details

property	value
status	complete
benchmark	quicksortSize.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n026.star.cs.uiowa.edu
space	Frederiksen_Others

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	291.578654051 seconds
cpu usage	1126.82393873
max memory	1.5440392192E10

stage attributes

key	value
output-size	27114
starexec-result	WORST_CASE(Omega(n^1), ?)

output

/export/starexec/sandbox2/solver/bin/starexec_run_complexity /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^1), ?) proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, INF). (0) CpxRelTRS (1) STerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 159 ms] (2) CpxRelTRS (3) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (4) CpxRelTRS (5) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (6) typed CpxTrs (7) OrderProof [LOWER BOUND(ID), 0 ms] (8) typed CpxTrs (9) RewriteLemmaProof [LOWER BOUND(ID), 306 ms] (10) typed CpxTrs (11) RewriteLemmaProof [LOWER BOUND(ID), 36 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), 46 ms] (18) typed CpxTrs (19) RewriteLemmaProof [LOWER BOUND(ID), 41 ms] (20) typed CpxTrs (21) RewriteLemmaProof [LOWER BOUND(ID), 75 ms] (22) typed CpxTrs ---------------------------------------- (0) 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: quicksort(Cons(x, Cons(x', xs))) -> part(x, Cons(x', xs)) quicksort(Cons(x, Nil)) -> Cons(x, Nil) quicksort(Nil) -> Nil partLt(x', Cons(x, xs)) -> partLt[Ite][True][Ite](<(x, x'), x', Cons(x, xs)) partLt(x, Nil) -> Nil partGt(x', Cons(x, xs)) -> partGt[Ite][True][Ite](>(x, x'), x', Cons(x, xs)) partGt(x, Nil) -> Nil app(Cons(x, xs), ys) -> Cons(x, app(xs, ys)) app(Nil, ys) -> ys notEmpty(Cons(x, xs)) -> True notEmpty(Nil) -> False part(x, xs) -> app(quicksort(partLt(x, xs)), Cons(x, quicksort(partGt(x, xs)))) goal(xs) -> quicksort(xs) The (relative) TRS S consists of the following rules: <(S(x), S(y)) -> <(x, y) <(0, S(y)) -> True <(x, 0) -> False >(S(x), S(y)) -> >(x, y) >(0, y) -> False >(S(x), 0) -> True partLt[Ite][True][Ite](True, x', Cons(x, xs)) -> Cons(x, partLt(x', xs)) partGt[Ite][True][Ite](True, x', Cons(x, xs)) -> Cons(x, partGt(x', xs)) partLt[Ite][True][Ite](False, x', Cons(x, xs)) -> partLt(x', xs) partGt[Ite][True][Ite](False, x', Cons(x, xs)) -> partGt(x', xs) Rewrite Strategy: INNERMOST ---------------------------------------- (1) STerminationProof (BOTH CONCRETE BOUNDS(ID, ID)) proved termination of relative rules ---------------------------------------- (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: quicksort(Cons(x, Cons(x', xs))) -> part(x, Cons(x', xs)) quicksort(Cons(x, Nil)) -> Cons(x, Nil) quicksort(Nil) -> Nil partLt(x', Cons(x, xs)) -> partLt[Ite][True][Ite](<(x, x'), x', Cons(x, xs)) partLt(x, Nil) -> Nil partGt(x', Cons(x, xs)) -> partGt[Ite][True][Ite](>(x, x'), x', Cons(x, xs)) partGt(x, Nil) -> Nil app(Cons(x, xs), ys) -> Cons(x, app(xs, ys)) app(Nil, ys) -> ys notEmpty(Cons(x, xs)) -> True notEmpty(Nil) -> False part(x, xs) -> app(quicksort(partLt(x, xs)), Cons(x, quicksort(partGt(x, xs)))) popout

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job log

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actions

all output return to Runti Compl Inner Rewri 22807