MAYBE
We are left with following problem, upon which TcT provides the
certificate MAYBE.
Strict Trs:
{ f(0()) -> 1()
, f(s(x)) -> g(f(x))
, f(s(x)) -> +(f(x), s(f(x)))
, g(x) -> +(x, s(x)) }
Obligation:
innermost runtime complexity
Answer:
MAYBE
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) 'Best' failed due to the following reason:
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 input cannot be shown compatible
2) 'Polynomial Path Order (PS) (timeout of 60 seconds)' failed due
to the following reason:
The input cannot be shown compatible
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 minimal-enrichment and initial automaton 'match''
failed due to the following reason:
match-boundness of the problem could not be verified.
2) 'Bounds with perSymbol-enrichment and initial automaton 'match''
failed due to the following reason:
match-boundness of the problem could not be verified.
2) 'WithProblem (timeout of 60 seconds)' failed due to the
following reason:
We add the following dependency tuples:
Strict DPs:
{ f^#(0()) -> c_1()
, f^#(s(x)) -> c_2(g^#(f(x)), f^#(x))
, f^#(s(x)) -> c_3(f^#(x), f^#(x))
, g^#(x) -> c_4() }
and mark the set of starting terms.
We are left with following problem, upon which TcT provides the
certificate MAYBE.
Strict DPs:
{ f^#(0()) -> c_1()
, f^#(s(x)) -> c_2(g^#(f(x)), f^#(x))
, f^#(s(x)) -> c_3(f^#(x), f^#(x))
, g^#(x) -> c_4() }
Weak Trs:
{ f(0()) -> 1()
, f(s(x)) -> g(f(x))
, f(s(x)) -> +(f(x), s(f(x)))
, g(x) -> +(x, s(x)) }
Obligation:
innermost runtime complexity
Answer:
MAYBE
We estimate the number of application of {1,4} by applications of
Pre({1,4}) = {2,3}. Here rules are labeled as follows:
DPs:
{ 1: f^#(0()) -> c_1()
, 2: f^#(s(x)) -> c_2(g^#(f(x)), f^#(x))
, 3: f^#(s(x)) -> c_3(f^#(x), f^#(x))
, 4: g^#(x) -> c_4() }
We are left with following problem, upon which TcT provides the
certificate MAYBE.
Strict DPs:
{ f^#(s(x)) -> c_2(g^#(f(x)), f^#(x))
, f^#(s(x)) -> c_3(f^#(x), f^#(x)) }
Weak DPs:
{ f^#(0()) -> c_1()
, g^#(x) -> c_4() }
Weak Trs:
{ f(0()) -> 1()
, f(s(x)) -> g(f(x))
, f(s(x)) -> +(f(x), s(f(x)))
, g(x) -> +(x, s(x)) }
Obligation:
innermost runtime complexity
Answer:
MAYBE
The following weak DPs constitute a sub-graph of the DG that is
closed under successors. The DPs are removed.
{ f^#(0()) -> c_1()
, g^#(x) -> c_4() }
We are left with following problem, upon which TcT provides the
certificate MAYBE.
Strict DPs:
{ f^#(s(x)) -> c_2(g^#(f(x)), f^#(x))
, f^#(s(x)) -> c_3(f^#(x), f^#(x)) }
Weak Trs:
{ f(0()) -> 1()
, f(s(x)) -> g(f(x))
, f(s(x)) -> +(f(x), s(f(x)))
, g(x) -> +(x, s(x)) }
Obligation:
innermost runtime complexity
Answer:
MAYBE
Due to missing edges in the dependency-graph, the right-hand sides
of following rules could be simplified:
{ f^#(s(x)) -> c_2(g^#(f(x)), f^#(x)) }
We are left with following problem, upon which TcT provides the
certificate MAYBE.
Strict DPs:
{ f^#(s(x)) -> c_1(f^#(x), f^#(x))
, f^#(s(x)) -> c_2(f^#(x)) }
Weak Trs:
{ f(0()) -> 1()
, f(s(x)) -> g(f(x))
, f(s(x)) -> +(f(x), s(f(x)))
, g(x) -> +(x, s(x)) }
Obligation:
innermost runtime complexity
Answer:
MAYBE
No rule is usable, rules are removed from the input problem.
We are left with following problem, upon which TcT provides the
certificate MAYBE.
Strict DPs:
{ f^#(s(x)) -> c_1(f^#(x), f^#(x))
, f^#(s(x)) -> c_2(f^#(x)) }
Obligation:
innermost runtime complexity
Answer:
MAYBE
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) 'Polynomial Path Order (PS)' failed due to the following reason:
The input cannot be shown compatible
2) 'Polynomial Path Order (PS)' failed due to the following reason:
The input cannot be shown compatible
3) 'Fastest (timeout of 5 seconds)' failed due to the following
reason:
None of the processors succeeded.
Details of failed attempt(s):
-----------------------------
1) 'Bounds with minimal-enrichment and initial automaton 'match''
failed due to the following reason:
match-boundness of the problem could not be verified.
2) 'Bounds with perSymbol-enrichment and initial automaton 'match''
failed due to the following reason:
match-boundness of the problem could not be verified.
Arrrr..