MAYBE
We are left with following problem, upon which TcT provides the
certificate MAYBE.
Strict Trs:
{ p(0()) -> 0()
, p(s(x)) -> x
, le(0(), y) -> true()
, le(s(x), 0()) -> false()
, le(s(x), s(y)) -> le(x, y)
, minus(x, y) -> if(le(x, y), x, y)
, if(true(), x, y) -> 0()
, if(false(), x, y) -> s(minus(p(x), y)) }
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) '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.
2) 'Innermost Weak Dependency Pairs (timeout of 60 seconds)' failed
due to the following reason:
We add the following weak dependency pairs:
Strict DPs:
{ p^#(0()) -> c_1()
, p^#(s(x)) -> c_2(x)
, le^#(0(), y) -> c_3()
, le^#(s(x), 0()) -> c_4()
, le^#(s(x), s(y)) -> c_5(le^#(x, y))
, minus^#(x, y) -> c_6(if^#(le(x, y), x, y))
, if^#(true(), x, y) -> c_7()
, if^#(false(), x, y) -> c_8(minus^#(p(x), y)) }
and mark the set of starting terms.
We are left with following problem, upon which TcT provides the
certificate MAYBE.
Strict DPs:
{ p^#(0()) -> c_1()
, p^#(s(x)) -> c_2(x)
, le^#(0(), y) -> c_3()
, le^#(s(x), 0()) -> c_4()
, le^#(s(x), s(y)) -> c_5(le^#(x, y))
, minus^#(x, y) -> c_6(if^#(le(x, y), x, y))
, if^#(true(), x, y) -> c_7()
, if^#(false(), x, y) -> c_8(minus^#(p(x), y)) }
Strict Trs:
{ p(0()) -> 0()
, p(s(x)) -> x
, le(0(), y) -> true()
, le(s(x), 0()) -> false()
, le(s(x), s(y)) -> le(x, y)
, minus(x, y) -> if(le(x, y), x, y)
, if(true(), x, y) -> 0()
, if(false(), x, y) -> s(minus(p(x), y)) }
Obligation:
runtime complexity
Answer:
MAYBE
We estimate the number of application of {1,3,4,7} by applications
of Pre({1,3,4,7}) = {2,5,6}. Here rules are labeled as follows:
DPs:
{ 1: p^#(0()) -> c_1()
, 2: p^#(s(x)) -> c_2(x)
, 3: le^#(0(), y) -> c_3()
, 4: le^#(s(x), 0()) -> c_4()
, 5: le^#(s(x), s(y)) -> c_5(le^#(x, y))
, 6: minus^#(x, y) -> c_6(if^#(le(x, y), x, y))
, 7: if^#(true(), x, y) -> c_7()
, 8: if^#(false(), x, y) -> c_8(minus^#(p(x), y)) }
We are left with following problem, upon which TcT provides the
certificate MAYBE.
Strict DPs:
{ p^#(s(x)) -> c_2(x)
, le^#(s(x), s(y)) -> c_5(le^#(x, y))
, minus^#(x, y) -> c_6(if^#(le(x, y), x, y))
, if^#(false(), x, y) -> c_8(minus^#(p(x), y)) }
Strict Trs:
{ p(0()) -> 0()
, p(s(x)) -> x
, le(0(), y) -> true()
, le(s(x), 0()) -> false()
, le(s(x), s(y)) -> le(x, y)
, minus(x, y) -> if(le(x, y), x, y)
, if(true(), x, y) -> 0()
, if(false(), x, y) -> s(minus(p(x), y)) }
Weak DPs:
{ p^#(0()) -> c_1()
, le^#(0(), y) -> c_3()
, le^#(s(x), 0()) -> c_4()
, if^#(true(), x, y) -> c_7() }
Obligation:
runtime complexity
Answer:
MAYBE
Empty strict component of the problem is NOT empty.
Arrrr..