Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307854

details

property	value
status	complete
benchmark	gcd.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n148.star.cs.uiowa.edu
space	Mixed_TRS

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	291.529 seconds
cpu usage	310.053
user time	308.331
system time	1.7223
max virtual memory	1.8279384E7
max residence set size	5225616.0

stage attributes

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

output

309.99/291.48	WORST_CASE(Omega(n^1), ?)
309.99/291.49	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
309.99/291.49	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
309.99/291.49	
309.99/291.49	
309.99/291.49	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF).
309.99/291.49	
309.99/291.49	(0) CpxTRS
309.99/291.49	(1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
309.99/291.49	(2) CpxTRS
309.99/291.49	(3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
309.99/291.49	(4) typed CpxTrs
309.99/291.49	(5) OrderProof [LOWER BOUND(ID), 0 ms]
309.99/291.49	(6) typed CpxTrs
309.99/291.49	(7) RewriteLemmaProof [LOWER BOUND(ID), 324 ms]
309.99/291.49	(8) BEST
309.99/291.49	    (9) proven lower bound
309.99/291.49	        (10) LowerBoundPropagationProof [FINISHED, 0 ms]
309.99/291.49	        (11) BOUNDS(n^1, INF)
309.99/291.49	    (12) typed CpxTrs
309.99/291.49	        (13) RewriteLemmaProof [LOWER BOUND(ID), 58 ms]
309.99/291.49	        (14) typed CpxTrs
309.99/291.49	        (15) RewriteLemmaProof [LOWER BOUND(ID), 13 ms]
309.99/291.49	        (16) typed CpxTrs
309.99/291.49	
309.99/291.49	
309.99/291.49	----------------------------------------
309.99/291.49	
309.99/291.49	(0)
309.99/291.49	Obligation:
309.99/291.49	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF).
309.99/291.49	
309.99/291.49	
309.99/291.49	The TRS R consists of the following rules:
309.99/291.49	
309.99/291.49	   min(x, 0) -> 0
309.99/291.49	   min(0, y) -> 0
309.99/291.49	   min(s(x), s(y)) -> s(min(x, y))
309.99/291.49	   max(x, 0) -> x
309.99/291.49	   max(0, y) -> y
309.99/291.49	   max(s(x), s(y)) -> s(max(x, y))
309.99/291.49	   -(x, 0) -> x
309.99/291.49	   -(s(x), s(y)) -> -(x, y)
309.99/291.49	   gcd(s(x), 0) -> s(x)
309.99/291.49	   gcd(0, s(x)) -> s(x)
309.99/291.49	   gcd(s(x), s(y)) -> gcd(-(max(x, y), min(x, y)), s(min(x, y)))
309.99/291.49	
309.99/291.49	S is empty.
309.99/291.49	Rewrite Strategy: FULL
309.99/291.49	----------------------------------------
309.99/291.49	
309.99/291.49	(1) RenamingProof (BOTH BOUNDS(ID, ID))
309.99/291.49	Renamed function symbols to avoid clashes with predefined symbol.
309.99/291.49	----------------------------------------
309.99/291.49	
309.99/291.49	(2)
309.99/291.49	Obligation:
309.99/291.49	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF).
309.99/291.49	
309.99/291.49	
309.99/291.49	The TRS R consists of the following rules:
309.99/291.49	
309.99/291.49	   min(x, 0') -> 0'
309.99/291.49	   min(0', y) -> 0'
309.99/291.49	   min(s(x), s(y)) -> s(min(x, y))
309.99/291.49	   max(x, 0') -> x
309.99/291.49	   max(0', y) -> y
309.99/291.49	   max(s(x), s(y)) -> s(max(x, y))
309.99/291.49	   -(x, 0') -> x
309.99/291.49	   -(s(x), s(y)) -> -(x, y)
309.99/291.49	   gcd(s(x), 0') -> s(x)
309.99/291.49	   gcd(0', s(x)) -> s(x)
309.99/291.49	   gcd(s(x), s(y)) -> gcd(-(max(x, y), min(x, y)), s(min(x, y)))
309.99/291.49	
309.99/291.49	S is empty.
309.99/291.49	Rewrite Strategy: FULL
309.99/291.49	----------------------------------------
309.99/291.49	
309.99/291.49	(3) TypeInferenceProof (BOTH BOUNDS(ID, ID))
309.99/291.49	Infered types.
309.99/291.49	----------------------------------------
309.99/291.49	
309.99/291.49	(4)
309.99/291.49	Obligation:
309.99/291.49	TRS:
309.99/291.49	Rules:
309.99/291.49	min(x, 0') -> 0'
309.99/291.49	min(0', y) -> 0'
309.99/291.49	min(s(x), s(y)) -> s(min(x, y))
309.99/291.49	max(x, 0') -> x
309.99/291.49	max(0', y) -> y
309.99/291.49	max(s(x), s(y)) -> s(max(x, y))
309.99/291.49	-(x, 0') -> x
309.99/291.49	-(s(x), s(y)) -> -(x, y)
309.99/291.49	gcd(s(x), 0') -> s(x)
309.99/291.49	gcd(0', s(x)) -> s(x)
309.99/291.49	gcd(s(x), s(y)) -> gcd(-(max(x, y), min(x, y)), s(min(x, y)))
309.99/291.49	
309.99/291.49	Types:
309.99/291.49	min :: 0':s -> 0':s -> 0':s

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