Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307754

details

property	value
status	complete
benchmark	thiemann40.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n134.star.cs.uiowa.edu
space	AProVE_07

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	291.56 seconds
cpu usage	305.426
user time	303.439
system time	1.9865
max virtual memory	1.82817E7
max residence set size	5407420.0

stage attributes

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

output

305.36/291.51	WORST_CASE(Omega(n^1), ?)
305.36/291.52	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
305.36/291.52	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
305.36/291.52	
305.36/291.52	
305.36/291.52	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF).
305.36/291.52	
305.36/291.52	(0) CpxTRS
305.36/291.52	(1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
305.36/291.52	(2) TRS for Loop Detection
305.36/291.52	(3) DecreasingLoopProof [LOWER BOUND(ID), 55 ms]
305.36/291.52	(4) BEST
305.36/291.52	    (5) proven lower bound
305.36/291.52	        (6) LowerBoundPropagationProof [FINISHED, 0 ms]
305.36/291.52	        (7) BOUNDS(n^1, INF)
305.36/291.52	    (8) TRS for Loop Detection
305.36/291.52	
305.36/291.52	
305.36/291.52	----------------------------------------
305.36/291.52	
305.36/291.52	(0)
305.36/291.52	Obligation:
305.36/291.52	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF).
305.36/291.52	
305.36/291.52	
305.36/291.52	The TRS R consists of the following rules:
305.36/291.52	
305.36/291.52	   nonZero(0) -> false
305.36/291.52	   nonZero(s(x)) -> true
305.36/291.52	   p(0) -> 0
305.36/291.52	   p(s(x)) -> x
305.36/291.52	   id_inc(x) -> x
305.36/291.52	   id_inc(x) -> s(x)
305.36/291.52	   random(x) -> rand(x, 0)
305.36/291.52	   rand(x, y) -> if(nonZero(x), x, y)
305.36/291.52	   if(false, x, y) -> y
305.36/291.52	   if(true, x, y) -> rand(p(x), id_inc(y))
305.36/291.52	
305.36/291.52	S is empty.
305.36/291.52	Rewrite Strategy: FULL
305.36/291.52	----------------------------------------
305.36/291.52	
305.36/291.52	(1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID))
305.36/291.52	Transformed a relative TRS into a decreasing-loop problem.
305.36/291.52	----------------------------------------
305.36/291.52	
305.36/291.52	(2)
305.36/291.52	Obligation:
305.36/291.52	Analyzing the following TRS for decreasing loops:
305.36/291.52	
305.36/291.52	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF).
305.36/291.52	
305.36/291.52	
305.36/291.52	The TRS R consists of the following rules:
305.36/291.52	
305.36/291.52	   nonZero(0) -> false
305.36/291.52	   nonZero(s(x)) -> true
305.36/291.52	   p(0) -> 0
305.36/291.52	   p(s(x)) -> x
305.36/291.52	   id_inc(x) -> x
305.36/291.52	   id_inc(x) -> s(x)
305.36/291.52	   random(x) -> rand(x, 0)
305.36/291.52	   rand(x, y) -> if(nonZero(x), x, y)
305.36/291.52	   if(false, x, y) -> y
305.36/291.52	   if(true, x, y) -> rand(p(x), id_inc(y))
305.36/291.52	
305.36/291.52	S is empty.
305.36/291.52	Rewrite Strategy: FULL
305.36/291.52	----------------------------------------
305.36/291.52	
305.36/291.52	(3) DecreasingLoopProof (LOWER BOUND(ID))
305.36/291.52	The following loop(s) give(s) rise to the lower bound Omega(n^1):
305.36/291.52	
305.36/291.52	The rewrite sequence
305.36/291.52	
305.36/291.52	rand(s(x1_0), y) ->^+ rand(x1_0, id_inc(y))
305.36/291.52	
305.36/291.52	gives rise to a decreasing loop by considering the right hand sides subterm at position [].
305.36/291.52	
305.36/291.52	The pumping substitution is [x1_0 / s(x1_0)].
305.36/291.52	
305.36/291.52	The result substitution is [y / id_inc(y)].
305.36/291.52	
305.36/291.52	
305.36/291.52	
305.36/291.52	
305.36/291.52	----------------------------------------
305.36/291.52	
305.36/291.52	(4)
305.36/291.52	Complex Obligation (BEST)
305.36/291.52	
305.36/291.52	----------------------------------------
305.36/291.52	
305.36/291.52	(5)
305.36/291.52	Obligation:
305.36/291.52	Proved the lower bound n^1 for the following obligation:
305.36/291.52	
305.36/291.52	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF).
305.36/291.52	
305.36/291.52

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