MAYBE
We are left with following problem, upon which TcT provides the
certificate MAYBE.
Strict Trs:
{ equal0(Nil()) -> number42(Nil())
, equal0(Cons(x, xs)) -> equal0(Cons(x, xs))
, number42(x) ->
Cons(Nil(),
Cons(Nil(),
Cons(Nil(),
Cons(Nil(),
Cons(Nil(),
Cons(Nil(),
Cons(Nil(),
Cons(Nil(),
Cons(Nil(),
Cons(Nil(),
Cons(Nil(),
Cons(Nil(),
Cons(Nil(),
Cons(Nil(),
Cons(Nil(),
Cons(Nil(),
Cons(Nil(),
Cons(Nil(),
Cons(Nil(),
Cons(Nil(),
Cons(Nil(),
Cons(Nil(),
Cons(Nil(),
Cons(Nil(),
Cons(Nil(),
Cons(Nil(),
Cons(Nil(),
Cons(Nil(),
Cons(Nil(),
Cons(Nil(),
Cons(Nil(),
Cons(Nil(),
Cons(Nil(),
Cons(Nil(),
Cons(Nil(),
Cons(Nil(),
Cons(Nil(),
Cons(Nil(),
Cons(Nil(),
Cons(Nil(),
Cons(Nil(),
Cons(Nil(),
Nil()))))))))))))))))))))))))))))))))))))))))))
, goal(x) -> equal0(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:
{ equal0^#(Nil()) -> c_1(number42^#(Nil()))
, equal0^#(Cons(x, xs)) -> c_2(equal0^#(Cons(x, xs)))
, number42^#(x) -> c_3()
, goal^#(x) -> c_4(equal0^#(x)) }
and mark the set of starting terms.
We are left with following problem, upon which TcT provides the
certificate MAYBE.
Strict DPs:
{ equal0^#(Nil()) -> c_1(number42^#(Nil()))
, equal0^#(Cons(x, xs)) -> c_2(equal0^#(Cons(x, xs)))
, number42^#(x) -> c_3()
, goal^#(x) -> c_4(equal0^#(x)) }
Strict Trs:
{ equal0(Nil()) -> number42(Nil())
, equal0(Cons(x, xs)) -> equal0(Cons(x, xs))
, number42(x) ->
Cons(Nil(),
Cons(Nil(),
Cons(Nil(),
Cons(Nil(),
Cons(Nil(),
Cons(Nil(),
Cons(Nil(),
Cons(Nil(),
Cons(Nil(),
Cons(Nil(),
Cons(Nil(),
Cons(Nil(),
Cons(Nil(),
Cons(Nil(),
Cons(Nil(),
Cons(Nil(),
Cons(Nil(),
Cons(Nil(),
Cons(Nil(),
Cons(Nil(),
Cons(Nil(),
Cons(Nil(),
Cons(Nil(),
Cons(Nil(),
Cons(Nil(),
Cons(Nil(),
Cons(Nil(),
Cons(Nil(),
Cons(Nil(),
Cons(Nil(),
Cons(Nil(),
Cons(Nil(),
Cons(Nil(),
Cons(Nil(),
Cons(Nil(),
Cons(Nil(),
Cons(Nil(),
Cons(Nil(),
Cons(Nil(),
Cons(Nil(),
Cons(Nil(),
Cons(Nil(),
Nil()))))))))))))))))))))))))))))))))))))))))))
, goal(x) -> equal0(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:
{ equal0^#(Nil()) -> c_1(number42^#(Nil()))
, equal0^#(Cons(x, xs)) -> c_2(equal0^#(Cons(x, xs)))
, number42^#(x) -> c_3()
, goal^#(x) -> c_4(equal0^#(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_1) = {1}, Uargs(c_2) = {1}, Uargs(c_4) = {1}
TcT has computed the following constructor-restricted matrix
interpretation.
[Nil] = [0]
[0]
[Cons](x1, x2) = [1 0] x1 + [1 0] x2 + [0]
[0 0] [0 0] [0]
[equal0^#](x1) = [0]
[0]
[c_1](x1) = [1 0] x1 + [1]
[0 1] [0]
[number42^#](x1) = [1 2] x1 + [0]
[2 1] [0]
[c_2](x1) = [1 0] x1 + [1]
[0 1] [1]
[c_3] = [1]
[0]
[goal^#](x1) = [1 2] x1 + [2]
[2 1] [2]
[c_4](x1) = [1 0] x1 + [1]
[0 1] [2]
The following symbols are considered usable
{equal0^#, number42^#, goal^#}
The order satisfies the following ordering constraints:
[equal0^#(Nil())] = [0]
[0]
? [1]
[0]
= [c_1(number42^#(Nil()))]
[equal0^#(Cons(x, xs))] = [0]
[0]
? [1]
[1]
= [c_2(equal0^#(Cons(x, xs)))]
[number42^#(x)] = [1 2] x + [0]
[2 1] [0]
? [1]
[0]
= [c_3()]
[goal^#(x)] = [1 2] x + [2]
[2 1] [2]
> [1]
[2]
= [c_4(equal0^#(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:
{ equal0^#(Nil()) -> c_1(number42^#(Nil()))
, equal0^#(Cons(x, xs)) -> c_2(equal0^#(Cons(x, xs)))
, number42^#(x) -> c_3() }
Weak DPs: { goal^#(x) -> c_4(equal0^#(x)) }
Obligation:
innermost runtime complexity
Answer:
MAYBE
We estimate the number of application of {3} by applications of
Pre({3}) = {1}. Here rules are labeled as follows:
DPs:
{ 1: equal0^#(Nil()) -> c_1(number42^#(Nil()))
, 2: equal0^#(Cons(x, xs)) -> c_2(equal0^#(Cons(x, xs)))
, 3: number42^#(x) -> c_3()
, 4: goal^#(x) -> c_4(equal0^#(x)) }
We are left with following problem, upon which TcT provides the
certificate MAYBE.
Strict DPs:
{ equal0^#(Nil()) -> c_1(number42^#(Nil()))
, equal0^#(Cons(x, xs)) -> c_2(equal0^#(Cons(x, xs))) }
Weak DPs:
{ number42^#(x) -> c_3()
, goal^#(x) -> c_4(equal0^#(x)) }
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.
{ number42^#(x) -> c_3() }
We are left with following problem, upon which TcT provides the
certificate MAYBE.
Strict DPs:
{ equal0^#(Nil()) -> c_1(number42^#(Nil()))
, equal0^#(Cons(x, xs)) -> c_2(equal0^#(Cons(x, xs))) }
Weak DPs: { goal^#(x) -> c_4(equal0^#(x)) }
Obligation:
innermost runtime complexity
Answer:
MAYBE
Due to missing edges in the dependency-graph, the right-hand sides
of following rules could be simplified:
{ equal0^#(Nil()) -> c_1(number42^#(Nil())) }
We are left with following problem, upon which TcT provides the
certificate MAYBE.
Strict DPs:
{ equal0^#(Nil()) -> c_1()
, equal0^#(Cons(x, xs)) -> c_2(equal0^#(Cons(x, xs))) }
Weak DPs: { goal^#(x) -> c_3(equal0^#(x)) }
Obligation:
innermost runtime complexity
Answer:
MAYBE
Consider the dependency graph
1: equal0^#(Nil()) -> c_1()
2: equal0^#(Cons(x, xs)) -> c_2(equal0^#(Cons(x, xs)))
-->_1 equal0^#(Cons(x, xs)) -> c_2(equal0^#(Cons(x, xs))) :2
3: goal^#(x) -> c_3(equal0^#(x))
-->_1 equal0^#(Cons(x, xs)) -> c_2(equal0^#(Cons(x, xs))) :2
-->_1 equal0^#(Nil()) -> c_1() :1
Following roots of the dependency graph are removed, as the
considered set of starting terms is closed under reduction with
respect to these rules (modulo compound contexts).
{ goal^#(x) -> c_3(equal0^#(x)) }
We are left with following problem, upon which TcT provides the
certificate MAYBE.
Strict DPs:
{ equal0^#(Nil()) -> c_1()
, equal0^#(Cons(x, xs)) -> c_2(equal0^#(Cons(x, xs))) }
Obligation:
innermost runtime complexity
Answer:
MAYBE
Consider the dependency graph
1: equal0^#(Nil()) -> c_1()
2: equal0^#(Cons(x, xs)) -> c_2(equal0^#(Cons(x, xs)))
-->_1 equal0^#(Cons(x, xs)) -> c_2(equal0^#(Cons(x, xs))) :2
Following roots of the dependency graph are removed, as the
considered set of starting terms is closed under reduction with
respect to these rules (modulo compound contexts).
{ equal0^#(Nil()) -> c_1() }
We are left with following problem, upon which TcT provides the
certificate MAYBE.
Strict DPs: { equal0^#(Cons(x, xs)) -> c_2(equal0^#(Cons(x, xs))) }
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) 'Fastest (timeout of 5 seconds)' failed due to the following
reason:
Computation stopped due to timeout after 5.0 seconds.
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:
Computation stopped due to timeout after 30.0 seconds.
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..