Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313722

details

property	value
status	complete
benchmark	thiemann23.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n139.star.cs.uiowa.edu
space	AProVE_07

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	13.5593 seconds
cpu usage	46.044
user time	43.7906
system time	2.25342
max virtual memory	1.895118E7
max residence set size	4498440.0

stage attributes

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

output

45.65/13.49	WORST_CASE(Omega(n^1), O(n^1))
45.65/13.50	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
45.65/13.50	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
45.65/13.50	
45.65/13.50	
45.65/13.50	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
45.65/13.50	
45.65/13.50	(0) CpxTRS
45.65/13.50	(1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
45.65/13.50	(2) CpxWeightedTrs
45.65/13.50	    (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
45.65/13.50	    (4) CpxTypedWeightedTrs
45.65/13.50	    (5) CompletionProof [UPPER BOUND(ID), 0 ms]
45.65/13.50	    (6) CpxTypedWeightedCompleteTrs
45.65/13.50	    (7) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
45.65/13.50	    (8) CpxRNTS
45.65/13.50	    (9) CompleteCoflocoProof [FINISHED, 198 ms]
45.65/13.50	    (10) BOUNDS(1, n^1)
45.65/13.50	(11) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
45.65/13.50	(12) TRS for Loop Detection
45.65/13.50	    (13) DecreasingLoopProof [LOWER BOUND(ID), 0 ms]
45.65/13.50	    (14) BEST
45.65/13.50	        (15) proven lower bound
45.65/13.50	            (16) LowerBoundPropagationProof [FINISHED, 0 ms]
45.65/13.50	            (17) BOUNDS(n^1, INF)
45.65/13.50	        (18) TRS for Loop Detection
45.65/13.50	
45.65/13.50	
45.65/13.50	----------------------------------------
45.65/13.50	
45.65/13.50	(0)
45.65/13.50	Obligation:
45.65/13.50	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
45.65/13.50	
45.65/13.50	
45.65/13.50	The TRS R consists of the following rules:
45.65/13.50	
45.65/13.50	   digits -> d(0)
45.65/13.50	   d(x) -> if(le(x, s(s(s(s(s(s(s(s(s(0)))))))))), x)
45.65/13.50	   if(true, x) -> cons(x, d(s(x)))
45.65/13.50	   if(false, x) -> nil
45.65/13.50	   le(0, y) -> true
45.65/13.50	   le(s(x), 0) -> false
45.65/13.50	   le(s(x), s(y)) -> le(x, y)
45.65/13.50	
45.65/13.50	S is empty.
45.65/13.50	Rewrite Strategy: INNERMOST
45.65/13.50	----------------------------------------
45.65/13.50	
45.65/13.50	(1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID))
45.65/13.50	Transformed relative TRS to weighted TRS
45.65/13.50	----------------------------------------
45.65/13.50	
45.65/13.50	(2)
45.65/13.50	Obligation:
45.65/13.50	The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^1).
45.65/13.50	
45.65/13.50	
45.65/13.50	The TRS R consists of the following rules:
45.65/13.50	
45.65/13.50	   digits -> d(0) [1]
45.65/13.50	   d(x) -> if(le(x, s(s(s(s(s(s(s(s(s(0)))))))))), x) [1]
45.65/13.50	   if(true, x) -> cons(x, d(s(x))) [1]
45.65/13.50	   if(false, x) -> nil [1]
45.65/13.50	   le(0, y) -> true [1]
45.65/13.50	   le(s(x), 0) -> false [1]
45.65/13.50	   le(s(x), s(y)) -> le(x, y) [1]
45.65/13.50	
45.65/13.50	Rewrite Strategy: INNERMOST
45.65/13.50	----------------------------------------
45.65/13.50	
45.65/13.50	(3) TypeInferenceProof (BOTH BOUNDS(ID, ID))
45.65/13.50	Infered types.
45.65/13.50	----------------------------------------
45.65/13.50	
45.65/13.50	(4)
45.65/13.50	Obligation:
45.65/13.50	Runtime Complexity Weighted TRS with Types.
45.65/13.50	The TRS R consists of the following rules:
45.65/13.50	
45.65/13.50	   digits -> d(0) [1]
45.65/13.50	   d(x) -> if(le(x, s(s(s(s(s(s(s(s(s(0)))))))))), x) [1]
45.65/13.50	   if(true, x) -> cons(x, d(s(x))) [1]
45.65/13.50	   if(false, x) -> nil [1]
45.65/13.50	   le(0, y) -> true [1]
45.65/13.50	   le(s(x), 0) -> false [1]
45.65/13.50	   le(s(x), s(y)) -> le(x, y) [1]
45.65/13.50	
45.65/13.50	The TRS has the following type information:
45.65/13.50	digits :: cons:nil
45.65/13.50	d :: 0:s -> cons:nil
45.65/13.50	0 :: 0:s
45.65/13.50	if :: true:false -> 0:s -> cons:nil
45.65/13.50	le :: 0:s -> 0:s -> true:false
45.65/13.50	s :: 0:s -> 0:s
45.65/13.50	true :: true:false
45.65/13.50	cons :: 0:s -> cons:nil -> cons:nil
45.65/13.50	false :: true:false
45.65/13.50	nil :: cons:nil
45.65/13.50

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