WORST_CASE(?,O(n^1)) * Step 1: NaturalPI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: f(0(),x2) -> 0() f(S(x),x2) -> f(x2,x) - 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: none Following symbols are considered usable: {f} TcT has computed the following interpretation: p(0) = 3 p(S) = 1 + x1 p(f) = 1 + x1 + x2 Following rules are strictly oriented: f(0(),x2) = 4 + x2 > 3 = 0() f(S(x),x2) = 2 + x + x2 > 1 + x + x2 = f(x2,x) Following rules are (at-least) weakly oriented: WORST_CASE(?,O(n^1))