details

property	value
status	complete
benchmark	jones6.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	Mixed_TRS

run statistics

property	value
solver	AProVE21
configuration	standard
runtime (wallclock)	2.19329190254 seconds
cpu usage	5.719107044
max memory	4.85613568E8

stage attributes

key	value
output-size	2206
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 74 ms] (2) QTRS (3) QTRSRRRProof [EQUIVALENT, 0 ms] (4) QTRS (5)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: f(a, empty) -> g(a, empty) f(a, cons(x, k)) -> f(cons(x, a), k) g(empty, d) -> d g(cons(x, k), d) -> g(k, cons(x, d)) Q is empty. ---------------------------------------- (1) QTRSRRRProof (EQUIVALENT) Used ordering: Polynomial interpretation [POLO]: POL(cons(x_1, x_2)) = 1 + x_1 + x_2 POL(empty) = 2 POL(f(x_1, x_2)) = 1 + x_1 + 2*x_2 POL(g(x_1, x_2)) = x_1 + x_2 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: f(a, empty) -> g(a, empty) f(a, cons(x, k)) -> f(cons(x, a), k) g(empty, d) -> d ---------------------------------------- (2) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: g(cons(x, k), d) -> g(k, cons(x, d)) Q is empty. ---------------------------------------- (3) QTRSRRRProof (EQUIVALENT) Used ordering: Knuth-Bendix order [KBO] with precedence:cons_2 > g_2 and weight map: cons_2=0 g_2=0 The variable weight is 1With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: g(cons(x, k), d) -> g(k, cons(x, d)) ---------------------------------------- (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