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Runti Compl Inner Rewri 22807 pair #381904707
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
n071.star.cs.uiowa.edu
space
Frederiksen_Others
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.549784184 seconds
cpu usage
346.489343825
max memory
5.65950464E9
stage attributes
key
value
output-size
75311
starexec-result
WORST_CASE(Omega(n^1), O(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^1), O(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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^2). (0) CpxRelTRS (1) STerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 164 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) InliningProof [UPPER BOUND(ID), 85 ms] (16) CpxRNTS (17) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] (18) CpxRNTS (19) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms] (20) CpxRNTS (21) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (22) CpxRNTS (23) IntTrsBoundProof [UPPER BOUND(ID), 456 ms] (24) CpxRNTS (25) IntTrsBoundProof [UPPER BOUND(ID), 108 ms] (26) CpxRNTS (27) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (28) CpxRNTS (29) IntTrsBoundProof [UPPER BOUND(ID), 259 ms] (30) CpxRNTS (31) IntTrsBoundProof [UPPER BOUND(ID), 5 ms] (32) CpxRNTS (33) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (34) CpxRNTS (35) IntTrsBoundProof [UPPER BOUND(ID), 3141 ms] (36) CpxRNTS (37) IntTrsBoundProof [UPPER BOUND(ID), 1106 ms] (38) CpxRNTS (39) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (40) CpxRNTS (41) IntTrsBoundProof [UPPER BOUND(ID), 381 ms] (42) CpxRNTS (43) IntTrsBoundProof [UPPER BOUND(ID), 105 ms] (44) CpxRNTS (45) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (46) CpxRNTS (47) IntTrsBoundProof [UPPER BOUND(ID), 351 ms] (48) CpxRNTS (49) IntTrsBoundProof [UPPER BOUND(ID), 176 ms] (50) CpxRNTS (51) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (52) CpxRNTS (53) IntTrsBoundProof [UPPER BOUND(ID), 167 ms] (54) CpxRNTS (55) IntTrsBoundProof [UPPER BOUND(ID), 13 ms] (56) CpxRNTS (57) FinalProof [FINISHED, 0 ms] (58) BOUNDS(1, n^2) (59) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (60) TRS for Loop Detection (61) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] (62) BEST (63) proven lower bound (64) LowerBoundPropagationProof [FINISHED, 0 ms] (65) BOUNDS(n^1, INF) (66) 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:
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