Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308410

details

property	value
status	complete
benchmark	2.07.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n159.star.cs.uiowa.edu
space	SK90

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	8.20882 seconds
cpu usage	20.5475
user time	19.3619
system time	1.18556
max virtual memory	1.9209448E7
max residence set size	3240368.0

stage attributes

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

output

20.36/7.30	WORST_CASE(Omega(n^1), O(n^1))
20.36/7.31	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
20.36/7.31	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
20.36/7.31	
20.36/7.31	
20.36/7.31	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
20.36/7.31	
20.36/7.31	(0) CpxTRS
20.36/7.31	(1) NestedDefinedSymbolProof [UPPER BOUND(ID), 0 ms]
20.36/7.31	(2) CpxTRS
20.36/7.31	    (3) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms]
20.36/7.31	    (4) CpxTRS
20.36/7.31	    (5) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
20.36/7.31	    (6) CpxWeightedTrs
20.36/7.31	    (7) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
20.36/7.31	    (8) CpxTypedWeightedTrs
20.36/7.31	    (9) CompletionProof [UPPER BOUND(ID), 0 ms]
20.36/7.31	    (10) CpxTypedWeightedCompleteTrs
20.36/7.31	    (11) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
20.36/7.31	    (12) CpxTypedWeightedCompleteTrs
20.36/7.31	    (13) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
20.36/7.31	    (14) CpxRNTS
20.36/7.31	    (15) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms]
20.36/7.31	    (16) CpxRNTS
20.36/7.31	    (17) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms]
20.36/7.31	    (18) CpxRNTS
20.36/7.31	    (19) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
20.36/7.31	    (20) CpxRNTS
20.36/7.31	    (21) IntTrsBoundProof [UPPER BOUND(ID), 1093 ms]
20.36/7.31	    (22) CpxRNTS
20.36/7.31	    (23) IntTrsBoundProof [UPPER BOUND(ID), 202 ms]
20.36/7.31	    (24) CpxRNTS
20.36/7.31	    (25) FinalProof [FINISHED, 0 ms]
20.36/7.31	    (26) BOUNDS(1, n^1)
20.36/7.31	(27) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
20.36/7.31	(28) TRS for Loop Detection
20.36/7.31	    (29) DecreasingLoopProof [LOWER BOUND(ID), 0 ms]
20.36/7.31	    (30) BEST
20.36/7.31	        (31) proven lower bound
20.36/7.31	            (32) LowerBoundPropagationProof [FINISHED, 0 ms]
20.36/7.31	            (33) BOUNDS(n^1, INF)
20.36/7.31	        (34) TRS for Loop Detection
20.36/7.31	
20.36/7.31	
20.36/7.31	----------------------------------------
20.36/7.31	
20.36/7.31	(0)
20.36/7.31	Obligation:
20.36/7.31	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
20.36/7.31	
20.36/7.31	
20.36/7.31	The TRS R consists of the following rules:
20.36/7.31	
20.36/7.31	   f(0, y) -> y
20.36/7.31	   f(x, 0) -> x
20.36/7.31	   f(i(x), y) -> i(x)
20.36/7.31	   f(f(x, y), z) -> f(x, f(y, z))
20.36/7.31	   f(g(x, y), z) -> g(f(x, z), f(y, z))
20.36/7.31	   f(1, g(x, y)) -> x
20.36/7.31	   f(2, g(x, y)) -> y
20.36/7.31	
20.36/7.31	S is empty.
20.36/7.31	Rewrite Strategy: FULL
20.36/7.31	----------------------------------------
20.36/7.31	
20.36/7.31	(1) NestedDefinedSymbolProof (UPPER BOUND(ID))
20.36/7.31	The TRS does not nest defined symbols.
20.36/7.31	Hence, the left-hand sides of the following rules are not basic-reachable and can be removed:
20.36/7.31	f(f(x, y), z) -> f(x, f(y, z))
20.36/7.31	
20.36/7.31	----------------------------------------
20.36/7.31	
20.36/7.31	(2)
20.36/7.31	Obligation:
20.36/7.31	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, n^1).
20.36/7.31	
20.36/7.31	
20.36/7.31	The TRS R consists of the following rules:
20.36/7.31	
20.36/7.31	   f(0, y) -> y
20.36/7.31	   f(x, 0) -> x
20.36/7.31	   f(i(x), y) -> i(x)
20.36/7.31	   f(g(x, y), z) -> g(f(x, z), f(y, z))
20.36/7.31	   f(1, g(x, y)) -> x
20.36/7.31	   f(2, g(x, y)) -> y
20.36/7.31	
20.36/7.31	S is empty.
20.36/7.31	Rewrite Strategy: FULL
20.36/7.31	----------------------------------------
20.36/7.31	
20.36/7.31	(3) RcToIrcProof (BOTH BOUNDS(ID, ID))
20.36/7.31	Converted rc-obligation to irc-obligation.
20.36/7.31	
20.36/7.31	As the TRS does not nest defined symbols, we have rc = irc.
20.36/7.31	----------------------------------------
20.36/7.31	
20.36/7.31	(4)
20.36/7.31	Obligation:
20.36/7.31	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, n^1).
20.36/7.31

popout

output may be truncated. 'popout' for the full output.

job log

popout

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