* Step 1: WeightGap WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: *(x,+(y,z)) -> +(*(x,y),*(x,z)) - Signature: {*/2} / {+/2} - Obligation: runtime complexity wrt. defined symbols {*} and constructors {+} + Applied Processor: WeightGap {wgDimension = 1, wgDegree = 1, wgKind = Algebraic, wgUArgs = UArgs, wgOn = WgOnAny} + Details: The weightgap principle applies using the following nonconstant growth matrix-interpretation: 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: all TcT has computed the following interpretation: p(*) = [6] x2 + [1] p(+) = [1] x1 + [1] x2 + [2] Following rules are strictly oriented: *(x,+(y,z)) = [6] y + [6] z + [13] > [6] y + [6] z + [4] = +(*(x,y),*(x,z)) Following rules are (at-least) weakly oriented: Further, it can be verified that all rules not oriented are covered by the weightgap condition. * Step 2: EmptyProcessor WORST_CASE(?,O(1)) + Considered Problem: - Weak TRS: *(x,+(y,z)) -> +(*(x,y),*(x,z)) - Signature: {*/2} / {+/2} - Obligation: 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))