Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308265

details

property	value
status	complete
benchmark	Ex6_Luc98_Z.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n081.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	9.9766 seconds
cpu usage	20.1999
user time	18.7017
system time	1.49818
max virtual memory	1.9008048E7
max residence set size	3390992.0

stage attributes

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

output

19.78/6.27	WORST_CASE(Omega(n^1), O(n^1))
20.03/6.29	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
20.03/6.29	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
20.03/6.29	
20.03/6.29	
20.03/6.29	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
20.03/6.29	
20.03/6.29	(0) CpxTRS
20.03/6.29	(1) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms]
20.03/6.29	(2) CpxTRS
20.03/6.29	    (3) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
20.03/6.29	    (4) CpxWeightedTrs
20.03/6.29	    (5) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
20.03/6.29	    (6) CpxTypedWeightedTrs
20.03/6.29	    (7) CompletionProof [UPPER BOUND(ID), 0 ms]
20.03/6.29	    (8) CpxTypedWeightedCompleteTrs
20.03/6.29	    (9) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
20.03/6.29	    (10) CpxTypedWeightedCompleteTrs
20.03/6.29	    (11) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
20.03/6.29	    (12) CpxRNTS
20.03/6.29	    (13) InliningProof [UPPER BOUND(ID), 84 ms]
20.03/6.29	    (14) CpxRNTS
20.03/6.29	    (15) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms]
20.03/6.29	    (16) CpxRNTS
20.03/6.29	    (17) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms]
20.03/6.29	    (18) CpxRNTS
20.03/6.29	    (19) ResultPropagationProof [UPPER BOUND(ID), 1 ms]
20.03/6.29	    (20) CpxRNTS
20.03/6.29	    (21) IntTrsBoundProof [UPPER BOUND(ID), 210 ms]
20.03/6.29	    (22) CpxRNTS
20.03/6.29	    (23) IntTrsBoundProof [UPPER BOUND(ID), 0 ms]
20.03/6.29	    (24) CpxRNTS
20.03/6.29	    (25) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
20.03/6.29	    (26) CpxRNTS
20.03/6.29	    (27) IntTrsBoundProof [UPPER BOUND(ID), 757 ms]
20.03/6.29	    (28) CpxRNTS
20.03/6.29	    (29) IntTrsBoundProof [UPPER BOUND(ID), 66 ms]
20.03/6.29	    (30) CpxRNTS
20.03/6.29	    (31) FinalProof [FINISHED, 0 ms]
20.03/6.29	    (32) BOUNDS(1, n^1)
20.03/6.29	(33) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
20.03/6.29	(34) TRS for Loop Detection
20.03/6.29	    (35) DecreasingLoopProof [LOWER BOUND(ID), 0 ms]
20.03/6.29	    (36) BEST
20.03/6.29	        (37) proven lower bound
20.03/6.29	            (38) LowerBoundPropagationProof [FINISHED, 0 ms]
20.03/6.29	            (39) BOUNDS(n^1, INF)
20.03/6.29	        (40) TRS for Loop Detection
20.03/6.29	
20.03/6.29	
20.03/6.29	----------------------------------------
20.03/6.29	
20.03/6.29	(0)
20.03/6.29	Obligation:
20.03/6.29	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
20.03/6.29	
20.03/6.29	
20.03/6.29	The TRS R consists of the following rules:
20.03/6.29	
20.03/6.29	   first(0, X) -> nil
20.03/6.29	   first(s(X), cons(Y, Z)) -> cons(Y, n__first(X, activate(Z)))
20.03/6.29	   from(X) -> cons(X, n__from(s(X)))
20.03/6.29	   first(X1, X2) -> n__first(X1, X2)
20.03/6.29	   from(X) -> n__from(X)
20.03/6.29	   activate(n__first(X1, X2)) -> first(X1, X2)
20.03/6.29	   activate(n__from(X)) -> from(X)
20.03/6.29	   activate(X) -> X
20.03/6.29	
20.03/6.29	S is empty.
20.03/6.29	Rewrite Strategy: FULL
20.03/6.29	----------------------------------------
20.03/6.29	
20.03/6.29	(1) RcToIrcProof (BOTH BOUNDS(ID, ID))
20.03/6.29	Converted rc-obligation to irc-obligation.
20.03/6.29	
20.03/6.29	As the TRS does not nest defined symbols, we have rc = irc.
20.03/6.29	----------------------------------------
20.03/6.29	
20.03/6.29	(2)
20.03/6.29	Obligation:
20.03/6.29	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, n^1).
20.03/6.29	
20.03/6.29	
20.03/6.29	The TRS R consists of the following rules:
20.03/6.29	
20.03/6.29	   first(0, X) -> nil
20.03/6.29	   first(s(X), cons(Y, Z)) -> cons(Y, n__first(X, activate(Z)))
20.03/6.29	   from(X) -> cons(X, n__from(s(X)))
20.03/6.29	   first(X1, X2) -> n__first(X1, X2)
20.03/6.29	   from(X) -> n__from(X)
20.03/6.29	   activate(n__first(X1, X2)) -> first(X1, X2)
20.03/6.29	   activate(n__from(X)) -> from(X)
20.03/6.29	   activate(X) -> X
20.03/6.29	
20.03/6.29	S is empty.
20.03/6.29	Rewrite Strategy: INNERMOST
20.03/6.29	----------------------------------------
20.03/6.29	
20.03/6.29	(3) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID))
20.03/6.29	Transformed relative TRS to weighted TRS

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