MAYBE
We are left with following problem, upon which TcT provides the
certificate MAYBE.
Strict Trs:
{ f(x, y, g(z)) -> g(f(x, y, z))
, f(x, g(y), z) -> g(f(x, y, z))
, f(0(), 1(), x) -> f(g(x), g(x), x)
, f(g(x), y, z) -> g(f(x, y, z)) }
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:
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:
The weightgap principle applies (using the following nonconstant
growth matrix-interpretation)
The following argument positions are usable:
Uargs(g) = {1}
TcT has computed the following matrix interpretation satisfying
not(EDA) and not(IDA(1)).
[f](x1, x2, x3) = [0 4] x3 + [0]
[0 1] [0]
[0] = [7]
[0]
[1] = [7]
[0]
[g](x1) = [1 0] x1 + [0]
[0 1] [2]
The following symbols are considered usable
{f}
The order satisfies the following ordering constraints:
[f(x, y, g(z))] = [0 4] z + [8]
[0 1] [2]
> [0 4] z + [0]
[0 1] [2]
= [g(f(x, y, z))]
[f(x, g(y), z)] = [0 4] z + [0]
[0 1] [0]
? [0 4] z + [0]
[0 1] [2]
= [g(f(x, y, z))]
[f(0(), 1(), x)] = [0 4] x + [0]
[0 1] [0]
>= [0 4] x + [0]
[0 1] [0]
= [f(g(x), g(x), x)]
[f(g(x), y, z)] = [0 4] z + [0]
[0 1] [0]
? [0 4] z + [0]
[0 1] [2]
= [g(f(x, y, z))]
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:
{ f(x, g(y), z) -> g(f(x, y, z))
, f(0(), 1(), x) -> f(g(x), g(x), x)
, f(g(x), y, z) -> g(f(x, y, z)) }
Weak Trs: { f(x, y, g(z)) -> g(f(x, y, z)) }
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) '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.
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^#(x, y, g(z)) -> c_1(f^#(x, y, z))
, f^#(x, g(y), z) -> c_2(f^#(x, y, z))
, f^#(0(), 1(), x) -> c_3(f^#(g(x), g(x), x))
, f^#(g(x), y, z) -> c_4(f^#(x, y, z)) }
and mark the set of starting terms.
We are left with following problem, upon which TcT provides the
certificate MAYBE.
Strict DPs:
{ f^#(x, y, g(z)) -> c_1(f^#(x, y, z))
, f^#(x, g(y), z) -> c_2(f^#(x, y, z))
, f^#(0(), 1(), x) -> c_3(f^#(g(x), g(x), x))
, f^#(g(x), y, z) -> c_4(f^#(x, y, z)) }
Strict Trs:
{ f(x, y, g(z)) -> g(f(x, y, z))
, f(x, g(y), z) -> g(f(x, y, z))
, f(0(), 1(), x) -> f(g(x), g(x), x)
, f(g(x), y, z) -> g(f(x, y, z)) }
Obligation:
runtime complexity
Answer:
MAYBE
Empty strict component of the problem is NOT empty.
Arrrr..