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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307600
details
property
value
status
complete
benchmark
qsortlast.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n082.star.cs.uiowa.edu
space
AProVE_09_Inductive
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.538 seconds
cpu usage
311.594
user time
309.723
system time
1.87099
max virtual memory
1.828152E7
max residence set size
5220268.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
311.48/291.49 WORST_CASE(Omega(n^1), ?) 311.48/291.49 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 311.48/291.49 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 311.48/291.49 311.48/291.49 311.48/291.49 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 311.48/291.49 311.48/291.49 (0) CpxTRS 311.48/291.49 (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 311.48/291.49 (2) CpxTRS 311.48/291.49 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 311.48/291.49 (4) typed CpxTrs 311.48/291.49 (5) OrderProof [LOWER BOUND(ID), 0 ms] 311.48/291.49 (6) typed CpxTrs 311.48/291.49 (7) RewriteLemmaProof [LOWER BOUND(ID), 217 ms] 311.48/291.49 (8) BEST 311.48/291.49 (9) proven lower bound 311.48/291.49 (10) LowerBoundPropagationProof [FINISHED, 0 ms] 311.48/291.49 (11) BOUNDS(n^1, INF) 311.48/291.49 (12) typed CpxTrs 311.48/291.49 (13) RewriteLemmaProof [LOWER BOUND(ID), 86 ms] 311.48/291.49 (14) typed CpxTrs 311.48/291.49 (15) RewriteLemmaProof [LOWER BOUND(ID), 47 ms] 311.48/291.49 (16) typed CpxTrs 311.48/291.49 (17) RewriteLemmaProof [LOWER BOUND(ID), 0 ms] 311.48/291.49 (18) typed CpxTrs 311.48/291.49 311.48/291.49 311.48/291.49 ---------------------------------------- 311.48/291.49 311.48/291.49 (0) 311.48/291.49 Obligation: 311.48/291.49 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 311.48/291.49 311.48/291.49 311.48/291.49 The TRS R consists of the following rules: 311.48/291.49 311.48/291.49 qsort(nil) -> nil 311.48/291.49 qsort(cons(x, xs)) -> append(qsort(filterlow(last(cons(x, xs)), cons(x, xs))), cons(last(cons(x, xs)), qsort(filterhigh(last(cons(x, xs)), cons(x, xs))))) 311.48/291.49 filterlow(n, nil) -> nil 311.48/291.49 filterlow(n, cons(x, xs)) -> if1(ge(n, x), n, x, xs) 311.48/291.49 if1(true, n, x, xs) -> filterlow(n, xs) 311.48/291.49 if1(false, n, x, xs) -> cons(x, filterlow(n, xs)) 311.48/291.49 filterhigh(n, nil) -> nil 311.48/291.49 filterhigh(n, cons(x, xs)) -> if2(ge(x, n), n, x, xs) 311.48/291.49 if2(true, n, x, xs) -> filterhigh(n, xs) 311.48/291.49 if2(false, n, x, xs) -> cons(x, filterhigh(n, xs)) 311.48/291.49 ge(x, 0) -> true 311.48/291.49 ge(0, s(x)) -> false 311.48/291.49 ge(s(x), s(y)) -> ge(x, y) 311.48/291.49 append(nil, ys) -> ys 311.48/291.49 append(cons(x, xs), ys) -> cons(x, append(xs, ys)) 311.48/291.49 last(nil) -> 0 311.48/291.49 last(cons(x, nil)) -> x 311.48/291.49 last(cons(x, cons(y, xs))) -> last(cons(y, xs)) 311.48/291.49 311.48/291.49 S is empty. 311.48/291.49 Rewrite Strategy: FULL 311.48/291.49 ---------------------------------------- 311.48/291.49 311.48/291.49 (1) RenamingProof (BOTH BOUNDS(ID, ID)) 311.48/291.49 Renamed function symbols to avoid clashes with predefined symbol. 311.48/291.50 ---------------------------------------- 311.48/291.50 311.48/291.50 (2) 311.48/291.50 Obligation: 311.48/291.50 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 311.48/291.50 311.48/291.50 311.48/291.50 The TRS R consists of the following rules: 311.48/291.50 311.48/291.50 qsort(nil) -> nil 311.48/291.50 qsort(cons(x, xs)) -> append(qsort(filterlow(last(cons(x, xs)), cons(x, xs))), cons(last(cons(x, xs)), qsort(filterhigh(last(cons(x, xs)), cons(x, xs))))) 311.48/291.50 filterlow(n, nil) -> nil 311.48/291.50 filterlow(n, cons(x, xs)) -> if1(ge(n, x), n, x, xs) 311.48/291.50 if1(true, n, x, xs) -> filterlow(n, xs) 311.48/291.50 if1(false, n, x, xs) -> cons(x, filterlow(n, xs)) 311.48/291.50 filterhigh(n, nil) -> nil 311.48/291.50 filterhigh(n, cons(x, xs)) -> if2(ge(x, n), n, x, xs) 311.48/291.50 if2(true, n, x, xs) -> filterhigh(n, xs) 311.48/291.50 if2(false, n, x, xs) -> cons(x, filterhigh(n, xs)) 311.48/291.50 ge(x, 0') -> true 311.48/291.50 ge(0', s(x)) -> false 311.48/291.50 ge(s(x), s(y)) -> ge(x, y) 311.48/291.50 append(nil, ys) -> ys 311.48/291.50 append(cons(x, xs), ys) -> cons(x, append(xs, ys)) 311.48/291.50 last(nil) -> 0' 311.48/291.50 last(cons(x, nil)) -> x 311.48/291.50 last(cons(x, cons(y, xs))) -> last(cons(y, xs)) 311.48/291.50 311.48/291.50 S is empty. 311.48/291.50 Rewrite Strategy: FULL 311.48/291.50 ---------------------------------------- 311.48/291.50 311.48/291.50 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 311.48/291.50 Infered types. 311.48/291.50 ---------------------------------------- 311.48/291.50 311.48/291.50 (4) 311.48/291.50 Obligation:
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