details

property	value
status	complete
benchmark	cade16.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n144.star.cs.uiowa.edu
space	GTSSK07

run statistics

property	value
solver	AProVE
configuration	rcdcRelativeAlsoLower
runtime (wallclock)	295.063 seconds
cpu usage	1148.9
user time	1137.7
system time	11.1979
max virtual memory	3.794938E7
max residence set size	1.516524E7

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, INF).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), 274 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), 522 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), 706 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: nthtail(n, l) -> cond(ge(n, length(l)), n, l) cond(true, n, l) -> l cond(false, n, l) -> tail(nthtail(s(n), l)) tail(nil) -> nil tail(cons(x, l)) -> l length(nil) -> 0 length(cons(x, l)) -> s(length(l)) ge(u, 0) -> true ge(0, s(v)) -> false ge(s(u), s(v)) -> ge(u, v) 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(true) -> true encArg(false) -> false encArg(s(x_1)) -> s(encArg(x_1)) encArg(nil) -> nil encArg(cons(x_1, x_2)) -> cons(encArg(x_1), encArg(x_2)) encArg(0) -> 0 encArg(cons_nthtail(x_1, x_2)) -> nthtail(encArg(x_1), encArg(x_2)) encArg(cons_cond(x_1, x_2, x_3)) -> cond(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_tail(x_1)) -> tail(encArg(x_1)) encArg(cons_length(x_1)) -> length(encArg(x_1)) encArg(cons_ge(x_1, x_2)) -> ge(encArg(x_1), encArg(x_2)) encode_nthtail(x_1, x_2) -> nthtail(encArg(x_1), encArg(x_2)) encode_cond(x_1, x_2, x_3) -> cond(encArg(x_1), encArg(x_2), encArg(x_3)) encode_ge(x_1, x_2) -> ge(encArg(x_1), encArg(x_2)) encode_length(x_1) -> length(encArg(x_1)) encode_true -> true encode_false -> false encode_tail(x_1) -> tail(encArg(x_1)) encode_s(x_1) -> s(encArg(x_1)) encode_nil -> nil encode_cons(x_1, x_2) -> cons(encArg(x_1), encArg(x_2)) encode_0 -> 0 ---------------------------------------- (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: nthtail(n, l) -> cond(ge(n, length(l)), n, l) cond(true, n, l) -> l cond(false, n, l) -> tail(nthtail(s(n), l)) tail(nil) -> nil tail(cons(x, l)) -> l length(nil) -> 0 length(cons(x, l)) -> s(length(l)) ge(u, 0) -> true ge(0, s(v)) -> false ge(s(u), s(v)) -> ge(u, v) The (relative) TRS S consists of the following rules: popout

output may be truncated. 'popout' for the full output.

job log

popout

actions

all output return to Derivational Complexity: TRS Innermost