Spaces
Explore
Communities
Statistics
Reports
Cluster
Status
Help
Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308473
details
property
value
status
complete
benchmark
aprove03.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n094.star.cs.uiowa.edu
space
Secret_07_TRS
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.58 seconds
cpu usage
308.091
user time
306.286
system time
1.80547
max virtual memory
1.828142E7
max residence set size
5200460.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
307.99/291.53 WORST_CASE(Omega(n^1), ?) 307.99/291.54 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 307.99/291.54 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 307.99/291.54 307.99/291.54 307.99/291.54 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 307.99/291.54 307.99/291.54 (0) CpxTRS 307.99/291.54 (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 307.99/291.54 (2) TRS for Loop Detection 307.99/291.54 (3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 307.99/291.54 (4) BEST 307.99/291.54 (5) proven lower bound 307.99/291.54 (6) LowerBoundPropagationProof [FINISHED, 0 ms] 307.99/291.54 (7) BOUNDS(n^1, INF) 307.99/291.54 (8) TRS for Loop Detection 307.99/291.54 307.99/291.54 307.99/291.54 ---------------------------------------- 307.99/291.54 307.99/291.54 (0) 307.99/291.54 Obligation: 307.99/291.54 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 307.99/291.54 307.99/291.54 307.99/291.54 The TRS R consists of the following rules: 307.99/291.54 307.99/291.54 average(x, y) -> if(ge(x, y), x, y) 307.99/291.54 if(true, x, y) -> averIter(y, x, y) 307.99/291.54 if(false, x, y) -> averIter(x, y, x) 307.99/291.54 averIter(x, y, z) -> ifIter(ge(x, y), x, y, z) 307.99/291.54 ifIter(true, x, y, z) -> z 307.99/291.54 ifIter(false, x, y, z) -> averIter(plus(x, s(s(s(0)))), plus(y, s(0)), plus(z, s(0))) 307.99/291.54 append(nil, y) -> y 307.99/291.54 append(cons(n, x), y) -> cons(n, app(x, y)) 307.99/291.54 low(n, nil) -> nil 307.99/291.54 low(n, cons(m, x)) -> if_low(ge(m, n), n, cons(m, x)) 307.99/291.54 if_low(false, n, cons(m, x)) -> cons(m, low(n, x)) 307.99/291.54 if_low(true, n, cons(m, x)) -> low(n, x) 307.99/291.54 high(n, nil) -> nil 307.99/291.54 high(n, cons(m, x)) -> if_high(ge(m, n), n, cons(m, x)) 307.99/291.54 if_high(false, n, cons(m, x)) -> high(n, x) 307.99/291.54 if_high(true, n, cons(m, x)) -> cons(average(m, m), high(n, x)) 307.99/291.54 quicksort(x) -> ifquick(isempty(x), x) 307.99/291.54 ifquick(true, x) -> nil 307.99/291.54 ifquick(false, x) -> append(quicksort(low(head(x), tail(x))), cons(tail(x), quicksort(high(head(x), tail(x))))) 307.99/291.54 plus(0, y) -> y 307.99/291.54 plus(s(x), y) -> s(plus(x, y)) 307.99/291.54 isempty(nil) -> true 307.99/291.54 isempty(cons(n, x)) -> false 307.99/291.54 head(nil) -> error 307.99/291.54 head(cons(n, x)) -> n 307.99/291.54 tail(nil) -> nil 307.99/291.54 tail(cons(n, x)) -> x 307.99/291.54 ge(x, 0) -> true 307.99/291.54 ge(0, s(y)) -> false 307.99/291.54 ge(s(x), s(y)) -> ge(x, y) 307.99/291.54 a -> b 307.99/291.54 a -> c 307.99/291.54 307.99/291.54 S is empty. 307.99/291.54 Rewrite Strategy: FULL 307.99/291.54 ---------------------------------------- 307.99/291.54 307.99/291.54 (1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) 307.99/291.54 Transformed a relative TRS into a decreasing-loop problem. 307.99/291.54 ---------------------------------------- 307.99/291.54 307.99/291.54 (2) 307.99/291.54 Obligation: 307.99/291.54 Analyzing the following TRS for decreasing loops: 307.99/291.54 307.99/291.54 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 307.99/291.54 307.99/291.54 307.99/291.54 The TRS R consists of the following rules: 307.99/291.54 307.99/291.54 average(x, y) -> if(ge(x, y), x, y) 307.99/291.54 if(true, x, y) -> averIter(y, x, y) 307.99/291.54 if(false, x, y) -> averIter(x, y, x) 307.99/291.54 averIter(x, y, z) -> ifIter(ge(x, y), x, y, z) 307.99/291.54 ifIter(true, x, y, z) -> z 307.99/291.54 ifIter(false, x, y, z) -> averIter(plus(x, s(s(s(0)))), plus(y, s(0)), plus(z, s(0))) 307.99/291.54 append(nil, y) -> y 307.99/291.54 append(cons(n, x), y) -> cons(n, app(x, y)) 307.99/291.54 low(n, nil) -> nil 307.99/291.54 low(n, cons(m, x)) -> if_low(ge(m, n), n, cons(m, x)) 307.99/291.54 if_low(false, n, cons(m, x)) -> cons(m, low(n, x)) 307.99/291.54 if_low(true, n, cons(m, x)) -> low(n, x) 307.99/291.54 high(n, nil) -> nil 307.99/291.54 high(n, cons(m, x)) -> if_high(ge(m, n), n, cons(m, x)) 307.99/291.54 if_high(false, n, cons(m, x)) -> high(n, x) 307.99/291.54 if_high(true, n, cons(m, x)) -> cons(average(m, m), high(n, x)) 307.99/291.54 quicksort(x) -> ifquick(isempty(x), x) 307.99/291.54 ifquick(true, x) -> nil 307.99/291.54 ifquick(false, x) -> append(quicksort(low(head(x), tail(x))), cons(tail(x), quicksort(high(head(x), tail(x))))) 307.99/291.54 plus(0, y) -> y 307.99/291.54 plus(s(x), y) -> s(plus(x, y)) 307.99/291.54 isempty(nil) -> true 307.99/291.54 isempty(cons(n, x)) -> false
popout
output may be truncated. 'popout' for the full output.
job log
popout
actions
all output
return to Runtime_Complexity_Full_Rewriting 2019-04-01 06.11
