WORST_CASE(?,O(n^1)) * Step 1: NaturalMI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: p(m,n,s(r)) -> p(m,r,n) p(m,0(),0()) -> m p(m,s(n),0()) -> p(0(),n,m) - Signature: {p/3} / {0/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {p} and constructors {0,s} + Applied Processor: NaturalMI {miDimension = 1, miDegree = 1, 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: {p} TcT has computed the following interpretation: p(0) = [0] p(p) = [2] x1 + [2] x2 + [2] x3 + [10] p(s) = [1] x1 + [2] Following rules are strictly oriented: p(m,n,s(r)) = [2] m + [2] n + [2] r + [14] > [2] m + [2] n + [2] r + [10] = p(m,r,n) p(m,0(),0()) = [2] m + [10] > [1] m + [0] = m p(m,s(n),0()) = [2] m + [2] n + [14] > [2] m + [2] n + [10] = p(0(),n,m) Following rules are (at-least) weakly oriented: WORST_CASE(?,O(n^1))