* Step 1: WeightGap 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: 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(g) = {1} Following symbols are considered usable: all TcT has computed the following interpretation: p(f) = [8] x1 + [0] p(g) = [1] x1 + [1] Following rules are strictly oriented: f(g(x),y,y) = [8] x + [8] > [8] x + [1] = g(f(x,x,y)) 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: 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))