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TRS Innermost pair #516979363
details
property
value
status
complete
benchmark
Ex9_BLR02_L.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n136.star.cs.uiowa.edu
space
Transformed_CSR_innermost_04
run statistics
property
value
solver
AProVE21
configuration
standard
runtime (wallclock)
3.1676299572 seconds
cpu usage
5.710428073
max memory
4.73407488E8
stage attributes
key
value
output-size
2813
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 90 ms] (2) QTRS (3) QTRSRRRProof [EQUIVALENT, 0 ms] (4) QTRS (5)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: filter(cons(X), 0, M) -> cons(0) filter(cons(X), s(N), M) -> cons(X) sieve(cons(0)) -> cons(0) sieve(cons(s(N))) -> cons(s(N)) nats(N) -> cons(N) zprimes -> sieve(nats(s(s(0)))) The set Q consists of the following terms: filter(cons(x0), 0, x1) filter(cons(x0), s(x1), x2) sieve(cons(0)) sieve(cons(s(x0))) nats(x0) zprimes ---------------------------------------- (1) QTRSRRRProof (EQUIVALENT) Used ordering: Polynomial interpretation [POLO]: POL(0) = 0 POL(cons(x_1)) = x_1 POL(filter(x_1, x_2, x_3)) = 1 + 2*x_1 + x_2 + x_3 POL(nats(x_1)) = 2*x_1 POL(s(x_1)) = x_1 POL(sieve(x_1)) = 1 + 2*x_1 POL(zprimes) = 2 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: filter(cons(X), 0, M) -> cons(0) filter(cons(X), s(N), M) -> cons(X) sieve(cons(0)) -> cons(0) sieve(cons(s(N))) -> cons(s(N)) zprimes -> sieve(nats(s(s(0)))) ---------------------------------------- (2) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: nats(N) -> cons(N) The set Q consists of the following terms: filter(cons(x0), 0, x1) filter(cons(x0), s(x1), x2) sieve(cons(0)) sieve(cons(s(x0))) nats(x0) zprimes ---------------------------------------- (3) QTRSRRRProof (EQUIVALENT) Used ordering: nats/1(YES) cons/1)YES( Quasi precedence: trivial
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