SRS_Standard 2019-03-29 03.29 pair #432289297

details

property	value
status	complete
benchmark	2.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n006.star.cs.uiowa.edu
space	Mixed_SRS

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	3.97561 seconds
cpu usage	12.1975
user time	11.5292
system time	0.668315
max virtual memory	4.0184384E7
max residence set size	1895976.0

stage attributes

key	value
starexec-result	YES

output

12.01/3.90	YES
12.01/3.91	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
12.01/3.91	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
12.01/3.91	
12.01/3.91	
12.01/3.91	Termination w.r.t. Q of the given QTRS could be proven:
12.01/3.91	
12.01/3.91	(0) QTRS
12.01/3.91	(1) QTRS Reverse [EQUIVALENT, 0 ms]
12.01/3.91	(2) QTRS
12.01/3.91	(3) DependencyPairsProof [EQUIVALENT, 16 ms]
12.01/3.91	(4) QDP
12.01/3.91	(5) QDPOrderProof [EQUIVALENT, 12 ms]
12.01/3.91	(6) QDP
12.01/3.91	(7) QDPOrderProof [EQUIVALENT, 74 ms]
12.01/3.91	(8) QDP
12.01/3.91	(9) DependencyGraphProof [EQUIVALENT, 0 ms]
12.01/3.91	(10) TRUE
12.01/3.91	
12.01/3.91	
12.01/3.91	----------------------------------------
12.01/3.91	
12.01/3.91	(0)
12.01/3.91	Obligation:
12.01/3.91	Q restricted rewrite system:
12.01/3.91	The TRS R consists of the following rules:
12.01/3.91	
12.01/3.91	   a(a(a(x1))) -> a(a(b(x1)))
12.01/3.91	   b(a(b(x1))) -> a(b(a(x1)))
12.01/3.91	
12.01/3.91	Q is empty.
12.01/3.91	
12.01/3.91	----------------------------------------
12.01/3.91	
12.01/3.91	(1) QTRS Reverse (EQUIVALENT)
12.01/3.91	We applied the QTRS Reverse Processor [REVERSE].
12.01/3.91	----------------------------------------
12.01/3.91	
12.01/3.91	(2)
12.01/3.91	Obligation:
12.01/3.91	Q restricted rewrite system:
12.01/3.91	The TRS R consists of the following rules:
12.01/3.91	
12.01/3.91	   a(a(a(x1))) -> b(a(a(x1)))
12.01/3.91	   b(a(b(x1))) -> a(b(a(x1)))
12.01/3.91	
12.01/3.91	Q is empty.
12.01/3.91	
12.01/3.91	----------------------------------------
12.01/3.91	
12.01/3.91	(3) DependencyPairsProof (EQUIVALENT)
12.01/3.91	Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem.
12.01/3.91	----------------------------------------
12.01/3.91	
12.01/3.91	(4)
12.01/3.91	Obligation:
12.01/3.91	Q DP problem:
12.01/3.91	The TRS P consists of the following rules:
12.01/3.91	
12.01/3.91	   A(a(a(x1))) -> B(a(a(x1)))
12.01/3.91	   B(a(b(x1))) -> A(b(a(x1)))
12.01/3.91	   B(a(b(x1))) -> B(a(x1))
12.01/3.91	   B(a(b(x1))) -> A(x1)
12.01/3.91	
12.01/3.91	The TRS R consists of the following rules:
12.01/3.91	
12.01/3.91	   a(a(a(x1))) -> b(a(a(x1)))
12.01/3.91	   b(a(b(x1))) -> a(b(a(x1)))
12.01/3.91	
12.01/3.91	Q is empty.
12.01/3.91	We have to consider all minimal (P,Q,R)-chains.
12.01/3.91	----------------------------------------
12.01/3.91	
12.01/3.91	(5) QDPOrderProof (EQUIVALENT)
12.01/3.91	We use the reduction pair processor [LPAR04,JAR06].
12.01/3.91	
12.01/3.91	
12.01/3.91	The following pairs can be oriented strictly and are deleted.
12.01/3.91	
12.01/3.91	   B(a(b(x1))) -> B(a(x1))
12.01/3.91	   B(a(b(x1))) -> A(x1)
12.01/3.91	The remaining pairs can at least be oriented weakly.
12.01/3.91	Used ordering:  Polynomial interpretation [POLO]:
12.01/3.91	
12.01/3.91	   POL(A(x_1)) = x_1
12.01/3.91	   POL(B(x_1)) = x_1
12.01/3.91	   POL(a(x_1)) = 1 + x_1
12.01/3.91	   POL(b(x_1)) = 1 + x_1
12.01/3.91	
12.01/3.91	The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:
12.01/3.91	
12.01/3.91	   b(a(b(x1))) -> a(b(a(x1)))
12.01/3.91	   a(a(a(x1))) -> b(a(a(x1)))
12.01/3.91	
12.01/3.91	
12.01/3.91	----------------------------------------
12.01/3.91	
12.01/3.91	(6)
12.01/3.91	Obligation:
12.01/3.91	Q DP problem:

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