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Runtime Complexity: TRS Innermost pair #487111674
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
n142.star.cs.uiowa.edu
space
raML
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.581 seconds
cpu usage
1043.59
user time
1027.18
system time
16.41
max virtual memory
5.6908912E7
max residence set size
1.5109384E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
WORST_CASE(Omega(n^1), ?) proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, INF). (0) CpxRelTRS (1) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 213 ms] (2) CpxRelTRS (3) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (4) CpxRelTRS (5) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (6) typed CpxTrs (7) OrderProof [LOWER BOUND(ID), 0 ms] (8) typed CpxTrs (9) RewriteLemmaProof [LOWER BOUND(ID), 1889 ms] (10) typed CpxTrs (11) RewriteLemmaProof [LOWER BOUND(ID), 99 ms] (12) BEST (13) proven lower bound (14) LowerBoundPropagationProof [FINISHED, 0 ms] (15) BOUNDS(n^1, INF) (16) typed CpxTrs (17) RewriteLemmaProof [LOWER BOUND(ID), 121 ms] (18) typed CpxTrs ---------------------------------------- (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) SInnermostTerminationProof (BOTH CONCRETE BOUNDS(ID, ID)) proved innermost 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)
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