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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307739
details
property
value
status
complete
benchmark
otto06.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n044.star.cs.uiowa.edu
space
AProVE_07
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.524 seconds
cpu usage
315.807
user time
313.857
system time
1.94999
max virtual memory
1.8281832E7
max residence set size
5360932.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
315.71/291.48 WORST_CASE(Omega(n^1), ?) 315.71/291.49 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 315.71/291.49 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 315.71/291.49 315.71/291.49 315.71/291.49 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 315.71/291.49 315.71/291.49 (0) CpxTRS 315.71/291.49 (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 315.71/291.49 (2) TRS for Loop Detection 315.71/291.49 (3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 315.71/291.49 (4) BEST 315.71/291.49 (5) proven lower bound 315.71/291.49 (6) LowerBoundPropagationProof [FINISHED, 0 ms] 315.71/291.49 (7) BOUNDS(n^1, INF) 315.71/291.49 (8) TRS for Loop Detection 315.71/291.49 315.71/291.49 315.71/291.49 ---------------------------------------- 315.71/291.49 315.71/291.49 (0) 315.71/291.49 Obligation: 315.71/291.49 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 315.71/291.49 315.71/291.49 315.71/291.49 The TRS R consists of the following rules: 315.71/291.49 315.71/291.49 app(x, y) -> helpa(0, plus(length(x), length(y)), x, y) 315.71/291.49 plus(x, 0) -> x 315.71/291.49 plus(x, s(y)) -> s(plus(x, y)) 315.71/291.49 length(nil) -> 0 315.71/291.49 length(cons(x, y)) -> s(length(y)) 315.71/291.49 helpa(c, l, ys, zs) -> if(ge(c, l), c, l, ys, zs) 315.71/291.49 ge(x, 0) -> true 315.71/291.49 ge(0, s(x)) -> false 315.71/291.49 ge(s(x), s(y)) -> ge(x, y) 315.71/291.49 if(true, c, l, ys, zs) -> nil 315.71/291.49 if(false, c, l, ys, zs) -> helpb(c, l, greater(ys, zs), smaller(ys, zs)) 315.71/291.49 greater(ys, zs) -> helpc(ge(length(ys), length(zs)), ys, zs) 315.71/291.49 smaller(ys, zs) -> helpc(ge(length(ys), length(zs)), zs, ys) 315.71/291.49 helpc(true, ys, zs) -> ys 315.71/291.49 helpc(false, ys, zs) -> zs 315.71/291.49 helpb(c, l, cons(y, ys), zs) -> cons(y, helpa(s(c), l, ys, zs)) 315.71/291.49 315.71/291.49 S is empty. 315.71/291.49 Rewrite Strategy: FULL 315.71/291.49 ---------------------------------------- 315.71/291.49 315.71/291.49 (1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) 315.71/291.49 Transformed a relative TRS into a decreasing-loop problem. 315.71/291.49 ---------------------------------------- 315.71/291.49 315.71/291.49 (2) 315.71/291.49 Obligation: 315.71/291.49 Analyzing the following TRS for decreasing loops: 315.71/291.49 315.71/291.49 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 315.71/291.49 315.71/291.49 315.71/291.49 The TRS R consists of the following rules: 315.71/291.49 315.71/291.49 app(x, y) -> helpa(0, plus(length(x), length(y)), x, y) 315.71/291.49 plus(x, 0) -> x 315.71/291.49 plus(x, s(y)) -> s(plus(x, y)) 315.71/291.49 length(nil) -> 0 315.71/291.49 length(cons(x, y)) -> s(length(y)) 315.71/291.49 helpa(c, l, ys, zs) -> if(ge(c, l), c, l, ys, zs) 315.71/291.49 ge(x, 0) -> true 315.71/291.49 ge(0, s(x)) -> false 315.71/291.49 ge(s(x), s(y)) -> ge(x, y) 315.71/291.49 if(true, c, l, ys, zs) -> nil 315.71/291.49 if(false, c, l, ys, zs) -> helpb(c, l, greater(ys, zs), smaller(ys, zs)) 315.71/291.49 greater(ys, zs) -> helpc(ge(length(ys), length(zs)), ys, zs) 315.71/291.49 smaller(ys, zs) -> helpc(ge(length(ys), length(zs)), zs, ys) 315.71/291.49 helpc(true, ys, zs) -> ys 315.71/291.49 helpc(false, ys, zs) -> zs 315.71/291.49 helpb(c, l, cons(y, ys), zs) -> cons(y, helpa(s(c), l, ys, zs)) 315.71/291.49 315.71/291.49 S is empty. 315.71/291.49 Rewrite Strategy: FULL 315.71/291.49 ---------------------------------------- 315.71/291.49 315.71/291.49 (3) DecreasingLoopProof (LOWER BOUND(ID)) 315.71/291.49 The following loop(s) give(s) rise to the lower bound Omega(n^1): 315.71/291.49 315.71/291.49 The rewrite sequence 315.71/291.49 315.71/291.49 plus(x, s(y)) ->^+ s(plus(x, y)) 315.71/291.49 315.71/291.49 gives rise to a decreasing loop by considering the right hand sides subterm at position [0]. 315.71/291.49 315.71/291.49 The pumping substitution is [y / s(y)]. 315.71/291.49 315.71/291.49 The result substitution is [ ]. 315.71/291.49 315.71/291.49 315.71/291.49 315.71/291.49 315.71/291.49 ---------------------------------------- 315.71/291.49
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