SRS_Standard 2019-03-29 03.29 pair #432292201

details

property	value
status	complete
benchmark	z093.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n109.star.cs.uiowa.edu
space	Zantema_04

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	2.54534 seconds
cpu usage	6.50117
user time	6.16573
system time	0.335436
max virtual memory	3.7771224E7
max residence set size	957828.0

stage attributes

key	value
starexec-result	YES

output

5.76/2.35	YES
6.34/2.49	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
6.34/2.49	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
6.34/2.49	
6.34/2.49	
6.34/2.49	Termination w.r.t. Q of the given QTRS could be proven:
6.34/2.49	
6.34/2.49	(0) QTRS
6.34/2.49	(1) QTRSRRRProof [EQUIVALENT, 41 ms]
6.34/2.49	(2) QTRS
6.34/2.49	(3) Overlay + Local Confluence [EQUIVALENT, 5 ms]
6.34/2.49	(4) QTRS
6.34/2.49	(5) DependencyPairsProof [EQUIVALENT, 23 ms]
6.34/2.49	(6) QDP
6.34/2.49	(7) UsableRulesProof [EQUIVALENT, 1 ms]
6.34/2.49	(8) QDP
6.34/2.49	(9) QReductionProof [EQUIVALENT, 0 ms]
6.34/2.49	(10) QDP
6.34/2.49	(11) QDPSizeChangeProof [EQUIVALENT, 0 ms]
6.34/2.49	(12) YES
6.34/2.49	
6.34/2.49	
6.34/2.49	----------------------------------------
6.34/2.49	
6.34/2.49	(0)
6.34/2.49	Obligation:
6.34/2.49	Q restricted rewrite system:
6.34/2.49	The TRS R consists of the following rules:
6.34/2.49	
6.34/2.49	   b(c(x1)) -> c(b(x1))
6.34/2.49	   c(b(x1)) -> a(a(a(x1)))
6.34/2.49	   a(a(a(a(x1)))) -> b(c(x1))
6.34/2.49	
6.34/2.49	Q is empty.
6.34/2.49	
6.34/2.49	----------------------------------------
6.34/2.49	
6.34/2.49	(1) QTRSRRRProof (EQUIVALENT)
6.34/2.49	Used ordering:
6.34/2.49	Polynomial interpretation [POLO]:
6.34/2.49	
6.34/2.49	   POL(a(x_1)) = 2 + x_1
6.34/2.49	   POL(b(x_1)) = x_1
6.34/2.49	   POL(c(x_1)) = 7 + x_1
6.34/2.49	With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
6.34/2.49	
6.34/2.49	   c(b(x1)) -> a(a(a(x1)))
6.34/2.49	   a(a(a(a(x1)))) -> b(c(x1))
6.34/2.49	
6.34/2.49	
6.34/2.49	
6.34/2.49	
6.34/2.49	----------------------------------------
6.34/2.49	
6.34/2.49	(2)
6.34/2.49	Obligation:
6.34/2.49	Q restricted rewrite system:
6.34/2.49	The TRS R consists of the following rules:
6.34/2.49	
6.34/2.49	   b(c(x1)) -> c(b(x1))
6.34/2.49	
6.34/2.49	Q is empty.
6.34/2.49	
6.34/2.49	----------------------------------------
6.34/2.49	
6.34/2.49	(3) Overlay + Local Confluence (EQUIVALENT)
6.34/2.49	The TRS is overlay and locally confluent. By [NOC] we can switch to innermost.
6.34/2.49	----------------------------------------
6.34/2.49	
6.34/2.49	(4)
6.34/2.49	Obligation:
6.34/2.49	Q restricted rewrite system:
6.34/2.49	The TRS R consists of the following rules:
6.34/2.49	
6.34/2.49	   b(c(x1)) -> c(b(x1))
6.34/2.49	
6.34/2.49	The set Q consists of the following terms:
6.34/2.49	
6.34/2.49	   b(c(x0))
6.34/2.49	
6.34/2.49	
6.34/2.49	----------------------------------------
6.34/2.49	
6.34/2.49	(5) DependencyPairsProof (EQUIVALENT)
6.34/2.49	Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem.
6.34/2.49	----------------------------------------
6.34/2.49	
6.34/2.49	(6)
6.34/2.49	Obligation:
6.34/2.49	Q DP problem:
6.34/2.49	The TRS P consists of the following rules:
6.34/2.49	
6.34/2.49	   B(c(x1)) -> B(x1)
6.34/2.49	
6.34/2.49	The TRS R consists of the following rules:
6.34/2.49	
6.34/2.49	   b(c(x1)) -> c(b(x1))
6.34/2.49	
6.34/2.49	The set Q consists of the following terms:
6.34/2.49

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