Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307725

details

property	value
status	complete
benchmark	#3.7.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n005.star.cs.uiowa.edu
space	AG01

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	6.30889 seconds
cpu usage	21.1103
user time	19.6756
system time	1.43469
max virtual memory	3.6978568E7
max residence set size	3926924.0

stage attributes

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

output

20.87/6.24	WORST_CASE(Omega(n^1), O(n^1))
20.87/6.25	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
20.87/6.25	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
20.87/6.25	
20.87/6.25	
20.87/6.25	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
20.87/6.25	
20.87/6.25	(0) CpxTRS
20.87/6.25	(1) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms]
20.87/6.25	(2) CpxTRS
20.87/6.25	    (3) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
20.87/6.25	    (4) CpxWeightedTrs
20.87/6.25	    (5) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
20.87/6.25	    (6) CpxTypedWeightedTrs
20.87/6.25	    (7) CompletionProof [UPPER BOUND(ID), 0 ms]
20.87/6.25	    (8) CpxTypedWeightedCompleteTrs
20.87/6.25	    (9) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
20.87/6.25	    (10) CpxRNTS
20.87/6.25	    (11) CompleteCoflocoProof [FINISHED, 128 ms]
20.87/6.25	    (12) BOUNDS(1, n^1)
20.87/6.25	(13) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
20.87/6.25	(14) TRS for Loop Detection
20.87/6.25	    (15) DecreasingLoopProof [LOWER BOUND(ID), 0 ms]
20.87/6.25	    (16) BEST
20.87/6.25	        (17) proven lower bound
20.87/6.25	            (18) LowerBoundPropagationProof [FINISHED, 0 ms]
20.87/6.25	            (19) BOUNDS(n^1, INF)
20.87/6.25	        (20) TRS for Loop Detection
20.87/6.25	
20.87/6.25	
20.87/6.25	----------------------------------------
20.87/6.25	
20.87/6.25	(0)
20.87/6.25	Obligation:
20.87/6.25	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
20.87/6.25	
20.87/6.25	
20.87/6.25	The TRS R consists of the following rules:
20.87/6.25	
20.87/6.25	   half(0) -> 0
20.87/6.25	   half(s(s(x))) -> s(half(x))
20.87/6.25	   log(s(0)) -> 0
20.87/6.25	   log(s(s(x))) -> s(log(s(half(x))))
20.87/6.25	
20.87/6.25	S is empty.
20.87/6.25	Rewrite Strategy: FULL
20.87/6.25	----------------------------------------
20.87/6.25	
20.87/6.25	(1) RcToIrcProof (BOTH BOUNDS(ID, ID))
20.87/6.25	Converted rc-obligation to irc-obligation.
20.87/6.25	
20.87/6.25	As the TRS is a non-duplicating overlay system, we have rc = irc.
20.87/6.25	----------------------------------------
20.87/6.25	
20.87/6.25	(2)
20.87/6.25	Obligation:
20.87/6.25	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, n^1).
20.87/6.25	
20.87/6.25	
20.87/6.25	The TRS R consists of the following rules:
20.87/6.25	
20.87/6.25	   half(0) -> 0
20.87/6.25	   half(s(s(x))) -> s(half(x))
20.87/6.25	   log(s(0)) -> 0
20.87/6.25	   log(s(s(x))) -> s(log(s(half(x))))
20.87/6.25	
20.87/6.25	S is empty.
20.87/6.25	Rewrite Strategy: INNERMOST
20.87/6.25	----------------------------------------
20.87/6.25	
20.87/6.25	(3) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID))
20.87/6.25	Transformed relative TRS to weighted TRS
20.87/6.25	----------------------------------------
20.87/6.25	
20.87/6.25	(4)
20.87/6.25	Obligation:
20.87/6.25	The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^1).
20.87/6.25	
20.87/6.25	
20.87/6.25	The TRS R consists of the following rules:
20.87/6.25	
20.87/6.25	   half(0) -> 0 [1]
20.87/6.25	   half(s(s(x))) -> s(half(x)) [1]
20.87/6.25	   log(s(0)) -> 0 [1]
20.87/6.25	   log(s(s(x))) -> s(log(s(half(x)))) [1]
20.87/6.25	
20.87/6.25	Rewrite Strategy: INNERMOST
20.87/6.25	----------------------------------------
20.87/6.25	
20.87/6.25	(5) TypeInferenceProof (BOTH BOUNDS(ID, ID))
20.87/6.25	Infered types.
20.87/6.25	----------------------------------------
20.87/6.25	
20.87/6.25	(6)
20.87/6.25	Obligation:
20.87/6.25	Runtime Complexity Weighted TRS with Types.
20.87/6.25	The TRS R consists of the following rules:
20.87/6.25	
20.87/6.25	   half(0) -> 0 [1]
20.87/6.25	   half(s(s(x))) -> s(half(x)) [1]

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