Runti Compl Inner Rewri 22807 pair #381904685

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	n047.star.cs.uiowa.edu
space	raML

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	291.86123395 seconds
cpu usage	405.841018253
max memory	1.1414528E10

stage attributes

key	value
output-size	62111
starexec-result	WORST_CASE(Omega(n^1), O(n^2))

output

/export/starexec/sandbox2/solver/bin/starexec_run_complexity /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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WORST_CASE(Omega(n^1), O(n^2))
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, n^2).

(0) CpxRelTRS
(1) STerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 229 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), 0 ms]
    (10) CpxRNTS
    (11) CompleteCoflocoProof [FINISHED, 3882 ms]
    (12) BOUNDS(1, n^2)
(13) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
(14) TRS for Loop Detection
    (15) DecreasingLoopProof [LOWER BOUND(ID), 69 ms]
    (16) BEST
        (17) proven lower bound
            (18) LowerBoundPropagationProof [FINISHED, 0 ms]
            (19) BOUNDS(n^1, INF)
        (20) TRS for Loop Detection


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(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
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(1) STerminationProof (BOTH CONCRETE BOUNDS(ID, ID))
proved termination of relative rules
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(2)
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:

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