WORST_CASE(?,O(n^1)) * Step 1: NaturalMI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: a__c() -> c() a__c() -> d() a__g(X) -> a__h(X) a__g(X) -> g(X) a__h(X) -> h(X) a__h(d()) -> a__g(c()) mark(c()) -> a__c() mark(d()) -> d() mark(g(X)) -> a__g(X) mark(h(X)) -> a__h(X) - Signature: {a__c/0,a__g/1,a__h/1,mark/1} / {c/0,d/0,g/1,h/1} - Obligation: innermost runtime complexity wrt. defined symbols {a__c,a__g,a__h,mark} and constructors {c,d,g,h} + 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__g,a__h,mark} TcT has computed the following interpretation: p(a__c) = [4] p(a__g) = [8] x1 + [5] p(a__h) = [1] x1 + [4] p(c) = [0] p(d) = [3] p(g) = [1] x1 + [1] p(h) = [1] x1 + [3] p(mark) = [8] x1 + [6] Following rules are strictly oriented: a__c() = [4] > [0] = c() a__c() = [4] > [3] = d() a__g(X) = [8] X + [5] > [1] X + [4] = a__h(X) a__g(X) = [8] X + [5] > [1] X + [1] = g(X) a__h(X) = [1] X + [4] > [1] X + [3] = h(X) a__h(d()) = [7] > [5] = a__g(c()) mark(c()) = [6] > [4] = a__c() mark(d()) = [30] > [3] = d() mark(g(X)) = [8] X + [14] > [8] X + [5] = a__g(X) mark(h(X)) = [8] X + [30] > [1] X + [4] = a__h(X) Following rules are (at-least) weakly oriented: WORST_CASE(?,O(n^1))