MAYBE
We are left with following problem, upon which TcT provides the
certificate MAYBE.
Strict Trs:
{ 2nd(cons(X, cons(Y, Z))) -> Y
, from(X) -> cons(X, from(s(X))) }
Obligation:
runtime complexity
Answer:
MAYBE
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 weak dependency pairs:
Strict DPs:
{ 2nd^#(cons(X, cons(Y, Z))) -> c_1(Y)
, from^#(X) -> c_2(X, 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^#(cons(X, cons(Y, Z))) -> c_1(Y)
, from^#(X) -> c_2(X, from^#(s(X))) }
Strict Trs:
{ 2nd(cons(X, cons(Y, Z))) -> Y
, from(X) -> cons(X, from(s(X))) }
Obligation:
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^#(cons(X, cons(Y, Z))) -> c_1(Y)
, from^#(X) -> c_2(X, from^#(s(X))) }
Obligation:
runtime complexity
Answer:
MAYBE
The weightgap principle applies (using the following constant
growth matrix-interpretation)
The following argument positions are usable:
Uargs(c_2) = {2}
TcT has computed the following constructor-restricted matrix
interpretation.
[cons](x1, x2) = [1 0] x1 + [0]
[0 0] [0]
[s](x1) = [1 1] x1 + [2]
[0 0] [2]
[2nd^#](x1) = [2]
[2]
[c_1](x1) = [1]
[2]
[from^#](x1) = [1 1] x1 + [2]
[1 1] [2]
[c_2](x1, x2) = [0 0] x1 + [1 0] x2 + [1]
[1 2] [0 1] [1]
The following symbols are considered usable
{2nd^#, from^#}
The order satisfies the following ordering constraints:
[2nd^#(cons(X, cons(Y, Z)))] = [2]
[2]
> [1]
[2]
= [c_1(Y)]
[from^#(X)] = [1 1] X + [2]
[1 1] [2]
? [1 1] X + [7]
[2 3] [7]
= [c_2(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 DPs: { from^#(X) -> c_2(X, from^#(s(X))) }
Weak DPs: { 2nd^#(cons(X, cons(Y, Z))) -> c_1(Y) }
Obligation:
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) 'Inspecting Problem...' 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 processor is inapplicable, reason:
Processor only applicable for innermost runtime complexity analysis
2) '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.
3) 'Polynomial Path Order (PS)' failed due to the following reason:
The processor is inapplicable, reason:
Processor only applicable for innermost runtime complexity analysis
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(cons) = {2}
TcT has computed the following matrix interpretation satisfying
not(EDA) and not(IDA(1)).
[2nd](x1) = [1] x1 + [1]
[cons](x1, x2) = [1] x1 + [1] x2 + [7]
[from](x1) = [1] x1 + [3]
[s](x1) = [3]
The following symbols are considered usable
{2nd, from}
The order satisfies the following ordering constraints:
[2nd(cons(X, cons(Y, Z)))] = [1] X + [1] Y + [1] Z + [15]
> [1] Y + [0]
= [Y]
[from(X)] = [1] X + [3]
? [1] X + [13]
= [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(cons(X, cons(Y, Z))) -> Y }
Obligation:
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 processor is inapplicable, reason:
Processor only applicable for innermost runtime complexity analysis
2) 'bsearch-popstar (timeout of 60 seconds)' failed due to the
following reason:
The processor is inapplicable, reason:
Processor only applicable for innermost runtime complexity analysis
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.
3) 'Innermost Weak Dependency Pairs (timeout of 60 seconds)' failed
due to the following reason:
We add the following weak dependency pairs:
Strict DPs:
{ 2nd^#(cons(X, cons(Y, Z))) -> c_1(Y)
, from^#(X) -> c_2(X, 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^#(cons(X, cons(Y, Z))) -> c_1(Y)
, from^#(X) -> c_2(X, from^#(s(X))) }
Strict Trs:
{ 2nd(cons(X, cons(Y, Z))) -> Y
, from(X) -> cons(X, from(s(X))) }
Obligation:
runtime complexity
Answer:
MAYBE
Empty strict component of the problem is NOT empty.
Arrrr..