WORST_CASE(?,O(n^1)) * Step 1: Ara WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: a__c(X) -> c(X) a__c(X) -> d(X) a__f(X) -> f(X) a__f(f(X)) -> a__c(f(g(f(X)))) a__h(X) -> a__c(d(X)) a__h(X) -> h(X) mark(c(X)) -> a__c(X) mark(d(X)) -> d(X) mark(f(X)) -> a__f(mark(X)) mark(g(X)) -> g(X) mark(h(X)) -> a__h(mark(X)) - Signature: {a__c/1,a__f/1,a__h/1,mark/1} / {c/1,d/1,f/1,g/1,h/1} - Obligation: innermost runtime complexity wrt. defined symbols {a__c,a__f,a__h,mark} and constructors {c,d,f,g,h} + Applied Processor: Ara {heuristics_ = NoHeuristics, minDegree = 1, maxDegree = 3, araTimeout = 60, araFindStrictRules = Nothing, araSmtSolver = Z3} + Details: Signatures used: ---------------- a__c :: [A(0)] -(2)-> A(7) a__f :: [A(7)] -(11)-> A(7) a__h :: [A(7)] -(8)-> A(7) c :: [A(0)] -(0)-> A(13) c :: [A(0)] -(0)-> A(7) d :: [A(0)] -(0)-> A(13) d :: [A(0)] -(0)-> A(7) d :: [A(0)] -(0)-> A(14) d :: [A(0)] -(0)-> A(8) f :: [A(7)] -(7)-> A(7) f :: [A(13)] -(13)-> A(13) f :: [A(0)] -(0)-> A(0) g :: [A(0)] -(0)-> A(13) g :: [A(0)] -(0)-> A(6) g :: [A(0)] -(0)-> A(8) h :: [A(13)] -(13)-> A(13) h :: [A(7)] -(7)-> A(7) mark :: [A(13)] -(3)-> A(7) Cost-free Signatures used: -------------------------- a__c :: [A_cf(0)] -(0)-> A_cf(0) a__f :: [A_cf(0)] -(0)-> A_cf(0) a__h :: [A_cf(0)] -(0)-> A_cf(0) c :: [A_cf(0)] -(0)-> A_cf(0) d :: [A_cf(0)] -(0)-> A_cf(0) f :: [A_cf(0)] -(0)-> A_cf(0) g :: [A_cf(0)] -(0)-> A_cf(0) h :: [A_cf(0)] -(0)-> A_cf(0) mark :: [A_cf(0)] -(0)-> A_cf(0) Base Constructor Signatures used: --------------------------------- c_A :: [A(0)] -(0)-> A(1) d_A :: [A(0)] -(0)-> A(1) f_A :: [A(1)] -(1)-> A(1) g_A :: [A(0)] -(0)-> A(1) h_A :: [A(1)] -(1)-> A(1) * Step 2: Open MAYBE - Strict TRS: a__c(X) -> c(X) a__c(X) -> d(X) a__f(X) -> f(X) a__f(f(X)) -> a__c(f(g(f(X)))) a__h(X) -> a__c(d(X)) a__h(X) -> h(X) mark(c(X)) -> a__c(X) mark(d(X)) -> d(X) mark(f(X)) -> a__f(mark(X)) mark(g(X)) -> g(X) mark(h(X)) -> a__h(mark(X)) - Signature: {a__c/1,a__f/1,a__h/1,mark/1} / {c/1,d/1,f/1,g/1,h/1} - Obligation: innermost runtime complexity wrt. defined symbols {a__c,a__f,a__h,mark} and constructors {c,d,f,g,h} Following problems could not be solved: - Strict TRS: a__c(X) -> c(X) a__c(X) -> d(X) a__f(X) -> f(X) a__f(f(X)) -> a__c(f(g(f(X)))) a__h(X) -> a__c(d(X)) a__h(X) -> h(X) mark(c(X)) -> a__c(X) mark(d(X)) -> d(X) mark(f(X)) -> a__f(mark(X)) mark(g(X)) -> g(X) mark(h(X)) -> a__h(mark(X)) - Signature: {a__c/1,a__f/1,a__h/1,mark/1} / {c/1,d/1,f/1,g/1,h/1} - Obligation: innermost runtime complexity wrt. defined symbols {a__c,a__f,a__h,mark} and constructors {c,d,f,g,h} WORST_CASE(?,O(n^1))