YES 8.762
H-Termination proof of /home/matraf/haskell/eval_FullyBlown_Fast/FiniteMap.hs
H-Termination of the given Haskell-Program with start terms could successfully be proven:
↳ HASKELL
↳ LR
mainModule FiniteMap
|
| ((fmToList_LE :: Ord b => FiniteMap b a -> b -> [(b,a)]) :: Ord b => FiniteMap b a -> b -> [(b,a)]) |
module FiniteMap where
| | import qualified Maybe
import qualified Prelude
|
| | data FiniteMap b a = EmptyFM | Branch b a Int (FiniteMap b a) (FiniteMap b a)
|
| | instance (Eq a, Eq b) => Eq (FiniteMap b a) where
|
|
|
| (==) | fm_1 fm_2 | = | sizeFM fm_1 == sizeFM fm_2 && fmToList fm_1 == fmToList fm_2 |
|
|
| | fmToList :: FiniteMap a b -> [(a,b)]
| fmToList | fm | = | foldFM (\key elt rest ->(key,elt) : rest) [] fm |
|
| | fmToList_LE :: Ord a => FiniteMap a b -> a -> [(a,b)]
| fmToList_LE | fm fr | = | foldFM_LE (\key elt rest ->(key,elt) : rest) [] fr fm |
|
| | foldFM :: (c -> b -> a -> a) -> a -> FiniteMap c b -> a
| foldFM | k z EmptyFM | = | z |
| foldFM | k z (Branch key elt _ fm_l fm_r) | = | foldFM k (k key elt (foldFM k z fm_r)) fm_l |
|
| | foldFM_LE :: Ord b => (b -> a -> c -> c) -> c -> b -> FiniteMap b a -> c
| foldFM_LE | k z fr EmptyFM | = | z |
| foldFM_LE | k z fr (Branch key elt _ fm_l fm_r) | |
| | | key <= fr | = |
| foldFM_LE k (k key elt (foldFM_LE k z fr fm_l)) fr fm_r |
|
| | | otherwise | = |
|
|
|
| | sizeFM :: FiniteMap a b -> Int
| sizeFM | EmptyFM | = | 0 |
| sizeFM | (Branch _ _ size _ _) | = | size |
|
module Maybe where
| | import qualified FiniteMap
import qualified Prelude
|
Lambda Reductions:
The following Lambda expression
\keyeltrest→(key,elt) : rest
is transformed to
| fmToList0 | key elt rest | = (key,elt) : rest |
The following Lambda expression
\keyeltrest→(key,elt) : rest
is transformed to
| fmToList_LE0 | key elt rest | = (key,elt) : rest |
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
mainModule FiniteMap
|
| ((fmToList_LE :: Ord b => FiniteMap b a -> b -> [(b,a)]) :: Ord b => FiniteMap b a -> b -> [(b,a)]) |
module FiniteMap where
| | import qualified Maybe
import qualified Prelude
|
| | data FiniteMap b a = EmptyFM | Branch b a Int (FiniteMap b a) (FiniteMap b a)
|
| | instance (Eq a, Eq b) => Eq (FiniteMap a b) where
|
|
|
| (==) | fm_1 fm_2 | = | sizeFM fm_1 == sizeFM fm_2 && fmToList fm_1 == fmToList fm_2 |
|
|
| | fmToList :: FiniteMap a b -> [(a,b)]
| fmToList | fm | = | foldFM fmToList0 [] fm |
|
| |
| fmToList0 | key elt rest | = | (key,elt) : rest |
|
| | fmToList_LE :: Ord a => FiniteMap a b -> a -> [(a,b)]
| fmToList_LE | fm fr | = | foldFM_LE fmToList_LE0 [] fr fm |
|
| |
| fmToList_LE0 | key elt rest | = | (key,elt) : rest |
|
| | foldFM :: (b -> c -> a -> a) -> a -> FiniteMap b c -> a
| foldFM | k z EmptyFM | = | z |
| foldFM | k z (Branch key elt _ fm_l fm_r) | = | foldFM k (k key elt (foldFM k z fm_r)) fm_l |
|
| | foldFM_LE :: Ord a => (a -> c -> b -> b) -> b -> a -> FiniteMap a c -> b
| foldFM_LE | k z fr EmptyFM | = | z |
| foldFM_LE | k z fr (Branch key elt _ fm_l fm_r) | |
| | | key <= fr | = |
| foldFM_LE k (k key elt (foldFM_LE k z fr fm_l)) fr fm_r |
|
| | | otherwise | = |
|
|
|
| | sizeFM :: FiniteMap a b -> Int
| sizeFM | EmptyFM | = | 0 |
| sizeFM | (Branch _ _ size _ _) | = | size |
|
module Maybe where
| | import qualified FiniteMap
import qualified Prelude
|
Case Reductions:
The following Case expression
| case | compare x y of |
| | EQ | → o |
| | LT | → LT |
| | GT | → GT |
is transformed to
| primCompAux0 | o EQ | = o |
| primCompAux0 | o LT | = LT |
| primCompAux0 | o GT | = GT |
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
mainModule FiniteMap
|
| ((fmToList_LE :: Ord a => FiniteMap a b -> a -> [(a,b)]) :: Ord a => FiniteMap a b -> a -> [(a,b)]) |
module FiniteMap where
| | import qualified Maybe
import qualified Prelude
|
| | data FiniteMap b a = EmptyFM | Branch b a Int (FiniteMap b a) (FiniteMap b a)
|
| | instance (Eq a, Eq b) => Eq (FiniteMap a b) where
|
|
|
| (==) | fm_1 fm_2 | = | sizeFM fm_1 == sizeFM fm_2 && fmToList fm_1 == fmToList fm_2 |
|
|
| | fmToList :: FiniteMap b a -> [(b,a)]
| fmToList | fm | = | foldFM fmToList0 [] fm |
|
| |
| fmToList0 | key elt rest | = | (key,elt) : rest |
|
| | fmToList_LE :: Ord a => FiniteMap a b -> a -> [(a,b)]
| fmToList_LE | fm fr | = | foldFM_LE fmToList_LE0 [] fr fm |
|
| |
| fmToList_LE0 | key elt rest | = | (key,elt) : rest |
|
| | foldFM :: (a -> c -> b -> b) -> b -> FiniteMap a c -> b
| foldFM | k z EmptyFM | = | z |
| foldFM | k z (Branch key elt _ fm_l fm_r) | = | foldFM k (k key elt (foldFM k z fm_r)) fm_l |
|
| | foldFM_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 Maybe where
| | import qualified FiniteMap
import qualified Prelude
|
If Reductions:
The following If expression
if primGEqNatS x y then Succ (primDivNatS (primMinusNatS x y) (Succ y)) else Zero
is transformed to
| primDivNatS0 | x y True | = Succ (primDivNatS (primMinusNatS x y) (Succ y)) |
| primDivNatS0 | x y False | = Zero |
The following If expression
if primGEqNatS x y then primModNatS (primMinusNatS x y) (Succ y) else Succ x
is transformed to
| primModNatS0 | x y True | = primModNatS (primMinusNatS x y) (Succ y) |
| primModNatS0 | x y False | = Succ x |
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
mainModule FiniteMap
|
| ((fmToList_LE :: Ord a => FiniteMap a b -> a -> [(a,b)]) :: Ord a => FiniteMap a b -> a -> [(a,b)]) |
module FiniteMap where
| | import qualified Maybe
import qualified Prelude
|
| | data FiniteMap a b = EmptyFM | Branch a b Int (FiniteMap a b) (FiniteMap a b)
|
| | instance (Eq a, Eq b) => Eq (FiniteMap a b) where
|
|
|
| (==) | fm_1 fm_2 | = | sizeFM fm_1 == sizeFM fm_2 && fmToList fm_1 == fmToList fm_2 |
|
|
| | fmToList :: FiniteMap a b -> [(a,b)]
| fmToList | fm | = | foldFM fmToList0 [] fm |
|
| |
| fmToList0 | key elt rest | = | (key,elt) : rest |
|
| | fmToList_LE :: Ord b => FiniteMap b a -> b -> [(b,a)]
| fmToList_LE | fm fr | = | foldFM_LE fmToList_LE0 [] fr fm |
|
| |
| fmToList_LE0 | key elt rest | = | (key,elt) : rest |
|
| | foldFM :: (a -> b -> c -> c) -> c -> FiniteMap a b -> c
| foldFM | k z EmptyFM | = | z |
| foldFM | k z (Branch key elt _ fm_l fm_r) | = | foldFM k (k key elt (foldFM k z fm_r)) fm_l |
|
| | foldFM_LE :: Ord c => (c -> a -> b -> b) -> b -> c -> FiniteMap c a -> b
| foldFM_LE | k z fr EmptyFM | = | z |
| foldFM_LE | k z fr (Branch key elt _ fm_l fm_r) | |
| | | key <= fr | = |
| foldFM_LE k (k key elt (foldFM_LE k z fr fm_l)) fr fm_r |
|
| | | otherwise | = |
|
|
|
| | sizeFM :: FiniteMap a b -> Int
| sizeFM | EmptyFM | = | 0 |
| sizeFM | (Branch _ _ size _ _) | = | size |
|
module Maybe where
| | import qualified FiniteMap
import qualified Prelude
|
Replaced joker patterns by fresh variables and removed binding patterns.
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
mainModule FiniteMap
|
| ((fmToList_LE :: Ord b => FiniteMap b a -> b -> [(b,a)]) :: Ord b => FiniteMap b a -> b -> [(b,a)]) |
module FiniteMap where
| | import qualified Maybe
import qualified Prelude
|
| | data FiniteMap b a = EmptyFM | Branch b a Int (FiniteMap b a) (FiniteMap b a)
|
| | instance (Eq a, Eq b) => Eq (FiniteMap b a) where
|
|
|
| (==) | fm_1 fm_2 | = | sizeFM fm_1 == sizeFM fm_2 && fmToList fm_1 == fmToList fm_2 |
|
|
| | fmToList :: FiniteMap b a -> [(b,a)]
| fmToList | fm | = | foldFM fmToList0 [] fm |
|
| |
| fmToList0 | key elt rest | = | (key,elt) : rest |
|
| | fmToList_LE :: Ord b => FiniteMap b a -> b -> [(b,a)]
| fmToList_LE | fm fr | = | foldFM_LE fmToList_LE0 [] fr fm |
|
| |
| fmToList_LE0 | key elt rest | = | (key,elt) : rest |
|
| | foldFM :: (a -> c -> b -> b) -> b -> FiniteMap a c -> b
| foldFM | k z EmptyFM | = | z |
| foldFM | k z (Branch key elt vw fm_l fm_r) | = | foldFM k (k key elt (foldFM k z fm_r)) fm_l |
|
| | foldFM_LE :: Ord b => (b -> c -> a -> a) -> a -> b -> FiniteMap b c -> a
| foldFM_LE | k z fr EmptyFM | = | z |
| foldFM_LE | k z fr (Branch key elt 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 b a -> Int
| sizeFM | EmptyFM | = | 0 |
| sizeFM | (Branch vy vz size wu wv) | = | size |
|
module Maybe where
| | import qualified FiniteMap
import qualified Prelude
|
Cond Reductions:
The following Function with conditions
| foldFM_LE | k z fr EmptyFM | = z |
| foldFM_LE | k z fr (Branch key elt vx fm_l fm_r) |
| | | key <= fr |
| = | foldFM_LE k (k key elt (foldFM_LE k z fr fm_l)) fr fm_r |
|
| | | otherwise | |
|
is transformed to
| foldFM_LE | k z fr EmptyFM | = foldFM_LE3 k z fr EmptyFM |
| foldFM_LE | k z fr (Branch key elt vx fm_l fm_r) | = foldFM_LE2 k z fr (Branch key elt vx fm_l fm_r) |
| foldFM_LE1 | k z fr key elt vx fm_l fm_r True | = foldFM_LE k (k key elt (foldFM_LE k z fr fm_l)) fr fm_r |
| foldFM_LE1 | k z fr key elt vx fm_l fm_r False | = foldFM_LE0 k z fr key elt vx fm_l fm_r otherwise |
| foldFM_LE0 | k z fr key elt vx fm_l fm_r True | = foldFM_LE k z fr fm_l |
| foldFM_LE2 | k z fr (Branch key elt vx fm_l fm_r) | = foldFM_LE1 k z fr key elt vx fm_l fm_r (key <= fr) |
| foldFM_LE3 | k z fr EmptyFM | = z |
| foldFM_LE3 | vvu vvv vvw vvx | = foldFM_LE2 vvu vvv vvw vvx |
The following Function with conditions
| compare | x y |
| | | x == y | |
| | | x <= y | |
| | | otherwise | |
|
is transformed to
| compare | x y | = compare3 x y |
| compare1 | x y True | = LT |
| compare1 | x y False | = compare0 x y otherwise |
| compare2 | x y True | = EQ |
| compare2 | x y False | = compare1 x y (x <= y) |
| compare3 | x y | = compare2 x y (x == y) |
The following Function with conditions
| gcd' | x 0 | = x |
| gcd' | x y | = gcd' y (x `rem` y) |
is transformed to
| gcd' | x vvy | = gcd'2 x vvy |
| gcd' | x y | = gcd'0 x y |
| gcd'0 | x y | = gcd' y (x `rem` y) |
| gcd'1 | True x vvy | = x |
| gcd'1 | vvz vwu vwv | = gcd'0 vwu vwv |
| gcd'2 | x vvy | = gcd'1 (vvy == 0) x vvy |
| gcd'2 | vww vwx | = gcd'0 vww vwx |
The following Function with conditions
| gcd | 0 0 | = error [] |
| gcd | x y | =
| gcd' (abs x) (abs y) |
| where |
| gcd' | x 0 | = x |
| gcd' | x y | = gcd' y (x `rem` y) |
|
|
is transformed to
| gcd | vwy vwz | = gcd3 vwy vwz |
| gcd | x y | = gcd0 x y |
| gcd0 | x y | =
| gcd' (abs x) (abs y) |
| where |
| gcd' | x vvy | = gcd'2 x vvy |
| gcd' | x y | = gcd'0 x y |
|
|
| gcd'0 | x y | = gcd' y (x `rem` y) |
|
|
| gcd'1 | True x vvy | = x |
| gcd'1 | vvz vwu vwv | = gcd'0 vwu vwv |
|
|
| gcd'2 | x vvy | = gcd'1 (vvy == 0) x vvy |
| gcd'2 | vww vwx | = gcd'0 vww vwx |
|
|
| gcd1 | True vwy vwz | = error [] |
| gcd1 | vxu vxv vxw | = gcd0 vxv vxw |
| gcd2 | True vwy vwz | = gcd1 (vwz == 0) vwy vwz |
| gcd2 | vxx vxy vxz | = gcd0 vxy vxz |
| gcd3 | vwy vwz | = gcd2 (vwy == 0) vwy vwz |
| gcd3 | vyu vyv | = gcd0 vyu vyv |
The following Function with conditions
is transformed to
| absReal0 | x True | = `negate` x |
| absReal1 | x True | = x |
| absReal1 | x False | = absReal0 x otherwise |
| absReal2 | x | = absReal1 x (x >= 0) |
The following Function with conditions
is transformed to
| undefined0 | True | = undefined |
| undefined1 | | = undefined0 False |
The following Function with conditions
| reduce | x y |
| | | y == 0 | |
| | | otherwise |
| = | x `quot` d :% (y `quot` d) |
|
|
| where | |
|
is transformed to
| reduce2 | x y | =
| reduce1 x y (y == 0) |
| where | |
|
| reduce0 | x y True | = x `quot` d :% (y `quot` d) |
|
|
| reduce1 | x y True | = error [] |
| reduce1 | x y False | = reduce0 x y otherwise |
|
|
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
mainModule FiniteMap
|
| ((fmToList_LE :: Ord b => FiniteMap b a -> b -> [(b,a)]) :: Ord b => FiniteMap b a -> b -> [(b,a)]) |
module FiniteMap where
| | import qualified Maybe
import qualified Prelude
|
| | data FiniteMap a b = EmptyFM | Branch a b Int (FiniteMap a b) (FiniteMap a b)
|
| | instance (Eq a, Eq b) => Eq (FiniteMap b a) where
|
|
|
| (==) | fm_1 fm_2 | = | sizeFM fm_1 == sizeFM fm_2 && fmToList fm_1 == fmToList fm_2 |
|
|
| | fmToList :: FiniteMap a b -> [(a,b)]
| fmToList | fm | = | foldFM fmToList0 [] fm |
|
| |
| fmToList0 | key elt rest | = | (key,elt) : rest |
|
| | fmToList_LE :: Ord b => FiniteMap b a -> b -> [(b,a)]
| fmToList_LE | fm fr | = | foldFM_LE fmToList_LE0 [] fr fm |
|
| |
| fmToList_LE0 | key elt rest | = | (key,elt) : rest |
|
| | foldFM :: (b -> c -> a -> a) -> a -> FiniteMap b c -> a
| foldFM | k z EmptyFM | = | z |
| foldFM | k z (Branch key elt vw fm_l fm_r) | = | foldFM k (k key elt (foldFM k z fm_r)) fm_l |
|
| | foldFM_LE :: Ord c => (c -> b -> a -> a) -> a -> c -> FiniteMap c b -> a
| foldFM_LE | k z fr EmptyFM | = | foldFM_LE3 k z fr EmptyFM |
| foldFM_LE | k z fr (Branch key elt vx fm_l fm_r) | = | foldFM_LE2 k z fr (Branch key elt vx fm_l fm_r) |
|
| |
| foldFM_LE0 | k z fr key elt vx fm_l fm_r True | = | foldFM_LE k z fr fm_l |
|
| |
| foldFM_LE1 | k z fr key elt vx fm_l fm_r True | = | foldFM_LE k (k key elt (foldFM_LE k z fr fm_l)) fr fm_r |
| foldFM_LE1 | k z fr key elt vx fm_l fm_r False | = | foldFM_LE0 k z fr key elt vx fm_l fm_r otherwise |
|
| |
| foldFM_LE2 | k z fr (Branch key elt vx fm_l fm_r) | = | foldFM_LE1 k z fr key elt vx fm_l fm_r (key <= fr) |
|
| |
| foldFM_LE3 | k z fr EmptyFM | = | z |
| foldFM_LE3 | vvu vvv vvw vvx | = | foldFM_LE2 vvu vvv vvw vvx |
|
| | sizeFM :: FiniteMap b a -> Int
| sizeFM | EmptyFM | = | 0 |
| sizeFM | (Branch vy vz size wu wv) | = | size |
|
module Maybe where
| | import qualified FiniteMap
import qualified Prelude
|
Let/Where Reductions:
The bindings of the following Let/Where expression
| reduce1 x y (y == 0) |
| where | |
|
| reduce0 | x y True | = x `quot` d :% (y `quot` d) |
|
|
| reduce1 | x y True | = error [] |
| reduce1 | x y False | = reduce0 x y otherwise |
|
are unpacked to the following functions on top level
| reduce2Reduce0 | vyw vyx x y True | = x `quot` reduce2D vyw vyx :% (y `quot` reduce2D vyw vyx) |
| reduce2D | vyw vyx | = gcd vyw vyx |
| reduce2Reduce1 | vyw vyx x y True | = error [] |
| reduce2Reduce1 | vyw vyx x y False | = reduce2Reduce0 vyw vyx x y otherwise |
The bindings of the following Let/Where expression
| gcd' (abs x) (abs y) |
| where |
| gcd' | x vvy | = gcd'2 x vvy |
| gcd' | x y | = gcd'0 x y |
|
|
| gcd'0 | x y | = gcd' y (x `rem` y) |
|
|
| gcd'1 | True x vvy | = x |
| gcd'1 | vvz vwu vwv | = gcd'0 vwu vwv |
|
|
| gcd'2 | x vvy | = gcd'1 (vvy == 0) x vvy |
| gcd'2 | vww vwx | = gcd'0 vww vwx |
|
are unpacked to the following functions on top level
| gcd0Gcd'0 | x y | = gcd0Gcd' y (x `rem` y) |
| gcd0Gcd'1 | True x vvy | = x |
| gcd0Gcd'1 | vvz vwu vwv | = gcd0Gcd'0 vwu vwv |
| gcd0Gcd' | x vvy | = gcd0Gcd'2 x vvy |
| gcd0Gcd' | x y | = gcd0Gcd'0 x y |
| gcd0Gcd'2 | x vvy | = gcd0Gcd'1 (vvy == 0) x vvy |
| gcd0Gcd'2 | vww vwx | = gcd0Gcd'0 vww vwx |
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
mainModule FiniteMap
|
| ((fmToList_LE :: Ord b => FiniteMap b a -> b -> [(b,a)]) :: Ord b => FiniteMap b a -> b -> [(b,a)]) |
module FiniteMap where
| | import qualified Maybe
import qualified Prelude
|
| | data FiniteMap b a = EmptyFM | Branch b a Int (FiniteMap b a) (FiniteMap b a)
|
| | instance (Eq a, Eq b) => Eq (FiniteMap b a) where
|
|
|
| (==) | fm_1 fm_2 | = | sizeFM fm_1 == sizeFM fm_2 && fmToList fm_1 == fmToList fm_2 |
|
|
| | fmToList :: FiniteMap b a -> [(b,a)]
| fmToList | fm | = | foldFM fmToList0 [] fm |
|
| |
| fmToList0 | key elt rest | = | (key,elt) : rest |
|
| | fmToList_LE :: Ord b => FiniteMap b a -> b -> [(b,a)]
| fmToList_LE | fm fr | = | foldFM_LE fmToList_LE0 [] fr fm |
|
| |
| fmToList_LE0 | key elt rest | = | (key,elt) : rest |
|
| | foldFM :: (b -> a -> c -> c) -> c -> FiniteMap b a -> c
| foldFM | k z EmptyFM | = | z |
| foldFM | k z (Branch key elt vw fm_l fm_r) | = | foldFM k (k key elt (foldFM k z fm_r)) fm_l |
|
| | foldFM_LE :: Ord c => (c -> b -> a -> a) -> a -> c -> FiniteMap c b -> a
| foldFM_LE | k z fr EmptyFM | = | foldFM_LE3 k z fr EmptyFM |
| foldFM_LE | k z fr (Branch key elt vx fm_l fm_r) | = | foldFM_LE2 k z fr (Branch key elt vx fm_l fm_r) |
|
| |
| foldFM_LE0 | k z fr key elt vx fm_l fm_r True | = | foldFM_LE k z fr fm_l |
|
| |
| foldFM_LE1 | k z fr key elt vx fm_l fm_r True | = | foldFM_LE k (k key elt (foldFM_LE k z fr fm_l)) fr fm_r |
| foldFM_LE1 | k z fr key elt vx fm_l fm_r False | = | foldFM_LE0 k z fr key elt vx fm_l fm_r otherwise |
|
| |
| foldFM_LE2 | k z fr (Branch key elt vx fm_l fm_r) | = | foldFM_LE1 k z fr key elt vx fm_l fm_r (key <= fr) |
|
| |
| foldFM_LE3 | k z fr EmptyFM | = | z |
| foldFM_LE3 | vvu vvv vvw vvx | = | foldFM_LE2 vvu vvv vvw vvx |
|
| | sizeFM :: FiniteMap b a -> Int
| sizeFM | EmptyFM | = | 0 |
| sizeFM | (Branch vy vz size wu wv) | = | size |
|
module Maybe where
| | import qualified FiniteMap
import qualified Prelude
|
Num Reduction: All numbers are transformed to thier corresponding representation with Pos, Neg, Succ and Zero.
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
mainModule FiniteMap
|
| (fmToList_LE :: Ord b => FiniteMap b a -> b -> [(b,a)]) |
module FiniteMap where
| | import qualified Maybe
import qualified Prelude
|
| | data FiniteMap b a = EmptyFM | Branch b a Int (FiniteMap b a) (FiniteMap b a)
|
| | instance (Eq a, Eq b) => Eq (FiniteMap a b) where
|
|
|
| (==) | fm_1 fm_2 | = | sizeFM fm_1 == sizeFM fm_2 && fmToList fm_1 == fmToList fm_2 |
|
|
| | fmToList :: FiniteMap b a -> [(b,a)]
| fmToList | fm | = | foldFM fmToList0 [] fm |
|
| |
| fmToList0 | key elt rest | = | (key,elt) : rest |
|
| | fmToList_LE :: Ord b => FiniteMap b a -> b -> [(b,a)]
| fmToList_LE | fm fr | = | foldFM_LE fmToList_LE0 [] fr fm |
|
| |
| fmToList_LE0 | key elt rest | = | (key,elt) : rest |
|
| | foldFM :: (b -> a -> c -> c) -> c -> FiniteMap b a -> c
| foldFM | k z EmptyFM | = | z |
| foldFM | k z (Branch key elt vw fm_l fm_r) | = | foldFM k (k key elt (foldFM k z fm_r)) fm_l |
|
| | foldFM_LE :: Ord c => (c -> a -> b -> b) -> b -> c -> FiniteMap c a -> b
| foldFM_LE | k z fr EmptyFM | = | foldFM_LE3 k z fr EmptyFM |
| foldFM_LE | k z fr (Branch key elt vx fm_l fm_r) | = | foldFM_LE2 k z fr (Branch key elt vx fm_l fm_r) |
|
| |
| foldFM_LE0 | k z fr key elt vx fm_l fm_r True | = | foldFM_LE k z fr fm_l |
|
| |
| foldFM_LE1 | k z fr key elt vx fm_l fm_r True | = | foldFM_LE k (k key elt (foldFM_LE k z fr fm_l)) fr fm_r |
| foldFM_LE1 | k z fr key elt vx fm_l fm_r False | = | foldFM_LE0 k z fr key elt vx fm_l fm_r otherwise |
|
| |
| foldFM_LE2 | k z fr (Branch key elt vx fm_l fm_r) | = | foldFM_LE1 k z fr key elt vx fm_l fm_r (key <= fr) |
|
| |
| foldFM_LE3 | k z fr EmptyFM | = | z |
| foldFM_LE3 | vvu vvv vvw vvx | = | foldFM_LE2 vvu vvv vvw vvx |
|
| | sizeFM :: FiniteMap b a -> Int
| sizeFM | EmptyFM | = | Pos Zero |
| sizeFM | (Branch vy vz size wu wv) | = | size |
|
module Maybe where
| | import qualified FiniteMap
import qualified Prelude
|
Haskell To QDPs
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDPSizeChangeProof
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_primCmpNat(Succ(vyy3000), Succ(vyy400)) → new_primCmpNat(vyy3000, vyy400)
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(vyy3000), Succ(vyy400)) → new_primCmpNat(vyy3000, vyy400)
The graph contains the following edges 1 > 1, 2 > 2
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDPSizeChangeProof
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_foldFM(vyy790, vyy791, vyy125, Branch(vyy7930, vyy7931, vyy7932, vyy7933, vyy7934), h, ba) → new_foldFM(vyy7930, vyy7931, new_foldFM0(vyy790, vyy791, vyy125, vyy7934, h, ba), vyy7933, h, ba)
new_foldFM(vyy790, vyy791, vyy125, Branch(vyy7930, vyy7931, vyy7932, vyy7933, vyy7934), h, ba) → new_foldFM(vyy790, vyy791, vyy125, vyy7934, h, ba)
The TRS R consists of the following rules:
new_foldFM0(vyy790, vyy791, vyy125, EmptyFM, h, ba) → :(@2(vyy790, vyy791), vyy125)
new_foldFM0(vyy790, vyy791, vyy125, Branch(vyy7930, vyy7931, vyy7932, vyy7933, vyy7934), h, ba) → new_foldFM0(vyy7930, vyy7931, new_foldFM0(vyy790, vyy791, vyy125, vyy7934, h, ba), vyy7933, h, ba)
The set Q consists of the following terms:
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
We have to consider all minimal (P,Q,R)-chains.
By using the subterm criterion [20] together with the size-change analysis [32] we have proven that there are no infinite chains for this DP problem. From the DPs we obtained the following set of size-change graphs:
- new_foldFM(vyy790, vyy791, vyy125, Branch(vyy7930, vyy7931, vyy7932, vyy7933, vyy7934), h, ba) → new_foldFM(vyy7930, vyy7931, new_foldFM0(vyy790, vyy791, vyy125, vyy7934, h, ba), vyy7933, h, ba)
The graph contains the following edges 4 > 1, 4 > 2, 4 > 4, 5 >= 5, 6 >= 6
- new_foldFM(vyy790, vyy791, vyy125, Branch(vyy7930, vyy7931, vyy7932, vyy7933, vyy7934), h, ba) → new_foldFM(vyy790, vyy791, vyy125, vyy7934, h, ba)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 > 4, 5 >= 5, 6 >= 6
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDPSizeChangeProof
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_foldFM1(Branch(vyy790, vyy791, vyy792, vyy793, vyy794), h, ba) → new_foldFM1(vyy794, 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(vyy790, vyy791, vyy792, vyy793, vyy794), h, ba) → new_foldFM1(vyy794, h, ba)
The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDPSizeChangeProof
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_primPlusNat(Succ(vyy12600), Succ(vyy41000)) → new_primPlusNat(vyy12600, vyy41000)
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(vyy12600), Succ(vyy41000)) → new_primPlusNat(vyy12600, vyy41000)
The graph contains the following edges 1 > 1, 2 > 2
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDPSizeChangeProof
↳ QDP
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_primMulNat(Succ(vyy30100), Succ(vyy4100)) → new_primMulNat(vyy30100, Succ(vyy4100))
R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By using the subterm criterion [20] together with the size-change analysis [32] we have proven that there are no infinite chains for this DP problem. From the DPs we obtained the following set of size-change graphs:
- new_primMulNat(Succ(vyy30100), Succ(vyy4100)) → new_primMulNat(vyy30100, Succ(vyy4100))
The graph contains the following edges 1 > 1, 2 >= 2
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDPSizeChangeProof
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_primEqNat(Succ(vyy7800), Succ(vyy7900)) → new_primEqNat(vyy7800, vyy7900)
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(vyy7800), Succ(vyy7900)) → new_primEqNat(vyy7800, vyy7900)
The graph contains the following edges 1 > 1, 2 > 2
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ Rewriting
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_esEs4(Just(vyy780), Just(vyy790), app(ty_Maybe, bgf)) → new_esEs4(vyy780, vyy790, bgf)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(app(app(ty_@3, bg), bh), ca)) → new_esEs3(vyy780, vyy790, bg, bh, ca)
new_esEs1(Left(vyy780), Left(vyy790), app(app(ty_FiniteMap, cf), cg), da) → new_esEs0(vyy780, vyy790, cf, cg)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(ty_Maybe, bcd), bbb, bbc) → new_esEs4(vyy780, vyy790, bcd)
new_esEs4(Just(vyy780), Just(vyy790), app(app(ty_FiniteMap, bfd), bfe)) → new_esEs0(vyy780, vyy790, bfd, bfe)
new_esEs1(Left(vyy780), Left(vyy790), app(app(ty_Either, db), dc), da) → new_esEs1(vyy780, vyy790, db, dc)
new_esEs2(@2(vyy780, vyy781), @2(vyy790, vyy791), hd, app(app(app(ty_@3, bad), bae), baf)) → new_esEs3(vyy781, vyy791, bad, bae, baf)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bce, app(ty_[], bdd), bbc) → new_esEs(vyy781, vyy791, bdd)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(app(ty_Either, bbd), bbe), bbb, bbc) → new_esEs1(vyy780, vyy790, bbd, bbe)
new_esEs1(Left(vyy780), Left(vyy790), app(app(ty_@2, dd), de), da) → new_esEs2(vyy780, vyy790, dd, de)
new_esEs2(@2(vyy780, vyy781), @2(vyy790, vyy791), hd, app(ty_Maybe, bag)) → new_esEs4(vyy781, vyy791, bag)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(app(ty_FiniteMap, bah), bba), bbb, bbc) → new_esEs0(vyy780, vyy790, bah, bba)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bce, app(app(ty_Either, bch), bda), bbc) → new_esEs1(vyy781, vyy791, bch, bda)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bce, app(ty_Maybe, bdh), bbc) → new_esEs4(vyy781, vyy791, bdh)
new_esEs2(@2(vyy780, vyy781), @2(vyy790, vyy791), app(ty_Maybe, hc), gb) → new_esEs4(vyy780, vyy790, hc)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(ty_Maybe, cb)) → new_esEs4(vyy780, vyy790, cb)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(app(ty_@2, bbf), bbg), bbb, bbc) → new_esEs2(vyy780, vyy790, bbf, bbg)
new_esEs4(Just(vyy780), Just(vyy790), app(app(app(ty_@3, bgc), bgd), bge)) → new_esEs3(vyy780, vyy790, bgc, bgd, bge)
new_esEs2(@2(vyy780, vyy781), @2(vyy790, vyy791), app(app(ty_FiniteMap, fh), ga), gb) → new_esEs0(vyy780, vyy790, fh, ga)
new_esEs1(Right(vyy780), Right(vyy790), ec, app(ty_[], fb)) → new_esEs(vyy780, vyy790, fb)
new_esEs0(vyy78, vyy79, cd, ce) → new_esEs(new_fmToList(vyy78, cd, ce), new_fmToList(vyy79, cd, ce), app(app(ty_@2, cd), ce))
new_esEs2(@2(vyy780, vyy781), @2(vyy790, vyy791), app(app(ty_Either, gc), gd), gb) → new_esEs1(vyy780, vyy790, gc, gd)
new_esEs2(@2(vyy780, vyy781), @2(vyy790, vyy791), app(app(app(ty_@3, gh), ha), hb), gb) → new_esEs3(vyy780, vyy790, gh, ha, hb)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bce, app(app(ty_FiniteMap, bcf), bcg), bbc) → new_esEs0(vyy781, vyy791, bcf, bcg)
new_esEs1(Left(vyy780), Left(vyy790), app(ty_Maybe, eb), da) → new_esEs4(vyy780, vyy790, eb)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bce, bbb, app(app(app(ty_@3, beh), bfa), bfb)) → new_esEs3(vyy782, vyy792, beh, bfa, bfb)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bce, bbb, app(ty_[], beg)) → new_esEs(vyy782, vyy792, beg)
new_esEs2(@2(vyy780, vyy781), @2(vyy790, vyy791), hd, app(app(ty_@2, baa), bab)) → new_esEs2(vyy781, vyy791, baa, bab)
new_esEs2(@2(vyy780, vyy781), @2(vyy790, vyy791), hd, app(app(ty_FiniteMap, he), hf)) → new_esEs0(vyy781, vyy791, he, hf)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(app(ty_@2, bd), be)) → new_esEs2(vyy780, vyy790, bd, be)
new_esEs2(@2(vyy780, vyy781), @2(vyy790, vyy791), app(app(ty_@2, ge), gf), gb) → new_esEs2(vyy780, vyy790, ge, gf)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(ty_[], bbh), bbb, bbc) → new_esEs(vyy780, vyy790, bbh)
new_esEs1(Right(vyy780), Right(vyy790), ec, app(app(ty_Either, ef), eg)) → new_esEs1(vyy780, vyy790, ef, eg)
new_esEs1(Right(vyy780), Right(vyy790), ec, app(ty_Maybe, fg)) → new_esEs4(vyy780, vyy790, fg)
new_esEs2(@2(vyy780, vyy781), @2(vyy790, vyy791), hd, app(app(ty_Either, hg), hh)) → new_esEs1(vyy781, vyy791, hg, hh)
new_esEs4(Just(vyy780), Just(vyy790), app(app(ty_@2, bfh), bga)) → new_esEs2(vyy780, vyy790, bfh, bga)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bce, bbb, app(ty_Maybe, bfc)) → new_esEs4(vyy782, vyy792, bfc)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bce, app(app(app(ty_@3, bde), bdf), bdg), bbc) → new_esEs3(vyy781, vyy791, bde, bdf, bdg)
new_esEs1(Right(vyy780), Right(vyy790), ec, app(app(ty_FiniteMap, ed), ee)) → new_esEs0(vyy780, vyy790, ed, ee)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), cc) → new_esEs(vyy781, vyy791, cc)
new_esEs2(@2(vyy780, vyy781), @2(vyy790, vyy791), hd, app(ty_[], bac)) → new_esEs(vyy781, vyy791, bac)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bce, bbb, app(app(ty_@2, bee), bef)) → new_esEs2(vyy782, vyy792, bee, bef)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bce, app(app(ty_@2, bdb), bdc), bbc) → new_esEs2(vyy781, vyy791, bdb, bdc)
new_esEs1(Right(vyy780), Right(vyy790), ec, app(app(app(ty_@3, fc), fd), ff)) → new_esEs3(vyy780, vyy790, fc, fd, ff)
new_esEs1(Right(vyy780), Right(vyy790), ec, app(app(ty_@2, eh), fa)) → new_esEs2(vyy780, vyy790, eh, fa)
new_esEs2(@2(vyy780, vyy781), @2(vyy790, vyy791), app(ty_[], gg), gb) → new_esEs(vyy780, vyy790, gg)
new_esEs4(Just(vyy780), Just(vyy790), app(ty_[], bgb)) → new_esEs(vyy780, vyy790, bgb)
new_esEs4(Just(vyy780), Just(vyy790), app(app(ty_Either, bff), bfg)) → new_esEs1(vyy780, vyy790, bff, bfg)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bce, bbb, app(app(ty_Either, bec), bed)) → new_esEs1(vyy782, vyy792, bec, bed)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(app(ty_Either, bb), bc)) → new_esEs1(vyy780, vyy790, bb, bc)
new_esEs1(Left(vyy780), Left(vyy790), app(ty_[], df), da) → new_esEs(vyy780, vyy790, df)
new_esEs1(Left(vyy780), Left(vyy790), app(app(app(ty_@3, dg), dh), ea), da) → new_esEs3(vyy780, vyy790, dg, dh, ea)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(ty_[], bf)) → new_esEs(vyy780, vyy790, bf)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bce, bbb, app(app(ty_FiniteMap, bea), beb)) → new_esEs0(vyy782, vyy792, bea, beb)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(app(app(ty_@3, bca), bcb), bcc), bbb, bbc) → new_esEs3(vyy780, vyy790, bca, bcb, bcc)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(app(ty_FiniteMap, h), ba)) → new_esEs0(vyy780, vyy790, h, ba)
The TRS R consists of the following rules:
new_foldFM0(vyy790, vyy791, vyy125, EmptyFM, cd, ce) → :(@2(vyy790, vyy791), vyy125)
new_foldFM0(vyy790, vyy791, vyy125, Branch(vyy7930, vyy7931, vyy7932, vyy7933, vyy7934), cd, ce) → new_foldFM0(vyy7930, vyy7931, new_foldFM0(vyy790, vyy791, vyy125, vyy7934, cd, ce), vyy7933, cd, ce)
new_fmToList(vyy79, cd, ce) → new_foldFM2(vyy79, cd, ce)
new_foldFM2(Branch(vyy790, vyy791, vyy792, vyy793, vyy794), cd, ce) → new_foldFM0(vyy790, vyy791, new_foldFM2(vyy794, cd, ce), vyy793, cd, ce)
new_foldFM2(EmptyFM, cd, ce) → []
The set Q consists of the following terms:
new_fmToList(x0, x1, x2)
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_foldFM2(EmptyFM, x0, x1)
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_esEs0(vyy78, vyy79, cd, ce) → new_esEs(new_fmToList(vyy78, cd, ce), new_fmToList(vyy79, cd, ce), app(app(ty_@2, cd), ce)) at position [0] we obtained the following new rules:
new_esEs0(vyy78, vyy79, cd, ce) → new_esEs(new_foldFM2(vyy78, cd, ce), new_fmToList(vyy79, cd, ce), app(app(ty_@2, cd), ce))
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ Rewriting
↳ QDP
↳ Rewriting
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_esEs4(Just(vyy780), Just(vyy790), app(ty_Maybe, bgf)) → new_esEs4(vyy780, vyy790, bgf)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(ty_Maybe, bcd), bbb, bbc) → new_esEs4(vyy780, vyy790, bcd)
new_esEs1(Left(vyy780), Left(vyy790), app(app(ty_FiniteMap, cf), cg), da) → new_esEs0(vyy780, vyy790, cf, cg)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(app(app(ty_@3, bg), bh), ca)) → new_esEs3(vyy780, vyy790, bg, bh, ca)
new_esEs4(Just(vyy780), Just(vyy790), app(app(ty_FiniteMap, bfd), bfe)) → new_esEs0(vyy780, vyy790, bfd, bfe)
new_esEs2(@2(vyy780, vyy781), @2(vyy790, vyy791), hd, app(app(app(ty_@3, bad), bae), baf)) → new_esEs3(vyy781, vyy791, bad, bae, baf)
new_esEs1(Left(vyy780), Left(vyy790), app(app(ty_Either, db), dc), da) → new_esEs1(vyy780, vyy790, db, dc)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bce, app(ty_[], bdd), bbc) → new_esEs(vyy781, vyy791, bdd)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(app(ty_Either, bbd), bbe), bbb, bbc) → new_esEs1(vyy780, vyy790, bbd, bbe)
new_esEs2(@2(vyy780, vyy781), @2(vyy790, vyy791), hd, app(ty_Maybe, bag)) → new_esEs4(vyy781, vyy791, bag)
new_esEs1(Left(vyy780), Left(vyy790), app(app(ty_@2, dd), de), da) → new_esEs2(vyy780, vyy790, dd, de)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(app(ty_FiniteMap, bah), bba), bbb, bbc) → new_esEs0(vyy780, vyy790, bah, bba)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bce, app(app(ty_Either, bch), bda), bbc) → new_esEs1(vyy781, vyy791, bch, bda)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bce, app(ty_Maybe, bdh), bbc) → new_esEs4(vyy781, vyy791, bdh)
new_esEs2(@2(vyy780, vyy781), @2(vyy790, vyy791), app(ty_Maybe, hc), gb) → new_esEs4(vyy780, vyy790, hc)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(ty_Maybe, cb)) → new_esEs4(vyy780, vyy790, cb)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(app(ty_@2, bbf), bbg), bbb, bbc) → new_esEs2(vyy780, vyy790, bbf, bbg)
new_esEs4(Just(vyy780), Just(vyy790), app(app(app(ty_@3, bgc), bgd), bge)) → new_esEs3(vyy780, vyy790, bgc, bgd, bge)
new_esEs2(@2(vyy780, vyy781), @2(vyy790, vyy791), app(app(ty_FiniteMap, fh), ga), gb) → new_esEs0(vyy780, vyy790, fh, ga)
new_esEs1(Right(vyy780), Right(vyy790), ec, app(ty_[], fb)) → new_esEs(vyy780, vyy790, fb)
new_esEs2(@2(vyy780, vyy781), @2(vyy790, vyy791), app(app(ty_Either, gc), gd), gb) → new_esEs1(vyy780, vyy790, gc, gd)
new_esEs2(@2(vyy780, vyy781), @2(vyy790, vyy791), app(app(app(ty_@3, gh), ha), hb), gb) → new_esEs3(vyy780, vyy790, gh, ha, hb)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bce, app(app(ty_FiniteMap, bcf), bcg), bbc) → new_esEs0(vyy781, vyy791, bcf, bcg)
new_esEs1(Left(vyy780), Left(vyy790), app(ty_Maybe, eb), da) → new_esEs4(vyy780, vyy790, eb)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bce, bbb, app(app(app(ty_@3, beh), bfa), bfb)) → new_esEs3(vyy782, vyy792, beh, bfa, bfb)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bce, bbb, app(ty_[], beg)) → new_esEs(vyy782, vyy792, beg)
new_esEs2(@2(vyy780, vyy781), @2(vyy790, vyy791), hd, app(app(ty_@2, baa), bab)) → new_esEs2(vyy781, vyy791, baa, bab)
new_esEs2(@2(vyy780, vyy781), @2(vyy790, vyy791), hd, app(app(ty_FiniteMap, he), hf)) → new_esEs0(vyy781, vyy791, he, hf)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(app(ty_@2, bd), be)) → new_esEs2(vyy780, vyy790, bd, be)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(ty_[], bbh), bbb, bbc) → new_esEs(vyy780, vyy790, bbh)
new_esEs2(@2(vyy780, vyy781), @2(vyy790, vyy791), app(app(ty_@2, ge), gf), gb) → new_esEs2(vyy780, vyy790, ge, gf)
new_esEs1(Right(vyy780), Right(vyy790), ec, app(app(ty_Either, ef), eg)) → new_esEs1(vyy780, vyy790, ef, eg)
new_esEs1(Right(vyy780), Right(vyy790), ec, app(ty_Maybe, fg)) → new_esEs4(vyy780, vyy790, fg)
new_esEs2(@2(vyy780, vyy781), @2(vyy790, vyy791), hd, app(app(ty_Either, hg), hh)) → new_esEs1(vyy781, vyy791, hg, hh)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bce, bbb, app(ty_Maybe, bfc)) → new_esEs4(vyy782, vyy792, bfc)
new_esEs4(Just(vyy780), Just(vyy790), app(app(ty_@2, bfh), bga)) → new_esEs2(vyy780, vyy790, bfh, bga)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bce, app(app(app(ty_@3, bde), bdf), bdg), bbc) → new_esEs3(vyy781, vyy791, bde, bdf, bdg)
new_esEs1(Right(vyy780), Right(vyy790), ec, app(app(ty_FiniteMap, ed), ee)) → new_esEs0(vyy780, vyy790, ed, ee)
new_esEs2(@2(vyy780, vyy781), @2(vyy790, vyy791), hd, app(ty_[], bac)) → new_esEs(vyy781, vyy791, bac)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), cc) → new_esEs(vyy781, vyy791, cc)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bce, bbb, app(app(ty_@2, bee), bef)) → new_esEs2(vyy782, vyy792, bee, bef)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bce, app(app(ty_@2, bdb), bdc), bbc) → new_esEs2(vyy781, vyy791, bdb, bdc)
new_esEs0(vyy78, vyy79, cd, ce) → new_esEs(new_foldFM2(vyy78, cd, ce), new_fmToList(vyy79, cd, ce), app(app(ty_@2, cd), ce))
new_esEs1(Right(vyy780), Right(vyy790), ec, app(app(app(ty_@3, fc), fd), ff)) → new_esEs3(vyy780, vyy790, fc, fd, ff)
new_esEs1(Right(vyy780), Right(vyy790), ec, app(app(ty_@2, eh), fa)) → new_esEs2(vyy780, vyy790, eh, fa)
new_esEs2(@2(vyy780, vyy781), @2(vyy790, vyy791), app(ty_[], gg), gb) → new_esEs(vyy780, vyy790, gg)
new_esEs4(Just(vyy780), Just(vyy790), app(ty_[], bgb)) → new_esEs(vyy780, vyy790, bgb)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bce, bbb, app(app(ty_Either, bec), bed)) → new_esEs1(vyy782, vyy792, bec, bed)
new_esEs4(Just(vyy780), Just(vyy790), app(app(ty_Either, bff), bfg)) → new_esEs1(vyy780, vyy790, bff, bfg)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(app(ty_Either, bb), bc)) → new_esEs1(vyy780, vyy790, bb, bc)
new_esEs1(Left(vyy780), Left(vyy790), app(ty_[], df), da) → new_esEs(vyy780, vyy790, df)
new_esEs1(Left(vyy780), Left(vyy790), app(app(app(ty_@3, dg), dh), ea), da) → new_esEs3(vyy780, vyy790, dg, dh, ea)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(ty_[], bf)) → new_esEs(vyy780, vyy790, bf)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(app(app(ty_@3, bca), bcb), bcc), bbb, bbc) → new_esEs3(vyy780, vyy790, bca, bcb, bcc)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bce, bbb, app(app(ty_FiniteMap, bea), beb)) → new_esEs0(vyy782, vyy792, bea, beb)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(app(ty_FiniteMap, h), ba)) → new_esEs0(vyy780, vyy790, h, ba)
The TRS R consists of the following rules:
new_foldFM0(vyy790, vyy791, vyy125, EmptyFM, cd, ce) → :(@2(vyy790, vyy791), vyy125)
new_foldFM0(vyy790, vyy791, vyy125, Branch(vyy7930, vyy7931, vyy7932, vyy7933, vyy7934), cd, ce) → new_foldFM0(vyy7930, vyy7931, new_foldFM0(vyy790, vyy791, vyy125, vyy7934, cd, ce), vyy7933, cd, ce)
new_fmToList(vyy79, cd, ce) → new_foldFM2(vyy79, cd, ce)
new_foldFM2(Branch(vyy790, vyy791, vyy792, vyy793, vyy794), cd, ce) → new_foldFM0(vyy790, vyy791, new_foldFM2(vyy794, cd, ce), vyy793, cd, ce)
new_foldFM2(EmptyFM, cd, ce) → []
The set Q consists of the following terms:
new_fmToList(x0, x1, x2)
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_foldFM2(EmptyFM, x0, x1)
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_esEs0(vyy78, vyy79, cd, ce) → new_esEs(new_foldFM2(vyy78, cd, ce), new_fmToList(vyy79, cd, ce), app(app(ty_@2, cd), ce)) at position [1] we obtained the following new rules:
new_esEs0(vyy78, vyy79, cd, ce) → new_esEs(new_foldFM2(vyy78, cd, ce), new_foldFM2(vyy79, cd, ce), app(app(ty_@2, cd), ce))
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ Rewriting
↳ QDP
↳ Rewriting
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_esEs4(Just(vyy780), Just(vyy790), app(ty_Maybe, bgf)) → new_esEs4(vyy780, vyy790, bgf)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(app(app(ty_@3, bg), bh), ca)) → new_esEs3(vyy780, vyy790, bg, bh, ca)
new_esEs1(Left(vyy780), Left(vyy790), app(app(ty_FiniteMap, cf), cg), da) → new_esEs0(vyy780, vyy790, cf, cg)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(ty_Maybe, bcd), bbb, bbc) → new_esEs4(vyy780, vyy790, bcd)
new_esEs4(Just(vyy780), Just(vyy790), app(app(ty_FiniteMap, bfd), bfe)) → new_esEs0(vyy780, vyy790, bfd, bfe)
new_esEs1(Left(vyy780), Left(vyy790), app(app(ty_Either, db), dc), da) → new_esEs1(vyy780, vyy790, db, dc)
new_esEs2(@2(vyy780, vyy781), @2(vyy790, vyy791), hd, app(app(app(ty_@3, bad), bae), baf)) → new_esEs3(vyy781, vyy791, bad, bae, baf)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bce, app(ty_[], bdd), bbc) → new_esEs(vyy781, vyy791, bdd)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(app(ty_Either, bbd), bbe), bbb, bbc) → new_esEs1(vyy780, vyy790, bbd, bbe)
new_esEs1(Left(vyy780), Left(vyy790), app(app(ty_@2, dd), de), da) → new_esEs2(vyy780, vyy790, dd, de)
new_esEs2(@2(vyy780, vyy781), @2(vyy790, vyy791), hd, app(ty_Maybe, bag)) → new_esEs4(vyy781, vyy791, bag)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(app(ty_FiniteMap, bah), bba), bbb, bbc) → new_esEs0(vyy780, vyy790, bah, bba)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bce, app(app(ty_Either, bch), bda), bbc) → new_esEs1(vyy781, vyy791, bch, bda)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bce, app(ty_Maybe, bdh), bbc) → new_esEs4(vyy781, vyy791, bdh)
new_esEs2(@2(vyy780, vyy781), @2(vyy790, vyy791), app(ty_Maybe, hc), gb) → new_esEs4(vyy780, vyy790, hc)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(ty_Maybe, cb)) → new_esEs4(vyy780, vyy790, cb)
new_esEs0(vyy78, vyy79, cd, ce) → new_esEs(new_foldFM2(vyy78, cd, ce), new_foldFM2(vyy79, cd, ce), app(app(ty_@2, cd), ce))
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(app(ty_@2, bbf), bbg), bbb, bbc) → new_esEs2(vyy780, vyy790, bbf, bbg)
new_esEs4(Just(vyy780), Just(vyy790), app(app(app(ty_@3, bgc), bgd), bge)) → new_esEs3(vyy780, vyy790, bgc, bgd, bge)
new_esEs2(@2(vyy780, vyy781), @2(vyy790, vyy791), app(app(ty_FiniteMap, fh), ga), gb) → new_esEs0(vyy780, vyy790, fh, ga)
new_esEs1(Right(vyy780), Right(vyy790), ec, app(ty_[], fb)) → new_esEs(vyy780, vyy790, fb)
new_esEs2(@2(vyy780, vyy781), @2(vyy790, vyy791), app(app(ty_Either, gc), gd), gb) → new_esEs1(vyy780, vyy790, gc, gd)
new_esEs2(@2(vyy780, vyy781), @2(vyy790, vyy791), app(app(app(ty_@3, gh), ha), hb), gb) → new_esEs3(vyy780, vyy790, gh, ha, hb)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bce, app(app(ty_FiniteMap, bcf), bcg), bbc) → new_esEs0(vyy781, vyy791, bcf, bcg)
new_esEs1(Left(vyy780), Left(vyy790), app(ty_Maybe, eb), da) → new_esEs4(vyy780, vyy790, eb)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bce, bbb, app(app(app(ty_@3, beh), bfa), bfb)) → new_esEs3(vyy782, vyy792, beh, bfa, bfb)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bce, bbb, app(ty_[], beg)) → new_esEs(vyy782, vyy792, beg)
new_esEs2(@2(vyy780, vyy781), @2(vyy790, vyy791), hd, app(app(ty_@2, baa), bab)) → new_esEs2(vyy781, vyy791, baa, bab)
new_esEs2(@2(vyy780, vyy781), @2(vyy790, vyy791), hd, app(app(ty_FiniteMap, he), hf)) → new_esEs0(vyy781, vyy791, he, hf)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(app(ty_@2, bd), be)) → new_esEs2(vyy780, vyy790, bd, be)
new_esEs2(@2(vyy780, vyy781), @2(vyy790, vyy791), app(app(ty_@2, ge), gf), gb) → new_esEs2(vyy780, vyy790, ge, gf)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(ty_[], bbh), bbb, bbc) → new_esEs(vyy780, vyy790, bbh)
new_esEs1(Right(vyy780), Right(vyy790), ec, app(app(ty_Either, ef), eg)) → new_esEs1(vyy780, vyy790, ef, eg)
new_esEs1(Right(vyy780), Right(vyy790), ec, app(ty_Maybe, fg)) → new_esEs4(vyy780, vyy790, fg)
new_esEs2(@2(vyy780, vyy781), @2(vyy790, vyy791), hd, app(app(ty_Either, hg), hh)) → new_esEs1(vyy781, vyy791, hg, hh)
new_esEs4(Just(vyy780), Just(vyy790), app(app(ty_@2, bfh), bga)) → new_esEs2(vyy780, vyy790, bfh, bga)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bce, bbb, app(ty_Maybe, bfc)) → new_esEs4(vyy782, vyy792, bfc)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bce, app(app(app(ty_@3, bde), bdf), bdg), bbc) → new_esEs3(vyy781, vyy791, bde, bdf, bdg)
new_esEs1(Right(vyy780), Right(vyy790), ec, app(app(ty_FiniteMap, ed), ee)) → new_esEs0(vyy780, vyy790, ed, ee)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), cc) → new_esEs(vyy781, vyy791, cc)
new_esEs2(@2(vyy780, vyy781), @2(vyy790, vyy791), hd, app(ty_[], bac)) → new_esEs(vyy781, vyy791, bac)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bce, bbb, app(app(ty_@2, bee), bef)) → new_esEs2(vyy782, vyy792, bee, bef)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bce, app(app(ty_@2, bdb), bdc), bbc) → new_esEs2(vyy781, vyy791, bdb, bdc)
new_esEs1(Right(vyy780), Right(vyy790), ec, app(app(app(ty_@3, fc), fd), ff)) → new_esEs3(vyy780, vyy790, fc, fd, ff)
new_esEs1(Right(vyy780), Right(vyy790), ec, app(app(ty_@2, eh), fa)) → new_esEs2(vyy780, vyy790, eh, fa)
new_esEs2(@2(vyy780, vyy781), @2(vyy790, vyy791), app(ty_[], gg), gb) → new_esEs(vyy780, vyy790, gg)
new_esEs4(Just(vyy780), Just(vyy790), app(ty_[], bgb)) → new_esEs(vyy780, vyy790, bgb)
new_esEs4(Just(vyy780), Just(vyy790), app(app(ty_Either, bff), bfg)) → new_esEs1(vyy780, vyy790, bff, bfg)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bce, bbb, app(app(ty_Either, bec), bed)) → new_esEs1(vyy782, vyy792, bec, bed)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(app(ty_Either, bb), bc)) → new_esEs1(vyy780, vyy790, bb, bc)
new_esEs1(Left(vyy780), Left(vyy790), app(ty_[], df), da) → new_esEs(vyy780, vyy790, df)
new_esEs1(Left(vyy780), Left(vyy790), app(app(app(ty_@3, dg), dh), ea), da) → new_esEs3(vyy780, vyy790, dg, dh, ea)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(ty_[], bf)) → new_esEs(vyy780, vyy790, bf)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bce, bbb, app(app(ty_FiniteMap, bea), beb)) → new_esEs0(vyy782, vyy792, bea, beb)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(app(app(ty_@3, bca), bcb), bcc), bbb, bbc) → new_esEs3(vyy780, vyy790, bca, bcb, bcc)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(app(ty_FiniteMap, h), ba)) → new_esEs0(vyy780, vyy790, h, ba)
The TRS R consists of the following rules:
new_foldFM0(vyy790, vyy791, vyy125, EmptyFM, cd, ce) → :(@2(vyy790, vyy791), vyy125)
new_foldFM0(vyy790, vyy791, vyy125, Branch(vyy7930, vyy7931, vyy7932, vyy7933, vyy7934), cd, ce) → new_foldFM0(vyy7930, vyy7931, new_foldFM0(vyy790, vyy791, vyy125, vyy7934, cd, ce), vyy7933, cd, ce)
new_fmToList(vyy79, cd, ce) → new_foldFM2(vyy79, cd, ce)
new_foldFM2(Branch(vyy790, vyy791, vyy792, vyy793, vyy794), cd, ce) → new_foldFM0(vyy790, vyy791, new_foldFM2(vyy794, cd, ce), vyy793, cd, ce)
new_foldFM2(EmptyFM, cd, ce) → []
The set Q consists of the following terms:
new_fmToList(x0, x1, x2)
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_foldFM2(EmptyFM, x0, x1)
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
We have to consider all minimal (P,Q,R)-chains.
As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [15] we can delete all non-usable rules [17] from R.
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ Rewriting
↳ QDP
↳ Rewriting
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QReductionProof
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_esEs4(Just(vyy780), Just(vyy790), app(ty_Maybe, bgf)) → new_esEs4(vyy780, vyy790, bgf)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(app(app(ty_@3, bg), bh), ca)) → new_esEs3(vyy780, vyy790, bg, bh, ca)
new_esEs1(Left(vyy780), Left(vyy790), app(app(ty_FiniteMap, cf), cg), da) → new_esEs0(vyy780, vyy790, cf, cg)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(ty_Maybe, bcd), bbb, bbc) → new_esEs4(vyy780, vyy790, bcd)
new_esEs4(Just(vyy780), Just(vyy790), app(app(ty_FiniteMap, bfd), bfe)) → new_esEs0(vyy780, vyy790, bfd, bfe)
new_esEs1(Left(vyy780), Left(vyy790), app(app(ty_Either, db), dc), da) → new_esEs1(vyy780, vyy790, db, dc)
new_esEs2(@2(vyy780, vyy781), @2(vyy790, vyy791), hd, app(app(app(ty_@3, bad), bae), baf)) → new_esEs3(vyy781, vyy791, bad, bae, baf)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bce, app(ty_[], bdd), bbc) → new_esEs(vyy781, vyy791, bdd)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(app(ty_Either, bbd), bbe), bbb, bbc) → new_esEs1(vyy780, vyy790, bbd, bbe)
new_esEs1(Left(vyy780), Left(vyy790), app(app(ty_@2, dd), de), da) → new_esEs2(vyy780, vyy790, dd, de)
new_esEs2(@2(vyy780, vyy781), @2(vyy790, vyy791), hd, app(ty_Maybe, bag)) → new_esEs4(vyy781, vyy791, bag)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(app(ty_FiniteMap, bah), bba), bbb, bbc) → new_esEs0(vyy780, vyy790, bah, bba)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bce, app(app(ty_Either, bch), bda), bbc) → new_esEs1(vyy781, vyy791, bch, bda)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bce, app(ty_Maybe, bdh), bbc) → new_esEs4(vyy781, vyy791, bdh)
new_esEs2(@2(vyy780, vyy781), @2(vyy790, vyy791), app(ty_Maybe, hc), gb) → new_esEs4(vyy780, vyy790, hc)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(ty_Maybe, cb)) → new_esEs4(vyy780, vyy790, cb)
new_esEs0(vyy78, vyy79, cd, ce) → new_esEs(new_foldFM2(vyy78, cd, ce), new_foldFM2(vyy79, cd, ce), app(app(ty_@2, cd), ce))
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(app(ty_@2, bbf), bbg), bbb, bbc) → new_esEs2(vyy780, vyy790, bbf, bbg)
new_esEs4(Just(vyy780), Just(vyy790), app(app(app(ty_@3, bgc), bgd), bge)) → new_esEs3(vyy780, vyy790, bgc, bgd, bge)
new_esEs2(@2(vyy780, vyy781), @2(vyy790, vyy791), app(app(ty_FiniteMap, fh), ga), gb) → new_esEs0(vyy780, vyy790, fh, ga)
new_esEs1(Right(vyy780), Right(vyy790), ec, app(ty_[], fb)) → new_esEs(vyy780, vyy790, fb)
new_esEs2(@2(vyy780, vyy781), @2(vyy790, vyy791), app(app(ty_Either, gc), gd), gb) → new_esEs1(vyy780, vyy790, gc, gd)
new_esEs2(@2(vyy780, vyy781), @2(vyy790, vyy791), app(app(app(ty_@3, gh), ha), hb), gb) → new_esEs3(vyy780, vyy790, gh, ha, hb)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bce, app(app(ty_FiniteMap, bcf), bcg), bbc) → new_esEs0(vyy781, vyy791, bcf, bcg)
new_esEs1(Left(vyy780), Left(vyy790), app(ty_Maybe, eb), da) → new_esEs4(vyy780, vyy790, eb)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bce, bbb, app(app(app(ty_@3, beh), bfa), bfb)) → new_esEs3(vyy782, vyy792, beh, bfa, bfb)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bce, bbb, app(ty_[], beg)) → new_esEs(vyy782, vyy792, beg)
new_esEs2(@2(vyy780, vyy781), @2(vyy790, vyy791), hd, app(app(ty_@2, baa), bab)) → new_esEs2(vyy781, vyy791, baa, bab)
new_esEs2(@2(vyy780, vyy781), @2(vyy790, vyy791), hd, app(app(ty_FiniteMap, he), hf)) → new_esEs0(vyy781, vyy791, he, hf)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(app(ty_@2, bd), be)) → new_esEs2(vyy780, vyy790, bd, be)
new_esEs2(@2(vyy780, vyy781), @2(vyy790, vyy791), app(app(ty_@2, ge), gf), gb) → new_esEs2(vyy780, vyy790, ge, gf)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(ty_[], bbh), bbb, bbc) → new_esEs(vyy780, vyy790, bbh)
new_esEs1(Right(vyy780), Right(vyy790), ec, app(app(ty_Either, ef), eg)) → new_esEs1(vyy780, vyy790, ef, eg)
new_esEs1(Right(vyy780), Right(vyy790), ec, app(ty_Maybe, fg)) → new_esEs4(vyy780, vyy790, fg)
new_esEs2(@2(vyy780, vyy781), @2(vyy790, vyy791), hd, app(app(ty_Either, hg), hh)) → new_esEs1(vyy781, vyy791, hg, hh)
new_esEs4(Just(vyy780), Just(vyy790), app(app(ty_@2, bfh), bga)) → new_esEs2(vyy780, vyy790, bfh, bga)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bce, bbb, app(ty_Maybe, bfc)) → new_esEs4(vyy782, vyy792, bfc)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bce, app(app(app(ty_@3, bde), bdf), bdg), bbc) → new_esEs3(vyy781, vyy791, bde, bdf, bdg)
new_esEs1(Right(vyy780), Right(vyy790), ec, app(app(ty_FiniteMap, ed), ee)) → new_esEs0(vyy780, vyy790, ed, ee)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), cc) → new_esEs(vyy781, vyy791, cc)
new_esEs2(@2(vyy780, vyy781), @2(vyy790, vyy791), hd, app(ty_[], bac)) → new_esEs(vyy781, vyy791, bac)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bce, bbb, app(app(ty_@2, bee), bef)) → new_esEs2(vyy782, vyy792, bee, bef)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bce, app(app(ty_@2, bdb), bdc), bbc) → new_esEs2(vyy781, vyy791, bdb, bdc)
new_esEs1(Right(vyy780), Right(vyy790), ec, app(app(app(ty_@3, fc), fd), ff)) → new_esEs3(vyy780, vyy790, fc, fd, ff)
new_esEs1(Right(vyy780), Right(vyy790), ec, app(app(ty_@2, eh), fa)) → new_esEs2(vyy780, vyy790, eh, fa)
new_esEs2(@2(vyy780, vyy781), @2(vyy790, vyy791), app(ty_[], gg), gb) → new_esEs(vyy780, vyy790, gg)
new_esEs4(Just(vyy780), Just(vyy790), app(ty_[], bgb)) → new_esEs(vyy780, vyy790, bgb)
new_esEs4(Just(vyy780), Just(vyy790), app(app(ty_Either, bff), bfg)) → new_esEs1(vyy780, vyy790, bff, bfg)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bce, bbb, app(app(ty_Either, bec), bed)) → new_esEs1(vyy782, vyy792, bec, bed)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(app(ty_Either, bb), bc)) → new_esEs1(vyy780, vyy790, bb, bc)
new_esEs1(Left(vyy780), Left(vyy790), app(ty_[], df), da) → new_esEs(vyy780, vyy790, df)
new_esEs1(Left(vyy780), Left(vyy790), app(app(app(ty_@3, dg), dh), ea), da) → new_esEs3(vyy780, vyy790, dg, dh, ea)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(ty_[], bf)) → new_esEs(vyy780, vyy790, bf)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bce, bbb, app(app(ty_FiniteMap, bea), beb)) → new_esEs0(vyy782, vyy792, bea, beb)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(app(app(ty_@3, bca), bcb), bcc), bbb, bbc) → new_esEs3(vyy780, vyy790, bca, bcb, bcc)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(app(ty_FiniteMap, h), ba)) → new_esEs0(vyy780, vyy790, h, ba)
The TRS R consists of the following rules:
new_foldFM2(Branch(vyy790, vyy791, vyy792, vyy793, vyy794), cd, ce) → new_foldFM0(vyy790, vyy791, new_foldFM2(vyy794, cd, ce), vyy793, cd, ce)
new_foldFM2(EmptyFM, cd, ce) → []
new_foldFM0(vyy790, vyy791, vyy125, EmptyFM, cd, ce) → :(@2(vyy790, vyy791), vyy125)
new_foldFM0(vyy790, vyy791, vyy125, Branch(vyy7930, vyy7931, vyy7932, vyy7933, vyy7934), cd, ce) → new_foldFM0(vyy7930, vyy7931, new_foldFM0(vyy790, vyy791, vyy125, vyy7934, cd, ce), vyy7933, cd, ce)
The set Q consists of the following terms:
new_fmToList(x0, x1, x2)
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_foldFM2(EmptyFM, x0, x1)
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
We have to consider all minimal (P,Q,R)-chains.
We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.
new_fmToList(x0, x1, x2)
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ Rewriting
↳ QDP
↳ Rewriting
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QReductionProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_esEs4(Just(vyy780), Just(vyy790), app(ty_Maybe, bgf)) → new_esEs4(vyy780, vyy790, bgf)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(app(app(ty_@3, bg), bh), ca)) → new_esEs3(vyy780, vyy790, bg, bh, ca)
new_esEs1(Left(vyy780), Left(vyy790), app(app(ty_FiniteMap, cf), cg), da) → new_esEs0(vyy780, vyy790, cf, cg)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(ty_Maybe, bcd), bbb, bbc) → new_esEs4(vyy780, vyy790, bcd)
new_esEs4(Just(vyy780), Just(vyy790), app(app(ty_FiniteMap, bfd), bfe)) → new_esEs0(vyy780, vyy790, bfd, bfe)
new_esEs1(Left(vyy780), Left(vyy790), app(app(ty_Either, db), dc), da) → new_esEs1(vyy780, vyy790, db, dc)
new_esEs2(@2(vyy780, vyy781), @2(vyy790, vyy791), hd, app(app(app(ty_@3, bad), bae), baf)) → new_esEs3(vyy781, vyy791, bad, bae, baf)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bce, app(ty_[], bdd), bbc) → new_esEs(vyy781, vyy791, bdd)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(app(ty_Either, bbd), bbe), bbb, bbc) → new_esEs1(vyy780, vyy790, bbd, bbe)
new_esEs1(Left(vyy780), Left(vyy790), app(app(ty_@2, dd), de), da) → new_esEs2(vyy780, vyy790, dd, de)
new_esEs2(@2(vyy780, vyy781), @2(vyy790, vyy791), hd, app(ty_Maybe, bag)) → new_esEs4(vyy781, vyy791, bag)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(app(ty_FiniteMap, bah), bba), bbb, bbc) → new_esEs0(vyy780, vyy790, bah, bba)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bce, app(app(ty_Either, bch), bda), bbc) → new_esEs1(vyy781, vyy791, bch, bda)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bce, app(ty_Maybe, bdh), bbc) → new_esEs4(vyy781, vyy791, bdh)
new_esEs2(@2(vyy780, vyy781), @2(vyy790, vyy791), app(ty_Maybe, hc), gb) → new_esEs4(vyy780, vyy790, hc)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(ty_Maybe, cb)) → new_esEs4(vyy780, vyy790, cb)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(app(ty_@2, bbf), bbg), bbb, bbc) → new_esEs2(vyy780, vyy790, bbf, bbg)
new_esEs0(vyy78, vyy79, cd, ce) → new_esEs(new_foldFM2(vyy78, cd, ce), new_foldFM2(vyy79, cd, ce), app(app(ty_@2, cd), ce))
new_esEs4(Just(vyy780), Just(vyy790), app(app(app(ty_@3, bgc), bgd), bge)) → new_esEs3(vyy780, vyy790, bgc, bgd, bge)
new_esEs2(@2(vyy780, vyy781), @2(vyy790, vyy791), app(app(ty_FiniteMap, fh), ga), gb) → new_esEs0(vyy780, vyy790, fh, ga)
new_esEs1(Right(vyy780), Right(vyy790), ec, app(ty_[], fb)) → new_esEs(vyy780, vyy790, fb)
new_esEs2(@2(vyy780, vyy781), @2(vyy790, vyy791), app(app(ty_Either, gc), gd), gb) → new_esEs1(vyy780, vyy790, gc, gd)
new_esEs2(@2(vyy780, vyy781), @2(vyy790, vyy791), app(app(app(ty_@3, gh), ha), hb), gb) → new_esEs3(vyy780, vyy790, gh, ha, hb)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bce, app(app(ty_FiniteMap, bcf), bcg), bbc) → new_esEs0(vyy781, vyy791, bcf, bcg)
new_esEs1(Left(vyy780), Left(vyy790), app(ty_Maybe, eb), da) → new_esEs4(vyy780, vyy790, eb)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bce, bbb, app(app(app(ty_@3, beh), bfa), bfb)) → new_esEs3(vyy782, vyy792, beh, bfa, bfb)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bce, bbb, app(ty_[], beg)) → new_esEs(vyy782, vyy792, beg)
new_esEs2(@2(vyy780, vyy781), @2(vyy790, vyy791), hd, app(app(ty_@2, baa), bab)) → new_esEs2(vyy781, vyy791, baa, bab)
new_esEs2(@2(vyy780, vyy781), @2(vyy790, vyy791), hd, app(app(ty_FiniteMap, he), hf)) → new_esEs0(vyy781, vyy791, he, hf)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(app(ty_@2, bd), be)) → new_esEs2(vyy780, vyy790, bd, be)
new_esEs2(@2(vyy780, vyy781), @2(vyy790, vyy791), app(app(ty_@2, ge), gf), gb) → new_esEs2(vyy780, vyy790, ge, gf)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(ty_[], bbh), bbb, bbc) → new_esEs(vyy780, vyy790, bbh)
new_esEs1(Right(vyy780), Right(vyy790), ec, app(app(ty_Either, ef), eg)) → new_esEs1(vyy780, vyy790, ef, eg)
new_esEs1(Right(vyy780), Right(vyy790), ec, app(ty_Maybe, fg)) → new_esEs4(vyy780, vyy790, fg)
new_esEs2(@2(vyy780, vyy781), @2(vyy790, vyy791), hd, app(app(ty_Either, hg), hh)) → new_esEs1(vyy781, vyy791, hg, hh)
new_esEs4(Just(vyy780), Just(vyy790), app(app(ty_@2, bfh), bga)) → new_esEs2(vyy780, vyy790, bfh, bga)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bce, bbb, app(ty_Maybe, bfc)) → new_esEs4(vyy782, vyy792, bfc)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bce, app(app(app(ty_@3, bde), bdf), bdg), bbc) → new_esEs3(vyy781, vyy791, bde, bdf, bdg)
new_esEs1(Right(vyy780), Right(vyy790), ec, app(app(ty_FiniteMap, ed), ee)) → new_esEs0(vyy780, vyy790, ed, ee)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), cc) → new_esEs(vyy781, vyy791, cc)
new_esEs2(@2(vyy780, vyy781), @2(vyy790, vyy791), hd, app(ty_[], bac)) → new_esEs(vyy781, vyy791, bac)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bce, bbb, app(app(ty_@2, bee), bef)) → new_esEs2(vyy782, vyy792, bee, bef)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bce, app(app(ty_@2, bdb), bdc), bbc) → new_esEs2(vyy781, vyy791, bdb, bdc)
new_esEs1(Right(vyy780), Right(vyy790), ec, app(app(app(ty_@3, fc), fd), ff)) → new_esEs3(vyy780, vyy790, fc, fd, ff)
new_esEs1(Right(vyy780), Right(vyy790), ec, app(app(ty_@2, eh), fa)) → new_esEs2(vyy780, vyy790, eh, fa)
new_esEs2(@2(vyy780, vyy781), @2(vyy790, vyy791), app(ty_[], gg), gb) → new_esEs(vyy780, vyy790, gg)
new_esEs4(Just(vyy780), Just(vyy790), app(ty_[], bgb)) → new_esEs(vyy780, vyy790, bgb)
new_esEs4(Just(vyy780), Just(vyy790), app(app(ty_Either, bff), bfg)) → new_esEs1(vyy780, vyy790, bff, bfg)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bce, bbb, app(app(ty_Either, bec), bed)) → new_esEs1(vyy782, vyy792, bec, bed)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(app(ty_Either, bb), bc)) → new_esEs1(vyy780, vyy790, bb, bc)
new_esEs1(Left(vyy780), Left(vyy790), app(ty_[], df), da) → new_esEs(vyy780, vyy790, df)
new_esEs1(Left(vyy780), Left(vyy790), app(app(app(ty_@3, dg), dh), ea), da) → new_esEs3(vyy780, vyy790, dg, dh, ea)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(ty_[], bf)) → new_esEs(vyy780, vyy790, bf)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(app(app(ty_@3, bca), bcb), bcc), bbb, bbc) → new_esEs3(vyy780, vyy790, bca, bcb, bcc)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bce, bbb, app(app(ty_FiniteMap, bea), beb)) → new_esEs0(vyy782, vyy792, bea, beb)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(app(ty_FiniteMap, h), ba)) → new_esEs0(vyy780, vyy790, h, ba)
The TRS R consists of the following rules:
new_foldFM2(Branch(vyy790, vyy791, vyy792, vyy793, vyy794), cd, ce) → new_foldFM0(vyy790, vyy791, new_foldFM2(vyy794, cd, ce), vyy793, cd, ce)
new_foldFM2(EmptyFM, cd, ce) → []
new_foldFM0(vyy790, vyy791, vyy125, EmptyFM, cd, ce) → :(@2(vyy790, vyy791), vyy125)
new_foldFM0(vyy790, vyy791, vyy125, Branch(vyy7930, vyy7931, vyy7932, vyy7933, vyy7934), cd, ce) → new_foldFM0(vyy7930, vyy7931, new_foldFM0(vyy790, vyy791, vyy125, vyy7934, cd, ce), vyy7933, cd, ce)
The set Q consists of the following terms:
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_foldFM2(EmptyFM, x0, x1)
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
We have to consider all minimal (P,Q,R)-chains.
We use the reduction pair processor [15].
The following pairs can be oriented strictly and are deleted.
new_esEs4(Just(vyy780), Just(vyy790), app(ty_Maybe, bgf)) → new_esEs4(vyy780, vyy790, bgf)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(app(app(ty_@3, bg), bh), ca)) → new_esEs3(vyy780, vyy790, bg, bh, ca)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(ty_Maybe, bcd), bbb, bbc) → new_esEs4(vyy780, vyy790, bcd)
new_esEs2(@2(vyy780, vyy781), @2(vyy790, vyy791), hd, app(app(app(ty_@3, bad), bae), baf)) → new_esEs3(vyy781, vyy791, bad, bae, baf)
new_esEs2(@2(vyy780, vyy781), @2(vyy790, vyy791), hd, app(ty_Maybe, bag)) → new_esEs4(vyy781, vyy791, bag)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bce, app(ty_Maybe, bdh), bbc) → new_esEs4(vyy781, vyy791, bdh)
new_esEs2(@2(vyy780, vyy781), @2(vyy790, vyy791), app(ty_Maybe, hc), gb) → new_esEs4(vyy780, vyy790, hc)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(ty_Maybe, cb)) → new_esEs4(vyy780, vyy790, cb)
new_esEs0(vyy78, vyy79, cd, ce) → new_esEs(new_foldFM2(vyy78, cd, ce), new_foldFM2(vyy79, cd, ce), app(app(ty_@2, cd), ce))
new_esEs4(Just(vyy780), Just(vyy790), app(app(app(ty_@3, bgc), bgd), bge)) → new_esEs3(vyy780, vyy790, bgc, bgd, bge)
new_esEs2(@2(vyy780, vyy781), @2(vyy790, vyy791), app(app(app(ty_@3, gh), ha), hb), gb) → new_esEs3(vyy780, vyy790, gh, ha, hb)
new_esEs1(Left(vyy780), Left(vyy790), app(ty_Maybe, eb), da) → new_esEs4(vyy780, vyy790, eb)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bce, bbb, app(app(app(ty_@3, beh), bfa), bfb)) → new_esEs3(vyy782, vyy792, beh, bfa, bfb)
new_esEs1(Right(vyy780), Right(vyy790), ec, app(ty_Maybe, fg)) → new_esEs4(vyy780, vyy790, fg)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bce, bbb, app(ty_Maybe, bfc)) → new_esEs4(vyy782, vyy792, bfc)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bce, app(app(app(ty_@3, bde), bdf), bdg), bbc) → new_esEs3(vyy781, vyy791, bde, bdf, bdg)
new_esEs1(Right(vyy780), Right(vyy790), ec, app(app(app(ty_@3, fc), fd), ff)) → new_esEs3(vyy780, vyy790, fc, fd, ff)
new_esEs1(Left(vyy780), Left(vyy790), app(app(app(ty_@3, dg), dh), ea), da) → new_esEs3(vyy780, vyy790, dg, dh, ea)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(app(app(ty_@3, bca), bcb), bcc), bbb, bbc) → new_esEs3(vyy780, vyy790, bca, bcb, bcc)
The remaining pairs can at least be oriented weakly.
new_esEs1(Left(vyy780), Left(vyy790), app(app(ty_FiniteMap, cf), cg), da) → new_esEs0(vyy780, vyy790, cf, cg)
new_esEs4(Just(vyy780), Just(vyy790), app(app(ty_FiniteMap, bfd), bfe)) → new_esEs0(vyy780, vyy790, bfd, bfe)
new_esEs1(Left(vyy780), Left(vyy790), app(app(ty_Either, db), dc), da) → new_esEs1(vyy780, vyy790, db, dc)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bce, app(ty_[], bdd), bbc) → new_esEs(vyy781, vyy791, bdd)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(app(ty_Either, bbd), bbe), bbb, bbc) → new_esEs1(vyy780, vyy790, bbd, bbe)
new_esEs1(Left(vyy780), Left(vyy790), app(app(ty_@2, dd), de), da) → new_esEs2(vyy780, vyy790, dd, de)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(app(ty_FiniteMap, bah), bba), bbb, bbc) → new_esEs0(vyy780, vyy790, bah, bba)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bce, app(app(ty_Either, bch), bda), bbc) → new_esEs1(vyy781, vyy791, bch, bda)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(app(ty_@2, bbf), bbg), bbb, bbc) → new_esEs2(vyy780, vyy790, bbf, bbg)
new_esEs2(@2(vyy780, vyy781), @2(vyy790, vyy791), app(app(ty_FiniteMap, fh), ga), gb) → new_esEs0(vyy780, vyy790, fh, ga)
new_esEs1(Right(vyy780), Right(vyy790), ec, app(ty_[], fb)) → new_esEs(vyy780, vyy790, fb)
new_esEs2(@2(vyy780, vyy781), @2(vyy790, vyy791), app(app(ty_Either, gc), gd), gb) → new_esEs1(vyy780, vyy790, gc, gd)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bce, app(app(ty_FiniteMap, bcf), bcg), bbc) → new_esEs0(vyy781, vyy791, bcf, bcg)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bce, bbb, app(ty_[], beg)) → new_esEs(vyy782, vyy792, beg)
new_esEs2(@2(vyy780, vyy781), @2(vyy790, vyy791), hd, app(app(ty_@2, baa), bab)) → new_esEs2(vyy781, vyy791, baa, bab)
new_esEs2(@2(vyy780, vyy781), @2(vyy790, vyy791), hd, app(app(ty_FiniteMap, he), hf)) → new_esEs0(vyy781, vyy791, he, hf)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(app(ty_@2, bd), be)) → new_esEs2(vyy780, vyy790, bd, be)
new_esEs2(@2(vyy780, vyy781), @2(vyy790, vyy791), app(app(ty_@2, ge), gf), gb) → new_esEs2(vyy780, vyy790, ge, gf)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(ty_[], bbh), bbb, bbc) → new_esEs(vyy780, vyy790, bbh)
new_esEs1(Right(vyy780), Right(vyy790), ec, app(app(ty_Either, ef), eg)) → new_esEs1(vyy780, vyy790, ef, eg)
new_esEs2(@2(vyy780, vyy781), @2(vyy790, vyy791), hd, app(app(ty_Either, hg), hh)) → new_esEs1(vyy781, vyy791, hg, hh)
new_esEs4(Just(vyy780), Just(vyy790), app(app(ty_@2, bfh), bga)) → new_esEs2(vyy780, vyy790, bfh, bga)
new_esEs1(Right(vyy780), Right(vyy790), ec, app(app(ty_FiniteMap, ed), ee)) → new_esEs0(vyy780, vyy790, ed, ee)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), cc) → new_esEs(vyy781, vyy791, cc)
new_esEs2(@2(vyy780, vyy781), @2(vyy790, vyy791), hd, app(ty_[], bac)) → new_esEs(vyy781, vyy791, bac)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bce, bbb, app(app(ty_@2, bee), bef)) → new_esEs2(vyy782, vyy792, bee, bef)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bce, app(app(ty_@2, bdb), bdc), bbc) → new_esEs2(vyy781, vyy791, bdb, bdc)
new_esEs1(Right(vyy780), Right(vyy790), ec, app(app(ty_@2, eh), fa)) → new_esEs2(vyy780, vyy790, eh, fa)
new_esEs2(@2(vyy780, vyy781), @2(vyy790, vyy791), app(ty_[], gg), gb) → new_esEs(vyy780, vyy790, gg)
new_esEs4(Just(vyy780), Just(vyy790), app(ty_[], bgb)) → new_esEs(vyy780, vyy790, bgb)
new_esEs4(Just(vyy780), Just(vyy790), app(app(ty_Either, bff), bfg)) → new_esEs1(vyy780, vyy790, bff, bfg)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bce, bbb, app(app(ty_Either, bec), bed)) → new_esEs1(vyy782, vyy792, bec, bed)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(app(ty_Either, bb), bc)) → new_esEs1(vyy780, vyy790, bb, bc)
new_esEs1(Left(vyy780), Left(vyy790), app(ty_[], df), da) → new_esEs(vyy780, vyy790, df)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(ty_[], bf)) → new_esEs(vyy780, vyy790, bf)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bce, bbb, app(app(ty_FiniteMap, bea), beb)) → new_esEs0(vyy782, vyy792, bea, beb)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(app(ty_FiniteMap, h), ba)) → new_esEs0(vyy780, vyy790, h, ba)
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)) = x3
POL(new_esEs0(x1, x2, x3, x4)) = 1 + x3 + x4
POL(new_esEs1(x1, x2, x3, x4)) = x3 + x4
POL(new_esEs2(x1, x2, x3, x4)) = x3 + x4
POL(new_esEs3(x1, x2, x3, x4, x5)) = x3 + x4 + x5
POL(new_esEs4(x1, x2, x3)) = x3
POL(new_foldFM0(x1, x2, x3, x4, x5, x6)) = 0
POL(new_foldFM2(x1, x2, x3)) = 0
POL(ty_@2) = 0
POL(ty_@3) = 1
POL(ty_Either) = 0
POL(ty_FiniteMap) = 1
POL(ty_Maybe) = 1
POL(ty_[]) = 0
The following usable rules [17] were oriented:
none
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ Rewriting
↳ QDP
↳ Rewriting
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QReductionProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bce, app(app(ty_FiniteMap, bcf), bcg), bbc) → new_esEs0(vyy781, vyy791, bcf, bcg)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bce, bbb, app(ty_[], beg)) → new_esEs(vyy782, vyy792, beg)
new_esEs2(@2(vyy780, vyy781), @2(vyy790, vyy791), hd, app(app(ty_@2, baa), bab)) → new_esEs2(vyy781, vyy791, baa, bab)
new_esEs2(@2(vyy780, vyy781), @2(vyy790, vyy791), hd, app(app(ty_FiniteMap, he), hf)) → new_esEs0(vyy781, vyy791, he, hf)
new_esEs1(Left(vyy780), Left(vyy790), app(app(ty_FiniteMap, cf), cg), da) → new_esEs0(vyy780, vyy790, cf, cg)
new_esEs4(Just(vyy780), Just(vyy790), app(app(ty_FiniteMap, bfd), bfe)) → new_esEs0(vyy780, vyy790, bfd, bfe)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(app(ty_@2, bd), be)) → new_esEs2(vyy780, vyy790, bd, be)
new_esEs2(@2(vyy780, vyy781), @2(vyy790, vyy791), app(app(ty_@2, ge), gf), gb) → new_esEs2(vyy780, vyy790, ge, gf)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(ty_[], bbh), bbb, bbc) → new_esEs(vyy780, vyy790, bbh)
new_esEs1(Left(vyy780), Left(vyy790), app(app(ty_Either, db), dc), da) → new_esEs1(vyy780, vyy790, db, dc)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bce, app(ty_[], bdd), bbc) → new_esEs(vyy781, vyy791, bdd)
new_esEs1(Right(vyy780), Right(vyy790), ec, app(app(ty_Either, ef), eg)) → new_esEs1(vyy780, vyy790, ef, eg)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(app(ty_Either, bbd), bbe), bbb, bbc) → new_esEs1(vyy780, vyy790, bbd, bbe)
new_esEs1(Left(vyy780), Left(vyy790), app(app(ty_@2, dd), de), da) → new_esEs2(vyy780, vyy790, dd, de)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(app(ty_FiniteMap, bah), bba), bbb, bbc) → new_esEs0(vyy780, vyy790, bah, bba)
new_esEs2(@2(vyy780, vyy781), @2(vyy790, vyy791), hd, app(app(ty_Either, hg), hh)) → new_esEs1(vyy781, vyy791, hg, hh)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bce, app(app(ty_Either, bch), bda), bbc) → new_esEs1(vyy781, vyy791, bch, bda)
new_esEs4(Just(vyy780), Just(vyy790), app(app(ty_@2, bfh), bga)) → new_esEs2(vyy780, vyy790, bfh, bga)
new_esEs1(Right(vyy780), Right(vyy790), ec, app(app(ty_FiniteMap, ed), ee)) → new_esEs0(vyy780, vyy790, ed, ee)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), cc) → new_esEs(vyy781, vyy791, cc)
new_esEs2(@2(vyy780, vyy781), @2(vyy790, vyy791), hd, app(ty_[], bac)) → new_esEs(vyy781, vyy791, bac)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bce, bbb, app(app(ty_@2, bee), bef)) → new_esEs2(vyy782, vyy792, bee, bef)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bce, app(app(ty_@2, bdb), bdc), bbc) → new_esEs2(vyy781, vyy791, bdb, bdc)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), app(app(ty_@2, bbf), bbg), bbb, bbc) → new_esEs2(vyy780, vyy790, bbf, bbg)
new_esEs1(Right(vyy780), Right(vyy790), ec, app(app(ty_@2, eh), fa)) → new_esEs2(vyy780, vyy790, eh, fa)
new_esEs2(@2(vyy780, vyy781), @2(vyy790, vyy791), app(app(ty_FiniteMap, fh), ga), gb) → new_esEs0(vyy780, vyy790, fh, ga)
new_esEs2(@2(vyy780, vyy781), @2(vyy790, vyy791), app(ty_[], gg), gb) → new_esEs(vyy780, vyy790, gg)
new_esEs4(Just(vyy780), Just(vyy790), app(ty_[], bgb)) → new_esEs(vyy780, vyy790, bgb)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bce, bbb, app(app(ty_Either, bec), bed)) → new_esEs1(vyy782, vyy792, bec, bed)
new_esEs4(Just(vyy780), Just(vyy790), app(app(ty_Either, bff), bfg)) → new_esEs1(vyy780, vyy790, bff, bfg)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(app(ty_Either, bb), bc)) → new_esEs1(vyy780, vyy790, bb, bc)
new_esEs1(Right(vyy780), Right(vyy790), ec, app(ty_[], fb)) → new_esEs(vyy780, vyy790, fb)
new_esEs1(Left(vyy780), Left(vyy790), app(ty_[], df), da) → new_esEs(vyy780, vyy790, df)
new_esEs2(@2(vyy780, vyy781), @2(vyy790, vyy791), app(app(ty_Either, gc), gd), gb) → new_esEs1(vyy780, vyy790, gc, gd)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(ty_[], bf)) → new_esEs(vyy780, vyy790, bf)
new_esEs3(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bce, bbb, app(app(ty_FiniteMap, bea), beb)) → new_esEs0(vyy782, vyy792, bea, beb)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(app(ty_FiniteMap, h), ba)) → new_esEs0(vyy780, vyy790, h, ba)
The TRS R consists of the following rules:
new_foldFM2(Branch(vyy790, vyy791, vyy792, vyy793, vyy794), cd, ce) → new_foldFM0(vyy790, vyy791, new_foldFM2(vyy794, cd, ce), vyy793, cd, ce)
new_foldFM2(EmptyFM, cd, ce) → []
new_foldFM0(vyy790, vyy791, vyy125, EmptyFM, cd, ce) → :(@2(vyy790, vyy791), vyy125)
new_foldFM0(vyy790, vyy791, vyy125, Branch(vyy7930, vyy7931, vyy7932, vyy7933, vyy7934), cd, ce) → new_foldFM0(vyy7930, vyy7931, new_foldFM0(vyy790, vyy791, vyy125, vyy7934, cd, ce), vyy7933, cd, ce)
The set Q consists of the following terms:
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_foldFM2(EmptyFM, x0, x1)
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph [15,17,22] contains 1 SCC with 21 less nodes.
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ Rewriting
↳ QDP
↳ Rewriting
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QReductionProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_esEs2(@2(vyy780, vyy781), @2(vyy790, vyy791), hd, app(ty_[], bac)) → new_esEs(vyy781, vyy791, bac)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), cc) → new_esEs(vyy781, vyy791, cc)
new_esEs2(@2(vyy780, vyy781), @2(vyy790, vyy791), hd, app(app(ty_@2, baa), bab)) → new_esEs2(vyy781, vyy791, baa, bab)
new_esEs1(Right(vyy780), Right(vyy790), ec, app(app(ty_@2, eh), fa)) → new_esEs2(vyy780, vyy790, eh, fa)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(app(ty_@2, bd), be)) → new_esEs2(vyy780, vyy790, bd, be)
new_esEs2(@2(vyy780, vyy781), @2(vyy790, vyy791), app(app(ty_@2, ge), gf), gb) → new_esEs2(vyy780, vyy790, ge, gf)
new_esEs2(@2(vyy780, vyy781), @2(vyy790, vyy791), app(ty_[], gg), gb) → new_esEs(vyy780, vyy790, gg)
new_esEs1(Left(vyy780), Left(vyy790), app(app(ty_Either, db), dc), da) → new_esEs1(vyy780, vyy790, db, dc)
new_esEs1(Right(vyy780), Right(vyy790), ec, app(app(ty_Either, ef), eg)) → new_esEs1(vyy780, vyy790, ef, eg)
new_esEs1(Right(vyy780), Right(vyy790), ec, app(ty_[], fb)) → new_esEs(vyy780, vyy790, fb)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(app(ty_Either, bb), bc)) → new_esEs1(vyy780, vyy790, bb, bc)
new_esEs1(Left(vyy780), Left(vyy790), app(ty_[], df), da) → new_esEs(vyy780, vyy790, df)
new_esEs1(Left(vyy780), Left(vyy790), app(app(ty_@2, dd), de), da) → new_esEs2(vyy780, vyy790, dd, de)
new_esEs2(@2(vyy780, vyy781), @2(vyy790, vyy791), app(app(ty_Either, gc), gd), gb) → new_esEs1(vyy780, vyy790, gc, gd)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(ty_[], bf)) → new_esEs(vyy780, vyy790, bf)
new_esEs2(@2(vyy780, vyy781), @2(vyy790, vyy791), hd, app(app(ty_Either, hg), hh)) → new_esEs1(vyy781, vyy791, hg, hh)
The TRS R consists of the following rules:
new_foldFM2(Branch(vyy790, vyy791, vyy792, vyy793, vyy794), cd, ce) → new_foldFM0(vyy790, vyy791, new_foldFM2(vyy794, cd, ce), vyy793, cd, ce)
new_foldFM2(EmptyFM, cd, ce) → []
new_foldFM0(vyy790, vyy791, vyy125, EmptyFM, cd, ce) → :(@2(vyy790, vyy791), vyy125)
new_foldFM0(vyy790, vyy791, vyy125, Branch(vyy7930, vyy7931, vyy7932, vyy7933, vyy7934), cd, ce) → new_foldFM0(vyy7930, vyy7931, new_foldFM0(vyy790, vyy791, vyy125, vyy7934, cd, ce), vyy7933, cd, ce)
The set Q consists of the following terms:
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_foldFM2(EmptyFM, x0, x1)
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
We have to consider all minimal (P,Q,R)-chains.
As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [15] we can delete all non-usable rules [17] from R.
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ Rewriting
↳ QDP
↳ Rewriting
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QReductionProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QReductionProof
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_esEs2(@2(vyy780, vyy781), @2(vyy790, vyy791), hd, app(ty_[], bac)) → new_esEs(vyy781, vyy791, bac)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), cc) → new_esEs(vyy781, vyy791, cc)
new_esEs2(@2(vyy780, vyy781), @2(vyy790, vyy791), hd, app(app(ty_@2, baa), bab)) → new_esEs2(vyy781, vyy791, baa, bab)
new_esEs1(Right(vyy780), Right(vyy790), ec, app(app(ty_@2, eh), fa)) → new_esEs2(vyy780, vyy790, eh, fa)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(app(ty_@2, bd), be)) → new_esEs2(vyy780, vyy790, bd, be)
new_esEs2(@2(vyy780, vyy781), @2(vyy790, vyy791), app(app(ty_@2, ge), gf), gb) → new_esEs2(vyy780, vyy790, ge, gf)
new_esEs2(@2(vyy780, vyy781), @2(vyy790, vyy791), app(ty_[], gg), gb) → new_esEs(vyy780, vyy790, gg)
new_esEs1(Left(vyy780), Left(vyy790), app(app(ty_Either, db), dc), da) → new_esEs1(vyy780, vyy790, db, dc)
new_esEs1(Right(vyy780), Right(vyy790), ec, app(app(ty_Either, ef), eg)) → new_esEs1(vyy780, vyy790, ef, eg)
new_esEs1(Right(vyy780), Right(vyy790), ec, app(ty_[], fb)) → new_esEs(vyy780, vyy790, fb)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(app(ty_Either, bb), bc)) → new_esEs1(vyy780, vyy790, bb, bc)
new_esEs1(Left(vyy780), Left(vyy790), app(ty_[], df), da) → new_esEs(vyy780, vyy790, df)
new_esEs1(Left(vyy780), Left(vyy790), app(app(ty_@2, dd), de), da) → new_esEs2(vyy780, vyy790, dd, de)
new_esEs2(@2(vyy780, vyy781), @2(vyy790, vyy791), app(app(ty_Either, gc), gd), gb) → new_esEs1(vyy780, vyy790, gc, gd)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(ty_[], bf)) → new_esEs(vyy780, vyy790, bf)
new_esEs2(@2(vyy780, vyy781), @2(vyy790, vyy791), hd, app(app(ty_Either, hg), hh)) → new_esEs1(vyy781, vyy791, hg, hh)
R is empty.
The set Q consists of the following terms:
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_foldFM2(EmptyFM, x0, x1)
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
We have to consider all minimal (P,Q,R)-chains.
We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_foldFM2(EmptyFM, x0, x1)
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ Rewriting
↳ QDP
↳ Rewriting
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QReductionProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QReductionProof
↳ QDP
↳ QDPSizeChangeProof
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_esEs2(@2(vyy780, vyy781), @2(vyy790, vyy791), hd, app(ty_[], bac)) → new_esEs(vyy781, vyy791, bac)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), cc) → new_esEs(vyy781, vyy791, cc)
new_esEs2(@2(vyy780, vyy781), @2(vyy790, vyy791), hd, app(app(ty_@2, baa), bab)) → new_esEs2(vyy781, vyy791, baa, bab)
new_esEs1(Right(vyy780), Right(vyy790), ec, app(app(ty_@2, eh), fa)) → new_esEs2(vyy780, vyy790, eh, fa)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(app(ty_@2, bd), be)) → new_esEs2(vyy780, vyy790, bd, be)
new_esEs2(@2(vyy780, vyy781), @2(vyy790, vyy791), app(app(ty_@2, ge), gf), gb) → new_esEs2(vyy780, vyy790, ge, gf)
new_esEs2(@2(vyy780, vyy781), @2(vyy790, vyy791), app(ty_[], gg), gb) → new_esEs(vyy780, vyy790, gg)
new_esEs1(Left(vyy780), Left(vyy790), app(app(ty_Either, db), dc), da) → new_esEs1(vyy780, vyy790, db, dc)
new_esEs1(Right(vyy780), Right(vyy790), ec, app(app(ty_Either, ef), eg)) → new_esEs1(vyy780, vyy790, ef, eg)
new_esEs1(Right(vyy780), Right(vyy790), ec, app(ty_[], fb)) → new_esEs(vyy780, vyy790, fb)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(app(ty_Either, bb), bc)) → new_esEs1(vyy780, vyy790, bb, bc)
new_esEs1(Left(vyy780), Left(vyy790), app(ty_[], df), da) → new_esEs(vyy780, vyy790, df)
new_esEs1(Left(vyy780), Left(vyy790), app(app(ty_@2, dd), de), da) → new_esEs2(vyy780, vyy790, dd, de)
new_esEs2(@2(vyy780, vyy781), @2(vyy790, vyy791), app(app(ty_Either, gc), gd), gb) → new_esEs1(vyy780, vyy790, gc, gd)
new_esEs2(@2(vyy780, vyy781), @2(vyy790, vyy791), hd, app(app(ty_Either, hg), hh)) → new_esEs1(vyy781, vyy791, hg, hh)
new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(ty_[], bf)) → new_esEs(vyy780, vyy790, bf)
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_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(app(ty_@2, bd), be)) → new_esEs2(vyy780, vyy790, bd, be)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
- new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(app(ty_Either, bb), bc)) → new_esEs1(vyy780, vyy790, bb, bc)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
- new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), cc) → new_esEs(vyy781, vyy791, cc)
The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3
- new_esEs(:(vyy780, vyy781), :(vyy790, vyy791), app(ty_[], bf)) → new_esEs(vyy780, vyy790, bf)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
- new_esEs2(@2(vyy780, vyy781), @2(vyy790, vyy791), hd, app(app(ty_@2, baa), bab)) → new_esEs2(vyy781, vyy791, baa, bab)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
- new_esEs2(@2(vyy780, vyy781), @2(vyy790, vyy791), app(app(ty_@2, ge), gf), gb) → new_esEs2(vyy780, vyy790, ge, gf)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
- new_esEs1(Right(vyy780), Right(vyy790), ec, app(app(ty_@2, eh), fa)) → new_esEs2(vyy780, vyy790, eh, fa)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
- new_esEs1(Left(vyy780), Left(vyy790), app(app(ty_@2, dd), de), da) → new_esEs2(vyy780, vyy790, dd, de)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
- new_esEs2(@2(vyy780, vyy781), @2(vyy790, vyy791), hd, app(ty_[], bac)) → new_esEs(vyy781, vyy791, bac)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
- new_esEs2(@2(vyy780, vyy781), @2(vyy790, vyy791), app(ty_[], gg), gb) → new_esEs(vyy780, vyy790, gg)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
- new_esEs1(Right(vyy780), Right(vyy790), ec, app(ty_[], fb)) → new_esEs(vyy780, vyy790, fb)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
- new_esEs1(Left(vyy780), Left(vyy790), app(ty_[], df), da) → new_esEs(vyy780, vyy790, df)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
- new_esEs2(@2(vyy780, vyy781), @2(vyy790, vyy791), app(app(ty_Either, gc), gd), gb) → new_esEs1(vyy780, vyy790, gc, gd)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
- new_esEs2(@2(vyy780, vyy781), @2(vyy790, vyy791), hd, app(app(ty_Either, hg), hh)) → new_esEs1(vyy781, vyy791, hg, hh)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
- new_esEs1(Left(vyy780), Left(vyy790), app(app(ty_Either, db), dc), da) → new_esEs1(vyy780, vyy790, db, dc)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
- new_esEs1(Right(vyy780), Right(vyy790), ec, app(app(ty_Either, ef), eg)) → new_esEs1(vyy780, vyy790, ef, eg)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDPSizeChangeProof
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_lt3(vyy300, vyy40, ef) → new_compare22(vyy300, vyy40, new_esEs8(vyy300, vyy40, ef), ef)
new_ltEs1(Left(vyy300), Left(vyy40), app(ty_[], gf), ge) → new_ltEs0(vyy300, vyy40, gf)
new_ltEs2(@2(vyy300, vyy301), @2(vyy40, vyy41), app(app(ty_@2, bcg), bch), bcc) → new_lt2(vyy300, vyy40, bcg, bch)
new_ltEs0(:(vyy300, vyy301), :(vyy40, vyy41), eg) → new_compare(vyy301, vyy41, eg)
new_ltEs1(Left(vyy300), Left(vyy40), app(app(ty_@2, ha), hb), ge) → new_ltEs2(vyy300, vyy40, ha, hb)
new_ltEs1(Left(vyy300), Left(vyy40), app(app(ty_Either, gg), gh), ge) → new_ltEs1(vyy300, vyy40, gg, gh)
new_primCompAux(vyy300, vyy40, vyy107, app(app(app(ty_@3, eh), fa), fb)) → new_compare1(vyy300, vyy40, eh, fa, fb)
new_ltEs(@3(vyy300, vyy301, vyy302), @3(vyy40, vyy41, vyy42), h, ba, app(app(ty_@2, bh), ca)) → new_ltEs2(vyy302, vyy42, bh, ca)
new_ltEs1(Right(vyy300), Right(vyy40), hd, app(app(ty_@2, bac), bad)) → new_ltEs2(vyy300, vyy40, bac, bad)
new_ltEs2(@2(vyy300, vyy301), @2(vyy40, vyy41), baf, app(app(app(ty_@3, bag), bah), bba)) → new_ltEs(vyy301, vyy41, bag, bah, bba)
new_ltEs2(@2(vyy300, vyy301), @2(vyy40, vyy41), app(ty_[], bcd), bcc) → new_lt0(vyy300, vyy40, bcd)
new_lt(vyy300, vyy40, df, dg, dh) → new_compare2(vyy300, vyy40, new_esEs5(vyy300, vyy40, df, dg, dh), df, dg, dh)
new_compare20(vyy300, vyy40, False, eb, ec) → new_ltEs1(vyy300, vyy40, eb, ec)
new_ltEs2(@2(vyy300, vyy301), @2(vyy40, vyy41), baf, app(app(ty_Either, bbc), bbd)) → new_ltEs1(vyy301, vyy41, bbc, bbd)
new_compare1(vyy300, vyy40, df, dg, dh) → new_compare2(vyy300, vyy40, new_esEs5(vyy300, vyy40, df, dg, dh), df, dg, dh)
new_ltEs(@3(vyy300, vyy301, vyy302), @3(vyy40, vyy41, vyy42), h, ba, app(ty_[], be)) → new_ltEs0(vyy302, vyy42, be)
new_ltEs(@3(vyy300, vyy301, vyy302), @3(vyy40, vyy41, vyy42), app(ty_Maybe, ef), ba, cf) → new_compare22(vyy300, vyy40, new_esEs8(vyy300, vyy40, ef), ef)
new_compare5(vyy300, vyy40, ef) → new_compare22(vyy300, vyy40, new_esEs8(vyy300, vyy40, ef), ef)
new_ltEs2(@2(vyy300, vyy301), @2(vyy40, vyy41), app(app(ty_Either, bce), bcf), bcc) → new_lt1(vyy300, vyy40, bce, bcf)
new_ltEs3(Just(vyy300), Just(vyy40), app(app(ty_@2, bdh), bea)) → new_ltEs2(vyy300, vyy40, bdh, bea)
new_ltEs1(Left(vyy300), Left(vyy40), app(app(app(ty_@3, gb), gc), gd), ge) → new_ltEs(vyy300, vyy40, gb, gc, gd)
new_primCompAux(vyy300, vyy40, vyy107, app(ty_[], fc)) → new_compare(vyy300, vyy40, fc)
new_compare22(vyy300, vyy40, False, ef) → new_ltEs3(vyy300, vyy40, ef)
new_compare3(vyy300, vyy40, eb, ec) → new_compare20(vyy300, vyy40, new_esEs6(vyy300, vyy40, eb, ec), eb, ec)
new_ltEs(@3(vyy300, vyy301, vyy302), @3(vyy40, vyy41, vyy42), app(app(ty_Either, eb), ec), ba, cf) → new_compare20(vyy300, vyy40, new_esEs6(vyy300, vyy40, eb, ec), eb, ec)
new_lt0(vyy300, vyy40, ea) → new_compare(vyy300, vyy40, ea)
new_ltEs2(@2(vyy300, vyy301), @2(vyy40, vyy41), app(ty_Maybe, bda), bcc) → new_lt3(vyy300, vyy40, bda)
new_ltEs2(@2(vyy300, vyy301), @2(vyy40, vyy41), baf, app(ty_[], bbb)) → new_ltEs0(vyy301, vyy41, bbb)
new_ltEs3(Just(vyy300), Just(vyy40), app(app(app(ty_@3, bdb), bdc), bdd)) → new_ltEs(vyy300, vyy40, bdb, bdc, bdd)
new_lt2(vyy300, vyy40, ed, ee) → new_compare21(vyy300, vyy40, new_esEs7(vyy300, vyy40, ed, ee), ed, ee)
new_compare21(vyy300, vyy40, False, ed, ee) → new_ltEs2(vyy300, vyy40, ed, ee)
new_ltEs1(Right(vyy300), Right(vyy40), hd, app(app(app(ty_@3, he), hf), hg)) → new_ltEs(vyy300, vyy40, he, hf, hg)
new_ltEs0(:(vyy300, vyy301), :(vyy40, vyy41), eg) → new_primCompAux(vyy300, vyy40, new_compare0(vyy301, vyy41, eg), eg)
new_ltEs(@3(vyy300, vyy301, vyy302), @3(vyy40, vyy41, vyy42), h, app(app(ty_@2, dc), dd), cf) → new_lt2(vyy301, vyy41, dc, dd)
new_ltEs(@3(vyy300, vyy301, vyy302), @3(vyy40, vyy41, vyy42), app(app(app(ty_@3, df), dg), dh), ba, cf) → new_compare2(vyy300, vyy40, new_esEs5(vyy300, vyy40, df, dg, dh), df, dg, dh)
new_compare4(vyy300, vyy40, ed, ee) → new_compare21(vyy300, vyy40, new_esEs7(vyy300, vyy40, ed, ee), ed, ee)
new_ltEs(@3(vyy300, vyy301, vyy302), @3(vyy40, vyy41, vyy42), h, app(ty_[], cg), cf) → new_lt0(vyy301, vyy41, cg)
new_ltEs2(@2(vyy300, vyy301), @2(vyy40, vyy41), app(app(app(ty_@3, bbh), bca), bcb), bcc) → new_lt(vyy300, vyy40, bbh, bca, bcb)
new_ltEs(@3(vyy300, vyy301, vyy302), @3(vyy40, vyy41, vyy42), h, app(app(app(ty_@3, cc), cd), ce), cf) → new_lt(vyy301, vyy41, cc, cd, ce)
new_ltEs(@3(vyy300, vyy301, vyy302), @3(vyy40, vyy41, vyy42), h, ba, app(ty_Maybe, cb)) → new_ltEs3(vyy302, vyy42, cb)
new_ltEs1(Right(vyy300), Right(vyy40), hd, app(ty_Maybe, bae)) → new_ltEs3(vyy300, vyy40, bae)
new_ltEs2(@2(vyy300, vyy301), @2(vyy40, vyy41), baf, app(app(ty_@2, bbe), bbf)) → new_ltEs2(vyy301, vyy41, bbe, bbf)
new_ltEs3(Just(vyy300), Just(vyy40), app(ty_[], bde)) → new_ltEs0(vyy300, vyy40, bde)
new_compare(:(vyy300, vyy301), :(vyy40, vyy41), eg) → new_compare(vyy301, vyy41, eg)
new_primCompAux(vyy300, vyy40, vyy107, app(app(ty_Either, fd), ff)) → new_compare3(vyy300, vyy40, fd, ff)
new_compare2(vyy300, vyy40, False, df, dg, dh) → new_ltEs(vyy300, vyy40, df, dg, dh)
new_compare(:(vyy300, vyy301), :(vyy40, vyy41), eg) → new_primCompAux(vyy300, vyy40, new_compare0(vyy301, vyy41, eg), eg)
new_ltEs1(Left(vyy300), Left(vyy40), app(ty_Maybe, hc), ge) → new_ltEs3(vyy300, vyy40, hc)
new_ltEs1(Right(vyy300), Right(vyy40), hd, app(app(ty_Either, baa), bab)) → new_ltEs1(vyy300, vyy40, baa, bab)
new_primCompAux(vyy300, vyy40, vyy107, app(app(ty_@2, fg), fh)) → new_compare4(vyy300, vyy40, fg, fh)
new_primCompAux(vyy300, vyy40, vyy107, app(ty_Maybe, ga)) → new_compare5(vyy300, vyy40, ga)
new_ltEs(@3(vyy300, vyy301, vyy302), @3(vyy40, vyy41, vyy42), app(ty_[], ea), ba, cf) → new_compare(vyy300, vyy40, ea)
new_ltEs3(Just(vyy300), Just(vyy40), app(app(ty_Either, bdf), bdg)) → new_ltEs1(vyy300, vyy40, bdf, bdg)
new_lt1(vyy300, vyy40, eb, ec) → new_compare20(vyy300, vyy40, new_esEs6(vyy300, vyy40, eb, ec), eb, ec)
new_ltEs(@3(vyy300, vyy301, vyy302), @3(vyy40, vyy41, vyy42), h, ba, app(app(app(ty_@3, bb), bc), bd)) → new_ltEs(vyy302, vyy42, bb, bc, bd)
new_ltEs2(@2(vyy300, vyy301), @2(vyy40, vyy41), baf, app(ty_Maybe, bbg)) → new_ltEs3(vyy301, vyy41, bbg)
new_ltEs(@3(vyy300, vyy301, vyy302), @3(vyy40, vyy41, vyy42), h, app(ty_Maybe, de), cf) → new_lt3(vyy301, vyy41, de)
new_ltEs(@3(vyy300, vyy301, vyy302), @3(vyy40, vyy41, vyy42), app(app(ty_@2, ed), ee), ba, cf) → new_compare21(vyy300, vyy40, new_esEs7(vyy300, vyy40, ed, ee), ed, ee)
new_ltEs1(Right(vyy300), Right(vyy40), hd, app(ty_[], hh)) → new_ltEs0(vyy300, vyy40, hh)
new_ltEs(@3(vyy300, vyy301, vyy302), @3(vyy40, vyy41, vyy42), h, ba, app(app(ty_Either, bf), bg)) → new_ltEs1(vyy302, vyy42, bf, bg)
new_ltEs3(Just(vyy300), Just(vyy40), app(ty_Maybe, beb)) → new_ltEs3(vyy300, vyy40, beb)
new_ltEs(@3(vyy300, vyy301, vyy302), @3(vyy40, vyy41, vyy42), h, app(app(ty_Either, da), db), cf) → new_lt1(vyy301, vyy41, da, db)
The TRS R consists of the following rules:
new_lt7(vyy301, vyy41, ty_Int) → new_lt10(vyy301, vyy41)
new_esEs6(Right(vyy780), Right(vyy790), cfh, ty_Char) → new_esEs25(vyy780, vyy790)
new_compare112(vyy300, vyy40, True, ef) → LT
new_ltEs19(vyy301, vyy41, ty_Integer) → new_ltEs16(vyy301, vyy41)
new_ltEs14(Left(vyy300), Left(vyy40), ty_Integer, ge) → new_ltEs16(vyy300, vyy40)
new_compare26(vyy300, vyy40, False, eb, ec) → new_compare111(vyy300, vyy40, new_ltEs14(vyy300, vyy40, eb, ec), eb, ec)
new_esEs6(Right(vyy780), Right(vyy790), cfh, ty_Float) → new_esEs23(vyy780, vyy790)
new_esEs8(Just(vyy780), Just(vyy790), app(app(ty_Either, cch), cda)) → new_esEs6(vyy780, vyy790, cch, cda)
new_lt7(vyy301, vyy41, ty_Char) → new_lt4(vyy301, vyy41)
new_compare30(vyy300, vyy40, app(ty_Ratio, ccc)) → new_compare15(vyy300, vyy40, ccc)
new_lt20(vyy300, vyy40, ty_Int) → new_lt10(vyy300, vyy40)
new_lt8(vyy300, vyy40, ty_Int) → new_lt10(vyy300, vyy40)
new_compare15(:%(vyy300, vyy301), :%(vyy40, vyy41), ty_Integer) → new_compare16(new_sr0(vyy300, vyy41), new_sr0(vyy40, vyy301))
new_compare23(vyy300, vyy40, False) → new_compare10(vyy300, vyy40, new_ltEs11(vyy300, vyy40))
new_esEs29(vyy78, vyy79, ty_@0) → new_esEs13(vyy78, vyy79)
new_lt20(vyy300, vyy40, app(ty_Ratio, cca)) → new_lt16(vyy300, vyy40, cca)
new_ltEs6(vyy30, vyy4) → new_not(new_compare13(vyy30, vyy4))
new_lt8(vyy300, vyy40, app(app(app(ty_@3, df), dg), dh)) → new_lt9(vyy300, vyy40, df, dg, dh)
new_ltEs18(Just(vyy300), Just(vyy40), app(ty_Maybe, beb)) → new_ltEs18(vyy300, vyy40, beb)
new_ltEs5(EQ, GT) → True
new_ltEs15(vyy30, vyy4, ccb) → new_not(new_compare15(vyy30, vyy4, ccb))
new_lt8(vyy300, vyy40, app(ty_[], ea)) → new_lt13(vyy300, vyy40, ea)
new_esEs8(Just(vyy780), Just(vyy790), app(app(ty_FiniteMap, cce), ccf)) → new_esEs21(vyy780, vyy790, cce, ccf)
new_esEs6(Right(vyy780), Right(vyy790), cfh, app(ty_Maybe, chd)) → new_esEs8(vyy780, vyy790, chd)
new_lt20(vyy300, vyy40, ty_@0) → new_lt6(vyy300, vyy40)
new_esEs29(vyy78, vyy79, app(ty_[], dcg)) → new_esEs22(vyy78, vyy79, dcg)
new_primMulNat0(Zero, Zero) → Zero
new_ltEs14(Left(vyy300), Left(vyy40), app(ty_[], gf), ge) → new_ltEs12(vyy300, vyy40, gf)
new_esEs6(Right(vyy780), Right(vyy790), cfh, app(app(ty_@2, cgf), cgg)) → new_esEs7(vyy780, vyy790, cgf, cgg)
new_esEs27(vyy781, vyy791, ty_Bool) → new_esEs9(vyy781, vyy791)
new_esEs26(vyy780, vyy790, app(ty_[], daf)) → new_esEs22(vyy780, vyy790, daf)
new_compare30(vyy300, vyy40, app(app(ty_Either, fd), ff)) → new_compare18(vyy300, vyy40, fd, ff)
new_esEs6(Left(vyy780), Left(vyy790), app(ty_[], cfc), cee) → new_esEs22(vyy780, vyy790, cfc)
new_compare30(vyy300, vyy40, ty_Integer) → new_compare16(vyy300, vyy40)
new_esEs19(vyy781, vyy791, ty_Int) → new_esEs10(vyy781, vyy791)
new_esEs27(vyy781, vyy791, ty_Integer) → new_esEs12(vyy781, vyy791)
new_compare19(vyy300, vyy40, ef) → new_compare28(vyy300, vyy40, new_esEs8(vyy300, vyy40, ef), ef)
new_not(GT) → False
new_esEs20(vyy782, vyy792, app(ty_Ratio, cac)) → new_esEs14(vyy782, vyy792, cac)
new_lt20(vyy300, vyy40, ty_Double) → new_lt14(vyy300, vyy40)
new_esEs20(vyy782, vyy792, ty_Ordering) → new_esEs17(vyy782, vyy792)
new_lt8(vyy300, vyy40, app(ty_Ratio, cbg)) → new_lt16(vyy300, vyy40, cbg)
new_compare30(vyy300, vyy40, ty_Ordering) → new_compare29(vyy300, vyy40)
new_compare0(:(vyy300, vyy301), :(vyy40, vyy41), eg) → new_primCompAux0(vyy300, vyy40, new_compare0(vyy301, vyy41, eg), eg)
new_compare30(vyy300, vyy40, ty_Bool) → new_compare6(vyy300, vyy40)
new_compare30(vyy300, vyy40, ty_Double) → new_compare17(vyy300, vyy40)
new_ltEs5(EQ, LT) → False
new_ltEs14(Left(vyy300), Left(vyy40), ty_@0, ge) → new_ltEs10(vyy300, vyy40)
new_lt6(vyy300, vyy40) → new_esEs11(new_compare14(vyy300, vyy40))
new_lt20(vyy300, vyy40, ty_Float) → new_lt12(vyy300, vyy40)
new_esEs27(vyy781, vyy791, app(ty_[], dcb)) → new_esEs22(vyy781, vyy791, dcb)
new_esEs29(vyy78, vyy79, ty_Bool) → new_esEs9(vyy78, vyy79)
new_esEs12(Integer(vyy780), Integer(vyy790)) → new_primEqInt(vyy780, vyy790)
new_ltEs9(vyy30, vyy4) → new_not(new_compare8(vyy30, vyy4))
new_esEs27(vyy781, vyy791, ty_Double) → new_esEs24(vyy781, vyy791)
new_esEs18(vyy780, vyy790, ty_Float) → new_esEs23(vyy780, vyy790)
new_lt20(vyy300, vyy40, app(ty_[], bcd)) → new_lt13(vyy300, vyy40, bcd)
new_esEs19(vyy781, vyy791, app(app(app(ty_@3, bhe), bhf), bhg)) → new_esEs5(vyy781, vyy791, bhe, bhf, bhg)
new_pePe(False, vyy78, vyy79, vyy97, ded) → new_asAs(new_esEs29(vyy78, vyy79, ded), vyy97)
new_esEs28(vyy780, vyy790, ty_Integer) → new_esEs12(vyy780, vyy790)
new_esEs28(vyy780, vyy790, app(app(app(ty_@3, ddh), dea), deb)) → new_esEs5(vyy780, vyy790, ddh, dea, deb)
new_esEs6(Left(vyy780), Left(vyy790), ty_Integer, cee) → new_esEs12(vyy780, vyy790)
new_esEs28(vyy780, vyy790, ty_Bool) → new_esEs9(vyy780, vyy790)
new_ltEs18(Just(vyy300), Just(vyy40), app(app(app(ty_@3, bdb), bdc), bdd)) → new_ltEs7(vyy300, vyy40, bdb, bdc, bdd)
new_foldFM0(vyy790, vyy791, vyy125, EmptyFM, bec, bed) → :(@2(vyy790, vyy791), vyy125)
new_lt7(vyy301, vyy41, ty_Ordering) → new_lt11(vyy301, vyy41)
new_esEs20(vyy782, vyy792, ty_Char) → new_esEs25(vyy782, vyy792)
new_lt20(vyy300, vyy40, ty_Char) → new_lt4(vyy300, vyy40)
new_ltEs4(vyy30, vyy4) → new_not(new_compare7(vyy30, vyy4))
new_ltEs14(Right(vyy300), Right(vyy40), hd, ty_@0) → new_ltEs10(vyy300, vyy40)
new_esEs6(Right(vyy780), Right(vyy790), cfh, ty_@0) → new_esEs13(vyy780, vyy790)
new_esEs6(Right(vyy780), Right(vyy790), cfh, app(ty_Ratio, cgc)) → new_esEs14(vyy780, vyy790, cgc)
new_esEs18(vyy780, vyy790, app(app(ty_@2, bff), bfg)) → new_esEs7(vyy780, vyy790, bff, bfg)
new_ltEs14(Right(vyy300), Right(vyy40), hd, app(app(ty_@2, bac), bad)) → new_ltEs17(vyy300, vyy40, bac, bad)
new_compare23(vyy300, vyy40, True) → EQ
new_compare27(vyy300, vyy40, df, dg, dh) → new_compare210(vyy300, vyy40, new_esEs5(vyy300, vyy40, df, dg, dh), df, dg, dh)
new_esEs28(vyy780, vyy790, ty_@0) → new_esEs13(vyy780, vyy790)
new_esEs26(vyy780, vyy790, ty_@0) → new_esEs13(vyy780, vyy790)
new_esEs24(Double(vyy780, vyy781), Double(vyy790, vyy791)) → new_esEs10(new_sr(vyy780, vyy790), new_sr(vyy781, vyy791))
new_esEs20(vyy782, vyy792, ty_Double) → new_esEs24(vyy782, vyy792)
new_compare14(@0, @0) → EQ
new_esEs8(Just(vyy780), Just(vyy790), ty_Ordering) → new_esEs17(vyy780, vyy790)
new_compare210(vyy300, vyy40, False, df, dg, dh) → new_compare110(vyy300, vyy40, new_ltEs7(vyy300, vyy40, df, dg, dh), df, dg, dh)
new_ltEs11(False, True) → True
new_ltEs8(vyy302, vyy42, ty_Double) → new_ltEs13(vyy302, vyy42)
new_esEs29(vyy78, vyy79, app(ty_Maybe, ccd)) → new_esEs8(vyy78, vyy79, ccd)
new_esEs18(vyy780, vyy790, app(app(ty_Either, bfd), bfe)) → new_esEs6(vyy780, vyy790, bfd, bfe)
new_primCmpNat0(Zero, Succ(vyy400)) → LT
new_esEs16(vyy781, vyy791, ty_Integer) → new_esEs12(vyy781, vyy791)
new_ltEs19(vyy301, vyy41, app(ty_Ratio, cbh)) → new_ltEs15(vyy301, vyy41, cbh)
new_ltEs18(Just(vyy300), Just(vyy40), ty_Char) → new_ltEs9(vyy300, vyy40)
new_esEs6(Left(vyy780), Left(vyy790), ty_Bool, cee) → new_esEs9(vyy780, vyy790)
new_esEs19(vyy781, vyy791, ty_Float) → new_esEs23(vyy781, vyy791)
new_esEs17(LT, LT) → True
new_esEs6(Right(vyy780), Left(vyy790), cfh, cee) → False
new_esEs6(Left(vyy780), Right(vyy790), cfh, cee) → False
new_esEs18(vyy780, vyy790, ty_@0) → new_esEs13(vyy780, vyy790)
new_esEs7(@2(vyy780, vyy781), @2(vyy790, vyy791), che, chf) → new_asAs(new_esEs26(vyy780, vyy790, che), new_esEs27(vyy781, vyy791, chf))
new_esEs6(Right(vyy780), Right(vyy790), cfh, ty_Integer) → new_esEs12(vyy780, vyy790)
new_esEs29(vyy78, vyy79, app(app(ty_@2, che), chf)) → new_esEs7(vyy78, vyy79, che, chf)
new_compare0([], [], eg) → EQ
new_primEqNat0(Zero, Zero) → True
new_esEs29(vyy78, vyy79, app(app(ty_FiniteMap, bec), bed)) → new_esEs21(vyy78, vyy79, bec, bed)
new_ltEs14(Left(vyy300), Left(vyy40), ty_Ordering, ge) → new_ltEs5(vyy300, vyy40)
new_ltEs14(Right(vyy300), Right(vyy40), hd, ty_Float) → new_ltEs6(vyy300, vyy40)
new_ltEs14(Right(vyy300), Right(vyy40), hd, ty_Ordering) → new_ltEs5(vyy300, vyy40)
new_compare30(vyy300, vyy40, ty_Int) → new_compare7(vyy300, vyy40)
new_compare111(vyy300, vyy40, False, eb, ec) → GT
new_esEs27(vyy781, vyy791, ty_Float) → new_esEs23(vyy781, vyy791)
new_esEs6(Right(vyy780), Right(vyy790), cfh, ty_Bool) → new_esEs9(vyy780, vyy790)
new_esEs6(Right(vyy780), Right(vyy790), cfh, app(app(ty_Either, cgd), cge)) → new_esEs6(vyy780, vyy790, cgd, cge)
new_ltEs17(@2(vyy300, vyy301), @2(vyy40, vyy41), baf, bcc) → new_pePe(new_lt20(vyy300, vyy40, baf), vyy300, vyy40, new_ltEs19(vyy301, vyy41, bcc), baf)
new_sr(vyy301, vyy41) → new_primMulInt(vyy301, vyy41)
new_esEs29(vyy78, vyy79, ty_Float) → new_esEs23(vyy78, vyy79)
new_compare7(vyy30, vyy4) → new_primCmpInt(vyy30, vyy4)
new_esEs28(vyy780, vyy790, app(app(ty_Either, ddc), ddd)) → new_esEs6(vyy780, vyy790, ddc, ddd)
new_esEs18(vyy780, vyy790, app(app(app(ty_@3, bga), bgb), bgc)) → new_esEs5(vyy780, vyy790, bga, bgb, bgc)
new_ltEs8(vyy302, vyy42, ty_Int) → new_ltEs4(vyy302, vyy42)
new_ltEs8(vyy302, vyy42, app(ty_[], be)) → new_ltEs12(vyy302, vyy42, be)
new_lt7(vyy301, vyy41, ty_Double) → new_lt14(vyy301, vyy41)
new_ltEs14(Right(vyy300), Right(vyy40), hd, ty_Char) → new_ltEs9(vyy300, vyy40)
new_esEs8(Just(vyy780), Just(vyy790), ty_Bool) → new_esEs9(vyy780, vyy790)
new_primPlusNat0(Succ(vyy1260), vyy4100) → Succ(Succ(new_primPlusNat1(vyy1260, vyy4100)))
new_ltEs5(LT, LT) → True
new_lt8(vyy300, vyy40, ty_Integer) → new_lt17(vyy300, vyy40)
new_lt8(vyy300, vyy40, ty_@0) → new_lt6(vyy300, vyy40)
new_esEs26(vyy780, vyy790, ty_Bool) → new_esEs9(vyy780, vyy790)
new_ltEs8(vyy302, vyy42, app(app(app(ty_@3, bb), bc), bd)) → new_ltEs7(vyy302, vyy42, bb, bc, bd)
new_esEs8(Just(vyy780), Nothing, ccd) → False
new_esEs8(Nothing, Just(vyy790), ccd) → False
new_esEs26(vyy780, vyy790, ty_Integer) → new_esEs12(vyy780, vyy790)
new_esEs29(vyy78, vyy79, ty_Double) → new_esEs24(vyy78, vyy79)
new_lt8(vyy300, vyy40, ty_Double) → new_lt14(vyy300, vyy40)
new_lt20(vyy300, vyy40, app(app(ty_@2, bcg), bch)) → new_lt18(vyy300, vyy40, bcg, bch)
new_esEs8(Just(vyy780), Just(vyy790), ty_Float) → new_esEs23(vyy780, vyy790)
new_primEqInt(Neg(Succ(vyy7800)), Neg(Succ(vyy7900))) → new_primEqNat0(vyy7800, vyy7900)
new_compare25(vyy300, vyy40, True) → EQ
new_esEs26(vyy780, vyy790, ty_Double) → new_esEs24(vyy780, vyy790)
new_ltEs19(vyy301, vyy41, app(app(ty_@2, bbe), bbf)) → new_ltEs17(vyy301, vyy41, bbe, bbf)
new_esEs26(vyy780, vyy790, app(ty_Maybe, dbb)) → new_esEs8(vyy780, vyy790, dbb)
new_esEs27(vyy781, vyy791, app(app(ty_FiniteMap, dbc), dbd)) → new_esEs21(vyy781, vyy791, dbc, dbd)
new_esEs28(vyy780, vyy790, ty_Char) → new_esEs25(vyy780, vyy790)
new_lt20(vyy300, vyy40, app(ty_Maybe, bda)) → new_lt19(vyy300, vyy40, bda)
new_primPlusNat1(Zero, Succ(vyy41000)) → Succ(vyy41000)
new_primPlusNat1(Succ(vyy12600), Zero) → Succ(vyy12600)
new_lt8(vyy300, vyy40, ty_Char) → new_lt4(vyy300, vyy40)
new_esEs19(vyy781, vyy791, ty_Double) → new_esEs24(vyy781, vyy791)
new_esEs11(LT) → True
new_ltEs14(Right(vyy300), Left(vyy40), hd, ge) → False
new_ltEs8(vyy302, vyy42, app(app(ty_Either, bf), bg)) → new_ltEs14(vyy302, vyy42, bf, bg)
new_esEs28(vyy780, vyy790, app(ty_Maybe, dec)) → new_esEs8(vyy780, vyy790, dec)
new_ltEs18(Just(vyy300), Just(vyy40), app(ty_Ratio, def)) → new_ltEs15(vyy300, vyy40, def)
new_ltEs18(Just(vyy300), Just(vyy40), app(app(ty_@2, bdh), bea)) → new_ltEs17(vyy300, vyy40, bdh, bea)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs17(EQ, EQ) → True
new_esEs6(Left(vyy780), Left(vyy790), ty_Ordering, cee) → new_esEs17(vyy780, vyy790)
new_lt8(vyy300, vyy40, app(app(ty_@2, ed), ee)) → new_lt18(vyy300, vyy40, ed, ee)
new_lt19(vyy300, vyy40, ef) → new_esEs11(new_compare19(vyy300, vyy40, ef))
new_ltEs14(Right(vyy300), Right(vyy40), hd, app(ty_[], hh)) → new_ltEs12(vyy300, vyy40, hh)
new_esEs28(vyy780, vyy790, ty_Ordering) → new_esEs17(vyy780, vyy790)
new_esEs19(vyy781, vyy791, ty_Integer) → new_esEs12(vyy781, vyy791)
new_esEs6(Right(vyy780), Right(vyy790), cfh, app(ty_[], cgh)) → new_esEs22(vyy780, vyy790, cgh)
new_primEqInt(Neg(Zero), Neg(Succ(vyy7900))) → False
new_primEqInt(Neg(Succ(vyy7800)), Neg(Zero)) → False
new_esEs26(vyy780, vyy790, ty_Float) → new_esEs23(vyy780, vyy790)
new_lt8(vyy300, vyy40, ty_Bool) → new_lt5(vyy300, vyy40)
new_ltEs18(Just(vyy300), Just(vyy40), ty_Ordering) → new_ltEs5(vyy300, vyy40)
new_esEs6(Left(vyy780), Left(vyy790), app(ty_Ratio, cef), cee) → new_esEs14(vyy780, vyy790, cef)
new_compare26(vyy300, vyy40, True, eb, ec) → EQ
new_compare9(vyy300, vyy40, ed, ee) → new_compare24(vyy300, vyy40, new_esEs7(vyy300, vyy40, ed, ee), ed, ee)
new_lt7(vyy301, vyy41, ty_Float) → new_lt12(vyy301, vyy41)
new_esEs28(vyy780, vyy790, ty_Double) → new_esEs24(vyy780, vyy790)
new_lt7(vyy301, vyy41, ty_Integer) → new_lt17(vyy301, vyy41)
new_compare24(vyy300, vyy40, True, ed, ee) → EQ
new_lt5(vyy300, vyy40) → new_esEs11(new_compare6(vyy300, vyy40))
new_esEs18(vyy780, vyy790, ty_Bool) → new_esEs9(vyy780, vyy790)
new_ltEs13(vyy30, vyy4) → new_not(new_compare17(vyy30, vyy4))
new_foldFM0(vyy790, vyy791, vyy125, Branch(vyy7930, vyy7931, vyy7932, vyy7933, vyy7934), bec, bed) → new_foldFM0(vyy7930, vyy7931, new_foldFM0(vyy790, vyy791, vyy125, vyy7934, bec, bed), vyy7933, bec, bed)
new_esEs19(vyy781, vyy791, app(ty_Maybe, bhh)) → new_esEs8(vyy781, vyy791, bhh)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_lt8(vyy300, vyy40, ty_Float) → new_lt12(vyy300, vyy40)
new_esEs19(vyy781, vyy791, ty_Bool) → new_esEs9(vyy781, vyy791)
new_lt8(vyy300, vyy40, app(app(ty_Either, eb), ec)) → new_lt15(vyy300, vyy40, eb, ec)
new_esEs28(vyy780, vyy790, app(app(ty_@2, dde), ddf)) → new_esEs7(vyy780, vyy790, dde, ddf)
new_lt7(vyy301, vyy41, app(app(ty_Either, da), db)) → new_lt15(vyy301, vyy41, da, db)
new_ltEs14(Left(vyy300), Left(vyy40), ty_Double, ge) → new_ltEs13(vyy300, vyy40)
new_primCmpNat0(Succ(vyy3000), Succ(vyy400)) → new_primCmpNat0(vyy3000, vyy400)
new_ltEs5(EQ, EQ) → True
new_sizeFM(EmptyFM, bec, bed) → Pos(Zero)
new_ltEs8(vyy302, vyy42, app(app(ty_@2, bh), ca)) → new_ltEs17(vyy302, vyy42, bh, ca)
new_ltEs8(vyy302, vyy42, app(ty_Ratio, cbe)) → new_ltEs15(vyy302, vyy42, cbe)
new_primEqInt(Pos(Succ(vyy7800)), Pos(Succ(vyy7900))) → new_primEqNat0(vyy7800, vyy7900)
new_ltEs19(vyy301, vyy41, app(app(app(ty_@3, bag), bah), bba)) → new_ltEs7(vyy301, vyy41, bag, bah, bba)
new_esEs16(vyy781, vyy791, ty_Int) → new_esEs10(vyy781, vyy791)
new_esEs18(vyy780, vyy790, ty_Int) → new_esEs10(vyy780, vyy790)
new_ltEs8(vyy302, vyy42, ty_Ordering) → new_ltEs5(vyy302, vyy42)
new_ltEs14(Right(vyy300), Right(vyy40), hd, ty_Double) → new_ltEs13(vyy300, vyy40)
new_esEs20(vyy782, vyy792, app(ty_Maybe, cbd)) → new_esEs8(vyy782, vyy792, cbd)
new_esEs6(Left(vyy780), Left(vyy790), app(app(app(ty_@3, cfd), cfe), cff), cee) → new_esEs5(vyy780, vyy790, cfd, cfe, cff)
new_compare29(vyy300, vyy40) → new_compare25(vyy300, vyy40, new_esEs17(vyy300, vyy40))
new_esEs20(vyy782, vyy792, ty_Int) → new_esEs10(vyy782, vyy792)
new_ltEs11(True, False) → False
new_esEs20(vyy782, vyy792, app(app(ty_FiniteMap, caa), cab)) → new_esEs21(vyy782, vyy792, caa, cab)
new_esEs19(vyy781, vyy791, app(app(ty_Either, bgh), bha)) → new_esEs6(vyy781, vyy791, bgh, bha)
new_esEs8(Just(vyy780), Just(vyy790), ty_Integer) → new_esEs12(vyy780, vyy790)
new_esEs18(vyy780, vyy790, ty_Char) → new_esEs25(vyy780, vyy790)
new_esEs17(GT, LT) → False
new_esEs17(LT, GT) → False
new_primEqNat0(Succ(vyy7800), Succ(vyy7900)) → new_primEqNat0(vyy7800, vyy7900)
new_esEs17(GT, EQ) → False
new_esEs17(EQ, GT) → False
new_lt16(vyy300, vyy40, cbg) → new_esEs11(new_compare15(vyy300, vyy40, cbg))
new_compare15(:%(vyy300, vyy301), :%(vyy40, vyy41), ty_Int) → new_compare7(new_sr(vyy300, vyy41), new_sr(vyy40, vyy301))
new_esEs23(Float(vyy780, vyy781), Float(vyy790, vyy791)) → new_esEs10(new_sr(vyy780, vyy790), new_sr(vyy781, vyy791))
new_esEs29(vyy78, vyy79, ty_Int) → new_esEs10(vyy78, vyy79)
new_compare17(Double(vyy300, vyy301), Double(vyy40, vyy41)) → new_compare7(new_sr(vyy300, vyy40), new_sr(vyy301, vyy41))
new_lt20(vyy300, vyy40, ty_Integer) → new_lt17(vyy300, vyy40)
new_primCompAux00(vyy111, LT) → LT
new_lt8(vyy300, vyy40, app(ty_Maybe, ef)) → new_lt19(vyy300, vyy40, ef)
new_ltEs14(Left(vyy300), Left(vyy40), app(ty_Ratio, cea), ge) → new_ltEs15(vyy300, vyy40, cea)
new_primCmpInt(Neg(Succ(vyy3000)), Neg(vyy40)) → new_primCmpNat0(vyy40, Succ(vyy3000))
new_esEs27(vyy781, vyy791, app(app(app(ty_@3, dcc), dcd), dce)) → new_esEs5(vyy781, vyy791, dcc, dcd, dce)
new_ltEs18(Just(vyy300), Just(vyy40), ty_@0) → new_ltEs10(vyy300, vyy40)
new_esEs19(vyy781, vyy791, ty_Ordering) → new_esEs17(vyy781, vyy791)
new_primEqInt(Pos(Zero), Pos(Succ(vyy7900))) → False
new_primEqInt(Pos(Succ(vyy7800)), Pos(Zero)) → False
new_ltEs5(GT, LT) → False
new_primCmpNat0(Zero, Zero) → EQ
new_ltEs18(Nothing, Nothing, dee) → True
new_primCmpNat0(Succ(vyy3000), Zero) → GT
new_esEs6(Right(vyy780), Right(vyy790), cfh, ty_Double) → new_esEs24(vyy780, vyy790)
new_lt20(vyy300, vyy40, ty_Bool) → new_lt5(vyy300, vyy40)
new_ltEs14(Right(vyy300), Right(vyy40), hd, ty_Bool) → new_ltEs11(vyy300, vyy40)
new_esEs19(vyy781, vyy791, ty_@0) → new_esEs13(vyy781, vyy791)
new_primCmpInt(Neg(Zero), Pos(Succ(vyy400))) → LT
new_compare11(vyy300, vyy40, True, ed, ee) → LT
new_compare210(vyy300, vyy40, True, df, dg, dh) → EQ
new_lt17(vyy300, vyy40) → new_esEs11(new_compare16(vyy300, vyy40))
new_sr0(Integer(vyy400), Integer(vyy3010)) → Integer(new_primMulInt(vyy400, vyy3010))
new_primPlusNat1(Succ(vyy12600), Succ(vyy41000)) → Succ(Succ(new_primPlusNat1(vyy12600, vyy41000)))
new_primEqInt(Neg(Succ(vyy7800)), Pos(vyy790)) → False
new_primEqInt(Pos(Succ(vyy7800)), Neg(vyy790)) → False
new_esEs18(vyy780, vyy790, app(ty_Ratio, bfc)) → new_esEs14(vyy780, vyy790, bfc)
new_ltEs18(Just(vyy300), Just(vyy40), ty_Integer) → new_ltEs16(vyy300, vyy40)
new_ltEs14(Left(vyy300), Left(vyy40), ty_Float, ge) → new_ltEs6(vyy300, vyy40)
new_foldFM2(EmptyFM, bec, bed) → []
new_ltEs14(Right(vyy300), Right(vyy40), hd, ty_Integer) → new_ltEs16(vyy300, vyy40)
new_lt13(vyy300, vyy40, ea) → new_esEs11(new_compare0(vyy300, vyy40, ea))
new_esEs18(vyy780, vyy790, ty_Double) → new_esEs24(vyy780, vyy790)
new_compare18(vyy300, vyy40, eb, ec) → new_compare26(vyy300, vyy40, new_esEs6(vyy300, vyy40, eb, ec), eb, ec)
new_esEs6(Left(vyy780), Left(vyy790), ty_@0, cee) → new_esEs13(vyy780, vyy790)
new_primEqInt(Neg(Zero), Pos(Succ(vyy7900))) → False
new_primEqInt(Pos(Zero), Neg(Succ(vyy7900))) → False
new_esEs26(vyy780, vyy790, ty_Int) → new_esEs10(vyy780, vyy790)
new_lt7(vyy301, vyy41, app(app(app(ty_@3, cc), cd), ce)) → new_lt9(vyy301, vyy41, cc, cd, ce)
new_esEs13(@0, @0) → True
new_esEs8(Just(vyy780), Just(vyy790), app(app(ty_@2, cdb), cdc)) → new_esEs7(vyy780, vyy790, cdb, cdc)
new_primCompAux00(vyy111, EQ) → vyy111
new_primCmpInt(Pos(Zero), Pos(Succ(vyy400))) → new_primCmpNat0(Zero, Succ(vyy400))
new_esEs27(vyy781, vyy791, app(app(ty_@2, dbh), dca)) → new_esEs7(vyy781, vyy791, dbh, dca)
new_compare12(vyy300, vyy40, False) → GT
new_lt20(vyy300, vyy40, app(app(app(ty_@3, bbh), bca), bcb)) → new_lt9(vyy300, vyy40, bbh, bca, bcb)
new_esEs28(vyy780, vyy790, app(app(ty_FiniteMap, dch), dda)) → new_esEs21(vyy780, vyy790, dch, dda)
new_esEs19(vyy781, vyy791, app(ty_Ratio, bgg)) → new_esEs14(vyy781, vyy791, bgg)
new_lt9(vyy300, vyy40, df, dg, dh) → new_esEs11(new_compare27(vyy300, vyy40, df, dg, dh))
new_lt7(vyy301, vyy41, app(app(ty_@2, dc), dd)) → new_lt18(vyy301, vyy41, dc, dd)
new_esEs22([], [], dcg) → True
new_esEs27(vyy781, vyy791, app(ty_Maybe, dcf)) → new_esEs8(vyy781, vyy791, dcf)
new_esEs28(vyy780, vyy790, app(ty_Ratio, ddb)) → new_esEs14(vyy780, vyy790, ddb)
new_ltEs8(vyy302, vyy42, ty_@0) → new_ltEs10(vyy302, vyy42)
new_esEs6(Left(vyy780), Left(vyy790), app(app(ty_@2, cfa), cfb), cee) → new_esEs7(vyy780, vyy790, cfa, cfb)
new_esEs6(Left(vyy780), Left(vyy790), app(app(ty_FiniteMap, cec), ced), cee) → new_esEs21(vyy780, vyy790, cec, ced)
new_esEs6(Left(vyy780), Left(vyy790), app(app(ty_Either, ceg), ceh), cee) → new_esEs6(vyy780, vyy790, ceg, ceh)
new_compare16(Integer(vyy300), Integer(vyy40)) → new_primCmpInt(vyy300, vyy40)
new_ltEs14(Right(vyy300), Right(vyy40), hd, app(ty_Maybe, bae)) → new_ltEs18(vyy300, vyy40, bae)
new_esEs6(Right(vyy780), Right(vyy790), cfh, ty_Ordering) → new_esEs17(vyy780, vyy790)
new_ltEs18(Just(vyy300), Nothing, dee) → False
new_compare30(vyy300, vyy40, app(app(ty_@2, fg), fh)) → new_compare9(vyy300, vyy40, fg, fh)
new_primCmpInt(Pos(Succ(vyy3000)), Pos(vyy40)) → new_primCmpNat0(Succ(vyy3000), vyy40)
new_primPlusNat0(Zero, vyy4100) → Succ(vyy4100)
new_ltEs18(Just(vyy300), Just(vyy40), ty_Float) → new_ltEs6(vyy300, vyy40)
new_esEs26(vyy780, vyy790, app(ty_Ratio, daa)) → new_esEs14(vyy780, vyy790, daa)
new_esEs19(vyy781, vyy791, app(app(ty_@2, bhb), bhc)) → new_esEs7(vyy781, vyy791, bhb, bhc)
new_esEs29(vyy78, vyy79, ty_Integer) → new_esEs12(vyy78, vyy79)
new_compare25(vyy300, vyy40, False) → new_compare12(vyy300, vyy40, new_ltEs5(vyy300, vyy40))
new_ltEs19(vyy301, vyy41, app(ty_[], bbb)) → new_ltEs12(vyy301, vyy41, bbb)
new_ltEs18(Just(vyy300), Just(vyy40), ty_Double) → new_ltEs13(vyy300, vyy40)
new_compare30(vyy300, vyy40, ty_@0) → new_compare14(vyy300, vyy40)
new_esEs29(vyy78, vyy79, ty_Char) → new_esEs25(vyy78, vyy79)
new_esEs5(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bef, beg, beh) → new_asAs(new_esEs18(vyy780, vyy790, bef), new_asAs(new_esEs19(vyy781, vyy791, beg), new_esEs20(vyy782, vyy792, beh)))
new_esEs8(Just(vyy780), Just(vyy790), app(ty_Ratio, ccg)) → new_esEs14(vyy780, vyy790, ccg)
new_esEs6(Right(vyy780), Right(vyy790), cfh, app(app(ty_FiniteMap, cga), cgb)) → new_esEs21(vyy780, vyy790, cga, cgb)
new_not0 → True
new_compare0(:(vyy300, vyy301), [], eg) → GT
new_ltEs11(False, False) → True
new_ltEs19(vyy301, vyy41, ty_Float) → new_ltEs6(vyy301, vyy41)
new_lt10(vyy300, vyy40) → new_esEs11(new_compare7(vyy300, vyy40))
new_esEs27(vyy781, vyy791, app(app(ty_Either, dbf), dbg)) → new_esEs6(vyy781, vyy791, dbf, dbg)
new_esEs9(True, True) → True
new_compare11(vyy300, vyy40, False, ed, ee) → GT
new_esEs15(vyy780, vyy790, ty_Int) → new_esEs10(vyy780, vyy790)
new_esEs20(vyy782, vyy792, app(app(app(ty_@3, cba), cbb), cbc)) → new_esEs5(vyy782, vyy792, cba, cbb, cbc)
new_primCmpInt(Pos(Succ(vyy3000)), Neg(vyy40)) → GT
new_esEs11(GT) → False
new_ltEs14(Left(vyy300), Left(vyy40), ty_Char, ge) → new_ltEs9(vyy300, vyy40)
new_primMulInt(Pos(vyy3010), Pos(vyy410)) → Pos(new_primMulNat0(vyy3010, vyy410))
new_ltEs5(LT, GT) → True
new_compare6(vyy300, vyy40) → new_compare23(vyy300, vyy40, new_esEs9(vyy300, vyy40))
new_primMulInt(Neg(vyy3010), Neg(vyy410)) → Pos(new_primMulNat0(vyy3010, vyy410))
new_esEs19(vyy781, vyy791, app(app(ty_FiniteMap, bge), bgf)) → new_esEs21(vyy781, vyy791, bge, bgf)
new_primEqNat0(Succ(vyy7800), Zero) → False
new_primEqNat0(Zero, Succ(vyy7900)) → False
new_ltEs14(Left(vyy300), Left(vyy40), ty_Bool, ge) → new_ltEs11(vyy300, vyy40)
new_esEs26(vyy780, vyy790, app(app(ty_@2, dad), dae)) → new_esEs7(vyy780, vyy790, dad, dae)
new_ltEs7(@3(vyy300, vyy301, vyy302), @3(vyy40, vyy41, vyy42), h, ba, cf) → new_pePe(new_lt8(vyy300, vyy40, h), vyy300, vyy40, new_pePe(new_lt7(vyy301, vyy41, ba), vyy301, vyy41, new_ltEs8(vyy302, vyy42, cf), ba), h)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs20(vyy782, vyy792, app(app(ty_Either, cad), cae)) → new_esEs6(vyy782, vyy792, cad, cae)
new_ltEs14(Right(vyy300), Right(vyy40), hd, ty_Int) → new_ltEs4(vyy300, vyy40)
new_sizeFM(Branch(vyy790, vyy791, vyy792, vyy793, vyy794), bec, bed) → vyy792
new_esEs29(vyy78, vyy79, app(app(ty_Either, cfh), cee)) → new_esEs6(vyy78, vyy79, cfh, cee)
new_lt7(vyy301, vyy41, ty_@0) → new_lt6(vyy301, vyy41)
new_pePe(True, vyy78, vyy79, vyy97, ded) → True
new_foldFM2(Branch(vyy790, vyy791, vyy792, vyy793, vyy794), bec, bed) → new_foldFM0(vyy790, vyy791, new_foldFM2(vyy794, bec, bed), vyy793, bec, bed)
new_ltEs19(vyy301, vyy41, ty_Char) → new_ltEs9(vyy301, vyy41)
new_esEs6(Left(vyy780), Left(vyy790), ty_Char, cee) → new_esEs25(vyy780, vyy790)
new_esEs29(vyy78, vyy79, app(app(app(ty_@3, bef), beg), beh)) → new_esEs5(vyy78, vyy79, bef, beg, beh)
new_esEs8(Just(vyy780), Just(vyy790), app(ty_[], cdd)) → new_esEs22(vyy780, vyy790, cdd)
new_esEs8(Just(vyy780), Just(vyy790), ty_@0) → new_esEs13(vyy780, vyy790)
new_primCmpInt(Neg(Zero), Neg(Succ(vyy400))) → new_primCmpNat0(Succ(vyy400), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(vyy400))) → GT
new_esEs20(vyy782, vyy792, ty_Bool) → new_esEs9(vyy782, vyy792)
new_compare24(vyy300, vyy40, False, ed, ee) → new_compare11(vyy300, vyy40, new_ltEs17(vyy300, vyy40, ed, ee), ed, ee)
new_ltEs14(Left(vyy300), Left(vyy40), app(ty_Maybe, hc), ge) → new_ltEs18(vyy300, vyy40, hc)
new_lt15(vyy300, vyy40, eb, ec) → new_esEs11(new_compare18(vyy300, vyy40, eb, ec))
new_lt7(vyy301, vyy41, ty_Bool) → new_lt5(vyy301, vyy41)
new_ltEs18(Just(vyy300), Just(vyy40), app(app(ty_Either, bdf), bdg)) → new_ltEs14(vyy300, vyy40, bdf, bdg)
new_lt4(vyy300, vyy40) → new_esEs11(new_compare8(vyy300, vyy40))
new_esEs18(vyy780, vyy790, ty_Integer) → new_esEs12(vyy780, vyy790)
new_ltEs18(Just(vyy300), Just(vyy40), app(ty_[], bde)) → new_ltEs12(vyy300, vyy40, bde)
new_esEs9(False, True) → False
new_esEs9(True, False) → False
new_ltEs10(vyy30, vyy4) → new_not(new_compare14(vyy30, vyy4))
new_ltEs14(Left(vyy300), Left(vyy40), app(app(ty_@2, ha), hb), ge) → new_ltEs17(vyy300, vyy40, ha, hb)
new_esEs22(:(vyy780, vyy781), :(vyy790, vyy791), dcg) → new_asAs(new_esEs28(vyy780, vyy790, dcg), new_esEs22(vyy781, vyy791, dcg))
new_esEs18(vyy780, vyy790, ty_Ordering) → new_esEs17(vyy780, vyy790)
new_ltEs14(Right(vyy300), Right(vyy40), hd, app(ty_Ratio, ceb)) → new_ltEs15(vyy300, vyy40, ceb)
new_esEs28(vyy780, vyy790, app(ty_[], ddg)) → new_esEs22(vyy780, vyy790, ddg)
new_esEs8(Nothing, Nothing, ccd) → True
new_primCompAux0(vyy300, vyy40, vyy107, eg) → new_primCompAux00(vyy107, new_compare30(vyy300, vyy40, eg))
new_esEs19(vyy781, vyy791, ty_Char) → new_esEs25(vyy781, vyy791)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs27(vyy781, vyy791, app(ty_Ratio, dbe)) → new_esEs14(vyy781, vyy791, dbe)
new_compare30(vyy300, vyy40, ty_Float) → new_compare13(vyy300, vyy40)
new_compare13(Float(vyy300, vyy301), Float(vyy40, vyy41)) → new_compare7(new_sr(vyy300, vyy40), new_sr(vyy301, vyy41))
new_ltEs8(vyy302, vyy42, app(ty_Maybe, cb)) → new_ltEs18(vyy302, vyy42, cb)
new_ltEs14(Left(vyy300), Right(vyy40), hd, ge) → True
new_ltEs8(vyy302, vyy42, ty_Float) → new_ltEs6(vyy302, vyy42)
new_esEs22(:(vyy780, vyy781), [], dcg) → False
new_esEs22([], :(vyy790, vyy791), dcg) → False
new_compare30(vyy300, vyy40, app(ty_[], fc)) → new_compare0(vyy300, vyy40, fc)
new_asAs(False, vyy106) → False
new_ltEs11(True, True) → True
new_esEs28(vyy780, vyy790, ty_Float) → new_esEs23(vyy780, vyy790)
new_compare30(vyy300, vyy40, ty_Char) → new_compare8(vyy300, vyy40)
new_primMulInt(Neg(vyy3010), Pos(vyy410)) → Neg(new_primMulNat0(vyy3010, vyy410))
new_primMulInt(Pos(vyy3010), Neg(vyy410)) → Neg(new_primMulNat0(vyy3010, vyy410))
new_ltEs19(vyy301, vyy41, app(app(ty_Either, bbc), bbd)) → new_ltEs14(vyy301, vyy41, bbc, bbd)
new_primMulNat0(Zero, Succ(vyy4100)) → Zero
new_primMulNat0(Succ(vyy30100), Zero) → Zero
new_ltEs14(Right(vyy300), Right(vyy40), hd, app(app(app(ty_@3, he), hf), hg)) → new_ltEs7(vyy300, vyy40, he, hf, hg)
new_ltEs5(LT, EQ) → True
new_esEs18(vyy780, vyy790, app(ty_[], bfh)) → new_esEs22(vyy780, vyy790, bfh)
new_ltEs16(vyy30, vyy4) → new_not(new_compare16(vyy30, vyy4))
new_esEs27(vyy781, vyy791, ty_Char) → new_esEs25(vyy781, vyy791)
new_lt18(vyy300, vyy40, ed, ee) → new_esEs11(new_compare9(vyy300, vyy40, ed, ee))
new_ltEs19(vyy301, vyy41, ty_@0) → new_ltEs10(vyy301, vyy41)
new_ltEs18(Nothing, Just(vyy40), dee) → True
new_compare12(vyy300, vyy40, True) → LT
new_esEs20(vyy782, vyy792, app(ty_[], cah)) → new_esEs22(vyy782, vyy792, cah)
new_esEs8(Just(vyy780), Just(vyy790), app(app(app(ty_@3, cde), cdf), cdg)) → new_esEs5(vyy780, vyy790, cde, cdf, cdg)
new_not(EQ) → new_not0
new_compare110(vyy300, vyy40, True, df, dg, dh) → LT
new_esEs27(vyy781, vyy791, ty_@0) → new_esEs13(vyy781, vyy791)
new_esEs6(Left(vyy780), Left(vyy790), ty_Float, cee) → new_esEs23(vyy780, vyy790)
new_ltEs14(Right(vyy300), Right(vyy40), hd, app(app(ty_Either, baa), bab)) → new_ltEs14(vyy300, vyy40, baa, bab)
new_esEs18(vyy780, vyy790, app(ty_Maybe, bgd)) → new_esEs8(vyy780, vyy790, bgd)
new_lt7(vyy301, vyy41, app(ty_Ratio, cbf)) → new_lt16(vyy301, vyy41, cbf)
new_esEs6(Right(vyy780), Right(vyy790), cfh, ty_Int) → new_esEs10(vyy780, vyy790)
new_esEs17(EQ, LT) → False
new_esEs17(LT, EQ) → False
new_lt7(vyy301, vyy41, app(ty_[], cg)) → new_lt13(vyy301, vyy41, cg)
new_esEs6(Left(vyy780), Left(vyy790), app(ty_Maybe, cfg), cee) → new_esEs8(vyy780, vyy790, cfg)
new_esEs20(vyy782, vyy792, ty_Integer) → new_esEs12(vyy782, vyy792)
new_esEs9(False, False) → True
new_esEs25(Char(vyy780), Char(vyy790)) → new_primEqNat0(vyy780, vyy790)
new_esEs14(:%(vyy780, vyy781), :%(vyy790, vyy791), bee) → new_asAs(new_esEs15(vyy780, vyy790, bee), new_esEs16(vyy781, vyy791, bee))
new_ltEs14(Left(vyy300), Left(vyy40), app(app(ty_Either, gg), gh), ge) → new_ltEs14(vyy300, vyy40, gg, gh)
new_ltEs18(Just(vyy300), Just(vyy40), ty_Bool) → new_ltEs11(vyy300, vyy40)
new_compare30(vyy300, vyy40, app(ty_Maybe, ga)) → new_compare19(vyy300, vyy40, ga)
new_ltEs14(Left(vyy300), Left(vyy40), ty_Int, ge) → new_ltEs4(vyy300, vyy40)
new_esEs19(vyy781, vyy791, app(ty_[], bhd)) → new_esEs22(vyy781, vyy791, bhd)
new_lt20(vyy300, vyy40, ty_Ordering) → new_lt11(vyy300, vyy40)
new_esEs26(vyy780, vyy790, ty_Ordering) → new_esEs17(vyy780, vyy790)
new_not(LT) → new_not0
new_lt20(vyy300, vyy40, app(app(ty_Either, bce), bcf)) → new_lt15(vyy300, vyy40, bce, bcf)
new_ltEs19(vyy301, vyy41, ty_Double) → new_ltEs13(vyy301, vyy41)
new_lt11(vyy300, vyy40) → new_esEs11(new_compare29(vyy300, vyy40))
new_esEs27(vyy781, vyy791, ty_Ordering) → new_esEs17(vyy781, vyy791)
new_esEs29(vyy78, vyy79, ty_Ordering) → new_esEs17(vyy78, vyy79)
new_esEs11(EQ) → False
new_compare112(vyy300, vyy40, False, ef) → GT
new_esEs8(Just(vyy780), Just(vyy790), ty_Double) → new_esEs24(vyy780, vyy790)
new_compare28(vyy300, vyy40, False, ef) → new_compare112(vyy300, vyy40, new_ltEs18(vyy300, vyy40, ef), ef)
new_esEs28(vyy780, vyy790, ty_Int) → new_esEs10(vyy780, vyy790)
new_esEs21(vyy78, vyy79, bec, bed) → new_asAs(new_esEs10(new_sizeFM(vyy78, bec, bed), new_sizeFM(vyy79, bec, bed)), new_esEs22(new_fmToList(vyy78, bec, bed), new_fmToList(vyy79, bec, bed), app(app(ty_@2, bec), bed)))
new_ltEs14(Left(vyy300), Left(vyy40), app(app(app(ty_@3, gb), gc), gd), ge) → new_ltEs7(vyy300, vyy40, gb, gc, gd)
new_esEs20(vyy782, vyy792, app(app(ty_@2, caf), cag)) → new_esEs7(vyy782, vyy792, caf, cag)
new_esEs26(vyy780, vyy790, app(app(ty_Either, dab), dac)) → new_esEs6(vyy780, vyy790, dab, dac)
new_ltEs19(vyy301, vyy41, ty_Ordering) → new_ltEs5(vyy301, vyy41)
new_primPlusNat1(Zero, Zero) → Zero
new_compare111(vyy300, vyy40, True, eb, ec) → LT
new_compare0([], :(vyy40, vyy41), eg) → LT
new_esEs15(vyy780, vyy790, ty_Integer) → new_esEs12(vyy780, vyy790)
new_esEs8(Just(vyy780), Just(vyy790), ty_Int) → new_esEs10(vyy780, vyy790)
new_asAs(True, vyy106) → vyy106
new_lt8(vyy300, vyy40, ty_Ordering) → new_lt11(vyy300, vyy40)
new_esEs26(vyy780, vyy790, app(app(app(ty_@3, dag), dah), dba)) → new_esEs5(vyy780, vyy790, dag, dah, dba)
new_primMulNat0(Succ(vyy30100), Succ(vyy4100)) → new_primPlusNat0(new_primMulNat0(vyy30100, Succ(vyy4100)), vyy4100)
new_ltEs5(GT, GT) → True
new_esEs18(vyy780, vyy790, app(app(ty_FiniteMap, bfa), bfb)) → new_esEs21(vyy780, vyy790, bfa, bfb)
new_esEs17(GT, GT) → True
new_esEs6(Left(vyy780), Left(vyy790), ty_Double, cee) → new_esEs24(vyy780, vyy790)
new_esEs27(vyy781, vyy791, ty_Int) → new_esEs10(vyy781, vyy791)
new_esEs8(Just(vyy780), Just(vyy790), app(ty_Maybe, cdh)) → new_esEs8(vyy780, vyy790, cdh)
new_esEs26(vyy780, vyy790, ty_Char) → new_esEs25(vyy780, vyy790)
new_ltEs8(vyy302, vyy42, ty_Char) → new_ltEs9(vyy302, vyy42)
new_fmToList(vyy79, bec, bed) → new_foldFM2(vyy79, bec, bed)
new_compare28(vyy300, vyy40, True, ef) → EQ
new_esEs26(vyy780, vyy790, app(app(ty_FiniteMap, chg), chh)) → new_esEs21(vyy780, vyy790, chg, chh)
new_ltEs8(vyy302, vyy42, ty_Integer) → new_ltEs16(vyy302, vyy42)
new_compare10(vyy300, vyy40, True) → LT
new_esEs29(vyy78, vyy79, app(ty_Ratio, bee)) → new_esEs14(vyy78, vyy79, bee)
new_ltEs12(vyy30, vyy4, eg) → new_not(new_compare0(vyy30, vyy4, eg))
new_compare110(vyy300, vyy40, False, df, dg, dh) → GT
new_lt12(vyy300, vyy40) → new_esEs11(new_compare13(vyy300, vyy40))
new_compare10(vyy300, vyy40, False) → GT
new_primCompAux00(vyy111, GT) → GT
new_esEs10(vyy78, vyy79) → new_primEqInt(vyy78, vyy79)
new_compare8(Char(vyy300), Char(vyy40)) → new_primCmpNat0(vyy300, vyy40)
new_lt7(vyy301, vyy41, app(ty_Maybe, de)) → new_lt19(vyy301, vyy41, de)
new_ltEs19(vyy301, vyy41, ty_Int) → new_ltEs4(vyy301, vyy41)
new_esEs8(Just(vyy780), Just(vyy790), ty_Char) → new_esEs25(vyy780, vyy790)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs6(Right(vyy780), Right(vyy790), cfh, app(app(app(ty_@3, cha), chb), chc)) → new_esEs5(vyy780, vyy790, cha, chb, chc)
new_lt14(vyy300, vyy40) → new_esEs11(new_compare17(vyy300, vyy40))
new_esEs20(vyy782, vyy792, ty_@0) → new_esEs13(vyy782, vyy792)
new_ltEs5(GT, EQ) → False
new_compare30(vyy300, vyy40, app(app(app(ty_@3, eh), fa), fb)) → new_compare27(vyy300, vyy40, eh, fa, fb)
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_ltEs8(vyy302, vyy42, ty_Bool) → new_ltEs11(vyy302, vyy42)
new_ltEs19(vyy301, vyy41, app(ty_Maybe, bbg)) → new_ltEs18(vyy301, vyy41, bbg)
new_ltEs18(Just(vyy300), Just(vyy40), ty_Int) → new_ltEs4(vyy300, vyy40)
new_ltEs19(vyy301, vyy41, ty_Bool) → new_ltEs11(vyy301, vyy41)
new_primCmpInt(Neg(Succ(vyy3000)), Pos(vyy40)) → LT
new_esEs6(Left(vyy780), Left(vyy790), ty_Int, cee) → new_esEs10(vyy780, vyy790)
new_esEs20(vyy782, vyy792, ty_Float) → new_esEs23(vyy782, vyy792)
The set Q consists of the following terms:
new_lt8(x0, x1, ty_Int)
new_lt7(x0, x1, ty_Bool)
new_esEs17(LT, GT)
new_esEs17(GT, LT)
new_esEs13(@0, @0)
new_ltEs14(Right(x0), Right(x1), x2, ty_Bool)
new_esEs23(Float(x0, x1), Float(x2, x3))
new_primPlusNat1(Zero, Succ(x0))
new_esEs7(@2(x0, x1), @2(x2, x3), x4, x5)
new_lt14(x0, x1)
new_compare30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs12(x0, x1, x2)
new_ltEs14(Right(x0), Right(x1), x2, ty_Int)
new_ltEs17(@2(x0, x1), @2(x2, x3), x4, x5)
new_compare0([], :(x0, x1), x2)
new_ltEs15(x0, x1, x2)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_lt20(x0, x1, app(ty_[], x2))
new_esEs16(x0, x1, ty_Integer)
new_esEs18(x0, x1, ty_Ordering)
new_compare9(x0, x1, x2, x3)
new_esEs17(LT, LT)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare28(x0, x1, False, x2)
new_lt20(x0, x1, ty_@0)
new_ltEs14(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs8(Just(x0), Just(x1), app(ty_[], x2))
new_esEs28(x0, x1, ty_Ordering)
new_compare30(x0, x1, ty_Double)
new_ltEs14(Right(x0), Right(x1), x2, ty_Double)
new_esEs29(x0, x1, ty_Float)
new_ltEs14(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs20(x0, x1, ty_Int)
new_esEs18(x0, x1, ty_Int)
new_compare13(Float(x0, x1), Float(x2, x3))
new_esEs19(x0, x1, ty_@0)
new_asAs(True, x0)
new_esEs18(x0, x1, ty_@0)
new_lt20(x0, x1, ty_Bool)
new_primMulNat0(Succ(x0), Zero)
new_esEs20(x0, x1, ty_Double)
new_esEs6(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_ltEs14(Right(x0), Right(x1), x2, ty_Ordering)
new_primMulInt(Pos(x0), Pos(x1))
new_compare6(x0, x1)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_asAs(False, x0)
new_esEs6(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
new_ltEs8(x0, x1, app(ty_[], x2))
new_esEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs14(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_lt5(x0, x1)
new_esEs28(x0, x1, ty_Float)
new_ltEs18(Just(x0), Just(x1), ty_Double)
new_esEs6(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_ltEs14(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_ltEs14(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs17(EQ, GT)
new_esEs17(GT, EQ)
new_ltEs5(GT, EQ)
new_ltEs5(EQ, GT)
new_ltEs8(x0, x1, app(ty_Ratio, x2))
new_esEs22([], [], x0)
new_lt19(x0, x1, x2)
new_esEs6(Left(x0), Left(x1), ty_@0, x2)
new_esEs20(x0, x1, ty_Bool)
new_compare27(x0, x1, x2, x3, x4)
new_esEs20(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_compare7(x0, x1)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_lt7(x0, x1, app(ty_[], x2))
new_ltEs8(x0, x1, ty_@0)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_esEs6(Left(x0), Left(x1), ty_Double, x2)
new_esEs11(EQ)
new_esEs17(GT, GT)
new_compare15(:%(x0, x1), :%(x2, x3), ty_Integer)
new_lt8(x0, x1, app(ty_Maybe, x2))
new_primCompAux00(x0, GT)
new_esEs8(Just(x0), Just(x1), ty_Int)
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs19(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs6(x0, x1)
new_ltEs5(EQ, LT)
new_ltEs5(LT, EQ)
new_esEs18(x0, x1, app(app(ty_@2, x2), x3))
new_compare110(x0, x1, True, x2, x3, x4)
new_primEqNat0(Zero, Zero)
new_esEs20(x0, x1, ty_Char)
new_esEs6(Left(x0), Left(x1), ty_Bool, x2)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_esEs6(Right(x0), Right(x1), x2, ty_Int)
new_compare8(Char(x0), Char(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs27(x0, x1, ty_Char)
new_esEs28(x0, x1, ty_Char)
new_esEs24(Double(x0, x1), Double(x2, x3))
new_esEs6(Right(x0), Right(x1), x2, ty_Double)
new_esEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs9(True, True)
new_esEs20(x0, x1, ty_Ordering)
new_esEs6(Left(x0), Left(x1), app(app(ty_FiniteMap, x2), x3), x4)
new_primEqNat0(Zero, Succ(x0))
new_primMulNat0(Succ(x0), Succ(x1))
new_ltEs18(Just(x0), Just(x1), app(ty_Ratio, x2))
new_ltEs14(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_primMulNat0(Zero, Zero)
new_esEs29(x0, x1, app(ty_[], x2))
new_esEs8(Just(x0), Just(x1), ty_Float)
new_esEs21(x0, x1, x2, x3)
new_esEs20(x0, x1, app(ty_[], x2))
new_ltEs14(Right(x0), Right(x1), x2, ty_Char)
new_ltEs14(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_lt20(x0, x1, ty_Double)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs8(Nothing, Nothing, x0)
new_compare30(x0, x1, ty_@0)
new_esEs29(x0, x1, ty_Ordering)
new_esEs6(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs29(x0, x1, ty_Int)
new_ltEs18(Just(x0), Just(x1), ty_Integer)
new_ltEs14(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt8(x0, x1, ty_Integer)
new_ltEs18(Nothing, Nothing, x0)
new_esEs28(x0, x1, ty_Double)
new_esEs6(Left(x0), Right(x1), x2, x3)
new_esEs6(Right(x0), Left(x1), x2, x3)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_esEs26(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_lt12(x0, x1)
new_esEs15(x0, x1, ty_Integer)
new_compare16(Integer(x0), Integer(x1))
new_foldFM2(EmptyFM, x0, x1)
new_esEs22(:(x0, x1), :(x2, x3), x4)
new_primMulNat0(Zero, Succ(x0))
new_lt7(x0, x1, ty_@0)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs18(Just(x0), Just(x1), ty_Ordering)
new_ltEs18(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs8(Just(x0), Just(x1), ty_Bool)
new_lt8(x0, x1, app(ty_[], x2))
new_lt7(x0, x1, ty_Int)
new_compare26(x0, x1, True, x2, x3)
new_lt7(x0, x1, app(ty_Ratio, x2))
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_compare24(x0, x1, True, x2, x3)
new_ltEs8(x0, x1, ty_Ordering)
new_esEs19(x0, x1, ty_Integer)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs20(x0, x1, ty_@0)
new_esEs8(Just(x0), Just(x1), ty_Char)
new_ltEs18(Just(x0), Just(x1), app(ty_[], x2))
new_esEs28(x0, x1, ty_Integer)
new_primCmpNat0(Zero, Succ(x0))
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare30(x0, x1, ty_Int)
new_compare30(x0, x1, ty_Ordering)
new_compare17(Double(x0, x1), Double(x2, x3))
new_compare30(x0, x1, ty_Bool)
new_primMulInt(Neg(x0), Neg(x1))
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_ltEs9(x0, x1)
new_sr(x0, x1)
new_lt8(x0, x1, ty_Char)
new_primPlusNat0(Zero, x0)
new_compare25(x0, x1, False)
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_lt18(x0, x1, x2, x3)
new_esEs29(x0, x1, ty_Double)
new_ltEs8(x0, x1, ty_Bool)
new_esEs26(x0, x1, app(ty_[], x2))
new_esEs26(x0, x1, ty_Integer)
new_compare30(x0, x1, app(ty_Ratio, x2))
new_ltEs14(Left(x0), Left(x1), ty_Char, x2)
new_primPlusNat1(Zero, Zero)
new_esEs8(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs18(x0, x1, ty_Char)
new_not0
new_esEs19(x0, x1, ty_Ordering)
new_ltEs19(x0, x1, ty_Ordering)
new_esEs11(GT)
new_ltEs14(Left(x0), Left(x1), ty_Float, x2)
new_esEs19(x0, x1, app(ty_Ratio, x2))
new_compare112(x0, x1, True, x2)
new_esEs6(Right(x0), Right(x1), x2, ty_Char)
new_esEs18(x0, x1, ty_Bool)
new_primCompAux0(x0, x1, x2, x3)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs22(:(x0, x1), [], x2)
new_esEs10(x0, x1)
new_esEs14(:%(x0, x1), :%(x2, x3), x4)
new_esEs27(x0, x1, ty_Float)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs19(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_esEs8(Just(x0), Nothing, x1)
new_esEs19(x0, x1, app(ty_[], x2))
new_ltEs7(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_primCmpNat0(Succ(x0), Succ(x1))
new_lt4(x0, x1)
new_lt13(x0, x1, x2)
new_ltEs14(Right(x0), Right(x1), x2, ty_@0)
new_ltEs14(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs29(x0, x1, ty_Bool)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_esEs26(x0, x1, ty_Bool)
new_esEs29(x0, x1, ty_@0)
new_ltEs14(Right(x0), Right(x1), x2, ty_Float)
new_esEs28(x0, x1, ty_Int)
new_ltEs8(x0, x1, ty_Char)
new_lt20(x0, x1, ty_Int)
new_esEs18(x0, x1, app(ty_[], x2))
new_esEs8(Just(x0), Just(x1), ty_Integer)
new_esEs27(x0, x1, ty_Ordering)
new_primEqNat0(Succ(x0), Zero)
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_esEs6(Left(x0), Left(x1), ty_Char, x2)
new_not(GT)
new_esEs8(Just(x0), Just(x1), ty_Ordering)
new_esEs26(x0, x1, ty_Char)
new_esEs6(Left(x0), Left(x1), ty_Float, x2)
new_lt17(x0, x1)
new_compare30(x0, x1, app(app(ty_@2, x2), x3))
new_esEs8(Just(x0), Just(x1), ty_@0)
new_compare23(x0, x1, True)
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_compare210(x0, x1, False, x2, x3, x4)
new_compare0(:(x0, x1), [], x2)
new_primEqInt(Neg(Zero), Pos(Zero))
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_esEs27(x0, x1, ty_Int)
new_esEs27(x0, x1, ty_Integer)
new_ltEs11(False, False)
new_ltEs14(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_lt7(x0, x1, ty_Float)
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primPlusNat1(Succ(x0), Zero)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_ltEs19(x0, x1, ty_Bool)
new_lt15(x0, x1, x2, x3)
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_esEs6(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs28(x0, x1, ty_Bool)
new_primCompAux00(x0, LT)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_ltEs8(x0, x1, app(app(ty_Either, x2), x3))
new_lt8(x0, x1, app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_esEs6(Left(x0), Left(x1), app(ty_[], x2), x3)
new_primEqInt(Neg(Zero), Neg(Zero))
new_compare14(@0, @0)
new_esEs6(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_ltEs8(x0, x1, ty_Double)
new_lt16(x0, x1, x2)
new_lt10(x0, x1)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_esEs6(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_ltEs18(Just(x0), Just(x1), ty_@0)
new_ltEs14(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs14(Right(x0), Left(x1), x2, x3)
new_ltEs14(Left(x0), Right(x1), x2, x3)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_lt8(x0, x1, ty_@0)
new_lt8(x0, x1, ty_Ordering)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_ltEs11(False, True)
new_ltEs11(True, False)
new_esEs26(x0, x1, ty_Double)
new_primPlusNat0(Succ(x0), x1)
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_compare25(x0, x1, True)
new_ltEs16(x0, x1)
new_esEs20(x0, x1, ty_Float)
new_lt11(x0, x1)
new_esEs15(x0, x1, ty_Int)
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_esEs6(Right(x0), Right(x1), x2, ty_Bool)
new_esEs12(Integer(x0), Integer(x1))
new_lt7(x0, x1, app(app(ty_Either, x2), x3))
new_compare110(x0, x1, False, x2, x3, x4)
new_lt20(x0, x1, ty_Char)
new_esEs6(Left(x0), Left(x1), ty_Integer, x2)
new_primCompAux00(x0, EQ)
new_compare19(x0, x1, x2)
new_esEs18(x0, x1, ty_Float)
new_ltEs13(x0, x1)
new_compare11(x0, x1, True, x2, x3)
new_ltEs18(Just(x0), Nothing, x1)
new_esEs29(x0, x1, ty_Char)
new_esEs6(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs28(x0, x1, ty_@0)
new_esEs19(x0, x1, ty_Bool)
new_esEs27(x0, x1, ty_Double)
new_compare10(x0, x1, False)
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
new_compare0(:(x0, x1), :(x2, x3), x4)
new_esEs6(Right(x0), Right(x1), x2, ty_Float)
new_esEs22([], :(x0, x1), x2)
new_ltEs5(GT, LT)
new_ltEs5(LT, GT)
new_ltEs8(x0, x1, ty_Float)
new_esEs18(x0, x1, app(ty_Maybe, x2))
new_esEs6(Right(x0), Right(x1), x2, ty_Integer)
new_esEs8(Just(x0), Just(x1), app(app(ty_FiniteMap, x2), x3))
new_compare112(x0, x1, False, x2)
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_lt7(x0, x1, ty_Double)
new_primCmpNat0(Zero, Zero)
new_ltEs4(x0, x1)
new_esEs19(x0, x1, ty_Float)
new_esEs29(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs27(x0, x1, ty_@0)
new_esEs18(x0, x1, app(app(ty_Either, x2), x3))
new_esEs5(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_ltEs14(Left(x0), Left(x1), ty_Int, x2)
new_ltEs19(x0, x1, ty_@0)
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs18(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_ltEs8(x0, x1, ty_Int)
new_ltEs18(Just(x0), Just(x1), ty_Char)
new_compare30(x0, x1, ty_Char)
new_esEs9(False, False)
new_esEs18(x0, x1, ty_Double)
new_compare30(x0, x1, app(ty_[], x2))
new_esEs18(x0, x1, app(ty_Ratio, x2))
new_ltEs19(x0, x1, ty_Float)
new_compare11(x0, x1, False, x2, x3)
new_pePe(False, x0, x1, x2, x3)
new_lt20(x0, x1, ty_Integer)
new_esEs27(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_lt20(x0, x1, ty_Ordering)
new_compare0([], [], x0)
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_compare111(x0, x1, True, x2, x3)
new_lt8(x0, x1, ty_Double)
new_ltEs8(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs18(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_ltEs5(GT, GT)
new_compare15(:%(x0, x1), :%(x2, x3), ty_Int)
new_esEs18(x0, x1, ty_Integer)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_ltEs19(x0, x1, ty_Integer)
new_esEs11(LT)
new_ltEs14(Left(x0), Left(x1), ty_Integer, x2)
new_esEs16(x0, x1, ty_Int)
new_compare30(x0, x1, app(app(ty_Either, x2), x3))
new_esEs8(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_ltEs8(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs26(x0, x1, ty_Ordering)
new_compare30(x0, x1, app(ty_Maybe, x2))
new_compare24(x0, x1, False, x2, x3)
new_esEs26(x0, x1, ty_Float)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs27(x0, x1, app(ty_[], x2))
new_ltEs18(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs28(x0, x1, app(ty_[], x2))
new_esEs29(x0, x1, ty_Integer)
new_ltEs19(x0, x1, app(ty_[], x2))
new_esEs6(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_lt7(x0, x1, app(app(ty_@2, x2), x3))
new_esEs28(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_lt7(x0, x1, ty_Ordering)
new_pePe(True, x0, x1, x2, x3)
new_lt7(x0, x1, ty_Integer)
new_not(EQ)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs18(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs26(x0, x1, ty_Int)
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs18(Just(x0), Just(x1), ty_Bool)
new_lt7(x0, x1, ty_Char)
new_compare28(x0, x1, True, x2)
new_lt8(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_esEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, ty_Float)
new_lt9(x0, x1, x2, x3, x4)
new_esEs20(x0, x1, ty_Integer)
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_ltEs14(Left(x0), Left(x1), ty_Double, x2)
new_compare18(x0, x1, x2, x3)
new_ltEs14(Left(x0), Left(x1), ty_Bool, x2)
new_sizeFM(EmptyFM, x0, x1)
new_lt8(x0, x1, app(app(ty_Either, x2), x3))
new_esEs19(x0, x1, app(app(ty_Either, x2), x3))
new_sr0(Integer(x0), Integer(x1))
new_primCmpNat0(Succ(x0), Zero)
new_esEs19(x0, x1, ty_Char)
new_ltEs5(EQ, EQ)
new_esEs19(x0, x1, ty_Int)
new_compare12(x0, x1, False)
new_ltEs10(x0, x1)
new_ltEs14(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs9(True, False)
new_esEs9(False, True)
new_esEs8(Just(x0), Just(x1), ty_Double)
new_esEs6(Left(x0), Left(x1), ty_Int, x2)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_ltEs8(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_compare111(x0, x1, False, x2, x3)
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_compare10(x0, x1, True)
new_lt7(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs8(Nothing, Just(x0), x1)
new_ltEs19(x0, x1, ty_Int)
new_esEs6(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs8(x0, x1, ty_Integer)
new_ltEs14(Right(x0), Right(x1), x2, ty_Integer)
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_compare12(x0, x1, True)
new_ltEs19(x0, x1, ty_Char)
new_ltEs14(Left(x0), Left(x1), ty_@0, x2)
new_esEs8(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_ltEs18(Just(x0), Just(x1), ty_Int)
new_esEs27(x0, x1, ty_Bool)
new_compare210(x0, x1, True, x2, x3, x4)
new_esEs8(Just(x0), Just(x1), app(ty_Ratio, x2))
new_lt8(x0, x1, ty_Bool)
new_primEqInt(Pos(Zero), Pos(Zero))
new_ltEs14(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_lt7(x0, x1, app(ty_Maybe, x2))
new_esEs19(x0, x1, ty_Double)
new_esEs6(Right(x0), Right(x1), x2, ty_@0)
new_primEqNat0(Succ(x0), Succ(x1))
new_lt8(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs8(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_lt6(x0, x1)
new_esEs17(EQ, EQ)
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_FiniteMap, x3), x4))
new_compare30(x0, x1, ty_Float)
new_esEs17(EQ, LT)
new_esEs17(LT, EQ)
new_compare26(x0, x1, False, x2, x3)
new_esEs6(Right(x0), Right(x1), x2, app(ty_[], x3))
new_fmToList(x0, x1, x2)
new_esEs25(Char(x0), Char(x1))
new_compare23(x0, x1, False)
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_not(LT)
new_ltEs11(True, True)
new_lt8(x0, x1, ty_Float)
new_ltEs18(Nothing, Just(x0), x1)
new_ltEs19(x0, x1, ty_Double)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_ltEs5(LT, LT)
new_compare30(x0, x1, ty_Integer)
new_esEs26(x0, x1, ty_@0)
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_compare29(x0, x1)
new_ltEs18(Just(x0), Just(x1), ty_Float)
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_compare22(vyy300, vyy40, False, ef) → new_ltEs3(vyy300, vyy40, ef)
The graph contains the following edges 1 >= 1, 2 >= 2, 4 >= 3
- new_lt2(vyy300, vyy40, ed, ee) → new_compare21(vyy300, vyy40, new_esEs7(vyy300, vyy40, ed, ee), ed, ee)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 4, 4 >= 5
- new_ltEs2(@2(vyy300, vyy301), @2(vyy40, vyy41), app(ty_Maybe, bda), bcc) → new_lt3(vyy300, vyy40, bda)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
- new_ltEs(@3(vyy300, vyy301, vyy302), @3(vyy40, vyy41, vyy42), h, app(ty_Maybe, de), cf) → new_lt3(vyy301, vyy41, de)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
- new_ltEs2(@2(vyy300, vyy301), @2(vyy40, vyy41), baf, app(app(ty_Either, bbc), bbd)) → new_ltEs1(vyy301, vyy41, bbc, bbd)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
- new_ltEs2(@2(vyy300, vyy301), @2(vyy40, vyy41), baf, app(app(ty_@2, bbe), bbf)) → new_ltEs2(vyy301, vyy41, bbe, bbf)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
- new_ltEs2(@2(vyy300, vyy301), @2(vyy40, vyy41), baf, app(ty_[], bbb)) → new_ltEs0(vyy301, vyy41, bbb)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
- new_ltEs0(:(vyy300, vyy301), :(vyy40, vyy41), eg) → new_primCompAux(vyy300, vyy40, new_compare0(vyy301, vyy41, eg), eg)
The graph contains the following edges 1 > 1, 2 > 2, 3 >= 4
- new_ltEs0(:(vyy300, vyy301), :(vyy40, vyy41), eg) → new_compare(vyy301, vyy41, eg)
The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3
- new_compare(:(vyy300, vyy301), :(vyy40, vyy41), eg) → new_primCompAux(vyy300, vyy40, new_compare0(vyy301, vyy41, eg), eg)
The graph contains the following edges 1 > 1, 2 > 2, 3 >= 4
- new_compare(:(vyy300, vyy301), :(vyy40, vyy41), eg) → new_compare(vyy301, vyy41, eg)
The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3
- new_compare1(vyy300, vyy40, df, dg, dh) → new_compare2(vyy300, vyy40, new_esEs5(vyy300, vyy40, df, dg, dh), df, dg, dh)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 4, 4 >= 5, 5 >= 6
- new_ltEs2(@2(vyy300, vyy301), @2(vyy40, vyy41), baf, app(app(app(ty_@3, bag), bah), bba)) → new_ltEs(vyy301, vyy41, bag, bah, bba)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5
- new_ltEs(@3(vyy300, vyy301, vyy302), @3(vyy40, vyy41, vyy42), h, ba, app(app(ty_Either, bf), bg)) → new_ltEs1(vyy302, vyy42, bf, bg)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4
- new_ltEs(@3(vyy300, vyy301, vyy302), @3(vyy40, vyy41, vyy42), h, ba, app(app(ty_@2, bh), ca)) → new_ltEs2(vyy302, vyy42, bh, ca)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4
- new_ltEs(@3(vyy300, vyy301, vyy302), @3(vyy40, vyy41, vyy42), h, ba, app(ty_[], be)) → new_ltEs0(vyy302, vyy42, be)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3
- new_ltEs3(Just(vyy300), Just(vyy40), app(ty_[], bde)) → new_ltEs0(vyy300, vyy40, bde)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
- new_ltEs(@3(vyy300, vyy301, vyy302), @3(vyy40, vyy41, vyy42), h, ba, app(app(app(ty_@3, bb), bc), bd)) → new_ltEs(vyy302, vyy42, bb, bc, bd)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4, 5 > 5
- new_ltEs2(@2(vyy300, vyy301), @2(vyy40, vyy41), app(app(app(ty_@3, bbh), bca), bcb), bcc) → new_lt(vyy300, vyy40, bbh, bca, bcb)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
- new_compare2(vyy300, vyy40, False, df, dg, dh) → new_ltEs(vyy300, vyy40, df, dg, dh)
The graph contains the following edges 1 >= 1, 2 >= 2, 4 >= 3, 5 >= 4, 6 >= 5
- new_ltEs3(Just(vyy300), Just(vyy40), app(app(app(ty_@3, bdb), bdc), bdd)) → new_ltEs(vyy300, vyy40, bdb, bdc, bdd)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
- new_ltEs(@3(vyy300, vyy301, vyy302), @3(vyy40, vyy41, vyy42), h, app(app(app(ty_@3, cc), cd), ce), cf) → new_lt(vyy301, vyy41, cc, cd, ce)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5
- new_ltEs(@3(vyy300, vyy301, vyy302), @3(vyy40, vyy41, vyy42), app(app(ty_Either, eb), ec), ba, cf) → new_compare20(vyy300, vyy40, new_esEs6(vyy300, vyy40, eb, ec), eb, ec)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 4, 3 > 5
- new_lt0(vyy300, vyy40, ea) → new_compare(vyy300, vyy40, ea)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3
- new_primCompAux(vyy300, vyy40, vyy107, app(app(app(ty_@3, eh), fa), fb)) → new_compare1(vyy300, vyy40, eh, fa, fb)
The graph contains the following edges 1 >= 1, 2 >= 2, 4 > 3, 4 > 4, 4 > 5
- new_primCompAux(vyy300, vyy40, vyy107, app(ty_Maybe, ga)) → new_compare5(vyy300, vyy40, ga)
The graph contains the following edges 1 >= 1, 2 >= 2, 4 > 3
- new_ltEs2(@2(vyy300, vyy301), @2(vyy40, vyy41), baf, app(ty_Maybe, bbg)) → new_ltEs3(vyy301, vyy41, bbg)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
- new_ltEs(@3(vyy300, vyy301, vyy302), @3(vyy40, vyy41, vyy42), h, ba, app(ty_Maybe, cb)) → new_ltEs3(vyy302, vyy42, cb)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3
- new_ltEs3(Just(vyy300), Just(vyy40), app(ty_Maybe, beb)) → new_ltEs3(vyy300, vyy40, beb)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
- new_lt1(vyy300, vyy40, eb, ec) → new_compare20(vyy300, vyy40, new_esEs6(vyy300, vyy40, eb, ec), eb, ec)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 4, 4 >= 5
- new_compare3(vyy300, vyy40, eb, ec) → new_compare20(vyy300, vyy40, new_esEs6(vyy300, vyy40, eb, ec), eb, ec)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 4, 4 >= 5
- new_ltEs3(Just(vyy300), Just(vyy40), app(app(ty_Either, bdf), bdg)) → new_ltEs1(vyy300, vyy40, bdf, bdg)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
- new_compare20(vyy300, vyy40, False, eb, ec) → new_ltEs1(vyy300, vyy40, eb, ec)
The graph contains the following edges 1 >= 1, 2 >= 2, 4 >= 3, 5 >= 4
- new_ltEs3(Just(vyy300), Just(vyy40), app(app(ty_@2, bdh), bea)) → new_ltEs2(vyy300, vyy40, bdh, bea)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
- new_compare21(vyy300, vyy40, False, ed, ee) → new_ltEs2(vyy300, vyy40, ed, ee)
The graph contains the following edges 1 >= 1, 2 >= 2, 4 >= 3, 5 >= 4
- new_ltEs(@3(vyy300, vyy301, vyy302), @3(vyy40, vyy41, vyy42), app(ty_Maybe, ef), ba, cf) → new_compare22(vyy300, vyy40, new_esEs8(vyy300, vyy40, ef), ef)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 4
- new_primCompAux(vyy300, vyy40, vyy107, app(app(ty_Either, fd), ff)) → new_compare3(vyy300, vyy40, fd, ff)
The graph contains the following edges 1 >= 1, 2 >= 2, 4 > 3, 4 > 4
- new_ltEs2(@2(vyy300, vyy301), @2(vyy40, vyy41), app(ty_[], bcd), bcc) → new_lt0(vyy300, vyy40, bcd)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
- new_ltEs(@3(vyy300, vyy301, vyy302), @3(vyy40, vyy41, vyy42), h, app(ty_[], cg), cf) → new_lt0(vyy301, vyy41, cg)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
- new_lt3(vyy300, vyy40, ef) → new_compare22(vyy300, vyy40, new_esEs8(vyy300, vyy40, ef), ef)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 4
- new_compare5(vyy300, vyy40, ef) → new_compare22(vyy300, vyy40, new_esEs8(vyy300, vyy40, ef), ef)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 4
- new_ltEs2(@2(vyy300, vyy301), @2(vyy40, vyy41), app(app(ty_@2, bcg), bch), bcc) → new_lt2(vyy300, vyy40, bcg, bch)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
- new_ltEs2(@2(vyy300, vyy301), @2(vyy40, vyy41), app(app(ty_Either, bce), bcf), bcc) → new_lt1(vyy300, vyy40, bce, bcf)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
- new_ltEs(@3(vyy300, vyy301, vyy302), @3(vyy40, vyy41, vyy42), h, app(app(ty_@2, dc), dd), cf) → new_lt2(vyy301, vyy41, dc, dd)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
- new_ltEs(@3(vyy300, vyy301, vyy302), @3(vyy40, vyy41, vyy42), app(app(ty_@2, ed), ee), ba, cf) → new_compare21(vyy300, vyy40, new_esEs7(vyy300, vyy40, ed, ee), ed, ee)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 4, 3 > 5
- new_compare4(vyy300, vyy40, ed, ee) → new_compare21(vyy300, vyy40, new_esEs7(vyy300, vyy40, ed, ee), ed, ee)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 4, 4 >= 5
- new_lt(vyy300, vyy40, df, dg, dh) → new_compare2(vyy300, vyy40, new_esEs5(vyy300, vyy40, df, dg, dh), df, dg, dh)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 4, 4 >= 5, 5 >= 6
- new_primCompAux(vyy300, vyy40, vyy107, app(app(ty_@2, fg), fh)) → new_compare4(vyy300, vyy40, fg, fh)
The graph contains the following edges 1 >= 1, 2 >= 2, 4 > 3, 4 > 4
- new_primCompAux(vyy300, vyy40, vyy107, app(ty_[], fc)) → new_compare(vyy300, vyy40, fc)
The graph contains the following edges 1 >= 1, 2 >= 2, 4 > 3
- new_ltEs(@3(vyy300, vyy301, vyy302), @3(vyy40, vyy41, vyy42), app(ty_[], ea), ba, cf) → new_compare(vyy300, vyy40, ea)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
- new_ltEs(@3(vyy300, vyy301, vyy302), @3(vyy40, vyy41, vyy42), app(app(app(ty_@3, df), dg), dh), ba, cf) → new_compare2(vyy300, vyy40, new_esEs5(vyy300, vyy40, df, dg, dh), df, dg, dh)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 4, 3 > 5, 3 > 6
- new_ltEs(@3(vyy300, vyy301, vyy302), @3(vyy40, vyy41, vyy42), h, app(app(ty_Either, da), db), cf) → new_lt1(vyy301, vyy41, da, db)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
- new_ltEs1(Left(vyy300), Left(vyy40), app(app(ty_Either, gg), gh), ge) → new_ltEs1(vyy300, vyy40, gg, gh)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
- new_ltEs1(Right(vyy300), Right(vyy40), hd, app(app(ty_Either, baa), bab)) → new_ltEs1(vyy300, vyy40, baa, bab)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
- new_ltEs1(Left(vyy300), Left(vyy40), app(app(ty_@2, ha), hb), ge) → new_ltEs2(vyy300, vyy40, ha, hb)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
- new_ltEs1(Right(vyy300), Right(vyy40), hd, app(app(ty_@2, bac), bad)) → new_ltEs2(vyy300, vyy40, bac, bad)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
- new_ltEs1(Left(vyy300), Left(vyy40), app(ty_[], gf), ge) → new_ltEs0(vyy300, vyy40, gf)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
- new_ltEs1(Right(vyy300), Right(vyy40), hd, app(ty_[], hh)) → new_ltEs0(vyy300, vyy40, hh)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
- new_ltEs1(Left(vyy300), Left(vyy40), app(app(app(ty_@3, gb), gc), gd), ge) → new_ltEs(vyy300, vyy40, gb, gc, gd)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
- new_ltEs1(Right(vyy300), Right(vyy40), hd, app(app(app(ty_@3, he), hf), hg)) → new_ltEs(vyy300, vyy40, he, hf, hg)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5
- new_ltEs1(Right(vyy300), Right(vyy40), hd, app(ty_Maybe, bae)) → new_ltEs3(vyy300, vyy40, bae)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
- new_ltEs1(Left(vyy300), Left(vyy40), app(ty_Maybe, hc), ge) → new_ltEs3(vyy300, vyy40, hc)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDPSizeChangeProof
Q DP problem:
The TRS P consists of the following rules:
new_foldFM_LE1(vyy61, vyy62, vyy63, vyy64, vyy65, vyy66, EmptyFM, True, h, ba) → new_foldFM_LE(vyy61, vyy62, vyy66, h, ba)
new_foldFM_LE1(vyy61, vyy62, vyy63, vyy64, vyy65, Branch(vyy660, vyy661, vyy662, vyy663, vyy664), vyy67, False, h, ba) → new_foldFM_LE1(vyy61, vyy62, vyy660, vyy661, vyy662, vyy663, vyy664, new_ltEs20(vyy660, vyy62, h), h, ba)
new_foldFM_LE2(vyy63, vyy64, vyy96, vyy62, vyy670, vyy671, vyy672, vyy673, vyy674, h, ba) → new_foldFM_LE1(new_fmToList_LE0(vyy63, vyy64, vyy96, h, ba), vyy62, vyy670, vyy671, vyy672, vyy673, vyy674, new_ltEs21(vyy670, vyy62, h), h, ba)
new_foldFM_LE1(vyy61, vyy62, vyy63, vyy64, vyy65, vyy66, Branch(vyy670, vyy671, vyy672, vyy673, vyy674), True, h, ba) → new_foldFM_LE2(vyy63, vyy64, new_foldFM_LE0(vyy61, vyy62, vyy66, h, ba), vyy62, vyy670, vyy671, vyy672, vyy673, vyy674, h, ba)
new_foldFM_LE(vyy61, vyy62, Branch(vyy660, vyy661, vyy662, vyy663, vyy664), h, ba) → new_foldFM_LE1(vyy61, vyy62, vyy660, vyy661, vyy662, vyy663, vyy664, new_ltEs20(vyy660, vyy62, h), h, ba)
new_foldFM_LE1(vyy61, vyy62, vyy63, vyy64, vyy65, vyy66, Branch(vyy670, vyy671, vyy672, vyy673, vyy674), True, h, ba) → new_foldFM_LE(vyy61, vyy62, vyy66, h, ba)
The TRS R consists of the following rules:
new_lt7(vyy301, vyy41, ty_Int) → new_lt10(vyy301, vyy41)
new_ltEs20(vyy660, vyy62, app(ty_Maybe, gb)) → new_ltEs18(vyy660, vyy62, gb)
new_esEs6(Right(vyy780), Right(vyy790), bcf, ty_Char) → new_esEs25(vyy780, vyy790)
new_ltEs19(vyy301, vyy41, ty_Integer) → new_ltEs16(vyy301, vyy41)
new_compare112(vyy300, vyy40, True, gf) → LT
new_compare26(vyy300, vyy40, False, ef, eg) → new_compare111(vyy300, vyy40, new_ltEs14(vyy300, vyy40, ef, eg), ef, eg)
new_ltEs14(Left(vyy300), Left(vyy40), ty_Integer, dah) → new_ltEs16(vyy300, vyy40)
new_esEs6(Right(vyy780), Right(vyy790), bcf, ty_Float) → new_esEs23(vyy780, vyy790)
new_ltEs21(vyy670, vyy62, app(ty_[], fc)) → new_ltEs12(vyy670, vyy62, fc)
new_lt7(vyy301, vyy41, ty_Char) → new_lt4(vyy301, vyy41)
new_esEs8(Just(vyy780), Just(vyy790), app(app(ty_Either, hf), hg)) → new_esEs6(vyy780, vyy790, hf, hg)
new_compare30(vyy300, vyy40, app(ty_Ratio, daa)) → new_compare15(vyy300, vyy40, daa)
new_lt20(vyy300, vyy40, ty_Int) → new_lt10(vyy300, vyy40)
new_lt8(vyy300, vyy40, ty_Int) → new_lt10(vyy300, vyy40)
new_compare15(:%(vyy300, vyy301), :%(vyy40, vyy41), ty_Integer) → new_compare16(new_sr0(vyy300, vyy41), new_sr0(vyy40, vyy301))
new_compare23(vyy300, vyy40, False) → new_compare10(vyy300, vyy40, new_ltEs11(vyy300, vyy40))
new_esEs29(vyy78, vyy79, ty_@0) → new_esEs13(vyy78, vyy79)
new_lt20(vyy300, vyy40, app(ty_Ratio, dh)) → new_lt16(vyy300, vyy40, dh)
new_ltEs6(vyy30, vyy4) → new_not(new_compare13(vyy30, vyy4))
new_ltEs20(vyy660, vyy62, ty_Int) → new_ltEs4(vyy660, vyy62)
new_lt8(vyy300, vyy40, app(app(app(ty_@3, gg), gh), ha)) → new_lt9(vyy300, vyy40, gg, gh, ha)
new_ltEs18(Just(vyy300), Just(vyy40), app(ty_Maybe, bhg)) → new_ltEs18(vyy300, vyy40, bhg)
new_ltEs5(EQ, GT) → True
new_ltEs15(vyy30, vyy4, ee) → new_not(new_compare15(vyy30, vyy4, ee))
new_lt8(vyy300, vyy40, app(ty_[], ge)) → new_lt13(vyy300, vyy40, ge)
new_esEs8(Just(vyy780), Just(vyy790), app(app(ty_FiniteMap, hc), hd)) → new_esEs21(vyy780, vyy790, hc, hd)
new_esEs6(Right(vyy780), Right(vyy790), bcf, app(ty_Maybe, dgb)) → new_esEs8(vyy780, vyy790, dgb)
new_ltEs20(vyy660, vyy62, app(ty_Ratio, fg)) → new_ltEs15(vyy660, vyy62, fg)
new_lt20(vyy300, vyy40, ty_@0) → new_lt6(vyy300, vyy40)
new_esEs29(vyy78, vyy79, app(ty_[], bag)) → new_esEs22(vyy78, vyy79, bag)
new_primMulNat0(Zero, Zero) → Zero
new_ltEs14(Left(vyy300), Left(vyy40), app(ty_[], dba), dah) → new_ltEs12(vyy300, vyy40, dba)
new_esEs27(vyy781, vyy791, ty_Bool) → new_esEs9(vyy781, vyy791)
new_esEs6(Right(vyy780), Right(vyy790), bcf, app(app(ty_@2, dfd), dfe)) → new_esEs7(vyy780, vyy790, dfd, dfe)
new_esEs26(vyy780, vyy790, app(ty_[], bed)) → new_esEs22(vyy780, vyy790, bed)
new_compare30(vyy300, vyy40, app(app(ty_Either, chg), chh)) → new_compare18(vyy300, vyy40, chg, chh)
new_esEs6(Left(vyy780), Left(vyy790), app(ty_[], deb), bcg) → new_esEs22(vyy780, vyy790, deb)
new_compare30(vyy300, vyy40, ty_Integer) → new_compare16(vyy300, vyy40)
new_esEs19(vyy781, vyy791, ty_Int) → new_esEs10(vyy781, vyy791)
new_esEs27(vyy781, vyy791, ty_Integer) → new_esEs12(vyy781, vyy791)
new_compare19(vyy300, vyy40, gf) → new_compare28(vyy300, vyy40, new_esEs8(vyy300, vyy40, gf), gf)
new_not(GT) → False
new_esEs20(vyy782, vyy792, app(ty_Ratio, cdb)) → new_esEs14(vyy782, vyy792, cdb)
new_lt20(vyy300, vyy40, ty_Double) → new_lt14(vyy300, vyy40)
new_esEs20(vyy782, vyy792, ty_Ordering) → new_esEs17(vyy782, vyy792)
new_ltEs20(vyy660, vyy62, app(app(ty_@2, fh), ga)) → new_ltEs17(vyy660, vyy62, fh, ga)
new_lt8(vyy300, vyy40, app(ty_Ratio, ed)) → new_lt16(vyy300, vyy40, ed)
new_compare30(vyy300, vyy40, ty_Ordering) → new_compare29(vyy300, vyy40)
new_compare0(:(vyy300, vyy301), :(vyy40, vyy41), bb) → new_primCompAux0(vyy300, vyy40, new_compare0(vyy301, vyy41, bb), bb)
new_compare30(vyy300, vyy40, ty_Bool) → new_compare6(vyy300, vyy40)
new_compare30(vyy300, vyy40, ty_Double) → new_compare17(vyy300, vyy40)
new_ltEs5(EQ, LT) → False
new_lt6(vyy300, vyy40) → new_esEs11(new_compare14(vyy300, vyy40))
new_ltEs14(Left(vyy300), Left(vyy40), ty_@0, dah) → new_ltEs10(vyy300, vyy40)
new_lt20(vyy300, vyy40, ty_Float) → new_lt12(vyy300, vyy40)
new_ltEs20(vyy660, vyy62, ty_Integer) → new_ltEs16(vyy660, vyy62)
new_esEs27(vyy781, vyy791, app(ty_[], bfh)) → new_esEs22(vyy781, vyy791, bfh)
new_ltEs21(vyy670, vyy62, app(app(ty_@2, fh), ga)) → new_ltEs17(vyy670, vyy62, fh, ga)
new_esEs29(vyy78, vyy79, ty_Bool) → new_esEs9(vyy78, vyy79)
new_esEs12(Integer(vyy780), Integer(vyy790)) → new_primEqInt(vyy780, vyy790)
new_esEs27(vyy781, vyy791, ty_Double) → new_esEs24(vyy781, vyy791)
new_ltEs9(vyy30, vyy4) → new_not(new_compare8(vyy30, vyy4))
new_esEs18(vyy780, vyy790, ty_Float) → new_esEs23(vyy780, vyy790)
new_lt20(vyy300, vyy40, app(ty_[], de)) → new_lt13(vyy300, vyy40, de)
new_esEs19(vyy781, vyy791, app(app(app(ty_@3, ccd), cce), ccf)) → new_esEs5(vyy781, vyy791, ccd, cce, ccf)
new_pePe(False, vyy78, vyy79, vyy97, bcd) → new_asAs(new_esEs29(vyy78, vyy79, bcd), vyy97)
new_esEs28(vyy780, vyy790, ty_Integer) → new_esEs12(vyy780, vyy790)
new_esEs28(vyy780, vyy790, app(app(app(ty_@3, bbh), bca), bcb)) → new_esEs5(vyy780, vyy790, bbh, bca, bcb)
new_ltEs18(Just(vyy300), Just(vyy40), app(app(app(ty_@3, bgf), bgg), bgh)) → new_ltEs7(vyy300, vyy40, bgf, bgg, bgh)
new_esEs28(vyy780, vyy790, ty_Bool) → new_esEs9(vyy780, vyy790)
new_esEs6(Left(vyy780), Left(vyy790), ty_Integer, bcg) → new_esEs12(vyy780, vyy790)
new_foldFM0(vyy790, vyy791, vyy125, EmptyFM, gc, gd) → :(@2(vyy790, vyy791), vyy125)
new_lt7(vyy301, vyy41, ty_Ordering) → new_lt11(vyy301, vyy41)
new_esEs20(vyy782, vyy792, ty_Char) → new_esEs25(vyy782, vyy792)
new_lt20(vyy300, vyy40, ty_Char) → new_lt4(vyy300, vyy40)
new_ltEs4(vyy30, vyy4) → new_not(new_compare7(vyy30, vyy4))
new_ltEs14(Right(vyy300), Right(vyy40), dbh, ty_@0) → new_ltEs10(vyy300, vyy40)
new_esEs6(Right(vyy780), Right(vyy790), bcf, ty_@0) → new_esEs13(vyy780, vyy790)
new_esEs18(vyy780, vyy790, app(app(ty_@2, cae), caf)) → new_esEs7(vyy780, vyy790, cae, caf)
new_esEs6(Right(vyy780), Right(vyy790), bcf, app(ty_Ratio, dfa)) → new_esEs14(vyy780, vyy790, dfa)
new_ltEs14(Right(vyy300), Right(vyy40), dbh, app(app(ty_@2, dch), dda)) → new_ltEs17(vyy300, vyy40, dch, dda)
new_compare23(vyy300, vyy40, True) → EQ
new_ltEs20(vyy660, vyy62, ty_@0) → new_ltEs10(vyy660, vyy62)
new_compare27(vyy300, vyy40, gg, gh, ha) → new_compare210(vyy300, vyy40, new_esEs5(vyy300, vyy40, gg, gh, ha), gg, gh, ha)
new_esEs28(vyy780, vyy790, ty_@0) → new_esEs13(vyy780, vyy790)
new_esEs26(vyy780, vyy790, ty_@0) → new_esEs13(vyy780, vyy790)
new_esEs20(vyy782, vyy792, ty_Double) → new_esEs24(vyy782, vyy792)
new_esEs24(Double(vyy780, vyy781), Double(vyy790, vyy791)) → new_esEs10(new_sr(vyy780, vyy790), new_sr(vyy781, vyy791))
new_compare14(@0, @0) → EQ
new_esEs8(Just(vyy780), Just(vyy790), ty_Ordering) → new_esEs17(vyy780, vyy790)
new_ltEs11(False, True) → True
new_compare210(vyy300, vyy40, False, gg, gh, ha) → new_compare110(vyy300, vyy40, new_ltEs7(vyy300, vyy40, gg, gh, ha), gg, gh, ha)
new_ltEs8(vyy302, vyy42, ty_Double) → new_ltEs13(vyy302, vyy42)
new_esEs29(vyy78, vyy79, app(ty_Maybe, hb)) → new_esEs8(vyy78, vyy79, hb)
new_ltEs20(vyy660, vyy62, app(ty_[], fc)) → new_ltEs12(vyy660, vyy62, fc)
new_esEs18(vyy780, vyy790, app(app(ty_Either, cac), cad)) → new_esEs6(vyy780, vyy790, cac, cad)
new_ltEs21(vyy670, vyy62, app(app(app(ty_@3, eh), fa), fb)) → new_ltEs7(vyy670, vyy62, eh, fa, fb)
new_esEs16(vyy781, vyy791, ty_Integer) → new_esEs12(vyy781, vyy791)
new_primCmpNat0(Zero, Succ(vyy400)) → LT
new_ltEs19(vyy301, vyy41, app(ty_Ratio, ce)) → new_ltEs15(vyy301, vyy41, ce)
new_ltEs18(Just(vyy300), Just(vyy40), ty_Char) → new_ltEs9(vyy300, vyy40)
new_esEs6(Left(vyy780), Left(vyy790), ty_Bool, bcg) → new_esEs9(vyy780, vyy790)
new_esEs19(vyy781, vyy791, ty_Float) → new_esEs23(vyy781, vyy791)
new_esEs17(LT, LT) → True
new_esEs18(vyy780, vyy790, ty_@0) → new_esEs13(vyy780, vyy790)
new_esEs6(Left(vyy780), Right(vyy790), bcf, bcg) → False
new_esEs6(Right(vyy780), Left(vyy790), bcf, bcg) → False
new_esEs7(@2(vyy780, vyy781), @2(vyy790, vyy791), bch, bda) → new_asAs(new_esEs26(vyy780, vyy790, bch), new_esEs27(vyy781, vyy791, bda))
new_esEs6(Right(vyy780), Right(vyy790), bcf, ty_Integer) → new_esEs12(vyy780, vyy790)
new_esEs29(vyy78, vyy79, app(app(ty_@2, bch), bda)) → new_esEs7(vyy78, vyy79, bch, bda)
new_compare0([], [], bb) → EQ
new_primEqNat0(Zero, Zero) → True
new_ltEs21(vyy670, vyy62, ty_Double) → new_ltEs13(vyy670, vyy62)
new_esEs29(vyy78, vyy79, app(app(ty_FiniteMap, gc), gd)) → new_esEs21(vyy78, vyy79, gc, gd)
new_ltEs14(Left(vyy300), Left(vyy40), ty_Ordering, dah) → new_ltEs5(vyy300, vyy40)
new_ltEs21(vyy670, vyy62, ty_@0) → new_ltEs10(vyy670, vyy62)
new_ltEs14(Right(vyy300), Right(vyy40), dbh, ty_Float) → new_ltEs6(vyy300, vyy40)
new_ltEs14(Right(vyy300), Right(vyy40), dbh, ty_Ordering) → new_ltEs5(vyy300, vyy40)
new_compare111(vyy300, vyy40, False, ef, eg) → GT
new_compare30(vyy300, vyy40, ty_Int) → new_compare7(vyy300, vyy40)
new_esEs27(vyy781, vyy791, ty_Float) → new_esEs23(vyy781, vyy791)
new_esEs6(Right(vyy780), Right(vyy790), bcf, ty_Bool) → new_esEs9(vyy780, vyy790)
new_esEs6(Right(vyy780), Right(vyy790), bcf, app(app(ty_Either, dfb), dfc)) → new_esEs6(vyy780, vyy790, dfb, dfc)
new_ltEs17(@2(vyy300, vyy301), @2(vyy40, vyy41), be, bf) → new_pePe(new_lt20(vyy300, vyy40, be), vyy300, vyy40, new_ltEs19(vyy301, vyy41, bf), be)
new_sr(vyy301, vyy41) → new_primMulInt(vyy301, vyy41)
new_compare7(vyy30, vyy4) → new_primCmpInt(vyy30, vyy4)
new_esEs29(vyy78, vyy79, ty_Float) → new_esEs23(vyy78, vyy79)
new_esEs28(vyy780, vyy790, app(app(ty_Either, bbc), bbd)) → new_esEs6(vyy780, vyy790, bbc, bbd)
new_esEs18(vyy780, vyy790, app(app(app(ty_@3, cah), cba), cbb)) → new_esEs5(vyy780, vyy790, cah, cba, cbb)
new_ltEs8(vyy302, vyy42, app(ty_[], cfb)) → new_ltEs12(vyy302, vyy42, cfb)
new_ltEs8(vyy302, vyy42, ty_Int) → new_ltEs4(vyy302, vyy42)
new_lt7(vyy301, vyy41, ty_Double) → new_lt14(vyy301, vyy41)
new_ltEs21(vyy670, vyy62, ty_Ordering) → new_ltEs5(vyy670, vyy62)
new_ltEs14(Right(vyy300), Right(vyy40), dbh, ty_Char) → new_ltEs9(vyy300, vyy40)
new_esEs8(Just(vyy780), Just(vyy790), ty_Bool) → new_esEs9(vyy780, vyy790)
new_primPlusNat0(Succ(vyy1260), vyy4100) → Succ(Succ(new_primPlusNat1(vyy1260, vyy4100)))
new_ltEs5(LT, LT) → True
new_lt8(vyy300, vyy40, ty_Integer) → new_lt17(vyy300, vyy40)
new_lt8(vyy300, vyy40, ty_@0) → new_lt6(vyy300, vyy40)
new_ltEs21(vyy670, vyy62, ty_Integer) → new_ltEs16(vyy670, vyy62)
new_ltEs8(vyy302, vyy42, app(app(app(ty_@3, ceg), ceh), cfa)) → new_ltEs7(vyy302, vyy42, ceg, ceh, cfa)
new_esEs26(vyy780, vyy790, ty_Bool) → new_esEs9(vyy780, vyy790)
new_esEs26(vyy780, vyy790, ty_Integer) → new_esEs12(vyy780, vyy790)
new_esEs8(Nothing, Just(vyy790), hb) → False
new_esEs8(Just(vyy780), Nothing, hb) → False
new_esEs29(vyy78, vyy79, ty_Double) → new_esEs24(vyy78, vyy79)
new_lt20(vyy300, vyy40, app(app(ty_@2, ea), eb)) → new_lt18(vyy300, vyy40, ea, eb)
new_lt8(vyy300, vyy40, ty_Double) → new_lt14(vyy300, vyy40)
new_esEs8(Just(vyy780), Just(vyy790), ty_Float) → new_esEs23(vyy780, vyy790)
new_compare25(vyy300, vyy40, True) → EQ
new_esEs26(vyy780, vyy790, ty_Double) → new_esEs24(vyy780, vyy790)
new_primEqInt(Neg(Succ(vyy7800)), Neg(Succ(vyy7900))) → new_primEqNat0(vyy7800, vyy7900)
new_ltEs19(vyy301, vyy41, app(app(ty_@2, cf), cg)) → new_ltEs17(vyy301, vyy41, cf, cg)
new_esEs27(vyy781, vyy791, app(app(ty_FiniteMap, bfa), bfb)) → new_esEs21(vyy781, vyy791, bfa, bfb)
new_esEs26(vyy780, vyy790, app(ty_Maybe, beh)) → new_esEs8(vyy780, vyy790, beh)
new_esEs28(vyy780, vyy790, ty_Char) → new_esEs25(vyy780, vyy790)
new_ltEs20(vyy660, vyy62, ty_Char) → new_ltEs9(vyy660, vyy62)
new_lt20(vyy300, vyy40, app(ty_Maybe, ec)) → new_lt19(vyy300, vyy40, ec)
new_lt8(vyy300, vyy40, ty_Char) → new_lt4(vyy300, vyy40)
new_primPlusNat1(Succ(vyy12600), Zero) → Succ(vyy12600)
new_primPlusNat1(Zero, Succ(vyy41000)) → Succ(vyy41000)
new_esEs19(vyy781, vyy791, ty_Double) → new_esEs24(vyy781, vyy791)
new_esEs11(LT) → True
new_ltEs8(vyy302, vyy42, app(app(ty_Either, cfc), cfd)) → new_ltEs14(vyy302, vyy42, cfc, cfd)
new_ltEs14(Right(vyy300), Left(vyy40), dbh, dah) → False
new_esEs28(vyy780, vyy790, app(ty_Maybe, bcc)) → new_esEs8(vyy780, vyy790, bcc)
new_ltEs18(Just(vyy300), Just(vyy40), app(ty_Ratio, bhd)) → new_ltEs15(vyy300, vyy40, bhd)
new_ltEs18(Just(vyy300), Just(vyy40), app(app(ty_@2, bhe), bhf)) → new_ltEs17(vyy300, vyy40, bhe, bhf)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs17(EQ, EQ) → True
new_ltEs20(vyy660, vyy62, ty_Bool) → new_ltEs11(vyy660, vyy62)
new_esEs6(Left(vyy780), Left(vyy790), ty_Ordering, bcg) → new_esEs17(vyy780, vyy790)
new_lt8(vyy300, vyy40, app(app(ty_@2, bc), bd)) → new_lt18(vyy300, vyy40, bc, bd)
new_lt19(vyy300, vyy40, gf) → new_esEs11(new_compare19(vyy300, vyy40, gf))
new_esEs28(vyy780, vyy790, ty_Ordering) → new_esEs17(vyy780, vyy790)
new_ltEs14(Right(vyy300), Right(vyy40), dbh, app(ty_[], dcd)) → new_ltEs12(vyy300, vyy40, dcd)
new_esEs19(vyy781, vyy791, ty_Integer) → new_esEs12(vyy781, vyy791)
new_esEs6(Right(vyy780), Right(vyy790), bcf, app(ty_[], dff)) → new_esEs22(vyy780, vyy790, dff)
new_esEs26(vyy780, vyy790, ty_Float) → new_esEs23(vyy780, vyy790)
new_primEqInt(Neg(Succ(vyy7800)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(vyy7900))) → False
new_lt8(vyy300, vyy40, ty_Bool) → new_lt5(vyy300, vyy40)
new_ltEs18(Just(vyy300), Just(vyy40), ty_Ordering) → new_ltEs5(vyy300, vyy40)
new_esEs6(Left(vyy780), Left(vyy790), app(ty_Ratio, dde), bcg) → new_esEs14(vyy780, vyy790, dde)
new_compare26(vyy300, vyy40, True, ef, eg) → EQ
new_lt7(vyy301, vyy41, ty_Float) → new_lt12(vyy301, vyy41)
new_compare9(vyy300, vyy40, bc, bd) → new_compare24(vyy300, vyy40, new_esEs7(vyy300, vyy40, bc, bd), bc, bd)
new_esEs28(vyy780, vyy790, ty_Double) → new_esEs24(vyy780, vyy790)
new_lt7(vyy301, vyy41, ty_Integer) → new_lt17(vyy301, vyy41)
new_ltEs21(vyy670, vyy62, app(app(ty_Either, fd), ff)) → new_ltEs14(vyy670, vyy62, fd, ff)
new_compare24(vyy300, vyy40, True, bc, bd) → EQ
new_lt5(vyy300, vyy40) → new_esEs11(new_compare6(vyy300, vyy40))
new_esEs18(vyy780, vyy790, ty_Bool) → new_esEs9(vyy780, vyy790)
new_ltEs13(vyy30, vyy4) → new_not(new_compare17(vyy30, vyy4))
new_foldFM0(vyy790, vyy791, vyy125, Branch(vyy7930, vyy7931, vyy7932, vyy7933, vyy7934), gc, gd) → new_foldFM0(vyy7930, vyy7931, new_foldFM0(vyy790, vyy791, vyy125, vyy7934, gc, gd), vyy7933, gc, gd)
new_esEs19(vyy781, vyy791, app(ty_Maybe, ccg)) → new_esEs8(vyy781, vyy791, ccg)
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_lt8(vyy300, vyy40, ty_Float) → new_lt12(vyy300, vyy40)
new_esEs19(vyy781, vyy791, ty_Bool) → new_esEs9(vyy781, vyy791)
new_esEs28(vyy780, vyy790, app(app(ty_@2, bbe), bbf)) → new_esEs7(vyy780, vyy790, bbe, bbf)
new_lt8(vyy300, vyy40, app(app(ty_Either, ef), eg)) → new_lt15(vyy300, vyy40, ef, eg)
new_lt7(vyy301, vyy41, app(app(ty_Either, cge), cgf)) → new_lt15(vyy301, vyy41, cge, cgf)
new_primCmpNat0(Succ(vyy3000), Succ(vyy400)) → new_primCmpNat0(vyy3000, vyy400)
new_ltEs14(Left(vyy300), Left(vyy40), ty_Double, dah) → new_ltEs13(vyy300, vyy40)
new_ltEs8(vyy302, vyy42, app(app(ty_@2, cff), cfg)) → new_ltEs17(vyy302, vyy42, cff, cfg)
new_sizeFM(EmptyFM, gc, gd) → Pos(Zero)
new_ltEs5(EQ, EQ) → True
new_ltEs8(vyy302, vyy42, app(ty_Ratio, cfe)) → new_ltEs15(vyy302, vyy42, cfe)
new_primEqInt(Pos(Succ(vyy7800)), Pos(Succ(vyy7900))) → new_primEqNat0(vyy7800, vyy7900)
new_ltEs19(vyy301, vyy41, app(app(app(ty_@3, bg), bh), ca)) → new_ltEs7(vyy301, vyy41, bg, bh, ca)
new_esEs16(vyy781, vyy791, ty_Int) → new_esEs10(vyy781, vyy791)
new_esEs18(vyy780, vyy790, ty_Int) → new_esEs10(vyy780, vyy790)
new_ltEs8(vyy302, vyy42, ty_Ordering) → new_ltEs5(vyy302, vyy42)
new_ltEs14(Right(vyy300), Right(vyy40), dbh, ty_Double) → new_ltEs13(vyy300, vyy40)
new_esEs20(vyy782, vyy792, app(ty_Maybe, cec)) → new_esEs8(vyy782, vyy792, cec)
new_esEs6(Left(vyy780), Left(vyy790), app(app(app(ty_@3, dec), ded), dee), bcg) → new_esEs5(vyy780, vyy790, dec, ded, dee)
new_compare29(vyy300, vyy40) → new_compare25(vyy300, vyy40, new_esEs17(vyy300, vyy40))
new_esEs20(vyy782, vyy792, ty_Int) → new_esEs10(vyy782, vyy792)
new_esEs20(vyy782, vyy792, app(app(ty_FiniteMap, cch), cda)) → new_esEs21(vyy782, vyy792, cch, cda)
new_ltEs11(True, False) → False
new_esEs19(vyy781, vyy791, app(app(ty_Either, cbg), cbh)) → new_esEs6(vyy781, vyy791, cbg, cbh)
new_esEs18(vyy780, vyy790, ty_Char) → new_esEs25(vyy780, vyy790)
new_esEs17(GT, LT) → False
new_esEs17(LT, GT) → False
new_esEs8(Just(vyy780), Just(vyy790), ty_Integer) → new_esEs12(vyy780, vyy790)
new_ltEs20(vyy660, vyy62, app(app(app(ty_@3, eh), fa), fb)) → new_ltEs7(vyy660, vyy62, eh, fa, fb)
new_primEqNat0(Succ(vyy7800), Succ(vyy7900)) → new_primEqNat0(vyy7800, vyy7900)
new_esEs17(GT, EQ) → False
new_esEs17(EQ, GT) → False
new_ltEs21(vyy670, vyy62, ty_Char) → new_ltEs9(vyy670, vyy62)
new_lt16(vyy300, vyy40, ed) → new_esEs11(new_compare15(vyy300, vyy40, ed))
new_compare15(:%(vyy300, vyy301), :%(vyy40, vyy41), ty_Int) → new_compare7(new_sr(vyy300, vyy41), new_sr(vyy40, vyy301))
new_esEs23(Float(vyy780, vyy781), Float(vyy790, vyy791)) → new_esEs10(new_sr(vyy780, vyy790), new_sr(vyy781, vyy791))
new_esEs29(vyy78, vyy79, ty_Int) → new_esEs10(vyy78, vyy79)
new_compare17(Double(vyy300, vyy301), Double(vyy40, vyy41)) → new_compare7(new_sr(vyy300, vyy40), new_sr(vyy301, vyy41))
new_lt20(vyy300, vyy40, ty_Integer) → new_lt17(vyy300, vyy40)
new_primCompAux00(vyy111, LT) → LT
new_lt8(vyy300, vyy40, app(ty_Maybe, gf)) → new_lt19(vyy300, vyy40, gf)
new_ltEs14(Left(vyy300), Left(vyy40), app(ty_Ratio, dbd), dah) → new_ltEs15(vyy300, vyy40, dbd)
new_primCmpInt(Neg(Succ(vyy3000)), Neg(vyy40)) → new_primCmpNat0(vyy40, Succ(vyy3000))
new_ltEs21(vyy670, vyy62, ty_Int) → new_ltEs4(vyy670, vyy62)
new_esEs27(vyy781, vyy791, app(app(app(ty_@3, bga), bgb), bgc)) → new_esEs5(vyy781, vyy791, bga, bgb, bgc)
new_ltEs18(Just(vyy300), Just(vyy40), ty_@0) → new_ltEs10(vyy300, vyy40)
new_esEs19(vyy781, vyy791, ty_Ordering) → new_esEs17(vyy781, vyy791)
new_primEqInt(Pos(Succ(vyy7800)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(vyy7900))) → False
new_ltEs5(GT, LT) → False
new_primCmpNat0(Zero, Zero) → EQ
new_ltEs18(Nothing, Nothing, bge) → True
new_primCmpNat0(Succ(vyy3000), Zero) → GT
new_esEs6(Right(vyy780), Right(vyy790), bcf, ty_Double) → new_esEs24(vyy780, vyy790)
new_lt20(vyy300, vyy40, ty_Bool) → new_lt5(vyy300, vyy40)
new_ltEs20(vyy660, vyy62, ty_Ordering) → new_ltEs5(vyy660, vyy62)
new_ltEs14(Right(vyy300), Right(vyy40), dbh, ty_Bool) → new_ltEs11(vyy300, vyy40)
new_esEs19(vyy781, vyy791, ty_@0) → new_esEs13(vyy781, vyy791)
new_primCmpInt(Neg(Zero), Pos(Succ(vyy400))) → LT
new_compare11(vyy300, vyy40, True, bc, bd) → LT
new_compare210(vyy300, vyy40, True, gg, gh, ha) → EQ
new_lt17(vyy300, vyy40) → new_esEs11(new_compare16(vyy300, vyy40))
new_sr0(Integer(vyy400), Integer(vyy3010)) → Integer(new_primMulInt(vyy400, vyy3010))
new_primPlusNat1(Succ(vyy12600), Succ(vyy41000)) → Succ(Succ(new_primPlusNat1(vyy12600, vyy41000)))
new_primEqInt(Pos(Succ(vyy7800)), Neg(vyy790)) → False
new_primEqInt(Neg(Succ(vyy7800)), Pos(vyy790)) → False
new_esEs18(vyy780, vyy790, app(ty_Ratio, cab)) → new_esEs14(vyy780, vyy790, cab)
new_ltEs18(Just(vyy300), Just(vyy40), ty_Integer) → new_ltEs16(vyy300, vyy40)
new_ltEs14(Left(vyy300), Left(vyy40), ty_Float, dah) → new_ltEs6(vyy300, vyy40)
new_foldFM2(EmptyFM, gc, gd) → []
new_ltEs14(Right(vyy300), Right(vyy40), dbh, ty_Integer) → new_ltEs16(vyy300, vyy40)
new_lt13(vyy300, vyy40, ge) → new_esEs11(new_compare0(vyy300, vyy40, ge))
new_foldFM_LE10(vyy61, vyy62, vyy63, vyy64, vyy65, vyy66, vyy67, False, h, ba) → new_foldFM_LE0(vyy61, vyy62, vyy66, h, ba)
new_esEs18(vyy780, vyy790, ty_Double) → new_esEs24(vyy780, vyy790)
new_compare18(vyy300, vyy40, ef, eg) → new_compare26(vyy300, vyy40, new_esEs6(vyy300, vyy40, ef, eg), ef, eg)
new_esEs6(Left(vyy780), Left(vyy790), ty_@0, bcg) → new_esEs13(vyy780, vyy790)
new_esEs26(vyy780, vyy790, ty_Int) → new_esEs10(vyy780, vyy790)
new_primEqInt(Pos(Zero), Neg(Succ(vyy7900))) → False
new_primEqInt(Neg(Zero), Pos(Succ(vyy7900))) → False
new_lt7(vyy301, vyy41, app(app(app(ty_@3, cga), cgb), cgc)) → new_lt9(vyy301, vyy41, cga, cgb, cgc)
new_esEs13(@0, @0) → True
new_ltEs20(vyy660, vyy62, ty_Float) → new_ltEs6(vyy660, vyy62)
new_esEs8(Just(vyy780), Just(vyy790), app(app(ty_@2, hh), baa)) → new_esEs7(vyy780, vyy790, hh, baa)
new_primCmpInt(Pos(Zero), Pos(Succ(vyy400))) → new_primCmpNat0(Zero, Succ(vyy400))
new_primCompAux00(vyy111, EQ) → vyy111
new_esEs27(vyy781, vyy791, app(app(ty_@2, bff), bfg)) → new_esEs7(vyy781, vyy791, bff, bfg)
new_compare12(vyy300, vyy40, False) → GT
new_lt20(vyy300, vyy40, app(app(app(ty_@3, db), dc), dd)) → new_lt9(vyy300, vyy40, db, dc, dd)
new_esEs28(vyy780, vyy790, app(app(ty_FiniteMap, bah), bba)) → new_esEs21(vyy780, vyy790, bah, bba)
new_esEs19(vyy781, vyy791, app(ty_Ratio, cbf)) → new_esEs14(vyy781, vyy791, cbf)
new_lt9(vyy300, vyy40, gg, gh, ha) → new_esEs11(new_compare27(vyy300, vyy40, gg, gh, ha))
new_lt7(vyy301, vyy41, app(app(ty_@2, cgh), cha)) → new_lt18(vyy301, vyy41, cgh, cha)
new_esEs22([], [], bag) → True
new_esEs27(vyy781, vyy791, app(ty_Maybe, bgd)) → new_esEs8(vyy781, vyy791, bgd)
new_esEs28(vyy780, vyy790, app(ty_Ratio, bbb)) → new_esEs14(vyy780, vyy790, bbb)
new_ltEs8(vyy302, vyy42, ty_@0) → new_ltEs10(vyy302, vyy42)
new_esEs6(Left(vyy780), Left(vyy790), app(app(ty_@2, ddh), dea), bcg) → new_esEs7(vyy780, vyy790, ddh, dea)
new_esEs6(Left(vyy780), Left(vyy790), app(app(ty_FiniteMap, ddc), ddd), bcg) → new_esEs21(vyy780, vyy790, ddc, ddd)
new_esEs6(Left(vyy780), Left(vyy790), app(app(ty_Either, ddf), ddg), bcg) → new_esEs6(vyy780, vyy790, ddf, ddg)
new_compare16(Integer(vyy300), Integer(vyy40)) → new_primCmpInt(vyy300, vyy40)
new_ltEs14(Right(vyy300), Right(vyy40), dbh, app(ty_Maybe, ddb)) → new_ltEs18(vyy300, vyy40, ddb)
new_ltEs18(Just(vyy300), Nothing, bge) → False
new_esEs6(Right(vyy780), Right(vyy790), bcf, ty_Ordering) → new_esEs17(vyy780, vyy790)
new_compare30(vyy300, vyy40, app(app(ty_@2, dab), dac)) → new_compare9(vyy300, vyy40, dab, dac)
new_primCmpInt(Pos(Succ(vyy3000)), Pos(vyy40)) → new_primCmpNat0(Succ(vyy3000), vyy40)
new_ltEs18(Just(vyy300), Just(vyy40), ty_Float) → new_ltEs6(vyy300, vyy40)
new_primPlusNat0(Zero, vyy4100) → Succ(vyy4100)
new_esEs19(vyy781, vyy791, app(app(ty_@2, cca), ccb)) → new_esEs7(vyy781, vyy791, cca, ccb)
new_esEs26(vyy780, vyy790, app(ty_Ratio, bdg)) → new_esEs14(vyy780, vyy790, bdg)
new_esEs29(vyy78, vyy79, ty_Integer) → new_esEs12(vyy78, vyy79)
new_compare25(vyy300, vyy40, False) → new_compare12(vyy300, vyy40, new_ltEs5(vyy300, vyy40))
new_ltEs18(Just(vyy300), Just(vyy40), ty_Double) → new_ltEs13(vyy300, vyy40)
new_ltEs19(vyy301, vyy41, app(ty_[], cb)) → new_ltEs12(vyy301, vyy41, cb)
new_compare30(vyy300, vyy40, ty_@0) → new_compare14(vyy300, vyy40)
new_esEs29(vyy78, vyy79, ty_Char) → new_esEs25(vyy78, vyy79)
new_esEs5(@3(vyy780, vyy781, vyy782), @3(vyy790, vyy791, vyy792), bdb, bdc, bdd) → new_asAs(new_esEs18(vyy780, vyy790, bdb), new_asAs(new_esEs19(vyy781, vyy791, bdc), new_esEs20(vyy782, vyy792, bdd)))
new_esEs8(Just(vyy780), Just(vyy790), app(ty_Ratio, he)) → new_esEs14(vyy780, vyy790, he)
new_esEs6(Right(vyy780), Right(vyy790), bcf, app(app(ty_FiniteMap, deg), deh)) → new_esEs21(vyy780, vyy790, deg, deh)
new_not0 → True
new_compare0(:(vyy300, vyy301), [], bb) → GT
new_ltEs11(False, False) → True
new_ltEs19(vyy301, vyy41, ty_Float) → new_ltEs6(vyy301, vyy41)
new_esEs27(vyy781, vyy791, app(app(ty_Either, bfd), bfe)) → new_esEs6(vyy781, vyy791, bfd, bfe)
new_lt10(vyy300, vyy40) → new_esEs11(new_compare7(vyy300, vyy40))
new_esEs9(True, True) → True
new_esEs15(vyy780, vyy790, ty_Int) → new_esEs10(vyy780, vyy790)
new_compare11(vyy300, vyy40, False, bc, bd) → GT
new_esEs20(vyy782, vyy792, app(app(app(ty_@3, cdh), cea), ceb)) → new_esEs5(vyy782, vyy792, cdh, cea, ceb)
new_primCmpInt(Pos(Succ(vyy3000)), Neg(vyy40)) → GT
new_foldFM_LE20(vyy63, vyy64, vyy96, vyy62, vyy670, vyy671, vyy672, vyy673, vyy674, h, ba) → new_foldFM_LE10(new_fmToList_LE0(vyy63, vyy64, vyy96, h, ba), vyy62, vyy670, vyy671, vyy672, vyy673, vyy674, new_ltEs21(vyy670, vyy62, h), h, ba)
new_esEs11(GT) → False
new_primMulInt(Pos(vyy3010), Pos(vyy410)) → Pos(new_primMulNat0(vyy3010, vyy410))
new_ltEs14(Left(vyy300), Left(vyy40), ty_Char, dah) → new_ltEs9(vyy300, vyy40)
new_ltEs5(LT, GT) → True
new_compare6(vyy300, vyy40) → new_compare23(vyy300, vyy40, new_esEs9(vyy300, vyy40))
new_primMulInt(Neg(vyy3010), Neg(vyy410)) → Pos(new_primMulNat0(vyy3010, vyy410))
new_esEs19(vyy781, vyy791, app(app(ty_FiniteMap, cbd), cbe)) → new_esEs21(vyy781, vyy791, cbd, cbe)
new_primEqNat0(Zero, Succ(vyy7900)) → False
new_primEqNat0(Succ(vyy7800), Zero) → False
new_ltEs14(Left(vyy300), Left(vyy40), ty_Bool, dah) → new_ltEs11(vyy300, vyy40)
new_esEs26(vyy780, vyy790, app(app(ty_@2, beb), bec)) → new_esEs7(vyy780, vyy790, beb, bec)
new_ltEs7(@3(vyy300, vyy301, vyy302), @3(vyy40, vyy41, vyy42), ced, cee, cef) → new_pePe(new_lt8(vyy300, vyy40, ced), vyy300, vyy40, new_pePe(new_lt7(vyy301, vyy41, cee), vyy301, vyy41, new_ltEs8(vyy302, vyy42, cef), cee), ced)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_ltEs21(vyy670, vyy62, ty_Float) → new_ltEs6(vyy670, vyy62)
new_esEs20(vyy782, vyy792, app(app(ty_Either, cdc), cdd)) → new_esEs6(vyy782, vyy792, cdc, cdd)
new_ltEs14(Right(vyy300), Right(vyy40), dbh, ty_Int) → new_ltEs4(vyy300, vyy40)
new_sizeFM(Branch(vyy790, vyy791, vyy792, vyy793, vyy794), gc, gd) → vyy792
new_esEs29(vyy78, vyy79, app(app(ty_Either, bcf), bcg)) → new_esEs6(vyy78, vyy79, bcf, bcg)
new_foldFM_LE10(vyy61, vyy62, vyy63, vyy64, vyy65, vyy66, EmptyFM, True, h, ba) → new_foldFM_LE3(vyy63, vyy64, new_foldFM_LE0(vyy61, vyy62, vyy66, h, ba), vyy62, h, ba)
new_ltEs21(vyy670, vyy62, app(ty_Maybe, gb)) → new_ltEs18(vyy670, vyy62, gb)
new_lt7(vyy301, vyy41, ty_@0) → new_lt6(vyy301, vyy41)
new_pePe(True, vyy78, vyy79, vyy97, bcd) → True
new_ltEs19(vyy301, vyy41, ty_Char) → new_ltEs9(vyy301, vyy41)
new_foldFM2(Branch(vyy790, vyy791, vyy792, vyy793, vyy794), gc, gd) → new_foldFM0(vyy790, vyy791, new_foldFM2(vyy794, gc, gd), vyy793, gc, gd)
new_esEs6(Left(vyy780), Left(vyy790), ty_Char, bcg) → new_esEs25(vyy780, vyy790)
new_esEs29(vyy78, vyy79, app(app(app(ty_@3, bdb), bdc), bdd)) → new_esEs5(vyy78, vyy79, bdb, bdc, bdd)
new_esEs8(Just(vyy780), Just(vyy790), ty_@0) → new_esEs13(vyy780, vyy790)
new_esEs8(Just(vyy780), Just(vyy790), app(ty_[], bab)) → new_esEs22(vyy780, vyy790, bab)
new_primCmpInt(Neg(Zero), Neg(Succ(vyy400))) → new_primCmpNat0(Succ(vyy400), Zero)
new_esEs20(vyy782, vyy792, ty_Bool) → new_esEs9(vyy782, vyy792)
new_primCmpInt(Pos(Zero), Neg(Succ(vyy400))) → GT
new_compare24(vyy300, vyy40, False, bc, bd) → new_compare11(vyy300, vyy40, new_ltEs17(vyy300, vyy40, bc, bd), bc, bd)
new_ltEs14(Left(vyy300), Left(vyy40), app(ty_Maybe, dbg), dah) → new_ltEs18(vyy300, vyy40, dbg)
new_foldFM_LE3(vyy63, vyy64, vyy95, vyy62, h, ba) → new_fmToList_LE0(vyy63, vyy64, vyy95, h, ba)
new_lt15(vyy300, vyy40, ef, eg) → new_esEs11(new_compare18(vyy300, vyy40, ef, eg))
new_lt7(vyy301, vyy41, ty_Bool) → new_lt5(vyy301, vyy41)
new_ltEs18(Just(vyy300), Just(vyy40), app(app(ty_Either, bhb), bhc)) → new_ltEs14(vyy300, vyy40, bhb, bhc)
new_lt4(vyy300, vyy40) → new_esEs11(new_compare8(vyy300, vyy40))
new_esEs18(vyy780, vyy790, ty_Integer) → new_esEs12(vyy780, vyy790)
new_ltEs18(Just(vyy300), Just(vyy40), app(ty_[], bha)) → new_ltEs12(vyy300, vyy40, bha)
new_esEs9(False, True) → False
new_esEs9(True, False) → False
new_ltEs10(vyy30, vyy4) → new_not(new_compare14(vyy30, vyy4))
new_esEs22(:(vyy780, vyy781), :(vyy790, vyy791), bag) → new_asAs(new_esEs28(vyy780, vyy790, bag), new_esEs22(vyy781, vyy791, bag))
new_ltEs14(Left(vyy300), Left(vyy40), app(app(ty_@2, dbe), dbf), dah) → new_ltEs17(vyy300, vyy40, dbe, dbf)
new_esEs18(vyy780, vyy790, ty_Ordering) → new_esEs17(vyy780, vyy790)
new_esEs28(vyy780, vyy790, app(ty_[], bbg)) → new_esEs22(vyy780, vyy790, bbg)
new_ltEs14(Right(vyy300), Right(vyy40), dbh, app(ty_Ratio, dcg)) → new_ltEs15(vyy300, vyy40, dcg)
new_esEs19(vyy781, vyy791, ty_Char) → new_esEs25(vyy781, vyy791)
new_esEs8(Nothing, Nothing, hb) → True
new_primCompAux0(vyy300, vyy40, vyy107, bb) → new_primCompAux00(vyy107, new_compare30(vyy300, vyy40, bb))
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs27(vyy781, vyy791, app(ty_Ratio, bfc)) → new_esEs14(vyy781, vyy791, bfc)
new_compare30(vyy300, vyy40, ty_Float) → new_compare13(vyy300, vyy40)
new_compare13(Float(vyy300, vyy301), Float(vyy40, vyy41)) → new_compare7(new_sr(vyy300, vyy40), new_sr(vyy301, vyy41))
new_ltEs8(vyy302, vyy42, app(ty_Maybe, cfh)) → new_ltEs18(vyy302, vyy42, cfh)
new_ltEs14(Left(vyy300), Right(vyy40), dbh, dah) → True
new_ltEs8(vyy302, vyy42, ty_Float) → new_ltEs6(vyy302, vyy42)
new_esEs22(:(vyy780, vyy781), [], bag) → False
new_esEs22([], :(vyy790, vyy791), bag) → False
new_compare30(vyy300, vyy40, app(ty_[], chf)) → new_compare0(vyy300, vyy40, chf)
new_ltEs20(vyy660, vyy62, app(app(ty_Either, fd), ff)) → new_ltEs14(vyy660, vyy62, fd, ff)
new_asAs(False, vyy106) → False
new_ltEs11(True, True) → True
new_esEs28(vyy780, vyy790, ty_Float) → new_esEs23(vyy780, vyy790)
new_compare30(vyy300, vyy40, ty_Char) → new_compare8(vyy300, vyy40)
new_primMulInt(Neg(vyy3010), Pos(vyy410)) → Neg(new_primMulNat0(vyy3010, vyy410))
new_primMulInt(Pos(vyy3010), Neg(vyy410)) → Neg(new_primMulNat0(vyy3010, vyy410))
new_ltEs19(vyy301, vyy41, app(app(ty_Either, cc), cd)) → new_ltEs14(vyy301, vyy41, cc, cd)
new_ltEs21(vyy670, vyy62, ty_Bool) → new_ltEs11(vyy670, vyy62)
new_primMulNat0(Zero, Succ(vyy4100)) → Zero
new_primMulNat0(Succ(vyy30100), Zero) → Zero
new_foldFM_LE0(vyy61, vyy62, Branch(vyy660, vyy661, vyy662, vyy663, vyy664), h, ba) → new_foldFM_LE10(vyy61, vyy62, vyy660, vyy661, vyy662, vyy663, vyy664, new_ltEs20(vyy660, vyy62, h), h, ba)
new_ltEs14(Right(vyy300), Right(vyy40), dbh, app(app(app(ty_@3, dca), dcb), dcc)) → new_ltEs7(vyy300, vyy40, dca, dcb, dcc)
new_ltEs5(LT, EQ) → True
new_esEs18(vyy780, vyy790, app(ty_[], cag)) → new_esEs22(vyy780, vyy790, cag)
new_esEs27(vyy781, vyy791, ty_Char) → new_esEs25(vyy781, vyy791)
new_ltEs16(vyy30, vyy4) → new_not(new_compare16(vyy30, vyy4))
new_lt18(vyy300, vyy40, bc, bd) → new_esEs11(new_compare9(vyy300, vyy40, bc, bd))
new_ltEs19(vyy301, vyy41, ty_@0) → new_ltEs10(vyy301, vyy41)
new_ltEs18(Nothing, Just(vyy40), bge) → True
new_esEs20(vyy782, vyy792, app(ty_[], cdg)) → new_esEs22(vyy782, vyy792, cdg)
new_compare12(vyy300, vyy40, True) → LT
new_esEs27(vyy781, vyy791, ty_@0) → new_esEs13(vyy781, vyy791)
new_not(EQ) → new_not0
new_esEs8(Just(vyy780), Just(vyy790), app(app(app(ty_@3, bac), bad), bae)) → new_esEs5(vyy780, vyy790, bac, bad, bae)
new_compare110(vyy300, vyy40, True, gg, gh, ha) → LT
new_ltEs21(vyy670, vyy62, app(ty_Ratio, fg)) → new_ltEs15(vyy670, vyy62, fg)
new_lt7(vyy301, vyy41, app(ty_Ratio, cgg)) → new_lt16(vyy301, vyy41, cgg)
new_esEs18(vyy780, vyy790, app(ty_Maybe, cbc)) → new_esEs8(vyy780, vyy790, cbc)
new_ltEs14(Right(vyy300), Right(vyy40), dbh, app(app(ty_Either, dce), dcf)) → new_ltEs14(vyy300, vyy40, dce, dcf)
new_esEs6(Left(vyy780), Left(vyy790), ty_Float, bcg) → new_esEs23(vyy780, vyy790)
new_esEs6(Right(vyy780), Right(vyy790), bcf, ty_Int) → new_esEs10(vyy780, vyy790)
new_foldFM_LE10(vyy61, vyy62, vyy63, vyy64, vyy65, vyy66, Branch(vyy670, vyy671, vyy672, vyy673, vyy674), True, h, ba) → new_foldFM_LE20(vyy63, vyy64, new_foldFM_LE0(vyy61, vyy62, vyy66, h, ba), vyy62, vyy670, vyy671, vyy672, vyy673, vyy674, h, ba)
new_lt7(vyy301, vyy41, app(ty_[], cgd)) → new_lt13(vyy301, vyy41, cgd)
new_esEs17(EQ, LT) → False
new_esEs17(LT, EQ) → False
new_esEs6(Left(vyy780), Left(vyy790), app(ty_Maybe, def), bcg) → new_esEs8(vyy780, vyy790, def)
new_esEs20(vyy782, vyy792, ty_Integer) → new_esEs12(vyy782, vyy792)
new_esEs9(False, False) → True
new_esEs25(Char(vyy780), Char(vyy790)) → new_primEqNat0(vyy780, vyy790)
new_esEs14(:%(vyy780, vyy781), :%(vyy790, vyy791), bce) → new_asAs(new_esEs15(vyy780, vyy790, bce), new_esEs16(vyy781, vyy791, bce))
new_ltEs18(Just(vyy300), Just(vyy40), ty_Bool) → new_ltEs11(vyy300, vyy40)
new_ltEs14(Left(vyy300), Left(vyy40), app(app(ty_Either, dbb), dbc), dah) → new_ltEs14(vyy300, vyy40, dbb, dbc)
new_compare30(vyy300, vyy40, app(ty_Maybe, dad)) → new_compare19(vyy300, vyy40, dad)
new_ltEs14(Left(vyy300), Left(vyy40), ty_Int, dah) → new_ltEs4(vyy300, vyy40)
new_esEs19(vyy781, vyy791, app(ty_[], ccc)) → new_esEs22(vyy781, vyy791, ccc)
new_lt20(vyy300, vyy40, ty_Ordering) → new_lt11(vyy300, vyy40)
new_esEs26(vyy780, vyy790, ty_Ordering) → new_esEs17(vyy780, vyy790)
new_not(LT) → new_not0
new_lt20(vyy300, vyy40, app(app(ty_Either, df), dg)) → new_lt15(vyy300, vyy40, df, dg)
new_ltEs19(vyy301, vyy41, ty_Double) → new_ltEs13(vyy301, vyy41)
new_esEs27(vyy781, vyy791, ty_Ordering) → new_esEs17(vyy781, vyy791)
new_lt11(vyy300, vyy40) → new_esEs11(new_compare29(vyy300, vyy40))
new_ltEs20(vyy660, vyy62, ty_Double) → new_ltEs13(vyy660, vyy62)
new_esEs29(vyy78, vyy79, ty_Ordering) → new_esEs17(vyy78, vyy79)
new_esEs11(EQ) → False
new_compare112(vyy300, vyy40, False, gf) → GT
new_compare28(vyy300, vyy40, False, gf) → new_compare112(vyy300, vyy40, new_ltEs18(vyy300, vyy40, gf), gf)
new_esEs8(Just(vyy780), Just(vyy790), ty_Double) → new_esEs24(vyy780, vyy790)
new_esEs28(vyy780, vyy790, ty_Int) → new_esEs10(vyy780, vyy790)
new_esEs21(vyy78, vyy79, gc, gd) → new_asAs(new_esEs10(new_sizeFM(vyy78, gc, gd), new_sizeFM(vyy79, gc, gd)), new_esEs22(new_fmToList(vyy78, gc, gd), new_fmToList(vyy79, gc, gd), app(app(ty_@2, gc), gd)))
new_ltEs14(Left(vyy300), Left(vyy40), app(app(app(ty_@3, dae), daf), dag), dah) → new_ltEs7(vyy300, vyy40, dae, daf, dag)
new_esEs20(vyy782, vyy792, app(app(ty_@2, cde), cdf)) → new_esEs7(vyy782, vyy792, cde, cdf)
new_esEs26(vyy780, vyy790, app(app(ty_Either, bdh), bea)) → new_esEs6(vyy780, vyy790, bdh, bea)
new_ltEs19(vyy301, vyy41, ty_Ordering) → new_ltEs5(vyy301, vyy41)
new_esEs15(vyy780, vyy790, ty_Integer) → new_esEs12(vyy780, vyy790)
new_compare111(vyy300, vyy40, True, ef, eg) → LT
new_compare0([], :(vyy40, vyy41), bb) → LT
new_primPlusNat1(Zero, Zero) → Zero
new_esEs8(Just(vyy780), Just(vyy790), ty_Int) → new_esEs10(vyy780, vyy790)
new_asAs(True, vyy106) → vyy106
new_lt8(vyy300, vyy40, ty_Ordering) → new_lt11(vyy300, vyy40)
new_esEs26(vyy780, vyy790, app(app(app(ty_@3, bee), bef), beg)) → new_esEs5(vyy780, vyy790, bee, bef, beg)
new_primMulNat0(Succ(vyy30100), Succ(vyy4100)) → new_primPlusNat0(new_primMulNat0(vyy30100, Succ(vyy4100)), vyy4100)
new_esEs18(vyy780, vyy790, app(app(ty_FiniteMap, bhh), caa)) → new_esEs21(vyy780, vyy790, bhh, caa)
new_ltEs5(GT, GT) → True
new_esEs17(GT, GT) → True
new_esEs6(Left(vyy780), Left(vyy790), ty_Double, bcg) → new_esEs24(vyy780, vyy790)
new_esEs27(vyy781, vyy791, ty_Int) → new_esEs10(vyy781, vyy791)
new_esEs8(Just(vyy780), Just(vyy790), app(ty_Maybe, baf)) → new_esEs8(vyy780, vyy790, baf)
new_esEs26(vyy780, vyy790, ty_Char) → new_esEs25(vyy780, vyy790)
new_ltEs8(vyy302, vyy42, ty_Char) → new_ltEs9(vyy302, vyy42)
new_fmToList(vyy79, gc, gd) → new_foldFM2(vyy79, gc, gd)
new_compare28(vyy300, vyy40, True, gf) → EQ
new_esEs26(vyy780, vyy790, app(app(ty_FiniteMap, bde), bdf)) → new_esEs21(vyy780, vyy790, bde, bdf)
new_ltEs8(vyy302, vyy42, ty_Integer) → new_ltEs16(vyy302, vyy42)
new_esEs29(vyy78, vyy79, app(ty_Ratio, bce)) → new_esEs14(vyy78, vyy79, bce)
new_compare10(vyy300, vyy40, True) → LT
new_fmToList_LE0(vyy63, vyy64, vyy95, h, ba) → :(@2(vyy63, vyy64), vyy95)
new_ltEs12(vyy30, vyy4, bb) → new_not(new_compare0(vyy30, vyy4, bb))
new_compare110(vyy300, vyy40, False, gg, gh, ha) → GT
new_lt12(vyy300, vyy40) → new_esEs11(new_compare13(vyy300, vyy40))
new_compare10(vyy300, vyy40, False) → GT
new_esEs10(vyy78, vyy79) → new_primEqInt(vyy78, vyy79)
new_primCompAux00(vyy111, GT) → GT
new_lt7(vyy301, vyy41, app(ty_Maybe, chb)) → new_lt19(vyy301, vyy41, chb)
new_ltEs19(vyy301, vyy41, ty_Int) → new_ltEs4(vyy301, vyy41)
new_compare8(Char(vyy300), Char(vyy40)) → new_primCmpNat0(vyy300, vyy40)
new_esEs8(Just(vyy780), Just(vyy790), ty_Char) → new_esEs25(vyy780, vyy790)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_lt14(vyy300, vyy40) → new_esEs11(new_compare17(vyy300, vyy40))
new_esEs6(Right(vyy780), Right(vyy790), bcf, app(app(app(ty_@3, dfg), dfh), dga)) → new_esEs5(vyy780, vyy790, dfg, dfh, dga)
new_esEs20(vyy782, vyy792, ty_@0) → new_esEs13(vyy782, vyy792)
new_ltEs5(GT, EQ) → False
new_compare30(vyy300, vyy40, app(app(app(ty_@3, chc), chd), che)) → new_compare27(vyy300, vyy40, chc, chd, che)
new_foldFM_LE0(vyy61, vyy62, EmptyFM, h, ba) → vyy61
new_ltEs8(vyy302, vyy42, ty_Bool) → new_ltEs11(vyy302, vyy42)
new_ltEs19(vyy301, vyy41, app(ty_Maybe, da)) → new_ltEs18(vyy301, vyy41, da)
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_ltEs18(Just(vyy300), Just(vyy40), ty_Int) → new_ltEs4(vyy300, vyy40)
new_ltEs19(vyy301, vyy41, ty_Bool) → new_ltEs11(vyy301, vyy41)
new_primCmpInt(Neg(Succ(vyy3000)), Pos(vyy40)) → LT
new_esEs20(vyy782, vyy792, ty_Float) → new_esEs23(vyy782, vyy792)
new_esEs6(Left(vyy780), Left(vyy790), ty_Int, bcg) → new_esEs10(vyy780, vyy790)
The set Q consists of the following terms:
new_esEs6(Left(x0), Left(x1), ty_Int, x2)
new_lt8(x0, x1, ty_Int)
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_lt7(x0, x1, ty_Bool)
new_esEs17(LT, GT)
new_esEs17(GT, LT)
new_esEs13(@0, @0)
new_esEs6(Right(x0), Right(x1), x2, ty_@0)
new_esEs23(Float(x0, x1), Float(x2, x3))
new_primPlusNat1(Zero, Succ(x0))
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_lt14(x0, x1)
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_lt20(x0, x1, app(ty_[], x2))
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_foldFM_LE0(x0, x1, EmptyFM, x2, x3)
new_ltEs20(x0, x1, ty_Integer)
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_ltEs14(Left(x0), Left(x1), ty_Int, x2)
new_lt7(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs16(x0, x1, ty_Integer)
new_esEs18(x0, x1, ty_Ordering)
new_esEs17(LT, LT)
new_esEs6(Left(x0), Left(x1), ty_Ordering, x2)
new_lt20(x0, x1, ty_@0)
new_esEs6(Left(x0), Right(x1), x2, x3)
new_esEs6(Right(x0), Left(x1), x2, x3)
new_compare30(x0, x1, app(ty_Ratio, x2))
new_esEs28(x0, x1, ty_Ordering)
new_compare30(x0, x1, ty_Double)
new_esEs6(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs29(x0, x1, ty_Float)
new_ltEs14(Right(x0), Right(x1), x2, ty_Float)
new_esEs20(x0, x1, ty_Int)
new_compare110(x0, x1, False, x2, x3, x4)
new_esEs18(x0, x1, ty_Int)
new_compare13(Float(x0, x1), Float(x2, x3))
new_ltEs14(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs19(x0, x1, ty_@0)
new_compare11(x0, x1, False, x2, x3)
new_asAs(True, x0)
new_esEs18(x0, x1, ty_@0)
new_primMulNat0(Succ(x0), Zero)
new_lt20(x0, x1, ty_Bool)
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs20(x0, x1, ty_Double)
new_primMulInt(Pos(x0), Pos(x1))
new_compare6(x0, x1)
new_asAs(False, x0)
new_esEs18(x0, x1, app(ty_[], x2))
new_compare26(x0, x1, False, x2, x3)
new_esEs28(x0, x1, ty_Float)
new_lt5(x0, x1)
new_esEs6(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs18(Just(x0), Just(x1), ty_Double)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs17(EQ, GT)
new_esEs17(GT, EQ)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs5(GT, EQ)
new_ltEs5(EQ, GT)
new_ltEs14(Right(x0), Right(x1), x2, ty_Bool)
new_compare0(:(x0, x1), :(x2, x3), x4)
new_esEs18(x0, x1, app(app(ty_@2, x2), x3))
new_foldFM_LE3(x0, x1, x2, x3, x4, x5)
new_esEs29(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs20(x0, x1, ty_Bool)
new_esEs22(:(x0, x1), [], x2)
new_ltEs14(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_compare30(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs21(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs7(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_compare30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare7(x0, x1)
new_ltEs8(x0, x1, ty_@0)
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
new_esEs26(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs11(EQ)
new_esEs17(GT, GT)
new_esEs6(Left(x0), Left(x1), app(ty_[], x2), x3)
new_ltEs21(x0, x1, ty_Integer)
new_lt18(x0, x1, x2, x3)
new_compare15(:%(x0, x1), :%(x2, x3), ty_Integer)
new_compare0([], :(x0, x1), x2)
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_primCompAux00(x0, GT)
new_esEs8(Just(x0), Just(x1), ty_Int)
new_ltEs20(x0, x1, ty_@0)
new_ltEs6(x0, x1)
new_ltEs5(LT, EQ)
new_ltEs5(EQ, LT)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_primEqNat0(Zero, Zero)
new_esEs20(x0, x1, ty_Char)
new_ltEs21(x0, x1, ty_Bool)
new_compare111(x0, x1, True, x2, x3)
new_esEs6(Left(x0), Left(x1), ty_@0, x2)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_compare8(Char(x0), Char(x1))
new_esEs27(x0, x1, ty_Char)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs28(x0, x1, ty_Char)
new_esEs24(Double(x0, x1), Double(x2, x3))
new_ltEs14(Right(x0), Right(x1), x2, ty_Int)
new_esEs9(True, True)
new_ltEs21(x0, x1, app(ty_[], x2))
new_esEs27(x0, x1, app(ty_[], x2))
new_esEs20(x0, x1, ty_Ordering)
new_ltEs18(Just(x0), Nothing, x1)
new_esEs6(Right(x0), Right(x1), x2, app(ty_[], x3))
new_primEqNat0(Zero, Succ(x0))
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_primMulNat0(Succ(x0), Succ(x1))
new_esEs8(Just(x0), Just(x1), app(ty_Ratio, x2))
new_ltEs8(x0, x1, app(ty_Maybe, x2))
new_compare30(x0, x1, app(ty_[], x2))
new_esEs29(x0, x1, app(ty_[], x2))
new_primMulNat0(Zero, Zero)
new_ltEs14(Left(x0), Left(x1), ty_Integer, x2)
new_esEs8(Just(x0), Just(x1), ty_Float)
new_ltEs14(Left(x0), Left(x1), ty_@0, x2)
new_esEs8(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_lt7(x0, x1, app(ty_Ratio, x2))
new_lt20(x0, x1, ty_Double)
new_ltEs14(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs19(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_ltEs20(x0, x1, ty_Char)
new_esEs6(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_lt7(x0, x1, app(app(ty_Either, x2), x3))
new_compare30(x0, x1, ty_@0)
new_esEs29(x0, x1, ty_Ordering)
new_ltEs18(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs29(x0, x1, ty_Int)
new_ltEs18(Just(x0), Just(x1), ty_Integer)
new_ltEs21(x0, x1, ty_Double)
new_ltEs8(x0, x1, app(ty_Ratio, x2))
new_esEs28(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_lt8(x0, x1, ty_Integer)
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_esEs28(x0, x1, ty_Double)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_esEs22([], :(x0, x1), x2)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_lt12(x0, x1)
new_esEs15(x0, x1, ty_Integer)
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_compare16(Integer(x0), Integer(x1))
new_esEs6(Right(x0), Right(x1), x2, ty_Ordering)
new_primMulNat0(Zero, Succ(x0))
new_esEs6(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_lt7(x0, x1, ty_@0)
new_ltEs18(Just(x0), Just(x1), ty_Ordering)
new_esEs8(Just(x0), Just(x1), ty_Bool)
new_esEs8(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_lt7(x0, x1, ty_Int)
new_esEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, x2, x3)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs8(x0, x1, ty_Ordering)
new_esEs19(x0, x1, app(app(ty_Either, x2), x3))
new_lt15(x0, x1, x2, x3)
new_esEs19(x0, x1, ty_Integer)
new_ltEs19(x0, x1, app(ty_[], x2))
new_esEs20(x0, x1, ty_@0)
new_esEs8(Just(x0), Just(x1), ty_Char)
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_primCmpNat0(Zero, Succ(x0))
new_esEs28(x0, x1, ty_Integer)
new_compare26(x0, x1, True, x2, x3)
new_compare30(x0, x1, ty_Int)
new_compare30(x0, x1, ty_Ordering)
new_compare17(Double(x0, x1), Double(x2, x3))
new_compare30(x0, x1, ty_Bool)
new_primMulInt(Neg(x0), Neg(x1))
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
new_ltEs14(Left(x0), Left(x1), ty_Double, x2)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs9(x0, x1)
new_compare30(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs18(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_sr(x0, x1)
new_lt8(x0, x1, ty_Char)
new_primPlusNat0(Zero, x0)
new_compare25(x0, x1, False)
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Right(x0), Right(x1), x2, ty_Double)
new_esEs29(x0, x1, ty_Double)
new_ltEs8(x0, x1, ty_Bool)
new_esEs26(x0, x1, app(ty_[], x2))
new_fmToList(x0, x1, x2)
new_esEs26(x0, x1, ty_Integer)
new_esEs8(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs21(x0, x1, ty_@0)
new_primPlusNat1(Zero, Zero)
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs18(x0, x1, ty_Char)
new_not0
new_esEs6(Right(x0), Right(x1), x2, ty_Char)
new_esEs19(x0, x1, ty_Ordering)
new_ltEs19(x0, x1, ty_Ordering)
new_esEs11(GT)
new_esEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs20(x0, x1, ty_Bool)
new_esEs6(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs18(x0, x1, ty_Bool)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_ltEs14(Right(x0), Right(x1), x2, ty_Integer)
new_ltEs14(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_ltEs14(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs10(x0, x1)
new_esEs6(Left(x0), Left(x1), ty_Char, x2)
new_esEs27(x0, x1, ty_Float)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_lt7(x0, x1, app(app(ty_@2, x2), x3))
new_primCmpNat0(Succ(x0), Succ(x1))
new_lt4(x0, x1)
new_foldFM_LE10(x0, x1, x2, x3, x4, x5, EmptyFM, True, x6, x7)
new_esEs8(Just(x0), Nothing, x1)
new_esEs29(x0, x1, ty_Bool)
new_lt7(x0, x1, app(ty_[], x2))
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_esEs26(x0, x1, ty_Bool)
new_esEs29(x0, x1, ty_@0)
new_esEs28(x0, x1, ty_Int)
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs8(x0, x1, ty_Char)
new_ltEs14(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_lt20(x0, x1, ty_Int)
new_ltEs21(x0, x1, app(ty_Ratio, x2))
new_compare27(x0, x1, x2, x3, x4)
new_esEs8(Just(x0), Just(x1), ty_Integer)
new_esEs18(x0, x1, app(app(ty_Either, x2), x3))
new_esEs6(Left(x0), Left(x1), ty_Integer, x2)
new_esEs27(x0, x1, ty_Ordering)
new_primEqNat0(Succ(x0), Zero)
new_lt8(x0, x1, app(app(ty_Either, x2), x3))
new_compare18(x0, x1, x2, x3)
new_not(GT)
new_esEs8(Just(x0), Just(x1), ty_Ordering)
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs8(x0, x1, app(app(ty_@2, x2), x3))
new_lt8(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, ty_Char)
new_lt17(x0, x1)
new_esEs8(Just(x0), Just(x1), ty_@0)
new_compare23(x0, x1, True)
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_ltEs14(Left(x0), Left(x1), app(ty_[], x2), x3)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_lt9(x0, x1, x2, x3, x4)
new_esEs27(x0, x1, ty_Int)
new_esEs27(x0, x1, ty_Integer)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs11(False, False)
new_lt7(x0, x1, ty_Float)
new_primPlusNat1(Succ(x0), Zero)
new_ltEs19(x0, x1, ty_Bool)
new_lt8(x0, x1, app(app(ty_@2, x2), x3))
new_esEs6(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_compare9(x0, x1, x2, x3)
new_esEs28(x0, x1, ty_Bool)
new_primCompAux00(x0, LT)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_compare210(x0, x1, False, x2, x3, x4)
new_ltEs20(x0, x1, ty_Float)
new_primEqInt(Neg(Zero), Neg(Zero))
new_esEs5(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_ltEs14(Right(x0), Right(x1), x2, ty_Ordering)
new_compare14(@0, @0)
new_compare111(x0, x1, False, x2, x3)
new_ltEs8(x0, x1, ty_Double)
new_lt10(x0, x1)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs18(Nothing, Nothing, x0)
new_ltEs18(Just(x0), Just(x1), ty_@0)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_ltEs14(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_lt8(x0, x1, ty_@0)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_lt8(x0, x1, ty_Ordering)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_ltEs11(False, True)
new_ltEs11(True, False)
new_esEs26(x0, x1, ty_Double)
new_primPlusNat0(Succ(x0), x1)
new_ltEs16(x0, x1)
new_compare25(x0, x1, True)
new_ltEs18(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs20(x0, x1, ty_Float)
new_lt7(x0, x1, app(ty_Maybe, x2))
new_compare28(x0, x1, False, x2)
new_lt11(x0, x1)
new_foldFM_LE10(x0, x1, x2, x3, x4, x5, Branch(x6, x7, x8, x9, x10), True, x11, x12)
new_esEs15(x0, x1, ty_Int)
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_esEs12(Integer(x0), Integer(x1))
new_ltEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs6(Left(x0), Left(x1), ty_Float, x2)
new_lt20(x0, x1, ty_Char)
new_ltEs8(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs14(Right(x0), Right(x1), x2, ty_Double)
new_primCompAux00(x0, EQ)
new_esEs18(x0, x1, ty_Float)
new_ltEs13(x0, x1)
new_esEs29(x0, x1, ty_Char)
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_esEs28(x0, x1, ty_@0)
new_esEs19(x0, x1, ty_Bool)
new_ltEs15(x0, x1, x2)
new_esEs27(x0, x1, ty_Double)
new_sizeFM(EmptyFM, x0, x1)
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_FiniteMap, x3), x4))
new_compare10(x0, x1, False)
new_esEs18(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_ltEs14(Left(x0), Left(x1), ty_Bool, x2)
new_ltEs14(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_foldFM2(EmptyFM, x0, x1)
new_ltEs14(Right(x0), Right(x1), x2, ty_@0)
new_ltEs14(Left(x0), Left(x1), ty_Char, x2)
new_ltEs21(x0, x1, ty_Int)
new_ltEs5(GT, LT)
new_ltEs5(LT, GT)
new_esEs8(Just(x0), Just(x1), app(ty_Maybe, x2))
new_ltEs8(x0, x1, ty_Float)
new_esEs6(Left(x0), Left(x1), ty_Bool, x2)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs18(Nothing, Just(x0), x1)
new_lt7(x0, x1, ty_Double)
new_primCmpNat0(Zero, Zero)
new_esEs19(x0, x1, ty_Float)
new_ltEs4(x0, x1)
new_esEs22(:(x0, x1), :(x2, x3), x4)
new_lt19(x0, x1, x2)
new_esEs27(x0, x1, ty_@0)
new_ltEs19(x0, x1, ty_@0)
new_ltEs8(x0, x1, ty_Int)
new_ltEs18(Just(x0), Just(x1), ty_Char)
new_compare30(x0, x1, ty_Char)
new_esEs9(False, False)
new_ltEs8(x0, x1, app(ty_[], x2))
new_esEs18(x0, x1, ty_Double)
new_lt8(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs19(x0, x1, app(ty_[], x2))
new_pePe(False, x0, x1, x2, x3)
new_ltEs19(x0, x1, ty_Float)
new_ltEs12(x0, x1, x2)
new_compare0([], [], x0)
new_lt20(x0, x1, ty_Integer)
new_lt20(x0, x1, ty_Ordering)
new_lt16(x0, x1, x2)
new_ltEs21(x0, x1, ty_Char)
new_ltEs8(x0, x1, app(app(ty_Either, x2), x3))
new_lt8(x0, x1, ty_Double)
new_esEs8(Just(x0), Just(x1), app(app(ty_FiniteMap, x2), x3))
new_esEs6(Right(x0), Right(x1), x2, ty_Float)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs18(x0, x1, app(ty_Ratio, x2))
new_ltEs5(GT, GT)
new_compare15(:%(x0, x1), :%(x2, x3), ty_Int)
new_ltEs14(Left(x0), Left(x1), ty_Float, x2)
new_esEs18(x0, x1, ty_Integer)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_ltEs21(x0, x1, ty_Ordering)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_ltEs19(x0, x1, ty_Integer)
new_esEs11(LT)
new_esEs16(x0, x1, ty_Int)
new_ltEs18(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs6(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_foldFM_LE10(x0, x1, x2, x3, x4, x5, x6, False, x7, x8)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_compare19(x0, x1, x2)
new_esEs26(x0, x1, ty_Ordering)
new_ltEs14(Right(x0), Right(x1), x2, ty_Char)
new_esEs22([], [], x0)
new_esEs6(Left(x0), Left(x1), app(app(ty_FiniteMap, x2), x3), x4)
new_esEs26(x0, x1, ty_Float)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_esEs29(x0, x1, ty_Integer)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_compare24(x0, x1, True, x2, x3)
new_pePe(True, x0, x1, x2, x3)
new_ltEs14(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_lt7(x0, x1, ty_Ordering)
new_not(EQ)
new_lt7(x0, x1, ty_Integer)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs26(x0, x1, ty_Int)
new_ltEs14(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_ltEs18(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs18(Just(x0), Just(x1), ty_Bool)
new_lt7(x0, x1, ty_Char)
new_compare11(x0, x1, True, x2, x3)
new_ltEs18(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_lt20(x0, x1, ty_Float)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_ltEs14(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs6(Left(x0), Left(x1), ty_Double, x2)
new_compare30(x0, x1, app(ty_Maybe, x2))
new_esEs20(x0, x1, ty_Integer)
new_esEs6(Right(x0), Right(x1), x2, ty_Int)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs8(Nothing, Just(x0), x1)
new_sr0(Integer(x0), Integer(x1))
new_primCmpNat0(Succ(x0), Zero)
new_esEs19(x0, x1, ty_Char)
new_ltEs5(EQ, EQ)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_esEs19(x0, x1, ty_Int)
new_compare12(x0, x1, False)
new_esEs6(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_lt8(x0, x1, app(ty_Ratio, x2))
new_compare0(:(x0, x1), [], x2)
new_ltEs10(x0, x1)
new_lt13(x0, x1, x2)
new_esEs14(:%(x0, x1), :%(x2, x3), x4)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs14(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_foldFM_LE20(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_compare28(x0, x1, True, x2)
new_esEs9(True, False)
new_esEs9(False, True)
new_esEs8(Just(x0), Just(x1), ty_Double)
new_ltEs20(x0, x1, app(ty_[], x2))
new_esEs19(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_compare10(x0, x1, True)
new_esEs6(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_primCompAux0(x0, x1, x2, x3)
new_ltEs19(x0, x1, ty_Int)
new_ltEs8(x0, x1, ty_Integer)
new_ltEs20(x0, x1, ty_Ordering)
new_esEs27(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_compare12(x0, x1, True)
new_ltEs19(x0, x1, ty_Char)
new_compare24(x0, x1, False, x2, x3)
new_ltEs18(Just(x0), Just(x1), ty_Int)
new_esEs27(x0, x1, ty_Bool)
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, ty_Double)
new_ltEs20(x0, x1, ty_Int)
new_lt8(x0, x1, ty_Bool)
new_ltEs21(x0, x1, ty_Float)
new_compare110(x0, x1, True, x2, x3, x4)
new_primEqInt(Pos(Zero), Pos(Zero))
new_esEs20(x0, x1, app(ty_[], x2))
new_esEs18(x0, x1, app(ty_Maybe, x2))
new_esEs8(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs19(x0, x1, ty_Double)
new_primEqNat0(Succ(x0), Succ(x1))
new_ltEs21(x0, x1, app(ty_Maybe, x2))
new_fmToList_LE0(x0, x1, x2, x3, x4)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_lt8(x0, x1, app(ty_[], x2))
new_ltEs14(Right(x0), Left(x1), x2, x3)
new_lt6(x0, x1)
new_ltEs14(Left(x0), Right(x1), x2, x3)
new_esEs17(EQ, EQ)
new_compare112(x0, x1, False, x2)
new_esEs6(Right(x0), Right(x1), x2, ty_Integer)
new_compare30(x0, x1, ty_Float)
new_esEs17(EQ, LT)
new_esEs17(LT, EQ)
new_esEs8(Nothing, Nothing, x0)
new_esEs25(Char(x0), Char(x1))
new_foldFM_LE0(x0, x1, Branch(x2, x3, x4, x5, x6), x7, x8)
new_compare23(x0, x1, False)
new_compare112(x0, x1, True, x2)
new_not(LT)
new_ltEs11(True, True)
new_lt8(x0, x1, ty_Float)
new_ltEs19(x0, x1, ty_Double)
new_ltEs17(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs7(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs20(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_ltEs5(LT, LT)
new_compare30(x0, x1, ty_Integer)
new_esEs26(x0, x1, ty_@0)
new_compare29(x0, x1)
new_compare210(x0, x1, True, x2, x3, x4)
new_esEs28(x0, x1, app(ty_[], x2))
new_ltEs18(Just(x0), Just(x1), ty_Float)
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(vyy61, vyy62, Branch(vyy660, vyy661, vyy662, vyy663, vyy664), h, ba) → new_foldFM_LE1(vyy61, vyy62, vyy660, vyy661, vyy662, vyy663, vyy664, new_ltEs20(vyy660, vyy62, h), h, ba)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 3 > 4, 3 > 5, 3 > 6, 3 > 7, 4 >= 9, 5 >= 10
- new_foldFM_LE1(vyy61, vyy62, vyy63, vyy64, vyy65, Branch(vyy660, vyy661, vyy662, vyy663, vyy664), vyy67, False, h, ba) → new_foldFM_LE1(vyy61, vyy62, vyy660, vyy661, vyy662, vyy663, vyy664, new_ltEs20(vyy660, vyy62, h), h, ba)
The graph contains the following edges 1 >= 1, 2 >= 2, 6 > 3, 6 > 4, 6 > 5, 6 > 6, 6 > 7, 9 >= 9, 10 >= 10
- new_foldFM_LE2(vyy63, vyy64, vyy96, vyy62, vyy670, vyy671, vyy672, vyy673, vyy674, h, ba) → new_foldFM_LE1(new_fmToList_LE0(vyy63, vyy64, vyy96, h, ba), vyy62, vyy670, vyy671, vyy672, vyy673, vyy674, new_ltEs21(vyy670, vyy62, h), h, ba)
The graph contains the following edges 4 >= 2, 5 >= 3, 6 >= 4, 7 >= 5, 8 >= 6, 9 >= 7, 10 >= 9, 11 >= 10
- new_foldFM_LE1(vyy61, vyy62, vyy63, vyy64, vyy65, vyy66, Branch(vyy670, vyy671, vyy672, vyy673, vyy674), True, h, ba) → new_foldFM_LE2(vyy63, vyy64, new_foldFM_LE0(vyy61, vyy62, vyy66, h, ba), vyy62, vyy670, vyy671, vyy672, vyy673, vyy674, h, ba)
The graph contains the following edges 3 >= 1, 4 >= 2, 2 >= 4, 7 > 5, 7 > 6, 7 > 7, 7 > 8, 7 > 9, 9 >= 10, 10 >= 11
- new_foldFM_LE1(vyy61, vyy62, vyy63, vyy64, vyy65, vyy66, EmptyFM, True, h, ba) → new_foldFM_LE(vyy61, vyy62, vyy66, h, ba)
The graph contains the following edges 1 >= 1, 2 >= 2, 6 >= 3, 9 >= 4, 10 >= 5
- new_foldFM_LE1(vyy61, vyy62, vyy63, vyy64, vyy65, vyy66, Branch(vyy670, vyy671, vyy672, vyy673, vyy674), True, h, ba) → new_foldFM_LE(vyy61, vyy62, vyy66, h, ba)
The graph contains the following edges 1 >= 1, 2 >= 2, 6 >= 3, 9 >= 4, 10 >= 5