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TRS Standard pair #487072278
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
n070.star.cs.uiowa.edu
space
Secret_07_TRS
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.86928 seconds
cpu usage
4.40221
user time
4.21421
system time
0.187998
max virtual memory
1.8408912E7
max residence set size
260288.0
stage attributes
key
value
starexec-result
YES
output
YES proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 175 ms] (2) QTRS (3) QTRSRRRProof [EQUIVALENT, 0 ms] (4)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: 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) 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(b(x, y), z) -> b(x, b(y, z))
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