Funct Progr 77531 pair #381920454

details

property	value
status	complete
benchmark	Maybe_mapMaybe_1.hs
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n039.star.cs.uiowa.edu
space	full_haskell

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	4.7974460125 seconds
cpu usage	10.950171566
max memory	6.473728E8

stage attributes

key	value
output-size	8405
starexec-result	YES

output

/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.hs /export/starexec/sandbox2/output/output_files


--------------------------------------------------------------------------------


YES
proof of /export/starexec/sandbox2/benchmark/theBenchmark.hs
# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


H-Termination with start terms of the given HASKELL could be proven:

(0) HASKELL
(1) CR [EQUIVALENT, 0 ms]
(2) HASKELL
(3) BR [EQUIVALENT, 0 ms]
(4) HASKELL
(5) COR [EQUIVALENT, 0 ms]
(6) HASKELL
(7) LetRed [EQUIVALENT, 0 ms]
(8) HASKELL
(9) Narrow [SOUND, 0 ms]
(10) QDP
(11) QDPSizeChangeProof [EQUIVALENT, 0 ms]
(12) YES


----------------------------------------

(0)
Obligation:
mainModule Main 
module Maybe where {
import qualified Main;
import qualified Prelude;
mapMaybe :: (b  ->  Maybe a)  ->  [b]  ->  [a];
mapMaybe _ [] = [];
mapMaybe f (x : xs) = let { 
rs = mapMaybe f xs;
} in case f x of { 
Nothing-> rs; 
Just r-> r : rs; 
 } ;

}
module Main where {
import qualified Maybe;
import qualified Prelude;
}

----------------------------------------

(1) CR (EQUIVALENT)
Case Reductions:
The following Case expression
"case f x of {
Nothing  -> rs;
Just r  -> r : rs}
"
is transformed to
"mapMaybe0 Nothing = rs;
mapMaybe0 (Just r) = r : rs;
"

----------------------------------------

(2)
Obligation:
mainModule Main 
module Maybe where {
import qualified Main;
import qualified Prelude;
mapMaybe :: (a  ->  Maybe b)  ->  [a]  ->  [b];
mapMaybe _ [] = [];
mapMaybe f (x : xs) = let { 
mapMaybe0 Nothing = rs;
mapMaybe0 (Just r) = r : rs;
rs = mapMaybe f xs;
} in mapMaybe0 (f x);

}
module Main where {
import qualified Maybe;
import qualified Prelude;
}

----------------------------------------

(3) BR (EQUIVALENT)
Replaced joker patterns by fresh variables and removed binding patterns.
----------------------------------------

(4)
Obligation:
mainModule Main 
module Maybe where {
import qualified Main;
import qualified Prelude;
mapMaybe :: (b  ->  Maybe a)  ->  [b]  ->  [a];

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