Spaces
Explore
Communities
Statistics
Reports
Cluster
Status
Help
Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313676
details
property
value
status
complete
benchmark
quicksort.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n071.star.cs.uiowa.edu
space
AProVE_06
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.696 seconds
cpu usage
1125.71
user time
1103.29
system time
22.4145
max virtual memory
3.852882E7
max residence set size
1.5351528E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^2), ?)
output
1125.33/291.54 WORST_CASE(Omega(n^2), ?) 1125.47/291.58 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 1125.47/291.58 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1125.47/291.58 1125.47/291.58 1125.47/291.58 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). 1125.47/291.58 1125.47/291.58 (0) CpxTRS 1125.47/291.58 (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 1125.47/291.58 (2) CpxTRS 1125.47/291.58 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 1125.47/291.58 (4) typed CpxTrs 1125.47/291.58 (5) OrderProof [LOWER BOUND(ID), 0 ms] 1125.47/291.58 (6) typed CpxTrs 1125.47/291.58 (7) RewriteLemmaProof [LOWER BOUND(ID), 280 ms] 1125.47/291.58 (8) BEST 1125.47/291.58 (9) proven lower bound 1125.47/291.58 (10) LowerBoundPropagationProof [FINISHED, 0 ms] 1125.47/291.58 (11) BOUNDS(n^1, INF) 1125.47/291.58 (12) typed CpxTrs 1125.47/291.58 (13) RewriteLemmaProof [LOWER BOUND(ID), 61 ms] 1125.47/291.58 (14) typed CpxTrs 1125.47/291.58 (15) RewriteLemmaProof [LOWER BOUND(ID), 40 ms] 1125.47/291.58 (16) typed CpxTrs 1125.47/291.58 (17) RewriteLemmaProof [LOWER BOUND(ID), 10 ms] 1125.47/291.58 (18) typed CpxTrs 1125.47/291.58 (19) RewriteLemmaProof [LOWER BOUND(ID), 241 ms] 1125.47/291.58 (20) proven lower bound 1125.47/291.58 (21) LowerBoundPropagationProof [FINISHED, 0 ms] 1125.47/291.58 (22) BOUNDS(n^2, INF) 1125.47/291.58 1125.47/291.58 1125.47/291.58 ---------------------------------------- 1125.47/291.58 1125.47/291.58 (0) 1125.47/291.58 Obligation: 1125.47/291.58 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). 1125.47/291.58 1125.47/291.58 1125.47/291.58 The TRS R consists of the following rules: 1125.47/291.58 1125.47/291.58 le(0, y) -> true 1125.47/291.58 le(s(x), 0) -> false 1125.47/291.58 le(s(x), s(y)) -> le(x, y) 1125.47/291.58 app(nil, y) -> y 1125.47/291.58 app(add(n, x), y) -> add(n, app(x, y)) 1125.47/291.58 low(n, nil) -> nil 1125.47/291.58 low(n, add(m, x)) -> if_low(le(m, n), n, add(m, x)) 1125.47/291.58 if_low(true, n, add(m, x)) -> add(m, low(n, x)) 1125.47/291.58 if_low(false, n, add(m, x)) -> low(n, x) 1125.47/291.58 high(n, nil) -> nil 1125.47/291.58 high(n, add(m, x)) -> if_high(le(m, n), n, add(m, x)) 1125.47/291.58 if_high(true, n, add(m, x)) -> high(n, x) 1125.47/291.58 if_high(false, n, add(m, x)) -> add(m, high(n, x)) 1125.47/291.58 head(add(n, x)) -> n 1125.47/291.58 tail(add(n, x)) -> x 1125.47/291.58 isempty(nil) -> true 1125.47/291.58 isempty(add(n, x)) -> false 1125.47/291.58 quicksort(x) -> if_qs(isempty(x), low(head(x), tail(x)), head(x), high(head(x), tail(x))) 1125.47/291.58 if_qs(true, x, n, y) -> nil 1125.47/291.58 if_qs(false, x, n, y) -> app(quicksort(x), add(n, quicksort(y))) 1125.47/291.58 1125.47/291.58 S is empty. 1125.47/291.58 Rewrite Strategy: INNERMOST 1125.47/291.58 ---------------------------------------- 1125.47/291.58 1125.47/291.58 (1) RenamingProof (BOTH BOUNDS(ID, ID)) 1125.47/291.58 Renamed function symbols to avoid clashes with predefined symbol. 1125.47/291.58 ---------------------------------------- 1125.47/291.58 1125.47/291.58 (2) 1125.47/291.58 Obligation: 1125.47/291.58 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). 1125.47/291.58 1125.47/291.58 1125.47/291.58 The TRS R consists of the following rules: 1125.47/291.58 1125.47/291.58 le(0', y) -> true 1125.47/291.58 le(s(x), 0') -> false 1125.47/291.58 le(s(x), s(y)) -> le(x, y) 1125.47/291.58 app(nil, y) -> y 1125.47/291.58 app(add(n, x), y) -> add(n, app(x, y)) 1125.47/291.58 low(n, nil) -> nil 1125.47/291.58 low(n, add(m, x)) -> if_low(le(m, n), n, add(m, x)) 1125.47/291.58 if_low(true, n, add(m, x)) -> add(m, low(n, x)) 1125.47/291.58 if_low(false, n, add(m, x)) -> low(n, x) 1125.47/291.58 high(n, nil) -> nil 1125.47/291.58 high(n, add(m, x)) -> if_high(le(m, n), n, add(m, x)) 1125.47/291.58 if_high(true, n, add(m, x)) -> high(n, x) 1125.47/291.58 if_high(false, n, add(m, x)) -> add(m, high(n, x)) 1125.47/291.58 head(add(n, x)) -> n 1125.47/291.58 tail(add(n, x)) -> x 1125.47/291.58 isempty(nil) -> true 1125.47/291.58 isempty(add(n, x)) -> false 1125.47/291.58 quicksort(x) -> if_qs(isempty(x), low(head(x), tail(x)), head(x), high(head(x), tail(x))) 1125.47/291.58 if_qs(true, x, n, y) -> nil 1125.47/291.58 if_qs(false, x, n, y) -> app(quicksort(x), add(n, quicksort(y))) 1125.47/291.58 1125.47/291.58 S is empty. 1125.47/291.58 Rewrite Strategy: INNERMOST
popout
output may be truncated. 'popout' for the full output.
job log
popout
actions
all output
return to Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40