details

property	value
status	complete
benchmark	duplicates.raml.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n137.star.cs.uiowa.edu
space	raML

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	291.533 seconds
cpu usage	408.066
user time	399.531
system time	8.53417
max virtual memory	1.9387712E7
max residence set size	1.1211408E7

stage attributes

key	value
starexec-result	WORST_CASE(Omega(n^1), O(n^2))

output

WORST_CASE(Omega(n^1), O(n^2)) proof of /export/starexec/sandbox2/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^2). (0) CpxRelTRS (1) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 161 ms] (2) CpxRelTRS (3) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (4) CpxWeightedTrs (5) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (6) CpxTypedWeightedTrs (7) CompletionProof [UPPER BOUND(ID), 0 ms] (8) CpxTypedWeightedCompleteTrs (9) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 7 ms] (10) CpxRNTS (11) CompleteCoflocoProof [FINISHED, 3877 ms] (12) BOUNDS(1, n^2) (13) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (14) CpxRelTRS (15) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (16) typed CpxTrs (17) OrderProof [LOWER BOUND(ID), 0 ms] (18) typed CpxTrs (19) RewriteLemmaProof [LOWER BOUND(ID), 24.9 s] (20) typed CpxTrs (21) RewriteLemmaProof [LOWER BOUND(ID), 70 ms] (22) BEST (23) proven lower bound (24) LowerBoundPropagationProof [FINISHED, 0 ms] (25) BOUNDS(n^1, INF) (26) typed CpxTrs (27) RewriteLemmaProof [LOWER BOUND(ID), 61 ms] (28) typed CpxTrs ---------------------------------------- (0) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^2). The TRS R consists of the following rules: #equal(@x, @y) -> #eq(@x, @y) and(@x, @y) -> #and(@x, @y) eq(@l1, @l2) -> eq#1(@l1, @l2) eq#1(::(@x, @xs), @l2) -> eq#3(@l2, @x, @xs) eq#1(nil, @l2) -> eq#2(@l2) eq#2(::(@y, @ys)) -> #false eq#2(nil) -> #true eq#3(::(@y, @ys), @x, @xs) -> and(#equal(@x, @y), eq(@xs, @ys)) eq#3(nil, @x, @xs) -> #false nub(@l) -> nub#1(@l) nub#1(::(@x, @xs)) -> ::(@x, nub(remove(@x, @xs))) nub#1(nil) -> nil remove(@x, @l) -> remove#1(@l, @x) remove#1(::(@y, @ys), @x) -> remove#2(eq(@x, @y), @x, @y, @ys) remove#1(nil, @x) -> nil remove#2(#false, @x, @y, @ys) -> ::(@y, remove(@x, @ys)) remove#2(#true, @x, @y, @ys) -> remove(@x, @ys) The (relative) TRS S consists of the following rules: #and(#false, #false) -> #false #and(#false, #true) -> #false #and(#true, #false) -> #false #and(#true, #true) -> #true #eq(#0, #0) -> #true #eq(#0, #neg(@y)) -> #false #eq(#0, #pos(@y)) -> #false #eq(#0, #s(@y)) -> #false #eq(#neg(@x), #0) -> #false #eq(#neg(@x), #neg(@y)) -> #eq(@x, @y) #eq(#neg(@x), #pos(@y)) -> #false #eq(#pos(@x), #0) -> #false #eq(#pos(@x), #neg(@y)) -> #false #eq(#pos(@x), #pos(@y)) -> #eq(@x, @y) #eq(#s(@x), #0) -> #false #eq(#s(@x), #s(@y)) -> #eq(@x, @y) #eq(::(@x_1, @x_2), ::(@y_1, @y_2)) -> #and(#eq(@x_1, @y_1), #eq(@x_2, @y_2)) #eq(::(@x_1, @x_2), nil) -> #false #eq(nil, ::(@y_1, @y_2)) -> #false #eq(nil, nil) -> #true 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, n^2). popout

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job log

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actions

all output return to Runtime Complexity: TRS Innermost