details

property	value
status	complete
benchmark	2.61.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n192.star.cs.uiowa.edu
space	SK90

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	1.56177592278 seconds
cpu usage	3.384280699
max memory	2.18189824E8

stage attributes

key	value
output-size	2047
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 0 ms] (2) QTRS (3) RisEmptyProof [EQUIVALENT, 0 ms] (4) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: f(j(x, y), y) -> g(f(x, k(y))) f(x, h1(y, z)) -> h2(0, x, h1(y, z)) g(h2(x, y, h1(z, u))) -> h2(s(x), y, h1(z, u)) h2(x, j(y, h1(z, u)), h1(z, u)) -> h2(s(x), y, h1(s(z), u)) i(f(x, h(y))) -> y i(h2(s(x), y, h1(x, z))) -> z k(h(x)) -> h1(0, x) k(h1(x, y)) -> h1(s(x), y) Q is empty. ---------------------------------------- (1) QTRSRRRProof (EQUIVALENT) Used ordering: Knuth-Bendix order [KBO] with precedence:h_1 > i_1 > s_1 > 0 > f_2 > g_1 > j_2 > h2_3 > k_1 > h1_2 and weight map: 0=5 g_1=4 k_1=4 s_1=4 i_1=1 h_1=1 j_2=7 f_2=5 h2_3=0 h1_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: f(j(x, y), y) -> g(f(x, k(y))) f(x, h1(y, z)) -> h2(0, x, h1(y, z)) g(h2(x, y, h1(z, u))) -> h2(s(x), y, h1(z, u)) h2(x, j(y, h1(z, u)), h1(z, u)) -> h2(s(x), y, h1(s(z), u)) i(f(x, h(y))) -> y i(h2(s(x), y, h1(x, z))) -> z k(h(x)) -> h1(0, x) k(h1(x, y)) -> h1(s(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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