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Runti Compl Inner Rewri 22807 pair #381905053
details
property
value
status
complete
benchmark
quicksort.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n046.star.cs.uiowa.edu
space
Frederiksen_Glenstrup
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
293.822266102 seconds
cpu usage
1140.19140776
max memory
1.5274635264E10
stage attributes
key
value
output-size
7632
starexec-result
WORST_CASE(Omega(n^1), ?)
output
/export/starexec/sandbox/solver/bin/starexec_run_complexity /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^1), ?) proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, INF). (0) CpxRelTRS (1) STerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 399 ms] (2) CpxRelTRS (3) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (4) TRS for Loop Detection (5) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] (6) BEST (7) proven lower bound (8) LowerBoundPropagationProof [FINISHED, 0 ms] (9) BOUNDS(n^1, INF) (10) TRS for Loop Detection ---------------------------------------- (0) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, INF). The TRS R consists of the following rules: quicksort(Cons(x, Cons(x', xs))) -> part(x, Cons(x, Cons(x', xs)), Cons(x, Nil), Nil) quicksort(Cons(x, Nil)) -> Cons(x, Nil) quicksort(Nil) -> Nil part(x', Cons(x, xs), xs1, xs2) -> part[Ite][True][Ite](>(x', x), x', Cons(x, xs), xs1, xs2) part(x, Nil, xs1, xs2) -> app(quicksort(xs1), quicksort(xs2)) app(Cons(x, xs), ys) -> Cons(x, app(xs, ys)) app(Nil, ys) -> ys notEmpty(Cons(x, xs)) -> True notEmpty(Nil) -> False goal(xs) -> quicksort(xs) The (relative) TRS S consists of the following rules: <(S(x), S(y)) -> <(x, y) <(0, S(y)) -> True <(x, 0) -> False >(S(x), S(y)) -> >(x, y) >(0, y) -> False >(S(x), 0) -> True part[Ite][True][Ite](True, x', Cons(x, xs), xs1, xs2) -> part(x', xs, Cons(x, xs1), xs2) part[Ite][True][Ite](False, x', Cons(x, xs), xs1, xs2) -> part[Ite][True][Ite][False][Ite](<(x', x), x', Cons(x, xs), xs1, xs2) Rewrite Strategy: INNERMOST ---------------------------------------- (1) STerminationProof (BOTH CONCRETE BOUNDS(ID, ID)) proved termination of relative rules ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, INF). The TRS R consists of the following rules: quicksort(Cons(x, Cons(x', xs))) -> part(x, Cons(x, Cons(x', xs)), Cons(x, Nil), Nil) quicksort(Cons(x, Nil)) -> Cons(x, Nil) quicksort(Nil) -> Nil part(x', Cons(x, xs), xs1, xs2) -> part[Ite][True][Ite](>(x', x), x', Cons(x, xs), xs1, xs2) part(x, Nil, xs1, xs2) -> app(quicksort(xs1), quicksort(xs2)) app(Cons(x, xs), ys) -> Cons(x, app(xs, ys)) app(Nil, ys) -> ys notEmpty(Cons(x, xs)) -> True notEmpty(Nil) -> False goal(xs) -> quicksort(xs) The (relative) TRS S consists of the following rules: <(S(x), S(y)) -> <(x, y) <(0, S(y)) -> True <(x, 0) -> False >(S(x), S(y)) -> >(x, y) >(0, y) -> False >(S(x), 0) -> True part[Ite][True][Ite](True, x', Cons(x, xs), xs1, xs2) -> part(x', xs, Cons(x, xs1), xs2) part[Ite][True][Ite](False, x', Cons(x, xs), xs1, xs2) -> part[Ite][True][Ite][False][Ite](<(x', x), x', Cons(x, xs), xs1, xs2) Rewrite Strategy: INNERMOST ---------------------------------------- (3) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) Transformed a relative TRS into a decreasing-loop problem. ----------------------------------------
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