Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313670

details

property	value
status	complete
benchmark	tower_sizeChange.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n156.star.cs.uiowa.edu
space	AProVE_06

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	291.569 seconds
cpu usage	1104.25
user time	1093.4
system time	10.8482
max virtual memory	3.7640344E7
max residence set size	1.1463528E7

stage attributes

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

output

1104.00/291.50	WORST_CASE(Omega(n^1), ?)
1104.00/291.51	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
1104.00/291.51	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
1104.00/291.51	
1104.00/291.51	
1104.00/291.51	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF).
1104.00/291.51	
1104.00/291.51	(0) CpxTRS
1104.00/291.51	(1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
1104.00/291.51	(2) CpxTRS
1104.00/291.51	(3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
1104.00/291.51	(4) typed CpxTrs
1104.00/291.51	(5) OrderProof [LOWER BOUND(ID), 0 ms]
1104.00/291.51	(6) typed CpxTrs
1104.00/291.51	(7) RewriteLemmaProof [LOWER BOUND(ID), 325 ms]
1104.00/291.51	(8) BEST
1104.00/291.51	    (9) proven lower bound
1104.00/291.51	        (10) LowerBoundPropagationProof [FINISHED, 0 ms]
1104.00/291.51	        (11) BOUNDS(n^1, INF)
1104.00/291.51	    (12) typed CpxTrs
1104.00/291.51	        (13) RewriteLemmaProof [LOWER BOUND(ID), 65 ms]
1104.00/291.51	        (14) typed CpxTrs
1104.00/291.51	        (15) RewriteLemmaProof [LOWER BOUND(ID), 584 ms]
1104.00/291.51	        (16) typed CpxTrs
1104.00/291.51	
1104.00/291.51	
1104.00/291.51	----------------------------------------
1104.00/291.51	
1104.00/291.51	(0)
1104.00/291.51	Obligation:
1104.00/291.51	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF).
1104.00/291.51	
1104.00/291.51	
1104.00/291.51	The TRS R consists of the following rules:
1104.00/291.51	
1104.00/291.51	   tower(x) -> f(a, x, s(0))
1104.00/291.51	   f(a, 0, y) -> y
1104.00/291.51	   f(a, s(x), y) -> f(b, y, s(x))
1104.00/291.51	   f(b, y, x) -> f(a, half(x), exp(y))
1104.00/291.51	   exp(0) -> s(0)
1104.00/291.51	   exp(s(x)) -> double(exp(x))
1104.00/291.51	   double(0) -> 0
1104.00/291.51	   double(s(x)) -> s(s(double(x)))
1104.00/291.51	   half(0) -> double(0)
1104.00/291.51	   half(s(0)) -> half(0)
1104.00/291.51	   half(s(s(x))) -> s(half(x))
1104.00/291.51	
1104.00/291.51	S is empty.
1104.00/291.51	Rewrite Strategy: INNERMOST
1104.00/291.51	----------------------------------------
1104.00/291.51	
1104.00/291.51	(1) RenamingProof (BOTH BOUNDS(ID, ID))
1104.00/291.51	Renamed function symbols to avoid clashes with predefined symbol.
1104.00/291.51	----------------------------------------
1104.00/291.51	
1104.00/291.51	(2)
1104.00/291.51	Obligation:
1104.00/291.51	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF).
1104.00/291.51	
1104.00/291.51	
1104.00/291.51	The TRS R consists of the following rules:
1104.00/291.51	
1104.00/291.51	   tower(x) -> f(a, x, s(0'))
1104.00/291.51	   f(a, 0', y) -> y
1104.00/291.51	   f(a, s(x), y) -> f(b, y, s(x))
1104.00/291.51	   f(b, y, x) -> f(a, half(x), exp(y))
1104.00/291.51	   exp(0') -> s(0')
1104.00/291.51	   exp(s(x)) -> double(exp(x))
1104.00/291.51	   double(0') -> 0'
1104.00/291.51	   double(s(x)) -> s(s(double(x)))
1104.00/291.51	   half(0') -> double(0')
1104.00/291.51	   half(s(0')) -> half(0')
1104.00/291.51	   half(s(s(x))) -> s(half(x))
1104.00/291.51	
1104.00/291.51	S is empty.
1104.00/291.51	Rewrite Strategy: INNERMOST
1104.00/291.51	----------------------------------------
1104.00/291.51	
1104.00/291.51	(3) TypeInferenceProof (BOTH BOUNDS(ID, ID))
1104.00/291.51	Infered types.
1104.00/291.51	----------------------------------------
1104.00/291.51	
1104.00/291.51	(4)
1104.00/291.51	Obligation:
1104.00/291.51	Innermost TRS:
1104.00/291.51	Rules:
1104.00/291.51	tower(x) -> f(a, x, s(0'))
1104.00/291.51	f(a, 0', y) -> y
1104.00/291.51	f(a, s(x), y) -> f(b, y, s(x))
1104.00/291.51	f(b, y, x) -> f(a, half(x), exp(y))
1104.00/291.51	exp(0') -> s(0')
1104.00/291.51	exp(s(x)) -> double(exp(x))
1104.00/291.51	double(0') -> 0'
1104.00/291.51	double(s(x)) -> s(s(double(x)))
1104.00/291.51	half(0') -> double(0')
1104.00/291.51	half(s(0')) -> half(0')
1104.00/291.51	half(s(s(x))) -> s(half(x))
1104.00/291.51	
1104.00/291.51	Types:
1104.00/291.51	tower :: 0':s -> 0':s

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actions all output return to Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40