WORST_CASE(?,O(n^2)) * Step 1: Ara WORST_CASE(?,O(n^2)) + Considered Problem: - Strict TRS: f(0()) -> cons(0()) f(s(0())) -> f(p(s(0()))) p(s(X)) -> X - Signature: {f/1,p/1} / {0/0,cons/1,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {f,p} and constructors {0,cons,s} + Applied Processor: Ara {heuristics_ = NoHeuristics, minDegree = 1, maxDegree = 3, araTimeout = 60, araFindStrictRules = Nothing, araSmtSolver = Z3} + Details: Signatures used: ---------------- 0 :: [] -(0)-> A(9, 5) 0 :: [] -(0)-> A(14, 5) 0 :: [] -(0)-> A(11, 15) 0 :: [] -(0)-> A(15, 15) cons :: [A(4, 0)] -(0)-> A(3, 1) f :: [A(9, 5)] -(8)-> A(0, 0) p :: [A(0, 15)] -(1)-> A(15, 15) s :: [A(14, 5)] -(9)-> A(9, 5) s :: [A(15, 15)] -(0)-> A(0, 15) Cost-free Signatures used: -------------------------- 0 :: [] -(0)-> A_cf(5, 1) 0 :: [] -(0)-> A_cf(6, 1) 0 :: [] -(0)-> A_cf(15, 11) 0 :: [] -(0)-> A_cf(11, 11) cons :: [A_cf(14, 0)] -(0)-> A_cf(1, 13) f :: [A_cf(5, 1)] -(3)-> A_cf(0, 0) p :: [A_cf(0, 6)] -(0)-> A_cf(6, 3) s :: [A_cf(6, 1)] -(5)-> A_cf(5, 1) s :: [A_cf(6, 6)] -(0)-> A_cf(0, 6) s :: [A_cf(8, 8)] -(0)-> A_cf(0, 8) Base Constructor Signatures used: --------------------------------- 0_A :: [] -(0)-> A(1, 0) 0_A :: [] -(0)-> A(0, 1) cons_A :: [A(1, 0)] -(0)-> A(1, 0) cons_A :: [A(1, 0)] -(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(0()) -> cons(0()) f(s(0())) -> f(p(s(0()))) p(s(X)) -> X - Signature: {f/1,p/1} / {0/0,cons/1,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {f,p} and constructors {0,cons,s} Following problems could not be solved: - Strict TRS: f(0()) -> cons(0()) f(s(0())) -> f(p(s(0()))) p(s(X)) -> X - Signature: {f/1,p/1} / {0/0,cons/1,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {f,p} and constructors {0,cons,s} WORST_CASE(?,O(n^2))