YES 8.815
H-Termination proof of /home/matraf/haskell/eval_FullyBlown_Fast/FiniteMap.hs
H-Termination of the given Haskell-Program with start terms could successfully be proven:
↳ HASKELL
↳ LR
mainModule FiniteMap
|
| ((foldFM_LE :: Ord c => (c -> b -> a -> a) -> a -> c -> FiniteMap c b -> a) :: Ord c => (c -> b -> a -> a) -> a -> c -> FiniteMap c b -> a) |
module FiniteMap where
| | import qualified Maybe
import qualified Prelude
|
| | data FiniteMap a b = EmptyFM | Branch a b Int (FiniteMap a b) (FiniteMap a b)
|
| | instance (Eq a, Eq b) => Eq (FiniteMap a b) where
|
|
|
| (==) | fm_1 fm_2 | = | sizeFM fm_1 == sizeFM fm_2 && fmToList fm_1 == fmToList fm_2 |
|
|
| | fmToList :: FiniteMap b a -> [(b,a)]
| fmToList | fm | = | foldFM (\key elt rest ->(key,elt) : rest) [] fm |
|
| | foldFM :: (c -> b -> a -> a) -> a -> FiniteMap c b -> a
| foldFM | k z EmptyFM | = | z |
| foldFM | k z (Branch key elt _ fm_l fm_r) | = | foldFM k (k key elt (foldFM k z fm_r)) fm_l |
|
| | foldFM_LE :: Ord c => (c -> b -> a -> a) -> a -> c -> FiniteMap c b -> a
| foldFM_LE | k z fr EmptyFM | = | z |
| foldFM_LE | k z fr (Branch key elt _ fm_l fm_r) | |
| | | key <= fr | = |
| foldFM_LE k (k key elt (foldFM_LE k z fr fm_l)) fr fm_r |
|
| | | otherwise | = |
|
|
|
| | sizeFM :: FiniteMap a b -> Int
| sizeFM | EmptyFM | = | 0 |
| sizeFM | (Branch _ _ size _ _) | = | size |
|
module Maybe where
| | import qualified FiniteMap
import qualified Prelude
|
Lambda Reductions:
The following Lambda expression
\keyeltrest→(key,elt) : rest
is transformed to
| fmToList0 | key elt rest | = (key,elt) : rest |
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
mainModule FiniteMap
|
| ((foldFM_LE :: Ord c => (c -> a -> b -> b) -> b -> c -> FiniteMap c a -> b) :: Ord c => (c -> a -> b -> b) -> b -> c -> FiniteMap c a -> b) |
module FiniteMap where
| | import qualified Maybe
import qualified Prelude
|
| | data FiniteMap a b = EmptyFM | Branch a b Int (FiniteMap a b) (FiniteMap a b)
|
| | instance (Eq a, Eq b) => Eq (FiniteMap a b) where
|
|
|
| (==) | fm_1 fm_2 | = | sizeFM fm_1 == sizeFM fm_2 && fmToList fm_1 == fmToList fm_2 |
|
|
| | fmToList :: FiniteMap b a -> [(b,a)]
| fmToList | fm | = | foldFM fmToList0 [] fm |
|
| |
| fmToList0 | key elt rest | = | (key,elt) : rest |
|
| | foldFM :: (c -> a -> b -> b) -> b -> FiniteMap c a -> b
| foldFM | k z EmptyFM | = | z |
| foldFM | k z (Branch key elt _ fm_l fm_r) | = | foldFM k (k key elt (foldFM k z fm_r)) fm_l |
|
| | foldFM_LE :: Ord c => (c -> a -> b -> b) -> b -> c -> FiniteMap c a -> b
| foldFM_LE | k z fr EmptyFM | = | z |
| foldFM_LE | k z fr (Branch key elt _ fm_l fm_r) | |
| | | key <= fr | = |
| foldFM_LE k (k key elt (foldFM_LE k z fr fm_l)) fr fm_r |
|
| | | otherwise | = |
|
|
|
| | sizeFM :: FiniteMap b a -> Int
| sizeFM | EmptyFM | = | 0 |
| sizeFM | (Branch _ _ size _ _) | = | size |
|
module Maybe where
| | import qualified FiniteMap
import qualified Prelude
|
Case Reductions:
The following Case expression
| case | compare x y of |
| | EQ | → o |
| | LT | → LT |
| | GT | → GT |
is transformed to
| primCompAux0 | o EQ | = o |
| primCompAux0 | o LT | = LT |
| primCompAux0 | o GT | = GT |
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
mainModule FiniteMap
|
| ((foldFM_LE :: Ord c => (c -> a -> b -> b) -> b -> c -> FiniteMap c a -> b) :: Ord c => (c -> a -> b -> b) -> b -> c -> FiniteMap c a -> b) |
module FiniteMap where
| | import qualified Maybe
import qualified Prelude
|
| | data FiniteMap b a = EmptyFM | Branch b a Int (FiniteMap b a) (FiniteMap b a)
|
| | instance (Eq a, Eq b) => Eq (FiniteMap a b) where
|
|
|
| (==) | fm_1 fm_2 | = | sizeFM fm_1 == sizeFM fm_2 && fmToList fm_1 == fmToList fm_2 |
|
|
| | fmToList :: FiniteMap a b -> [(a,b)]
| fmToList | fm | = | foldFM fmToList0 [] fm |
|
| |
| fmToList0 | key elt rest | = | (key,elt) : rest |
|
| | foldFM :: (c -> a -> b -> b) -> b -> FiniteMap c a -> b
| foldFM | k z EmptyFM | = | z |
| foldFM | k z (Branch key elt _ fm_l fm_r) | = | foldFM k (k key elt (foldFM k z fm_r)) fm_l |
|
| | foldFM_LE :: Ord b => (b -> a -> c -> c) -> c -> b -> FiniteMap b a -> c
| foldFM_LE | k z fr EmptyFM | = | z |
| foldFM_LE | k z fr (Branch key elt _ fm_l fm_r) | |
| | | key <= fr | = |
| foldFM_LE k (k key elt (foldFM_LE k z fr fm_l)) fr fm_r |
|
| | | otherwise | = |
|
|
|
| | sizeFM :: FiniteMap b a -> Int
| sizeFM | EmptyFM | = | 0 |
| sizeFM | (Branch _ _ size _ _) | = | size |
|
module Maybe where
| | import qualified FiniteMap
import qualified Prelude
|
If Reductions:
The following If expression
if primGEqNatS x y then Succ (primDivNatS (primMinusNatS x y) (Succ y)) else Zero
is transformed to
| primDivNatS0 | x y True | = Succ (primDivNatS (primMinusNatS x y) (Succ y)) |
| primDivNatS0 | x y False | = Zero |
The following If expression
if primGEqNatS x y then primModNatS (primMinusNatS x y) (Succ y) else Succ x
is transformed to
| primModNatS0 | x y True | = primModNatS (primMinusNatS x y) (Succ y) |
| primModNatS0 | x y False | = Succ x |
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
mainModule FiniteMap
|
| ((foldFM_LE :: Ord a => (a -> c -> b -> b) -> b -> a -> FiniteMap a c -> b) :: Ord a => (a -> c -> b -> b) -> b -> a -> FiniteMap a c -> b) |
module FiniteMap where
| | import qualified Maybe
import qualified Prelude
|
| | data FiniteMap a b = EmptyFM | Branch a b Int (FiniteMap a b) (FiniteMap a b)
|
| | instance (Eq a, Eq b) => Eq (FiniteMap a b) where
|
|
|
| (==) | fm_1 fm_2 | = | sizeFM fm_1 == sizeFM fm_2 && fmToList fm_1 == fmToList fm_2 |
|
|
| | fmToList :: FiniteMap b a -> [(b,a)]
| fmToList | fm | = | foldFM fmToList0 [] fm |
|
| |
| fmToList0 | key elt rest | = | (key,elt) : rest |
|
| | foldFM :: (c -> a -> b -> b) -> b -> FiniteMap c a -> b
| foldFM | k z EmptyFM | = | z |
| foldFM | k z (Branch key elt _ fm_l fm_r) | = | foldFM k (k key elt (foldFM k z fm_r)) fm_l |
|
| | foldFM_LE :: Ord c => (c -> a -> b -> b) -> b -> c -> FiniteMap c a -> b
| foldFM_LE | k z fr EmptyFM | = | z |
| foldFM_LE | k z fr (Branch key elt _ fm_l fm_r) | |
| | | key <= fr | = |
| foldFM_LE k (k key elt (foldFM_LE k z fr fm_l)) fr fm_r |
|
| | | otherwise | = |
|
|
|
| | sizeFM :: FiniteMap b a -> Int
| sizeFM | EmptyFM | = | 0 |
| sizeFM | (Branch _ _ size _ _) | = | size |
|
module Maybe where
| | import qualified FiniteMap
import qualified Prelude
|
Replaced joker patterns by fresh variables and removed binding patterns.
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
mainModule FiniteMap
|
| ((foldFM_LE :: Ord b => (b -> a -> c -> c) -> c -> b -> FiniteMap b a -> c) :: Ord b => (b -> a -> c -> c) -> c -> b -> FiniteMap b a -> c) |
module FiniteMap where
| | import qualified Maybe
import qualified Prelude
|
| | data FiniteMap b a = EmptyFM | Branch b a Int (FiniteMap b a) (FiniteMap b a)
|
| | instance (Eq a, Eq b) => Eq (FiniteMap b a) where
|
|
|
| (==) | fm_1 fm_2 | = | sizeFM fm_1 == sizeFM fm_2 && fmToList fm_1 == fmToList fm_2 |
|
|
| | fmToList :: FiniteMap b a -> [(b,a)]
| fmToList | fm | = | foldFM fmToList0 [] fm |
|
| |
| fmToList0 | key elt rest | = | (key,elt) : rest |
|
| | foldFM :: (c -> a -> b -> b) -> b -> FiniteMap c a -> b
| foldFM | k z EmptyFM | = | z |
| foldFM | k z (Branch key elt vw fm_l fm_r) | = | foldFM k (k key elt (foldFM k z fm_r)) fm_l |
|
| | foldFM_LE :: Ord a => (a -> b -> c -> c) -> c -> a -> FiniteMap a b -> c
| foldFM_LE | k z fr EmptyFM | = | z |
| foldFM_LE | k z fr (Branch key elt 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
|
| ((foldFM_LE :: Ord a => (a -> c -> b -> b) -> b -> a -> FiniteMap a c -> b) :: Ord a => (a -> c -> b -> b) -> b -> a -> FiniteMap a c -> b) |
module FiniteMap where
| | import qualified Maybe
import qualified Prelude
|
| | data FiniteMap a b = EmptyFM | Branch a b Int (FiniteMap a b) (FiniteMap a b)
|
| | instance (Eq a, Eq b) => Eq (FiniteMap b a) where
|
|
|
| (==) | fm_1 fm_2 | = | sizeFM fm_1 == sizeFM fm_2 && fmToList fm_1 == fmToList fm_2 |
|
|
| | fmToList :: FiniteMap a b -> [(a,b)]
| fmToList | fm | = | foldFM fmToList0 [] fm |
|
| |
| fmToList0 | key elt rest | = | (key,elt) : rest |
|
| | foldFM :: (a -> 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 | = | foldFM_LE3 k z fr EmptyFM |
| foldFM_LE | k z fr (Branch key elt vx fm_l fm_r) | = | foldFM_LE2 k z fr (Branch key elt vx fm_l fm_r) |
|
| |
| foldFM_LE0 | k z fr key elt vx fm_l fm_r True | = | foldFM_LE k z fr fm_l |
|
| |
| foldFM_LE1 | k z fr key elt vx fm_l fm_r True | = | foldFM_LE k (k key elt (foldFM_LE k z fr fm_l)) fr fm_r |
| foldFM_LE1 | k z fr key elt vx fm_l fm_r False | = | foldFM_LE0 k z fr key elt vx fm_l fm_r otherwise |
|
| |
| foldFM_LE2 | k z fr (Branch key elt vx fm_l fm_r) | = | foldFM_LE1 k z fr key elt vx fm_l fm_r (key <= fr) |
|
| |
| foldFM_LE3 | k z fr EmptyFM | = | z |
| foldFM_LE3 | vvu vvv vvw vvx | = | foldFM_LE2 vvu vvv vvw vvx |
|
| | sizeFM :: FiniteMap a b -> Int
| sizeFM | EmptyFM | = | 0 |
| sizeFM | (Branch vy vz size wu wv) | = | size |
|
module Maybe where
| | import qualified FiniteMap
import qualified Prelude
|
Let/Where Reductions:
The bindings of the following Let/Where expression
| reduce1 x y (y == 0) |
| where | |
|
| reduce0 | x y True | = x `quot` d :% (y `quot` d) |
|
|
| reduce1 | x y True | = error [] |
| reduce1 | x y False | = reduce0 x y otherwise |
|
are unpacked to the following functions on top level
| reduce2Reduce1 | vyw vyx x y True | = error [] |
| reduce2Reduce1 | vyw vyx x y False | = reduce2Reduce0 vyw vyx x y otherwise |
| reduce2Reduce0 | vyw vyx x y True | = x `quot` reduce2D vyw vyx :% (y `quot` reduce2D vyw vyx) |
| reduce2D | vyw vyx | = gcd vyw vyx |
The bindings of the following Let/Where expression
| gcd' (abs x) (abs y) |
| where |
| gcd' | x vvy | = gcd'2 x vvy |
| gcd' | x y | = gcd'0 x y |
|
|
| gcd'0 | x y | = gcd' y (x `rem` y) |
|
|
| gcd'1 | True x vvy | = x |
| gcd'1 | vvz vwu vwv | = gcd'0 vwu vwv |
|
|
| gcd'2 | x vvy | = gcd'1 (vvy == 0) x vvy |
| gcd'2 | vww vwx | = gcd'0 vww vwx |
|
are unpacked to the following functions on top level
| gcd0Gcd' | 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 |
| gcd0Gcd'0 | x y | = gcd0Gcd' y (x `rem` y) |
| gcd0Gcd'1 | True x vvy | = x |
| gcd0Gcd'1 | vvz vwu vwv | = gcd0Gcd'0 vwu vwv |
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
mainModule FiniteMap
|
| ((foldFM_LE :: Ord a => (a -> b -> c -> c) -> c -> a -> FiniteMap a b -> c) :: Ord a => (a -> b -> c -> c) -> c -> a -> FiniteMap a b -> c) |
module FiniteMap where
| | import qualified Maybe
import qualified Prelude
|
| | data FiniteMap b a = EmptyFM | Branch b a Int (FiniteMap b a) (FiniteMap b a)
|
| | instance (Eq a, Eq b) => Eq (FiniteMap a b) where
|
|
|
| (==) | fm_1 fm_2 | = | sizeFM fm_1 == sizeFM fm_2 && fmToList fm_1 == fmToList fm_2 |
|
|
| | fmToList :: FiniteMap a b -> [(a,b)]
| fmToList | fm | = | foldFM fmToList0 [] fm |
|
| |
| fmToList0 | key elt rest | = | (key,elt) : rest |
|
| | foldFM :: (c -> a -> b -> b) -> b -> FiniteMap c a -> b
| foldFM | k z EmptyFM | = | z |
| foldFM | k z (Branch key elt vw fm_l fm_r) | = | foldFM k (k key elt (foldFM k z fm_r)) fm_l |
|
| | foldFM_LE :: Ord a => (a -> b -> c -> c) -> c -> a -> FiniteMap a b -> c
| foldFM_LE | k z fr EmptyFM | = | foldFM_LE3 k z fr EmptyFM |
| foldFM_LE | k z fr (Branch key elt vx fm_l fm_r) | = | foldFM_LE2 k z fr (Branch key elt vx fm_l fm_r) |
|
| |
| foldFM_LE0 | k z fr key elt vx fm_l fm_r True | = | foldFM_LE k z fr fm_l |
|
| |
| foldFM_LE1 | k z fr key elt vx fm_l fm_r True | = | foldFM_LE k (k key elt (foldFM_LE k z fr fm_l)) fr fm_r |
| foldFM_LE1 | k z fr key elt vx fm_l fm_r False | = | foldFM_LE0 k z fr key elt vx fm_l fm_r otherwise |
|
| |
| foldFM_LE2 | k z fr (Branch key elt vx fm_l fm_r) | = | foldFM_LE1 k z fr key elt vx fm_l fm_r (key <= fr) |
|
| |
| foldFM_LE3 | k z fr EmptyFM | = | z |
| foldFM_LE3 | vvu vvv vvw vvx | = | foldFM_LE2 vvu vvv vvw vvx |
|
| | sizeFM :: FiniteMap b a -> Int
| sizeFM | EmptyFM | = | 0 |
| sizeFM | (Branch vy vz size wu wv) | = | size |
|
module Maybe where
| | import qualified FiniteMap
import qualified Prelude
|
Num Reduction: All numbers are transformed to thier corresponding representation with Pos, Neg, Succ and Zero.
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
mainModule FiniteMap
|
| (foldFM_LE :: Ord a => (a -> b -> c -> c) -> c -> a -> FiniteMap a b -> c) |
module FiniteMap where
| | import qualified Maybe
import qualified Prelude
|
| | data FiniteMap a b = EmptyFM | Branch a b Int (FiniteMap a b) (FiniteMap a b)
|
| | instance (Eq a, Eq b) => Eq (FiniteMap a b) where
|
|
|
| (==) | fm_1 fm_2 | = | sizeFM fm_1 == sizeFM fm_2 && fmToList fm_1 == fmToList fm_2 |
|
|
| | fmToList :: FiniteMap b a -> [(b,a)]
| fmToList | fm | = | foldFM fmToList0 [] fm |
|
| |
| fmToList0 | key elt rest | = | (key,elt) : rest |
|
| | foldFM :: (b -> c -> a -> a) -> a -> FiniteMap b c -> a
| foldFM | k z EmptyFM | = | z |
| foldFM | k z (Branch key elt vw fm_l fm_r) | = | foldFM k (k key elt (foldFM k z fm_r)) fm_l |
|
| | foldFM_LE :: Ord b => (b -> a -> c -> c) -> c -> b -> FiniteMap b a -> c
| foldFM_LE | k z fr EmptyFM | = | foldFM_LE3 k z fr EmptyFM |
| foldFM_LE | k z fr (Branch key elt vx fm_l fm_r) | = | foldFM_LE2 k z fr (Branch key elt vx fm_l fm_r) |
|
| |
| foldFM_LE0 | k z fr key elt vx fm_l fm_r True | = | foldFM_LE k z fr fm_l |
|
| |
| foldFM_LE1 | k z fr key elt vx fm_l fm_r True | = | foldFM_LE k (k key elt (foldFM_LE k z fr fm_l)) fr fm_r |
| foldFM_LE1 | k z fr key elt vx fm_l fm_r False | = | foldFM_LE0 k z fr key elt vx fm_l fm_r otherwise |
|
| |
| foldFM_LE2 | k z fr (Branch key elt vx fm_l fm_r) | = | foldFM_LE1 k z fr key elt vx fm_l fm_r (key <= fr) |
|
| |
| foldFM_LE3 | k z fr EmptyFM | = | z |
| foldFM_LE3 | vvu vvv vvw vvx | = | foldFM_LE2 vvu vvv vvw vvx |
|
| | sizeFM :: FiniteMap a b -> Int
| sizeFM | EmptyFM | = | 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(vyy6000), Succ(vyy500)) → new_primCmpNat(vyy6000, vyy500)
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(vyy6000), Succ(vyy500)) → new_primCmpNat(vyy6000, vyy500)
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(vyy350, vyy351, vyy80, Branch(vyy3530, vyy3531, vyy3532, vyy3533, vyy3534), h, ba) → new_foldFM(vyy3530, vyy3531, new_foldFM0(vyy350, vyy351, vyy80, vyy3534, h, ba), vyy3533, h, ba)
new_foldFM(vyy350, vyy351, vyy80, Branch(vyy3530, vyy3531, vyy3532, vyy3533, vyy3534), h, ba) → new_foldFM(vyy350, vyy351, vyy80, vyy3534, h, ba)
The TRS R consists of the following rules:
new_foldFM0(vyy350, vyy351, vyy80, EmptyFM, h, ba) → :(@2(vyy350, vyy351), vyy80)
new_foldFM0(vyy350, vyy351, vyy80, Branch(vyy3530, vyy3531, vyy3532, vyy3533, vyy3534), h, ba) → new_foldFM0(vyy3530, vyy3531, new_foldFM0(vyy350, vyy351, vyy80, vyy3534, h, ba), vyy3533, h, ba)
The set Q consists of the following terms:
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
We have to consider all minimal (P,Q,R)-chains.
By using the subterm criterion [20] together with the size-change analysis [32] we have proven that there are no infinite chains for this DP problem. From the DPs we obtained the following set of size-change graphs:
- new_foldFM(vyy350, vyy351, vyy80, Branch(vyy3530, vyy3531, vyy3532, vyy3533, vyy3534), h, ba) → new_foldFM(vyy3530, vyy3531, new_foldFM0(vyy350, vyy351, vyy80, vyy3534, h, ba), vyy3533, h, ba)
The graph contains the following edges 4 > 1, 4 > 2, 4 > 4, 5 >= 5, 6 >= 6
- new_foldFM(vyy350, vyy351, vyy80, Branch(vyy3530, vyy3531, vyy3532, vyy3533, vyy3534), h, ba) → new_foldFM(vyy350, vyy351, vyy80, vyy3534, 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(vyy350, vyy351, vyy352, vyy353, vyy354), h, ba) → new_foldFM1(vyy354, 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(vyy350, vyy351, vyy352, vyy353, vyy354), h, ba) → new_foldFM1(vyy354, 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(vyy8100), Succ(vyy51000)) → new_primPlusNat(vyy8100, vyy51000)
R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By using the subterm criterion [20] together with the size-change analysis [32] we have proven that there are no infinite chains for this DP problem. From the DPs we obtained the following set of size-change graphs:
- new_primPlusNat(Succ(vyy8100), Succ(vyy51000)) → new_primPlusNat(vyy8100, vyy51000)
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(vyy60100), Succ(vyy5100)) → new_primMulNat(vyy60100, Succ(vyy5100))
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(vyy60100), Succ(vyy5100)) → new_primMulNat(vyy60100, Succ(vyy5100))
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(vyy3500), Succ(vyy3600)) → new_primEqNat(vyy3500, vyy3600)
R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By using the subterm criterion [20] together with the size-change analysis [32] we have proven that there are no infinite chains for this DP problem. From the DPs we obtained the following set of size-change graphs:
- new_primEqNat(Succ(vyy3500), Succ(vyy3600)) → new_primEqNat(vyy3500, vyy3600)
The graph contains the following edges 1 > 1, 2 > 2
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ Rewriting
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_esEs3(Just(vyy350), Just(vyy360), app(app(ty_@2, bbb), bbc)) → new_esEs1(vyy350, vyy360, bbb, bbc)
new_esEs2(Right(vyy350), Right(vyy360), hd, app(ty_[], bac)) → new_esEs(vyy350, vyy360, bac)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), bcc, app(ty_[], beg), beb) → new_esEs(vyy351, vyy361, beg)
new_esEs2(Left(vyy350), Left(vyy360), app(app(app(ty_@3, ha), hb), hc), gb) → new_esEs4(vyy350, vyy360, ha, hb, hc)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), bcc, app(app(ty_FiniteMap, bdh), bea), beb) → new_esEs0(vyy351, vyy361, bdh, bea)
new_esEs2(Left(vyy350), Left(vyy360), app(app(ty_Either, ge), gf), gb) → new_esEs2(vyy350, vyy360, ge, gf)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), bcc, bcd, app(ty_[], bdc)) → new_esEs(vyy352, vyy362, bdc)
new_esEs1(@2(vyy350, vyy351), @2(vyy360, vyy361), cf, app(app(ty_@2, db), dc)) → new_esEs1(vyy351, vyy361, db, dc)
new_esEs1(@2(vyy350, vyy351), @2(vyy360, vyy361), cf, app(app(app(ty_@3, dh), ea), eb)) → new_esEs4(vyy351, vyy361, dh, ea, eb)
new_esEs2(Right(vyy350), Right(vyy360), hd, app(app(ty_Either, baa), bab)) → new_esEs2(vyy350, vyy360, baa, bab)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), app(app(app(ty_@3, bgd), bge), bgf), bcd, beb) → new_esEs4(vyy350, vyy360, bgd, bge, bgf)
new_esEs(:(vyy350, vyy351), :(vyy360, vyy361), app(ty_Maybe, bh)) → new_esEs3(vyy350, vyy360, bh)
new_esEs2(Right(vyy350), Right(vyy360), hd, app(ty_Maybe, bad)) → new_esEs3(vyy350, vyy360, bad)
new_esEs1(@2(vyy350, vyy351), @2(vyy360, vyy361), cf, app(app(ty_Either, dd), de)) → new_esEs2(vyy351, vyy361, dd, de)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), app(ty_[], bgb), bcd, beb) → new_esEs(vyy350, vyy360, bgb)
new_esEs3(Just(vyy350), Just(vyy360), app(app(app(ty_@3, bbh), bca), bcb)) → new_esEs4(vyy350, vyy360, bbh, bca, bcb)
new_esEs2(Left(vyy350), Left(vyy360), app(ty_Maybe, gh), gb) → new_esEs3(vyy350, vyy360, gh)
new_esEs0(vyy35, vyy36, cd, ce) → new_esEs(new_fmToList(vyy35, cd, ce), new_fmToList(vyy36, cd, ce), app(app(ty_@2, cd), ce))
new_esEs2(Left(vyy350), Left(vyy360), app(app(ty_FiniteMap, fh), ga), gb) → new_esEs0(vyy350, vyy360, fh, ga)
new_esEs2(Right(vyy350), Right(vyy360), hd, app(app(ty_FiniteMap, he), hf)) → new_esEs0(vyy350, vyy360, he, hf)
new_esEs2(Left(vyy350), Left(vyy360), app(app(ty_@2, gc), gd), gb) → new_esEs1(vyy350, vyy360, gc, gd)
new_esEs1(@2(vyy350, vyy351), @2(vyy360, vyy361), cf, app(ty_Maybe, dg)) → new_esEs3(vyy351, vyy361, dg)
new_esEs1(@2(vyy350, vyy351), @2(vyy360, vyy361), app(app(ty_FiniteMap, ec), ed), ee) → new_esEs0(vyy350, vyy360, ec, ed)
new_esEs2(Left(vyy350), Left(vyy360), app(ty_[], gg), gb) → new_esEs(vyy350, vyy360, gg)
new_esEs1(@2(vyy350, vyy351), @2(vyy360, vyy361), app(app(ty_Either, eh), fa), ee) → new_esEs2(vyy350, vyy360, eh, fa)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), bcc, app(app(ty_Either, bee), bef), beb) → new_esEs2(vyy351, vyy361, bee, bef)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), bcc, app(app(app(ty_@3, bfa), bfb), bfc), beb) → new_esEs4(vyy351, vyy361, bfa, bfb, bfc)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), bcc, bcd, app(app(ty_@2, bcg), bch)) → new_esEs1(vyy352, vyy362, bcg, bch)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), app(app(ty_Either, bfh), bga), bcd, beb) → new_esEs2(vyy350, vyy360, bfh, bga)
new_esEs1(@2(vyy350, vyy351), @2(vyy360, vyy361), cf, app(app(ty_FiniteMap, cg), da)) → new_esEs0(vyy351, vyy361, cg, da)
new_esEs1(@2(vyy350, vyy351), @2(vyy360, vyy361), app(ty_Maybe, fc), ee) → new_esEs3(vyy350, vyy360, fc)
new_esEs2(Right(vyy350), Right(vyy360), hd, app(app(ty_@2, hg), hh)) → new_esEs1(vyy350, vyy360, hg, hh)
new_esEs3(Just(vyy350), Just(vyy360), app(app(ty_Either, bbd), bbe)) → new_esEs2(vyy350, vyy360, bbd, bbe)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), bcc, bcd, app(ty_Maybe, bdd)) → new_esEs3(vyy352, vyy362, bdd)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), bcc, bcd, app(app(ty_FiniteMap, bce), bcf)) → new_esEs0(vyy352, vyy362, bce, bcf)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), bcc, app(app(ty_@2, bec), bed), beb) → new_esEs1(vyy351, vyy361, bec, bed)
new_esEs1(@2(vyy350, vyy351), @2(vyy360, vyy361), app(app(app(ty_@3, fd), ff), fg), ee) → new_esEs4(vyy350, vyy360, fd, ff, fg)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), bcc, bcd, app(app(app(ty_@3, bde), bdf), bdg)) → new_esEs4(vyy352, vyy362, bde, bdf, bdg)
new_esEs1(@2(vyy350, vyy351), @2(vyy360, vyy361), cf, app(ty_[], df)) → new_esEs(vyy351, vyy361, df)
new_esEs1(@2(vyy350, vyy351), @2(vyy360, vyy361), app(ty_[], fb), ee) → new_esEs(vyy350, vyy360, fb)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), app(app(ty_@2, bff), bfg), bcd, beb) → new_esEs1(vyy350, vyy360, bff, bfg)
new_esEs3(Just(vyy350), Just(vyy360), app(ty_[], bbf)) → new_esEs(vyy350, vyy360, bbf)
new_esEs(:(vyy350, vyy351), :(vyy360, vyy361), app(app(ty_@2, bc), bd)) → new_esEs1(vyy350, vyy360, bc, bd)
new_esEs2(Right(vyy350), Right(vyy360), hd, app(app(app(ty_@3, bae), baf), bag)) → new_esEs4(vyy350, vyy360, bae, baf, bag)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), app(app(ty_FiniteMap, bfd), bfe), bcd, beb) → new_esEs0(vyy350, vyy360, bfd, bfe)
new_esEs(:(vyy350, vyy351), :(vyy360, vyy361), h) → new_esEs(vyy351, vyy361, h)
new_esEs(:(vyy350, vyy351), :(vyy360, vyy361), app(app(ty_Either, be), bf)) → new_esEs2(vyy350, vyy360, be, bf)
new_esEs1(@2(vyy350, vyy351), @2(vyy360, vyy361), app(app(ty_@2, ef), eg), ee) → new_esEs1(vyy350, vyy360, ef, eg)
new_esEs3(Just(vyy350), Just(vyy360), app(ty_Maybe, bbg)) → new_esEs3(vyy350, vyy360, bbg)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), app(ty_Maybe, bgc), bcd, beb) → new_esEs3(vyy350, vyy360, bgc)
new_esEs(:(vyy350, vyy351), :(vyy360, vyy361), app(app(app(ty_@3, ca), cb), cc)) → new_esEs4(vyy350, vyy360, ca, cb, cc)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), bcc, bcd, app(app(ty_Either, bda), bdb)) → new_esEs2(vyy352, vyy362, bda, bdb)
new_esEs(:(vyy350, vyy351), :(vyy360, vyy361), app(ty_[], bg)) → new_esEs(vyy350, vyy360, bg)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), bcc, app(ty_Maybe, beh), beb) → new_esEs3(vyy351, vyy361, beh)
new_esEs3(Just(vyy350), Just(vyy360), app(app(ty_FiniteMap, bah), bba)) → new_esEs0(vyy350, vyy360, bah, bba)
new_esEs(:(vyy350, vyy351), :(vyy360, vyy361), app(app(ty_FiniteMap, ba), bb)) → new_esEs0(vyy350, vyy360, ba, bb)
The TRS R consists of the following rules:
new_foldFM0(vyy350, vyy351, vyy80, EmptyFM, cd, ce) → :(@2(vyy350, vyy351), vyy80)
new_foldFM0(vyy350, vyy351, vyy80, Branch(vyy3530, vyy3531, vyy3532, vyy3533, vyy3534), cd, ce) → new_foldFM0(vyy3530, vyy3531, new_foldFM0(vyy350, vyy351, vyy80, vyy3534, cd, ce), vyy3533, cd, ce)
new_fmToList(vyy35, cd, ce) → new_foldFM2(vyy35, cd, ce)
new_foldFM2(Branch(vyy350, vyy351, vyy352, vyy353, vyy354), cd, ce) → new_foldFM0(vyy350, vyy351, new_foldFM2(vyy354, cd, ce), vyy353, cd, ce)
new_foldFM2(EmptyFM, cd, ce) → []
The set Q consists of the following terms:
new_fmToList(x0, x1, x2)
new_foldFM2(EmptyFM, x0, x1)
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_esEs0(vyy35, vyy36, cd, ce) → new_esEs(new_fmToList(vyy35, cd, ce), new_fmToList(vyy36, cd, ce), app(app(ty_@2, cd), ce)) at position [0] we obtained the following new rules:
new_esEs0(vyy35, vyy36, cd, ce) → new_esEs(new_foldFM2(vyy35, cd, ce), new_fmToList(vyy36, 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_esEs3(Just(vyy350), Just(vyy360), app(app(ty_@2, bbb), bbc)) → new_esEs1(vyy350, vyy360, bbb, bbc)
new_esEs2(Right(vyy350), Right(vyy360), hd, app(ty_[], bac)) → new_esEs(vyy350, vyy360, bac)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), bcc, app(ty_[], beg), beb) → new_esEs(vyy351, vyy361, beg)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), bcc, app(app(ty_FiniteMap, bdh), bea), beb) → new_esEs0(vyy351, vyy361, bdh, bea)
new_esEs2(Left(vyy350), Left(vyy360), app(app(app(ty_@3, ha), hb), hc), gb) → new_esEs4(vyy350, vyy360, ha, hb, hc)
new_esEs2(Left(vyy350), Left(vyy360), app(app(ty_Either, ge), gf), gb) → new_esEs2(vyy350, vyy360, ge, gf)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), bcc, bcd, app(ty_[], bdc)) → new_esEs(vyy352, vyy362, bdc)
new_esEs1(@2(vyy350, vyy351), @2(vyy360, vyy361), cf, app(app(ty_@2, db), dc)) → new_esEs1(vyy351, vyy361, db, dc)
new_esEs1(@2(vyy350, vyy351), @2(vyy360, vyy361), cf, app(app(app(ty_@3, dh), ea), eb)) → new_esEs4(vyy351, vyy361, dh, ea, eb)
new_esEs2(Right(vyy350), Right(vyy360), hd, app(app(ty_Either, baa), bab)) → new_esEs2(vyy350, vyy360, baa, bab)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), app(app(app(ty_@3, bgd), bge), bgf), bcd, beb) → new_esEs4(vyy350, vyy360, bgd, bge, bgf)
new_esEs(:(vyy350, vyy351), :(vyy360, vyy361), app(ty_Maybe, bh)) → new_esEs3(vyy350, vyy360, bh)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), app(ty_[], bgb), bcd, beb) → new_esEs(vyy350, vyy360, bgb)
new_esEs1(@2(vyy350, vyy351), @2(vyy360, vyy361), cf, app(app(ty_Either, dd), de)) → new_esEs2(vyy351, vyy361, dd, de)
new_esEs2(Right(vyy350), Right(vyy360), hd, app(ty_Maybe, bad)) → new_esEs3(vyy350, vyy360, bad)
new_esEs2(Left(vyy350), Left(vyy360), app(ty_Maybe, gh), gb) → new_esEs3(vyy350, vyy360, gh)
new_esEs3(Just(vyy350), Just(vyy360), app(app(app(ty_@3, bbh), bca), bcb)) → new_esEs4(vyy350, vyy360, bbh, bca, bcb)
new_esEs2(Left(vyy350), Left(vyy360), app(app(ty_FiniteMap, fh), ga), gb) → new_esEs0(vyy350, vyy360, fh, ga)
new_esEs2(Left(vyy350), Left(vyy360), app(app(ty_@2, gc), gd), gb) → new_esEs1(vyy350, vyy360, gc, gd)
new_esEs2(Right(vyy350), Right(vyy360), hd, app(app(ty_FiniteMap, he), hf)) → new_esEs0(vyy350, vyy360, he, hf)
new_esEs2(Left(vyy350), Left(vyy360), app(ty_[], gg), gb) → new_esEs(vyy350, vyy360, gg)
new_esEs1(@2(vyy350, vyy351), @2(vyy360, vyy361), app(app(ty_FiniteMap, ec), ed), ee) → new_esEs0(vyy350, vyy360, ec, ed)
new_esEs1(@2(vyy350, vyy351), @2(vyy360, vyy361), cf, app(ty_Maybe, dg)) → new_esEs3(vyy351, vyy361, dg)
new_esEs1(@2(vyy350, vyy351), @2(vyy360, vyy361), app(app(ty_Either, eh), fa), ee) → new_esEs2(vyy350, vyy360, eh, fa)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), bcc, app(app(ty_Either, bee), bef), beb) → new_esEs2(vyy351, vyy361, bee, bef)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), bcc, app(app(app(ty_@3, bfa), bfb), bfc), beb) → new_esEs4(vyy351, vyy361, bfa, bfb, bfc)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), bcc, bcd, app(app(ty_@2, bcg), bch)) → new_esEs1(vyy352, vyy362, bcg, bch)
new_esEs1(@2(vyy350, vyy351), @2(vyy360, vyy361), cf, app(app(ty_FiniteMap, cg), da)) → new_esEs0(vyy351, vyy361, cg, da)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), app(app(ty_Either, bfh), bga), bcd, beb) → new_esEs2(vyy350, vyy360, bfh, bga)
new_esEs2(Right(vyy350), Right(vyy360), hd, app(app(ty_@2, hg), hh)) → new_esEs1(vyy350, vyy360, hg, hh)
new_esEs1(@2(vyy350, vyy351), @2(vyy360, vyy361), app(ty_Maybe, fc), ee) → new_esEs3(vyy350, vyy360, fc)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), bcc, bcd, app(ty_Maybe, bdd)) → new_esEs3(vyy352, vyy362, bdd)
new_esEs3(Just(vyy350), Just(vyy360), app(app(ty_Either, bbd), bbe)) → new_esEs2(vyy350, vyy360, bbd, bbe)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), bcc, app(app(ty_@2, bec), bed), beb) → new_esEs1(vyy351, vyy361, bec, bed)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), bcc, bcd, app(app(ty_FiniteMap, bce), bcf)) → new_esEs0(vyy352, vyy362, bce, bcf)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), bcc, bcd, app(app(app(ty_@3, bde), bdf), bdg)) → new_esEs4(vyy352, vyy362, bde, bdf, bdg)
new_esEs1(@2(vyy350, vyy351), @2(vyy360, vyy361), app(app(app(ty_@3, fd), ff), fg), ee) → new_esEs4(vyy350, vyy360, fd, ff, fg)
new_esEs1(@2(vyy350, vyy351), @2(vyy360, vyy361), cf, app(ty_[], df)) → new_esEs(vyy351, vyy361, df)
new_esEs1(@2(vyy350, vyy351), @2(vyy360, vyy361), app(ty_[], fb), ee) → new_esEs(vyy350, vyy360, fb)
new_esEs3(Just(vyy350), Just(vyy360), app(ty_[], bbf)) → new_esEs(vyy350, vyy360, bbf)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), app(app(ty_@2, bff), bfg), bcd, beb) → new_esEs1(vyy350, vyy360, bff, bfg)
new_esEs2(Right(vyy350), Right(vyy360), hd, app(app(app(ty_@3, bae), baf), bag)) → new_esEs4(vyy350, vyy360, bae, baf, bag)
new_esEs(:(vyy350, vyy351), :(vyy360, vyy361), app(app(ty_@2, bc), bd)) → new_esEs1(vyy350, vyy360, bc, bd)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), app(app(ty_FiniteMap, bfd), bfe), bcd, beb) → new_esEs0(vyy350, vyy360, bfd, bfe)
new_esEs(:(vyy350, vyy351), :(vyy360, vyy361), h) → new_esEs(vyy351, vyy361, h)
new_esEs(:(vyy350, vyy351), :(vyy360, vyy361), app(app(ty_Either, be), bf)) → new_esEs2(vyy350, vyy360, be, bf)
new_esEs0(vyy35, vyy36, cd, ce) → new_esEs(new_foldFM2(vyy35, cd, ce), new_fmToList(vyy36, cd, ce), app(app(ty_@2, cd), ce))
new_esEs3(Just(vyy350), Just(vyy360), app(ty_Maybe, bbg)) → new_esEs3(vyy350, vyy360, bbg)
new_esEs1(@2(vyy350, vyy351), @2(vyy360, vyy361), app(app(ty_@2, ef), eg), ee) → new_esEs1(vyy350, vyy360, ef, eg)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), app(ty_Maybe, bgc), bcd, beb) → new_esEs3(vyy350, vyy360, bgc)
new_esEs(:(vyy350, vyy351), :(vyy360, vyy361), app(app(app(ty_@3, ca), cb), cc)) → new_esEs4(vyy350, vyy360, ca, cb, cc)
new_esEs(:(vyy350, vyy351), :(vyy360, vyy361), app(ty_[], bg)) → new_esEs(vyy350, vyy360, bg)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), bcc, bcd, app(app(ty_Either, bda), bdb)) → new_esEs2(vyy352, vyy362, bda, bdb)
new_esEs(:(vyy350, vyy351), :(vyy360, vyy361), app(app(ty_FiniteMap, ba), bb)) → new_esEs0(vyy350, vyy360, ba, bb)
new_esEs3(Just(vyy350), Just(vyy360), app(app(ty_FiniteMap, bah), bba)) → new_esEs0(vyy350, vyy360, bah, bba)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), bcc, app(ty_Maybe, beh), beb) → new_esEs3(vyy351, vyy361, beh)
The TRS R consists of the following rules:
new_foldFM0(vyy350, vyy351, vyy80, EmptyFM, cd, ce) → :(@2(vyy350, vyy351), vyy80)
new_foldFM0(vyy350, vyy351, vyy80, Branch(vyy3530, vyy3531, vyy3532, vyy3533, vyy3534), cd, ce) → new_foldFM0(vyy3530, vyy3531, new_foldFM0(vyy350, vyy351, vyy80, vyy3534, cd, ce), vyy3533, cd, ce)
new_fmToList(vyy35, cd, ce) → new_foldFM2(vyy35, cd, ce)
new_foldFM2(Branch(vyy350, vyy351, vyy352, vyy353, vyy354), cd, ce) → new_foldFM0(vyy350, vyy351, new_foldFM2(vyy354, cd, ce), vyy353, cd, ce)
new_foldFM2(EmptyFM, cd, ce) → []
The set Q consists of the following terms:
new_fmToList(x0, x1, x2)
new_foldFM2(EmptyFM, x0, x1)
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_esEs0(vyy35, vyy36, cd, ce) → new_esEs(new_foldFM2(vyy35, cd, ce), new_fmToList(vyy36, cd, ce), app(app(ty_@2, cd), ce)) at position [1] we obtained the following new rules:
new_esEs0(vyy35, vyy36, cd, ce) → new_esEs(new_foldFM2(vyy35, cd, ce), new_foldFM2(vyy36, 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_esEs3(Just(vyy350), Just(vyy360), app(app(ty_@2, bbb), bbc)) → new_esEs1(vyy350, vyy360, bbb, bbc)
new_esEs2(Right(vyy350), Right(vyy360), hd, app(ty_[], bac)) → new_esEs(vyy350, vyy360, bac)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), bcc, app(ty_[], beg), beb) → new_esEs(vyy351, vyy361, beg)
new_esEs2(Left(vyy350), Left(vyy360), app(app(app(ty_@3, ha), hb), hc), gb) → new_esEs4(vyy350, vyy360, ha, hb, hc)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), bcc, app(app(ty_FiniteMap, bdh), bea), beb) → new_esEs0(vyy351, vyy361, bdh, bea)
new_esEs2(Left(vyy350), Left(vyy360), app(app(ty_Either, ge), gf), gb) → new_esEs2(vyy350, vyy360, ge, gf)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), bcc, bcd, app(ty_[], bdc)) → new_esEs(vyy352, vyy362, bdc)
new_esEs1(@2(vyy350, vyy351), @2(vyy360, vyy361), cf, app(app(ty_@2, db), dc)) → new_esEs1(vyy351, vyy361, db, dc)
new_esEs1(@2(vyy350, vyy351), @2(vyy360, vyy361), cf, app(app(app(ty_@3, dh), ea), eb)) → new_esEs4(vyy351, vyy361, dh, ea, eb)
new_esEs0(vyy35, vyy36, cd, ce) → new_esEs(new_foldFM2(vyy35, cd, ce), new_foldFM2(vyy36, cd, ce), app(app(ty_@2, cd), ce))
new_esEs2(Right(vyy350), Right(vyy360), hd, app(app(ty_Either, baa), bab)) → new_esEs2(vyy350, vyy360, baa, bab)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), app(app(app(ty_@3, bgd), bge), bgf), bcd, beb) → new_esEs4(vyy350, vyy360, bgd, bge, bgf)
new_esEs(:(vyy350, vyy351), :(vyy360, vyy361), app(ty_Maybe, bh)) → new_esEs3(vyy350, vyy360, bh)
new_esEs2(Right(vyy350), Right(vyy360), hd, app(ty_Maybe, bad)) → new_esEs3(vyy350, vyy360, bad)
new_esEs1(@2(vyy350, vyy351), @2(vyy360, vyy361), cf, app(app(ty_Either, dd), de)) → new_esEs2(vyy351, vyy361, dd, de)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), app(ty_[], bgb), bcd, beb) → new_esEs(vyy350, vyy360, bgb)
new_esEs3(Just(vyy350), Just(vyy360), app(app(app(ty_@3, bbh), bca), bcb)) → new_esEs4(vyy350, vyy360, bbh, bca, bcb)
new_esEs2(Left(vyy350), Left(vyy360), app(ty_Maybe, gh), gb) → new_esEs3(vyy350, vyy360, gh)
new_esEs2(Left(vyy350), Left(vyy360), app(app(ty_FiniteMap, fh), ga), gb) → new_esEs0(vyy350, vyy360, fh, ga)
new_esEs2(Right(vyy350), Right(vyy360), hd, app(app(ty_FiniteMap, he), hf)) → new_esEs0(vyy350, vyy360, he, hf)
new_esEs2(Left(vyy350), Left(vyy360), app(app(ty_@2, gc), gd), gb) → new_esEs1(vyy350, vyy360, gc, gd)
new_esEs1(@2(vyy350, vyy351), @2(vyy360, vyy361), cf, app(ty_Maybe, dg)) → new_esEs3(vyy351, vyy361, dg)
new_esEs1(@2(vyy350, vyy351), @2(vyy360, vyy361), app(app(ty_FiniteMap, ec), ed), ee) → new_esEs0(vyy350, vyy360, ec, ed)
new_esEs2(Left(vyy350), Left(vyy360), app(ty_[], gg), gb) → new_esEs(vyy350, vyy360, gg)
new_esEs1(@2(vyy350, vyy351), @2(vyy360, vyy361), app(app(ty_Either, eh), fa), ee) → new_esEs2(vyy350, vyy360, eh, fa)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), bcc, app(app(ty_Either, bee), bef), beb) → new_esEs2(vyy351, vyy361, bee, bef)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), bcc, app(app(app(ty_@3, bfa), bfb), bfc), beb) → new_esEs4(vyy351, vyy361, bfa, bfb, bfc)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), bcc, bcd, app(app(ty_@2, bcg), bch)) → new_esEs1(vyy352, vyy362, bcg, bch)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), app(app(ty_Either, bfh), bga), bcd, beb) → new_esEs2(vyy350, vyy360, bfh, bga)
new_esEs1(@2(vyy350, vyy351), @2(vyy360, vyy361), cf, app(app(ty_FiniteMap, cg), da)) → new_esEs0(vyy351, vyy361, cg, da)
new_esEs1(@2(vyy350, vyy351), @2(vyy360, vyy361), app(ty_Maybe, fc), ee) → new_esEs3(vyy350, vyy360, fc)
new_esEs2(Right(vyy350), Right(vyy360), hd, app(app(ty_@2, hg), hh)) → new_esEs1(vyy350, vyy360, hg, hh)
new_esEs3(Just(vyy350), Just(vyy360), app(app(ty_Either, bbd), bbe)) → new_esEs2(vyy350, vyy360, bbd, bbe)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), bcc, bcd, app(ty_Maybe, bdd)) → new_esEs3(vyy352, vyy362, bdd)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), bcc, bcd, app(app(ty_FiniteMap, bce), bcf)) → new_esEs0(vyy352, vyy362, bce, bcf)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), bcc, app(app(ty_@2, bec), bed), beb) → new_esEs1(vyy351, vyy361, bec, bed)
new_esEs1(@2(vyy350, vyy351), @2(vyy360, vyy361), app(app(app(ty_@3, fd), ff), fg), ee) → new_esEs4(vyy350, vyy360, fd, ff, fg)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), bcc, bcd, app(app(app(ty_@3, bde), bdf), bdg)) → new_esEs4(vyy352, vyy362, bde, bdf, bdg)
new_esEs1(@2(vyy350, vyy351), @2(vyy360, vyy361), cf, app(ty_[], df)) → new_esEs(vyy351, vyy361, df)
new_esEs1(@2(vyy350, vyy351), @2(vyy360, vyy361), app(ty_[], fb), ee) → new_esEs(vyy350, vyy360, fb)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), app(app(ty_@2, bff), bfg), bcd, beb) → new_esEs1(vyy350, vyy360, bff, bfg)
new_esEs3(Just(vyy350), Just(vyy360), app(ty_[], bbf)) → new_esEs(vyy350, vyy360, bbf)
new_esEs(:(vyy350, vyy351), :(vyy360, vyy361), app(app(ty_@2, bc), bd)) → new_esEs1(vyy350, vyy360, bc, bd)
new_esEs2(Right(vyy350), Right(vyy360), hd, app(app(app(ty_@3, bae), baf), bag)) → new_esEs4(vyy350, vyy360, bae, baf, bag)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), app(app(ty_FiniteMap, bfd), bfe), bcd, beb) → new_esEs0(vyy350, vyy360, bfd, bfe)
new_esEs(:(vyy350, vyy351), :(vyy360, vyy361), h) → new_esEs(vyy351, vyy361, h)
new_esEs(:(vyy350, vyy351), :(vyy360, vyy361), app(app(ty_Either, be), bf)) → new_esEs2(vyy350, vyy360, be, bf)
new_esEs1(@2(vyy350, vyy351), @2(vyy360, vyy361), app(app(ty_@2, ef), eg), ee) → new_esEs1(vyy350, vyy360, ef, eg)
new_esEs3(Just(vyy350), Just(vyy360), app(ty_Maybe, bbg)) → new_esEs3(vyy350, vyy360, bbg)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), app(ty_Maybe, bgc), bcd, beb) → new_esEs3(vyy350, vyy360, bgc)
new_esEs(:(vyy350, vyy351), :(vyy360, vyy361), app(app(app(ty_@3, ca), cb), cc)) → new_esEs4(vyy350, vyy360, ca, cb, cc)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), bcc, bcd, app(app(ty_Either, bda), bdb)) → new_esEs2(vyy352, vyy362, bda, bdb)
new_esEs(:(vyy350, vyy351), :(vyy360, vyy361), app(ty_[], bg)) → new_esEs(vyy350, vyy360, bg)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), bcc, app(ty_Maybe, beh), beb) → new_esEs3(vyy351, vyy361, beh)
new_esEs3(Just(vyy350), Just(vyy360), app(app(ty_FiniteMap, bah), bba)) → new_esEs0(vyy350, vyy360, bah, bba)
new_esEs(:(vyy350, vyy351), :(vyy360, vyy361), app(app(ty_FiniteMap, ba), bb)) → new_esEs0(vyy350, vyy360, ba, bb)
The TRS R consists of the following rules:
new_foldFM0(vyy350, vyy351, vyy80, EmptyFM, cd, ce) → :(@2(vyy350, vyy351), vyy80)
new_foldFM0(vyy350, vyy351, vyy80, Branch(vyy3530, vyy3531, vyy3532, vyy3533, vyy3534), cd, ce) → new_foldFM0(vyy3530, vyy3531, new_foldFM0(vyy350, vyy351, vyy80, vyy3534, cd, ce), vyy3533, cd, ce)
new_fmToList(vyy35, cd, ce) → new_foldFM2(vyy35, cd, ce)
new_foldFM2(Branch(vyy350, vyy351, vyy352, vyy353, vyy354), cd, ce) → new_foldFM0(vyy350, vyy351, new_foldFM2(vyy354, cd, ce), vyy353, cd, ce)
new_foldFM2(EmptyFM, cd, ce) → []
The set Q consists of the following terms:
new_fmToList(x0, x1, x2)
new_foldFM2(EmptyFM, x0, x1)
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
We have to consider all minimal (P,Q,R)-chains.
As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [15] we can delete all non-usable rules [17] from R.
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ Rewriting
↳ QDP
↳ Rewriting
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QReductionProof
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_esEs3(Just(vyy350), Just(vyy360), app(app(ty_@2, bbb), bbc)) → new_esEs1(vyy350, vyy360, bbb, bbc)
new_esEs2(Right(vyy350), Right(vyy360), hd, app(ty_[], bac)) → new_esEs(vyy350, vyy360, bac)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), bcc, app(ty_[], beg), beb) → new_esEs(vyy351, vyy361, beg)
new_esEs2(Left(vyy350), Left(vyy360), app(app(app(ty_@3, ha), hb), hc), gb) → new_esEs4(vyy350, vyy360, ha, hb, hc)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), bcc, app(app(ty_FiniteMap, bdh), bea), beb) → new_esEs0(vyy351, vyy361, bdh, bea)
new_esEs2(Left(vyy350), Left(vyy360), app(app(ty_Either, ge), gf), gb) → new_esEs2(vyy350, vyy360, ge, gf)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), bcc, bcd, app(ty_[], bdc)) → new_esEs(vyy352, vyy362, bdc)
new_esEs1(@2(vyy350, vyy351), @2(vyy360, vyy361), cf, app(app(ty_@2, db), dc)) → new_esEs1(vyy351, vyy361, db, dc)
new_esEs1(@2(vyy350, vyy351), @2(vyy360, vyy361), cf, app(app(app(ty_@3, dh), ea), eb)) → new_esEs4(vyy351, vyy361, dh, ea, eb)
new_esEs0(vyy35, vyy36, cd, ce) → new_esEs(new_foldFM2(vyy35, cd, ce), new_foldFM2(vyy36, cd, ce), app(app(ty_@2, cd), ce))
new_esEs2(Right(vyy350), Right(vyy360), hd, app(app(ty_Either, baa), bab)) → new_esEs2(vyy350, vyy360, baa, bab)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), app(app(app(ty_@3, bgd), bge), bgf), bcd, beb) → new_esEs4(vyy350, vyy360, bgd, bge, bgf)
new_esEs(:(vyy350, vyy351), :(vyy360, vyy361), app(ty_Maybe, bh)) → new_esEs3(vyy350, vyy360, bh)
new_esEs2(Right(vyy350), Right(vyy360), hd, app(ty_Maybe, bad)) → new_esEs3(vyy350, vyy360, bad)
new_esEs1(@2(vyy350, vyy351), @2(vyy360, vyy361), cf, app(app(ty_Either, dd), de)) → new_esEs2(vyy351, vyy361, dd, de)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), app(ty_[], bgb), bcd, beb) → new_esEs(vyy350, vyy360, bgb)
new_esEs3(Just(vyy350), Just(vyy360), app(app(app(ty_@3, bbh), bca), bcb)) → new_esEs4(vyy350, vyy360, bbh, bca, bcb)
new_esEs2(Left(vyy350), Left(vyy360), app(ty_Maybe, gh), gb) → new_esEs3(vyy350, vyy360, gh)
new_esEs2(Left(vyy350), Left(vyy360), app(app(ty_FiniteMap, fh), ga), gb) → new_esEs0(vyy350, vyy360, fh, ga)
new_esEs2(Right(vyy350), Right(vyy360), hd, app(app(ty_FiniteMap, he), hf)) → new_esEs0(vyy350, vyy360, he, hf)
new_esEs2(Left(vyy350), Left(vyy360), app(app(ty_@2, gc), gd), gb) → new_esEs1(vyy350, vyy360, gc, gd)
new_esEs1(@2(vyy350, vyy351), @2(vyy360, vyy361), cf, app(ty_Maybe, dg)) → new_esEs3(vyy351, vyy361, dg)
new_esEs1(@2(vyy350, vyy351), @2(vyy360, vyy361), app(app(ty_FiniteMap, ec), ed), ee) → new_esEs0(vyy350, vyy360, ec, ed)
new_esEs2(Left(vyy350), Left(vyy360), app(ty_[], gg), gb) → new_esEs(vyy350, vyy360, gg)
new_esEs1(@2(vyy350, vyy351), @2(vyy360, vyy361), app(app(ty_Either, eh), fa), ee) → new_esEs2(vyy350, vyy360, eh, fa)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), bcc, app(app(ty_Either, bee), bef), beb) → new_esEs2(vyy351, vyy361, bee, bef)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), bcc, app(app(app(ty_@3, bfa), bfb), bfc), beb) → new_esEs4(vyy351, vyy361, bfa, bfb, bfc)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), bcc, bcd, app(app(ty_@2, bcg), bch)) → new_esEs1(vyy352, vyy362, bcg, bch)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), app(app(ty_Either, bfh), bga), bcd, beb) → new_esEs2(vyy350, vyy360, bfh, bga)
new_esEs1(@2(vyy350, vyy351), @2(vyy360, vyy361), cf, app(app(ty_FiniteMap, cg), da)) → new_esEs0(vyy351, vyy361, cg, da)
new_esEs1(@2(vyy350, vyy351), @2(vyy360, vyy361), app(ty_Maybe, fc), ee) → new_esEs3(vyy350, vyy360, fc)
new_esEs2(Right(vyy350), Right(vyy360), hd, app(app(ty_@2, hg), hh)) → new_esEs1(vyy350, vyy360, hg, hh)
new_esEs3(Just(vyy350), Just(vyy360), app(app(ty_Either, bbd), bbe)) → new_esEs2(vyy350, vyy360, bbd, bbe)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), bcc, bcd, app(ty_Maybe, bdd)) → new_esEs3(vyy352, vyy362, bdd)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), bcc, bcd, app(app(ty_FiniteMap, bce), bcf)) → new_esEs0(vyy352, vyy362, bce, bcf)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), bcc, app(app(ty_@2, bec), bed), beb) → new_esEs1(vyy351, vyy361, bec, bed)
new_esEs1(@2(vyy350, vyy351), @2(vyy360, vyy361), app(app(app(ty_@3, fd), ff), fg), ee) → new_esEs4(vyy350, vyy360, fd, ff, fg)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), bcc, bcd, app(app(app(ty_@3, bde), bdf), bdg)) → new_esEs4(vyy352, vyy362, bde, bdf, bdg)
new_esEs1(@2(vyy350, vyy351), @2(vyy360, vyy361), cf, app(ty_[], df)) → new_esEs(vyy351, vyy361, df)
new_esEs1(@2(vyy350, vyy351), @2(vyy360, vyy361), app(ty_[], fb), ee) → new_esEs(vyy350, vyy360, fb)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), app(app(ty_@2, bff), bfg), bcd, beb) → new_esEs1(vyy350, vyy360, bff, bfg)
new_esEs3(Just(vyy350), Just(vyy360), app(ty_[], bbf)) → new_esEs(vyy350, vyy360, bbf)
new_esEs(:(vyy350, vyy351), :(vyy360, vyy361), app(app(ty_@2, bc), bd)) → new_esEs1(vyy350, vyy360, bc, bd)
new_esEs2(Right(vyy350), Right(vyy360), hd, app(app(app(ty_@3, bae), baf), bag)) → new_esEs4(vyy350, vyy360, bae, baf, bag)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), app(app(ty_FiniteMap, bfd), bfe), bcd, beb) → new_esEs0(vyy350, vyy360, bfd, bfe)
new_esEs(:(vyy350, vyy351), :(vyy360, vyy361), h) → new_esEs(vyy351, vyy361, h)
new_esEs(:(vyy350, vyy351), :(vyy360, vyy361), app(app(ty_Either, be), bf)) → new_esEs2(vyy350, vyy360, be, bf)
new_esEs1(@2(vyy350, vyy351), @2(vyy360, vyy361), app(app(ty_@2, ef), eg), ee) → new_esEs1(vyy350, vyy360, ef, eg)
new_esEs3(Just(vyy350), Just(vyy360), app(ty_Maybe, bbg)) → new_esEs3(vyy350, vyy360, bbg)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), app(ty_Maybe, bgc), bcd, beb) → new_esEs3(vyy350, vyy360, bgc)
new_esEs(:(vyy350, vyy351), :(vyy360, vyy361), app(app(app(ty_@3, ca), cb), cc)) → new_esEs4(vyy350, vyy360, ca, cb, cc)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), bcc, bcd, app(app(ty_Either, bda), bdb)) → new_esEs2(vyy352, vyy362, bda, bdb)
new_esEs(:(vyy350, vyy351), :(vyy360, vyy361), app(ty_[], bg)) → new_esEs(vyy350, vyy360, bg)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), bcc, app(ty_Maybe, beh), beb) → new_esEs3(vyy351, vyy361, beh)
new_esEs3(Just(vyy350), Just(vyy360), app(app(ty_FiniteMap, bah), bba)) → new_esEs0(vyy350, vyy360, bah, bba)
new_esEs(:(vyy350, vyy351), :(vyy360, vyy361), app(app(ty_FiniteMap, ba), bb)) → new_esEs0(vyy350, vyy360, ba, bb)
The TRS R consists of the following rules:
new_foldFM2(Branch(vyy350, vyy351, vyy352, vyy353, vyy354), cd, ce) → new_foldFM0(vyy350, vyy351, new_foldFM2(vyy354, cd, ce), vyy353, cd, ce)
new_foldFM2(EmptyFM, cd, ce) → []
new_foldFM0(vyy350, vyy351, vyy80, EmptyFM, cd, ce) → :(@2(vyy350, vyy351), vyy80)
new_foldFM0(vyy350, vyy351, vyy80, Branch(vyy3530, vyy3531, vyy3532, vyy3533, vyy3534), cd, ce) → new_foldFM0(vyy3530, vyy3531, new_foldFM0(vyy350, vyy351, vyy80, vyy3534, cd, ce), vyy3533, cd, ce)
The set Q consists of the following terms:
new_fmToList(x0, x1, x2)
new_foldFM2(EmptyFM, x0, x1)
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
We have to consider all minimal (P,Q,R)-chains.
We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.
new_fmToList(x0, x1, x2)
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ Rewriting
↳ QDP
↳ Rewriting
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QReductionProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_esEs3(Just(vyy350), Just(vyy360), app(app(ty_@2, bbb), bbc)) → new_esEs1(vyy350, vyy360, bbb, bbc)
new_esEs2(Right(vyy350), Right(vyy360), hd, app(ty_[], bac)) → new_esEs(vyy350, vyy360, bac)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), bcc, app(ty_[], beg), beb) → new_esEs(vyy351, vyy361, beg)
new_esEs2(Left(vyy350), Left(vyy360), app(app(app(ty_@3, ha), hb), hc), gb) → new_esEs4(vyy350, vyy360, ha, hb, hc)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), bcc, app(app(ty_FiniteMap, bdh), bea), beb) → new_esEs0(vyy351, vyy361, bdh, bea)
new_esEs2(Left(vyy350), Left(vyy360), app(app(ty_Either, ge), gf), gb) → new_esEs2(vyy350, vyy360, ge, gf)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), bcc, bcd, app(ty_[], bdc)) → new_esEs(vyy352, vyy362, bdc)
new_esEs1(@2(vyy350, vyy351), @2(vyy360, vyy361), cf, app(app(ty_@2, db), dc)) → new_esEs1(vyy351, vyy361, db, dc)
new_esEs1(@2(vyy350, vyy351), @2(vyy360, vyy361), cf, app(app(app(ty_@3, dh), ea), eb)) → new_esEs4(vyy351, vyy361, dh, ea, eb)
new_esEs0(vyy35, vyy36, cd, ce) → new_esEs(new_foldFM2(vyy35, cd, ce), new_foldFM2(vyy36, cd, ce), app(app(ty_@2, cd), ce))
new_esEs2(Right(vyy350), Right(vyy360), hd, app(app(ty_Either, baa), bab)) → new_esEs2(vyy350, vyy360, baa, bab)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), app(app(app(ty_@3, bgd), bge), bgf), bcd, beb) → new_esEs4(vyy350, vyy360, bgd, bge, bgf)
new_esEs(:(vyy350, vyy351), :(vyy360, vyy361), app(ty_Maybe, bh)) → new_esEs3(vyy350, vyy360, bh)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), app(ty_[], bgb), bcd, beb) → new_esEs(vyy350, vyy360, bgb)
new_esEs1(@2(vyy350, vyy351), @2(vyy360, vyy361), cf, app(app(ty_Either, dd), de)) → new_esEs2(vyy351, vyy361, dd, de)
new_esEs2(Right(vyy350), Right(vyy360), hd, app(ty_Maybe, bad)) → new_esEs3(vyy350, vyy360, bad)
new_esEs2(Left(vyy350), Left(vyy360), app(ty_Maybe, gh), gb) → new_esEs3(vyy350, vyy360, gh)
new_esEs3(Just(vyy350), Just(vyy360), app(app(app(ty_@3, bbh), bca), bcb)) → new_esEs4(vyy350, vyy360, bbh, bca, bcb)
new_esEs2(Left(vyy350), Left(vyy360), app(app(ty_FiniteMap, fh), ga), gb) → new_esEs0(vyy350, vyy360, fh, ga)
new_esEs2(Left(vyy350), Left(vyy360), app(app(ty_@2, gc), gd), gb) → new_esEs1(vyy350, vyy360, gc, gd)
new_esEs2(Right(vyy350), Right(vyy360), hd, app(app(ty_FiniteMap, he), hf)) → new_esEs0(vyy350, vyy360, he, hf)
new_esEs2(Left(vyy350), Left(vyy360), app(ty_[], gg), gb) → new_esEs(vyy350, vyy360, gg)
new_esEs1(@2(vyy350, vyy351), @2(vyy360, vyy361), app(app(ty_FiniteMap, ec), ed), ee) → new_esEs0(vyy350, vyy360, ec, ed)
new_esEs1(@2(vyy350, vyy351), @2(vyy360, vyy361), cf, app(ty_Maybe, dg)) → new_esEs3(vyy351, vyy361, dg)
new_esEs1(@2(vyy350, vyy351), @2(vyy360, vyy361), app(app(ty_Either, eh), fa), ee) → new_esEs2(vyy350, vyy360, eh, fa)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), bcc, app(app(ty_Either, bee), bef), beb) → new_esEs2(vyy351, vyy361, bee, bef)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), bcc, app(app(app(ty_@3, bfa), bfb), bfc), beb) → new_esEs4(vyy351, vyy361, bfa, bfb, bfc)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), bcc, bcd, app(app(ty_@2, bcg), bch)) → new_esEs1(vyy352, vyy362, bcg, bch)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), app(app(ty_Either, bfh), bga), bcd, beb) → new_esEs2(vyy350, vyy360, bfh, bga)
new_esEs1(@2(vyy350, vyy351), @2(vyy360, vyy361), cf, app(app(ty_FiniteMap, cg), da)) → new_esEs0(vyy351, vyy361, cg, da)
new_esEs1(@2(vyy350, vyy351), @2(vyy360, vyy361), app(ty_Maybe, fc), ee) → new_esEs3(vyy350, vyy360, fc)
new_esEs2(Right(vyy350), Right(vyy360), hd, app(app(ty_@2, hg), hh)) → new_esEs1(vyy350, vyy360, hg, hh)
new_esEs3(Just(vyy350), Just(vyy360), app(app(ty_Either, bbd), bbe)) → new_esEs2(vyy350, vyy360, bbd, bbe)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), bcc, bcd, app(ty_Maybe, bdd)) → new_esEs3(vyy352, vyy362, bdd)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), bcc, bcd, app(app(ty_FiniteMap, bce), bcf)) → new_esEs0(vyy352, vyy362, bce, bcf)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), bcc, app(app(ty_@2, bec), bed), beb) → new_esEs1(vyy351, vyy361, bec, bed)
new_esEs1(@2(vyy350, vyy351), @2(vyy360, vyy361), app(app(app(ty_@3, fd), ff), fg), ee) → new_esEs4(vyy350, vyy360, fd, ff, fg)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), bcc, bcd, app(app(app(ty_@3, bde), bdf), bdg)) → new_esEs4(vyy352, vyy362, bde, bdf, bdg)
new_esEs1(@2(vyy350, vyy351), @2(vyy360, vyy361), cf, app(ty_[], df)) → new_esEs(vyy351, vyy361, df)
new_esEs1(@2(vyy350, vyy351), @2(vyy360, vyy361), app(ty_[], fb), ee) → new_esEs(vyy350, vyy360, fb)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), app(app(ty_@2, bff), bfg), bcd, beb) → new_esEs1(vyy350, vyy360, bff, bfg)
new_esEs3(Just(vyy350), Just(vyy360), app(ty_[], bbf)) → new_esEs(vyy350, vyy360, bbf)
new_esEs(:(vyy350, vyy351), :(vyy360, vyy361), app(app(ty_@2, bc), bd)) → new_esEs1(vyy350, vyy360, bc, bd)
new_esEs2(Right(vyy350), Right(vyy360), hd, app(app(app(ty_@3, bae), baf), bag)) → new_esEs4(vyy350, vyy360, bae, baf, bag)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), app(app(ty_FiniteMap, bfd), bfe), bcd, beb) → new_esEs0(vyy350, vyy360, bfd, bfe)
new_esEs(:(vyy350, vyy351), :(vyy360, vyy361), h) → new_esEs(vyy351, vyy361, h)
new_esEs(:(vyy350, vyy351), :(vyy360, vyy361), app(app(ty_Either, be), bf)) → new_esEs2(vyy350, vyy360, be, bf)
new_esEs1(@2(vyy350, vyy351), @2(vyy360, vyy361), app(app(ty_@2, ef), eg), ee) → new_esEs1(vyy350, vyy360, ef, eg)
new_esEs3(Just(vyy350), Just(vyy360), app(ty_Maybe, bbg)) → new_esEs3(vyy350, vyy360, bbg)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), app(ty_Maybe, bgc), bcd, beb) → new_esEs3(vyy350, vyy360, bgc)
new_esEs(:(vyy350, vyy351), :(vyy360, vyy361), app(app(app(ty_@3, ca), cb), cc)) → new_esEs4(vyy350, vyy360, ca, cb, cc)
new_esEs(:(vyy350, vyy351), :(vyy360, vyy361), app(ty_[], bg)) → new_esEs(vyy350, vyy360, bg)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), bcc, bcd, app(app(ty_Either, bda), bdb)) → new_esEs2(vyy352, vyy362, bda, bdb)
new_esEs(:(vyy350, vyy351), :(vyy360, vyy361), app(app(ty_FiniteMap, ba), bb)) → new_esEs0(vyy350, vyy360, ba, bb)
new_esEs3(Just(vyy350), Just(vyy360), app(app(ty_FiniteMap, bah), bba)) → new_esEs0(vyy350, vyy360, bah, bba)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), bcc, app(ty_Maybe, beh), beb) → new_esEs3(vyy351, vyy361, beh)
The TRS R consists of the following rules:
new_foldFM2(Branch(vyy350, vyy351, vyy352, vyy353, vyy354), cd, ce) → new_foldFM0(vyy350, vyy351, new_foldFM2(vyy354, cd, ce), vyy353, cd, ce)
new_foldFM2(EmptyFM, cd, ce) → []
new_foldFM0(vyy350, vyy351, vyy80, EmptyFM, cd, ce) → :(@2(vyy350, vyy351), vyy80)
new_foldFM0(vyy350, vyy351, vyy80, Branch(vyy3530, vyy3531, vyy3532, vyy3533, vyy3534), cd, ce) → new_foldFM0(vyy3530, vyy3531, new_foldFM0(vyy350, vyy351, vyy80, vyy3534, cd, ce), vyy3533, cd, ce)
The set Q consists of the following terms:
new_foldFM2(EmptyFM, x0, x1)
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
We have to consider all minimal (P,Q,R)-chains.
We use the reduction pair processor [15].
The following pairs can be oriented strictly and are deleted.
new_esEs3(Just(vyy350), Just(vyy360), app(app(ty_@2, bbb), bbc)) → new_esEs1(vyy350, vyy360, bbb, bbc)
new_esEs2(Left(vyy350), Left(vyy360), app(app(ty_Either, ge), gf), gb) → new_esEs2(vyy350, vyy360, ge, gf)
new_esEs1(@2(vyy350, vyy351), @2(vyy360, vyy361), cf, app(app(ty_@2, db), dc)) → new_esEs1(vyy351, vyy361, db, dc)
new_esEs1(@2(vyy350, vyy351), @2(vyy360, vyy361), cf, app(app(app(ty_@3, dh), ea), eb)) → new_esEs4(vyy351, vyy361, dh, ea, eb)
new_esEs2(Right(vyy350), Right(vyy360), hd, app(app(ty_Either, baa), bab)) → new_esEs2(vyy350, vyy360, baa, bab)
new_esEs1(@2(vyy350, vyy351), @2(vyy360, vyy361), cf, app(app(ty_Either, dd), de)) → new_esEs2(vyy351, vyy361, dd, de)
new_esEs3(Just(vyy350), Just(vyy360), app(app(app(ty_@3, bbh), bca), bcb)) → new_esEs4(vyy350, vyy360, bbh, bca, bcb)
new_esEs1(@2(vyy350, vyy351), @2(vyy360, vyy361), app(app(ty_FiniteMap, ec), ed), ee) → new_esEs0(vyy350, vyy360, ec, ed)
new_esEs1(@2(vyy350, vyy351), @2(vyy360, vyy361), cf, app(ty_Maybe, dg)) → new_esEs3(vyy351, vyy361, dg)
new_esEs1(@2(vyy350, vyy351), @2(vyy360, vyy361), app(app(ty_Either, eh), fa), ee) → new_esEs2(vyy350, vyy360, eh, fa)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), bcc, app(app(ty_Either, bee), bef), beb) → new_esEs2(vyy351, vyy361, bee, bef)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), app(app(ty_Either, bfh), bga), bcd, beb) → new_esEs2(vyy350, vyy360, bfh, bga)
new_esEs1(@2(vyy350, vyy351), @2(vyy360, vyy361), cf, app(app(ty_FiniteMap, cg), da)) → new_esEs0(vyy351, vyy361, cg, da)
new_esEs1(@2(vyy350, vyy351), @2(vyy360, vyy361), app(ty_Maybe, fc), ee) → new_esEs3(vyy350, vyy360, fc)
new_esEs3(Just(vyy350), Just(vyy360), app(app(ty_Either, bbd), bbe)) → new_esEs2(vyy350, vyy360, bbd, bbe)
new_esEs1(@2(vyy350, vyy351), @2(vyy360, vyy361), app(app(app(ty_@3, fd), ff), fg), ee) → new_esEs4(vyy350, vyy360, fd, ff, fg)
new_esEs1(@2(vyy350, vyy351), @2(vyy360, vyy361), cf, app(ty_[], df)) → new_esEs(vyy351, vyy361, df)
new_esEs1(@2(vyy350, vyy351), @2(vyy360, vyy361), app(ty_[], fb), ee) → new_esEs(vyy350, vyy360, fb)
new_esEs3(Just(vyy350), Just(vyy360), app(ty_[], bbf)) → new_esEs(vyy350, vyy360, bbf)
new_esEs(:(vyy350, vyy351), :(vyy360, vyy361), app(app(ty_Either, be), bf)) → new_esEs2(vyy350, vyy360, be, bf)
new_esEs1(@2(vyy350, vyy351), @2(vyy360, vyy361), app(app(ty_@2, ef), eg), ee) → new_esEs1(vyy350, vyy360, ef, eg)
new_esEs3(Just(vyy350), Just(vyy360), app(ty_Maybe, bbg)) → new_esEs3(vyy350, vyy360, bbg)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), bcc, bcd, app(app(ty_Either, bda), bdb)) → new_esEs2(vyy352, vyy362, bda, bdb)
new_esEs3(Just(vyy350), Just(vyy360), app(app(ty_FiniteMap, bah), bba)) → new_esEs0(vyy350, vyy360, bah, bba)
The remaining pairs can at least be oriented weakly.
new_esEs2(Right(vyy350), Right(vyy360), hd, app(ty_[], bac)) → new_esEs(vyy350, vyy360, bac)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), bcc, app(ty_[], beg), beb) → new_esEs(vyy351, vyy361, beg)
new_esEs2(Left(vyy350), Left(vyy360), app(app(app(ty_@3, ha), hb), hc), gb) → new_esEs4(vyy350, vyy360, ha, hb, hc)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), bcc, app(app(ty_FiniteMap, bdh), bea), beb) → new_esEs0(vyy351, vyy361, bdh, bea)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), bcc, bcd, app(ty_[], bdc)) → new_esEs(vyy352, vyy362, bdc)
new_esEs0(vyy35, vyy36, cd, ce) → new_esEs(new_foldFM2(vyy35, cd, ce), new_foldFM2(vyy36, cd, ce), app(app(ty_@2, cd), ce))
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), app(app(app(ty_@3, bgd), bge), bgf), bcd, beb) → new_esEs4(vyy350, vyy360, bgd, bge, bgf)
new_esEs(:(vyy350, vyy351), :(vyy360, vyy361), app(ty_Maybe, bh)) → new_esEs3(vyy350, vyy360, bh)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), app(ty_[], bgb), bcd, beb) → new_esEs(vyy350, vyy360, bgb)
new_esEs2(Right(vyy350), Right(vyy360), hd, app(ty_Maybe, bad)) → new_esEs3(vyy350, vyy360, bad)
new_esEs2(Left(vyy350), Left(vyy360), app(ty_Maybe, gh), gb) → new_esEs3(vyy350, vyy360, gh)
new_esEs2(Left(vyy350), Left(vyy360), app(app(ty_FiniteMap, fh), ga), gb) → new_esEs0(vyy350, vyy360, fh, ga)
new_esEs2(Left(vyy350), Left(vyy360), app(app(ty_@2, gc), gd), gb) → new_esEs1(vyy350, vyy360, gc, gd)
new_esEs2(Right(vyy350), Right(vyy360), hd, app(app(ty_FiniteMap, he), hf)) → new_esEs0(vyy350, vyy360, he, hf)
new_esEs2(Left(vyy350), Left(vyy360), app(ty_[], gg), gb) → new_esEs(vyy350, vyy360, gg)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), bcc, app(app(app(ty_@3, bfa), bfb), bfc), beb) → new_esEs4(vyy351, vyy361, bfa, bfb, bfc)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), bcc, bcd, app(app(ty_@2, bcg), bch)) → new_esEs1(vyy352, vyy362, bcg, bch)
new_esEs2(Right(vyy350), Right(vyy360), hd, app(app(ty_@2, hg), hh)) → new_esEs1(vyy350, vyy360, hg, hh)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), bcc, bcd, app(ty_Maybe, bdd)) → new_esEs3(vyy352, vyy362, bdd)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), bcc, bcd, app(app(ty_FiniteMap, bce), bcf)) → new_esEs0(vyy352, vyy362, bce, bcf)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), bcc, app(app(ty_@2, bec), bed), beb) → new_esEs1(vyy351, vyy361, bec, bed)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), bcc, bcd, app(app(app(ty_@3, bde), bdf), bdg)) → new_esEs4(vyy352, vyy362, bde, bdf, bdg)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), app(app(ty_@2, bff), bfg), bcd, beb) → new_esEs1(vyy350, vyy360, bff, bfg)
new_esEs(:(vyy350, vyy351), :(vyy360, vyy361), app(app(ty_@2, bc), bd)) → new_esEs1(vyy350, vyy360, bc, bd)
new_esEs2(Right(vyy350), Right(vyy360), hd, app(app(app(ty_@3, bae), baf), bag)) → new_esEs4(vyy350, vyy360, bae, baf, bag)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), app(app(ty_FiniteMap, bfd), bfe), bcd, beb) → new_esEs0(vyy350, vyy360, bfd, bfe)
new_esEs(:(vyy350, vyy351), :(vyy360, vyy361), h) → new_esEs(vyy351, vyy361, h)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), app(ty_Maybe, bgc), bcd, beb) → new_esEs3(vyy350, vyy360, bgc)
new_esEs(:(vyy350, vyy351), :(vyy360, vyy361), app(app(app(ty_@3, ca), cb), cc)) → new_esEs4(vyy350, vyy360, ca, cb, cc)
new_esEs(:(vyy350, vyy351), :(vyy360, vyy361), app(ty_[], bg)) → new_esEs(vyy350, vyy360, bg)
new_esEs(:(vyy350, vyy351), :(vyy360, vyy361), app(app(ty_FiniteMap, ba), bb)) → new_esEs0(vyy350, vyy360, ba, bb)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), bcc, app(ty_Maybe, beh), beb) → new_esEs3(vyy351, vyy361, beh)
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)) = 1 + x3 + x4
POL(new_esEs2(x1, x2, x3, x4)) = x3 + x4
POL(new_esEs3(x1, x2, x3)) = 1 + x3
POL(new_esEs4(x1, x2, x3, x4, x5)) = x3 + x4 + x5
POL(new_foldFM0(x1, x2, x3, x4, x5, x6)) = 0
POL(new_foldFM2(x1, x2, x3)) = 0
POL(ty_@2) = 1
POL(ty_@3) = 0
POL(ty_Either) = 1
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_esEs2(Left(vyy350), Left(vyy360), app(ty_[], gg), gb) → new_esEs(vyy350, vyy360, gg)
new_esEs2(Right(vyy350), Right(vyy360), hd, app(ty_[], bac)) → new_esEs(vyy350, vyy360, bac)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), bcc, app(app(app(ty_@3, bfa), bfb), bfc), beb) → new_esEs4(vyy351, vyy361, bfa, bfb, bfc)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), bcc, app(ty_[], beg), beb) → new_esEs(vyy351, vyy361, beg)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), bcc, app(app(ty_FiniteMap, bdh), bea), beb) → new_esEs0(vyy351, vyy361, bdh, bea)
new_esEs2(Left(vyy350), Left(vyy360), app(app(app(ty_@3, ha), hb), hc), gb) → new_esEs4(vyy350, vyy360, ha, hb, hc)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), bcc, bcd, app(app(ty_@2, bcg), bch)) → new_esEs1(vyy352, vyy362, bcg, bch)
new_esEs2(Right(vyy350), Right(vyy360), hd, app(app(ty_@2, hg), hh)) → new_esEs1(vyy350, vyy360, hg, hh)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), bcc, bcd, app(ty_Maybe, bdd)) → new_esEs3(vyy352, vyy362, bdd)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), bcc, bcd, app(app(ty_FiniteMap, bce), bcf)) → new_esEs0(vyy352, vyy362, bce, bcf)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), bcc, app(app(ty_@2, bec), bed), beb) → new_esEs1(vyy351, vyy361, bec, bed)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), bcc, bcd, app(app(app(ty_@3, bde), bdf), bdg)) → new_esEs4(vyy352, vyy362, bde, bdf, bdg)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), bcc, bcd, app(ty_[], bdc)) → new_esEs(vyy352, vyy362, bdc)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), app(app(ty_@2, bff), bfg), bcd, beb) → new_esEs1(vyy350, vyy360, bff, bfg)
new_esEs(:(vyy350, vyy351), :(vyy360, vyy361), app(app(ty_@2, bc), bd)) → new_esEs1(vyy350, vyy360, bc, bd)
new_esEs2(Right(vyy350), Right(vyy360), hd, app(app(app(ty_@3, bae), baf), bag)) → new_esEs4(vyy350, vyy360, bae, baf, bag)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), app(app(ty_FiniteMap, bfd), bfe), bcd, beb) → new_esEs0(vyy350, vyy360, bfd, bfe)
new_esEs(:(vyy350, vyy351), :(vyy360, vyy361), h) → new_esEs(vyy351, vyy361, h)
new_esEs0(vyy35, vyy36, cd, ce) → new_esEs(new_foldFM2(vyy35, cd, ce), new_foldFM2(vyy36, cd, ce), app(app(ty_@2, cd), ce))
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), app(app(app(ty_@3, bgd), bge), bgf), bcd, beb) → new_esEs4(vyy350, vyy360, bgd, bge, bgf)
new_esEs(:(vyy350, vyy351), :(vyy360, vyy361), app(ty_Maybe, bh)) → new_esEs3(vyy350, vyy360, bh)
new_esEs2(Right(vyy350), Right(vyy360), hd, app(ty_Maybe, bad)) → new_esEs3(vyy350, vyy360, bad)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), app(ty_[], bgb), bcd, beb) → new_esEs(vyy350, vyy360, bgb)
new_esEs2(Left(vyy350), Left(vyy360), app(ty_Maybe, gh), gb) → new_esEs3(vyy350, vyy360, gh)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), app(ty_Maybe, bgc), bcd, beb) → new_esEs3(vyy350, vyy360, bgc)
new_esEs(:(vyy350, vyy351), :(vyy360, vyy361), app(app(app(ty_@3, ca), cb), cc)) → new_esEs4(vyy350, vyy360, ca, cb, cc)
new_esEs2(Left(vyy350), Left(vyy360), app(app(ty_FiniteMap, fh), ga), gb) → new_esEs0(vyy350, vyy360, fh, ga)
new_esEs(:(vyy350, vyy351), :(vyy360, vyy361), app(ty_[], bg)) → new_esEs(vyy350, vyy360, bg)
new_esEs2(Left(vyy350), Left(vyy360), app(app(ty_@2, gc), gd), gb) → new_esEs1(vyy350, vyy360, gc, gd)
new_esEs2(Right(vyy350), Right(vyy360), hd, app(app(ty_FiniteMap, he), hf)) → new_esEs0(vyy350, vyy360, he, hf)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), bcc, app(ty_Maybe, beh), beb) → new_esEs3(vyy351, vyy361, beh)
new_esEs(:(vyy350, vyy351), :(vyy360, vyy361), app(app(ty_FiniteMap, ba), bb)) → new_esEs0(vyy350, vyy360, ba, bb)
The TRS R consists of the following rules:
new_foldFM2(Branch(vyy350, vyy351, vyy352, vyy353, vyy354), cd, ce) → new_foldFM0(vyy350, vyy351, new_foldFM2(vyy354, cd, ce), vyy353, cd, ce)
new_foldFM2(EmptyFM, cd, ce) → []
new_foldFM0(vyy350, vyy351, vyy80, EmptyFM, cd, ce) → :(@2(vyy350, vyy351), vyy80)
new_foldFM0(vyy350, vyy351, vyy80, Branch(vyy3530, vyy3531, vyy3532, vyy3533, vyy3534), cd, ce) → new_foldFM0(vyy3530, vyy3531, new_foldFM0(vyy350, vyy351, vyy80, vyy3534, cd, ce), vyy3533, cd, ce)
The set Q consists of the following terms:
new_foldFM2(EmptyFM, x0, x1)
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph [15,17,22] contains 1 SCC with 18 less nodes.
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ Rewriting
↳ QDP
↳ Rewriting
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QReductionProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), app(app(ty_FiniteMap, bfd), bfe), bcd, beb) → new_esEs0(vyy350, vyy360, bfd, bfe)
new_esEs(:(vyy350, vyy351), :(vyy360, vyy361), h) → new_esEs(vyy351, vyy361, h)
new_esEs0(vyy35, vyy36, cd, ce) → new_esEs(new_foldFM2(vyy35, cd, ce), new_foldFM2(vyy36, cd, ce), app(app(ty_@2, cd), ce))
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), bcc, app(app(app(ty_@3, bfa), bfb), bfc), beb) → new_esEs4(vyy351, vyy361, bfa, bfb, bfc)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), bcc, app(ty_[], beg), beb) → new_esEs(vyy351, vyy361, beg)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), bcc, app(app(ty_FiniteMap, bdh), bea), beb) → new_esEs0(vyy351, vyy361, bdh, bea)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), app(app(app(ty_@3, bgd), bge), bgf), bcd, beb) → new_esEs4(vyy350, vyy360, bgd, bge, bgf)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), app(ty_[], bgb), bcd, beb) → new_esEs(vyy350, vyy360, bgb)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), bcc, bcd, app(app(ty_FiniteMap, bce), bcf)) → new_esEs0(vyy352, vyy362, bce, bcf)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), bcc, bcd, app(app(app(ty_@3, bde), bdf), bdg)) → new_esEs4(vyy352, vyy362, bde, bdf, bdg)
new_esEs(:(vyy350, vyy351), :(vyy360, vyy361), app(app(app(ty_@3, ca), cb), cc)) → new_esEs4(vyy350, vyy360, ca, cb, cc)
new_esEs(:(vyy350, vyy351), :(vyy360, vyy361), app(ty_[], bg)) → new_esEs(vyy350, vyy360, bg)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), bcc, bcd, app(ty_[], bdc)) → new_esEs(vyy352, vyy362, bdc)
new_esEs(:(vyy350, vyy351), :(vyy360, vyy361), app(app(ty_FiniteMap, ba), bb)) → new_esEs0(vyy350, vyy360, ba, bb)
The TRS R consists of the following rules:
new_foldFM2(Branch(vyy350, vyy351, vyy352, vyy353, vyy354), cd, ce) → new_foldFM0(vyy350, vyy351, new_foldFM2(vyy354, cd, ce), vyy353, cd, ce)
new_foldFM2(EmptyFM, cd, ce) → []
new_foldFM0(vyy350, vyy351, vyy80, EmptyFM, cd, ce) → :(@2(vyy350, vyy351), vyy80)
new_foldFM0(vyy350, vyy351, vyy80, Branch(vyy3530, vyy3531, vyy3532, vyy3533, vyy3534), cd, ce) → new_foldFM0(vyy3530, vyy3531, new_foldFM0(vyy350, vyy351, vyy80, vyy3534, cd, ce), vyy3533, cd, ce)
The set Q consists of the following terms:
new_foldFM2(EmptyFM, x0, x1)
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
We have to consider all minimal (P,Q,R)-chains.
We use the reduction pair processor [15].
The following pairs can be oriented strictly and are deleted.
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), app(app(ty_FiniteMap, bfd), bfe), bcd, beb) → new_esEs0(vyy350, vyy360, bfd, bfe)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), bcc, app(app(app(ty_@3, bfa), bfb), bfc), beb) → new_esEs4(vyy351, vyy361, bfa, bfb, bfc)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), bcc, app(ty_[], beg), beb) → new_esEs(vyy351, vyy361, beg)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), bcc, app(app(ty_FiniteMap, bdh), bea), beb) → new_esEs0(vyy351, vyy361, bdh, bea)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), app(app(app(ty_@3, bgd), bge), bgf), bcd, beb) → new_esEs4(vyy350, vyy360, bgd, bge, bgf)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), app(ty_[], bgb), bcd, beb) → new_esEs(vyy350, vyy360, bgb)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), bcc, bcd, app(app(ty_FiniteMap, bce), bcf)) → new_esEs0(vyy352, vyy362, bce, bcf)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), bcc, bcd, app(app(app(ty_@3, bde), bdf), bdg)) → new_esEs4(vyy352, vyy362, bde, bdf, bdg)
new_esEs4(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), bcc, bcd, app(ty_[], bdc)) → new_esEs(vyy352, vyy362, bdc)
The remaining pairs can at least be oriented weakly.
new_esEs(:(vyy350, vyy351), :(vyy360, vyy361), h) → new_esEs(vyy351, vyy361, h)
new_esEs0(vyy35, vyy36, cd, ce) → new_esEs(new_foldFM2(vyy35, cd, ce), new_foldFM2(vyy36, cd, ce), app(app(ty_@2, cd), ce))
new_esEs(:(vyy350, vyy351), :(vyy360, vyy361), app(app(app(ty_@3, ca), cb), cc)) → new_esEs4(vyy350, vyy360, ca, cb, cc)
new_esEs(:(vyy350, vyy351), :(vyy360, vyy361), app(ty_[], bg)) → new_esEs(vyy350, vyy360, bg)
new_esEs(:(vyy350, vyy351), :(vyy360, vyy361), app(app(ty_FiniteMap, ba), bb)) → new_esEs0(vyy350, vyy360, ba, bb)
Used ordering: Polynomial interpretation [25]:
POL(:(x1, x2)) = x1 + x2
POL(@2(x1, x2)) = 0
POL(@3(x1, x2, x3)) = 1 + x1 + x2 + x3
POL(Branch(x1, x2, x3, x4, x5)) = 0
POL(EmptyFM) = 0
POL([]) = 0
POL(app(x1, x2)) = 0
POL(new_esEs(x1, x2, x3)) = x1
POL(new_esEs0(x1, x2, x3, x4)) = x1
POL(new_esEs4(x1, x2, x3, x4, x5)) = x1
POL(new_foldFM0(x1, x2, x3, x4, x5, x6)) = x3
POL(new_foldFM2(x1, x2, x3)) = 0
POL(ty_@2) = 0
POL(ty_@3) = 0
POL(ty_FiniteMap) = 0
POL(ty_[]) = 0
The following usable rules [17] were oriented:
new_foldFM2(EmptyFM, cd, ce) → []
new_foldFM2(Branch(vyy350, vyy351, vyy352, vyy353, vyy354), cd, ce) → new_foldFM0(vyy350, vyy351, new_foldFM2(vyy354, cd, ce), vyy353, cd, ce)
new_foldFM0(vyy350, vyy351, vyy80, Branch(vyy3530, vyy3531, vyy3532, vyy3533, vyy3534), cd, ce) → new_foldFM0(vyy3530, vyy3531, new_foldFM0(vyy350, vyy351, vyy80, vyy3534, cd, ce), vyy3533, cd, ce)
new_foldFM0(vyy350, vyy351, vyy80, EmptyFM, cd, ce) → :(@2(vyy350, vyy351), vyy80)
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ Rewriting
↳ QDP
↳ Rewriting
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QReductionProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_esEs(:(vyy350, vyy351), :(vyy360, vyy361), h) → new_esEs(vyy351, vyy361, h)
new_esEs0(vyy35, vyy36, cd, ce) → new_esEs(new_foldFM2(vyy35, cd, ce), new_foldFM2(vyy36, cd, ce), app(app(ty_@2, cd), ce))
new_esEs(:(vyy350, vyy351), :(vyy360, vyy361), app(app(app(ty_@3, ca), cb), cc)) → new_esEs4(vyy350, vyy360, ca, cb, cc)
new_esEs(:(vyy350, vyy351), :(vyy360, vyy361), app(ty_[], bg)) → new_esEs(vyy350, vyy360, bg)
new_esEs(:(vyy350, vyy351), :(vyy360, vyy361), app(app(ty_FiniteMap, ba), bb)) → new_esEs0(vyy350, vyy360, ba, bb)
The TRS R consists of the following rules:
new_foldFM2(Branch(vyy350, vyy351, vyy352, vyy353, vyy354), cd, ce) → new_foldFM0(vyy350, vyy351, new_foldFM2(vyy354, cd, ce), vyy353, cd, ce)
new_foldFM2(EmptyFM, cd, ce) → []
new_foldFM0(vyy350, vyy351, vyy80, EmptyFM, cd, ce) → :(@2(vyy350, vyy351), vyy80)
new_foldFM0(vyy350, vyy351, vyy80, Branch(vyy3530, vyy3531, vyy3532, vyy3533, vyy3534), cd, ce) → new_foldFM0(vyy3530, vyy3531, new_foldFM0(vyy350, vyy351, vyy80, vyy3534, cd, ce), vyy3533, cd, ce)
The set Q consists of the following terms:
new_foldFM2(EmptyFM, x0, x1)
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph [15,17,22] contains 1 SCC with 1 less node.
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ Rewriting
↳ QDP
↳ Rewriting
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QReductionProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_esEs(:(vyy350, vyy351), :(vyy360, vyy361), h) → new_esEs(vyy351, vyy361, h)
new_esEs0(vyy35, vyy36, cd, ce) → new_esEs(new_foldFM2(vyy35, cd, ce), new_foldFM2(vyy36, cd, ce), app(app(ty_@2, cd), ce))
new_esEs(:(vyy350, vyy351), :(vyy360, vyy361), app(ty_[], bg)) → new_esEs(vyy350, vyy360, bg)
new_esEs(:(vyy350, vyy351), :(vyy360, vyy361), app(app(ty_FiniteMap, ba), bb)) → new_esEs0(vyy350, vyy360, ba, bb)
The TRS R consists of the following rules:
new_foldFM2(Branch(vyy350, vyy351, vyy352, vyy353, vyy354), cd, ce) → new_foldFM0(vyy350, vyy351, new_foldFM2(vyy354, cd, ce), vyy353, cd, ce)
new_foldFM2(EmptyFM, cd, ce) → []
new_foldFM0(vyy350, vyy351, vyy80, EmptyFM, cd, ce) → :(@2(vyy350, vyy351), vyy80)
new_foldFM0(vyy350, vyy351, vyy80, Branch(vyy3530, vyy3531, vyy3532, vyy3533, vyy3534), cd, ce) → new_foldFM0(vyy3530, vyy3531, new_foldFM0(vyy350, vyy351, vyy80, vyy3534, cd, ce), vyy3533, cd, ce)
The set Q consists of the following terms:
new_foldFM2(EmptyFM, x0, x1)
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
We have to consider all minimal (P,Q,R)-chains.
We use the reduction pair processor [15].
The following pairs can be oriented strictly and are deleted.
new_esEs(:(vyy350, vyy351), :(vyy360, vyy361), app(app(ty_FiniteMap, ba), bb)) → new_esEs0(vyy350, vyy360, ba, bb)
The remaining pairs can at least be oriented weakly.
new_esEs(:(vyy350, vyy351), :(vyy360, vyy361), h) → new_esEs(vyy351, vyy361, h)
new_esEs0(vyy35, vyy36, cd, ce) → new_esEs(new_foldFM2(vyy35, cd, ce), new_foldFM2(vyy36, cd, ce), app(app(ty_@2, cd), ce))
new_esEs(:(vyy350, vyy351), :(vyy360, vyy361), app(ty_[], bg)) → new_esEs(vyy350, vyy360, bg)
Used ordering: Polynomial interpretation [25]:
POL(:(x1, x2)) = 0
POL(@2(x1, x2)) = 0
POL(Branch(x1, x2, x3, x4, x5)) = 0
POL(EmptyFM) = 0
POL([]) = 0
POL(app(x1, x2)) = x1 + x2
POL(new_esEs(x1, x2, x3)) = x3
POL(new_esEs0(x1, x2, x3, x4)) = x3 + x4
POL(new_foldFM0(x1, x2, x3, x4, x5, x6)) = 0
POL(new_foldFM2(x1, x2, x3)) = 0
POL(ty_@2) = 0
POL(ty_FiniteMap) = 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
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_esEs(:(vyy350, vyy351), :(vyy360, vyy361), h) → new_esEs(vyy351, vyy361, h)
new_esEs0(vyy35, vyy36, cd, ce) → new_esEs(new_foldFM2(vyy35, cd, ce), new_foldFM2(vyy36, cd, ce), app(app(ty_@2, cd), ce))
new_esEs(:(vyy350, vyy351), :(vyy360, vyy361), app(ty_[], bg)) → new_esEs(vyy350, vyy360, bg)
The TRS R consists of the following rules:
new_foldFM2(Branch(vyy350, vyy351, vyy352, vyy353, vyy354), cd, ce) → new_foldFM0(vyy350, vyy351, new_foldFM2(vyy354, cd, ce), vyy353, cd, ce)
new_foldFM2(EmptyFM, cd, ce) → []
new_foldFM0(vyy350, vyy351, vyy80, EmptyFM, cd, ce) → :(@2(vyy350, vyy351), vyy80)
new_foldFM0(vyy350, vyy351, vyy80, Branch(vyy3530, vyy3531, vyy3532, vyy3533, vyy3534), cd, ce) → new_foldFM0(vyy3530, vyy3531, new_foldFM0(vyy350, vyy351, vyy80, vyy3534, cd, ce), vyy3533, cd, ce)
The set Q consists of the following terms:
new_foldFM2(EmptyFM, x0, x1)
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph [15,17,22] contains 1 SCC with 1 less node.
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ Rewriting
↳ QDP
↳ Rewriting
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QReductionProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_esEs(:(vyy350, vyy351), :(vyy360, vyy361), h) → new_esEs(vyy351, vyy361, h)
new_esEs(:(vyy350, vyy351), :(vyy360, vyy361), app(ty_[], bg)) → new_esEs(vyy350, vyy360, bg)
The TRS R consists of the following rules:
new_foldFM2(Branch(vyy350, vyy351, vyy352, vyy353, vyy354), cd, ce) → new_foldFM0(vyy350, vyy351, new_foldFM2(vyy354, cd, ce), vyy353, cd, ce)
new_foldFM2(EmptyFM, cd, ce) → []
new_foldFM0(vyy350, vyy351, vyy80, EmptyFM, cd, ce) → :(@2(vyy350, vyy351), vyy80)
new_foldFM0(vyy350, vyy351, vyy80, Branch(vyy3530, vyy3531, vyy3532, vyy3533, vyy3534), cd, ce) → new_foldFM0(vyy3530, vyy3531, new_foldFM0(vyy350, vyy351, vyy80, vyy3534, cd, ce), vyy3533, cd, ce)
The set Q consists of the following terms:
new_foldFM2(EmptyFM, x0, x1)
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
We have to consider all minimal (P,Q,R)-chains.
As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [15] we can delete all non-usable rules [17] from R.
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ Rewriting
↳ QDP
↳ Rewriting
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QReductionProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QReductionProof
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_esEs(:(vyy350, vyy351), :(vyy360, vyy361), h) → new_esEs(vyy351, vyy361, h)
new_esEs(:(vyy350, vyy351), :(vyy360, vyy361), app(ty_[], bg)) → new_esEs(vyy350, vyy360, bg)
R is empty.
The set Q consists of the following terms:
new_foldFM2(EmptyFM, x0, x1)
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
We have to consider all minimal (P,Q,R)-chains.
We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.
new_foldFM2(EmptyFM, x0, x1)
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ Rewriting
↳ QDP
↳ Rewriting
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QReductionProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QReductionProof
↳ QDP
↳ QDPSizeChangeProof
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_esEs(:(vyy350, vyy351), :(vyy360, vyy361), h) → new_esEs(vyy351, vyy361, h)
new_esEs(:(vyy350, vyy351), :(vyy360, vyy361), app(ty_[], bg)) → new_esEs(vyy350, vyy360, bg)
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(:(vyy350, vyy351), :(vyy360, vyy361), h) → new_esEs(vyy351, vyy361, h)
The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3
- new_esEs(:(vyy350, vyy351), :(vyy360, vyy361), app(ty_[], bg)) → new_esEs(vyy350, vyy360, bg)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDPSizeChangeProof
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_ltEs2(@2(vyy600, vyy601), @2(vyy50, vyy51), app(app(ty_@2, bcf), bcg), bca) → new_lt2(vyy600, vyy50, bcf, bcg)
new_ltEs2(@2(vyy600, vyy601), @2(vyy50, vyy51), app(ty_[], bch), bca) → new_lt3(vyy600, vyy50, bch)
new_ltEs2(@2(vyy600, vyy601), @2(vyy50, vyy51), bae, app(app(ty_Either, baf), bag)) → new_ltEs(vyy601, vyy51, baf, bag)
new_primCompAux(vyy600, vyy50, vyy62, app(app(ty_@2, bdh), bea)) → new_compare5(vyy600, vyy50, bdh, bea)
new_compare2(vyy600, vyy50, False, gc, gd) → new_ltEs(vyy600, vyy50, gc, gd)
new_ltEs(Left(vyy600), Left(vyy50), app(app(ty_Either, h), ba), bb) → new_ltEs(vyy600, vyy50, h, ba)
new_ltEs(Right(vyy600), Right(vyy50), cb, app(app(ty_Either, cc), cd)) → new_ltEs(vyy600, vyy50, cc, cd)
new_compare3(vyy600, vyy50, ge, gf, gg) → new_compare20(vyy600, vyy50, new_esEs6(vyy600, vyy50, ge, gf, gg), ge, gf, gg)
new_ltEs0(@3(vyy600, vyy601, vyy602), @3(vyy50, vyy51, vyy52), de, df, app(ty_[], eg)) → new_ltEs3(vyy602, vyy52, eg)
new_ltEs1(Just(vyy600), Just(vyy50), app(ty_Maybe, baa)) → new_ltEs1(vyy600, vyy50, baa)
new_compare1(vyy600, vyy50, gc, gd) → new_compare2(vyy600, vyy50, new_esEs5(vyy600, vyy50, gc, gd), gc, gd)
new_ltEs0(@3(vyy600, vyy601, vyy602), @3(vyy50, vyy51, vyy52), app(app(app(ty_@3, ge), gf), gg), df, fb) → new_compare20(vyy600, vyy50, new_esEs6(vyy600, vyy50, ge, gf, gg), ge, gf, gg)
new_primCompAux(vyy600, vyy50, vyy62, app(ty_[], beb)) → new_compare(vyy600, vyy50, beb)
new_ltEs3(:(vyy600, vyy601), :(vyy50, vyy51), bda) → new_compare(vyy601, vyy51, bda)
new_ltEs1(Just(vyy600), Just(vyy50), app(app(app(ty_@3, hf), hg), hh)) → new_ltEs0(vyy600, vyy50, hf, hg, hh)
new_ltEs2(@2(vyy600, vyy601), @2(vyy50, vyy51), bae, app(ty_[], bbf)) → new_ltEs3(vyy601, vyy51, bbf)
new_ltEs0(@3(vyy600, vyy601, vyy602), @3(vyy50, vyy51, vyy52), app(app(ty_@2, ha), hb), df, fb) → new_compare22(vyy600, vyy50, new_esEs8(vyy600, vyy50, ha, hb), ha, hb)
new_ltEs0(@3(vyy600, vyy601, vyy602), @3(vyy50, vyy51, vyy52), app(ty_[], hc), df, fb) → new_compare(vyy600, vyy50, hc)
new_ltEs0(@3(vyy600, vyy601, vyy602), @3(vyy50, vyy51, vyy52), de, df, app(ty_Maybe, ed)) → new_ltEs1(vyy602, vyy52, ed)
new_ltEs0(@3(vyy600, vyy601, vyy602), @3(vyy50, vyy51, vyy52), de, app(app(app(ty_@3, fc), fd), ff), fb) → new_lt0(vyy601, vyy51, fc, fd, ff)
new_ltEs2(@2(vyy600, vyy601), @2(vyy50, vyy51), app(app(ty_Either, bbg), bbh), bca) → new_lt(vyy600, vyy50, bbg, bbh)
new_ltEs(Left(vyy600), Left(vyy50), app(ty_[], ca), bb) → new_ltEs3(vyy600, vyy50, ca)
new_primCompAux(vyy600, vyy50, vyy62, app(app(ty_Either, bdb), bdc)) → new_compare1(vyy600, vyy50, bdb, bdc)
new_ltEs0(@3(vyy600, vyy601, vyy602), @3(vyy50, vyy51, vyy52), de, app(app(ty_@2, fh), ga), fb) → new_lt2(vyy601, vyy51, fh, ga)
new_ltEs0(@3(vyy600, vyy601, vyy602), @3(vyy50, vyy51, vyy52), app(app(ty_Either, gc), gd), df, fb) → new_compare2(vyy600, vyy50, new_esEs5(vyy600, vyy50, gc, gd), gc, gd)
new_ltEs1(Just(vyy600), Just(vyy50), app(app(ty_Either, hd), he)) → new_ltEs(vyy600, vyy50, hd, he)
new_ltEs2(@2(vyy600, vyy601), @2(vyy50, vyy51), app(ty_Maybe, bce), bca) → new_lt1(vyy600, vyy50, bce)
new_ltEs(Right(vyy600), Right(vyy50), cb, app(ty_[], dd)) → new_ltEs3(vyy600, vyy50, dd)
new_ltEs1(Just(vyy600), Just(vyy50), app(app(ty_@2, bab), bac)) → new_ltEs2(vyy600, vyy50, bab, bac)
new_ltEs0(@3(vyy600, vyy601, vyy602), @3(vyy50, vyy51, vyy52), de, app(app(ty_Either, eh), fa), fb) → new_lt(vyy601, vyy51, eh, fa)
new_ltEs0(@3(vyy600, vyy601, vyy602), @3(vyy50, vyy51, vyy52), de, df, app(app(app(ty_@3, ea), eb), ec)) → new_ltEs0(vyy602, vyy52, ea, eb, ec)
new_ltEs2(@2(vyy600, vyy601), @2(vyy50, vyy51), bae, app(ty_Maybe, bbc)) → new_ltEs1(vyy601, vyy51, bbc)
new_lt2(vyy600, vyy50, ha, hb) → new_compare22(vyy600, vyy50, new_esEs8(vyy600, vyy50, ha, hb), ha, hb)
new_lt1(vyy600, vyy50, gh) → new_compare21(vyy600, vyy50, new_esEs7(vyy600, vyy50, gh), gh)
new_ltEs2(@2(vyy600, vyy601), @2(vyy50, vyy51), bae, app(app(ty_@2, bbd), bbe)) → new_ltEs2(vyy601, vyy51, bbd, bbe)
new_ltEs2(@2(vyy600, vyy601), @2(vyy50, vyy51), app(app(app(ty_@3, bcb), bcc), bcd), bca) → new_lt0(vyy600, vyy50, bcb, bcc, bcd)
new_ltEs0(@3(vyy600, vyy601, vyy602), @3(vyy50, vyy51, vyy52), de, df, app(app(ty_@2, ee), ef)) → new_ltEs2(vyy602, vyy52, ee, ef)
new_ltEs0(@3(vyy600, vyy601, vyy602), @3(vyy50, vyy51, vyy52), app(ty_Maybe, gh), df, fb) → new_compare21(vyy600, vyy50, new_esEs7(vyy600, vyy50, gh), gh)
new_compare(:(vyy600, vyy601), :(vyy50, vyy51), bda) → new_compare(vyy601, vyy51, bda)
new_lt3(vyy600, vyy50, hc) → new_compare(vyy600, vyy50, hc)
new_ltEs(Left(vyy600), Left(vyy50), app(ty_Maybe, bf), bb) → new_ltEs1(vyy600, vyy50, bf)
new_primCompAux(vyy600, vyy50, vyy62, app(app(app(ty_@3, bdd), bde), bdf)) → new_compare3(vyy600, vyy50, bdd, bde, bdf)
new_ltEs3(:(vyy600, vyy601), :(vyy50, vyy51), bda) → new_primCompAux(vyy600, vyy50, new_compare0(vyy601, vyy51, bda), bda)
new_ltEs1(Just(vyy600), Just(vyy50), app(ty_[], bad)) → new_ltEs3(vyy600, vyy50, bad)
new_compare(:(vyy600, vyy601), :(vyy50, vyy51), bda) → new_primCompAux(vyy600, vyy50, new_compare0(vyy601, vyy51, bda), bda)
new_ltEs0(@3(vyy600, vyy601, vyy602), @3(vyy50, vyy51, vyy52), de, df, app(app(ty_Either, dg), dh)) → new_ltEs(vyy602, vyy52, dg, dh)
new_compare4(vyy600, vyy50, gh) → new_compare21(vyy600, vyy50, new_esEs7(vyy600, vyy50, gh), gh)
new_ltEs(Right(vyy600), Right(vyy50), cb, app(app(ty_@2, db), dc)) → new_ltEs2(vyy600, vyy50, db, dc)
new_ltEs0(@3(vyy600, vyy601, vyy602), @3(vyy50, vyy51, vyy52), de, app(ty_[], gb), fb) → new_lt3(vyy601, vyy51, gb)
new_primCompAux(vyy600, vyy50, vyy62, app(ty_Maybe, bdg)) → new_compare4(vyy600, vyy50, bdg)
new_ltEs2(@2(vyy600, vyy601), @2(vyy50, vyy51), bae, app(app(app(ty_@3, bah), bba), bbb)) → new_ltEs0(vyy601, vyy51, bah, bba, bbb)
new_ltEs0(@3(vyy600, vyy601, vyy602), @3(vyy50, vyy51, vyy52), de, app(ty_Maybe, fg), fb) → new_lt1(vyy601, vyy51, fg)
new_compare5(vyy600, vyy50, ha, hb) → new_compare22(vyy600, vyy50, new_esEs8(vyy600, vyy50, ha, hb), ha, hb)
new_ltEs(Left(vyy600), Left(vyy50), app(app(app(ty_@3, bc), bd), be), bb) → new_ltEs0(vyy600, vyy50, bc, bd, be)
new_compare22(vyy600, vyy50, False, ha, hb) → new_ltEs2(vyy600, vyy50, ha, hb)
new_lt0(vyy600, vyy50, ge, gf, gg) → new_compare20(vyy600, vyy50, new_esEs6(vyy600, vyy50, ge, gf, gg), ge, gf, gg)
new_compare20(vyy600, vyy50, False, ge, gf, gg) → new_ltEs0(vyy600, vyy50, ge, gf, gg)
new_ltEs(Left(vyy600), Left(vyy50), app(app(ty_@2, bg), bh), bb) → new_ltEs2(vyy600, vyy50, bg, bh)
new_ltEs(Right(vyy600), Right(vyy50), cb, app(app(app(ty_@3, ce), cf), cg)) → new_ltEs0(vyy600, vyy50, ce, cf, cg)
new_lt(vyy600, vyy50, gc, gd) → new_compare2(vyy600, vyy50, new_esEs5(vyy600, vyy50, gc, gd), gc, gd)
new_ltEs(Right(vyy600), Right(vyy50), cb, app(ty_Maybe, da)) → new_ltEs1(vyy600, vyy50, da)
new_compare21(vyy600, vyy50, False, gh) → new_ltEs1(vyy600, vyy50, gh)
The TRS R consists of the following rules:
new_ltEs18(vyy601, vyy51, app(ty_Ratio, bhh)) → new_ltEs15(vyy601, vyy51, bhh)
new_esEs7(Just(vyy350), Just(vyy360), app(ty_Maybe, bfd)) → new_esEs7(vyy350, vyy360, bfd)
new_esEs23(vyy350, vyy360, ty_Integer) → new_esEs13(vyy350, vyy360)
new_compare29(vyy600, vyy50, ha, hb) → new_compare25(vyy600, vyy50, new_esEs8(vyy600, vyy50, ha, hb), ha, hb)
new_esEs25(vyy351, vyy361, ty_Int) → new_esEs19(vyy351, vyy361)
new_esEs24(vyy352, vyy362, app(app(ty_Either, cbe), cbf)) → new_esEs5(vyy352, vyy362, cbe, cbf)
new_esEs24(vyy352, vyy362, ty_Float) → new_esEs12(vyy352, vyy362)
new_ltEs18(vyy601, vyy51, ty_Float) → new_ltEs8(vyy601, vyy51)
new_ltEs4(Right(vyy600), Right(vyy50), cb, app(ty_[], dd)) → new_ltEs11(vyy600, vyy50, dd)
new_ltEs17(LT, LT) → True
new_esEs24(vyy352, vyy362, ty_Char) → new_esEs15(vyy352, vyy362)
new_compare8(Integer(vyy600), Integer(vyy50)) → new_primCmpInt(vyy600, vyy50)
new_ltEs4(Right(vyy600), Right(vyy50), cb, app(ty_Maybe, da)) → new_ltEs5(vyy600, vyy50, da)
new_lt5(vyy600, vyy50, app(app(ty_@2, bcf), bcg)) → new_lt11(vyy600, vyy50, bcf, bcg)
new_lt5(vyy600, vyy50, app(app(app(ty_@3, bcb), bcc), bcd)) → new_lt7(vyy600, vyy50, bcb, bcc, bcd)
new_ltEs18(vyy601, vyy51, ty_Integer) → new_ltEs14(vyy601, vyy51)
new_ltEs4(Left(vyy600), Left(vyy50), app(ty_[], ca), bb) → new_ltEs11(vyy600, vyy50, ca)
new_esEs29(vyy35, vyy36, ty_Integer) → new_esEs13(vyy35, vyy36)
new_lt20(vyy600, vyy50, app(ty_Ratio, daf)) → new_lt16(vyy600, vyy50, daf)
new_esEs27(vyy351, vyy361, app(ty_Maybe, cgf)) → new_esEs7(vyy351, vyy361, cgf)
new_ltEs4(Left(vyy600), Left(vyy50), app(app(app(ty_@3, bc), bd), be), bb) → new_ltEs6(vyy600, vyy50, bc, bd, be)
new_compare210(vyy600, vyy50, False, ge, gf, gg) → new_compare13(vyy600, vyy50, new_ltEs6(vyy600, vyy50, ge, gf, gg), ge, gf, gg)
new_esEs5(Right(vyy350), Right(vyy360), dcf, ty_Char) → new_esEs15(vyy350, vyy360)
new_compare31(vyy600, vyy50, ty_@0) → new_compare6(vyy600, vyy50)
new_ltEs5(Just(vyy600), Just(vyy50), ty_Double) → new_ltEs9(vyy600, vyy50)
new_primMulNat0(Zero, Zero) → Zero
new_ltEs5(Just(vyy600), Just(vyy50), ty_Ordering) → new_ltEs17(vyy600, vyy50)
new_esEs24(vyy352, vyy362, ty_Integer) → new_esEs13(vyy352, vyy362)
new_lt5(vyy600, vyy50, ty_Ordering) → new_lt18(vyy600, vyy50)
new_compare13(vyy600, vyy50, False, ge, gf, gg) → GT
new_esEs5(Right(vyy350), Right(vyy360), dcf, ty_@0) → new_esEs20(vyy350, vyy360)
new_sr(Integer(vyy500), Integer(vyy6010)) → Integer(new_primMulInt(vyy500, vyy6010))
new_esEs25(vyy351, vyy361, app(app(ty_FiniteMap, ccd), cce)) → new_esEs11(vyy351, vyy361, ccd, cce)
new_ltEs19(vyy602, vyy52, ty_Double) → new_ltEs9(vyy602, vyy52)
new_ltEs5(Just(vyy600), Just(vyy50), app(app(ty_@2, bab), bac)) → new_ltEs10(vyy600, vyy50, bab, bac)
new_esEs24(vyy352, vyy362, app(app(ty_FiniteMap, cah), cba)) → new_esEs11(vyy352, vyy362, cah, cba)
new_lt19(vyy601, vyy51, app(ty_Maybe, fg)) → new_lt9(vyy601, vyy51, fg)
new_ltEs19(vyy602, vyy52, ty_Integer) → new_ltEs14(vyy602, vyy52)
new_ltEs4(Right(vyy600), Right(vyy50), cb, app(app(app(ty_@3, ce), cf), cg)) → new_ltEs6(vyy600, vyy50, ce, cf, cg)
new_esEs9(LT) → True
new_esEs29(vyy35, vyy36, ty_@0) → new_esEs20(vyy35, vyy36)
new_compare24(vyy600, vyy50, False) → new_compare10(vyy600, vyy50, new_ltEs13(vyy600, vyy50))
new_compare31(vyy600, vyy50, app(app(app(ty_@3, bdd), bde), bdf)) → new_compare18(vyy600, vyy50, bdd, bde, bdf)
new_esEs21(vyy350, vyy360, ty_Integer) → new_esEs13(vyy350, vyy360)
new_esEs26(vyy350, vyy360, ty_Char) → new_esEs15(vyy350, vyy360)
new_lt20(vyy600, vyy50, app(app(ty_@2, ha), hb)) → new_lt11(vyy600, vyy50, ha, hb)
new_ltEs4(Right(vyy600), Right(vyy50), cb, ty_Integer) → new_ltEs14(vyy600, vyy50)
new_lt12(vyy600, vyy50, hc) → new_esEs9(new_compare0(vyy600, vyy50, hc))
new_not(GT) → False
new_esEs26(vyy350, vyy360, ty_Ordering) → new_esEs10(vyy350, vyy360)
new_esEs29(vyy35, vyy36, app(ty_Maybe, bec)) → new_esEs7(vyy35, vyy36, bec)
new_esEs27(vyy351, vyy361, app(app(ty_@2, cfh), cga)) → new_esEs8(vyy351, vyy361, cfh, cga)
new_ltEs4(Left(vyy600), Left(vyy50), app(app(ty_@2, bg), bh), bb) → new_ltEs10(vyy600, vyy50, bg, bh)
new_esEs27(vyy351, vyy361, ty_Char) → new_esEs15(vyy351, vyy361)
new_lt5(vyy600, vyy50, ty_Integer) → new_lt15(vyy600, vyy50)
new_ltEs19(vyy602, vyy52, ty_@0) → new_ltEs7(vyy602, vyy52)
new_ltEs4(Left(vyy600), Left(vyy50), ty_Float, bb) → new_ltEs8(vyy600, vyy50)
new_esEs21(vyy350, vyy360, ty_Double) → new_esEs18(vyy350, vyy360)
new_ltEs5(Just(vyy600), Just(vyy50), ty_@0) → new_ltEs7(vyy600, vyy50)
new_ltEs13(True, False) → False
new_esEs27(vyy351, vyy361, ty_Integer) → new_esEs13(vyy351, vyy361)
new_ltEs4(Left(vyy600), Left(vyy50), ty_Int, bb) → new_ltEs16(vyy600, vyy50)
new_ltEs4(Left(vyy600), Left(vyy50), ty_Ordering, bb) → new_ltEs17(vyy600, vyy50)
new_ltEs5(Just(vyy600), Just(vyy50), app(ty_Ratio, bga)) → new_ltEs15(vyy600, vyy50, bga)
new_ltEs4(Left(vyy600), Left(vyy50), ty_Char, bb) → new_ltEs12(vyy600, vyy50)
new_pePe(False, vyy35, vyy36, vyy52, dec) → new_asAs(new_esEs29(vyy35, vyy36, dec), vyy52)
new_compare31(vyy600, vyy50, ty_Char) → new_compare30(vyy600, vyy50)
new_foldFM0(vyy350, vyy351, vyy80, EmptyFM, cab, cac) → :(@2(vyy350, vyy351), vyy80)
new_ltEs17(EQ, LT) → False
new_esEs21(vyy350, vyy360, app(app(ty_@2, bgf), bgg)) → new_esEs8(vyy350, vyy360, bgf, bgg)
new_esEs5(Right(vyy350), Right(vyy360), dcf, app(app(app(ty_@3, ddh), dea), deb)) → new_esEs6(vyy350, vyy360, ddh, dea, deb)
new_lt20(vyy600, vyy50, ty_Bool) → new_lt14(vyy600, vyy50)
new_ltEs19(vyy602, vyy52, app(app(ty_Either, dg), dh)) → new_ltEs4(vyy602, vyy52, dg, dh)
new_ltEs4(Right(vyy600), Right(vyy50), cb, ty_Char) → new_ltEs12(vyy600, vyy50)
new_esEs26(vyy350, vyy360, app(app(ty_@2, ceb), cec)) → new_esEs8(vyy350, vyy360, ceb, cec)
new_esEs20(@0, @0) → True
new_compare6(@0, @0) → EQ
new_lt19(vyy601, vyy51, ty_Double) → new_lt10(vyy601, vyy51)
new_esEs25(vyy351, vyy361, ty_Bool) → new_esEs14(vyy351, vyy361)
new_ltEs5(Just(vyy600), Just(vyy50), app(app(app(ty_@3, hf), hg), hh)) → new_ltEs6(vyy600, vyy50, hf, hg, hh)
new_lt19(vyy601, vyy51, app(ty_Ratio, dee)) → new_lt16(vyy601, vyy51, dee)
new_ltEs11(vyy60, vyy5, bda) → new_not(new_compare0(vyy60, vyy5, bda))
new_ltEs19(vyy602, vyy52, app(ty_[], eg)) → new_ltEs11(vyy602, vyy52, eg)
new_compare31(vyy600, vyy50, app(app(ty_@2, bdh), bea)) → new_compare29(vyy600, vyy50, bdh, bea)
new_esEs24(vyy352, vyy362, app(ty_Maybe, cbh)) → new_esEs7(vyy352, vyy362, cbh)
new_esEs6(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), cae, caf, cag) → new_asAs(new_esEs26(vyy350, vyy360, cae), new_asAs(new_esEs25(vyy351, vyy361, caf), new_esEs24(vyy352, vyy362, cag)))
new_esEs28(vyy350, vyy360, ty_@0) → new_esEs20(vyy350, vyy360)
new_ltEs5(Just(vyy600), Just(vyy50), ty_Bool) → new_ltEs13(vyy600, vyy50)
new_compare9(vyy60, vyy5) → new_primCmpInt(vyy60, vyy5)
new_ltEs4(Right(vyy600), Right(vyy50), cb, app(app(ty_Either, cc), cd)) → new_ltEs4(vyy600, vyy50, cc, cd)
new_esEs27(vyy351, vyy361, app(ty_[], cge)) → new_esEs17(vyy351, vyy361, cge)
new_ltEs18(vyy601, vyy51, ty_Int) → new_ltEs16(vyy601, vyy51)
new_lt5(vyy600, vyy50, app(app(ty_Either, bbg), bbh)) → new_lt6(vyy600, vyy50, bbg, bbh)
new_lt5(vyy600, vyy50, ty_Char) → new_lt13(vyy600, vyy50)
new_esEs28(vyy350, vyy360, app(ty_Ratio, chf)) → new_esEs16(vyy350, vyy360, chf)
new_compare111(vyy600, vyy50, False) → GT
new_compare111(vyy600, vyy50, True) → LT
new_ltEs4(Left(vyy600), Right(vyy50), cb, bb) → True
new_lt19(vyy601, vyy51, app(ty_[], gb)) → new_lt12(vyy601, vyy51, gb)
new_ltEs6(@3(vyy600, vyy601, vyy602), @3(vyy50, vyy51, vyy52), de, df, fb) → new_pePe(new_lt20(vyy600, vyy50, de), vyy600, vyy50, new_pePe(new_lt19(vyy601, vyy51, df), vyy601, vyy51, new_ltEs19(vyy602, vyy52, fb), df), de)
new_esEs27(vyy351, vyy361, ty_Int) → new_esEs19(vyy351, vyy361)
new_esEs21(vyy350, vyy360, ty_Bool) → new_esEs14(vyy350, vyy360)
new_primCmpNat0(Zero, Succ(vyy500)) → LT
new_ltEs19(vyy602, vyy52, app(ty_Ratio, ded)) → new_ltEs15(vyy602, vyy52, ded)
new_lt5(vyy600, vyy50, ty_Float) → new_lt8(vyy600, vyy50)
new_esEs11(vyy35, vyy36, cab, cac) → new_asAs(new_esEs19(new_sizeFM(vyy35, cab, cac), new_sizeFM(vyy36, cab, cac)), new_esEs17(new_fmToList(vyy35, cab, cac), new_fmToList(vyy36, cab, cac), app(app(ty_@2, cab), cac)))
new_compare31(vyy600, vyy50, app(app(ty_Either, bdb), bdc)) → new_compare17(vyy600, vyy50, bdb, bdc)
new_esEs25(vyy351, vyy361, app(app(ty_Either, cda), cdb)) → new_esEs5(vyy351, vyy361, cda, cdb)
new_esEs8(@2(vyy350, vyy351), @2(vyy360, vyy361), cfd, cfe) → new_asAs(new_esEs28(vyy350, vyy360, cfd), new_esEs27(vyy351, vyy361, cfe))
new_ltEs13(False, True) → True
new_ltEs18(vyy601, vyy51, app(ty_Maybe, bbc)) → new_ltEs5(vyy601, vyy51, bbc)
new_esEs10(LT, LT) → True
new_esEs10(EQ, GT) → False
new_esEs10(GT, EQ) → False
new_compare15(Float(vyy600, vyy601), Float(vyy50, vyy51)) → new_compare9(new_sr0(vyy600, vyy50), new_sr0(vyy601, vyy51))
new_esEs5(Right(vyy350), Right(vyy360), dcf, app(app(ty_@2, dda), ddb)) → new_esEs8(vyy350, vyy360, dda, ddb)
new_lt19(vyy601, vyy51, app(app(ty_@2, fh), ga)) → new_lt11(vyy601, vyy51, fh, ga)
new_compare0([], [], bda) → EQ
new_primEqNat0(Zero, Zero) → True
new_compare16(vyy600, vyy50) → new_compare24(vyy600, vyy50, new_esEs14(vyy600, vyy50))
new_ltEs19(vyy602, vyy52, ty_Float) → new_ltEs8(vyy602, vyy52)
new_ltEs4(Right(vyy600), Right(vyy50), cb, ty_Double) → new_ltEs9(vyy600, vyy50)
new_ltEs7(vyy60, vyy5) → new_not(new_compare6(vyy60, vyy5))
new_lt5(vyy600, vyy50, app(ty_[], bch)) → new_lt12(vyy600, vyy50, bch)
new_ltEs17(GT, LT) → False
new_esEs15(Char(vyy350), Char(vyy360)) → new_primEqNat0(vyy350, vyy360)
new_esEs21(vyy350, vyy360, app(app(ty_FiniteMap, bgd), bge)) → new_esEs11(vyy350, vyy360, bgd, bge)
new_compare12(vyy600, vyy50, False, ha, hb) → GT
new_esEs12(Float(vyy350, vyy351), Float(vyy360, vyy361)) → new_esEs19(new_sr0(vyy350, vyy360), new_sr0(vyy351, vyy361))
new_esEs7(Just(vyy350), Just(vyy360), ty_Int) → new_esEs19(vyy350, vyy360)
new_esEs27(vyy351, vyy361, ty_@0) → new_esEs20(vyy351, vyy361)
new_primPlusNat0(Succ(vyy810), vyy5100) → Succ(Succ(new_primPlusNat1(vyy810, vyy5100)))
new_lt19(vyy601, vyy51, ty_@0) → new_lt4(vyy601, vyy51)
new_esEs26(vyy350, vyy360, app(app(app(ty_@3, cfa), cfb), cfc)) → new_esEs6(vyy350, vyy360, cfa, cfb, cfc)
new_lt5(vyy600, vyy50, ty_@0) → new_lt4(vyy600, vyy50)
new_esEs13(Integer(vyy350), Integer(vyy360)) → new_primEqInt(vyy350, vyy360)
new_ltEs4(Left(vyy600), Left(vyy50), app(ty_Maybe, bf), bb) → new_ltEs5(vyy600, vyy50, bf)
new_lt5(vyy600, vyy50, app(ty_Ratio, caa)) → new_lt16(vyy600, vyy50, caa)
new_esEs10(EQ, EQ) → True
new_primEqInt(Neg(Succ(vyy3500)), Neg(Succ(vyy3600))) → new_primEqNat0(vyy3500, vyy3600)
new_ltEs19(vyy602, vyy52, app(app(ty_@2, ee), ef)) → new_ltEs10(vyy602, vyy52, ee, ef)
new_lt19(vyy601, vyy51, ty_Char) → new_lt13(vyy601, vyy51)
new_esEs5(Right(vyy350), Right(vyy360), dcf, app(app(ty_FiniteMap, dcg), dch)) → new_esEs11(vyy350, vyy360, dcg, dch)
new_ltEs4(Right(vyy600), Right(vyy50), cb, ty_Float) → new_ltEs8(vyy600, vyy50)
new_esEs25(vyy351, vyy361, app(app(ty_@2, ccf), ccg)) → new_esEs8(vyy351, vyy361, ccf, ccg)
new_lt10(vyy600, vyy50) → new_esEs9(new_compare14(vyy600, vyy50))
new_esEs9(GT) → False
new_ltEs5(Just(vyy600), Nothing, bfh) → False
new_ltEs17(LT, GT) → True
new_esEs28(vyy350, vyy360, ty_Char) → new_esEs15(vyy350, vyy360)
new_ltEs5(Just(vyy600), Just(vyy50), ty_Float) → new_ltEs8(vyy600, vyy50)
new_esEs24(vyy352, vyy362, ty_Bool) → new_esEs14(vyy352, vyy362)
new_primPlusNat1(Zero, Succ(vyy51000)) → Succ(vyy51000)
new_primPlusNat1(Succ(vyy8100), Zero) → Succ(vyy8100)
new_esEs21(vyy350, vyy360, ty_Ordering) → new_esEs10(vyy350, vyy360)
new_lt17(vyy600, vyy50) → new_esEs9(new_compare9(vyy600, vyy50))
new_esEs5(Left(vyy350), Left(vyy360), ty_Bool, dba) → new_esEs14(vyy350, vyy360)
new_esEs29(vyy35, vyy36, app(app(ty_Either, dcf), dba)) → new_esEs5(vyy35, vyy36, dcf, dba)
new_esEs21(vyy350, vyy360, ty_Char) → new_esEs15(vyy350, vyy360)
new_compare31(vyy600, vyy50, ty_Ordering) → new_compare19(vyy600, vyy50)
new_ltEs4(Left(vyy600), Left(vyy50), ty_Double, bb) → new_ltEs9(vyy600, vyy50)
new_esEs9(EQ) → False
new_ltEs8(vyy60, vyy5) → new_not(new_compare15(vyy60, vyy5))
new_esEs7(Just(vyy350), Just(vyy360), ty_@0) → new_esEs20(vyy350, vyy360)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs24(vyy352, vyy362, app(app(app(ty_@3, cca), ccb), ccc)) → new_esEs6(vyy352, vyy362, cca, ccb, ccc)
new_esEs5(Left(vyy350), Left(vyy360), app(ty_Maybe, dcb), dba) → new_esEs7(vyy350, vyy360, dcb)
new_esEs27(vyy351, vyy361, app(app(ty_Either, cgc), cgd)) → new_esEs5(vyy351, vyy361, cgc, cgd)
new_lt19(vyy601, vyy51, ty_Integer) → new_lt15(vyy601, vyy51)
new_ltEs4(Left(vyy600), Left(vyy50), app(app(ty_Either, h), ba), bb) → new_ltEs4(vyy600, vyy50, h, ba)
new_primEqInt(Neg(Succ(vyy3500)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(vyy3600))) → False
new_primCompAux0(vyy66, GT) → GT
new_ltEs19(vyy602, vyy52, ty_Char) → new_ltEs12(vyy602, vyy52)
new_lt18(vyy600, vyy50) → new_esEs9(new_compare19(vyy600, vyy50))
new_compare7(:%(vyy600, vyy601), :%(vyy50, vyy51), ty_Int) → new_compare9(new_sr0(vyy600, vyy51), new_sr0(vyy50, vyy601))
new_ltEs17(EQ, EQ) → True
new_foldFM0(vyy350, vyy351, vyy80, Branch(vyy3530, vyy3531, vyy3532, vyy3533, vyy3534), cab, cac) → new_foldFM0(vyy3530, vyy3531, new_foldFM0(vyy350, vyy351, vyy80, vyy3534, cab, cac), vyy3533, cab, cac)
new_ltEs19(vyy602, vyy52, ty_Ordering) → new_ltEs17(vyy602, vyy52)
new_esEs24(vyy352, vyy362, ty_Ordering) → new_esEs10(vyy352, vyy362)
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_ltEs19(vyy602, vyy52, ty_Bool) → new_ltEs13(vyy602, vyy52)
new_ltEs18(vyy601, vyy51, app(app(ty_@2, bbd), bbe)) → new_ltEs10(vyy601, vyy51, bbd, bbe)
new_esEs28(vyy350, vyy360, ty_Int) → new_esEs19(vyy350, vyy360)
new_primCmpNat0(Succ(vyy6000), Succ(vyy500)) → new_primCmpNat0(vyy6000, vyy500)
new_compare23(vyy600, vyy50, False, gc, gd) → new_compare11(vyy600, vyy50, new_ltEs4(vyy600, vyy50, gc, gd), gc, gd)
new_sizeFM(EmptyFM, cab, cac) → Pos(Zero)
new_primEqInt(Pos(Succ(vyy3500)), Pos(Succ(vyy3600))) → new_primEqNat0(vyy3500, vyy3600)
new_lt20(vyy600, vyy50, app(ty_[], hc)) → new_lt12(vyy600, vyy50, hc)
new_esEs21(vyy350, vyy360, ty_Int) → new_esEs19(vyy350, vyy360)
new_esEs24(vyy352, vyy362, app(ty_Ratio, cbd)) → new_esEs16(vyy352, vyy362, cbd)
new_compare12(vyy600, vyy50, True, ha, hb) → LT
new_ltEs16(vyy60, vyy5) → new_not(new_compare9(vyy60, vyy5))
new_esEs14(True, False) → False
new_esEs14(False, True) → False
new_ltEs4(Right(vyy600), Right(vyy50), cb, ty_Bool) → new_ltEs13(vyy600, vyy50)
new_esEs7(Just(vyy350), Just(vyy360), app(app(ty_@2, bef), beg)) → new_esEs8(vyy350, vyy360, bef, beg)
new_esEs5(Right(vyy350), Right(vyy360), dcf, app(app(ty_Either, ddd), dde)) → new_esEs5(vyy350, vyy360, ddd, dde)
new_ltEs10(@2(vyy600, vyy601), @2(vyy50, vyy51), bae, bca) → new_pePe(new_lt5(vyy600, vyy50, bae), vyy600, vyy50, new_ltEs18(vyy601, vyy51, bca), bae)
new_primEqNat0(Succ(vyy3500), Succ(vyy3600)) → new_primEqNat0(vyy3500, vyy3600)
new_esEs5(Left(vyy350), Left(vyy360), ty_Char, dba) → new_esEs15(vyy350, vyy360)
new_compare31(vyy600, vyy50, ty_Double) → new_compare14(vyy600, vyy50)
new_esEs27(vyy351, vyy361, ty_Float) → new_esEs12(vyy351, vyy361)
new_compare26(vyy600, vyy50, False, gh) → new_compare110(vyy600, vyy50, new_ltEs5(vyy600, vyy50, gh), gh)
new_esEs5(Right(vyy350), Right(vyy360), dcf, app(ty_Ratio, ddc)) → new_esEs16(vyy350, vyy360, ddc)
new_esEs5(Left(vyy350), Left(vyy360), ty_Double, dba) → new_esEs18(vyy350, vyy360)
new_primCmpInt(Neg(Succ(vyy6000)), Neg(vyy50)) → new_primCmpNat0(vyy50, Succ(vyy6000))
new_lt20(vyy600, vyy50, ty_@0) → new_lt4(vyy600, vyy50)
new_esEs5(Left(vyy350), Left(vyy360), ty_Int, dba) → new_esEs19(vyy350, vyy360)
new_compare19(vyy600, vyy50) → new_compare27(vyy600, vyy50, new_esEs10(vyy600, vyy50))
new_esEs7(Nothing, Nothing, bec) → True
new_ltEs4(Left(vyy600), Left(vyy50), ty_Bool, bb) → new_ltEs13(vyy600, vyy50)
new_lt5(vyy600, vyy50, ty_Int) → new_lt17(vyy600, vyy50)
new_primEqInt(Pos(Succ(vyy3500)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(vyy3600))) → False
new_ltEs5(Nothing, Just(vyy50), bfh) → True
new_lt20(vyy600, vyy50, ty_Int) → new_lt17(vyy600, vyy50)
new_esEs22(vyy351, vyy361, ty_Integer) → new_esEs13(vyy351, vyy361)
new_lt6(vyy600, vyy50, gc, gd) → new_esEs9(new_compare17(vyy600, vyy50, gc, gd))
new_esEs26(vyy350, vyy360, app(app(ty_FiniteMap, cdh), cea)) → new_esEs11(vyy350, vyy360, cdh, cea)
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(vyy6000), Zero) → GT
new_esEs29(vyy35, vyy36, ty_Double) → new_esEs18(vyy35, vyy36)
new_lt5(vyy600, vyy50, ty_Double) → new_lt10(vyy600, vyy50)
new_primCmpInt(Neg(Zero), Pos(Succ(vyy500))) → LT
new_ltEs18(vyy601, vyy51, app(ty_[], bbf)) → new_ltEs11(vyy601, vyy51, bbf)
new_esEs7(Just(vyy350), Just(vyy360), app(app(ty_Either, bfa), bfb)) → new_esEs5(vyy350, vyy360, bfa, bfb)
new_esEs24(vyy352, vyy362, ty_Double) → new_esEs18(vyy352, vyy362)
new_compare11(vyy600, vyy50, True, gc, gd) → LT
new_compare210(vyy600, vyy50, True, ge, gf, gg) → EQ
new_ltEs5(Just(vyy600), Just(vyy50), ty_Int) → new_ltEs16(vyy600, vyy50)
new_lt20(vyy600, vyy50, ty_Char) → new_lt13(vyy600, vyy50)
new_primPlusNat1(Succ(vyy8100), Succ(vyy51000)) → Succ(Succ(new_primPlusNat1(vyy8100, vyy51000)))
new_ltEs4(Left(vyy600), Left(vyy50), app(ty_Ratio, dag), bb) → new_ltEs15(vyy600, vyy50, dag)
new_primEqInt(Pos(Succ(vyy3500)), Neg(vyy360)) → False
new_primEqInt(Neg(Succ(vyy3500)), Pos(vyy360)) → False
new_esEs28(vyy350, vyy360, app(app(ty_Either, chg), chh)) → new_esEs5(vyy350, vyy360, chg, chh)
new_esEs7(Nothing, Just(vyy360), bec) → False
new_esEs7(Just(vyy350), Nothing, bec) → False
new_ltEs18(vyy601, vyy51, app(app(ty_Either, baf), bag)) → new_ltEs4(vyy601, vyy51, baf, bag)
new_esEs28(vyy350, vyy360, app(app(ty_FiniteMap, chb), chc)) → new_esEs11(vyy350, vyy360, chb, chc)
new_foldFM2(EmptyFM, cab, cac) → []
new_esEs26(vyy350, vyy360, ty_Double) → new_esEs18(vyy350, vyy360)
new_esEs16(:%(vyy350, vyy351), :%(vyy360, vyy361), cad) → new_asAs(new_esEs23(vyy350, vyy360, cad), new_esEs22(vyy351, vyy361, cad))
new_esEs26(vyy350, vyy360, app(ty_Ratio, ced)) → new_esEs16(vyy350, vyy360, ced)
new_lt5(vyy600, vyy50, app(ty_Maybe, bce)) → new_lt9(vyy600, vyy50, bce)
new_primEqInt(Pos(Zero), Neg(Succ(vyy3600))) → False
new_primEqInt(Neg(Zero), Pos(Succ(vyy3600))) → False
new_esEs26(vyy350, vyy360, app(ty_[], ceg)) → new_esEs17(vyy350, vyy360, ceg)
new_compare25(vyy600, vyy50, False, ha, hb) → new_compare12(vyy600, vyy50, new_ltEs10(vyy600, vyy50, ha, hb), ha, hb)
new_esEs26(vyy350, vyy360, ty_Float) → new_esEs12(vyy350, vyy360)
new_primCmpInt(Pos(Zero), Pos(Succ(vyy500))) → new_primCmpNat0(Zero, Succ(vyy500))
new_compare18(vyy600, vyy50, ge, gf, gg) → new_compare210(vyy600, vyy50, new_esEs6(vyy600, vyy50, ge, gf, gg), ge, gf, gg)
new_lt16(vyy600, vyy50, daf) → new_esEs9(new_compare7(vyy600, vyy50, daf))
new_compare24(vyy600, vyy50, True) → EQ
new_ltEs18(vyy601, vyy51, ty_Ordering) → new_ltEs17(vyy601, vyy51)
new_esEs28(vyy350, vyy360, ty_Float) → new_esEs12(vyy350, vyy360)
new_esEs21(vyy350, vyy360, app(ty_[], bhc)) → new_esEs17(vyy350, vyy360, bhc)
new_esEs27(vyy351, vyy361, app(ty_Ratio, cgb)) → new_esEs16(vyy351, vyy361, cgb)
new_esEs28(vyy350, vyy360, ty_Ordering) → new_esEs10(vyy350, vyy360)
new_compare26(vyy600, vyy50, True, gh) → EQ
new_lt13(vyy600, vyy50) → new_esEs9(new_compare30(vyy600, vyy50))
new_primCompAux0(vyy66, LT) → LT
new_compare17(vyy600, vyy50, gc, gd) → new_compare23(vyy600, vyy50, new_esEs5(vyy600, vyy50, gc, gd), gc, gd)
new_esEs25(vyy351, vyy361, ty_Float) → new_esEs12(vyy351, vyy361)
new_esEs7(Just(vyy350), Just(vyy360), ty_Ordering) → new_esEs10(vyy350, vyy360)
new_esEs23(vyy350, vyy360, ty_Int) → new_esEs19(vyy350, vyy360)
new_esEs5(Left(vyy350), Left(vyy360), app(app(ty_@2, dbd), dbe), dba) → new_esEs8(vyy350, vyy360, dbd, dbe)
new_ltEs4(Right(vyy600), Left(vyy50), cb, bb) → False
new_esEs5(Right(vyy350), Right(vyy360), dcf, ty_Ordering) → new_esEs10(vyy350, vyy360)
new_primCmpInt(Pos(Succ(vyy6000)), Pos(vyy50)) → new_primCmpNat0(Succ(vyy6000), vyy50)
new_primPlusNat0(Zero, vyy5100) → Succ(vyy5100)
new_compare110(vyy600, vyy50, True, gh) → LT
new_esEs29(vyy35, vyy36, app(ty_[], bgc)) → new_esEs17(vyy35, vyy36, bgc)
new_compare31(vyy600, vyy50, app(ty_Maybe, bdg)) → new_compare28(vyy600, vyy50, bdg)
new_ltEs18(vyy601, vyy51, app(app(app(ty_@3, bah), bba), bbb)) → new_ltEs6(vyy601, vyy51, bah, bba, bbb)
new_esEs29(vyy35, vyy36, app(app(ty_@2, cfd), cfe)) → new_esEs8(vyy35, vyy36, cfd, cfe)
new_esEs21(vyy350, vyy360, ty_@0) → new_esEs20(vyy350, vyy360)
new_esEs5(Left(vyy350), Left(vyy360), ty_@0, dba) → new_esEs20(vyy350, vyy360)
new_lt4(vyy600, vyy50) → new_esEs9(new_compare6(vyy600, vyy50))
new_esEs26(vyy350, vyy360, ty_Bool) → new_esEs14(vyy350, vyy360)
new_esEs25(vyy351, vyy361, app(ty_Ratio, cch)) → new_esEs16(vyy351, vyy361, cch)
new_lt20(vyy600, vyy50, app(app(ty_Either, gc), gd)) → new_lt6(vyy600, vyy50, gc, gd)
new_compare14(Double(vyy600, vyy601), Double(vyy50, vyy51)) → new_compare9(new_sr0(vyy600, vyy50), new_sr0(vyy601, vyy51))
new_not0 → True
new_compare0(:(vyy600, vyy601), [], bda) → GT
new_esEs24(vyy352, vyy362, app(ty_[], cbg)) → new_esEs17(vyy352, vyy362, cbg)
new_ltEs19(vyy602, vyy52, app(app(app(ty_@3, ea), eb), ec)) → new_ltEs6(vyy602, vyy52, ea, eb, ec)
new_lt20(vyy600, vyy50, app(app(app(ty_@3, ge), gf), gg)) → new_lt7(vyy600, vyy50, ge, gf, gg)
new_lt20(vyy600, vyy50, ty_Ordering) → new_lt18(vyy600, vyy50)
new_esEs26(vyy350, vyy360, app(app(ty_Either, cee), cef)) → new_esEs5(vyy350, vyy360, cee, cef)
new_esEs27(vyy351, vyy361, app(app(ty_FiniteMap, cff), cfg)) → new_esEs11(vyy351, vyy361, cff, cfg)
new_compare11(vyy600, vyy50, False, gc, gd) → GT
new_primCmpInt(Pos(Succ(vyy6000)), Neg(vyy50)) → GT
new_esEs28(vyy350, vyy360, app(ty_Maybe, dab)) → new_esEs7(vyy350, vyy360, dab)
new_esEs21(vyy350, vyy360, app(ty_Maybe, bhd)) → new_esEs7(vyy350, vyy360, bhd)
new_esEs5(Left(vyy350), Left(vyy360), ty_Ordering, dba) → new_esEs10(vyy350, vyy360)
new_primMulInt(Pos(vyy6010), Pos(vyy510)) → Pos(new_primMulNat0(vyy6010, vyy510))
new_compare7(:%(vyy600, vyy601), :%(vyy50, vyy51), ty_Integer) → new_compare8(new_sr(vyy600, vyy51), new_sr(vyy50, vyy601))
new_esEs5(Right(vyy350), Left(vyy360), dcf, dba) → False
new_esEs5(Left(vyy350), Right(vyy360), dcf, dba) → False
new_primMulInt(Neg(vyy6010), Neg(vyy510)) → Pos(new_primMulNat0(vyy6010, vyy510))
new_esEs18(Double(vyy350, vyy351), Double(vyy360, vyy361)) → new_esEs19(new_sr0(vyy350, vyy360), new_sr0(vyy351, vyy361))
new_esEs29(vyy35, vyy36, ty_Char) → new_esEs15(vyy35, vyy36)
new_ltEs4(Right(vyy600), Right(vyy50), cb, app(app(ty_@2, db), dc)) → new_ltEs10(vyy600, vyy50, db, dc)
new_primEqNat0(Succ(vyy3500), Zero) → False
new_primEqNat0(Zero, Succ(vyy3600)) → False
new_ltEs5(Nothing, Nothing, bfh) → True
new_compare31(vyy600, vyy50, ty_Integer) → new_compare8(vyy600, vyy50)
new_compare25(vyy600, vyy50, True, ha, hb) → EQ
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs28(vyy350, vyy360, app(app(app(ty_@3, dac), dad), dae)) → new_esEs6(vyy350, vyy360, dac, dad, dae)
new_ltEs18(vyy601, vyy51, ty_@0) → new_ltEs7(vyy601, vyy51)
new_esEs27(vyy351, vyy361, app(app(app(ty_@3, cgg), cgh), cha)) → new_esEs6(vyy351, vyy361, cgg, cgh, cha)
new_sizeFM(Branch(vyy350, vyy351, vyy352, vyy353, vyy354), cab, cac) → vyy352
new_pePe(True, vyy35, vyy36, vyy52, dec) → True
new_ltEs4(Left(vyy600), Left(vyy50), ty_Integer, bb) → new_ltEs14(vyy600, vyy50)
new_foldFM2(Branch(vyy350, vyy351, vyy352, vyy353, vyy354), cab, cac) → new_foldFM0(vyy350, vyy351, new_foldFM2(vyy354, cab, cac), vyy353, cab, cac)
new_ltEs4(Right(vyy600), Right(vyy50), cb, app(ty_Ratio, dah)) → new_ltEs15(vyy600, vyy50, dah)
new_ltEs19(vyy602, vyy52, app(ty_Maybe, ed)) → new_ltEs5(vyy602, vyy52, ed)
new_lt9(vyy600, vyy50, gh) → new_esEs9(new_compare28(vyy600, vyy50, gh))
new_esEs7(Just(vyy350), Just(vyy360), ty_Float) → new_esEs12(vyy350, vyy360)
new_primCmpInt(Neg(Zero), Neg(Succ(vyy500))) → new_primCmpNat0(Succ(vyy500), Zero)
new_compare23(vyy600, vyy50, True, gc, gd) → EQ
new_primCmpInt(Pos(Zero), Neg(Succ(vyy500))) → GT
new_ltEs4(Right(vyy600), Right(vyy50), cb, ty_@0) → new_ltEs7(vyy600, vyy50)
new_compare28(vyy600, vyy50, gh) → new_compare26(vyy600, vyy50, new_esEs7(vyy600, vyy50, gh), gh)
new_esEs5(Right(vyy350), Right(vyy360), dcf, ty_Double) → new_esEs18(vyy350, vyy360)
new_compare110(vyy600, vyy50, False, gh) → GT
new_esEs5(Left(vyy350), Left(vyy360), ty_Integer, dba) → new_esEs13(vyy350, vyy360)
new_compare0(:(vyy600, vyy601), :(vyy50, vyy51), bda) → new_primCompAux1(vyy600, vyy50, new_compare0(vyy601, vyy51, bda), bda)
new_ltEs4(Left(vyy600), Left(vyy50), ty_@0, bb) → new_ltEs7(vyy600, vyy50)
new_lt20(vyy600, vyy50, app(ty_Maybe, gh)) → new_lt9(vyy600, vyy50, gh)
new_sr0(vyy601, vyy51) → new_primMulInt(vyy601, vyy51)
new_compare31(vyy600, vyy50, app(ty_Ratio, def)) → new_compare7(vyy600, vyy50, def)
new_esEs21(vyy350, vyy360, ty_Float) → new_esEs12(vyy350, vyy360)
new_esEs29(vyy35, vyy36, ty_Int) → new_esEs19(vyy35, vyy36)
new_esEs7(Just(vyy350), Just(vyy360), ty_Char) → new_esEs15(vyy350, vyy360)
new_esEs25(vyy351, vyy361, app(ty_Maybe, cdd)) → new_esEs7(vyy351, vyy361, cdd)
new_esEs7(Just(vyy350), Just(vyy360), app(app(app(ty_@3, bfe), bff), bfg)) → new_esEs6(vyy350, vyy360, bfe, bff, bfg)
new_ltEs9(vyy60, vyy5) → new_not(new_compare14(vyy60, vyy5))
new_esEs19(vyy35, vyy36) → new_primEqInt(vyy35, vyy36)
new_esEs27(vyy351, vyy361, ty_Double) → new_esEs18(vyy351, vyy361)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_lt11(vyy600, vyy50, ha, hb) → new_esEs9(new_compare29(vyy600, vyy50, ha, hb))
new_primCompAux1(vyy600, vyy50, vyy62, bda) → new_primCompAux0(vyy62, new_compare31(vyy600, vyy50, bda))
new_lt19(vyy601, vyy51, ty_Bool) → new_lt14(vyy601, vyy51)
new_lt7(vyy600, vyy50, ge, gf, gg) → new_esEs9(new_compare18(vyy600, vyy50, ge, gf, gg))
new_ltEs15(vyy60, vyy5, bgb) → new_not(new_compare7(vyy60, vyy5, bgb))
new_asAs(False, vyy61) → False
new_esEs5(Left(vyy350), Left(vyy360), ty_Float, dba) → new_esEs12(vyy350, vyy360)
new_ltEs4(Right(vyy600), Right(vyy50), cb, ty_Ordering) → new_ltEs17(vyy600, vyy50)
new_primMulInt(Pos(vyy6010), Neg(vyy510)) → Neg(new_primMulNat0(vyy6010, vyy510))
new_primMulInt(Neg(vyy6010), Pos(vyy510)) → Neg(new_primMulNat0(vyy6010, vyy510))
new_primMulNat0(Zero, Succ(vyy5100)) → Zero
new_primMulNat0(Succ(vyy60100), Zero) → Zero
new_esEs7(Just(vyy350), Just(vyy360), ty_Double) → new_esEs18(vyy350, vyy360)
new_esEs21(vyy350, vyy360, app(app(ty_Either, bha), bhb)) → new_esEs5(vyy350, vyy360, bha, bhb)
new_esEs26(vyy350, vyy360, ty_Integer) → new_esEs13(vyy350, vyy360)
new_lt19(vyy601, vyy51, ty_Ordering) → new_lt18(vyy601, vyy51)
new_esEs5(Left(vyy350), Left(vyy360), app(app(app(ty_@3, dcc), dcd), dce), dba) → new_esEs6(vyy350, vyy360, dcc, dcd, dce)
new_ltEs4(Right(vyy600), Right(vyy50), cb, ty_Int) → new_ltEs16(vyy600, vyy50)
new_esEs25(vyy351, vyy361, ty_Ordering) → new_esEs10(vyy351, vyy361)
new_esEs10(GT, GT) → True
new_esEs26(vyy350, vyy360, app(ty_Maybe, ceh)) → new_esEs7(vyy350, vyy360, ceh)
new_esEs17(:(vyy350, vyy351), :(vyy360, vyy361), bgc) → new_asAs(new_esEs21(vyy350, vyy360, bgc), new_esEs17(vyy351, vyy361, bgc))
new_lt19(vyy601, vyy51, ty_Float) → new_lt8(vyy601, vyy51)
new_esEs28(vyy350, vyy360, ty_Bool) → new_esEs14(vyy350, vyy360)
new_esEs5(Right(vyy350), Right(vyy360), dcf, ty_Integer) → new_esEs13(vyy350, vyy360)
new_ltEs5(Just(vyy600), Just(vyy50), app(ty_Maybe, baa)) → new_ltEs5(vyy600, vyy50, baa)
new_esEs28(vyy350, vyy360, ty_Double) → new_esEs18(vyy350, vyy360)
new_not(EQ) → new_not0
new_lt20(vyy600, vyy50, ty_Float) → new_lt8(vyy600, vyy50)
new_esEs25(vyy351, vyy361, ty_Integer) → new_esEs13(vyy351, vyy361)
new_compare31(vyy600, vyy50, app(ty_[], beb)) → new_compare0(vyy600, vyy50, beb)
new_esEs29(vyy35, vyy36, app(ty_Ratio, cad)) → new_esEs16(vyy35, vyy36, cad)
new_esEs5(Right(vyy350), Right(vyy360), dcf, ty_Int) → new_esEs19(vyy350, vyy360)
new_esEs25(vyy351, vyy361, app(ty_[], cdc)) → new_esEs17(vyy351, vyy361, cdc)
new_ltEs18(vyy601, vyy51, ty_Char) → new_ltEs12(vyy601, vyy51)
new_esEs25(vyy351, vyy361, app(app(app(ty_@3, cde), cdf), cdg)) → new_esEs6(vyy351, vyy361, cde, cdf, cdg)
new_esEs28(vyy350, vyy360, ty_Integer) → new_esEs13(vyy350, vyy360)
new_lt14(vyy600, vyy50) → new_esEs9(new_compare16(vyy600, vyy50))
new_ltEs17(GT, GT) → True
new_ltEs5(Just(vyy600), Just(vyy50), ty_Integer) → new_ltEs14(vyy600, vyy50)
new_compare27(vyy600, vyy50, True) → EQ
new_esEs14(True, True) → True
new_esEs29(vyy35, vyy36, ty_Ordering) → new_esEs10(vyy35, vyy36)
new_ltEs19(vyy602, vyy52, ty_Int) → new_ltEs16(vyy602, vyy52)
new_esEs27(vyy351, vyy361, ty_Bool) → new_esEs14(vyy351, vyy361)
new_esEs21(vyy350, vyy360, app(ty_Ratio, bgh)) → new_esEs16(vyy350, vyy360, bgh)
new_ltEs17(GT, EQ) → False
new_ltEs5(Just(vyy600), Just(vyy50), ty_Char) → new_ltEs12(vyy600, vyy50)
new_lt19(vyy601, vyy51, app(app(app(ty_@3, fc), fd), ff)) → new_lt7(vyy601, vyy51, fc, fd, ff)
new_esEs28(vyy350, vyy360, app(ty_[], daa)) → new_esEs17(vyy350, vyy360, daa)
new_esEs7(Just(vyy350), Just(vyy360), app(ty_Ratio, beh)) → new_esEs16(vyy350, vyy360, beh)
new_ltEs13(True, True) → True
new_esEs5(Left(vyy350), Left(vyy360), app(ty_Ratio, dbf), dba) → new_esEs16(vyy350, vyy360, dbf)
new_esEs27(vyy351, vyy361, ty_Ordering) → new_esEs10(vyy351, vyy361)
new_esEs7(Just(vyy350), Just(vyy360), app(ty_[], bfc)) → new_esEs17(vyy350, vyy360, bfc)
new_ltEs13(False, False) → True
new_ltEs14(vyy60, vyy5) → new_not(new_compare8(vyy60, vyy5))
new_esEs7(Just(vyy350), Just(vyy360), ty_Integer) → new_esEs13(vyy350, vyy360)
new_esEs25(vyy351, vyy361, ty_Char) → new_esEs15(vyy351, vyy361)
new_esEs5(Right(vyy350), Right(vyy360), dcf, ty_Bool) → new_esEs14(vyy350, vyy360)
new_esEs22(vyy351, vyy361, ty_Int) → new_esEs19(vyy351, vyy361)
new_ltEs18(vyy601, vyy51, ty_Bool) → new_ltEs13(vyy601, vyy51)
new_esEs5(Left(vyy350), Left(vyy360), app(app(ty_FiniteMap, dbb), dbc), dba) → new_esEs11(vyy350, vyy360, dbb, dbc)
new_not(LT) → new_not0
new_esEs26(vyy350, vyy360, ty_Int) → new_esEs19(vyy350, vyy360)
new_esEs25(vyy351, vyy361, ty_Double) → new_esEs18(vyy351, vyy361)
new_lt20(vyy600, vyy50, ty_Integer) → new_lt15(vyy600, vyy50)
new_esEs5(Left(vyy350), Left(vyy360), app(app(ty_Either, dbg), dbh), dba) → new_esEs5(vyy350, vyy360, dbg, dbh)
new_ltEs5(Just(vyy600), Just(vyy50), app(app(ty_Either, hd), he)) → new_ltEs4(vyy600, vyy50, hd, he)
new_esEs29(vyy35, vyy36, app(app(app(ty_@3, cae), caf), cag)) → new_esEs6(vyy35, vyy36, cae, caf, cag)
new_esEs14(False, False) → True
new_esEs10(LT, GT) → False
new_esEs10(GT, LT) → False
new_esEs7(Just(vyy350), Just(vyy360), app(app(ty_FiniteMap, bed), bee)) → new_esEs11(vyy350, vyy360, bed, bee)
new_esEs10(LT, EQ) → False
new_esEs10(EQ, LT) → False
new_compare31(vyy600, vyy50, ty_Float) → new_compare15(vyy600, vyy50)
new_esEs28(vyy350, vyy360, app(app(ty_@2, chd), che)) → new_esEs8(vyy350, vyy360, chd, che)
new_compare31(vyy600, vyy50, ty_Bool) → new_compare16(vyy600, vyy50)
new_primPlusNat1(Zero, Zero) → Zero
new_compare0([], :(vyy50, vyy51), bda) → LT
new_esEs21(vyy350, vyy360, app(app(app(ty_@3, bhe), bhf), bhg)) → new_esEs6(vyy350, vyy360, bhe, bhf, bhg)
new_esEs5(Left(vyy350), Left(vyy360), app(ty_[], dca), dba) → new_esEs17(vyy350, vyy360, dca)
new_asAs(True, vyy61) → vyy61
new_lt8(vyy600, vyy50) → new_esEs9(new_compare15(vyy600, vyy50))
new_lt15(vyy600, vyy50) → new_esEs9(new_compare8(vyy600, vyy50))
new_primMulNat0(Succ(vyy60100), Succ(vyy5100)) → new_primPlusNat0(new_primMulNat0(vyy60100, Succ(vyy5100)), vyy5100)
new_ltEs17(LT, EQ) → True
new_compare30(Char(vyy600), Char(vyy50)) → new_primCmpNat0(vyy600, vyy50)
new_esEs29(vyy35, vyy36, ty_Float) → new_esEs12(vyy35, vyy36)
new_compare31(vyy600, vyy50, ty_Int) → new_compare9(vyy600, vyy50)
new_esEs24(vyy352, vyy362, ty_Int) → new_esEs19(vyy352, vyy362)
new_esEs17([], [], bgc) → True
new_esEs17([], :(vyy360, vyy361), bgc) → False
new_esEs17(:(vyy350, vyy351), [], bgc) → False
new_esEs7(Just(vyy350), Just(vyy360), ty_Bool) → new_esEs14(vyy350, vyy360)
new_fmToList(vyy35, cab, cac) → new_foldFM2(vyy35, cab, cac)
new_lt19(vyy601, vyy51, ty_Int) → new_lt17(vyy601, vyy51)
new_esEs29(vyy35, vyy36, app(app(ty_FiniteMap, cab), cac)) → new_esEs11(vyy35, vyy36, cab, cac)
new_esEs24(vyy352, vyy362, app(app(ty_@2, cbb), cbc)) → new_esEs8(vyy352, vyy362, cbb, cbc)
new_compare10(vyy600, vyy50, True) → LT
new_esEs26(vyy350, vyy360, ty_@0) → new_esEs20(vyy350, vyy360)
new_esEs29(vyy35, vyy36, ty_Bool) → new_esEs14(vyy35, vyy36)
new_ltEs17(EQ, GT) → True
new_lt19(vyy601, vyy51, app(app(ty_Either, eh), fa)) → new_lt6(vyy601, vyy51, eh, fa)
new_compare13(vyy600, vyy50, True, ge, gf, gg) → LT
new_lt5(vyy600, vyy50, ty_Bool) → new_lt14(vyy600, vyy50)
new_esEs5(Right(vyy350), Right(vyy360), dcf, ty_Float) → new_esEs12(vyy350, vyy360)
new_compare10(vyy600, vyy50, False) → GT
new_esEs25(vyy351, vyy361, ty_@0) → new_esEs20(vyy351, vyy361)
new_lt20(vyy600, vyy50, ty_Double) → new_lt10(vyy600, vyy50)
new_ltEs18(vyy601, vyy51, ty_Double) → new_ltEs9(vyy601, vyy51)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCompAux0(vyy66, EQ) → vyy66
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_esEs5(Right(vyy350), Right(vyy360), dcf, app(ty_Maybe, ddg)) → new_esEs7(vyy350, vyy360, ddg)
new_primCmpInt(Neg(Succ(vyy6000)), Pos(vyy50)) → LT
new_esEs24(vyy352, vyy362, ty_@0) → new_esEs20(vyy352, vyy362)
new_ltEs5(Just(vyy600), Just(vyy50), app(ty_[], bad)) → new_ltEs11(vyy600, vyy50, bad)
new_ltEs12(vyy60, vyy5) → new_not(new_compare30(vyy60, vyy5))
new_compare27(vyy600, vyy50, False) → new_compare111(vyy600, vyy50, new_ltEs17(vyy600, vyy50))
new_esEs5(Right(vyy350), Right(vyy360), dcf, app(ty_[], ddf)) → new_esEs17(vyy350, vyy360, ddf)
The set Q consists of the following terms:
new_lt19(x0, x1, ty_Int)
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_compare10(x0, x1, True)
new_ltEs5(Just(x0), Just(x1), ty_Bool)
new_ltEs19(x0, x1, ty_Int)
new_ltEs5(Just(x0), Just(x1), ty_Ordering)
new_esEs25(x0, x1, ty_Int)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs28(x0, x1, ty_Bool)
new_ltEs19(x0, x1, app(ty_[], x2))
new_compare28(x0, x1, x2)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs5(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_lt5(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs7(Just(x0), Just(x1), ty_Char)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs5(Left(x0), Left(x1), ty_Char, x2)
new_lt5(x0, x1, ty_Double)
new_primPlusNat0(Succ(x0), x1)
new_ltEs5(Just(x0), Just(x1), ty_Int)
new_lt5(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, ty_Int)
new_esEs23(x0, x1, ty_Integer)
new_lt11(x0, x1, x2, x3)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs4(Left(x0), Right(x1), x2, x3)
new_ltEs4(Right(x0), Left(x1), x2, x3)
new_esEs9(EQ)
new_esEs5(Right(x0), Right(x1), x2, ty_Double)
new_ltEs17(EQ, GT)
new_ltEs17(GT, EQ)
new_esEs17(:(x0, x1), :(x2, x3), x4)
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpNat0(Zero, Succ(x0))
new_esEs21(x0, x1, ty_Double)
new_esEs15(Char(x0), Char(x1))
new_lt20(x0, x1, ty_Char)
new_ltEs4(Right(x0), Right(x1), x2, ty_Float)
new_esEs10(EQ, GT)
new_esEs10(GT, EQ)
new_ltEs4(Left(x0), Left(x1), ty_Integer, x2)
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs5(Left(x0), Left(x1), app(app(ty_FiniteMap, x2), x3), x4)
new_ltEs8(x0, x1)
new_esEs26(x0, x1, ty_Char)
new_esEs10(LT, EQ)
new_esEs10(EQ, LT)
new_compare31(x0, x1, ty_Integer)
new_ltEs18(x0, x1, app(app(ty_Either, x2), x3))
new_lt8(x0, x1)
new_ltEs4(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_esEs5(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs5(Just(x0), Just(x1), app(ty_Maybe, x2))
new_ltEs5(Just(x0), Just(x1), ty_Integer)
new_esEs5(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs28(x0, x1, ty_Integer)
new_esEs6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs29(x0, x1, app(ty_[], x2))
new_compare7(:%(x0, x1), :%(x2, x3), ty_Integer)
new_compare24(x0, x1, True)
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs5(Left(x0), Left(x1), ty_Bool, x2)
new_esEs27(x0, x1, ty_Double)
new_esEs27(x0, x1, ty_Float)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_compare11(x0, x1, False, x2, x3)
new_ltEs4(Right(x0), Right(x1), x2, ty_Ordering)
new_compare29(x0, x1, x2, x3)
new_esEs7(Just(x0), Just(x1), ty_Integer)
new_esEs5(Left(x0), Left(x1), ty_Integer, x2)
new_esEs17([], :(x0, x1), x2)
new_compare16(x0, x1)
new_lt12(x0, x1, x2)
new_ltEs5(Nothing, Just(x0), x1)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_compare0([], :(x0, x1), x2)
new_lt15(x0, x1)
new_ltEs5(Just(x0), Just(x1), ty_Float)
new_esEs29(x0, x1, ty_Integer)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_compare30(Char(x0), Char(x1))
new_ltEs4(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_compare0(:(x0, x1), [], x2)
new_lt5(x0, x1, ty_Float)
new_pePe(False, x0, x1, x2, x3)
new_esEs17(:(x0, x1), [], x2)
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_esEs7(Just(x0), Just(x1), ty_Double)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs21(x0, x1, ty_Int)
new_esEs14(True, True)
new_lt19(x0, x1, app(ty_Maybe, x2))
new_ltEs4(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_fmToList(x0, x1, x2)
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primEqNat0(Zero, Zero)
new_sr(Integer(x0), Integer(x1))
new_compare11(x0, x1, True, x2, x3)
new_lt13(x0, x1)
new_compare210(x0, x1, True, x2, x3, x4)
new_compare0(:(x0, x1), :(x2, x3), x4)
new_esEs24(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_lt5(x0, x1, ty_Bool)
new_esEs7(Just(x0), Just(x1), ty_@0)
new_esEs5(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_ltEs18(x0, x1, ty_Bool)
new_compare13(x0, x1, False, x2, x3, x4)
new_ltEs5(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs21(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare31(x0, x1, ty_Int)
new_lt9(x0, x1, x2)
new_primCmpNat0(Succ(x0), Zero)
new_esEs29(x0, x1, ty_Float)
new_primMulNat0(Zero, Zero)
new_esEs29(x0, x1, ty_Char)
new_foldFM2(EmptyFM, x0, x1)
new_lt5(x0, x1, ty_@0)
new_esEs25(x0, x1, ty_Integer)
new_ltEs19(x0, x1, ty_Char)
new_esEs7(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs25(x0, x1, ty_Double)
new_primCompAux0(x0, GT)
new_ltEs14(x0, x1)
new_ltEs18(x0, x1, app(ty_[], x2))
new_ltEs4(Left(x0), Left(x1), ty_Double, x2)
new_esEs5(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs26(x0, x1, ty_Ordering)
new_esEs24(x0, x1, ty_Integer)
new_compare0([], [], x0)
new_esEs28(x0, x1, ty_@0)
new_esEs5(Left(x0), Left(x1), ty_Float, x2)
new_esEs5(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs10(LT, GT)
new_esEs10(GT, LT)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpNat0(Succ(x0), Succ(x1))
new_esEs21(x0, x1, ty_Bool)
new_lt20(x0, x1, ty_Bool)
new_esEs27(x0, x1, ty_Int)
new_primPlusNat0(Zero, x0)
new_primCompAux0(x0, EQ)
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs4(Left(x0), Left(x1), ty_@0, x2)
new_esEs24(x0, x1, ty_Ordering)
new_esEs25(x0, x1, ty_Ordering)
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_ltEs5(Just(x0), Just(x1), ty_@0)
new_primCompAux0(x0, LT)
new_esEs28(x0, x1, app(ty_[], x2))
new_esEs26(x0, x1, app(ty_[], x2))
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_esEs7(Just(x0), Just(x1), ty_Ordering)
new_ltEs5(Just(x0), Nothing, x1)
new_lt18(x0, x1)
new_compare14(Double(x0, x1), Double(x2, x3))
new_esEs24(x0, x1, ty_@0)
new_ltEs4(Left(x0), Left(x1), ty_Bool, x2)
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_esEs5(Left(x0), Left(x1), ty_@0, x2)
new_primEqNat0(Zero, Succ(x0))
new_esEs16(:%(x0, x1), :%(x2, x3), x4)
new_ltEs4(Right(x0), Right(x1), x2, ty_Integer)
new_esEs26(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs5(Left(x0), Left(x1), ty_Int, x2)
new_esEs22(x0, x1, ty_Int)
new_lt20(x0, x1, app(ty_[], x2))
new_ltEs15(x0, x1, x2)
new_esEs27(x0, x1, ty_Integer)
new_esEs25(x0, x1, ty_Char)
new_ltEs18(x0, x1, ty_Float)
new_compare31(x0, x1, ty_Char)
new_esEs25(x0, x1, ty_Float)
new_primPlusNat1(Zero, Zero)
new_ltEs13(True, True)
new_not0
new_esEs29(x0, x1, ty_@0)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_compare27(x0, x1, True)
new_esEs5(Right(x0), Right(x1), x2, ty_Integer)
new_esEs9(GT)
new_compare9(x0, x1)
new_esEs13(Integer(x0), Integer(x1))
new_compare111(x0, x1, True)
new_ltEs19(x0, x1, ty_Ordering)
new_esEs10(EQ, EQ)
new_esEs27(x0, x1, ty_Char)
new_ltEs19(x0, x1, ty_Float)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_lt19(x0, x1, ty_Bool)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_ltEs13(False, False)
new_esEs28(x0, x1, ty_Int)
new_ltEs4(Left(x0), Left(x1), ty_Float, x2)
new_lt5(x0, x1, ty_Integer)
new_ltEs13(False, True)
new_ltEs13(True, False)
new_esEs12(Float(x0, x1), Float(x2, x3))
new_esEs27(x0, x1, ty_Bool)
new_esEs25(x0, x1, ty_Bool)
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs18(x0, x1, ty_@0)
new_esEs24(x0, x1, ty_Int)
new_esEs7(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs25(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_lt20(x0, x1, ty_Int)
new_esEs7(Just(x0), Nothing, x1)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_esEs7(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs5(Left(x0), Left(x1), app(ty_[], x2), x3)
new_not(GT)
new_esEs21(x0, x1, ty_Float)
new_lt19(x0, x1, ty_Char)
new_lt17(x0, x1)
new_lt20(x0, x1, ty_Integer)
new_esEs27(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_esEs7(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs17(GT, GT)
new_compare27(x0, x1, False)
new_lt5(x0, x1, ty_Ordering)
new_asAs(False, x0)
new_esEs26(x0, x1, ty_Float)
new_primEqNat0(Succ(x0), Zero)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_ltEs4(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs5(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_ltEs18(x0, x1, ty_Int)
new_asAs(True, x0)
new_esEs7(Just(x0), Just(x1), app(ty_[], x2))
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_compare31(x0, x1, app(ty_Ratio, x2))
new_ltEs4(Right(x0), Right(x1), x2, ty_@0)
new_esEs5(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_ltEs5(Just(x0), Just(x1), ty_Double)
new_primMulNat0(Succ(x0), Succ(x1))
new_lt5(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs4(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs5(Left(x0), Right(x1), x2, x3)
new_esEs5(Right(x0), Left(x1), x2, x3)
new_esEs26(x0, x1, ty_Double)
new_esEs5(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_lt5(x0, x1, app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_lt20(x0, x1, app(ty_Maybe, x2))
new_compare23(x0, x1, False, x2, x3)
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_primEqInt(Neg(Zero), Neg(Zero))
new_esEs5(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs7(Nothing, Nothing, x0)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_esEs14(False, True)
new_esEs14(True, False)
new_lt16(x0, x1, x2)
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs4(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_ltEs5(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs4(Right(x0), Right(x1), x2, ty_Bool)
new_esEs26(x0, x1, ty_Integer)
new_esEs5(Right(x0), Right(x1), x2, ty_Char)
new_compare8(Integer(x0), Integer(x1))
new_compare31(x0, x1, app(ty_[], x2))
new_compare7(:%(x0, x1), :%(x2, x3), ty_Int)
new_esEs28(x0, x1, ty_Float)
new_compare12(x0, x1, False, x2, x3)
new_esEs5(Right(x0), Right(x1), x2, ty_Int)
new_ltEs4(Left(x0), Left(x1), ty_Ordering, x2)
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_ltEs10(@2(x0, x1), @2(x2, x3), x4, x5)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_lt10(x0, x1)
new_ltEs4(Right(x0), Right(x1), x2, app(ty_[], x3))
new_compare110(x0, x1, True, x2)
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
new_esEs10(LT, LT)
new_lt19(x0, x1, ty_Double)
new_ltEs5(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_ltEs18(x0, x1, ty_Ordering)
new_esEs24(x0, x1, ty_Double)
new_primEqNat0(Succ(x0), Succ(x1))
new_ltEs4(Left(x0), Left(x1), ty_Char, x2)
new_esEs9(LT)
new_lt20(x0, x1, ty_Ordering)
new_esEs18(Double(x0, x1), Double(x2, x3))
new_esEs29(x0, x1, ty_Ordering)
new_compare6(@0, @0)
new_ltEs4(Right(x0), Right(x1), x2, ty_Char)
new_compare23(x0, x1, True, x2, x3)
new_primPlusNat1(Succ(x0), Zero)
new_ltEs19(x0, x1, ty_@0)
new_esEs29(x0, x1, ty_Int)
new_ltEs6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_compare31(x0, x1, ty_Ordering)
new_ltEs5(Just(x0), Just(x1), ty_Char)
new_compare31(x0, x1, app(app(ty_@2, x2), x3))
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_esEs26(x0, x1, ty_@0)
new_compare25(x0, x1, False, x2, x3)
new_esEs28(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
new_esEs5(Right(x0), Right(x1), x2, ty_Float)
new_esEs7(Just(x0), Just(x1), ty_Bool)
new_lt5(x0, x1, app(ty_Ratio, x2))
new_primCmpNat0(Zero, Zero)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_ltEs4(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_esEs21(x0, x1, ty_Char)
new_esEs29(x0, x1, ty_Bool)
new_esEs21(x0, x1, app(ty_[], x2))
new_esEs24(x0, x1, ty_Char)
new_esEs7(Just(x0), Just(x1), ty_Float)
new_esEs8(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs26(x0, x1, ty_Bool)
new_ltEs5(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_compare13(x0, x1, True, x2, x3, x4)
new_ltEs17(LT, GT)
new_esEs24(x0, x1, ty_Bool)
new_ltEs17(GT, LT)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_ltEs9(x0, x1)
new_lt19(x0, x1, ty_Integer)
new_esEs22(x0, x1, ty_Integer)
new_lt20(x0, x1, ty_Float)
new_pePe(True, x0, x1, x2, x3)
new_esEs7(Just(x0), Just(x1), ty_Int)
new_lt19(x0, x1, app(ty_Ratio, x2))
new_compare31(x0, x1, ty_Float)
new_esEs29(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs5(Right(x0), Right(x1), x2, ty_@0)
new_esEs27(x0, x1, app(ty_[], x2))
new_esEs5(Right(x0), Right(x1), x2, app(app(ty_FiniteMap, x3), x4))
new_compare110(x0, x1, False, x2)
new_esEs5(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_sr0(x0, x1)
new_esEs10(GT, GT)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_compare111(x0, x1, False)
new_esEs17([], [], x0)
new_esEs5(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_esEs24(x0, x1, app(ty_[], x2))
new_lt7(x0, x1, x2, x3, x4)
new_ltEs19(x0, x1, ty_Double)
new_ltEs18(x0, x1, app(app(ty_@2, x2), x3))
new_compare18(x0, x1, x2, x3, x4)
new_compare24(x0, x1, False)
new_esEs21(x0, x1, ty_Integer)
new_esEs25(x0, x1, ty_@0)
new_esEs28(x0, x1, ty_Ordering)
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Neg(x0), Neg(x1))
new_lt19(x0, x1, ty_Float)
new_ltEs5(Just(x0), Just(x1), app(ty_Ratio, x2))
new_not(EQ)
new_ltEs19(x0, x1, ty_Integer)
new_compare19(x0, x1)
new_esEs5(Right(x0), Right(x1), x2, app(ty_[], x3))
new_lt19(x0, x1, app(ty_[], x2))
new_compare31(x0, x1, app(ty_Maybe, x2))
new_lt14(x0, x1)
new_esEs7(Just(x0), Just(x1), app(app(ty_FiniteMap, x2), x3))
new_primMulNat0(Succ(x0), Zero)
new_ltEs5(Nothing, Nothing, x0)
new_compare15(Float(x0, x1), Float(x2, x3))
new_ltEs4(Left(x0), Left(x1), ty_Int, x2)
new_ltEs4(Right(x0), Right(x1), x2, ty_Double)
new_compare25(x0, x1, True, x2, x3)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_compare12(x0, x1, True, x2, x3)
new_lt20(x0, x1, ty_Double)
new_compare10(x0, x1, False)
new_compare210(x0, x1, False, x2, x3, x4)
new_esEs26(x0, x1, ty_Int)
new_compare26(x0, x1, True, x2)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs11(x0, x1, x2)
new_lt5(x0, x1, ty_Int)
new_lt19(x0, x1, ty_Ordering)
new_primCompAux1(x0, x1, x2, x3)
new_ltEs4(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, ty_@0)
new_esEs19(x0, x1)
new_esEs21(x0, x1, ty_Ordering)
new_esEs28(x0, x1, ty_Double)
new_esEs24(x0, x1, ty_Float)
new_ltEs18(x0, x1, ty_Char)
new_esEs20(@0, @0)
new_esEs21(x0, x1, ty_@0)
new_compare31(x0, x1, ty_Bool)
new_esEs5(Left(x0), Left(x1), ty_Double, x2)
new_ltEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs27(x0, x1, ty_Ordering)
new_lt6(x0, x1, x2, x3)
new_lt5(x0, x1, app(ty_[], x2))
new_sizeFM(EmptyFM, x0, x1)
new_ltEs4(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_lt5(x0, x1, ty_Char)
new_ltEs12(x0, x1)
new_ltEs17(LT, EQ)
new_ltEs17(EQ, LT)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs11(x0, x1, x2, x3)
new_compare31(x0, x1, ty_@0)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs18(x0, x1, app(ty_Ratio, x2))
new_ltEs19(x0, x1, ty_Bool)
new_lt19(x0, x1, ty_@0)
new_ltEs18(x0, x1, ty_Double)
new_ltEs16(x0, x1)
new_lt4(x0, x1)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_ltEs4(Right(x0), Right(x1), x2, ty_Int)
new_compare31(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs4(Left(x0), Left(x1), app(ty_[], x2), x3)
new_primPlusNat1(Zero, Succ(x0))
new_esEs14(False, False)
new_primEqInt(Pos(Zero), Pos(Zero))
new_esEs5(Right(x0), Right(x1), x2, ty_Bool)
new_esEs27(x0, x1, ty_@0)
new_compare26(x0, x1, False, x2)
new_esEs7(Nothing, Just(x0), x1)
new_compare17(x0, x1, x2, x3)
new_compare31(x0, x1, ty_Double)
new_esEs28(x0, x1, ty_Char)
new_ltEs4(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_ltEs7(x0, x1)
new_esEs29(x0, x1, ty_Double)
new_ltEs17(EQ, EQ)
new_compare31(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs17(LT, LT)
new_ltEs18(x0, x1, ty_Integer)
new_primPlusNat1(Succ(x0), Succ(x1))
new_not(LT)
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_esEs7(Just(x0), Just(x1), app(ty_Ratio, x2))
new_ltEs18(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, app(ty_[], x2))
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
We have to consider all minimal (P,Q,R)-chains.
By using the subterm criterion [20] together with the size-change analysis [32] we have proven that there are no infinite chains for this DP problem. From the DPs we obtained the following set of size-change graphs:
- new_lt2(vyy600, vyy50, ha, hb) → new_compare22(vyy600, vyy50, new_esEs8(vyy600, vyy50, ha, hb), ha, hb)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 4, 4 >= 5
- new_lt3(vyy600, vyy50, hc) → new_compare(vyy600, vyy50, hc)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3
- new_compare5(vyy600, vyy50, ha, hb) → new_compare22(vyy600, vyy50, new_esEs8(vyy600, vyy50, ha, hb), ha, hb)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 4, 4 >= 5
- new_compare20(vyy600, vyy50, False, ge, gf, gg) → new_ltEs0(vyy600, vyy50, ge, gf, gg)
The graph contains the following edges 1 >= 1, 2 >= 2, 4 >= 3, 5 >= 4, 6 >= 5
- new_primCompAux(vyy600, vyy50, vyy62, app(app(app(ty_@3, bdd), bde), bdf)) → new_compare3(vyy600, vyy50, bdd, bde, bdf)
The graph contains the following edges 1 >= 1, 2 >= 2, 4 > 3, 4 > 4, 4 > 5
- new_ltEs3(:(vyy600, vyy601), :(vyy50, vyy51), bda) → new_primCompAux(vyy600, vyy50, new_compare0(vyy601, vyy51, bda), bda)
The graph contains the following edges 1 > 1, 2 > 2, 3 >= 4
- new_compare(:(vyy600, vyy601), :(vyy50, vyy51), bda) → new_primCompAux(vyy600, vyy50, new_compare0(vyy601, vyy51, bda), bda)
The graph contains the following edges 1 > 1, 2 > 2, 3 >= 4
- new_ltEs3(:(vyy600, vyy601), :(vyy50, vyy51), bda) → new_compare(vyy601, vyy51, bda)
The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3
- new_ltEs1(Just(vyy600), Just(vyy50), app(app(ty_@2, bab), bac)) → new_ltEs2(vyy600, vyy50, bab, bac)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
- new_ltEs1(Just(vyy600), Just(vyy50), app(app(ty_Either, hd), he)) → new_ltEs(vyy600, vyy50, hd, he)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
- new_ltEs1(Just(vyy600), Just(vyy50), app(app(app(ty_@3, hf), hg), hh)) → new_ltEs0(vyy600, vyy50, hf, hg, hh)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
- new_ltEs1(Just(vyy600), Just(vyy50), app(ty_Maybe, baa)) → new_ltEs1(vyy600, vyy50, baa)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
- new_ltEs1(Just(vyy600), Just(vyy50), app(ty_[], bad)) → new_ltEs3(vyy600, vyy50, bad)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
- new_compare2(vyy600, vyy50, False, gc, gd) → new_ltEs(vyy600, vyy50, gc, gd)
The graph contains the following edges 1 >= 1, 2 >= 2, 4 >= 3, 5 >= 4
- new_primCompAux(vyy600, vyy50, vyy62, app(app(ty_Either, bdb), bdc)) → new_compare1(vyy600, vyy50, bdb, bdc)
The graph contains the following edges 1 >= 1, 2 >= 2, 4 > 3, 4 > 4
- new_ltEs0(@3(vyy600, vyy601, vyy602), @3(vyy50, vyy51, vyy52), de, df, app(app(ty_@2, ee), ef)) → new_ltEs2(vyy602, vyy52, ee, ef)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4
- new_ltEs0(@3(vyy600, vyy601, vyy602), @3(vyy50, vyy51, vyy52), app(app(ty_Either, gc), gd), df, fb) → new_compare2(vyy600, vyy50, new_esEs5(vyy600, vyy50, gc, gd), gc, gd)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 4, 3 > 5
- new_ltEs0(@3(vyy600, vyy601, vyy602), @3(vyy50, vyy51, vyy52), de, df, app(app(ty_Either, dg), dh)) → new_ltEs(vyy602, vyy52, dg, dh)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4
- new_ltEs2(@2(vyy600, vyy601), @2(vyy50, vyy51), bae, app(app(ty_Either, baf), bag)) → new_ltEs(vyy601, vyy51, baf, bag)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
- new_ltEs0(@3(vyy600, vyy601, vyy602), @3(vyy50, vyy51, vyy52), de, df, app(app(app(ty_@3, ea), eb), ec)) → new_ltEs0(vyy602, vyy52, ea, eb, ec)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4, 5 > 5
- new_ltEs2(@2(vyy600, vyy601), @2(vyy50, vyy51), bae, app(app(app(ty_@3, bah), bba), bbb)) → new_ltEs0(vyy601, vyy51, bah, bba, bbb)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5
- new_ltEs0(@3(vyy600, vyy601, vyy602), @3(vyy50, vyy51, vyy52), de, df, app(ty_Maybe, ed)) → new_ltEs1(vyy602, vyy52, ed)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3
- new_ltEs0(@3(vyy600, vyy601, vyy602), @3(vyy50, vyy51, vyy52), de, df, app(ty_[], eg)) → new_ltEs3(vyy602, vyy52, eg)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3
- new_compare(:(vyy600, vyy601), :(vyy50, vyy51), bda) → new_compare(vyy601, vyy51, bda)
The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3
- new_ltEs2(@2(vyy600, vyy601), @2(vyy50, vyy51), bae, app(ty_[], bbf)) → new_ltEs3(vyy601, vyy51, bbf)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
- new_compare22(vyy600, vyy50, False, ha, hb) → new_ltEs2(vyy600, vyy50, ha, hb)
The graph contains the following edges 1 >= 1, 2 >= 2, 4 >= 3, 5 >= 4
- new_ltEs2(@2(vyy600, vyy601), @2(vyy50, vyy51), bae, app(app(ty_@2, bbd), bbe)) → new_ltEs2(vyy601, vyy51, bbd, bbe)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
- new_lt0(vyy600, vyy50, ge, gf, gg) → new_compare20(vyy600, vyy50, new_esEs6(vyy600, vyy50, ge, gf, gg), ge, gf, gg)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 4, 4 >= 5, 5 >= 6
- new_lt(vyy600, vyy50, gc, gd) → new_compare2(vyy600, vyy50, new_esEs5(vyy600, vyy50, gc, gd), gc, gd)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 4, 4 >= 5
- new_compare1(vyy600, vyy50, gc, gd) → new_compare2(vyy600, vyy50, new_esEs5(vyy600, vyy50, gc, gd), gc, gd)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 4, 4 >= 5
- new_lt1(vyy600, vyy50, gh) → new_compare21(vyy600, vyy50, new_esEs7(vyy600, vyy50, gh), gh)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 4
- new_ltEs2(@2(vyy600, vyy601), @2(vyy50, vyy51), bae, app(ty_Maybe, bbc)) → new_ltEs1(vyy601, vyy51, bbc)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
- new_compare21(vyy600, vyy50, False, gh) → new_ltEs1(vyy600, vyy50, gh)
The graph contains the following edges 1 >= 1, 2 >= 2, 4 >= 3
- new_ltEs0(@3(vyy600, vyy601, vyy602), @3(vyy50, vyy51, vyy52), de, app(app(ty_@2, fh), ga), fb) → new_lt2(vyy601, vyy51, fh, ga)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
- new_ltEs2(@2(vyy600, vyy601), @2(vyy50, vyy51), app(app(ty_@2, bcf), bcg), bca) → new_lt2(vyy600, vyy50, bcf, bcg)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
- new_ltEs0(@3(vyy600, vyy601, vyy602), @3(vyy50, vyy51, vyy52), de, app(ty_Maybe, fg), fb) → new_lt1(vyy601, vyy51, fg)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
- new_ltEs2(@2(vyy600, vyy601), @2(vyy50, vyy51), app(ty_Maybe, bce), bca) → new_lt1(vyy600, vyy50, bce)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
- new_ltEs0(@3(vyy600, vyy601, vyy602), @3(vyy50, vyy51, vyy52), app(ty_[], hc), df, fb) → new_compare(vyy600, vyy50, hc)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
- new_primCompAux(vyy600, vyy50, vyy62, app(ty_[], beb)) → new_compare(vyy600, vyy50, beb)
The graph contains the following edges 1 >= 1, 2 >= 2, 4 > 3
- new_ltEs0(@3(vyy600, vyy601, vyy602), @3(vyy50, vyy51, vyy52), de, app(ty_[], gb), fb) → new_lt3(vyy601, vyy51, gb)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
- new_ltEs2(@2(vyy600, vyy601), @2(vyy50, vyy51), app(ty_[], bch), bca) → new_lt3(vyy600, vyy50, bch)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
- new_compare3(vyy600, vyy50, ge, gf, gg) → new_compare20(vyy600, vyy50, new_esEs6(vyy600, vyy50, ge, gf, gg), ge, gf, gg)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 4, 4 >= 5, 5 >= 6
- new_compare4(vyy600, vyy50, gh) → new_compare21(vyy600, vyy50, new_esEs7(vyy600, vyy50, gh), gh)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 4
- new_primCompAux(vyy600, vyy50, vyy62, app(ty_Maybe, bdg)) → new_compare4(vyy600, vyy50, bdg)
The graph contains the following edges 1 >= 1, 2 >= 2, 4 > 3
- new_primCompAux(vyy600, vyy50, vyy62, app(app(ty_@2, bdh), bea)) → new_compare5(vyy600, vyy50, bdh, bea)
The graph contains the following edges 1 >= 1, 2 >= 2, 4 > 3, 4 > 4
- new_ltEs0(@3(vyy600, vyy601, vyy602), @3(vyy50, vyy51, vyy52), app(app(ty_@2, ha), hb), df, fb) → new_compare22(vyy600, vyy50, new_esEs8(vyy600, vyy50, ha, hb), ha, hb)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 4, 3 > 5
- new_ltEs0(@3(vyy600, vyy601, vyy602), @3(vyy50, vyy51, vyy52), de, app(app(app(ty_@3, fc), fd), ff), fb) → new_lt0(vyy601, vyy51, fc, fd, ff)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5
- new_ltEs2(@2(vyy600, vyy601), @2(vyy50, vyy51), app(app(app(ty_@3, bcb), bcc), bcd), bca) → new_lt0(vyy600, vyy50, bcb, bcc, bcd)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
- new_ltEs2(@2(vyy600, vyy601), @2(vyy50, vyy51), app(app(ty_Either, bbg), bbh), bca) → new_lt(vyy600, vyy50, bbg, bbh)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
- new_ltEs0(@3(vyy600, vyy601, vyy602), @3(vyy50, vyy51, vyy52), app(app(app(ty_@3, ge), gf), gg), df, fb) → new_compare20(vyy600, vyy50, new_esEs6(vyy600, vyy50, ge, gf, gg), ge, gf, gg)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 4, 3 > 5, 3 > 6
- new_ltEs0(@3(vyy600, vyy601, vyy602), @3(vyy50, vyy51, vyy52), de, app(app(ty_Either, eh), fa), fb) → new_lt(vyy601, vyy51, eh, fa)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
- new_ltEs0(@3(vyy600, vyy601, vyy602), @3(vyy50, vyy51, vyy52), app(ty_Maybe, gh), df, fb) → new_compare21(vyy600, vyy50, new_esEs7(vyy600, vyy50, gh), gh)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 4
- new_ltEs(Right(vyy600), Right(vyy50), cb, app(app(ty_@2, db), dc)) → new_ltEs2(vyy600, vyy50, db, dc)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
- new_ltEs(Left(vyy600), Left(vyy50), app(app(ty_@2, bg), bh), bb) → new_ltEs2(vyy600, vyy50, bg, bh)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
- new_ltEs(Left(vyy600), Left(vyy50), app(app(ty_Either, h), ba), bb) → new_ltEs(vyy600, vyy50, h, ba)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
- new_ltEs(Right(vyy600), Right(vyy50), cb, app(app(ty_Either, cc), cd)) → new_ltEs(vyy600, vyy50, cc, cd)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
- new_ltEs(Left(vyy600), Left(vyy50), app(app(app(ty_@3, bc), bd), be), bb) → new_ltEs0(vyy600, vyy50, bc, bd, be)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
- new_ltEs(Right(vyy600), Right(vyy50), cb, app(app(app(ty_@3, ce), cf), cg)) → new_ltEs0(vyy600, vyy50, ce, cf, cg)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5
- new_ltEs(Left(vyy600), Left(vyy50), app(ty_Maybe, bf), bb) → new_ltEs1(vyy600, vyy50, bf)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
- new_ltEs(Right(vyy600), Right(vyy50), cb, app(ty_Maybe, da)) → new_ltEs1(vyy600, vyy50, da)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
- new_ltEs(Left(vyy600), Left(vyy50), app(ty_[], ca), bb) → new_ltEs3(vyy600, vyy50, ca)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
- new_ltEs(Right(vyy600), Right(vyy50), cb, app(ty_[], dd)) → new_ltEs3(vyy600, vyy50, dd)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 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(vyy17, vyy19, vyy20, vyy21, vyy22, vyy23, vyy24, True, h, ba, bb) → new_foldFM_LE(vyy17, vyy19, vyy24, h, ba, bb)
new_foldFM_LE1(vyy17, vyy19, vyy20, vyy21, vyy22, vyy23, vyy24, True, h, ba, bb) → new_foldFM_LE(vyy17, vyy19, vyy23, h, ba, bb)
new_foldFM_LE(vyy3, vyy5, Branch(vyy60, vyy61, vyy62, vyy63, vyy64), bc, bd, be) → new_foldFM_LE1(vyy3, vyy5, vyy60, vyy61, vyy62, vyy63, vyy64, new_ltEs20(vyy60, vyy5, bd), bc, bd, be)
new_foldFM_LE1(vyy17, vyy19, vyy20, vyy21, vyy22, vyy23, vyy24, False, h, ba, bb) → new_foldFM_LE(vyy17, vyy19, vyy23, h, ba, bb)
The TRS R consists of the following rules:
new_ltEs18(vyy601, vyy51, app(ty_Ratio, bah)) → new_ltEs15(vyy601, vyy51, bah)
new_esEs7(Just(vyy350), Just(vyy360), app(ty_Maybe, cg)) → new_esEs7(vyy350, vyy360, cg)
new_esEs23(vyy350, vyy360, ty_Integer) → new_esEs13(vyy350, vyy360)
new_compare29(vyy600, vyy50, fa, fb) → new_compare25(vyy600, vyy50, new_esEs8(vyy600, vyy50, fa, fb), fa, fb)
new_esEs25(vyy351, vyy361, ty_Int) → new_esEs19(vyy351, vyy361)
new_esEs24(vyy352, vyy362, app(app(ty_Either, bee), bef)) → new_esEs5(vyy352, vyy362, bee, bef)
new_esEs24(vyy352, vyy362, ty_Float) → new_esEs12(vyy352, vyy362)
new_ltEs18(vyy601, vyy51, ty_Float) → new_ltEs8(vyy601, vyy51)
new_ltEs4(Right(vyy600), Right(vyy50), bce, app(ty_[], cgb)) → new_ltEs11(vyy600, vyy50, cgb)
new_ltEs17(LT, LT) → True
new_esEs24(vyy352, vyy362, ty_Char) → new_esEs15(vyy352, vyy362)
new_compare8(Integer(vyy600), Integer(vyy50)) → new_primCmpInt(vyy600, vyy50)
new_ltEs4(Right(vyy600), Right(vyy50), bce, app(ty_Maybe, cfg)) → new_ltEs5(vyy600, vyy50, cfg)
new_lt5(vyy600, vyy50, app(app(ty_@2, bbg), bbh)) → new_lt11(vyy600, vyy50, bbg, bbh)
new_lt5(vyy600, vyy50, app(app(app(ty_@3, bbc), bbd), bbe)) → new_lt7(vyy600, vyy50, bbc, bbd, bbe)
new_ltEs18(vyy601, vyy51, ty_Integer) → new_ltEs14(vyy601, vyy51)
new_ltEs4(Left(vyy600), Left(vyy50), app(ty_[], ceh), bcf) → new_ltEs11(vyy600, vyy50, ceh)
new_esEs29(vyy35, vyy36, ty_Integer) → new_esEs13(vyy35, vyy36)
new_lt20(vyy600, vyy50, app(ty_Ratio, cdf)) → new_lt16(vyy600, vyy50, cdf)
new_esEs27(vyy351, vyy361, app(ty_Maybe, cbf)) → new_esEs7(vyy351, vyy361, cbf)
new_ltEs4(Left(vyy600), Left(vyy50), app(app(app(ty_@3, ceb), cec), ced), bcf) → new_ltEs6(vyy600, vyy50, ceb, cec, ced)
new_compare210(vyy600, vyy50, False, hb, hc, hd) → new_compare13(vyy600, vyy50, new_ltEs6(vyy600, vyy50, hb, hc, hd), hb, hc, hd)
new_esEs5(Right(vyy350), Right(vyy360), daa, ty_Char) → new_esEs15(vyy350, vyy360)
new_compare31(vyy600, vyy50, ty_@0) → new_compare6(vyy600, vyy50)
new_ltEs5(Just(vyy600), Just(vyy50), ty_Double) → new_ltEs9(vyy600, vyy50)
new_ltEs20(vyy60, vyy5, app(ty_Ratio, fc)) → new_ltEs15(vyy60, vyy5, fc)
new_primMulNat0(Zero, Zero) → Zero
new_esEs24(vyy352, vyy362, ty_Integer) → new_esEs13(vyy352, vyy362)
new_ltEs5(Just(vyy600), Just(vyy50), ty_Ordering) → new_ltEs17(vyy600, vyy50)
new_lt5(vyy600, vyy50, ty_Ordering) → new_lt18(vyy600, vyy50)
new_compare13(vyy600, vyy50, False, hb, hc, hd) → GT
new_esEs5(Right(vyy350), Right(vyy360), daa, ty_@0) → new_esEs20(vyy350, vyy360)
new_sr(Integer(vyy500), Integer(vyy6010)) → Integer(new_primMulInt(vyy500, vyy6010))
new_esEs25(vyy351, vyy361, app(app(ty_FiniteMap, bfd), bfe)) → new_esEs11(vyy351, vyy361, bfd, bfe)
new_ltEs19(vyy602, vyy52, ty_Double) → new_ltEs9(vyy602, vyy52)
new_ltEs5(Just(vyy600), Just(vyy50), app(app(ty_@2, ec), ed)) → new_ltEs10(vyy600, vyy50, ec, ed)
new_esEs24(vyy352, vyy362, app(app(ty_FiniteMap, bdh), bea)) → new_esEs11(vyy352, vyy362, bdh, bea)
new_lt19(vyy601, vyy51, app(ty_Maybe, ddf)) → new_lt9(vyy601, vyy51, ddf)
new_ltEs19(vyy602, vyy52, ty_Integer) → new_ltEs14(vyy602, vyy52)
new_ltEs4(Right(vyy600), Right(vyy50), bce, app(app(app(ty_@3, cfd), cfe), cff)) → new_ltEs6(vyy600, vyy50, cfd, cfe, cff)
new_esEs9(LT) → True
new_esEs29(vyy35, vyy36, ty_@0) → new_esEs20(vyy35, vyy36)
new_compare24(vyy600, vyy50, False) → new_compare10(vyy600, vyy50, new_ltEs13(vyy600, vyy50))
new_compare31(vyy600, vyy50, app(app(app(ty_@3, dee), def), deg)) → new_compare18(vyy600, vyy50, dee, def, deg)
new_esEs21(vyy350, vyy360, ty_Integer) → new_esEs13(vyy350, vyy360)
new_esEs26(vyy350, vyy360, ty_Char) → new_esEs15(vyy350, vyy360)
new_lt20(vyy600, vyy50, app(app(ty_@2, fa), fb)) → new_lt11(vyy600, vyy50, fa, fb)
new_ltEs4(Right(vyy600), Right(vyy50), bce, ty_Integer) → new_ltEs14(vyy600, vyy50)
new_lt12(vyy600, vyy50, cdg) → new_esEs9(new_compare0(vyy600, vyy50, cdg))
new_not(GT) → False
new_esEs26(vyy350, vyy360, ty_Ordering) → new_esEs10(vyy350, vyy360)
new_esEs29(vyy35, vyy36, app(ty_Maybe, bf)) → new_esEs7(vyy35, vyy36, bf)
new_esEs27(vyy351, vyy361, app(app(ty_@2, cah), cba)) → new_esEs8(vyy351, vyy361, cah, cba)
new_ltEs4(Left(vyy600), Left(vyy50), app(app(ty_@2, cef), ceg), bcf) → new_ltEs10(vyy600, vyy50, cef, ceg)
new_esEs27(vyy351, vyy361, ty_Char) → new_esEs15(vyy351, vyy361)
new_lt5(vyy600, vyy50, ty_Integer) → new_lt15(vyy600, vyy50)
new_ltEs19(vyy602, vyy52, ty_@0) → new_ltEs7(vyy602, vyy52)
new_ltEs4(Left(vyy600), Left(vyy50), ty_Float, bcf) → new_ltEs8(vyy600, vyy50)
new_esEs21(vyy350, vyy360, ty_Double) → new_esEs18(vyy350, vyy360)
new_ltEs5(Just(vyy600), Just(vyy50), ty_@0) → new_ltEs7(vyy600, vyy50)
new_ltEs13(True, False) → False
new_esEs27(vyy351, vyy361, ty_Integer) → new_esEs13(vyy351, vyy361)
new_ltEs4(Left(vyy600), Left(vyy50), ty_Int, bcf) → new_ltEs16(vyy600, vyy50)
new_ltEs4(Left(vyy600), Left(vyy50), ty_Ordering, bcf) → new_ltEs17(vyy600, vyy50)
new_ltEs5(Just(vyy600), Just(vyy50), app(ty_Ratio, ef)) → new_ltEs15(vyy600, vyy50, ef)
new_ltEs4(Left(vyy600), Left(vyy50), ty_Char, bcf) → new_ltEs12(vyy600, vyy50)
new_ltEs20(vyy60, vyy5, ty_Double) → new_ltEs9(vyy60, vyy5)
new_pePe(False, vyy35, vyy36, vyy52, dbf) → new_asAs(new_esEs29(vyy35, vyy36, dbf), vyy52)
new_compare31(vyy600, vyy50, ty_Char) → new_compare30(vyy600, vyy50)
new_foldFM0(vyy350, vyy351, vyy80, EmptyFM, bcc, bcd) → :(@2(vyy350, vyy351), vyy80)
new_ltEs17(EQ, LT) → False
new_esEs21(vyy350, vyy360, app(app(ty_@2, fh), ga)) → new_esEs8(vyy350, vyy360, fh, ga)
new_esEs5(Right(vyy350), Right(vyy360), daa, app(app(app(ty_@3, dbc), dbd), dbe)) → new_esEs6(vyy350, vyy360, dbc, dbd, dbe)
new_lt20(vyy600, vyy50, ty_Bool) → new_lt14(vyy600, vyy50)
new_ltEs19(vyy602, vyy52, app(app(ty_Either, dbg), dbh)) → new_ltEs4(vyy602, vyy52, dbg, dbh)
new_ltEs4(Right(vyy600), Right(vyy50), bce, ty_Char) → new_ltEs12(vyy600, vyy50)
new_esEs26(vyy350, vyy360, app(app(ty_@2, bhb), bhc)) → new_esEs8(vyy350, vyy360, bhb, bhc)
new_esEs20(@0, @0) → True
new_compare6(@0, @0) → EQ
new_lt19(vyy601, vyy51, ty_Double) → new_lt10(vyy601, vyy51)
new_esEs25(vyy351, vyy361, ty_Bool) → new_esEs14(vyy351, vyy361)
new_ltEs5(Just(vyy600), Just(vyy50), app(app(app(ty_@3, dg), dh), ea)) → new_ltEs6(vyy600, vyy50, dg, dh, ea)
new_lt19(vyy601, vyy51, app(ty_Ratio, deb)) → new_lt16(vyy601, vyy51, deb)
new_ltEs11(vyy60, vyy5, bdb) → new_not(new_compare0(vyy60, vyy5, bdb))
new_ltEs19(vyy602, vyy52, app(ty_[], dcg)) → new_ltEs11(vyy602, vyy52, dcg)
new_compare31(vyy600, vyy50, app(app(ty_@2, dfa), dfb)) → new_compare29(vyy600, vyy50, dfa, dfb)
new_esEs24(vyy352, vyy362, app(ty_Maybe, beh)) → new_esEs7(vyy352, vyy362, beh)
new_esEs6(@3(vyy350, vyy351, vyy352), @3(vyy360, vyy361, vyy362), bde, bdf, bdg) → new_asAs(new_esEs26(vyy350, vyy360, bde), new_asAs(new_esEs25(vyy351, vyy361, bdf), new_esEs24(vyy352, vyy362, bdg)))
new_ltEs20(vyy60, vyy5, app(app(ty_Either, bce), bcf)) → new_ltEs4(vyy60, vyy5, bce, bcf)
new_esEs28(vyy350, vyy360, ty_@0) → new_esEs20(vyy350, vyy360)
new_ltEs5(Just(vyy600), Just(vyy50), ty_Bool) → new_ltEs13(vyy600, vyy50)
new_compare9(vyy60, vyy5) → new_primCmpInt(vyy60, vyy5)
new_ltEs4(Right(vyy600), Right(vyy50), bce, app(app(ty_Either, cfb), cfc)) → new_ltEs4(vyy600, vyy50, cfb, cfc)
new_esEs27(vyy351, vyy361, app(ty_[], cbe)) → new_esEs17(vyy351, vyy361, cbe)
new_ltEs18(vyy601, vyy51, ty_Int) → new_ltEs16(vyy601, vyy51)
new_lt5(vyy600, vyy50, app(app(ty_Either, bba), bbb)) → new_lt6(vyy600, vyy50, bba, bbb)
new_lt5(vyy600, vyy50, ty_Char) → new_lt13(vyy600, vyy50)
new_esEs28(vyy350, vyy360, app(ty_Ratio, ccf)) → new_esEs16(vyy350, vyy360, ccf)
new_compare111(vyy600, vyy50, False) → GT
new_compare111(vyy600, vyy50, True) → LT
new_ltEs4(Left(vyy600), Right(vyy50), bce, bcf) → True
new_lt19(vyy601, vyy51, app(ty_[], dea)) → new_lt12(vyy601, vyy51, dea)
new_ltEs6(@3(vyy600, vyy601, vyy602), @3(vyy50, vyy51, vyy52), bcg, bch, bda) → new_pePe(new_lt20(vyy600, vyy50, bcg), vyy600, vyy50, new_pePe(new_lt19(vyy601, vyy51, bch), vyy601, vyy51, new_ltEs19(vyy602, vyy52, bda), bch), bcg)
new_esEs27(vyy351, vyy361, ty_Int) → new_esEs19(vyy351, vyy361)
new_esEs21(vyy350, vyy360, ty_Bool) → new_esEs14(vyy350, vyy360)
new_primCmpNat0(Zero, Succ(vyy500)) → LT
new_ltEs19(vyy602, vyy52, app(ty_Ratio, dch)) → new_ltEs15(vyy602, vyy52, dch)
new_lt5(vyy600, vyy50, ty_Float) → new_lt8(vyy600, vyy50)
new_esEs11(vyy35, vyy36, bcc, bcd) → new_asAs(new_esEs19(new_sizeFM(vyy35, bcc, bcd), new_sizeFM(vyy36, bcc, bcd)), new_esEs17(new_fmToList(vyy35, bcc, bcd), new_fmToList(vyy36, bcc, bcd), app(app(ty_@2, bcc), bcd)))
new_compare31(vyy600, vyy50, app(app(ty_Either, dec), ded)) → new_compare17(vyy600, vyy50, dec, ded)
new_esEs25(vyy351, vyy361, app(app(ty_Either, bga), bgb)) → new_esEs5(vyy351, vyy361, bga, bgb)
new_esEs8(@2(vyy350, vyy351), @2(vyy360, vyy361), cad, cae) → new_asAs(new_esEs28(vyy350, vyy360, cad), new_esEs27(vyy351, vyy361, cae))
new_ltEs13(False, True) → True
new_ltEs18(vyy601, vyy51, app(ty_Maybe, bad)) → new_ltEs5(vyy601, vyy51, bad)
new_esEs10(LT, LT) → True
new_esEs10(EQ, GT) → False
new_esEs10(GT, EQ) → False
new_compare15(Float(vyy600, vyy601), Float(vyy50, vyy51)) → new_compare9(new_sr0(vyy600, vyy50), new_sr0(vyy601, vyy51))
new_esEs5(Right(vyy350), Right(vyy360), daa, app(app(ty_@2, dad), dae)) → new_esEs8(vyy350, vyy360, dad, dae)
new_lt19(vyy601, vyy51, app(app(ty_@2, ddg), ddh)) → new_lt11(vyy601, vyy51, ddg, ddh)
new_compare0([], [], bdb) → EQ
new_primEqNat0(Zero, Zero) → True
new_compare16(vyy600, vyy50) → new_compare24(vyy600, vyy50, new_esEs14(vyy600, vyy50))
new_ltEs20(vyy60, vyy5, ty_@0) → new_ltEs7(vyy60, vyy5)
new_ltEs20(vyy60, vyy5, ty_Integer) → new_ltEs14(vyy60, vyy5)
new_ltEs20(vyy60, vyy5, ty_Float) → new_ltEs8(vyy60, vyy5)
new_ltEs19(vyy602, vyy52, ty_Float) → new_ltEs8(vyy602, vyy52)
new_ltEs4(Right(vyy600), Right(vyy50), bce, ty_Double) → new_ltEs9(vyy600, vyy50)
new_ltEs7(vyy60, vyy5) → new_not(new_compare6(vyy60, vyy5))
new_lt5(vyy600, vyy50, app(ty_[], bca)) → new_lt12(vyy600, vyy50, bca)
new_ltEs17(GT, LT) → False
new_esEs15(Char(vyy350), Char(vyy360)) → new_primEqNat0(vyy350, vyy360)
new_esEs21(vyy350, vyy360, app(app(ty_FiniteMap, ff), fg)) → new_esEs11(vyy350, vyy360, ff, fg)
new_compare12(vyy600, vyy50, False, fa, fb) → GT
new_esEs12(Float(vyy350, vyy351), Float(vyy360, vyy361)) → new_esEs19(new_sr0(vyy350, vyy360), new_sr0(vyy351, vyy361))
new_esEs7(Just(vyy350), Just(vyy360), ty_Int) → new_esEs19(vyy350, vyy360)
new_esEs27(vyy351, vyy361, ty_@0) → new_esEs20(vyy351, vyy361)
new_primPlusNat0(Succ(vyy810), vyy5100) → Succ(Succ(new_primPlusNat1(vyy810, vyy5100)))
new_lt19(vyy601, vyy51, ty_@0) → new_lt4(vyy601, vyy51)
new_esEs26(vyy350, vyy360, app(app(app(ty_@3, caa), cab), cac)) → new_esEs6(vyy350, vyy360, caa, cab, cac)
new_lt5(vyy600, vyy50, ty_@0) → new_lt4(vyy600, vyy50)
new_esEs13(Integer(vyy350), Integer(vyy360)) → new_primEqInt(vyy350, vyy360)
new_ltEs20(vyy60, vyy5, ty_Int) → new_ltEs16(vyy60, vyy5)
new_ltEs4(Left(vyy600), Left(vyy50), app(ty_Maybe, cee), bcf) → new_ltEs5(vyy600, vyy50, cee)
new_lt5(vyy600, vyy50, app(ty_Ratio, bcb)) → new_lt16(vyy600, vyy50, bcb)
new_esEs10(EQ, EQ) → True
new_primEqInt(Neg(Succ(vyy3500)), Neg(Succ(vyy3600))) → new_primEqNat0(vyy3500, vyy3600)
new_ltEs19(vyy602, vyy52, app(app(ty_@2, dce), dcf)) → new_ltEs10(vyy602, vyy52, dce, dcf)
new_lt19(vyy601, vyy51, ty_Char) → new_lt13(vyy601, vyy51)
new_esEs5(Right(vyy350), Right(vyy360), daa, app(app(ty_FiniteMap, dab), dac)) → new_esEs11(vyy350, vyy360, dab, dac)
new_ltEs4(Right(vyy600), Right(vyy50), bce, ty_Float) → new_ltEs8(vyy600, vyy50)
new_esEs25(vyy351, vyy361, app(app(ty_@2, bff), bfg)) → new_esEs8(vyy351, vyy361, bff, bfg)
new_lt10(vyy600, vyy50) → new_esEs9(new_compare14(vyy600, vyy50))
new_esEs9(GT) → False
new_ltEs5(Just(vyy600), Nothing, dd) → False
new_ltEs17(LT, GT) → True
new_esEs28(vyy350, vyy360, ty_Char) → new_esEs15(vyy350, vyy360)
new_esEs24(vyy352, vyy362, ty_Bool) → new_esEs14(vyy352, vyy362)
new_ltEs5(Just(vyy600), Just(vyy50), ty_Float) → new_ltEs8(vyy600, vyy50)
new_primPlusNat1(Zero, Succ(vyy51000)) → Succ(vyy51000)
new_primPlusNat1(Succ(vyy8100), Zero) → Succ(vyy8100)
new_esEs21(vyy350, vyy360, ty_Ordering) → new_esEs10(vyy350, vyy360)
new_lt17(vyy600, vyy50) → new_esEs9(new_compare9(vyy600, vyy50))
new_esEs5(Left(vyy350), Left(vyy360), ty_Bool, cgd) → new_esEs14(vyy350, vyy360)
new_esEs29(vyy35, vyy36, app(app(ty_Either, daa), cgd)) → new_esEs5(vyy35, vyy36, daa, cgd)
new_esEs21(vyy350, vyy360, ty_Char) → new_esEs15(vyy350, vyy360)
new_compare31(vyy600, vyy50, ty_Ordering) → new_compare19(vyy600, vyy50)
new_ltEs4(Left(vyy600), Left(vyy50), ty_Double, bcf) → new_ltEs9(vyy600, vyy50)
new_esEs9(EQ) → False
new_ltEs8(vyy60, vyy5) → new_not(new_compare15(vyy60, vyy5))
new_esEs7(Just(vyy350), Just(vyy360), ty_@0) → new_esEs20(vyy350, vyy360)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs24(vyy352, vyy362, app(app(app(ty_@3, bfa), bfb), bfc)) → new_esEs6(vyy352, vyy362, bfa, bfb, bfc)
new_esEs5(Left(vyy350), Left(vyy360), app(ty_Maybe, che), cgd) → new_esEs7(vyy350, vyy360, che)
new_esEs27(vyy351, vyy361, app(app(ty_Either, cbc), cbd)) → new_esEs5(vyy351, vyy361, cbc, cbd)
new_ltEs20(vyy60, vyy5, ty_Char) → new_ltEs12(vyy60, vyy5)
new_lt19(vyy601, vyy51, ty_Integer) → new_lt15(vyy601, vyy51)
new_ltEs4(Left(vyy600), Left(vyy50), app(app(ty_Either, cdh), cea), bcf) → new_ltEs4(vyy600, vyy50, cdh, cea)
new_primEqInt(Neg(Succ(vyy3500)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(vyy3600))) → False
new_primCompAux0(vyy66, GT) → GT
new_ltEs19(vyy602, vyy52, ty_Char) → new_ltEs12(vyy602, vyy52)
new_lt18(vyy600, vyy50) → new_esEs9(new_compare19(vyy600, vyy50))
new_compare7(:%(vyy600, vyy601), :%(vyy50, vyy51), ty_Int) → new_compare9(new_sr0(vyy600, vyy51), new_sr0(vyy50, vyy601))
new_ltEs17(EQ, EQ) → True
new_foldFM0(vyy350, vyy351, vyy80, Branch(vyy3530, vyy3531, vyy3532, vyy3533, vyy3534), bcc, bcd) → new_foldFM0(vyy3530, vyy3531, new_foldFM0(vyy350, vyy351, vyy80, vyy3534, bcc, bcd), vyy3533, bcc, bcd)
new_ltEs19(vyy602, vyy52, ty_Ordering) → new_ltEs17(vyy602, vyy52)
new_esEs24(vyy352, vyy362, ty_Ordering) → new_esEs10(vyy352, vyy362)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_ltEs19(vyy602, vyy52, ty_Bool) → new_ltEs13(vyy602, vyy52)
new_ltEs18(vyy601, vyy51, app(app(ty_@2, bae), baf)) → new_ltEs10(vyy601, vyy51, bae, baf)
new_esEs28(vyy350, vyy360, ty_Int) → new_esEs19(vyy350, vyy360)
new_primCmpNat0(Succ(vyy6000), Succ(vyy500)) → new_primCmpNat0(vyy6000, vyy500)
new_compare23(vyy600, vyy50, False, eg, eh) → new_compare11(vyy600, vyy50, new_ltEs4(vyy600, vyy50, eg, eh), eg, eh)
new_sizeFM(EmptyFM, bcc, bcd) → Pos(Zero)
new_primEqInt(Pos(Succ(vyy3500)), Pos(Succ(vyy3600))) → new_primEqNat0(vyy3500, vyy3600)
new_lt20(vyy600, vyy50, app(ty_[], cdg)) → new_lt12(vyy600, vyy50, cdg)
new_esEs24(vyy352, vyy362, app(ty_Ratio, bed)) → new_esEs16(vyy352, vyy362, bed)
new_esEs21(vyy350, vyy360, ty_Int) → new_esEs19(vyy350, vyy360)
new_compare12(vyy600, vyy50, True, fa, fb) → LT
new_esEs14(True, False) → False
new_esEs14(False, True) → False
new_ltEs16(vyy60, vyy5) → new_not(new_compare9(vyy60, vyy5))
new_ltEs4(Right(vyy600), Right(vyy50), bce, ty_Bool) → new_ltEs13(vyy600, vyy50)
new_esEs7(Just(vyy350), Just(vyy360), app(app(ty_@2, ca), cb)) → new_esEs8(vyy350, vyy360, ca, cb)
new_esEs5(Right(vyy350), Right(vyy360), daa, app(app(ty_Either, dag), dah)) → new_esEs5(vyy350, vyy360, dag, dah)
new_ltEs10(@2(vyy600, vyy601), @2(vyy50, vyy51), he, hf) → new_pePe(new_lt5(vyy600, vyy50, he), vyy600, vyy50, new_ltEs18(vyy601, vyy51, hf), he)
new_primEqNat0(Succ(vyy3500), Succ(vyy3600)) → new_primEqNat0(vyy3500, vyy3600)
new_esEs5(Left(vyy350), Left(vyy360), ty_Char, cgd) → new_esEs15(vyy350, vyy360)
new_compare31(vyy600, vyy50, ty_Double) → new_compare14(vyy600, vyy50)
new_esEs27(vyy351, vyy361, ty_Float) → new_esEs12(vyy351, vyy361)
new_compare26(vyy600, vyy50, False, bdd) → new_compare110(vyy600, vyy50, new_ltEs5(vyy600, vyy50, bdd), bdd)
new_esEs5(Right(vyy350), Right(vyy360), daa, app(ty_Ratio, daf)) → new_esEs16(vyy350, vyy360, daf)
new_esEs5(Left(vyy350), Left(vyy360), ty_Double, cgd) → new_esEs18(vyy350, vyy360)
new_primCmpInt(Neg(Succ(vyy6000)), Neg(vyy50)) → new_primCmpNat0(vyy50, Succ(vyy6000))
new_lt20(vyy600, vyy50, ty_@0) → new_lt4(vyy600, vyy50)
new_esEs5(Left(vyy350), Left(vyy360), ty_Int, cgd) → new_esEs19(vyy350, vyy360)
new_compare19(vyy600, vyy50) → new_compare27(vyy600, vyy50, new_esEs10(vyy600, vyy50))
new_esEs7(Nothing, Nothing, bf) → True
new_ltEs4(Left(vyy600), Left(vyy50), ty_Bool, bcf) → new_ltEs13(vyy600, vyy50)
new_lt5(vyy600, vyy50, ty_Int) → new_lt17(vyy600, vyy50)
new_primEqInt(Pos(Succ(vyy3500)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(vyy3600))) → False
new_ltEs5(Nothing, Just(vyy50), dd) → True
new_lt20(vyy600, vyy50, ty_Int) → new_lt17(vyy600, vyy50)
new_esEs22(vyy351, vyy361, ty_Integer) → new_esEs13(vyy351, vyy361)
new_lt6(vyy600, vyy50, eg, eh) → new_esEs9(new_compare17(vyy600, vyy50, eg, eh))
new_esEs26(vyy350, vyy360, app(app(ty_FiniteMap, bgh), bha)) → new_esEs11(vyy350, vyy360, bgh, bha)
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(vyy6000), Zero) → GT
new_esEs29(vyy35, vyy36, ty_Double) → new_esEs18(vyy35, vyy36)
new_lt5(vyy600, vyy50, ty_Double) → new_lt10(vyy600, vyy50)
new_ltEs18(vyy601, vyy51, app(ty_[], bag)) → new_ltEs11(vyy601, vyy51, bag)
new_esEs7(Just(vyy350), Just(vyy360), app(app(ty_Either, cd), ce)) → new_esEs5(vyy350, vyy360, cd, ce)
new_primCmpInt(Neg(Zero), Pos(Succ(vyy500))) → LT
new_esEs24(vyy352, vyy362, ty_Double) → new_esEs18(vyy352, vyy362)
new_compare11(vyy600, vyy50, True, eg, eh) → LT
new_compare210(vyy600, vyy50, True, hb, hc, hd) → EQ
new_ltEs5(Just(vyy600), Just(vyy50), ty_Int) → new_ltEs16(vyy600, vyy50)
new_lt20(vyy600, vyy50, ty_Char) → new_lt13(vyy600, vyy50)
new_primPlusNat1(Succ(vyy8100), Succ(vyy51000)) → Succ(Succ(new_primPlusNat1(vyy8100, vyy51000)))
new_ltEs4(Left(vyy600), Left(vyy50), app(ty_Ratio, cfa), bcf) → new_ltEs15(vyy600, vyy50, cfa)
new_primEqInt(Pos(Succ(vyy3500)), Neg(vyy360)) → False
new_primEqInt(Neg(Succ(vyy3500)), Pos(vyy360)) → False
new_esEs28(vyy350, vyy360, app(app(ty_Either, ccg), cch)) → new_esEs5(vyy350, vyy360, ccg, cch)
new_esEs7(Nothing, Just(vyy360), bf) → False
new_esEs7(Just(vyy350), Nothing, bf) → False
new_ltEs18(vyy601, vyy51, app(app(ty_Either, hg), hh)) → new_ltEs4(vyy601, vyy51, hg, hh)
new_esEs28(vyy350, vyy360, app(app(ty_FiniteMap, ccb), ccc)) → new_esEs11(vyy350, vyy360, ccb, ccc)
new_foldFM2(EmptyFM, bcc, bcd) → []
new_esEs26(vyy350, vyy360, ty_Double) → new_esEs18(vyy350, vyy360)
new_esEs16(:%(vyy350, vyy351), :%(vyy360, vyy361), bdc) → new_asAs(new_esEs23(vyy350, vyy360, bdc), new_esEs22(vyy351, vyy361, bdc))
new_esEs26(vyy350, vyy360, app(ty_Ratio, bhd)) → new_esEs16(vyy350, vyy360, bhd)
new_lt5(vyy600, vyy50, app(ty_Maybe, bbf)) → new_lt9(vyy600, vyy50, bbf)
new_primEqInt(Pos(Zero), Neg(Succ(vyy3600))) → False
new_primEqInt(Neg(Zero), Pos(Succ(vyy3600))) → False
new_esEs26(vyy350, vyy360, app(ty_[], bhg)) → new_esEs17(vyy350, vyy360, bhg)
new_compare25(vyy600, vyy50, False, fa, fb) → new_compare12(vyy600, vyy50, new_ltEs10(vyy600, vyy50, fa, fb), fa, fb)
new_esEs26(vyy350, vyy360, ty_Float) → new_esEs12(vyy350, vyy360)
new_primCmpInt(Pos(Zero), Pos(Succ(vyy500))) → new_primCmpNat0(Zero, Succ(vyy500))
new_compare18(vyy600, vyy50, hb, hc, hd) → new_compare210(vyy600, vyy50, new_esEs6(vyy600, vyy50, hb, hc, hd), hb, hc, hd)
new_lt16(vyy600, vyy50, cdf) → new_esEs9(new_compare7(vyy600, vyy50, cdf))
new_compare24(vyy600, vyy50, True) → EQ
new_ltEs18(vyy601, vyy51, ty_Ordering) → new_ltEs17(vyy601, vyy51)
new_esEs28(vyy350, vyy360, ty_Float) → new_esEs12(vyy350, vyy360)
new_esEs21(vyy350, vyy360, app(ty_[], ge)) → new_esEs17(vyy350, vyy360, ge)
new_esEs27(vyy351, vyy361, app(ty_Ratio, cbb)) → new_esEs16(vyy351, vyy361, cbb)
new_esEs28(vyy350, vyy360, ty_Ordering) → new_esEs10(vyy350, vyy360)
new_compare26(vyy600, vyy50, True, bdd) → EQ
new_lt13(vyy600, vyy50) → new_esEs9(new_compare30(vyy600, vyy50))
new_primCompAux0(vyy66, LT) → LT
new_compare17(vyy600, vyy50, eg, eh) → new_compare23(vyy600, vyy50, new_esEs5(vyy600, vyy50, eg, eh), eg, eh)
new_esEs25(vyy351, vyy361, ty_Float) → new_esEs12(vyy351, vyy361)
new_esEs7(Just(vyy350), Just(vyy360), ty_Ordering) → new_esEs10(vyy350, vyy360)
new_esEs23(vyy350, vyy360, ty_Int) → new_esEs19(vyy350, vyy360)
new_ltEs20(vyy60, vyy5, app(app(app(ty_@3, bcg), bch), bda)) → new_ltEs6(vyy60, vyy5, bcg, bch, bda)
new_esEs5(Left(vyy350), Left(vyy360), app(app(ty_@2, cgg), cgh), cgd) → new_esEs8(vyy350, vyy360, cgg, cgh)
new_ltEs4(Right(vyy600), Left(vyy50), bce, bcf) → False
new_esEs5(Right(vyy350), Right(vyy360), daa, ty_Ordering) → new_esEs10(vyy350, vyy360)
new_primCmpInt(Pos(Succ(vyy6000)), Pos(vyy50)) → new_primCmpNat0(Succ(vyy6000), vyy50)
new_primPlusNat0(Zero, vyy5100) → Succ(vyy5100)
new_compare110(vyy600, vyy50, True, bdd) → LT
new_esEs29(vyy35, vyy36, app(ty_[], fd)) → new_esEs17(vyy35, vyy36, fd)
new_compare31(vyy600, vyy50, app(ty_Maybe, deh)) → new_compare28(vyy600, vyy50, deh)
new_ltEs18(vyy601, vyy51, app(app(app(ty_@3, baa), bab), bac)) → new_ltEs6(vyy601, vyy51, baa, bab, bac)
new_esEs29(vyy35, vyy36, app(app(ty_@2, cad), cae)) → new_esEs8(vyy35, vyy36, cad, cae)
new_esEs21(vyy350, vyy360, ty_@0) → new_esEs20(vyy350, vyy360)
new_esEs5(Left(vyy350), Left(vyy360), ty_@0, cgd) → new_esEs20(vyy350, vyy360)
new_lt4(vyy600, vyy50) → new_esEs9(new_compare6(vyy600, vyy50))
new_esEs26(vyy350, vyy360, ty_Bool) → new_esEs14(vyy350, vyy360)
new_esEs25(vyy351, vyy361, app(ty_Ratio, bfh)) → new_esEs16(vyy351, vyy361, bfh)
new_lt20(vyy600, vyy50, app(app(ty_Either, eg), eh)) → new_lt6(vyy600, vyy50, eg, eh)
new_compare14(Double(vyy600, vyy601), Double(vyy50, vyy51)) → new_compare9(new_sr0(vyy600, vyy50), new_sr0(vyy601, vyy51))
new_not0 → True
new_compare0(:(vyy600, vyy601), [], bdb) → GT
new_esEs24(vyy352, vyy362, app(ty_[], beg)) → new_esEs17(vyy352, vyy362, beg)
new_ltEs19(vyy602, vyy52, app(app(app(ty_@3, dca), dcb), dcc)) → new_ltEs6(vyy602, vyy52, dca, dcb, dcc)
new_lt20(vyy600, vyy50, app(app(app(ty_@3, hb), hc), hd)) → new_lt7(vyy600, vyy50, hb, hc, hd)
new_lt20(vyy600, vyy50, ty_Ordering) → new_lt18(vyy600, vyy50)
new_esEs26(vyy350, vyy360, app(app(ty_Either, bhe), bhf)) → new_esEs5(vyy350, vyy360, bhe, bhf)
new_esEs27(vyy351, vyy361, app(app(ty_FiniteMap, caf), cag)) → new_esEs11(vyy351, vyy361, caf, cag)
new_ltEs20(vyy60, vyy5, app(ty_Maybe, dd)) → new_ltEs5(vyy60, vyy5, dd)
new_compare11(vyy600, vyy50, False, eg, eh) → GT
new_primCmpInt(Pos(Succ(vyy6000)), Neg(vyy50)) → GT
new_esEs28(vyy350, vyy360, app(ty_Maybe, cdb)) → new_esEs7(vyy350, vyy360, cdb)
new_esEs21(vyy350, vyy360, app(ty_Maybe, gf)) → new_esEs7(vyy350, vyy360, gf)
new_esEs5(Left(vyy350), Left(vyy360), ty_Ordering, cgd) → new_esEs10(vyy350, vyy360)
new_primMulInt(Pos(vyy6010), Pos(vyy510)) → Pos(new_primMulNat0(vyy6010, vyy510))
new_compare7(:%(vyy600, vyy601), :%(vyy50, vyy51), ty_Integer) → new_compare8(new_sr(vyy600, vyy51), new_sr(vyy50, vyy601))
new_esEs5(Right(vyy350), Left(vyy360), daa, cgd) → False
new_esEs5(Left(vyy350), Right(vyy360), daa, cgd) → False
new_primMulInt(Neg(vyy6010), Neg(vyy510)) → Pos(new_primMulNat0(vyy6010, vyy510))
new_esEs18(Double(vyy350, vyy351), Double(vyy360, vyy361)) → new_esEs19(new_sr0(vyy350, vyy360), new_sr0(vyy351, vyy361))
new_esEs29(vyy35, vyy36, ty_Char) → new_esEs15(vyy35, vyy36)
new_ltEs4(Right(vyy600), Right(vyy50), bce, app(app(ty_@2, cfh), cga)) → new_ltEs10(vyy600, vyy50, cfh, cga)
new_primEqNat0(Succ(vyy3500), Zero) → False
new_primEqNat0(Zero, Succ(vyy3600)) → False
new_ltEs5(Nothing, Nothing, dd) → True
new_compare31(vyy600, vyy50, ty_Integer) → new_compare8(vyy600, vyy50)
new_compare25(vyy600, vyy50, True, fa, fb) → EQ
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs28(vyy350, vyy360, app(app(app(ty_@3, cdc), cdd), cde)) → new_esEs6(vyy350, vyy360, cdc, cdd, cde)
new_ltEs18(vyy601, vyy51, ty_@0) → new_ltEs7(vyy601, vyy51)
new_esEs27(vyy351, vyy361, app(app(app(ty_@3, cbg), cbh), cca)) → new_esEs6(vyy351, vyy361, cbg, cbh, cca)
new_sizeFM(Branch(vyy350, vyy351, vyy352, vyy353, vyy354), bcc, bcd) → vyy352
new_pePe(True, vyy35, vyy36, vyy52, dbf) → True
new_ltEs4(Left(vyy600), Left(vyy50), ty_Integer, bcf) → new_ltEs14(vyy600, vyy50)
new_foldFM2(Branch(vyy350, vyy351, vyy352, vyy353, vyy354), bcc, bcd) → new_foldFM0(vyy350, vyy351, new_foldFM2(vyy354, bcc, bcd), vyy353, bcc, bcd)
new_ltEs4(Right(vyy600), Right(vyy50), bce, app(ty_Ratio, cgc)) → new_ltEs15(vyy600, vyy50, cgc)
new_ltEs19(vyy602, vyy52, app(ty_Maybe, dcd)) → new_ltEs5(vyy602, vyy52, dcd)
new_lt9(vyy600, vyy50, bdd) → new_esEs9(new_compare28(vyy600, vyy50, bdd))
new_esEs7(Just(vyy350), Just(vyy360), ty_Float) → new_esEs12(vyy350, vyy360)
new_compare23(vyy600, vyy50, True, eg, eh) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(vyy500))) → new_primCmpNat0(Succ(vyy500), Zero)
new_ltEs4(Right(vyy600), Right(vyy50), bce, ty_@0) → new_ltEs7(vyy600, vyy50)
new_primCmpInt(Pos(Zero), Neg(Succ(vyy500))) → GT
new_compare28(vyy600, vyy50, bdd) → new_compare26(vyy600, vyy50, new_esEs7(vyy600, vyy50, bdd), bdd)
new_esEs5(Right(vyy350), Right(vyy360), daa, ty_Double) → new_esEs18(vyy350, vyy360)
new_compare110(vyy600, vyy50, False, bdd) → GT
new_esEs5(Left(vyy350), Left(vyy360), ty_Integer, cgd) → new_esEs13(vyy350, vyy360)
new_compare0(:(vyy600, vyy601), :(vyy50, vyy51), bdb) → new_primCompAux1(vyy600, vyy50, new_compare0(vyy601, vyy51, bdb), bdb)
new_ltEs4(Left(vyy600), Left(vyy50), ty_@0, bcf) → new_ltEs7(vyy600, vyy50)
new_lt20(vyy600, vyy50, app(ty_Maybe, bdd)) → new_lt9(vyy600, vyy50, bdd)
new_sr0(vyy601, vyy51) → new_primMulInt(vyy601, vyy51)
new_compare31(vyy600, vyy50, app(ty_Ratio, dfd)) → new_compare7(vyy600, vyy50, dfd)
new_esEs21(vyy350, vyy360, ty_Float) → new_esEs12(vyy350, vyy360)
new_esEs29(vyy35, vyy36, ty_Int) → new_esEs19(vyy35, vyy36)
new_esEs7(Just(vyy350), Just(vyy360), ty_Char) → new_esEs15(vyy350, vyy360)
new_esEs25(vyy351, vyy361, app(ty_Maybe, bgd)) → new_esEs7(vyy351, vyy361, bgd)
new_esEs7(Just(vyy350), Just(vyy360), app(app(app(ty_@3, da), db), dc)) → new_esEs6(vyy350, vyy360, da, db, dc)
new_ltEs20(vyy60, vyy5, ty_Ordering) → new_ltEs17(vyy60, vyy5)
new_ltEs9(vyy60, vyy5) → new_not(new_compare14(vyy60, vyy5))
new_esEs19(vyy35, vyy36) → new_primEqInt(vyy35, vyy36)
new_esEs27(vyy351, vyy361, ty_Double) → new_esEs18(vyy351, vyy361)
new_lt11(vyy600, vyy50, fa, fb) → new_esEs9(new_compare29(vyy600, vyy50, fa, fb))
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCompAux1(vyy600, vyy50, vyy62, bdb) → new_primCompAux0(vyy62, new_compare31(vyy600, vyy50, bdb))
new_lt19(vyy601, vyy51, ty_Bool) → new_lt14(vyy601, vyy51)
new_lt7(vyy600, vyy50, hb, hc, hd) → new_esEs9(new_compare18(vyy600, vyy50, hb, hc, hd))
new_ltEs15(vyy60, vyy5, fc) → new_not(new_compare7(vyy60, vyy5, fc))
new_asAs(False, vyy61) → False
new_esEs5(Left(vyy350), Left(vyy360), ty_Float, cgd) → new_esEs12(vyy350, vyy360)
new_ltEs4(Right(vyy600), Right(vyy50), bce, ty_Ordering) → new_ltEs17(vyy600, vyy50)
new_primMulInt(Pos(vyy6010), Neg(vyy510)) → Neg(new_primMulNat0(vyy6010, vyy510))
new_primMulInt(Neg(vyy6010), Pos(vyy510)) → Neg(new_primMulNat0(vyy6010, vyy510))
new_ltEs20(vyy60, vyy5, app(ty_[], bdb)) → new_ltEs11(vyy60, vyy5, bdb)
new_primMulNat0(Zero, Succ(vyy5100)) → Zero
new_primMulNat0(Succ(vyy60100), Zero) → Zero
new_esEs7(Just(vyy350), Just(vyy360), ty_Double) → new_esEs18(vyy350, vyy360)
new_esEs21(vyy350, vyy360, app(app(ty_Either, gc), gd)) → new_esEs5(vyy350, vyy360, gc, gd)
new_esEs26(vyy350, vyy360, ty_Integer) → new_esEs13(vyy350, vyy360)
new_lt19(vyy601, vyy51, ty_Ordering) → new_lt18(vyy601, vyy51)
new_esEs5(Left(vyy350), Left(vyy360), app(app(app(ty_@3, chf), chg), chh), cgd) → new_esEs6(vyy350, vyy360, chf, chg, chh)
new_ltEs4(Right(vyy600), Right(vyy50), bce, ty_Int) → new_ltEs16(vyy600, vyy50)
new_esEs25(vyy351, vyy361, ty_Ordering) → new_esEs10(vyy351, vyy361)
new_esEs10(GT, GT) → True
new_esEs26(vyy350, vyy360, app(ty_Maybe, bhh)) → new_esEs7(vyy350, vyy360, bhh)
new_esEs17(:(vyy350, vyy351), :(vyy360, vyy361), fd) → new_asAs(new_esEs21(vyy350, vyy360, fd), new_esEs17(vyy351, vyy361, fd))
new_lt19(vyy601, vyy51, ty_Float) → new_lt8(vyy601, vyy51)
new_esEs28(vyy350, vyy360, ty_Bool) → new_esEs14(vyy350, vyy360)
new_esEs5(Right(vyy350), Right(vyy360), daa, ty_Integer) → new_esEs13(vyy350, vyy360)
new_ltEs5(Just(vyy600), Just(vyy50), app(ty_Maybe, eb)) → new_ltEs5(vyy600, vyy50, eb)
new_esEs28(vyy350, vyy360, ty_Double) → new_esEs18(vyy350, vyy360)
new_not(EQ) → new_not0
new_lt20(vyy600, vyy50, ty_Float) → new_lt8(vyy600, vyy50)
new_ltEs20(vyy60, vyy5, ty_Bool) → new_ltEs13(vyy60, vyy5)
new_esEs25(vyy351, vyy361, ty_Integer) → new_esEs13(vyy351, vyy361)
new_compare31(vyy600, vyy50, app(ty_[], dfc)) → new_compare0(vyy600, vyy50, dfc)
new_esEs29(vyy35, vyy36, app(ty_Ratio, bdc)) → new_esEs16(vyy35, vyy36, bdc)
new_esEs5(Right(vyy350), Right(vyy360), daa, ty_Int) → new_esEs19(vyy350, vyy360)
new_esEs25(vyy351, vyy361, app(ty_[], bgc)) → new_esEs17(vyy351, vyy361, bgc)
new_ltEs18(vyy601, vyy51, ty_Char) → new_ltEs12(vyy601, vyy51)
new_esEs25(vyy351, vyy361, app(app(app(ty_@3, bge), bgf), bgg)) → new_esEs6(vyy351, vyy361, bge, bgf, bgg)
new_esEs28(vyy350, vyy360, ty_Integer) → new_esEs13(vyy350, vyy360)
new_lt14(vyy600, vyy50) → new_esEs9(new_compare16(vyy600, vyy50))
new_ltEs17(GT, GT) → True
new_ltEs5(Just(vyy600), Just(vyy50), ty_Integer) → new_ltEs14(vyy600, vyy50)
new_compare27(vyy600, vyy50, True) → EQ
new_esEs14(True, True) → True
new_esEs29(vyy35, vyy36, ty_Ordering) → new_esEs10(vyy35, vyy36)
new_ltEs19(vyy602, vyy52, ty_Int) → new_ltEs16(vyy602, vyy52)
new_esEs27(vyy351, vyy361, ty_Bool) → new_esEs14(vyy351, vyy361)
new_esEs21(vyy350, vyy360, app(ty_Ratio, gb)) → new_esEs16(vyy350, vyy360, gb)
new_ltEs17(GT, EQ) → False
new_ltEs5(Just(vyy600), Just(vyy50), ty_Char) → new_ltEs12(vyy600, vyy50)
new_lt19(vyy601, vyy51, app(app(app(ty_@3, ddc), ddd), dde)) → new_lt7(vyy601, vyy51, ddc, ddd, dde)
new_esEs28(vyy350, vyy360, app(ty_[], cda)) → new_esEs17(vyy350, vyy360, cda)
new_esEs7(Just(vyy350), Just(vyy360), app(ty_Ratio, cc)) → new_esEs16(vyy350, vyy360, cc)
new_ltEs13(True, True) → True
new_esEs5(Left(vyy350), Left(vyy360), app(ty_Ratio, cha), cgd) → new_esEs16(vyy350, vyy360, cha)
new_esEs27(vyy351, vyy361, ty_Ordering) → new_esEs10(vyy351, vyy361)
new_esEs7(Just(vyy350), Just(vyy360), app(ty_[], cf)) → new_esEs17(vyy350, vyy360, cf)
new_ltEs13(False, False) → True
new_ltEs14(vyy60, vyy5) → new_not(new_compare8(vyy60, vyy5))
new_esEs7(Just(vyy350), Just(vyy360), ty_Integer) → new_esEs13(vyy350, vyy360)
new_esEs25(vyy351, vyy361, ty_Char) → new_esEs15(vyy351, vyy361)
new_esEs5(Right(vyy350), Right(vyy360), daa, ty_Bool) → new_esEs14(vyy350, vyy360)
new_esEs22(vyy351, vyy361, ty_Int) → new_esEs19(vyy351, vyy361)
new_ltEs18(vyy601, vyy51, ty_Bool) → new_ltEs13(vyy601, vyy51)
new_esEs5(Left(vyy350), Left(vyy360), app(app(ty_FiniteMap, cge), cgf), cgd) → new_esEs11(vyy350, vyy360, cge, cgf)
new_not(LT) → new_not0
new_esEs26(vyy350, vyy360, ty_Int) → new_esEs19(vyy350, vyy360)
new_esEs25(vyy351, vyy361, ty_Double) → new_esEs18(vyy351, vyy361)
new_lt20(vyy600, vyy50, ty_Integer) → new_lt15(vyy600, vyy50)
new_esEs5(Left(vyy350), Left(vyy360), app(app(ty_Either, chb), chc), cgd) → new_esEs5(vyy350, vyy360, chb, chc)
new_ltEs5(Just(vyy600), Just(vyy50), app(app(ty_Either, de), df)) → new_ltEs4(vyy600, vyy50, de, df)
new_esEs29(vyy35, vyy36, app(app(app(ty_@3, bde), bdf), bdg)) → new_esEs6(vyy35, vyy36, bde, bdf, bdg)
new_esEs14(False, False) → True
new_esEs10(LT, GT) → False
new_esEs10(GT, LT) → False
new_esEs7(Just(vyy350), Just(vyy360), app(app(ty_FiniteMap, bg), bh)) → new_esEs11(vyy350, vyy360, bg, bh)
new_esEs10(LT, EQ) → False
new_esEs10(EQ, LT) → False
new_compare31(vyy600, vyy50, ty_Float) → new_compare15(vyy600, vyy50)
new_esEs28(vyy350, vyy360, app(app(ty_@2, ccd), cce)) → new_esEs8(vyy350, vyy360, ccd, cce)
new_compare31(vyy600, vyy50, ty_Bool) → new_compare16(vyy600, vyy50)
new_primPlusNat1(Zero, Zero) → Zero
new_compare0([], :(vyy50, vyy51), bdb) → LT
new_esEs21(vyy350, vyy360, app(app(app(ty_@3, gg), gh), ha)) → new_esEs6(vyy350, vyy360, gg, gh, ha)
new_esEs5(Left(vyy350), Left(vyy360), app(ty_[], chd), cgd) → new_esEs17(vyy350, vyy360, chd)
new_asAs(True, vyy61) → vyy61
new_lt8(vyy600, vyy50) → new_esEs9(new_compare15(vyy600, vyy50))
new_lt15(vyy600, vyy50) → new_esEs9(new_compare8(vyy600, vyy50))
new_primMulNat0(Succ(vyy60100), Succ(vyy5100)) → new_primPlusNat0(new_primMulNat0(vyy60100, Succ(vyy5100)), vyy5100)
new_ltEs17(LT, EQ) → True
new_compare30(Char(vyy600), Char(vyy50)) → new_primCmpNat0(vyy600, vyy50)
new_esEs29(vyy35, vyy36, ty_Float) → new_esEs12(vyy35, vyy36)
new_compare31(vyy600, vyy50, ty_Int) → new_compare9(vyy600, vyy50)
new_esEs24(vyy352, vyy362, ty_Int) → new_esEs19(vyy352, vyy362)
new_esEs17([], [], fd) → True
new_esEs17([], :(vyy360, vyy361), fd) → False
new_esEs17(:(vyy350, vyy351), [], fd) → False
new_esEs7(Just(vyy350), Just(vyy360), ty_Bool) → new_esEs14(vyy350, vyy360)
new_fmToList(vyy35, bcc, bcd) → new_foldFM2(vyy35, bcc, bcd)
new_lt19(vyy601, vyy51, ty_Int) → new_lt17(vyy601, vyy51)
new_esEs29(vyy35, vyy36, app(app(ty_FiniteMap, bcc), bcd)) → new_esEs11(vyy35, vyy36, bcc, bcd)
new_esEs24(vyy352, vyy362, app(app(ty_@2, beb), bec)) → new_esEs8(vyy352, vyy362, beb, bec)
new_compare10(vyy600, vyy50, True) → LT
new_esEs26(vyy350, vyy360, ty_@0) → new_esEs20(vyy350, vyy360)
new_esEs29(vyy35, vyy36, ty_Bool) → new_esEs14(vyy35, vyy36)
new_ltEs17(EQ, GT) → True
new_lt19(vyy601, vyy51, app(app(ty_Either, dda), ddb)) → new_lt6(vyy601, vyy51, dda, ddb)
new_compare13(vyy600, vyy50, True, hb, hc, hd) → LT
new_lt5(vyy600, vyy50, ty_Bool) → new_lt14(vyy600, vyy50)
new_esEs5(Right(vyy350), Right(vyy360), daa, ty_Float) → new_esEs12(vyy350, vyy360)
new_compare10(vyy600, vyy50, False) → GT
new_esEs25(vyy351, vyy361, ty_@0) → new_esEs20(vyy351, vyy361)
new_lt20(vyy600, vyy50, ty_Double) → new_lt10(vyy600, vyy50)
new_ltEs18(vyy601, vyy51, ty_Double) → new_ltEs9(vyy601, vyy51)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCompAux0(vyy66, EQ) → vyy66
new_ltEs20(vyy60, vyy5, app(app(ty_@2, he), hf)) → new_ltEs10(vyy60, vyy5, he, hf)
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_esEs5(Right(vyy350), Right(vyy360), daa, app(ty_Maybe, dbb)) → new_esEs7(vyy350, vyy360, dbb)
new_primCmpInt(Neg(Succ(vyy6000)), Pos(vyy50)) → LT
new_esEs24(vyy352, vyy362, ty_@0) → new_esEs20(vyy352, vyy362)
new_ltEs5(Just(vyy600), Just(vyy50), app(ty_[], ee)) → new_ltEs11(vyy600, vyy50, ee)
new_ltEs12(vyy60, vyy5) → new_not(new_compare30(vyy60, vyy5))
new_compare27(vyy600, vyy50, False) → new_compare111(vyy600, vyy50, new_ltEs17(vyy600, vyy50))
new_esEs5(Right(vyy350), Right(vyy360), daa, app(ty_[], dba)) → new_esEs17(vyy350, vyy360, dba)
The set Q consists of the following terms:
new_lt19(x0, x1, ty_Int)
new_compare10(x0, x1, True)
new_ltEs5(Just(x0), Just(x1), ty_Bool)
new_ltEs19(x0, x1, ty_Int)
new_ltEs5(Just(x0), Just(x1), ty_Ordering)
new_esEs25(x0, x1, ty_Int)
new_compare13(x0, x1, True, x2, x3, x4)
new_ltEs18(x0, x1, app(app(ty_@2, x2), x3))
new_esEs5(Left(x0), Left(x1), ty_Float, x2)
new_esEs6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs28(x0, x1, ty_Bool)
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs5(Right(x0), Right(x1), x2, ty_Double)
new_esEs7(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs7(Just(x0), Just(x1), ty_Char)
new_esEs5(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_compare110(x0, x1, True, x2)
new_ltEs4(Left(x0), Left(x1), ty_Float, x2)
new_lt5(x0, x1, ty_Double)
new_compare31(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primPlusNat0(Succ(x0), x1)
new_ltEs5(Just(x0), Just(x1), ty_Int)
new_esEs23(x0, x1, ty_Int)
new_esEs23(x0, x1, ty_Integer)
new_foldFM0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_ltEs4(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs9(EQ)
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs17(EQ, GT)
new_ltEs17(GT, EQ)
new_esEs27(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_ltEs20(x0, x1, ty_Bool)
new_primCmpNat0(Zero, Succ(x0))
new_esEs21(x0, x1, ty_Double)
new_esEs27(x0, x1, app(ty_[], x2))
new_esEs15(Char(x0), Char(x1))
new_lt20(x0, x1, ty_Char)
new_ltEs20(x0, x1, ty_Ordering)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_esEs10(EQ, GT)
new_esEs10(GT, EQ)
new_esEs5(Left(x0), Left(x1), app(app(ty_FiniteMap, x2), x3), x4)
new_ltEs15(x0, x1, x2)
new_ltEs8(x0, x1)
new_esEs26(x0, x1, ty_Char)
new_esEs10(LT, EQ)
new_esEs10(EQ, LT)
new_compare31(x0, x1, ty_Integer)
new_esEs17([], [], x0)
new_lt8(x0, x1)
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare31(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_ltEs5(Just(x0), Just(x1), ty_Integer)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_ltEs20(x0, x1, ty_Integer)
new_compare11(x0, x1, True, x2, x3)
new_ltEs18(x0, x1, app(app(ty_Either, x2), x3))
new_compare0([], :(x0, x1), x2)
new_esEs28(x0, x1, ty_Integer)
new_compare7(:%(x0, x1), :%(x2, x3), ty_Integer)
new_compare24(x0, x1, True)
new_esEs5(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_ltEs5(Nothing, Nothing, x0)
new_esEs27(x0, x1, ty_Double)
new_esEs27(x0, x1, ty_Float)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_compare12(x0, x1, True, x2, x3)
new_compare23(x0, x1, True, x2, x3)
new_ltEs4(Left(x0), Left(x1), ty_Char, x2)
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs7(Just(x0), Just(x1), ty_Integer)
new_compare16(x0, x1)
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_lt15(x0, x1)
new_ltEs5(Just(x0), Just(x1), ty_Float)
new_esEs29(x0, x1, ty_Integer)
new_esEs26(x0, x1, app(ty_[], x2))
new_ltEs4(Left(x0), Left(x1), ty_Integer, x2)
new_compare30(Char(x0), Char(x1))
new_ltEs4(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_lt5(x0, x1, ty_Float)
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_esEs7(Just(x0), Just(x1), ty_Double)
new_ltEs20(x0, x1, ty_Char)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_ltEs4(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs21(x0, x1, ty_Int)
new_esEs14(True, True)
new_ltEs4(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs7(Just(x0), Just(x1), app(ty_[], x2))
new_compare13(x0, x1, False, x2, x3, x4)
new_esEs11(x0, x1, x2, x3)
new_primEqNat0(Zero, Zero)
new_sr(Integer(x0), Integer(x1))
new_ltEs5(Nothing, Just(x0), x1)
new_ltEs5(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_compare11(x0, x1, False, x2, x3)
new_esEs29(x0, x1, app(ty_[], x2))
new_lt13(x0, x1)
new_ltEs19(x0, x1, app(ty_[], x2))
new_lt5(x0, x1, ty_Bool)
new_esEs7(Just(x0), Just(x1), ty_@0)
new_ltEs4(Left(x0), Right(x1), x2, x3)
new_ltEs4(Right(x0), Left(x1), x2, x3)
new_ltEs18(x0, x1, ty_Bool)
new_ltEs4(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_ltEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt6(x0, x1, x2, x3)
new_compare31(x0, x1, ty_Int)
new_esEs5(Left(x0), Left(x1), ty_Char, x2)
new_esEs17(:(x0, x1), :(x2, x3), x4)
new_primCmpNat0(Succ(x0), Zero)
new_esEs29(x0, x1, ty_Float)
new_primMulNat0(Zero, Zero)
new_esEs29(x0, x1, ty_Char)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_lt5(x0, x1, ty_@0)
new_esEs25(x0, x1, ty_Integer)
new_esEs24(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_ltEs19(x0, x1, ty_Char)
new_compare29(x0, x1, x2, x3)
new_esEs25(x0, x1, ty_Double)
new_primCompAux0(x0, GT)
new_primCompAux1(x0, x1, x2, x3)
new_ltEs5(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_compare0([], [], x0)
new_foldFM2(EmptyFM, x0, x1)
new_ltEs14(x0, x1)
new_esEs7(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs26(x0, x1, ty_Ordering)
new_esEs17(:(x0, x1), [], x2)
new_ltEs4(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_pePe(True, x0, x1, x2, x3)
new_esEs24(x0, x1, ty_Integer)
new_esEs28(x0, x1, ty_@0)
new_compare31(x0, x1, app(app(ty_@2, x2), x3))
new_esEs10(LT, GT)
new_esEs10(GT, LT)
new_primCmpNat0(Succ(x0), Succ(x1))
new_lt11(x0, x1, x2, x3)
new_esEs21(x0, x1, ty_Bool)
new_lt20(x0, x1, ty_Bool)
new_esEs5(Right(x0), Right(x1), x2, ty_Bool)
new_esEs27(x0, x1, ty_Int)
new_esEs5(Left(x0), Right(x1), x2, x3)
new_esEs5(Right(x0), Left(x1), x2, x3)
new_primPlusNat0(Zero, x0)
new_primCompAux0(x0, EQ)
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_compare26(x0, x1, False, x2)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs24(x0, x1, ty_Ordering)
new_esEs7(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_compare210(x0, x1, True, x2, x3, x4)
new_esEs25(x0, x1, ty_Ordering)
new_lt20(x0, x1, app(ty_[], x2))
new_ltEs5(Just(x0), Just(x1), ty_@0)
new_primCompAux0(x0, LT)
new_ltEs5(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs7(Just(x0), Just(x1), ty_Ordering)
new_esEs5(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs5(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs4(Right(x0), Right(x1), x2, ty_Int)
new_lt18(x0, x1)
new_compare14(Double(x0, x1), Double(x2, x3))
new_esEs24(x0, x1, ty_@0)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt12(x0, x1, x2)
new_foldFM2(Branch(x0, x1, x2, x3, x4), x5, x6)
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, app(ty_Ratio, x2))
new_primEqNat0(Zero, Succ(x0))
new_ltEs20(x0, x1, ty_Int)
new_esEs5(Left(x0), Left(x1), ty_Integer, x2)
new_compare25(x0, x1, False, x2, x3)
new_ltEs20(x0, x1, ty_Double)
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_esEs22(x0, x1, ty_Int)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_compare17(x0, x1, x2, x3)
new_esEs27(x0, x1, ty_Integer)
new_esEs25(x0, x1, ty_Char)
new_ltEs18(x0, x1, ty_Float)
new_compare31(x0, x1, ty_Char)
new_esEs25(x0, x1, ty_Float)
new_ltEs4(Right(x0), Right(x1), x2, ty_@0)
new_primPlusNat1(Zero, Zero)
new_ltEs13(True, True)
new_not0
new_esEs29(x0, x1, ty_@0)
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_compare27(x0, x1, True)
new_esEs5(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_fmToList(x0, x1, x2)
new_esEs9(GT)
new_compare9(x0, x1)
new_esEs13(Integer(x0), Integer(x1))
new_compare111(x0, x1, True)
new_ltEs5(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, ty_Ordering)
new_esEs10(EQ, EQ)
new_esEs27(x0, x1, ty_Char)
new_ltEs19(x0, x1, ty_Float)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_lt19(x0, x1, ty_Bool)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_ltEs13(False, False)
new_esEs28(x0, x1, ty_Int)
new_lt19(x0, x1, app(ty_Maybe, x2))
new_esEs5(Right(x0), Right(x1), x2, app(app(ty_FiniteMap, x3), x4))
new_lt5(x0, x1, ty_Integer)
new_esEs5(Left(x0), Left(x1), app(ty_[], x2), x3)
new_ltEs13(False, True)
new_ltEs13(True, False)
new_ltEs4(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs12(Float(x0, x1), Float(x2, x3))
new_esEs27(x0, x1, ty_Bool)
new_ltEs4(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs25(x0, x1, ty_Bool)
new_compare0(:(x0, x1), :(x2, x3), x4)
new_ltEs18(x0, x1, ty_@0)
new_esEs24(x0, x1, ty_Int)
new_esEs5(Right(x0), Right(x1), x2, ty_Char)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_ltEs20(x0, x1, ty_@0)
new_compare31(x0, x1, app(ty_Maybe, x2))
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, ty_Int)
new_ltEs5(Just(x0), Nothing, x1)
new_ltEs4(Left(x0), Left(x1), ty_Bool, x2)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_not(GT)
new_esEs21(x0, x1, ty_Float)
new_lt19(x0, x1, ty_Char)
new_lt17(x0, x1)
new_lt20(x0, x1, ty_Integer)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_esEs5(Right(x0), Right(x1), x2, ty_Float)
new_lt19(x0, x1, app(ty_Ratio, x2))
new_esEs29(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_ltEs17(GT, GT)
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_compare27(x0, x1, False)
new_lt5(x0, x1, ty_Ordering)
new_asAs(False, x0)
new_esEs26(x0, x1, ty_Float)
new_lt5(x0, x1, app(ty_Ratio, x2))
new_foldFM0(x0, x1, x2, EmptyFM, x3, x4)
new_primEqNat0(Succ(x0), Zero)
new_ltEs18(x0, x1, ty_Int)
new_esEs8(@2(x0, x1), @2(x2, x3), x4, x5)
new_asAs(True, x0)
new_esEs21(x0, x1, app(ty_[], x2))
new_compare25(x0, x1, True, x2, x3)
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_ltEs4(Left(x0), Left(x1), ty_@0, x2)
new_ltEs5(Just(x0), Just(x1), ty_Double)
new_esEs26(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_primMulNat0(Succ(x0), Succ(x1))
new_esEs26(x0, x1, ty_Double)
new_compare210(x0, x1, False, x2, x3, x4)
new_ltEs5(Just(x0), Just(x1), app(ty_[], x2))
new_compare18(x0, x1, x2, x3, x4)
new_lt7(x0, x1, x2, x3, x4)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_ltEs4(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs25(x0, x1, app(ty_[], x2))
new_primEqInt(Neg(Zero), Neg(Zero))
new_esEs5(Right(x0), Right(x1), x2, ty_@0)
new_compare110(x0, x1, False, x2)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_esEs14(False, True)
new_esEs14(True, False)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs26(x0, x1, ty_Integer)
new_compare8(Integer(x0), Integer(x1))
new_compare7(:%(x0, x1), :%(x2, x3), ty_Int)
new_esEs28(x0, x1, ty_Float)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_ltEs6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_lt10(x0, x1)
new_compare31(x0, x1, app(ty_Ratio, x2))
new_esEs10(LT, LT)
new_lt19(x0, x1, ty_Double)
new_ltEs18(x0, x1, ty_Ordering)
new_esEs24(x0, x1, ty_Double)
new_ltEs4(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs9(LT)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs4(Right(x0), Right(x1), x2, ty_Char)
new_lt20(x0, x1, ty_Ordering)
new_esEs18(Double(x0, x1), Double(x2, x3))
new_esEs29(x0, x1, ty_Ordering)
new_compare6(@0, @0)
new_ltEs18(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_compare31(x0, x1, app(ty_[], x2))
new_primPlusNat1(Succ(x0), Zero)
new_ltEs19(x0, x1, ty_@0)
new_esEs29(x0, x1, ty_Int)
new_compare31(x0, x1, ty_Ordering)
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs5(Just(x0), Just(x1), ty_Char)
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_esEs26(x0, x1, ty_@0)
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs7(Just(x0), Just(x1), ty_Bool)
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_primCmpNat0(Zero, Zero)
new_esEs5(Left(x0), Left(x1), ty_Int, x2)
new_compare26(x0, x1, True, x2)
new_ltEs4(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs21(x0, x1, ty_Char)
new_esEs21(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_esEs29(x0, x1, ty_Bool)
new_esEs24(x0, x1, ty_Char)
new_esEs7(Just(x0), Just(x1), ty_Float)
new_esEs28(x0, x1, app(app(ty_FiniteMap, x2), x3))
new_compare23(x0, x1, False, x2, x3)
new_compare0(:(x0, x1), [], x2)
new_esEs24(x0, x1, app(ty_[], x2))
new_esEs26(x0, x1, ty_Bool)
new_ltEs17(LT, GT)
new_esEs24(x0, x1, ty_Bool)
new_ltEs17(GT, LT)
new_esEs5(Right(x0), Right(x1), x2, ty_Int)
new_esEs5(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_ltEs9(x0, x1)
new_lt19(x0, x1, ty_Integer)
new_esEs22(x0, x1, ty_Integer)
new_lt20(x0, x1, ty_Float)
new_esEs5(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs7(Just(x0), Just(x1), ty_Int)
new_compare31(x0, x1, ty_Float)
new_esEs5(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs5(Left(x0), Left(x1), ty_@0, x2)
new_esEs16(:%(x0, x1), :%(x2, x3), x4)
new_lt5(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_sr0(x0, x1)
new_pePe(False, x0, x1, x2, x3)
new_esEs10(GT, GT)
new_ltEs4(Right(x0), Right(x1), x2, ty_Float)
new_esEs7(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_compare111(x0, x1, False)
new_ltEs19(x0, x1, ty_Double)
new_esEs7(Just(x0), Just(x1), app(ty_Maybe, x2))
new_compare24(x0, x1, False)
new_sizeFM(EmptyFM, x0, x1)
new_lt5(x0, x1, app(ty_Maybe, x2))
new_esEs21(x0, x1, ty_Integer)
new_ltEs4(Left(x0), Left(x1), ty_Int, x2)
new_esEs25(x0, x1, ty_@0)
new_esEs28(x0, x1, ty_Ordering)
new_primMulNat0(Zero, Succ(x0))
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_primMulInt(Neg(x0), Neg(x1))
new_lt19(x0, x1, ty_Float)
new_compare12(x0, x1, False, x2, x3)
new_not(EQ)
new_ltEs19(x0, x1, ty_Integer)
new_compare19(x0, x1)
new_lt14(x0, x1)
new_primMulNat0(Succ(x0), Zero)
new_compare15(Float(x0, x1), Float(x2, x3))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_esEs5(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_lt5(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs4(Left(x0), Left(x1), ty_Double, x2)
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, ty_Double)
new_compare10(x0, x1, False)
new_ltEs20(x0, x1, ty_Float)
new_esEs26(x0, x1, ty_Int)
new_lt5(x0, x1, ty_Int)
new_esEs5(Right(x0), Right(x1), x2, ty_Integer)
new_lt5(x0, x1, app(app(ty_@2, x2), x3))
new_compare28(x0, x1, x2)
new_lt19(x0, x1, ty_Ordering)
new_ltEs20(x0, x1, app(ty_[], x2))
new_esEs17([], :(x0, x1), x2)
new_lt20(x0, x1, ty_@0)
new_esEs19(x0, x1)
new_esEs21(x0, x1, ty_Ordering)
new_esEs7(Nothing, Nothing, x0)
new_esEs28(x0, x1, ty_Double)
new_ltEs18(x0, x1, ty_Char)
new_esEs24(x0, x1, ty_Float)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_esEs20(@0, @0)
new_lt9(x0, x1, x2)
new_ltEs4(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs21(x0, x1, ty_@0)
new_compare31(x0, x1, ty_Bool)
new_esEs27(x0, x1, ty_Ordering)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs7(Just(x0), Just(x1), app(app(ty_FiniteMap, x2), x3))
new_lt5(x0, x1, ty_Char)
new_ltEs4(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_ltEs12(x0, x1)
new_ltEs17(LT, EQ)
new_ltEs17(EQ, LT)
new_esEs5(Left(x0), Left(x1), ty_Bool, x2)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_lt5(x0, x1, app(ty_[], x2))
new_compare31(x0, x1, ty_@0)
new_ltEs4(Right(x0), Right(x1), x2, ty_Bool)
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_primMulInt(Pos(x0), Pos(x1))
new_esEs5(Left(x0), Left(x1), ty_Double, x2)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs19(x0, x1, ty_Bool)
new_ltEs4(Right(x0), Right(x1), x2, ty_Integer)
new_lt19(x0, x1, ty_@0)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs18(x0, x1, ty_Double)
new_esEs5(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs16(x0, x1)
new_lt4(x0, x1)
new_esEs5(Right(x0), Right(x1), x2, ty_Ordering)
new_ltEs4(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_primPlusNat1(Zero, Succ(x0))
new_lt16(x0, x1, x2)
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs14(False, False)
new_primEqInt(Pos(Zero), Pos(Zero))
new_ltEs10(@2(x0, x1), @2(x2, x3), x4, x5)
new_ltEs5(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs27(x0, x1, ty_@0)
new_lt19(x0, x1, app(ty_[], x2))
new_ltEs18(x0, x1, app(ty_Ratio, x2))
new_compare31(x0, x1, ty_Double)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs28(x0, x1, ty_Char)
new_esEs5(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs7(Nothing, Just(x0), x1)
new_ltEs7(x0, x1)
new_esEs29(x0, x1, ty_Double)
new_esEs7(Just(x0), Nothing, x1)
new_ltEs17(EQ, EQ)
new_ltEs17(LT, LT)
new_ltEs18(x0, x1, ty_Integer)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs28(x0, x1, app(ty_[], x2))
new_not(LT)
new_ltEs18(x0, x1, app(ty_[], x2))
new_ltEs11(x0, x1, x2)
new_ltEs4(Right(x0), Right(x1), x2, ty_Double)
new_esEs5(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_ltEs20(x0, x1, app(ty_Maybe, x2))
We have to consider all minimal (P,Q,R)-chains.
By using the subterm criterion [20] together with the size-change analysis [32] we have proven that there are no infinite chains for this DP problem. From the DPs we obtained the following set of size-change graphs:
- new_foldFM_LE(vyy3, vyy5, Branch(vyy60, vyy61, vyy62, vyy63, vyy64), bc, bd, be) → new_foldFM_LE1(vyy3, vyy5, vyy60, vyy61, vyy62, vyy63, vyy64, new_ltEs20(vyy60, vyy5, bd), bc, bd, be)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 3 > 4, 3 > 5, 3 > 6, 3 > 7, 4 >= 9, 5 >= 10, 6 >= 11
- new_foldFM_LE1(vyy17, vyy19, vyy20, vyy21, vyy22, vyy23, vyy24, True, h, ba, bb) → new_foldFM_LE(vyy17, vyy19, vyy24, h, ba, bb)
The graph contains the following edges 1 >= 1, 2 >= 2, 7 >= 3, 9 >= 4, 10 >= 5, 11 >= 6
- new_foldFM_LE1(vyy17, vyy19, vyy20, vyy21, vyy22, vyy23, vyy24, True, h, ba, bb) → new_foldFM_LE(vyy17, vyy19, vyy23, h, ba, bb)
The graph contains the following edges 1 >= 1, 2 >= 2, 6 >= 3, 9 >= 4, 10 >= 5, 11 >= 6
- new_foldFM_LE1(vyy17, vyy19, vyy20, vyy21, vyy22, vyy23, vyy24, False, h, ba, bb) → new_foldFM_LE(vyy17, vyy19, vyy23, h, ba, bb)
The graph contains the following edges 1 >= 1, 2 >= 2, 6 >= 3, 9 >= 4, 10 >= 5, 11 >= 6