Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307691

details

property	value
status	complete
benchmark	#3.56.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n141.star.cs.uiowa.edu
space	AG01

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	7.11955 seconds
cpu usage	22.8394
user time	21.452
system time	1.38743
max virtual memory	1.9032184E7
max residence set size	3685084.0

stage attributes

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

output

22.73/7.06	WORST_CASE(Omega(n^1), O(n^1))
22.73/7.07	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
22.73/7.07	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
22.73/7.07	
22.73/7.07	
22.73/7.07	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
22.73/7.07	
22.73/7.07	(0) CpxTRS
22.73/7.07	(1) DependencyGraphProof [UPPER BOUND(ID), 0 ms]
22.73/7.07	(2) CpxTRS
22.73/7.07	    (3) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms]
22.73/7.07	    (4) CpxTRS
22.73/7.07	    (5) CpxTrsMatchBoundsTAProof [FINISHED, 0 ms]
22.73/7.07	    (6) BOUNDS(1, n^1)
22.73/7.07	(7) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
22.73/7.07	(8) TRS for Loop Detection
22.73/7.07	    (9) DecreasingLoopProof [LOWER BOUND(ID), 0 ms]
22.73/7.07	    (10) BEST
22.73/7.07	        (11) proven lower bound
22.73/7.07	            (12) LowerBoundPropagationProof [FINISHED, 0 ms]
22.73/7.07	            (13) BOUNDS(n^1, INF)
22.73/7.07	        (14) TRS for Loop Detection
22.73/7.07	
22.73/7.07	
22.73/7.07	----------------------------------------
22.73/7.07	
22.73/7.07	(0)
22.73/7.07	Obligation:
22.73/7.07	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
22.73/7.07	
22.73/7.07	
22.73/7.07	The TRS R consists of the following rules:
22.73/7.07	
22.73/7.07	   g(c(x, s(y))) -> g(c(s(x), y))
22.73/7.07	   f(c(s(x), y)) -> f(c(x, s(y)))
22.73/7.07	   f(f(x)) -> f(d(f(x)))
22.73/7.07	   f(x) -> x
22.73/7.07	
22.73/7.07	S is empty.
22.73/7.07	Rewrite Strategy: FULL
22.73/7.07	----------------------------------------
22.73/7.07	
22.73/7.07	(1) DependencyGraphProof (UPPER BOUND(ID))
22.73/7.07	The following rules are not reachable from basic terms in the dependency graph and can be removed:
22.73/7.07	
22.73/7.07	f(f(x)) -> f(d(f(x)))
22.73/7.07	
22.73/7.07	----------------------------------------
22.73/7.07	
22.73/7.07	(2)
22.73/7.07	Obligation:
22.73/7.07	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, n^1).
22.73/7.07	
22.73/7.07	
22.73/7.07	The TRS R consists of the following rules:
22.73/7.07	
22.73/7.07	   g(c(x, s(y))) -> g(c(s(x), y))
22.73/7.07	   f(c(s(x), y)) -> f(c(x, s(y)))
22.73/7.07	   f(x) -> x
22.73/7.07	
22.73/7.07	S is empty.
22.73/7.07	Rewrite Strategy: FULL
22.73/7.07	----------------------------------------
22.73/7.07	
22.73/7.07	(3) RelTrsToTrsProof (UPPER BOUND(ID))
22.73/7.07	transformed relative TRS to TRS
22.73/7.07	----------------------------------------
22.73/7.07	
22.73/7.07	(4)
22.73/7.07	Obligation:
22.73/7.07	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, n^1).
22.73/7.07	
22.73/7.07	
22.73/7.07	The TRS R consists of the following rules:
22.73/7.07	
22.73/7.07	   g(c(x, s(y))) -> g(c(s(x), y))
22.73/7.07	   f(c(s(x), y)) -> f(c(x, s(y)))
22.73/7.07	   f(x) -> x
22.73/7.07	
22.73/7.07	S is empty.
22.73/7.07	Rewrite Strategy: FULL
22.73/7.07	----------------------------------------
22.73/7.07	
22.73/7.07	(5) CpxTrsMatchBoundsTAProof (FINISHED)
22.73/7.07	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. 
22.73/7.07	
22.73/7.07	The compatible tree automaton used to show the Match-Boundedness (for constructor-based start-terms) is represented by: 
22.73/7.07	final states : [1, 2]
22.73/7.07	transitions: 
22.73/7.07	c0(0, 0) -> 0
22.73/7.07	s0(0) -> 0
22.73/7.07	g0(0) -> 1
22.73/7.07	f0(0) -> 2
22.73/7.07	s1(0) -> 4
22.73/7.07	c1(4, 0) -> 3
22.73/7.07	g1(3) -> 1
22.73/7.07	s1(0) -> 6
22.73/7.07	c1(0, 6) -> 5
22.73/7.07	f1(5) -> 2
22.73/7.07	s1(4) -> 4

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