WORST_CASE(?,O(n^1)) * Step 1: NaturalMI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: fold#3(Cons(x4,x2)) -> plus#2(x4,fold#3(x2)) fold#3(Nil()) -> 0() main(x1) -> fold#3(x1) plus#2(0(),x12) -> x12 plus#2(S(x4),x2) -> S(plus#2(x4,x2)) - Signature: {fold#3/1,main/1,plus#2/2} / {0/0,Cons/2,Nil/0,S/1} - Obligation: innermost runtime complexity wrt. defined symbols {fold#3,main,plus#2} and constructors {0,Cons,Nil,S} + 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: uargs(S) = {1}, uargs(plus#2) = {2} Following symbols are considered usable: {fold#3,main,plus#2} TcT has computed the following interpretation: p(0) = [4] p(Cons) = [1] x1 + [1] x2 + [1] p(Nil) = [3] p(S) = [1] x1 + [1] p(fold#3) = [8] x1 + [0] p(main) = [8] x1 + [3] p(plus#2) = [2] x1 + [1] x2 + [0] Following rules are strictly oriented: fold#3(Cons(x4,x2)) = [8] x2 + [8] x4 + [8] > [8] x2 + [2] x4 + [0] = plus#2(x4,fold#3(x2)) fold#3(Nil()) = [24] > [4] = 0() main(x1) = [8] x1 + [3] > [8] x1 + [0] = fold#3(x1) plus#2(0(),x12) = [1] x12 + [8] > [1] x12 + [0] = x12 plus#2(S(x4),x2) = [1] x2 + [2] x4 + [2] > [1] x2 + [2] x4 + [1] = S(plus#2(x4,x2)) Following rules are (at-least) weakly oriented: WORST_CASE(?,O(n^1))