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Runti Compl Inner Rewri 22807 pair #381904367
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
n071.star.cs.uiowa.edu
space
AProVE_06
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.57015419 seconds
cpu usage
1143.61153358
max memory
1.5988658176E10
stage attributes
key
value
output-size
25295
starexec-result
WORST_CASE(Omega(n^2), ?)
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^2), ?) proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^2, INF).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), 262 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), 102 ms] (14) typed CpxTrs (15) RewriteLemmaProof [LOWER BOUND(ID), 70 ms] (16) typed CpxTrs (17) RewriteLemmaProof [LOWER BOUND(ID), 65 ms] (18) typed CpxTrs (19) RewriteLemmaProof [LOWER BOUND(ID), 225 ms] (20) proven lower bound (21) LowerBoundPropagationProof [FINISHED, 0 ms] (22) BOUNDS(n^2, INF) ---------------------------------------- (0) Obligation: The Runtime Complexity (innermost) 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: INNERMOST ---------------------------------------- (1) RenamingProof (BOTH BOUNDS(ID, ID)) Renamed function symbols to avoid clashes with predefined symbol. ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) 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
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