YES 0.717
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
| ((join :: [[a]] -> [a]) :: [[a]] -> [a]) |
module Monad where
| import qualified Maybe import qualified Prelude
|
| join :: Monad a => 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
| ((join :: [[a]] -> [a]) :: [[a]] -> [a]) |
module Maybe where
| import qualified Monad import qualified Prelude
|
module Monad where
| import qualified Maybe import qualified Prelude
|
| join :: Monad b => 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
module Monad where
| import qualified Maybe import qualified Prelude
|
| join :: Monad a => 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
↳ QDPSizeChangeProof
Q DP problem:
The TRS P consists of the following rules:
new_gtGtEs(:(vy30, vy31), h) → new_gtGtEs(vy31, 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(:(vy30, vy31), h) → new_gtGtEs(vy31, h)
The graph contains the following edges 1 > 1, 2 >= 2