WORST_CASE(?,O(n^1)) * Step 1: Ara WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: g(f(x),y) -> f(h(x,y)) h(x,y) -> g(x,f(y)) - Signature: {g/2,h/2} / {f/1} - Obligation: innermost runtime complexity wrt. defined symbols {g,h} and constructors {f} + Applied Processor: Ara {heuristics_ = NoHeuristics, minDegree = 1, maxDegree = 3, araTimeout = 60, araFindStrictRules = Nothing, araSmtSolver = Z3} + Details: Signatures used: ---------------- f :: [A(11)] -(11)-> A(11) f :: [A(2)] -(2)-> A(2) f :: [A(0)] -(0)-> A(0) g :: [A(11) x A(0)] -(3)-> A(2) h :: [A(11) x A(0)] -(9)-> A(2) Cost-free Signatures used: -------------------------- f :: [A_cf(0)] -(0)-> A_cf(0) g :: [A_cf(0) x A_cf(0)] -(0)-> A_cf(0) h :: [A_cf(0) x A_cf(0)] -(0)-> A_cf(0) Base Constructor Signatures used: --------------------------------- f_A :: [A(1)] -(1)-> A(1) * Step 2: Open MAYBE - Strict TRS: g(f(x),y) -> f(h(x,y)) h(x,y) -> g(x,f(y)) - Signature: {g/2,h/2} / {f/1} - Obligation: innermost runtime complexity wrt. defined symbols {g,h} and constructors {f} Following problems could not be solved: - Strict TRS: g(f(x),y) -> f(h(x,y)) h(x,y) -> g(x,f(y)) - Signature: {g/2,h/2} / {f/1} - Obligation: innermost runtime complexity wrt. defined symbols {g,h} and constructors {f} WORST_CASE(?,O(n^1))