Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308543

details

property	value
status	complete
benchmark	z26.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n002.star.cs.uiowa.edu
space	Zantema_05

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	5.28792 seconds
cpu usage	16.3669
user time	15.1775
system time	1.18933
max virtual memory	1.9075428E7
max residence set size	3521212.0

stage attributes

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

output

16.22/5.23	WORST_CASE(Omega(n^1), O(n^1))
16.22/5.24	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
16.22/5.24	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
16.22/5.24	
16.22/5.24	
16.22/5.24	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
16.22/5.24	
16.22/5.24	(0) CpxTRS
16.22/5.24	(1) NestedDefinedSymbolProof [UPPER BOUND(ID), 0 ms]
16.22/5.24	(2) CpxTRS
16.22/5.24	    (3) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms]
16.22/5.24	    (4) CpxTRS
16.22/5.24	    (5) CpxTrsMatchBoundsTAProof [FINISHED, 18 ms]
16.22/5.24	    (6) BOUNDS(1, n^1)
16.22/5.24	(7) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
16.22/5.24	(8) TRS for Loop Detection
16.22/5.24	    (9) DecreasingLoopProof [LOWER BOUND(ID), 0 ms]
16.22/5.24	    (10) BEST
16.22/5.24	        (11) proven lower bound
16.22/5.24	            (12) LowerBoundPropagationProof [FINISHED, 0 ms]
16.22/5.24	            (13) BOUNDS(n^1, INF)
16.22/5.24	        (14) TRS for Loop Detection
16.22/5.24	
16.22/5.24	
16.22/5.24	----------------------------------------
16.22/5.24	
16.22/5.24	(0)
16.22/5.24	Obligation:
16.22/5.24	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
16.22/5.24	
16.22/5.24	
16.22/5.24	The TRS R consists of the following rules:
16.22/5.24	
16.22/5.24	   a(a(f(x, y))) -> f(a(b(a(b(a(x))))), a(b(a(b(a(y))))))
16.22/5.24	   f(a(x), a(y)) -> a(f(x, y))
16.22/5.24	   f(b(x), b(y)) -> b(f(x, y))
16.22/5.24	
16.22/5.24	S is empty.
16.22/5.24	Rewrite Strategy: FULL
16.22/5.24	----------------------------------------
16.22/5.24	
16.22/5.24	(1) NestedDefinedSymbolProof (UPPER BOUND(ID))
16.22/5.24	The TRS does not nest defined symbols.
16.22/5.24	Hence, the left-hand sides of the following rules are not basic-reachable and can be removed:
16.22/5.24	a(a(f(x, y))) -> f(a(b(a(b(a(x))))), a(b(a(b(a(y))))))
16.22/5.24	f(a(x), a(y)) -> a(f(x, y))
16.22/5.24	
16.22/5.24	----------------------------------------
16.22/5.24	
16.22/5.24	(2)
16.22/5.24	Obligation:
16.22/5.24	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, n^1).
16.22/5.24	
16.22/5.24	
16.22/5.24	The TRS R consists of the following rules:
16.22/5.24	
16.22/5.24	   f(b(x), b(y)) -> b(f(x, y))
16.22/5.24	
16.22/5.24	S is empty.
16.22/5.24	Rewrite Strategy: FULL
16.22/5.24	----------------------------------------
16.22/5.24	
16.22/5.24	(3) RelTrsToTrsProof (UPPER BOUND(ID))
16.22/5.24	transformed relative TRS to TRS
16.22/5.24	----------------------------------------
16.22/5.24	
16.22/5.24	(4)
16.22/5.24	Obligation:
16.22/5.24	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, n^1).
16.22/5.24	
16.22/5.24	
16.22/5.24	The TRS R consists of the following rules:
16.22/5.24	
16.22/5.24	   f(b(x), b(y)) -> b(f(x, y))
16.22/5.24	
16.22/5.24	S is empty.
16.22/5.24	Rewrite Strategy: FULL
16.22/5.24	----------------------------------------
16.22/5.24	
16.22/5.24	(5) CpxTrsMatchBoundsTAProof (FINISHED)
16.22/5.24	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. 
16.22/5.24	
16.22/5.24	The compatible tree automaton used to show the Match-Boundedness (for constructor-based start-terms) is represented by: 
16.22/5.24	final states : [1]
16.22/5.24	transitions: 
16.22/5.24	b0(0) -> 0
16.22/5.24	f0(0, 0) -> 1
16.22/5.24	f1(0, 0) -> 2
16.22/5.24	b1(2) -> 1
16.22/5.24	b1(2) -> 2
16.22/5.24	
16.22/5.24	----------------------------------------
16.22/5.24	
16.22/5.24	(6)
16.22/5.24	BOUNDS(1, n^1)
16.22/5.24	
16.22/5.24	----------------------------------------
16.22/5.24	
16.22/5.24	(7) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID))
16.22/5.24	Transformed a relative TRS into a decreasing-loop problem.

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