WORST_CASE(?,O(n^1)) * Step 1: NaturalMI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: f(g(x),y,y) -> g(f(x,x,y)) - Signature: {f/3} / {g/1} - Obligation: innermost runtime complexity wrt. defined symbols {f} and constructors {g} + Applied Processor: NaturalMI {miDimension = 1, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Just any strict-rules} + Details: We apply a matrix interpretation of kind constructor based matrix interpretation: The following argument positions are considered usable: uargs(g) = {1} Following symbols are considered usable: {f} TcT has computed the following interpretation: p(f) = [2] x1 + [8] x3 + [2] p(g) = [1] x1 + [8] Following rules are strictly oriented: f(g(x),y,y) = [2] x + [8] y + [18] > [2] x + [8] y + [10] = g(f(x,x,y)) Following rules are (at-least) weakly oriented: * Step 2: EmptyProcessor WORST_CASE(?,O(1)) + Considered Problem: - Weak TRS: f(g(x),y,y) -> g(f(x,x,y)) - Signature: {f/3} / {g/1} - Obligation: innermost runtime complexity wrt. defined symbols {f} and constructors {g} + Applied Processor: EmptyProcessor + Details: The problem is already closed. The intended complexity is O(1). WORST_CASE(?,O(n^1))