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Runti Compl Inner Rewri 22807 pair #381904178
details
property
value
status
complete
benchmark
aprove02.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
Secret_07_TRS
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.554416895 seconds
cpu usage
1133.17980078
max memory
1.5561920512E10
stage attributes
key
value
output-size
187605
starexec-result
WORST_CASE(Omega(n^1), O(n^5))
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^5)) 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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^5). (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, 52.1 s] (10) BOUNDS(1, n^5) (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^5). The TRS R consists of the following rules: plus(x, y) -> ifPlus(isZero(x), x, inc(y)) ifPlus(true, x, y) -> p(y) ifPlus(false, x, y) -> plus(p(x), y) times(x, y) -> timesIter(0, x, y, 0) timesIter(i, x, y, z) -> ifTimes(ge(i, x), i, x, y, z) ifTimes(true, i, x, y, z) -> z ifTimes(false, i, x, y, z) -> timesIter(inc(i), x, y, plus(z, y)) isZero(0) -> true isZero(s(0)) -> false isZero(s(s(x))) -> isZero(s(x)) inc(0) -> s(0) inc(s(x)) -> s(inc(x)) inc(x) -> s(x) p(0) -> 0 p(s(x)) -> x p(s(s(x))) -> s(p(s(x))) ge(x, 0) -> true ge(0, s(y)) -> false ge(s(x), s(y)) -> ge(x, y) f0(0, y, x) -> f1(x, y, x) f1(x, y, z) -> f2(x, y, z) f2(x, 1, z) -> f0(x, z, z) f0(x, y, z) -> d f1(x, y, z) -> c 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^5). The TRS R consists of the following rules: plus(x, y) -> ifPlus(isZero(x), x, inc(y)) [1] ifPlus(true, x, y) -> p(y) [1] ifPlus(false, x, y) -> plus(p(x), y) [1] times(x, y) -> timesIter(0, x, y, 0) [1] timesIter(i, x, y, z) -> ifTimes(ge(i, x), i, x, y, z) [1] ifTimes(true, i, x, y, z) -> z [1] ifTimes(false, i, x, y, z) -> timesIter(inc(i), x, y, plus(z, y)) [1] isZero(0) -> true [1] isZero(s(0)) -> false [1] isZero(s(s(x))) -> isZero(s(x)) [1] inc(0) -> s(0) [1] inc(s(x)) -> s(inc(x)) [1] inc(x) -> s(x) [1] p(0) -> 0 [1] p(s(x)) -> x [1] p(s(s(x))) -> s(p(s(x))) [1] ge(x, 0) -> true [1]
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