YES 0.728
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
↳ BR
mainModule Monad
| ((msum :: MonadPlus a => [a b] -> a b) :: MonadPlus a => [a b] -> a b) |
module Monad where
| import qualified Maybe import qualified Prelude
|
| class Monad a => MonadPlus a where
|
| mplus :: MonadPlus a => a b -> a b -> a b
mzero :: MonadPlus a => a b
|
|
| instance MonadPlus Maybe where
|
|
mplus | Nothing ys | = | ys |
mplus | xs _ys | = | xs |
|
instance MonadPlus [] where
|
| msum :: MonadPlus a => [a b] -> a b
|
module Maybe where
| import qualified Monad import qualified Prelude
|
Replaced joker patterns by fresh variables and removed binding patterns.
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
mainModule Monad
| ((msum :: MonadPlus b => [b a] -> b a) :: MonadPlus b => [b a] -> b a) |
module Maybe where
| import qualified Monad import qualified Prelude
|
module Monad where
| import qualified Maybe import qualified Prelude
|
| class Monad a => MonadPlus a where
|
| mplus :: MonadPlus a => a b -> a b -> a b
mzero :: MonadPlus a => a b
|
|
| instance MonadPlus Maybe where
|
|
mplus | Nothing ys | = | ys |
mplus | xs _ys | = | xs |
|
instance MonadPlus [] where
|
| msum :: MonadPlus b => [b a] -> b a
|
Cond Reductions:
The following Function with conditions
is transformed to
undefined0 | True | = undefined |
undefined1 | | = undefined0 False |
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ Narrow
mainModule Monad
| (msum :: MonadPlus a => [a b] -> a b) |
module Monad where
| import qualified Maybe import qualified Prelude
|
| class Monad a => MonadPlus a where
|
| mplus :: MonadPlus a => a b -> a b -> a b
mzero :: MonadPlus a => a b
|
|
| instance MonadPlus Maybe where
|
|
mplus | Nothing ys | = | ys |
mplus | xs _ys | = | xs |
|
instance MonadPlus [] where
|
| msum :: MonadPlus a => [a b] -> a b
|
module Maybe where
| import qualified Monad import qualified Prelude
|
Haskell To QDPs
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDPSizeChangeProof
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_psPs(:(vy300, vy301), vy4, h) → new_psPs(vy301, vy4, 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_psPs(:(vy300, vy301), vy4, h) → new_psPs(vy301, vy4, h)
The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ DependencyGraphProof
Q DP problem:
The TRS P consists of the following rules:
new_foldr(:(vy30, vy31), ty_[], h) → new_foldr(vy31, ty_[], h)
new_foldr(:(vy30, vy31), ty_Maybe, h) → new_foldr(vy31, ty_Maybe, h)
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 2 SCCs.
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPSizeChangeProof
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_foldr(:(vy30, vy31), ty_Maybe, h) → new_foldr(vy31, ty_Maybe, 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_foldr(:(vy30, vy31), ty_Maybe, h) → new_foldr(vy31, ty_Maybe, h)
The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPSizeChangeProof
Q DP problem:
The TRS P consists of the following rules:
new_foldr(:(vy30, vy31), ty_[], h) → new_foldr(vy31, ty_[], 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_foldr(:(vy30, vy31), ty_[], h) → new_foldr(vy31, ty_[], h)
The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3