TRS_Innermost 2019-03-28 22.12 pair #432271252

details

property	value
status	complete
benchmark	Ex4_7_77_Bor03_GM.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n038.star.cs.uiowa.edu
space	Transformed_CSR_innermost_04

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	1.63605 seconds
cpu usage	3.58821
user time	3.42495
system time	0.163259
max virtual memory	1.8343124E7
max residence set size	233228.0

stage attributes

key	value
starexec-result	YES

output

3.43/1.59	YES
3.43/1.60	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
3.43/1.60	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.43/1.60	
3.43/1.60	
3.43/1.60	Termination w.r.t. Q of the given QTRS could be proven:
3.43/1.60	
3.43/1.60	(0) QTRS
3.43/1.60	(1) QTRSRRRProof [EQUIVALENT, 24 ms]
3.43/1.60	(2) QTRS
3.43/1.60	(3) RisEmptyProof [EQUIVALENT, 0 ms]
3.43/1.60	(4) YES
3.43/1.60	
3.43/1.60	
3.43/1.60	----------------------------------------
3.43/1.60	
3.43/1.60	(0)
3.43/1.60	Obligation:
3.43/1.60	Q restricted rewrite system:
3.43/1.60	The TRS R consists of the following rules:
3.43/1.60	
3.43/1.60	   a__zeros -> cons(0, zeros)
3.43/1.60	   a__tail(cons(X, XS)) -> mark(XS)
3.43/1.60	   mark(zeros) -> a__zeros
3.43/1.60	   mark(tail(X)) -> a__tail(mark(X))
3.43/1.60	   mark(cons(X1, X2)) -> cons(mark(X1), X2)
3.43/1.60	   mark(0) -> 0
3.43/1.60	   a__zeros -> zeros
3.43/1.60	   a__tail(X) -> tail(X)
3.43/1.60	
3.43/1.60	The set Q consists of the following terms:
3.43/1.60	
3.43/1.60	   a__zeros
3.43/1.60	   mark(zeros)
3.43/1.60	   mark(tail(x0))
3.43/1.60	   mark(cons(x0, x1))
3.43/1.60	   mark(0)
3.43/1.60	   a__tail(x0)
3.43/1.60	
3.43/1.60	
3.43/1.60	----------------------------------------
3.43/1.60	
3.43/1.60	(1) QTRSRRRProof (EQUIVALENT)
3.43/1.60	Used ordering:
3.43/1.60	Knuth-Bendix order [KBO] with precedence:mark_1 > a__tail_1 > tail_1 > a__zeros > zeros > cons_2 > 0
3.43/1.60	
3.43/1.60	and weight map:
3.43/1.60	
3.43/1.60	   a__zeros=4
3.43/1.60	   0=1
3.43/1.60	   zeros=1
3.43/1.60	   a__tail_1=2
3.43/1.60	   mark_1=3
3.43/1.60	   tail_1=2
3.43/1.60	   cons_2=1
3.43/1.60	
3.43/1.60	The variable weight is 1With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
3.43/1.60	
3.43/1.60	   a__zeros -> cons(0, zeros)
3.43/1.60	   a__tail(cons(X, XS)) -> mark(XS)
3.43/1.60	   mark(zeros) -> a__zeros
3.43/1.60	   mark(tail(X)) -> a__tail(mark(X))
3.43/1.60	   mark(cons(X1, X2)) -> cons(mark(X1), X2)
3.43/1.60	   mark(0) -> 0
3.43/1.60	   a__zeros -> zeros
3.43/1.60	   a__tail(X) -> tail(X)
3.43/1.60	
3.43/1.60	
3.43/1.60	
3.43/1.60	
3.43/1.60	----------------------------------------
3.43/1.60	
3.43/1.60	(2)
3.43/1.60	Obligation:
3.43/1.60	Q restricted rewrite system:
3.43/1.60	R is empty.
3.43/1.60	The set Q consists of the following terms:
3.43/1.60	
3.43/1.60	   a__zeros
3.43/1.60	   mark(zeros)
3.43/1.60	   mark(tail(x0))
3.43/1.60	   mark(cons(x0, x1))
3.43/1.60	   mark(0)
3.43/1.60	   a__tail(x0)
3.43/1.60	
3.43/1.60	
3.43/1.60	----------------------------------------
3.43/1.60	
3.43/1.60	(3) RisEmptyProof (EQUIVALENT)
3.43/1.60	The TRS R is empty. Hence, termination is trivially proven.
3.43/1.60	----------------------------------------
3.43/1.60	
3.43/1.60	(4)
3.43/1.60	YES
3.43/1.63	EOF

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