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Runti Compl Full Rewri 10127 pair #381903497
details
property
value
status
complete
benchmark
Ex9_BLR02_C.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n035.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
292.131523132 seconds
cpu usage
331.06618452
max memory
8.395337728E9
stage attributes
key
value
output-size
31083
starexec-result
WORST_CASE(Omega(n^1), ?)
output
/export/starexec/sandbox/solver/bin/starexec_run_complexity /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^1), ?) proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). (0) CpxTRS (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxTRS (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (4) typed CpxTrs (5) OrderProof [LOWER BOUND(ID), 0 ms] (6) typed CpxTrs (7) RewriteLemmaProof [LOWER BOUND(ID), 446 ms] (8) BEST (9) proven lower bound (10) LowerBoundPropagationProof [FINISHED, 0 ms] (11) BOUNDS(n^1, INF) (12) typed CpxTrs (13) RewriteLemmaProof [LOWER BOUND(ID), 121 ms] (14) typed CpxTrs (15) RewriteLemmaProof [LOWER BOUND(ID), 118 ms] (16) typed CpxTrs (17) RewriteLemmaProof [LOWER BOUND(ID), 76 ms] (18) typed CpxTrs (19) RewriteLemmaProof [LOWER BOUND(ID), 28 ms] (20) typed CpxTrs ---------------------------------------- (0) Obligation: The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). The TRS R consists of the following rules: active(filter(cons(X, Y), 0, M)) -> mark(cons(0, filter(Y, M, M))) active(filter(cons(X, Y), s(N), M)) -> mark(cons(X, filter(Y, N, M))) active(sieve(cons(0, Y))) -> mark(cons(0, sieve(Y))) active(sieve(cons(s(N), Y))) -> mark(cons(s(N), sieve(filter(Y, N, N)))) active(nats(N)) -> mark(cons(N, nats(s(N)))) active(zprimes) -> mark(sieve(nats(s(s(0))))) active(filter(X1, X2, X3)) -> filter(active(X1), X2, X3) active(filter(X1, X2, X3)) -> filter(X1, active(X2), X3) active(filter(X1, X2, X3)) -> filter(X1, X2, active(X3)) active(cons(X1, X2)) -> cons(active(X1), X2) active(s(X)) -> s(active(X)) active(sieve(X)) -> sieve(active(X)) active(nats(X)) -> nats(active(X)) filter(mark(X1), X2, X3) -> mark(filter(X1, X2, X3)) filter(X1, mark(X2), X3) -> mark(filter(X1, X2, X3)) filter(X1, X2, mark(X3)) -> mark(filter(X1, X2, X3)) cons(mark(X1), X2) -> mark(cons(X1, X2)) s(mark(X)) -> mark(s(X)) sieve(mark(X)) -> mark(sieve(X)) nats(mark(X)) -> mark(nats(X)) proper(filter(X1, X2, X3)) -> filter(proper(X1), proper(X2), proper(X3)) proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)) proper(0) -> ok(0) proper(s(X)) -> s(proper(X)) proper(sieve(X)) -> sieve(proper(X)) proper(nats(X)) -> nats(proper(X)) proper(zprimes) -> ok(zprimes) filter(ok(X1), ok(X2), ok(X3)) -> ok(filter(X1, X2, X3)) cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)) s(ok(X)) -> ok(s(X)) sieve(ok(X)) -> ok(sieve(X)) nats(ok(X)) -> ok(nats(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) S is empty. Rewrite Strategy: FULL ---------------------------------------- (1) RenamingProof (BOTH BOUNDS(ID, ID)) Renamed function symbols to avoid clashes with predefined symbol. ---------------------------------------- (2) Obligation: The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). The TRS R consists of the following rules: active(filter(cons(X, Y), 0', M)) -> mark(cons(0', filter(Y, M, M))) active(filter(cons(X, Y), s(N), M)) -> mark(cons(X, filter(Y, N, M))) active(sieve(cons(0', Y))) -> mark(cons(0', sieve(Y))) active(sieve(cons(s(N), Y))) -> mark(cons(s(N), sieve(filter(Y, N, N)))) active(nats(N)) -> mark(cons(N, nats(s(N))))
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