WORST_CASE(?,O(n^1)) * Step 1: NaturalMI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: *(x,+(y,z)) -> +(*(x,y),*(x,z)) - Signature: {*/2} / {+/2} - Obligation: innermost runtime complexity wrt. defined symbols {*} and constructors {+} + 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(+) = {1,2} Following symbols are considered usable: {*} TcT has computed the following interpretation: p(*) = [4] x2 + [8] p(+) = [1] x1 + [1] x2 + [3] Following rules are strictly oriented: *(x,+(y,z)) = [4] y + [4] z + [20] > [4] y + [4] z + [19] = +(*(x,y),*(x,z)) Following rules are (at-least) weakly oriented: * Step 2: EmptyProcessor WORST_CASE(?,O(1)) + Considered Problem: - Weak TRS: *(x,+(y,z)) -> +(*(x,y),*(x,z)) - Signature: {*/2} / {+/2} - Obligation: innermost runtime complexity wrt. defined symbols {*} and constructors {+} + Applied Processor: EmptyProcessor + Details: The problem is already closed. The intended complexity is O(1). WORST_CASE(?,O(n^1))