WORST_CASE(?,O(n^1)) * Step 1: Ara WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: f(cons(x,k),l) -> g(k,l,cons(x,k)) f(empty(),l) -> l g(a,b,c) -> f(a,cons(b,c)) - Signature: {f/2,g/3} / {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(2) x A(2)] -(2)-> A(2) cons :: [A(0) x A(0)] -(0)-> A(0) empty :: [] -(0)-> A(2) f :: [A(2) x A(0)] -(4)-> A(0) g :: [A(2) x A(0) x A(0)] -(5)-> 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) 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(cons(x,k),l) -> g(k,l,cons(x,k)) f(empty(),l) -> l g(a,b,c) -> f(a,cons(b,c)) - Signature: {f/2,g/3} / {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(cons(x,k),l) -> g(k,l,cons(x,k)) f(empty(),l) -> l g(a,b,c) -> f(a,cons(b,c)) - Signature: {f/2,g/3} / {cons/2,empty/0} - Obligation: innermost runtime complexity wrt. defined symbols {f,g} and constructors {cons,empty} WORST_CASE(?,O(n^1))