Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308441

details

property	value
status	complete
benchmark	2.16.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n161.star.cs.uiowa.edu
space	SK90

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	8.77658 seconds
cpu usage	26.367
user time	24.6001
system time	1.76684
max virtual memory	1.9080616E7
max residence set size	3939116.0

stage attributes

key	value
starexec-result	WORST_CASE(Omega(n^2), O(n^2))

output

26.12/8.71	WORST_CASE(Omega(n^2), O(n^2))
26.12/8.73	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
26.12/8.73	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
26.12/8.73	
26.12/8.73	
26.12/8.73	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^2, n^2).
26.12/8.73	
26.12/8.73	(0) CpxTRS
26.12/8.73	(1) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms]
26.12/8.73	(2) CpxTRS
26.12/8.73	    (3) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
26.12/8.73	    (4) CpxWeightedTrs
26.12/8.73	    (5) CpxWeightedTrsRenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
26.12/8.73	    (6) CpxWeightedTrs
26.12/8.73	    (7) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
26.12/8.73	    (8) CpxTypedWeightedTrs
26.12/8.73	    (9) CompletionProof [UPPER BOUND(ID), 0 ms]
26.12/8.73	    (10) CpxTypedWeightedCompleteTrs
26.12/8.73	    (11) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
26.12/8.73	    (12) CpxTypedWeightedCompleteTrs
26.12/8.73	    (13) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
26.12/8.73	    (14) CpxRNTS
26.12/8.73	    (15) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms]
26.12/8.73	    (16) CpxRNTS
26.12/8.73	    (17) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms]
26.12/8.73	    (18) CpxRNTS
26.12/8.73	    (19) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
26.12/8.73	    (20) CpxRNTS
26.12/8.73	    (21) IntTrsBoundProof [UPPER BOUND(ID), 360 ms]
26.12/8.73	    (22) CpxRNTS
26.12/8.73	    (23) IntTrsBoundProof [UPPER BOUND(ID), 75 ms]
26.12/8.73	    (24) CpxRNTS
26.12/8.73	    (25) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
26.12/8.73	    (26) CpxRNTS
26.12/8.73	    (27) IntTrsBoundProof [UPPER BOUND(ID), 836 ms]
26.12/8.73	    (28) CpxRNTS
26.12/8.73	    (29) IntTrsBoundProof [UPPER BOUND(ID), 370 ms]
26.12/8.73	    (30) CpxRNTS
26.12/8.73	    (31) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
26.12/8.73	    (32) CpxRNTS
26.12/8.73	    (33) IntTrsBoundProof [UPPER BOUND(ID), 740 ms]
26.12/8.73	    (34) CpxRNTS
26.12/8.73	    (35) IntTrsBoundProof [UPPER BOUND(ID), 0 ms]
26.12/8.73	    (36) CpxRNTS
26.12/8.73	    (37) FinalProof [FINISHED, 0 ms]
26.12/8.73	    (38) BOUNDS(1, n^2)
26.12/8.73	(39) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
26.12/8.73	(40) CpxTRS
26.12/8.73	    (41) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
26.12/8.73	    (42) typed CpxTrs
26.12/8.73	    (43) OrderProof [LOWER BOUND(ID), 0 ms]
26.12/8.73	    (44) typed CpxTrs
26.12/8.73	    (45) RewriteLemmaProof [LOWER BOUND(ID), 284 ms]
26.12/8.73	    (46) BEST
26.12/8.73	        (47) proven lower bound
26.12/8.73	            (48) LowerBoundPropagationProof [FINISHED, 0 ms]
26.12/8.73	            (49) BOUNDS(n^1, INF)
26.12/8.73	        (50) typed CpxTrs
26.12/8.73	            (51) RewriteLemmaProof [LOWER BOUND(ID), 777 ms]
26.12/8.73	            (52) proven lower bound
26.12/8.73	            (53) LowerBoundPropagationProof [FINISHED, 0 ms]
26.12/8.73	            (54) BOUNDS(n^2, INF)
26.12/8.73	
26.12/8.73	
26.12/8.73	----------------------------------------
26.12/8.73	
26.12/8.73	(0)
26.12/8.73	Obligation:
26.12/8.73	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^2, n^2).
26.12/8.73	
26.12/8.73	
26.12/8.73	The TRS R consists of the following rules:
26.12/8.73	
26.12/8.73	   f(0) -> 1
26.12/8.73	   f(s(x)) -> g(x, s(x))
26.12/8.73	   g(0, y) -> y
26.12/8.73	   g(s(x), y) -> g(x, +(y, s(x)))
26.12/8.73	   +(x, 0) -> x
26.12/8.73	   +(x, s(y)) -> s(+(x, y))
26.12/8.73	   g(s(x), y) -> g(x, s(+(y, x)))
26.12/8.73	
26.12/8.73	S is empty.
26.12/8.73	Rewrite Strategy: FULL
26.12/8.73	----------------------------------------
26.12/8.73	
26.12/8.73	(1) RcToIrcProof (BOTH BOUNDS(ID, ID))
26.12/8.73	Converted rc-obligation to irc-obligation.
26.12/8.73	
26.12/8.73	The duplicating contexts are:
26.12/8.73	f(s([]))
26.12/8.73	g(s([]), y)
26.12/8.73	
26.12/8.73	
26.12/8.73	The defined contexts are:
26.12/8.73	g(x0, [])
26.12/8.73	g(x0, s([]))
26.12/8.73	+([], s(x1))
26.12/8.73	+([], x1)
26.12/8.73	
26.12/8.73

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