WORST_CASE(?,O(n^1)) * Step 1: NaturalPI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: g(x,h(y,z)) -> h(g(x,y),z) g(f(x,y),z) -> f(x,g(y,z)) g(h(x,y),z) -> g(x,f(y,z)) - Signature: {g/2} / {f/2,h/2} - Obligation: innermost runtime complexity wrt. defined symbols {g} and constructors {f,h} + 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) = {2}, uargs(h) = {1} Following symbols are considered usable: {g} TcT has computed the following interpretation: p(f) = 4 + x2 p(g) = 4*x1 + 3*x2 p(h) = 6 + x1 + x2 Following rules are strictly oriented: g(x,h(y,z)) = 18 + 4*x + 3*y + 3*z > 6 + 4*x + 3*y + z = h(g(x,y),z) g(f(x,y),z) = 16 + 4*y + 3*z > 4 + 4*y + 3*z = f(x,g(y,z)) g(h(x,y),z) = 24 + 4*x + 4*y + 3*z > 12 + 4*x + 3*z = g(x,f(y,z)) Following rules are (at-least) weakly oriented: WORST_CASE(?,O(n^1))