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Runti Compl Inner Rewri 22807 pair #381904429
details
property
value
status
complete
benchmark
aprove06.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n040.star.cs.uiowa.edu
space
Secret_07_TRS
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.809617996 seconds
cpu usage
1127.02577938
max memory
6.713520128E9
stage attributes
key
value
output-size
5975
starexec-result
WORST_CASE(Omega(n^1), ?)
output
/export/starexec/sandbox2/solver/bin/starexec_run_complexity /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^1), ?) proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). (0) CpxTRS (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (2) TRS for Loop Detection (3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] (4) BEST (5) proven lower bound (6) LowerBoundPropagationProof [FINISHED, 0 ms] (7) BOUNDS(n^1, INF) (8) TRS for Loop Detection ---------------------------------------- (0) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). The TRS R consists of the following rules: le(s(x), 0) -> false le(0, y) -> true le(s(x), s(y)) -> le(x, y) double(0) -> 0 double(s(x)) -> s(s(double(x))) log(0) -> logError log(s(x)) -> loop(s(x), s(0), 0) loop(x, s(y), z) -> if(le(x, s(y)), x, s(y), z) if(true, x, y, z) -> z if(false, x, y, z) -> loop(x, double(y), s(z)) maplog(xs) -> mapIter(xs, nil) mapIter(xs, ys) -> ifmap(isempty(xs), xs, ys) ifmap(true, xs, ys) -> ys ifmap(false, xs, ys) -> mapIter(droplast(xs), cons(log(last(xs)), ys)) isempty(nil) -> true isempty(cons(x, xs)) -> false last(nil) -> error last(cons(x, nil)) -> x last(cons(x, cons(y, xs))) -> last(cons(y, xs)) droplast(nil) -> nil droplast(cons(x, nil)) -> nil droplast(cons(x, cons(y, xs))) -> cons(x, droplast(cons(y, xs))) a -> b a -> c S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) Transformed a relative TRS into a decreasing-loop problem. ---------------------------------------- (2) Obligation: Analyzing the following TRS for decreasing loops: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). The TRS R consists of the following rules: le(s(x), 0) -> false le(0, y) -> true le(s(x), s(y)) -> le(x, y) double(0) -> 0 double(s(x)) -> s(s(double(x))) log(0) -> logError log(s(x)) -> loop(s(x), s(0), 0) loop(x, s(y), z) -> if(le(x, s(y)), x, s(y), z) if(true, x, y, z) -> z if(false, x, y, z) -> loop(x, double(y), s(z)) maplog(xs) -> mapIter(xs, nil) mapIter(xs, ys) -> ifmap(isempty(xs), xs, ys) ifmap(true, xs, ys) -> ys ifmap(false, xs, ys) -> mapIter(droplast(xs), cons(log(last(xs)), ys)) isempty(nil) -> true isempty(cons(x, xs)) -> false last(nil) -> error last(cons(x, nil)) -> x last(cons(x, cons(y, xs))) -> last(cons(y, xs)) droplast(nil) -> nil droplast(cons(x, nil)) -> nil droplast(cons(x, cons(y, xs))) -> cons(x, droplast(cons(y, xs))) a -> b a -> c
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