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Runti Compl Inner Rewri 22807 pair #381904992
details
property
value
status
complete
benchmark
4.17.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n042.star.cs.uiowa.edu
space
SK90
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
5.78222894669 seconds
cpu usage
19.063291751
max memory
4.224630784E9
stage attributes
key
value
output-size
13399
starexec-result
WORST_CASE(Omega(n^2), O(n^2))
output
/export/starexec/sandbox/solver/bin/starexec_run_complexity /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^2), O(n^2)) proof of /export/starexec/sandbox/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^2, n^2).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), 0 ms] (8) CpxRNTS (9) CompleteCoflocoProof [FINISHED, 138 ms] (10) BOUNDS(1, n^2) (11) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (12) CpxTRS (13) SlicingProof [LOWER BOUND(ID), 0 ms] (14) CpxTRS (15) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (16) typed CpxTrs (17) OrderProof [LOWER BOUND(ID), 0 ms] (18) typed CpxTrs (19) RewriteLemmaProof [LOWER BOUND(ID), 289 ms] (20) BEST (21) proven lower bound (22) LowerBoundPropagationProof [FINISHED, 0 ms] (23) BOUNDS(n^1, INF) (24) typed CpxTrs (25) RewriteLemmaProof [LOWER BOUND(ID), 2074 ms] (26) proven lower bound (27) LowerBoundPropagationProof [FINISHED, 0 ms] (28) 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: fac(s(x)) -> *(fac(p(s(x))), s(x)) p(s(0)) -> 0 p(s(s(x))) -> s(p(s(x))) 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: fac(s(x)) -> *(fac(p(s(x))), s(x)) [1] p(s(0)) -> 0 [1] p(s(s(x))) -> s(p(s(x))) [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: fac(s(x)) -> *(fac(p(s(x))), s(x)) [1] p(s(0)) -> 0 [1] p(s(s(x))) -> s(p(s(x))) [1] The TRS has the following type information: fac :: s:0 -> * s :: s:0 -> s:0 * :: * -> s:0 -> * p :: s:0 -> s:0 0 :: s:0 Rewrite Strategy: INNERMOST
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