MAYBE
We are left with following problem, upon which TcT provides the
certificate MAYBE.
Strict Trs:
{ log(x, s(s(y))) -> cond(le(x, s(s(y))), x, y)
, cond(true(), x, y) -> s(0())
, cond(false(), x, y) -> double(log(x, square(s(s(y)))))
, le(s(u), s(v)) -> le(u, v)
, le(s(u), 0()) -> false()
, le(0(), v) -> true()
, double(s(x)) -> s(s(double(x)))
, double(0()) -> 0()
, square(s(x)) -> s(plus(square(x), double(x)))
, square(0()) -> 0()
, plus(n, s(m)) -> s(plus(n, m))
, plus(n, 0()) -> n }
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:
Computation stopped due to timeout after 30.0 seconds.
2) '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) 'Best' failed due to the following reason:
None of the processors succeeded.
Details of failed attempt(s):
-----------------------------
1) '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
2) '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
3) 'Innermost Weak Dependency Pairs (timeout of 60 seconds)' failed
due to the following reason:
We add the following weak dependency pairs:
Strict DPs:
{ log^#(x, s(s(y))) -> c_1(cond^#(le(x, s(s(y))), x, y))
, cond^#(true(), x, y) -> c_2()
, cond^#(false(), x, y) -> c_3(double^#(log(x, square(s(s(y))))))
, double^#(s(x)) -> c_7(double^#(x))
, double^#(0()) -> c_8()
, le^#(s(u), s(v)) -> c_4(le^#(u, v))
, le^#(s(u), 0()) -> c_5()
, le^#(0(), v) -> c_6()
, square^#(s(x)) -> c_9(plus^#(square(x), double(x)))
, square^#(0()) -> c_10()
, plus^#(n, s(m)) -> c_11(plus^#(n, m))
, plus^#(n, 0()) -> c_12(n) }
and mark the set of starting terms.
We are left with following problem, upon which TcT provides the
certificate MAYBE.
Strict DPs:
{ log^#(x, s(s(y))) -> c_1(cond^#(le(x, s(s(y))), x, y))
, cond^#(true(), x, y) -> c_2()
, cond^#(false(), x, y) -> c_3(double^#(log(x, square(s(s(y))))))
, double^#(s(x)) -> c_7(double^#(x))
, double^#(0()) -> c_8()
, le^#(s(u), s(v)) -> c_4(le^#(u, v))
, le^#(s(u), 0()) -> c_5()
, le^#(0(), v) -> c_6()
, square^#(s(x)) -> c_9(plus^#(square(x), double(x)))
, square^#(0()) -> c_10()
, plus^#(n, s(m)) -> c_11(plus^#(n, m))
, plus^#(n, 0()) -> c_12(n) }
Strict Trs:
{ log(x, s(s(y))) -> cond(le(x, s(s(y))), x, y)
, cond(true(), x, y) -> s(0())
, cond(false(), x, y) -> double(log(x, square(s(s(y)))))
, le(s(u), s(v)) -> le(u, v)
, le(s(u), 0()) -> false()
, le(0(), v) -> true()
, double(s(x)) -> s(s(double(x)))
, double(0()) -> 0()
, square(s(x)) -> s(plus(square(x), double(x)))
, square(0()) -> 0()
, plus(n, s(m)) -> s(plus(n, m))
, plus(n, 0()) -> n }
Obligation:
runtime complexity
Answer:
MAYBE
We estimate the number of application of {2,5,7,8,10} by
applications of Pre({2,5,7,8,10}) = {1,3,4,6,12}. Here rules are
labeled as follows:
DPs:
{ 1: log^#(x, s(s(y))) -> c_1(cond^#(le(x, s(s(y))), x, y))
, 2: cond^#(true(), x, y) -> c_2()
, 3: cond^#(false(), x, y) ->
c_3(double^#(log(x, square(s(s(y))))))
, 4: double^#(s(x)) -> c_7(double^#(x))
, 5: double^#(0()) -> c_8()
, 6: le^#(s(u), s(v)) -> c_4(le^#(u, v))
, 7: le^#(s(u), 0()) -> c_5()
, 8: le^#(0(), v) -> c_6()
, 9: square^#(s(x)) -> c_9(plus^#(square(x), double(x)))
, 10: square^#(0()) -> c_10()
, 11: plus^#(n, s(m)) -> c_11(plus^#(n, m))
, 12: plus^#(n, 0()) -> c_12(n) }
We are left with following problem, upon which TcT provides the
certificate MAYBE.
Strict DPs:
{ log^#(x, s(s(y))) -> c_1(cond^#(le(x, s(s(y))), x, y))
, cond^#(false(), x, y) -> c_3(double^#(log(x, square(s(s(y))))))
, double^#(s(x)) -> c_7(double^#(x))
, le^#(s(u), s(v)) -> c_4(le^#(u, v))
, square^#(s(x)) -> c_9(plus^#(square(x), double(x)))
, plus^#(n, s(m)) -> c_11(plus^#(n, m))
, plus^#(n, 0()) -> c_12(n) }
Strict Trs:
{ log(x, s(s(y))) -> cond(le(x, s(s(y))), x, y)
, cond(true(), x, y) -> s(0())
, cond(false(), x, y) -> double(log(x, square(s(s(y)))))
, le(s(u), s(v)) -> le(u, v)
, le(s(u), 0()) -> false()
, le(0(), v) -> true()
, double(s(x)) -> s(s(double(x)))
, double(0()) -> 0()
, square(s(x)) -> s(plus(square(x), double(x)))
, square(0()) -> 0()
, plus(n, s(m)) -> s(plus(n, m))
, plus(n, 0()) -> n }
Weak DPs:
{ cond^#(true(), x, y) -> c_2()
, double^#(0()) -> c_8()
, le^#(s(u), 0()) -> c_5()
, le^#(0(), v) -> c_6()
, square^#(0()) -> c_10() }
Obligation:
runtime complexity
Answer:
MAYBE
Empty strict component of the problem is NOT empty.
Arrrr..