WORST_CASE(?,O(n^1)) * Step 1: NaturalPI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: f(X,X) -> c(X) f(X,c(X)) -> f(s(X),X) f(s(X),X) -> f(X,a(X)) - Signature: {f/2} / {a/1,c/1,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {f} and constructors {a,c,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(a) = 0 p(c) = 9 p(f) = 12 + x1 + x2 p(s) = 4 Following rules are strictly oriented: f(X,X) = 12 + 2*X > 9 = c(X) f(X,c(X)) = 21 + X > 16 + X = f(s(X),X) f(s(X),X) = 16 + X > 12 + X = f(X,a(X)) Following rules are (at-least) weakly oriented: WORST_CASE(?,O(n^1))