WORST_CASE(?,O(n^1)) * Step 1: NaturalPI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: f(0(),y) -> 0() f(s(x),y) -> f(f(x,y),y) - Signature: {f/2} / {0/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {f} and constructors {0,s} + Applied Processor: NaturalPI {shape = StronglyLinear, restrict = NoRestrict, uargs = UArgs, urules = URules, selector = Nothing} + Details: We apply a polynomial interpretation of kind constructor-based(stronglyLinear): The following argument positions are considered usable: uargs(f) = {1} Following symbols are considered usable: {f} TcT has computed the following interpretation: p(0) = 0 p(f) = 4 + x1 p(s) = 6 + x1 Following rules are strictly oriented: f(0(),y) = 4 > 0 = 0() f(s(x),y) = 10 + x > 8 + x = f(f(x,y),y) Following rules are (at-least) weakly oriented: WORST_CASE(?,O(n^1))