YES 0.8220000000000001
H-Termination proof of /home/matraf/haskell/eval_FullyBlown_Fast/Monad.hs
H-Termination of the given Haskell-Program with start terms could successfully be proven:
↳ HASKELL
↳ LR
mainModule Monad
| ((zipWithM_ :: (a -> c -> [b]) -> [a] -> [c] -> [()]) :: (a -> c -> [b]) -> [a] -> [c] -> [()]) |
module Monad where
| import qualified Maybe import qualified Prelude
|
| zipWithM_ :: Monad c => (d -> b -> c a) -> [d] -> [b] -> c ()
zipWithM_ | f xs ys | = | sequence_ (zipWith f xs ys) |
|
module Maybe where
| import qualified Monad import qualified Prelude
|
Lambda Reductions:
The following Lambda expression
\_→q
is transformed to
↳ HASKELL
↳ LR
↳ HASKELL
↳ BR
mainModule Monad
| ((zipWithM_ :: (c -> b -> [a]) -> [c] -> [b] -> [()]) :: (c -> b -> [a]) -> [c] -> [b] -> [()]) |
module Maybe where
| import qualified Monad import qualified Prelude
|
module Monad where
| import qualified Maybe import qualified Prelude
|
| zipWithM_ :: Monad c => (b -> d -> c a) -> [b] -> [d] -> c ()
zipWithM_ | f xs ys | = | sequence_ (zipWith f xs ys) |
|
Replaced joker patterns by fresh variables and removed binding patterns.
↳ HASKELL
↳ LR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
mainModule Monad
| ((zipWithM_ :: (b -> a -> [c]) -> [b] -> [a] -> [()]) :: (b -> a -> [c]) -> [b] -> [a] -> [()]) |
module Monad where
| import qualified Maybe import qualified Prelude
|
| zipWithM_ :: Monad a => (c -> d -> a b) -> [c] -> [d] -> a ()
zipWithM_ | f xs ys | = | sequence_ (zipWith f xs ys) |
|
module Maybe where
| import qualified Monad import qualified Prelude
|
Cond Reductions:
The following Function with conditions
is transformed to
undefined0 | True | = undefined |
undefined1 | | = undefined0 False |
↳ HASKELL
↳ LR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ Narrow
mainModule Monad
| (zipWithM_ :: (c -> b -> [a]) -> [c] -> [b] -> [()]) |
module Maybe where
| import qualified Monad import qualified Prelude
|
module Monad where
| import qualified Maybe import qualified Prelude
|
| zipWithM_ :: Monad d => (c -> a -> d b) -> [c] -> [a] -> d ()
zipWithM_ | f xs ys | = | sequence_ (zipWith f xs ys) |
|
Haskell To QDPs
↳ HASKELL
↳ LR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDPSizeChangeProof
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_psPs(:(ww60, ww61), ww9) → new_psPs(ww61, ww9)
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_psPs(:(ww60, ww61), ww9) → new_psPs(ww61, ww9)
The graph contains the following edges 1 > 1, 2 >= 2
↳ HASKELL
↳ LR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDPSizeChangeProof
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_gtGtEs(:(ww80, ww81), ww6, h) → new_gtGtEs(ww81, ww6, h)
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_gtGtEs(:(ww80, ww81), ww6, h) → new_gtGtEs(ww81, ww6, h)
The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3
↳ HASKELL
↳ LR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDPSizeChangeProof
Q DP problem:
The TRS P consists of the following rules:
new_foldr(ww3, :(ww40, ww41), :(ww50, ww51), h, ba, bb) → new_foldr(ww3, ww41, ww51, h, ba, bb)
R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By using the subterm criterion [20] together with the size-change analysis [32] we have proven that there are no infinite chains for this DP problem. From the DPs we obtained the following set of size-change graphs:
- new_foldr(ww3, :(ww40, ww41), :(ww50, ww51), h, ba, bb) → new_foldr(ww3, ww41, ww51, h, ba, bb)
The graph contains the following edges 1 >= 1, 2 > 2, 3 > 3, 4 >= 4, 5 >= 5, 6 >= 6