WORST_CASE(?,O(n^1)) * Step 1: Ara 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: Ara {heuristics_ = NoHeuristics, minDegree = 1, maxDegree = 3, araTimeout = 60, araFindStrictRules = Nothing, araSmtSolver = Z3} + Details: Signatures used: ---------------- a__c :: [] -(14)-> A(0) a__f :: [A(5)] -(4)-> A(0) c :: [] -(0)-> A(8) c :: [] -(0)-> A(5) c :: [] -(0)-> A(0) f :: [A(8)] -(8)-> A(8) f :: [A(3)] -(3)-> A(3) g :: [A(5)] -(5)-> A(5) g :: [A(8)] -(8)-> A(8) g :: [A(0)] -(0)-> A(0) mark :: [A(8)] -(15)-> A(0) Cost-free Signatures used: -------------------------- Base Constructor Signatures used: --------------------------------- c_A :: [] -(0)-> A(1) f_A :: [A(1)] -(1)-> A(1) g_A :: [A(1)] -(1)-> A(1) * Step 2: Open MAYBE - 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} Following problems could not be solved: - 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} WORST_CASE(?,O(n^1))