details

property	value
status	complete
benchmark	quicksortPtime.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n148.star.cs.uiowa.edu
space	Frederiksen_Others

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	291.674 seconds
cpu usage	349.352
user time	345.251
system time	4.10049
max virtual memory	5.7207292E7
max residence set size	5652136.0

stage attributes

key	value
starexec-result	WORST_CASE(Omega(n^1), O(n^2))

output

WORST_CASE(Omega(n^1), O(n^2)) proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^2). (0) CpxRelTRS (1) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 321 ms] (2) CpxRelTRS (3) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (4) CpxWeightedTrs (5) CpxWeightedTrsRenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (6) CpxWeightedTrs (7) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (8) CpxTypedWeightedTrs (9) CompletionProof [UPPER BOUND(ID), 0 ms] (10) CpxTypedWeightedCompleteTrs (11) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (12) CpxTypedWeightedCompleteTrs (13) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (14) CpxRNTS (15) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] (16) CpxRNTS (17) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms] (18) CpxRNTS (19) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (20) CpxRNTS (21) IntTrsBoundProof [UPPER BOUND(ID), 167 ms] (22) CpxRNTS (23) IntTrsBoundProof [UPPER BOUND(ID), 57 ms] (24) CpxRNTS (25) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (26) CpxRNTS (27) IntTrsBoundProof [UPPER BOUND(ID), 337 ms] (28) CpxRNTS (29) IntTrsBoundProof [UPPER BOUND(ID), 95 ms] (30) CpxRNTS (31) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (32) CpxRNTS (33) IntTrsBoundProof [UPPER BOUND(ID), 313 ms] (34) CpxRNTS (35) IntTrsBoundProof [UPPER BOUND(ID), 65 ms] (36) CpxRNTS (37) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (38) CpxRNTS (39) IntTrsBoundProof [UPPER BOUND(ID), 271 ms] (40) CpxRNTS (41) IntTrsBoundProof [UPPER BOUND(ID), 24 ms] (42) CpxRNTS (43) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (44) CpxRNTS (45) IntTrsBoundProof [UPPER BOUND(ID), 3143 ms] (46) CpxRNTS (47) IntTrsBoundProof [UPPER BOUND(ID), 1277 ms] (48) CpxRNTS (49) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (50) CpxRNTS (51) IntTrsBoundProof [UPPER BOUND(ID), 472 ms] (52) CpxRNTS (53) IntTrsBoundProof [UPPER BOUND(ID), 246 ms] (54) CpxRNTS (55) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (56) CpxRNTS (57) IntTrsBoundProof [UPPER BOUND(ID), 227 ms] (58) CpxRNTS (59) IntTrsBoundProof [UPPER BOUND(ID), 43 ms] (60) CpxRNTS (61) FinalProof [FINISHED, 0 ms] (62) BOUNDS(1, n^2) (63) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (64) TRS for Loop Detection (65) DecreasingLoopProof [LOWER BOUND(ID), 7 ms] (66) BEST (67) proven lower bound (68) LowerBoundPropagationProof [FINISHED, 0 ms] (69) BOUNDS(n^1, INF) (70) TRS for Loop Detection ---------------------------------------- (0) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^2). The TRS R consists of the following rules: qs(x', Cons(x, xs)) -> app(Cons(x, Nil), Cons(x', quicksort(xs))) quicksort(Cons(x, Cons(x', xs))) -> qs(x, part(x, Cons(x', xs), Nil, Nil)) quicksort(Cons(x, Nil)) -> Cons(x, Nil) quicksort(Nil) -> Nil part(x', Cons(x, xs), xs1, xs2) -> part[Ite](>(x', x), x', Cons(x, xs), xs1, xs2) part(x, Nil, xs1, xs2) -> app(xs1, xs2) app(Cons(x, xs), ys) -> Cons(x, app(xs, ys)) app(Nil, ys) -> ys notEmpty(Cons(x, xs)) -> True notEmpty(Nil) -> False popout

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

job log

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actions

all output return to Runtime Complexity: TRS Innermost