WORST_CASE(?,O(n^1)) * Step 1: NaturalMI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: f(0(),x2) -> 0() f(S(x),x2) -> f(x2,x) - 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: none Following symbols are considered usable: {f} TcT has computed the following interpretation: p(0) = [2] p(S) = [1] x1 + [2] p(f) = [4] x1 + [4] x2 + [0] Following rules are strictly oriented: f(0(),x2) = [4] x2 + [8] > [2] = 0() f(S(x),x2) = [4] x + [4] x2 + [8] > [4] x + [4] x2 + [0] = f(x2,x) Following rules are (at-least) weakly oriented: WORST_CASE(?,O(n^1))