WORST_CASE(?,O(n^1)) * Step 1: NaturalPI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: f(x,y) -> g(x,y) g(h(x),y) -> h(f(x,y)) g(h(x),y) -> h(g(x,y)) - Signature: {f/2,g/2} / {h/1} - Obligation: innermost runtime complexity wrt. defined symbols {f,g} and constructors {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(h) = {1} Following symbols are considered usable: {f,g} TcT has computed the following interpretation: p(f) = 15 + 4*x1 p(g) = 8 + 4*x1 p(h) = 5 + x1 Following rules are strictly oriented: f(x,y) = 15 + 4*x > 8 + 4*x = g(x,y) g(h(x),y) = 28 + 4*x > 20 + 4*x = h(f(x,y)) g(h(x),y) = 28 + 4*x > 13 + 4*x = h(g(x,y)) Following rules are (at-least) weakly oriented: WORST_CASE(?,O(n^1))