details

property	value
status	complete
benchmark	aprove07.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	Secret_07_TRS

run statistics

property	value
solver	AProVE
configuration	rcdcRelativeAlsoLower
runtime (wallclock)	296.606 seconds
cpu usage	1162.85
user time	1152.29
system time	10.5601
max virtual memory	1.9662784E7
max residence set size	1.5027E7

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, INF).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), 705 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: plus(x, y) -> plusIter(x, y, 0) plusIter(x, y, z) -> ifPlus(le(x, z), x, y, z) ifPlus(true, x, y, z) -> y ifPlus(false, x, y, z) -> plusIter(x, s(y), s(z)) le(s(x), 0) -> false le(0, y) -> true le(s(x), s(y)) -> le(x, y) sum(xs) -> sumIter(xs, 0) sumIter(xs, x) -> ifSum(isempty(xs), xs, x, plus(x, head(xs))) ifSum(true, xs, x, y) -> x ifSum(false, xs, x, y) -> sumIter(tail(xs), y) isempty(nil) -> true isempty(cons(x, xs)) -> false head(nil) -> error head(cons(x, xs)) -> x tail(nil) -> nil tail(cons(x, xs)) -> 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(0) -> 0 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(error) -> error encArg(b) -> b encArg(c) -> c encArg(cons_plus(x_1, x_2)) -> plus(encArg(x_1), encArg(x_2)) encArg(cons_plusIter(x_1, x_2, x_3)) -> plusIter(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_ifPlus(x_1, x_2, x_3, x_4)) -> ifPlus(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4)) encArg(cons_le(x_1, x_2)) -> le(encArg(x_1), encArg(x_2)) encArg(cons_sum(x_1)) -> sum(encArg(x_1)) encArg(cons_sumIter(x_1, x_2)) -> sumIter(encArg(x_1), encArg(x_2)) encArg(cons_ifSum(x_1, x_2, x_3, x_4)) -> ifSum(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4)) encArg(cons_isempty(x_1)) -> isempty(encArg(x_1)) encArg(cons_head(x_1)) -> head(encArg(x_1)) encArg(cons_tail(x_1)) -> tail(encArg(x_1)) encArg(cons_a) -> a encode_plus(x_1, x_2) -> plus(encArg(x_1), encArg(x_2)) encode_plusIter(x_1, x_2, x_3) -> plusIter(encArg(x_1), encArg(x_2), encArg(x_3)) encode_0 -> 0 encode_ifPlus(x_1, x_2, x_3, x_4) -> ifPlus(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4)) encode_le(x_1, x_2) -> le(encArg(x_1), encArg(x_2)) encode_true -> true encode_false -> false encode_s(x_1) -> s(encArg(x_1)) encode_sum(x_1) -> sum(encArg(x_1)) encode_sumIter(x_1, x_2) -> sumIter(encArg(x_1), encArg(x_2)) encode_ifSum(x_1, x_2, x_3, x_4) -> ifSum(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4)) encode_isempty(x_1) -> isempty(encArg(x_1)) encode_head(x_1) -> head(encArg(x_1)) encode_tail(x_1) -> tail(encArg(x_1)) encode_nil -> nil encode_cons(x_1, x_2) -> cons(encArg(x_1), encArg(x_2)) encode_error -> error encode_a -> a encode_b -> b encode_c -> c popout

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

job log

popout

actions

all output return to Derivational Complexity: TRS Innermost