WORST_CASE(?,O(n^1)) * Step 1: Ara WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: f(a,cons(x,k)) -> f(cons(x,a),k) f(a,empty()) -> g(a,empty()) g(cons(x,k),d) -> g(k,cons(x,d)) g(empty(),d) -> d - Signature: {f/2,g/2} / {cons/2,empty/0} - Obligation: innermost runtime complexity wrt. defined symbols {f,g} and constructors {cons,empty} + Applied Processor: Ara {heuristics_ = NoHeuristics, minDegree = 1, maxDegree = 3, araTimeout = 60, araFindStrictRules = Nothing, araSmtSolver = MiniSMT} + Details: Signatures used: ---------------- cons :: [A(12) x A(12)] -(12)-> A(12) cons :: [A(4) x A(4)] -(4)-> A(4) cons :: [A(8) x A(8)] -(8)-> A(8) cons :: [A(0) x A(0)] -(0)-> A(0) empty :: [] -(0)-> A(12) empty :: [] -(0)-> A(4) empty :: [] -(0)-> A(8) f :: [A(8) x A(12)] -(4)-> A(0) g :: [A(4) x A(0)] -(2)-> A(0) Cost-free Signatures used: -------------------------- cons :: [A_cf(0) x A_cf(0)] -(0)-> A_cf(0) empty :: [] -(0)-> A_cf(0) f :: [A_cf(0) x A_cf(0)] -(0)-> A_cf(0) g :: [A_cf(0) x A_cf(0)] -(0)-> A_cf(0) Base Constructor Signatures used: --------------------------------- cons_A :: [A(1) x A(1)] -(1)-> A(1) empty_A :: [] -(0)-> A(1) * Step 2: Open MAYBE - Strict TRS: f(a,cons(x,k)) -> f(cons(x,a),k) f(a,empty()) -> g(a,empty()) g(cons(x,k),d) -> g(k,cons(x,d)) g(empty(),d) -> d - Signature: {f/2,g/2} / {cons/2,empty/0} - Obligation: innermost runtime complexity wrt. defined symbols {f,g} and constructors {cons,empty} Following problems could not be solved: - Strict TRS: f(a,cons(x,k)) -> f(cons(x,a),k) f(a,empty()) -> g(a,empty()) g(cons(x,k),d) -> g(k,cons(x,d)) g(empty(),d) -> d - Signature: {f/2,g/2} / {cons/2,empty/0} - Obligation: innermost runtime complexity wrt. defined symbols {f,g} and constructors {cons,empty} WORST_CASE(?,O(n^1))