WORST_CASE(?,O(n^1)) * Step 1: NaturalPI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: goal(xs,ys) -> revapp(xs,ys) revapp(Cons(x,xs),rest) -> revapp(xs,Cons(x,rest)) revapp(Nil(),rest) -> rest - Signature: {goal/2,revapp/2} / {Cons/2,Nil/0} - Obligation: innermost runtime complexity wrt. defined symbols {goal,revapp} 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: none Following symbols are considered usable: {goal,revapp} TcT has computed the following interpretation: p(Cons) = 5 + x2 p(Nil) = 2 p(goal) = 13 + 8*x1 + 3*x2 p(revapp) = 6*x1 + 2*x2 Following rules are strictly oriented: goal(xs,ys) = 13 + 8*xs + 3*ys > 6*xs + 2*ys = revapp(xs,ys) revapp(Cons(x,xs),rest) = 30 + 2*rest + 6*xs > 10 + 2*rest + 6*xs = revapp(xs,Cons(x,rest)) revapp(Nil(),rest) = 12 + 2*rest > rest = rest Following rules are (at-least) weakly oriented: WORST_CASE(?,O(n^1))