WORST_CASE(?,O(n^1)) * Step 1: NaturalMI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: f(s(x),y,y) -> f(y,x,s(x)) g(x,y) -> x g(x,y) -> y - Signature: {f/3,g/2} / {s/1} - Obligation: innermost runtime complexity wrt. defined symbols {f,g} and constructors {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(f) = [4] x1 + [4] x2 + [3] p(g) = [8] x1 + [2] x2 + [4] p(s) = [1] x1 + [7] Following rules are strictly oriented: f(s(x),y,y) = [4] x + [4] y + [31] > [4] x + [4] y + [3] = f(y,x,s(x)) g(x,y) = [8] x + [2] y + [4] > [1] x + [0] = x g(x,y) = [8] x + [2] y + [4] > [1] y + [0] = y Following rules are (at-least) weakly oriented: WORST_CASE(?,O(n^1))