WORST_CASE(?,O(n^1)) * Step 1: NaturalPI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: f(x,x,y) -> x f(x,y,y) -> y f(x,y,g(y)) -> x f(f(x,y,z),u,f(x,y,v)) -> f(x,y,f(z,u,v)) f(g(x),x,y) -> y - Signature: {f/3} / {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(f) = {3} Following symbols are considered usable: {f} TcT has computed the following interpretation: p(f) = 1 + 2*x1 + 4*x3 p(g) = 2 + x1 Following rules are strictly oriented: f(x,x,y) = 1 + 2*x + 4*y > x = x f(x,y,y) = 1 + 2*x + 4*y > y = y f(x,y,g(y)) = 9 + 2*x + 4*y > x = x f(f(x,y,z),u,f(x,y,v)) = 7 + 16*v + 12*x + 8*z > 5 + 16*v + 2*x + 8*z = f(x,y,f(z,u,v)) f(g(x),x,y) = 5 + 2*x + 4*y > y = y Following rules are (at-least) weakly oriented: WORST_CASE(?,O(n^1))