details

property	value
status	complete
benchmark	secret3.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n071.star.cs.uiowa.edu
space	Secret_07_TRS

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	1.7384519577 seconds
cpu usage	3.864499535
max memory	1.97083136E8

stage attributes

key	value
output-size	2072
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 115 ms] (2) QTRS (3) RisEmptyProof [EQUIVALENT, 0 ms] (4) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: 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), l)) a(h, h, x) -> s(x) a(x, s(y), h) -> a(x, y, s(h)) a(x, s(y), s(z)) -> a(x, y, a(x, s(y), z)) a(s(x), h, z) -> a(x, z, z) Q is empty. ---------------------------------------- (1) QTRSRRRProof (EQUIVALENT) Used ordering: Quasi precedence: app_2 > cons_2 > [a_3, h] > s_1 > nil sum_1 > cons_2 > [a_3, h] > s_1 > nil Status: app_2: [2,1] nil: multiset status cons_2: [2,1] sum_1: multiset status a_3: [1,2,3] h: multiset status s_1: multiset status With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: 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), l)) a(h, h, x) -> s(x) a(x, s(y), h) -> a(x, y, s(h)) a(x, s(y), s(z)) -> a(x, y, a(x, s(y), z)) a(s(x), h, z) -> a(x, z, z) ---------------------------------------- (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 Stand 20472