YES 0.727
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 :: (c -> a -> IO b) -> [c] -> [a] -> IO [b]) :: (c -> a -> IO b) -> [c] -> [a] -> IO [b]) |
module Monad where
| import qualified Maybe import qualified Prelude
|
| zipWithM :: Monad b => (c -> a -> b d) -> [c] -> [a] -> b [d]
zipWithM | f xs ys | = | sequence (zipWith f xs ys) |
|
module Maybe where
| import qualified Monad import qualified Prelude
|
Lambda Reductions:
The following Lambda expression
\xs→return (x : xs)
is transformed to
sequence0 | x xs | = return (x : xs) |
The following Lambda expression
\x→sequence cs >>= sequence0 x
is transformed to
sequence1 | cs x | = sequence cs >>= sequence0 x |
↳ HASKELL
↳ LR
↳ HASKELL
↳ BR
mainModule Monad
| ((zipWithM :: (b -> c -> IO a) -> [b] -> [c] -> IO [a]) :: (b -> c -> IO a) -> [b] -> [c] -> IO [a]) |
module Maybe where
| import qualified Monad import qualified Prelude
|
module Monad where
| import qualified Maybe import qualified Prelude
|
| zipWithM :: Monad c => (d -> a -> c b) -> [d] -> [a] -> c [b]
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 :: (c -> a -> IO b) -> [c] -> [a] -> IO [b]) :: (c -> a -> IO b) -> [c] -> [a] -> IO [b]) |
module Monad where
| import qualified Maybe import qualified Prelude
|
| zipWithM :: Monad a => (d -> c -> a b) -> [d] -> [c] -> a [b]
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 :: (b -> c -> IO a) -> [b] -> [c] -> IO [a]) |
module Maybe where
| import qualified Monad import qualified Prelude
|
module Monad where
| import qualified Maybe import qualified Prelude
|
| zipWithM :: Monad d => (a -> b -> d c) -> [a] -> [b] -> d [c]
zipWithM | f xs ys | = | sequence (zipWith f xs ys) |
|
Haskell To QDPs
↳ HASKELL
↳ LR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ Narrow
↳ QDP
↳ DependencyGraphProof
Q DP problem:
The TRS P consists of the following rules:
new_sequence1(wv3, wv41, wv51, wv6, h, ba, bb) → new_sequence(wv3, wv41, wv51, h, ba, bb)
new_sequence(wv3, :(wv40, wv41), :(wv50, wv51), h, ba, bb) → new_sequence(wv3, wv41, wv51, h, ba, bb)
R is empty.
Q is empty.
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
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ Narrow
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPSizeChangeProof
Q DP problem:
The TRS P consists of the following rules:
new_sequence(wv3, :(wv40, wv41), :(wv50, wv51), h, ba, bb) → new_sequence(wv3, wv41, wv51, 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_sequence(wv3, :(wv40, wv41), :(wv50, wv51), h, ba, bb) → new_sequence(wv3, wv41, wv51, h, ba, bb)
The graph contains the following edges 1 >= 1, 2 > 2, 3 > 3, 4 >= 4, 5 >= 5, 6 >= 6