Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308527

details

property	value
status	complete
benchmark	#4.32.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n170.star.cs.uiowa.edu
space	Strategy_removed_AG01

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	5.44742 seconds
cpu usage	18.0351
user time	17.0467
system time	0.988333
max virtual memory	1.8742832E7
max residence set size	3208468.0

stage attributes

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

output

17.76/5.38	WORST_CASE(Omega(n^1), O(n^1))
17.94/5.39	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
17.94/5.39	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
17.94/5.39	
17.94/5.39	
17.94/5.39	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
17.94/5.39	
17.94/5.39	(0) CpxTRS
17.94/5.39	(1) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms]
17.94/5.39	(2) CpxTRS
17.94/5.39	    (3) CpxTrsToCdtProof [UPPER BOUND(ID), 7 ms]
17.94/5.39	    (4) CdtProblem
17.94/5.39	    (5) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 65 ms]
17.94/5.39	    (6) CdtProblem
17.94/5.39	    (7) CdtInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
17.94/5.39	    (8) CdtProblem
17.94/5.39	    (9) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
17.94/5.39	    (10) CdtProblem
17.94/5.39	    (11) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms]
17.94/5.39	    (12) CdtProblem
17.94/5.39	    (13) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 4 ms]
17.94/5.39	    (14) CdtProblem
17.94/5.39	    (15) SIsEmptyProof [BOTH BOUNDS(ID, ID), 0 ms]
17.94/5.39	    (16) BOUNDS(1, 1)
17.94/5.39	(17) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
17.94/5.39	(18) TRS for Loop Detection
17.94/5.39	    (19) DecreasingLoopProof [LOWER BOUND(ID), 0 ms]
17.94/5.39	    (20) BEST
17.94/5.39	        (21) proven lower bound
17.94/5.39	            (22) LowerBoundPropagationProof [FINISHED, 0 ms]
17.94/5.39	            (23) BOUNDS(n^1, INF)
17.94/5.39	        (24) TRS for Loop Detection
17.94/5.39	
17.94/5.39	
17.94/5.39	----------------------------------------
17.94/5.39	
17.94/5.39	(0)
17.94/5.39	Obligation:
17.94/5.39	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
17.94/5.39	
17.94/5.39	
17.94/5.39	The TRS R consists of the following rules:
17.94/5.39	
17.94/5.39	   f(x, c(y)) -> f(x, s(f(y, y)))
17.94/5.39	   f(s(x), s(y)) -> f(x, s(c(s(y))))
17.94/5.39	
17.94/5.39	S is empty.
17.94/5.39	Rewrite Strategy: FULL
17.94/5.39	----------------------------------------
17.94/5.39	
17.94/5.39	(1) RcToIrcProof (BOTH BOUNDS(ID, ID))
17.94/5.39	Converted rc-obligation to irc-obligation.
17.94/5.39	
17.94/5.39	The duplicating contexts are:
17.94/5.39	f(x, c([]))
17.94/5.39	
17.94/5.39	
17.94/5.39	The defined contexts are:
17.94/5.39	f(x0, s([]))
17.94/5.39	f(x0, s(c(s([]))))
17.94/5.39	
17.94/5.39	
17.94/5.39	As the TRS is an overlay system and the defined contexts and the duplicating contexts don't overlap, we have rc = irc.
17.94/5.39	----------------------------------------
17.94/5.39	
17.94/5.39	(2)
17.94/5.39	Obligation:
17.94/5.39	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, n^1).
17.94/5.39	
17.94/5.39	
17.94/5.39	The TRS R consists of the following rules:
17.94/5.39	
17.94/5.39	   f(x, c(y)) -> f(x, s(f(y, y)))
17.94/5.39	   f(s(x), s(y)) -> f(x, s(c(s(y))))
17.94/5.39	
17.94/5.39	S is empty.
17.94/5.39	Rewrite Strategy: INNERMOST
17.94/5.39	----------------------------------------
17.94/5.39	
17.94/5.39	(3) CpxTrsToCdtProof (UPPER BOUND(ID))
17.94/5.39	Converted Cpx (relative) TRS to CDT
17.94/5.39	----------------------------------------
17.94/5.39	
17.94/5.39	(4)
17.94/5.39	Obligation:
17.94/5.39	Complexity Dependency Tuples Problem
17.94/5.39	
17.94/5.39	Rules:
17.94/5.39	   f(z0, c(z1)) -> f(z0, s(f(z1, z1)))
17.94/5.39	   f(s(z0), s(z1)) -> f(z0, s(c(s(z1))))
17.94/5.39	Tuples:
17.94/5.39	   F(z0, c(z1)) -> c1(F(z0, s(f(z1, z1))), F(z1, z1))
17.94/5.39	   F(s(z0), s(z1)) -> c2(F(z0, s(c(s(z1)))))
17.94/5.39	S tuples:
17.94/5.39	   F(z0, c(z1)) -> c1(F(z0, s(f(z1, z1))), F(z1, z1))
17.94/5.39	   F(s(z0), s(z1)) -> c2(F(z0, s(c(s(z1)))))
17.94/5.39	K tuples:none
17.94/5.39	Defined Rule Symbols:   f_2
17.94/5.39	
17.94/5.39	Defined Pair Symbols:   F_2

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