Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307871

details

property	value
status	complete
benchmark	double.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n046.star.cs.uiowa.edu
space	Secret_06_TRS

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	291.561 seconds
cpu usage	313.184
user time	311.211
system time	1.97236
max virtual memory	1.8279384E7
max residence set size	5338856.0

stage attributes

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

output

313.12/291.51	WORST_CASE(Omega(n^1), ?)
313.12/291.52	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
313.12/291.52	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
313.12/291.52	
313.12/291.52	
313.12/291.52	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF).
313.12/291.52	
313.12/291.52	(0) CpxTRS
313.12/291.52	(1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
313.12/291.52	(2) TRS for Loop Detection
313.12/291.52	(3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms]
313.12/291.52	(4) BEST
313.12/291.52	    (5) proven lower bound
313.12/291.52	        (6) LowerBoundPropagationProof [FINISHED, 0 ms]
313.12/291.52	        (7) BOUNDS(n^1, INF)
313.12/291.52	    (8) TRS for Loop Detection
313.12/291.52	
313.12/291.52	
313.12/291.52	----------------------------------------
313.12/291.52	
313.12/291.52	(0)
313.12/291.52	Obligation:
313.12/291.52	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF).
313.12/291.52	
313.12/291.52	
313.12/291.52	The TRS R consists of the following rules:
313.12/291.52	
313.12/291.52	   double(x) -> permute(x, x, a)
313.12/291.52	   permute(x, y, a) -> permute(isZero(x), x, b)
313.12/291.52	   permute(false, x, b) -> permute(ack(x, x), p(x), c)
313.12/291.52	   permute(true, x, b) -> 0
313.12/291.52	   permute(y, x, c) -> s(s(permute(x, y, a)))
313.12/291.52	   p(0) -> 0
313.12/291.52	   p(s(x)) -> x
313.12/291.52	   ack(0, x) -> plus(x, s(0))
313.12/291.52	   ack(s(x), 0) -> ack(x, s(0))
313.12/291.52	   ack(s(x), s(y)) -> ack(x, ack(s(x), y))
313.12/291.52	   plus(0, y) -> y
313.12/291.52	   plus(s(x), y) -> plus(x, s(y))
313.12/291.52	   plus(x, s(s(y))) -> s(plus(s(x), y))
313.12/291.52	   plus(x, s(0)) -> s(x)
313.12/291.52	   plus(x, 0) -> x
313.12/291.52	   isZero(0) -> true
313.12/291.52	   isZero(s(x)) -> false
313.12/291.52	
313.12/291.52	S is empty.
313.12/291.52	Rewrite Strategy: FULL
313.12/291.52	----------------------------------------
313.12/291.52	
313.12/291.52	(1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID))
313.12/291.52	Transformed a relative TRS into a decreasing-loop problem.
313.12/291.52	----------------------------------------
313.12/291.52	
313.12/291.52	(2)
313.12/291.52	Obligation:
313.12/291.52	Analyzing the following TRS for decreasing loops:
313.12/291.52	
313.12/291.52	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF).
313.12/291.52	
313.12/291.52	
313.12/291.52	The TRS R consists of the following rules:
313.12/291.52	
313.12/291.52	   double(x) -> permute(x, x, a)
313.12/291.52	   permute(x, y, a) -> permute(isZero(x), x, b)
313.12/291.52	   permute(false, x, b) -> permute(ack(x, x), p(x), c)
313.12/291.52	   permute(true, x, b) -> 0
313.12/291.52	   permute(y, x, c) -> s(s(permute(x, y, a)))
313.12/291.52	   p(0) -> 0
313.12/291.52	   p(s(x)) -> x
313.12/291.52	   ack(0, x) -> plus(x, s(0))
313.12/291.52	   ack(s(x), 0) -> ack(x, s(0))
313.12/291.52	   ack(s(x), s(y)) -> ack(x, ack(s(x), y))
313.12/291.52	   plus(0, y) -> y
313.12/291.52	   plus(s(x), y) -> plus(x, s(y))
313.12/291.52	   plus(x, s(s(y))) -> s(plus(s(x), y))
313.12/291.52	   plus(x, s(0)) -> s(x)
313.12/291.52	   plus(x, 0) -> x
313.12/291.52	   isZero(0) -> true
313.12/291.52	   isZero(s(x)) -> false
313.12/291.52	
313.12/291.52	S is empty.
313.12/291.52	Rewrite Strategy: FULL
313.12/291.52	----------------------------------------
313.12/291.52	
313.12/291.52	(3) DecreasingLoopProof (LOWER BOUND(ID))
313.12/291.52	The following loop(s) give(s) rise to the lower bound Omega(n^1):
313.12/291.52	
313.12/291.52	The rewrite sequence
313.12/291.52	
313.12/291.52	plus(x, s(s(y))) ->^+ s(plus(s(x), y))
313.12/291.52	
313.12/291.52	gives rise to a decreasing loop by considering the right hand sides subterm at position [0].
313.12/291.52	
313.12/291.52	The pumping substitution is [y / s(s(y))].
313.12/291.52	
313.12/291.52	The result substitution is [x / s(x)].
313.12/291.52	
313.12/291.52	
313.12/291.52	
313.12/291.52

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