MAYBE
We are left with following problem, upon which TcT provides the
certificate MAYBE.
Strict Trs:
{ 2nd(cons1(X, cons(Y, Z))) -> Y
, 2nd(cons(X, X1)) -> 2nd(cons1(X, X1))
, from(X) -> cons(X, from(s(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) '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(cons) = {2}
TcT has computed the following matrix interpretation satisfying
not(EDA) and not(IDA(1)).
[2nd](x1) = [1] x1 + [0]
[cons1](x1, x2) = [1] x1 + [1] x2 + [4]
[cons](x1, x2) = [1] x1 + [1] x2 + [0]
[from](x1) = [1] x1 + [0]
[s](x1) = [0]
The following symbols are considered usable
{2nd, from}
The order satisfies the following ordering constraints:
[2nd(cons1(X, cons(Y, Z)))] = [1] X + [1] Y + [1] Z + [4]
> [1] Y + [0]
= [Y]
[2nd(cons(X, X1))] = [1] X + [1] X1 + [0]
? [1] X + [1] X1 + [4]
= [2nd(cons1(X, X1))]
[from(X)] = [1] X + [0]
>= [1] X + [0]
= [cons(X, from(s(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:
{ 2nd(cons(X, X1)) -> 2nd(cons1(X, X1))
, from(X) -> cons(X, from(s(X))) }
Weak Trs: { 2nd(cons1(X, cons(Y, Z))) -> 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(cons) = {2}
TcT has computed the following matrix interpretation satisfying
not(EDA) and not(IDA(1)).
[2nd](x1) = [1] x1 + [4]
[cons1](x1, x2) = [1] x1 + [1] x2 + [0]
[cons](x1, x2) = [1] x1 + [1] x2 + [4]
[from](x1) = [1] x1 + [0]
[s](x1) = [0]
The following symbols are considered usable
{2nd, from}
The order satisfies the following ordering constraints:
[2nd(cons1(X, cons(Y, Z)))] = [1] X + [1] Y + [1] Z + [8]
> [1] Y + [0]
= [Y]
[2nd(cons(X, X1))] = [1] X + [1] X1 + [8]
> [1] X + [1] X1 + [4]
= [2nd(cons1(X, X1))]
[from(X)] = [1] X + [0]
? [1] X + [4]
= [cons(X, from(s(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: { from(X) -> cons(X, from(s(X))) }
Weak Trs:
{ 2nd(cons1(X, cons(Y, Z))) -> Y
, 2nd(cons(X, X1)) -> 2nd(cons1(X, X1)) }
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) '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
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.
2) 'WithProblem (timeout of 60 seconds)' failed due to the
following reason:
We add the following innermost weak dependency pairs:
Strict DPs:
{ 2nd^#(cons1(X, cons(Y, Z))) -> c_1()
, 2nd^#(cons(X, X1)) -> c_2(2nd^#(cons1(X, X1)))
, from^#(X) -> c_3(from^#(s(X))) }
and mark the set of starting terms.
We are left with following problem, upon which TcT provides the
certificate MAYBE.
Strict DPs:
{ 2nd^#(cons1(X, cons(Y, Z))) -> c_1()
, 2nd^#(cons(X, X1)) -> c_2(2nd^#(cons1(X, X1)))
, from^#(X) -> c_3(from^#(s(X))) }
Strict Trs:
{ 2nd(cons1(X, cons(Y, Z))) -> Y
, 2nd(cons(X, X1)) -> 2nd(cons1(X, X1))
, from(X) -> cons(X, from(s(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:
{ 2nd^#(cons1(X, cons(Y, Z))) -> c_1()
, 2nd^#(cons(X, X1)) -> c_2(2nd^#(cons1(X, X1)))
, from^#(X) -> c_3(from^#(s(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_2) = {1}, Uargs(c_3) = {1}
TcT has computed the following constructor-restricted matrix
interpretation.
[cons1](x1, x2) = [1 0] x1 + [0]
[0 0] [2]
[cons](x1, x2) = [1 0] x1 + [1 0] x2 + [0]
[0 0] [0 0] [0]
[s](x1) = [1 1] x1 + [1]
[0 0] [1]
[2nd^#](x1) = [0 2] x1 + [0]
[0 0] [0]
[c_1] = [1]
[0]
[c_2](x1) = [1 0] x1 + [1]
[0 1] [2]
[from^#](x1) = [1 1] x1 + [2]
[2 2] [2]
[c_3](x1) = [1 0] x1 + [2]
[0 1] [1]
The following symbols are considered usable
{2nd^#, from^#}
The order satisfies the following ordering constraints:
[2nd^#(cons1(X, cons(Y, Z)))] = [4]
[0]
> [1]
[0]
= [c_1()]
[2nd^#(cons(X, X1))] = [0]
[0]
? [5]
[2]
= [c_2(2nd^#(cons1(X, X1)))]
[from^#(X)] = [1 1] X + [2]
[2 2] [2]
? [1 1] X + [6]
[2 2] [7]
= [c_3(from^#(s(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:
{ 2nd^#(cons(X, X1)) -> c_2(2nd^#(cons1(X, X1)))
, from^#(X) -> c_3(from^#(s(X))) }
Weak DPs: { 2nd^#(cons1(X, cons(Y, Z))) -> c_1() }
Obligation:
innermost runtime complexity
Answer:
MAYBE
We estimate the number of application of {1} by applications of
Pre({1}) = {}. Here rules are labeled as follows:
DPs:
{ 1: 2nd^#(cons(X, X1)) -> c_2(2nd^#(cons1(X, X1)))
, 2: from^#(X) -> c_3(from^#(s(X)))
, 3: 2nd^#(cons1(X, cons(Y, Z))) -> c_1() }
We are left with following problem, upon which TcT provides the
certificate MAYBE.
Strict DPs: { from^#(X) -> c_3(from^#(s(X))) }
Weak DPs:
{ 2nd^#(cons1(X, cons(Y, Z))) -> c_1()
, 2nd^#(cons(X, X1)) -> c_2(2nd^#(cons1(X, X1))) }
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.
{ 2nd^#(cons1(X, cons(Y, Z))) -> c_1()
, 2nd^#(cons(X, X1)) -> c_2(2nd^#(cons1(X, X1))) }
We are left with following problem, upon which TcT provides the
certificate MAYBE.
Strict DPs: { from^#(X) -> c_3(from^#(s(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) '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
Arrrr..