MAYBE
We are left with following problem, upon which TcT provides the
certificate MAYBE.
Strict Trs:
{ f(X) -> if(X, c(), f(true()))
, if(true(), X, Y) -> X
, if(false(), X, Y) -> Y }
Obligation:
runtime complexity
Answer:
MAYBE
The input is overlay and right-linear. Switching to innermost
rewriting.
We are left with following problem, upon which TcT provides the
certificate MAYBE.
Strict Trs:
{ f(X) -> if(X, c(), f(true()))
, if(true(), X, Y) -> X
, if(false(), X, Y) -> Y }
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 dependency tuples:
Strict DPs:
{ f^#(X) -> c_1(if^#(X, c(), f(true())), f^#(true()))
, if^#(true(), X, Y) -> c_2()
, if^#(false(), X, Y) -> c_3() }
and mark the set of starting terms.
We are left with following problem, upon which TcT provides the
certificate MAYBE.
Strict DPs:
{ f^#(X) -> c_1(if^#(X, c(), f(true())), f^#(true()))
, if^#(true(), X, Y) -> c_2()
, if^#(false(), X, Y) -> c_3() }
Weak Trs:
{ f(X) -> if(X, c(), f(true()))
, if(true(), X, Y) -> X
, if(false(), X, Y) -> Y }
Obligation:
innermost runtime complexity
Answer:
MAYBE
We estimate the number of application of {2,3} by applications of
Pre({2,3}) = {1}. Here rules are labeled as follows:
DPs:
{ 1: f^#(X) -> c_1(if^#(X, c(), f(true())), f^#(true()))
, 2: if^#(true(), X, Y) -> c_2()
, 3: if^#(false(), X, Y) -> c_3() }
We are left with following problem, upon which TcT provides the
certificate MAYBE.
Strict DPs: { f^#(X) -> c_1(if^#(X, c(), f(true())), f^#(true())) }
Weak DPs:
{ if^#(true(), X, Y) -> c_2()
, if^#(false(), X, Y) -> c_3() }
Weak Trs:
{ f(X) -> if(X, c(), f(true()))
, if(true(), X, Y) -> X
, if(false(), X, Y) -> Y }
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.
{ if^#(true(), X, Y) -> c_2()
, if^#(false(), X, Y) -> c_3() }
We are left with following problem, upon which TcT provides the
certificate MAYBE.
Strict DPs: { f^#(X) -> c_1(if^#(X, c(), f(true())), f^#(true())) }
Weak Trs:
{ f(X) -> if(X, c(), f(true()))
, if(true(), X, Y) -> X
, if(false(), X, Y) -> Y }
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^#(X) -> c_1(if^#(X, c(), f(true())), f^#(true())) }
We are left with following problem, upon which TcT provides the
certificate MAYBE.
Strict DPs: { f^#(X) -> c_1(f^#(true())) }
Weak Trs:
{ f(X) -> if(X, c(), f(true()))
, if(true(), X, Y) -> X
, if(false(), X, Y) -> Y }
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^#(X) -> c_1(f^#(true())) }
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) 'Fastest (timeout of 5 seconds) (timeout of 60 seconds)' failed
due to the following reason:
Computation stopped due to timeout after 5.0 seconds.
2) '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(if) = {3}
TcT has computed the following matrix interpretation satisfying
not(EDA) and not(IDA(1)).
[f](x1) = [1] x1 + [0]
[if](x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [0]
[c] = [0]
[true] = [0]
[false] = [1]
The following symbols are considered usable
{f, if}
The order satisfies the following ordering constraints:
[f(X)] = [1] X + [0]
>= [1] X + [0]
= [if(X, c(), f(true()))]
[if(true(), X, Y)] = [1] X + [1] Y + [0]
>= [1] X + [0]
= [X]
[if(false(), X, Y)] = [1] X + [1] Y + [1]
> [1] Y + [0]
= [Y]
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) -> if(X, c(), f(true()))
, if(true(), X, Y) -> X }
Weak Trs: { if(false(), X, Y) -> Y }
Obligation:
innermost runtime complexity
Answer:
MAYBE
The weightgap principle applies (using the following nonconstant
growth matrix-interpretation)
The following argument positions are usable:
Uargs(if) = {3}
TcT has computed the following matrix interpretation satisfying
not(EDA) and not(IDA(1)).
[f](x1) = [1] x1 + [4]
[if](x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [0]
[c] = [0]
[true] = [4]
[false] = [7]
The following symbols are considered usable
{f, if}
The order satisfies the following ordering constraints:
[f(X)] = [1] X + [4]
? [1] X + [8]
= [if(X, c(), f(true()))]
[if(true(), X, Y)] = [1] X + [1] Y + [4]
> [1] X + [0]
= [X]
[if(false(), X, Y)] = [1] X + [1] Y + [7]
> [1] Y + [0]
= [Y]
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) -> if(X, c(), f(true())) }
Weak Trs:
{ if(true(), X, Y) -> X
, if(false(), X, Y) -> Y }
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.
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..