SRS_Standard 2019-03-29 03.29 pair #432292369

details

property	value
status	complete
benchmark	z115.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n063.star.cs.uiowa.edu
space	Zantema_04

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	3.89055 seconds
cpu usage	11.7216
user time	11.1884
system time	0.533276
max virtual memory	9.5929776E7
max residence set size	1545500.0

stage attributes

key	value
starexec-result	YES

output

11.38/3.75	YES
11.38/3.78	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
11.38/3.78	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
11.38/3.78	
11.38/3.78	
11.38/3.78	Termination w.r.t. Q of the given QTRS could be proven:
11.38/3.78	
11.38/3.78	(0) QTRS
11.38/3.78	(1) QTRSRRRProof [EQUIVALENT, 35 ms]
11.38/3.78	(2) QTRS
11.38/3.78	(3) DependencyPairsProof [EQUIVALENT, 26 ms]
11.38/3.78	(4) QDP
11.38/3.78	(5) QDPOrderProof [EQUIVALENT, 26 ms]
11.38/3.78	(6) QDP
11.38/3.78	(7) DependencyGraphProof [EQUIVALENT, 0 ms]
11.38/3.78	(8) TRUE
11.38/3.78	
11.38/3.78	
11.38/3.78	----------------------------------------
11.38/3.78	
11.38/3.78	(0)
11.38/3.78	Obligation:
11.38/3.78	Q restricted rewrite system:
11.38/3.78	The TRS R consists of the following rules:
11.38/3.78	
11.38/3.78	   a(a(x1)) -> d(c(x1))
11.38/3.78	   a(b(x1)) -> c(c(c(x1)))
11.38/3.78	   b(b(x1)) -> a(c(c(x1)))
11.38/3.78	   c(c(x1)) -> b(x1)
11.38/3.78	   c(d(x1)) -> a(a(x1))
11.38/3.78	   d(d(x1)) -> b(a(c(x1)))
11.38/3.78	
11.38/3.78	Q is empty.
11.38/3.78	
11.38/3.78	----------------------------------------
11.38/3.78	
11.38/3.78	(1) QTRSRRRProof (EQUIVALENT)
11.38/3.78	Used ordering:
11.38/3.78	Polynomial interpretation [POLO]:
11.38/3.78	
11.38/3.78	   POL(a(x_1)) = 15 + x_1
11.38/3.78	   POL(b(x_1)) = 17 + x_1
11.38/3.78	   POL(c(x_1)) = 9 + x_1
11.38/3.78	   POL(d(x_1)) = 21 + x_1
11.38/3.78	With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
11.38/3.78	
11.38/3.78	   a(b(x1)) -> c(c(c(x1)))
11.38/3.78	   b(b(x1)) -> a(c(c(x1)))
11.38/3.78	   c(c(x1)) -> b(x1)
11.38/3.78	   d(d(x1)) -> b(a(c(x1)))
11.38/3.78	
11.38/3.78	
11.38/3.78	
11.38/3.78	
11.38/3.78	----------------------------------------
11.38/3.78	
11.38/3.78	(2)
11.38/3.78	Obligation:
11.38/3.78	Q restricted rewrite system:
11.38/3.78	The TRS R consists of the following rules:
11.38/3.78	
11.38/3.78	   a(a(x1)) -> d(c(x1))
11.38/3.78	   c(d(x1)) -> a(a(x1))
11.38/3.78	
11.38/3.78	Q is empty.
11.38/3.78	
11.38/3.78	----------------------------------------
11.38/3.78	
11.38/3.78	(3) DependencyPairsProof (EQUIVALENT)
11.38/3.78	Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem.
11.38/3.78	----------------------------------------
11.38/3.78	
11.38/3.78	(4)
11.38/3.78	Obligation:
11.38/3.78	Q DP problem:
11.38/3.78	The TRS P consists of the following rules:
11.38/3.78	
11.38/3.78	   A(a(x1)) -> C(x1)
11.38/3.78	   C(d(x1)) -> A(a(x1))
11.38/3.78	   C(d(x1)) -> A(x1)
11.38/3.78	
11.38/3.78	The TRS R consists of the following rules:
11.38/3.78	
11.38/3.78	   a(a(x1)) -> d(c(x1))
11.38/3.78	   c(d(x1)) -> a(a(x1))
11.38/3.78	
11.38/3.78	Q is empty.
11.38/3.78	We have to consider all minimal (P,Q,R)-chains.
11.38/3.78	----------------------------------------
11.38/3.78	
11.38/3.78	(5) QDPOrderProof (EQUIVALENT)
11.38/3.78	We use the reduction pair processor [LPAR04,JAR06].
11.38/3.78	
11.38/3.78	
11.38/3.78	The following pairs can be oriented strictly and are deleted.
11.38/3.78	
11.38/3.78	   C(d(x1)) -> A(a(x1))
11.38/3.78	   C(d(x1)) -> A(x1)
11.38/3.78	The remaining pairs can at least be oriented weakly.
11.38/3.78	Used ordering:  Polynomial interpretation [POLO]:

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