WORST_CASE(?,O(n^1)) * Step 1: NaturalPI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: goal(x) -> list(x) list(Cons(x,xs)) -> list(xs) list(Nil()) -> True() list(Nil()) -> isEmpty[Match](Nil()) notEmpty(Cons(x,xs)) -> True() notEmpty(Nil()) -> False() - Signature: {goal/1,list/1,notEmpty/1} / {Cons/2,False/0,Nil/0,True/0,isEmpty[Match]/1} - Obligation: innermost runtime complexity wrt. defined symbols {goal,list,notEmpty} and constructors {Cons,False,Nil,True ,isEmpty[Match]} + Applied Processor: NaturalPI {shape = StronglyLinear, restrict = NoRestrict, uargs = UArgs, urules = URules, selector = Nothing} + Details: We apply a polynomial interpretation of kind constructor-based(stronglyLinear): The following argument positions are considered usable: none Following symbols are considered usable: {goal,list,notEmpty} TcT has computed the following interpretation: p(Cons) = 2 + x1 + x2 p(False) = 14 p(Nil) = 14 p(True) = 5 p(goal) = 3 + x1 p(isEmpty[Match]) = 10 p(list) = x1 p(notEmpty) = 13 + x1 Following rules are strictly oriented: goal(x) = 3 + x > x = list(x) list(Cons(x,xs)) = 2 + x + xs > xs = list(xs) list(Nil()) = 14 > 5 = True() list(Nil()) = 14 > 10 = isEmpty[Match](Nil()) notEmpty(Cons(x,xs)) = 15 + x + xs > 5 = True() notEmpty(Nil()) = 27 > 14 = False() Following rules are (at-least) weakly oriented: WORST_CASE(?,O(n^1))