WORST_CASE(?,O(n^1)) * Step 1: NaturalMI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: f(0(),y) -> 0() f(s(x),y) -> f(f(x,y),y) - Signature: {f/2} / {0/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {f} 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(f) = {1} Following symbols are considered usable: {f} TcT has computed the following interpretation: p(0) = [4] p(f) = [1] x1 + [4] p(s) = [1] x1 + [12] Following rules are strictly oriented: f(0(),y) = [8] > [4] = 0() f(s(x),y) = [1] x + [16] > [1] x + [8] = f(f(x,y),y) Following rules are (at-least) weakly oriented: WORST_CASE(?,O(n^1))