TRS_Innermost 2019-03-28 22.12 pair #432271336

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	n050.star.cs.uiowa.edu
space	Transformed_CSR_innermost_04

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	1.65583 seconds
cpu usage	6.61522
user time	6.34446
system time	0.270762
max virtual memory	1.8277356E7
max residence set size	227292.0

stage attributes

key	value
starexec-result	YES

output

3.15/1.63	YES
3.15/1.64	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.15/1.64	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.15/1.64	
3.15/1.64	
3.15/1.64	Termination w.r.t. Q of the given QTRS could be proven:
3.15/1.64	
3.15/1.64	(0) QTRS
3.15/1.64	(1) QTRSRRRProof [EQUIVALENT, 26 ms]
3.15/1.64	(2) QTRS
3.15/1.64	(3) RisEmptyProof [EQUIVALENT, 0 ms]
3.15/1.64	(4) YES
3.15/1.64	
3.15/1.64	
3.15/1.64	----------------------------------------
3.15/1.64	
3.15/1.64	(0)
3.15/1.64	Obligation:
3.15/1.64	Q restricted rewrite system:
3.15/1.64	The TRS R consists of the following rules:
3.15/1.64	
3.15/1.64	   terms(N) -> cons(recip(sqr(N)))
3.15/1.64	   sqr(0) -> 0
3.15/1.64	   sqr(s) -> s
3.15/1.64	   dbl(0) -> 0
3.15/1.64	   dbl(s) -> s
3.15/1.64	   add(0, X) -> X
3.15/1.64	   add(s, Y) -> s
3.15/1.64	   first(0, X) -> nil
3.15/1.64	   first(s, cons(Y)) -> cons(Y)
3.15/1.64	
3.15/1.64	The set Q consists of the following terms:
3.15/1.64	
3.15/1.64	   terms(x0)
3.15/1.64	   sqr(0)
3.15/1.64	   sqr(s)
3.15/1.64	   dbl(0)
3.15/1.64	   dbl(s)
3.15/1.64	   add(0, x0)
3.15/1.64	   add(s, x0)
3.15/1.64	   first(0, x0)
3.15/1.64	   first(s, cons(x0))
3.15/1.64	
3.15/1.64	
3.15/1.64	----------------------------------------
3.15/1.64	
3.15/1.64	(1) QTRSRRRProof (EQUIVALENT)
3.15/1.64	Used ordering:
3.15/1.64	Knuth-Bendix order [KBO] with precedence:dbl_1 > first_2 > nil > add_2 > s > 0 > recip_1 > sqr_1 > terms_1 > cons_1
3.15/1.64	
3.15/1.64	and weight map:
3.15/1.64	
3.15/1.64	   0=1
3.15/1.64	   s=1
3.15/1.64	   nil=2
3.15/1.64	   terms_1=3
3.15/1.64	   cons_1=1
3.15/1.64	   recip_1=1
3.15/1.64	   sqr_1=1
3.15/1.64	   dbl_1=0
3.15/1.64	   add_2=0
3.15/1.64	   first_2=0
3.15/1.64	
3.15/1.64	The variable weight is 1With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
3.15/1.64	
3.15/1.64	   terms(N) -> cons(recip(sqr(N)))
3.15/1.64	   sqr(0) -> 0
3.15/1.64	   sqr(s) -> s
3.15/1.64	   dbl(0) -> 0
3.15/1.64	   dbl(s) -> s
3.15/1.64	   add(0, X) -> X
3.15/1.64	   add(s, Y) -> s
3.15/1.64	   first(0, X) -> nil
3.15/1.64	   first(s, cons(Y)) -> cons(Y)
3.15/1.64	
3.15/1.64	
3.15/1.64	
3.15/1.64	
3.15/1.64	----------------------------------------
3.15/1.64	
3.15/1.64	(2)
3.15/1.64	Obligation:
3.15/1.64	Q restricted rewrite system:
3.15/1.64	R is empty.
3.15/1.64	The set Q consists of the following terms:
3.15/1.64	
3.15/1.64	   terms(x0)
3.15/1.64	   sqr(0)
3.15/1.64	   sqr(s)
3.15/1.64	   dbl(0)
3.15/1.64	   dbl(s)
3.15/1.64	   add(0, x0)
3.15/1.64	   add(s, x0)
3.15/1.64	   first(0, x0)
3.15/1.64	   first(s, cons(x0))
3.15/1.64	
3.15/1.64	
3.15/1.64	----------------------------------------
3.15/1.64	
3.15/1.64	(3) RisEmptyProof (EQUIVALENT)

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