MAYBE
We are left with following problem, upon which TcT provides the
certificate MAYBE.
Strict Trs:
{ f(S(x)) -> x
, f(0()) -> 0()
, g(x) -> g(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) 'WithProblem (timeout of 60 seconds)' failed due to the
following reason:
We add the following innermost weak dependency pairs:
Strict DPs:
{ f^#(S(x)) -> c_1()
, f^#(0()) -> c_2()
, g^#(x) -> c_3(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^#(S(x)) -> c_1()
, f^#(0()) -> c_2()
, g^#(x) -> c_3(g^#(x)) }
Strict Trs:
{ f(S(x)) -> x
, f(0()) -> 0()
, g(x) -> g(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^#(0()) -> c_2()
, g^#(x) -> c_3(g^#(x)) }
Obligation:
innermost runtime complexity
Answer:
MAYBE
The weightgap principle applies (using the following constant
growth matrix-interpretation)
The following argument positions are usable:
Uargs(c_3) = {1}
TcT has computed the following constructor-restricted matrix
interpretation.
[S](x1) = [1]
[2]
[0] = [1]
[1]
[f^#](x1) = [1 1] x1 + [2]
[1 1] [1]
[c_1] = [0]
[0]
[c_2] = [1]
[1]
[g^#](x1) = [2 1] x1 + [2]
[1 1] [2]
[c_3](x1) = [1 0] x1 + [1]
[0 1] [2]
The following symbols are considered usable
{f^#, g^#}
The order satisfies the following ordering constraints:
[f^#(S(x))] = [5]
[4]
> [0]
[0]
= [c_1()]
[f^#(0())] = [4]
[3]
> [1]
[1]
= [c_2()]
[g^#(x)] = [2 1] x + [2]
[1 1] [2]
? [2 1] x + [3]
[1 1] [4]
= [c_3(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 DPs: { g^#(x) -> c_3(g^#(x)) }
Weak DPs:
{ f^#(S(x)) -> c_1()
, f^#(0()) -> c_2() }
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^#(S(x)) -> c_1()
, f^#(0()) -> c_2() }
We are left with following problem, upon which TcT provides the
certificate MAYBE.
Strict DPs: { g^#(x) -> c_3(g^#(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) 'Fastest (timeout of 5 seconds)' failed due to the following
reason:
Computation stopped due to timeout after 5.0 seconds.
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) 'Polynomial Path Order (PS)' failed due to the following reason:
The input cannot be shown compatible
3) 'Polynomial Path Order (PS)' failed due to the following reason:
The input cannot be shown compatible
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:
none
TcT has computed the following matrix interpretation satisfying
not(EDA) and not(IDA(1)).
[f](x1) = [1] x1 + [7]
[S](x1) = [1] x1 + [7]
[0] = [7]
[g](x1) = [1] x1 + [0]
The following symbols are considered usable
{f, g}
The order satisfies the following ordering constraints:
[f(S(x))] = [1] x + [14]
> [1] x + [0]
= [x]
[f(0())] = [14]
> [7]
= [0()]
[g(x)] = [1] x + [0]
>= [1] x + [0]
= [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) -> g(x) }
Weak Trs:
{ f(S(x)) -> x
, f(0()) -> 0() }
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) '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 input cannot be shown compatible
2) 'bsearch-popstar (timeout of 60 seconds)' failed due to the
following reason:
The input cannot be shown compatible
Arrrr..