WORST_CASE(?,O(n^1)) * Step 1: NaturalMI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: g(x,s(y)) -> g(f(x,y),0()) g(0(),f(x,x)) -> x g(f(x,y),0()) -> f(g(x,0()),g(y,0())) g(s(x),y) -> g(f(x,y),0()) - Signature: {g/2} / {0/0,f/2,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {g} and constructors {0,f,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) = {1,2} Following symbols are considered usable: {g} TcT has computed the following interpretation: p(0) = [0] p(f) = [1] x1 + [1] x2 + [1] p(g) = [2] x1 + [3] x2 + [0] p(s) = [1] x1 + [3] Following rules are strictly oriented: g(x,s(y)) = [2] x + [3] y + [9] > [2] x + [2] y + [2] = g(f(x,y),0()) g(0(),f(x,x)) = [6] x + [3] > [1] x + [0] = x g(f(x,y),0()) = [2] x + [2] y + [2] > [2] x + [2] y + [1] = f(g(x,0()),g(y,0())) g(s(x),y) = [2] x + [3] y + [6] > [2] x + [2] y + [2] = g(f(x,y),0()) Following rules are (at-least) weakly oriented: WORST_CASE(?,O(n^1))