Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308520

details

property	value
status	complete
benchmark	#4.30b.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n160.star.cs.uiowa.edu
space	Strategy_removed_AG01

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	13.8995 seconds
cpu usage	46.5458
user time	44.7142
system time	1.8316
max virtual memory	3.750946E7
max residence set size	3909488.0

stage attributes

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

output

46.14/13.83	WORST_CASE(Omega(n^1), O(n^1))
46.46/13.85	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
46.46/13.85	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
46.46/13.85	
46.46/13.85	
46.46/13.85	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
46.46/13.85	
46.46/13.85	(0) CpxTRS
46.46/13.85	(1) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms]
46.46/13.85	(2) CpxTRS
46.46/13.85	    (3) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
46.46/13.85	    (4) CpxWeightedTrs
46.46/13.85	    (5) TypeInferenceProof [BOTH BOUNDS(ID, ID), 2 ms]
46.46/13.85	    (6) CpxTypedWeightedTrs
46.46/13.85	    (7) CompletionProof [UPPER BOUND(ID), 0 ms]
46.46/13.85	    (8) CpxTypedWeightedCompleteTrs
46.46/13.85	    (9) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
46.46/13.85	    (10) CpxRNTS
46.46/13.85	    (11) CompleteCoflocoProof [FINISHED, 504 ms]
46.46/13.85	    (12) BOUNDS(1, n^1)
46.46/13.85	(13) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
46.46/13.85	(14) CpxTRS
46.46/13.85	    (15) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
46.46/13.85	    (16) typed CpxTrs
46.46/13.85	    (17) OrderProof [LOWER BOUND(ID), 0 ms]
46.46/13.85	    (18) typed CpxTrs
46.46/13.85	    (19) RewriteLemmaProof [LOWER BOUND(ID), 298 ms]
46.46/13.85	    (20) BEST
46.46/13.85	        (21) proven lower bound
46.46/13.85	            (22) LowerBoundPropagationProof [FINISHED, 0 ms]
46.46/13.85	            (23) BOUNDS(n^1, INF)
46.46/13.85	        (24) typed CpxTrs
46.46/13.85	            (25) RewriteLemmaProof [LOWER BOUND(ID), 84 ms]
46.46/13.85	            (26) typed CpxTrs
46.46/13.85	
46.46/13.85	
46.46/13.85	----------------------------------------
46.46/13.85	
46.46/13.85	(0)
46.46/13.85	Obligation:
46.46/13.85	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
46.46/13.85	
46.46/13.85	
46.46/13.85	The TRS R consists of the following rules:
46.46/13.85	
46.46/13.85	   le(0, y) -> true
46.46/13.85	   le(s(x), 0) -> false
46.46/13.85	   le(s(x), s(y)) -> le(x, y)
46.46/13.85	   minus(x, 0) -> x
46.46/13.85	   minus(s(x), s(y)) -> minus(x, y)
46.46/13.85	   mod(0, y) -> 0
46.46/13.85	   mod(s(x), 0) -> 0
46.46/13.85	   mod(s(x), s(y)) -> if_mod(le(y, x), s(x), s(y))
46.46/13.85	   if_mod(true, x, y) -> mod(minus(x, y), y)
46.46/13.85	   if_mod(false, s(x), s(y)) -> s(x)
46.46/13.85	
46.46/13.85	S is empty.
46.46/13.85	Rewrite Strategy: FULL
46.46/13.85	----------------------------------------
46.46/13.85	
46.46/13.85	(1) RcToIrcProof (BOTH BOUNDS(ID, ID))
46.46/13.85	Converted rc-obligation to irc-obligation.
46.46/13.85	
46.46/13.85	The duplicating contexts are:
46.46/13.85	mod(s(x), s([]))
46.46/13.85	mod(s([]), s(y))
46.46/13.85	if_mod(true, x, [])
46.46/13.85	
46.46/13.85	
46.46/13.85	The defined contexts are:
46.46/13.85	if_mod([], s(x1), s(x2))
46.46/13.85	mod([], x1)
46.46/13.85	le(x0, [])
46.46/13.85	if_mod(x0, s([]), s(x2))
46.46/13.85	minus([], x1)
46.46/13.85	
46.46/13.85	
46.46/13.85	[] just represents basic- or constructor-terms in the following defined contexts:
46.46/13.85	if_mod([], s(x1), s(x2))
46.46/13.85	mod([], x1)
46.46/13.85	
46.46/13.85	
46.46/13.85	As the TRS is an overlay system and the defined contexts and the duplicating contexts don't overlap, we have rc = irc.
46.46/13.85	----------------------------------------
46.46/13.85	
46.46/13.85	(2)
46.46/13.85	Obligation:
46.46/13.85	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, n^1).
46.46/13.85	
46.46/13.85	
46.46/13.85	The TRS R consists of the following rules:
46.46/13.85	
46.46/13.85	   le(0, y) -> true
46.46/13.85	   le(s(x), 0) -> false
46.46/13.85	   le(s(x), s(y)) -> le(x, y)
46.46/13.85	   minus(x, 0) -> x
46.46/13.85	   minus(s(x), s(y)) -> minus(x, y)
46.46/13.85	   mod(0, y) -> 0
46.46/13.85	   mod(s(x), 0) -> 0
46.46/13.85	   mod(s(x), s(y)) -> if_mod(le(y, x), s(x), s(y))

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actions all output return to Runtime_Complexity_Full_Rewriting 2019-04-01 06.11