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	n140.star.cs.uiowa.edu
space	Frederiksen_Glenstrup

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	291.636 seconds
cpu usage	1115.49
user time	1101.25
system time	14.239
max virtual memory	3.804342E7
max residence set size	1.5019852E7

stage attributes

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

output

WORST_CASE(Omega(n^1), ?) 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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, INF). (0) CpxRelTRS (1) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 373 ms] (2) CpxRelTRS (3) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (4) CpxRelTRS (5) SlicingProof [LOWER BOUND(ID), 0 ms] (6) CpxRelTRS (7) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (8) typed CpxTrs (9) OrderProof [LOWER BOUND(ID), 0 ms] (10) typed CpxTrs (11) RewriteLemmaProof [LOWER BOUND(ID), 248 ms] (12) typed CpxTrs (13) RewriteLemmaProof [LOWER BOUND(ID), 69 ms] (14) BEST (15) proven lower bound (16) LowerBoundPropagationProof [FINISHED, 0 ms] (17) BOUNDS(n^1, INF) (18) typed CpxTrs (19) RewriteLemmaProof [LOWER BOUND(ID), 47 ms] (20) 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, Cons(x', xs)), Cons(x, Nil), Nil) quicksort(Cons(x, Nil)) -> Cons(x, Nil) quicksort(Nil) -> Nil part(x', Cons(x, xs), xs1, xs2) -> part[Ite][True][Ite](>(x', x), x', Cons(x, xs), xs1, xs2) part(x, Nil, xs1, xs2) -> app(quicksort(xs1), quicksort(xs2)) app(Cons(x, xs), ys) -> Cons(x, app(xs, ys)) app(Nil, ys) -> ys notEmpty(Cons(x, xs)) -> True notEmpty(Nil) -> False 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 part[Ite][True][Ite](True, x', Cons(x, xs), xs1, xs2) -> part(x', xs, Cons(x, xs1), xs2) part[Ite][True][Ite](False, x', Cons(x, xs), xs1, xs2) -> part[Ite][True][Ite][False][Ite](<(x', x), x', Cons(x, xs), xs1, xs2) Rewrite Strategy: INNERMOST ---------------------------------------- (1) SInnermostTerminationProof (BOTH CONCRETE BOUNDS(ID, ID)) proved innermost 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, Cons(x', xs)), Cons(x, Nil), Nil) quicksort(Cons(x, Nil)) -> Cons(x, Nil) quicksort(Nil) -> Nil part(x', Cons(x, xs), xs1, xs2) -> part[Ite][True][Ite](>(x', x), x', Cons(x, xs), xs1, xs2) part(x, Nil, xs1, xs2) -> app(quicksort(xs1), quicksort(xs2)) app(Cons(x, xs), ys) -> Cons(x, app(xs, ys)) app(Nil, ys) -> ys notEmpty(Cons(x, xs)) -> True notEmpty(Nil) -> False 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 part[Ite][True][Ite](True, x', Cons(x, xs), xs1, xs2) -> part(x', xs, Cons(x, xs1), xs2) part[Ite][True][Ite](False, x', Cons(x, xs), xs1, xs2) -> part[Ite][True][Ite][False][Ite](<(x', x), x', Cons(x, xs), xs1, xs2) Rewrite Strategy: INNERMOST ---------------------------------------- popout

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

job log

popout

actions

all output return to Runtime Complexity: TRS Innermost