MAYBE We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { cons(x, cons(y, z)) -> big() , inf(x) -> cons(x, inf(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) 'WithProblem (timeout of 60 seconds)' failed due to the following reason: We add the following dependency tuples: Strict DPs: { cons^#(x, cons(y, z)) -> c_1() , inf^#(x) -> c_2(cons^#(x, inf(s(x))), inf^#(s(x))) } and mark the set of starting terms. We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { cons^#(x, cons(y, z)) -> c_1() , inf^#(x) -> c_2(cons^#(x, inf(s(x))), inf^#(s(x))) } Weak Trs: { cons(x, cons(y, z)) -> big() , inf(x) -> cons(x, inf(s(x))) } Obligation: innermost runtime complexity Answer: MAYBE We estimate the number of application of {1} by applications of Pre({1}) = {2}. Here rules are labeled as follows: DPs: { 1: cons^#(x, cons(y, z)) -> c_1() , 2: inf^#(x) -> c_2(cons^#(x, inf(s(x))), inf^#(s(x))) } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { inf^#(x) -> c_2(cons^#(x, inf(s(x))), inf^#(s(x))) } Weak DPs: { cons^#(x, cons(y, z)) -> c_1() } Weak Trs: { cons(x, cons(y, z)) -> big() , inf(x) -> cons(x, inf(s(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. { cons^#(x, cons(y, z)) -> c_1() } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { inf^#(x) -> c_2(cons^#(x, inf(s(x))), inf^#(s(x))) } Weak Trs: { cons(x, cons(y, z)) -> big() , inf(x) -> cons(x, inf(s(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: { inf^#(x) -> c_2(cons^#(x, inf(s(x))), inf^#(s(x))) } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { inf^#(x) -> c_1(inf^#(s(x))) } Weak Trs: { cons(x, cons(y, z)) -> big() , inf(x) -> cons(x, inf(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: { inf^#(x) -> c_1(inf^#(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 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)). [cons](x1, x2) = [1] x1 + [1] x2 + [3] [big] = [5] [inf](x1) = [1] x1 + [5] [s](x1) = [6] The following symbols are considered usable {cons, inf} The order satisfies the following ordering constraints: [cons(x, cons(y, z))] = [1] x + [1] y + [1] z + [6] > [5] = [big()] [inf(x)] = [1] x + [5] ? [1] x + [14] = [cons(x, inf(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: { inf(x) -> cons(x, inf(s(x))) } Weak Trs: { cons(x, cons(y, z)) -> big() } 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: 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: 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 input cannot be shown compatible 2) 'bsearch-popstar (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 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. Arrrr..