Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307787

details

property	value
status	complete
benchmark	thiemann20.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n141.star.cs.uiowa.edu
space	AProVE_07

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	291.536 seconds
cpu usage	311.239
user time	309.343
system time	1.89645
max virtual memory	1.8281476E7
max residence set size	5240876.0

stage attributes

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

output

311.12/291.48	WORST_CASE(Omega(n^1), ?)
311.12/291.49	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
311.12/291.49	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
311.12/291.49	
311.12/291.49	
311.12/291.49	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF).
311.12/291.49	
311.12/291.49	(0) CpxTRS
311.12/291.49	(1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
311.12/291.49	(2) CpxTRS
311.12/291.49	(3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
311.12/291.49	(4) typed CpxTrs
311.12/291.49	(5) OrderProof [LOWER BOUND(ID), 0 ms]
311.12/291.49	(6) typed CpxTrs
311.12/291.49	(7) RewriteLemmaProof [LOWER BOUND(ID), 287 ms]
311.12/291.49	(8) BEST
311.12/291.49	    (9) proven lower bound
311.12/291.49	        (10) LowerBoundPropagationProof [FINISHED, 0 ms]
311.12/291.49	        (11) BOUNDS(n^1, INF)
311.12/291.49	    (12) typed CpxTrs
311.12/291.49	        (13) RewriteLemmaProof [LOWER BOUND(ID), 76 ms]
311.12/291.49	        (14) typed CpxTrs
311.12/291.49	        (15) RewriteLemmaProof [LOWER BOUND(ID), 44 ms]
311.12/291.49	        (16) typed CpxTrs
311.12/291.49	
311.12/291.49	
311.12/291.49	----------------------------------------
311.12/291.49	
311.12/291.49	(0)
311.12/291.49	Obligation:
311.12/291.49	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF).
311.12/291.49	
311.12/291.49	
311.12/291.49	The TRS R consists of the following rules:
311.12/291.49	
311.12/291.49	   gt(0, y) -> false
311.12/291.49	   gt(s(x), 0) -> true
311.12/291.49	   gt(s(x), s(y)) -> gt(x, y)
311.12/291.49	   plus(0, y) -> y
311.12/291.49	   plus(s(x), y) -> s(plus(x, y))
311.12/291.49	   double(0) -> 0
311.12/291.49	   double(s(x)) -> s(s(double(x)))
311.12/291.49	   average(x, y) -> aver(plus(x, y), 0)
311.12/291.49	   aver(sum, z) -> if(gt(sum, double(z)), sum, z)
311.12/291.49	   if(true, sum, z) -> aver(sum, s(z))
311.12/291.49	   if(false, sum, z) -> z
311.12/291.49	
311.12/291.49	S is empty.
311.12/291.49	Rewrite Strategy: FULL
311.12/291.49	----------------------------------------
311.12/291.49	
311.12/291.49	(1) RenamingProof (BOTH BOUNDS(ID, ID))
311.12/291.49	Renamed function symbols to avoid clashes with predefined symbol.
311.12/291.49	----------------------------------------
311.12/291.49	
311.12/291.49	(2)
311.12/291.49	Obligation:
311.12/291.49	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF).
311.12/291.49	
311.12/291.49	
311.12/291.49	The TRS R consists of the following rules:
311.12/291.49	
311.12/291.49	   gt(0', y) -> false
311.12/291.49	   gt(s(x), 0') -> true
311.12/291.49	   gt(s(x), s(y)) -> gt(x, y)
311.12/291.49	   plus(0', y) -> y
311.12/291.49	   plus(s(x), y) -> s(plus(x, y))
311.12/291.49	   double(0') -> 0'
311.12/291.49	   double(s(x)) -> s(s(double(x)))
311.12/291.49	   average(x, y) -> aver(plus(x, y), 0')
311.12/291.49	   aver(sum, z) -> if(gt(sum, double(z)), sum, z)
311.12/291.49	   if(true, sum, z) -> aver(sum, s(z))
311.12/291.49	   if(false, sum, z) -> z
311.12/291.49	
311.12/291.49	S is empty.
311.12/291.49	Rewrite Strategy: FULL
311.12/291.49	----------------------------------------
311.12/291.49	
311.12/291.49	(3) TypeInferenceProof (BOTH BOUNDS(ID, ID))
311.12/291.49	Infered types.
311.12/291.49	----------------------------------------
311.12/291.49	
311.12/291.49	(4)
311.12/291.49	Obligation:
311.12/291.49	TRS:
311.12/291.49	Rules:
311.12/291.49	gt(0', y) -> false
311.12/291.49	gt(s(x), 0') -> true
311.12/291.49	gt(s(x), s(y)) -> gt(x, y)
311.12/291.49	plus(0', y) -> y
311.12/291.49	plus(s(x), y) -> s(plus(x, y))
311.12/291.49	double(0') -> 0'
311.12/291.49	double(s(x)) -> s(s(double(x)))
311.12/291.49	average(x, y) -> aver(plus(x, y), 0')
311.12/291.49	aver(sum, z) -> if(gt(sum, double(z)), sum, z)
311.12/291.49	if(true, sum, z) -> aver(sum, s(z))
311.12/291.49	if(false, sum, z) -> z
311.12/291.49	
311.12/291.49	Types:
311.12/291.49	gt :: 0':s -> 0':s -> false:true

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