WORST_CASE(?,O(n^1)) * Step 1: NaturalMI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: f(0()) -> s(0()) f(s(x)) -> s(s(g(x))) g(0()) -> 0() g(s(x)) -> f(x) - 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 = 1, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Nothing} + Details: We apply a matrix interpretation of kind constructor based matrix interpretation: The following argument positions are considered usable: uargs(s) = {1} Following symbols are considered usable: {f,g} TcT has computed the following interpretation: p(0) = [0] p(f) = [8] x1 + [13] p(g) = [8] x1 + [15] p(s) = [1] x1 + [1] Following rules are strictly oriented: f(0()) = [13] > [1] = s(0()) f(s(x)) = [8] x + [21] > [8] x + [17] = s(s(g(x))) g(0()) = [15] > [0] = 0() g(s(x)) = [8] x + [23] > [8] x + [13] = f(x) Following rules are (at-least) weakly oriented: WORST_CASE(?,O(n^1))