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Runti Compl Inner Rewri 22807 pair #381904162
details
property
value
status
complete
benchmark
parting04_maxsort_h.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n038.star.cs.uiowa.edu
space
AProVE_08
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
292.723972082 seconds
cpu usage
1046.1379618
max memory
1.5347818496E10
stage attributes
key
value
output-size
21151
starexec-result
WORST_CASE(Omega(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), ?) 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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^2, INF).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), 333 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), 30 ms] (14) typed CpxTrs (15) RewriteLemmaProof [LOWER BOUND(ID), 71 ms] (16) typed CpxTrs (17) RewriteLemmaProof [LOWER BOUND(ID), 55 ms] (18) typed CpxTrs (19) RewriteLemmaProof [LOWER BOUND(ID), 63 ms] (20) proven lower bound (21) LowerBoundPropagationProof [FINISHED, 0 ms] (22) BOUNDS(n^2, 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: max(nil) -> 0 max(cons(x, nil)) -> x max(cons(x, cons(y, xs))) -> if1(ge(x, y), x, y, xs) if1(true, x, y, xs) -> max(cons(x, xs)) if1(false, x, y, xs) -> max(cons(y, xs)) del(x, nil) -> nil del(x, cons(y, xs)) -> if2(eq(x, y), x, y, xs) if2(true, x, y, xs) -> xs if2(false, x, y, xs) -> cons(y, del(x, xs)) eq(0, 0) -> true eq(0, s(y)) -> false eq(s(x), 0) -> false eq(s(x), s(y)) -> eq(x, y) sort(nil) -> nil sort(cons(x, xs)) -> cons(max(cons(x, xs)), sort(h(del(max(cons(x, xs)), cons(x, xs))))) ge(0, 0) -> true ge(s(x), 0) -> true ge(0, s(x)) -> false ge(s(x), s(y)) -> ge(x, y) h(nil) -> nil h(cons(x, xs)) -> cons(x, h(xs)) 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: max(nil) -> 0' max(cons(x, nil)) -> x max(cons(x, cons(y, xs))) -> if1(ge(x, y), x, y, xs) if1(true, x, y, xs) -> max(cons(x, xs)) if1(false, x, y, xs) -> max(cons(y, xs)) del(x, nil) -> nil del(x, cons(y, xs)) -> if2(eq(x, y), x, y, xs) if2(true, x, y, xs) -> xs if2(false, x, y, xs) -> cons(y, del(x, xs)) eq(0', 0') -> true eq(0', s(y)) -> false eq(s(x), 0') -> false eq(s(x), s(y)) -> eq(x, y) sort(nil) -> nil sort(cons(x, xs)) -> cons(max(cons(x, xs)), sort(h(del(max(cons(x, xs)), cons(x, xs))))) ge(0', 0') -> true
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