WORST_CASE(?,O(n^1)) * Step 1: NaturalPI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: append(Cons(x,xs),ys) -> Cons(x,append(xs,ys)) append(Nil(),ys) -> ys goal(x,y) -> append(x,y) - Signature: {append/2,goal/2} / {Cons/2,Nil/0} - Obligation: innermost runtime complexity wrt. defined symbols {append,goal} and constructors {Cons,Nil} + 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(Cons) = {2} Following symbols are considered usable: {append,goal} TcT has computed the following interpretation: p(Cons) = 5 + x1 + x2 p(Nil) = 2 p(append) = 8 + 4*x1 + 12*x2 p(goal) = 13 + 13*x1 + 12*x2 Following rules are strictly oriented: append(Cons(x,xs),ys) = 28 + 4*x + 4*xs + 12*ys > 13 + x + 4*xs + 12*ys = Cons(x,append(xs,ys)) append(Nil(),ys) = 16 + 12*ys > ys = ys goal(x,y) = 13 + 13*x + 12*y > 8 + 4*x + 12*y = append(x,y) Following rules are (at-least) weakly oriented: WORST_CASE(?,O(n^1))