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Runti Compl Inner Rewri 22807 pair #381904635
details
property
value
status
complete
benchmark
mergesort.raml.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n050.star.cs.uiowa.edu
space
raML
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.801408052 seconds
cpu usage
1059.92277014
max memory
1.5644434432E10
stage attributes
key
value
output-size
11415
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, INF). (0) CpxRelTRS (1) STerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 197 ms] (2) CpxRelTRS (3) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (4) TRS for Loop Detection (5) DecreasingLoopProof [LOWER BOUND(ID), 126 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: #less(@x, @y) -> #cklt(#compare(@x, @y)) merge(@l1, @l2) -> merge#1(@l1, @l2) merge#1(::(@x, @xs), @l2) -> merge#2(@l2, @x, @xs) merge#1(nil, @l2) -> @l2 merge#2(::(@y, @ys), @x, @xs) -> merge#3(#less(@x, @y), @x, @xs, @y, @ys) merge#2(nil, @x, @xs) -> ::(@x, @xs) merge#3(#false, @x, @xs, @y, @ys) -> ::(@y, merge(::(@x, @xs), @ys)) merge#3(#true, @x, @xs, @y, @ys) -> ::(@x, merge(@xs, ::(@y, @ys))) mergesort(@l) -> mergesort#1(@l) mergesort#1(::(@x1, @xs)) -> mergesort#2(@xs, @x1) mergesort#1(nil) -> nil mergesort#2(::(@x2, @xs'), @x1) -> mergesort#3(msplit(::(@x1, ::(@x2, @xs')))) mergesort#2(nil, @x1) -> ::(@x1, nil) mergesort#3(tuple#2(@l1, @l2)) -> merge(mergesort(@l1), mergesort(@l2)) msplit(@l) -> msplit#1(@l) msplit#1(::(@x1, @xs)) -> msplit#2(@xs, @x1) msplit#1(nil) -> tuple#2(nil, nil) msplit#2(::(@x2, @xs'), @x1) -> msplit#3(msplit(@xs'), @x1, @x2) msplit#2(nil, @x1) -> tuple#2(::(@x1, nil), nil) msplit#3(tuple#2(@l1, @l2), @x1, @x2) -> tuple#2(::(@x1, @l1), ::(@x2, @l2)) The (relative) TRS S consists of the following rules: #cklt(#EQ) -> #false #cklt(#GT) -> #false #cklt(#LT) -> #true #compare(#0, #0) -> #EQ #compare(#0, #neg(@y)) -> #GT #compare(#0, #pos(@y)) -> #LT #compare(#0, #s(@y)) -> #LT #compare(#neg(@x), #0) -> #LT #compare(#neg(@x), #neg(@y)) -> #compare(@y, @x) #compare(#neg(@x), #pos(@y)) -> #LT #compare(#pos(@x), #0) -> #GT #compare(#pos(@x), #neg(@y)) -> #GT #compare(#pos(@x), #pos(@y)) -> #compare(@x, @y) #compare(#s(@x), #0) -> #GT #compare(#s(@x), #s(@y)) -> #compare(@x, @y) 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: #less(@x, @y) -> #cklt(#compare(@x, @y)) merge(@l1, @l2) -> merge#1(@l1, @l2) merge#1(::(@x, @xs), @l2) -> merge#2(@l2, @x, @xs) merge#1(nil, @l2) -> @l2 merge#2(::(@y, @ys), @x, @xs) -> merge#3(#less(@x, @y), @x, @xs, @y, @ys) merge#2(nil, @x, @xs) -> ::(@x, @xs) merge#3(#false, @x, @xs, @y, @ys) -> ::(@y, merge(::(@x, @xs), @ys)) merge#3(#true, @x, @xs, @y, @ys) -> ::(@x, merge(@xs, ::(@y, @ys))) mergesort(@l) -> mergesort#1(@l) mergesort#1(::(@x1, @xs)) -> mergesort#2(@xs, @x1) mergesort#1(nil) -> nil mergesort#2(::(@x2, @xs'), @x1) -> mergesort#3(msplit(::(@x1, ::(@x2, @xs'))))
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