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	n141.star.cs.uiowa.edu
space	Transformed_CSR_innermost_04

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	1.74603 seconds
cpu usage	3.99073
user time	3.81081
system time	0.179911
max virtual memory	1.834908E7
max residence set size	245916.0

stage attributes

key	value
starexec-result	YES

output

YES proof of /export/starexec/sandbox/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 149 ms] (2) QTRS (3) QTRSRRRProof [EQUIVALENT, 0 ms] (4) QTRS (5) RisEmptyProof [EQUIVALENT, 0 ms] (6) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: a__eq(0, 0) -> true a__eq(s(X), s(Y)) -> a__eq(X, Y) a__eq(X, Y) -> false a__inf(X) -> cons(X, inf(s(X))) a__take(0, X) -> nil a__take(s(X), cons(Y, L)) -> cons(Y, take(X, L)) a__length(nil) -> 0 a__length(cons(X, L)) -> s(length(L)) mark(eq(X1, X2)) -> a__eq(X1, X2) mark(inf(X)) -> a__inf(mark(X)) mark(take(X1, X2)) -> a__take(mark(X1), mark(X2)) mark(length(X)) -> a__length(mark(X)) mark(0) -> 0 mark(true) -> true mark(s(X)) -> s(X) mark(false) -> false mark(cons(X1, X2)) -> cons(X1, X2) mark(nil) -> nil a__eq(X1, X2) -> eq(X1, X2) a__inf(X) -> inf(X) a__take(X1, X2) -> take(X1, X2) a__length(X) -> length(X) The set Q consists of the following terms: a__eq(x0, x1) a__inf(x0) mark(eq(x0, x1)) mark(inf(x0)) mark(take(x0, x1)) mark(length(x0)) mark(0) mark(true) mark(s(x0)) mark(false) mark(cons(x0, x1)) mark(nil) a__take(x0, x1) a__length(x0) ---------------------------------------- (1) QTRSRRRProof (EQUIVALENT) Used ordering: Quasi precedence: [a__eq_2, a__length_1, length_1, mark_1] > true > [s_1, cons_2, inf_1] [a__eq_2, a__length_1, length_1, mark_1] > false > [s_1, cons_2, inf_1] [a__eq_2, a__length_1, length_1, mark_1] > a__inf_1 > [s_1, cons_2, inf_1] [a__eq_2, a__length_1, length_1, mark_1] > a__take_2 > nil > 0 > [s_1, cons_2, inf_1] [a__eq_2, a__length_1, length_1, mark_1] > a__take_2 > take_2 > [s_1, cons_2, inf_1] [a__eq_2, a__length_1, length_1, mark_1] > eq_2 > [s_1, cons_2, inf_1] Status: a__eq_2: multiset status 0: multiset status true: multiset status s_1: multiset status false: multiset status a__inf_1: multiset status cons_2: multiset status inf_1: multiset status a__take_2: multiset status nil: multiset status take_2: multiset status a__length_1: multiset status length_1: multiset status mark_1: multiset status eq_2: multiset status With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: a__eq(0, 0) -> true a__eq(s(X), s(Y)) -> a__eq(X, Y) a__eq(X, Y) -> false a__inf(X) -> cons(X, inf(s(X))) popout

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all output return to TRS Innermost