Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307956

details

property	value
status	complete
benchmark	test76.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n172.star.cs.uiowa.edu
space	Strategy_removed_mixed_05

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	10.4347 seconds
cpu usage	19.7402
user time	18.1152
system time	1.62498
max virtual memory	1.9076696E7
max residence set size	3929796.0

stage attributes

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

output

19.55/7.09	WORST_CASE(Omega(n^1), O(n^1))
19.55/7.10	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
19.55/7.10	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
19.55/7.10	
19.55/7.10	
19.55/7.10	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
19.55/7.10	
19.55/7.10	(0) CpxTRS
19.55/7.10	(1) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms]
19.55/7.10	(2) CpxTRS
19.55/7.10	    (3) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms]
19.55/7.10	    (4) CdtProblem
19.55/7.10	    (5) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
19.55/7.10	    (6) CdtProblem
19.55/7.10	    (7) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms]
19.55/7.10	    (8) CdtProblem
19.55/7.10	    (9) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
19.55/7.10	    (10) CdtProblem
19.55/7.10	    (11) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
19.55/7.10	    (12) CdtProblem
19.55/7.10	    (13) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
19.55/7.10	    (14) CdtProblem
19.55/7.10	    (15) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms]
19.55/7.10	    (16) CdtProblem
19.55/7.10	    (17) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms]
19.55/7.10	    (18) CdtProblem
19.55/7.10	    (19) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 0 ms]
19.55/7.10	    (20) CdtProblem
19.55/7.10	    (21) SIsEmptyProof [BOTH BOUNDS(ID, ID), 0 ms]
19.55/7.10	    (22) BOUNDS(1, 1)
19.55/7.10	(23) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
19.55/7.10	(24) CpxTRS
19.55/7.10	    (25) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
19.55/7.10	    (26) typed CpxTrs
19.55/7.10	    (27) OrderProof [LOWER BOUND(ID), 0 ms]
19.55/7.10	    (28) typed CpxTrs
19.55/7.10	    (29) RewriteLemmaProof [LOWER BOUND(ID), 283 ms]
19.55/7.10	    (30) BEST
19.55/7.10	        (31) proven lower bound
19.55/7.10	            (32) LowerBoundPropagationProof [FINISHED, 0 ms]
19.55/7.10	            (33) BOUNDS(n^1, INF)
19.55/7.10	        (34) typed CpxTrs
19.55/7.10	
19.55/7.10	
19.55/7.10	----------------------------------------
19.55/7.10	
19.55/7.10	(0)
19.55/7.10	Obligation:
19.55/7.10	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
19.55/7.10	
19.55/7.10	
19.55/7.10	The TRS R consists of the following rules:
19.55/7.10	
19.55/7.10	   +(X, 0) -> X
19.55/7.10	   +(X, s(Y)) -> s(+(X, Y))
19.55/7.10	   f(0, s(0), X) -> f(X, +(X, X), X)
19.55/7.10	   g(X, Y) -> X
19.55/7.10	   g(X, Y) -> Y
19.55/7.10	
19.55/7.10	S is empty.
19.55/7.10	Rewrite Strategy: FULL
19.55/7.10	----------------------------------------
19.55/7.10	
19.55/7.10	(1) RcToIrcProof (BOTH BOUNDS(ID, ID))
19.55/7.10	Converted rc-obligation to irc-obligation.
19.55/7.10	
19.55/7.10	The duplicating contexts are:
19.55/7.10	f(0, s(0), [])
19.55/7.10	
19.55/7.10	
19.55/7.10	The defined contexts are:
19.55/7.10	f(x0, [], x2)
19.55/7.10	
19.55/7.10	
19.55/7.10	As the TRS is an overlay system and the defined contexts and the duplicating contexts don't overlap, we have rc = irc.
19.55/7.10	----------------------------------------
19.55/7.10	
19.55/7.10	(2)
19.55/7.10	Obligation:
19.55/7.10	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, n^1).
19.55/7.10	
19.55/7.10	
19.55/7.10	The TRS R consists of the following rules:
19.55/7.10	
19.55/7.10	   +(X, 0) -> X
19.55/7.10	   +(X, s(Y)) -> s(+(X, Y))
19.55/7.10	   f(0, s(0), X) -> f(X, +(X, X), X)
19.55/7.10	   g(X, Y) -> X
19.55/7.10	   g(X, Y) -> Y
19.55/7.10	
19.55/7.10	S is empty.
19.55/7.10	Rewrite Strategy: INNERMOST
19.55/7.10	----------------------------------------
19.55/7.10	
19.55/7.10	(3) CpxTrsToCdtProof (UPPER BOUND(ID))
19.55/7.10	Converted Cpx (relative) TRS to CDT
19.55/7.10	----------------------------------------
19.55/7.10	
19.55/7.10	(4)
19.55/7.10	Obligation:

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