TRS_Innermost 2019-03-28 22.12 pair #432271016

details

property	value
status	complete
benchmark	Ex9_BLR02_C.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n086.star.cs.uiowa.edu
space	Transformed_CSR_innermost_04

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	1.79026 seconds
cpu usage	3.8468
user time	3.67106
system time	0.17574
max virtual memory	1.8343352E7
max residence set size	235396.0

stage attributes

key	value
starexec-result	YES

output

3.62/1.73	YES
3.77/1.74	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.77/1.74	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.77/1.74	
3.77/1.74	
3.77/1.74	Termination w.r.t. Q of the given QTRS could be proven:
3.77/1.74	
3.77/1.74	(0) QTRS
3.77/1.74	(1) QTRSToCSRProof [SOUND, 0 ms]
3.77/1.74	(2) CSR
3.77/1.74	(3) CSRRRRProof [EQUIVALENT, 87 ms]
3.77/1.74	(4) CSR
3.77/1.74	(5) CSRRRRProof [EQUIVALENT, 0 ms]
3.77/1.74	(6) CSR
3.77/1.74	(7) RisEmptyProof [EQUIVALENT, 0 ms]
3.77/1.74	(8) YES
3.77/1.74	
3.77/1.74	
3.77/1.74	----------------------------------------
3.77/1.74	
3.77/1.74	(0)
3.77/1.74	Obligation:
3.77/1.74	Q restricted rewrite system:
3.77/1.74	The TRS R consists of the following rules:
3.77/1.74	
3.77/1.74	   active(filter(cons(X, Y), 0, M)) -> mark(cons(0, filter(Y, M, M)))
3.77/1.74	   active(filter(cons(X, Y), s(N), M)) -> mark(cons(X, filter(Y, N, M)))
3.77/1.74	   active(sieve(cons(0, Y))) -> mark(cons(0, sieve(Y)))
3.77/1.74	   active(sieve(cons(s(N), Y))) -> mark(cons(s(N), sieve(filter(Y, N, N))))
3.77/1.74	   active(nats(N)) -> mark(cons(N, nats(s(N))))
3.77/1.74	   active(zprimes) -> mark(sieve(nats(s(s(0)))))
3.77/1.74	   active(filter(X1, X2, X3)) -> filter(active(X1), X2, X3)
3.77/1.74	   active(filter(X1, X2, X3)) -> filter(X1, active(X2), X3)
3.77/1.74	   active(filter(X1, X2, X3)) -> filter(X1, X2, active(X3))
3.77/1.74	   active(cons(X1, X2)) -> cons(active(X1), X2)
3.77/1.74	   active(s(X)) -> s(active(X))
3.77/1.74	   active(sieve(X)) -> sieve(active(X))
3.77/1.74	   active(nats(X)) -> nats(active(X))
3.77/1.74	   filter(mark(X1), X2, X3) -> mark(filter(X1, X2, X3))
3.77/1.74	   filter(X1, mark(X2), X3) -> mark(filter(X1, X2, X3))
3.77/1.74	   filter(X1, X2, mark(X3)) -> mark(filter(X1, X2, X3))
3.77/1.74	   cons(mark(X1), X2) -> mark(cons(X1, X2))
3.77/1.74	   s(mark(X)) -> mark(s(X))
3.77/1.74	   sieve(mark(X)) -> mark(sieve(X))
3.77/1.74	   nats(mark(X)) -> mark(nats(X))
3.77/1.74	   proper(filter(X1, X2, X3)) -> filter(proper(X1), proper(X2), proper(X3))
3.77/1.74	   proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
3.77/1.74	   proper(0) -> ok(0)
3.77/1.74	   proper(s(X)) -> s(proper(X))
3.77/1.74	   proper(sieve(X)) -> sieve(proper(X))
3.77/1.74	   proper(nats(X)) -> nats(proper(X))
3.77/1.74	   proper(zprimes) -> ok(zprimes)
3.77/1.74	   filter(ok(X1), ok(X2), ok(X3)) -> ok(filter(X1, X2, X3))
3.77/1.74	   cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
3.77/1.74	   s(ok(X)) -> ok(s(X))
3.77/1.74	   sieve(ok(X)) -> ok(sieve(X))
3.77/1.74	   nats(ok(X)) -> ok(nats(X))
3.77/1.74	   top(mark(X)) -> top(proper(X))
3.77/1.74	   top(ok(X)) -> top(active(X))
3.77/1.74	
3.77/1.74	The set Q consists of the following terms:
3.77/1.74	
3.77/1.74	   active(nats(x0))
3.77/1.74	   active(zprimes)
3.77/1.74	   active(filter(x0, x1, x2))
3.77/1.74	   active(cons(x0, x1))
3.77/1.74	   active(s(x0))
3.77/1.74	   active(sieve(x0))
3.77/1.74	   filter(mark(x0), x1, x2)
3.77/1.74	   filter(x0, mark(x1), x2)
3.77/1.74	   filter(x0, x1, mark(x2))
3.77/1.74	   cons(mark(x0), x1)
3.77/1.74	   s(mark(x0))
3.77/1.74	   sieve(mark(x0))
3.77/1.74	   nats(mark(x0))
3.77/1.74	   proper(filter(x0, x1, x2))
3.77/1.74	   proper(cons(x0, x1))
3.77/1.74	   proper(0)
3.77/1.74	   proper(s(x0))
3.77/1.74	   proper(sieve(x0))
3.77/1.74	   proper(nats(x0))
3.77/1.74	   proper(zprimes)
3.77/1.74	   filter(ok(x0), ok(x1), ok(x2))
3.77/1.74	   cons(ok(x0), ok(x1))
3.77/1.74	   s(ok(x0))
3.77/1.74	   sieve(ok(x0))
3.77/1.74	   nats(ok(x0))
3.77/1.74	   top(mark(x0))
3.77/1.74	   top(ok(x0))
3.77/1.74	
3.77/1.74	
3.77/1.74	----------------------------------------
3.77/1.74	
3.77/1.74	(1) QTRSToCSRProof (SOUND)
3.77/1.74	The following Q TRS is given: Q restricted rewrite system:
3.77/1.74	The TRS R consists of the following rules:
3.77/1.74	
3.77/1.74	   active(filter(cons(X, Y), 0, M)) -> mark(cons(0, filter(Y, M, M)))
3.77/1.74	   active(filter(cons(X, Y), s(N), M)) -> mark(cons(X, filter(Y, N, M)))
3.77/1.74	   active(sieve(cons(0, Y))) -> mark(cons(0, sieve(Y)))

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