, Succ(x0))
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
new_ltEs4(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_compare3([], :(x0, x1), x2)
new_ltEs7(x0, x1, ty_Char)
new_esEs26(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs18(EQ, GT)
new_esEs18(GT, EQ)
new_ltEs4(Left(x0), Left(x1), ty_Double, x2)
new_primCmpNat1(Succ(x0), Zero)
new_ltEs4(Left(x0), Left(x1), ty_Int, x2)
new_lt4(x0, x1, ty_Char)
new_esEs8(Right(x0), Right(x1), x2, ty_Float)
new_compare3([], [], x0)
new_esEs27(x0, x1, ty_@0)
new_ltEs20(x0, x1, ty_@0)
new_ltEs20(x0, x1, ty_Ordering)
new_compare34(x0, x1, app(ty_Ratio, x2))
new_esEs18(EQ, EQ)
new_ltEs4(Right(x0), Right(x1), x2, ty_Bool)
new_compare16(x0, x1)
new_ltEs19(x0, x1, ty_Float)
new_primCmpNat1(Zero, Zero)
new_compare10(x0, x1, False, x2, x3)
new_esEs27(x0, x1, ty_Int)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_compare8(x0, x1, x2)
new_compare25(x0, x1, True)
new_esEs25(x0, x1, app(ty_[], x2))
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_esEs14(True, True)
new_esEs27(x0, x1, app(ty_[], x2))
new_esEs27(x0, x1, ty_Float)
new_lt20(x0, x1, ty_Ordering)
new_esEs26(x0, x1, ty_Double)
new_esEs8(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_lt4(x0, x1, app(ty_Ratio, x2))
new_compare34(x0, x1, ty_Ordering)
new_ltEs14(EQ, EQ)
new_primEqNat0(Zero, Zero)
new_esEs27(x0, x1, ty_Double)
new_esEs8(Left(x0), Left(x1), app(ty_[], x2), x3)
new_lt5(x0, x1, app(app(ty_Either, x2), x3))
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_lt20(x0, x1, ty_Double)
new_esEs7(Just(x0), Just(x1), ty_Int)
new_compare34(x0, x1, app(ty_[], x2))
new_esEs24(x0, x1, ty_@0)
new_esEs26(x0, x1, ty_Bool)
new_compare3(:(x0, x1), :(x2, x3), x4)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_compare31(x0, x1, x2, x3)
new_esEs23(x0, x1, ty_Integer)
new_primMulNat0(Zero, Zero)
new_ltEs18(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_ltEs4(Right(x0), Right(x1), x2, ty_Float)
new_primCmpNat0(x0, Succ(x1))
new_esEs21(x0, x1, ty_Float)
new_ltEs17(x0, x1)
new_esEs6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs20(x0, x1, ty_Char)
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_esEs26(x0, x1, ty_@0)
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_primMulNat0(Succ(x0), Zero)
new_lt14(x0, x1, x2)
new_ltEs18(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_compare34(x0, x1, ty_Bool)
new_primCompAux00(x0, LT)
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare34(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs7(Just(x0), Just(x1), app(ty_[], x2))
new_lt5(x0, x1, ty_Ordering)
new_primPlusNat0(Zero, x0)
new_esEs25(x0, x1, ty_Float)
new_compare34(x0, x1, ty_Integer)
new_lt4(x0, x1, ty_@0)
new_esEs27(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_ltEs7(x0, x1, ty_Float)
new_esEs8(Left(x0), Left(x1), ty_Int, x2)
new_ltEs19(x0, x1, ty_Ordering)
new_sr(Integer(x0), Integer(x1))
new_esEs8(Right(x0), Right(x1), x2, app(app(ty_FiniteMap, x3), x4))
new_compare19(x0, x1, True)
new_esEs27(x0, x1, ty_Ordering)
new_ltEs19(x0, x1, ty_Bool)
new_esEs8(Right(x0), Left(x1), x2, x3)
new_esEs8(Left(x0), Right(x1), x2, x3)
new_esEs8(Right(x0), Right(x1), x2, ty_Bool)
new_compare34(x0, x1, app(ty_Maybe, x2))
new_compare34(x0, x1, ty_Char)
new_ltEs4(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_ltEs4(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_primEqNat0(Succ(x0), Zero)
new_ltEs18(Just(x0), Just(x1), ty_Int)
new_esEs12(:%(x0, x1), :%(x2, x3), x4)
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, ty_Bool)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_ltEs7(x0, x1, ty_Integer)
new_lt7(x0, x1, x2, x3)
new_esEs23(x0, x1, ty_@0)
new_ltEs18(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs16(x0, x1, x2, x3)
new_esEs8(Right(x0), Right(x1), x2, ty_@0)
new_lt5(x0, x1, ty_Float)
new_compare23(x0, x1, True, x2, x3)
new_esEs20(x0, x1, ty_Ordering)
new_esEs8(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_compare28(x0, x1, False, x2, x3)
new_esEs8(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_compare17(Double(x0, x1), Double(x2, x3))
new_esEs13(Char(x0), Char(x1))
new_esEs25(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_lt20(x0, x1, ty_Char)
new_ltEs4(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs25(x0, x1, ty_Ordering)
new_lt20(x0, x1, ty_Integer)
new_ltEs20(x0, x1, ty_Char)
new_ltEs4(Right(x0), Right(x1), x2, ty_Double)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_ltEs18(Just(x0), Just(x1), ty_Float)
new_ltEs7(x0, x1, ty_@0)
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs28(x0, x1, ty_Integer)
new_esEs21(x0, x1, ty_Char)
new_primPlusNat1(Zero, Zero)
new_lt4(x0, x1, app(app(ty_Either, x2), x3))
new_compare6(:%(x0, x1), :%(x2, x3), ty_Integer)
new_not0
new_ltEs19(x0, x1, ty_Char)
new_primPlusNat1(Zero, Succ(x0))
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs7(Just(x0), Just(x1), ty_Integer)
new_lt5(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs14(LT, LT)
new_lt5(x0, x1, app(ty_Ratio, x2))
new_esEs8(Right(x0), Right(x1), x2, ty_Integer)
new_fmToList(x0, x1, x2)
new_ltEs13(x0, x1)
new_esEs26(x0, x1, ty_Integer)
new_compare34(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs7(x0, x1, ty_Bool)
new_esEs7(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_lt4(x0, x1, ty_Float)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_lt20(x0, x1, app(ty_Ratio, x2))
new_compare34(x0, x1, ty_@0)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_compare34(x0, x1, ty_Int)
new_lt5(x0, x1, ty_Double)
new_esEs18(GT, GT)
new_lt5(x0, x1, ty_Bool)
new_lt12(x0, x1)
new_compare13(x0, x1, False, x2, x3)
new_ltEs4(Left(x0), Right(x1), x2, x3)
new_ltEs4(Right(x0), Left(x1), x2, x3)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_primCompAux00(x0, EQ)
new_lt4(x0, x1, app(app(ty_@2, x2), x3))
new_esEs20(x0, x1, ty_@0)
new_lt6(x0, x1)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_esEs25(x0, x1, ty_Double)
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_not(GT)
new_ltEs8(x0, x1)
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_esEs8(Left(x0), Left(x1), ty_Double, x2)
new_esEs7(Just(x0), Just(x1), app(app(ty_FiniteMap, x2), x3))
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_lt20(x0, x1, ty_Float)
new_compare15(x0, x1)
new_ltEs4(Left(x0), Left(x1), ty_Char, x2)
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_ltEs10(x0, x1)
new_esEs23(x0, x1, ty_Float)
new_ltEs14(LT, EQ)
new_ltEs16(x0, x1)
new_ltEs14(EQ, LT)
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs8(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_ltEs11(False, False)
new_ltEs4(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_sr0(x0, x1)
new_ltEs7(x0, x1, app(app(ty_@2, x2), x3))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_lt5(x0, x1, ty_Integer)
new_compare26(x0, x1, False, x2, x3, x4)
new_esEs7(Just(x0), Nothing, x1)
new_compare24(x0, x1, True, x2)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_lt4(x0, x1, ty_Ordering)
new_primEqInt(Neg(Zero), Neg(Zero))
new_ltEs20(x0, x1, ty_Float)
new_foldFM2(EmptyFM, x0, x1)
new_lt5(x0, x1, app(ty_[], x2))
new_ltEs11(False, True)
new_ltEs11(True, False)
new_esEs26(x0, x1, ty_Ordering)
new_esEs14(False, True)
new_esEs14(True, False)
new_lt15(x0, x1, x2)
new_esEs21(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_esEs8(Left(x0), Left(x1), ty_Ordering, x2)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_ltEs5(x0, x1, x2)
new_ltEs18(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs18(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs17(x0, x1)
new_esEs26(x0, x1, app(ty_[], x2))
new_primCmpNat2(Succ(x0), x1)
new_ltEs18(Just(x0), Just(x1), ty_Integer)
new_esEs7(Just(x0), Just(x1), app(ty_Maybe, x2))
new_compare29(Char(x0), Char(x1))
new_primPlusNat0(Succ(x0), x1)
new_compare7(@0, @0)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_ltEs7(x0, x1, app(ty_[], x2))
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_ltEs4(Left(x0), Left(x1), ty_Float, x2)
new_compare23(x0, x1, False, x2, x3)
new_primCmpNat2(Zero, x0)
new_compare9(x0, x1)
new_lt4(x0, x1, app(ty_[], x2))
new_compare33(x0, x1, x2, x3, x4)
new_primCmpNat1(Succ(x0), Succ(x1))
new_primCmpNat0(x0, Zero)
new_esEs24(x0, x1, ty_Char)
new_esEs8(Left(x0), Left(x1), app(app(ty_FiniteMap, x2), x3), x4)
new_esEs8(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs7(Just(x0), Just(x1), ty_Double)
new_esEs20(x0, x1, app(ty_[], x2))
new_ltEs4(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs4(Right(x0), Right(x1), x2, ty_Int)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, ty_Double)
new_ltEs7(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs20(x0, x1, app(ty_[], x2))
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_esEs8(Right(x0), Right(x1), x2, ty_Int)
new_compare26(x0, x1, True, x2, x3, x4)
new_lt4(x0, x1, ty_Int)
new_esEs21(x0, x1, ty_Ordering)
new_esEs10(:(x0, x1), :(x2, x3), x4)
new_ltEs14(EQ, GT)
new_ltEs14(GT, EQ)
new_ltEs12(x0, x1)
new_esEs7(Nothing, Just(x0), x1)
new_primCompAux0(x0, x1, x2, x3)
new_esEs20(x0, x1, ty_Double)
new_lt18(x0, x1, x2)
new_esEs8(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs26(x0, x1, ty_Int)
new_sizeFM(EmptyFM, x0, x1)
new_ltEs18(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs24(x0, x1, ty_Float)
new_primMulNat0(Succ(x0), Succ(x1))
new_esEs20(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(EQ)
new_ltEs4(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_compare34(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs18(Just(x0), Just(x1), ty_Bool)
new_esEs7(Just(x0), Just(x1), ty_Float)
new_asAs(True, x0)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_primCmpNat1(Zero, Succ(x0))
new_lt5(x0, x1, ty_@0)
new_esEs18(EQ, LT)
new_esEs18(LT, EQ)
new_esEs23(x0, x1, ty_Bool)
new_lt5(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs14(LT, GT)
new_ltEs14(GT, LT)
new_primCompAux00(x0, GT)
new_compare25(x0, x1, False)
new_ltEs4(Right(x0), Right(x1), x2, ty_@0)
new_esEs20(x0, x1, ty_Int)
new_compare34(x0, x1, ty_Float)
new_esEs27(x0, x1, ty_Char)
new_lt20(x0, x1, app(ty_[], x2))
new_esEs23(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_compare32(x0, x1, x2, x3)
new_ltEs7(x0, x1, app(ty_Ratio, x2))
new_lt4(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt17(x0, x1)
new_esEs26(x0, x1, ty_Float)
new_ltEs4(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_ltEs14(GT, GT)
new_lt20(x0, x1, ty_Bool)
new_ltEs18(Just(x0), Just(x1), ty_Char)
new_esEs5(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs25(x0, x1, ty_Bool)
new_esEs19(Double(x0, x1), Double(x2, x3))
new_lt5(x0, x1, ty_Char)
new_not(EQ)
new_esEs10(:(x0, x1), [], x2)
new_esEs10([], :(x0, x1), x2)
new_ltEs20(x0, x1, ty_Double)
new_lt4(x0, x1, ty_Double)
new_compare12(Integer(x0), Integer(x1))
new_esEs7(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_lt10(x0, x1, x2, x3, x4)
new_esEs28(x0, x1, ty_Int)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_ltEs7(x0, x1, ty_Double)
new_lt16(x0, x1)
new_esEs22(GT)
new_ltEs18(Just(x0), Just(x1), ty_Ordering)
new_lt9(x0, x1)
new_esEs15(Integer(x0), Integer(x1))
new_lt5(x0, x1, app(ty_Maybe, x2))
new_compare24(x0, x1, False, x2)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(Nothing, Nothing, x0)
new_esEs8(Left(x0), Left(x1), ty_@0, x2)
new_ltEs4(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs23(x0, x1, app(ty_[], x2))
new_esEs25(x0, x1, ty_Integer)
new_esEs20(x0, x1, ty_Integer)
new_compare18(x0, x1, True)
new_compare11(x0, x1, True, x2)
new_compare18(x0, x1, False)
new_pePe(True, x0, x1, x2, x3)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare6(:%(x0, x1), :%(x2, x3), ty_Int)
new_compare30(Float(x0, x1), Float(x2, x3))
new_lt11(x0, x1)
new_ltEs18(Just(x0), Nothing, x1)
new_esEs27(x0, x1, ty_Bool)
new_esEs18(GT, LT)
new_esEs18(LT, GT)
new_ltEs19(x0, x1, ty_@0)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs21(x0, x1, app(ty_[], x2))
new_esEs9(Float(x0, x1), Float(x2, x3))
new_esEs10([], [], x0)
new_ltEs7(x0, x1, ty_Ordering)
new_ltEs4(Left(x0), Left(x1), ty_Ordering, x2)
new_ltEs18(Nothing, Just(x0), x1)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_esEs25(x0, x1, ty_Char)
new_esEs29(x0, x1, ty_Int)
new_ltEs19(x0, x1, ty_Double)
new_compare14(x0, x1, False, x2, x3, x4)
new_esEs27(x0, x1, ty_Integer)
new_esEs7(Just(x0), Just(x1), ty_@0)
new_lt4(x0, x1, ty_Bool)
new_ltEs4(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_ltEs4(Left(x0), Left(x1), ty_@0, x2)
new_esEs8(Left(x0), Left(x1), ty_Char, x2)
new_ltEs19(x0, x1, ty_Int)
new_compare28(x0, x1, True, x2, x3)
new_esEs14(False, False)
new_ltEs4(Right(x0), Right(x1), x2, ty_Char)
new_primEqInt(Pos(Zero), Pos(Zero))
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_esEs25(x0, x1, ty_@0)
new_lt19(x0, x1, x2, x3)
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_esEs21(x0, x1, ty_Double)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs4(Left(x0), Left(x1), app(ty_[], x2), x3)
new_ltEs20(x0, x1, ty_Int)
new_ltEs18(Just(x0), Just(x1), ty_@0)
new_esEs24(x0, x1, ty_Int)
new_lt20(x0, x1, ty_@0)
new_ltEs4(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs7(Just(x0), Just(x1), ty_Ordering)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, ty_Int)
new_esEs8(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs25(x0, x1, ty_Int)
new_esEs24(x0, x1, ty_Bool)
new_esEs8(Left(x0), Left(x1), ty_Float, x2)
new_ltEs4(Left(x0), Left(x1), ty_Integer, x2)
new_primPlusNat1(Succ(x0), Zero)
new_ltEs15(x0, x1, x2)
new_primMulInt(Pos(x0), Pos(x1))
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs18(Just(x0), Just(x1), ty_Double)
new_not(LT)
new_ltEs11(True, True)
new_esEs8(Right(x0), Right(x1), x2, ty_Char)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_pePe(False, x0, x1, x2, x3)
new_ltEs7(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
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
↳ QDPSizeChangeProof
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_foldFM_LE1(vyy17, vyy19, vyy20, vyy21, vyy22, vyy23, vyy24, False, bc, bd, be) → new_foldFM_LE(vyy17, Just(vyy19), vyy23, bc, bd, be)
new_foldFM_LE(vyy3, Just(vyy50), Branch(Just(vyy600), vyy61, vyy62, vyy63, vyy64), h, ba, bb) → new_foldFM_LE1(vyy3, vyy50, vyy600, vyy61, vyy62, vyy63, vyy64, new_ltEs20(vyy600, vyy50, ba), h, ba, bb)
new_foldFM_LE1(vyy17, vyy19, vyy20, vyy21, vyy22, vyy23, vyy24, True, bc, bd, be) → new_foldFM_LE(vyy17, Just(vyy19), vyy24, bc, bd, be)
new_foldFM_LE1(vyy17, vyy19, vyy20, vyy21, vyy22, vyy23, vyy24, True, bc, bd, be) → new_foldFM_LE(vyy17, Just(vyy19), vyy23, bc, bd, be)
new_foldFM_LE(vyy3, Just(vyy50), Branch(Nothing, vyy61, vyy62, vyy63, vyy64), h, ba, bb) → new_foldFM_LE(vyy3, Just(vyy50), vyy64, h, ba, bb)
new_foldFM_LE(vyy3, Just(vyy50), Branch(Nothing, vyy61, vyy62, vyy63, vyy64), h, ba, bb) → new_foldFM_LE(vyy3, Just(vyy50), vyy63, h, ba, bb)
The TRS R consists of the following rules:
new_compare34(vyy6000, vyy500, app(app(ty_Either, dfc), dfd)) → new_compare32(vyy6000, vyy500, dfc, dfd)
new_esEs7(Just(vyy440), Just(vyy450), app(ty_Maybe, ca)) → new_esEs7(vyy440, vyy450, ca)
new_ltEs20(vyy600, vyy50, app(ty_Maybe, baa)) → new_ltEs18(vyy600, vyy50, baa)
new_esEs20(vyy440, vyy450, app(ty_Maybe, bbh)) → new_esEs7(vyy440, vyy450, bbh)
new_esEs23(vyy440, vyy450, ty_Ordering) → new_esEs18(vyy440, vyy450)
new_compare3(:(vyy6000, vyy6001), :(vyy500, vyy501), bhd) → new_primCompAux0(vyy6000, vyy500, new_compare3(vyy6001, vyy501, bhd), bhd)
new_lt20(vyy6000, vyy500, ty_Int) → new_lt16(vyy6000, vyy500)
new_primCmpNat2(Zero, vyy60000) → LT
new_ltEs9(@2(vyy6000, vyy6001), @2(vyy500, vyy501), cee, cef) → new_pePe(new_lt20(vyy6000, vyy500, cee), vyy6000, vyy500, new_ltEs19(vyy6001, vyy501, cef), cee)
new_esEs18(LT, LT) → True
new_esEs20(vyy440, vyy450, ty_Double) → new_esEs19(vyy440, vyy450)
new_lt4(vyy6000, vyy500, ty_Int) → new_lt16(vyy6000, vyy500)
new_lt20(vyy6000, vyy500, app(app(ty_Either, dd), de)) → new_lt19(vyy6000, vyy500, dd, de)
new_ltEs4(Left(vyy6000), Left(vyy500), app(ty_Maybe, dbb), ceh) → new_ltEs18(vyy6000, vyy500, dbb)
new_esEs25(vyy441, vyy451, ty_Ordering) → new_esEs18(vyy441, vyy451)
new_ltEs14(GT, GT) → True
new_primCmpNat1(Zero, Succ(vyy50000)) → LT
new_ltEs18(Just(vyy6000), Just(vyy500), ty_Float) → new_ltEs8(vyy6000, vyy500)
new_compare10(vyy6000, vyy500, True, dd, de) → LT
new_primCompAux0(vyy6000, vyy500, vyy56, bhd) → new_primCompAux00(vyy56, new_compare34(vyy6000, vyy500, bhd))
new_ltEs18(Just(vyy6000), Just(vyy500), app(ty_Maybe, bba)) → new_ltEs18(vyy6000, vyy500, bba)
new_esEs18(LT, EQ) → False
new_esEs18(EQ, LT) → False
new_esEs27(vyy44, vyy45, app(ty_Maybe, bf)) → new_esEs7(vyy44, vyy45, bf)
new_esEs20(vyy440, vyy450, ty_Float) → new_esEs9(vyy440, vyy450)
new_esEs23(vyy440, vyy450, ty_Bool) → new_esEs14(vyy440, vyy450)
new_ltEs18(Just(vyy6000), Just(vyy500), ty_@0) → new_ltEs17(vyy6000, vyy500)
new_ltEs4(Left(vyy6000), Left(vyy500), app(app(app(ty_@3, dae), daf), dag), ceh) → new_ltEs6(vyy6000, vyy500, dae, daf, dag)
new_esEs8(Left(vyy440), Left(vyy450), ty_Integer, cfc) → new_esEs15(vyy440, vyy450)
new_compare14(vyy6000, vyy500, True, bfd, bfe, bff) → LT
new_ltEs19(vyy6001, vyy501, app(ty_Ratio, ddd)) → new_ltEs5(vyy6001, vyy501, ddd)
new_esEs7(Just(vyy440), Just(vyy450), ty_Double) → new_esEs19(vyy440, vyy450)
new_primMulNat0(Zero, Zero) → Zero
new_lt4(vyy6000, vyy500, ty_Double) → new_lt8(vyy6000, vyy500)
new_compare32(vyy6000, vyy500, dd, de) → new_compare23(vyy6000, vyy500, new_esEs8(vyy6000, vyy500, dd, de), dd, de)
new_esEs8(Left(vyy440), Left(vyy450), app(app(ty_FiniteMap, cgd), cge), cfc) → new_esEs16(vyy440, vyy450, cgd, cge)
new_sr(Integer(vyy60000), Integer(vyy5010)) → Integer(new_primMulInt(vyy60000, vyy5010))
new_esEs21(vyy441, vyy451, app(app(ty_Either, bdb), bdc)) → new_esEs8(vyy441, vyy451, bdb, bdc)
new_ltEs4(Right(vyy6000), Right(vyy500), ceg, ty_Integer) → new_ltEs12(vyy6000, vyy500)
new_esEs21(vyy441, vyy451, app(ty_[], bdh)) → new_esEs10(vyy441, vyy451, bdh)
new_lt20(vyy6000, vyy500, ty_Float) → new_lt6(vyy6000, vyy500)
new_ltEs4(Left(vyy6000), Left(vyy500), app(app(ty_@2, dac), dad), ceh) → new_ltEs9(vyy6000, vyy500, dac, dad)
new_ltEs4(Right(vyy6000), Right(vyy500), ceg, app(app(app(ty_@3, dbg), dbh), dca)) → new_ltEs6(vyy6000, vyy500, dbg, dbh, dca)
new_esEs24(vyy440, vyy450, ty_Integer) → new_esEs15(vyy440, vyy450)
new_esEs16(vyy44, vyy45, beh, bfa) → new_asAs(new_esEs17(new_sizeFM(vyy44, beh, bfa), new_sizeFM(vyy45, beh, bfa)), new_esEs10(new_fmToList(vyy44, beh, bfa), new_fmToList(vyy45, beh, bfa), app(app(ty_@2, beh), bfa)))
new_esEs21(vyy441, vyy451, app(app(ty_FiniteMap, bed), bee)) → new_esEs16(vyy441, vyy451, bed, bee)
new_not(GT) → False
new_lt5(vyy6001, vyy501, ty_Ordering) → new_lt13(vyy6001, vyy501)
new_esEs8(Right(vyy440), Right(vyy450), cgf, app(app(ty_FiniteMap, daa), dab)) → new_esEs16(vyy440, vyy450, daa, dab)
new_esEs26(vyy442, vyy452, ty_Float) → new_esEs9(vyy442, vyy452)
new_ltEs4(Right(vyy6000), Right(vyy500), ceg, app(ty_Maybe, dcd)) → new_ltEs18(vyy6000, vyy500, dcd)
new_lt4(vyy6000, vyy500, app(ty_[], eh)) → new_lt15(vyy6000, vyy500, eh)
new_ltEs4(Left(vyy6000), Left(vyy500), ty_Float, ceh) → new_ltEs8(vyy6000, vyy500)
new_esEs26(vyy442, vyy452, app(ty_[], cdf)) → new_esEs10(vyy442, vyy452, cdf)
new_lt4(vyy6000, vyy500, app(ty_Maybe, fa)) → new_lt18(vyy6000, vyy500, fa)
new_ltEs4(Right(vyy6000), Right(vyy500), ceg, app(ty_Ratio, dcb)) → new_ltEs5(vyy6000, vyy500, dcb)
new_esEs8(Left(vyy440), Left(vyy450), ty_Bool, cfc) → new_esEs14(vyy440, vyy450)
new_esEs24(vyy440, vyy450, app(app(ty_@2, cag), cah)) → new_esEs5(vyy440, vyy450, cag, cah)
new_esEs8(Left(vyy440), Left(vyy450), app(app(ty_@2, cga), cgb), cfc) → new_esEs5(vyy440, vyy450, cga, cgb)
new_primCmpNat1(Succ(vyy600000), Succ(vyy50000)) → new_primCmpNat1(vyy600000, vyy50000)
new_esEs9(Float(vyy440, vyy441), Float(vyy450, vyy451)) → new_esEs17(new_sr0(vyy440, vyy450), new_sr0(vyy441, vyy451))
new_ltEs4(Left(vyy6000), Left(vyy500), ty_Int, ceh) → new_ltEs16(vyy6000, vyy500)
new_esEs15(Integer(vyy440), Integer(vyy450)) → new_primEqInt(vyy440, vyy450)
new_esEs18(LT, GT) → False
new_esEs18(GT, LT) → False
new_ltEs7(vyy6002, vyy502, app(ty_Maybe, hf)) → new_ltEs18(vyy6002, vyy502, hf)
new_compare34(vyy6000, vyy500, app(app(app(ty_@3, dee), def), deg)) → new_compare33(vyy6000, vyy500, dee, def, deg)
new_esEs26(vyy442, vyy452, ty_Char) → new_esEs13(vyy442, vyy452)
new_esEs21(vyy441, vyy451, ty_Int) → new_esEs17(vyy441, vyy451)
new_ltEs7(vyy6002, vyy502, app(app(ty_@2, gg), gh)) → new_ltEs9(vyy6002, vyy502, gg, gh)
new_foldFM0(vyy450, vyy451, vyy74, EmptyFM, beh, bfa) → :(@2(vyy450, vyy451), vyy74)
new_esEs29(vyy441, vyy451, ty_Integer) → new_esEs15(vyy441, vyy451)
new_esEs25(vyy441, vyy451, app(ty_[], ccb)) → new_esEs10(vyy441, vyy451, ccb)
new_ltEs19(vyy6001, vyy501, app(app(ty_Either, ddg), ddh)) → new_ltEs4(vyy6001, vyy501, ddg, ddh)
new_compare34(vyy6000, vyy500, app(ty_[], dfa)) → new_compare3(vyy6000, vyy500, dfa)
new_compare27(vyy6000, vyy500, False) → new_compare18(vyy6000, vyy500, new_ltEs14(vyy6000, vyy500))
new_compare34(vyy6000, vyy500, ty_Integer) → new_compare12(vyy6000, vyy500)
new_esEs25(vyy441, vyy451, ty_Bool) → new_esEs14(vyy441, vyy451)
new_lt5(vyy6001, vyy501, ty_@0) → new_lt17(vyy6001, vyy501)
new_ltEs7(vyy6002, vyy502, ty_Double) → new_ltEs10(vyy6002, vyy502)
new_ltEs14(GT, EQ) → False
new_esEs22(EQ) → False
new_esEs23(vyy440, vyy450, app(app(ty_Either, bfh), bga)) → new_esEs8(vyy440, vyy450, bfh, bga)
new_esEs20(vyy440, vyy450, app(ty_Ratio, bcg)) → new_esEs12(vyy440, vyy450, bcg)
new_esEs26(vyy442, vyy452, app(app(ty_Either, cch), cda)) → new_esEs8(vyy442, vyy452, cch, cda)
new_esEs27(vyy44, vyy45, app(app(ty_FiniteMap, beh), bfa)) → new_esEs16(vyy44, vyy45, beh, bfa)
new_esEs24(vyy440, vyy450, app(ty_Maybe, cab)) → new_esEs7(vyy440, vyy450, cab)
new_compare34(vyy6000, vyy500, app(app(ty_@2, dec), ded)) → new_compare31(vyy6000, vyy500, dec, ded)
new_esEs24(vyy440, vyy450, ty_@0) → new_esEs11(vyy440, vyy450)
new_ltEs20(vyy600, vyy50, app(app(ty_Either, ceg), ceh)) → new_ltEs4(vyy600, vyy50, ceg, ceh)
new_lt20(vyy6000, vyy500, app(app(app(ty_@3, bfd), bfe), bff)) → new_lt10(vyy6000, vyy500, bfd, bfe, bff)
new_esEs23(vyy440, vyy450, app(ty_Maybe, bgb)) → new_esEs7(vyy440, vyy450, bgb)
new_ltEs7(vyy6002, vyy502, app(ty_[], he)) → new_ltEs15(vyy6002, vyy502, he)
new_lt5(vyy6001, vyy501, app(app(app(ty_@3, fg), fh), ga)) → new_lt10(vyy6001, vyy501, fg, fh, ga)
new_ltEs4(Right(vyy6000), Right(vyy500), ceg, app(app(ty_Either, dce), dcf)) → new_ltEs4(vyy6000, vyy500, dce, dcf)
new_ltEs20(vyy600, vyy50, ty_Integer) → new_ltEs12(vyy600, vyy50)
new_compare13(vyy6000, vyy500, False, bfb, bfc) → GT
new_ltEs18(Just(vyy6000), Just(vyy500), app(ty_Ratio, bag)) → new_ltEs5(vyy6000, vyy500, bag)
new_ltEs11(False, True) → True
new_esEs20(vyy440, vyy450, app(app(ty_@2, bce), bcf)) → new_esEs5(vyy440, vyy450, bce, bcf)
new_compare19(vyy6000, vyy500, True) → LT
new_lt20(vyy6000, vyy500, app(app(ty_@2, bfb), bfc)) → new_lt7(vyy6000, vyy500, bfb, bfc)
new_ltEs4(Left(vyy6000), Right(vyy500), ceg, ceh) → True
new_esEs21(vyy441, vyy451, ty_Bool) → new_esEs14(vyy441, vyy451)
new_lt4(vyy6000, vyy500, app(app(ty_Either, fb), fc)) → new_lt19(vyy6000, vyy500, fb, fc)
new_esEs21(vyy441, vyy451, ty_Char) → new_esEs13(vyy441, vyy451)
new_compare24(vyy6000, vyy500, False, beg) → new_compare11(vyy6000, vyy500, new_ltEs18(vyy6000, vyy500, beg), beg)
new_ltEs15(vyy600, vyy50, bhd) → new_not(new_compare3(vyy600, vyy50, bhd))
new_esEs7(Just(vyy440), Just(vyy450), ty_Int) → new_esEs17(vyy440, vyy450)
new_esEs21(vyy441, vyy451, ty_Double) → new_esEs19(vyy441, vyy451)
new_lt14(vyy6000, vyy500, bef) → new_esEs22(new_compare6(vyy6000, vyy500, bef))
new_esEs20(vyy440, vyy450, ty_Ordering) → new_esEs18(vyy440, vyy450)
new_esEs20(vyy440, vyy450, ty_@0) → new_esEs11(vyy440, vyy450)
new_esEs23(vyy440, vyy450, ty_Double) → new_esEs19(vyy440, vyy450)
new_compare34(vyy6000, vyy500, ty_@0) → new_compare7(vyy6000, vyy500)
new_esEs20(vyy440, vyy450, app(app(app(ty_@3, bca), bcb), bcc)) → new_esEs6(vyy440, vyy450, bca, bcb, bcc)
new_lt4(vyy6000, vyy500, app(app(ty_@2, eb), ec)) → new_lt7(vyy6000, vyy500, eb, ec)
new_esEs8(Left(vyy440), Left(vyy450), ty_Char, cfc) → new_esEs13(vyy440, vyy450)
new_ltEs18(Just(vyy6000), Just(vyy500), app(app(app(ty_@3, bad), bae), baf)) → new_ltEs6(vyy6000, vyy500, bad, bae, baf)
new_primEqNat0(Zero, Zero) → True
new_esEs27(vyy44, vyy45, ty_Ordering) → new_esEs18(vyy44, vyy45)
new_esEs23(vyy440, vyy450, ty_@0) → new_esEs11(vyy440, vyy450)
new_esEs8(Right(vyy440), Right(vyy450), cgf, ty_Double) → new_esEs19(vyy440, vyy450)
new_lt15(vyy6000, vyy500, ced) → new_esEs22(new_compare3(vyy6000, vyy500, ced))
new_ltEs4(Right(vyy6000), Right(vyy500), ceg, ty_Ordering) → new_ltEs14(vyy6000, vyy500)
new_compare11(vyy6000, vyy500, True, beg) → LT
new_esEs8(Right(vyy440), Right(vyy450), cgf, ty_@0) → new_esEs11(vyy440, vyy450)
new_ltEs4(Right(vyy6000), Right(vyy500), ceg, app(app(ty_@2, dbe), dbf)) → new_ltEs9(vyy6000, vyy500, dbe, dbf)
new_ltEs20(vyy600, vyy50, ty_Float) → new_ltEs8(vyy600, vyy50)
new_esEs27(vyy44, vyy45, ty_Char) → new_esEs13(vyy44, vyy45)
new_ltEs19(vyy6001, vyy501, ty_Float) → new_ltEs8(vyy6001, vyy501)
new_compare17(Double(vyy6000, vyy6001), Double(vyy500, vyy501)) → new_compare16(new_sr0(vyy6000, vyy500), new_sr0(vyy6001, vyy501))
new_ltEs18(Just(vyy6000), Just(vyy500), ty_Int) → new_ltEs16(vyy6000, vyy500)
new_esEs7(Just(vyy440), Just(vyy450), app(app(ty_FiniteMap, db), dc)) → new_esEs16(vyy440, vyy450, db, dc)
new_esEs13(Char(vyy440), Char(vyy450)) → new_primEqInt(vyy440, vyy450)
new_ltEs20(vyy600, vyy50, app(app(ty_@2, cee), cef)) → new_ltEs9(vyy600, vyy50, cee, cef)
new_ltEs18(Just(vyy6000), Just(vyy500), ty_Double) → new_ltEs10(vyy6000, vyy500)
new_ltEs14(EQ, LT) → False
new_primCmpNat1(Zero, Zero) → EQ
new_esEs25(vyy441, vyy451, ty_Int) → new_esEs17(vyy441, vyy451)
new_primCmpInt(Neg(Zero), Neg(Succ(vyy5000))) → new_primCmpNat0(vyy5000, Zero)
new_esEs8(Left(vyy440), Left(vyy450), ty_Double, cfc) → new_esEs19(vyy440, vyy450)
new_esEs8(Right(vyy440), Right(vyy450), cgf, ty_Char) → new_esEs13(vyy440, vyy450)
new_primPlusNat0(Succ(vyy750), vyy50000) → Succ(Succ(new_primPlusNat1(vyy750, vyy50000)))
new_esEs21(vyy441, vyy451, ty_Float) → new_esEs9(vyy441, vyy451)
new_esEs7(Just(vyy440), Just(vyy450), app(ty_[], ce)) → new_esEs10(vyy440, vyy450, ce)
new_esEs23(vyy440, vyy450, ty_Float) → new_esEs9(vyy440, vyy450)
new_esEs26(vyy442, vyy452, app(app(app(ty_@3, cdc), cdd), cde)) → new_esEs6(vyy442, vyy452, cdc, cdd, cde)
new_ltEs7(vyy6002, vyy502, ty_Ordering) → new_ltEs14(vyy6002, vyy502)
new_ltEs19(vyy6001, vyy501, ty_Double) → new_ltEs10(vyy6001, vyy501)
new_esEs18(EQ, GT) → False
new_esEs18(GT, EQ) → False
new_lt20(vyy6000, vyy500, ty_Bool) → new_lt9(vyy6000, vyy500)
new_primCmpNat1(Succ(vyy600000), Zero) → GT
new_ltEs20(vyy600, vyy50, ty_Int) → new_ltEs16(vyy600, vyy50)
new_primEqInt(Neg(Succ(vyy4400)), Neg(Succ(vyy4500))) → new_primEqNat0(vyy4400, vyy4500)
new_compare25(vyy6000, vyy500, True) → EQ
new_ltEs4(Right(vyy6000), Right(vyy500), ceg, ty_Float) → new_ltEs8(vyy6000, vyy500)
new_compare13(vyy6000, vyy500, True, bfb, bfc) → LT
new_esEs25(vyy441, vyy451, app(app(ty_FiniteMap, ccf), ccg)) → new_esEs16(vyy441, vyy451, ccf, ccg)
new_esEs24(vyy440, vyy450, ty_Bool) → new_esEs14(vyy440, vyy450)
new_primPlusNat1(Succ(vyy7500), Zero) → Succ(vyy7500)
new_primPlusNat1(Zero, Succ(vyy500000)) → Succ(vyy500000)
new_ltEs4(Left(vyy6000), Left(vyy500), ty_Bool, ceh) → new_ltEs11(vyy6000, vyy500)
new_esEs8(Right(vyy440), Right(vyy450), cgf, app(app(ty_Either, cgg), cgh)) → new_esEs8(vyy440, vyy450, cgg, cgh)
new_esEs8(Right(vyy440), Left(vyy450), cgf, cfc) → False
new_esEs8(Left(vyy440), Right(vyy450), cgf, cfc) → False
new_lt4(vyy6000, vyy500, ty_Char) → new_lt12(vyy6000, vyy500)
new_compare3([], :(vyy500, vyy501), bhd) → LT
new_esEs20(vyy440, vyy450, app(app(ty_Either, bbf), bbg)) → new_esEs8(vyy440, vyy450, bbf, bbg)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_lt20(vyy6000, vyy500, app(ty_Maybe, beg)) → new_lt18(vyy6000, vyy500, beg)
new_ltEs20(vyy600, vyy50, ty_Bool) → new_ltEs11(vyy600, vyy50)
new_esEs24(vyy440, vyy450, app(app(app(ty_@3, cac), cad), cae)) → new_esEs6(vyy440, vyy450, cac, cad, cae)
new_compare3(:(vyy6000, vyy6001), [], bhd) → GT
new_lt5(vyy6001, vyy501, ty_Integer) → new_lt11(vyy6001, vyy501)
new_lt5(vyy6001, vyy501, app(app(ty_@2, fd), ff)) → new_lt7(vyy6001, vyy501, fd, ff)
new_compare18(vyy6000, vyy500, False) → GT
new_lt5(vyy6001, vyy501, ty_Int) → new_lt16(vyy6001, vyy501)
new_esEs29(vyy441, vyy451, ty_Int) → new_esEs17(vyy441, vyy451)
new_ltEs4(Left(vyy6000), Left(vyy500), app(app(ty_Either, dbc), dbd), ceh) → new_ltEs4(vyy6000, vyy500, dbc, dbd)
new_primEqInt(Neg(Succ(vyy4400)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(vyy4500))) → False
new_lt20(vyy6000, vyy500, ty_Integer) → new_lt11(vyy6000, vyy500)
new_esEs26(vyy442, vyy452, app(app(ty_FiniteMap, ceb), cec)) → new_esEs16(vyy442, vyy452, ceb, cec)
new_ltEs7(vyy6002, vyy502, app(ty_Ratio, hd)) → new_ltEs5(vyy6002, vyy502, hd)
new_lt20(vyy6000, vyy500, ty_Ordering) → new_lt13(vyy6000, vyy500)
new_esEs8(Left(vyy440), Left(vyy450), app(ty_[], cfh), cfc) → new_esEs10(vyy440, vyy450, cfh)
new_esEs27(vyy44, vyy45, app(app(ty_Either, cgf), cfc)) → new_esEs8(vyy44, vyy45, cgf, cfc)
new_esEs12(:%(vyy440, vyy441), :%(vyy450, vyy451), deb) → new_asAs(new_esEs28(vyy440, vyy450, deb), new_esEs29(vyy441, vyy451, deb))
new_compare34(vyy6000, vyy500, ty_Char) → new_compare29(vyy6000, vyy500)
new_foldFM0(vyy450, vyy451, vyy74, Branch(vyy4530, vyy4531, vyy4532, vyy4533, vyy4534), beh, bfa) → new_foldFM0(vyy4530, vyy4531, new_foldFM0(vyy450, vyy451, vyy74, vyy4534, beh, bfa), vyy4533, beh, bfa)
new_ltEs20(vyy600, vyy50, app(ty_Ratio, df)) → new_ltEs5(vyy600, vyy50, df)
new_compare34(vyy6000, vyy500, ty_Double) → new_compare17(vyy6000, vyy500)
new_esEs26(vyy442, vyy452, ty_@0) → new_esEs11(vyy442, vyy452)
new_compare25(vyy6000, vyy500, False) → new_compare19(vyy6000, vyy500, new_ltEs11(vyy6000, vyy500))
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_esEs24(vyy440, vyy450, ty_Ordering) → new_esEs18(vyy440, vyy450)
new_esEs10(:(vyy440, vyy441), [], bfg) → False
new_esEs10([], :(vyy450, vyy451), bfg) → False
new_lt20(vyy6000, vyy500, ty_Double) → new_lt8(vyy6000, vyy500)
new_sizeFM(EmptyFM, beh, bfa) → Pos(Zero)
new_compare11(vyy6000, vyy500, False, beg) → GT
new_compare6(:%(vyy6000, vyy6001), :%(vyy500, vyy501), ty_Integer) → new_compare12(new_sr(vyy6000, vyy501), new_sr(vyy500, vyy6001))
new_primEqInt(Pos(Succ(vyy4400)), Pos(Succ(vyy4500))) → new_primEqNat0(vyy4400, vyy4500)
new_compare10(vyy6000, vyy500, False, dd, de) → GT
new_esEs24(vyy440, vyy450, app(app(ty_FiniteMap, cbb), cbc)) → new_esEs16(vyy440, vyy450, cbb, cbc)
new_esEs24(vyy440, vyy450, app(app(ty_Either, bhh), caa)) → new_esEs8(vyy440, vyy450, bhh, caa)
new_esEs8(Left(vyy440), Left(vyy450), app(ty_Maybe, cfd), cfc) → new_esEs7(vyy440, vyy450, cfd)
new_esEs7(Just(vyy440), Just(vyy450), ty_Float) → new_esEs9(vyy440, vyy450)
new_esEs14(True, False) → False
new_esEs14(False, True) → False
new_ltEs4(Right(vyy6000), Right(vyy500), ceg, app(ty_[], dcc)) → new_ltEs15(vyy6000, vyy500, dcc)
new_esEs26(vyy442, vyy452, ty_Integer) → new_esEs15(vyy442, vyy452)
new_ltEs11(True, False) → False
new_ltEs18(Just(vyy6000), Just(vyy500), app(app(ty_Either, bbb), bbc)) → new_ltEs4(vyy6000, vyy500, bbb, bbc)
new_esEs8(Left(vyy440), Left(vyy450), app(app(app(ty_@3, cfe), cff), cfg), cfc) → new_esEs6(vyy440, vyy450, cfe, cff, cfg)
new_esEs10([], [], bfg) → True
new_esEs24(vyy440, vyy450, ty_Int) → new_esEs17(vyy440, vyy450)
new_primEqNat0(Succ(vyy44000), Succ(vyy45000)) → new_primEqNat0(vyy44000, vyy45000)
new_compare7(@0, @0) → EQ
new_esEs21(vyy441, vyy451, app(ty_Ratio, bec)) → new_esEs12(vyy441, vyy451, bec)
new_compare34(vyy6000, vyy500, ty_Float) → new_compare30(vyy6000, vyy500)
new_ltEs18(Just(vyy6000), Just(vyy500), ty_Ordering) → new_ltEs14(vyy6000, vyy500)
new_primCompAux00(vyy60, LT) → LT
new_ltEs4(Left(vyy6000), Left(vyy500), ty_Char, ceh) → new_ltEs13(vyy6000, vyy500)
new_esEs24(vyy440, vyy450, app(ty_Ratio, cba)) → new_esEs12(vyy440, vyy450, cba)
new_esEs24(vyy440, vyy450, ty_Float) → new_esEs9(vyy440, vyy450)
new_esEs23(vyy440, vyy450, app(app(ty_FiniteMap, bhb), bhc)) → new_esEs16(vyy440, vyy450, bhb, bhc)
new_ltEs20(vyy600, vyy50, ty_Ordering) → new_ltEs14(vyy600, vyy50)
new_esEs5(@2(vyy440, vyy441), @2(vyy450, vyy451), bbd, bbe) → new_asAs(new_esEs20(vyy440, vyy450, bbd), new_esEs21(vyy441, vyy451, bbe))
new_esEs7(Nothing, Nothing, bf) → True
new_esEs8(Right(vyy440), Right(vyy450), cgf, ty_Float) → new_esEs9(vyy440, vyy450)
new_primEqInt(Pos(Succ(vyy4400)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(vyy4500))) → False
new_ltEs12(vyy600, vyy50) → new_not(new_compare12(vyy600, vyy50))
new_esEs23(vyy440, vyy450, ty_Char) → new_esEs13(vyy440, vyy450)
new_compare34(vyy6000, vyy500, ty_Int) → new_compare16(vyy6000, vyy500)
new_esEs8(Right(vyy440), Right(vyy450), cgf, ty_Bool) → new_esEs14(vyy440, vyy450)
new_lt10(vyy6000, vyy500, bfd, bfe, bff) → new_esEs22(new_compare33(vyy6000, vyy500, bfd, bfe, bff))
new_ltEs4(Right(vyy6000), Right(vyy500), ceg, ty_@0) → new_ltEs17(vyy6000, vyy500)
new_ltEs18(Nothing, Nothing, baa) → True
new_compare18(vyy6000, vyy500, True) → LT
new_esEs23(vyy440, vyy450, app(app(ty_@2, bgg), bgh)) → new_esEs5(vyy440, vyy450, bgg, bgh)
new_esEs6(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), bhe, bhf, bhg) → new_asAs(new_esEs24(vyy440, vyy450, bhe), new_asAs(new_esEs25(vyy441, vyy451, bhf), new_esEs26(vyy442, vyy452, bhg)))
new_primCmpInt(Neg(Zero), Pos(Succ(vyy5000))) → LT
new_esEs8(Right(vyy440), Right(vyy450), cgf, ty_Ordering) → new_esEs18(vyy440, vyy450)
new_compare19(vyy6000, vyy500, False) → GT
new_ltEs7(vyy6002, vyy502, ty_Int) → new_ltEs16(vyy6002, vyy502)
new_lt4(vyy6000, vyy500, ty_Float) → new_lt6(vyy6000, vyy500)
new_compare14(vyy6000, vyy500, False, bfd, bfe, bff) → GT
new_compare28(vyy6000, vyy500, False, bfb, bfc) → new_compare13(vyy6000, vyy500, new_ltEs9(vyy6000, vyy500, bfb, bfc), bfb, bfc)
new_ltEs7(vyy6002, vyy502, ty_Bool) → new_ltEs11(vyy6002, vyy502)
new_compare26(vyy6000, vyy500, False, bfd, bfe, bff) → new_compare14(vyy6000, vyy500, new_ltEs6(vyy6000, vyy500, bfd, bfe, bff), bfd, bfe, bff)
new_primPlusNat1(Succ(vyy7500), Succ(vyy500000)) → Succ(Succ(new_primPlusNat1(vyy7500, vyy500000)))
new_ltEs20(vyy600, vyy50, ty_Char) → new_ltEs13(vyy600, vyy50)
new_compare28(vyy6000, vyy500, True, bfb, bfc) → EQ
new_esEs7(Just(vyy440), Just(vyy450), ty_Integer) → new_esEs15(vyy440, vyy450)
new_primEqInt(Pos(Succ(vyy4400)), Neg(vyy450)) → False
new_primEqInt(Neg(Succ(vyy4400)), Pos(vyy450)) → False
new_esEs7(Nothing, Just(vyy450), bf) → False
new_esEs7(Just(vyy440), Nothing, bf) → False
new_esEs20(vyy440, vyy450, ty_Char) → new_esEs13(vyy440, vyy450)
new_foldFM2(EmptyFM, beh, bfa) → []
new_compare34(vyy6000, vyy500, ty_Ordering) → new_compare15(vyy6000, vyy500)
new_compare34(vyy6000, vyy500, ty_Bool) → new_compare9(vyy6000, vyy500)
new_lt17(vyy6000, vyy500) → new_esEs22(new_compare7(vyy6000, vyy500))
new_ltEs20(vyy600, vyy50, ty_Double) → new_ltEs10(vyy600, vyy50)
new_compare31(vyy6000, vyy500, bfb, bfc) → new_compare28(vyy6000, vyy500, new_esEs5(vyy6000, vyy500, bfb, bfc), bfb, bfc)
new_esEs7(Just(vyy440), Just(vyy450), app(app(ty_Either, bg), bh)) → new_esEs8(vyy440, vyy450, bg, bh)
new_lt5(vyy6001, vyy501, ty_Bool) → new_lt9(vyy6001, vyy501)
new_esEs23(vyy440, vyy450, app(ty_Ratio, bha)) → new_esEs12(vyy440, vyy450, bha)
new_esEs26(vyy442, vyy452, ty_Int) → new_esEs17(vyy442, vyy452)
new_primEqInt(Pos(Zero), Neg(Succ(vyy4500))) → False
new_primEqInt(Neg(Zero), Pos(Succ(vyy4500))) → False
new_ltEs19(vyy6001, vyy501, app(app(ty_@2, dcg), dch)) → new_ltEs9(vyy6001, vyy501, dcg, dch)
new_primCmpNat2(Succ(vyy5000), vyy60000) → new_primCmpNat1(vyy5000, vyy60000)
new_esEs21(vyy441, vyy451, ty_Integer) → new_esEs15(vyy441, vyy451)
new_primCompAux00(vyy60, EQ) → vyy60
new_pePe(False, vyy44, vyy45, vyy46, dea) → new_asAs(new_esEs27(vyy44, vyy45, dea), vyy46)
new_esEs8(Left(vyy440), Left(vyy450), app(ty_Ratio, cgc), cfc) → new_esEs12(vyy440, vyy450, cgc)
new_esEs26(vyy442, vyy452, ty_Ordering) → new_esEs18(vyy442, vyy452)
new_esEs8(Left(vyy440), Left(vyy450), ty_@0, cfc) → new_esEs11(vyy440, vyy450)
new_esEs21(vyy441, vyy451, ty_Ordering) → new_esEs18(vyy441, vyy451)
new_ltEs4(Left(vyy6000), Left(vyy500), app(ty_[], dba), ceh) → new_ltEs15(vyy6000, vyy500, dba)
new_esEs8(Left(vyy440), Left(vyy450), ty_Int, cfc) → new_esEs17(vyy440, vyy450)
new_esEs26(vyy442, vyy452, app(app(ty_@2, cdg), cdh)) → new_esEs5(vyy442, vyy452, cdg, cdh)
new_esEs20(vyy440, vyy450, app(app(ty_FiniteMap, bch), bda)) → new_esEs16(vyy440, vyy450, bch, bda)
new_esEs24(vyy440, vyy450, ty_Char) → new_esEs13(vyy440, vyy450)
new_esEs21(vyy441, vyy451, app(app(ty_@2, bea), beb)) → new_esEs5(vyy441, vyy451, bea, beb)
new_ltEs20(vyy600, vyy50, app(app(app(ty_@3, dg), dh), ea)) → new_ltEs6(vyy600, vyy50, dg, dh, ea)
new_ltEs4(Right(vyy6000), Left(vyy500), ceg, ceh) → False
new_ltEs5(vyy600, vyy50, df) → new_not(new_compare6(vyy600, vyy50, df))
new_compare24(vyy6000, vyy500, True, beg) → EQ
new_ltEs18(Just(vyy6000), Nothing, baa) → False
new_primPlusNat0(Zero, vyy50000) → Succ(vyy50000)
new_ltEs17(vyy600, vyy50) → new_not(new_compare7(vyy600, vyy50))
new_compare15(vyy6000, vyy500) → new_compare27(vyy6000, vyy500, new_esEs18(vyy6000, vyy500))
new_ltEs18(Just(vyy6000), Just(vyy500), app(ty_[], bah)) → new_ltEs15(vyy6000, vyy500, bah)
new_esEs25(vyy441, vyy451, ty_Integer) → new_esEs15(vyy441, vyy451)
new_ltEs14(LT, LT) → True
new_esEs26(vyy442, vyy452, ty_Bool) → new_esEs14(vyy442, vyy452)
new_ltEs7(vyy6002, vyy502, app(app(app(ty_@3, ha), hb), hc)) → new_ltEs6(vyy6002, vyy502, ha, hb, hc)
new_ltEs4(Left(vyy6000), Left(vyy500), ty_Integer, ceh) → new_ltEs12(vyy6000, vyy500)
new_lt20(vyy6000, vyy500, app(ty_Ratio, bef)) → new_lt14(vyy6000, vyy500, bef)
new_not0 → True
new_ltEs19(vyy6001, vyy501, app(app(app(ty_@3, dda), ddb), ddc)) → new_ltEs6(vyy6001, vyy501, dda, ddb, ddc)
new_esEs23(vyy440, vyy450, app(ty_[], bgf)) → new_esEs10(vyy440, vyy450, bgf)
new_lt12(vyy6000, vyy500) → new_esEs22(new_compare29(vyy6000, vyy500))
new_ltEs11(False, False) → True
new_esEs19(Double(vyy440, vyy441), Double(vyy450, vyy451)) → new_esEs17(new_sr0(vyy440, vyy450), new_sr0(vyy441, vyy451))
new_compare12(Integer(vyy6000), Integer(vyy500)) → new_primCmpInt(vyy6000, vyy500)
new_ltEs7(vyy6002, vyy502, ty_Float) → new_ltEs8(vyy6002, vyy502)
new_esEs18(GT, GT) → True
new_ltEs19(vyy6001, vyy501, app(ty_[], dde)) → new_ltEs15(vyy6001, vyy501, dde)
new_ltEs20(vyy600, vyy50, ty_@0) → new_ltEs17(vyy600, vyy50)
new_lt4(vyy6000, vyy500, ty_Integer) → new_lt11(vyy6000, vyy500)
new_ltEs19(vyy6001, vyy501, ty_Integer) → new_ltEs12(vyy6001, vyy501)
new_primCmpInt(Pos(Succ(vyy60000)), Neg(vyy500)) → GT
new_esEs21(vyy441, vyy451, app(ty_Maybe, bdd)) → new_esEs7(vyy441, vyy451, bdd)
new_primMulInt(Pos(vyy60000), Pos(vyy5000)) → Pos(new_primMulNat0(vyy60000, vyy5000))
new_ltEs4(Left(vyy6000), Left(vyy500), app(ty_Ratio, dah), ceh) → new_ltEs5(vyy6000, vyy500, dah)
new_esEs8(Right(vyy440), Right(vyy450), cgf, app(app(app(ty_@3, chb), chc), chd)) → new_esEs6(vyy440, vyy450, chb, chc, chd)
new_primMulInt(Neg(vyy60000), Neg(vyy5000)) → Pos(new_primMulNat0(vyy60000, vyy5000))
new_esEs20(vyy440, vyy450, ty_Integer) → new_esEs15(vyy440, vyy450)
new_primEqNat0(Zero, Succ(vyy45000)) → False
new_primEqNat0(Succ(vyy44000), Zero) → False
new_esEs7(Just(vyy440), Just(vyy450), ty_Char) → new_esEs13(vyy440, vyy450)
new_lt5(vyy6001, vyy501, app(ty_[], gc)) → new_lt15(vyy6001, vyy501, gc)
new_esEs8(Right(vyy440), Right(vyy450), cgf, app(ty_Ratio, chh)) → new_esEs12(vyy440, vyy450, chh)
new_esEs17(vyy44, vyy45) → new_primEqInt(vyy44, vyy45)
new_esEs27(vyy44, vyy45, ty_@0) → new_esEs11(vyy44, vyy45)
new_ltEs7(vyy6002, vyy502, ty_Integer) → new_ltEs12(vyy6002, vyy502)
new_esEs20(vyy440, vyy450, ty_Bool) → new_esEs14(vyy440, vyy450)
new_lt20(vyy6000, vyy500, ty_@0) → new_lt17(vyy6000, vyy500)
new_esEs20(vyy440, vyy450, app(ty_[], bcd)) → new_esEs10(vyy440, vyy450, bcd)
new_compare23(vyy6000, vyy500, False, dd, de) → new_compare10(vyy6000, vyy500, new_ltEs4(vyy6000, vyy500, dd, de), dd, de)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_primCmpInt(Pos(Succ(vyy60000)), Pos(vyy500)) → new_primCmpNat0(vyy60000, vyy500)
new_esEs27(vyy44, vyy45, app(app(app(ty_@3, bhe), bhf), bhg)) → new_esEs6(vyy44, vyy45, bhe, bhf, bhg)
new_ltEs7(vyy6002, vyy502, app(app(ty_Either, hg), hh)) → new_ltEs4(vyy6002, vyy502, hg, hh)
new_esEs11(@0, @0) → True
new_esEs25(vyy441, vyy451, ty_@0) → new_esEs11(vyy441, vyy451)
new_esEs27(vyy44, vyy45, app(app(ty_@2, bbd), bbe)) → new_esEs5(vyy44, vyy45, bbd, bbe)
new_primCmpNat0(vyy60000, Zero) → GT
new_ltEs19(vyy6001, vyy501, ty_Char) → new_ltEs13(vyy6001, vyy501)
new_esEs27(vyy44, vyy45, ty_Int) → new_esEs17(vyy44, vyy45)
new_sizeFM(Branch(vyy450, vyy451, vyy452, vyy453, vyy454), beh, bfa) → vyy452
new_compare30(Float(vyy6000, vyy6001), Float(vyy500, vyy501)) → new_compare16(new_sr0(vyy6000, vyy500), new_sr0(vyy6001, vyy501))
new_ltEs4(Right(vyy6000), Right(vyy500), ceg, ty_Double) → new_ltEs10(vyy6000, vyy500)
new_ltEs19(vyy6001, vyy501, ty_@0) → new_ltEs17(vyy6001, vyy501)
new_esEs23(vyy440, vyy450, ty_Int) → new_esEs17(vyy440, vyy450)
new_pePe(True, vyy44, vyy45, vyy46, dea) → True
new_esEs24(vyy440, vyy450, ty_Double) → new_esEs19(vyy440, vyy450)
new_foldFM2(Branch(vyy450, vyy451, vyy452, vyy453, vyy454), beh, bfa) → new_foldFM0(vyy450, vyy451, new_foldFM2(vyy454, beh, bfa), vyy453, beh, bfa)
new_compare23(vyy6000, vyy500, True, dd, de) → EQ
new_lt5(vyy6001, vyy501, ty_Float) → new_lt6(vyy6001, vyy501)
new_primCmpInt(Pos(Zero), Neg(Succ(vyy5000))) → GT
new_compare8(vyy6000, vyy500, beg) → new_compare24(vyy6000, vyy500, new_esEs7(vyy6000, vyy500, beg), beg)
new_sr0(vyy6000, vyy500) → new_primMulInt(vyy6000, vyy500)
new_esEs10(:(vyy440, vyy441), :(vyy450, vyy451), bfg) → new_asAs(new_esEs23(vyy440, vyy450, bfg), new_esEs10(vyy441, vyy451, bfg))
new_esEs27(vyy44, vyy45, app(ty_Ratio, deb)) → new_esEs12(vyy44, vyy45, deb)
new_ltEs19(vyy6001, vyy501, ty_Ordering) → new_ltEs14(vyy6001, vyy501)
new_esEs8(Left(vyy440), Left(vyy450), app(app(ty_Either, cfa), cfb), cfc) → new_esEs8(vyy440, vyy450, cfa, cfb)
new_esEs25(vyy441, vyy451, app(ty_Maybe, cbf)) → new_esEs7(vyy441, vyy451, cbf)
new_esEs7(Just(vyy440), Just(vyy450), app(app(app(ty_@3, cb), cc), cd)) → new_esEs6(vyy440, vyy450, cb, cc, cd)
new_esEs24(vyy440, vyy450, app(ty_[], caf)) → new_esEs10(vyy440, vyy450, caf)
new_lt4(vyy6000, vyy500, ty_Ordering) → new_lt13(vyy6000, vyy500)
new_lt6(vyy6000, vyy500) → new_esEs22(new_compare30(vyy6000, vyy500))
new_lt9(vyy6000, vyy500) → new_esEs22(new_compare9(vyy6000, vyy500))
new_lt20(vyy6000, vyy500, app(ty_[], ced)) → new_lt15(vyy6000, vyy500, ced)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_compare29(Char(vyy6000), Char(vyy500)) → new_primCmpInt(vyy6000, vyy500)
new_esEs7(Just(vyy440), Just(vyy450), ty_@0) → new_esEs11(vyy440, vyy450)
new_ltEs18(Just(vyy6000), Just(vyy500), app(app(ty_@2, bab), bac)) → new_ltEs9(vyy6000, vyy500, bab, bac)
new_ltEs10(vyy600, vyy50) → new_not(new_compare17(vyy600, vyy50))
new_compare34(vyy6000, vyy500, app(ty_Maybe, dfb)) → new_compare8(vyy6000, vyy500, dfb)
new_lt18(vyy6000, vyy500, beg) → new_esEs22(new_compare8(vyy6000, vyy500, beg))
new_esEs28(vyy440, vyy450, ty_Int) → new_esEs17(vyy440, vyy450)
new_asAs(False, vyy55) → False
new_ltEs11(True, True) → True
new_compare3([], [], bhd) → EQ
new_primMulInt(Pos(vyy60000), Neg(vyy5000)) → Neg(new_primMulNat0(vyy60000, vyy5000))
new_primMulInt(Neg(vyy60000), Pos(vyy5000)) → Neg(new_primMulNat0(vyy60000, vyy5000))
new_primCmpInt(Neg(Succ(vyy60000)), Neg(vyy500)) → new_primCmpNat2(vyy500, vyy60000)
new_compare16(vyy600, vyy50) → new_primCmpInt(vyy600, vyy50)
new_primMulNat0(Succ(vyy600000), Zero) → Zero
new_primMulNat0(Zero, Succ(vyy50000)) → Zero
new_esEs23(vyy440, vyy450, app(app(app(ty_@3, bgc), bgd), bge)) → new_esEs6(vyy440, vyy450, bgc, bgd, bge)
new_lt4(vyy6000, vyy500, app(app(app(ty_@3, ed), ee), ef)) → new_lt10(vyy6000, vyy500, ed, ee, ef)
new_ltEs16(vyy600, vyy50) → new_not(new_compare16(vyy600, vyy50))
new_ltEs4(Right(vyy6000), Right(vyy500), ceg, ty_Int) → new_ltEs16(vyy6000, vyy500)
new_esEs8(Right(vyy440), Right(vyy450), cgf, ty_Int) → new_esEs17(vyy440, vyy450)
new_esEs26(vyy442, vyy452, app(ty_Maybe, cdb)) → new_esEs7(vyy442, vyy452, cdb)
new_ltEs18(Nothing, Just(vyy500), baa) → True
new_ltEs14(GT, LT) → False
new_not(EQ) → new_not0
new_esEs28(vyy440, vyy450, ty_Integer) → new_esEs15(vyy440, vyy450)
new_primCmpInt(Pos(Zero), Pos(Succ(vyy5000))) → new_primCmpNat2(Zero, vyy5000)
new_esEs25(vyy441, vyy451, app(app(app(ty_@3, cbg), cbh), cca)) → new_esEs6(vyy441, vyy451, cbg, cbh, cca)
new_lt8(vyy6000, vyy500) → new_esEs22(new_compare17(vyy6000, vyy500))
new_esEs23(vyy440, vyy450, ty_Integer) → new_esEs15(vyy440, vyy450)
new_esEs27(vyy44, vyy45, app(ty_[], bfg)) → new_esEs10(vyy44, vyy45, bfg)
new_compare27(vyy6000, vyy500, True) → EQ
new_esEs14(True, True) → True
new_ltEs19(vyy6001, vyy501, ty_Int) → new_ltEs16(vyy6001, vyy501)
new_ltEs4(Left(vyy6000), Left(vyy500), ty_Ordering, ceh) → new_ltEs14(vyy6000, vyy500)
new_ltEs18(Just(vyy6000), Just(vyy500), ty_Integer) → new_ltEs12(vyy6000, vyy500)
new_ltEs6(@3(vyy6000, vyy6001, vyy6002), @3(vyy500, vyy501, vyy502), dg, dh, ea) → new_pePe(new_lt4(vyy6000, vyy500, dg), vyy6000, vyy500, new_pePe(new_lt5(vyy6001, vyy501, dh), vyy6001, vyy501, new_ltEs7(vyy6002, vyy502, ea), dh), dg)
new_esEs27(vyy44, vyy45, ty_Bool) → new_esEs14(vyy44, vyy45)
new_esEs26(vyy442, vyy452, ty_Double) → new_esEs19(vyy442, vyy452)
new_lt19(vyy6000, vyy500, dd, de) → new_esEs22(new_compare32(vyy6000, vyy500, dd, de))
new_esEs26(vyy442, vyy452, app(ty_Ratio, cea)) → new_esEs12(vyy442, vyy452, cea)
new_ltEs18(Just(vyy6000), Just(vyy500), ty_Bool) → new_ltEs11(vyy6000, vyy500)
new_ltEs7(vyy6002, vyy502, ty_@0) → new_ltEs17(vyy6002, vyy502)
new_lt5(vyy6001, vyy501, app(app(ty_Either, ge), gf)) → new_lt19(vyy6001, vyy501, ge, gf)
new_ltEs20(vyy600, vyy50, app(ty_[], bhd)) → new_ltEs15(vyy600, vyy50, bhd)
new_ltEs4(Right(vyy6000), Right(vyy500), ceg, ty_Char) → new_ltEs13(vyy6000, vyy500)
new_esEs20(vyy440, vyy450, ty_Int) → new_esEs17(vyy440, vyy450)
new_esEs25(vyy441, vyy451, app(app(ty_@2, ccc), ccd)) → new_esEs5(vyy441, vyy451, ccc, ccd)
new_ltEs14(LT, GT) → True
new_esEs27(vyy44, vyy45, ty_Float) → new_esEs9(vyy44, vyy45)
new_not(LT) → new_not0
new_esEs8(Right(vyy440), Right(vyy450), cgf, ty_Integer) → new_esEs15(vyy440, vyy450)
new_lt5(vyy6001, vyy501, app(ty_Maybe, gd)) → new_lt18(vyy6001, vyy501, gd)
new_ltEs14(LT, EQ) → True
new_compare9(vyy6000, vyy500) → new_compare25(vyy6000, vyy500, new_esEs14(vyy6000, vyy500))
new_lt16(vyy6000, vyy500) → new_esEs22(new_compare16(vyy6000, vyy500))
new_lt13(vyy6000, vyy500) → new_esEs22(new_compare15(vyy6000, vyy500))
new_ltEs4(Right(vyy6000), Right(vyy500), ceg, ty_Bool) → new_ltEs11(vyy6000, vyy500)
new_lt4(vyy6000, vyy500, ty_Bool) → new_lt9(vyy6000, vyy500)
new_esEs14(False, False) → True
new_esEs8(Left(vyy440), Left(vyy450), ty_Float, cfc) → new_esEs9(vyy440, vyy450)
new_esEs7(Just(vyy440), Just(vyy450), app(app(ty_@2, cf), cg)) → new_esEs5(vyy440, vyy450, cf, cg)
new_lt20(vyy6000, vyy500, ty_Char) → new_lt12(vyy6000, vyy500)
new_ltEs7(vyy6002, vyy502, ty_Char) → new_ltEs13(vyy6002, vyy502)
new_esEs22(GT) → False
new_lt5(vyy6001, vyy501, ty_Double) → new_lt8(vyy6001, vyy501)
new_esEs25(vyy441, vyy451, ty_Double) → new_esEs19(vyy441, vyy451)
new_compare26(vyy6000, vyy500, True, bfd, bfe, bff) → EQ
new_esEs21(vyy441, vyy451, ty_@0) → new_esEs11(vyy441, vyy451)
new_ltEs4(Left(vyy6000), Left(vyy500), ty_Double, ceh) → new_ltEs10(vyy6000, vyy500)
new_primPlusNat1(Zero, Zero) → Zero
new_esEs21(vyy441, vyy451, app(app(app(ty_@3, bde), bdf), bdg)) → new_esEs6(vyy441, vyy451, bde, bdf, bdg)
new_asAs(True, vyy55) → vyy55
new_ltEs14(EQ, EQ) → True
new_primMulNat0(Succ(vyy600000), Succ(vyy50000)) → new_primPlusNat0(new_primMulNat0(vyy600000, Succ(vyy50000)), vyy50000)
new_lt5(vyy6001, vyy501, app(ty_Ratio, gb)) → new_lt14(vyy6001, vyy501, gb)
new_ltEs8(vyy600, vyy50) → new_not(new_compare30(vyy600, vyy50))
new_esEs7(Just(vyy440), Just(vyy450), ty_Bool) → new_esEs14(vyy440, vyy450)
new_compare6(:%(vyy6000, vyy6001), :%(vyy500, vyy501), ty_Int) → new_compare16(new_sr0(vyy6000, vyy501), new_sr0(vyy500, vyy6001))
new_fmToList(vyy45, beh, bfa) → new_foldFM2(vyy45, beh, bfa)
new_esEs8(Right(vyy440), Right(vyy450), cgf, app(app(ty_@2, chf), chg)) → new_esEs5(vyy440, vyy450, chf, chg)
new_ltEs13(vyy600, vyy50) → new_not(new_compare29(vyy600, vyy50))
new_esEs8(Left(vyy440), Left(vyy450), ty_Ordering, cfc) → new_esEs18(vyy440, vyy450)
new_lt11(vyy6000, vyy500) → new_esEs22(new_compare12(vyy6000, vyy500))
new_primCompAux00(vyy60, GT) → GT
new_ltEs18(Just(vyy6000), Just(vyy500), ty_Char) → new_ltEs13(vyy6000, vyy500)
new_esEs8(Right(vyy440), Right(vyy450), cgf, app(ty_[], che)) → new_esEs10(vyy440, vyy450, che)
new_compare33(vyy6000, vyy500, bfd, bfe, bff) → new_compare26(vyy6000, vyy500, new_esEs6(vyy6000, vyy500, bfd, bfe, bff), bfd, bfe, bff)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_ltEs14(EQ, GT) → True
new_esEs7(Just(vyy440), Just(vyy450), ty_Ordering) → new_esEs18(vyy440, vyy450)
new_lt4(vyy6000, vyy500, ty_@0) → new_lt17(vyy6000, vyy500)
new_ltEs4(Left(vyy6000), Left(vyy500), ty_@0, ceh) → new_ltEs17(vyy6000, vyy500)
new_lt5(vyy6001, vyy501, ty_Char) → new_lt12(vyy6001, vyy501)
new_esEs22(LT) → True
new_lt7(vyy6000, vyy500, bfb, bfc) → new_esEs22(new_compare31(vyy6000, vyy500, bfb, bfc))
new_lt4(vyy6000, vyy500, app(ty_Ratio, eg)) → new_lt14(vyy6000, vyy500, eg)
new_compare34(vyy6000, vyy500, app(ty_Ratio, deh)) → new_compare6(vyy6000, vyy500, deh)
new_esEs25(vyy441, vyy451, ty_Float) → new_esEs9(vyy441, vyy451)
new_esEs25(vyy441, vyy451, app(ty_Ratio, cce)) → new_esEs12(vyy441, vyy451, cce)
new_esEs7(Just(vyy440), Just(vyy450), app(ty_Ratio, da)) → new_esEs12(vyy440, vyy450, da)
new_primCmpNat0(vyy60000, Succ(vyy5000)) → new_primCmpNat1(vyy60000, vyy5000)
new_ltEs19(vyy6001, vyy501, app(ty_Maybe, ddf)) → new_ltEs18(vyy6001, vyy501, ddf)
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_esEs8(Right(vyy440), Right(vyy450), cgf, app(ty_Maybe, cha)) → new_esEs7(vyy440, vyy450, cha)
new_esEs25(vyy441, vyy451, app(app(ty_Either, cbd), cbe)) → new_esEs8(vyy441, vyy451, cbd, cbe)
new_esEs27(vyy44, vyy45, ty_Integer) → new_esEs15(vyy44, vyy45)
new_ltEs19(vyy6001, vyy501, ty_Bool) → new_ltEs11(vyy6001, vyy501)
new_esEs18(EQ, EQ) → True
new_esEs25(vyy441, vyy451, ty_Char) → new_esEs13(vyy441, vyy451)
new_primCmpInt(Neg(Succ(vyy60000)), Pos(vyy500)) → LT
new_esEs27(vyy44, vyy45, ty_Double) → new_esEs19(vyy44, vyy45)
The set Q consists of the following terms:
new_esEs21(x0, x1, ty_Int)
new_ltEs7(x0, x1, app(ty_Maybe, x2))
new_esEs8(Left(x0), Left(x1), ty_Integer, x2)
new_ltEs20(x0, x1, ty_Integer)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_esEs24(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_primPlusNat1(Succ(x0), Succ(x1))
new_ltEs7(x0, x1, ty_Int)
new_compare11(x0, x1, False, x2)
new_asAs(False, x0)
new_lt5(x0, x1, ty_Int)
new_lt8(x0, x1)
new_esEs8(Left(x0), Left(x1), ty_Bool, x2)
new_compare3(:(x0, x1), [], x2)
new_esEs7(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_esEs18(LT, LT)
new_esEs20(x0, x1, ty_Bool)
new_esEs7(Just(x0), Just(x1), ty_Char)
new_esEs24(x0, x1, ty_Ordering)
new_esEs21(x0, x1, ty_Bool)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs8(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_esEs8(Right(x0), Right(x1), x2, ty_Double)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_compare34(x0, x1, ty_Double)
new_esEs8(Right(x0), Right(x1), x2, ty_Ordering)
new_compare14(x0, x1, True, x2, x3, x4)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_esEs23(x0, x1, ty_Ordering)
new_esEs8(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs21(x0, x1, ty_@0)
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs26(x0, x1, ty_Char)
new_ltEs19(x0, x1, ty_Integer)
new_lt4(x0, x1, ty_Integer)
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs24(x0, x1, ty_Integer)
new_ltEs18(Nothing, Nothing, x0)
new_esEs20(x0, x1, ty_Float)
new_lt4(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare27(x0, x1, True)
new_esEs8(Right(x0), Right(x1), x2, app(ty_[], x3))
new_primMulNat0(Zero, Succ(x0))
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs7(Just(x0), Just(x1), ty_Bool)
new_esEs24(x0, x1, ty_Double)
new_ltEs4(Left(x0), Left(x1), ty_Bool, x2)
new_esEs23(x0, x1, ty_Char)
new_esEs11(@0, @0)
new_esEs22(LT)
new_compare13(x0, x1, True, x2, x3)
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_esEs29(x0, x1, ty_Integer)
new_ltEs4(Right(x0), Right(x1), x2, ty_Integer)
new_compare27(x0, x1, False)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_esEs8(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs21(x0, x1, ty_Integer)
new_esEs24(x0, x1, app(ty_[], x2))
new_ltEs4(Right(x0), Right(x1), x2, ty_Ordering)
new_compare10(x0, x1, True, x2, x3)
new_ltEs19(x0, x1, app(ty_[], x2))
new_compare19(x0, x1, False)
new_ltEs9(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_lt20(x0, x1, ty_Int)
new_esEs7(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_lt13(x0, x1)
new_primEqNat0(Zero, Succ(x0))
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
new_ltEs4(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_compare3([], :(x0, x1), x2)
new_ltEs7(x0, x1, ty_Char)
new_esEs26(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs18(EQ, GT)
new_esEs18(GT, EQ)
new_ltEs4(Left(x0), Left(x1), ty_Double, x2)
new_primCmpNat1(Succ(x0), Zero)
new_ltEs4(Left(x0), Left(x1), ty_Int, x2)
new_lt4(x0, x1, ty_Char)
new_esEs8(Right(x0), Right(x1), x2, ty_Float)
new_compare3([], [], x0)
new_esEs27(x0, x1, ty_@0)
new_ltEs20(x0, x1, ty_@0)
new_ltEs20(x0, x1, ty_Ordering)
new_compare34(x0, x1, app(ty_Ratio, x2))
new_esEs18(EQ, EQ)
new_ltEs4(Right(x0), Right(x1), x2, ty_Bool)
new_compare16(x0, x1)
new_ltEs19(x0, x1, ty_Float)
new_primCmpNat1(Zero, Zero)
new_compare10(x0, x1, False, x2, x3)
new_esEs27(x0, x1, ty_Int)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_compare8(x0, x1, x2)
new_compare25(x0, x1, True)
new_esEs25(x0, x1, app(ty_[], x2))
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_esEs14(True, True)
new_esEs27(x0, x1, app(ty_[], x2))
new_esEs27(x0, x1, ty_Float)
new_lt20(x0, x1, ty_Ordering)
new_esEs26(x0, x1, ty_Double)
new_esEs8(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_lt4(x0, x1, app(ty_Ratio, x2))
new_compare34(x0, x1, ty_Ordering)
new_ltEs14(EQ, EQ)
new_primEqNat0(Zero, Zero)
new_esEs27(x0, x1, ty_Double)
new_esEs8(Left(x0), Left(x1), app(ty_[], x2), x3)
new_lt5(x0, x1, app(app(ty_Either, x2), x3))
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_lt20(x0, x1, ty_Double)
new_esEs7(Just(x0), Just(x1), ty_Int)
new_compare34(x0, x1, app(ty_[], x2))
new_esEs24(x0, x1, ty_@0)
new_esEs26(x0, x1, ty_Bool)
new_compare3(:(x0, x1), :(x2, x3), x4)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_compare31(x0, x1, x2, x3)
new_esEs23(x0, x1, ty_Integer)
new_primMulNat0(Zero, Zero)
new_ltEs18(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_ltEs4(Right(x0), Right(x1), x2, ty_Float)
new_primCmpNat0(x0, Succ(x1))
new_esEs21(x0, x1, ty_Float)
new_ltEs17(x0, x1)
new_esEs6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs20(x0, x1, ty_Char)
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_esEs26(x0, x1, ty_@0)
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_primMulNat0(Succ(x0), Zero)
new_lt14(x0, x1, x2)
new_ltEs18(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_compare34(x0, x1, ty_Bool)
new_primCompAux00(x0, LT)
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare34(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs7(Just(x0), Just(x1), app(ty_[], x2))
new_lt5(x0, x1, ty_Ordering)
new_primPlusNat0(Zero, x0)
new_esEs25(x0, x1, ty_Float)
new_compare34(x0, x1, ty_Integer)
new_lt4(x0, x1, ty_@0)
new_esEs27(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_ltEs7(x0, x1, ty_Float)
new_esEs8(Left(x0), Left(x1), ty_Int, x2)
new_ltEs19(x0, x1, ty_Ordering)
new_sr(Integer(x0), Integer(x1))
new_esEs8(Right(x0), Right(x1), x2, app(app(ty_FiniteMap, x3), x4))
new_compare19(x0, x1, True)
new_esEs27(x0, x1, ty_Ordering)
new_ltEs19(x0, x1, ty_Bool)
new_esEs8(Right(x0), Left(x1), x2, x3)
new_esEs8(Left(x0), Right(x1), x2, x3)
new_esEs8(Right(x0), Right(x1), x2, ty_Bool)
new_compare34(x0, x1, app(ty_Maybe, x2))
new_compare34(x0, x1, ty_Char)
new_ltEs4(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_ltEs4(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_primEqNat0(Succ(x0), Zero)
new_ltEs18(Just(x0), Just(x1), ty_Int)
new_esEs12(:%(x0, x1), :%(x2, x3), x4)
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, ty_Bool)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_ltEs7(x0, x1, ty_Integer)
new_lt7(x0, x1, x2, x3)
new_esEs23(x0, x1, ty_@0)
new_ltEs18(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs16(x0, x1, x2, x3)
new_esEs8(Right(x0), Right(x1), x2, ty_@0)
new_lt5(x0, x1, ty_Float)
new_compare23(x0, x1, True, x2, x3)
new_esEs20(x0, x1, ty_Ordering)
new_esEs8(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_compare28(x0, x1, False, x2, x3)
new_esEs8(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_compare17(Double(x0, x1), Double(x2, x3))
new_esEs13(Char(x0), Char(x1))
new_esEs25(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_lt20(x0, x1, ty_Char)
new_ltEs4(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs25(x0, x1, ty_Ordering)
new_lt20(x0, x1, ty_Integer)
new_ltEs20(x0, x1, ty_Char)
new_ltEs4(Right(x0), Right(x1), x2, ty_Double)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_ltEs18(Just(x0), Just(x1), ty_Float)
new_ltEs7(x0, x1, ty_@0)
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs28(x0, x1, ty_Integer)
new_esEs21(x0, x1, ty_Char)
new_primPlusNat1(Zero, Zero)
new_lt4(x0, x1, app(app(ty_Either, x2), x3))
new_compare6(:%(x0, x1), :%(x2, x3), ty_Integer)
new_not0
new_ltEs19(x0, x1, ty_Char)
new_primPlusNat1(Zero, Succ(x0))
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs7(Just(x0), Just(x1), ty_Integer)
new_lt5(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs14(LT, LT)
new_lt5(x0, x1, app(ty_Ratio, x2))
new_esEs8(Right(x0), Right(x1), x2, ty_Integer)
new_fmToList(x0, x1, x2)
new_ltEs13(x0, x1)
new_esEs26(x0, x1, ty_Integer)
new_compare34(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs7(x0, x1, ty_Bool)
new_esEs7(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_lt4(x0, x1, ty_Float)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_lt20(x0, x1, app(ty_Ratio, x2))
new_compare34(x0, x1, ty_@0)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_compare34(x0, x1, ty_Int)
new_lt5(x0, x1, ty_Double)
new_esEs18(GT, GT)
new_lt5(x0, x1, ty_Bool)
new_lt12(x0, x1)
new_compare13(x0, x1, False, x2, x3)
new_ltEs4(Left(x0), Right(x1), x2, x3)
new_ltEs4(Right(x0), Left(x1), x2, x3)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_primCompAux00(x0, EQ)
new_lt4(x0, x1, app(app(ty_@2, x2), x3))
new_esEs20(x0, x1, ty_@0)
new_lt6(x0, x1)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_esEs25(x0, x1, ty_Double)
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_not(GT)
new_ltEs8(x0, x1)
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_esEs8(Left(x0), Left(x1), ty_Double, x2)
new_esEs7(Just(x0), Just(x1), app(app(ty_FiniteMap, x2), x3))
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_lt20(x0, x1, ty_Float)
new_compare15(x0, x1)
new_ltEs4(Left(x0), Left(x1), ty_Char, x2)
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_ltEs10(x0, x1)
new_esEs23(x0, x1, ty_Float)
new_ltEs14(LT, EQ)
new_ltEs16(x0, x1)
new_ltEs14(EQ, LT)
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs8(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_ltEs11(False, False)
new_ltEs4(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_sr0(x0, x1)
new_ltEs7(x0, x1, app(app(ty_@2, x2), x3))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_lt5(x0, x1, ty_Integer)
new_compare26(x0, x1, False, x2, x3, x4)
new_esEs7(Just(x0), Nothing, x1)
new_compare24(x0, x1, True, x2)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_lt4(x0, x1, ty_Ordering)
new_primEqInt(Neg(Zero), Neg(Zero))
new_ltEs20(x0, x1, ty_Float)
new_foldFM2(EmptyFM, x0, x1)
new_lt5(x0, x1, app(ty_[], x2))
new_ltEs11(False, True)
new_ltEs11(True, False)
new_esEs26(x0, x1, ty_Ordering)
new_esEs14(False, True)
new_esEs14(True, False)
new_lt15(x0, x1, x2)
new_esEs21(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_esEs8(Left(x0), Left(x1), ty_Ordering, x2)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_ltEs5(x0, x1, x2)
new_ltEs18(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs18(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs17(x0, x1)
new_esEs26(x0, x1, app(ty_[], x2))
new_primCmpNat2(Succ(x0), x1)
new_ltEs18(Just(x0), Just(x1), ty_Integer)
new_esEs7(Just(x0), Just(x1), app(ty_Maybe, x2))
new_compare29(Char(x0), Char(x1))
new_primPlusNat0(Succ(x0), x1)
new_compare7(@0, @0)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_ltEs7(x0, x1, app(ty_[], x2))
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_ltEs4(Left(x0), Left(x1), ty_Float, x2)
new_compare23(x0, x1, False, x2, x3)
new_primCmpNat2(Zero, x0)
new_compare9(x0, x1)
new_lt4(x0, x1, app(ty_[], x2))
new_compare33(x0, x1, x2, x3, x4)
new_primCmpNat1(Succ(x0), Succ(x1))
new_primCmpNat0(x0, Zero)
new_esEs24(x0, x1, ty_Char)
new_esEs8(Left(x0), Left(x1), app(app(ty_FiniteMap, x2), x3), x4)
new_esEs8(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs7(Just(x0), Just(x1), ty_Double)
new_esEs20(x0, x1, app(ty_[], x2))
new_ltEs4(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs4(Right(x0), Right(x1), x2, ty_Int)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, ty_Double)
new_ltEs7(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs20(x0, x1, app(ty_[], x2))
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_esEs8(Right(x0), Right(x1), x2, ty_Int)
new_compare26(x0, x1, True, x2, x3, x4)
new_lt4(x0, x1, ty_Int)
new_esEs21(x0, x1, ty_Ordering)
new_esEs10(:(x0, x1), :(x2, x3), x4)
new_ltEs14(EQ, GT)
new_ltEs14(GT, EQ)
new_ltEs12(x0, x1)
new_esEs7(Nothing, Just(x0), x1)
new_primCompAux0(x0, x1, x2, x3)
new_esEs20(x0, x1, ty_Double)
new_lt18(x0, x1, x2)
new_esEs8(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs26(x0, x1, ty_Int)
new_sizeFM(EmptyFM, x0, x1)
new_ltEs18(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs24(x0, x1, ty_Float)
new_primMulNat0(Succ(x0), Succ(x1))
new_esEs20(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(EQ)
new_ltEs4(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_compare34(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs18(Just(x0), Just(x1), ty_Bool)
new_esEs7(Just(x0), Just(x1), ty_Float)
new_asAs(True, x0)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_primCmpNat1(Zero, Succ(x0))
new_lt5(x0, x1, ty_@0)
new_esEs18(EQ, LT)
new_esEs18(LT, EQ)
new_esEs23(x0, x1, ty_Bool)
new_lt5(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs14(LT, GT)
new_ltEs14(GT, LT)
new_primCompAux00(x0, GT)
new_compare25(x0, x1, False)
new_ltEs4(Right(x0), Right(x1), x2, ty_@0)
new_esEs20(x0, x1, ty_Int)
new_compare34(x0, x1, ty_Float)
new_esEs27(x0, x1, ty_Char)
new_lt20(x0, x1, app(ty_[], x2))
new_esEs23(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_compare32(x0, x1, x2, x3)
new_ltEs7(x0, x1, app(ty_Ratio, x2))
new_lt4(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt17(x0, x1)
new_esEs26(x0, x1, ty_Float)
new_ltEs4(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_ltEs14(GT, GT)
new_lt20(x0, x1, ty_Bool)
new_ltEs18(Just(x0), Just(x1), ty_Char)
new_esEs5(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs25(x0, x1, ty_Bool)
new_esEs19(Double(x0, x1), Double(x2, x3))
new_lt5(x0, x1, ty_Char)
new_not(EQ)
new_esEs10(:(x0, x1), [], x2)
new_esEs10([], :(x0, x1), x2)
new_ltEs20(x0, x1, ty_Double)
new_lt4(x0, x1, ty_Double)
new_compare12(Integer(x0), Integer(x1))
new_esEs7(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_lt10(x0, x1, x2, x3, x4)
new_esEs28(x0, x1, ty_Int)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_ltEs7(x0, x1, ty_Double)
new_lt16(x0, x1)
new_esEs22(GT)
new_ltEs18(Just(x0), Just(x1), ty_Ordering)
new_lt9(x0, x1)
new_esEs15(Integer(x0), Integer(x1))
new_lt5(x0, x1, app(ty_Maybe, x2))
new_compare24(x0, x1, False, x2)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(Nothing, Nothing, x0)
new_esEs8(Left(x0), Left(x1), ty_@0, x2)
new_ltEs4(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs23(x0, x1, app(ty_[], x2))
new_esEs25(x0, x1, ty_Integer)
new_esEs20(x0, x1, ty_Integer)
new_compare18(x0, x1, True)
new_compare11(x0, x1, True, x2)
new_compare18(x0, x1, False)
new_pePe(True, x0, x1, x2, x3)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare6(:%(x0, x1), :%(x2, x3), ty_Int)
new_compare30(Float(x0, x1), Float(x2, x3))
new_lt11(x0, x1)
new_ltEs18(Just(x0), Nothing, x1)
new_esEs27(x0, x1, ty_Bool)
new_esEs18(GT, LT)
new_esEs18(LT, GT)
new_ltEs19(x0, x1, ty_@0)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs21(x0, x1, app(ty_[], x2))
new_esEs9(Float(x0, x1), Float(x2, x3))
new_esEs10([], [], x0)
new_ltEs7(x0, x1, ty_Ordering)
new_ltEs4(Left(x0), Left(x1), ty_Ordering, x2)
new_ltEs18(Nothing, Just(x0), x1)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_esEs25(x0, x1, ty_Char)
new_esEs29(x0, x1, ty_Int)
new_ltEs19(x0, x1, ty_Double)
new_compare14(x0, x1, False, x2, x3, x4)
new_esEs27(x0, x1, ty_Integer)
new_esEs7(Just(x0), Just(x1), ty_@0)
new_lt4(x0, x1, ty_Bool)
new_ltEs4(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_ltEs4(Left(x0), Left(x1), ty_@0, x2)
new_esEs8(Left(x0), Left(x1), ty_Char, x2)
new_ltEs19(x0, x1, ty_Int)
new_compare28(x0, x1, True, x2, x3)
new_esEs14(False, False)
new_ltEs4(Right(x0), Right(x1), x2, ty_Char)
new_primEqInt(Pos(Zero), Pos(Zero))
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_esEs25(x0, x1, ty_@0)
new_lt19(x0, x1, x2, x3)
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_esEs21(x0, x1, ty_Double)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs4(Left(x0), Left(x1), app(ty_[], x2), x3)
new_ltEs20(x0, x1, ty_Int)
new_ltEs18(Just(x0), Just(x1), ty_@0)
new_esEs24(x0, x1, ty_Int)
new_lt20(x0, x1, ty_@0)
new_ltEs4(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs7(Just(x0), Just(x1), ty_Ordering)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, ty_Int)
new_esEs8(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs25(x0, x1, ty_Int)
new_esEs24(x0, x1, ty_Bool)
new_esEs8(Left(x0), Left(x1), ty_Float, x2)
new_ltEs4(Left(x0), Left(x1), ty_Integer, x2)
new_primPlusNat1(Succ(x0), Zero)
new_ltEs15(x0, x1, x2)
new_primMulInt(Pos(x0), Pos(x1))
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs18(Just(x0), Just(x1), ty_Double)
new_not(LT)
new_ltEs11(True, True)
new_esEs8(Right(x0), Right(x1), x2, ty_Char)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_pePe(False, x0, x1, x2, x3)
new_ltEs7(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
We have to consider all minimal (P,Q,R)-chains.
By using the subterm criterion [20] together with the size-change analysis [32] we have proven that there are no infinite chains for this DP problem. From the DPs we obtained the following set of size-change graphs:
- new_foldFM_LE(vyy3, Just(vyy50), Branch(Just(vyy600), vyy61, vyy62, vyy63, vyy64), h, ba, bb) → new_foldFM_LE1(vyy3, vyy50, vyy600, vyy61, vyy62, vyy63, vyy64, new_ltEs20(vyy600, vyy50, ba), h, ba, bb)
The graph contains the following edges 1 >= 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5, 3 > 6, 3 > 7, 4 >= 9, 5 >= 10, 6 >= 11
- new_foldFM_LE1(vyy17, vyy19, vyy20, vyy21, vyy22, vyy23, vyy24, False, bc, bd, be) → new_foldFM_LE(vyy17, Just(vyy19), vyy23, bc, bd, be)
The graph contains the following edges 1 >= 1, 6 >= 3, 9 >= 4, 10 >= 5, 11 >= 6
- new_foldFM_LE1(vyy17, vyy19, vyy20, vyy21, vyy22, vyy23, vyy24, True, bc, bd, be) → new_foldFM_LE(vyy17, Just(vyy19), vyy23, bc, bd, be)
The graph contains the following edges 1 >= 1, 6 >= 3, 9 >= 4, 10 >= 5, 11 >= 6
- new_foldFM_LE1(vyy17, vyy19, vyy20, vyy21, vyy22, vyy23, vyy24, True, bc, bd, be) → new_foldFM_LE(vyy17, Just(vyy19), vyy24, bc, bd, be)
The graph contains the following edges 1 >= 1, 7 >= 3, 9 >= 4, 10 >= 5, 11 >= 6
- new_foldFM_LE(vyy3, Just(vyy50), Branch(Nothing, vyy61, vyy62, vyy63, vyy64), h, ba, bb) → new_foldFM_LE(vyy3, Just(vyy50), vyy64, h, ba, bb)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 >= 4, 5 >= 5, 6 >= 6
- new_foldFM_LE(vyy3, Just(vyy50), Branch(Nothing, vyy61, vyy62, vyy63, vyy64), h, ba, bb) → new_foldFM_LE(vyy3, Just(vyy50), vyy63, h, ba, bb)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 >= 4, 5 >= 5, 6 >= 6
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_foldFM_LE(vyy3, Nothing, Branch(Just(vyy600), vyy61, vyy62, vyy63, vyy64), h, ba, bb) → new_foldFM_LE(vyy3, Nothing, vyy63, h, ba, bb)
new_foldFM_LE(vyy3, Nothing, Branch(Nothing, vyy61, vyy62, vyy63, vyy64), h, ba, bb) → new_foldFM_LE(vyy3, Nothing, vyy64, h, ba, bb)
new_foldFM_LE(vyy3, Nothing, Branch(Nothing, vyy61, vyy62, vyy63, vyy64), h, ba, bb) → new_foldFM_LE(vyy3, Nothing, vyy63, h, ba, bb)
The TRS R consists of the following rules:
new_compare34(vyy6000, vyy500, app(app(ty_Either, dfc), dfd)) → new_compare32(vyy6000, vyy500, dfc, dfd)
new_esEs7(Just(vyy440), Just(vyy450), app(ty_Maybe, ca)) → new_esEs7(vyy440, vyy450, ca)
new_ltEs20(vyy600, vyy50, app(ty_Maybe, baa)) → new_ltEs18(vyy600, vyy50, baa)
new_esEs20(vyy440, vyy450, app(ty_Maybe, bbh)) → new_esEs7(vyy440, vyy450, bbh)
new_esEs23(vyy440, vyy450, ty_Ordering) → new_esEs18(vyy440, vyy450)
new_compare3(:(vyy6000, vyy6001), :(vyy500, vyy501), bhd) → new_primCompAux0(vyy6000, vyy500, new_compare3(vyy6001, vyy501, bhd), bhd)
new_lt20(vyy6000, vyy500, ty_Int) → new_lt16(vyy6000, vyy500)
new_primCmpNat2(Zero, vyy60000) → LT
new_ltEs9(@2(vyy6000, vyy6001), @2(vyy500, vyy501), cee, cef) → new_pePe(new_lt20(vyy6000, vyy500, cee), vyy6000, vyy500, new_ltEs19(vyy6001, vyy501, cef), cee)
new_esEs18(LT, LT) → True
new_esEs20(vyy440, vyy450, ty_Double) → new_esEs19(vyy440, vyy450)
new_lt4(vyy6000, vyy500, ty_Int) → new_lt16(vyy6000, vyy500)
new_lt20(vyy6000, vyy500, app(app(ty_Either, dd), de)) → new_lt19(vyy6000, vyy500, dd, de)
new_ltEs4(Left(vyy6000), Left(vyy500), app(ty_Maybe, dbb), ceh) → new_ltEs18(vyy6000, vyy500, dbb)
new_esEs25(vyy441, vyy451, ty_Ordering) → new_esEs18(vyy441, vyy451)
new_ltEs14(GT, GT) → True
new_primCmpNat1(Zero, Succ(vyy50000)) → LT
new_ltEs18(Just(vyy6000), Just(vyy500), ty_Float) → new_ltEs8(vyy6000, vyy500)
new_compare10(vyy6000, vyy500, True, dd, de) → LT
new_primCompAux0(vyy6000, vyy500, vyy56, bhd) → new_primCompAux00(vyy56, new_compare34(vyy6000, vyy500, bhd))
new_ltEs18(Just(vyy6000), Just(vyy500), app(ty_Maybe, bba)) → new_ltEs18(vyy6000, vyy500, bba)
new_esEs18(LT, EQ) → False
new_esEs18(EQ, LT) → False
new_esEs27(vyy44, vyy45, app(ty_Maybe, bf)) → new_esEs7(vyy44, vyy45, bf)
new_esEs20(vyy440, vyy450, ty_Float) → new_esEs9(vyy440, vyy450)
new_esEs23(vyy440, vyy450, ty_Bool) → new_esEs14(vyy440, vyy450)
new_ltEs18(Just(vyy6000), Just(vyy500), ty_@0) → new_ltEs17(vyy6000, vyy500)
new_ltEs4(Left(vyy6000), Left(vyy500), app(app(app(ty_@3, dae), daf), dag), ceh) → new_ltEs6(vyy6000, vyy500, dae, daf, dag)
new_esEs8(Left(vyy440), Left(vyy450), ty_Integer, cfc) → new_esEs15(vyy440, vyy450)
new_compare14(vyy6000, vyy500, True, bfd, bfe, bff) → LT
new_ltEs19(vyy6001, vyy501, app(ty_Ratio, ddd)) → new_ltEs5(vyy6001, vyy501, ddd)
new_esEs7(Just(vyy440), Just(vyy450), ty_Double) → new_esEs19(vyy440, vyy450)
new_primMulNat0(Zero, Zero) → Zero
new_lt4(vyy6000, vyy500, ty_Double) → new_lt8(vyy6000, vyy500)
new_compare32(vyy6000, vyy500, dd, de) → new_compare23(vyy6000, vyy500, new_esEs8(vyy6000, vyy500, dd, de), dd, de)
new_esEs8(Left(vyy440), Left(vyy450), app(app(ty_FiniteMap, cgd), cge), cfc) → new_esEs16(vyy440, vyy450, cgd, cge)
new_sr(Integer(vyy60000), Integer(vyy5010)) → Integer(new_primMulInt(vyy60000, vyy5010))
new_esEs21(vyy441, vyy451, app(app(ty_Either, bdb), bdc)) → new_esEs8(vyy441, vyy451, bdb, bdc)
new_ltEs4(Right(vyy6000), Right(vyy500), ceg, ty_Integer) → new_ltEs12(vyy6000, vyy500)
new_esEs21(vyy441, vyy451, app(ty_[], bdh)) → new_esEs10(vyy441, vyy451, bdh)
new_lt20(vyy6000, vyy500, ty_Float) → new_lt6(vyy6000, vyy500)
new_ltEs4(Left(vyy6000), Left(vyy500), app(app(ty_@2, dac), dad), ceh) → new_ltEs9(vyy6000, vyy500, dac, dad)
new_ltEs4(Right(vyy6000), Right(vyy500), ceg, app(app(app(ty_@3, dbg), dbh), dca)) → new_ltEs6(vyy6000, vyy500, dbg, dbh, dca)
new_esEs24(vyy440, vyy450, ty_Integer) → new_esEs15(vyy440, vyy450)
new_esEs16(vyy44, vyy45, beh, bfa) → new_asAs(new_esEs17(new_sizeFM(vyy44, beh, bfa), new_sizeFM(vyy45, beh, bfa)), new_esEs10(new_fmToList(vyy44, beh, bfa), new_fmToList(vyy45, beh, bfa), app(app(ty_@2, beh), bfa)))
new_esEs21(vyy441, vyy451, app(app(ty_FiniteMap, bed), bee)) → new_esEs16(vyy441, vyy451, bed, bee)
new_not(GT) → False
new_lt5(vyy6001, vyy501, ty_Ordering) → new_lt13(vyy6001, vyy501)
new_esEs8(Right(vyy440), Right(vyy450), cgf, app(app(ty_FiniteMap, daa), dab)) → new_esEs16(vyy440, vyy450, daa, dab)
new_esEs26(vyy442, vyy452, ty_Float) → new_esEs9(vyy442, vyy452)
new_ltEs4(Right(vyy6000), Right(vyy500), ceg, app(ty_Maybe, dcd)) → new_ltEs18(vyy6000, vyy500, dcd)
new_lt4(vyy6000, vyy500, app(ty_[], eh)) → new_lt15(vyy6000, vyy500, eh)
new_ltEs4(Left(vyy6000), Left(vyy500), ty_Float, ceh) → new_ltEs8(vyy6000, vyy500)
new_esEs26(vyy442, vyy452, app(ty_[], cdf)) → new_esEs10(vyy442, vyy452, cdf)
new_lt4(vyy6000, vyy500, app(ty_Maybe, fa)) → new_lt18(vyy6000, vyy500, fa)
new_ltEs4(Right(vyy6000), Right(vyy500), ceg, app(ty_Ratio, dcb)) → new_ltEs5(vyy6000, vyy500, dcb)
new_esEs8(Left(vyy440), Left(vyy450), ty_Bool, cfc) → new_esEs14(vyy440, vyy450)
new_esEs24(vyy440, vyy450, app(app(ty_@2, cag), cah)) → new_esEs5(vyy440, vyy450, cag, cah)
new_esEs8(Left(vyy440), Left(vyy450), app(app(ty_@2, cga), cgb), cfc) → new_esEs5(vyy440, vyy450, cga, cgb)
new_primCmpNat1(Succ(vyy600000), Succ(vyy50000)) → new_primCmpNat1(vyy600000, vyy50000)
new_esEs9(Float(vyy440, vyy441), Float(vyy450, vyy451)) → new_esEs17(new_sr0(vyy440, vyy450), new_sr0(vyy441, vyy451))
new_ltEs4(Left(vyy6000), Left(vyy500), ty_Int, ceh) → new_ltEs16(vyy6000, vyy500)
new_esEs15(Integer(vyy440), Integer(vyy450)) → new_primEqInt(vyy440, vyy450)
new_esEs18(LT, GT) → False
new_esEs18(GT, LT) → False
new_ltEs7(vyy6002, vyy502, app(ty_Maybe, hf)) → new_ltEs18(vyy6002, vyy502, hf)
new_compare34(vyy6000, vyy500, app(app(app(ty_@3, dee), def), deg)) → new_compare33(vyy6000, vyy500, dee, def, deg)
new_esEs26(vyy442, vyy452, ty_Char) → new_esEs13(vyy442, vyy452)
new_esEs21(vyy441, vyy451, ty_Int) → new_esEs17(vyy441, vyy451)
new_ltEs7(vyy6002, vyy502, app(app(ty_@2, gg), gh)) → new_ltEs9(vyy6002, vyy502, gg, gh)
new_foldFM0(vyy450, vyy451, vyy74, EmptyFM, beh, bfa) → :(@2(vyy450, vyy451), vyy74)
new_esEs29(vyy441, vyy451, ty_Integer) → new_esEs15(vyy441, vyy451)
new_esEs25(vyy441, vyy451, app(ty_[], ccb)) → new_esEs10(vyy441, vyy451, ccb)
new_ltEs19(vyy6001, vyy501, app(app(ty_Either, ddg), ddh)) → new_ltEs4(vyy6001, vyy501, ddg, ddh)
new_compare34(vyy6000, vyy500, app(ty_[], dfa)) → new_compare3(vyy6000, vyy500, dfa)
new_compare27(vyy6000, vyy500, False) → new_compare18(vyy6000, vyy500, new_ltEs14(vyy6000, vyy500))
new_compare34(vyy6000, vyy500, ty_Integer) → new_compare12(vyy6000, vyy500)
new_esEs25(vyy441, vyy451, ty_Bool) → new_esEs14(vyy441, vyy451)
new_lt5(vyy6001, vyy501, ty_@0) → new_lt17(vyy6001, vyy501)
new_ltEs7(vyy6002, vyy502, ty_Double) → new_ltEs10(vyy6002, vyy502)
new_ltEs14(GT, EQ) → False
new_esEs22(EQ) → False
new_esEs23(vyy440, vyy450, app(app(ty_Either, bfh), bga)) → new_esEs8(vyy440, vyy450, bfh, bga)
new_esEs20(vyy440, vyy450, app(ty_Ratio, bcg)) → new_esEs12(vyy440, vyy450, bcg)
new_esEs26(vyy442, vyy452, app(app(ty_Either, cch), cda)) → new_esEs8(vyy442, vyy452, cch, cda)
new_esEs27(vyy44, vyy45, app(app(ty_FiniteMap, beh), bfa)) → new_esEs16(vyy44, vyy45, beh, bfa)
new_esEs24(vyy440, vyy450, app(ty_Maybe, cab)) → new_esEs7(vyy440, vyy450, cab)
new_compare34(vyy6000, vyy500, app(app(ty_@2, dec), ded)) → new_compare31(vyy6000, vyy500, dec, ded)
new_esEs24(vyy440, vyy450, ty_@0) → new_esEs11(vyy440, vyy450)
new_ltEs20(vyy600, vyy50, app(app(ty_Either, ceg), ceh)) → new_ltEs4(vyy600, vyy50, ceg, ceh)
new_lt20(vyy6000, vyy500, app(app(app(ty_@3, bfd), bfe), bff)) → new_lt10(vyy6000, vyy500, bfd, bfe, bff)
new_esEs23(vyy440, vyy450, app(ty_Maybe, bgb)) → new_esEs7(vyy440, vyy450, bgb)
new_ltEs7(vyy6002, vyy502, app(ty_[], he)) → new_ltEs15(vyy6002, vyy502, he)
new_lt5(vyy6001, vyy501, app(app(app(ty_@3, fg), fh), ga)) → new_lt10(vyy6001, vyy501, fg, fh, ga)
new_ltEs4(Right(vyy6000), Right(vyy500), ceg, app(app(ty_Either, dce), dcf)) → new_ltEs4(vyy6000, vyy500, dce, dcf)
new_ltEs20(vyy600, vyy50, ty_Integer) → new_ltEs12(vyy600, vyy50)
new_compare13(vyy6000, vyy500, False, bfb, bfc) → GT
new_ltEs18(Just(vyy6000), Just(vyy500), app(ty_Ratio, bag)) → new_ltEs5(vyy6000, vyy500, bag)
new_ltEs11(False, True) → True
new_esEs20(vyy440, vyy450, app(app(ty_@2, bce), bcf)) → new_esEs5(vyy440, vyy450, bce, bcf)
new_compare19(vyy6000, vyy500, True) → LT
new_lt20(vyy6000, vyy500, app(app(ty_@2, bfb), bfc)) → new_lt7(vyy6000, vyy500, bfb, bfc)
new_ltEs4(Left(vyy6000), Right(vyy500), ceg, ceh) → True
new_esEs21(vyy441, vyy451, ty_Bool) → new_esEs14(vyy441, vyy451)
new_lt4(vyy6000, vyy500, app(app(ty_Either, fb), fc)) → new_lt19(vyy6000, vyy500, fb, fc)
new_esEs21(vyy441, vyy451, ty_Char) → new_esEs13(vyy441, vyy451)
new_compare24(vyy6000, vyy500, False, beg) → new_compare11(vyy6000, vyy500, new_ltEs18(vyy6000, vyy500, beg), beg)
new_ltEs15(vyy600, vyy50, bhd) → new_not(new_compare3(vyy600, vyy50, bhd))
new_esEs7(Just(vyy440), Just(vyy450), ty_Int) → new_esEs17(vyy440, vyy450)
new_esEs21(vyy441, vyy451, ty_Double) → new_esEs19(vyy441, vyy451)
new_lt14(vyy6000, vyy500, bef) → new_esEs22(new_compare6(vyy6000, vyy500, bef))
new_esEs20(vyy440, vyy450, ty_Ordering) → new_esEs18(vyy440, vyy450)
new_esEs20(vyy440, vyy450, ty_@0) → new_esEs11(vyy440, vyy450)
new_esEs23(vyy440, vyy450, ty_Double) → new_esEs19(vyy440, vyy450)
new_compare34(vyy6000, vyy500, ty_@0) → new_compare7(vyy6000, vyy500)
new_esEs20(vyy440, vyy450, app(app(app(ty_@3, bca), bcb), bcc)) → new_esEs6(vyy440, vyy450, bca, bcb, bcc)
new_lt4(vyy6000, vyy500, app(app(ty_@2, eb), ec)) → new_lt7(vyy6000, vyy500, eb, ec)
new_esEs8(Left(vyy440), Left(vyy450), ty_Char, cfc) → new_esEs13(vyy440, vyy450)
new_ltEs18(Just(vyy6000), Just(vyy500), app(app(app(ty_@3, bad), bae), baf)) → new_ltEs6(vyy6000, vyy500, bad, bae, baf)
new_primEqNat0(Zero, Zero) → True
new_esEs27(vyy44, vyy45, ty_Ordering) → new_esEs18(vyy44, vyy45)
new_esEs23(vyy440, vyy450, ty_@0) → new_esEs11(vyy440, vyy450)
new_esEs8(Right(vyy440), Right(vyy450), cgf, ty_Double) → new_esEs19(vyy440, vyy450)
new_lt15(vyy6000, vyy500, ced) → new_esEs22(new_compare3(vyy6000, vyy500, ced))
new_ltEs4(Right(vyy6000), Right(vyy500), ceg, ty_Ordering) → new_ltEs14(vyy6000, vyy500)
new_compare11(vyy6000, vyy500, True, beg) → LT
new_esEs8(Right(vyy440), Right(vyy450), cgf, ty_@0) → new_esEs11(vyy440, vyy450)
new_ltEs4(Right(vyy6000), Right(vyy500), ceg, app(app(ty_@2, dbe), dbf)) → new_ltEs9(vyy6000, vyy500, dbe, dbf)
new_ltEs20(vyy600, vyy50, ty_Float) → new_ltEs8(vyy600, vyy50)
new_esEs27(vyy44, vyy45, ty_Char) → new_esEs13(vyy44, vyy45)
new_ltEs19(vyy6001, vyy501, ty_Float) → new_ltEs8(vyy6001, vyy501)
new_compare17(Double(vyy6000, vyy6001), Double(vyy500, vyy501)) → new_compare16(new_sr0(vyy6000, vyy500), new_sr0(vyy6001, vyy501))
new_ltEs18(Just(vyy6000), Just(vyy500), ty_Int) → new_ltEs16(vyy6000, vyy500)
new_esEs7(Just(vyy440), Just(vyy450), app(app(ty_FiniteMap, db), dc)) → new_esEs16(vyy440, vyy450, db, dc)
new_esEs13(Char(vyy440), Char(vyy450)) → new_primEqInt(vyy440, vyy450)
new_ltEs20(vyy600, vyy50, app(app(ty_@2, cee), cef)) → new_ltEs9(vyy600, vyy50, cee, cef)
new_ltEs18(Just(vyy6000), Just(vyy500), ty_Double) → new_ltEs10(vyy6000, vyy500)
new_ltEs14(EQ, LT) → False
new_primCmpNat1(Zero, Zero) → EQ
new_esEs25(vyy441, vyy451, ty_Int) → new_esEs17(vyy441, vyy451)
new_primCmpInt(Neg(Zero), Neg(Succ(vyy5000))) → new_primCmpNat0(vyy5000, Zero)
new_esEs8(Left(vyy440), Left(vyy450), ty_Double, cfc) → new_esEs19(vyy440, vyy450)
new_esEs8(Right(vyy440), Right(vyy450), cgf, ty_Char) → new_esEs13(vyy440, vyy450)
new_primPlusNat0(Succ(vyy750), vyy50000) → Succ(Succ(new_primPlusNat1(vyy750, vyy50000)))
new_esEs21(vyy441, vyy451, ty_Float) → new_esEs9(vyy441, vyy451)
new_esEs7(Just(vyy440), Just(vyy450), app(ty_[], ce)) → new_esEs10(vyy440, vyy450, ce)
new_esEs23(vyy440, vyy450, ty_Float) → new_esEs9(vyy440, vyy450)
new_esEs26(vyy442, vyy452, app(app(app(ty_@3, cdc), cdd), cde)) → new_esEs6(vyy442, vyy452, cdc, cdd, cde)
new_ltEs7(vyy6002, vyy502, ty_Ordering) → new_ltEs14(vyy6002, vyy502)
new_ltEs19(vyy6001, vyy501, ty_Double) → new_ltEs10(vyy6001, vyy501)
new_esEs18(EQ, GT) → False
new_esEs18(GT, EQ) → False
new_lt20(vyy6000, vyy500, ty_Bool) → new_lt9(vyy6000, vyy500)
new_primCmpNat1(Succ(vyy600000), Zero) → GT
new_ltEs20(vyy600, vyy50, ty_Int) → new_ltEs16(vyy600, vyy50)
new_primEqInt(Neg(Succ(vyy4400)), Neg(Succ(vyy4500))) → new_primEqNat0(vyy4400, vyy4500)
new_compare25(vyy6000, vyy500, True) → EQ
new_ltEs4(Right(vyy6000), Right(vyy500), ceg, ty_Float) → new_ltEs8(vyy6000, vyy500)
new_compare13(vyy6000, vyy500, True, bfb, bfc) → LT
new_esEs25(vyy441, vyy451, app(app(ty_FiniteMap, ccf), ccg)) → new_esEs16(vyy441, vyy451, ccf, ccg)
new_esEs24(vyy440, vyy450, ty_Bool) → new_esEs14(vyy440, vyy450)
new_primPlusNat1(Succ(vyy7500), Zero) → Succ(vyy7500)
new_primPlusNat1(Zero, Succ(vyy500000)) → Succ(vyy500000)
new_ltEs4(Left(vyy6000), Left(vyy500), ty_Bool, ceh) → new_ltEs11(vyy6000, vyy500)
new_esEs8(Right(vyy440), Right(vyy450), cgf, app(app(ty_Either, cgg), cgh)) → new_esEs8(vyy440, vyy450, cgg, cgh)
new_esEs8(Right(vyy440), Left(vyy450), cgf, cfc) → False
new_esEs8(Left(vyy440), Right(vyy450), cgf, cfc) → False
new_lt4(vyy6000, vyy500, ty_Char) → new_lt12(vyy6000, vyy500)
new_compare3([], :(vyy500, vyy501), bhd) → LT
new_esEs20(vyy440, vyy450, app(app(ty_Either, bbf), bbg)) → new_esEs8(vyy440, vyy450, bbf, bbg)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_lt20(vyy6000, vyy500, app(ty_Maybe, beg)) → new_lt18(vyy6000, vyy500, beg)
new_ltEs20(vyy600, vyy50, ty_Bool) → new_ltEs11(vyy600, vyy50)
new_esEs24(vyy440, vyy450, app(app(app(ty_@3, cac), cad), cae)) → new_esEs6(vyy440, vyy450, cac, cad, cae)
new_compare3(:(vyy6000, vyy6001), [], bhd) → GT
new_lt5(vyy6001, vyy501, ty_Integer) → new_lt11(vyy6001, vyy501)
new_lt5(vyy6001, vyy501, app(app(ty_@2, fd), ff)) → new_lt7(vyy6001, vyy501, fd, ff)
new_compare18(vyy6000, vyy500, False) → GT
new_lt5(vyy6001, vyy501, ty_Int) → new_lt16(vyy6001, vyy501)
new_esEs29(vyy441, vyy451, ty_Int) → new_esEs17(vyy441, vyy451)
new_ltEs4(Left(vyy6000), Left(vyy500), app(app(ty_Either, dbc), dbd), ceh) → new_ltEs4(vyy6000, vyy500, dbc, dbd)
new_primEqInt(Neg(Succ(vyy4400)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(vyy4500))) → False
new_lt20(vyy6000, vyy500, ty_Integer) → new_lt11(vyy6000, vyy500)
new_esEs26(vyy442, vyy452, app(app(ty_FiniteMap, ceb), cec)) → new_esEs16(vyy442, vyy452, ceb, cec)
new_ltEs7(vyy6002, vyy502, app(ty_Ratio, hd)) → new_ltEs5(vyy6002, vyy502, hd)
new_lt20(vyy6000, vyy500, ty_Ordering) → new_lt13(vyy6000, vyy500)
new_esEs8(Left(vyy440), Left(vyy450), app(ty_[], cfh), cfc) → new_esEs10(vyy440, vyy450, cfh)
new_esEs27(vyy44, vyy45, app(app(ty_Either, cgf), cfc)) → new_esEs8(vyy44, vyy45, cgf, cfc)
new_esEs12(:%(vyy440, vyy441), :%(vyy450, vyy451), deb) → new_asAs(new_esEs28(vyy440, vyy450, deb), new_esEs29(vyy441, vyy451, deb))
new_compare34(vyy6000, vyy500, ty_Char) → new_compare29(vyy6000, vyy500)
new_foldFM0(vyy450, vyy451, vyy74, Branch(vyy4530, vyy4531, vyy4532, vyy4533, vyy4534), beh, bfa) → new_foldFM0(vyy4530, vyy4531, new_foldFM0(vyy450, vyy451, vyy74, vyy4534, beh, bfa), vyy4533, beh, bfa)
new_ltEs20(vyy600, vyy50, app(ty_Ratio, df)) → new_ltEs5(vyy600, vyy50, df)
new_compare34(vyy6000, vyy500, ty_Double) → new_compare17(vyy6000, vyy500)
new_esEs26(vyy442, vyy452, ty_@0) → new_esEs11(vyy442, vyy452)
new_compare25(vyy6000, vyy500, False) → new_compare19(vyy6000, vyy500, new_ltEs11(vyy6000, vyy500))
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_esEs24(vyy440, vyy450, ty_Ordering) → new_esEs18(vyy440, vyy450)
new_esEs10(:(vyy440, vyy441), [], bfg) → False
new_esEs10([], :(vyy450, vyy451), bfg) → False
new_lt20(vyy6000, vyy500, ty_Double) → new_lt8(vyy6000, vyy500)
new_sizeFM(EmptyFM, beh, bfa) → Pos(Zero)
new_compare11(vyy6000, vyy500, False, beg) → GT
new_compare6(:%(vyy6000, vyy6001), :%(vyy500, vyy501), ty_Integer) → new_compare12(new_sr(vyy6000, vyy501), new_sr(vyy500, vyy6001))
new_primEqInt(Pos(Succ(vyy4400)), Pos(Succ(vyy4500))) → new_primEqNat0(vyy4400, vyy4500)
new_compare10(vyy6000, vyy500, False, dd, de) → GT
new_esEs24(vyy440, vyy450, app(app(ty_FiniteMap, cbb), cbc)) → new_esEs16(vyy440, vyy450, cbb, cbc)
new_esEs24(vyy440, vyy450, app(app(ty_Either, bhh), caa)) → new_esEs8(vyy440, vyy450, bhh, caa)
new_esEs8(Left(vyy440), Left(vyy450), app(ty_Maybe, cfd), cfc) → new_esEs7(vyy440, vyy450, cfd)
new_esEs7(Just(vyy440), Just(vyy450), ty_Float) → new_esEs9(vyy440, vyy450)
new_esEs14(True, False) → False
new_esEs14(False, True) → False
new_ltEs4(Right(vyy6000), Right(vyy500), ceg, app(ty_[], dcc)) → new_ltEs15(vyy6000, vyy500, dcc)
new_esEs26(vyy442, vyy452, ty_Integer) → new_esEs15(vyy442, vyy452)
new_ltEs11(True, False) → False
new_ltEs18(Just(vyy6000), Just(vyy500), app(app(ty_Either, bbb), bbc)) → new_ltEs4(vyy6000, vyy500, bbb, bbc)
new_esEs8(Left(vyy440), Left(vyy450), app(app(app(ty_@3, cfe), cff), cfg), cfc) → new_esEs6(vyy440, vyy450, cfe, cff, cfg)
new_esEs10([], [], bfg) → True
new_esEs24(vyy440, vyy450, ty_Int) → new_esEs17(vyy440, vyy450)
new_primEqNat0(Succ(vyy44000), Succ(vyy45000)) → new_primEqNat0(vyy44000, vyy45000)
new_compare7(@0, @0) → EQ
new_esEs21(vyy441, vyy451, app(ty_Ratio, bec)) → new_esEs12(vyy441, vyy451, bec)
new_compare34(vyy6000, vyy500, ty_Float) → new_compare30(vyy6000, vyy500)
new_ltEs18(Just(vyy6000), Just(vyy500), ty_Ordering) → new_ltEs14(vyy6000, vyy500)
new_primCompAux00(vyy60, LT) → LT
new_ltEs4(Left(vyy6000), Left(vyy500), ty_Char, ceh) → new_ltEs13(vyy6000, vyy500)
new_esEs24(vyy440, vyy450, app(ty_Ratio, cba)) → new_esEs12(vyy440, vyy450, cba)
new_esEs24(vyy440, vyy450, ty_Float) → new_esEs9(vyy440, vyy450)
new_esEs23(vyy440, vyy450, app(app(ty_FiniteMap, bhb), bhc)) → new_esEs16(vyy440, vyy450, bhb, bhc)
new_ltEs20(vyy600, vyy50, ty_Ordering) → new_ltEs14(vyy600, vyy50)
new_esEs5(@2(vyy440, vyy441), @2(vyy450, vyy451), bbd, bbe) → new_asAs(new_esEs20(vyy440, vyy450, bbd), new_esEs21(vyy441, vyy451, bbe))
new_esEs7(Nothing, Nothing, bf) → True
new_esEs8(Right(vyy440), Right(vyy450), cgf, ty_Float) → new_esEs9(vyy440, vyy450)
new_primEqInt(Pos(Succ(vyy4400)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(vyy4500))) → False
new_ltEs12(vyy600, vyy50) → new_not(new_compare12(vyy600, vyy50))
new_esEs23(vyy440, vyy450, ty_Char) → new_esEs13(vyy440, vyy450)
new_compare34(vyy6000, vyy500, ty_Int) → new_compare16(vyy6000, vyy500)
new_esEs8(Right(vyy440), Right(vyy450), cgf, ty_Bool) → new_esEs14(vyy440, vyy450)
new_lt10(vyy6000, vyy500, bfd, bfe, bff) → new_esEs22(new_compare33(vyy6000, vyy500, bfd, bfe, bff))
new_ltEs4(Right(vyy6000), Right(vyy500), ceg, ty_@0) → new_ltEs17(vyy6000, vyy500)
new_ltEs18(Nothing, Nothing, baa) → True
new_compare18(vyy6000, vyy500, True) → LT
new_esEs23(vyy440, vyy450, app(app(ty_@2, bgg), bgh)) → new_esEs5(vyy440, vyy450, bgg, bgh)
new_esEs6(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), bhe, bhf, bhg) → new_asAs(new_esEs24(vyy440, vyy450, bhe), new_asAs(new_esEs25(vyy441, vyy451, bhf), new_esEs26(vyy442, vyy452, bhg)))
new_primCmpInt(Neg(Zero), Pos(Succ(vyy5000))) → LT
new_esEs8(Right(vyy440), Right(vyy450), cgf, ty_Ordering) → new_esEs18(vyy440, vyy450)
new_compare19(vyy6000, vyy500, False) → GT
new_ltEs7(vyy6002, vyy502, ty_Int) → new_ltEs16(vyy6002, vyy502)
new_lt4(vyy6000, vyy500, ty_Float) → new_lt6(vyy6000, vyy500)
new_compare14(vyy6000, vyy500, False, bfd, bfe, bff) → GT
new_compare28(vyy6000, vyy500, False, bfb, bfc) → new_compare13(vyy6000, vyy500, new_ltEs9(vyy6000, vyy500, bfb, bfc), bfb, bfc)
new_ltEs7(vyy6002, vyy502, ty_Bool) → new_ltEs11(vyy6002, vyy502)
new_compare26(vyy6000, vyy500, False, bfd, bfe, bff) → new_compare14(vyy6000, vyy500, new_ltEs6(vyy6000, vyy500, bfd, bfe, bff), bfd, bfe, bff)
new_primPlusNat1(Succ(vyy7500), Succ(vyy500000)) → Succ(Succ(new_primPlusNat1(vyy7500, vyy500000)))
new_ltEs20(vyy600, vyy50, ty_Char) → new_ltEs13(vyy600, vyy50)
new_compare28(vyy6000, vyy500, True, bfb, bfc) → EQ
new_esEs7(Just(vyy440), Just(vyy450), ty_Integer) → new_esEs15(vyy440, vyy450)
new_primEqInt(Pos(Succ(vyy4400)), Neg(vyy450)) → False
new_primEqInt(Neg(Succ(vyy4400)), Pos(vyy450)) → False
new_esEs7(Nothing, Just(vyy450), bf) → False
new_esEs7(Just(vyy440), Nothing, bf) → False
new_esEs20(vyy440, vyy450, ty_Char) → new_esEs13(vyy440, vyy450)
new_foldFM2(EmptyFM, beh, bfa) → []
new_compare34(vyy6000, vyy500, ty_Ordering) → new_compare15(vyy6000, vyy500)
new_compare34(vyy6000, vyy500, ty_Bool) → new_compare9(vyy6000, vyy500)
new_lt17(vyy6000, vyy500) → new_esEs22(new_compare7(vyy6000, vyy500))
new_ltEs20(vyy600, vyy50, ty_Double) → new_ltEs10(vyy600, vyy50)
new_compare31(vyy6000, vyy500, bfb, bfc) → new_compare28(vyy6000, vyy500, new_esEs5(vyy6000, vyy500, bfb, bfc), bfb, bfc)
new_esEs7(Just(vyy440), Just(vyy450), app(app(ty_Either, bg), bh)) → new_esEs8(vyy440, vyy450, bg, bh)
new_lt5(vyy6001, vyy501, ty_Bool) → new_lt9(vyy6001, vyy501)
new_esEs23(vyy440, vyy450, app(ty_Ratio, bha)) → new_esEs12(vyy440, vyy450, bha)
new_esEs26(vyy442, vyy452, ty_Int) → new_esEs17(vyy442, vyy452)
new_primEqInt(Pos(Zero), Neg(Succ(vyy4500))) → False
new_primEqInt(Neg(Zero), Pos(Succ(vyy4500))) → False
new_ltEs19(vyy6001, vyy501, app(app(ty_@2, dcg), dch)) → new_ltEs9(vyy6001, vyy501, dcg, dch)
new_primCmpNat2(Succ(vyy5000), vyy60000) → new_primCmpNat1(vyy5000, vyy60000)
new_esEs21(vyy441, vyy451, ty_Integer) → new_esEs15(vyy441, vyy451)
new_primCompAux00(vyy60, EQ) → vyy60
new_pePe(False, vyy44, vyy45, vyy46, dea) → new_asAs(new_esEs27(vyy44, vyy45, dea), vyy46)
new_esEs8(Left(vyy440), Left(vyy450), app(ty_Ratio, cgc), cfc) → new_esEs12(vyy440, vyy450, cgc)
new_esEs26(vyy442, vyy452, ty_Ordering) → new_esEs18(vyy442, vyy452)
new_esEs8(Left(vyy440), Left(vyy450), ty_@0, cfc) → new_esEs11(vyy440, vyy450)
new_esEs21(vyy441, vyy451, ty_Ordering) → new_esEs18(vyy441, vyy451)
new_ltEs4(Left(vyy6000), Left(vyy500), app(ty_[], dba), ceh) → new_ltEs15(vyy6000, vyy500, dba)
new_esEs8(Left(vyy440), Left(vyy450), ty_Int, cfc) → new_esEs17(vyy440, vyy450)
new_esEs26(vyy442, vyy452, app(app(ty_@2, cdg), cdh)) → new_esEs5(vyy442, vyy452, cdg, cdh)
new_esEs20(vyy440, vyy450, app(app(ty_FiniteMap, bch), bda)) → new_esEs16(vyy440, vyy450, bch, bda)
new_esEs24(vyy440, vyy450, ty_Char) → new_esEs13(vyy440, vyy450)
new_esEs21(vyy441, vyy451, app(app(ty_@2, bea), beb)) → new_esEs5(vyy441, vyy451, bea, beb)
new_ltEs20(vyy600, vyy50, app(app(app(ty_@3, dg), dh), ea)) → new_ltEs6(vyy600, vyy50, dg, dh, ea)
new_ltEs4(Right(vyy6000), Left(vyy500), ceg, ceh) → False
new_ltEs5(vyy600, vyy50, df) → new_not(new_compare6(vyy600, vyy50, df))
new_compare24(vyy6000, vyy500, True, beg) → EQ
new_ltEs18(Just(vyy6000), Nothing, baa) → False
new_primPlusNat0(Zero, vyy50000) → Succ(vyy50000)
new_ltEs17(vyy600, vyy50) → new_not(new_compare7(vyy600, vyy50))
new_compare15(vyy6000, vyy500) → new_compare27(vyy6000, vyy500, new_esEs18(vyy6000, vyy500))
new_ltEs18(Just(vyy6000), Just(vyy500), app(ty_[], bah)) → new_ltEs15(vyy6000, vyy500, bah)
new_esEs25(vyy441, vyy451, ty_Integer) → new_esEs15(vyy441, vyy451)
new_ltEs14(LT, LT) → True
new_esEs26(vyy442, vyy452, ty_Bool) → new_esEs14(vyy442, vyy452)
new_ltEs7(vyy6002, vyy502, app(app(app(ty_@3, ha), hb), hc)) → new_ltEs6(vyy6002, vyy502, ha, hb, hc)
new_ltEs4(Left(vyy6000), Left(vyy500), ty_Integer, ceh) → new_ltEs12(vyy6000, vyy500)
new_lt20(vyy6000, vyy500, app(ty_Ratio, bef)) → new_lt14(vyy6000, vyy500, bef)
new_not0 → True
new_ltEs19(vyy6001, vyy501, app(app(app(ty_@3, dda), ddb), ddc)) → new_ltEs6(vyy6001, vyy501, dda, ddb, ddc)
new_esEs23(vyy440, vyy450, app(ty_[], bgf)) → new_esEs10(vyy440, vyy450, bgf)
new_lt12(vyy6000, vyy500) → new_esEs22(new_compare29(vyy6000, vyy500))
new_ltEs11(False, False) → True
new_esEs19(Double(vyy440, vyy441), Double(vyy450, vyy451)) → new_esEs17(new_sr0(vyy440, vyy450), new_sr0(vyy441, vyy451))
new_compare12(Integer(vyy6000), Integer(vyy500)) → new_primCmpInt(vyy6000, vyy500)
new_ltEs7(vyy6002, vyy502, ty_Float) → new_ltEs8(vyy6002, vyy502)
new_esEs18(GT, GT) → True
new_ltEs19(vyy6001, vyy501, app(ty_[], dde)) → new_ltEs15(vyy6001, vyy501, dde)
new_ltEs20(vyy600, vyy50, ty_@0) → new_ltEs17(vyy600, vyy50)
new_lt4(vyy6000, vyy500, ty_Integer) → new_lt11(vyy6000, vyy500)
new_ltEs19(vyy6001, vyy501, ty_Integer) → new_ltEs12(vyy6001, vyy501)
new_primCmpInt(Pos(Succ(vyy60000)), Neg(vyy500)) → GT
new_esEs21(vyy441, vyy451, app(ty_Maybe, bdd)) → new_esEs7(vyy441, vyy451, bdd)
new_primMulInt(Pos(vyy60000), Pos(vyy5000)) → Pos(new_primMulNat0(vyy60000, vyy5000))
new_ltEs4(Left(vyy6000), Left(vyy500), app(ty_Ratio, dah), ceh) → new_ltEs5(vyy6000, vyy500, dah)
new_esEs8(Right(vyy440), Right(vyy450), cgf, app(app(app(ty_@3, chb), chc), chd)) → new_esEs6(vyy440, vyy450, chb, chc, chd)
new_primMulInt(Neg(vyy60000), Neg(vyy5000)) → Pos(new_primMulNat0(vyy60000, vyy5000))
new_esEs20(vyy440, vyy450, ty_Integer) → new_esEs15(vyy440, vyy450)
new_primEqNat0(Zero, Succ(vyy45000)) → False
new_primEqNat0(Succ(vyy44000), Zero) → False
new_esEs7(Just(vyy440), Just(vyy450), ty_Char) → new_esEs13(vyy440, vyy450)
new_lt5(vyy6001, vyy501, app(ty_[], gc)) → new_lt15(vyy6001, vyy501, gc)
new_esEs8(Right(vyy440), Right(vyy450), cgf, app(ty_Ratio, chh)) → new_esEs12(vyy440, vyy450, chh)
new_esEs17(vyy44, vyy45) → new_primEqInt(vyy44, vyy45)
new_esEs27(vyy44, vyy45, ty_@0) → new_esEs11(vyy44, vyy45)
new_ltEs7(vyy6002, vyy502, ty_Integer) → new_ltEs12(vyy6002, vyy502)
new_esEs20(vyy440, vyy450, ty_Bool) → new_esEs14(vyy440, vyy450)
new_lt20(vyy6000, vyy500, ty_@0) → new_lt17(vyy6000, vyy500)
new_esEs20(vyy440, vyy450, app(ty_[], bcd)) → new_esEs10(vyy440, vyy450, bcd)
new_compare23(vyy6000, vyy500, False, dd, de) → new_compare10(vyy6000, vyy500, new_ltEs4(vyy6000, vyy500, dd, de), dd, de)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_primCmpInt(Pos(Succ(vyy60000)), Pos(vyy500)) → new_primCmpNat0(vyy60000, vyy500)
new_esEs27(vyy44, vyy45, app(app(app(ty_@3, bhe), bhf), bhg)) → new_esEs6(vyy44, vyy45, bhe, bhf, bhg)
new_ltEs7(vyy6002, vyy502, app(app(ty_Either, hg), hh)) → new_ltEs4(vyy6002, vyy502, hg, hh)
new_esEs11(@0, @0) → True
new_esEs25(vyy441, vyy451, ty_@0) → new_esEs11(vyy441, vyy451)
new_esEs27(vyy44, vyy45, app(app(ty_@2, bbd), bbe)) → new_esEs5(vyy44, vyy45, bbd, bbe)
new_primCmpNat0(vyy60000, Zero) → GT
new_ltEs19(vyy6001, vyy501, ty_Char) → new_ltEs13(vyy6001, vyy501)
new_esEs27(vyy44, vyy45, ty_Int) → new_esEs17(vyy44, vyy45)
new_sizeFM(Branch(vyy450, vyy451, vyy452, vyy453, vyy454), beh, bfa) → vyy452
new_compare30(Float(vyy6000, vyy6001), Float(vyy500, vyy501)) → new_compare16(new_sr0(vyy6000, vyy500), new_sr0(vyy6001, vyy501))
new_ltEs4(Right(vyy6000), Right(vyy500), ceg, ty_Double) → new_ltEs10(vyy6000, vyy500)
new_ltEs19(vyy6001, vyy501, ty_@0) → new_ltEs17(vyy6001, vyy501)
new_esEs23(vyy440, vyy450, ty_Int) → new_esEs17(vyy440, vyy450)
new_pePe(True, vyy44, vyy45, vyy46, dea) → True
new_esEs24(vyy440, vyy450, ty_Double) → new_esEs19(vyy440, vyy450)
new_foldFM2(Branch(vyy450, vyy451, vyy452, vyy453, vyy454), beh, bfa) → new_foldFM0(vyy450, vyy451, new_foldFM2(vyy454, beh, bfa), vyy453, beh, bfa)
new_compare23(vyy6000, vyy500, True, dd, de) → EQ
new_lt5(vyy6001, vyy501, ty_Float) → new_lt6(vyy6001, vyy501)
new_primCmpInt(Pos(Zero), Neg(Succ(vyy5000))) → GT
new_compare8(vyy6000, vyy500, beg) → new_compare24(vyy6000, vyy500, new_esEs7(vyy6000, vyy500, beg), beg)
new_sr0(vyy6000, vyy500) → new_primMulInt(vyy6000, vyy500)
new_esEs10(:(vyy440, vyy441), :(vyy450, vyy451), bfg) → new_asAs(new_esEs23(vyy440, vyy450, bfg), new_esEs10(vyy441, vyy451, bfg))
new_esEs27(vyy44, vyy45, app(ty_Ratio, deb)) → new_esEs12(vyy44, vyy45, deb)
new_ltEs19(vyy6001, vyy501, ty_Ordering) → new_ltEs14(vyy6001, vyy501)
new_esEs8(Left(vyy440), Left(vyy450), app(app(ty_Either, cfa), cfb), cfc) → new_esEs8(vyy440, vyy450, cfa, cfb)
new_esEs25(vyy441, vyy451, app(ty_Maybe, cbf)) → new_esEs7(vyy441, vyy451, cbf)
new_esEs7(Just(vyy440), Just(vyy450), app(app(app(ty_@3, cb), cc), cd)) → new_esEs6(vyy440, vyy450, cb, cc, cd)
new_esEs24(vyy440, vyy450, app(ty_[], caf)) → new_esEs10(vyy440, vyy450, caf)
new_lt4(vyy6000, vyy500, ty_Ordering) → new_lt13(vyy6000, vyy500)
new_lt6(vyy6000, vyy500) → new_esEs22(new_compare30(vyy6000, vyy500))
new_lt9(vyy6000, vyy500) → new_esEs22(new_compare9(vyy6000, vyy500))
new_lt20(vyy6000, vyy500, app(ty_[], ced)) → new_lt15(vyy6000, vyy500, ced)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_compare29(Char(vyy6000), Char(vyy500)) → new_primCmpInt(vyy6000, vyy500)
new_esEs7(Just(vyy440), Just(vyy450), ty_@0) → new_esEs11(vyy440, vyy450)
new_ltEs18(Just(vyy6000), Just(vyy500), app(app(ty_@2, bab), bac)) → new_ltEs9(vyy6000, vyy500, bab, bac)
new_ltEs10(vyy600, vyy50) → new_not(new_compare17(vyy600, vyy50))
new_compare34(vyy6000, vyy500, app(ty_Maybe, dfb)) → new_compare8(vyy6000, vyy500, dfb)
new_lt18(vyy6000, vyy500, beg) → new_esEs22(new_compare8(vyy6000, vyy500, beg))
new_esEs28(vyy440, vyy450, ty_Int) → new_esEs17(vyy440, vyy450)
new_asAs(False, vyy55) → False
new_ltEs11(True, True) → True
new_compare3([], [], bhd) → EQ
new_primMulInt(Pos(vyy60000), Neg(vyy5000)) → Neg(new_primMulNat0(vyy60000, vyy5000))
new_primMulInt(Neg(vyy60000), Pos(vyy5000)) → Neg(new_primMulNat0(vyy60000, vyy5000))
new_primCmpInt(Neg(Succ(vyy60000)), Neg(vyy500)) → new_primCmpNat2(vyy500, vyy60000)
new_compare16(vyy600, vyy50) → new_primCmpInt(vyy600, vyy50)
new_primMulNat0(Succ(vyy600000), Zero) → Zero
new_primMulNat0(Zero, Succ(vyy50000)) → Zero
new_esEs23(vyy440, vyy450, app(app(app(ty_@3, bgc), bgd), bge)) → new_esEs6(vyy440, vyy450, bgc, bgd, bge)
new_lt4(vyy6000, vyy500, app(app(app(ty_@3, ed), ee), ef)) → new_lt10(vyy6000, vyy500, ed, ee, ef)
new_ltEs16(vyy600, vyy50) → new_not(new_compare16(vyy600, vyy50))
new_ltEs4(Right(vyy6000), Right(vyy500), ceg, ty_Int) → new_ltEs16(vyy6000, vyy500)
new_esEs8(Right(vyy440), Right(vyy450), cgf, ty_Int) → new_esEs17(vyy440, vyy450)
new_esEs26(vyy442, vyy452, app(ty_Maybe, cdb)) → new_esEs7(vyy442, vyy452, cdb)
new_ltEs18(Nothing, Just(vyy500), baa) → True
new_ltEs14(GT, LT) → False
new_not(EQ) → new_not0
new_esEs28(vyy440, vyy450, ty_Integer) → new_esEs15(vyy440, vyy450)
new_primCmpInt(Pos(Zero), Pos(Succ(vyy5000))) → new_primCmpNat2(Zero, vyy5000)
new_esEs25(vyy441, vyy451, app(app(app(ty_@3, cbg), cbh), cca)) → new_esEs6(vyy441, vyy451, cbg, cbh, cca)
new_lt8(vyy6000, vyy500) → new_esEs22(new_compare17(vyy6000, vyy500))
new_esEs23(vyy440, vyy450, ty_Integer) → new_esEs15(vyy440, vyy450)
new_esEs27(vyy44, vyy45, app(ty_[], bfg)) → new_esEs10(vyy44, vyy45, bfg)
new_compare27(vyy6000, vyy500, True) → EQ
new_esEs14(True, True) → True
new_ltEs19(vyy6001, vyy501, ty_Int) → new_ltEs16(vyy6001, vyy501)
new_ltEs4(Left(vyy6000), Left(vyy500), ty_Ordering, ceh) → new_ltEs14(vyy6000, vyy500)
new_ltEs18(Just(vyy6000), Just(vyy500), ty_Integer) → new_ltEs12(vyy6000, vyy500)
new_ltEs6(@3(vyy6000, vyy6001, vyy6002), @3(vyy500, vyy501, vyy502), dg, dh, ea) → new_pePe(new_lt4(vyy6000, vyy500, dg), vyy6000, vyy500, new_pePe(new_lt5(vyy6001, vyy501, dh), vyy6001, vyy501, new_ltEs7(vyy6002, vyy502, ea), dh), dg)
new_esEs27(vyy44, vyy45, ty_Bool) → new_esEs14(vyy44, vyy45)
new_esEs26(vyy442, vyy452, ty_Double) → new_esEs19(vyy442, vyy452)
new_lt19(vyy6000, vyy500, dd, de) → new_esEs22(new_compare32(vyy6000, vyy500, dd, de))
new_esEs26(vyy442, vyy452, app(ty_Ratio, cea)) → new_esEs12(vyy442, vyy452, cea)
new_ltEs18(Just(vyy6000), Just(vyy500), ty_Bool) → new_ltEs11(vyy6000, vyy500)
new_ltEs7(vyy6002, vyy502, ty_@0) → new_ltEs17(vyy6002, vyy502)
new_lt5(vyy6001, vyy501, app(app(ty_Either, ge), gf)) → new_lt19(vyy6001, vyy501, ge, gf)
new_ltEs20(vyy600, vyy50, app(ty_[], bhd)) → new_ltEs15(vyy600, vyy50, bhd)
new_ltEs4(Right(vyy6000), Right(vyy500), ceg, ty_Char) → new_ltEs13(vyy6000, vyy500)
new_esEs20(vyy440, vyy450, ty_Int) → new_esEs17(vyy440, vyy450)
new_esEs25(vyy441, vyy451, app(app(ty_@2, ccc), ccd)) → new_esEs5(vyy441, vyy451, ccc, ccd)
new_ltEs14(LT, GT) → True
new_esEs27(vyy44, vyy45, ty_Float) → new_esEs9(vyy44, vyy45)
new_not(LT) → new_not0
new_esEs8(Right(vyy440), Right(vyy450), cgf, ty_Integer) → new_esEs15(vyy440, vyy450)
new_lt5(vyy6001, vyy501, app(ty_Maybe, gd)) → new_lt18(vyy6001, vyy501, gd)
new_ltEs14(LT, EQ) → True
new_compare9(vyy6000, vyy500) → new_compare25(vyy6000, vyy500, new_esEs14(vyy6000, vyy500))
new_lt16(vyy6000, vyy500) → new_esEs22(new_compare16(vyy6000, vyy500))
new_lt13(vyy6000, vyy500) → new_esEs22(new_compare15(vyy6000, vyy500))
new_ltEs4(Right(vyy6000), Right(vyy500), ceg, ty_Bool) → new_ltEs11(vyy6000, vyy500)
new_lt4(vyy6000, vyy500, ty_Bool) → new_lt9(vyy6000, vyy500)
new_esEs14(False, False) → True
new_esEs8(Left(vyy440), Left(vyy450), ty_Float, cfc) → new_esEs9(vyy440, vyy450)
new_esEs7(Just(vyy440), Just(vyy450), app(app(ty_@2, cf), cg)) → new_esEs5(vyy440, vyy450, cf, cg)
new_lt20(vyy6000, vyy500, ty_Char) → new_lt12(vyy6000, vyy500)
new_ltEs7(vyy6002, vyy502, ty_Char) → new_ltEs13(vyy6002, vyy502)
new_esEs22(GT) → False
new_lt5(vyy6001, vyy501, ty_Double) → new_lt8(vyy6001, vyy501)
new_esEs25(vyy441, vyy451, ty_Double) → new_esEs19(vyy441, vyy451)
new_compare26(vyy6000, vyy500, True, bfd, bfe, bff) → EQ
new_esEs21(vyy441, vyy451, ty_@0) → new_esEs11(vyy441, vyy451)
new_ltEs4(Left(vyy6000), Left(vyy500), ty_Double, ceh) → new_ltEs10(vyy6000, vyy500)
new_primPlusNat1(Zero, Zero) → Zero
new_esEs21(vyy441, vyy451, app(app(app(ty_@3, bde), bdf), bdg)) → new_esEs6(vyy441, vyy451, bde, bdf, bdg)
new_asAs(True, vyy55) → vyy55
new_ltEs14(EQ, EQ) → True
new_primMulNat0(Succ(vyy600000), Succ(vyy50000)) → new_primPlusNat0(new_primMulNat0(vyy600000, Succ(vyy50000)), vyy50000)
new_lt5(vyy6001, vyy501, app(ty_Ratio, gb)) → new_lt14(vyy6001, vyy501, gb)
new_ltEs8(vyy600, vyy50) → new_not(new_compare30(vyy600, vyy50))
new_esEs7(Just(vyy440), Just(vyy450), ty_Bool) → new_esEs14(vyy440, vyy450)
new_compare6(:%(vyy6000, vyy6001), :%(vyy500, vyy501), ty_Int) → new_compare16(new_sr0(vyy6000, vyy501), new_sr0(vyy500, vyy6001))
new_fmToList(vyy45, beh, bfa) → new_foldFM2(vyy45, beh, bfa)
new_esEs8(Right(vyy440), Right(vyy450), cgf, app(app(ty_@2, chf), chg)) → new_esEs5(vyy440, vyy450, chf, chg)
new_ltEs13(vyy600, vyy50) → new_not(new_compare29(vyy600, vyy50))
new_esEs8(Left(vyy440), Left(vyy450), ty_Ordering, cfc) → new_esEs18(vyy440, vyy450)
new_lt11(vyy6000, vyy500) → new_esEs22(new_compare12(vyy6000, vyy500))
new_primCompAux00(vyy60, GT) → GT
new_ltEs18(Just(vyy6000), Just(vyy500), ty_Char) → new_ltEs13(vyy6000, vyy500)
new_esEs8(Right(vyy440), Right(vyy450), cgf, app(ty_[], che)) → new_esEs10(vyy440, vyy450, che)
new_compare33(vyy6000, vyy500, bfd, bfe, bff) → new_compare26(vyy6000, vyy500, new_esEs6(vyy6000, vyy500, bfd, bfe, bff), bfd, bfe, bff)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_ltEs14(EQ, GT) → True
new_esEs7(Just(vyy440), Just(vyy450), ty_Ordering) → new_esEs18(vyy440, vyy450)
new_lt4(vyy6000, vyy500, ty_@0) → new_lt17(vyy6000, vyy500)
new_ltEs4(Left(vyy6000), Left(vyy500), ty_@0, ceh) → new_ltEs17(vyy6000, vyy500)
new_lt5(vyy6001, vyy501, ty_Char) → new_lt12(vyy6001, vyy501)
new_esEs22(LT) → True
new_lt7(vyy6000, vyy500, bfb, bfc) → new_esEs22(new_compare31(vyy6000, vyy500, bfb, bfc))
new_lt4(vyy6000, vyy500, app(ty_Ratio, eg)) → new_lt14(vyy6000, vyy500, eg)
new_compare34(vyy6000, vyy500, app(ty_Ratio, deh)) → new_compare6(vyy6000, vyy500, deh)
new_esEs25(vyy441, vyy451, ty_Float) → new_esEs9(vyy441, vyy451)
new_esEs25(vyy441, vyy451, app(ty_Ratio, cce)) → new_esEs12(vyy441, vyy451, cce)
new_esEs7(Just(vyy440), Just(vyy450), app(ty_Ratio, da)) → new_esEs12(vyy440, vyy450, da)
new_primCmpNat0(vyy60000, Succ(vyy5000)) → new_primCmpNat1(vyy60000, vyy5000)
new_ltEs19(vyy6001, vyy501, app(ty_Maybe, ddf)) → new_ltEs18(vyy6001, vyy501, ddf)
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_esEs8(Right(vyy440), Right(vyy450), cgf, app(ty_Maybe, cha)) → new_esEs7(vyy440, vyy450, cha)
new_esEs25(vyy441, vyy451, app(app(ty_Either, cbd), cbe)) → new_esEs8(vyy441, vyy451, cbd, cbe)
new_esEs27(vyy44, vyy45, ty_Integer) → new_esEs15(vyy44, vyy45)
new_ltEs19(vyy6001, vyy501, ty_Bool) → new_ltEs11(vyy6001, vyy501)
new_esEs18(EQ, EQ) → True
new_esEs25(vyy441, vyy451, ty_Char) → new_esEs13(vyy441, vyy451)
new_primCmpInt(Neg(Succ(vyy60000)), Pos(vyy500)) → LT
new_esEs27(vyy44, vyy45, ty_Double) → new_esEs19(vyy44, vyy45)
The set Q consists of the following terms:
new_esEs21(x0, x1, ty_Int)
new_ltEs7(x0, x1, app(ty_Maybe, x2))
new_esEs8(Left(x0), Left(x1), ty_Integer, x2)
new_ltEs20(x0, x1, ty_Integer)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_esEs24(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_primPlusNat1(Succ(x0), Succ(x1))
new_ltEs7(x0, x1, ty_Int)
new_compare11(x0, x1, False, x2)
new_asAs(False, x0)
new_lt5(x0, x1, ty_Int)
new_lt8(x0, x1)
new_esEs8(Left(x0), Left(x1), ty_Bool, x2)
new_compare3(:(x0, x1), [], x2)
new_esEs7(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_esEs18(LT, LT)
new_esEs20(x0, x1, ty_Bool)
new_esEs7(Just(x0), Just(x1), ty_Char)
new_esEs24(x0, x1, ty_Ordering)
new_esEs21(x0, x1, ty_Bool)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs8(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_esEs8(Right(x0), Right(x1), x2, ty_Double)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_compare34(x0, x1, ty_Double)
new_esEs8(Right(x0), Right(x1), x2, ty_Ordering)
new_compare14(x0, x1, True, x2, x3, x4)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_esEs23(x0, x1, ty_Ordering)
new_esEs8(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs21(x0, x1, ty_@0)
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs26(x0, x1, ty_Char)
new_ltEs19(x0, x1, ty_Integer)
new_lt4(x0, x1, ty_Integer)
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs24(x0, x1, ty_Integer)
new_ltEs18(Nothing, Nothing, x0)
new_esEs20(x0, x1, ty_Float)
new_lt4(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare27(x0, x1, True)
new_esEs8(Right(x0), Right(x1), x2, app(ty_[], x3))
new_primMulNat0(Zero, Succ(x0))
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs7(Just(x0), Just(x1), ty_Bool)
new_esEs24(x0, x1, ty_Double)
new_ltEs4(Left(x0), Left(x1), ty_Bool, x2)
new_esEs23(x0, x1, ty_Char)
new_esEs11(@0, @0)
new_esEs22(LT)
new_compare13(x0, x1, True, x2, x3)
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_esEs29(x0, x1, ty_Integer)
new_ltEs4(Right(x0), Right(x1), x2, ty_Integer)
new_compare27(x0, x1, False)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_esEs8(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs21(x0, x1, ty_Integer)
new_esEs24(x0, x1, app(ty_[], x2))
new_ltEs4(Right(x0), Right(x1), x2, ty_Ordering)
new_compare10(x0, x1, True, x2, x3)
new_ltEs19(x0, x1, app(ty_[], x2))
new_compare19(x0, x1, False)
new_ltEs9(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_lt20(x0, x1, ty_Int)
new_esEs7(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_lt13(x0, x1)
new_primEqNat0(Zero, Succ(x0))
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
new_ltEs4(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_compare3([], :(x0, x1), x2)
new_ltEs7(x0, x1, ty_Char)
new_esEs26(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs18(EQ, GT)
new_esEs18(GT, EQ)
new_ltEs4(Left(x0), Left(x1), ty_Double, x2)
new_primCmpNat1(Succ(x0), Zero)
new_ltEs4(Left(x0), Left(x1), ty_Int, x2)
new_lt4(x0, x1, ty_Char)
new_esEs8(Right(x0), Right(x1), x2, ty_Float)
new_compare3([], [], x0)
new_esEs27(x0, x1, ty_@0)
new_ltEs20(x0, x1, ty_@0)
new_ltEs20(x0, x1, ty_Ordering)
new_compare34(x0, x1, app(ty_Ratio, x2))
new_esEs18(EQ, EQ)
new_ltEs4(Right(x0), Right(x1), x2, ty_Bool)
new_compare16(x0, x1)
new_ltEs19(x0, x1, ty_Float)
new_primCmpNat1(Zero, Zero)
new_compare10(x0, x1, False, x2, x3)
new_esEs27(x0, x1, ty_Int)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_compare8(x0, x1, x2)
new_compare25(x0, x1, True)
new_esEs25(x0, x1, app(ty_[], x2))
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_esEs14(True, True)
new_esEs27(x0, x1, app(ty_[], x2))
new_esEs27(x0, x1, ty_Float)
new_lt20(x0, x1, ty_Ordering)
new_esEs26(x0, x1, ty_Double)
new_esEs8(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_lt4(x0, x1, app(ty_Ratio, x2))
new_compare34(x0, x1, ty_Ordering)
new_ltEs14(EQ, EQ)
new_primEqNat0(Zero, Zero)
new_esEs27(x0, x1, ty_Double)
new_esEs8(Left(x0), Left(x1), app(ty_[], x2), x3)
new_lt5(x0, x1, app(app(ty_Either, x2), x3))
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_lt20(x0, x1, ty_Double)
new_esEs7(Just(x0), Just(x1), ty_Int)
new_compare34(x0, x1, app(ty_[], x2))
new_esEs24(x0, x1, ty_@0)
new_esEs26(x0, x1, ty_Bool)
new_compare3(:(x0, x1), :(x2, x3), x4)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_compare31(x0, x1, x2, x3)
new_esEs23(x0, x1, ty_Integer)
new_primMulNat0(Zero, Zero)
new_ltEs18(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_ltEs4(Right(x0), Right(x1), x2, ty_Float)
new_primCmpNat0(x0, Succ(x1))
new_esEs21(x0, x1, ty_Float)
new_ltEs17(x0, x1)
new_esEs6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs20(x0, x1, ty_Char)
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_esEs26(x0, x1, ty_@0)
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_primMulNat0(Succ(x0), Zero)
new_lt14(x0, x1, x2)
new_ltEs18(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_compare34(x0, x1, ty_Bool)
new_primCompAux00(x0, LT)
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare34(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs7(Just(x0), Just(x1), app(ty_[], x2))
new_lt5(x0, x1, ty_Ordering)
new_primPlusNat0(Zero, x0)
new_esEs25(x0, x1, ty_Float)
new_compare34(x0, x1, ty_Integer)
new_lt4(x0, x1, ty_@0)
new_esEs27(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_ltEs7(x0, x1, ty_Float)
new_esEs8(Left(x0), Left(x1), ty_Int, x2)
new_ltEs19(x0, x1, ty_Ordering)
new_sr(Integer(x0), Integer(x1))
new_esEs8(Right(x0), Right(x1), x2, app(app(ty_FiniteMap, x3), x4))
new_compare19(x0, x1, True)
new_esEs27(x0, x1, ty_Ordering)
new_ltEs19(x0, x1, ty_Bool)
new_esEs8(Right(x0), Left(x1), x2, x3)
new_esEs8(Left(x0), Right(x1), x2, x3)
new_esEs8(Right(x0), Right(x1), x2, ty_Bool)
new_compare34(x0, x1, app(ty_Maybe, x2))
new_compare34(x0, x1, ty_Char)
new_ltEs4(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_ltEs4(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_primEqNat0(Succ(x0), Zero)
new_ltEs18(Just(x0), Just(x1), ty_Int)
new_esEs12(:%(x0, x1), :%(x2, x3), x4)
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, ty_Bool)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_ltEs7(x0, x1, ty_Integer)
new_lt7(x0, x1, x2, x3)
new_esEs23(x0, x1, ty_@0)
new_ltEs18(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs16(x0, x1, x2, x3)
new_esEs8(Right(x0), Right(x1), x2, ty_@0)
new_lt5(x0, x1, ty_Float)
new_compare23(x0, x1, True, x2, x3)
new_esEs20(x0, x1, ty_Ordering)
new_esEs8(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_compare28(x0, x1, False, x2, x3)
new_esEs8(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_compare17(Double(x0, x1), Double(x2, x3))
new_esEs13(Char(x0), Char(x1))
new_esEs25(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_lt20(x0, x1, ty_Char)
new_ltEs4(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs25(x0, x1, ty_Ordering)
new_lt20(x0, x1, ty_Integer)
new_ltEs20(x0, x1, ty_Char)
new_ltEs4(Right(x0), Right(x1), x2, ty_Double)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_ltEs18(Just(x0), Just(x1), ty_Float)
new_ltEs7(x0, x1, ty_@0)
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs28(x0, x1, ty_Integer)
new_esEs21(x0, x1, ty_Char)
new_primPlusNat1(Zero, Zero)
new_lt4(x0, x1, app(app(ty_Either, x2), x3))
new_compare6(:%(x0, x1), :%(x2, x3), ty_Integer)
new_not0
new_ltEs19(x0, x1, ty_Char)
new_primPlusNat1(Zero, Succ(x0))
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs7(Just(x0), Just(x1), ty_Integer)
new_lt5(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs14(LT, LT)
new_lt5(x0, x1, app(ty_Ratio, x2))
new_esEs8(Right(x0), Right(x1), x2, ty_Integer)
new_fmToList(x0, x1, x2)
new_ltEs13(x0, x1)
new_esEs26(x0, x1, ty_Integer)
new_compare34(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs7(x0, x1, ty_Bool)
new_esEs7(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_lt4(x0, x1, ty_Float)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_lt20(x0, x1, app(ty_Ratio, x2))
new_compare34(x0, x1, ty_@0)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_compare34(x0, x1, ty_Int)
new_lt5(x0, x1, ty_Double)
new_esEs18(GT, GT)
new_lt5(x0, x1, ty_Bool)
new_lt12(x0, x1)
new_compare13(x0, x1, False, x2, x3)
new_ltEs4(Left(x0), Right(x1), x2, x3)
new_ltEs4(Right(x0), Left(x1), x2, x3)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_primCompAux00(x0, EQ)
new_lt4(x0, x1, app(app(ty_@2, x2), x3))
new_esEs20(x0, x1, ty_@0)
new_lt6(x0, x1)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_esEs25(x0, x1, ty_Double)
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_not(GT)
new_ltEs8(x0, x1)
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_esEs8(Left(x0), Left(x1), ty_Double, x2)
new_esEs7(Just(x0), Just(x1), app(app(ty_FiniteMap, x2), x3))
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_lt20(x0, x1, ty_Float)
new_compare15(x0, x1)
new_ltEs4(Left(x0), Left(x1), ty_Char, x2)
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_ltEs10(x0, x1)
new_esEs23(x0, x1, ty_Float)
new_ltEs14(LT, EQ)
new_ltEs16(x0, x1)
new_ltEs14(EQ, LT)
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs8(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_ltEs11(False, False)
new_ltEs4(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_sr0(x0, x1)
new_ltEs7(x0, x1, app(app(ty_@2, x2), x3))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_lt5(x0, x1, ty_Integer)
new_compare26(x0, x1, False, x2, x3, x4)
new_esEs7(Just(x0), Nothing, x1)
new_compare24(x0, x1, True, x2)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_lt4(x0, x1, ty_Ordering)
new_primEqInt(Neg(Zero), Neg(Zero))
new_ltEs20(x0, x1, ty_Float)
new_foldFM2(EmptyFM, x0, x1)
new_lt5(x0, x1, app(ty_[], x2))
new_ltEs11(False, True)
new_ltEs11(True, False)
new_esEs26(x0, x1, ty_Ordering)
new_esEs14(False, True)
new_esEs14(True, False)
new_lt15(x0, x1, x2)
new_esEs21(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_esEs8(Left(x0), Left(x1), ty_Ordering, x2)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_ltEs5(x0, x1, x2)
new_ltEs18(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs18(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs17(x0, x1)
new_esEs26(x0, x1, app(ty_[], x2))
new_primCmpNat2(Succ(x0), x1)
new_ltEs18(Just(x0), Just(x1), ty_Integer)
new_esEs7(Just(x0), Just(x1), app(ty_Maybe, x2))
new_compare29(Char(x0), Char(x1))
new_primPlusNat0(Succ(x0), x1)
new_compare7(@0, @0)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_ltEs7(x0, x1, app(ty_[], x2))
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_ltEs4(Left(x0), Left(x1), ty_Float, x2)
new_compare23(x0, x1, False, x2, x3)
new_primCmpNat2(Zero, x0)
new_compare9(x0, x1)
new_lt4(x0, x1, app(ty_[], x2))
new_compare33(x0, x1, x2, x3, x4)
new_primCmpNat1(Succ(x0), Succ(x1))
new_primCmpNat0(x0, Zero)
new_esEs24(x0, x1, ty_Char)
new_esEs8(Left(x0), Left(x1), app(app(ty_FiniteMap, x2), x3), x4)
new_esEs8(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs7(Just(x0), Just(x1), ty_Double)
new_esEs20(x0, x1, app(ty_[], x2))
new_ltEs4(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs4(Right(x0), Right(x1), x2, ty_Int)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, ty_Double)
new_ltEs7(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs20(x0, x1, app(ty_[], x2))
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_esEs8(Right(x0), Right(x1), x2, ty_Int)
new_compare26(x0, x1, True, x2, x3, x4)
new_lt4(x0, x1, ty_Int)
new_esEs21(x0, x1, ty_Ordering)
new_esEs10(:(x0, x1), :(x2, x3), x4)
new_ltEs14(EQ, GT)
new_ltEs14(GT, EQ)
new_ltEs12(x0, x1)
new_esEs7(Nothing, Just(x0), x1)
new_primCompAux0(x0, x1, x2, x3)
new_esEs20(x0, x1, ty_Double)
new_lt18(x0, x1, x2)
new_esEs8(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs26(x0, x1, ty_Int)
new_sizeFM(EmptyFM, x0, x1)
new_ltEs18(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs24(x0, x1, ty_Float)
new_primMulNat0(Succ(x0), Succ(x1))
new_esEs20(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(EQ)
new_ltEs4(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_compare34(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs18(Just(x0), Just(x1), ty_Bool)
new_esEs7(Just(x0), Just(x1), ty_Float)
new_asAs(True, x0)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_primCmpNat1(Zero, Succ(x0))
new_lt5(x0, x1, ty_@0)
new_esEs18(EQ, LT)
new_esEs18(LT, EQ)
new_esEs23(x0, x1, ty_Bool)
new_lt5(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs14(LT, GT)
new_ltEs14(GT, LT)
new_primCompAux00(x0, GT)
new_compare25(x0, x1, False)
new_ltEs4(Right(x0), Right(x1), x2, ty_@0)
new_esEs20(x0, x1, ty_Int)
new_compare34(x0, x1, ty_Float)
new_esEs27(x0, x1, ty_Char)
new_lt20(x0, x1, app(ty_[], x2))
new_esEs23(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_compare32(x0, x1, x2, x3)
new_ltEs7(x0, x1, app(ty_Ratio, x2))
new_lt4(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt17(x0, x1)
new_esEs26(x0, x1, ty_Float)
new_ltEs4(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_ltEs14(GT, GT)
new_lt20(x0, x1, ty_Bool)
new_ltEs18(Just(x0), Just(x1), ty_Char)
new_esEs5(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs25(x0, x1, ty_Bool)
new_esEs19(Double(x0, x1), Double(x2, x3))
new_lt5(x0, x1, ty_Char)
new_not(EQ)
new_esEs10(:(x0, x1), [], x2)
new_esEs10([], :(x0, x1), x2)
new_ltEs20(x0, x1, ty_Double)
new_lt4(x0, x1, ty_Double)
new_compare12(Integer(x0), Integer(x1))
new_esEs7(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_lt10(x0, x1, x2, x3, x4)
new_esEs28(x0, x1, ty_Int)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_ltEs7(x0, x1, ty_Double)
new_lt16(x0, x1)
new_esEs22(GT)
new_ltEs18(Just(x0), Just(x1), ty_Ordering)
new_lt9(x0, x1)
new_esEs15(Integer(x0), Integer(x1))
new_lt5(x0, x1, app(ty_Maybe, x2))
new_compare24(x0, x1, False, x2)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(Nothing, Nothing, x0)
new_esEs8(Left(x0), Left(x1), ty_@0, x2)
new_ltEs4(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs23(x0, x1, app(ty_[], x2))
new_esEs25(x0, x1, ty_Integer)
new_esEs20(x0, x1, ty_Integer)
new_compare18(x0, x1, True)
new_compare11(x0, x1, True, x2)
new_compare18(x0, x1, False)
new_pePe(True, x0, x1, x2, x3)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare6(:%(x0, x1), :%(x2, x3), ty_Int)
new_compare30(Float(x0, x1), Float(x2, x3))
new_lt11(x0, x1)
new_ltEs18(Just(x0), Nothing, x1)
new_esEs27(x0, x1, ty_Bool)
new_esEs18(GT, LT)
new_esEs18(LT, GT)
new_ltEs19(x0, x1, ty_@0)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs21(x0, x1, app(ty_[], x2))
new_esEs9(Float(x0, x1), Float(x2, x3))
new_esEs10([], [], x0)
new_ltEs7(x0, x1, ty_Ordering)
new_ltEs4(Left(x0), Left(x1), ty_Ordering, x2)
new_ltEs18(Nothing, Just(x0), x1)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_esEs25(x0, x1, ty_Char)
new_esEs29(x0, x1, ty_Int)
new_ltEs19(x0, x1, ty_Double)
new_compare14(x0, x1, False, x2, x3, x4)
new_esEs27(x0, x1, ty_Integer)
new_esEs7(Just(x0), Just(x1), ty_@0)
new_lt4(x0, x1, ty_Bool)
new_ltEs4(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_ltEs4(Left(x0), Left(x1), ty_@0, x2)
new_esEs8(Left(x0), Left(x1), ty_Char, x2)
new_ltEs19(x0, x1, ty_Int)
new_compare28(x0, x1, True, x2, x3)
new_esEs14(False, False)
new_ltEs4(Right(x0), Right(x1), x2, ty_Char)
new_primEqInt(Pos(Zero), Pos(Zero))
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_esEs25(x0, x1, ty_@0)
new_lt19(x0, x1, x2, x3)
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_esEs21(x0, x1, ty_Double)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs4(Left(x0), Left(x1), app(ty_[], x2), x3)
new_ltEs20(x0, x1, ty_Int)
new_ltEs18(Just(x0), Just(x1), ty_@0)
new_esEs24(x0, x1, ty_Int)
new_lt20(x0, x1, ty_@0)
new_ltEs4(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs7(Just(x0), Just(x1), ty_Ordering)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, ty_Int)
new_esEs8(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs25(x0, x1, ty_Int)
new_esEs24(x0, x1, ty_Bool)
new_esEs8(Left(x0), Left(x1), ty_Float, x2)
new_ltEs4(Left(x0), Left(x1), ty_Integer, x2)
new_primPlusNat1(Succ(x0), Zero)
new_ltEs15(x0, x1, x2)
new_primMulInt(Pos(x0), Pos(x1))
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs18(Just(x0), Just(x1), ty_Double)
new_not(LT)
new_ltEs11(True, True)
new_esEs8(Right(x0), Right(x1), x2, ty_Char)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_pePe(False, x0, x1, x2, x3)
new_ltEs7(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
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
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QReductionProof
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_foldFM_LE(vyy3, Nothing, Branch(Just(vyy600), vyy61, vyy62, vyy63, vyy64), h, ba, bb) → new_foldFM_LE(vyy3, Nothing, vyy63, h, ba, bb)
new_foldFM_LE(vyy3, Nothing, Branch(Nothing, vyy61, vyy62, vyy63, vyy64), h, ba, bb) → new_foldFM_LE(vyy3, Nothing, vyy64, h, ba, bb)
new_foldFM_LE(vyy3, Nothing, Branch(Nothing, vyy61, vyy62, vyy63, vyy64), h, ba, bb) → new_foldFM_LE(vyy3, Nothing, vyy63, h, ba, bb)
R is empty.
The set Q consists of the following terms:
new_esEs21(x0, x1, ty_Int)
new_ltEs7(x0, x1, app(ty_Maybe, x2))
new_esEs8(Left(x0), Left(x1), ty_Integer, x2)
new_ltEs20(x0, x1, ty_Integer)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_esEs24(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_primPlusNat1(Succ(x0), Succ(x1))
new_ltEs7(x0, x1, ty_Int)
new_compare11(x0, x1, False, x2)
new_asAs(False, x0)
new_lt5(x0, x1, ty_Int)
new_lt8(x0, x1)
new_esEs8(Left(x0), Left(x1), ty_Bool, x2)
new_compare3(:(x0, x1), [], x2)
new_esEs7(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_esEs18(LT, LT)
new_esEs20(x0, x1, ty_Bool)
new_esEs7(Just(x0), Just(x1), ty_Char)
new_esEs24(x0, x1, ty_Ordering)
new_esEs21(x0, x1, ty_Bool)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs8(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_esEs8(Right(x0), Right(x1), x2, ty_Double)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_compare34(x0, x1, ty_Double)
new_esEs8(Right(x0), Right(x1), x2, ty_Ordering)
new_compare14(x0, x1, True, x2, x3, x4)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_esEs23(x0, x1, ty_Ordering)
new_esEs8(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs21(x0, x1, ty_@0)
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs26(x0, x1, ty_Char)
new_ltEs19(x0, x1, ty_Integer)
new_lt4(x0, x1, ty_Integer)
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs24(x0, x1, ty_Integer)
new_ltEs18(Nothing, Nothing, x0)
new_esEs20(x0, x1, ty_Float)
new_lt4(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare27(x0, x1, True)
new_esEs8(Right(x0), Right(x1), x2, app(ty_[], x3))
new_primMulNat0(Zero, Succ(x0))
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs7(Just(x0), Just(x1), ty_Bool)
new_esEs24(x0, x1, ty_Double)
new_ltEs4(Left(x0), Left(x1), ty_Bool, x2)
new_esEs23(x0, x1, ty_Char)
new_esEs11(@0, @0)
new_esEs22(LT)
new_compare13(x0, x1, True, x2, x3)
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_esEs29(x0, x1, ty_Integer)
new_ltEs4(Right(x0), Right(x1), x2, ty_Integer)
new_compare27(x0, x1, False)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_esEs8(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs21(x0, x1, ty_Integer)
new_esEs24(x0, x1, app(ty_[], x2))
new_ltEs4(Right(x0), Right(x1), x2, ty_Ordering)
new_compare10(x0, x1, True, x2, x3)
new_ltEs19(x0, x1, app(ty_[], x2))
new_compare19(x0, x1, False)
new_ltEs9(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_lt20(x0, x1, ty_Int)
new_esEs7(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_lt13(x0, x1)
new_primEqNat0(Zero, Succ(x0))
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
new_ltEs4(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_compare3([], :(x0, x1), x2)
new_ltEs7(x0, x1, ty_Char)
new_esEs26(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs18(EQ, GT)
new_esEs18(GT, EQ)
new_ltEs4(Left(x0), Left(x1), ty_Double, x2)
new_primCmpNat1(Succ(x0), Zero)
new_ltEs4(Left(x0), Left(x1), ty_Int, x2)
new_lt4(x0, x1, ty_Char)
new_esEs8(Right(x0), Right(x1), x2, ty_Float)
new_compare3([], [], x0)
new_esEs27(x0, x1, ty_@0)
new_ltEs20(x0, x1, ty_@0)
new_ltEs20(x0, x1, ty_Ordering)
new_compare34(x0, x1, app(ty_Ratio, x2))
new_esEs18(EQ, EQ)
new_ltEs4(Right(x0), Right(x1), x2, ty_Bool)
new_compare16(x0, x1)
new_ltEs19(x0, x1, ty_Float)
new_primCmpNat1(Zero, Zero)
new_compare10(x0, x1, False, x2, x3)
new_esEs27(x0, x1, ty_Int)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_compare8(x0, x1, x2)
new_compare25(x0, x1, True)
new_esEs25(x0, x1, app(ty_[], x2))
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_esEs14(True, True)
new_esEs27(x0, x1, app(ty_[], x2))
new_esEs27(x0, x1, ty_Float)
new_lt20(x0, x1, ty_Ordering)
new_esEs26(x0, x1, ty_Double)
new_esEs8(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_lt4(x0, x1, app(ty_Ratio, x2))
new_compare34(x0, x1, ty_Ordering)
new_ltEs14(EQ, EQ)
new_primEqNat0(Zero, Zero)
new_esEs27(x0, x1, ty_Double)
new_esEs8(Left(x0), Left(x1), app(ty_[], x2), x3)
new_lt5(x0, x1, app(app(ty_Either, x2), x3))
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_lt20(x0, x1, ty_Double)
new_esEs7(Just(x0), Just(x1), ty_Int)
new_compare34(x0, x1, app(ty_[], x2))
new_esEs24(x0, x1, ty_@0)
new_esEs26(x0, x1, ty_Bool)
new_compare3(:(x0, x1), :(x2, x3), x4)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_compare31(x0, x1, x2, x3)
new_esEs23(x0, x1, ty_Integer)
new_primMulNat0(Zero, Zero)
new_ltEs18(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_ltEs4(Right(x0), Right(x1), x2, ty_Float)
new_primCmpNat0(x0, Succ(x1))
new_esEs21(x0, x1, ty_Float)
new_ltEs17(x0, x1)
new_esEs6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs20(x0, x1, ty_Char)
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_esEs26(x0, x1, ty_@0)
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_primMulNat0(Succ(x0), Zero)
new_lt14(x0, x1, x2)
new_ltEs18(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_compare34(x0, x1, ty_Bool)
new_primCompAux00(x0, LT)
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare34(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs7(Just(x0), Just(x1), app(ty_[], x2))
new_lt5(x0, x1, ty_Ordering)
new_primPlusNat0(Zero, x0)
new_esEs25(x0, x1, ty_Float)
new_compare34(x0, x1, ty_Integer)
new_lt4(x0, x1, ty_@0)
new_esEs27(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_ltEs7(x0, x1, ty_Float)
new_esEs8(Left(x0), Left(x1), ty_Int, x2)
new_ltEs19(x0, x1, ty_Ordering)
new_sr(Integer(x0), Integer(x1))
new_esEs8(Right(x0), Right(x1), x2, app(app(ty_FiniteMap, x3), x4))
new_compare19(x0, x1, True)
new_esEs27(x0, x1, ty_Ordering)
new_ltEs19(x0, x1, ty_Bool)
new_esEs8(Right(x0), Left(x1), x2, x3)
new_esEs8(Left(x0), Right(x1), x2, x3)
new_esEs8(Right(x0), Right(x1), x2, ty_Bool)
new_compare34(x0, x1, app(ty_Maybe, x2))
new_compare34(x0, x1, ty_Char)
new_ltEs4(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_ltEs4(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_primEqNat0(Succ(x0), Zero)
new_ltEs18(Just(x0), Just(x1), ty_Int)
new_esEs12(:%(x0, x1), :%(x2, x3), x4)
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, ty_Bool)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_ltEs7(x0, x1, ty_Integer)
new_lt7(x0, x1, x2, x3)
new_esEs23(x0, x1, ty_@0)
new_ltEs18(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs16(x0, x1, x2, x3)
new_esEs8(Right(x0), Right(x1), x2, ty_@0)
new_lt5(x0, x1, ty_Float)
new_compare23(x0, x1, True, x2, x3)
new_esEs20(x0, x1, ty_Ordering)
new_esEs8(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_compare28(x0, x1, False, x2, x3)
new_esEs8(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_compare17(Double(x0, x1), Double(x2, x3))
new_esEs13(Char(x0), Char(x1))
new_esEs25(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_lt20(x0, x1, ty_Char)
new_ltEs4(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs25(x0, x1, ty_Ordering)
new_lt20(x0, x1, ty_Integer)
new_ltEs20(x0, x1, ty_Char)
new_ltEs4(Right(x0), Right(x1), x2, ty_Double)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_ltEs18(Just(x0), Just(x1), ty_Float)
new_ltEs7(x0, x1, ty_@0)
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs28(x0, x1, ty_Integer)
new_esEs21(x0, x1, ty_Char)
new_primPlusNat1(Zero, Zero)
new_lt4(x0, x1, app(app(ty_Either, x2), x3))
new_compare6(:%(x0, x1), :%(x2, x3), ty_Integer)
new_not0
new_ltEs19(x0, x1, ty_Char)
new_primPlusNat1(Zero, Succ(x0))
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs7(Just(x0), Just(x1), ty_Integer)
new_lt5(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs14(LT, LT)
new_lt5(x0, x1, app(ty_Ratio, x2))
new_esEs8(Right(x0), Right(x1), x2, ty_Integer)
new_fmToList(x0, x1, x2)
new_ltEs13(x0, x1)
new_esEs26(x0, x1, ty_Integer)
new_compare34(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs7(x0, x1, ty_Bool)
new_esEs7(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_lt4(x0, x1, ty_Float)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_lt20(x0, x1, app(ty_Ratio, x2))
new_compare34(x0, x1, ty_@0)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_compare34(x0, x1, ty_Int)
new_lt5(x0, x1, ty_Double)
new_esEs18(GT, GT)
new_lt5(x0, x1, ty_Bool)
new_lt12(x0, x1)
new_compare13(x0, x1, False, x2, x3)
new_ltEs4(Left(x0), Right(x1), x2, x3)
new_ltEs4(Right(x0), Left(x1), x2, x3)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_primCompAux00(x0, EQ)
new_lt4(x0, x1, app(app(ty_@2, x2), x3))
new_esEs20(x0, x1, ty_@0)
new_lt6(x0, x1)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_esEs25(x0, x1, ty_Double)
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_not(GT)
new_ltEs8(x0, x1)
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_esEs8(Left(x0), Left(x1), ty_Double, x2)
new_esEs7(Just(x0), Just(x1), app(app(ty_FiniteMap, x2), x3))
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_lt20(x0, x1, ty_Float)
new_compare15(x0, x1)
new_ltEs4(Left(x0), Left(x1), ty_Char, x2)
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_ltEs10(x0, x1)
new_esEs23(x0, x1, ty_Float)
new_ltEs14(LT, EQ)
new_ltEs16(x0, x1)
new_ltEs14(EQ, LT)
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs8(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_ltEs11(False, False)
new_ltEs4(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_sr0(x0, x1)
new_ltEs7(x0, x1, app(app(ty_@2, x2), x3))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_lt5(x0, x1, ty_Integer)
new_compare26(x0, x1, False, x2, x3, x4)
new_esEs7(Just(x0), Nothing, x1)
new_compare24(x0, x1, True, x2)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_lt4(x0, x1, ty_Ordering)
new_primEqInt(Neg(Zero), Neg(Zero))
new_ltEs20(x0, x1, ty_Float)
new_foldFM2(EmptyFM, x0, x1)
new_lt5(x0, x1, app(ty_[], x2))
new_ltEs11(False, True)
new_ltEs11(True, False)
new_esEs26(x0, x1, ty_Ordering)
new_esEs14(False, True)
new_esEs14(True, False)
new_lt15(x0, x1, x2)
new_esEs21(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_esEs8(Left(x0), Left(x1), ty_Ordering, x2)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_ltEs5(x0, x1, x2)
new_ltEs18(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs18(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs17(x0, x1)
new_esEs26(x0, x1, app(ty_[], x2))
new_primCmpNat2(Succ(x0), x1)
new_ltEs18(Just(x0), Just(x1), ty_Integer)
new_esEs7(Just(x0), Just(x1), app(ty_Maybe, x2))
new_compare29(Char(x0), Char(x1))
new_primPlusNat0(Succ(x0), x1)
new_compare7(@0, @0)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_ltEs7(x0, x1, app(ty_[], x2))
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_ltEs4(Left(x0), Left(x1), ty_Float, x2)
new_compare23(x0, x1, False, x2, x3)
new_primCmpNat2(Zero, x0)
new_compare9(x0, x1)
new_lt4(x0, x1, app(ty_[], x2))
new_compare33(x0, x1, x2, x3, x4)
new_primCmpNat1(Succ(x0), Succ(x1))
new_primCmpNat0(x0, Zero)
new_esEs24(x0, x1, ty_Char)
new_esEs8(Left(x0), Left(x1), app(app(ty_FiniteMap, x2), x3), x4)
new_esEs8(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs7(Just(x0), Just(x1), ty_Double)
new_esEs20(x0, x1, app(ty_[], x2))
new_ltEs4(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs4(Right(x0), Right(x1), x2, ty_Int)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, ty_Double)
new_ltEs7(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs20(x0, x1, app(ty_[], x2))
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_esEs8(Right(x0), Right(x1), x2, ty_Int)
new_compare26(x0, x1, True, x2, x3, x4)
new_lt4(x0, x1, ty_Int)
new_esEs21(x0, x1, ty_Ordering)
new_esEs10(:(x0, x1), :(x2, x3), x4)
new_ltEs14(EQ, GT)
new_ltEs14(GT, EQ)
new_ltEs12(x0, x1)
new_esEs7(Nothing, Just(x0), x1)
new_primCompAux0(x0, x1, x2, x3)
new_esEs20(x0, x1, ty_Double)
new_lt18(x0, x1, x2)
new_esEs8(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs26(x0, x1, ty_Int)
new_sizeFM(EmptyFM, x0, x1)
new_ltEs18(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs24(x0, x1, ty_Float)
new_primMulNat0(Succ(x0), Succ(x1))
new_esEs20(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(EQ)
new_ltEs4(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_compare34(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs18(Just(x0), Just(x1), ty_Bool)
new_esEs7(Just(x0), Just(x1), ty_Float)
new_asAs(True, x0)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_primCmpNat1(Zero, Succ(x0))
new_lt5(x0, x1, ty_@0)
new_esEs18(EQ, LT)
new_esEs18(LT, EQ)
new_esEs23(x0, x1, ty_Bool)
new_lt5(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs14(LT, GT)
new_ltEs14(GT, LT)
new_primCompAux00(x0, GT)
new_compare25(x0, x1, False)
new_ltEs4(Right(x0), Right(x1), x2, ty_@0)
new_esEs20(x0, x1, ty_Int)
new_compare34(x0, x1, ty_Float)
new_esEs27(x0, x1, ty_Char)
new_lt20(x0, x1, app(ty_[], x2))
new_esEs23(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_compare32(x0, x1, x2, x3)
new_ltEs7(x0, x1, app(ty_Ratio, x2))
new_lt4(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt17(x0, x1)
new_esEs26(x0, x1, ty_Float)
new_ltEs4(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_ltEs14(GT, GT)
new_lt20(x0, x1, ty_Bool)
new_ltEs18(Just(x0), Just(x1), ty_Char)
new_esEs5(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs25(x0, x1, ty_Bool)
new_esEs19(Double(x0, x1), Double(x2, x3))
new_lt5(x0, x1, ty_Char)
new_not(EQ)
new_esEs10(:(x0, x1), [], x2)
new_esEs10([], :(x0, x1), x2)
new_ltEs20(x0, x1, ty_Double)
new_lt4(x0, x1, ty_Double)
new_compare12(Integer(x0), Integer(x1))
new_esEs7(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_lt10(x0, x1, x2, x3, x4)
new_esEs28(x0, x1, ty_Int)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_ltEs7(x0, x1, ty_Double)
new_lt16(x0, x1)
new_esEs22(GT)
new_ltEs18(Just(x0), Just(x1), ty_Ordering)
new_lt9(x0, x1)
new_esEs15(Integer(x0), Integer(x1))
new_lt5(x0, x1, app(ty_Maybe, x2))
new_compare24(x0, x1, False, x2)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(Nothing, Nothing, x0)
new_esEs8(Left(x0), Left(x1), ty_@0, x2)
new_ltEs4(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs23(x0, x1, app(ty_[], x2))
new_esEs25(x0, x1, ty_Integer)
new_esEs20(x0, x1, ty_Integer)
new_compare18(x0, x1, True)
new_compare11(x0, x1, True, x2)
new_compare18(x0, x1, False)
new_pePe(True, x0, x1, x2, x3)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare6(:%(x0, x1), :%(x2, x3), ty_Int)
new_compare30(Float(x0, x1), Float(x2, x3))
new_lt11(x0, x1)
new_ltEs18(Just(x0), Nothing, x1)
new_esEs27(x0, x1, ty_Bool)
new_esEs18(GT, LT)
new_esEs18(LT, GT)
new_ltEs19(x0, x1, ty_@0)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs21(x0, x1, app(ty_[], x2))
new_esEs9(Float(x0, x1), Float(x2, x3))
new_esEs10([], [], x0)
new_ltEs7(x0, x1, ty_Ordering)
new_ltEs4(Left(x0), Left(x1), ty_Ordering, x2)
new_ltEs18(Nothing, Just(x0), x1)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_esEs25(x0, x1, ty_Char)
new_esEs29(x0, x1, ty_Int)
new_ltEs19(x0, x1, ty_Double)
new_compare14(x0, x1, False, x2, x3, x4)
new_esEs27(x0, x1, ty_Integer)
new_esEs7(Just(x0), Just(x1), ty_@0)
new_lt4(x0, x1, ty_Bool)
new_ltEs4(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_ltEs4(Left(x0), Left(x1), ty_@0, x2)
new_esEs8(Left(x0), Left(x1), ty_Char, x2)
new_ltEs19(x0, x1, ty_Int)
new_compare28(x0, x1, True, x2, x3)
new_esEs14(False, False)
new_ltEs4(Right(x0), Right(x1), x2, ty_Char)
new_primEqInt(Pos(Zero), Pos(Zero))
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_esEs25(x0, x1, ty_@0)
new_lt19(x0, x1, x2, x3)
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_esEs21(x0, x1, ty_Double)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs4(Left(x0), Left(x1), app(ty_[], x2), x3)
new_ltEs20(x0, x1, ty_Int)
new_ltEs18(Just(x0), Just(x1), ty_@0)
new_esEs24(x0, x1, ty_Int)
new_lt20(x0, x1, ty_@0)
new_ltEs4(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs7(Just(x0), Just(x1), ty_Ordering)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, ty_Int)
new_esEs8(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs25(x0, x1, ty_Int)
new_esEs24(x0, x1, ty_Bool)
new_esEs8(Left(x0), Left(x1), ty_Float, x2)
new_ltEs4(Left(x0), Left(x1), ty_Integer, x2)
new_primPlusNat1(Succ(x0), Zero)
new_ltEs15(x0, x1, x2)
new_primMulInt(Pos(x0), Pos(x1))
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs18(Just(x0), Just(x1), ty_Double)
new_not(LT)
new_ltEs11(True, True)
new_esEs8(Right(x0), Right(x1), x2, ty_Char)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_pePe(False, x0, x1, x2, x3)
new_ltEs7(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
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_esEs21(x0, x1, ty_Int)
new_ltEs7(x0, x1, app(ty_Maybe, x2))
new_esEs8(Left(x0), Left(x1), ty_Integer, x2)
new_ltEs20(x0, x1, ty_Integer)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_esEs24(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_primPlusNat1(Succ(x0), Succ(x1))
new_ltEs7(x0, x1, ty_Int)
new_compare11(x0, x1, False, x2)
new_asAs(False, x0)
new_lt5(x0, x1, ty_Int)
new_lt8(x0, x1)
new_esEs8(Left(x0), Left(x1), ty_Bool, x2)
new_compare3(:(x0, x1), [], x2)
new_esEs7(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_esEs18(LT, LT)
new_esEs20(x0, x1, ty_Bool)
new_esEs7(Just(x0), Just(x1), ty_Char)
new_esEs24(x0, x1, ty_Ordering)
new_esEs21(x0, x1, ty_Bool)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs8(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_esEs8(Right(x0), Right(x1), x2, ty_Double)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_compare34(x0, x1, ty_Double)
new_esEs8(Right(x0), Right(x1), x2, ty_Ordering)
new_compare14(x0, x1, True, x2, x3, x4)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_esEs23(x0, x1, ty_Ordering)
new_esEs8(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs21(x0, x1, ty_@0)
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs26(x0, x1, ty_Char)
new_ltEs19(x0, x1, ty_Integer)
new_lt4(x0, x1, ty_Integer)
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs24(x0, x1, ty_Integer)
new_ltEs18(Nothing, Nothing, x0)
new_esEs20(x0, x1, ty_Float)
new_lt4(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare27(x0, x1, True)
new_esEs8(Right(x0), Right(x1), x2, app(ty_[], x3))
new_primMulNat0(Zero, Succ(x0))
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs7(Just(x0), Just(x1), ty_Bool)
new_esEs24(x0, x1, ty_Double)
new_ltEs4(Left(x0), Left(x1), ty_Bool, x2)
new_esEs23(x0, x1, ty_Char)
new_esEs11(@0, @0)
new_esEs22(LT)
new_compare13(x0, x1, True, x2, x3)
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_esEs29(x0, x1, ty_Integer)
new_ltEs4(Right(x0), Right(x1), x2, ty_Integer)
new_compare27(x0, x1, False)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_esEs8(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs21(x0, x1, ty_Integer)
new_esEs24(x0, x1, app(ty_[], x2))
new_ltEs4(Right(x0), Right(x1), x2, ty_Ordering)
new_compare10(x0, x1, True, x2, x3)
new_ltEs19(x0, x1, app(ty_[], x2))
new_compare19(x0, x1, False)
new_ltEs9(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_lt20(x0, x1, ty_Int)
new_esEs7(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_lt13(x0, x1)
new_primEqNat0(Zero, Succ(x0))
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
new_ltEs4(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_compare3([], :(x0, x1), x2)
new_ltEs7(x0, x1, ty_Char)
new_esEs26(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs18(EQ, GT)
new_esEs18(GT, EQ)
new_ltEs4(Left(x0), Left(x1), ty_Double, x2)
new_primCmpNat1(Succ(x0), Zero)
new_ltEs4(Left(x0), Left(x1), ty_Int, x2)
new_lt4(x0, x1, ty_Char)
new_esEs8(Right(x0), Right(x1), x2, ty_Float)
new_compare3([], [], x0)
new_esEs27(x0, x1, ty_@0)
new_ltEs20(x0, x1, ty_@0)
new_ltEs20(x0, x1, ty_Ordering)
new_compare34(x0, x1, app(ty_Ratio, x2))
new_esEs18(EQ, EQ)
new_ltEs4(Right(x0), Right(x1), x2, ty_Bool)
new_compare16(x0, x1)
new_ltEs19(x0, x1, ty_Float)
new_primCmpNat1(Zero, Zero)
new_compare10(x0, x1, False, x2, x3)
new_esEs27(x0, x1, ty_Int)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_compare8(x0, x1, x2)
new_compare25(x0, x1, True)
new_esEs25(x0, x1, app(ty_[], x2))
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_esEs14(True, True)
new_esEs27(x0, x1, app(ty_[], x2))
new_esEs27(x0, x1, ty_Float)
new_lt20(x0, x1, ty_Ordering)
new_esEs26(x0, x1, ty_Double)
new_esEs8(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_lt4(x0, x1, app(ty_Ratio, x2))
new_compare34(x0, x1, ty_Ordering)
new_ltEs14(EQ, EQ)
new_primEqNat0(Zero, Zero)
new_esEs27(x0, x1, ty_Double)
new_esEs8(Left(x0), Left(x1), app(ty_[], x2), x3)
new_lt5(x0, x1, app(app(ty_Either, x2), x3))
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_lt20(x0, x1, ty_Double)
new_esEs7(Just(x0), Just(x1), ty_Int)
new_compare34(x0, x1, app(ty_[], x2))
new_esEs24(x0, x1, ty_@0)
new_esEs26(x0, x1, ty_Bool)
new_compare3(:(x0, x1), :(x2, x3), x4)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_compare31(x0, x1, x2, x3)
new_esEs23(x0, x1, ty_Integer)
new_primMulNat0(Zero, Zero)
new_ltEs18(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_ltEs4(Right(x0), Right(x1), x2, ty_Float)
new_primCmpNat0(x0, Succ(x1))
new_esEs21(x0, x1, ty_Float)
new_ltEs17(x0, x1)
new_esEs6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs20(x0, x1, ty_Char)
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_esEs26(x0, x1, ty_@0)
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_primMulNat0(Succ(x0), Zero)
new_lt14(x0, x1, x2)
new_ltEs18(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_compare34(x0, x1, ty_Bool)
new_primCompAux00(x0, LT)
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare34(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs7(Just(x0), Just(x1), app(ty_[], x2))
new_lt5(x0, x1, ty_Ordering)
new_primPlusNat0(Zero, x0)
new_esEs25(x0, x1, ty_Float)
new_compare34(x0, x1, ty_Integer)
new_lt4(x0, x1, ty_@0)
new_esEs27(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_ltEs7(x0, x1, ty_Float)
new_esEs8(Left(x0), Left(x1), ty_Int, x2)
new_ltEs19(x0, x1, ty_Ordering)
new_sr(Integer(x0), Integer(x1))
new_esEs8(Right(x0), Right(x1), x2, app(app(ty_FiniteMap, x3), x4))
new_compare19(x0, x1, True)
new_esEs27(x0, x1, ty_Ordering)
new_ltEs19(x0, x1, ty_Bool)
new_esEs8(Right(x0), Left(x1), x2, x3)
new_esEs8(Left(x0), Right(x1), x2, x3)
new_esEs8(Right(x0), Right(x1), x2, ty_Bool)
new_compare34(x0, x1, app(ty_Maybe, x2))
new_compare34(x0, x1, ty_Char)
new_ltEs4(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_ltEs4(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_primEqNat0(Succ(x0), Zero)
new_ltEs18(Just(x0), Just(x1), ty_Int)
new_esEs12(:%(x0, x1), :%(x2, x3), x4)
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, ty_Bool)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_ltEs7(x0, x1, ty_Integer)
new_lt7(x0, x1, x2, x3)
new_esEs23(x0, x1, ty_@0)
new_ltEs18(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs16(x0, x1, x2, x3)
new_esEs8(Right(x0), Right(x1), x2, ty_@0)
new_lt5(x0, x1, ty_Float)
new_compare23(x0, x1, True, x2, x3)
new_esEs20(x0, x1, ty_Ordering)
new_esEs8(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_compare28(x0, x1, False, x2, x3)
new_esEs8(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_compare17(Double(x0, x1), Double(x2, x3))
new_esEs13(Char(x0), Char(x1))
new_esEs25(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_lt20(x0, x1, ty_Char)
new_ltEs4(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs25(x0, x1, ty_Ordering)
new_lt20(x0, x1, ty_Integer)
new_ltEs20(x0, x1, ty_Char)
new_ltEs4(Right(x0), Right(x1), x2, ty_Double)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_ltEs18(Just(x0), Just(x1), ty_Float)
new_ltEs7(x0, x1, ty_@0)
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs28(x0, x1, ty_Integer)
new_esEs21(x0, x1, ty_Char)
new_primPlusNat1(Zero, Zero)
new_lt4(x0, x1, app(app(ty_Either, x2), x3))
new_compare6(:%(x0, x1), :%(x2, x3), ty_Integer)
new_not0
new_ltEs19(x0, x1, ty_Char)
new_primPlusNat1(Zero, Succ(x0))
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs7(Just(x0), Just(x1), ty_Integer)
new_lt5(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs14(LT, LT)
new_lt5(x0, x1, app(ty_Ratio, x2))
new_esEs8(Right(x0), Right(x1), x2, ty_Integer)
new_fmToList(x0, x1, x2)
new_ltEs13(x0, x1)
new_esEs26(x0, x1, ty_Integer)
new_compare34(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs7(x0, x1, ty_Bool)
new_esEs7(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_lt4(x0, x1, ty_Float)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_lt20(x0, x1, app(ty_Ratio, x2))
new_compare34(x0, x1, ty_@0)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_compare34(x0, x1, ty_Int)
new_lt5(x0, x1, ty_Double)
new_esEs18(GT, GT)
new_lt5(x0, x1, ty_Bool)
new_lt12(x0, x1)
new_compare13(x0, x1, False, x2, x3)
new_ltEs4(Left(x0), Right(x1), x2, x3)
new_ltEs4(Right(x0), Left(x1), x2, x3)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_primCompAux00(x0, EQ)
new_lt4(x0, x1, app(app(ty_@2, x2), x3))
new_esEs20(x0, x1, ty_@0)
new_lt6(x0, x1)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_esEs25(x0, x1, ty_Double)
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_not(GT)
new_ltEs8(x0, x1)
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_esEs8(Left(x0), Left(x1), ty_Double, x2)
new_esEs7(Just(x0), Just(x1), app(app(ty_FiniteMap, x2), x3))
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_lt20(x0, x1, ty_Float)
new_compare15(x0, x1)
new_ltEs4(Left(x0), Left(x1), ty_Char, x2)
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_ltEs10(x0, x1)
new_esEs23(x0, x1, ty_Float)
new_ltEs14(LT, EQ)
new_ltEs16(x0, x1)
new_ltEs14(EQ, LT)
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs8(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_ltEs11(False, False)
new_ltEs4(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_sr0(x0, x1)
new_ltEs7(x0, x1, app(app(ty_@2, x2), x3))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_lt5(x0, x1, ty_Integer)
new_compare26(x0, x1, False, x2, x3, x4)
new_esEs7(Just(x0), Nothing, x1)
new_compare24(x0, x1, True, x2)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_lt4(x0, x1, ty_Ordering)
new_primEqInt(Neg(Zero), Neg(Zero))
new_ltEs20(x0, x1, ty_Float)
new_foldFM2(EmptyFM, x0, x1)
new_lt5(x0, x1, app(ty_[], x2))
new_ltEs11(False, True)
new_ltEs11(True, False)
new_esEs26(x0, x1, ty_Ordering)
new_esEs14(False, True)
new_esEs14(True, False)
new_lt15(x0, x1, x2)
new_esEs21(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_esEs8(Left(x0), Left(x1), ty_Ordering, x2)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_ltEs5(x0, x1, x2)
new_ltEs18(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs18(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs17(x0, x1)
new_esEs26(x0, x1, app(ty_[], x2))
new_primCmpNat2(Succ(x0), x1)
new_ltEs18(Just(x0), Just(x1), ty_Integer)
new_esEs7(Just(x0), Just(x1), app(ty_Maybe, x2))
new_compare29(Char(x0), Char(x1))
new_primPlusNat0(Succ(x0), x1)
new_compare7(@0, @0)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_ltEs7(x0, x1, app(ty_[], x2))
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_ltEs4(Left(x0), Left(x1), ty_Float, x2)
new_compare23(x0, x1, False, x2, x3)
new_primCmpNat2(Zero, x0)
new_compare9(x0, x1)
new_lt4(x0, x1, app(ty_[], x2))
new_compare33(x0, x1, x2, x3, x4)
new_primCmpNat1(Succ(x0), Succ(x1))
new_primCmpNat0(x0, Zero)
new_esEs24(x0, x1, ty_Char)
new_esEs8(Left(x0), Left(x1), app(app(ty_FiniteMap, x2), x3), x4)
new_esEs8(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs7(Just(x0), Just(x1), ty_Double)
new_esEs20(x0, x1, app(ty_[], x2))
new_ltEs4(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs4(Right(x0), Right(x1), x2, ty_Int)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, ty_Double)
new_ltEs7(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs20(x0, x1, app(ty_[], x2))
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_esEs8(Right(x0), Right(x1), x2, ty_Int)
new_compare26(x0, x1, True, x2, x3, x4)
new_lt4(x0, x1, ty_Int)
new_esEs21(x0, x1, ty_Ordering)
new_esEs10(:(x0, x1), :(x2, x3), x4)
new_ltEs14(EQ, GT)
new_ltEs14(GT, EQ)
new_ltEs12(x0, x1)
new_esEs7(Nothing, Just(x0), x1)
new_primCompAux0(x0, x1, x2, x3)
new_esEs20(x0, x1, ty_Double)
new_lt18(x0, x1, x2)
new_esEs8(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs26(x0, x1, ty_Int)
new_sizeFM(EmptyFM, x0, x1)
new_ltEs18(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs24(x0, x1, ty_Float)
new_primMulNat0(Succ(x0), Succ(x1))
new_esEs20(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(EQ)
new_ltEs4(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_compare34(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs18(Just(x0), Just(x1), ty_Bool)
new_esEs7(Just(x0), Just(x1), ty_Float)
new_asAs(True, x0)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_primCmpNat1(Zero, Succ(x0))
new_lt5(x0, x1, ty_@0)
new_esEs18(EQ, LT)
new_esEs18(LT, EQ)
new_esEs23(x0, x1, ty_Bool)
new_lt5(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs14(LT, GT)
new_ltEs14(GT, LT)
new_primCompAux00(x0, GT)
new_compare25(x0, x1, False)
new_ltEs4(Right(x0), Right(x1), x2, ty_@0)
new_esEs20(x0, x1, ty_Int)
new_compare34(x0, x1, ty_Float)
new_esEs27(x0, x1, ty_Char)
new_lt20(x0, x1, app(ty_[], x2))
new_esEs23(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_compare32(x0, x1, x2, x3)
new_ltEs7(x0, x1, app(ty_Ratio, x2))
new_lt4(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt17(x0, x1)
new_esEs26(x0, x1, ty_Float)
new_ltEs4(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_ltEs14(GT, GT)
new_lt20(x0, x1, ty_Bool)
new_ltEs18(Just(x0), Just(x1), ty_Char)
new_esEs5(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs25(x0, x1, ty_Bool)
new_esEs19(Double(x0, x1), Double(x2, x3))
new_lt5(x0, x1, ty_Char)
new_not(EQ)
new_esEs10(:(x0, x1), [], x2)
new_esEs10([], :(x0, x1), x2)
new_ltEs20(x0, x1, ty_Double)
new_lt4(x0, x1, ty_Double)
new_compare12(Integer(x0), Integer(x1))
new_esEs7(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_lt10(x0, x1, x2, x3, x4)
new_esEs28(x0, x1, ty_Int)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_ltEs7(x0, x1, ty_Double)
new_lt16(x0, x1)
new_esEs22(GT)
new_ltEs18(Just(x0), Just(x1), ty_Ordering)
new_lt9(x0, x1)
new_esEs15(Integer(x0), Integer(x1))
new_lt5(x0, x1, app(ty_Maybe, x2))
new_compare24(x0, x1, False, x2)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(Nothing, Nothing, x0)
new_esEs8(Left(x0), Left(x1), ty_@0, x2)
new_ltEs4(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs23(x0, x1, app(ty_[], x2))
new_esEs25(x0, x1, ty_Integer)
new_esEs20(x0, x1, ty_Integer)
new_compare18(x0, x1, True)
new_compare11(x0, x1, True, x2)
new_compare18(x0, x1, False)
new_pePe(True, x0, x1, x2, x3)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare6(:%(x0, x1), :%(x2, x3), ty_Int)
new_compare30(Float(x0, x1), Float(x2, x3))
new_lt11(x0, x1)
new_ltEs18(Just(x0), Nothing, x1)
new_esEs27(x0, x1, ty_Bool)
new_esEs18(GT, LT)
new_esEs18(LT, GT)
new_ltEs19(x0, x1, ty_@0)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs21(x0, x1, app(ty_[], x2))
new_esEs9(Float(x0, x1), Float(x2, x3))
new_esEs10([], [], x0)
new_ltEs7(x0, x1, ty_Ordering)
new_ltEs4(Left(x0), Left(x1), ty_Ordering, x2)
new_ltEs18(Nothing, Just(x0), x1)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_esEs25(x0, x1, ty_Char)
new_esEs29(x0, x1, ty_Int)
new_ltEs19(x0, x1, ty_Double)
new_compare14(x0, x1, False, x2, x3, x4)
new_esEs27(x0, x1, ty_Integer)
new_esEs7(Just(x0), Just(x1), ty_@0)
new_lt4(x0, x1, ty_Bool)
new_ltEs4(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_ltEs4(Left(x0), Left(x1), ty_@0, x2)
new_esEs8(Left(x0), Left(x1), ty_Char, x2)
new_ltEs19(x0, x1, ty_Int)
new_compare28(x0, x1, True, x2, x3)
new_esEs14(False, False)
new_ltEs4(Right(x0), Right(x1), x2, ty_Char)
new_primEqInt(Pos(Zero), Pos(Zero))
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_esEs25(x0, x1, ty_@0)
new_lt19(x0, x1, x2, x3)
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_esEs21(x0, x1, ty_Double)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs4(Left(x0), Left(x1), app(ty_[], x2), x3)
new_ltEs20(x0, x1, ty_Int)
new_ltEs18(Just(x0), Just(x1), ty_@0)
new_esEs24(x0, x1, ty_Int)
new_lt20(x0, x1, ty_@0)
new_ltEs4(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs7(Just(x0), Just(x1), ty_Ordering)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, ty_Int)
new_esEs8(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs25(x0, x1, ty_Int)
new_esEs24(x0, x1, ty_Bool)
new_esEs8(Left(x0), Left(x1), ty_Float, x2)
new_ltEs4(Left(x0), Left(x1), ty_Integer, x2)
new_primPlusNat1(Succ(x0), Zero)
new_ltEs15(x0, x1, x2)
new_primMulInt(Pos(x0), Pos(x1))
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs18(Just(x0), Just(x1), ty_Double)
new_not(LT)
new_ltEs11(True, True)
new_esEs8(Right(x0), Right(x1), x2, ty_Char)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_pePe(False, x0, x1, x2, x3)
new_ltEs7(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
↳ 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
↳ UsableRulesProof
↳ QDP
↳ QReductionProof
↳ QDP
↳ QDPSizeChangeProof
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_foldFM_LE(vyy3, Nothing, Branch(Just(vyy600), vyy61, vyy62, vyy63, vyy64), h, ba, bb) → new_foldFM_LE(vyy3, Nothing, vyy63, h, ba, bb)
new_foldFM_LE(vyy3, Nothing, Branch(Nothing, vyy61, vyy62, vyy63, vyy64), h, ba, bb) → new_foldFM_LE(vyy3, Nothing, vyy64, h, ba, bb)
new_foldFM_LE(vyy3, Nothing, Branch(Nothing, vyy61, vyy62, vyy63, vyy64), h, ba, bb) → new_foldFM_LE(vyy3, Nothing, vyy63, h, ba, bb)
R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By using the subterm criterion [20] together with the size-change analysis [32] we have proven that there are no infinite chains for this DP problem. From the DPs we obtained the following set of size-change graphs:
- new_foldFM_LE(vyy3, Nothing, Branch(Just(vyy600), vyy61, vyy62, vyy63, vyy64), h, ba, bb) → new_foldFM_LE(vyy3, Nothing, vyy63, h, ba, bb)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 >= 4, 5 >= 5, 6 >= 6
- new_foldFM_LE(vyy3, Nothing, Branch(Nothing, vyy61, vyy62, vyy63, vyy64), h, ba, bb) → new_foldFM_LE(vyy3, Nothing, vyy64, h, ba, bb)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 2, 3 > 3, 4 >= 4, 5 >= 5, 6 >= 6
- new_foldFM_LE(vyy3, Nothing, Branch(Nothing, vyy61, vyy62, vyy63, vyy64), h, ba, bb) → new_foldFM_LE(vyy3, Nothing, vyy63, h, ba, bb)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 2, 3 > 3, 4 >= 4, 5 >= 5, 6 >= 6
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDPSizeChangeProof
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_foldFM(vyy450, vyy451, vyy74, Branch(vyy4530, vyy4531, vyy4532, vyy4533, vyy4534), h, ba) → new_foldFM(vyy4530, vyy4531, new_foldFM0(vyy450, vyy451, vyy74, vyy4534, h, ba), vyy4533, h, ba)
new_foldFM(vyy450, vyy451, vyy74, Branch(vyy4530, vyy4531, vyy4532, vyy4533, vyy4534), h, ba) → new_foldFM(vyy450, vyy451, vyy74, vyy4534, h, ba)
The TRS R consists of the following rules:
new_foldFM0(vyy450, vyy451, vyy74, EmptyFM, h, ba) → :(@2(vyy450, vyy451), vyy74)
new_foldFM0(vyy450, vyy451, vyy74, Branch(vyy4530, vyy4531, vyy4532, vyy4533, vyy4534), h, ba) → new_foldFM0(vyy4530, vyy4531, new_foldFM0(vyy450, vyy451, vyy74, vyy4534, h, ba), vyy4533, h, ba)
The set Q consists of the following terms:
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
We have to consider all minimal (P,Q,R)-chains.
By using the subterm criterion [20] together with the size-change analysis [32] we have proven that there are no infinite chains for this DP problem. From the DPs we obtained the following set of size-change graphs:
- new_foldFM(vyy450, vyy451, vyy74, Branch(vyy4530, vyy4531, vyy4532, vyy4533, vyy4534), h, ba) → new_foldFM(vyy4530, vyy4531, new_foldFM0(vyy450, vyy451, vyy74, vyy4534, h, ba), vyy4533, h, ba)
The graph contains the following edges 4 > 1, 4 > 2, 4 > 4, 5 >= 5, 6 >= 6
- new_foldFM(vyy450, vyy451, vyy74, Branch(vyy4530, vyy4531, vyy4532, vyy4533, vyy4534), h, ba) → new_foldFM(vyy450, vyy451, vyy74, vyy4534, h, ba)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 > 4, 5 >= 5, 6 >= 6
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDPSizeChangeProof
Q DP problem:
The TRS P consists of the following rules:
new_ltEs0(@3(vyy6000, vyy6001, vyy6002), @3(vyy500, vyy501, vyy502), eh, dg, app(app(ty_Either, hb), hc)) → new_ltEs3(vyy6002, vyy502, hb, hc)
new_ltEs1(:(vyy6000, vyy6001), :(vyy500, vyy501), hd) → new_compare(vyy6001, vyy501, hd)
new_ltEs3(Left(vyy6000), Left(vyy500), app(app(ty_Either, bcg), bch), bca) → new_ltEs3(vyy6000, vyy500, bcg, bch)
new_compare22(vyy6000, vyy500, False, bh, ca) → new_ltEs3(vyy6000, vyy500, bh, ca)
new_compare2(vyy6000, vyy500, False, h, ba) → new_ltEs(vyy6000, vyy500, h, ba)
new_compare(:(vyy6000, vyy6001), :(vyy500, vyy501), hd) → new_primCompAux(vyy6000, vyy500, new_compare3(vyy6001, vyy501, hd), hd)
new_primCompAux(vyy6000, vyy500, vyy56, app(app(app(ty_@3, hg), hh), baa)) → new_compare1(vyy6000, vyy500, hg, hh, baa)
new_ltEs(@2(vyy6000, vyy6001), @2(vyy500, vyy501), cb, app(ty_[], da)) → new_ltEs1(vyy6001, vyy501, da)
new_ltEs0(@3(vyy6000, vyy6001, vyy6002), @3(vyy500, vyy501, vyy502), app(app(app(ty_@3, ea), eb), ec), dg, dh) → new_lt0(vyy6000, vyy500, ea, eb, ec)
new_ltEs(@2(vyy6000, vyy6001), @2(vyy500, vyy501), app(app(ty_@2, h), ba), bb) → new_compare2(vyy6000, vyy500, new_esEs5(vyy6000, vyy500, h, ba), h, ba)
new_ltEs(@2(vyy6000, vyy6001), @2(vyy500, vyy501), cb, app(ty_Maybe, db)) → new_ltEs2(vyy6001, vyy501, db)
new_ltEs0(@3(vyy6000, vyy6001, vyy6002), @3(vyy500, vyy501, vyy502), eh, dg, app(app(ty_@2, gc), gd)) → new_ltEs(vyy6002, vyy502, gc, gd)
new_ltEs0(@3(vyy6000, vyy6001, vyy6002), @3(vyy500, vyy501, vyy502), app(ty_Maybe, ee), dg, dh) → new_lt2(vyy6000, vyy500, ee)
new_ltEs3(Right(vyy6000), Right(vyy500), bda, app(app(app(ty_@3, bdd), bde), bdf)) → new_ltEs0(vyy6000, vyy500, bdd, bde, bdf)
new_primCompAux(vyy6000, vyy500, vyy56, app(app(ty_@2, he), hf)) → new_compare0(vyy6000, vyy500, he, hf)
new_ltEs1(:(vyy6000, vyy6001), :(vyy500, vyy501), hd) → new_primCompAux(vyy6000, vyy500, new_compare3(vyy6001, vyy501, hd), hd)
new_compare0(vyy6000, vyy500, h, ba) → new_compare2(vyy6000, vyy500, new_esEs5(vyy6000, vyy500, h, ba), h, ba)
new_lt3(vyy6000, vyy500, bh, ca) → new_compare22(vyy6000, vyy500, new_esEs8(vyy6000, vyy500, bh, ca), bh, ca)
new_ltEs2(Just(vyy6000), Just(vyy500), app(app(ty_Either, bbe), bbf)) → new_ltEs3(vyy6000, vyy500, bbe, bbf)
new_primCompAux(vyy6000, vyy500, vyy56, app(ty_[], bab)) → new_compare(vyy6000, vyy500, bab)
new_ltEs(@2(vyy6000, vyy6001), @2(vyy500, vyy501), app(ty_[], bf), bb) → new_compare(vyy6000, vyy500, bf)
new_ltEs2(Just(vyy6000), Just(vyy500), app(app(app(ty_@3, bah), bba), bbb)) → new_ltEs0(vyy6000, vyy500, bah, bba, bbb)
new_primCompAux(vyy6000, vyy500, vyy56, app(app(ty_Either, bad), bae)) → new_compare5(vyy6000, vyy500, bad, bae)
new_ltEs0(@3(vyy6000, vyy6001, vyy6002), @3(vyy500, vyy501, vyy502), eh, app(app(app(ty_@3, fc), fd), ff), dh) → new_lt0(vyy6001, vyy501, fc, fd, ff)
new_compare1(vyy6000, vyy500, bc, bd, be) → new_compare20(vyy6000, vyy500, new_esEs6(vyy6000, vyy500, bc, bd, be), bc, bd, be)
new_ltEs3(Right(vyy6000), Right(vyy500), bda, app(app(ty_Either, bea), beb)) → new_ltEs3(vyy6000, vyy500, bea, beb)
new_lt2(vyy6000, vyy500, bg) → new_compare21(vyy6000, vyy500, new_esEs7(vyy6000, vyy500, bg), bg)
new_ltEs2(Just(vyy6000), Just(vyy500), app(ty_[], bbc)) → new_ltEs1(vyy6000, vyy500, bbc)
new_ltEs3(Left(vyy6000), Left(vyy500), app(app(ty_@2, bbg), bbh), bca) → new_ltEs(vyy6000, vyy500, bbg, bbh)
new_ltEs3(Right(vyy6000), Right(vyy500), bda, app(ty_Maybe, bdh)) → new_ltEs2(vyy6000, vyy500, bdh)
new_ltEs0(@3(vyy6000, vyy6001, vyy6002), @3(vyy500, vyy501, vyy502), app(ty_[], ed), dg, dh) → new_lt1(vyy6000, vyy500, ed)
new_ltEs3(Right(vyy6000), Right(vyy500), bda, app(ty_[], bdg)) → new_ltEs1(vyy6000, vyy500, bdg)
new_ltEs0(@3(vyy6000, vyy6001, vyy6002), @3(vyy500, vyy501, vyy502), eh, dg, app(app(app(ty_@3, ge), gf), gg)) → new_ltEs0(vyy6002, vyy502, ge, gf, gg)
new_ltEs0(@3(vyy6000, vyy6001, vyy6002), @3(vyy500, vyy501, vyy502), eh, app(app(ty_@2, fa), fb), dh) → new_lt(vyy6001, vyy501, fa, fb)
new_ltEs0(@3(vyy6000, vyy6001, vyy6002), @3(vyy500, vyy501, vyy502), eh, dg, app(ty_[], gh)) → new_ltEs1(vyy6002, vyy502, gh)
new_lt1(vyy6000, vyy500, bf) → new_compare(vyy6000, vyy500, bf)
new_ltEs(@2(vyy6000, vyy6001), @2(vyy500, vyy501), app(ty_Maybe, bg), bb) → new_compare21(vyy6000, vyy500, new_esEs7(vyy6000, vyy500, bg), bg)
new_ltEs2(Just(vyy6000), Just(vyy500), app(app(ty_@2, baf), bag)) → new_ltEs(vyy6000, vyy500, baf, bag)
new_ltEs0(@3(vyy6000, vyy6001, vyy6002), @3(vyy500, vyy501, vyy502), eh, dg, app(ty_Maybe, ha)) → new_ltEs2(vyy6002, vyy502, ha)
new_ltEs2(Just(vyy6000), Just(vyy500), app(ty_Maybe, bbd)) → new_ltEs2(vyy6000, vyy500, bbd)
new_compare(:(vyy6000, vyy6001), :(vyy500, vyy501), hd) → new_compare(vyy6001, vyy501, hd)
new_compare21(vyy6000, vyy500, False, bg) → new_ltEs2(vyy6000, vyy500, bg)
new_ltEs(@2(vyy6000, vyy6001), @2(vyy500, vyy501), cb, app(app(ty_Either, dc), dd)) → new_ltEs3(vyy6001, vyy501, dc, dd)
new_ltEs(@2(vyy6000, vyy6001), @2(vyy500, vyy501), cb, app(app(ty_@2, cc), cd)) → new_ltEs(vyy6001, vyy501, cc, cd)
new_ltEs3(Right(vyy6000), Right(vyy500), bda, app(app(ty_@2, bdb), bdc)) → new_ltEs(vyy6000, vyy500, bdb, bdc)
new_ltEs3(Left(vyy6000), Left(vyy500), app(ty_[], bce), bca) → new_ltEs1(vyy6000, vyy500, bce)
new_compare4(vyy6000, vyy500, bg) → new_compare21(vyy6000, vyy500, new_esEs7(vyy6000, vyy500, bg), bg)
new_ltEs(@2(vyy6000, vyy6001), @2(vyy500, vyy501), app(app(ty_Either, bh), ca), bb) → new_compare22(vyy6000, vyy500, new_esEs8(vyy6000, vyy500, bh, ca), bh, ca)
new_primCompAux(vyy6000, vyy500, vyy56, app(ty_Maybe, bac)) → new_compare4(vyy6000, vyy500, bac)
new_compare5(vyy6000, vyy500, bh, ca) → new_compare22(vyy6000, vyy500, new_esEs8(vyy6000, vyy500, bh, ca), bh, ca)
new_ltEs(@2(vyy6000, vyy6001), @2(vyy500, vyy501), app(app(app(ty_@3, bc), bd), be), bb) → new_compare20(vyy6000, vyy500, new_esEs6(vyy6000, vyy500, bc, bd, be), bc, bd, be)
new_ltEs0(@3(vyy6000, vyy6001, vyy6002), @3(vyy500, vyy501, vyy502), app(app(ty_Either, ef), eg), dg, dh) → new_lt3(vyy6000, vyy500, ef, eg)
new_ltEs0(@3(vyy6000, vyy6001, vyy6002), @3(vyy500, vyy501, vyy502), eh, app(ty_Maybe, fh), dh) → new_lt2(vyy6001, vyy501, fh)
new_lt0(vyy6000, vyy500, bc, bd, be) → new_compare20(vyy6000, vyy500, new_esEs6(vyy6000, vyy500, bc, bd, be), bc, bd, be)
new_compare20(vyy6000, vyy500, False, bc, bd, be) → new_ltEs0(vyy6000, vyy500, bc, bd, be)
new_ltEs0(@3(vyy6000, vyy6001, vyy6002), @3(vyy500, vyy501, vyy502), eh, app(app(ty_Either, ga), gb), dh) → new_lt3(vyy6001, vyy501, ga, gb)
new_ltEs(@2(vyy6000, vyy6001), @2(vyy500, vyy501), cb, app(app(app(ty_@3, ce), cf), cg)) → new_ltEs0(vyy6001, vyy501, ce, cf, cg)
new_ltEs0(@3(vyy6000, vyy6001, vyy6002), @3(vyy500, vyy501, vyy502), eh, app(ty_[], fg), dh) → new_lt1(vyy6001, vyy501, fg)
new_lt(vyy6000, vyy500, h, ba) → new_compare2(vyy6000, vyy500, new_esEs5(vyy6000, vyy500, h, ba), h, ba)
new_ltEs3(Left(vyy6000), Left(vyy500), app(app(app(ty_@3, bcb), bcc), bcd), bca) → new_ltEs0(vyy6000, vyy500, bcb, bcc, bcd)
new_ltEs3(Left(vyy6000), Left(vyy500), app(ty_Maybe, bcf), bca) → new_ltEs2(vyy6000, vyy500, bcf)
new_ltEs0(@3(vyy6000, vyy6001, vyy6002), @3(vyy500, vyy501, vyy502), app(app(ty_@2, de), df), dg, dh) → new_lt(vyy6000, vyy500, de, df)
The TRS R consists of the following rules:
new_compare34(vyy6000, vyy500, app(app(ty_Either, bad), bae)) → new_compare32(vyy6000, vyy500, bad, bae)
new_esEs7(Just(vyy440), Just(vyy450), app(ty_Maybe, bef)) → new_esEs7(vyy440, vyy450, bef)
new_esEs20(vyy440, vyy450, app(ty_Maybe, bhb)) → new_esEs7(vyy440, vyy450, bhb)
new_esEs23(vyy440, vyy450, ty_Ordering) → new_esEs18(vyy440, vyy450)
new_compare3(:(vyy6000, vyy6001), :(vyy500, vyy501), hd) → new_primCompAux0(vyy6000, vyy500, new_compare3(vyy6001, vyy501, hd), hd)
new_lt20(vyy6000, vyy500, ty_Int) → new_lt16(vyy6000, vyy500)
new_primCmpNat2(Zero, vyy60000) → LT
new_ltEs9(@2(vyy6000, vyy6001), @2(vyy500, vyy501), cb, bb) → new_pePe(new_lt20(vyy6000, vyy500, cb), vyy6000, vyy500, new_ltEs19(vyy6001, vyy501, bb), cb)
new_esEs18(LT, LT) → True
new_esEs20(vyy440, vyy450, ty_Double) → new_esEs19(vyy440, vyy450)
new_lt4(vyy6000, vyy500, ty_Int) → new_lt16(vyy6000, vyy500)
new_lt20(vyy6000, vyy500, app(app(ty_Either, bh), ca)) → new_lt19(vyy6000, vyy500, bh, ca)
new_ltEs4(Left(vyy6000), Left(vyy500), app(ty_Maybe, bcf), bca) → new_ltEs18(vyy6000, vyy500, bcf)
new_esEs25(vyy441, vyy451, ty_Ordering) → new_esEs18(vyy441, vyy451)
new_ltEs14(GT, GT) → True
new_primCmpNat1(Zero, Succ(vyy50000)) → LT
new_ltEs18(Just(vyy6000), Just(vyy500), ty_Float) → new_ltEs8(vyy6000, vyy500)
new_compare10(vyy6000, vyy500, True, bh, ca) → LT
new_primCompAux0(vyy6000, vyy500, vyy56, hd) → new_primCompAux00(vyy56, new_compare34(vyy6000, vyy500, hd))
new_ltEs18(Just(vyy6000), Just(vyy500), app(ty_Maybe, bbd)) → new_ltEs18(vyy6000, vyy500, bbd)
new_esEs18(LT, EQ) → False
new_esEs18(EQ, LT) → False
new_esEs27(vyy44, vyy45, app(ty_Maybe, bec)) → new_esEs7(vyy44, vyy45, bec)
new_esEs20(vyy440, vyy450, ty_Float) → new_esEs9(vyy440, vyy450)
new_esEs23(vyy440, vyy450, ty_Bool) → new_esEs14(vyy440, vyy450)
new_ltEs18(Just(vyy6000), Just(vyy500), ty_@0) → new_ltEs17(vyy6000, vyy500)
new_ltEs4(Left(vyy6000), Left(vyy500), app(app(app(ty_@3, bcb), bcc), bcd), bca) → new_ltEs6(vyy6000, vyy500, bcb, bcc, bcd)
new_esEs8(Left(vyy440), Left(vyy450), ty_Integer, dba) → new_esEs15(vyy440, vyy450)
new_compare14(vyy6000, vyy500, True, bc, bd, be) → LT
new_ltEs19(vyy6001, vyy501, app(ty_Ratio, dec)) → new_ltEs5(vyy6001, vyy501, dec)
new_esEs7(Just(vyy440), Just(vyy450), ty_Double) → new_esEs19(vyy440, vyy450)
new_primMulNat0(Zero, Zero) → Zero
new_lt4(vyy6000, vyy500, ty_Double) → new_lt8(vyy6000, vyy500)
new_compare32(vyy6000, vyy500, bh, ca) → new_compare23(vyy6000, vyy500, new_esEs8(vyy6000, vyy500, bh, ca), bh, ca)
new_esEs8(Left(vyy440), Left(vyy450), app(app(ty_FiniteMap, dcb), dcc), dba) → new_esEs16(vyy440, vyy450, dcb, dcc)
new_sr(Integer(vyy60000), Integer(vyy5010)) → Integer(new_primMulInt(vyy60000, vyy5010))
new_esEs21(vyy441, vyy451, app(app(ty_Either, cad), cae)) → new_esEs8(vyy441, vyy451, cad, cae)
new_ltEs4(Right(vyy6000), Right(vyy500), bda, ty_Integer) → new_ltEs12(vyy6000, vyy500)
new_esEs21(vyy441, vyy451, app(ty_[], cbb)) → new_esEs10(vyy441, vyy451, cbb)
new_lt20(vyy6000, vyy500, ty_Float) → new_lt6(vyy6000, vyy500)
new_ltEs4(Left(vyy6000), Left(vyy500), app(app(ty_@2, bbg), bbh), bca) → new_ltEs9(vyy6000, vyy500, bbg, bbh)
new_ltEs4(Right(vyy6000), Right(vyy500), bda, app(app(app(ty_@3, bdd), bde), bdf)) → new_ltEs6(vyy6000, vyy500, bdd, bde, bdf)
new_esEs24(vyy440, vyy450, ty_Integer) → new_esEs15(vyy440, vyy450)
new_esEs16(vyy44, vyy45, cca, ccb) → new_asAs(new_esEs17(new_sizeFM(vyy44, cca, ccb), new_sizeFM(vyy45, cca, ccb)), new_esEs10(new_fmToList(vyy44, cca, ccb), new_fmToList(vyy45, cca, ccb), app(app(ty_@2, cca), ccb)))
new_esEs21(vyy441, vyy451, app(app(ty_FiniteMap, cbf), cbg)) → new_esEs16(vyy441, vyy451, cbf, cbg)
new_not(GT) → False
new_lt5(vyy6001, vyy501, ty_Ordering) → new_lt13(vyy6001, vyy501)
new_esEs8(Right(vyy440), Right(vyy450), dcd, app(app(ty_FiniteMap, ddg), ddh)) → new_esEs16(vyy440, vyy450, ddg, ddh)
new_esEs26(vyy442, vyy452, ty_Float) → new_esEs9(vyy442, vyy452)
new_ltEs4(Right(vyy6000), Right(vyy500), bda, app(ty_Maybe, bdh)) → new_ltEs18(vyy6000, vyy500, bdh)
new_lt4(vyy6000, vyy500, app(ty_[], ed)) → new_lt15(vyy6000, vyy500, ed)
new_ltEs4(Left(vyy6000), Left(vyy500), ty_Float, bca) → new_ltEs8(vyy6000, vyy500)
new_esEs26(vyy442, vyy452, app(ty_[], daa)) → new_esEs10(vyy442, vyy452, daa)
new_lt4(vyy6000, vyy500, app(ty_Maybe, ee)) → new_lt18(vyy6000, vyy500, ee)
new_ltEs4(Right(vyy6000), Right(vyy500), bda, app(ty_Ratio, deb)) → new_ltEs5(vyy6000, vyy500, deb)
new_esEs8(Left(vyy440), Left(vyy450), ty_Bool, dba) → new_esEs14(vyy440, vyy450)
new_esEs24(vyy440, vyy450, app(app(ty_@2, cfb), cfc)) → new_esEs5(vyy440, vyy450, cfb, cfc)
new_esEs8(Left(vyy440), Left(vyy450), app(app(ty_@2, dbg), dbh), dba) → new_esEs5(vyy440, vyy450, dbg, dbh)
new_primCmpNat1(Succ(vyy600000), Succ(vyy50000)) → new_primCmpNat1(vyy600000, vyy50000)
new_esEs9(Float(vyy440, vyy441), Float(vyy450, vyy451)) → new_esEs17(new_sr0(vyy440, vyy450), new_sr0(vyy441, vyy451))
new_ltEs4(Left(vyy6000), Left(vyy500), ty_Int, bca) → new_ltEs16(vyy6000, vyy500)
new_esEs15(Integer(vyy440), Integer(vyy450)) → new_primEqInt(vyy440, vyy450)
new_esEs18(LT, GT) → False
new_esEs18(GT, LT) → False
new_ltEs7(vyy6002, vyy502, app(ty_Maybe, ha)) → new_ltEs18(vyy6002, vyy502, ha)
new_compare34(vyy6000, vyy500, app(app(app(ty_@3, hg), hh), baa)) → new_compare33(vyy6000, vyy500, hg, hh, baa)
new_esEs26(vyy442, vyy452, ty_Char) → new_esEs13(vyy442, vyy452)
new_esEs21(vyy441, vyy451, ty_Int) → new_esEs17(vyy441, vyy451)
new_ltEs7(vyy6002, vyy502, app(app(ty_@2, gc), gd)) → new_ltEs9(vyy6002, vyy502, gc, gd)
new_foldFM0(vyy450, vyy451, vyy74, EmptyFM, cca, ccb) → :(@2(vyy450, vyy451), vyy74)
new_esEs29(vyy441, vyy451, ty_Integer) → new_esEs15(vyy441, vyy451)
new_esEs25(vyy441, vyy451, app(ty_[], cge)) → new_esEs10(vyy441, vyy451, cge)
new_ltEs19(vyy6001, vyy501, app(app(ty_Either, dc), dd)) → new_ltEs4(vyy6001, vyy501, dc, dd)
new_compare34(vyy6000, vyy500, app(ty_[], bab)) → new_compare3(vyy6000, vyy500, bab)
new_compare27(vyy6000, vyy500, False) → new_compare18(vyy6000, vyy500, new_ltEs14(vyy6000, vyy500))
new_compare34(vyy6000, vyy500, ty_Integer) → new_compare12(vyy6000, vyy500)
new_esEs25(vyy441, vyy451, ty_Bool) → new_esEs14(vyy441, vyy451)
new_lt5(vyy6001, vyy501, ty_@0) → new_lt17(vyy6001, vyy501)
new_ltEs7(vyy6002, vyy502, ty_Double) → new_ltEs10(vyy6002, vyy502)
new_ltEs14(GT, EQ) → False
new_esEs22(EQ) → False
new_esEs23(vyy440, vyy450, app(app(ty_Either, ccd), cce)) → new_esEs8(vyy440, vyy450, ccd, cce)
new_esEs20(vyy440, vyy450, app(ty_Ratio, caa)) → new_esEs12(vyy440, vyy450, caa)
new_esEs26(vyy442, vyy452, app(app(ty_Either, chc), chd)) → new_esEs8(vyy442, vyy452, chc, chd)
new_esEs27(vyy44, vyy45, app(app(ty_FiniteMap, cca), ccb)) → new_esEs16(vyy44, vyy45, cca, ccb)
new_esEs24(vyy440, vyy450, app(ty_Maybe, cee)) → new_esEs7(vyy440, vyy450, cee)
new_compare34(vyy6000, vyy500, app(app(ty_@2, he), hf)) → new_compare31(vyy6000, vyy500, he, hf)
new_esEs24(vyy440, vyy450, ty_@0) → new_esEs11(vyy440, vyy450)
new_lt20(vyy6000, vyy500, app(app(app(ty_@3, bc), bd), be)) → new_lt10(vyy6000, vyy500, bc, bd, be)
new_esEs23(vyy440, vyy450, app(ty_Maybe, ccf)) → new_esEs7(vyy440, vyy450, ccf)
new_ltEs7(vyy6002, vyy502, app(ty_[], gh)) → new_ltEs15(vyy6002, vyy502, gh)
new_lt5(vyy6001, vyy501, app(app(app(ty_@3, fc), fd), ff)) → new_lt10(vyy6001, vyy501, fc, fd, ff)
new_ltEs4(Right(vyy6000), Right(vyy500), bda, app(app(ty_Either, bea), beb)) → new_ltEs4(vyy6000, vyy500, bea, beb)
new_compare13(vyy6000, vyy500, False, h, ba) → GT
new_ltEs18(Just(vyy6000), Just(vyy500), app(ty_Ratio, bge)) → new_ltEs5(vyy6000, vyy500, bge)
new_ltEs11(False, True) → True
new_esEs20(vyy440, vyy450, app(app(ty_@2, bhg), bhh)) → new_esEs5(vyy440, vyy450, bhg, bhh)
new_compare19(vyy6000, vyy500, True) → LT
new_lt20(vyy6000, vyy500, app(app(ty_@2, h), ba)) → new_lt7(vyy6000, vyy500, h, ba)
new_ltEs4(Left(vyy6000), Right(vyy500), bda, bca) → True
new_esEs21(vyy441, vyy451, ty_Bool) → new_esEs14(vyy441, vyy451)
new_lt4(vyy6000, vyy500, app(app(ty_Either, ef), eg)) → new_lt19(vyy6000, vyy500, ef, eg)
new_esEs21(vyy441, vyy451, ty_Char) → new_esEs13(vyy441, vyy451)
new_compare24(vyy6000, vyy500, False, bg) → new_compare11(vyy6000, vyy500, new_ltEs18(vyy6000, vyy500, bg), bg)
new_ltEs15(vyy600, vyy50, hd) → new_not(new_compare3(vyy600, vyy50, hd))
new_esEs7(Just(vyy440), Just(vyy450), ty_Int) → new_esEs17(vyy440, vyy450)
new_esEs21(vyy441, vyy451, ty_Double) → new_esEs19(vyy441, vyy451)
new_lt14(vyy6000, vyy500, cbh) → new_esEs22(new_compare6(vyy6000, vyy500, cbh))
new_esEs20(vyy440, vyy450, ty_Ordering) → new_esEs18(vyy440, vyy450)
new_esEs20(vyy440, vyy450, ty_@0) → new_esEs11(vyy440, vyy450)
new_esEs23(vyy440, vyy450, ty_Double) → new_esEs19(vyy440, vyy450)
new_compare34(vyy6000, vyy500, ty_@0) → new_compare7(vyy6000, vyy500)
new_esEs20(vyy440, vyy450, app(app(app(ty_@3, bhc), bhd), bhe)) → new_esEs6(vyy440, vyy450, bhc, bhd, bhe)
new_lt4(vyy6000, vyy500, app(app(ty_@2, de), df)) → new_lt7(vyy6000, vyy500, de, df)
new_esEs8(Left(vyy440), Left(vyy450), ty_Char, dba) → new_esEs13(vyy440, vyy450)
new_ltEs18(Just(vyy6000), Just(vyy500), app(app(app(ty_@3, bah), bba), bbb)) → new_ltEs6(vyy6000, vyy500, bah, bba, bbb)
new_primEqNat0(Zero, Zero) → True
new_esEs27(vyy44, vyy45, ty_Ordering) → new_esEs18(vyy44, vyy45)
new_esEs23(vyy440, vyy450, ty_@0) → new_esEs11(vyy440, vyy450)
new_esEs8(Right(vyy440), Right(vyy450), dcd, ty_Double) → new_esEs19(vyy440, vyy450)
new_lt15(vyy6000, vyy500, bf) → new_esEs22(new_compare3(vyy6000, vyy500, bf))
new_ltEs4(Right(vyy6000), Right(vyy500), bda, ty_Ordering) → new_ltEs14(vyy6000, vyy500)
new_compare11(vyy6000, vyy500, True, bg) → LT
new_esEs8(Right(vyy440), Right(vyy450), dcd, ty_@0) → new_esEs11(vyy440, vyy450)
new_ltEs4(Right(vyy6000), Right(vyy500), bda, app(app(ty_@2, bdb), bdc)) → new_ltEs9(vyy6000, vyy500, bdb, bdc)
new_esEs27(vyy44, vyy45, ty_Char) → new_esEs13(vyy44, vyy45)
new_ltEs19(vyy6001, vyy501, ty_Float) → new_ltEs8(vyy6001, vyy501)
new_compare17(Double(vyy6000, vyy6001), Double(vyy500, vyy501)) → new_compare16(new_sr0(vyy6000, vyy500), new_sr0(vyy6001, vyy501))
new_ltEs18(Just(vyy6000), Just(vyy500), ty_Int) → new_ltEs16(vyy6000, vyy500)
new_esEs7(Just(vyy440), Just(vyy450), app(app(ty_FiniteMap, bff), bfg)) → new_esEs16(vyy440, vyy450, bff, bfg)
new_esEs13(Char(vyy440), Char(vyy450)) → new_primEqInt(vyy440, vyy450)
new_ltEs18(Just(vyy6000), Just(vyy500), ty_Double) → new_ltEs10(vyy6000, vyy500)
new_ltEs14(EQ, LT) → False
new_primCmpNat1(Zero, Zero) → EQ
new_esEs25(vyy441, vyy451, ty_Int) → new_esEs17(vyy441, vyy451)
new_primCmpInt(Neg(Zero), Neg(Succ(vyy5000))) → new_primCmpNat0(vyy5000, Zero)
new_esEs8(Left(vyy440), Left(vyy450), ty_Double, dba) → new_esEs19(vyy440, vyy450)
new_esEs8(Right(vyy440), Right(vyy450), dcd, ty_Char) → new_esEs13(vyy440, vyy450)
new_primPlusNat0(Succ(vyy750), vyy50000) → Succ(Succ(new_primPlusNat1(vyy750, vyy50000)))
new_esEs21(vyy441, vyy451, ty_Float) → new_esEs9(vyy441, vyy451)
new_esEs7(Just(vyy440), Just(vyy450), app(ty_[], bfb)) → new_esEs10(vyy440, vyy450, bfb)
new_esEs23(vyy440, vyy450, ty_Float) → new_esEs9(vyy440, vyy450)
new_esEs26(vyy442, vyy452, app(app(app(ty_@3, chf), chg), chh)) → new_esEs6(vyy442, vyy452, chf, chg, chh)
new_ltEs7(vyy6002, vyy502, ty_Ordering) → new_ltEs14(vyy6002, vyy502)
new_ltEs19(vyy6001, vyy501, ty_Double) → new_ltEs10(vyy6001, vyy501)
new_esEs18(EQ, GT) → False
new_esEs18(GT, EQ) → False
new_lt20(vyy6000, vyy500, ty_Bool) → new_lt9(vyy6000, vyy500)
new_primCmpNat1(Succ(vyy600000), Zero) → GT
new_primEqInt(Neg(Succ(vyy4400)), Neg(Succ(vyy4500))) → new_primEqNat0(vyy4400, vyy4500)
new_compare25(vyy6000, vyy500, True) → EQ
new_ltEs4(Right(vyy6000), Right(vyy500), bda, ty_Float) → new_ltEs8(vyy6000, vyy500)
new_compare13(vyy6000, vyy500, True, h, ba) → LT
new_esEs25(vyy441, vyy451, app(app(ty_FiniteMap, cha), chb)) → new_esEs16(vyy441, vyy451, cha, chb)
new_esEs24(vyy440, vyy450, ty_Bool) → new_esEs14(vyy440, vyy450)
new_primPlusNat1(Succ(vyy7500), Zero) → Succ(vyy7500)
new_primPlusNat1(Zero, Succ(vyy500000)) → Succ(vyy500000)
new_ltEs4(Left(vyy6000), Left(vyy500), ty_Bool, bca) → new_ltEs11(vyy6000, vyy500)
new_esEs8(Right(vyy440), Right(vyy450), dcd, app(app(ty_Either, dce), dcf)) → new_esEs8(vyy440, vyy450, dce, dcf)
new_esEs8(Right(vyy440), Left(vyy450), dcd, dba) → False
new_esEs8(Left(vyy440), Right(vyy450), dcd, dba) → False
new_lt4(vyy6000, vyy500, ty_Char) → new_lt12(vyy6000, vyy500)
new_compare3([], :(vyy500, vyy501), hd) → LT
new_esEs20(vyy440, vyy450, app(app(ty_Either, bgh), bha)) → new_esEs8(vyy440, vyy450, bgh, bha)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_lt20(vyy6000, vyy500, app(ty_Maybe, bg)) → new_lt18(vyy6000, vyy500, bg)
new_esEs24(vyy440, vyy450, app(app(app(ty_@3, cef), ceg), ceh)) → new_esEs6(vyy440, vyy450, cef, ceg, ceh)
new_compare3(:(vyy6000, vyy6001), [], hd) → GT
new_lt5(vyy6001, vyy501, ty_Integer) → new_lt11(vyy6001, vyy501)
new_lt5(vyy6001, vyy501, app(app(ty_@2, fa), fb)) → new_lt7(vyy6001, vyy501, fa, fb)
new_compare18(vyy6000, vyy500, False) → GT
new_lt5(vyy6001, vyy501, ty_Int) → new_lt16(vyy6001, vyy501)
new_esEs29(vyy441, vyy451, ty_Int) → new_esEs17(vyy441, vyy451)
new_ltEs4(Left(vyy6000), Left(vyy500), app(app(ty_Either, bcg), bch), bca) → new_ltEs4(vyy6000, vyy500, bcg, bch)
new_primEqInt(Neg(Succ(vyy4400)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(vyy4500))) → False
new_lt20(vyy6000, vyy500, ty_Integer) → new_lt11(vyy6000, vyy500)
new_esEs26(vyy442, vyy452, app(app(ty_FiniteMap, dae), daf)) → new_esEs16(vyy442, vyy452, dae, daf)
new_ltEs7(vyy6002, vyy502, app(ty_Ratio, bgc)) → new_ltEs5(vyy6002, vyy502, bgc)
new_lt20(vyy6000, vyy500, ty_Ordering) → new_lt13(vyy6000, vyy500)
new_esEs27(vyy44, vyy45, app(app(ty_Either, dcd), dba)) → new_esEs8(vyy44, vyy45, dcd, dba)
new_esEs8(Left(vyy440), Left(vyy450), app(ty_[], dbf), dba) → new_esEs10(vyy440, vyy450, dbf)
new_esEs12(:%(vyy440, vyy441), :%(vyy450, vyy451), dee) → new_asAs(new_esEs28(vyy440, vyy450, dee), new_esEs29(vyy441, vyy451, dee))
new_compare34(vyy6000, vyy500, ty_Char) → new_compare29(vyy6000, vyy500)
new_foldFM0(vyy450, vyy451, vyy74, Branch(vyy4530, vyy4531, vyy4532, vyy4533, vyy4534), cca, ccb) → new_foldFM0(vyy4530, vyy4531, new_foldFM0(vyy450, vyy451, vyy74, vyy4534, cca, ccb), vyy4533, cca, ccb)
new_compare34(vyy6000, vyy500, ty_Double) → new_compare17(vyy6000, vyy500)
new_esEs26(vyy442, vyy452, ty_@0) → new_esEs11(vyy442, vyy452)
new_compare25(vyy6000, vyy500, False) → new_compare19(vyy6000, vyy500, new_ltEs11(vyy6000, vyy500))
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_esEs24(vyy440, vyy450, ty_Ordering) → new_esEs18(vyy440, vyy450)
new_esEs10(:(vyy440, vyy441), [], ccc) → False
new_esEs10([], :(vyy450, vyy451), ccc) → False
new_lt20(vyy6000, vyy500, ty_Double) → new_lt8(vyy6000, vyy500)
new_sizeFM(EmptyFM, cca, ccb) → Pos(Zero)
new_compare11(vyy6000, vyy500, False, bg) → GT
new_compare6(:%(vyy6000, vyy6001), :%(vyy500, vyy501), ty_Integer) → new_compare12(new_sr(vyy6000, vyy501), new_sr(vyy500, vyy6001))
new_primEqInt(Pos(Succ(vyy4400)), Pos(Succ(vyy4500))) → new_primEqNat0(vyy4400, vyy4500)
new_compare10(vyy6000, vyy500, False, bh, ca) → GT
new_esEs24(vyy440, vyy450, app(app(ty_FiniteMap, cfe), cff)) → new_esEs16(vyy440, vyy450, cfe, cff)
new_esEs24(vyy440, vyy450, app(app(ty_Either, cec), ced)) → new_esEs8(vyy440, vyy450, cec, ced)
new_esEs8(Left(vyy440), Left(vyy450), app(ty_Maybe, dbb), dba) → new_esEs7(vyy440, vyy450, dbb)
new_esEs7(Just(vyy440), Just(vyy450), ty_Float) → new_esEs9(vyy440, vyy450)
new_esEs14(True, False) → False
new_esEs14(False, True) → False
new_ltEs4(Right(vyy6000), Right(vyy500), bda, app(ty_[], bdg)) → new_ltEs15(vyy6000, vyy500, bdg)
new_esEs26(vyy442, vyy452, ty_Integer) → new_esEs15(vyy442, vyy452)
new_ltEs11(True, False) → False
new_ltEs18(Just(vyy6000), Just(vyy500), app(app(ty_Either, bbe), bbf)) → new_ltEs4(vyy6000, vyy500, bbe, bbf)
new_esEs8(Left(vyy440), Left(vyy450), app(app(app(ty_@3, dbc), dbd), dbe), dba) → new_esEs6(vyy440, vyy450, dbc, dbd, dbe)
new_esEs10([], [], ccc) → True
new_esEs24(vyy440, vyy450, ty_Int) → new_esEs17(vyy440, vyy450)
new_primEqNat0(Succ(vyy44000), Succ(vyy45000)) → new_primEqNat0(vyy44000, vyy45000)
new_compare7(@0, @0) → EQ
new_esEs21(vyy441, vyy451, app(ty_Ratio, cbe)) → new_esEs12(vyy441, vyy451, cbe)
new_compare34(vyy6000, vyy500, ty_Float) → new_compare30(vyy6000, vyy500)
new_ltEs18(Just(vyy6000), Just(vyy500), ty_Ordering) → new_ltEs14(vyy6000, vyy500)
new_primCompAux00(vyy60, LT) → LT
new_ltEs4(Left(vyy6000), Left(vyy500), ty_Char, bca) → new_ltEs13(vyy6000, vyy500)
new_esEs24(vyy440, vyy450, app(ty_Ratio, cfd)) → new_esEs12(vyy440, vyy450, cfd)
new_esEs24(vyy440, vyy450, ty_Float) → new_esEs9(vyy440, vyy450)
new_esEs23(vyy440, vyy450, app(app(ty_FiniteMap, cdf), cdg)) → new_esEs16(vyy440, vyy450, cdf, cdg)
new_esEs5(@2(vyy440, vyy441), @2(vyy450, vyy451), bgf, bgg) → new_asAs(new_esEs20(vyy440, vyy450, bgf), new_esEs21(vyy441, vyy451, bgg))
new_esEs7(Nothing, Nothing, bec) → True
new_esEs8(Right(vyy440), Right(vyy450), dcd, ty_Float) → new_esEs9(vyy440, vyy450)
new_primEqInt(Pos(Succ(vyy4400)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(vyy4500))) → False
new_ltEs12(vyy600, vyy50) → new_not(new_compare12(vyy600, vyy50))
new_esEs23(vyy440, vyy450, ty_Char) → new_esEs13(vyy440, vyy450)
new_compare34(vyy6000, vyy500, ty_Int) → new_compare16(vyy6000, vyy500)
new_esEs8(Right(vyy440), Right(vyy450), dcd, ty_Bool) → new_esEs14(vyy440, vyy450)
new_lt10(vyy6000, vyy500, bc, bd, be) → new_esEs22(new_compare33(vyy6000, vyy500, bc, bd, be))
new_ltEs4(Right(vyy6000), Right(vyy500), bda, ty_@0) → new_ltEs17(vyy6000, vyy500)
new_ltEs18(Nothing, Nothing, bgd) → True
new_compare18(vyy6000, vyy500, True) → LT
new_esEs23(vyy440, vyy450, app(app(ty_@2, cdc), cdd)) → new_esEs5(vyy440, vyy450, cdc, cdd)
new_esEs6(@3(vyy440, vyy441, vyy442), @3(vyy450, vyy451, vyy452), cdh, cea, ceb) → new_asAs(new_esEs24(vyy440, vyy450, cdh), new_asAs(new_esEs25(vyy441, vyy451, cea), new_esEs26(vyy442, vyy452, ceb)))
new_primCmpInt(Neg(Zero), Pos(Succ(vyy5000))) → LT
new_esEs8(Right(vyy440), Right(vyy450), dcd, ty_Ordering) → new_esEs18(vyy440, vyy450)
new_compare19(vyy6000, vyy500, False) → GT
new_ltEs7(vyy6002, vyy502, ty_Int) → new_ltEs16(vyy6002, vyy502)
new_lt4(vyy6000, vyy500, ty_Float) → new_lt6(vyy6000, vyy500)
new_compare14(vyy6000, vyy500, False, bc, bd, be) → GT
new_compare28(vyy6000, vyy500, False, h, ba) → new_compare13(vyy6000, vyy500, new_ltEs9(vyy6000, vyy500, h, ba), h, ba)
new_ltEs7(vyy6002, vyy502, ty_Bool) → new_ltEs11(vyy6002, vyy502)
new_compare26(vyy6000, vyy500, False, bc, bd, be) → new_compare14(vyy6000, vyy500, new_ltEs6(vyy6000, vyy500, bc, bd, be), bc, bd, be)
new_primPlusNat1(Succ(vyy7500), Succ(vyy500000)) → Succ(Succ(new_primPlusNat1(vyy7500, vyy500000)))
new_compare28(vyy6000, vyy500, True, h, ba) → EQ
new_esEs7(Just(vyy440), Just(vyy450), ty_Integer) → new_esEs15(vyy440, vyy450)
new_primEqInt(Pos(Succ(vyy4400)), Neg(vyy450)) → False
new_primEqInt(Neg(Succ(vyy4400)), Pos(vyy450)) → False
new_esEs7(Nothing, Just(vyy450), bec) → False
new_esEs7(Just(vyy440), Nothing, bec) → False
new_esEs20(vyy440, vyy450, ty_Char) → new_esEs13(vyy440, vyy450)
new_foldFM2(EmptyFM, cca, ccb) → []
new_compare34(vyy6000, vyy500, ty_Ordering) → new_compare15(vyy6000, vyy500)
new_compare34(vyy6000, vyy500, ty_Bool) → new_compare9(vyy6000, vyy500)
new_lt17(vyy6000, vyy500) → new_esEs22(new_compare7(vyy6000, vyy500))
new_compare31(vyy6000, vyy500, h, ba) → new_compare28(vyy6000, vyy500, new_esEs5(vyy6000, vyy500, h, ba), h, ba)
new_esEs7(Just(vyy440), Just(vyy450), app(app(ty_Either, bed), bee)) → new_esEs8(vyy440, vyy450, bed, bee)
new_lt5(vyy6001, vyy501, ty_Bool) → new_lt9(vyy6001, vyy501)
new_esEs23(vyy440, vyy450, app(ty_Ratio, cde)) → new_esEs12(vyy440, vyy450, cde)
new_esEs26(vyy442, vyy452, ty_Int) → new_esEs17(vyy442, vyy452)
new_primEqInt(Pos(Zero), Neg(Succ(vyy4500))) → False
new_primEqInt(Neg(Zero), Pos(Succ(vyy4500))) → False
new_ltEs19(vyy6001, vyy501, app(app(ty_@2, cc), cd)) → new_ltEs9(vyy6001, vyy501, cc, cd)
new_primCmpNat2(Succ(vyy5000), vyy60000) → new_primCmpNat1(vyy5000, vyy60000)
new_esEs21(vyy441, vyy451, ty_Integer) → new_esEs15(vyy441, vyy451)
new_primCompAux00(vyy60, EQ) → vyy60
new_pePe(False, vyy44, vyy45, vyy46, ded) → new_asAs(new_esEs27(vyy44, vyy45, ded), vyy46)
new_esEs8(Left(vyy440), Left(vyy450), app(ty_Ratio, dca), dba) → new_esEs12(vyy440, vyy450, dca)
new_esEs26(vyy442, vyy452, ty_Ordering) → new_esEs18(vyy442, vyy452)
new_esEs8(Left(vyy440), Left(vyy450), ty_@0, dba) → new_esEs11(vyy440, vyy450)
new_esEs21(vyy441, vyy451, ty_Ordering) → new_esEs18(vyy441, vyy451)
new_ltEs4(Left(vyy6000), Left(vyy500), app(ty_[], bce), bca) → new_ltEs15(vyy6000, vyy500, bce)
new_esEs8(Left(vyy440), Left(vyy450), ty_Int, dba) → new_esEs17(vyy440, vyy450)
new_esEs26(vyy442, vyy452, app(app(ty_@2, dab), dac)) → new_esEs5(vyy442, vyy452, dab, dac)
new_esEs20(vyy440, vyy450, app(app(ty_FiniteMap, cab), cac)) → new_esEs16(vyy440, vyy450, cab, cac)
new_esEs24(vyy440, vyy450, ty_Char) → new_esEs13(vyy440, vyy450)
new_esEs21(vyy441, vyy451, app(app(ty_@2, cbc), cbd)) → new_esEs5(vyy441, vyy451, cbc, cbd)
new_ltEs4(Right(vyy6000), Left(vyy500), bda, bca) → False
new_ltEs5(vyy600, vyy50, bfh) → new_not(new_compare6(vyy600, vyy50, bfh))
new_compare24(vyy6000, vyy500, True, bg) → EQ
new_ltEs18(Just(vyy6000), Nothing, bgd) → False
new_primPlusNat0(Zero, vyy50000) → Succ(vyy50000)
new_ltEs17(vyy600, vyy50) → new_not(new_compare7(vyy600, vyy50))
new_compare15(vyy6000, vyy500) → new_compare27(vyy6000, vyy500, new_esEs18(vyy6000, vyy500))
new_ltEs18(Just(vyy6000), Just(vyy500), app(ty_[], bbc)) → new_ltEs15(vyy6000, vyy500, bbc)
new_esEs25(vyy441, vyy451, ty_Integer) → new_esEs15(vyy441, vyy451)
new_ltEs14(LT, LT) → True
new_esEs26(vyy442, vyy452, ty_Bool) → new_esEs14(vyy442, vyy452)
new_ltEs7(vyy6002, vyy502, app(app(app(ty_@3, ge), gf), gg)) → new_ltEs6(vyy6002, vyy502, ge, gf, gg)
new_ltEs4(Left(vyy6000), Left(vyy500), ty_Integer, bca) → new_ltEs12(vyy6000, vyy500)
new_lt20(vyy6000, vyy500, app(ty_Ratio, cbh)) → new_lt14(vyy6000, vyy500, cbh)
new_not0 → True
new_ltEs19(vyy6001, vyy501, app(app(app(ty_@3, ce), cf), cg)) → new_ltEs6(vyy6001, vyy501, ce, cf, cg)
new_esEs23(vyy440, vyy450, app(ty_[], cdb)) → new_esEs10(vyy440, vyy450, cdb)
new_lt12(vyy6000, vyy500) → new_esEs22(new_compare29(vyy6000, vyy500))
new_ltEs11(False, False) → True
new_esEs19(Double(vyy440, vyy441), Double(vyy450, vyy451)) → new_esEs17(new_sr0(vyy440, vyy450), new_sr0(vyy441, vyy451))
new_compare12(Integer(vyy6000), Integer(vyy500)) → new_primCmpInt(vyy6000, vyy500)
new_ltEs7(vyy6002, vyy502, ty_Float) → new_ltEs8(vyy6002, vyy502)
new_esEs18(GT, GT) → True
new_ltEs19(vyy6001, vyy501, app(ty_[], da)) → new_ltEs15(vyy6001, vyy501, da)
new_ltEs19(vyy6001, vyy501, ty_Integer) → new_ltEs12(vyy6001, vyy501)
new_lt4(vyy6000, vyy500, ty_Integer) → new_lt11(vyy6000, vyy500)
new_primCmpInt(Pos(Succ(vyy60000)), Neg(vyy500)) → GT
new_esEs21(vyy441, vyy451, app(ty_Maybe, caf)) → new_esEs7(vyy441, vyy451, caf)
new_primMulInt(Pos(vyy60000), Pos(vyy5000)) → Pos(new_primMulNat0(vyy60000, vyy5000))
new_ltEs4(Left(vyy6000), Left(vyy500), app(ty_Ratio, dea), bca) → new_ltEs5(vyy6000, vyy500, dea)
new_esEs8(Right(vyy440), Right(vyy450), dcd, app(app(app(ty_@3, dch), dda), ddb)) → new_esEs6(vyy440, vyy450, dch, dda, ddb)
new_primMulInt(Neg(vyy60000), Neg(vyy5000)) → Pos(new_primMulNat0(vyy60000, vyy5000))
new_esEs20(vyy440, vyy450, ty_Integer) → new_esEs15(vyy440, vyy450)
new_primEqNat0(Zero, Succ(vyy45000)) → False
new_primEqNat0(Succ(vyy44000), Zero) → False
new_esEs7(Just(vyy440), Just(vyy450), ty_Char) → new_esEs13(vyy440, vyy450)
new_lt5(vyy6001, vyy501, app(ty_[], fg)) → new_lt15(vyy6001, vyy501, fg)
new_esEs8(Right(vyy440), Right(vyy450), dcd, app(ty_Ratio, ddf)) → new_esEs12(vyy440, vyy450, ddf)
new_esEs17(vyy44, vyy45) → new_primEqInt(vyy44, vyy45)
new_esEs27(vyy44, vyy45, ty_@0) → new_esEs11(vyy44, vyy45)
new_ltEs7(vyy6002, vyy502, ty_Integer) → new_ltEs12(vyy6002, vyy502)
new_esEs20(vyy440, vyy450, ty_Bool) → new_esEs14(vyy440, vyy450)
new_lt20(vyy6000, vyy500, ty_@0) → new_lt17(vyy6000, vyy500)
new_esEs20(vyy440, vyy450, app(ty_[], bhf)) → new_esEs10(vyy440, vyy450, bhf)
new_compare23(vyy6000, vyy500, False, bh, ca) → new_compare10(vyy6000, vyy500, new_ltEs4(vyy6000, vyy500, bh, ca), bh, ca)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_primCmpInt(Pos(Succ(vyy60000)), Pos(vyy500)) → new_primCmpNat0(vyy60000, vyy500)
new_esEs27(vyy44, vyy45, app(app(app(ty_@3, cdh), cea), ceb)) → new_esEs6(vyy44, vyy45, cdh, cea, ceb)
new_ltEs7(vyy6002, vyy502, app(app(ty_Either, hb), hc)) → new_ltEs4(vyy6002, vyy502, hb, hc)
new_esEs11(@0, @0) → True
new_esEs25(vyy441, vyy451, ty_@0) → new_esEs11(vyy441, vyy451)
new_esEs27(vyy44, vyy45, app(app(ty_@2, bgf), bgg)) → new_esEs5(vyy44, vyy45, bgf, bgg)
new_primCmpNat0(vyy60000, Zero) → GT
new_ltEs19(vyy6001, vyy501, ty_Char) → new_ltEs13(vyy6001, vyy501)
new_sizeFM(Branch(vyy450, vyy451, vyy452, vyy453, vyy454), cca, ccb) → vyy452
new_esEs27(vyy44, vyy45, ty_Int) → new_esEs17(vyy44, vyy45)
new_compare30(Float(vyy6000, vyy6001), Float(vyy500, vyy501)) → new_compare16(new_sr0(vyy6000, vyy500), new_sr0(vyy6001, vyy501))
new_ltEs4(Right(vyy6000), Right(vyy500), bda, ty_Double) → new_ltEs10(vyy6000, vyy500)
new_ltEs19(vyy6001, vyy501, ty_@0) → new_ltEs17(vyy6001, vyy501)
new_esEs23(vyy440, vyy450, ty_Int) → new_esEs17(vyy440, vyy450)
new_pePe(True, vyy44, vyy45, vyy46, ded) → True
new_esEs24(vyy440, vyy450, ty_Double) → new_esEs19(vyy440, vyy450)
new_foldFM2(Branch(vyy450, vyy451, vyy452, vyy453, vyy454), cca, ccb) → new_foldFM0(vyy450, vyy451, new_foldFM2(vyy454, cca, ccb), vyy453, cca, ccb)
new_compare23(vyy6000, vyy500, True, bh, ca) → EQ
new_lt5(vyy6001, vyy501, ty_Float) → new_lt6(vyy6001, vyy501)
new_primCmpInt(Pos(Zero), Neg(Succ(vyy5000))) → GT
new_compare8(vyy6000, vyy500, bg) → new_compare24(vyy6000, vyy500, new_esEs7(vyy6000, vyy500, bg), bg)
new_sr0(vyy6000, vyy500) → new_primMulInt(vyy6000, vyy500)
new_esEs10(:(vyy440, vyy441), :(vyy450, vyy451), ccc) → new_asAs(new_esEs23(vyy440, vyy450, ccc), new_esEs10(vyy441, vyy451, ccc))
new_esEs27(vyy44, vyy45, app(ty_Ratio, dee)) → new_esEs12(vyy44, vyy45, dee)
new_ltEs19(vyy6001, vyy501, ty_Ordering) → new_ltEs14(vyy6001, vyy501)
new_esEs8(Left(vyy440), Left(vyy450), app(app(ty_Either, dag), dah), dba) → new_esEs8(vyy440, vyy450, dag, dah)
new_esEs25(vyy441, vyy451, app(ty_Maybe, cga)) → new_esEs7(vyy441, vyy451, cga)
new_esEs7(Just(vyy440), Just(vyy450), app(app(app(ty_@3, beg), beh), bfa)) → new_esEs6(vyy440, vyy450, beg, beh, bfa)
new_esEs24(vyy440, vyy450, app(ty_[], cfa)) → new_esEs10(vyy440, vyy450, cfa)
new_lt4(vyy6000, vyy500, ty_Ordering) → new_lt13(vyy6000, vyy500)
new_lt6(vyy6000, vyy500) → new_esEs22(new_compare30(vyy6000, vyy500))
new_lt9(vyy6000, vyy500) → new_esEs22(new_compare9(vyy6000, vyy500))
new_lt20(vyy6000, vyy500, app(ty_[], bf)) → new_lt15(vyy6000, vyy500, bf)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_compare29(Char(vyy6000), Char(vyy500)) → new_primCmpInt(vyy6000, vyy500)
new_esEs7(Just(vyy440), Just(vyy450), ty_@0) → new_esEs11(vyy440, vyy450)
new_ltEs18(Just(vyy6000), Just(vyy500), app(app(ty_@2, baf), bag)) → new_ltEs9(vyy6000, vyy500, baf, bag)
new_ltEs10(vyy600, vyy50) → new_not(new_compare17(vyy600, vyy50))
new_compare34(vyy6000, vyy500, app(ty_Maybe, bac)) → new_compare8(vyy6000, vyy500, bac)
new_lt18(vyy6000, vyy500, bg) → new_esEs22(new_compare8(vyy6000, vyy500, bg))
new_esEs28(vyy440, vyy450, ty_Int) → new_esEs17(vyy440, vyy450)
new_asAs(False, vyy55) → False
new_ltEs11(True, True) → True
new_compare3([], [], hd) → EQ
new_primMulInt(Pos(vyy60000), Neg(vyy5000)) → Neg(new_primMulNat0(vyy60000, vyy5000))
new_primMulInt(Neg(vyy60000), Pos(vyy5000)) → Neg(new_primMulNat0(vyy60000, vyy5000))
new_primCmpInt(Neg(Succ(vyy60000)), Neg(vyy500)) → new_primCmpNat2(vyy500, vyy60000)
new_compare16(vyy600, vyy50) → new_primCmpInt(vyy600, vyy50)
new_primMulNat0(Succ(vyy600000), Zero) → Zero
new_primMulNat0(Zero, Succ(vyy50000)) → Zero
new_esEs23(vyy440, vyy450, app(app(app(ty_@3, ccg), cch), cda)) → new_esEs6(vyy440, vyy450, ccg, cch, cda)
new_lt4(vyy6000, vyy500, app(app(app(ty_@3, ea), eb), ec)) → new_lt10(vyy6000, vyy500, ea, eb, ec)
new_ltEs16(vyy600, vyy50) → new_not(new_compare16(vyy600, vyy50))
new_ltEs4(Right(vyy6000), Right(vyy500), bda, ty_Int) → new_ltEs16(vyy6000, vyy500)
new_esEs8(Right(vyy440), Right(vyy450), dcd, ty_Int) → new_esEs17(vyy440, vyy450)
new_esEs26(vyy442, vyy452, app(ty_Maybe, che)) → new_esEs7(vyy442, vyy452, che)
new_ltEs18(Nothing, Just(vyy500), bgd) → True
new_ltEs14(GT, LT) → False
new_not(EQ) → new_not0
new_esEs28(vyy440, vyy450, ty_Integer) → new_esEs15(vyy440, vyy450)
new_primCmpInt(Pos(Zero), Pos(Succ(vyy5000))) → new_primCmpNat2(Zero, vyy5000)
new_esEs25(vyy441, vyy451, app(app(app(ty_@3, cgb), cgc), cgd)) → new_esEs6(vyy441, vyy451, cgb, cgc, cgd)
new_lt8(vyy6000, vyy500) → new_esEs22(new_compare17(vyy6000, vyy500))
new_esEs23(vyy440, vyy450, ty_Integer) → new_esEs15(vyy440, vyy450)
new_esEs27(vyy44, vyy45, app(ty_[], ccc)) → new_esEs10(vyy44, vyy45, ccc)
new_compare27(vyy6000, vyy500, True) → EQ
new_ltEs19(vyy6001, vyy501, ty_Int) → new_ltEs16(vyy6001, vyy501)
new_esEs14(True, True) → True
new_ltEs4(Left(vyy6000), Left(vyy500), ty_Ordering, bca) → new_ltEs14(vyy6000, vyy500)
new_ltEs18(Just(vyy6000), Just(vyy500), ty_Integer) → new_ltEs12(vyy6000, vyy500)
new_ltEs6(@3(vyy6000, vyy6001, vyy6002), @3(vyy500, vyy501, vyy502), eh, dg, dh) → new_pePe(new_lt4(vyy6000, vyy500, eh), vyy6000, vyy500, new_pePe(new_lt5(vyy6001, vyy501, dg), vyy6001, vyy501, new_ltEs7(vyy6002, vyy502, dh), dg), eh)
new_esEs27(vyy44, vyy45, ty_Bool) → new_esEs14(vyy44, vyy45)
new_esEs26(vyy442, vyy452, ty_Double) → new_esEs19(vyy442, vyy452)
new_lt19(vyy6000, vyy500, bh, ca) → new_esEs22(new_compare32(vyy6000, vyy500, bh, ca))
new_esEs26(vyy442, vyy452, app(ty_Ratio, dad)) → new_esEs12(vyy442, vyy452, dad)
new_ltEs18(Just(vyy6000), Just(vyy500), ty_Bool) → new_ltEs11(vyy6000, vyy500)
new_ltEs7(vyy6002, vyy502, ty_@0) → new_ltEs17(vyy6002, vyy502)
new_lt5(vyy6001, vyy501, app(app(ty_Either, ga), gb)) → new_lt19(vyy6001, vyy501, ga, gb)
new_ltEs4(Right(vyy6000), Right(vyy500), bda, ty_Char) → new_ltEs13(vyy6000, vyy500)
new_esEs20(vyy440, vyy450, ty_Int) → new_esEs17(vyy440, vyy450)
new_esEs25(vyy441, vyy451, app(app(ty_@2, cgf), cgg)) → new_esEs5(vyy441, vyy451, cgf, cgg)
new_ltEs14(LT, GT) → True
new_esEs27(vyy44, vyy45, ty_Float) → new_esEs9(vyy44, vyy45)
new_not(LT) → new_not0
new_esEs8(Right(vyy440), Right(vyy450), dcd, ty_Integer) → new_esEs15(vyy440, vyy450)
new_lt5(vyy6001, vyy501, app(ty_Maybe, fh)) → new_lt18(vyy6001, vyy501, fh)
new_ltEs14(LT, EQ) → True
new_compare9(vyy6000, vyy500) → new_compare25(vyy6000, vyy500, new_esEs14(vyy6000, vyy500))
new_lt16(vyy6000, vyy500) → new_esEs22(new_compare16(vyy6000, vyy500))
new_lt13(vyy6000, vyy500) → new_esEs22(new_compare15(vyy6000, vyy500))
new_ltEs4(Right(vyy6000), Right(vyy500), bda, ty_Bool) → new_ltEs11(vyy6000, vyy500)
new_lt4(vyy6000, vyy500, ty_Bool) → new_lt9(vyy6000, vyy500)
new_esEs14(False, False) → True
new_esEs8(Left(vyy440), Left(vyy450), ty_Float, dba) → new_esEs9(vyy440, vyy450)
new_esEs7(Just(vyy440), Just(vyy450), app(app(ty_@2, bfc), bfd)) → new_esEs5(vyy440, vyy450, bfc, bfd)
new_lt20(vyy6000, vyy500, ty_Char) → new_lt12(vyy6000, vyy500)
new_ltEs7(vyy6002, vyy502, ty_Char) → new_ltEs13(vyy6002, vyy502)
new_esEs22(GT) → False
new_lt5(vyy6001, vyy501, ty_Double) → new_lt8(vyy6001, vyy501)
new_esEs25(vyy441, vyy451, ty_Double) → new_esEs19(vyy441, vyy451)
new_compare26(vyy6000, vyy500, True, bc, bd, be) → EQ
new_esEs21(vyy441, vyy451, ty_@0) → new_esEs11(vyy441, vyy451)
new_ltEs4(Left(vyy6000), Left(vyy500), ty_Double, bca) → new_ltEs10(vyy6000, vyy500)
new_primPlusNat1(Zero, Zero) → Zero
new_esEs21(vyy441, vyy451, app(app(app(ty_@3, cag), cah), cba)) → new_esEs6(vyy441, vyy451, cag, cah, cba)
new_asAs(True, vyy55) → vyy55
new_ltEs14(EQ, EQ) → True
new_primMulNat0(Succ(vyy600000), Succ(vyy50000)) → new_primPlusNat0(new_primMulNat0(vyy600000, Succ(vyy50000)), vyy50000)
new_lt5(vyy6001, vyy501, app(ty_Ratio, bgb)) → new_lt14(vyy6001, vyy501, bgb)
new_ltEs8(vyy600, vyy50) → new_not(new_compare30(vyy600, vyy50))
new_esEs7(Just(vyy440), Just(vyy450), ty_Bool) → new_esEs14(vyy440, vyy450)
new_compare6(:%(vyy6000, vyy6001), :%(vyy500, vyy501), ty_Int) → new_compare16(new_sr0(vyy6000, vyy501), new_sr0(vyy500, vyy6001))
new_fmToList(vyy45, cca, ccb) → new_foldFM2(vyy45, cca, ccb)
new_esEs8(Right(vyy440), Right(vyy450), dcd, app(app(ty_@2, ddd), dde)) → new_esEs5(vyy440, vyy450, ddd, dde)
new_ltEs13(vyy600, vyy50) → new_not(new_compare29(vyy600, vyy50))
new_esEs8(Left(vyy440), Left(vyy450), ty_Ordering, dba) → new_esEs18(vyy440, vyy450)
new_lt11(vyy6000, vyy500) → new_esEs22(new_compare12(vyy6000, vyy500))
new_primCompAux00(vyy60, GT) → GT
new_ltEs18(Just(vyy6000), Just(vyy500), ty_Char) → new_ltEs13(vyy6000, vyy500)
new_esEs8(Right(vyy440), Right(vyy450), dcd, app(ty_[], ddc)) → new_esEs10(vyy440, vyy450, ddc)
new_compare33(vyy6000, vyy500, bc, bd, be) → new_compare26(vyy6000, vyy500, new_esEs6(vyy6000, vyy500, bc, bd, be), bc, bd, be)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_ltEs14(EQ, GT) → True
new_esEs7(Just(vyy440), Just(vyy450), ty_Ordering) → new_esEs18(vyy440, vyy450)
new_lt4(vyy6000, vyy500, ty_@0) → new_lt17(vyy6000, vyy500)
new_ltEs4(Left(vyy6000), Left(vyy500), ty_@0, bca) → new_ltEs17(vyy6000, vyy500)
new_lt5(vyy6001, vyy501, ty_Char) → new_lt12(vyy6001, vyy501)
new_esEs22(LT) → True
new_lt7(vyy6000, vyy500, h, ba) → new_esEs22(new_compare31(vyy6000, vyy500, h, ba))
new_lt4(vyy6000, vyy500, app(ty_Ratio, bga)) → new_lt14(vyy6000, vyy500, bga)
new_compare34(vyy6000, vyy500, app(ty_Ratio, def)) → new_compare6(vyy6000, vyy500, def)
new_esEs25(vyy441, vyy451, ty_Float) → new_esEs9(vyy441, vyy451)
new_esEs25(vyy441, vyy451, app(ty_Ratio, cgh)) → new_esEs12(vyy441, vyy451, cgh)
new_ltEs19(vyy6001, vyy501, app(ty_Maybe, db)) → new_ltEs18(vyy6001, vyy501, db)
new_esEs7(Just(vyy440), Just(vyy450), app(ty_Ratio, bfe)) → new_esEs12(vyy440, vyy450, bfe)
new_primCmpNat0(vyy60000, Succ(vyy5000)) → new_primCmpNat1(vyy60000, vyy5000)
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_esEs8(Right(vyy440), Right(vyy450), dcd, app(ty_Maybe, dcg)) → new_esEs7(vyy440, vyy450, dcg)
new_esEs25(vyy441, vyy451, app(app(ty_Either, cfg), cfh)) → new_esEs8(vyy441, vyy451, cfg, cfh)
new_esEs27(vyy44, vyy45, ty_Integer) → new_esEs15(vyy44, vyy45)
new_ltEs19(vyy6001, vyy501, ty_Bool) → new_ltEs11(vyy6001, vyy501)
new_esEs18(EQ, EQ) → True
new_esEs25(vyy441, vyy451, ty_Char) → new_esEs13(vyy441, vyy451)
new_primCmpInt(Neg(Succ(vyy60000)), Pos(vyy500)) → LT
new_esEs27(vyy44, vyy45, ty_Double) → new_esEs19(vyy44, vyy45)
The set Q consists of the following terms:
new_esEs21(x0, x1, ty_Int)
new_lt7(x0, x1, x2, x3)
new_lt19(x0, x1, x2, x3)
new_esEs27(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_ltEs4(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_ltEs18(Just(x0), Nothing, x1)
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primPlusNat1(Succ(x0), Succ(x1))
new_lt4(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs7(x0, x1, ty_Int)
new_esEs27(x0, x1, app(ty_[], x2))
new_esEs8(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_asAs(False, x0)
new_lt5(x0, x1, ty_Int)
new_compare8(x0, x1, x2)
new_lt8(x0, x1)
new_compare3(:(x0, x1), [], x2)
new_esEs18(LT, LT)
new_esEs20(x0, x1, ty_Bool)
new_esEs7(Just(x0), Just(x1), ty_Char)
new_esEs24(x0, x1, ty_Ordering)
new_esEs21(x0, x1, ty_Bool)
new_esEs8(Right(x0), Left(x1), x2, x3)
new_esEs8(Left(x0), Right(x1), x2, x3)
new_compare34(x0, x1, ty_Double)
new_fmToList(x0, x1, x2)
new_ltEs7(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs23(x0, x1, ty_Ordering)
new_esEs21(x0, x1, ty_@0)
new_compare28(x0, x1, False, x2, x3)
new_esEs26(x0, x1, ty_Char)
new_ltEs18(Nothing, Nothing, x0)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_ltEs19(x0, x1, ty_Integer)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_lt4(x0, x1, ty_Integer)
new_esEs24(x0, x1, ty_Integer)
new_compare26(x0, x1, True, x2, x3, x4)
new_esEs20(x0, x1, ty_Float)
new_compare14(x0, x1, True, x2, x3, x4)
new_compare27(x0, x1, True)
new_primCompAux0(x0, x1, x2, x3)
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_primMulNat0(Zero, Succ(x0))
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs7(Just(x0), Just(x1), ty_Bool)
new_esEs24(x0, x1, ty_Double)
new_esEs23(x0, x1, ty_Char)
new_lt5(x0, x1, app(app(ty_Either, x2), x3))
new_esEs11(@0, @0)
new_esEs22(LT)
new_esEs20(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs29(x0, x1, ty_Integer)
new_compare31(x0, x1, x2, x3)
new_compare27(x0, x1, False)
new_esEs8(Left(x0), Left(x1), ty_Bool, x2)
new_esEs21(x0, x1, ty_Integer)
new_ltEs7(x0, x1, app(ty_Ratio, x2))
new_compare11(x0, x1, True, x2)
new_ltEs7(x0, x1, app(app(ty_Either, x2), x3))
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_compare19(x0, x1, False)
new_lt20(x0, x1, ty_Int)
new_lt13(x0, x1)
new_primEqNat0(Zero, Succ(x0))
new_esEs21(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_compare34(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_lt5(x0, x1, app(ty_Ratio, x2))
new_ltEs7(x0, x1, ty_Char)
new_lt4(x0, x1, app(app(ty_Either, x2), x3))
new_esEs18(EQ, GT)
new_esEs18(GT, EQ)
new_esEs8(Left(x0), Left(x1), ty_Integer, x2)
new_ltEs4(Left(x0), Left(x1), ty_Double, x2)
new_primCmpNat1(Succ(x0), Zero)
new_lt4(x0, x1, ty_Char)
new_foldFM2(EmptyFM, x0, x1)
new_esEs27(x0, x1, ty_@0)
new_esEs8(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs8(Right(x0), Right(x1), x2, ty_Bool)
new_esEs18(EQ, EQ)
new_esEs24(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_compare16(x0, x1)
new_ltEs19(x0, x1, ty_Float)
new_primCmpNat1(Zero, Zero)
new_esEs8(Right(x0), Right(x1), x2, app(app(ty_FiniteMap, x3), x4))
new_esEs27(x0, x1, ty_Int)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_compare25(x0, x1, True)
new_esEs8(Left(x0), Left(x1), ty_Float, x2)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare34(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt5(x0, x1, app(ty_Maybe, x2))
new_esEs8(Left(x0), Left(x1), ty_Ordering, x2)
new_compare34(x0, x1, app(ty_[], x2))
new_esEs14(True, True)
new_esEs27(x0, x1, ty_Float)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, ty_Ordering)
new_esEs26(x0, x1, ty_Double)
new_lt5(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs4(Left(x0), Right(x1), x2, x3)
new_ltEs4(Right(x0), Left(x1), x2, x3)
new_esEs8(Left(x0), Left(x1), ty_Int, x2)
new_lt5(x0, x1, app(ty_[], x2))
new_compare34(x0, x1, ty_Ordering)
new_ltEs14(EQ, EQ)
new_primEqNat0(Zero, Zero)
new_esEs27(x0, x1, ty_Double)
new_sizeFM(EmptyFM, x0, x1)
new_esEs10(:(x0, x1), :(x2, x3), x4)
new_ltEs4(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_lt20(x0, x1, ty_Double)
new_lt4(x0, x1, app(ty_[], x2))
new_ltEs4(Left(x0), Left(x1), ty_@0, x2)
new_compare13(x0, x1, False, x2, x3)
new_esEs7(Just(x0), Just(x1), ty_Int)
new_esEs24(x0, x1, ty_@0)
new_esEs26(x0, x1, ty_Bool)
new_compare24(x0, x1, False, x2)
new_lt14(x0, x1, x2)
new_esEs23(x0, x1, ty_Integer)
new_esEs7(Just(x0), Just(x1), app(app(ty_FiniteMap, x2), x3))
new_primMulNat0(Zero, Zero)
new_primCmpNat0(x0, Succ(x1))
new_esEs21(x0, x1, ty_Float)
new_ltEs17(x0, x1)
new_esEs20(x0, x1, ty_Char)
new_esEs26(x0, x1, ty_@0)
new_primMulNat0(Succ(x0), Zero)
new_compare10(x0, x1, True, x2, x3)
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_compare34(x0, x1, ty_Bool)
new_primCompAux00(x0, LT)
new_compare10(x0, x1, False, x2, x3)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
new_lt5(x0, x1, ty_Ordering)
new_esEs8(Left(x0), Left(x1), ty_Double, x2)
new_primPlusNat0(Zero, x0)
new_ltEs4(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs25(x0, x1, ty_Float)
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs4(Right(x0), Right(x1), x2, ty_Bool)
new_esEs21(x0, x1, app(ty_[], x2))
new_compare34(x0, x1, ty_Integer)
new_lt4(x0, x1, ty_@0)
new_ltEs4(Right(x0), Right(x1), x2, ty_Ordering)
new_ltEs7(x0, x1, ty_Float)
new_ltEs19(x0, x1, ty_Ordering)
new_sr(Integer(x0), Integer(x1))
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_esEs8(Left(x0), Left(x1), app(app(ty_FiniteMap, x2), x3), x4)
new_compare19(x0, x1, True)
new_esEs25(x0, x1, app(ty_[], x2))
new_esEs27(x0, x1, ty_Ordering)
new_ltEs19(x0, x1, ty_Bool)
new_compare34(x0, x1, ty_Char)
new_ltEs4(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_primEqNat0(Succ(x0), Zero)
new_ltEs4(Left(x0), Left(x1), app(ty_[], x2), x3)
new_ltEs18(Just(x0), Just(x1), ty_Int)
new_ltEs7(x0, x1, app(ty_[], x2))
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs7(x0, x1, ty_Integer)
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_esEs23(x0, x1, ty_@0)
new_lt5(x0, x1, ty_Float)
new_esEs8(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs26(x0, x1, app(ty_[], x2))
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs20(x0, x1, ty_Ordering)
new_esEs10([], :(x0, x1), x2)
new_lt4(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs4(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_compare32(x0, x1, x2, x3)
new_compare17(Double(x0, x1), Double(x2, x3))
new_lt4(x0, x1, app(ty_Maybe, x2))
new_esEs13(Char(x0), Char(x1))
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, ty_Char)
new_esEs20(x0, x1, app(ty_[], x2))
new_compare3([], [], x0)
new_esEs25(x0, x1, ty_Ordering)
new_lt20(x0, x1, ty_Integer)
new_compare14(x0, x1, False, x2, x3, x4)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_ltEs18(Just(x0), Just(x1), ty_Float)
new_ltEs7(x0, x1, ty_@0)
new_esEs28(x0, x1, ty_Integer)
new_esEs21(x0, x1, ty_Char)
new_primPlusNat1(Zero, Zero)
new_compare6(:%(x0, x1), :%(x2, x3), ty_Integer)
new_not0
new_compare23(x0, x1, True, x2, x3)
new_ltEs19(x0, x1, ty_Char)
new_primPlusNat1(Zero, Succ(x0))
new_esEs7(Just(x0), Just(x1), ty_Integer)
new_ltEs4(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_ltEs14(LT, LT)
new_compare34(x0, x1, app(ty_Maybe, x2))
new_compare33(x0, x1, x2, x3, x4)
new_ltEs13(x0, x1)
new_esEs26(x0, x1, ty_Integer)
new_compare34(x0, x1, app(ty_Ratio, x2))
new_ltEs7(x0, x1, ty_Bool)
new_ltEs7(x0, x1, app(ty_Maybe, x2))
new_lt10(x0, x1, x2, x3, x4)
new_esEs7(Just(x0), Nothing, x1)
new_lt4(x0, x1, ty_Float)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_compare34(x0, x1, ty_@0)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_pePe(True, x0, x1, x2, x3)
new_compare34(x0, x1, ty_Int)
new_lt5(x0, x1, ty_Double)
new_esEs18(GT, GT)
new_ltEs4(Left(x0), Left(x1), ty_Integer, x2)
new_lt5(x0, x1, ty_Bool)
new_lt12(x0, x1)
new_ltEs18(Nothing, Just(x0), x1)
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs4(Right(x0), Right(x1), x2, ty_Char)
new_lt5(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCompAux00(x0, EQ)
new_compare3(:(x0, x1), :(x2, x3), x4)
new_esEs20(x0, x1, ty_@0)
new_lt6(x0, x1)
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs25(x0, x1, ty_Double)
new_ltEs19(x0, x1, app(ty_[], x2))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_not(GT)
new_ltEs8(x0, x1)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs15(x0, x1, x2)
new_lt20(x0, x1, app(ty_[], x2))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs18(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs8(Right(x0), Right(x1), x2, ty_@0)
new_lt20(x0, x1, ty_Float)
new_compare15(x0, x1)
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_ltEs10(x0, x1)
new_esEs23(x0, x1, ty_Float)
new_compare3([], :(x0, x1), x2)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_ltEs14(LT, EQ)
new_ltEs14(EQ, LT)
new_primEqNat0(Succ(x0), Succ(x1))
new_ltEs16(x0, x1)
new_ltEs4(Left(x0), Left(x1), ty_Float, x2)
new_esEs8(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_compare13(x0, x1, True, x2, x3)
new_ltEs11(False, False)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_sr0(x0, x1)
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs18(Just(x0), Just(x1), app(ty_Ratio, x2))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_lt5(x0, x1, ty_Integer)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_esEs8(Right(x0), Right(x1), x2, ty_Double)
new_esEs8(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_lt4(x0, x1, ty_Ordering)
new_primEqInt(Neg(Zero), Neg(Zero))
new_esEs7(Nothing, Nothing, x0)
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
new_ltEs11(False, True)
new_ltEs11(True, False)
new_ltEs4(Right(x0), Right(x1), x2, ty_Int)
new_ltEs4(Right(x0), Right(x1), x2, ty_Integer)
new_esEs26(x0, x1, ty_Ordering)
new_esEs14(False, True)
new_esEs14(True, False)
new_ltEs4(Right(x0), Right(x1), x2, app(ty_[], x3))
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs23(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs17(x0, x1)
new_primCmpNat2(Succ(x0), x1)
new_ltEs18(Just(x0), Just(x1), ty_Integer)
new_esEs8(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs8(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_compare29(Char(x0), Char(x1))
new_primPlusNat0(Succ(x0), x1)
new_compare7(@0, @0)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_esEs8(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_primCmpNat2(Zero, x0)
new_compare9(x0, x1)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_primCmpNat1(Succ(x0), Succ(x1))
new_primCmpNat0(x0, Zero)
new_esEs24(x0, x1, ty_Char)
new_esEs7(Just(x0), Just(x1), ty_Double)
new_esEs8(Right(x0), Right(x1), x2, ty_Int)
new_esEs7(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_compare34(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, ty_Double)
new_compare26(x0, x1, False, x2, x3, x4)
new_esEs7(Just(x0), Just(x1), app(ty_[], x2))
new_esEs23(x0, x1, app(ty_[], x2))
new_lt4(x0, x1, app(ty_Ratio, x2))
new_lt4(x0, x1, ty_Int)
new_esEs21(x0, x1, ty_Ordering)
new_ltEs14(EQ, GT)
new_ltEs14(GT, EQ)
new_esEs10(:(x0, x1), [], x2)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_ltEs4(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs12(x0, x1)
new_esEs8(Left(x0), Left(x1), ty_Char, x2)
new_esEs20(x0, x1, ty_Double)
new_esEs7(Just(x0), Just(x1), app(ty_Ratio, x2))
new_ltEs6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs26(x0, x1, ty_Int)
new_ltEs4(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs26(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs8(Right(x0), Right(x1), x2, ty_Float)
new_esEs25(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs24(x0, x1, ty_Float)
new_primMulNat0(Succ(x0), Succ(x1))
new_esEs22(EQ)
new_ltEs18(Just(x0), Just(x1), ty_Bool)
new_esEs24(x0, x1, app(ty_[], x2))
new_esEs7(Just(x0), Just(x1), ty_Float)
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_asAs(True, x0)
new_primCmpNat1(Zero, Succ(x0))
new_lt5(x0, x1, ty_@0)
new_ltEs4(Left(x0), Left(x1), ty_Char, x2)
new_esEs18(EQ, LT)
new_esEs18(LT, EQ)
new_esEs23(x0, x1, ty_Bool)
new_ltEs14(LT, GT)
new_ltEs14(GT, LT)
new_primCompAux00(x0, GT)
new_pePe(False, x0, x1, x2, x3)
new_esEs7(Just(x0), Just(x1), app(ty_Maybe, x2))
new_ltEs4(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_compare25(x0, x1, False)
new_esEs20(x0, x1, ty_Int)
new_esEs8(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_compare34(x0, x1, ty_Float)
new_esEs27(x0, x1, ty_Char)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs4(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_lt18(x0, x1, x2)
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_ltEs18(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_lt17(x0, x1)
new_esEs26(x0, x1, ty_Float)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs14(GT, GT)
new_esEs5(@2(x0, x1), @2(x2, x3), x4, x5)
new_lt20(x0, x1, ty_Bool)
new_ltEs18(Just(x0), Just(x1), ty_Char)
new_esEs8(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_ltEs18(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs25(x0, x1, ty_Bool)
new_esEs19(Double(x0, x1), Double(x2, x3))
new_lt5(x0, x1, ty_Char)
new_not(EQ)
new_ltEs4(Right(x0), Right(x1), x2, ty_Double)
new_lt4(x0, x1, ty_Double)
new_compare12(Integer(x0), Integer(x1))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_esEs28(x0, x1, ty_Int)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_ltEs7(x0, x1, ty_Double)
new_lt16(x0, x1)
new_esEs22(GT)
new_ltEs4(Left(x0), Left(x1), ty_Int, x2)
new_ltEs18(Just(x0), Just(x1), ty_Ordering)
new_esEs7(Nothing, Just(x0), x1)
new_lt9(x0, x1)
new_esEs15(Integer(x0), Integer(x1))
new_esEs8(Right(x0), Right(x1), x2, ty_Ordering)
new_ltEs9(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs25(x0, x1, ty_Integer)
new_esEs20(x0, x1, ty_Integer)
new_ltEs5(x0, x1, x2)
new_compare18(x0, x1, True)
new_esEs16(x0, x1, x2, x3)
new_compare18(x0, x1, False)
new_compare6(:%(x0, x1), :%(x2, x3), ty_Int)
new_compare30(Float(x0, x1), Float(x2, x3))
new_lt11(x0, x1)
new_ltEs4(Right(x0), Right(x1), x2, ty_@0)
new_esEs12(:%(x0, x1), :%(x2, x3), x4)
new_esEs27(x0, x1, ty_Bool)
new_esEs18(GT, LT)
new_esEs18(LT, GT)
new_ltEs19(x0, x1, ty_@0)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs9(Float(x0, x1), Float(x2, x3))
new_ltEs7(x0, x1, ty_Ordering)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_lt15(x0, x1, x2)
new_esEs8(Right(x0), Right(x1), x2, ty_Integer)
new_ltEs4(Right(x0), Right(x1), x2, ty_Float)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_lt20(x0, x1, app(ty_Ratio, x2))
new_esEs25(x0, x1, ty_Char)
new_esEs29(x0, x1, ty_Int)
new_ltEs19(x0, x1, ty_Double)
new_esEs6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs27(x0, x1, ty_Integer)
new_esEs7(Just(x0), Just(x1), ty_@0)
new_lt4(x0, x1, ty_Bool)
new_ltEs7(x0, x1, app(app(ty_@2, x2), x3))
new_compare23(x0, x1, False, x2, x3)
new_ltEs4(Left(x0), Left(x1), ty_Bool, x2)
new_ltEs19(x0, x1, ty_Int)
new_esEs8(Left(x0), Left(x1), ty_@0, x2)
new_esEs14(False, False)
new_esEs8(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_primEqInt(Pos(Zero), Pos(Zero))
new_esEs25(x0, x1, ty_@0)
new_ltEs4(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs21(x0, x1, ty_Double)
new_ltEs18(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs18(Just(x0), Just(x1), ty_@0)
new_esEs24(x0, x1, ty_Int)
new_lt20(x0, x1, ty_@0)
new_esEs7(Just(x0), Just(x1), ty_Ordering)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_ltEs18(Just(x0), Just(x1), app(ty_[], x2))
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, ty_Int)
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_esEs25(x0, x1, ty_Int)
new_esEs24(x0, x1, ty_Bool)
new_primPlusNat1(Succ(x0), Zero)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs8(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_primMulInt(Pos(x0), Pos(x1))
new_compare28(x0, x1, True, x2, x3)
new_ltEs18(Just(x0), Just(x1), ty_Double)
new_not(LT)
new_ltEs11(True, True)
new_esEs7(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_compare11(x0, x1, False, x2)
new_compare24(x0, x1, True, x2)
new_esEs10([], [], x0)
new_esEs8(Right(x0), Right(x1), x2, ty_Char)
We have to consider all minimal (P,Q,R)-chains.
By using the subterm criterion [20] together with the size-change analysis [32] we have proven that there are no infinite chains for this DP problem. From the DPs we obtained the following set of size-change graphs:
- new_ltEs(@2(vyy6000, vyy6001), @2(vyy500, vyy501), cb, app(app(app(ty_@3, ce), cf), cg)) → new_ltEs0(vyy6001, vyy501, ce, cf, cg)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5
- new_ltEs(@2(vyy6000, vyy6001), @2(vyy500, vyy501), cb, app(ty_[], da)) → new_ltEs1(vyy6001, vyy501, da)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
- new_ltEs(@2(vyy6000, vyy6001), @2(vyy500, vyy501), cb, app(app(ty_Either, dc), dd)) → new_ltEs3(vyy6001, vyy501, dc, dd)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
- new_ltEs(@2(vyy6000, vyy6001), @2(vyy500, vyy501), app(app(ty_Either, bh), ca), bb) → new_compare22(vyy6000, vyy500, new_esEs8(vyy6000, vyy500, bh, ca), bh, ca)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 4, 3 > 5
- new_ltEs(@2(vyy6000, vyy6001), @2(vyy500, vyy501), app(app(ty_@2, h), ba), bb) → new_compare2(vyy6000, vyy500, new_esEs5(vyy6000, vyy500, h, ba), h, ba)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 4, 3 > 5
- new_compare(:(vyy6000, vyy6001), :(vyy500, vyy501), hd) → new_compare(vyy6001, vyy501, hd)
The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3
- new_compare(:(vyy6000, vyy6001), :(vyy500, vyy501), hd) → new_primCompAux(vyy6000, vyy500, new_compare3(vyy6001, vyy501, hd), hd)
The graph contains the following edges 1 > 1, 2 > 2, 3 >= 4
- new_ltEs(@2(vyy6000, vyy6001), @2(vyy500, vyy501), app(ty_[], bf), bb) → new_compare(vyy6000, vyy500, bf)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
- new_primCompAux(vyy6000, vyy500, vyy56, app(ty_[], bab)) → new_compare(vyy6000, vyy500, bab)
The graph contains the following edges 1 >= 1, 2 >= 2, 4 > 3
- new_compare1(vyy6000, vyy500, bc, bd, be) → new_compare20(vyy6000, vyy500, new_esEs6(vyy6000, vyy500, bc, bd, be), bc, bd, be)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 4, 4 >= 5, 5 >= 6
- new_ltEs1(:(vyy6000, vyy6001), :(vyy500, vyy501), hd) → new_primCompAux(vyy6000, vyy500, new_compare3(vyy6001, vyy501, hd), hd)
The graph contains the following edges 1 > 1, 2 > 2, 3 >= 4
- new_ltEs(@2(vyy6000, vyy6001), @2(vyy500, vyy501), cb, app(app(ty_@2, cc), cd)) → new_ltEs(vyy6001, vyy501, cc, cd)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
- new_ltEs1(:(vyy6000, vyy6001), :(vyy500, vyy501), hd) → new_compare(vyy6001, vyy501, hd)
The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3
- new_lt1(vyy6000, vyy500, bf) → new_compare(vyy6000, vyy500, bf)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3
- new_lt0(vyy6000, vyy500, bc, bd, be) → new_compare20(vyy6000, vyy500, new_esEs6(vyy6000, vyy500, bc, bd, be), bc, bd, be)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 4, 4 >= 5, 5 >= 6
- new_compare2(vyy6000, vyy500, False, h, ba) → new_ltEs(vyy6000, vyy500, h, ba)
The graph contains the following edges 1 >= 1, 2 >= 2, 4 >= 3, 5 >= 4
- new_ltEs2(Just(vyy6000), Just(vyy500), app(app(app(ty_@3, bah), bba), bbb)) → new_ltEs0(vyy6000, vyy500, bah, bba, bbb)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
- new_ltEs2(Just(vyy6000), Just(vyy500), app(ty_[], bbc)) → new_ltEs1(vyy6000, vyy500, bbc)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
- new_ltEs0(@3(vyy6000, vyy6001, vyy6002), @3(vyy500, vyy501, vyy502), eh, dg, app(ty_[], gh)) → new_ltEs1(vyy6002, vyy502, gh)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3
- new_ltEs2(Just(vyy6000), Just(vyy500), app(app(ty_Either, bbe), bbf)) → new_ltEs3(vyy6000, vyy500, bbe, bbf)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
- new_ltEs2(Just(vyy6000), Just(vyy500), app(app(ty_@2, baf), bag)) → new_ltEs(vyy6000, vyy500, baf, bag)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
- new_ltEs0(@3(vyy6000, vyy6001, vyy6002), @3(vyy500, vyy501, vyy502), eh, dg, app(app(ty_@2, gc), gd)) → new_ltEs(vyy6002, vyy502, gc, gd)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4
- new_ltEs2(Just(vyy6000), Just(vyy500), app(ty_Maybe, bbd)) → new_ltEs2(vyy6000, vyy500, bbd)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
- new_lt2(vyy6000, vyy500, bg) → new_compare21(vyy6000, vyy500, new_esEs7(vyy6000, vyy500, bg), bg)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 4
- new_ltEs0(@3(vyy6000, vyy6001, vyy6002), @3(vyy500, vyy501, vyy502), eh, dg, app(app(app(ty_@3, ge), gf), gg)) → new_ltEs0(vyy6002, vyy502, ge, gf, gg)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4, 5 > 5
- new_compare20(vyy6000, vyy500, False, bc, bd, be) → new_ltEs0(vyy6000, vyy500, bc, bd, be)
The graph contains the following edges 1 >= 1, 2 >= 2, 4 >= 3, 5 >= 4, 6 >= 5
- new_ltEs0(@3(vyy6000, vyy6001, vyy6002), @3(vyy500, vyy501, vyy502), eh, dg, app(app(ty_Either, hb), hc)) → new_ltEs3(vyy6002, vyy502, hb, hc)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4
- new_compare22(vyy6000, vyy500, False, bh, ca) → new_ltEs3(vyy6000, vyy500, bh, ca)
The graph contains the following edges 1 >= 1, 2 >= 2, 4 >= 3, 5 >= 4
- new_compare0(vyy6000, vyy500, h, ba) → new_compare2(vyy6000, vyy500, new_esEs5(vyy6000, vyy500, h, ba), h, ba)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 4, 4 >= 5
- new_lt(vyy6000, vyy500, h, ba) → new_compare2(vyy6000, vyy500, new_esEs5(vyy6000, vyy500, h, ba), h, ba)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 4, 4 >= 5
- new_primCompAux(vyy6000, vyy500, vyy56, app(app(ty_@2, he), hf)) → new_compare0(vyy6000, vyy500, he, hf)
The graph contains the following edges 1 >= 1, 2 >= 2, 4 > 3, 4 > 4
- new_ltEs(@2(vyy6000, vyy6001), @2(vyy500, vyy501), cb, app(ty_Maybe, db)) → new_ltEs2(vyy6001, vyy501, db)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
- new_ltEs0(@3(vyy6000, vyy6001, vyy6002), @3(vyy500, vyy501, vyy502), eh, dg, app(ty_Maybe, ha)) → new_ltEs2(vyy6002, vyy502, ha)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3
- new_compare21(vyy6000, vyy500, False, bg) → new_ltEs2(vyy6000, vyy500, bg)
The graph contains the following edges 1 >= 1, 2 >= 2, 4 >= 3
- new_compare4(vyy6000, vyy500, bg) → new_compare21(vyy6000, vyy500, new_esEs7(vyy6000, vyy500, bg), bg)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 4
- new_compare5(vyy6000, vyy500, bh, ca) → new_compare22(vyy6000, vyy500, new_esEs8(vyy6000, vyy500, bh, ca), bh, ca)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 4, 4 >= 5
- new_lt3(vyy6000, vyy500, bh, ca) →