Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307995

details

property	value
status	complete
benchmark	Ex24_GM04_GM.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n150.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	7.58478 seconds
cpu usage	20.6897
user time	19.0659
system time	1.62381
max virtual memory	1.8910156E7
max residence set size	3765060.0

stage attributes

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

output

20.46/7.53	WORST_CASE(Omega(n^1), O(n^1))
20.46/7.54	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
20.46/7.54	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
20.46/7.54	
20.46/7.54	
20.46/7.54	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
20.46/7.54	
20.46/7.54	(0) CpxTRS
20.46/7.54	(1) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms]
20.46/7.54	(2) CpxTRS
20.46/7.54	    (3) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
20.46/7.54	    (4) CpxWeightedTrs
20.46/7.54	    (5) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
20.46/7.54	    (6) CpxTypedWeightedTrs
20.46/7.54	    (7) CompletionProof [UPPER BOUND(ID), 0 ms]
20.46/7.54	    (8) CpxTypedWeightedCompleteTrs
20.46/7.54	    (9) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
20.46/7.54	    (10) CpxTypedWeightedCompleteTrs
20.46/7.54	    (11) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
20.46/7.54	    (12) CpxRNTS
20.46/7.54	    (13) InliningProof [UPPER BOUND(ID), 125 ms]
20.46/7.54	    (14) CpxRNTS
20.46/7.54	    (15) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms]
20.46/7.54	    (16) CpxRNTS
20.46/7.54	    (17) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms]
20.46/7.54	    (18) CpxRNTS
20.46/7.54	    (19) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
20.46/7.54	    (20) CpxRNTS
20.46/7.54	    (21) IntTrsBoundProof [UPPER BOUND(ID), 124 ms]
20.46/7.54	    (22) CpxRNTS
20.46/7.54	    (23) IntTrsBoundProof [UPPER BOUND(ID), 33 ms]
20.46/7.54	    (24) CpxRNTS
20.46/7.54	    (25) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
20.46/7.54	    (26) CpxRNTS
20.46/7.54	    (27) IntTrsBoundProof [UPPER BOUND(ID), 139 ms]
20.46/7.54	    (28) CpxRNTS
20.46/7.54	    (29) IntTrsBoundProof [UPPER BOUND(ID), 43 ms]
20.46/7.54	    (30) CpxRNTS
20.46/7.54	    (31) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
20.46/7.54	    (32) CpxRNTS
20.46/7.54	    (33) IntTrsBoundProof [UPPER BOUND(ID), 334 ms]
20.46/7.54	    (34) CpxRNTS
20.46/7.54	    (35) IntTrsBoundProof [UPPER BOUND(ID), 94 ms]
20.46/7.54	    (36) CpxRNTS
20.46/7.54	    (37) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
20.46/7.54	    (38) CpxRNTS
20.46/7.54	    (39) IntTrsBoundProof [UPPER BOUND(ID), 422 ms]
20.46/7.54	    (40) CpxRNTS
20.46/7.54	    (41) IntTrsBoundProof [UPPER BOUND(ID), 51 ms]
20.46/7.54	    (42) CpxRNTS
20.46/7.54	    (43) FinalProof [FINISHED, 0 ms]
20.46/7.54	    (44) BOUNDS(1, n^1)
20.46/7.54	(45) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
20.46/7.54	(46) TRS for Loop Detection
20.46/7.54	    (47) DecreasingLoopProof [LOWER BOUND(ID), 0 ms]
20.46/7.54	    (48) BEST
20.46/7.54	        (49) proven lower bound
20.46/7.54	            (50) LowerBoundPropagationProof [FINISHED, 0 ms]
20.46/7.54	            (51) BOUNDS(n^1, INF)
20.46/7.54	        (52) TRS for Loop Detection
20.46/7.54	
20.46/7.54	
20.46/7.54	----------------------------------------
20.46/7.54	
20.46/7.54	(0)
20.46/7.54	Obligation:
20.46/7.54	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
20.46/7.54	
20.46/7.54	
20.46/7.54	The TRS R consists of the following rules:
20.46/7.54	
20.46/7.54	   a__f(X, g(X), Y) -> a__f(Y, Y, Y)
20.46/7.54	   a__g(b) -> c
20.46/7.54	   a__b -> c
20.46/7.54	   mark(f(X1, X2, X3)) -> a__f(X1, X2, X3)
20.46/7.54	   mark(g(X)) -> a__g(mark(X))
20.46/7.54	   mark(b) -> a__b
20.46/7.54	   mark(c) -> c
20.46/7.54	   a__f(X1, X2, X3) -> f(X1, X2, X3)
20.46/7.54	   a__g(X) -> g(X)
20.46/7.54	   a__b -> b
20.46/7.54	
20.46/7.54	S is empty.
20.46/7.54	Rewrite Strategy: FULL
20.46/7.54	----------------------------------------
20.46/7.54	
20.46/7.54	(1) RcToIrcProof (BOTH BOUNDS(ID, ID))
20.46/7.54	Converted rc-obligation to irc-obligation.
20.46/7.54	
20.46/7.54	The duplicating contexts are:
20.46/7.54	a__f(X, g(X), [])
20.46/7.54	
20.46/7.54	
20.46/7.54	The defined contexts are:
20.46/7.54	a__g([])
20.46/7.54	
20.46/7.54	
20.46/7.54	As the TRS is an overlay system and the defined contexts and the duplicating contexts don't overlap, we have rc = irc.
20.46/7.54	----------------------------------------
20.46/7.54

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