details

property	value
status	complete
benchmark	23.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n059.star.cs.uiowa.edu
space	Various_04

run statistics

property	value
solver	AProVE21
configuration	standard
runtime (wallclock)	2.16490387917 seconds
cpu usage	5.66318471
max memory	4.75430912E8

stage attributes

key	value
output-size	2234
starexec-result	YES

output

/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox2/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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 71 ms] (2) QTRS (3) QTRSRRRProof [EQUIVALENT, 0 ms] (4) QTRS (5)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: g(0, f(x, x)) -> x g(x, s(y)) -> g(f(x, y), 0) g(s(x), y) -> g(f(x, y), 0) g(f(x, y), 0) -> f(g(x, 0), g(y, 0)) Q is empty. ---------------------------------------- (1) QTRSRRRProof (EQUIVALENT) Used ordering: Polynomial interpretation [POLO]: POL(0) = 0 POL(f(x_1, x_2)) = 1 + x_1 + x_2 POL(g(x_1, x_2)) = 2*x_1 + 2*x_2 POL(s(x_1)) = 1 + x_1 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: g(0, f(x, x)) -> x g(f(x, y), 0) -> f(g(x, 0), g(y, 0)) ---------------------------------------- (2) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: g(x, s(y)) -> g(f(x, y), 0) g(s(x), y) -> g(f(x, y), 0) Q is empty. ---------------------------------------- (3) QTRSRRRProof (EQUIVALENT) Used ordering: Polynomial interpretation [POLO]: POL(0) = 0 POL(f(x_1, x_2)) = 1 + x_1 + x_2 POL(g(x_1, x_2)) = 2*x_1 + 2*x_2 POL(s(x_1)) = 2 + 2*x_1 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: g(x, s(y)) -> g(f(x, y), 0) g(s(x), y) -> g(f(x, y), 0) ---------------------------------------- (4) Obligation: Q restricted rewrite system: R is empty. Q is empty. ---------------------------------------- (5) RisEmptyProof (EQUIVALENT) The TRS R is empty. Hence, termination is trivially proven. ---------------------------------------- (6) YES popout

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all output return to TRS Standard