Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308435

details

property	value
status	complete
benchmark	2.44.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n170.star.cs.uiowa.edu
space	SK90

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	8.24709 seconds
cpu usage	22.7882
user time	21.0206
system time	1.76765
max virtual memory	1.8881452E7
max residence set size	3832344.0

stage attributes

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

output

22.49/8.20	WORST_CASE(Omega(n^1), O(n^1))
22.72/8.21	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
22.72/8.21	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
22.72/8.21	
22.72/8.21	
22.72/8.21	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
22.72/8.21	
22.72/8.21	(0) CpxTRS
22.72/8.21	(1) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms]
22.72/8.21	(2) CpxTRS
22.72/8.21	    (3) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
22.72/8.21	    (4) CpxWeightedTrs
22.72/8.21	    (5) CpxWeightedTrsRenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
22.72/8.21	    (6) CpxWeightedTrs
22.72/8.21	    (7) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
22.72/8.21	    (8) CpxTypedWeightedTrs
22.72/8.21	    (9) CompletionProof [UPPER BOUND(ID), 0 ms]
22.72/8.21	    (10) CpxTypedWeightedCompleteTrs
22.72/8.21	    (11) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
22.72/8.21	    (12) CpxTypedWeightedCompleteTrs
22.72/8.21	    (13) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
22.72/8.21	    (14) CpxRNTS
22.72/8.21	    (15) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms]
22.72/8.21	    (16) CpxRNTS
22.72/8.21	    (17) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms]
22.72/8.21	    (18) CpxRNTS
22.72/8.21	    (19) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
22.72/8.21	    (20) CpxRNTS
22.72/8.21	    (21) IntTrsBoundProof [UPPER BOUND(ID), 344 ms]
22.72/8.21	    (22) CpxRNTS
22.72/8.21	    (23) IntTrsBoundProof [UPPER BOUND(ID), 107 ms]
22.72/8.21	    (24) CpxRNTS
22.72/8.21	    (25) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
22.72/8.21	    (26) CpxRNTS
22.72/8.21	    (27) IntTrsBoundProof [UPPER BOUND(ID), 1197 ms]
22.72/8.21	    (28) CpxRNTS
22.72/8.21	    (29) IntTrsBoundProof [UPPER BOUND(ID), 587 ms]
22.72/8.21	    (30) CpxRNTS
22.72/8.21	    (31) FinalProof [FINISHED, 0 ms]
22.72/8.21	    (32) BOUNDS(1, n^1)
22.72/8.21	(33) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
22.72/8.21	(34) CpxTRS
22.72/8.21	    (35) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
22.72/8.21	    (36) typed CpxTrs
22.72/8.21	    (37) OrderProof [LOWER BOUND(ID), 0 ms]
22.72/8.21	    (38) typed CpxTrs
22.72/8.21	    (39) RewriteLemmaProof [LOWER BOUND(ID), 409 ms]
22.72/8.21	    (40) proven lower bound
22.72/8.21	    (41) LowerBoundPropagationProof [FINISHED, 0 ms]
22.72/8.21	    (42) BOUNDS(n^1, INF)
22.72/8.21	
22.72/8.21	
22.72/8.21	----------------------------------------
22.72/8.21	
22.72/8.21	(0)
22.72/8.21	Obligation:
22.72/8.21	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
22.72/8.21	
22.72/8.21	
22.72/8.21	The TRS R consists of the following rules:
22.72/8.21	
22.72/8.21	   del(.(x, .(y, z))) -> f(=(x, y), x, y, z)
22.72/8.21	   f(true, x, y, z) -> del(.(y, z))
22.72/8.21	   f(false, x, y, z) -> .(x, del(.(y, z)))
22.72/8.21	   =(nil, nil) -> true
22.72/8.21	   =(.(x, y), nil) -> false
22.72/8.21	   =(nil, .(y, z)) -> false
22.72/8.21	   =(.(x, y), .(u, v)) -> and(=(x, u), =(y, v))
22.72/8.21	
22.72/8.21	S is empty.
22.72/8.21	Rewrite Strategy: FULL
22.72/8.21	----------------------------------------
22.72/8.21	
22.72/8.21	(1) RcToIrcProof (BOTH BOUNDS(ID, ID))
22.72/8.21	Converted rc-obligation to irc-obligation.
22.72/8.21	
22.72/8.21	The duplicating contexts are:
22.72/8.21	del(.([], .(y, z)))
22.72/8.21	del(.(x, .([], z)))
22.72/8.21	
22.72/8.21	
22.72/8.21	The defined contexts are:
22.72/8.21	f([], x1, x2, x3)
22.72/8.21	
22.72/8.21	
22.72/8.21	As the TRS is an overlay system and the defined contexts and the duplicating contexts don't overlap, we have rc = irc.
22.72/8.21	----------------------------------------
22.72/8.21	
22.72/8.21	(2)
22.72/8.21	Obligation:
22.72/8.21	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, n^1).
22.72/8.21	
22.72/8.21	
22.72/8.21	The TRS R consists of the following rules:
22.72/8.21	
22.72/8.21	   del(.(x, .(y, z))) -> f(=(x, y), x, y, z)
22.72/8.21	   f(true, x, y, z) -> del(.(y, z))
22.72/8.21	   f(false, x, y, z) -> .(x, del(.(y, z)))
22.72/8.21	   =(nil, nil) -> true
22.72/8.21	   =(.(x, y), nil) -> false

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