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Runti Compl Inner Rewri 22807 pair #381904177
details
property
value
status
complete
benchmark
polycounter-5.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n040.star.cs.uiowa.edu
space
TCT_12
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.458163977 seconds
cpu usage
1035.98751466
max memory
7.083421696E9
stage attributes
key
value
output-size
16095
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^5).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) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (8) CpxTypedWeightedCompleteTrs (9) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (10) CpxRNTS (11) SimplificationProof [BOTH BOUNDS(ID, ID), 3 ms] (12) CpxRNTS (13) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms] (14) CpxRNTS (15) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (16) CpxRNTS (17) IntTrsBoundProof [UPPER BOUND(ID), 3541 ms] (18) CpxRNTS (19) IntTrsBoundProof [UPPER BOUND(ID), 3507 ms] (20) CpxRNTS (21) FinalProof [FINISHED, 0 ms] (22) BOUNDS(1, n^5) (23) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (24) TRS for Loop Detection (25) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] (26) BEST (27) proven lower bound (28) LowerBoundPropagationProof [FINISHED, 0 ms] (29) BOUNDS(n^1, INF) (30) 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: f(s(x1), x2, x3, x4, x5) -> f(x1, x2, x3, x4, x5) f(0, s(x2), x3, x4, x5) -> f(x2, x2, x3, x4, x5) f(0, 0, s(x3), x4, x5) -> f(x3, x3, x3, x4, x5) f(0, 0, 0, s(x4), x5) -> f(x4, x4, x4, x4, x5) f(0, 0, 0, 0, s(x5)) -> f(x5, x5, x5, x5, x5) f(0, 0, 0, 0, 0) -> 0 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: f(s(x1), x2, x3, x4, x5) -> f(x1, x2, x3, x4, x5) [1] f(0, s(x2), x3, x4, x5) -> f(x2, x2, x3, x4, x5) [1] f(0, 0, s(x3), x4, x5) -> f(x3, x3, x3, x4, x5) [1] f(0, 0, 0, s(x4), x5) -> f(x4, x4, x4, x4, x5) [1] f(0, 0, 0, 0, s(x5)) -> f(x5, x5, x5, x5, x5) [1] f(0, 0, 0, 0, 0) -> 0 [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: f(s(x1), x2, x3, x4, x5) -> f(x1, x2, x3, x4, x5) [1] f(0, s(x2), x3, x4, x5) -> f(x2, x2, x3, x4, x5) [1] f(0, 0, s(x3), x4, x5) -> f(x3, x3, x3, x4, x5) [1] f(0, 0, 0, s(x4), x5) -> f(x4, x4, x4, x4, x5) [1]
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