Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307709

details

property	value
status	complete
benchmark	#3.15.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n100.star.cs.uiowa.edu
space	AG01

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	5.08505 seconds
cpu usage	16.264
user time	15.4454
system time	0.818558
max virtual memory	1.8874232E7
max residence set size	2149752.0

stage attributes

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

output

15.79/5.02	WORST_CASE(Omega(n^1), O(n^1))
16.19/5.04	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
16.19/5.04	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
16.19/5.04	
16.19/5.04	
16.19/5.04	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
16.19/5.04	
16.19/5.04	(0) CpxTRS
16.19/5.04	(1) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms]
16.19/5.04	(2) CpxTRS
16.19/5.04	    (3) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
16.19/5.04	    (4) CpxWeightedTrs
16.19/5.04	    (5) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
16.19/5.04	    (6) CpxTypedWeightedTrs
16.19/5.04	    (7) CompletionProof [UPPER BOUND(ID), 0 ms]
16.19/5.04	    (8) CpxTypedWeightedCompleteTrs
16.19/5.04	    (9) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
16.19/5.04	    (10) CpxTypedWeightedCompleteTrs
16.19/5.04	    (11) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
16.19/5.04	    (12) CpxRNTS
16.19/5.04	    (13) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms]
16.19/5.04	    (14) CpxRNTS
16.19/5.04	    (15) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms]
16.19/5.04	    (16) CpxRNTS
16.19/5.04	    (17) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
16.19/5.04	    (18) CpxRNTS
16.19/5.04	    (19) IntTrsBoundProof [UPPER BOUND(ID), 595 ms]
16.19/5.04	    (20) CpxRNTS
16.19/5.04	    (21) IntTrsBoundProof [UPPER BOUND(ID), 250 ms]
16.19/5.04	    (22) CpxRNTS
16.19/5.04	    (23) FinalProof [FINISHED, 0 ms]
16.19/5.04	    (24) BOUNDS(1, n^1)
16.19/5.04	(25) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
16.19/5.04	(26) TRS for Loop Detection
16.19/5.04	    (27) DecreasingLoopProof [LOWER BOUND(ID), 0 ms]
16.19/5.04	    (28) BEST
16.19/5.04	        (29) proven lower bound
16.19/5.04	            (30) LowerBoundPropagationProof [FINISHED, 0 ms]
16.19/5.04	            (31) BOUNDS(n^1, INF)
16.19/5.04	        (32) TRS for Loop Detection
16.19/5.04	
16.19/5.04	
16.19/5.04	----------------------------------------
16.19/5.04	
16.19/5.04	(0)
16.19/5.04	Obligation:
16.19/5.04	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
16.19/5.04	
16.19/5.04	
16.19/5.04	The TRS R consists of the following rules:
16.19/5.04	
16.19/5.04	   average(s(x), y) -> average(x, s(y))
16.19/5.04	   average(x, s(s(s(y)))) -> s(average(s(x), y))
16.19/5.04	   average(0, 0) -> 0
16.19/5.04	   average(0, s(0)) -> 0
16.19/5.04	   average(0, s(s(0))) -> s(0)
16.19/5.04	
16.19/5.04	S is empty.
16.19/5.04	Rewrite Strategy: FULL
16.19/5.04	----------------------------------------
16.19/5.04	
16.19/5.04	(1) RcToIrcProof (BOTH BOUNDS(ID, ID))
16.19/5.04	Converted rc-obligation to irc-obligation.
16.19/5.04	
16.19/5.04	As the TRS does not nest defined symbols, we have rc = irc.
16.19/5.04	----------------------------------------
16.19/5.04	
16.19/5.04	(2)
16.19/5.04	Obligation:
16.19/5.04	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, n^1).
16.19/5.04	
16.19/5.04	
16.19/5.04	The TRS R consists of the following rules:
16.19/5.04	
16.19/5.04	   average(s(x), y) -> average(x, s(y))
16.19/5.04	   average(x, s(s(s(y)))) -> s(average(s(x), y))
16.19/5.04	   average(0, 0) -> 0
16.19/5.04	   average(0, s(0)) -> 0
16.19/5.04	   average(0, s(s(0))) -> s(0)
16.19/5.04	
16.19/5.04	S is empty.
16.19/5.04	Rewrite Strategy: INNERMOST
16.19/5.04	----------------------------------------
16.19/5.04	
16.19/5.04	(3) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID))
16.19/5.04	Transformed relative TRS to weighted TRS
16.19/5.04	----------------------------------------
16.19/5.04	
16.19/5.04	(4)
16.19/5.04	Obligation:
16.19/5.04	The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^1).
16.19/5.04	
16.19/5.04	
16.19/5.04	The TRS R consists of the following rules:
16.19/5.04	
16.19/5.04	   average(s(x), y) -> average(x, s(y)) [1]
16.19/5.04	   average(x, s(s(s(y)))) -> s(average(s(x), y)) [1]
16.19/5.04	   average(0, 0) -> 0 [1]
16.19/5.04	   average(0, s(0)) -> 0 [1]
16.19/5.04	   average(0, s(s(0))) -> s(0) [1]

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