WORST_CASE(?,O(n^1)) * Step 1: NaturalMI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: f(X,X) -> c(X) f(X,c(X)) -> f(s(X),X) f(s(X),X) -> f(X,a(X)) - Signature: {f/2} / {a/1,c/1,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {f} and constructors {a,c,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(a) = [1] x1 + [0] p(c) = [1] x1 + [2] p(f) = [9] x1 + [6] x2 + [4] p(s) = [1] x1 + [1] Following rules are strictly oriented: f(X,X) = [15] X + [4] > [1] X + [2] = c(X) f(X,c(X)) = [15] X + [16] > [15] X + [13] = f(s(X),X) f(s(X),X) = [15] X + [13] > [15] X + [4] = f(X,a(X)) Following rules are (at-least) weakly oriented: WORST_CASE(?,O(n^1))