* Step 1: MI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: g(f(x),y) -> f(h(x,y)) h(x,y) -> g(x,f(y)) - Signature: {g/2,h/2} / {f/1} - Obligation: innermost runtime complexity wrt. defined symbols {g,h} and constructors {f} + Applied Processor: MI {miKind = MaximalMatrix (UpperTriangular (Multiplicity Nothing)), miDimension = 1, miUArgs = UArgs, miURules = URules, miSelector = Just any strict-rules} + Details: We apply a matrix interpretation of kind MaximalMatrix (UpperTriangular (Multiplicity Nothing)): The following argument positions are considered usable: uargs(f) = {1} Following symbols are considered usable: {g,h} TcT has computed the following interpretation: p(f) = [1] x_1 + [12] p(g) = [2] x_1 + [0] p(h) = [2] x_1 + [1] Following rules are strictly oriented: g(f(x),y) = [2] x + [24] > [2] x + [13] = f(h(x,y)) h(x,y) = [2] x + [1] > [2] x + [0] = g(x,f(y)) Following rules are (at-least) weakly oriented: * Step 2: EmptyProcessor WORST_CASE(?,O(1)) + Considered Problem: - Weak TRS: g(f(x),y) -> f(h(x,y)) h(x,y) -> g(x,f(y)) - Signature: {g/2,h/2} / {f/1} - Obligation: innermost runtime complexity wrt. defined symbols {g,h} and constructors {f} + Applied Processor: EmptyProcessor + Details: The problem is already closed. The intended complexity is O(1). WORST_CASE(?,O(n^1))