WORST_CASE(?,O(n^1)) * Step 1: NaturalPI WORST_CASE(?,O(n^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: NaturalPI {shape = Linear, restrict = NoRestrict, uargs = UArgs, urules = URules, selector = Nothing} + Details: We apply a polynomial interpretation of kind constructor-based(linear): 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) = 7 p(a__f) = 4 p(c) = 2 p(f) = 2 p(g) = 1 p(mark) = 6 + 2*x1 Following rules are strictly oriented: a__c() = 7 > 4 = a__f(g(c())) a__c() = 7 > 2 = c() a__f(X) = 4 > 2 = f(X) a__f(g(X)) = 4 > 1 = g(X) mark(c()) = 10 > 7 = a__c() mark(f(X)) = 10 > 4 = a__f(X) mark(g(X)) = 8 > 1 = g(X) Following rules are (at-least) weakly oriented: WORST_CASE(?,O(n^1))