details

property	value
status	complete
benchmark	#3.16.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n183.star.cs.uiowa.edu
space	AG01

run statistics

property	value
solver	AProVE21
configuration	standard
runtime (wallclock)	2.09212183952 seconds
cpu usage	5.394447826
max memory	4.71269376E8

stage attributes

key	value
output-size	1700
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 91 ms] (2) QTRS (3) RisEmptyProof [EQUIVALENT, 0 ms] (4) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: times(x, 0) -> 0 times(x, s(y)) -> plus(times(x, y), x) plus(x, 0) -> x plus(0, x) -> x plus(x, s(y)) -> s(plus(x, y)) plus(s(x), y) -> s(plus(x, y)) Q is empty. ---------------------------------------- (1) QTRSRRRProof (EQUIVALENT) Used ordering: Quasi precedence: times_2 > 0 > s_1 times_2 > plus_2 > s_1 Status: times_2: multiset status 0: multiset status s_1: multiset status plus_2: [1,2] With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: times(x, 0) -> 0 times(x, s(y)) -> plus(times(x, y), x) plus(x, 0) -> x plus(0, x) -> x plus(x, s(y)) -> s(plus(x, y)) plus(s(x), y) -> s(plus(x, y)) ---------------------------------------- (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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job log

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actions

all output return to TRS Standard