WORST_CASE(?,O(n^1)) * Step 1: NaturalMI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: f(g(X)) -> f(X) - Signature: {f/1} / {g/1} - Obligation: innermost runtime complexity wrt. defined symbols {f} and constructors {g} + Applied Processor: NaturalMI {miDimension = 2, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Nothing} + Details: We apply a matrix interpretation of kind constructor based matrix interpretation (containing no more than 1 non-zero interpretation-entries in the diagonal of the component-wise maxima): The following argument positions are considered usable: none Following symbols are considered usable: {f} TcT has computed the following interpretation: p(f) = [4 1] x1 + [2] [9 8] [12] p(g) = [1 1] x1 + [0] [0 0] [1] Following rules are strictly oriented: f(g(X)) = [4 4] X + [3] [9 9] [20] > [4 1] X + [2] [9 8] [12] = f(X) Following rules are (at-least) weakly oriented: WORST_CASE(?,O(n^1))