Haskell pair #487599438

details

property	value
status	complete
benchmark	FiniteMap_keysFM_GE_2.hs
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n145.star.cs.uiowa.edu
space	full_haskell

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	5.39670991898 seconds
cpu usage	12.716661313
max memory	7.03135744E8

stage attributes

key	value
output-size	22919
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


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

(0) HASKELL
(1) LR [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) AND
    (9) QDP
        (10) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (11) YES
    (12) QDP
        (13) TransformationProof [EQUIVALENT, 0 ms]
        (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 b a = EmptyFM  | Branch b a Int (FiniteMap b a) (FiniteMap b a) ;

instance (Eq a, Eq b) => Eq FiniteMap b a where { 
}
foldFM_GE :: Ord a => (a  ->  c  ->  b  ->  b)  ->  b  ->  a  ->  FiniteMap a c  ->  b;
foldFM_GE k z fr EmptyFM = z;
foldFM_GE k z fr (Branch key elt _ fm_l fm_r)  | key >= fr = foldFM_GE k (k key elt (foldFM_GE k z fr fm_r)) fr fm_l
 | otherwise = foldFM_GE k z fr fm_r;

keysFM_GE :: Ord a => FiniteMap a b  ->  a  ->  [a];
keysFM_GE fm fr = foldFM_GE (\key elt rest ->key : rest) [] fr fm;

}
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) LR (EQUIVALENT)
Lambda Reductions:
The following Lambda expression
"\keyeltrest->key : rest"
is transformed to
"keysFM_GE0 key elt rest = key : rest;
"

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

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

instance (Eq a, Eq b) => Eq FiniteMap b a where { 
}
foldFM_GE :: Ord b => (b  ->  c  ->  a  ->  a)  ->  a  ->  b  ->  FiniteMap b c  ->  a;
foldFM_GE k z fr EmptyFM = z;
foldFM_GE k z fr (Branch key elt _ fm_l fm_r)  | key >= fr = foldFM_GE k (k key elt (foldFM_GE k z fr fm_r)) fr fm_l
 | otherwise = foldFM_GE k z fr fm_r;

keysFM_GE :: Ord b => FiniteMap b a  ->  b  ->  [b];
keysFM_GE fm fr = foldFM_GE keysFM_GE0 [] fr fm;

keysFM_GE0 key elt rest = key : rest;

}
module Maybe where {

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