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Runti Compl Inner Rewri 22807 pair #381904004
details
property
value
status
complete
benchmark
division.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n038.star.cs.uiowa.edu
space
Secret_06_TRS
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.50774312 seconds
cpu usage
1014.77175826
max memory
1.1684421632E10
stage attributes
key
value
output-size
42908
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). (0) CpxTRS (1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxWeightedTrs (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 1 ms] (4) CpxTypedWeightedTrs (5) CompletionProof [UPPER BOUND(ID), 0 ms] (6) CpxTypedWeightedCompleteTrs (7) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (8) CpxRNTS (9) CompleteCoflocoProof [FINISHED, 3063 ms] (10) BOUNDS(1, n^2) (11) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (12) TRS for Loop Detection (13) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] (14) BEST (15) proven lower bound (16) LowerBoundPropagationProof [FINISHED, 0 ms] (17) BOUNDS(n^1, INF) (18) TRS for Loop Detection ---------------------------------------- (0) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). The TRS R consists of the following rules: division(x, y) -> div(x, y, 0) div(x, y, z) -> if(lt(x, y), x, y, inc(z)) if(true, x, y, z) -> z if(false, x, s(y), z) -> div(minus(x, s(y)), s(y), z) minus(x, 0) -> x minus(s(x), s(y)) -> minus(x, y) lt(x, 0) -> false lt(0, s(y)) -> true lt(s(x), s(y)) -> lt(x, y) inc(0) -> s(0) inc(s(x)) -> s(inc(x)) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) Transformed relative TRS to weighted TRS ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^2). The TRS R consists of the following rules: division(x, y) -> div(x, y, 0) [1] div(x, y, z) -> if(lt(x, y), x, y, inc(z)) [1] if(true, x, y, z) -> z [1] if(false, x, s(y), z) -> div(minus(x, s(y)), s(y), z) [1] minus(x, 0) -> x [1] minus(s(x), s(y)) -> minus(x, y) [1] lt(x, 0) -> false [1] lt(0, s(y)) -> true [1] lt(s(x), s(y)) -> lt(x, y) [1] inc(0) -> s(0) [1] inc(s(x)) -> s(inc(x)) [1] Rewrite Strategy: INNERMOST ---------------------------------------- (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (4) Obligation: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: division(x, y) -> div(x, y, 0) [1] div(x, y, z) -> if(lt(x, y), x, y, inc(z)) [1] if(true, x, y, z) -> z [1] if(false, x, s(y), z) -> div(minus(x, s(y)), s(y), z) [1] minus(x, 0) -> x [1] minus(s(x), s(y)) -> minus(x, y) [1]
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