YES 0.714
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
| ((liftM :: (a -> b) -> [a] -> [b]) :: (a -> b) -> [a] -> [b]) |
module Monad where
| import qualified Maybe import qualified Prelude
|
| liftM :: Monad c => (b -> a) -> c b -> c a
liftM | f m1 | = | m1 >>= (\x1 ->return (f x1)) |
|
module Maybe where
| import qualified Monad import qualified Prelude
|
Lambda Reductions:
The following Lambda expression
\x1→return (f x1)
is transformed to
liftM0 | f x1 | = return (f x1) |
↳ HASKELL
↳ LR
↳ HASKELL
↳ BR
mainModule Monad
| ((liftM :: (a -> b) -> [a] -> [b]) :: (a -> b) -> [a] -> [b]) |
module Maybe where
| import qualified Monad import qualified Prelude
|
module Monad where
| import qualified Maybe import qualified Prelude
|
| liftM :: Monad b => (a -> c) -> b a -> b c
liftM | f m1 | = | m1 >>= liftM0 f |
|
|
liftM0 | f x1 | = | return (f x1) |
|
Replaced joker patterns by fresh variables and removed binding patterns.
↳ HASKELL
↳ LR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
mainModule Monad
| ((liftM :: (a -> b) -> [a] -> [b]) :: (a -> b) -> [a] -> [b]) |
module Monad where
| import qualified Maybe import qualified Prelude
|
| liftM :: Monad a => (b -> c) -> a b -> a c
liftM | f m1 | = | m1 >>= liftM0 f |
|
|
liftM0 | f x1 | = | return (f x1) |
|
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
| (liftM :: (b -> a) -> [b] -> [a]) |
module Maybe where
| import qualified Monad import qualified Prelude
|
module Monad where
| import qualified Maybe import qualified Prelude
|
| liftM :: Monad b => (a -> c) -> b a -> b c
liftM | f m1 | = | m1 >>= liftM0 f |
|
|
liftM0 | f x1 | = | return (f x1) |
|
Haskell To QDPs
↳ HASKELL
↳ LR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ Narrow
↳ QDP
↳ QDPSizeChangeProof
Q DP problem:
The TRS P consists of the following rules:
new_gtGtEs(:(vy40, vy41), vy3, h, ba) → new_gtGtEs(vy41, vy3, 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_gtGtEs(:(vy40, vy41), vy3, h, ba) → new_gtGtEs(vy41, vy3, h, ba)
The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3, 4 >= 4