WORST_CASE(?,O(1)) * Step 1: NaturalMI WORST_CASE(?,O(1)) + Considered Problem: - Strict TRS: a__c() -> a__f(g(c())) a__c() -> c() a__f(X) -> f(X) a__f(g(X)) -> g(X) mark(c()) -> a__c() mark(f(X)) -> a__f(X) mark(g(X)) -> g(X) - Signature: {a__c/0,a__f/1,mark/1} / {c/0,f/1,g/1} - Obligation: innermost runtime complexity wrt. defined symbols {a__c,a__f,mark} and constructors {c,f,g} + 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: {a__c,a__f,mark} TcT has computed the following interpretation: p(a__c) = [11] p(a__f) = [9] p(c) = [2] p(f) = [1] p(g) = [5] p(mark) = [4] x1 + [11] Following rules are strictly oriented: a__c() = [11] > [9] = a__f(g(c())) a__c() = [11] > [2] = c() a__f(X) = [9] > [1] = f(X) a__f(g(X)) = [9] > [5] = g(X) mark(c()) = [19] > [11] = a__c() mark(f(X)) = [15] > [9] = a__f(X) mark(g(X)) = [31] > [5] = g(X) Following rules are (at-least) weakly oriented: WORST_CASE(?,O(1))