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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313703
details
property
value
status
complete
benchmark
otto03.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n182.star.cs.uiowa.edu
space
AProVE_07
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.499 seconds
cpu usage
884.106
user time
880.077
system time
4.02903
max virtual memory
5.699752E7
max residence set size
5422428.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^2))
output
883.94/291.44 WORST_CASE(Omega(n^1), O(n^2)) 884.02/291.45 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 884.02/291.45 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 884.02/291.45 884.02/291.45 884.02/291.45 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 884.02/291.45 884.02/291.45 (0) CpxTRS 884.02/291.45 (1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 884.02/291.45 (2) CpxWeightedTrs 884.02/291.45 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 884.02/291.45 (4) CpxTypedWeightedTrs 884.02/291.45 (5) CompletionProof [UPPER BOUND(ID), 0 ms] 884.02/291.45 (6) CpxTypedWeightedCompleteTrs 884.02/291.45 (7) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] 884.02/291.45 (8) CpxRNTS 884.02/291.45 (9) CompleteCoflocoProof [FINISHED, 319 ms] 884.02/291.45 (10) BOUNDS(1, n^2) 884.02/291.45 (11) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 884.02/291.45 (12) TRS for Loop Detection 884.02/291.45 (13) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 884.02/291.45 (14) BEST 884.02/291.45 (15) proven lower bound 884.02/291.45 (16) LowerBoundPropagationProof [FINISHED, 0 ms] 884.02/291.45 (17) BOUNDS(n^1, INF) 884.02/291.45 (18) TRS for Loop Detection 884.02/291.45 884.02/291.45 884.02/291.45 ---------------------------------------- 884.02/291.45 884.02/291.45 (0) 884.02/291.45 Obligation: 884.02/291.45 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 884.02/291.45 884.02/291.45 884.02/291.45 The TRS R consists of the following rules: 884.02/291.45 884.02/291.45 lt(0, s(x)) -> true 884.02/291.45 lt(x, 0) -> false 884.02/291.45 lt(s(x), s(y)) -> lt(x, y) 884.02/291.45 fac(x) -> help(x, 0) 884.02/291.45 help(x, c) -> if(lt(c, x), x, c) 884.02/291.45 if(true, x, c) -> times(s(c), help(x, s(c))) 884.02/291.45 if(false, x, c) -> s(0) 884.02/291.45 884.02/291.45 S is empty. 884.02/291.45 Rewrite Strategy: INNERMOST 884.02/291.45 ---------------------------------------- 884.02/291.45 884.02/291.45 (1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) 884.02/291.45 Transformed relative TRS to weighted TRS 884.02/291.45 ---------------------------------------- 884.02/291.45 884.02/291.45 (2) 884.02/291.45 Obligation: 884.02/291.45 The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^2). 884.02/291.45 884.02/291.45 884.02/291.45 The TRS R consists of the following rules: 884.02/291.45 884.02/291.45 lt(0, s(x)) -> true [1] 884.02/291.45 lt(x, 0) -> false [1] 884.02/291.45 lt(s(x), s(y)) -> lt(x, y) [1] 884.02/291.45 fac(x) -> help(x, 0) [1] 884.02/291.45 help(x, c) -> if(lt(c, x), x, c) [1] 884.02/291.45 if(true, x, c) -> times(s(c), help(x, s(c))) [1] 884.02/291.45 if(false, x, c) -> s(0) [1] 884.02/291.45 884.02/291.45 Rewrite Strategy: INNERMOST 884.02/291.45 ---------------------------------------- 884.02/291.45 884.02/291.45 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 884.02/291.45 Infered types. 884.02/291.45 ---------------------------------------- 884.02/291.45 884.02/291.45 (4) 884.02/291.45 Obligation: 884.02/291.45 Runtime Complexity Weighted TRS with Types. 884.02/291.45 The TRS R consists of the following rules: 884.02/291.45 884.02/291.45 lt(0, s(x)) -> true [1] 884.02/291.45 lt(x, 0) -> false [1] 884.02/291.45 lt(s(x), s(y)) -> lt(x, y) [1] 884.02/291.45 fac(x) -> help(x, 0) [1] 884.02/291.45 help(x, c) -> if(lt(c, x), x, c) [1] 884.02/291.45 if(true, x, c) -> times(s(c), help(x, s(c))) [1] 884.02/291.45 if(false, x, c) -> s(0) [1] 884.02/291.45 884.02/291.45 The TRS has the following type information: 884.02/291.45 lt :: 0:s:times -> 0:s:times -> true:false 884.02/291.45 0 :: 0:s:times 884.02/291.45 s :: 0:s:times -> 0:s:times 884.02/291.45 true :: true:false 884.02/291.45 false :: true:false 884.02/291.45 fac :: 0:s:times -> 0:s:times 884.02/291.45 help :: 0:s:times -> 0:s:times -> 0:s:times 884.02/291.45 if :: true:false -> 0:s:times -> 0:s:times -> 0:s:times 884.02/291.45 times :: 0:s:times -> 0:s:times -> 0:s:times 884.02/291.45 884.02/291.45 Rewrite Strategy: INNERMOST
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