details

property	value
status	complete
benchmark	2.42.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	SK90

run statistics

property	value
solver	AProVE
configuration	rcdcRelativeAlsoLower
runtime (wallclock)	291.893 seconds
cpu usage	1075.7
user time	1062.41
system time	13.2937
max virtual memory	3.7508396E7
max residence set size	1.5168404E7

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (full) of the given DCpxTrs could be proven to be BOUNDS(n^1, INF).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), 168 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), 230 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), 82 ms] (18) BOUNDS(1, INF) ---------------------------------------- (0) Obligation: The Derivational Complexity (full) of the given DCpxTrs could be proven to be BOUNDS(n^1, INF). The TRS R consists of the following rules: flatten(nil) -> nil flatten(unit(x)) -> flatten(x) flatten(++(x, y)) -> ++(flatten(x), flatten(y)) flatten(++(unit(x), y)) -> ++(flatten(x), flatten(y)) flatten(flatten(x)) -> flatten(x) rev(nil) -> nil rev(unit(x)) -> unit(x) rev(++(x, y)) -> ++(rev(y), rev(x)) rev(rev(x)) -> x ++(x, nil) -> x ++(nil, y) -> y ++(++(x, y), z) -> ++(x, ++(y, z)) S is empty. Rewrite Strategy: FULL ---------------------------------------- (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(nil) -> nil encArg(unit(x_1)) -> unit(encArg(x_1)) encArg(cons_flatten(x_1)) -> flatten(encArg(x_1)) encArg(cons_rev(x_1)) -> rev(encArg(x_1)) encArg(cons_++(x_1, x_2)) -> ++(encArg(x_1), encArg(x_2)) encode_flatten(x_1) -> flatten(encArg(x_1)) encode_nil -> nil encode_unit(x_1) -> unit(encArg(x_1)) encode_++(x_1, x_2) -> ++(encArg(x_1), encArg(x_2)) encode_rev(x_1) -> rev(encArg(x_1)) ---------------------------------------- (2) Obligation: The Runtime Complexity (full) of the given CpxRelTRS could be proven to be BOUNDS(n^1, INF). The TRS R consists of the following rules: flatten(nil) -> nil flatten(unit(x)) -> flatten(x) flatten(++(x, y)) -> ++(flatten(x), flatten(y)) flatten(++(unit(x), y)) -> ++(flatten(x), flatten(y)) flatten(flatten(x)) -> flatten(x) rev(nil) -> nil rev(unit(x)) -> unit(x) rev(++(x, y)) -> ++(rev(y), rev(x)) rev(rev(x)) -> x ++(x, nil) -> x ++(nil, y) -> y ++(++(x, y), z) -> ++(x, ++(y, z)) The (relative) TRS S consists of the following rules: encArg(nil) -> nil encArg(unit(x_1)) -> unit(encArg(x_1)) encArg(cons_flatten(x_1)) -> flatten(encArg(x_1)) encArg(cons_rev(x_1)) -> rev(encArg(x_1)) encArg(cons_++(x_1, x_2)) -> ++(encArg(x_1), encArg(x_2)) encode_flatten(x_1) -> flatten(encArg(x_1)) encode_nil -> nil popout

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

job log

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actions

all output return to Derivational Complexity: TRS