WORST_CASE(?,O(n^1)) * Step 1: NaturalMI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: dfsAcc#3(Leaf(x8),x16) -> Cons(x8,x16) dfsAcc#3(Node(x6,x4),x2) -> dfsAcc#3(x4,dfsAcc#3(x6,x2)) main(x1) -> revApp#2(dfsAcc#3(x1,Nil()),Nil()) revApp#2(Cons(x6,x4),x2) -> revApp#2(x4,Cons(x6,x2)) revApp#2(Nil(),x16) -> x16 - Signature: {dfsAcc#3/2,main/1,revApp#2/2} / {Cons/2,Leaf/1,Nil/0,Node/2} - Obligation: innermost runtime complexity wrt. defined symbols {dfsAcc#3,main,revApp#2} and constructors {Cons,Leaf,Nil ,Node} + 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(dfsAcc#3) = {2}, uargs(revApp#2) = {1} Following symbols are considered usable: {dfsAcc#3,main,revApp#2} TcT has computed the following interpretation: p(Cons) = [1] x2 + [1] p(Leaf) = [5] p(Nil) = [0] p(Node) = [1] x1 + [1] x2 + [1] p(dfsAcc#3) = [2] x1 + [1] x2 + [0] p(main) = [8] x1 + [9] p(revApp#2) = [4] x1 + [1] x2 + [1] Following rules are strictly oriented: dfsAcc#3(Leaf(x8),x16) = [1] x16 + [10] > [1] x16 + [1] = Cons(x8,x16) dfsAcc#3(Node(x6,x4),x2) = [1] x2 + [2] x4 + [2] x6 + [2] > [1] x2 + [2] x4 + [2] x6 + [0] = dfsAcc#3(x4,dfsAcc#3(x6,x2)) main(x1) = [8] x1 + [9] > [8] x1 + [1] = revApp#2(dfsAcc#3(x1,Nil()),Nil()) revApp#2(Cons(x6,x4),x2) = [1] x2 + [4] x4 + [5] > [1] x2 + [4] x4 + [2] = revApp#2(x4,Cons(x6,x2)) revApp#2(Nil(),x16) = [1] x16 + [1] > [1] x16 + [0] = x16 Following rules are (at-least) weakly oriented: WORST_CASE(?,O(n^1))