YES 0.912
H-Termination proof of /home/matraf/haskell/eval_FullyBlown_Fast/List.hs
H-Termination of the given Haskell-Program with start terms could successfully be proven:
↳ HASKELL
↳ BR
mainModule List
| ((isPrefixOf :: [Int] -> [Int] -> Bool) :: [Int] -> [Int] -> Bool) |
module List where
| import qualified Maybe import qualified Prelude
|
| isPrefixOf :: Eq a => [a] -> [a] -> Bool
isPrefixOf | [] _ | = | True |
isPrefixOf | _ [] | = | False |
isPrefixOf | (x : xs) (y : ys) | = | x == y && isPrefixOf xs ys |
|
module Maybe where
| import qualified List import qualified Prelude
|
Replaced joker patterns by fresh variables and removed binding patterns.
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
mainModule List
| ((isPrefixOf :: [Int] -> [Int] -> Bool) :: [Int] -> [Int] -> Bool) |
module List where
| import qualified Maybe import qualified Prelude
|
| isPrefixOf :: Eq a => [a] -> [a] -> Bool
isPrefixOf | [] vw | = | True |
isPrefixOf | vx [] | = | False |
isPrefixOf | (x : xs) (y : ys) | = | x == y && isPrefixOf xs ys |
|
module Maybe where
| import qualified List import qualified Prelude
|
Cond Reductions:
The following Function with conditions
is transformed to
undefined0 | True | = undefined |
undefined1 | | = undefined0 False |
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ Narrow
mainModule List
| (isPrefixOf :: [Int] -> [Int] -> Bool) |
module List where
| import qualified Maybe import qualified Prelude
|
| isPrefixOf :: Eq a => [a] -> [a] -> Bool
isPrefixOf | [] vw | = | True |
isPrefixOf | vx [] | = | False |
isPrefixOf | (x : xs) (y : ys) | = | x == y && isPrefixOf xs ys |
|
module Maybe where
| import qualified List 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_asAs(Succ(ww30000), Succ(ww40000), ww5) → new_asAs(ww30000, ww40000, ww5)
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_asAs(Succ(ww30000), Succ(ww40000), ww5) → new_asAs(ww30000, ww40000, ww5)
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_isPrefixOf(:(ww30, ww31), :(ww40, ww41)) → new_isPrefixOf(ww31, ww41)
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_isPrefixOf(:(ww30, ww31), :(ww40, ww41)) → new_isPrefixOf(ww31, ww41)
The graph contains the following edges 1 > 1, 2 > 2