WORST_CASE(?,O(n^2)) * Step 1: NaturalMI WORST_CASE(?,O(n^2)) + Considered Problem: - Strict TRS: h(x,c(y,z)) -> h(c(s(y),x),z) h(c(s(x),c(s(0()),y)),z) -> h(y,c(s(0()),c(x,z))) - Signature: {h/2} / {0/0,c/2,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {h} and constructors {0,c,s} + Applied Processor: NaturalMI {miDimension = 2, miDegree = 2, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Nothing} + Details: We apply a matrix interpretation of kind constructor based matrix interpretation: The following argument positions are considered usable: none Following symbols are considered usable: {h} TcT has computed the following interpretation: p(0) = [1] [3] p(c) = [1 4] x1 + [1 0] x2 + [0] [0 1] [0 1] [1] p(h) = [4 0] x1 + [0 4] x2 + [2] [4 0] [0 4] [0] p(s) = [0 1] x1 + [0] [0 0] [0] Following rules are strictly oriented: h(x,c(y,z)) = [4 0] x + [0 4] y + [0 4] z + [6] [4 0] [0 4] [0 4] [4] > [4 0] x + [0 4] y + [0 4] z + [2] [4 0] [0 4] [0 4] [0] = h(c(s(y),x),z) h(c(s(x),c(s(0()),y)),z) = [0 4] x + [4 0] y + [0 4] z + [14] [0 4] [4 0] [0 4] [12] > [0 4] x + [4 0] y + [0 4] z + [10] [0 4] [4 0] [0 4] [8] = h(y,c(s(0()),c(x,z))) Following rules are (at-least) weakly oriented: WORST_CASE(?,O(n^2))