details

property	value
status	complete
benchmark	secret4.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n192.star.cs.uiowa.edu
space	Secret_07_TRS

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	1.87458 seconds
cpu usage	4.00323
user time	3.81756
system time	0.185667
max virtual memory	1.8408912E7
max residence set size	250000.0

stage attributes

key	value
starexec-result	YES

output

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 144 ms] (2) QTRS (3) QTRSRRRProof [EQUIVALENT, 0 ms] (4)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(h, h, h, x) -> s(x) a(l, x, s(y), h) -> a(l, x, y, s(h)) a(l, x, s(y), s(z)) -> a(l, x, y, a(l, x, s(y), z)) a(l, s(x), h, z) -> a(l, x, z, z) a(s(l), h, h, z) -> a(l, z, h, z) +(x, h) -> x +(h, x) -> x +(s(x), s(y)) -> s(s(+(x, y))) +(+(x, y), z) -> +(x, +(y, z)) s(h) -> 1 app(nil, k) -> k app(l, nil) -> l app(cons(x, l), k) -> cons(x, app(l, k)) sum(cons(x, nil)) -> cons(x, nil) sum(cons(x, cons(y, l))) -> sum(cons(a(x, y, h, h), l)) Q is empty. ---------------------------------------- (1) QTRSRRRProof (EQUIVALENT) Used ordering: a/4(YES,YES,YES,YES) h/0) s/1(YES) +/2(YES,YES) 1/0) app/2(YES,YES) nil/0) cons/2(YES,YES) sum/1)YES( Quasi precedence: +_2 > [s_1, 1] > h app_2 > cons_2 > a_4 > [s_1, 1] > h app_2 > cons_2 > nil Status: a_4: [1,2,3,4] h: multiset status s_1: [1] +_2: [1,2] 1: multiset status app_2: [2,1] nil: multiset status cons_2: [2,1] With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: a(h, h, h, x) -> s(x) a(l, x, s(y), h) -> a(l, x, y, s(h)) a(l, x, s(y), s(z)) -> a(l, x, y, a(l, x, s(y), z)) a(l, s(x), h, z) -> a(l, x, z, z) a(s(l), h, h, z) -> a(l, z, h, z) +(x, h) -> x +(h, x) -> x +(s(x), s(y)) -> s(s(+(x, y))) +(+(x, y), z) -> +(x, +(y, z)) s(h) -> 1 app(nil, k) -> k app(l, nil) -> l app(cons(x, l), k) -> cons(x, app(l, k)) sum(cons(x, cons(y, l))) -> sum(cons(a(x, y, h, h), l)) ---------------------------------------- (2) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: sum(cons(x, nil)) -> cons(x, nil) popout

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job log

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actions

all output return to TRS Standard