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Runti Compl Inner Rewri 22807 pair #381904430
details
property
value
status
complete
benchmark
logarithm.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n056.star.cs.uiowa.edu
space
Secret_06_TRS
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.495682955 seconds
cpu usage
1125.65133816
max memory
1.5812784128E10
stage attributes
key
value
output-size
43875
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2).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), 0 ms] (4) CpxTypedWeightedTrs (5) CompletionProof [UPPER BOUND(ID), 0 ms] (6) CpxTypedWeightedCompleteTrs (7) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (8) CpxRNTS (9) CompleteCoflocoProof [FINISHED, 1804 ms] (10) BOUNDS(1, n^2) (11) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (12) CpxTRS (13) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (14) typed CpxTrs (15) OrderProof [LOWER BOUND(ID), 0 ms] (16) typed CpxTrs (17) RewriteLemmaProof [LOWER BOUND(ID), 289 ms] (18) BEST (19) proven lower bound (20) LowerBoundPropagationProof [FINISHED, 0 ms] (21) BOUNDS(n^1, INF) (22) typed CpxTrs (23) RewriteLemmaProof [LOWER BOUND(ID), 55 ms] (24) typed CpxTrs (25) RewriteLemmaProof [LOWER BOUND(ID), 0 ms] (26) typed CpxTrs ---------------------------------------- (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: half(0) -> 0 half(s(0)) -> 0 half(s(s(x))) -> s(half(x)) le(0, y) -> true le(s(x), 0) -> false le(s(x), s(y)) -> le(x, y) inc(s(x)) -> s(inc(x)) inc(0) -> s(0) logarithm(x) -> logIter(x, 0) logIter(x, y) -> if(le(s(0), x), le(s(s(0)), x), half(x), inc(y)) if(false, b, x, y) -> logZeroError if(true, false, x, s(y)) -> y if(true, true, x, y) -> logIter(x, y) f -> g f -> h 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: half(0) -> 0 [1] half(s(0)) -> 0 [1] half(s(s(x))) -> s(half(x)) [1] le(0, y) -> true [1] le(s(x), 0) -> false [1] le(s(x), s(y)) -> le(x, y) [1] inc(s(x)) -> s(inc(x)) [1] inc(0) -> s(0) [1] logarithm(x) -> logIter(x, 0) [1] logIter(x, y) -> if(le(s(0), x), le(s(s(0)), x), half(x), inc(y)) [1] if(false, b, x, y) -> logZeroError [1] if(true, false, x, s(y)) -> y [1] if(true, true, x, y) -> logIter(x, y) [1] f -> g [1] f -> h [1] Rewrite Strategy: INNERMOST ----------------------------------------
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