SRS_Standard 2019-03-29 03.29 pair #432294637

details

property	value
status	complete
benchmark	random-552.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n172.star.cs.uiowa.edu
space	Waldmann_19

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	5.43234 seconds
cpu usage	17.2917
user time	16.4608
system time	0.830891
max virtual memory	2.0489776E7
max residence set size	2448328.0

stage attributes

key	value
starexec-result	YES

output

16.72/5.32	YES
16.72/5.33	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
16.72/5.33	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
16.72/5.33	
16.72/5.33	
16.72/5.33	Termination w.r.t. Q of the given QTRS could be proven:
16.72/5.33	
16.72/5.33	(0) QTRS
16.72/5.33	(1) RootLabelingProof [EQUIVALENT, 0 ms]
16.72/5.33	(2) QTRS
16.72/5.33	(3) DependencyPairsProof [EQUIVALENT, 14 ms]
16.72/5.33	(4) QDP
16.72/5.33	(5) DependencyGraphProof [EQUIVALENT, 0 ms]
16.72/5.33	(6) QDP
16.72/5.33	(7) QDPOrderProof [EQUIVALENT, 128 ms]
16.72/5.33	(8) QDP
16.72/5.33	(9) PisEmptyProof [EQUIVALENT, 0 ms]
16.72/5.33	(10) YES
16.72/5.33	
16.72/5.33	
16.72/5.33	----------------------------------------
16.72/5.33	
16.72/5.33	(0)
16.72/5.33	Obligation:
16.72/5.33	Q restricted rewrite system:
16.72/5.33	The TRS R consists of the following rules:
16.72/5.33	
16.72/5.33	   a(b(b(a(x1)))) -> a(a(a(a(x1))))
16.72/5.33	   b(b(a(a(x1)))) -> b(a(a(a(x1))))
16.72/5.33	   b(b(a(a(x1)))) -> b(a(b(b(x1))))
16.72/5.33	
16.72/5.33	Q is empty.
16.72/5.33	
16.72/5.33	----------------------------------------
16.72/5.33	
16.72/5.33	(1) RootLabelingProof (EQUIVALENT)
16.72/5.33	We used plain root labeling [ROOTLAB] with the following heuristic:
16.72/5.33	LabelAll: All function symbols get labeled
16.72/5.33	
16.72/5.33	As Q is empty the root labeling was sound AND complete.
16.72/5.33	
16.72/5.33	----------------------------------------
16.72/5.33	
16.72/5.33	(2)
16.72/5.33	Obligation:
16.72/5.33	Q restricted rewrite system:
16.72/5.33	The TRS R consists of the following rules:
16.72/5.33	
16.72/5.33	   a_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x1)))) -> a_{a_1}(a_{a_1}(a_{a_1}(a_{a_1}(x1))))
16.72/5.33	   a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x1)))) -> a_{a_1}(a_{a_1}(a_{a_1}(a_{b_1}(x1))))
16.72/5.33	   b_{b_1}(b_{a_1}(a_{a_1}(a_{a_1}(x1)))) -> b_{a_1}(a_{a_1}(a_{a_1}(a_{a_1}(x1))))
16.72/5.33	   b_{b_1}(b_{a_1}(a_{a_1}(a_{b_1}(x1)))) -> b_{a_1}(a_{a_1}(a_{a_1}(a_{b_1}(x1))))
16.72/5.33	   b_{b_1}(b_{a_1}(a_{a_1}(a_{a_1}(x1)))) -> b_{a_1}(a_{b_1}(b_{b_1}(b_{a_1}(x1))))
16.72/5.33	   b_{b_1}(b_{a_1}(a_{a_1}(a_{b_1}(x1)))) -> b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(x1))))
16.72/5.33	
16.72/5.33	Q is empty.
16.72/5.33	
16.72/5.33	----------------------------------------
16.72/5.33	
16.72/5.33	(3) DependencyPairsProof (EQUIVALENT)
16.72/5.33	Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem.
16.72/5.33	----------------------------------------
16.72/5.33	
16.72/5.33	(4)
16.72/5.33	Obligation:
16.72/5.33	Q DP problem:
16.72/5.33	The TRS P consists of the following rules:
16.72/5.33	
16.72/5.33	   B_{B_1}(b_{a_1}(a_{a_1}(a_{a_1}(x1)))) -> A_{B_1}(b_{b_1}(b_{a_1}(x1)))
16.72/5.33	   B_{B_1}(b_{a_1}(a_{a_1}(a_{a_1}(x1)))) -> B_{B_1}(b_{a_1}(x1))
16.72/5.33	   B_{B_1}(b_{a_1}(a_{a_1}(a_{b_1}(x1)))) -> A_{B_1}(b_{b_1}(b_{b_1}(x1)))
16.72/5.33	   B_{B_1}(b_{a_1}(a_{a_1}(a_{b_1}(x1)))) -> B_{B_1}(b_{b_1}(x1))
16.72/5.33	   B_{B_1}(b_{a_1}(a_{a_1}(a_{b_1}(x1)))) -> B_{B_1}(x1)
16.72/5.33	
16.72/5.33	The TRS R consists of the following rules:
16.72/5.33	
16.72/5.33	   a_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x1)))) -> a_{a_1}(a_{a_1}(a_{a_1}(a_{a_1}(x1))))
16.72/5.33	   a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x1)))) -> a_{a_1}(a_{a_1}(a_{a_1}(a_{b_1}(x1))))
16.72/5.33	   b_{b_1}(b_{a_1}(a_{a_1}(a_{a_1}(x1)))) -> b_{a_1}(a_{a_1}(a_{a_1}(a_{a_1}(x1))))
16.72/5.33	   b_{b_1}(b_{a_1}(a_{a_1}(a_{b_1}(x1)))) -> b_{a_1}(a_{a_1}(a_{a_1}(a_{b_1}(x1))))
16.72/5.33	   b_{b_1}(b_{a_1}(a_{a_1}(a_{a_1}(x1)))) -> b_{a_1}(a_{b_1}(b_{b_1}(b_{a_1}(x1))))
16.72/5.33	   b_{b_1}(b_{a_1}(a_{a_1}(a_{b_1}(x1)))) -> b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(x1))))
16.72/5.33	
16.72/5.33	Q is empty.
16.72/5.33	We have to consider all minimal (P,Q,R)-chains.
16.72/5.33	----------------------------------------
16.72/5.33	
16.72/5.33	(5) DependencyGraphProof (EQUIVALENT)
16.72/5.33	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes.
16.72/5.33	----------------------------------------
16.72/5.33	
16.72/5.33	(6)
16.72/5.33	Obligation:
16.72/5.33	Q DP problem:
16.72/5.33	The TRS P consists of the following rules:
16.72/5.33	
16.72/5.33	   B_{B_1}(b_{a_1}(a_{a_1}(a_{b_1}(x1)))) -> B_{B_1}(b_{b_1}(x1))
16.72/5.33	   B_{B_1}(b_{a_1}(a_{a_1}(a_{a_1}(x1)))) -> B_{B_1}(b_{a_1}(x1))
16.72/5.33	   B_{B_1}(b_{a_1}(a_{a_1}(a_{b_1}(x1)))) -> B_{B_1}(x1)
16.72/5.33

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