Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307921

details

property	value
status	complete
benchmark	t012.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n132.star.cs.uiowa.edu
space	HirokawaMiddeldorp_04

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	292.252 seconds
cpu usage	1102.89
user time	1090.82
system time	12.0705
max virtual memory	3.7112632E7
max residence set size	1.5043076E7

stage attributes

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

output

1102.25/292.07	WORST_CASE(Omega(n^1), ?)
1102.25/292.08	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
1102.25/292.08	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
1102.25/292.08	
1102.25/292.08	
1102.25/292.08	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF).
1102.25/292.08	
1102.25/292.08	(0) CpxTRS
1102.25/292.08	(1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
1102.25/292.08	(2) CpxTRS
1102.25/292.08	(3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
1102.25/292.08	(4) typed CpxTrs
1102.25/292.08	(5) OrderProof [LOWER BOUND(ID), 0 ms]
1102.25/292.08	(6) typed CpxTrs
1102.25/292.08	(7) RewriteLemmaProof [LOWER BOUND(ID), 523 ms]
1102.25/292.08	(8) BEST
1102.25/292.08	    (9) proven lower bound
1102.25/292.08	        (10) LowerBoundPropagationProof [FINISHED, 0 ms]
1102.25/292.08	        (11) BOUNDS(n^1, INF)
1102.25/292.08	    (12) typed CpxTrs
1102.25/292.08	
1102.25/292.08	
1102.25/292.08	----------------------------------------
1102.25/292.08	
1102.25/292.08	(0)
1102.25/292.08	Obligation:
1102.25/292.08	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF).
1102.25/292.08	
1102.25/292.08	
1102.25/292.08	The TRS R consists of the following rules:
1102.25/292.08	
1102.25/292.08	   minus(minus(x)) -> x
1102.25/292.08	   minus(+(x, y)) -> *(minus(minus(minus(x))), minus(minus(minus(y))))
1102.25/292.08	   minus(*(x, y)) -> +(minus(minus(minus(x))), minus(minus(minus(y))))
1102.25/292.08	   f(minus(x)) -> minus(minus(minus(f(x))))
1102.25/292.08	
1102.25/292.08	S is empty.
1102.25/292.08	Rewrite Strategy: FULL
1102.25/292.08	----------------------------------------
1102.25/292.08	
1102.25/292.08	(1) RenamingProof (BOTH BOUNDS(ID, ID))
1102.25/292.08	Renamed function symbols to avoid clashes with predefined symbol.
1102.25/292.08	----------------------------------------
1102.25/292.08	
1102.25/292.08	(2)
1102.25/292.08	Obligation:
1102.25/292.08	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF).
1102.25/292.08	
1102.25/292.08	
1102.25/292.08	The TRS R consists of the following rules:
1102.25/292.08	
1102.25/292.08	   minus(minus(x)) -> x
1102.25/292.08	   minus(+'(x, y)) -> *'(minus(minus(minus(x))), minus(minus(minus(y))))
1102.25/292.08	   minus(*'(x, y)) -> +'(minus(minus(minus(x))), minus(minus(minus(y))))
1102.25/292.08	   f(minus(x)) -> minus(minus(minus(f(x))))
1102.25/292.08	
1102.25/292.08	S is empty.
1102.25/292.08	Rewrite Strategy: FULL
1102.25/292.08	----------------------------------------
1102.25/292.08	
1102.25/292.08	(3) TypeInferenceProof (BOTH BOUNDS(ID, ID))
1102.25/292.08	Infered types.
1102.25/292.08	----------------------------------------
1102.25/292.08	
1102.25/292.08	(4)
1102.25/292.08	Obligation:
1102.25/292.08	TRS:
1102.25/292.08	Rules:
1102.25/292.08	minus(minus(x)) -> x
1102.25/292.08	minus(+'(x, y)) -> *'(minus(minus(minus(x))), minus(minus(minus(y))))
1102.25/292.08	minus(*'(x, y)) -> +'(minus(minus(minus(x))), minus(minus(minus(y))))
1102.25/292.08	f(minus(x)) -> minus(minus(minus(f(x))))
1102.25/292.08	
1102.25/292.08	Types:
1102.25/292.08	minus :: +':*' -> +':*'
1102.25/292.08	+' :: +':*' -> +':*' -> +':*'
1102.25/292.08	*' :: +':*' -> +':*' -> +':*'
1102.25/292.08	f :: +':*' -> +':*'
1102.25/292.08	hole_+':*'1_0 :: +':*'
1102.25/292.08	gen_+':*'2_0 :: Nat -> +':*'
1102.25/292.08	
1102.25/292.08	----------------------------------------
1102.25/292.08	
1102.25/292.08	(5) OrderProof (LOWER BOUND(ID))
1102.25/292.08	Heuristically decided to analyse the following defined symbols:
1102.25/292.08	minus, f
1102.25/292.08	
1102.25/292.08	They will be analysed ascendingly in the following order:
1102.25/292.08	minus < f
1102.25/292.08	
1102.25/292.08	----------------------------------------
1102.25/292.08	
1102.25/292.08	(6)
1102.25/292.08	Obligation:
1102.25/292.08	TRS:
1102.25/292.08	Rules:
1102.25/292.08	minus(minus(x)) -> x
1102.25/292.08	minus(+'(x, y)) -> *'(minus(minus(minus(x))), minus(minus(minus(y))))
1102.25/292.08	minus(*'(x, y)) -> +'(minus(minus(minus(x))), minus(minus(minus(y))))
1102.25/292.08	f(minus(x)) -> minus(minus(minus(f(x))))

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