MAYBE We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { f(X) -> cons(X, f(g(X))) , g(0()) -> s(0()) , g(s(X)) -> s(s(g(X))) , sel(0(), cons(X, Y)) -> X , sel(s(X), cons(Y, Z)) -> sel(X, Z) } 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) = {1}, Uargs(cons) = {2}, Uargs(s) = {1} TcT has computed the following matrix interpretation satisfying not(EDA) and not(IDA(1)). [f](x1) = [1] x1 + [0] [cons](x1, x2) = [1] x1 + [1] x2 + [0] [g](x1) = [0] [0] = [4] [s](x1) = [1] x1 + [0] [sel](x1, x2) = [1] x2 + [1] The following symbols are considered usable {f, g, sel} The order satisfies the following ordering constraints: [f(X)] = [1] X + [0] >= [1] X + [0] = [cons(X, f(g(X)))] [g(0())] = [0] ? [4] = [s(0())] [g(s(X))] = [0] >= [0] = [s(s(g(X)))] [sel(0(), cons(X, Y))] = [1] X + [1] Y + [1] > [1] X + [0] = [X] [sel(s(X), cons(Y, Z))] = [1] Y + [1] Z + [1] >= [1] Z + [1] = [sel(X, Z)] 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(X) -> cons(X, f(g(X))) , g(0()) -> s(0()) , g(s(X)) -> s(s(g(X))) , sel(s(X), cons(Y, Z)) -> sel(X, Z) } Weak Trs: { sel(0(), cons(X, Y)) -> 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) = {1}, Uargs(cons) = {2}, Uargs(s) = {1} TcT has computed the following matrix interpretation satisfying not(EDA) and not(IDA(1)). [f](x1) = [1] x1 + [0] [cons](x1, x2) = [1] x1 + [1] x2 + [4] [g](x1) = [0] [0] = [4] [s](x1) = [1] x1 + [0] [sel](x1, x2) = [1] x2 + [7] The following symbols are considered usable {f, g, sel} The order satisfies the following ordering constraints: [f(X)] = [1] X + [0] ? [1] X + [4] = [cons(X, f(g(X)))] [g(0())] = [0] ? [4] = [s(0())] [g(s(X))] = [0] >= [0] = [s(s(g(X)))] [sel(0(), cons(X, Y))] = [1] X + [1] Y + [11] > [1] X + [0] = [X] [sel(s(X), cons(Y, Z))] = [1] Y + [1] Z + [11] > [1] Z + [7] = [sel(X, Z)] 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(X) -> cons(X, f(g(X))) , g(0()) -> s(0()) , g(s(X)) -> s(s(g(X))) } Weak Trs: { sel(0(), cons(X, Y)) -> X , sel(s(X), cons(Y, Z)) -> sel(X, Z) } 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) = {1}, Uargs(cons) = {2}, Uargs(s) = {1} TcT has computed the following matrix interpretation satisfying not(EDA) and not(IDA(1)). [f](x1) = [1] x1 + [7] [cons](x1, x2) = [1] x1 + [1] x2 + [6] [g](x1) = [1] [0] = [0] [s](x1) = [1] x1 + [0] [sel](x1, x2) = [1] x1 + [1] x2 + [7] The following symbols are considered usable {f, g, sel} The order satisfies the following ordering constraints: [f(X)] = [1] X + [7] ? [1] X + [14] = [cons(X, f(g(X)))] [g(0())] = [1] > [0] = [s(0())] [g(s(X))] = [1] >= [1] = [s(s(g(X)))] [sel(0(), cons(X, Y))] = [1] X + [1] Y + [13] > [1] X + [0] = [X] [sel(s(X), cons(Y, Z))] = [1] X + [1] Y + [1] Z + [13] > [1] X + [1] Z + [7] = [sel(X, Z)] 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(X) -> cons(X, f(g(X))) , g(s(X)) -> s(s(g(X))) } Weak Trs: { g(0()) -> s(0()) , sel(0(), cons(X, Y)) -> X , sel(s(X), cons(Y, Z)) -> sel(X, Z) } 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. Arrrr..