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Runti Compl Inner Rewri 22807 pair #381904219
details
property
value
status
complete
benchmark
thiemann40_modified.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n030.star.cs.uiowa.edu
space
AProVE_08
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
15.7065939903 seconds
cpu usage
57.206448594
max memory
4.506546176E9
stage attributes
key
value
output-size
21238
starexec-result
WORST_CASE(Omega(n^2), 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^2), 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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^2, n^2).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), 2 ms] (8) CpxRNTS (9) CompleteCoflocoProof [FINISHED, 403 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), 304 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), 74 ms] (24) proven lower bound (25) LowerBoundPropagationProof [FINISHED, 0 ms] (26) BOUNDS(n^2, INF) ---------------------------------------- (0) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^2, n^2). The TRS R consists of the following rules: nonZero(0) -> false nonZero(s(x)) -> true p(s(0)) -> 0 p(s(s(x))) -> s(p(s(x))) id_inc(x) -> x id_inc(x) -> s(x) random(x) -> rand(x, 0) rand(x, y) -> if(nonZero(x), x, y) if(false, x, y) -> y if(true, x, y) -> rand(p(x), id_inc(y)) 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: nonZero(0) -> false [1] nonZero(s(x)) -> true [1] p(s(0)) -> 0 [1] p(s(s(x))) -> s(p(s(x))) [1] id_inc(x) -> x [1] id_inc(x) -> s(x) [1] random(x) -> rand(x, 0) [1] rand(x, y) -> if(nonZero(x), x, y) [1] if(false, x, y) -> y [1] if(true, x, y) -> rand(p(x), id_inc(y)) [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:
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