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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307602
details
property
value
status
complete
benchmark
qsortmiddle.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n057.star.cs.uiowa.edu
space
AProVE_09_Inductive
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.626 seconds
cpu usage
311.887
user time
309.925
system time
1.96198
max virtual memory
1.8281488E7
max residence set size
5284076.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
311.79/291.57 WORST_CASE(Omega(n^1), ?) 311.79/291.58 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 311.79/291.58 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 311.79/291.58 311.79/291.58 311.79/291.58 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 311.79/291.58 311.79/291.58 (0) CpxTRS 311.79/291.58 (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 311.79/291.58 (2) TRS for Loop Detection 311.79/291.58 (3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 311.79/291.58 (4) BEST 311.79/291.58 (5) proven lower bound 311.79/291.58 (6) LowerBoundPropagationProof [FINISHED, 0 ms] 311.79/291.58 (7) BOUNDS(n^1, INF) 311.79/291.58 (8) TRS for Loop Detection 311.79/291.58 311.79/291.58 311.79/291.58 ---------------------------------------- 311.79/291.58 311.79/291.58 (0) 311.79/291.58 Obligation: 311.79/291.58 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 311.79/291.58 311.79/291.58 311.79/291.58 The TRS R consists of the following rules: 311.79/291.58 311.79/291.58 qsort(xs) -> qs(half(length(xs)), xs) 311.79/291.58 qs(n, nil) -> nil 311.79/291.58 qs(n, cons(x, xs)) -> append(qs(half(n), filterlow(get(n, cons(x, xs)), cons(x, xs))), cons(get(n, cons(x, xs)), qs(half(n), filterhigh(get(n, cons(x, xs)), cons(x, xs))))) 311.79/291.58 filterlow(n, nil) -> nil 311.79/291.58 filterlow(n, cons(x, xs)) -> if1(ge(n, x), n, x, xs) 311.79/291.58 if1(true, n, x, xs) -> filterlow(n, xs) 311.79/291.58 if1(false, n, x, xs) -> cons(x, filterlow(n, xs)) 311.79/291.58 filterhigh(n, nil) -> nil 311.79/291.58 filterhigh(n, cons(x, xs)) -> if2(ge(x, n), n, x, xs) 311.79/291.58 if2(true, n, x, xs) -> filterhigh(n, xs) 311.79/291.58 if2(false, n, x, xs) -> cons(x, filterhigh(n, xs)) 311.79/291.58 ge(x, 0) -> true 311.79/291.58 ge(0, s(x)) -> false 311.79/291.58 ge(s(x), s(y)) -> ge(x, y) 311.79/291.58 append(nil, ys) -> ys 311.79/291.58 append(cons(x, xs), ys) -> cons(x, append(xs, ys)) 311.79/291.58 length(nil) -> 0 311.79/291.58 length(cons(x, xs)) -> s(length(xs)) 311.79/291.58 half(0) -> 0 311.79/291.58 half(s(0)) -> 0 311.79/291.58 half(s(s(x))) -> s(half(x)) 311.79/291.58 get(n, nil) -> 0 311.79/291.58 get(n, cons(x, nil)) -> x 311.79/291.58 get(0, cons(x, cons(y, xs))) -> x 311.79/291.58 get(s(n), cons(x, cons(y, xs))) -> get(n, cons(y, xs)) 311.79/291.58 311.79/291.58 S is empty. 311.79/291.58 Rewrite Strategy: FULL 311.79/291.58 ---------------------------------------- 311.79/291.58 311.79/291.58 (1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) 311.79/291.58 Transformed a relative TRS into a decreasing-loop problem. 311.79/291.58 ---------------------------------------- 311.79/291.58 311.79/291.58 (2) 311.79/291.58 Obligation: 311.79/291.58 Analyzing the following TRS for decreasing loops: 311.79/291.58 311.79/291.58 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 311.79/291.58 311.79/291.58 311.79/291.58 The TRS R consists of the following rules: 311.79/291.58 311.79/291.58 qsort(xs) -> qs(half(length(xs)), xs) 311.79/291.58 qs(n, nil) -> nil 311.79/291.58 qs(n, cons(x, xs)) -> append(qs(half(n), filterlow(get(n, cons(x, xs)), cons(x, xs))), cons(get(n, cons(x, xs)), qs(half(n), filterhigh(get(n, cons(x, xs)), cons(x, xs))))) 311.79/291.58 filterlow(n, nil) -> nil 311.79/291.58 filterlow(n, cons(x, xs)) -> if1(ge(n, x), n, x, xs) 311.79/291.58 if1(true, n, x, xs) -> filterlow(n, xs) 311.79/291.58 if1(false, n, x, xs) -> cons(x, filterlow(n, xs)) 311.79/291.58 filterhigh(n, nil) -> nil 311.79/291.58 filterhigh(n, cons(x, xs)) -> if2(ge(x, n), n, x, xs) 311.79/291.58 if2(true, n, x, xs) -> filterhigh(n, xs) 311.79/291.58 if2(false, n, x, xs) -> cons(x, filterhigh(n, xs)) 311.79/291.58 ge(x, 0) -> true 311.79/291.58 ge(0, s(x)) -> false 311.79/291.58 ge(s(x), s(y)) -> ge(x, y) 311.79/291.58 append(nil, ys) -> ys 311.79/291.58 append(cons(x, xs), ys) -> cons(x, append(xs, ys)) 311.79/291.58 length(nil) -> 0 311.79/291.58 length(cons(x, xs)) -> s(length(xs)) 311.79/291.58 half(0) -> 0 311.79/291.58 half(s(0)) -> 0 311.79/291.58 half(s(s(x))) -> s(half(x)) 311.79/291.58 get(n, nil) -> 0 311.79/291.58 get(n, cons(x, nil)) -> x 311.79/291.58 get(0, cons(x, cons(y, xs))) -> x 311.79/291.58 get(s(n), cons(x, cons(y, xs))) -> get(n, cons(y, xs)) 311.79/291.58 311.79/291.58 S is empty. 311.79/291.58 Rewrite Strategy: FULL 311.79/291.58 ---------------------------------------- 311.79/291.58
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