SRS_Standard 2019-03-29 03.29 pair #432291871

details

property	value
status	complete
benchmark	z083.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n132.star.cs.uiowa.edu
space	Zantema_04

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	6.23812 seconds
cpu usage	20.7026
user time	19.8796
system time	0.822968
max virtual memory	2.1016372E7
max residence set size	2428512.0

stage attributes

key	value
starexec-result	YES

output

19.79/5.95	YES
20.30/6.10	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
20.30/6.10	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
20.30/6.10	
20.30/6.10	
20.30/6.10	Termination w.r.t. Q of the given QTRS could be proven:
20.30/6.10	
20.30/6.10	(0) QTRS
20.30/6.10	(1) QTRS Reverse [EQUIVALENT, 0 ms]
20.30/6.10	(2) QTRS
20.30/6.10	(3) QTRSRRRProof [EQUIVALENT, 3 ms]
20.30/6.10	(4) QTRS
20.30/6.10	(5) DependencyPairsProof [EQUIVALENT, 1 ms]
20.30/6.10	(6) QDP
20.30/6.10	(7) DependencyGraphProof [EQUIVALENT, 0 ms]
20.30/6.10	(8) AND
20.30/6.10	    (9) QDP
20.30/6.10	        (10) MRRProof [EQUIVALENT, 42 ms]
20.30/6.10	        (11) QDP
20.30/6.10	        (12) QDPOrderProof [EQUIVALENT, 0 ms]
20.30/6.10	        (13) QDP
20.30/6.10	        (14) PisEmptyProof [EQUIVALENT, 0 ms]
20.30/6.10	        (15) YES
20.30/6.10	    (16) QDP
20.30/6.10	        (17) UsableRulesProof [EQUIVALENT, 0 ms]
20.30/6.10	        (18) QDP
20.30/6.10	        (19) QDPSizeChangeProof [EQUIVALENT, 1 ms]
20.30/6.10	        (20) YES
20.30/6.10	
20.30/6.10	
20.30/6.10	----------------------------------------
20.30/6.10	
20.30/6.10	(0)
20.30/6.10	Obligation:
20.30/6.10	Q restricted rewrite system:
20.30/6.10	The TRS R consists of the following rules:
20.30/6.10	
20.30/6.10	   b(d(b(x1))) -> c(d(b(x1)))
20.30/6.10	   b(a(c(x1))) -> b(c(x1))
20.30/6.10	   a(d(x1)) -> d(c(x1))
20.30/6.10	   b(b(b(x1))) -> a(b(c(x1)))
20.30/6.10	   d(c(x1)) -> b(d(x1))
20.30/6.10	   d(c(x1)) -> d(b(d(x1)))
20.30/6.10	   d(a(c(x1))) -> b(b(x1))
20.30/6.10	
20.30/6.10	Q is empty.
20.30/6.10	
20.30/6.10	----------------------------------------
20.30/6.10	
20.30/6.10	(1) QTRS Reverse (EQUIVALENT)
20.30/6.10	We applied the QTRS Reverse Processor [REVERSE].
20.30/6.10	----------------------------------------
20.30/6.10	
20.30/6.10	(2)
20.30/6.10	Obligation:
20.30/6.10	Q restricted rewrite system:
20.30/6.10	The TRS R consists of the following rules:
20.30/6.10	
20.30/6.10	   b(d(b(x1))) -> b(d(c(x1)))
20.30/6.10	   c(a(b(x1))) -> c(b(x1))
20.30/6.10	   d(a(x1)) -> c(d(x1))
20.30/6.10	   b(b(b(x1))) -> c(b(a(x1)))
20.30/6.10	   c(d(x1)) -> d(b(x1))
20.30/6.10	   c(d(x1)) -> d(b(d(x1)))
20.30/6.10	   c(a(d(x1))) -> b(b(x1))
20.30/6.10	
20.30/6.10	Q is empty.
20.30/6.10	
20.30/6.10	----------------------------------------
20.30/6.10	
20.30/6.10	(3) QTRSRRRProof (EQUIVALENT)
20.30/6.10	Used ordering:
20.30/6.10	Polynomial interpretation [POLO]:
20.30/6.10	
20.30/6.10	   POL(a(x_1)) = 1 + x_1
20.30/6.10	   POL(b(x_1)) = 1 + x_1
20.30/6.10	   POL(c(x_1)) = 1 + x_1
20.30/6.10	   POL(d(x_1)) = x_1
20.30/6.10	With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
20.30/6.10	
20.30/6.10	   c(a(b(x1))) -> c(b(x1))
20.30/6.10	
20.30/6.10	
20.30/6.10	
20.30/6.10	
20.30/6.10	----------------------------------------
20.30/6.10	
20.30/6.10	(4)
20.30/6.10	Obligation:
20.30/6.10	Q restricted rewrite system:
20.30/6.10	The TRS R consists of the following rules:
20.30/6.10	
20.30/6.10	   b(d(b(x1))) -> b(d(c(x1)))
20.30/6.10	   d(a(x1)) -> c(d(x1))
20.30/6.10	   b(b(b(x1))) -> c(b(a(x1)))
20.30/6.10	   c(d(x1)) -> d(b(x1))
20.30/6.10	   c(d(x1)) -> d(b(d(x1)))
20.30/6.10	   c(a(d(x1))) -> b(b(x1))
20.30/6.10	
20.30/6.10	Q is empty.

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