Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313777

details

property	value
status	complete
benchmark	#3.42.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n065.star.cs.uiowa.edu
space	AG01

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	5.33518 seconds
cpu usage	17.7312
user time	16.2402
system time	1.49098
max virtual memory	1.9078304E7
max residence set size	3961184.0

stage attributes

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

output

17.44/5.27	WORST_CASE(Omega(n^1), O(n^1))
17.44/5.28	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
17.44/5.28	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
17.44/5.28	
17.44/5.28	
17.44/5.28	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
17.44/5.28	
17.44/5.28	(0) CpxTRS
17.44/5.28	(1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
17.44/5.28	(2) CpxWeightedTrs
17.44/5.28	    (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
17.44/5.28	    (4) CpxTypedWeightedTrs
17.44/5.28	    (5) CompletionProof [UPPER BOUND(ID), 0 ms]
17.44/5.28	    (6) CpxTypedWeightedCompleteTrs
17.44/5.28	    (7) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
17.44/5.28	    (8) CpxRNTS
17.44/5.28	    (9) CompleteCoflocoProof [FINISHED, 310 ms]
17.44/5.28	    (10) BOUNDS(1, n^1)
17.44/5.28	(11) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
17.44/5.28	(12) TRS for Loop Detection
17.44/5.28	    (13) DecreasingLoopProof [LOWER BOUND(ID), 0 ms]
17.44/5.28	    (14) BEST
17.44/5.28	        (15) proven lower bound
17.44/5.28	            (16) LowerBoundPropagationProof [FINISHED, 0 ms]
17.44/5.28	            (17) BOUNDS(n^1, INF)
17.44/5.28	        (18) TRS for Loop Detection
17.44/5.28	
17.44/5.28	
17.44/5.28	----------------------------------------
17.44/5.28	
17.44/5.28	(0)
17.44/5.28	Obligation:
17.44/5.28	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
17.44/5.28	
17.44/5.28	
17.44/5.28	The TRS R consists of the following rules:
17.44/5.28	
17.44/5.28	   half(0) -> 0
17.44/5.28	   half(s(0)) -> 0
17.44/5.28	   half(s(s(x))) -> s(half(x))
17.44/5.28	   lastbit(0) -> 0
17.44/5.28	   lastbit(s(0)) -> s(0)
17.44/5.28	   lastbit(s(s(x))) -> lastbit(x)
17.44/5.28	   conv(0) -> cons(nil, 0)
17.44/5.28	   conv(s(x)) -> cons(conv(half(s(x))), lastbit(s(x)))
17.44/5.28	
17.44/5.28	S is empty.
17.44/5.28	Rewrite Strategy: INNERMOST
17.44/5.28	----------------------------------------
17.44/5.28	
17.44/5.28	(1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID))
17.44/5.28	Transformed relative TRS to weighted TRS
17.44/5.28	----------------------------------------
17.44/5.28	
17.44/5.28	(2)
17.44/5.28	Obligation:
17.44/5.28	The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^1).
17.44/5.28	
17.44/5.28	
17.44/5.28	The TRS R consists of the following rules:
17.44/5.28	
17.44/5.28	   half(0) -> 0 [1]
17.44/5.28	   half(s(0)) -> 0 [1]
17.44/5.28	   half(s(s(x))) -> s(half(x)) [1]
17.44/5.28	   lastbit(0) -> 0 [1]
17.44/5.28	   lastbit(s(0)) -> s(0) [1]
17.44/5.28	   lastbit(s(s(x))) -> lastbit(x) [1]
17.44/5.28	   conv(0) -> cons(nil, 0) [1]
17.44/5.28	   conv(s(x)) -> cons(conv(half(s(x))), lastbit(s(x))) [1]
17.44/5.28	
17.44/5.28	Rewrite Strategy: INNERMOST
17.44/5.28	----------------------------------------
17.44/5.28	
17.44/5.28	(3) TypeInferenceProof (BOTH BOUNDS(ID, ID))
17.44/5.28	Infered types.
17.44/5.28	----------------------------------------
17.44/5.28	
17.44/5.28	(4)
17.44/5.28	Obligation:
17.44/5.28	Runtime Complexity Weighted TRS with Types.
17.44/5.28	The TRS R consists of the following rules:
17.44/5.28	
17.44/5.28	   half(0) -> 0 [1]
17.44/5.28	   half(s(0)) -> 0 [1]
17.44/5.28	   half(s(s(x))) -> s(half(x)) [1]
17.44/5.28	   lastbit(0) -> 0 [1]
17.44/5.28	   lastbit(s(0)) -> s(0) [1]
17.44/5.28	   lastbit(s(s(x))) -> lastbit(x) [1]
17.44/5.28	   conv(0) -> cons(nil, 0) [1]
17.44/5.28	   conv(s(x)) -> cons(conv(half(s(x))), lastbit(s(x))) [1]
17.44/5.28	
17.44/5.28	The TRS has the following type information:
17.44/5.28	half :: 0:s -> 0:s
17.44/5.28	0 :: 0:s
17.44/5.28	s :: 0:s -> 0:s
17.44/5.28	lastbit :: 0:s -> 0:s
17.44/5.28	conv :: 0:s -> nil:cons
17.44/5.28	cons :: nil:cons -> 0:s -> nil:cons
17.44/5.28	nil :: nil:cons
17.44/5.28

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actions all output return to Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40