WORST_CASE(?,O(n^1)) * Step 1: Ara WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: f(c(X,s(Y))) -> f(c(s(X),Y)) g(c(s(X),Y)) -> f(c(X,s(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 = Z3} + Details: Signatures used: ---------------- c :: [A(0) x A(7)] -(7)-> A(7) c :: [A(0) x A(15)] -(15)-> A(15) f :: [A(7)] -(7)-> A(15) g :: [A(15)] -(8)-> A(0) s :: [A(7)] -(7)-> A(7) s :: [A(0)] -(0)-> A(0) Cost-free Signatures used: -------------------------- c :: [A_cf(0) x A_cf(0)] -(0)-> A_cf(0) f :: [A_cf(0)] -(0)-> A_cf(0) s :: [A_cf(0)] -(0)-> A_cf(0) Base Constructor Signatures used: --------------------------------- c_A :: [A(0) x A(1)] -(1)-> A(1) s_A :: [A(1)] -(1)-> A(1) * Step 2: Open MAYBE - Strict TRS: f(c(X,s(Y))) -> f(c(s(X),Y)) g(c(s(X),Y)) -> f(c(X,s(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(X,s(Y))) -> f(c(s(X),Y)) g(c(s(X),Y)) -> f(c(X,s(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^1))