MAYBE
We are left with following problem, upon which TcT provides the
certificate MAYBE.
Strict Trs:
{ half(0()) -> 0()
, half(s(0())) -> 0()
, half(s(s(x))) -> s(half(x))
, le(0(), y) -> true()
, le(s(x), 0()) -> false()
, le(s(x), s(y)) -> le(x, y)
, inc(0()) -> s(0())
, inc(s(x)) -> s(inc(x))
, logarithm(x) -> logIter(x, 0())
, logIter(x, y) ->
if(le(s(0()), x), le(s(s(0())), x), half(x), inc(y))
, if(true(), true(), x, y) -> logIter(x, y)
, if(true(), false(), x, s(y)) -> y
, if(false(), b, x, y) -> logZeroError()
, f() -> g()
, f() -> h() }
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) '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) '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:
{ half^#(0()) -> c_1()
, half^#(s(0())) -> c_2()
, half^#(s(s(x))) -> c_3(half^#(x))
, le^#(0(), y) -> c_4()
, le^#(s(x), 0()) -> c_5()
, le^#(s(x), s(y)) -> c_6(le^#(x, y))
, inc^#(0()) -> c_7()
, inc^#(s(x)) -> c_8(inc^#(x))
, logarithm^#(x) -> c_9(logIter^#(x, 0()))
, logIter^#(x, y) ->
c_10(if^#(le(s(0()), x), le(s(s(0())), x), half(x), inc(y)))
, if^#(true(), true(), x, y) -> c_11(logIter^#(x, y))
, if^#(true(), false(), x, s(y)) -> c_12(y)
, if^#(false(), b, x, y) -> c_13()
, f^#() -> c_14()
, f^#() -> c_15() }
and mark the set of starting terms.
We are left with following problem, upon which TcT provides the
certificate MAYBE.
Strict DPs:
{ half^#(0()) -> c_1()
, half^#(s(0())) -> c_2()
, half^#(s(s(x))) -> c_3(half^#(x))
, le^#(0(), y) -> c_4()
, le^#(s(x), 0()) -> c_5()
, le^#(s(x), s(y)) -> c_6(le^#(x, y))
, inc^#(0()) -> c_7()
, inc^#(s(x)) -> c_8(inc^#(x))
, logarithm^#(x) -> c_9(logIter^#(x, 0()))
, logIter^#(x, y) ->
c_10(if^#(le(s(0()), x), le(s(s(0())), x), half(x), inc(y)))
, if^#(true(), true(), x, y) -> c_11(logIter^#(x, y))
, if^#(true(), false(), x, s(y)) -> c_12(y)
, if^#(false(), b, x, y) -> c_13()
, f^#() -> c_14()
, f^#() -> c_15() }
Strict Trs:
{ half(0()) -> 0()
, half(s(0())) -> 0()
, half(s(s(x))) -> s(half(x))
, le(0(), y) -> true()
, le(s(x), 0()) -> false()
, le(s(x), s(y)) -> le(x, y)
, inc(0()) -> s(0())
, inc(s(x)) -> s(inc(x))
, logarithm(x) -> logIter(x, 0())
, logIter(x, y) ->
if(le(s(0()), x), le(s(s(0())), x), half(x), inc(y))
, if(true(), true(), x, y) -> logIter(x, y)
, if(true(), false(), x, s(y)) -> y
, if(false(), b, x, y) -> logZeroError()
, f() -> g()
, f() -> h() }
Obligation:
runtime complexity
Answer:
MAYBE
We estimate the number of application of {1,2,4,5,7,13,14,15} by
applications of Pre({1,2,4,5,7,13,14,15}) = {3,6,8,10,12}. Here
rules are labeled as follows:
DPs:
{ 1: half^#(0()) -> c_1()
, 2: half^#(s(0())) -> c_2()
, 3: half^#(s(s(x))) -> c_3(half^#(x))
, 4: le^#(0(), y) -> c_4()
, 5: le^#(s(x), 0()) -> c_5()
, 6: le^#(s(x), s(y)) -> c_6(le^#(x, y))
, 7: inc^#(0()) -> c_7()
, 8: inc^#(s(x)) -> c_8(inc^#(x))
, 9: logarithm^#(x) -> c_9(logIter^#(x, 0()))
, 10: logIter^#(x, y) ->
c_10(if^#(le(s(0()), x), le(s(s(0())), x), half(x), inc(y)))
, 11: if^#(true(), true(), x, y) -> c_11(logIter^#(x, y))
, 12: if^#(true(), false(), x, s(y)) -> c_12(y)
, 13: if^#(false(), b, x, y) -> c_13()
, 14: f^#() -> c_14()
, 15: f^#() -> c_15() }
We are left with following problem, upon which TcT provides the
certificate MAYBE.
Strict DPs:
{ half^#(s(s(x))) -> c_3(half^#(x))
, le^#(s(x), s(y)) -> c_6(le^#(x, y))
, inc^#(s(x)) -> c_8(inc^#(x))
, logarithm^#(x) -> c_9(logIter^#(x, 0()))
, logIter^#(x, y) ->
c_10(if^#(le(s(0()), x), le(s(s(0())), x), half(x), inc(y)))
, if^#(true(), true(), x, y) -> c_11(logIter^#(x, y))
, if^#(true(), false(), x, s(y)) -> c_12(y) }
Strict Trs:
{ half(0()) -> 0()
, half(s(0())) -> 0()
, half(s(s(x))) -> s(half(x))
, le(0(), y) -> true()
, le(s(x), 0()) -> false()
, le(s(x), s(y)) -> le(x, y)
, inc(0()) -> s(0())
, inc(s(x)) -> s(inc(x))
, logarithm(x) -> logIter(x, 0())
, logIter(x, y) ->
if(le(s(0()), x), le(s(s(0())), x), half(x), inc(y))
, if(true(), true(), x, y) -> logIter(x, y)
, if(true(), false(), x, s(y)) -> y
, if(false(), b, x, y) -> logZeroError()
, f() -> g()
, f() -> h() }
Weak DPs:
{ half^#(0()) -> c_1()
, half^#(s(0())) -> c_2()
, le^#(0(), y) -> c_4()
, le^#(s(x), 0()) -> c_5()
, inc^#(0()) -> c_7()
, if^#(false(), b, x, y) -> c_13()
, f^#() -> c_14()
, f^#() -> c_15() }
Obligation:
runtime complexity
Answer:
MAYBE
Empty strict component of the problem is NOT empty.
Arrrr..