WORST_CASE(?,O(n^1)) * Step 1: NaturalPI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: f(g(x)) -> g(g(f(x))) f(g(x)) -> g(g(g(x))) - Signature: {f/1} / {g/1} - Obligation: innermost runtime complexity wrt. defined symbols {f} and constructors {g} + 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: uargs(g) = {1} Following symbols are considered usable: {f} TcT has computed the following interpretation: p(f) = 12 + 8*x1 p(g) = 2 + x1 Following rules are strictly oriented: f(g(x)) = 28 + 8*x > 16 + 8*x = g(g(f(x))) f(g(x)) = 28 + 8*x > 6 + x = g(g(g(x))) Following rules are (at-least) weakly oriented: WORST_CASE(?,O(n^1))