details

property	value
status	complete
benchmark	aprove06.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n148.star.cs.uiowa.edu
space	Secret_07_TRS

run statistics

property	value
solver	AProVE
configuration	rcdcRelativeAlsoLower
runtime (wallclock)	291.729 seconds
cpu usage	1145.53
user time	1135.24
system time	10.29
max virtual memory	1.9854148E7
max residence set size	1.50991E7

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, INF).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), 517 ms] (4) CpxRelTRS (5) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (6) TRS for Loop Detection (7) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] (8) BEST (9) proven lower bound (10) LowerBoundPropagationProof [FINISHED, 0 ms] (11) BOUNDS(n^1, INF) (12) TRS for Loop Detection ---------------------------------------- (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: le(s(x), 0) -> false le(0, y) -> true le(s(x), s(y)) -> le(x, y) double(0) -> 0 double(s(x)) -> s(s(double(x))) log(0) -> logError log(s(x)) -> loop(s(x), s(0), 0) loop(x, s(y), z) -> if(le(x, s(y)), x, s(y), z) if(true, x, y, z) -> z if(false, x, y, z) -> loop(x, double(y), s(z)) maplog(xs) -> mapIter(xs, nil) mapIter(xs, ys) -> ifmap(isempty(xs), xs, ys) ifmap(true, xs, ys) -> ys ifmap(false, xs, ys) -> mapIter(droplast(xs), cons(log(last(xs)), ys)) isempty(nil) -> true isempty(cons(x, xs)) -> false last(nil) -> error last(cons(x, nil)) -> x last(cons(x, cons(y, xs))) -> last(cons(y, xs)) droplast(nil) -> nil droplast(cons(x, nil)) -> nil droplast(cons(x, cons(y, xs))) -> cons(x, droplast(cons(y, xs))) a -> b a -> c 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(s(x_1)) -> s(encArg(x_1)) encArg(0) -> 0 encArg(false) -> false encArg(true) -> true encArg(logError) -> logError encArg(nil) -> nil encArg(cons(x_1, x_2)) -> cons(encArg(x_1), encArg(x_2)) encArg(error) -> error encArg(b) -> b encArg(c) -> c encArg(cons_le(x_1, x_2)) -> le(encArg(x_1), encArg(x_2)) encArg(cons_double(x_1)) -> double(encArg(x_1)) encArg(cons_log(x_1)) -> log(encArg(x_1)) encArg(cons_loop(x_1, x_2, x_3)) -> loop(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_if(x_1, x_2, x_3, x_4)) -> if(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4)) encArg(cons_maplog(x_1)) -> maplog(encArg(x_1)) encArg(cons_mapIter(x_1, x_2)) -> mapIter(encArg(x_1), encArg(x_2)) encArg(cons_ifmap(x_1, x_2, x_3)) -> ifmap(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_isempty(x_1)) -> isempty(encArg(x_1)) encArg(cons_last(x_1)) -> last(encArg(x_1)) encArg(cons_droplast(x_1)) -> droplast(encArg(x_1)) encArg(cons_a) -> a encode_le(x_1, x_2) -> le(encArg(x_1), encArg(x_2)) encode_s(x_1) -> s(encArg(x_1)) encode_0 -> 0 encode_false -> false encode_true -> true encode_double(x_1) -> double(encArg(x_1)) encode_log(x_1) -> log(encArg(x_1)) encode_logError -> logError encode_loop(x_1, x_2, x_3) -> loop(encArg(x_1), encArg(x_2), encArg(x_3)) encode_if(x_1, x_2, x_3, x_4) -> if(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4)) encode_maplog(x_1) -> maplog(encArg(x_1)) encode_mapIter(x_1, x_2) -> mapIter(encArg(x_1), encArg(x_2)) encode_nil -> nil encode_ifmap(x_1, x_2, x_3) -> ifmap(encArg(x_1), encArg(x_2), encArg(x_3)) encode_isempty(x_1) -> isempty(encArg(x_1)) popout

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

job log

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actions

all output return to Derivational Complexity: TRS Innermost