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Derivational Complexity: TRS Innermost pair #487109080
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
n140.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
rcdcRelativeAlsoLower
runtime (wallclock)
291.616 seconds
cpu usage
1141.97
user time
1129.24
system time
12.7282
max virtual memory
3.7456016E7
max residence set size
1.494512E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
WORST_CASE(Omega(n^1), ?) proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, INF). (0) DCpxTrs (1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxRelTRS (3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 339 ms] (4) CpxRelTRS (5) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (6) CpxRelTRS (7) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (8) typed CpxTrs (9) OrderProof [LOWER BOUND(ID), 0 ms] (10) typed CpxTrs (11) RewriteLemmaProof [LOWER BOUND(ID), 433 ms] (12) BEST (13) proven lower bound (14) LowerBoundPropagationProof [FINISHED, 0 ms] (15) BOUNDS(n^1, INF) (16) typed CpxTrs (17) RewriteLemmaProof [LOWER BOUND(ID), 193 ms] (18) typed CpxTrs (19) RewriteLemmaProof [LOWER BOUND(ID), 117 ms] (20) typed CpxTrs (21) RewriteLemmaProof [LOWER BOUND(ID), 102 ms] (22) typed CpxTrs (23) RewriteLemmaProof [LOWER BOUND(ID), 95 ms] (24) typed CpxTrs (25) RewriteLemmaProof [LOWER BOUND(ID), 1061 ms] (26) BOUNDS(1, INF) ---------------------------------------- (0) Obligation: The Derivational Complexity (innermost) of the given DCpxTrs 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: INNERMOST ---------------------------------------- (1) DerivationalComplexityToRuntimeComplexityProof (BOTH BOUNDS(ID, ID)) The following rules have been added to S to convert the given derivational complexity problem to a runtime complexity problem: encArg(0) -> 0 encArg(mark(x_1)) -> mark(encArg(x_1)) encArg(zprimes) -> zprimes encArg(ok(x_1)) -> ok(encArg(x_1)) encArg(cons_active(x_1)) -> active(encArg(x_1)) encArg(cons_filter(x_1, x_2, x_3)) -> filter(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_cons(x_1, x_2)) -> cons(encArg(x_1), encArg(x_2)) encArg(cons_s(x_1)) -> s(encArg(x_1)) encArg(cons_sieve(x_1)) -> sieve(encArg(x_1)) encArg(cons_nats(x_1)) -> nats(encArg(x_1)) encArg(cons_proper(x_1)) -> proper(encArg(x_1)) encArg(cons_top(x_1)) -> top(encArg(x_1)) encode_active(x_1) -> active(encArg(x_1))
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