MAYBE We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { f(X1, X2) -> n__f(X1, X2) , f(g(X), Y) -> f(X, n__f(g(X), activate(Y))) , activate(X) -> X , activate(n__f(X1, X2)) -> f(X1, X2) } 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: Computation stopped due to timeout after 60.0 seconds. 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(f) = {2}, Uargs(n__f) = {2} TcT has computed the following matrix interpretation satisfying not(EDA) and not(IDA(1)). [f](x1, x2) = [1] x2 + [4] [g](x1) = [1] x1 + [7] [n__f](x1, x2) = [1] x2 + [0] [activate](x1) = [1] x1 + [0] The following symbols are considered usable {f, activate} The order satisfies the following ordering constraints: [f(X1, X2)] = [1] X2 + [4] > [1] X2 + [0] = [n__f(X1, X2)] [f(g(X), Y)] = [1] Y + [4] >= [1] Y + [4] = [f(X, n__f(g(X), activate(Y)))] [activate(X)] = [1] X + [0] >= [1] X + [0] = [X] [activate(n__f(X1, X2))] = [1] X2 + [0] ? [1] X2 + [4] = [f(X1, X2)] 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: { f(g(X), Y) -> f(X, n__f(g(X), activate(Y))) , activate(X) -> X , activate(n__f(X1, X2)) -> f(X1, X2) } Weak Trs: { f(X1, X2) -> n__f(X1, X2) } Obligation: innermost runtime complexity Answer: MAYBE The weightgap principle applies (using the following nonconstant growth matrix-interpretation) The following argument positions are usable: Uargs(f) = {2}, Uargs(n__f) = {2} TcT has computed the following matrix interpretation satisfying not(EDA) and not(IDA(1)). [f](x1, x2) = [1] x2 + [4] [g](x1) = [1] x1 + [7] [n__f](x1, x2) = [1] x2 + [0] [activate](x1) = [1] x1 + [4] The following symbols are considered usable {f, activate} The order satisfies the following ordering constraints: [f(X1, X2)] = [1] X2 + [4] > [1] X2 + [0] = [n__f(X1, X2)] [f(g(X), Y)] = [1] Y + [4] ? [1] Y + [8] = [f(X, n__f(g(X), activate(Y)))] [activate(X)] = [1] X + [4] > [1] X + [0] = [X] [activate(n__f(X1, X2))] = [1] X2 + [4] >= [1] X2 + [4] = [f(X1, X2)] 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: { f(g(X), Y) -> f(X, n__f(g(X), activate(Y))) , activate(n__f(X1, X2)) -> f(X1, X2) } Weak Trs: { f(X1, X2) -> n__f(X1, X2) , activate(X) -> X } Obligation: innermost runtime complexity Answer: MAYBE The weightgap principle applies (using the following nonconstant growth matrix-interpretation) The following argument positions are usable: Uargs(f) = {2}, Uargs(n__f) = {2} TcT has computed the following matrix interpretation satisfying not(EDA) and not(IDA(1)). [f](x1, x2) = [1] x2 + [0] [g](x1) = [1] x1 + [7] [n__f](x1, x2) = [1] x2 + [0] [activate](x1) = [1] x1 + [1] The following symbols are considered usable {f, activate} The order satisfies the following ordering constraints: [f(X1, X2)] = [1] X2 + [0] >= [1] X2 + [0] = [n__f(X1, X2)] [f(g(X), Y)] = [1] Y + [0] ? [1] Y + [1] = [f(X, n__f(g(X), activate(Y)))] [activate(X)] = [1] X + [1] > [1] X + [0] = [X] [activate(n__f(X1, X2))] = [1] X2 + [1] > [1] X2 + [0] = [f(X1, X2)] 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: { f(g(X), Y) -> f(X, n__f(g(X), activate(Y))) } Weak Trs: { f(X1, X2) -> n__f(X1, X2) , activate(X) -> X , activate(n__f(X1, X2)) -> f(X1, X2) } 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. Arrrr..