Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313535

details

property	value
status	complete
benchmark	Ex26_Luc03b_L.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n099.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	1.57791 seconds
cpu usage	3.26448
user time	3.11461
system time	0.149874
max virtual memory	1.8273204E7
max residence set size	218100.0

stage attributes

key	value
starexec-result	WORST_CASE(?, O(1))

output

2.97/1.53	WORST_CASE(?, O(1))
2.97/1.54	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
2.97/1.54	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.97/1.54	
2.97/1.54	
2.97/1.54	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, 1).
2.97/1.54	
2.97/1.54	(0) CpxTRS
2.97/1.54	(1) NarrowingOnBasicTermsTerminatesProof [FINISHED, 0 ms]
2.97/1.54	(2) BOUNDS(1, 1)
2.97/1.54	
2.97/1.54	
2.97/1.54	----------------------------------------
2.97/1.54	
2.97/1.54	(0)
2.97/1.54	Obligation:
2.97/1.54	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, 1).
2.97/1.54	
2.97/1.54	
2.97/1.54	The TRS R consists of the following rules:
2.97/1.54	
2.97/1.54	   terms(N) -> cons(recip(sqr(N)))
2.97/1.54	   sqr(0) -> 0
2.97/1.54	   sqr(s) -> s
2.97/1.54	   dbl(0) -> 0
2.97/1.54	   dbl(s) -> s
2.97/1.54	   add(0, X) -> X
2.97/1.54	   add(s, Y) -> s
2.97/1.54	   first(0, X) -> nil
2.97/1.54	   first(s, cons(Y)) -> cons(Y)
2.97/1.54	
2.97/1.54	S is empty.
2.97/1.54	Rewrite Strategy: INNERMOST
2.97/1.54	----------------------------------------
2.97/1.54	
2.97/1.54	(1) NarrowingOnBasicTermsTerminatesProof (FINISHED)
2.97/1.54	Constant runtime complexity proven by termination of constructor-based narrowing.
2.97/1.54	
2.97/1.54	The maximal most general narrowing sequences give rise to the following rewrite sequences:
2.97/1.54	
2.97/1.54	first(s, cons(x0)) ->^* cons(x0)
2.97/1.54	
2.97/1.54	first(0, x0) ->^* nil
2.97/1.54	
2.97/1.54	dbl(s) ->^* s
2.97/1.54	
2.97/1.54	dbl(0) ->^* 0
2.97/1.54	
2.97/1.54	add(s, x0) ->^* s
2.97/1.54	
2.97/1.54	terms(s) ->^* cons(recip(s))
2.97/1.54	
2.97/1.54	terms(0) ->^* cons(recip(0))
2.97/1.54	
2.97/1.54	sqr(s) ->^* s
2.97/1.54	
2.97/1.54	sqr(0) ->^* 0
2.97/1.54	
2.97/1.54	
2.97/1.54	
2.97/1.54	
2.97/1.54	----------------------------------------
2.97/1.54	
2.97/1.54	(2)
2.97/1.54	BOUNDS(1, 1)
3.25/1.57	EOF

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