WORST_CASE(?,O(n^1)) * Step 1: Ara WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: g(x,h(y,z)) -> h(g(x,y),z) g(f(x,y),z) -> f(x,g(y,z)) g(h(x,y),z) -> g(x,f(y,z)) - Signature: {g/2} / {f/2,h/2} - Obligation: innermost runtime complexity wrt. defined symbols {g} and constructors {f,h} + Applied Processor: Ara {heuristics_ = NoHeuristics, minDegree = 1, maxDegree = 3, araTimeout = 60, araFindStrictRules = Nothing, araSmtSolver = MiniSMT} + Details: Signatures used: ---------------- f :: [A(0) x A(8)] -(8)-> A(8) f :: [A(0) x A(0)] -(0)-> A(0) f :: [A(0) x A(1)] -(1)-> A(1) g :: [A(8) x A(1)] -(4)-> A(0) h :: [A(1) x A(1)] -(1)-> A(1) h :: [A(8) x A(8)] -(8)-> A(8) h :: [A(0) x 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) x A_cf(0)] -(0)-> A_cf(0) Base Constructor Signatures used: --------------------------------- f_A :: [A(0) x A(1)] -(1)-> A(1) h_A :: [A(1) x A(1)] -(1)-> A(1) * Step 2: Open MAYBE - Strict TRS: g(x,h(y,z)) -> h(g(x,y),z) g(f(x,y),z) -> f(x,g(y,z)) g(h(x,y),z) -> g(x,f(y,z)) - Signature: {g/2} / {f/2,h/2} - Obligation: innermost runtime complexity wrt. defined symbols {g} and constructors {f,h} Following problems could not be solved: - Strict TRS: g(x,h(y,z)) -> h(g(x,y),z) g(f(x,y),z) -> f(x,g(y,z)) g(h(x,y),z) -> g(x,f(y,z)) - Signature: {g/2} / {f/2,h/2} - Obligation: innermost runtime complexity wrt. defined symbols {g} and constructors {f,h} WORST_CASE(?,O(n^1))