Runti Compl Inner Rewri 22807 pair #381904385

details

property	value
status	complete
benchmark	tpa06.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n041.star.cs.uiowa.edu
space	Secret_06_TRS

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	291.740135908 seconds
cpu usage	1142.16631375
max memory	1.88035072E10

stage attributes

key	value
output-size	135740
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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 CpxTRS could be proven to be BOUNDS(n^1, n^2).

(0) CpxTRS
(1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
(2) CpxWeightedTrs
    (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
    (4) CpxTypedWeightedTrs
    (5) CompletionProof [UPPER BOUND(ID), 0 ms]
    (6) CpxTypedWeightedCompleteTrs
    (7) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
    (8) CpxRNTS
    (9) CompleteCoflocoProof [FINISHED, 30.8 s]
    (10) BOUNDS(1, n^2)
(11) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
(12) TRS for Loop Detection
    (13) DecreasingLoopProof [LOWER BOUND(ID), 0 ms]
    (14) BEST
        (15) proven lower bound
            (16) LowerBoundPropagationProof [FINISHED, 0 ms]
            (17) BOUNDS(n^1, INF)
        (18) TRS for Loop Detection


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(0)
Obligation:
The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2).


The TRS R consists of the following rules:

   min(0, y) -> 0
   min(x, 0) -> 0
   min(s(x), s(y)) -> s(min(x, y))
   max(0, y) -> y
   max(x, 0) -> x
   max(s(x), s(y)) -> s(max(x, y))
   p(s(x)) -> x
   f(s(x), s(y), s(z)) -> f(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
   f(0, y, z) -> max(y, z)
   f(x, 0, z) -> max(x, z)
   f(x, y, 0) -> max(x, y)

S is empty.
Rewrite Strategy: INNERMOST
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(1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID))
Transformed relative TRS to weighted TRS
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(2)
Obligation:
The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^2).


The TRS R consists of the following rules:

   min(0, y) -> 0 [1]
   min(x, 0) -> 0 [1]
   min(s(x), s(y)) -> s(min(x, y)) [1]
   max(0, y) -> y [1]
   max(x, 0) -> x [1]
   max(s(x), s(y)) -> s(max(x, y)) [1]
   p(s(x)) -> x [1]
   f(s(x), s(y), s(z)) -> f(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z)))) [1]
   f(0, y, z) -> max(y, z) [1]
   f(x, 0, z) -> max(x, z) [1]
   f(x, y, 0) -> max(x, y) [1]

Rewrite Strategy: INNERMOST
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(3) TypeInferenceProof (BOTH BOUNDS(ID, ID))
Infered types.
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(4)
Obligation:
Runtime Complexity Weighted TRS with Types.
The TRS R consists of the following rules:

   min(0, y) -> 0 [1]
   min(x, 0) -> 0 [1]
   min(s(x), s(y)) -> s(min(x, y)) [1]
   max(0, y) -> y [1]
   max(x, 0) -> x [1]
   max(s(x), s(y)) -> s(max(x, y)) [1]

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