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	n142.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE
configuration	rcdcRelativeAlsoLower
runtime (wallclock)	291.487 seconds
cpu usage	314.07
user time	311.41
system time	2.66014
max virtual memory	3.771394E7
max residence set size	5176028.0

stage attributes

key	value
starexec-result	WORST_CASE(?, O(n^1))

output

WORST_CASE(?, O(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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(1, n^1). (0) DCpxTrs (1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxRelTRS (3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 207 ms] (4) CpxRelTRS (5) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (6) CpxTRS (7) CpxTrsMatchBoundsTAProof [FINISHED, 345 ms] (8) BOUNDS(1, n^1) ---------------------------------------- (0) Obligation: The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(1, n^1). 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)))) 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)) -> cons(encArg(x_1)) encArg(0) -> 0 encArg(s(x_1)) -> s(encArg(x_1)) encArg(cons_filter(x_1, x_2, x_3)) -> filter(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_sieve(x_1)) -> sieve(encArg(x_1)) encArg(cons_nats(x_1)) -> nats(encArg(x_1)) encArg(cons_zprimes) -> zprimes encode_filter(x_1, x_2, x_3) -> filter(encArg(x_1), encArg(x_2), encArg(x_3)) encode_cons(x_1) -> cons(encArg(x_1)) encode_0 -> 0 encode_s(x_1) -> s(encArg(x_1)) encode_sieve(x_1) -> sieve(encArg(x_1)) encode_nats(x_1) -> nats(encArg(x_1)) encode_zprimes -> zprimes ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, n^1). 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 (relative) TRS S consists of the following rules: encArg(cons(x_1)) -> cons(encArg(x_1)) encArg(0) -> 0 encArg(s(x_1)) -> s(encArg(x_1)) encArg(cons_filter(x_1, x_2, x_3)) -> filter(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_sieve(x_1)) -> sieve(encArg(x_1)) encArg(cons_nats(x_1)) -> nats(encArg(x_1)) encArg(cons_zprimes) -> zprimes encode_filter(x_1, x_2, x_3) -> filter(encArg(x_1), encArg(x_2), encArg(x_3)) encode_cons(x_1) -> cons(encArg(x_1)) encode_0 -> 0 encode_s(x_1) -> s(encArg(x_1)) encode_sieve(x_1) -> sieve(encArg(x_1)) encode_nats(x_1) -> nats(encArg(x_1)) encode_zprimes -> zprimes Rewrite Strategy: INNERMOST ---------------------------------------- (3) SInnermostTerminationProof (BOTH CONCRETE BOUNDS(ID, ID)) proved innermost termination of relative rules ---------------------------------------- (4) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, n^1). popout

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actions

all output return to Derivational Complexity: TRS Innermost