SRS_Standard 2019-03-29 03.29 pair #432294577

details

property	value
status	complete
benchmark	random-466.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n161.star.cs.uiowa.edu
space	Waldmann_19

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	5.95393 seconds
cpu usage	16.9767
user time	16.2797
system time	0.697054
max virtual memory	5.6798224E7
max residence set size	2080380.0

stage attributes

key	value
starexec-result	YES

output

16.30/5.08	YES
16.76/5.24	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
16.76/5.24	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
16.76/5.24	
16.76/5.24	
16.76/5.24	Termination w.r.t. Q of the given QTRS could be proven:
16.76/5.24	
16.76/5.24	(0) QTRS
16.76/5.24	(1) QTRS Reverse [EQUIVALENT, 0 ms]
16.76/5.24	(2) QTRS
16.76/5.24	(3) RootLabelingProof [EQUIVALENT, 0 ms]
16.76/5.24	(4) QTRS
16.76/5.24	(5) QTRSRRRProof [EQUIVALENT, 3 ms]
16.76/5.24	(6) QTRS
16.76/5.24	(7) QTRSRRRProof [EQUIVALENT, 1 ms]
16.76/5.24	(8) QTRS
16.76/5.24	(9) DependencyPairsProof [EQUIVALENT, 2 ms]
16.76/5.24	(10) QDP
16.76/5.24	(11) QDPSizeChangeProof [EQUIVALENT, 0 ms]
16.76/5.24	(12) YES
16.76/5.24	
16.76/5.24	
16.76/5.24	----------------------------------------
16.76/5.24	
16.76/5.24	(0)
16.76/5.24	Obligation:
16.76/5.24	Q restricted rewrite system:
16.76/5.24	The TRS R consists of the following rules:
16.76/5.24	
16.76/5.24	   a(a(b(a(x1)))) -> a(b(b(a(x1))))
16.76/5.24	   b(a(b(b(x1)))) -> b(b(a(b(x1))))
16.76/5.24	   b(a(b(a(x1)))) -> b(b(a(a(x1))))
16.76/5.24	
16.76/5.24	Q is empty.
16.76/5.24	
16.76/5.24	----------------------------------------
16.76/5.24	
16.76/5.24	(1) QTRS Reverse (EQUIVALENT)
16.76/5.24	We applied the QTRS Reverse Processor [REVERSE].
16.76/5.24	----------------------------------------
16.76/5.24	
16.76/5.24	(2)
16.76/5.24	Obligation:
16.76/5.24	Q restricted rewrite system:
16.76/5.24	The TRS R consists of the following rules:
16.76/5.24	
16.76/5.24	   a(b(a(a(x1)))) -> a(b(b(a(x1))))
16.76/5.24	   b(b(a(b(x1)))) -> b(a(b(b(x1))))
16.76/5.24	   a(b(a(b(x1)))) -> a(a(b(b(x1))))
16.76/5.24	
16.76/5.24	Q is empty.
16.76/5.24	
16.76/5.24	----------------------------------------
16.76/5.24	
16.76/5.24	(3) RootLabelingProof (EQUIVALENT)
16.76/5.24	We used plain root labeling [ROOTLAB] with the following heuristic:
16.76/5.24	LabelAll: All function symbols get labeled
16.76/5.24	
16.76/5.24	As Q is empty the root labeling was sound AND complete.
16.76/5.24	
16.76/5.24	----------------------------------------
16.76/5.24	
16.76/5.24	(4)
16.76/5.24	Obligation:
16.76/5.24	Q restricted rewrite system:
16.76/5.24	The TRS R consists of the following rules:
16.76/5.24	
16.76/5.24	   a_{b_1}(b_{a_1}(a_{a_1}(a_{a_1}(x1)))) -> a_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x1))))
16.76/5.24	   a_{b_1}(b_{a_1}(a_{a_1}(a_{b_1}(x1)))) -> a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x1))))
16.76/5.24	   b_{b_1}(b_{a_1}(a_{b_1}(b_{a_1}(x1)))) -> b_{a_1}(a_{b_1}(b_{b_1}(b_{a_1}(x1))))
16.76/5.24	   b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(x1)))) -> b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(x1))))
16.76/5.24	   a_{b_1}(b_{a_1}(a_{b_1}(b_{a_1}(x1)))) -> a_{a_1}(a_{b_1}(b_{b_1}(b_{a_1}(x1))))
16.76/5.24	   a_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(x1)))) -> a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(x1))))
16.76/5.24	
16.76/5.24	Q is empty.
16.76/5.24	
16.76/5.24	----------------------------------------
16.76/5.24	
16.76/5.24	(5) QTRSRRRProof (EQUIVALENT)
16.76/5.24	Used ordering:
16.76/5.24	Polynomial interpretation [POLO]:
16.76/5.24	
16.76/5.24	   POL(a_{a_1}(x_1)) = 1 + x_1
16.76/5.24	   POL(a_{b_1}(x_1)) = x_1
16.76/5.24	   POL(b_{a_1}(x_1)) = 1 + x_1
16.76/5.24	   POL(b_{b_1}(x_1)) = x_1
16.76/5.24	With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
16.76/5.24	
16.76/5.24	   a_{b_1}(b_{a_1}(a_{a_1}(a_{a_1}(x1)))) -> a_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x1))))
16.76/5.24	   a_{b_1}(b_{a_1}(a_{a_1}(a_{b_1}(x1)))) -> a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x1))))
16.76/5.24	
16.76/5.24	
16.76/5.24	
16.76/5.24	
16.76/5.24	----------------------------------------
16.76/5.24	
16.76/5.24	(6)
16.76/5.24	Obligation:
16.76/5.24	Q restricted rewrite system:
16.76/5.24	The TRS R consists of the following rules:

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