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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313311
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
n039.star.cs.uiowa.edu
space
Secret_07_TRS
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
292.068 seconds
cpu usage
1148.28
user time
1133.96
system time
14.3241
max virtual memory
5.8607088E7
max residence set size
1.5779656E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
1147.77/291.91 WORST_CASE(Omega(n^1), ?) 1148.12/291.94 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 1148.12/291.94 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1148.12/291.94 1148.12/291.94 1148.12/291.94 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1148.12/291.94 1148.12/291.94 (0) CpxTRS 1148.12/291.94 (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 1148.12/291.94 (2) TRS for Loop Detection 1148.12/291.94 (3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 1148.12/291.94 (4) BEST 1148.12/291.94 (5) proven lower bound 1148.12/291.94 (6) LowerBoundPropagationProof [FINISHED, 0 ms] 1148.12/291.94 (7) BOUNDS(n^1, INF) 1148.12/291.94 (8) TRS for Loop Detection 1148.12/291.94 1148.12/291.94 1148.12/291.94 ---------------------------------------- 1148.12/291.94 1148.12/291.94 (0) 1148.12/291.94 Obligation: 1148.12/291.94 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1148.12/291.94 1148.12/291.94 1148.12/291.94 The TRS R consists of the following rules: 1148.12/291.94 1148.12/291.94 average(x, y) -> if(ge(x, y), x, y) 1148.12/291.94 if(true, x, y) -> averIter(y, x, y) 1148.12/291.94 if(false, x, y) -> averIter(x, y, x) 1148.12/291.94 averIter(x, y, z) -> ifIter(ge(x, y), x, y, z) 1148.12/291.94 ifIter(true, x, y, z) -> z 1148.12/291.94 ifIter(false, x, y, z) -> averIter(plus(x, s(s(s(0)))), plus(y, s(0)), plus(z, s(0))) 1148.12/291.94 append(nil, y) -> y 1148.12/291.94 append(cons(n, x), y) -> cons(n, app(x, y)) 1148.12/291.94 low(n, nil) -> nil 1148.12/291.94 low(n, cons(m, x)) -> if_low(ge(m, n), n, cons(m, x)) 1148.12/291.94 if_low(false, n, cons(m, x)) -> cons(m, low(n, x)) 1148.12/291.94 if_low(true, n, cons(m, x)) -> low(n, x) 1148.12/291.94 high(n, nil) -> nil 1148.12/291.94 high(n, cons(m, x)) -> if_high(ge(m, n), n, cons(m, x)) 1148.12/291.94 if_high(false, n, cons(m, x)) -> high(n, x) 1148.12/291.94 if_high(true, n, cons(m, x)) -> cons(average(m, m), high(n, x)) 1148.12/291.94 quicksort(x) -> ifquick(isempty(x), x) 1148.12/291.94 ifquick(true, x) -> nil 1148.12/291.94 ifquick(false, x) -> append(quicksort(low(head(x), tail(x))), cons(tail(x), quicksort(high(head(x), tail(x))))) 1148.12/291.94 plus(0, y) -> y 1148.12/291.94 plus(s(x), y) -> s(plus(x, y)) 1148.12/291.94 isempty(nil) -> true 1148.12/291.94 isempty(cons(n, x)) -> false 1148.12/291.94 head(nil) -> error 1148.12/291.94 head(cons(n, x)) -> n 1148.12/291.94 tail(nil) -> nil 1148.12/291.94 tail(cons(n, x)) -> x 1148.12/291.94 ge(x, 0) -> true 1148.12/291.94 ge(0, s(y)) -> false 1148.12/291.94 ge(s(x), s(y)) -> ge(x, y) 1148.12/291.94 a -> b 1148.12/291.94 a -> c 1148.12/291.94 1148.12/291.94 S is empty. 1148.12/291.94 Rewrite Strategy: INNERMOST 1148.12/291.94 ---------------------------------------- 1148.12/291.94 1148.12/291.94 (1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) 1148.12/291.94 Transformed a relative TRS into a decreasing-loop problem. 1148.12/291.94 ---------------------------------------- 1148.12/291.94 1148.12/291.94 (2) 1148.12/291.94 Obligation: 1148.12/291.94 Analyzing the following TRS for decreasing loops: 1148.12/291.94 1148.12/291.94 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1148.12/291.94 1148.12/291.94 1148.12/291.94 The TRS R consists of the following rules: 1148.12/291.94 1148.12/291.94 average(x, y) -> if(ge(x, y), x, y) 1148.12/291.94 if(true, x, y) -> averIter(y, x, y) 1148.12/291.94 if(false, x, y) -> averIter(x, y, x) 1148.12/291.94 averIter(x, y, z) -> ifIter(ge(x, y), x, y, z) 1148.12/291.94 ifIter(true, x, y, z) -> z 1148.12/291.94 ifIter(false, x, y, z) -> averIter(plus(x, s(s(s(0)))), plus(y, s(0)), plus(z, s(0))) 1148.12/291.94 append(nil, y) -> y 1148.12/291.94 append(cons(n, x), y) -> cons(n, app(x, y)) 1148.12/291.94 low(n, nil) -> nil 1148.12/291.94 low(n, cons(m, x)) -> if_low(ge(m, n), n, cons(m, x)) 1148.12/291.94 if_low(false, n, cons(m, x)) -> cons(m, low(n, x)) 1148.12/291.94 if_low(true, n, cons(m, x)) -> low(n, x) 1148.12/291.94 high(n, nil) -> nil 1148.12/291.94 high(n, cons(m, x)) -> if_high(ge(m, n), n, cons(m, x)) 1148.12/291.94 if_high(false, n, cons(m, x)) -> high(n, x) 1148.12/291.94 if_high(true, n, cons(m, x)) -> cons(average(m, m), high(n, x)) 1148.12/291.94 quicksort(x) -> ifquick(isempty(x), x) 1148.12/291.94 ifquick(true, x) -> nil 1148.12/291.94 ifquick(false, x) -> append(quicksort(low(head(x), tail(x))), cons(tail(x), quicksort(high(head(x), tail(x))))) 1148.12/291.94 plus(0, y) -> y 1148.12/291.94 plus(s(x), y) -> s(plus(x, y)) 1148.12/291.94 isempty(nil) -> true 1148.12/291.94 isempty(cons(n, x)) -> false
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return to Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40
