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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313866
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
n080.star.cs.uiowa.edu
space
Frederiksen_Others
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.575 seconds
cpu usage
348.195
user time
344.755
system time
3.44006
max virtual memory
3.804208E7
max residence set size
5495940.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^2))
output
348.07/291.51 WORST_CASE(Omega(n^1), O(n^2)) 348.07/291.52 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 348.07/291.52 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 348.07/291.52 348.07/291.52 348.07/291.52 The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^2). 348.07/291.52 348.07/291.52 (0) CpxRelTRS 348.07/291.52 (1) STerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 159 ms] 348.07/291.52 (2) CpxRelTRS 348.07/291.52 (3) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] 348.07/291.52 (4) CdtProblem 348.07/291.52 (5) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] 348.07/291.52 (6) CdtProblem 348.07/291.52 (7) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] 348.07/291.52 (8) CdtProblem 348.07/291.52 (9) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms] 348.07/291.52 (10) CdtProblem 348.07/291.52 (11) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms] 348.07/291.52 (12) CdtProblem 348.07/291.52 (13) CdtKnowledgeProof [BOTH BOUNDS(ID, ID), 0 ms] 348.07/291.52 (14) CdtProblem 348.07/291.52 (15) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms] 348.07/291.52 (16) CdtProblem 348.07/291.52 (17) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 54 ms] 348.07/291.52 (18) CdtProblem 348.07/291.52 (19) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 24 ms] 348.07/291.52 (20) CdtProblem 348.07/291.52 (21) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 23 ms] 348.07/291.52 (22) CdtProblem 348.07/291.52 (23) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 67 ms] 348.07/291.52 (24) CdtProblem 348.07/291.52 (25) SIsEmptyProof [BOTH BOUNDS(ID, ID), 0 ms] 348.07/291.52 (26) BOUNDS(1, 1) 348.07/291.52 (27) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 348.07/291.52 (28) TRS for Loop Detection 348.07/291.52 (29) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 348.07/291.52 (30) BEST 348.07/291.52 (31) proven lower bound 348.07/291.52 (32) LowerBoundPropagationProof [FINISHED, 0 ms] 348.07/291.52 (33) BOUNDS(n^1, INF) 348.07/291.52 (34) TRS for Loop Detection 348.07/291.52 348.07/291.52 348.07/291.52 ---------------------------------------- 348.07/291.52 348.07/291.52 (0) 348.07/291.52 Obligation: 348.07/291.52 The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^2). 348.07/291.52 348.07/291.52 348.07/291.52 The TRS R consists of the following rules: 348.07/291.52 348.07/291.52 bsort(S(x'), Cons(x, xs)) -> bsort(x', bubble(x, xs)) 348.07/291.52 len(Cons(x, xs)) -> +(S(0), len(xs)) 348.07/291.52 bubble(x', Cons(x, xs)) -> bubble[Ite][False][Ite](<(x', x), x', Cons(x, xs)) 348.07/291.52 len(Nil) -> 0 348.07/291.52 bubble(x, Nil) -> Cons(x, Nil) 348.07/291.52 bsort(0, xs) -> xs 348.07/291.52 bubblesort(xs) -> bsort(len(xs), xs) 348.07/291.52 348.07/291.52 The (relative) TRS S consists of the following rules: 348.07/291.52 348.07/291.52 +(x, S(0)) -> S(x) 348.07/291.52 +(S(0), y) -> S(y) 348.07/291.52 <(S(x), S(y)) -> <(x, y) 348.07/291.52 <(0, S(y)) -> True 348.07/291.52 <(x, 0) -> False 348.07/291.52 bubble[Ite][False][Ite](False, x', Cons(x, xs)) -> Cons(x, bubble(x', xs)) 348.07/291.52 bubble[Ite][False][Ite](True, x', Cons(x, xs)) -> Cons(x', bubble(x, xs)) 348.07/291.52 348.07/291.52 Rewrite Strategy: INNERMOST 348.07/291.52 ---------------------------------------- 348.07/291.52 348.07/291.52 (1) STerminationProof (BOTH CONCRETE BOUNDS(ID, ID)) 348.07/291.52 proved termination of relative rules 348.07/291.52 ---------------------------------------- 348.07/291.52 348.07/291.52 (2) 348.07/291.52 Obligation: 348.07/291.52 The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^2). 348.07/291.52 348.07/291.52 348.07/291.52 The TRS R consists of the following rules: 348.07/291.52 348.07/291.52 bsort(S(x'), Cons(x, xs)) -> bsort(x', bubble(x, xs)) 348.07/291.52 len(Cons(x, xs)) -> +(S(0), len(xs)) 348.07/291.52 bubble(x', Cons(x, xs)) -> bubble[Ite][False][Ite](<(x', x), x', Cons(x, xs)) 348.07/291.52 len(Nil) -> 0 348.07/291.52 bubble(x, Nil) -> Cons(x, Nil) 348.07/291.52 bsort(0, xs) -> xs 348.07/291.52 bubblesort(xs) -> bsort(len(xs), xs) 348.07/291.52 348.07/291.52 The (relative) TRS S consists of the following rules: 348.07/291.52 348.07/291.52 +(x, S(0)) -> S(x) 348.07/291.52 +(S(0), y) -> S(y) 348.07/291.52 <(S(x), S(y)) -> <(x, y) 348.07/291.52 <(0, S(y)) -> True 348.07/291.52 <(x, 0) -> False
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