MAYBE
We are left with following problem, upon which TcT provides the
certificate MAYBE.
Strict Trs:
{ division(x, y) -> div(x, y, 0())
, div(x, y, z) -> if(lt(x, y), x, y, inc(z))
, if(true(), x, y, z) -> z
, if(false(), x, s(y), z) -> div(minus(x, s(y)), s(y), z)
, lt(x, 0()) -> false()
, lt(0(), s(y)) -> true()
, lt(s(x), s(y)) -> lt(x, y)
, inc(0()) -> s(0())
, inc(s(x)) -> s(inc(x))
, minus(x, 0()) -> x
, minus(s(x), s(y)) -> minus(x, y) }
Obligation:
runtime complexity
Answer:
MAYBE
None of the processors succeeded.
Details of failed attempt(s):
-----------------------------
1) 'WithProblem (timeout of 60 seconds)' failed due to the
following reason:
Computation stopped due to timeout after 60.0 seconds.
2) 'Best' failed due to the following reason:
None of the processors succeeded.
Details of failed attempt(s):
-----------------------------
1) 'WithProblem (timeout of 30 seconds) (timeout of 60 seconds)'
failed due to the following reason:
None of the processors succeeded.
Details of failed attempt(s):
-----------------------------
1) 'empty' failed due to the following reason:
Empty strict component of the problem is NOT empty.
2) 'WithProblem' failed due to the following reason:
None of the processors succeeded.
Details of failed attempt(s):
-----------------------------
1) 'empty' failed due to the following reason:
Empty strict component of the problem is NOT empty.
2) 'Fastest' failed due to the following reason:
None of the processors succeeded.
Details of failed attempt(s):
-----------------------------
1) 'WithProblem' failed due to the following reason:
None of the processors succeeded.
Details of failed attempt(s):
-----------------------------
1) 'empty' failed due to the following reason:
Empty strict component of the problem is NOT empty.
2) 'WithProblem' failed due to the following reason:
Empty strict component of the problem is NOT empty.
2) 'WithProblem' failed due to the following reason:
None of the processors succeeded.
Details of failed attempt(s):
-----------------------------
1) 'empty' failed due to the following reason:
Empty strict component of the problem is NOT empty.
2) 'WithProblem' failed due to the following reason:
None of the processors succeeded.
Details of failed attempt(s):
-----------------------------
1) 'empty' failed due to the following reason:
Empty strict component of the problem is NOT empty.
2) 'WithProblem' failed due to the following reason:
None of the processors succeeded.
Details of failed attempt(s):
-----------------------------
1) 'empty' failed due to the following reason:
Empty strict component of the problem is NOT empty.
2) 'WithProblem' failed due to the following reason:
Empty strict component of the problem is NOT empty.
2) 'Best' failed due to the following reason:
None of the processors succeeded.
Details of failed attempt(s):
-----------------------------
1) 'Polynomial Path Order (PS) (timeout of 60 seconds)' failed due
to the following reason:
The processor is inapplicable, reason:
Processor only applicable for innermost runtime complexity analysis
2) 'bsearch-popstar (timeout of 60 seconds)' failed due to the
following reason:
The processor is inapplicable, reason:
Processor only applicable for innermost runtime complexity analysis
3) 'Fastest (timeout of 5 seconds) (timeout of 60 seconds)' failed
due to the following reason:
None of the processors succeeded.
Details of failed attempt(s):
-----------------------------
1) 'Bounds with perSymbol-enrichment and initial automaton 'match''
failed due to the following reason:
match-boundness of the problem could not be verified.
2) 'Bounds with minimal-enrichment and initial automaton 'match''
failed due to the following reason:
match-boundness of the problem could not be verified.
3) 'Innermost Weak Dependency Pairs (timeout of 60 seconds)' failed
due to the following reason:
We add the following weak dependency pairs:
Strict DPs:
{ division^#(x, y) -> c_1(div^#(x, y, 0()))
, div^#(x, y, z) -> c_2(if^#(lt(x, y), x, y, inc(z)))
, if^#(true(), x, y, z) -> c_3(z)
, if^#(false(), x, s(y), z) -> c_4(div^#(minus(x, s(y)), s(y), z))
, lt^#(x, 0()) -> c_5()
, lt^#(0(), s(y)) -> c_6()
, lt^#(s(x), s(y)) -> c_7(lt^#(x, y))
, inc^#(0()) -> c_8()
, inc^#(s(x)) -> c_9(inc^#(x))
, minus^#(x, 0()) -> c_10(x)
, minus^#(s(x), s(y)) -> c_11(minus^#(x, y)) }
and mark the set of starting terms.
We are left with following problem, upon which TcT provides the
certificate MAYBE.
Strict DPs:
{ division^#(x, y) -> c_1(div^#(x, y, 0()))
, div^#(x, y, z) -> c_2(if^#(lt(x, y), x, y, inc(z)))
, if^#(true(), x, y, z) -> c_3(z)
, if^#(false(), x, s(y), z) -> c_4(div^#(minus(x, s(y)), s(y), z))
, lt^#(x, 0()) -> c_5()
, lt^#(0(), s(y)) -> c_6()
, lt^#(s(x), s(y)) -> c_7(lt^#(x, y))
, inc^#(0()) -> c_8()
, inc^#(s(x)) -> c_9(inc^#(x))
, minus^#(x, 0()) -> c_10(x)
, minus^#(s(x), s(y)) -> c_11(minus^#(x, y)) }
Strict Trs:
{ division(x, y) -> div(x, y, 0())
, div(x, y, z) -> if(lt(x, y), x, y, inc(z))
, if(true(), x, y, z) -> z
, if(false(), x, s(y), z) -> div(minus(x, s(y)), s(y), z)
, lt(x, 0()) -> false()
, lt(0(), s(y)) -> true()
, lt(s(x), s(y)) -> lt(x, y)
, inc(0()) -> s(0())
, inc(s(x)) -> s(inc(x))
, minus(x, 0()) -> x
, minus(s(x), s(y)) -> minus(x, y) }
Obligation:
runtime complexity
Answer:
MAYBE
We estimate the number of application of {5,6,8} by applications of
Pre({5,6,8}) = {3,7,9,10}. Here rules are labeled as follows:
DPs:
{ 1: division^#(x, y) -> c_1(div^#(x, y, 0()))
, 2: div^#(x, y, z) -> c_2(if^#(lt(x, y), x, y, inc(z)))
, 3: if^#(true(), x, y, z) -> c_3(z)
, 4: if^#(false(), x, s(y), z) ->
c_4(div^#(minus(x, s(y)), s(y), z))
, 5: lt^#(x, 0()) -> c_5()
, 6: lt^#(0(), s(y)) -> c_6()
, 7: lt^#(s(x), s(y)) -> c_7(lt^#(x, y))
, 8: inc^#(0()) -> c_8()
, 9: inc^#(s(x)) -> c_9(inc^#(x))
, 10: minus^#(x, 0()) -> c_10(x)
, 11: minus^#(s(x), s(y)) -> c_11(minus^#(x, y)) }
We are left with following problem, upon which TcT provides the
certificate MAYBE.
Strict DPs:
{ division^#(x, y) -> c_1(div^#(x, y, 0()))
, div^#(x, y, z) -> c_2(if^#(lt(x, y), x, y, inc(z)))
, if^#(true(), x, y, z) -> c_3(z)
, if^#(false(), x, s(y), z) -> c_4(div^#(minus(x, s(y)), s(y), z))
, lt^#(s(x), s(y)) -> c_7(lt^#(x, y))
, inc^#(s(x)) -> c_9(inc^#(x))
, minus^#(x, 0()) -> c_10(x)
, minus^#(s(x), s(y)) -> c_11(minus^#(x, y)) }
Strict Trs:
{ division(x, y) -> div(x, y, 0())
, div(x, y, z) -> if(lt(x, y), x, y, inc(z))
, if(true(), x, y, z) -> z
, if(false(), x, s(y), z) -> div(minus(x, s(y)), s(y), z)
, lt(x, 0()) -> false()
, lt(0(), s(y)) -> true()
, lt(s(x), s(y)) -> lt(x, y)
, inc(0()) -> s(0())
, inc(s(x)) -> s(inc(x))
, minus(x, 0()) -> x
, minus(s(x), s(y)) -> minus(x, y) }
Weak DPs:
{ lt^#(x, 0()) -> c_5()
, lt^#(0(), s(y)) -> c_6()
, inc^#(0()) -> c_8() }
Obligation:
runtime complexity
Answer:
MAYBE
Empty strict component of the problem is NOT empty.
Arrrr..