Haskell 2019-04-01 06.52 pair #433316881

details

property	value
status	complete
benchmark	FiniteMap_addToFM_C_4.hs
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n161.star.cs.uiowa.edu
space	full_haskell

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	9.19962 seconds
cpu usage	23.8108
user time	23.1531
system time	0.65775
max virtual memory	1.8287616E7
max residence set size	1822480.0

stage attributes

key	value
starexec-result	YES

output

19.88/7.73	YES
22.68/8.47	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
22.68/8.47	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
22.68/8.47	
22.68/8.47	
22.68/8.47	H-Termination with start terms of the given HASKELL could be proven:
22.68/8.47	
22.68/8.47	(0) HASKELL
22.68/8.47	(1) LR [EQUIVALENT, 0 ms]
22.68/8.47	(2) HASKELL
22.68/8.47	(3) CR [EQUIVALENT, 0 ms]
22.68/8.47	(4) HASKELL
22.68/8.47	(5) IFR [EQUIVALENT, 0 ms]
22.68/8.47	(6) HASKELL
22.68/8.47	(7) BR [EQUIVALENT, 0 ms]
22.68/8.47	(8) HASKELL
22.68/8.47	(9) COR [EQUIVALENT, 0 ms]
22.68/8.47	(10) HASKELL
22.68/8.47	(11) LetRed [EQUIVALENT, 0 ms]
22.68/8.47	(12) HASKELL
22.68/8.47	(13) NumRed [SOUND, 0 ms]
22.68/8.47	(14) HASKELL
22.68/8.47	(15) Narrow [SOUND, 0 ms]
22.68/8.47	(16) AND
22.68/8.47	    (17) QDP
22.68/8.47	        (18) QDPSizeChangeProof [EQUIVALENT, 0 ms]
22.68/8.47	        (19) YES
22.68/8.47	    (20) QDP
22.68/8.47	        (21) DependencyGraphProof [EQUIVALENT, 0 ms]
22.68/8.47	        (22) AND
22.68/8.47	            (23) QDP
22.68/8.47	                (24) QDPSizeChangeProof [EQUIVALENT, 0 ms]
22.68/8.47	                (25) YES
22.68/8.47	            (26) QDP
22.68/8.47	                (27) QDPSizeChangeProof [EQUIVALENT, 0 ms]
22.68/8.47	                (28) YES
22.68/8.47	    (29) QDP
22.68/8.47	        (30) DependencyGraphProof [EQUIVALENT, 0 ms]
22.68/8.47	        (31) QDP
22.68/8.47	        (32) QDPSizeChangeProof [EQUIVALENT, 307 ms]
22.68/8.48	        (33) YES
22.68/8.48	    (34) QDP
22.68/8.48	        (35) QDPSizeChangeProof [EQUIVALENT, 0 ms]
22.68/8.48	        (36) YES
22.68/8.48	    (37) QDP
22.68/8.48	        (38) QDPSizeChangeProof [EQUIVALENT, 0 ms]
22.68/8.48	        (39) YES
22.68/8.48	    (40) QDP
22.68/8.48	        (41) QDPSizeChangeProof [EQUIVALENT, 0 ms]
22.68/8.48	        (42) YES
22.68/8.48	    (43) QDP
22.68/8.48	        (44) QDPSizeChangeProof [EQUIVALENT, 0 ms]
22.68/8.48	        (45) YES
22.68/8.48	    (46) QDP
22.68/8.48	        (47) QDPSizeChangeProof [EQUIVALENT, 0 ms]
22.68/8.48	        (48) YES
22.68/8.48	
22.68/8.48	
22.68/8.48	----------------------------------------
22.68/8.48	
22.68/8.48	(0)
22.68/8.48	Obligation:
22.68/8.48	mainModule Main 
22.68/8.48	module FiniteMap where {
22.68/8.48	import qualified Main;
22.68/8.48	import qualified Maybe;
22.68/8.48	import qualified Prelude;
22.68/8.48	data FiniteMap b a = EmptyFM  | Branch b a Int (FiniteMap b a) (FiniteMap b a) ;
22.68/8.48	
22.68/8.48	instance (Eq a, Eq b) => Eq FiniteMap a b where { 
22.68/8.48	(==) fm_1 fm_2 = sizeFM fm_1 == sizeFM fm_2 && fmToList fm_1 == fmToList fm_2;
22.68/8.48	}
22.68/8.48	addToFM_C :: Ord b => (a  ->  a  ->  a)  ->  FiniteMap b a  ->  b  ->  a  ->  FiniteMap b a;
22.68/8.48	addToFM_C combiner EmptyFM key elt = unitFM key elt;
22.68/8.48	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
22.68/8.48	 | new_key > key = mkBalBranch key elt fm_l (addToFM_C combiner fm_r new_key new_elt)
22.68/8.48	 | otherwise = Branch new_key (combiner elt new_elt) size fm_l fm_r;
22.68/8.48	
22.68/8.48	emptyFM :: FiniteMap a b;
22.68/8.48	emptyFM = EmptyFM;
22.68/8.48	
22.68/8.48	findMax :: FiniteMap b a  ->  (b,a);
22.68/8.48	findMax (Branch key elt _ _ EmptyFM) = (key,elt);
22.68/8.48	findMax (Branch key elt _ _ fm_r) = findMax fm_r;
22.68/8.48	
22.68/8.48	findMin :: FiniteMap b a  ->  (b,a);
22.68/8.48	findMin (Branch key elt _ EmptyFM _) = (key,elt);
22.68/8.48	findMin (Branch key elt _ fm_l _) = findMin fm_l;
22.68/8.48	
22.68/8.48	fmToList :: FiniteMap a b  ->  [(a,b)];
22.68/8.48	fmToList fm = foldFM (\key elt rest ->(key,elt) : rest) [] fm;
22.68/8.48	
22.68/8.48	foldFM :: (c  ->  b  ->  a  ->  a)  ->  a  ->  FiniteMap c b  ->  a;
22.68/8.48	foldFM k z EmptyFM = z;
22.68/8.48	foldFM k z (Branch key elt _ fm_l fm_r) = foldFM k (k key elt (foldFM k z fm_r)) fm_l;
22.68/8.48	
22.68/8.48	mkBalBranch :: Ord a => a  ->  b  ->  FiniteMap a b  ->  FiniteMap a b  ->  FiniteMap a b;
22.68/8.48	mkBalBranch key elt fm_L fm_R  | size_l + size_r < 2 = mkBranch 1 key elt fm_L fm_R
22.68/8.48	 | size_r > sIZE_RATIO * size_l = case fm_R of { 
22.68/8.48	Branch _ _ _ fm_rl fm_rr | sizeFM fm_rl < 2 * sizeFM fm_rr -> single_L fm_L fm_R

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