Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307689

details

property	value
status	complete
benchmark	#3.49.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n009.star.cs.uiowa.edu
space	AG01

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	291.535 seconds
cpu usage	912.232
user time	905.696
system time	6.53546
max virtual memory	3.7829348E7
max residence set size	7425580.0

stage attributes

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

output

912.09/291.48	WORST_CASE(Omega(n^1), ?)
912.09/291.48	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
912.09/291.48	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
912.09/291.48	
912.09/291.48	
912.09/291.48	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF).
912.09/291.48	
912.09/291.48	(0) CpxTRS
912.09/291.48	(1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
912.09/291.48	(2) TRS for Loop Detection
912.09/291.48	(3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms]
912.09/291.48	(4) BEST
912.09/291.48	    (5) proven lower bound
912.09/291.48	        (6) LowerBoundPropagationProof [FINISHED, 0 ms]
912.09/291.48	        (7) BOUNDS(n^1, INF)
912.09/291.48	    (8) TRS for Loop Detection
912.09/291.48	
912.09/291.48	
912.09/291.48	----------------------------------------
912.09/291.48	
912.09/291.48	(0)
912.09/291.48	Obligation:
912.09/291.48	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF).
912.09/291.48	
912.09/291.48	
912.09/291.48	The TRS R consists of the following rules:
912.09/291.48	
912.09/291.48	   f(c(s(x), y)) -> f(c(x, s(y)))
912.09/291.48	   f(c(s(x), s(y))) -> g(c(x, y))
912.09/291.48	   g(c(x, s(y))) -> g(c(s(x), y))
912.09/291.48	   g(c(s(x), s(y))) -> f(c(x, y))
912.09/291.48	
912.09/291.48	S is empty.
912.09/291.48	Rewrite Strategy: FULL
912.09/291.48	----------------------------------------
912.09/291.48	
912.09/291.48	(1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID))
912.09/291.48	Transformed a relative TRS into a decreasing-loop problem.
912.09/291.48	----------------------------------------
912.09/291.48	
912.09/291.48	(2)
912.09/291.48	Obligation:
912.09/291.48	Analyzing the following TRS for decreasing loops:
912.09/291.48	
912.09/291.48	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF).
912.09/291.48	
912.09/291.48	
912.09/291.48	The TRS R consists of the following rules:
912.09/291.48	
912.09/291.48	   f(c(s(x), y)) -> f(c(x, s(y)))
912.09/291.48	   f(c(s(x), s(y))) -> g(c(x, y))
912.09/291.48	   g(c(x, s(y))) -> g(c(s(x), y))
912.09/291.48	   g(c(s(x), s(y))) -> f(c(x, y))
912.09/291.48	
912.09/291.48	S is empty.
912.09/291.48	Rewrite Strategy: FULL
912.09/291.48	----------------------------------------
912.09/291.48	
912.09/291.48	(3) DecreasingLoopProof (LOWER BOUND(ID))
912.09/291.48	The following loop(s) give(s) rise to the lower bound Omega(n^1):
912.09/291.48	
912.09/291.48	The rewrite sequence
912.09/291.48	
912.09/291.48	g(c(x, s(y))) ->^+ g(c(s(x), y))
912.09/291.48	
912.09/291.48	gives rise to a decreasing loop by considering the right hand sides subterm at position [].
912.09/291.48	
912.09/291.48	The pumping substitution is [y / s(y)].
912.09/291.48	
912.09/291.48	The result substitution is [x / s(x)].
912.09/291.48	
912.09/291.48	
912.09/291.48	
912.09/291.48	
912.09/291.48	----------------------------------------
912.09/291.48	
912.09/291.48	(4)
912.09/291.48	Complex Obligation (BEST)
912.09/291.48	
912.09/291.48	----------------------------------------
912.09/291.48	
912.09/291.48	(5)
912.09/291.48	Obligation:
912.09/291.48	Proved the lower bound n^1 for the following obligation:
912.09/291.48	
912.09/291.48	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF).
912.09/291.48	
912.09/291.48	
912.09/291.48	The TRS R consists of the following rules:
912.09/291.48	
912.09/291.48	   f(c(s(x), y)) -> f(c(x, s(y)))
912.09/291.48	   f(c(s(x), s(y))) -> g(c(x, y))
912.09/291.48	   g(c(x, s(y))) -> g(c(s(x), y))
912.09/291.48	   g(c(s(x), s(y))) -> f(c(x, y))
912.09/291.48	
912.09/291.48	S is empty.
912.09/291.48	Rewrite Strategy: FULL
912.09/291.48	----------------------------------------
912.09/291.48	
912.09/291.48	(6) LowerBoundPropagationProof (FINISHED)

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