Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307882

details

property	value
status	complete
benchmark	tpa2.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n135.star.cs.uiowa.edu
space	Secret_05_TRS

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	291.565 seconds
cpu usage	303.106
user time	300.87
system time	2.23625
max virtual memory	1.8279384E7
max residence set size	5326224.0

stage attributes

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

output

302.99/291.52	WORST_CASE(Omega(n^1), ?)
302.99/291.53	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
302.99/291.53	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
302.99/291.53	
302.99/291.53	
302.99/291.53	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF).
302.99/291.53	
302.99/291.53	(0) CpxTRS
302.99/291.53	(1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
302.99/291.53	(2) TRS for Loop Detection
302.99/291.53	(3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms]
302.99/291.53	(4) BEST
302.99/291.53	    (5) proven lower bound
302.99/291.53	        (6) LowerBoundPropagationProof [FINISHED, 0 ms]
302.99/291.53	        (7) BOUNDS(n^1, INF)
302.99/291.53	    (8) TRS for Loop Detection
302.99/291.53	
302.99/291.53	
302.99/291.53	----------------------------------------
302.99/291.53	
302.99/291.53	(0)
302.99/291.53	Obligation:
302.99/291.53	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF).
302.99/291.53	
302.99/291.53	
302.99/291.53	The TRS R consists of the following rules:
302.99/291.53	
302.99/291.53	   -(x, 0) -> x
302.99/291.53	   -(s(x), s(y)) -> -(x, y)
302.99/291.53	   p(s(x)) -> x
302.99/291.53	   f(s(x), y) -> f(p(-(s(x), y)), p(-(y, s(x))))
302.99/291.53	   f(x, s(y)) -> f(p(-(x, s(y))), p(-(s(y), x)))
302.99/291.53	
302.99/291.53	S is empty.
302.99/291.53	Rewrite Strategy: FULL
302.99/291.53	----------------------------------------
302.99/291.53	
302.99/291.53	(1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID))
302.99/291.53	Transformed a relative TRS into a decreasing-loop problem.
302.99/291.53	----------------------------------------
302.99/291.53	
302.99/291.53	(2)
302.99/291.53	Obligation:
302.99/291.53	Analyzing the following TRS for decreasing loops:
302.99/291.53	
302.99/291.53	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF).
302.99/291.53	
302.99/291.53	
302.99/291.53	The TRS R consists of the following rules:
302.99/291.53	
302.99/291.53	   -(x, 0) -> x
302.99/291.53	   -(s(x), s(y)) -> -(x, y)
302.99/291.53	   p(s(x)) -> x
302.99/291.53	   f(s(x), y) -> f(p(-(s(x), y)), p(-(y, s(x))))
302.99/291.53	   f(x, s(y)) -> f(p(-(x, s(y))), p(-(s(y), x)))
302.99/291.53	
302.99/291.53	S is empty.
302.99/291.53	Rewrite Strategy: FULL
302.99/291.53	----------------------------------------
302.99/291.53	
302.99/291.53	(3) DecreasingLoopProof (LOWER BOUND(ID))
302.99/291.53	The following loop(s) give(s) rise to the lower bound Omega(n^1):
302.99/291.53	
302.99/291.53	The rewrite sequence
302.99/291.53	
302.99/291.53	-(s(x), s(y)) ->^+ -(x, y)
302.99/291.53	
302.99/291.53	gives rise to a decreasing loop by considering the right hand sides subterm at position [].
302.99/291.53	
302.99/291.53	The pumping substitution is [x / s(x), y / s(y)].
302.99/291.53	
302.99/291.53	The result substitution is [ ].
302.99/291.53	
302.99/291.53	
302.99/291.53	
302.99/291.53	
302.99/291.53	----------------------------------------
302.99/291.53	
302.99/291.53	(4)
302.99/291.53	Complex Obligation (BEST)
302.99/291.53	
302.99/291.53	----------------------------------------
302.99/291.53	
302.99/291.53	(5)
302.99/291.53	Obligation:
302.99/291.53	Proved the lower bound n^1 for the following obligation:
302.99/291.53	
302.99/291.53	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF).
302.99/291.53	
302.99/291.53	
302.99/291.53	The TRS R consists of the following rules:
302.99/291.53	
302.99/291.53	   -(x, 0) -> x
302.99/291.53	   -(s(x), s(y)) -> -(x, y)
302.99/291.53	   p(s(x)) -> x
302.99/291.53	   f(s(x), y) -> f(p(-(s(x), y)), p(-(y, s(x))))
302.99/291.53	   f(x, s(y)) -> f(p(-(x, s(y))), p(-(s(y), x)))
302.99/291.53	
302.99/291.53	S is empty.
302.99/291.53	Rewrite Strategy: FULL

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