details

property	value
status	complete
benchmark	Ex9_BLR02_L.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n137.star.cs.uiowa.edu
space	Transformed_CSR_innermost_04

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	1.63258600235 seconds
cpu usage	3.47601824
max memory	2.21138944E8

stage attributes

key	value
output-size	2146
starexec-result	YES

output

/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 0 ms] (2) QTRS (3) RisEmptyProof [EQUIVALENT, 0 ms] (4) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: filter(cons(X), 0, M) -> cons(0) filter(cons(X), s(N), M) -> cons(X) sieve(cons(0)) -> cons(0) sieve(cons(s(N))) -> cons(s(N)) nats(N) -> cons(N) zprimes -> sieve(nats(s(s(0)))) The set Q consists of the following terms: filter(cons(x0), 0, x1) filter(cons(x0), s(x1), x2) sieve(cons(0)) sieve(cons(s(x0))) nats(x0) zprimes ---------------------------------------- (1) QTRSRRRProof (EQUIVALENT) Used ordering: Knuth-Bendix order [KBO] with precedence:sieve_1 > zprimes > s_1 > cons_1 > nats_1 > 0 > filter_3 and weight map: 0=3 zprimes=8 cons_1=1 s_1=1 sieve_1=0 nats_1=2 filter_3=0 The variable weight is 1With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: filter(cons(X), 0, M) -> cons(0) filter(cons(X), s(N), M) -> cons(X) sieve(cons(0)) -> cons(0) sieve(cons(s(N))) -> cons(s(N)) nats(N) -> cons(N) zprimes -> sieve(nats(s(s(0)))) ---------------------------------------- (2) Obligation: Q restricted rewrite system: R is empty. The set Q consists of the following terms: filter(cons(x0), 0, x1) filter(cons(x0), s(x1), x2) sieve(cons(0)) sieve(cons(s(x0))) nats(x0) zprimes ---------------------------------------- (3) RisEmptyProof (EQUIVALENT) The TRS R is empty. Hence, termination is trivially proven. ---------------------------------------- (4) YES popout

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

job log

popout

actions

all output return to TRS Innermost