Haskell pair #487599756

details

property	value
status	complete
benchmark	FiniteMap_addListToFM_1.hs
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n109.star.cs.uiowa.edu
space	full_haskell

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	19.0892620087 seconds
cpu usage	40.845964016
max memory	4.057235456E9

stage attributes

key	value
output-size	982885
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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) LR [EQUIVALENT, 0 ms]
(2) HASKELL
(3) CR [EQUIVALENT, 0 ms]
(4) HASKELL
(5) IFR [EQUIVALENT, 0 ms]
(6) HASKELL
(7) BR [EQUIVALENT, 5 ms]
(8) HASKELL
(9) COR [EQUIVALENT, 0 ms]
(10) HASKELL
(11) LetRed [EQUIVALENT, 1 ms]
(12) HASKELL
(13) NumRed [SOUND, 0 ms]
(14) HASKELL
(15) Narrow [SOUND, 0 ms]
(16) AND
    (17) QDP
        (18) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (19) YES
    (20) QDP
        (21) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (22) YES
    (23) QDP
        (24) QDPSizeChangeProof [EQUIVALENT, 5 ms]
        (25) YES
    (26) QDP
        (27) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (28) YES
    (29) QDP
        (30) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (31) YES
    (32) QDP
        (33) QDPSizeChangeProof [EQUIVALENT, 137 ms]
        (34) YES
    (35) QDP
        (36) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (37) YES
    (38) QDP
        (39) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (40) YES
    (41) QDP
        (42) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (43) 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 { 
(==) fm_1 fm_2 = sizeFM fm_1 == sizeFM fm_2 && fmToList fm_1 == fmToList fm_2;
}
addListToFM :: Ord b => FiniteMap b a  ->  [(b,a)]  ->  FiniteMap b a;
addListToFM fm key_elt_pairs = addListToFM_C (\old new ->new) fm key_elt_pairs;

addListToFM_C :: Ord b => (a  ->  a  ->  a)  ->  FiniteMap b a  ->  [(b,a)]  ->  FiniteMap b a;
addListToFM_C combiner fm key_elt_pairs = foldl add fm key_elt_pairs where { 
add fmap (key,elt) = addToFM_C combiner fmap key elt;
 };

addToFM_C :: Ord b => (a  ->  a  ->  a)  ->  FiniteMap b a  ->  b  ->  a  ->  FiniteMap b a;
addToFM_C combiner EmptyFM key elt = unitFM key elt;
addToFM_C combiner (Branch key elt size fm_l fm_r) new_key new_elt  | new_key < key = mkBalBranch key elt (addToFM_C combiner fm_l new_key new_elt) fm_r
 | new_key > key = mkBalBranch key elt fm_l (addToFM_C combiner fm_r new_key new_elt)
 | otherwise = Branch new_key (combiner elt new_elt) size fm_l fm_r;

emptyFM :: FiniteMap b a;
emptyFM = EmptyFM;

findMax :: FiniteMap a b  ->  (a,b);
findMax (Branch key elt _ _ EmptyFM) = (key,elt);
findMax (Branch key elt _ _ fm_r) = findMax fm_r;

findMin :: FiniteMap a b  ->  (a,b);
findMin (Branch key elt _ EmptyFM _) = (key,elt);
findMin (Branch key elt _ fm_l _) = findMin fm_l;

fmToList :: FiniteMap a b  ->  [(a,b)];
fmToList fm = foldFM (\key elt rest ->(key,elt) : rest) [] fm;

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