details

property	value
status	complete
benchmark	Ex9_BLR02_GM.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n141.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE
configuration	rcdcRelativeAlsoLower
runtime (wallclock)	291.587 seconds
cpu usage	1145.21
user time	1133.74
system time	11.4662
max virtual memory	3.8033416E7
max residence set size	1.4786728E7

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, INF).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), 1 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), 324 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), 2505 ms] (18) 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: a__filter(cons(X, Y), 0, M) -> cons(0, filter(Y, M, M)) a__filter(cons(X, Y), s(N), M) -> cons(mark(X), filter(Y, N, M)) a__sieve(cons(0, Y)) -> cons(0, sieve(Y)) a__sieve(cons(s(N), Y)) -> cons(s(mark(N)), sieve(filter(Y, N, N))) a__nats(N) -> cons(mark(N), nats(s(N))) a__zprimes -> a__sieve(a__nats(s(s(0)))) mark(filter(X1, X2, X3)) -> a__filter(mark(X1), mark(X2), mark(X3)) mark(sieve(X)) -> a__sieve(mark(X)) mark(nats(X)) -> a__nats(mark(X)) mark(zprimes) -> a__zprimes mark(cons(X1, X2)) -> cons(mark(X1), X2) mark(0) -> 0 mark(s(X)) -> s(mark(X)) a__filter(X1, X2, X3) -> filter(X1, X2, X3) a__sieve(X) -> sieve(X) a__nats(X) -> nats(X) a__zprimes -> zprimes 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(cons(x_1, x_2)) -> cons(encArg(x_1), encArg(x_2)) encArg(0) -> 0 encArg(filter(x_1, x_2, x_3)) -> filter(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(s(x_1)) -> s(encArg(x_1)) encArg(sieve(x_1)) -> sieve(encArg(x_1)) encArg(nats(x_1)) -> nats(encArg(x_1)) encArg(zprimes) -> zprimes encArg(cons_a__filter(x_1, x_2, x_3)) -> a__filter(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_a__sieve(x_1)) -> a__sieve(encArg(x_1)) encArg(cons_a__nats(x_1)) -> a__nats(encArg(x_1)) encArg(cons_a__zprimes) -> a__zprimes encArg(cons_mark(x_1)) -> mark(encArg(x_1)) encode_a__filter(x_1, x_2, x_3) -> a__filter(encArg(x_1), encArg(x_2), encArg(x_3)) encode_cons(x_1, x_2) -> cons(encArg(x_1), encArg(x_2)) encode_0 -> 0 encode_filter(x_1, x_2, x_3) -> filter(encArg(x_1), encArg(x_2), encArg(x_3)) encode_s(x_1) -> s(encArg(x_1)) encode_mark(x_1) -> mark(encArg(x_1)) encode_a__sieve(x_1) -> a__sieve(encArg(x_1)) encode_sieve(x_1) -> sieve(encArg(x_1)) encode_a__nats(x_1) -> a__nats(encArg(x_1)) encode_nats(x_1) -> nats(encArg(x_1)) encode_a__zprimes -> a__zprimes encode_zprimes -> zprimes ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, INF). The TRS R consists of the following rules: a__filter(cons(X, Y), 0, M) -> cons(0, filter(Y, M, M)) a__filter(cons(X, Y), s(N), M) -> cons(mark(X), filter(Y, N, M)) a__sieve(cons(0, Y)) -> cons(0, sieve(Y)) popout

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all output return to Derivational Complexity: TRS Innermost