Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313553

details

property	value
status	complete
benchmark	#4.37.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n086.star.cs.uiowa.edu
space	Strategy_removed_AG01

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	4.38688 seconds
cpu usage	13.1206
user time	12.0427
system time	1.07785
max virtual memory	1.9208424E7
max residence set size	3570868.0

stage attributes

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

output

12.76/4.33	WORST_CASE(Omega(n^1), O(n^1))
12.76/4.33	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
12.76/4.33	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
12.76/4.33	
12.76/4.33	
12.76/4.33	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
12.76/4.33	
12.76/4.33	(0) CpxTRS
12.76/4.33	(1) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms]
12.76/4.33	(2) CpxTRS
12.76/4.33	    (3) CpxTrsMatchBoundsTAProof [FINISHED, 0 ms]
12.76/4.33	    (4) BOUNDS(1, n^1)
12.76/4.33	(5) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
12.76/4.33	(6) TRS for Loop Detection
12.76/4.33	    (7) DecreasingLoopProof [LOWER BOUND(ID), 0 ms]
12.76/4.33	    (8) BEST
12.76/4.33	        (9) proven lower bound
12.76/4.33	            (10) LowerBoundPropagationProof [FINISHED, 0 ms]
12.76/4.33	            (11) BOUNDS(n^1, INF)
12.76/4.33	        (12) TRS for Loop Detection
12.76/4.33	
12.76/4.33	
12.76/4.33	----------------------------------------
12.76/4.33	
12.76/4.33	(0)
12.76/4.33	Obligation:
12.76/4.33	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
12.76/4.33	
12.76/4.33	
12.76/4.33	The TRS R consists of the following rules:
12.76/4.33	
12.76/4.33	   f(c(s(x), y)) -> f(c(x, s(y)))
12.76/4.33	   g(c(x, s(y))) -> g(c(s(x), y))
12.76/4.33	
12.76/4.33	S is empty.
12.76/4.33	Rewrite Strategy: INNERMOST
12.76/4.33	----------------------------------------
12.76/4.33	
12.76/4.33	(1) RelTrsToTrsProof (UPPER BOUND(ID))
12.76/4.33	transformed relative TRS to TRS
12.76/4.33	----------------------------------------
12.76/4.33	
12.76/4.33	(2)
12.76/4.33	Obligation:
12.76/4.33	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, n^1).
12.76/4.33	
12.76/4.33	
12.76/4.33	The TRS R consists of the following rules:
12.76/4.33	
12.76/4.33	   f(c(s(x), y)) -> f(c(x, s(y)))
12.76/4.33	   g(c(x, s(y))) -> g(c(s(x), y))
12.76/4.33	
12.76/4.33	S is empty.
12.76/4.33	Rewrite Strategy: INNERMOST
12.76/4.33	----------------------------------------
12.76/4.33	
12.76/4.33	(3) CpxTrsMatchBoundsTAProof (FINISHED)
12.76/4.33	A linear upper bound on the runtime complexity of the TRS R could be shown with a Match-Bound[TAB_LEFTLINEAR,TAB_NONLEFTLINEAR] (for contructor-based start-terms) of 1. 
12.76/4.33	
12.76/4.33	The compatible tree automaton used to show the Match-Boundedness (for constructor-based start-terms) is represented by: 
12.76/4.33	final states : [1, 2]
12.76/4.33	transitions: 
12.76/4.33	c0(0, 0) -> 0
12.76/4.33	s0(0) -> 0
12.76/4.33	f0(0) -> 1
12.76/4.33	g0(0) -> 2
12.76/4.33	s1(0) -> 4
12.76/4.33	c1(0, 4) -> 3
12.76/4.33	f1(3) -> 1
12.76/4.33	s1(0) -> 6
12.76/4.33	c1(6, 0) -> 5
12.76/4.33	g1(5) -> 2
12.76/4.33	s1(4) -> 4
12.76/4.33	s1(6) -> 6
12.76/4.33	
12.76/4.33	----------------------------------------
12.76/4.33	
12.76/4.33	(4)
12.76/4.33	BOUNDS(1, n^1)
12.76/4.33	
12.76/4.33	----------------------------------------
12.76/4.33	
12.76/4.33	(5) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID))
12.76/4.33	Transformed a relative TRS into a decreasing-loop problem.
12.76/4.33	----------------------------------------
12.76/4.33	
12.76/4.33	(6)
12.76/4.33	Obligation:
12.76/4.33	Analyzing the following TRS for decreasing loops:
12.76/4.33	
12.76/4.33	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
12.76/4.33	
12.76/4.33	
12.76/4.33	The TRS R consists of the following rules:
12.76/4.33	
12.76/4.33	   f(c(s(x), y)) -> f(c(x, s(y)))
12.76/4.33	   g(c(x, s(y))) -> g(c(s(x), y))
12.76/4.33	
12.76/4.33	S is empty.
12.76/4.33	Rewrite Strategy: INNERMOST

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