Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313748

details

property	value
status	complete
benchmark	#3.35.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n100.star.cs.uiowa.edu
space	AG01

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	4.5082 seconds
cpu usage	13.2514
user time	11.7913
system time	1.46015
max virtual memory	1.8938648E7
max residence set size	4037292.0

stage attributes

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

output

13.08/4.47	WORST_CASE(Omega(n^1), O(n^1))
13.19/4.48	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
13.19/4.48	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
13.19/4.48	
13.19/4.48	
13.19/4.48	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
13.19/4.48	
13.19/4.48	(0) CpxTRS
13.19/4.48	(1) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms]
13.19/4.48	(2) CpxTRS
13.19/4.48	    (3) CpxTrsMatchBoundsProof [FINISHED, 0 ms]
13.19/4.48	    (4) BOUNDS(1, n^1)
13.19/4.48	(5) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
13.19/4.48	(6) TRS for Loop Detection
13.19/4.48	    (7) DecreasingLoopProof [LOWER BOUND(ID), 0 ms]
13.19/4.48	    (8) BEST
13.19/4.48	        (9) proven lower bound
13.19/4.48	            (10) LowerBoundPropagationProof [FINISHED, 0 ms]
13.19/4.48	            (11) BOUNDS(n^1, INF)
13.19/4.48	        (12) TRS for Loop Detection
13.19/4.48	
13.19/4.48	
13.19/4.48	----------------------------------------
13.19/4.48	
13.19/4.48	(0)
13.19/4.48	Obligation:
13.19/4.48	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
13.19/4.48	
13.19/4.48	
13.19/4.48	The TRS R consists of the following rules:
13.19/4.48	
13.19/4.48	   g(s(x)) -> f(x)
13.19/4.48	   f(0) -> s(0)
13.19/4.48	   f(s(x)) -> s(s(g(x)))
13.19/4.48	   g(0) -> 0
13.19/4.48	
13.19/4.48	S is empty.
13.19/4.48	Rewrite Strategy: INNERMOST
13.19/4.48	----------------------------------------
13.19/4.48	
13.19/4.48	(1) RelTrsToTrsProof (UPPER BOUND(ID))
13.19/4.48	transformed relative TRS to TRS
13.19/4.48	----------------------------------------
13.19/4.48	
13.19/4.48	(2)
13.19/4.48	Obligation:
13.19/4.48	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, n^1).
13.19/4.48	
13.19/4.48	
13.19/4.48	The TRS R consists of the following rules:
13.19/4.48	
13.19/4.48	   g(s(x)) -> f(x)
13.19/4.48	   f(0) -> s(0)
13.19/4.48	   f(s(x)) -> s(s(g(x)))
13.19/4.48	   g(0) -> 0
13.19/4.48	
13.19/4.48	S is empty.
13.19/4.48	Rewrite Strategy: INNERMOST
13.19/4.48	----------------------------------------
13.19/4.48	
13.19/4.48	(3) CpxTrsMatchBoundsProof (FINISHED)
13.19/4.48	A linear upper bound on the runtime complexity of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 1. 
13.19/4.48	The certificate found is represented by the following graph.
13.19/4.48	
13.19/4.48	"[1, 2, 3, 4, 5]
13.19/4.48	{(1,2,[g_1|0, f_1|0, f_1|1, 0|1]), (1,3,[s_1|1]), (1,4,[s_1|1]), (2,2,[s_1|0, 0|0]), (3,2,[0|1]), (4,5,[s_1|1]), (5,2,[g_1|1, f_1|1, 0|1]), (5,3,[s_1|1]), (5,4,[s_1|1])}"
13.19/4.48	----------------------------------------
13.19/4.48	
13.19/4.48	(4)
13.19/4.48	BOUNDS(1, n^1)
13.19/4.48	
13.19/4.48	----------------------------------------
13.19/4.48	
13.19/4.48	(5) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID))
13.19/4.48	Transformed a relative TRS into a decreasing-loop problem.
13.19/4.48	----------------------------------------
13.19/4.48	
13.19/4.48	(6)
13.19/4.48	Obligation:
13.19/4.48	Analyzing the following TRS for decreasing loops:
13.19/4.48	
13.19/4.48	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
13.19/4.48	
13.19/4.48	
13.19/4.48	The TRS R consists of the following rules:
13.19/4.48	
13.19/4.48	   g(s(x)) -> f(x)
13.19/4.48	   f(0) -> s(0)
13.19/4.48	   f(s(x)) -> s(s(g(x)))
13.19/4.48	   g(0) -> 0
13.19/4.48	
13.19/4.48	S is empty.
13.19/4.48	Rewrite Strategy: INNERMOST
13.19/4.48	----------------------------------------
13.19/4.48	
13.19/4.48	(7) DecreasingLoopProof (LOWER BOUND(ID))
13.19/4.48	The following loop(s) give(s) rise to the lower bound Omega(n^1):
13.19/4.48	
13.19/4.48	The rewrite sequence
13.19/4.48

popout

output may be truncated. 'popout' for the full output.

job log

popout

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