MAYBE
We are left with following problem, upon which TcT provides the
certificate MAYBE.
Strict Trs:
{ fib(0()) -> 0()
, fib(s(0())) -> s(0())
, fib(s(s(x))) -> +(fib(s(x)), fib(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:
{ fib^#(0()) -> c_1()
, fib^#(s(0())) -> c_2()
, fib^#(s(s(x))) -> c_3(fib^#(s(x)), fib^#(x)) }
and mark the set of starting terms.
We are left with following problem, upon which TcT provides the
certificate MAYBE.
Strict DPs:
{ fib^#(0()) -> c_1()
, fib^#(s(0())) -> c_2()
, fib^#(s(s(x))) -> c_3(fib^#(s(x)), fib^#(x)) }
Strict Trs:
{ fib(0()) -> 0()
, fib(s(0())) -> s(0())
, fib(s(s(x))) -> +(fib(s(x)), fib(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:
{ fib^#(0()) -> c_1()
, fib^#(s(0())) -> c_2()
, fib^#(s(s(x))) -> c_3(fib^#(s(x)), fib^#(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, 2}
TcT has computed the following constructor-restricted matrix
interpretation.
[0] = [0]
[0]
[s](x1) = [0]
[0]
[fib^#](x1) = [1]
[0]
[c_1] = [0]
[0]
[c_2] = [0]
[0]
[c_3](x1, x2) = [1 0] x1 + [1 0] x2 + [1]
[0 1] [0 1] [2]
The following symbols are considered usable
{fib^#}
The order satisfies the following ordering constraints:
[fib^#(0())] = [1]
[0]
> [0]
[0]
= [c_1()]
[fib^#(s(0()))] = [1]
[0]
> [0]
[0]
= [c_2()]
[fib^#(s(s(x)))] = [1]
[0]
? [3]
[2]
= [c_3(fib^#(s(x)), fib^#(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: { fib^#(s(s(x))) -> c_3(fib^#(s(x)), fib^#(x)) }
Weak DPs:
{ fib^#(0()) -> c_1()
, fib^#(s(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.
{ fib^#(0()) -> c_1()
, fib^#(s(0())) -> c_2() }
We are left with following problem, upon which TcT provides the
certificate MAYBE.
Strict DPs: { fib^#(s(s(x))) -> c_3(fib^#(s(x)), fib^#(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 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) '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(+) = {1, 2}
TcT has computed the following matrix interpretation satisfying
not(EDA) and not(IDA(1)).
[fib](x1) = [7]
[0] = [3]
[s](x1) = [1] x1 + [3]
[+](x1, x2) = [1] x1 + [1] x2 + [0]
The following symbols are considered usable
{fib}
The order satisfies the following ordering constraints:
[fib(0())] = [7]
> [3]
= [0()]
[fib(s(0()))] = [7]
> [6]
= [s(0())]
[fib(s(s(x)))] = [7]
? [14]
= [+(fib(s(x)), fib(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: { fib(s(s(x))) -> +(fib(s(x)), fib(x)) }
Weak Trs:
{ fib(0()) -> 0()
, fib(s(0())) -> s(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) '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
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.
Arrrr..