details

property	value
status	complete
benchmark	bubblesort.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n147.star.cs.uiowa.edu
space	Frederiksen_Others

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	291.603 seconds
cpu usage	344.612
user time	340.821
system time	3.79087
max virtual memory	1.9379596E7
max residence set size	5748528.0

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^2).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), 160 ms] (2) CpxRelTRS (3) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] (4) CdtProblem (5) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (6) CdtProblem (7) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (8) CdtProblem (9) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms] (10) CdtProblem (11) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms] (12) CdtProblem (13) CdtKnowledgeProof [BOTH BOUNDS(ID, ID), 0 ms] (14) CdtProblem (15) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms] (16) CdtProblem (17) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 79 ms] (18) CdtProblem (19) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 40 ms] (20) CdtProblem (21) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 22 ms] (22) CdtProblem (23) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 180 ms] (24) CdtProblem (25) SIsEmptyProof [BOTH BOUNDS(ID, ID), 0 ms] (26) BOUNDS(1, 1) (27) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (28) TRS for Loop Detection (29) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] (30) BEST (31) proven lower bound (32) LowerBoundPropagationProof [FINISHED, 0 ms] (33) BOUNDS(n^1, INF) (34) 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: bsort(S(x'), Cons(x, xs)) -> bsort(x', bubble(x, xs)) len(Cons(x, xs)) -> +(S(0), len(xs)) bubble(x', Cons(x, xs)) -> bubble[Ite][False][Ite](<(x', x), x', Cons(x, xs)) len(Nil) -> 0 bubble(x, Nil) -> Cons(x, Nil) bsort(0, xs) -> xs bubblesort(xs) -> bsort(len(xs), xs) The (relative) TRS S consists of the following rules: +(x, S(0)) -> S(x) +(S(0), y) -> S(y) <(S(x), S(y)) -> <(x, y) <(0, S(y)) -> True <(x, 0) -> False bubble[Ite][False][Ite](False, x', Cons(x, xs)) -> Cons(x, bubble(x', xs)) bubble[Ite][False][Ite](True, x', Cons(x, xs)) -> Cons(x', bubble(x, xs)) 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, n^2). The TRS R consists of the following rules: bsort(S(x'), Cons(x, xs)) -> bsort(x', bubble(x, xs)) len(Cons(x, xs)) -> +(S(0), len(xs)) bubble(x', Cons(x, xs)) -> bubble[Ite][False][Ite](<(x', x), x', Cons(x, xs)) len(Nil) -> 0 bubble(x, Nil) -> Cons(x, Nil) bsort(0, xs) -> xs bubblesort(xs) -> bsort(len(xs), xs) The (relative) TRS S consists of the following rules: +(x, S(0)) -> S(x) +(S(0), y) -> S(y) <(S(x), S(y)) -> <(x, y) <(0, S(y)) -> True <(x, 0) -> 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