details

property	value
status	complete
benchmark	quick.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n149.star.cs.uiowa.edu
space	Rubio_04

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	291.611 seconds
cpu usage	309.44
user time	307.594
system time	1.84649
max virtual memory	1.828166E7
max residence set size	5221860.0

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^2, INF).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), 239 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), 60 ms] (14) typed CpxTrs (15) RewriteLemmaProof [LOWER BOUND(ID), 34 ms] (16) typed CpxTrs (17) RewriteLemmaProof [LOWER BOUND(ID), 25 ms] (18) typed CpxTrs (19) RewriteLemmaProof [LOWER BOUND(ID), 29 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(cons(N, L), Y) -> cons(N, app(L, Y)) low(N, nil) -> nil low(N, cons(M, L)) -> iflow(le(M, N), N, cons(M, L)) iflow(true, N, cons(M, L)) -> cons(M, low(N, L)) iflow(false, N, cons(M, L)) -> low(N, L) high(N, nil) -> nil high(N, cons(M, L)) -> ifhigh(le(M, N), N, cons(M, L)) ifhigh(true, N, cons(M, L)) -> high(N, L) ifhigh(false, N, cons(M, L)) -> cons(M, high(N, L)) quicksort(nil) -> nil quicksort(cons(N, L)) -> app(quicksort(low(N, L)), cons(N, quicksort(high(N, L)))) 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(cons(N, L), Y) -> cons(N, app(L, Y)) low(N, nil) -> nil low(N, cons(M, L)) -> iflow(le(M, N), N, cons(M, L)) iflow(true, N, cons(M, L)) -> cons(M, low(N, L)) iflow(false, N, cons(M, L)) -> low(N, L) high(N, nil) -> nil high(N, cons(M, L)) -> ifhigh(le(M, N), N, cons(M, L)) ifhigh(true, N, cons(M, L)) -> high(N, L) ifhigh(false, N, cons(M, L)) -> cons(M, high(N, L)) quicksort(nil) -> nil quicksort(cons(N, L)) -> app(quicksort(low(N, L)), cons(N, quicksort(high(N, L)))) S is empty. Rewrite Strategy: FULL ---------------------------------------- (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (4) Obligation: TRS: Rules: popout

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

job log

popout

actions

all output return to Runtime Complexity: TRS