WORST_CASE(?,O(n^1)) * Step 1: NaturalPI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: g(x,y) -> h(x,y) h(f(x),y) -> f(g(x,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) = 4 + x1 p(g) = 8 + 4*x1 p(h) = 4*x1 Following rules are strictly oriented: g(x,y) = 8 + 4*x > 4*x = h(x,y) h(f(x),y) = 16 + 4*x > 12 + 4*x = f(g(x,y)) Following rules are (at-least) weakly oriented: WORST_CASE(?,O(n^1))