details

property	value
status	complete
benchmark	quicksort.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n137.star.cs.uiowa.edu
space	AProVE_06

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	291.601 seconds
cpu usage	310.466
user time	308.74
system time	1.72601
max virtual memory	1.8281728E7
max residence set size	5261792.0

stage attributes

key	value
starexec-result	WORST_CASE(Omega(n^2), ?)

output

WORST_CASE(Omega(n^2), ?) proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). (0) CpxTRS (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxTRS (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (4) typed CpxTrs (5) OrderProof [LOWER BOUND(ID), 0 ms] (6) typed CpxTrs (7) RewriteLemmaProof [LOWER BOUND(ID), 274 ms] (8) BEST (9) proven lower bound (10) LowerBoundPropagationProof [FINISHED, 0 ms] (11) BOUNDS(n^1, INF) (12) typed CpxTrs (13) RewriteLemmaProof [LOWER BOUND(ID), 71 ms] (14) typed CpxTrs (15) RewriteLemmaProof [LOWER BOUND(ID), 49 ms] (16) typed CpxTrs (17) RewriteLemmaProof [LOWER BOUND(ID), 23 ms] (18) typed CpxTrs (19) RewriteLemmaProof [LOWER BOUND(ID), 139 ms] (20) proven lower bound (21) LowerBoundPropagationProof [FINISHED, 0 ms] (22) BOUNDS(n^2, INF) ---------------------------------------- (0) Obligation: The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). The TRS R consists of the following rules: le(0, y) -> true le(s(x), 0) -> false le(s(x), s(y)) -> le(x, y) app(nil, y) -> y app(add(n, x), y) -> add(n, app(x, y)) low(n, nil) -> nil low(n, add(m, x)) -> if_low(le(m, n), n, add(m, x)) if_low(true, n, add(m, x)) -> add(m, low(n, x)) if_low(false, n, add(m, x)) -> low(n, x) high(n, nil) -> nil high(n, add(m, x)) -> if_high(le(m, n), n, add(m, x)) if_high(true, n, add(m, x)) -> high(n, x) if_high(false, n, add(m, x)) -> add(m, high(n, x)) head(add(n, x)) -> n tail(add(n, x)) -> x isempty(nil) -> true isempty(add(n, x)) -> false quicksort(x) -> if_qs(isempty(x), low(head(x), tail(x)), head(x), high(head(x), tail(x))) if_qs(true, x, n, y) -> nil if_qs(false, x, n, y) -> app(quicksort(x), add(n, quicksort(y))) S is empty. Rewrite Strategy: FULL ---------------------------------------- (1) RenamingProof (BOTH BOUNDS(ID, ID)) Renamed function symbols to avoid clashes with predefined symbol. ---------------------------------------- (2) Obligation: The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). The TRS R consists of the following rules: le(0', y) -> true le(s(x), 0') -> false le(s(x), s(y)) -> le(x, y) app(nil, y) -> y app(add(n, x), y) -> add(n, app(x, y)) low(n, nil) -> nil low(n, add(m, x)) -> if_low(le(m, n), n, add(m, x)) if_low(true, n, add(m, x)) -> add(m, low(n, x)) if_low(false, n, add(m, x)) -> low(n, x) high(n, nil) -> nil high(n, add(m, x)) -> if_high(le(m, n), n, add(m, x)) if_high(true, n, add(m, x)) -> high(n, x) if_high(false, n, add(m, x)) -> add(m, high(n, x)) head(add(n, x)) -> n tail(add(n, x)) -> x isempty(nil) -> true isempty(add(n, x)) -> false quicksort(x) -> if_qs(isempty(x), low(head(x), tail(x)), head(x), high(head(x), tail(x))) if_qs(true, x, n, y) -> nil if_qs(false, x, n, y) -> app(quicksort(x), add(n, quicksort(y))) S is empty. Rewrite Strategy: FULL popout

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actions

all output return to Runtime Complexity: TRS