Haskell 2019-04-01 06.52 pair #433316254

details

property	value
status	complete
benchmark	FiniteMap_keysFM_LE_5.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)	6.26821 seconds
cpu usage	16.5533
user time	16.1143
system time	0.439021
max virtual memory	1.8285568E7
max residence set size	998716.0

stage attributes

key	value
starexec-result	YES

output

14.06/5.58	YES
16.17/6.21	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
16.17/6.21	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
16.17/6.21	
16.17/6.21	
16.17/6.21	H-Termination with start terms of the given HASKELL could be proven:
16.17/6.21	
16.17/6.21	(0) HASKELL
16.17/6.21	(1) LR [EQUIVALENT, 0 ms]
16.17/6.21	(2) HASKELL
16.17/6.21	(3) BR [EQUIVALENT, 0 ms]
16.17/6.21	(4) HASKELL
16.17/6.21	(5) COR [EQUIVALENT, 0 ms]
16.17/6.21	(6) HASKELL
16.17/6.21	(7) Narrow [SOUND, 0 ms]
16.17/6.21	(8) AND
16.17/6.21	    (9) QDP
16.17/6.21	        (10) TransformationProof [EQUIVALENT, 0 ms]
16.17/6.21	        (11) QDP
16.17/6.21	        (12) TransformationProof [EQUIVALENT, 0 ms]
16.17/6.21	        (13) QDP
16.17/6.21	        (14) TransformationProof [EQUIVALENT, 1 ms]
16.17/6.21	        (15) QDP
16.17/6.21	        (16) QDPSizeChangeProof [EQUIVALENT, 0 ms]
16.17/6.21	        (17) YES
16.17/6.21	    (18) QDP
16.17/6.21	        (19) TransformationProof [EQUIVALENT, 0 ms]
16.17/6.21	        (20) QDP
16.17/6.21	        (21) TransformationProof [EQUIVALENT, 0 ms]
16.17/6.21	        (22) QDP
16.17/6.21	        (23) TransformationProof [EQUIVALENT, 0 ms]
16.17/6.21	        (24) QDP
16.17/6.21	        (25) TransformationProof [EQUIVALENT, 0 ms]
16.17/6.21	        (26) QDP
16.17/6.21	        (27) TransformationProof [EQUIVALENT, 0 ms]
16.17/6.21	        (28) QDP
16.17/6.21	        (29) TransformationProof [EQUIVALENT, 0 ms]
16.17/6.21	        (30) QDP
16.17/6.21	        (31) TransformationProof [EQUIVALENT, 0 ms]
16.17/6.21	        (32) QDP
16.17/6.21	        (33) QDPSizeChangeProof [EQUIVALENT, 0 ms]
16.17/6.21	        (34) YES
16.17/6.21	    (35) QDP
16.17/6.21	        (36) TransformationProof [EQUIVALENT, 0 ms]
16.17/6.21	        (37) QDP
16.17/6.21	        (38) TransformationProof [EQUIVALENT, 0 ms]
16.17/6.21	        (39) QDP
16.17/6.21	        (40) QDPSizeChangeProof [EQUIVALENT, 0 ms]
16.17/6.21	        (41) YES
16.17/6.21	    (42) QDP
16.17/6.21	        (43) DependencyGraphProof [EQUIVALENT, 0 ms]
16.17/6.21	        (44) AND
16.17/6.21	            (45) QDP
16.17/6.21	                (46) QDPSizeChangeProof [EQUIVALENT, 0 ms]
16.17/6.21	                (47) YES
16.17/6.21	            (48) QDP
16.17/6.21	                (49) QDPSizeChangeProof [EQUIVALENT, 0 ms]
16.17/6.21	                (50) YES
16.17/6.21	
16.17/6.21	
16.17/6.21	----------------------------------------
16.17/6.21	
16.17/6.21	(0)
16.17/6.21	Obligation:
16.17/6.21	mainModule Main 
16.17/6.21	module FiniteMap where {
16.17/6.21	import qualified Main;
16.17/6.21	import qualified Maybe;
16.17/6.21	import qualified Prelude;
16.17/6.21	data FiniteMap a b = EmptyFM  | Branch a b Int (FiniteMap a b) (FiniteMap a b) ;
16.17/6.21	
16.17/6.21	instance (Eq a, Eq b) => Eq FiniteMap b a where { 
16.17/6.21	}
16.17/6.21	foldFM_LE :: Ord b => (b  ->  c  ->  a  ->  a)  ->  a  ->  b  ->  FiniteMap b c  ->  a;
16.17/6.21	foldFM_LE k z fr EmptyFM = z;
16.17/6.21	foldFM_LE k z fr (Branch key elt _ fm_l fm_r)  | key <= fr = foldFM_LE k (k key elt (foldFM_LE k z fr fm_l)) fr fm_r
16.17/6.21	 | otherwise = foldFM_LE k z fr fm_l;
16.17/6.21	
16.17/6.21	keysFM_LE :: Ord a => FiniteMap a b  ->  a  ->  [a];
16.17/6.21	keysFM_LE fm fr = foldFM_LE (\key elt rest ->key : rest) [] fr fm;
16.17/6.21	
16.17/6.21	}
16.17/6.21	module Maybe where {
16.17/6.21	import qualified FiniteMap;
16.17/6.21	import qualified Main;
16.17/6.21	import qualified Prelude;
16.17/6.21	}
16.17/6.21	module Main where {
16.17/6.21	import qualified FiniteMap;
16.17/6.21	import qualified Maybe;
16.17/6.21	import qualified Prelude;
16.17/6.21	}
16.17/6.21	
16.17/6.21	----------------------------------------
16.17/6.21	
16.17/6.21	(1) LR (EQUIVALENT)
16.17/6.21	Lambda Reductions:
16.17/6.21	The following Lambda expression
16.17/6.21	"\keyeltrest->key : rest"
16.17/6.21	is transformed to

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