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Runti Compl Full Rewri 10127 pair #381903223
details
property
value
status
complete
benchmark
otto13.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n027.star.cs.uiowa.edu
space
AProVE_07
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.79508996 seconds
cpu usage
1059.21164707
max memory
1.552058368E10
stage attributes
key
value
output-size
28341
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). (0) CpxTRS (1) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxTRS (3) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (4) CpxWeightedTrs (5) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (6) CpxTypedWeightedTrs (7) CompletionProof [UPPER BOUND(ID), 0 ms] (8) CpxTypedWeightedCompleteTrs (9) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (10) CpxRNTS (11) CompleteCoflocoProof [FINISHED, 1172 ms] (12) BOUNDS(1, n^2) (13) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (14) TRS for Loop Detection (15) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] (16) BEST (17) proven lower bound (18) LowerBoundPropagationProof [FINISHED, 0 ms] (19) BOUNDS(n^1, INF) (20) TRS for Loop Detection ---------------------------------------- (0) Obligation: The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). The TRS R consists of the following rules: le(0, y, z) -> greater(y, z) le(s(x), 0, z) -> false le(s(x), s(y), 0) -> false le(s(x), s(y), s(z)) -> le(x, y, z) greater(x, 0) -> first greater(0, s(y)) -> second greater(s(x), s(y)) -> greater(x, y) double(0) -> 0 double(s(x)) -> s(s(double(x))) triple(x) -> if(le(x, x, double(x)), x, 0, 0) if(false, x, y, z) -> true if(first, x, y, z) -> if(le(s(x), y, s(z)), s(x), y, s(z)) if(second, x, y, z) -> if(le(s(x), s(y), z), s(x), s(y), z) S is empty. Rewrite Strategy: FULL ---------------------------------------- (1) RcToIrcProof (BOTH BOUNDS(ID, ID)) Converted rc-obligation to irc-obligation. The duplicating contexts are: triple([]) if(first, [], y, z) if(first, x, [], z) if(first, x, y, []) if(second, [], y, z) if(second, x, [], z) if(second, x, y, []) The defined contexts are: if([], s(x1), x2, s(x3)) if([], s(x1), s(x2), x3) if([], x1, 0, 0) le(x0, x1, []) greater(x0, []) [] just represents basic- or constructor-terms in the following defined contexts: if([], s(x1), x2, s(x3)) if([], s(x1), s(x2), x3) As the TRS is an overlay system and the defined contexts and the duplicating contexts don't overlap, we have rc = irc. ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, n^2). The TRS R consists of the following rules: le(0, y, z) -> greater(y, z)
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