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: 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 + [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: 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) '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 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^#(cons(X, cons(Y, Z))) -> c_1() , from^#(X) -> c_2(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() , from^#(X) -> c_2(from^#(s(X))) } Strict Trs: { 2nd(cons(X, cons(Y, Z))) -> Y , 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^#(cons(X, cons(Y, Z))) -> c_1() , from^#(X) -> c_2(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} TcT has computed the following constructor-restricted matrix interpretation. [cons](x1, x2) = [0] [0] [s](x1) = [1 1] x1 + [1] [0 0] [1] [2nd^#](x1) = [2] [2] [c_1] = [1] [1] [from^#](x1) = [2 2] x1 + [2] [2 2] [2] [c_2](x1) = [1 0] x1 + [1] [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] [1] = [c_1()] [from^#(X)] = [2 2] X + [2] [2 2] [2] ? [2 2] X + [7] [2 2] [7] = [c_2(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(from^#(s(X))) } Weak DPs: { 2nd^#(cons(X, cons(Y, Z))) -> c_1() } 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^#(cons(X, cons(Y, Z))) -> c_1() } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { from^#(X) -> c_2(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..