TRS_Innermost 2019-03-28 22.12 pair #432270954

details

property	value
status	complete
benchmark	Ex1_GL02a_GM.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n167.star.cs.uiowa.edu
space	Transformed_CSR_innermost_04

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	1.80018 seconds
cpu usage	3.91528
user time	3.72368
system time	0.191605
max virtual memory	1.8408888E7
max residence set size	243968.0

stage attributes

key	value
starexec-result	YES

output

3.74/1.75	YES
3.74/1.76	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
3.74/1.76	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.74/1.76	
3.74/1.76	
3.74/1.76	Termination w.r.t. Q of the given QTRS could be proven:
3.74/1.76	
3.74/1.76	(0) QTRS
3.74/1.76	(1) QTRSRRRProof [EQUIVALENT, 119 ms]
3.74/1.76	(2) QTRS
3.74/1.76	(3) QTRSRRRProof [EQUIVALENT, 0 ms]
3.74/1.76	(4) QTRS
3.74/1.76	(5) RisEmptyProof [EQUIVALENT, 0 ms]
3.74/1.76	(6) YES
3.74/1.76	
3.74/1.76	
3.74/1.76	----------------------------------------
3.74/1.76	
3.74/1.76	(0)
3.74/1.76	Obligation:
3.74/1.76	Q restricted rewrite system:
3.74/1.76	The TRS R consists of the following rules:
3.74/1.76	
3.74/1.76	   a__eq(0, 0) -> true
3.74/1.76	   a__eq(s(X), s(Y)) -> a__eq(X, Y)
3.74/1.76	   a__eq(X, Y) -> false
3.74/1.76	   a__inf(X) -> cons(X, inf(s(X)))
3.74/1.76	   a__take(0, X) -> nil
3.74/1.76	   a__take(s(X), cons(Y, L)) -> cons(Y, take(X, L))
3.74/1.76	   a__length(nil) -> 0
3.74/1.76	   a__length(cons(X, L)) -> s(length(L))
3.74/1.76	   mark(eq(X1, X2)) -> a__eq(X1, X2)
3.74/1.76	   mark(inf(X)) -> a__inf(mark(X))
3.74/1.76	   mark(take(X1, X2)) -> a__take(mark(X1), mark(X2))
3.74/1.76	   mark(length(X)) -> a__length(mark(X))
3.74/1.76	   mark(0) -> 0
3.74/1.76	   mark(true) -> true
3.74/1.76	   mark(s(X)) -> s(X)
3.74/1.76	   mark(false) -> false
3.74/1.76	   mark(cons(X1, X2)) -> cons(X1, X2)
3.74/1.76	   mark(nil) -> nil
3.74/1.76	   a__eq(X1, X2) -> eq(X1, X2)
3.74/1.76	   a__inf(X) -> inf(X)
3.74/1.76	   a__take(X1, X2) -> take(X1, X2)
3.74/1.76	   a__length(X) -> length(X)
3.74/1.76	
3.74/1.76	The set Q consists of the following terms:
3.74/1.76	
3.74/1.76	   a__eq(x0, x1)
3.74/1.76	   a__inf(x0)
3.74/1.76	   mark(eq(x0, x1))
3.74/1.76	   mark(inf(x0))
3.74/1.76	   mark(take(x0, x1))
3.74/1.76	   mark(length(x0))
3.74/1.76	   mark(0)
3.74/1.76	   mark(true)
3.74/1.76	   mark(s(x0))
3.74/1.76	   mark(false)
3.74/1.76	   mark(cons(x0, x1))
3.74/1.76	   mark(nil)
3.74/1.76	   a__take(x0, x1)
3.74/1.76	   a__length(x0)
3.74/1.76	
3.74/1.76	
3.74/1.76	----------------------------------------
3.74/1.76	
3.74/1.76	(1) QTRSRRRProof (EQUIVALENT)
3.74/1.76	Used ordering:
3.74/1.76	Quasi precedence:
3.74/1.76	[a__eq_2, a__length_1, length_1, mark_1] > true > [s_1, cons_2, inf_1]
3.74/1.76	[a__eq_2, a__length_1, length_1, mark_1] > false > [s_1, cons_2, inf_1]
3.74/1.76	[a__eq_2, a__length_1, length_1, mark_1] > a__inf_1 > [s_1, cons_2, inf_1]
3.74/1.76	[a__eq_2, a__length_1, length_1, mark_1] > a__take_2 > nil > 0 > [s_1, cons_2, inf_1]
3.74/1.76	[a__eq_2, a__length_1, length_1, mark_1] > a__take_2 > take_2 > [s_1, cons_2, inf_1]
3.74/1.76	[a__eq_2, a__length_1, length_1, mark_1] > eq_2 > [s_1, cons_2, inf_1]
3.74/1.76	
3.74/1.76	
3.74/1.76	Status:
3.74/1.76	a__eq_2: multiset status
3.74/1.76	0: multiset status
3.74/1.76	true: multiset status
3.74/1.76	s_1: multiset status
3.74/1.76	false: multiset status
3.74/1.76	a__inf_1: multiset status
3.74/1.76	cons_2: multiset status
3.74/1.76	inf_1: multiset status
3.74/1.76	a__take_2: multiset status
3.74/1.76	nil: multiset status
3.74/1.76	take_2: multiset status
3.74/1.76	a__length_1: multiset status
3.74/1.76	length_1: multiset status
3.74/1.76	mark_1: multiset status
3.74/1.76	eq_2: multiset status
3.74/1.76	
3.74/1.76	With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
3.74/1.76	
3.74/1.76	   a__eq(0, 0) -> true
3.74/1.76	   a__eq(s(X), s(Y)) -> a__eq(X, Y)
3.74/1.76	   a__eq(X, Y) -> false
3.74/1.76	   a__inf(X) -> cons(X, inf(s(X)))

popout

output may be truncated. 'popout' for the full output.

job log

popout

actions all output return to TRS_Innermost 2019-03-28 22.12