Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313457

details

property	value
status	complete
benchmark	Ex15_Luc06_GM.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n058.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	4.35272 seconds
cpu usage	12.5784
user time	11.1455
system time	1.43293
max virtual memory	1.8480104E7
max residence set size	4089516.0

stage attributes

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

output

12.50/4.29	WORST_CASE(Omega(n^1), O(n^1))
12.50/4.30	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
12.50/4.30	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
12.50/4.30	
12.50/4.30	
12.50/4.30	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
12.50/4.30	
12.50/4.30	(0) CpxTRS
12.50/4.30	(1) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms]
12.50/4.30	(2) CpxTRS
12.50/4.30	    (3) CpxTrsMatchBoundsProof [FINISHED, 0 ms]
12.50/4.30	    (4) BOUNDS(1, n^1)
12.50/4.30	(5) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
12.50/4.30	(6) TRS for Loop Detection
12.50/4.30	    (7) DecreasingLoopProof [LOWER BOUND(ID), 0 ms]
12.50/4.30	    (8) BEST
12.50/4.30	        (9) proven lower bound
12.50/4.30	            (10) LowerBoundPropagationProof [FINISHED, 0 ms]
12.50/4.30	            (11) BOUNDS(n^1, INF)
12.50/4.30	        (12) TRS for Loop Detection
12.50/4.30	
12.50/4.30	
12.50/4.30	----------------------------------------
12.50/4.30	
12.50/4.30	(0)
12.50/4.30	Obligation:
12.50/4.30	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
12.50/4.30	
12.50/4.30	
12.50/4.30	The TRS R consists of the following rules:
12.50/4.30	
12.50/4.30	   a__f(f(a)) -> a__f(g(f(a)))
12.50/4.30	   mark(f(X)) -> a__f(X)
12.50/4.30	   mark(a) -> a
12.50/4.30	   mark(g(X)) -> g(mark(X))
12.50/4.30	   a__f(X) -> f(X)
12.50/4.30	
12.50/4.30	S is empty.
12.50/4.30	Rewrite Strategy: INNERMOST
12.50/4.30	----------------------------------------
12.50/4.30	
12.50/4.30	(1) RelTrsToTrsProof (UPPER BOUND(ID))
12.50/4.30	transformed relative TRS to TRS
12.50/4.30	----------------------------------------
12.50/4.30	
12.50/4.30	(2)
12.50/4.30	Obligation:
12.50/4.30	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, n^1).
12.50/4.30	
12.50/4.30	
12.50/4.30	The TRS R consists of the following rules:
12.50/4.30	
12.50/4.30	   a__f(f(a)) -> a__f(g(f(a)))
12.50/4.30	   mark(f(X)) -> a__f(X)
12.50/4.30	   mark(a) -> a
12.50/4.30	   mark(g(X)) -> g(mark(X))
12.50/4.30	   a__f(X) -> f(X)
12.50/4.30	
12.50/4.30	S is empty.
12.50/4.30	Rewrite Strategy: INNERMOST
12.50/4.30	----------------------------------------
12.50/4.30	
12.50/4.30	(3) CpxTrsMatchBoundsProof (FINISHED)
12.50/4.30	A linear upper bound on the runtime complexity of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 2. 
12.50/4.30	The certificate found is represented by the following graph.
12.50/4.30	
12.50/4.30	"[1, 2, 3, 4, 5, 6]
12.50/4.30	{(1,2,[a__f_1|0, mark_1|0, f_1|1, a__f_1|1, a|1, f_1|2]), (1,3,[a__f_1|1, f_1|2]), (1,6,[g_1|1]), (2,2,[f_1|0, a|0, g_1|0]), (3,4,[g_1|1]), (4,5,[f_1|1]), (5,2,[a|1]), (6,2,[mark_1|1, a__f_1|1, a|1, f_1|2]), (6,6,[g_1|1]), (6,3,[a__f_1|1, f_1|2])}"
12.50/4.30	----------------------------------------
12.50/4.30	
12.50/4.30	(4)
12.50/4.30	BOUNDS(1, n^1)
12.50/4.30	
12.50/4.30	----------------------------------------
12.50/4.30	
12.50/4.30	(5) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID))
12.50/4.30	Transformed a relative TRS into a decreasing-loop problem.
12.50/4.30	----------------------------------------
12.50/4.30	
12.50/4.30	(6)
12.50/4.30	Obligation:
12.50/4.30	Analyzing the following TRS for decreasing loops:
12.50/4.30	
12.50/4.30	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
12.50/4.30	
12.50/4.30	
12.50/4.30	The TRS R consists of the following rules:
12.50/4.30	
12.50/4.30	   a__f(f(a)) -> a__f(g(f(a)))
12.50/4.30	   mark(f(X)) -> a__f(X)
12.50/4.30	   mark(a) -> a
12.50/4.30	   mark(g(X)) -> g(mark(X))
12.50/4.30	   a__f(X) -> f(X)
12.50/4.30	
12.50/4.30	S is empty.
12.50/4.30	Rewrite Strategy: INNERMOST
12.50/4.30	----------------------------------------
12.50/4.30	
12.50/4.30	(7) DecreasingLoopProof (LOWER BOUND(ID))
12.50/4.30	The following loop(s) give(s) rise to the lower bound Omega(n^1):

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