Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313559

details

property	value
status	complete
benchmark	#4.28.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n138.star.cs.uiowa.edu
space	Strategy_removed_AG01

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	4.57495 seconds
cpu usage	14.4246
user time	13.6797
system time	0.744876
max virtual memory	1.901546E7
max residence set size	1972920.0

stage attributes

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

output

14.22/4.51	WORST_CASE(Omega(n^1), O(n^1))
14.22/4.53	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
14.22/4.53	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
14.22/4.53	
14.22/4.53	
14.22/4.53	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
14.22/4.53	
14.22/4.53	(0) CpxTRS
14.22/4.53	(1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
14.22/4.53	(2) CpxWeightedTrs
14.22/4.53	    (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 2 ms]
14.22/4.53	    (4) CpxTypedWeightedTrs
14.22/4.53	    (5) CompletionProof [UPPER BOUND(ID), 0 ms]
14.22/4.53	    (6) CpxTypedWeightedCompleteTrs
14.22/4.53	    (7) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 2 ms]
14.22/4.53	    (8) CpxRNTS
14.22/4.53	    (9) CompleteCoflocoProof [FINISHED, 190 ms]
14.22/4.53	    (10) BOUNDS(1, n^1)
14.22/4.53	(11) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
14.22/4.53	(12) TRS for Loop Detection
14.22/4.53	    (13) DecreasingLoopProof [LOWER BOUND(ID), 0 ms]
14.22/4.53	    (14) BEST
14.22/4.53	        (15) proven lower bound
14.22/4.53	            (16) LowerBoundPropagationProof [FINISHED, 0 ms]
14.22/4.53	            (17) BOUNDS(n^1, INF)
14.22/4.53	        (18) TRS for Loop Detection
14.22/4.53	
14.22/4.53	
14.22/4.53	----------------------------------------
14.22/4.53	
14.22/4.53	(0)
14.22/4.53	Obligation:
14.22/4.53	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
14.22/4.53	
14.22/4.53	
14.22/4.53	The TRS R consists of the following rules:
14.22/4.53	
14.22/4.53	   half(0) -> 0
14.22/4.53	   half(s(0)) -> 0
14.22/4.53	   half(s(s(x))) -> s(half(x))
14.22/4.53	   bits(0) -> 0
14.22/4.53	   bits(s(x)) -> s(bits(half(s(x))))
14.22/4.53	
14.22/4.53	S is empty.
14.22/4.53	Rewrite Strategy: INNERMOST
14.22/4.53	----------------------------------------
14.22/4.53	
14.22/4.53	(1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID))
14.22/4.53	Transformed relative TRS to weighted TRS
14.22/4.53	----------------------------------------
14.22/4.53	
14.22/4.53	(2)
14.22/4.53	Obligation:
14.22/4.53	The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^1).
14.22/4.53	
14.22/4.53	
14.22/4.53	The TRS R consists of the following rules:
14.22/4.53	
14.22/4.53	   half(0) -> 0 [1]
14.22/4.53	   half(s(0)) -> 0 [1]
14.22/4.53	   half(s(s(x))) -> s(half(x)) [1]
14.22/4.53	   bits(0) -> 0 [1]
14.22/4.53	   bits(s(x)) -> s(bits(half(s(x)))) [1]
14.22/4.53	
14.22/4.53	Rewrite Strategy: INNERMOST
14.22/4.53	----------------------------------------
14.22/4.53	
14.22/4.53	(3) TypeInferenceProof (BOTH BOUNDS(ID, ID))
14.22/4.53	Infered types.
14.22/4.53	----------------------------------------
14.22/4.53	
14.22/4.53	(4)
14.22/4.53	Obligation:
14.22/4.53	Runtime Complexity Weighted TRS with Types.
14.22/4.53	The TRS R consists of the following rules:
14.22/4.53	
14.22/4.53	   half(0) -> 0 [1]
14.22/4.53	   half(s(0)) -> 0 [1]
14.22/4.53	   half(s(s(x))) -> s(half(x)) [1]
14.22/4.53	   bits(0) -> 0 [1]
14.22/4.53	   bits(s(x)) -> s(bits(half(s(x)))) [1]
14.22/4.53	
14.22/4.53	The TRS has the following type information:
14.22/4.53	half :: 0:s -> 0:s
14.22/4.53	0 :: 0:s
14.22/4.53	s :: 0:s -> 0:s
14.22/4.53	bits :: 0:s -> 0:s
14.22/4.53	
14.22/4.53	Rewrite Strategy: INNERMOST
14.22/4.53	----------------------------------------
14.22/4.53	
14.22/4.53	(5) CompletionProof (UPPER BOUND(ID))
14.22/4.53	The TRS is a completely defined constructor system, as every type has a constant constructor and the following rules were added:
14.22/4.53	none
14.22/4.53	
14.22/4.53	And the following fresh constants: none
14.22/4.53	
14.22/4.53	----------------------------------------
14.22/4.53	
14.22/4.53	(6)

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