WORST_CASE(?,O(n^1)) * Step 1: NaturalMI 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: NaturalMI {miDimension = 1, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Nothing} + Details: We apply a matrix interpretation of kind constructor based matrix interpretation: The following argument positions are considered usable: none Following symbols are considered usable: {goal,list,notEmpty} TcT has computed the following interpretation: p(Cons) = [1] x1 + [1] x2 + [4] p(False) = [0] p(Nil) = [0] p(True) = [0] p(goal) = [2] x1 + [7] p(isEmpty[Match]) = [0] p(list) = [2] x1 + [5] p(notEmpty) = [15] Following rules are strictly oriented: goal(x) = [2] x + [7] > [2] x + [5] = list(x) list(Cons(x,xs)) = [2] x + [2] xs + [13] > [2] xs + [5] = list(xs) list(Nil()) = [5] > [0] = True() list(Nil()) = [5] > [0] = isEmpty[Match](Nil()) notEmpty(Cons(x,xs)) = [15] > [0] = True() notEmpty(Nil()) = [15] > [0] = False() Following rules are (at-least) weakly oriented: WORST_CASE(?,O(n^1))