Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307777

details

property	value
status	complete
benchmark	thiemann19.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n175.star.cs.uiowa.edu
space	AProVE_07

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	291.72 seconds
cpu usage	1126.19
user time	1113.14
system time	13.0504
max virtual memory	3.7643088E7
max residence set size	1.362624E7

stage attributes

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

output

1125.74/291.57	WORST_CASE(Omega(n^1), ?)
1125.87/291.62	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
1125.87/291.62	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
1125.87/291.62	
1125.87/291.62	
1125.87/291.62	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF).
1125.87/291.62	
1125.87/291.62	(0) CpxTRS
1125.87/291.62	(1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
1125.87/291.62	(2) TRS for Loop Detection
1125.87/291.62	(3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms]
1125.87/291.62	(4) BEST
1125.87/291.62	    (5) proven lower bound
1125.87/291.62	        (6) LowerBoundPropagationProof [FINISHED, 0 ms]
1125.87/291.62	        (7) BOUNDS(n^1, INF)
1125.87/291.62	    (8) TRS for Loop Detection
1125.87/291.62	
1125.87/291.62	
1125.87/291.62	----------------------------------------
1125.87/291.62	
1125.87/291.62	(0)
1125.87/291.62	Obligation:
1125.87/291.62	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF).
1125.87/291.62	
1125.87/291.62	
1125.87/291.62	The TRS R consists of the following rules:
1125.87/291.62	
1125.87/291.62	   1024 -> 1024_1(0)
1125.87/291.62	   1024_1(x) -> if(lt(x, 10), x)
1125.87/291.62	   if(true, x) -> double(1024_1(s(x)))
1125.87/291.62	   if(false, x) -> s(0)
1125.87/291.62	   lt(0, s(y)) -> true
1125.87/291.62	   lt(x, 0) -> false
1125.87/291.62	   lt(s(x), s(y)) -> lt(x, y)
1125.87/291.62	   double(0) -> 0
1125.87/291.62	   double(s(x)) -> s(s(double(x)))
1125.87/291.62	   10 -> double(s(double(s(s(0)))))
1125.87/291.62	
1125.87/291.62	S is empty.
1125.87/291.62	Rewrite Strategy: FULL
1125.87/291.62	----------------------------------------
1125.87/291.62	
1125.87/291.62	(1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID))
1125.87/291.62	Transformed a relative TRS into a decreasing-loop problem.
1125.87/291.62	----------------------------------------
1125.87/291.62	
1125.87/291.62	(2)
1125.87/291.62	Obligation:
1125.87/291.62	Analyzing the following TRS for decreasing loops:
1125.87/291.62	
1125.87/291.62	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF).
1125.87/291.62	
1125.87/291.62	
1125.87/291.62	The TRS R consists of the following rules:
1125.87/291.62	
1125.87/291.62	   1024 -> 1024_1(0)
1125.87/291.62	   1024_1(x) -> if(lt(x, 10), x)
1125.87/291.62	   if(true, x) -> double(1024_1(s(x)))
1125.87/291.62	   if(false, x) -> s(0)
1125.87/291.62	   lt(0, s(y)) -> true
1125.87/291.62	   lt(x, 0) -> false
1125.87/291.62	   lt(s(x), s(y)) -> lt(x, y)
1125.87/291.62	   double(0) -> 0
1125.87/291.62	   double(s(x)) -> s(s(double(x)))
1125.87/291.62	   10 -> double(s(double(s(s(0)))))
1125.87/291.62	
1125.87/291.62	S is empty.
1125.87/291.62	Rewrite Strategy: FULL
1125.87/291.62	----------------------------------------
1125.87/291.62	
1125.87/291.62	(3) DecreasingLoopProof (LOWER BOUND(ID))
1125.87/291.62	The following loop(s) give(s) rise to the lower bound Omega(n^1):
1125.87/291.62	
1125.87/291.62	The rewrite sequence
1125.87/291.62	
1125.87/291.62	lt(s(x), s(y)) ->^+ lt(x, y)
1125.87/291.62	
1125.87/291.62	gives rise to a decreasing loop by considering the right hand sides subterm at position [].
1125.87/291.62	
1125.87/291.62	The pumping substitution is [x / s(x), y / s(y)].
1125.87/291.62	
1125.87/291.62	The result substitution is [ ].
1125.87/291.62	
1125.87/291.62	
1125.87/291.62	
1125.87/291.62	
1125.87/291.62	----------------------------------------
1125.87/291.62	
1125.87/291.62	(4)
1125.87/291.62	Complex Obligation (BEST)
1125.87/291.62	
1125.87/291.62	----------------------------------------
1125.87/291.62	
1125.87/291.62	(5)
1125.87/291.62	Obligation:
1125.87/291.62	Proved the lower bound n^1 for the following obligation:
1125.87/291.62	
1125.87/291.62	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF).
1125.87/291.62	
1125.87/291.62

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