MAYBE
We are left with following problem, upon which TcT provides the
certificate MAYBE.
Strict Trs:
{ g(X) -> h(X)
, h(d()) -> g(c())
, c() -> d() }
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:
{ g^#(X) -> c_1(h^#(X))
, h^#(d()) -> c_2(g^#(c()))
, c^#() -> c_3() }
and mark the set of starting terms.
We are left with following problem, upon which TcT provides the
certificate MAYBE.
Strict DPs:
{ g^#(X) -> c_1(h^#(X))
, h^#(d()) -> c_2(g^#(c()))
, c^#() -> c_3() }
Strict Trs:
{ g(X) -> h(X)
, h(d()) -> g(c())
, c() -> d() }
Obligation:
innermost runtime complexity
Answer:
MAYBE
We replace rewrite rules by usable rules:
Strict Usable Rules: { c() -> d() }
We are left with following problem, upon which TcT provides the
certificate MAYBE.
Strict DPs:
{ g^#(X) -> c_1(h^#(X))
, h^#(d()) -> c_2(g^#(c()))
, c^#() -> c_3() }
Strict Trs: { c() -> d() }
Obligation:
innermost runtime complexity
Answer:
MAYBE
The weightgap principle applies (using the following constant
growth matrix-interpretation)
The following argument positions are usable:
Uargs(g^#) = {1}, Uargs(c_1) = {1}, Uargs(c_2) = {1}
TcT has computed the following constructor-restricted matrix
interpretation.
[c] = [1]
[2]
[d] = [0]
[2]
[g^#](x1) = [2 1] x1 + [2]
[2 1] [2]
[c_1](x1) = [1 0] x1 + [1]
[0 1] [1]
[h^#](x1) = [1 1] x1 + [2]
[1 1] [2]
[c_2](x1) = [1 0] x1 + [1]
[0 1] [1]
[c^#] = [1]
[1]
[c_3] = [1]
[1]
The following symbols are considered usable
{c, g^#, h^#, c^#}
The order satisfies the following ordering constraints:
[c()] = [1]
[2]
> [0]
[2]
= [d()]
[g^#(X)] = [2 1] X + [2]
[2 1] [2]
? [1 1] X + [3]
[1 1] [3]
= [c_1(h^#(X))]
[h^#(d())] = [4]
[4]
? [7]
[7]
= [c_2(g^#(c()))]
[c^#()] = [1]
[1]
>= [1]
[1]
= [c_3()]
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_1(h^#(X))
, h^#(d()) -> c_2(g^#(c()))
, c^#() -> c_3() }
Weak Trs: { c() -> d() }
Obligation:
innermost runtime complexity
Answer:
MAYBE
We estimate the number of application of {3} by applications of
Pre({3}) = {}. Here rules are labeled as follows:
DPs:
{ 1: g^#(X) -> c_1(h^#(X))
, 2: h^#(d()) -> c_2(g^#(c()))
, 3: c^#() -> c_3() }
We are left with following problem, upon which TcT provides the
certificate MAYBE.
Strict DPs:
{ g^#(X) -> c_1(h^#(X))
, h^#(d()) -> c_2(g^#(c())) }
Weak DPs: { c^#() -> c_3() }
Weak Trs: { c() -> d() }
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.
{ c^#() -> c_3() }
We are left with following problem, upon which TcT provides the
certificate MAYBE.
Strict DPs:
{ g^#(X) -> c_1(h^#(X))
, h^#(d()) -> c_2(g^#(c())) }
Weak Trs: { c() -> d() }
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(g) = {1}
TcT has computed the following matrix interpretation satisfying
not(EDA) and not(IDA(1)).
[g](x1) = [1] x1 + [7]
[h](x1) = [1] x1 + [7]
[c] = [3]
[d] = [7]
The following symbols are considered usable
{g, h, c}
The order satisfies the following ordering constraints:
[g(X)] = [1] X + [7]
>= [1] X + [7]
= [h(X)]
[h(d())] = [14]
> [10]
= [g(c())]
[c()] = [3]
? [7]
= [d()]
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) -> h(X)
, c() -> d() }
Weak Trs: { h(d()) -> g(c()) }
Obligation:
innermost runtime complexity
Answer:
MAYBE
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)).
[g](x1) = [1] x1 + [0]
[h](x1) = [1] x1 + [6]
[c] = [4]
[d] = [2]
The following symbols are considered usable
{g, h, c}
The order satisfies the following ordering constraints:
[g(X)] = [1] X + [0]
? [1] X + [6]
= [h(X)]
[h(d())] = [8]
> [4]
= [g(c())]
[c()] = [4]
> [2]
= [d()]
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) -> h(X) }
Weak Trs:
{ h(d()) -> g(c())
, c() -> d() }
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) 'bsearch-popstar (timeout of 60 seconds)' failed due to the
following reason:
The input cannot be shown compatible
2) 'Polynomial Path Order (PS) (timeout of 60 seconds)' failed due
to the following reason:
The input cannot be shown compatible
Arrrr..