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TRS Standard pair #516967535
details
property
value
status
complete
benchmark
secret1.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n145.star.cs.uiowa.edu
space
Secret_07_TRS
run statistics
property
value
solver
AProVE21
configuration
standard
runtime (wallclock)
2.32580685616 seconds
cpu usage
6.238425093
max memory
4.79244288E8
stage attributes
key
value
output-size
3194
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 161 ms] (2) QTRS (3) QTRSRRRProof [EQUIVALENT, 2 ms] (4) QTRS (5) RisEmptyProof [EQUIVALENT, 0 ms] (6) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: D(t) -> s(h) D(constant) -> h D(b(x, y)) -> b(D(x), D(y)) D(c(x, y)) -> b(c(y, D(x)), c(x, D(y))) D(m(x, y)) -> m(D(x), D(y)) D(opp(x)) -> opp(D(x)) D(div(x, y)) -> m(div(D(x), y), div(c(x, D(y)), pow(y, 2))) D(ln(x)) -> div(D(x), x) D(pow(x, y)) -> b(c(c(y, pow(x, m(y, 1))), D(x)), c(c(pow(x, y), ln(x)), D(y))) b(h, x) -> x b(x, h) -> x b(s(x), s(y)) -> s(s(b(x, y))) b(b(x, y), z) -> b(x, b(y, z)) Q is empty. ---------------------------------------- (1) QTRSRRRProof (EQUIVALENT) Used ordering: D/1(YES) t/0) s/1)YES( h/0) constant/0) b/2(YES,YES) c/2(YES,YES) m/2(YES,YES) opp/1(YES) div/2(YES,YES) pow/2(YES,YES) 2/0) ln/1(YES) 1/0) Quasi precedence: D_1 > h D_1 > c_2 > b_2 D_1 > m_2 D_1 > opp_1 D_1 > div_2 > [pow_2, ln_1] > b_2 D_1 > 2 D_1 > 1 t > h Status: D_1: multiset status t: multiset status h: multiset status constant: multiset status b_2: [1,2] c_2: multiset status m_2: multiset status opp_1: multiset status div_2: multiset status pow_2: multiset status 2: multiset status ln_1: multiset status 1: multiset status With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: D(t) -> s(h) D(constant) -> h D(b(x, y)) -> b(D(x), D(y)) D(c(x, y)) -> b(c(y, D(x)), c(x, D(y))) D(m(x, y)) -> m(D(x), D(y)) D(opp(x)) -> opp(D(x)) D(div(x, y)) -> m(div(D(x), y), div(c(x, D(y)), pow(y, 2))) D(ln(x)) -> div(D(x), x)
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