Haskell 2019-04-01 06.52 pair #433316272

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	n119.star.cs.uiowa.edu
space	full_haskell

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	5.42065 seconds
cpu usage	13.0976
user time	12.7258
system time	0.371769
max virtual memory	1.8285568E7
max residence set size	836916.0

stage attributes

key	value
starexec-result	YES

output

10.78/4.81	YES
12.94/5.38	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
12.94/5.38	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
12.94/5.38	
12.94/5.38	
12.94/5.38	H-Termination with start terms of the given HASKELL could be proven:
12.94/5.38	
12.94/5.38	(0) HASKELL
12.94/5.38	(1) CR [EQUIVALENT, 0 ms]
12.94/5.38	(2) HASKELL
12.94/5.38	(3) BR [EQUIVALENT, 0 ms]
12.94/5.38	(4) HASKELL
12.94/5.38	(5) COR [EQUIVALENT, 0 ms]
12.94/5.38	(6) HASKELL
12.94/5.38	(7) Narrow [SOUND, 0 ms]
12.94/5.38	(8) QDP
12.94/5.38	(9) DependencyGraphProof [EQUIVALENT, 0 ms]
12.94/5.38	(10) AND
12.94/5.38	    (11) QDP
12.94/5.38	        (12) QDPSizeChangeProof [EQUIVALENT, 0 ms]
12.94/5.38	        (13) YES
12.94/5.38	    (14) QDP
12.94/5.38	        (15) QDPSizeChangeProof [EQUIVALENT, 0 ms]
12.94/5.38	        (16) YES
12.94/5.38	
12.94/5.38	
12.94/5.38	----------------------------------------
12.94/5.38	
12.94/5.38	(0)
12.94/5.38	Obligation:
12.94/5.38	mainModule Main 
12.94/5.38	module FiniteMap where {
12.94/5.38	import qualified Main;
12.94/5.38	import qualified Maybe;
12.94/5.38	import qualified Prelude;
12.94/5.38	data FiniteMap a b = EmptyFM  | Branch a b Int (FiniteMap a b) (FiniteMap a b) ;
12.94/5.38	
12.94/5.38	instance (Eq a, Eq b) => Eq FiniteMap b a where { 
12.94/5.38	}
12.94/5.38	elemFM :: Ord b => b  ->  FiniteMap b a  ->  Bool;
12.94/5.38	elemFM key fm = case lookupFM fm key of { 
12.94/5.38	Nothing-> False; 
12.94/5.38	Just elt-> True; 
12.94/5.38	 } ;
12.94/5.38	
12.94/5.38	lookupFM :: Ord b => FiniteMap b a  ->  b  ->  Maybe a;
12.94/5.38	lookupFM EmptyFM key = Nothing;
12.94/5.38	lookupFM (Branch key elt _ fm_l fm_r) key_to_find  | key_to_find < key = lookupFM fm_l key_to_find
12.94/5.38	 | key_to_find > key = lookupFM fm_r key_to_find
12.94/5.38	 | otherwise = Just elt;
12.94/5.38	
12.94/5.38	}
12.94/5.38	module Maybe where {
12.94/5.38	import qualified FiniteMap;
12.94/5.38	import qualified Main;
12.94/5.38	import qualified Prelude;
12.94/5.38	}
12.94/5.38	module Main where {
12.94/5.38	import qualified FiniteMap;
12.94/5.38	import qualified Maybe;
12.94/5.38	import qualified Prelude;
12.94/5.38	}
12.94/5.38	
12.94/5.38	----------------------------------------
12.94/5.38	
12.94/5.38	(1) CR (EQUIVALENT)
12.94/5.38	Case Reductions:
12.94/5.38	The following Case expression
12.94/5.38	"case lookupFM fm key of {
12.94/5.38	Nothing  -> False;
12.94/5.38	Just elt  -> True}
12.94/5.38	"
12.94/5.38	is transformed to
12.94/5.38	"elemFM0 Nothing = False;
12.94/5.38	elemFM0 (Just elt) = True;
12.94/5.38	"
12.94/5.38	
12.94/5.38	----------------------------------------
12.94/5.38	
12.94/5.38	(2)
12.94/5.38	Obligation:
12.94/5.38	mainModule Main 
12.94/5.38	module FiniteMap where {
12.94/5.38	import qualified Main;
12.94/5.38	import qualified Maybe;
12.94/5.38	import qualified Prelude;
12.94/5.38	data FiniteMap a b = EmptyFM  | Branch a b Int (FiniteMap a b) (FiniteMap a b) ;
12.94/5.38	
12.94/5.38	instance (Eq a, Eq b) => Eq FiniteMap b a where { 
12.94/5.38	}
12.94/5.38	elemFM :: Ord b => b  ->  FiniteMap b a  ->  Bool;
12.94/5.38	elemFM key fm = elemFM0 (lookupFM fm key);
12.94/5.38	
12.94/5.38	elemFM0 Nothing = False;
12.94/5.38	elemFM0 (Just elt) = True;
12.94/5.38	
12.94/5.38	lookupFM :: Ord b => FiniteMap b a  ->  b  ->  Maybe a;
12.94/5.38	lookupFM EmptyFM key = Nothing;
12.94/5.38	lookupFM (Branch key elt _ fm_l fm_r) key_to_find  | key_to_find < key = lookupFM fm_l key_to_find
12.94/5.38	 | key_to_find > key = lookupFM fm_r key_to_find

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