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))
, lastbit(0()) -> 0()
, lastbit(s(0())) -> s(0())
, lastbit(s(s(x))) -> lastbit(x)
, zero(0()) -> true()
, zero(s(x)) -> false()
, conv(x) -> conviter(x, cons(0(), nil()))
, conviter(x, l) -> if(zero(x), x, l)
, if(true(), x, l) -> l
, if(false(), x, l) -> conviter(half(x), cons(lastbit(x), l)) }
Obligation:
runtime complexity
Answer:
MAYBE
None of the processors succeeded.
Details of failed attempt(s):
-----------------------------
1) '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:
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) '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.
2) '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))
, lastbit^#(0()) -> c_4()
, lastbit^#(s(0())) -> c_5()
, lastbit^#(s(s(x))) -> c_6(lastbit^#(x))
, zero^#(0()) -> c_7()
, zero^#(s(x)) -> c_8()
, conv^#(x) -> c_9(conviter^#(x, cons(0(), nil())))
, conviter^#(x, l) -> c_10(if^#(zero(x), x, l))
, if^#(true(), x, l) -> c_11(l)
, if^#(false(), x, l) ->
c_12(conviter^#(half(x), cons(lastbit(x), l))) }
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))
, lastbit^#(0()) -> c_4()
, lastbit^#(s(0())) -> c_5()
, lastbit^#(s(s(x))) -> c_6(lastbit^#(x))
, zero^#(0()) -> c_7()
, zero^#(s(x)) -> c_8()
, conv^#(x) -> c_9(conviter^#(x, cons(0(), nil())))
, conviter^#(x, l) -> c_10(if^#(zero(x), x, l))
, if^#(true(), x, l) -> c_11(l)
, if^#(false(), x, l) ->
c_12(conviter^#(half(x), cons(lastbit(x), l))) }
Strict Trs:
{ half(0()) -> 0()
, half(s(0())) -> 0()
, half(s(s(x))) -> s(half(x))
, lastbit(0()) -> 0()
, lastbit(s(0())) -> s(0())
, lastbit(s(s(x))) -> lastbit(x)
, zero(0()) -> true()
, zero(s(x)) -> false()
, conv(x) -> conviter(x, cons(0(), nil()))
, conviter(x, l) -> if(zero(x), x, l)
, if(true(), x, l) -> l
, if(false(), x, l) -> conviter(half(x), cons(lastbit(x), l)) }
Obligation:
runtime complexity
Answer:
MAYBE
We estimate the number of application of {1,2,4,5,7,8} by
applications of Pre({1,2,4,5,7,8}) = {3,6,11}. 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: lastbit^#(0()) -> c_4()
, 5: lastbit^#(s(0())) -> c_5()
, 6: lastbit^#(s(s(x))) -> c_6(lastbit^#(x))
, 7: zero^#(0()) -> c_7()
, 8: zero^#(s(x)) -> c_8()
, 9: conv^#(x) -> c_9(conviter^#(x, cons(0(), nil())))
, 10: conviter^#(x, l) -> c_10(if^#(zero(x), x, l))
, 11: if^#(true(), x, l) -> c_11(l)
, 12: if^#(false(), x, l) ->
c_12(conviter^#(half(x), cons(lastbit(x), l))) }
We are left with following problem, upon which TcT provides the
certificate MAYBE.
Strict DPs:
{ half^#(s(s(x))) -> c_3(half^#(x))
, lastbit^#(s(s(x))) -> c_6(lastbit^#(x))
, conv^#(x) -> c_9(conviter^#(x, cons(0(), nil())))
, conviter^#(x, l) -> c_10(if^#(zero(x), x, l))
, if^#(true(), x, l) -> c_11(l)
, if^#(false(), x, l) ->
c_12(conviter^#(half(x), cons(lastbit(x), l))) }
Strict Trs:
{ half(0()) -> 0()
, half(s(0())) -> 0()
, half(s(s(x))) -> s(half(x))
, lastbit(0()) -> 0()
, lastbit(s(0())) -> s(0())
, lastbit(s(s(x))) -> lastbit(x)
, zero(0()) -> true()
, zero(s(x)) -> false()
, conv(x) -> conviter(x, cons(0(), nil()))
, conviter(x, l) -> if(zero(x), x, l)
, if(true(), x, l) -> l
, if(false(), x, l) -> conviter(half(x), cons(lastbit(x), l)) }
Weak DPs:
{ half^#(0()) -> c_1()
, half^#(s(0())) -> c_2()
, lastbit^#(0()) -> c_4()
, lastbit^#(s(0())) -> c_5()
, zero^#(0()) -> c_7()
, zero^#(s(x)) -> c_8() }
Obligation:
runtime complexity
Answer:
MAYBE
Empty strict component of the problem is NOT empty.
Arrrr..