WORST_CASE(?,O(n^1)) * Step 1: NaturalMI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: f(x1,0()) -> g(x1,0()) f(y,S(x)) -> f(S(y),x) g(0(),x2) -> x2 g(S(x),y) -> g(x,S(y)) - Signature: {f/2,g/2} / {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: none Following symbols are considered usable: {f,g} TcT has computed the following interpretation: p(0) = [2] p(S) = [1] x1 + [2] p(f) = [12] x1 + [14] x2 + [0] p(g) = [9] x1 + [8] x2 + [0] Following rules are strictly oriented: f(x1,0()) = [12] x1 + [28] > [9] x1 + [16] = g(x1,0()) f(y,S(x)) = [14] x + [12] y + [28] > [14] x + [12] y + [24] = f(S(y),x) g(0(),x2) = [8] x2 + [18] > [1] x2 + [0] = x2 g(S(x),y) = [9] x + [8] y + [18] > [9] x + [8] y + [16] = g(x,S(y)) Following rules are (at-least) weakly oriented: WORST_CASE(?,O(n^1))