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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313912
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
n082.star.cs.uiowa.edu
space
AProVE_09_Inductive
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
292.92 seconds
cpu usage
1141.0
user time
1128.87
system time
12.1284
max virtual memory
3.8076268E7
max residence set size
1.4883148E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
1135.63/291.55 WORST_CASE(Omega(n^1), ?) 1140.84/292.85 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 1140.84/292.85 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1140.84/292.85 1140.84/292.85 1140.84/292.85 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1140.84/292.85 1140.84/292.85 (0) CpxTRS 1140.84/292.85 (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 1140.84/292.85 (2) TRS for Loop Detection 1140.84/292.85 (3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 1140.84/292.85 (4) BEST 1140.84/292.85 (5) proven lower bound 1140.84/292.85 (6) LowerBoundPropagationProof [FINISHED, 0 ms] 1140.84/292.85 (7) BOUNDS(n^1, INF) 1140.84/292.85 (8) TRS for Loop Detection 1140.84/292.85 1140.84/292.85 1140.84/292.85 ---------------------------------------- 1140.84/292.85 1140.84/292.85 (0) 1140.84/292.85 Obligation: 1140.84/292.85 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1140.84/292.85 1140.84/292.85 1140.84/292.85 The TRS R consists of the following rules: 1140.84/292.85 1140.84/292.85 qsort(xs) -> qs(half(length(xs)), xs) 1140.84/292.85 qs(n, nil) -> nil 1140.84/292.85 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))))) 1140.84/292.85 filterlow(n, nil) -> nil 1140.84/292.85 filterlow(n, cons(x, xs)) -> if1(ge(n, x), n, x, xs) 1140.84/292.85 if1(true, n, x, xs) -> filterlow(n, xs) 1140.84/292.85 if1(false, n, x, xs) -> cons(x, filterlow(n, xs)) 1140.84/292.85 filterhigh(n, nil) -> nil 1140.84/292.85 filterhigh(n, cons(x, xs)) -> if2(ge(x, n), n, x, xs) 1140.84/292.85 if2(true, n, x, xs) -> filterhigh(n, xs) 1140.84/292.85 if2(false, n, x, xs) -> cons(x, filterhigh(n, xs)) 1140.84/292.85 ge(x, 0) -> true 1140.84/292.85 ge(0, s(x)) -> false 1140.84/292.85 ge(s(x), s(y)) -> ge(x, y) 1140.84/292.85 append(nil, ys) -> ys 1140.84/292.85 append(cons(x, xs), ys) -> cons(x, append(xs, ys)) 1140.84/292.85 length(nil) -> 0 1140.84/292.85 length(cons(x, xs)) -> s(length(xs)) 1140.84/292.85 half(0) -> 0 1140.84/292.85 half(s(0)) -> 0 1140.84/292.85 half(s(s(x))) -> s(half(x)) 1140.84/292.85 get(n, nil) -> 0 1140.84/292.85 get(n, cons(x, nil)) -> x 1140.84/292.85 get(0, cons(x, cons(y, xs))) -> x 1140.84/292.85 get(s(n), cons(x, cons(y, xs))) -> get(n, cons(y, xs)) 1140.84/292.85 1140.84/292.85 S is empty. 1140.84/292.85 Rewrite Strategy: INNERMOST 1140.84/292.85 ---------------------------------------- 1140.84/292.85 1140.84/292.85 (1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) 1140.84/292.85 Transformed a relative TRS into a decreasing-loop problem. 1140.84/292.85 ---------------------------------------- 1140.84/292.85 1140.84/292.85 (2) 1140.84/292.85 Obligation: 1140.84/292.85 Analyzing the following TRS for decreasing loops: 1140.84/292.85 1140.84/292.85 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1140.84/292.85 1140.84/292.85 1140.84/292.85 The TRS R consists of the following rules: 1140.84/292.85 1140.84/292.85 qsort(xs) -> qs(half(length(xs)), xs) 1140.84/292.85 qs(n, nil) -> nil 1140.84/292.85 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))))) 1140.84/292.85 filterlow(n, nil) -> nil 1140.84/292.85 filterlow(n, cons(x, xs)) -> if1(ge(n, x), n, x, xs) 1140.84/292.85 if1(true, n, x, xs) -> filterlow(n, xs) 1140.84/292.85 if1(false, n, x, xs) -> cons(x, filterlow(n, xs)) 1140.84/292.85 filterhigh(n, nil) -> nil 1140.84/292.85 filterhigh(n, cons(x, xs)) -> if2(ge(x, n), n, x, xs) 1140.84/292.85 if2(true, n, x, xs) -> filterhigh(n, xs) 1140.84/292.85 if2(false, n, x, xs) -> cons(x, filterhigh(n, xs)) 1140.84/292.85 ge(x, 0) -> true 1140.84/292.85 ge(0, s(x)) -> false 1140.84/292.85 ge(s(x), s(y)) -> ge(x, y) 1140.84/292.85 append(nil, ys) -> ys 1140.84/292.85 append(cons(x, xs), ys) -> cons(x, append(xs, ys)) 1140.84/292.85 length(nil) -> 0 1140.84/292.85 length(cons(x, xs)) -> s(length(xs)) 1140.84/292.85 half(0) -> 0 1140.84/292.85 half(s(0)) -> 0 1140.84/292.85 half(s(s(x))) -> s(half(x)) 1140.84/292.85 get(n, nil) -> 0 1140.84/292.85 get(n, cons(x, nil)) -> x 1140.84/292.85 get(0, cons(x, cons(y, xs))) -> x 1140.84/292.85 get(s(n), cons(x, cons(y, xs))) -> get(n, cons(y, xs)) 1140.84/292.85 1140.84/292.85 S is empty. 1140.84/292.85 Rewrite Strategy: INNERMOST 1140.84/292.85 ---------------------------------------- 1140.84/292.85
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