WORST_CASE(?,O(n^1)) * Step 1: NaturalMI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: f(c(s(x),y)) -> f(c(x,s(y))) g(c(x,s(y))) -> g(c(s(x),y)) g(s(f(x))) -> g(f(x)) - Signature: {f/1,g/1} / {c/2,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {f,g} and constructors {c,s} + Applied Processor: NaturalMI {miDimension = 2, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Nothing} + Details: We apply a matrix interpretation of kind constructor based matrix interpretation (containing no more than 1 non-zero interpretation-entries in the diagonal of the component-wise maxima): The following argument positions are considered usable: none Following symbols are considered usable: {f,g} TcT has computed the following interpretation: p(c) = [0 0] x1 + [0 4] x2 + [0] [0 1] [0 0] [0] p(f) = [0 1] x1 + [0] [0 2] [0] p(g) = [1 3] x1 + [0] [1 0] [5] p(s) = [0 4] x1 + [4] [0 1] [2] Following rules are strictly oriented: f(c(s(x),y)) = [0 1] x + [2] [0 2] [4] > [0 1] x + [0] [0 2] [0] = f(c(x,s(y))) g(c(x,s(y))) = [0 3] x + [0 4] y + [8] [0 0] [0 4] [13] > [0 3] x + [0 4] y + [6] [0 0] [0 4] [5] = g(c(s(x),y)) g(s(f(x))) = [0 14] x + [10] [0 8] [9] > [0 7] x + [0] [0 1] [5] = g(f(x)) Following rules are (at-least) weakly oriented: WORST_CASE(?,O(n^1))