Runti Compl Full Rewri 10127 pair #381902230

details

property	value
status	complete
benchmark	tpa10.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n072.star.cs.uiowa.edu
space	Secret_06_TRS

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	291.480764866 seconds
cpu usage	312.088259741
max memory	5.475708928E9

stage attributes

key	value
output-size	16265
starexec-result	WORST_CASE(Omega(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^2), ?)
proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^2, INF).

(0) CpxTRS
(1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
(2) CpxTRS
(3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
(4) typed CpxTrs
(5) OrderProof [LOWER BOUND(ID), 0 ms]
(6) typed CpxTrs
(7) RewriteLemmaProof [LOWER BOUND(ID), 283 ms]
(8) BEST
    (9) proven lower bound
        (10) LowerBoundPropagationProof [FINISHED, 0 ms]
        (11) BOUNDS(n^1, INF)
    (12) typed CpxTrs
        (13) RewriteLemmaProof [LOWER BOUND(ID), 71 ms]
        (14) typed CpxTrs
        (15) RewriteLemmaProof [LOWER BOUND(ID), 32 ms]
        (16) typed CpxTrs
        (17) RewriteLemmaProof [LOWER BOUND(ID), 31 ms]
        (18) typed CpxTrs
        (19) RewriteLemmaProof [LOWER BOUND(ID), 46 ms]
        (20) BEST
            (21) proven lower bound
                (22) LowerBoundPropagationProof [FINISHED, 0 ms]
                (23) BOUNDS(n^2, INF)
            (24) typed CpxTrs


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


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

S is empty.
Rewrite Strategy: FULL
----------------------------------------

(1) RenamingProof (BOTH BOUNDS(ID, ID))
Renamed function symbols to avoid clashes with predefined symbol.
----------------------------------------

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


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))
   +'(0', y) -> y
   +'(s(x), y) -> s(+'(x, y))
   -(x, 0') -> x
   -(s(x), s(y)) -> -(x, y)
   *'(x, 0') -> 0'
   *'(x, s(y)) -> +'(x, *'(x, y))
   p(s(x)) -> x
   f(s(x), s(y)) -> f(-(min(s(x), s(y)), max(s(x), s(y))), *'(s(x), s(y)))

S is empty.
Rewrite Strategy: FULL
----------------------------------------

(3) TypeInferenceProof (BOTH BOUNDS(ID, ID))
Infered types.

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