Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313770

details

property	value
status	complete
benchmark	#3.7.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n159.star.cs.uiowa.edu
space	AG01

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	9.9044 seconds
cpu usage	23.7138
user time	22.2669
system time	1.44696
max virtual memory	1.9012412E7
max residence set size	4014216.0

stage attributes

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

output

21.57/6.33	WORST_CASE(Omega(n^1), O(n^1))
21.57/6.34	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
21.57/6.34	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
21.57/6.34	
21.57/6.34	
21.57/6.34	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
21.57/6.34	
21.57/6.34	(0) CpxTRS
21.57/6.34	(1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
21.57/6.34	(2) CpxWeightedTrs
21.57/6.34	    (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
21.57/6.34	    (4) CpxTypedWeightedTrs
21.57/6.34	    (5) CompletionProof [UPPER BOUND(ID), 0 ms]
21.57/6.34	    (6) CpxTypedWeightedCompleteTrs
21.57/6.34	    (7) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
21.57/6.34	    (8) CpxRNTS
21.57/6.34	    (9) CompleteCoflocoProof [FINISHED, 129 ms]
21.57/6.34	    (10) BOUNDS(1, n^1)
21.57/6.34	(11) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
21.57/6.34	(12) TRS for Loop Detection
21.57/6.34	    (13) DecreasingLoopProof [LOWER BOUND(ID), 0 ms]
21.57/6.34	    (14) BEST
21.57/6.34	        (15) proven lower bound
21.57/6.34	            (16) LowerBoundPropagationProof [FINISHED, 0 ms]
21.57/6.34	            (17) BOUNDS(n^1, INF)
21.57/6.34	        (18) TRS for Loop Detection
21.57/6.34	
21.57/6.34	
21.57/6.34	----------------------------------------
21.57/6.34	
21.57/6.34	(0)
21.57/6.34	Obligation:
21.57/6.34	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
21.57/6.34	
21.57/6.34	
21.57/6.34	The TRS R consists of the following rules:
21.57/6.34	
21.57/6.34	   half(0) -> 0
21.57/6.34	   half(s(s(x))) -> s(half(x))
21.57/6.34	   log(s(0)) -> 0
21.57/6.34	   log(s(s(x))) -> s(log(s(half(x))))
21.57/6.34	
21.57/6.34	S is empty.
21.57/6.34	Rewrite Strategy: INNERMOST
21.57/6.34	----------------------------------------
21.57/6.34	
21.57/6.34	(1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID))
21.57/6.34	Transformed relative TRS to weighted TRS
21.57/6.34	----------------------------------------
21.57/6.34	
21.57/6.34	(2)
21.57/6.34	Obligation:
21.57/6.34	The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^1).
21.57/6.34	
21.57/6.34	
21.57/6.34	The TRS R consists of the following rules:
21.57/6.34	
21.57/6.34	   half(0) -> 0 [1]
21.57/6.34	   half(s(s(x))) -> s(half(x)) [1]
21.57/6.34	   log(s(0)) -> 0 [1]
21.57/6.34	   log(s(s(x))) -> s(log(s(half(x)))) [1]
21.57/6.34	
21.57/6.34	Rewrite Strategy: INNERMOST
21.57/6.34	----------------------------------------
21.57/6.34	
21.57/6.34	(3) TypeInferenceProof (BOTH BOUNDS(ID, ID))
21.57/6.34	Infered types.
21.57/6.34	----------------------------------------
21.57/6.34	
21.57/6.34	(4)
21.57/6.34	Obligation:
21.57/6.34	Runtime Complexity Weighted TRS with Types.
21.57/6.34	The TRS R consists of the following rules:
21.57/6.34	
21.57/6.34	   half(0) -> 0 [1]
21.57/6.34	   half(s(s(x))) -> s(half(x)) [1]
21.57/6.34	   log(s(0)) -> 0 [1]
21.57/6.34	   log(s(s(x))) -> s(log(s(half(x)))) [1]
21.57/6.34	
21.57/6.34	The TRS has the following type information:
21.57/6.34	half :: 0:s -> 0:s
21.57/6.34	0 :: 0:s
21.57/6.34	s :: 0:s -> 0:s
21.57/6.34	log :: 0:s -> 0:s
21.57/6.34	
21.57/6.34	Rewrite Strategy: INNERMOST
21.57/6.34	----------------------------------------
21.57/6.34	
21.57/6.34	(5) CompletionProof (UPPER BOUND(ID))
21.57/6.34	The TRS is a completely defined constructor system, as every type has a constant constructor and the following rules were added:
21.57/6.34	
21.57/6.34	   half(v0) -> null_half [0]
21.57/6.34	   log(v0) -> null_log [0]
21.57/6.34	
21.57/6.34	And the following fresh constants:    null_half, null_log
21.57/6.34	
21.57/6.34	----------------------------------------
21.57/6.34	
21.57/6.34	(6)
21.57/6.34	Obligation:

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