TRS_Outermost 2019-04-01 06.45 pair #433314830

details

property	value
status	complete
benchmark	g_2_f_var.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n012.star.cs.uiowa.edu
space	Zantema_08

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	1.61095 seconds
cpu usage	3.8957
user time	3.70802
system time	0.18768
max virtual memory	1.8341532E7
max residence set size	294228.0

stage attributes

key	value
starexec-result	YES

output

3.73/1.55	YES
3.73/1.55	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
3.73/1.55	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.73/1.55	
3.73/1.55	
3.73/1.55	Outermost Termination of the given OTRS could be proven:
3.73/1.55	
3.73/1.55	(0) OTRS
3.73/1.55	(1) Raffelsieper-Zantema-Transformation [SOUND, 0 ms]
3.73/1.55	(2) QTRS
3.73/1.55	(3) QTRSRRRProof [EQUIVALENT, 36 ms]
3.73/1.55	(4) QTRS
3.73/1.55	(5) QTRSRRRProof [EQUIVALENT, 14 ms]
3.73/1.55	(6) QTRS
3.73/1.55	(7) AAECC Innermost [EQUIVALENT, 0 ms]
3.73/1.55	(8) QTRS
3.73/1.55	(9) DependencyPairsProof [EQUIVALENT, 0 ms]
3.73/1.55	(10) QDP
3.73/1.55	(11) DependencyGraphProof [EQUIVALENT, 0 ms]
3.73/1.55	(12) AND
3.73/1.55	    (13) QDP
3.73/1.55	        (14) UsableRulesProof [EQUIVALENT, 0 ms]
3.73/1.55	        (15) QDP
3.73/1.55	        (16) QReductionProof [EQUIVALENT, 0 ms]
3.73/1.55	        (17) QDP
3.73/1.55	        (18) QDPSizeChangeProof [EQUIVALENT, 0 ms]
3.73/1.55	        (19) YES
3.73/1.55	    (20) QDP
3.73/1.55	        (21) UsableRulesProof [EQUIVALENT, 0 ms]
3.73/1.55	        (22) QDP
3.73/1.55	        (23) QReductionProof [EQUIVALENT, 0 ms]
3.73/1.55	        (24) QDP
3.73/1.55	        (25) RFCMatchBoundsDPProof [EQUIVALENT, 0 ms]
3.73/1.55	        (26) YES
3.73/1.55	
3.73/1.55	
3.73/1.55	----------------------------------------
3.73/1.55	
3.73/1.55	(0)
3.73/1.55	Obligation:
3.73/1.55	Term rewrite system R:
3.73/1.55	The TRS R consists of the following rules:
3.73/1.55	
3.73/1.55	   f(x) -> g(f(x))
3.73/1.55	   g(g(f(x))) -> x
3.73/1.55	
3.73/1.55	
3.73/1.55	
3.73/1.55	Outermost Strategy.
3.73/1.55	
3.73/1.55	----------------------------------------
3.73/1.55	
3.73/1.55	(1) Raffelsieper-Zantema-Transformation (SOUND)
3.73/1.55	We applied the Raffelsieper-Zantema transformation  to transform the outermost TRS to a standard TRS.
3.73/1.55	----------------------------------------
3.73/1.55	
3.73/1.55	(2)
3.73/1.55	Obligation:
3.73/1.55	Q restricted rewrite system:
3.73/1.55	The TRS R consists of the following rules:
3.73/1.55	
3.73/1.55	   down(f(x)) -> up(g(f(x)))
3.73/1.55	   down(g(g(f(x)))) -> up(x)
3.73/1.55	   top(up(x)) -> top(down(x))
3.73/1.55	   down(g(f(y3))) -> g_flat(down(f(y3)))
3.73/1.55	   down(g(fresh_constant)) -> g_flat(down(fresh_constant))
3.73/1.55	   down(g(g(g(y7)))) -> g_flat(down(g(g(y7))))
3.73/1.55	   down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant)))
3.73/1.55	   f_flat(up(x_1)) -> up(f(x_1))
3.73/1.55	   g_flat(up(x_1)) -> up(g(x_1))
3.73/1.55	
3.73/1.55	Q is empty.
3.73/1.55	
3.73/1.55	----------------------------------------
3.73/1.55	
3.73/1.55	(3) QTRSRRRProof (EQUIVALENT)
3.73/1.55	Used ordering:
3.73/1.55	Polynomial interpretation [POLO]:
3.73/1.55	
3.73/1.55	   POL(down(x_1)) = 2*x_1
3.73/1.55	   POL(f(x_1)) = 2*x_1
3.73/1.55	   POL(f_flat(x_1)) = 1 + 2*x_1
3.73/1.56	   POL(fresh_constant) = 0
3.73/1.56	   POL(g(x_1)) = x_1
3.73/1.56	   POL(g_flat(x_1)) = x_1
3.73/1.56	   POL(top(x_1)) = 2*x_1
3.73/1.56	   POL(up(x_1)) = 2*x_1
3.73/1.56	With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
3.73/1.56	
3.73/1.56	   f_flat(up(x_1)) -> up(f(x_1))
3.73/1.56	
3.73/1.56	
3.73/1.56	
3.73/1.56	
3.73/1.56	----------------------------------------
3.73/1.56	
3.73/1.56	(4)
3.73/1.56	Obligation:
3.73/1.56	Q restricted rewrite system:
3.73/1.56	The TRS R consists of the following rules:

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actions all output return to TRS_Outermost 2019-04-01 06.45