MAYBE
We are left with following problem, upon which TcT provides the
certificate MAYBE.
Strict Trs:
{ f(f(x)) -> b()
, f(g(a())) -> a()
, g(x) -> f(g(x)) }
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:
The weightgap principle applies (using the following nonconstant
growth matrix-interpretation)
The following argument positions are usable:
Uargs(f) = {1}
TcT has computed the following matrix interpretation satisfying
not(EDA) and not(IDA(1)).
[f](x1) = [1] x1 + [1]
[g](x1) = [1] x1 + [7]
[a] = [7]
[b] = [1]
The following symbols are considered usable
{f, g}
The order satisfies the following ordering constraints:
[f(f(x))] = [1] x + [2]
> [1]
= [b()]
[f(g(a()))] = [15]
> [7]
= [a()]
[g(x)] = [1] x + [7]
? [1] x + [8]
= [f(g(x))]
Further, it can be verified that all rules not oriented are covered by the weightgap condition.
We are left with following problem, upon which TcT provides the
certificate MAYBE.
Strict Trs: { g(x) -> f(g(x)) }
Weak Trs:
{ f(f(x)) -> b()
, f(g(a())) -> a() }
Obligation:
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) '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) 'Fastest (timeout of 5 seconds) (timeout of 60 seconds)' failed
due to the following reason:
Computation stopped due to timeout after 5.0 seconds.
3) '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) 'Innermost Weak Dependency Pairs (timeout of 60 seconds)' failed
due to the following reason:
We add the following weak dependency pairs:
Strict DPs:
{ f^#(f(x)) -> c_1()
, f^#(g(a())) -> c_2()
, g^#(x) -> c_3(f^#(g(x))) }
and mark the set of starting terms.
We are left with following problem, upon which TcT provides the
certificate MAYBE.
Strict DPs:
{ f^#(f(x)) -> c_1()
, f^#(g(a())) -> c_2()
, g^#(x) -> c_3(f^#(g(x))) }
Strict Trs:
{ f(f(x)) -> b()
, f(g(a())) -> a()
, g(x) -> f(g(x)) }
Obligation:
runtime complexity
Answer:
MAYBE
We estimate the number of application of {1,2} by applications of
Pre({1,2}) = {3}. Here rules are labeled as follows:
DPs:
{ 1: f^#(f(x)) -> c_1()
, 2: f^#(g(a())) -> c_2()
, 3: g^#(x) -> c_3(f^#(g(x))) }
We are left with following problem, upon which TcT provides the
certificate MAYBE.
Strict DPs: { g^#(x) -> c_3(f^#(g(x))) }
Strict Trs:
{ f(f(x)) -> b()
, f(g(a())) -> a()
, g(x) -> f(g(x)) }
Weak DPs:
{ f^#(f(x)) -> c_1()
, f^#(g(a())) -> c_2() }
Obligation:
runtime complexity
Answer:
MAYBE
We estimate the number of application of {1} by applications of
Pre({1}) = {}. Here rules are labeled as follows:
DPs:
{ 1: g^#(x) -> c_3(f^#(g(x)))
, 2: f^#(f(x)) -> c_1()
, 3: f^#(g(a())) -> c_2() }
We are left with following problem, upon which TcT provides the
certificate MAYBE.
Strict Trs:
{ f(f(x)) -> b()
, f(g(a())) -> a()
, g(x) -> f(g(x)) }
Weak DPs:
{ f^#(f(x)) -> c_1()
, f^#(g(a())) -> c_2()
, g^#(x) -> c_3(f^#(g(x))) }
Obligation:
runtime complexity
Answer:
MAYBE
Empty strict component of the problem is NOT empty.
Arrrr..