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	n035.star.cs.uiowa.edu
space	CiME_04

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	1.78332090378 seconds
cpu usage	3.94097955
max memory	2.07056896E8

stage attributes

key	value
output-size	2463
starexec-result	YES

output

/export/starexec/sandbox/solver/bin/starexec_run_standard /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 113 ms] (2) QTRS (3) RisEmptyProof [EQUIVALENT, 0 ms] (4)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) popout

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