Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307929

details

property	value
status	complete
benchmark	cade09.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n084.star.cs.uiowa.edu
space	GTSSK07

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	291.579 seconds
cpu usage	307.144
user time	305.211
system time	1.93273
max virtual memory	1.8281052E7
max residence set size	5344228.0

stage attributes

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

output

306.99/291.50	WORST_CASE(Omega(n^1), ?)
306.99/291.50	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
306.99/291.50	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
306.99/291.50	
306.99/291.50	
306.99/291.50	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF).
306.99/291.50	
306.99/291.50	(0) CpxTRS
306.99/291.50	(1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
306.99/291.50	(2) TRS for Loop Detection
306.99/291.50	(3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms]
306.99/291.50	(4) BEST
306.99/291.50	    (5) proven lower bound
306.99/291.50	        (6) LowerBoundPropagationProof [FINISHED, 0 ms]
306.99/291.50	        (7) BOUNDS(n^1, INF)
306.99/291.50	    (8) TRS for Loop Detection
306.99/291.50	
306.99/291.50	
306.99/291.50	----------------------------------------
306.99/291.50	
306.99/291.50	(0)
306.99/291.50	Obligation:
306.99/291.50	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF).
306.99/291.50	
306.99/291.50	
306.99/291.50	The TRS R consists of the following rules:
306.99/291.50	
306.99/291.50	   f(true, x, y) -> f(gt(x, y), x, round(s(y)))
306.99/291.50	   round(0) -> 0
306.99/291.50	   round(s(0)) -> s(s(0))
306.99/291.50	   round(s(s(x))) -> s(s(round(x)))
306.99/291.50	   gt(0, v) -> false
306.99/291.50	   gt(s(u), 0) -> true
306.99/291.50	   gt(s(u), s(v)) -> gt(u, v)
306.99/291.50	
306.99/291.50	S is empty.
306.99/291.50	Rewrite Strategy: FULL
306.99/291.50	----------------------------------------
306.99/291.50	
306.99/291.50	(1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID))
306.99/291.50	Transformed a relative TRS into a decreasing-loop problem.
306.99/291.50	----------------------------------------
306.99/291.50	
306.99/291.50	(2)
306.99/291.50	Obligation:
306.99/291.50	Analyzing the following TRS for decreasing loops:
306.99/291.50	
306.99/291.50	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF).
306.99/291.50	
306.99/291.50	
306.99/291.50	The TRS R consists of the following rules:
306.99/291.50	
306.99/291.50	   f(true, x, y) -> f(gt(x, y), x, round(s(y)))
306.99/291.50	   round(0) -> 0
306.99/291.50	   round(s(0)) -> s(s(0))
306.99/291.50	   round(s(s(x))) -> s(s(round(x)))
306.99/291.50	   gt(0, v) -> false
306.99/291.50	   gt(s(u), 0) -> true
306.99/291.50	   gt(s(u), s(v)) -> gt(u, v)
306.99/291.50	
306.99/291.50	S is empty.
306.99/291.50	Rewrite Strategy: FULL
306.99/291.50	----------------------------------------
306.99/291.50	
306.99/291.50	(3) DecreasingLoopProof (LOWER BOUND(ID))
306.99/291.50	The following loop(s) give(s) rise to the lower bound Omega(n^1):
306.99/291.50	
306.99/291.50	The rewrite sequence
306.99/291.50	
306.99/291.50	gt(s(u), s(v)) ->^+ gt(u, v)
306.99/291.50	
306.99/291.50	gives rise to a decreasing loop by considering the right hand sides subterm at position [].
306.99/291.50	
306.99/291.50	The pumping substitution is [u / s(u), v / s(v)].
306.99/291.50	
306.99/291.50	The result substitution is [ ].
306.99/291.50	
306.99/291.50	
306.99/291.50	
306.99/291.50	
306.99/291.50	----------------------------------------
306.99/291.50	
306.99/291.51	(4)
306.99/291.51	Complex Obligation (BEST)
306.99/291.51	
306.99/291.51	----------------------------------------
306.99/291.51	
306.99/291.51	(5)
306.99/291.51	Obligation:
306.99/291.51	Proved the lower bound n^1 for the following obligation:
306.99/291.51	
306.99/291.51	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF).
306.99/291.51	
306.99/291.51	
306.99/291.51	The TRS R consists of the following rules:
306.99/291.51	
306.99/291.51	   f(true, x, y) -> f(gt(x, y), x, round(s(y)))
306.99/291.51	   round(0) -> 0
306.99/291.51	   round(s(0)) -> s(s(0))
306.99/291.51	   round(s(s(x))) -> s(s(round(x)))

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