Haskell pair #487598836

details

property	value
status	complete
benchmark	FiniteMap_elemFM_3.hs
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n140.star.cs.uiowa.edu
space	full_haskell

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	9.64981293678 seconds
cpu usage	13.233672775
max memory	7.03717376E8

stage attributes

key	value
output-size	38500
starexec-result	YES

output

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


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


YES
proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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) Narrow [SOUND, 0 ms]
(8) QDP
(9) DependencyGraphProof [EQUIVALENT, 0 ms]
(10) AND
    (11) QDP
        (12) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (13) YES
    (14) QDP
        (15) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (16) YES


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

(0)
Obligation:
mainModule Main 
module FiniteMap where {
import qualified Main;
import qualified Maybe;
import qualified Prelude;
data FiniteMap a b = EmptyFM  | Branch a b Int (FiniteMap a b) (FiniteMap a b) ;

instance (Eq a, Eq b) => Eq FiniteMap b a where { 
}
elemFM :: Ord b => b  ->  FiniteMap b a  ->  Bool;
elemFM key fm = case lookupFM fm key of { 
Nothing-> False; 
Just elt-> True; 
 } ;

lookupFM :: Ord b => FiniteMap b a  ->  b  ->  Maybe a;
lookupFM EmptyFM key = Nothing;
lookupFM (Branch key elt _ fm_l fm_r) key_to_find  | key_to_find < key = lookupFM fm_l key_to_find
 | key_to_find > key = lookupFM fm_r key_to_find
 | otherwise = Just elt;

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

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

(1) CR (EQUIVALENT)
Case Reductions:
The following Case expression
"case lookupFM fm key of {
Nothing  -> False;
Just elt  -> True}
"
is transformed to
"elemFM0 Nothing = False;
elemFM0 (Just elt) = True;
"

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

(2)
Obligation:
mainModule Main 
module FiniteMap where {
import qualified Main;
import qualified Maybe;
import qualified Prelude;
data FiniteMap a b = EmptyFM  | Branch a b Int (FiniteMap a b) (FiniteMap a b) ;

instance (Eq a, Eq b) => Eq FiniteMap a b where { 
}
elemFM :: Ord b => b  ->  FiniteMap b a  ->  Bool;
elemFM key fm = elemFM0 (lookupFM fm key);

elemFM0 Nothing = False;

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