WORST_CASE(?,O(n^1)) * Step 1: NaturalMI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: eq0(0(),0()) -> S(0()) eq0(0(),S(x)) -> 0() eq0(S(x),0()) -> 0() eq0(S(x'),S(x)) -> eq0(x',x) - Signature: {eq0/2} / {0/0,S/1} - Obligation: innermost runtime complexity wrt. defined symbols {eq0} 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: {eq0} TcT has computed the following interpretation: p(0) = [1] p(S) = [1] x1 + [1] p(eq0) = [8] x2 + [1] Following rules are strictly oriented: eq0(0(),0()) = [9] > [2] = S(0()) eq0(0(),S(x)) = [8] x + [9] > [1] = 0() eq0(S(x),0()) = [9] > [1] = 0() eq0(S(x'),S(x)) = [8] x + [9] > [8] x + [1] = eq0(x',x) Following rules are (at-least) weakly oriented: WORST_CASE(?,O(n^1))