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Runti Compl Inner Rewri 22807 pair #381903985
details
property
value
status
complete
benchmark
naiverev.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n039.star.cs.uiowa.edu
space
Frederiksen_Glenstrup
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
3.83373188972 seconds
cpu usage
11.599704137
max memory
1.607446528E9
stage attributes
key
value
output-size
17424
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^2, n^2).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), 0 ms] (8) CpxRNTS (9) CompleteCoflocoProof [FINISHED, 167 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), 312 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), 49 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: naiverev(Cons(x, xs)) -> app(naiverev(xs), Cons(x, Nil)) app(Cons(x, xs), ys) -> Cons(x, app(xs, ys)) notEmpty(Cons(x, xs)) -> True notEmpty(Nil) -> False naiverev(Nil) -> Nil app(Nil, ys) -> ys goal(xs) -> naiverev(xs) 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: naiverev(Cons(x, xs)) -> app(naiverev(xs), Cons(x, Nil)) [1] app(Cons(x, xs), ys) -> Cons(x, app(xs, ys)) [1] notEmpty(Cons(x, xs)) -> True [1] notEmpty(Nil) -> False [1] naiverev(Nil) -> Nil [1] app(Nil, ys) -> ys [1] goal(xs) -> naiverev(xs) [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: naiverev(Cons(x, xs)) -> app(naiverev(xs), Cons(x, Nil)) [1] app(Cons(x, xs), ys) -> Cons(x, app(xs, ys)) [1] notEmpty(Cons(x, xs)) -> True [1] notEmpty(Nil) -> False [1]
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