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Runti Compl Inner Rewri 22807 pair #381904336
details
property
value
status
complete
benchmark
aprove09.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n036.star.cs.uiowa.edu
space
Secret_07_TRS
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.51350379 seconds
cpu usage
1154.76329313
max memory
1.5233363968E10
stage attributes
key
value
output-size
84468
starexec-result
WORST_CASE(Omega(n^1), O(n^3))
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^3)) 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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^3). (0) CpxTRS (1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxWeightedTrs (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 2 ms] (4) CpxTypedWeightedTrs (5) CompletionProof [UPPER BOUND(ID), 0 ms] (6) CpxTypedWeightedCompleteTrs (7) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (8) CpxRNTS (9) CompleteCoflocoProof [FINISHED, 8018 ms] (10) BOUNDS(1, n^3) (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), 303 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), 21 ms] (24) typed CpxTrs (25) RewriteLemmaProof [LOWER BOUND(ID), 50 ms] (26) typed CpxTrs ---------------------------------------- (0) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^3). The TRS R consists of the following rules: div(x, y) -> div2(x, y, 0) div2(x, y, i) -> if1(le(y, 0), le(y, x), x, y, plus(i, 0), inc(i)) if1(true, b, x, y, i, j) -> divZeroError if1(false, b, x, y, i, j) -> if2(b, x, y, i, j) if2(true, x, y, i, j) -> div2(minus(x, y), y, j) if2(false, x, y, i, j) -> i inc(0) -> 0 inc(s(i)) -> s(inc(i)) le(s(x), 0) -> false le(0, y) -> true le(s(x), s(y)) -> le(x, y) minus(x, 0) -> x minus(0, y) -> 0 minus(s(x), s(y)) -> minus(x, y) plus(x, y) -> plusIter(x, y, 0) plusIter(x, y, z) -> ifPlus(le(x, z), x, y, z) ifPlus(true, x, y, z) -> y ifPlus(false, x, y, z) -> plusIter(x, s(y), s(z)) a -> c a -> d 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^3). The TRS R consists of the following rules: div(x, y) -> div2(x, y, 0) [1] div2(x, y, i) -> if1(le(y, 0), le(y, x), x, y, plus(i, 0), inc(i)) [1] if1(true, b, x, y, i, j) -> divZeroError [1] if1(false, b, x, y, i, j) -> if2(b, x, y, i, j) [1] if2(true, x, y, i, j) -> div2(minus(x, y), y, j) [1] if2(false, x, y, i, j) -> i [1] inc(0) -> 0 [1] inc(s(i)) -> s(inc(i)) [1] le(s(x), 0) -> false [1] le(0, y) -> true [1] le(s(x), s(y)) -> le(x, y) [1] minus(x, 0) -> x [1] minus(0, y) -> 0 [1]
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