YES 0.78
H-Termination proof of /home/matraf/haskell/eval_FullyBlown_Fast/empty.hs
H-Termination of the given Haskell-Program with start terms could successfully be proven:
↳ HASKELL
↳ BR
mainModule Main
| (((=<<) :: Monad c => (b -> c a) -> c b -> c a) :: Monad c => (b -> c a) -> c b -> c a) |
module Main where
Replaced joker patterns by fresh variables and removed binding patterns.
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
mainModule Main
| (((=<<) :: Monad b => (a -> b c) -> b a -> b c) :: Monad b => (a -> b c) -> b a -> b c) |
module Main where
Cond Reductions:
The following Function with conditions
is transformed to
undefined0 | True | = undefined |
undefined1 | | = undefined0 False |
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ Narrow
mainModule Main
| ((=<<) :: Monad c => (a -> c b) -> c a -> c b) |
module Main where
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(:(vx60, vx61), vx5, ba) → new_psPs(vx61, vx5, 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_psPs(:(vx60, vx61), vx5, ba) → new_psPs(vx61, vx5, ba)
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(:(vx40, vx41), vx3, ba, bb) → new_gtGtEs(vx41, vx3, 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_gtGtEs(:(vx40, vx41), vx3, ba, bb) → new_gtGtEs(vx41, vx3, ba, bb)
The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3, 4 >= 4