Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313353

details

property	value
status	complete
benchmark	t014.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n044.star.cs.uiowa.edu
space	HirokawaMiddeldorp_04

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	5.33721 seconds
cpu usage	16.9066
user time	15.5763
system time	1.33028
max virtual memory	1.9209036E7
max residence set size	4133072.0

stage attributes

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

output

16.66/5.26	WORST_CASE(Omega(n^1), O(n^1))
16.66/5.27	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
16.66/5.27	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
16.66/5.27	
16.66/5.27	
16.66/5.27	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
16.66/5.27	
16.66/5.27	(0) CpxTRS
16.66/5.27	(1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
16.66/5.27	(2) CpxWeightedTrs
16.66/5.27	    (3) CpxWeightedTrsRenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
16.66/5.27	    (4) CpxWeightedTrs
16.66/5.27	    (5) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
16.66/5.27	    (6) CpxTypedWeightedTrs
16.66/5.27	    (7) CompletionProof [UPPER BOUND(ID), 0 ms]
16.66/5.27	    (8) CpxTypedWeightedCompleteTrs
16.66/5.27	    (9) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 5 ms]
16.66/5.27	    (10) CpxRNTS
16.66/5.27	    (11) CompleteCoflocoProof [FINISHED, 360 ms]
16.66/5.27	    (12) BOUNDS(1, n^1)
16.66/5.27	(13) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
16.66/5.27	(14) CpxTRS
16.66/5.27	    (15) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
16.66/5.27	    (16) typed CpxTrs
16.66/5.27	    (17) OrderProof [LOWER BOUND(ID), 0 ms]
16.66/5.27	    (18) typed CpxTrs
16.66/5.27	    (19) RewriteLemmaProof [LOWER BOUND(ID), 321 ms]
16.66/5.27	    (20) BEST
16.66/5.27	        (21) proven lower bound
16.66/5.27	            (22) LowerBoundPropagationProof [FINISHED, 0 ms]
16.66/5.27	            (23) BOUNDS(n^1, INF)
16.66/5.27	        (24) typed CpxTrs
16.66/5.27	            (25) RewriteLemmaProof [LOWER BOUND(ID), 58 ms]
16.66/5.27	            (26) typed CpxTrs
16.66/5.27	
16.66/5.27	
16.66/5.27	----------------------------------------
16.66/5.27	
16.66/5.27	(0)
16.66/5.27	Obligation:
16.66/5.27	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
16.66/5.27	
16.66/5.27	
16.66/5.27	The TRS R consists of the following rules:
16.66/5.27	
16.66/5.27	   -(x, 0) -> x
16.66/5.27	   -(0, s(y)) -> 0
16.66/5.27	   -(s(x), s(y)) -> -(x, y)
16.66/5.27	   lt(x, 0) -> false
16.66/5.27	   lt(0, s(y)) -> true
16.66/5.27	   lt(s(x), s(y)) -> lt(x, y)
16.66/5.27	   if(true, x, y) -> x
16.66/5.27	   if(false, x, y) -> y
16.66/5.27	   div(x, 0) -> 0
16.66/5.27	   div(0, y) -> 0
16.66/5.27	   div(s(x), s(y)) -> if(lt(x, y), 0, s(div(-(x, y), s(y))))
16.66/5.27	
16.66/5.27	S is empty.
16.66/5.27	Rewrite Strategy: INNERMOST
16.66/5.27	----------------------------------------
16.66/5.27	
16.66/5.27	(1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID))
16.66/5.27	Transformed relative TRS to weighted TRS
16.66/5.27	----------------------------------------
16.66/5.27	
16.66/5.27	(2)
16.66/5.27	Obligation:
16.66/5.27	The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^1).
16.66/5.27	
16.66/5.27	
16.66/5.27	The TRS R consists of the following rules:
16.66/5.27	
16.66/5.27	   -(x, 0) -> x [1]
16.66/5.27	   -(0, s(y)) -> 0 [1]
16.66/5.27	   -(s(x), s(y)) -> -(x, y) [1]
16.66/5.27	   lt(x, 0) -> false [1]
16.66/5.27	   lt(0, s(y)) -> true [1]
16.66/5.27	   lt(s(x), s(y)) -> lt(x, y) [1]
16.66/5.27	   if(true, x, y) -> x [1]
16.66/5.27	   if(false, x, y) -> y [1]
16.66/5.27	   div(x, 0) -> 0 [1]
16.66/5.27	   div(0, y) -> 0 [1]
16.66/5.27	   div(s(x), s(y)) -> if(lt(x, y), 0, s(div(-(x, y), s(y)))) [1]
16.66/5.27	
16.66/5.27	Rewrite Strategy: INNERMOST
16.66/5.27	----------------------------------------
16.66/5.27	
16.66/5.27	(3) CpxWeightedTrsRenamingProof (BOTH BOUNDS(ID, ID))
16.66/5.27	Renamed defined symbols to avoid conflicts with arithmetic symbols:
16.66/5.27	
16.66/5.27	- => minus
16.66/5.27	
16.66/5.27	----------------------------------------
16.66/5.27	
16.66/5.27	(4)
16.66/5.27	Obligation:
16.66/5.27	The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^1).
16.66/5.27	
16.66/5.27	
16.66/5.27	The TRS R consists of the following rules:

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