TRS_Relative 2019-03-21 03.54 pair #429988698

details

property	value
status	complete
benchmark	rtL-pwl.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n078.star.cs.uiowa.edu
space	Relative_05

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	4.65764 seconds
cpu usage	15.0202
user time	14.2174
system time	0.802879
max virtual memory	1.8768452E7
max residence set size	2110584.0

stage attributes

key	value
starexec-result	YES

output

14.65/4.58	YES
14.65/4.61	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
14.65/4.61	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
14.65/4.61	
14.65/4.61	
14.65/4.61	Termination of the given RelTRS could be proven:
14.65/4.61	
14.65/4.61	(0) RelTRS
14.65/4.61	(1) RelTRSRRRProof [EQUIVALENT, 77 ms]
14.65/4.61	(2) RelTRS
14.65/4.61	(3) RelTRSRRRProof [EQUIVALENT, 53 ms]
14.65/4.61	(4) RelTRS
14.65/4.61	(5) RelTRSSemanticLabellingPOLOProof [EQUIVALENT, 213 ms]
14.65/4.61	(6) RelTRS
14.65/4.61	(7) RelTRSSemanticLabellingPOLOProof [EQUIVALENT, 159 ms]
14.65/4.61	(8) RelTRS
14.65/4.61	(9) RelTRSSemanticLabellingPOLOProof [EQUIVALENT, 71 ms]
14.65/4.61	(10) RelTRS
14.65/4.61	(11) RIsEmptyProof [EQUIVALENT, 0 ms]
14.65/4.61	(12) YES
14.65/4.61	
14.65/4.61	
14.65/4.61	----------------------------------------
14.65/4.61	
14.65/4.61	(0)
14.65/4.61	Obligation:
14.65/4.61	Relative term rewrite system:
14.65/4.61	The relative TRS consists of the following R rules:
14.65/4.61	
14.65/4.61	   top(ok(queue(old(x), bot))) -> top(check(queue(x, bot)))
14.65/4.61	   top(ok(queue(new(x), bot))) -> top(check(queue(x, bot)))
14.65/4.61	   top(ok(queue(bot, old(x)))) -> top(check(queue(bot, x)))
14.65/4.61	   top(ok(queue(bot, new(x)))) -> top(check(queue(bot, x)))
14.65/4.61	   top(ok(queue(old(x), old(y)))) -> top(check(queue(x, y)))
14.65/4.61	   top(ok(queue(old(x), new(y)))) -> top(check(queue(x, y)))
14.65/4.61	   top(ok(queue(new(x), old(y)))) -> top(check(queue(x, y)))
14.65/4.61	   top(ok(queue(new(x), new(y)))) -> top(check(queue(x, y)))
14.65/4.61	
14.65/4.61	The relative TRS consists of the following S rules:
14.65/4.61	
14.65/4.61	   top(ok(queue(old(x), y))) -> top(check(queue(x, y)))
14.65/4.61	   top(ok(queue(new(x), y))) -> top(check(queue(x, y)))
14.65/4.61	   bot -> new(bot)
14.65/4.61	   check(old(x)) -> ok(old(x))
14.65/4.61	   check(new(x)) -> new(check(x))
14.65/4.61	   check(queue(x, y)) -> queue(check(x), y)
14.65/4.61	   check(queue(x, y)) -> queue(x, check(y))
14.65/4.61	   old(ok(x)) -> ok(old(x))
14.65/4.61	   new(ok(x)) -> ok(new(x))
14.65/4.61	   queue(ok(x), y) -> ok(queue(x, y))
14.65/4.61	   queue(x, ok(y)) -> ok(queue(x, y))
14.65/4.61	
14.65/4.61	
14.65/4.61	----------------------------------------
14.65/4.61	
14.65/4.61	(1) RelTRSRRRProof (EQUIVALENT)
14.65/4.61	We used the following monotonic ordering for rule removal:
14.65/4.61	Polynomial interpretation [POLO]:
14.65/4.61	
14.65/4.61	   POL(bot) = 0
14.65/4.61	   POL(check(x_1)) = x_1
14.65/4.61	   POL(new(x_1)) = x_1
14.65/4.61	   POL(ok(x_1)) = x_1
14.65/4.61	   POL(old(x_1)) = 1 + x_1
14.65/4.61	   POL(queue(x_1, x_2)) = x_1 + x_2
14.65/4.61	   POL(top(x_1)) = x_1
14.65/4.61	With this ordering the following rules can be removed [MATRO] because they are oriented strictly:
14.65/4.61	Rules from R:
14.65/4.61	
14.65/4.61	   top(ok(queue(old(x), bot))) -> top(check(queue(x, bot)))
14.65/4.61	   top(ok(queue(bot, old(x)))) -> top(check(queue(bot, x)))
14.65/4.61	   top(ok(queue(old(x), old(y)))) -> top(check(queue(x, y)))
14.65/4.61	   top(ok(queue(old(x), new(y)))) -> top(check(queue(x, y)))
14.65/4.61	   top(ok(queue(new(x), old(y)))) -> top(check(queue(x, y)))
14.65/4.61	Rules from S:
14.65/4.61	
14.65/4.61	   top(ok(queue(old(x), y))) -> top(check(queue(x, y)))
14.65/4.61	
14.65/4.61	
14.65/4.61	
14.65/4.61	
14.65/4.61	----------------------------------------
14.65/4.61	
14.65/4.61	(2)
14.65/4.61	Obligation:
14.65/4.61	Relative term rewrite system:
14.65/4.61	The relative TRS consists of the following R rules:
14.65/4.61	
14.65/4.61	   top(ok(queue(new(x), bot))) -> top(check(queue(x, bot)))
14.65/4.61	   top(ok(queue(bot, new(x)))) -> top(check(queue(bot, x)))
14.65/4.61	   top(ok(queue(new(x), new(y)))) -> top(check(queue(x, y)))
14.65/4.61	
14.65/4.61	The relative TRS consists of the following S rules:
14.65/4.61	
14.65/4.61	   top(ok(queue(new(x), y))) -> top(check(queue(x, y)))
14.65/4.61	   bot -> new(bot)
14.65/4.61	   check(old(x)) -> ok(old(x))
14.65/4.61	   check(new(x)) -> new(check(x))
14.65/4.61	   check(queue(x, y)) -> queue(check(x), y)
14.65/4.61	   check(queue(x, y)) -> queue(x, check(y))

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job log

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