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Runti Compl Full Rewri 10127 pair #381902134
details
property
value
status
complete
benchmark
10.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n048.star.cs.uiowa.edu
space
Various_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.460887909 seconds
cpu usage
321.85797237
max memory
5.617045504E9
stage attributes
key
value
output-size
15299
starexec-result
WORST_CASE(Omega(n^1), ?)
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), ?) proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). (0) CpxTRS (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxTRS (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (4) typed CpxTrs (5) OrderProof [LOWER BOUND(ID), 0 ms] (6) typed CpxTrs (7) RewriteLemmaProof [LOWER BOUND(ID), 282 ms] (8) BEST (9) proven lower bound (10) LowerBoundPropagationProof [FINISHED, 0 ms] (11) BOUNDS(n^1, INF) (12) typed CpxTrs (13) RewriteLemmaProof [LOWER BOUND(ID), 69 ms] (14) typed CpxTrs (15) RewriteLemmaProof [LOWER BOUND(ID), 30 ms] (16) typed CpxTrs (17) RewriteLemmaProof [LOWER BOUND(ID), 52 ms] (18) typed CpxTrs (19) RewriteLemmaProof [LOWER BOUND(ID), 12 ms] (20) BOUNDS(1, INF) ---------------------------------------- (0) Obligation: The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). The TRS R consists of the following rules: +(0, y) -> y +(s(x), y) -> s(+(x, y)) ++(nil, ys) -> ys ++(:(x, xs), ys) -> :(x, ++(xs, ys)) sum(:(x, nil)) -> :(x, nil) sum(:(x, :(y, xs))) -> sum(:(+(x, y), xs)) sum(++(xs, :(x, :(y, ys)))) -> sum(++(xs, sum(:(x, :(y, ys))))) -(x, 0) -> x -(0, s(y)) -> 0 -(s(x), s(y)) -> -(x, y) quot(0, s(y)) -> 0 quot(s(x), s(y)) -> s(quot(-(x, y), s(y))) length(nil) -> 0 length(:(x, xs)) -> s(length(xs)) hd(:(x, xs)) -> x avg(xs) -> quot(hd(sum(xs)), length(xs)) S is empty. Rewrite Strategy: FULL ---------------------------------------- (1) RenamingProof (BOTH BOUNDS(ID, ID)) Renamed function symbols to avoid clashes with predefined symbol. ---------------------------------------- (2) Obligation: The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). The TRS R consists of the following rules: +'(0', y) -> y +'(s(x), y) -> s(+'(x, y)) ++(nil, ys) -> ys ++(:(x, xs), ys) -> :(x, ++(xs, ys)) sum(:(x, nil)) -> :(x, nil) sum(:(x, :(y, xs))) -> sum(:(+'(x, y), xs)) sum(++(xs, :(x, :(y, ys)))) -> sum(++(xs, sum(:(x, :(y, ys))))) -(x, 0') -> x -(0', s(y)) -> 0' -(s(x), s(y)) -> -(x, y) quot(0', s(y)) -> 0' quot(s(x), s(y)) -> s(quot(-(x, y), s(y))) length(nil) -> 0' length(:(x, xs)) -> s(length(xs)) hd(:(x, xs)) -> x avg(xs) -> quot(hd(sum(xs)), length(xs)) S is empty. Rewrite Strategy: FULL ---------------------------------------- (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types.
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