WORST_CASE(?,O(n^1)) * Step 1: NaturalPI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: f(x,g(x)) -> x f(x,h(y)) -> f(h(x),y) - Signature: {f/2} / {g/1,h/1} - Obligation: innermost runtime complexity wrt. defined symbols {f} and constructors {g,h} + Applied Processor: NaturalPI {shape = Linear, restrict = NoRestrict, uargs = UArgs, urules = URules, selector = Nothing} + Details: We apply a polynomial interpretation of kind constructor-based(linear): The following argument positions are considered usable: none Following symbols are considered usable: {f} TcT has computed the following interpretation: p(f) = 1 + 2*x2 p(g) = 4 + x1 p(h) = 8 + x1 Following rules are strictly oriented: f(x,g(x)) = 9 + 2*x > x = x f(x,h(y)) = 17 + 2*y > 1 + 2*y = f(h(x),y) Following rules are (at-least) weakly oriented: WORST_CASE(?,O(n^1))