WORST_CASE(?,O(n^1)) * Step 1: NaturalMI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: f(f(x)) -> f(x) f(s(x)) -> f(x) g(s(0())) -> g(f(s(0()))) - Signature: {f/1,g/1} / {0/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {f,g} and constructors {0,s} + 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: uargs(g) = {1} Following symbols are considered usable: {f,g} TcT has computed the following interpretation: p(0) = [2] [0] p(f) = [1 1] x1 + [8] [0 0] [0] p(g) = [1 14] x1 + [3] [0 0] [6] p(s) = [1 1] x1 + [1] [0 0] [1] Following rules are strictly oriented: f(f(x)) = [1 1] x + [16] [0 0] [0] > [1 1] x + [8] [0 0] [0] = f(x) f(s(x)) = [1 1] x + [10] [0 0] [0] > [1 1] x + [8] [0 0] [0] = f(x) g(s(0())) = [20] [6] > [15] [6] = g(f(s(0()))) Following rules are (at-least) weakly oriented: WORST_CASE(?,O(n^1))