Haskell 2019-04-01 06.52 pair #433315902

details

property	value
status	complete
benchmark	FiniteMap_lookupWithDefaultFM_2.hs
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n057.star.cs.uiowa.edu
space	full_haskell

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	5.00077 seconds
cpu usage	11.8218
user time	11.494
system time	0.327814
max virtual memory	1.828352E7
max residence set size	720964.0

stage attributes

key	value
starexec-result	YES

output

9.69/4.39	YES
11.78/4.96	proof of /export/starexec/sandbox2/benchmark/theBenchmark.hs
11.78/4.96	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
11.78/4.96	
11.78/4.96	
11.78/4.96	H-Termination with start terms of the given HASKELL could be proven:
11.78/4.96	
11.78/4.96	(0) HASKELL
11.78/4.96	(1) CR [EQUIVALENT, 0 ms]
11.78/4.96	(2) HASKELL
11.78/4.96	(3) BR [EQUIVALENT, 0 ms]
11.78/4.96	(4) HASKELL
11.78/4.96	(5) COR [EQUIVALENT, 0 ms]
11.78/4.96	(6) HASKELL
11.78/4.96	(7) Narrow [EQUIVALENT, 0 ms]
11.78/4.96	(8) YES
11.78/4.96	
11.78/4.96	
11.78/4.96	----------------------------------------
11.78/4.96	
11.78/4.96	(0)
11.78/4.96	Obligation:
11.78/4.96	mainModule Main 
11.78/4.96	module FiniteMap where {
11.78/4.96	import qualified Main;
11.78/4.96	import qualified Maybe;
11.78/4.96	import qualified Prelude;
11.78/4.96	data FiniteMap b a = EmptyFM  | Branch b a Int (FiniteMap b a) (FiniteMap b a) ;
11.78/4.96	
11.78/4.96	instance (Eq a, Eq b) => Eq FiniteMap a b where { 
11.78/4.96	}
11.78/4.96	lookupFM :: Ord a => FiniteMap a b  ->  a  ->  Maybe b;
11.78/4.96	lookupFM EmptyFM key = Nothing;
11.78/4.96	lookupFM (Branch key elt _ fm_l fm_r) key_to_find  | key_to_find < key = lookupFM fm_l key_to_find
11.78/4.96	 | key_to_find > key = lookupFM fm_r key_to_find
11.78/4.96	 | otherwise = Just elt;
11.78/4.96	
11.78/4.96	lookupWithDefaultFM :: Ord b => FiniteMap b a  ->  a  ->  b  ->  a;
11.78/4.96	lookupWithDefaultFM fm deflt key = case lookupFM fm key of { 
11.78/4.96	Nothing-> deflt; 
11.78/4.96	Just elt-> elt; 
11.78/4.96	 } ;
11.78/4.96	
11.78/4.96	}
11.78/4.96	module Maybe where {
11.78/4.96	import qualified FiniteMap;
11.78/4.96	import qualified Main;
11.78/4.96	import qualified Prelude;
11.78/4.96	}
11.78/4.96	module Main where {
11.78/4.96	import qualified FiniteMap;
11.78/4.96	import qualified Maybe;
11.78/4.96	import qualified Prelude;
11.78/4.96	}
11.78/4.96	
11.78/4.96	----------------------------------------
11.78/4.96	
11.78/4.96	(1) CR (EQUIVALENT)
11.78/4.96	Case Reductions:
11.78/4.96	The following Case expression
11.78/4.96	"case lookupFM fm key of {
11.78/4.96	Nothing  -> deflt;
11.78/4.96	Just elt  -> elt}
11.78/4.96	"
11.78/4.96	is transformed to
11.78/4.96	"lookupWithDefaultFM0 deflt Nothing = deflt;
11.78/4.96	lookupWithDefaultFM0 deflt (Just elt) = elt;
11.78/4.96	"
11.78/4.96	
11.78/4.96	----------------------------------------
11.78/4.96	
11.78/4.96	(2)
11.78/4.96	Obligation:
11.78/4.96	mainModule Main 
11.78/4.96	module FiniteMap where {
11.78/4.96	import qualified Main;
11.78/4.96	import qualified Maybe;
11.78/4.96	import qualified Prelude;
11.78/4.96	data FiniteMap b a = EmptyFM  | Branch b a Int (FiniteMap b a) (FiniteMap b a) ;
11.78/4.96	
11.78/4.96	instance (Eq a, Eq b) => Eq FiniteMap b a where { 
11.78/4.96	}
11.78/4.96	lookupFM :: Ord b => FiniteMap b a  ->  b  ->  Maybe a;
11.78/4.96	lookupFM EmptyFM key = Nothing;
11.78/4.96	lookupFM (Branch key elt _ fm_l fm_r) key_to_find  | key_to_find < key = lookupFM fm_l key_to_find
11.78/4.96	 | key_to_find > key = lookupFM fm_r key_to_find
11.78/4.96	 | otherwise = Just elt;
11.78/4.96	
11.78/4.96	lookupWithDefaultFM :: Ord b => FiniteMap b a  ->  a  ->  b  ->  a;
11.78/4.96	lookupWithDefaultFM fm deflt key = lookupWithDefaultFM0 deflt (lookupFM fm key);
11.78/4.96	
11.78/4.96	lookupWithDefaultFM0 deflt Nothing = deflt;
11.78/4.96	lookupWithDefaultFM0 deflt (Just elt) = elt;
11.78/4.96	
11.78/4.96	}
11.78/4.96	module Maybe where {
11.78/4.96	import qualified FiniteMap;
11.78/4.96	import qualified Main;
11.78/4.96	import qualified Prelude;
11.78/4.96	}

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