Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307735

details

property	value
status	complete
benchmark	#3.54.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n146.star.cs.uiowa.edu
space	AG01

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	291.523 seconds
cpu usage	779.817
user time	775.846
system time	3.97129
max virtual memory	3.7635088E7
max residence set size	7046944.0

stage attributes

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

output

779.70/291.48	WORST_CASE(Omega(n^1), ?)
779.70/291.49	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
779.70/291.49	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
779.70/291.49	
779.70/291.49	
779.70/291.49	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF).
779.70/291.49	
779.70/291.49	(0) CpxTRS
779.70/291.49	(1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
779.70/291.49	(2) CpxTRS
779.70/291.49	(3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
779.70/291.49	(4) typed CpxTrs
779.70/291.49	(5) OrderProof [LOWER BOUND(ID), 0 ms]
779.70/291.49	(6) typed CpxTrs
779.70/291.49	(7) RewriteLemmaProof [LOWER BOUND(ID), 463 ms]
779.70/291.49	(8) BEST
779.70/291.49	    (9) proven lower bound
779.70/291.49	        (10) LowerBoundPropagationProof [FINISHED, 0 ms]
779.70/291.49	        (11) BOUNDS(n^1, INF)
779.70/291.49	    (12) typed CpxTrs
779.70/291.49	
779.70/291.49	
779.70/291.49	----------------------------------------
779.70/291.49	
779.70/291.49	(0)
779.70/291.49	Obligation:
779.70/291.49	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF).
779.70/291.49	
779.70/291.49	
779.70/291.49	The TRS R consists of the following rules:
779.70/291.49	
779.70/291.49	   f(g(x)) -> g(f(f(x)))
779.70/291.49	   f(h(x)) -> h(g(x))
779.70/291.49	   f'(s(x), y, y) -> f'(y, x, s(x))
779.70/291.49	
779.70/291.49	S is empty.
779.70/291.49	Rewrite Strategy: FULL
779.70/291.49	----------------------------------------
779.70/291.49	
779.70/291.49	(1) RenamingProof (BOTH BOUNDS(ID, ID))
779.70/291.49	Renamed function symbols to avoid clashes with predefined symbol.
779.70/291.49	----------------------------------------
779.70/291.49	
779.70/291.49	(2)
779.70/291.49	Obligation:
779.70/291.49	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF).
779.70/291.49	
779.70/291.49	
779.70/291.49	The TRS R consists of the following rules:
779.70/291.49	
779.70/291.49	   f(g(x)) -> g(f(f(x)))
779.70/291.49	   f(h(x)) -> h(g(x))
779.70/291.49	   f'(s(x), y, y) -> f'(y, x, s(x))
779.70/291.49	
779.70/291.49	S is empty.
779.70/291.49	Rewrite Strategy: FULL
779.70/291.49	----------------------------------------
779.70/291.49	
779.70/291.49	(3) TypeInferenceProof (BOTH BOUNDS(ID, ID))
779.70/291.49	Infered types.
779.70/291.49	----------------------------------------
779.70/291.49	
779.70/291.49	(4)
779.70/291.49	Obligation:
779.70/291.49	TRS:
779.70/291.49	Rules:
779.70/291.49	f(g(x)) -> g(f(f(x)))
779.70/291.49	f(h(x)) -> h(g(x))
779.70/291.49	f'(s(x), y, y) -> f'(y, x, s(x))
779.70/291.49	
779.70/291.49	Types:
779.70/291.49	f :: g:h -> g:h
779.70/291.49	g :: g:h -> g:h
779.70/291.49	h :: g:h -> g:h
779.70/291.49	f' :: s -> s -> s -> f'
779.70/291.49	s :: s -> s
779.70/291.49	hole_g:h1_0 :: g:h
779.70/291.49	hole_f'2_0 :: f'
779.70/291.49	hole_s3_0 :: s
779.70/291.49	gen_g:h4_0 :: Nat -> g:h
779.70/291.49	gen_s5_0 :: Nat -> s
779.70/291.49	
779.70/291.49	----------------------------------------
779.70/291.49	
779.70/291.49	(5) OrderProof (LOWER BOUND(ID))
779.70/291.49	Heuristically decided to analyse the following defined symbols:
779.70/291.49	f, f'
779.70/291.49	----------------------------------------
779.70/291.49	
779.70/291.49	(6)
779.70/291.49	Obligation:
779.70/291.49	TRS:
779.70/291.49	Rules:
779.70/291.49	f(g(x)) -> g(f(f(x)))
779.70/291.49	f(h(x)) -> h(g(x))
779.70/291.49	f'(s(x), y, y) -> f'(y, x, s(x))
779.70/291.49	
779.70/291.49	Types:
779.70/291.49	f :: g:h -> g:h
779.70/291.49	g :: g:h -> g:h

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