Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313863

details

property	value
status	complete
benchmark	oddeven.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n092.star.cs.uiowa.edu
space	Frederiksen_Others

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	10.1391 seconds
cpu usage	20.5903
user time	18.8722
system time	1.71805
max virtual memory	1.9205948E7
max residence set size	4303856.0

stage attributes

key	value
starexec-result	WORST_CASE(Omega(n^1), O(n^1))

output

20.21/6.56	WORST_CASE(Omega(n^1), O(n^1))
20.53/9.95	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
20.53/9.95	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
20.53/9.95	
20.53/9.95	
20.53/9.95	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
20.53/9.95	
20.53/9.95	(0) CpxTRS
20.53/9.95	(1) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms]
20.53/9.95	(2) CpxTRS
20.53/9.95	    (3) CpxTrsMatchBoundsProof [FINISHED, 0 ms]
20.53/9.95	    (4) BOUNDS(1, n^1)
20.53/9.95	(5) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
20.53/9.95	(6) TRS for Loop Detection
20.53/9.95	    (7) DecreasingLoopProof [LOWER BOUND(ID), 0 ms]
20.53/9.95	    (8) BEST
20.53/9.95	        (9) proven lower bound
20.53/9.95	            (10) LowerBoundPropagationProof [FINISHED, 0 ms]
20.53/9.95	            (11) BOUNDS(n^1, INF)
20.53/9.95	        (12) TRS for Loop Detection
20.53/9.95	
20.53/9.95	
20.53/9.95	----------------------------------------
20.53/9.95	
20.53/9.95	(0)
20.53/9.95	Obligation:
20.53/9.95	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
20.53/9.95	
20.53/9.95	
20.53/9.95	The TRS R consists of the following rules:
20.53/9.95	
20.53/9.95	   odd(S(x)) -> even(x)
20.53/9.95	   even(S(x)) -> odd(x)
20.53/9.95	   odd(0) -> 0
20.53/9.95	   even(0) -> S(0)
20.53/9.95	
20.53/9.95	S is empty.
20.53/9.95	Rewrite Strategy: INNERMOST
20.55/10.03	----------------------------------------
20.55/10.03	
20.55/10.03	(1) RelTrsToTrsProof (UPPER BOUND(ID))
20.55/10.03	transformed relative TRS to TRS
20.55/10.03	----------------------------------------
20.55/10.03	
20.55/10.03	(2)
20.55/10.03	Obligation:
20.55/10.03	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, n^1).
20.55/10.03	
20.55/10.03	
20.55/10.03	The TRS R consists of the following rules:
20.55/10.03	
20.55/10.03	   odd(S(x)) -> even(x)
20.55/10.03	   even(S(x)) -> odd(x)
20.55/10.03	   odd(0) -> 0
20.55/10.03	   even(0) -> S(0)
20.55/10.03	
20.55/10.03	S is empty.
20.55/10.03	Rewrite Strategy: INNERMOST
20.55/10.03	----------------------------------------
20.55/10.03	
20.55/10.03	(3) CpxTrsMatchBoundsProof (FINISHED)
20.55/10.03	A linear upper bound on the runtime complexity of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 1. 
20.55/10.03	The certificate found is represented by the following graph.
20.55/10.03	
20.55/10.03	"[1, 2, 3]
20.55/10.03	{(1,2,[odd_1|0, even_1|0, even_1|1, 0|1, odd_1|1]), (1,3,[S_1|1]), (2,2,[S_1|0, 0|0]), (3,2,[0|1])}"
20.55/10.03	----------------------------------------
20.55/10.03	
20.55/10.03	(4)
20.55/10.03	BOUNDS(1, n^1)
20.55/10.03	
20.55/10.03	----------------------------------------
20.55/10.03	
20.55/10.03	(5) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID))
20.55/10.03	Transformed a relative TRS into a decreasing-loop problem.
20.55/10.03	----------------------------------------
20.55/10.03	
20.55/10.03	(6)
20.55/10.03	Obligation:
20.55/10.03	Analyzing the following TRS for decreasing loops:
20.55/10.03	
20.55/10.03	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
20.55/10.03	
20.55/10.03	
20.55/10.03	The TRS R consists of the following rules:
20.55/10.03	
20.55/10.03	   odd(S(x)) -> even(x)
20.55/10.03	   even(S(x)) -> odd(x)
20.55/10.03	   odd(0) -> 0
20.55/10.03	   even(0) -> S(0)
20.55/10.03	
20.55/10.03	S is empty.
20.55/10.03	Rewrite Strategy: INNERMOST
20.55/10.03	----------------------------------------
20.55/10.03	
20.55/10.03	(7) DecreasingLoopProof (LOWER BOUND(ID))
20.55/10.03	The following loop(s) give(s) rise to the lower bound Omega(n^1):
20.55/10.03	
20.55/10.03	The rewrite sequence
20.55/10.03

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actions all output return to Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40