Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308152

details

property	value
status	complete
benchmark	Ex16_Luc06_GM.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n050.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	9.41568 seconds
cpu usage	21.2952
user time	20.2236
system time	1.07156
max virtual memory	1.8943404E7
max residence set size	3136704.0

stage attributes

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

output

20.96/6.29	WORST_CASE(Omega(n^1), O(n^1))
20.96/6.30	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
20.96/6.30	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
20.96/6.30	
20.96/6.30	
20.96/6.30	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
20.96/6.30	
20.96/6.30	(0) CpxTRS
20.96/6.30	(1) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms]
20.96/6.30	(2) CpxTRS
20.96/6.30	    (3) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
20.96/6.30	    (4) CpxWeightedTrs
20.96/6.30	    (5) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
20.96/6.30	    (6) CpxTypedWeightedTrs
20.96/6.30	    (7) CompletionProof [UPPER BOUND(ID), 0 ms]
20.96/6.30	    (8) CpxTypedWeightedCompleteTrs
20.96/6.30	    (9) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
20.96/6.30	    (10) CpxRNTS
20.96/6.30	    (11) CompleteCoflocoProof [FINISHED, 176 ms]
20.96/6.30	    (12) BOUNDS(1, n^1)
20.96/6.30	(13) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
20.96/6.30	(14) CpxTRS
20.96/6.30	    (15) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
20.96/6.30	    (16) typed CpxTrs
20.96/6.30	    (17) OrderProof [LOWER BOUND(ID), 0 ms]
20.96/6.30	    (18) typed CpxTrs
20.96/6.30	    (19) RewriteLemmaProof [LOWER BOUND(ID), 3275 ms]
20.96/6.30	    (20) proven lower bound
20.96/6.30	    (21) LowerBoundPropagationProof [FINISHED, 0 ms]
20.96/6.30	    (22) BOUNDS(n^1, INF)
20.96/6.30	
20.96/6.30	
20.96/6.30	----------------------------------------
20.96/6.30	
20.96/6.30	(0)
20.96/6.30	Obligation:
20.96/6.30	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
20.96/6.30	
20.96/6.30	
20.96/6.30	The TRS R consists of the following rules:
20.96/6.30	
20.96/6.30	   a__f(X, X) -> a__f(a, b)
20.96/6.30	   a__b -> a
20.96/6.30	   mark(f(X1, X2)) -> a__f(mark(X1), X2)
20.96/6.30	   mark(b) -> a__b
20.96/6.30	   mark(a) -> a
20.96/6.30	   a__f(X1, X2) -> f(X1, X2)
20.96/6.30	   a__b -> b
20.96/6.30	
20.96/6.30	S is empty.
20.96/6.30	Rewrite Strategy: FULL
20.96/6.30	----------------------------------------
20.96/6.30	
20.96/6.30	(1) RcToIrcProof (BOTH BOUNDS(ID, ID))
20.96/6.30	Converted rc-obligation to irc-obligation.
20.96/6.30	
20.96/6.30	As the TRS is a non-duplicating overlay system, we have rc = irc.
20.96/6.30	----------------------------------------
20.96/6.30	
20.96/6.30	(2)
20.96/6.30	Obligation:
20.96/6.30	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, n^1).
20.96/6.30	
20.96/6.30	
20.96/6.30	The TRS R consists of the following rules:
20.96/6.30	
20.96/6.30	   a__f(X, X) -> a__f(a, b)
20.96/6.30	   a__b -> a
20.96/6.30	   mark(f(X1, X2)) -> a__f(mark(X1), X2)
20.96/6.30	   mark(b) -> a__b
20.96/6.30	   mark(a) -> a
20.96/6.30	   a__f(X1, X2) -> f(X1, X2)
20.96/6.30	   a__b -> b
20.96/6.30	
20.96/6.30	S is empty.
20.96/6.30	Rewrite Strategy: INNERMOST
20.96/6.30	----------------------------------------
20.96/6.30	
20.96/6.30	(3) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID))
20.96/6.30	Transformed relative TRS to weighted TRS
20.96/6.30	----------------------------------------
20.96/6.30	
20.96/6.30	(4)
20.96/6.30	Obligation:
20.96/6.30	The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^1).
20.96/6.30	
20.96/6.30	
20.96/6.30	The TRS R consists of the following rules:
20.96/6.30	
20.96/6.30	   a__f(X, X) -> a__f(a, b) [1]
20.96/6.30	   a__b -> a [1]
20.96/6.30	   mark(f(X1, X2)) -> a__f(mark(X1), X2) [1]
20.96/6.30	   mark(b) -> a__b [1]
20.96/6.30	   mark(a) -> a [1]
20.96/6.30	   a__f(X1, X2) -> f(X1, X2) [1]
20.96/6.30	   a__b -> b [1]
20.96/6.30	
20.96/6.30	Rewrite Strategy: INNERMOST
20.96/6.30	----------------------------------------
20.96/6.30

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