details

property	value
status	complete
benchmark	list-sum-prod-assoc-append.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n074.star.cs.uiowa.edu
space	CiME_04

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	1.74441 seconds
cpu usage	3.8775
user time	3.72383
system time	0.153676
max virtual memory	1.8349112E7
max residence set size	246296.0

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 118 ms] (2) QTRS (3) RisEmptyProof [EQUIVALENT, 0 ms] (4) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: +(x, 0) -> x +(0, x) -> x +(s(x), s(y)) -> s(s(+(x, y))) +(+(x, y), z) -> +(x, +(y, z)) *(x, 0) -> 0 *(0, x) -> 0 *(s(x), s(y)) -> s(+(*(x, y), +(x, y))) *(*(x, y), z) -> *(x, *(y, z)) app(nil, l) -> l app(cons(x, l1), l2) -> cons(x, app(l1, l2)) sum(nil) -> 0 sum(cons(x, l)) -> +(x, sum(l)) sum(app(l1, l2)) -> +(sum(l1), sum(l2)) prod(nil) -> s(0) prod(cons(x, l)) -> *(x, prod(l)) prod(app(l1, l2)) -> *(prod(l1), prod(l2)) Q is empty. ---------------------------------------- (1) QTRSRRRProof (EQUIVALENT) Used ordering: Quasi precedence: [*_2, app_2, sum_1, prod_1] > +_2 > [s_1, nil] [*_2, app_2, sum_1, prod_1] > 0 [*_2, app_2, sum_1, prod_1] > cons_2 Status: +_2: [1,2] 0: multiset status s_1: [1] *_2: [1,2] app_2: [1,2] nil: multiset status cons_2: multiset status sum_1: multiset status prod_1: [1] With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: +(x, 0) -> x +(0, x) -> x +(s(x), s(y)) -> s(s(+(x, y))) +(+(x, y), z) -> +(x, +(y, z)) *(x, 0) -> 0 *(0, x) -> 0 *(s(x), s(y)) -> s(+(*(x, y), +(x, y))) *(*(x, y), z) -> *(x, *(y, z)) app(nil, l) -> l app(cons(x, l1), l2) -> cons(x, app(l1, l2)) sum(nil) -> 0 sum(cons(x, l)) -> +(x, sum(l)) sum(app(l1, l2)) -> +(sum(l1), sum(l2)) prod(nil) -> s(0) prod(cons(x, l)) -> *(x, prod(l)) prod(app(l1, l2)) -> *(prod(l1), prod(l2)) ---------------------------------------- (2) Obligation: Q restricted rewrite system: R is empty. Q is empty. ---------------------------------------- (3) RisEmptyProof (EQUIVALENT) The TRS R is empty. Hence, termination is trivially proven. ---------------------------------------- (4) YES popout

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all output return to TRS Standard