WORST_CASE(?,O(n^1)) * Step 1: NaturalPI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: g(f(x),y) -> f(h(x,y)) h(x,y) -> g(x,f(y)) - Signature: {g/2,h/2} / {f/1} - Obligation: innermost runtime complexity wrt. defined symbols {g,h} and constructors {f} + 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(f) = {1} Following symbols are considered usable: {g,h} TcT has computed the following interpretation: p(f) = 2 + x1 p(g) = 8*x1 + x2 p(h) = 10 + 8*x1 + x2 Following rules are strictly oriented: g(f(x),y) = 16 + 8*x + y > 12 + 8*x + y = f(h(x,y)) h(x,y) = 10 + 8*x + y > 2 + 8*x + y = g(x,f(y)) Following rules are (at-least) weakly oriented: WORST_CASE(?,O(n^1))