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