Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307901

details

property	value
status	complete
benchmark	08.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n098.star.cs.uiowa.edu
space	Der95

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	5.70201 seconds
cpu usage	15.6435
user time	14.6099
system time	1.03353
max virtual memory	7.4891024E7
max residence set size	3062152.0

stage attributes

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

output

15.47/5.65	WORST_CASE(Omega(n^1), O(n^1))
15.59/5.66	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
15.59/5.66	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
15.59/5.66	
15.59/5.66	
15.59/5.66	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
15.59/5.66	
15.59/5.66	(0) CpxTRS
15.59/5.66	(1) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms]
15.59/5.66	(2) CpxTRS
15.59/5.66	    (3) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
15.59/5.66	    (4) CpxWeightedTrs
15.59/5.66	    (5) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
15.59/5.66	    (6) CpxTypedWeightedTrs
15.59/5.66	    (7) CompletionProof [UPPER BOUND(ID), 0 ms]
15.59/5.66	    (8) CpxTypedWeightedCompleteTrs
15.59/5.66	    (9) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
15.59/5.66	    (10) CpxTypedWeightedCompleteTrs
15.59/5.66	    (11) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
15.59/5.66	    (12) CpxRNTS
15.59/5.66	    (13) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms]
15.59/5.66	    (14) CpxRNTS
15.59/5.66	    (15) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms]
15.59/5.66	    (16) CpxRNTS
15.59/5.66	    (17) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
15.59/5.66	    (18) CpxRNTS
15.59/5.66	    (19) IntTrsBoundProof [UPPER BOUND(ID), 605 ms]
15.59/5.66	    (20) CpxRNTS
15.59/5.66	    (21) IntTrsBoundProof [UPPER BOUND(ID), 117 ms]
15.59/5.66	    (22) CpxRNTS
15.59/5.66	    (23) FinalProof [FINISHED, 0 ms]
15.59/5.66	    (24) BOUNDS(1, n^1)
15.59/5.66	(25) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
15.59/5.66	(26) CpxTRS
15.59/5.66	    (27) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
15.59/5.66	    (28) typed CpxTrs
15.59/5.66	    (29) OrderProof [LOWER BOUND(ID), 0 ms]
15.59/5.66	    (30) typed CpxTrs
15.59/5.66	    (31) RewriteLemmaProof [LOWER BOUND(ID), 641 ms]
15.59/5.66	    (32) proven lower bound
15.59/5.66	    (33) LowerBoundPropagationProof [FINISHED, 0 ms]
15.59/5.66	    (34) BOUNDS(n^1, INF)
15.59/5.66	
15.59/5.66	
15.59/5.66	----------------------------------------
15.59/5.66	
15.59/5.66	(0)
15.59/5.66	Obligation:
15.59/5.66	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
15.59/5.66	
15.59/5.66	
15.59/5.66	The TRS R consists of the following rules:
15.59/5.66	
15.59/5.66	   D(t) -> 1
15.59/5.66	   D(constant) -> 0
15.59/5.66	   D(+(x, y)) -> +(D(x), D(y))
15.59/5.66	   D(*(x, y)) -> +(*(y, D(x)), *(x, D(y)))
15.59/5.66	   D(-(x, y)) -> -(D(x), D(y))
15.59/5.66	
15.59/5.66	S is empty.
15.59/5.66	Rewrite Strategy: FULL
15.59/5.66	----------------------------------------
15.59/5.66	
15.59/5.66	(1) RcToIrcProof (BOTH BOUNDS(ID, ID))
15.59/5.66	Converted rc-obligation to irc-obligation.
15.59/5.66	
15.59/5.66	As the TRS does not nest defined symbols, we have rc = irc.
15.59/5.66	----------------------------------------
15.59/5.66	
15.59/5.66	(2)
15.59/5.66	Obligation:
15.59/5.66	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, n^1).
15.59/5.66	
15.59/5.66	
15.59/5.66	The TRS R consists of the following rules:
15.59/5.66	
15.59/5.66	   D(t) -> 1
15.59/5.66	   D(constant) -> 0
15.59/5.66	   D(+(x, y)) -> +(D(x), D(y))
15.59/5.66	   D(*(x, y)) -> +(*(y, D(x)), *(x, D(y)))
15.59/5.66	   D(-(x, y)) -> -(D(x), D(y))
15.59/5.66	
15.59/5.66	S is empty.
15.59/5.66	Rewrite Strategy: INNERMOST
15.59/5.66	----------------------------------------
15.59/5.66	
15.59/5.66	(3) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID))
15.59/5.66	Transformed relative TRS to weighted TRS
15.59/5.66	----------------------------------------
15.59/5.66	
15.59/5.66	(4)
15.59/5.66	Obligation:
15.59/5.66	The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^1).
15.59/5.66	
15.59/5.66	
15.59/5.66	The TRS R consists of the following rules:
15.59/5.66	
15.59/5.66	   D(t) -> 1 [1]
15.59/5.66	   D(constant) -> 0 [1]
15.59/5.66	   D(+(x, y)) -> +(D(x), D(y)) [1]

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