Runtime Complexity: TRS pair #487110994

details

property	value
status	complete
benchmark	otto13.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n144.star.cs.uiowa.edu
space	AProVE_07

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	291.558 seconds
cpu usage	1061.46
user time	1046.8
system time	14.6633
max virtual memory	5.6605384E7
max residence set size	1.4986944E7

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/sandbox/benchmark/theBenchmark.xml
# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


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

(0) CpxTRS
(1) RcToIrcProof [BOTH BOUNDS(ID, ID), 18 ms]
(2) CpxTRS
    (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, 1182 ms]
    (12) BOUNDS(1, n^2)
(13) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
(14) CpxTRS
    (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), 282 ms]
    (20) BEST
        (21) proven lower bound
            (22) LowerBoundPropagationProof [FINISHED, 0 ms]
            (23) BOUNDS(n^1, INF)
        (24) typed CpxTrs
            (25) RewriteLemmaProof [LOWER BOUND(ID), 89 ms]
            (26) typed CpxTrs
            (27) RewriteLemmaProof [LOWER BOUND(ID), 74 ms]
            (28) typed CpxTrs


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


The TRS R consists of the following rules:

   le(0, y, z) -> greater(y, z)
   le(s(x), 0, z) -> false
   le(s(x), s(y), 0) -> false
   le(s(x), s(y), s(z)) -> le(x, y, z)
   greater(x, 0) -> first
   greater(0, s(y)) -> second
   greater(s(x), s(y)) -> greater(x, y)
   double(0) -> 0
   double(s(x)) -> s(s(double(x)))
   triple(x) -> if(le(x, x, double(x)), x, 0, 0)
   if(false, x, y, z) -> true
   if(first, x, y, z) -> if(le(s(x), y, s(z)), s(x), y, s(z))
   if(second, x, y, z) -> if(le(s(x), s(y), z), s(x), s(y), z)

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

(1) RcToIrcProof (BOTH BOUNDS(ID, ID))
Converted rc-obligation to irc-obligation.

The duplicating contexts are:
triple([])
if(first, [], y, z)
if(first, x, [], z)
if(first, x, y, [])
if(second, [], y, z)
if(second, x, [], z)
if(second, x, y, [])


The defined contexts are:
if([], s(x1), x2, s(x3))
if([], s(x1), s(x2), x3)
if([], x1, 0, 0)
le(x0, x1, [])
greater(x0, [])


[] just represents basic- or constructor-terms in the following defined contexts:
if([], s(x1), x2, s(x3))
if([], s(x1), s(x2), x3)


As the TRS is an overlay system and the defined contexts and the duplicating contexts don't overlap, we have rc = irc.
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(2)
Obligation:
The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, n^2).


The TRS R consists of the following rules:

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