WORST_CASE(?,O(n^1)) * Step 1: NaturalPI 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: 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__g,a__h,mark} TcT has computed the following interpretation: p(a__c) = 3 p(a__g) = 3 + 10*x1 p(a__h) = 1 + 8*x1 p(c) = 0 p(d) = 2 p(g) = 1 + x1 p(h) = x1 p(mark) = 5 + 10*x1 Following rules are strictly oriented: a__c() = 3 > 0 = c() a__c() = 3 > 2 = d() a__g(X) = 3 + 10*X > 1 + 8*X = a__h(X) a__g(X) = 3 + 10*X > 1 + X = g(X) a__h(X) = 1 + 8*X > X = h(X) a__h(d()) = 17 > 3 = a__g(c()) mark(c()) = 5 > 3 = a__c() mark(d()) = 25 > 2 = d() mark(g(X)) = 15 + 10*X > 3 + 10*X = a__g(X) mark(h(X)) = 5 + 10*X > 1 + 8*X = a__h(X) Following rules are (at-least) weakly oriented: WORST_CASE(?,O(n^1))