WORST_CASE(?,O(n^1)) * Step 1: Ara WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: a__f(X) -> f(X) a__f(X) -> g(h(f(X))) mark(f(X)) -> a__f(mark(X)) mark(g(X)) -> g(X) mark(h(X)) -> h(mark(X)) - Signature: {a__f/1,mark/1} / {f/1,g/1,h/1} - Obligation: innermost runtime complexity wrt. defined symbols {a__f,mark} and constructors {f,g,h} + Applied Processor: Ara {heuristics_ = NoHeuristics, minDegree = 1, maxDegree = 3, araTimeout = 60, araFindStrictRules = Nothing, araSmtSolver = Z3} + Details: Signatures used: ---------------- a__f :: [A(0)] -(4)-> A(0) f :: [A(11)] -(11)-> A(11) f :: [A(0)] -(0)-> A(0) g :: [A(0)] -(11)-> A(11) g :: [A(0)] -(0)-> A(0) g :: [A(0)] -(4)-> A(4) h :: [A(11)] -(11)-> A(11) h :: [A(0)] -(0)-> A(0) mark :: [A(11)] -(0)-> A(0) Cost-free Signatures used: -------------------------- a__f :: [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: --------------------------------- f_A :: [A(1)] -(1)-> A(1) g_A :: [A(0)] -(1)-> A(1) h_A :: [A(1)] -(1)-> A(1) * Step 2: Open MAYBE - Strict TRS: a__f(X) -> f(X) a__f(X) -> g(h(f(X))) mark(f(X)) -> a__f(mark(X)) mark(g(X)) -> g(X) mark(h(X)) -> h(mark(X)) - Signature: {a__f/1,mark/1} / {f/1,g/1,h/1} - Obligation: innermost runtime complexity wrt. defined symbols {a__f,mark} and constructors {f,g,h} Following problems could not be solved: - Strict TRS: a__f(X) -> f(X) a__f(X) -> g(h(f(X))) mark(f(X)) -> a__f(mark(X)) mark(g(X)) -> g(X) mark(h(X)) -> h(mark(X)) - Signature: {a__f/1,mark/1} / {f/1,g/1,h/1} - Obligation: innermost runtime complexity wrt. defined symbols {a__f,mark} and constructors {f,g,h} WORST_CASE(?,O(n^1))