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Runti Compl Inner Rewri 22807 pair #381904369
details
property
value
status
complete
benchmark
list-sum-prod.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n046.star.cs.uiowa.edu
space
CiME_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.556855917 seconds
cpu usage
1135.03837376
max memory
1.2390862848E10
stage attributes
key
value
output-size
12426
starexec-result
WORST_CASE(Omega(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), ?) 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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^2, INF).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), 334 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), 5236 ms] (14) BEST (15) proven lower bound (16) LowerBoundPropagationProof [FINISHED, 0 ms] (17) BOUNDS(n^2, INF) (18) typed CpxTrs (19) RewriteLemmaProof [LOWER BOUND(ID), 5 ms] (20) typed CpxTrs (21) RewriteLemmaProof [LOWER BOUND(ID), 408 ms] (22) BOUNDS(1, INF) ---------------------------------------- (0) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). The TRS R consists of the following rules: +(x, 0) -> x +(0, x) -> x +(s(x), s(y)) -> s(s(+(x, y))) *(x, 0) -> 0 *(0, x) -> 0 *(s(x), s(y)) -> s(+(*(x, y), +(x, y))) sum(nil) -> 0 sum(cons(x, l)) -> +(x, sum(l)) prod(nil) -> s(0) prod(cons(x, l)) -> *(x, prod(l)) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (1) RenamingProof (BOTH BOUNDS(ID, ID)) Renamed function symbols to avoid clashes with predefined symbol. ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). The TRS R consists of the following rules: +'(x, 0') -> x +'(0', x) -> x +'(s(x), s(y)) -> s(s(+'(x, y))) *'(x, 0') -> 0' *'(0', x) -> 0' *'(s(x), s(y)) -> s(+'(*'(x, y), +'(x, y))) sum(nil) -> 0' sum(cons(x, l)) -> +'(x, sum(l)) prod(nil) -> s(0') prod(cons(x, l)) -> *'(x, prod(l)) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (4) Obligation: Innermost TRS: Rules: +'(x, 0') -> x +'(0', x) -> x +'(s(x), s(y)) -> s(s(+'(x, y))) *'(x, 0') -> 0'
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