Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307919

details

property	value
status	complete
benchmark	t014.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n110.star.cs.uiowa.edu
space	HirokawaMiddeldorp_04

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	9.42793 seconds
cpu usage	23.984
user time	22.0048
system time	1.97922
max virtual memory	5.5937932E7
max residence set size	4142844.0

stage attributes

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

output

23.71/9.02	WORST_CASE(Omega(n^1), O(n^1))
23.71/9.03	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
23.71/9.03	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
23.71/9.03	
23.71/9.03	
23.71/9.03	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
23.71/9.03	
23.71/9.03	(0) CpxTRS
23.71/9.03	(1) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms]
23.71/9.03	(2) CpxTRS
23.71/9.03	    (3) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
23.71/9.03	    (4) CpxWeightedTrs
23.71/9.03	    (5) CpxWeightedTrsRenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
23.71/9.03	    (6) CpxWeightedTrs
23.71/9.03	    (7) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
23.71/9.03	    (8) CpxTypedWeightedTrs
23.71/9.03	    (9) CompletionProof [UPPER BOUND(ID), 0 ms]
23.71/9.03	    (10) CpxTypedWeightedCompleteTrs
23.71/9.03	    (11) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
23.71/9.03	    (12) CpxRNTS
23.71/9.03	    (13) CompleteCoflocoProof [FINISHED, 360 ms]
23.71/9.03	    (14) BOUNDS(1, n^1)
23.71/9.03	(15) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
23.71/9.03	(16) CpxTRS
23.71/9.03	    (17) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
23.71/9.03	    (18) typed CpxTrs
23.71/9.03	    (19) OrderProof [LOWER BOUND(ID), 0 ms]
23.71/9.03	    (20) typed CpxTrs
23.71/9.03	    (21) RewriteLemmaProof [LOWER BOUND(ID), 329 ms]
23.71/9.03	    (22) BEST
23.71/9.03	        (23) proven lower bound
23.71/9.03	            (24) LowerBoundPropagationProof [FINISHED, 0 ms]
23.71/9.03	            (25) BOUNDS(n^1, INF)
23.71/9.03	        (26) typed CpxTrs
23.71/9.03	            (27) RewriteLemmaProof [LOWER BOUND(ID), 44 ms]
23.71/9.03	            (28) typed CpxTrs
23.71/9.03	
23.71/9.03	
23.71/9.03	----------------------------------------
23.71/9.03	
23.71/9.03	(0)
23.71/9.03	Obligation:
23.71/9.03	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
23.71/9.03	
23.71/9.03	
23.71/9.03	The TRS R consists of the following rules:
23.71/9.03	
23.71/9.03	   -(x, 0) -> x
23.71/9.03	   -(0, s(y)) -> 0
23.71/9.03	   -(s(x), s(y)) -> -(x, y)
23.71/9.03	   lt(x, 0) -> false
23.71/9.03	   lt(0, s(y)) -> true
23.71/9.03	   lt(s(x), s(y)) -> lt(x, y)
23.71/9.03	   if(true, x, y) -> x
23.71/9.03	   if(false, x, y) -> y
23.71/9.03	   div(x, 0) -> 0
23.71/9.03	   div(0, y) -> 0
23.71/9.03	   div(s(x), s(y)) -> if(lt(x, y), 0, s(div(-(x, y), s(y))))
23.71/9.03	
23.71/9.03	S is empty.
23.71/9.03	Rewrite Strategy: FULL
23.71/9.03	----------------------------------------
23.71/9.03	
23.71/9.03	(1) RcToIrcProof (BOTH BOUNDS(ID, ID))
23.71/9.03	Converted rc-obligation to irc-obligation.
23.71/9.03	
23.71/9.03	The duplicating contexts are:
23.71/9.03	div(s([]), s(y))
23.71/9.03	div(s(x), s([]))
23.71/9.03	
23.71/9.03	
23.71/9.03	The defined contexts are:
23.71/9.03	if([], 0, s(x1))
23.71/9.03	if(x0, 0, s([]))
23.71/9.03	div([], s(x1))
23.71/9.03	lt([], x1)
23.71/9.03	-([], x1)
23.71/9.03	
23.71/9.03	
23.71/9.03	[] just represents basic- or constructor-terms in the following defined contexts:
23.71/9.03	if([], 0, s(x1))
23.71/9.03	div([], s(x1))
23.71/9.03	
23.71/9.03	
23.71/9.03	As the TRS is an overlay system and the defined contexts and the duplicating contexts don't overlap, we have rc = irc.
23.71/9.03	----------------------------------------
23.71/9.03	
23.71/9.03	(2)
23.71/9.03	Obligation:
23.71/9.03	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, n^1).
23.71/9.03	
23.71/9.03	
23.71/9.03	The TRS R consists of the following rules:
23.71/9.03	
23.71/9.03	   -(x, 0) -> x
23.71/9.03	   -(0, s(y)) -> 0
23.71/9.03	   -(s(x), s(y)) -> -(x, y)
23.71/9.03	   lt(x, 0) -> false
23.71/9.03	   lt(0, s(y)) -> true
23.71/9.03	   lt(s(x), s(y)) -> lt(x, y)

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