WORST_CASE(?,O(n^1)) * Step 1: NaturalMI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: anchored(Cons(x,xs),y) -> anchored(xs,Cons(Cons(Nil(),Nil()),y)) anchored(Nil(),y) -> y goal(x,y) -> anchored(x,y) - Signature: {anchored/2,goal/2} / {Cons/2,Nil/0} - Obligation: innermost runtime complexity wrt. defined symbols {anchored,goal} and constructors {Cons,Nil} + 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: {anchored,goal} TcT has computed the following interpretation: p(Cons) = [1] x2 + [2] p(Nil) = [1] p(anchored) = [4] x1 + [3] x2 + [6] p(goal) = [4] x1 + [3] x2 + [7] Following rules are strictly oriented: anchored(Cons(x,xs),y) = [4] xs + [3] y + [14] > [4] xs + [3] y + [12] = anchored(xs,Cons(Cons(Nil(),Nil()),y)) anchored(Nil(),y) = [3] y + [10] > [1] y + [0] = y goal(x,y) = [4] x + [3] y + [7] > [4] x + [3] y + [6] = anchored(x,y) Following rules are (at-least) weakly oriented: WORST_CASE(?,O(n^1))