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