SRS_Standard 2019-03-29 03.29 pair #432289843

details

property	value
status	complete
benchmark	size-12-alpha-3-num-468.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n125.star.cs.uiowa.edu
space	Waldmann_07_size12

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	6.79292 seconds
cpu usage	22.9541
user time	21.9515
system time	1.00261
max virtual memory	6.0398476E7
max residence set size	2817396.0

stage attributes

key	value
starexec-result	YES

output

22.39/6.71	YES
22.77/6.73	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
22.77/6.73	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
22.77/6.73	
22.77/6.73	
22.77/6.73	Termination w.r.t. Q of the given QTRS could be proven:
22.77/6.73	
22.77/6.73	(0) QTRS
22.77/6.73	(1) DependencyPairsProof [EQUIVALENT, 25 ms]
22.77/6.73	(2) QDP
22.77/6.73	(3) DependencyGraphProof [EQUIVALENT, 6 ms]
22.77/6.73	(4) QDP
22.77/6.73	(5) QDPOrderProof [EQUIVALENT, 110 ms]
22.77/6.73	(6) QDP
22.77/6.73	(7) DependencyGraphProof [EQUIVALENT, 0 ms]
22.77/6.73	(8) QDP
22.77/6.73	(9) UsableRulesProof [EQUIVALENT, 0 ms]
22.77/6.73	(10) QDP
22.77/6.73	(11) QDPSizeChangeProof [EQUIVALENT, 0 ms]
22.77/6.73	(12) YES
22.77/6.73	
22.77/6.73	
22.77/6.73	----------------------------------------
22.77/6.73	
22.77/6.73	(0)
22.77/6.73	Obligation:
22.77/6.73	Q restricted rewrite system:
22.77/6.73	The TRS R consists of the following rules:
22.77/6.73	
22.77/6.73	   a(x1) -> b(c(b(c(x1))))
22.77/6.73	   b(b(x1)) -> x1
22.77/6.73	   c(c(b(x1))) -> a(c(x1))
22.77/6.73	
22.77/6.73	Q is empty.
22.77/6.73	
22.77/6.73	----------------------------------------
22.77/6.73	
22.77/6.73	(1) DependencyPairsProof (EQUIVALENT)
22.77/6.73	Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem.
22.77/6.73	----------------------------------------
22.77/6.73	
22.77/6.73	(2)
22.77/6.73	Obligation:
22.77/6.73	Q DP problem:
22.77/6.73	The TRS P consists of the following rules:
22.77/6.73	
22.77/6.73	   A(x1) -> B(c(b(c(x1))))
22.77/6.73	   A(x1) -> C(b(c(x1)))
22.77/6.73	   A(x1) -> B(c(x1))
22.77/6.73	   A(x1) -> C(x1)
22.77/6.73	   C(c(b(x1))) -> A(c(x1))
22.77/6.73	   C(c(b(x1))) -> C(x1)
22.77/6.73	
22.77/6.73	The TRS R consists of the following rules:
22.77/6.73	
22.77/6.73	   a(x1) -> b(c(b(c(x1))))
22.77/6.73	   b(b(x1)) -> x1
22.77/6.73	   c(c(b(x1))) -> a(c(x1))
22.77/6.73	
22.77/6.73	Q is empty.
22.77/6.73	We have to consider all minimal (P,Q,R)-chains.
22.77/6.73	----------------------------------------
22.77/6.73	
22.77/6.73	(3) DependencyGraphProof (EQUIVALENT)
22.77/6.73	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes.
22.77/6.73	----------------------------------------
22.77/6.73	
22.77/6.73	(4)
22.77/6.73	Obligation:
22.77/6.73	Q DP problem:
22.77/6.73	The TRS P consists of the following rules:
22.77/6.73	
22.77/6.73	   A(x1) -> C(b(c(x1)))
22.77/6.73	   C(c(b(x1))) -> A(c(x1))
22.77/6.73	   A(x1) -> C(x1)
22.77/6.73	   C(c(b(x1))) -> C(x1)
22.77/6.73	
22.77/6.73	The TRS R consists of the following rules:
22.77/6.73	
22.77/6.73	   a(x1) -> b(c(b(c(x1))))
22.77/6.73	   b(b(x1)) -> x1
22.77/6.73	   c(c(b(x1))) -> a(c(x1))
22.77/6.73	
22.77/6.73	Q is empty.
22.77/6.73	We have to consider all minimal (P,Q,R)-chains.
22.77/6.73	----------------------------------------
22.77/6.73	
22.77/6.73	(5) QDPOrderProof (EQUIVALENT)
22.77/6.73	We use the reduction pair processor [LPAR04,JAR06].
22.77/6.73	
22.77/6.73	
22.77/6.73	The following pairs can be oriented strictly and are deleted.
22.77/6.73	
22.77/6.73	   C(c(b(x1))) -> A(c(x1))
22.77/6.73	The remaining pairs can at least be oriented weakly.
22.77/6.73	Used ordering:  Matrix interpretation [MATRO] with arctic natural numbers [ARCTIC]:
22.77/6.73	
22.77/6.73	   <<<
22.77/6.73	 POL(A(x_1)) =  	[[1A]] 	 +  	[[1A, 0A, 0A]] 	* 	x_1
22.77/6.73	>>>

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