WORST_CASE(?,O(n^1)) * Step 1: Ara WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: f(0()) -> cons(0()) f(s(0())) -> f(p(s(0()))) p(s(0())) -> 0() - 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(15) 0 :: [] -(0)-> A(0) 0 :: [] -(0)-> A(14) cons :: [A(0)] -(0)-> A(12) f :: [A(15)] -(12)-> A(0) p :: [A(1)] -(0)-> A(15) s :: [A(0)] -(15)-> A(15) s :: [A(0)] -(1)-> A(1) Cost-free Signatures used: -------------------------- 0 :: [] -(0)-> A_cf(0) cons :: [A_cf(0)] -(0)-> A_cf(0) f :: [A_cf(0)] -(0)-> A_cf(0) p :: [A_cf(0)] -(0)-> A_cf(0) s :: [A_cf(0)] -(0)-> A_cf(0) Base Constructor Signatures used: --------------------------------- 0_A :: [] -(0)-> A(1) cons_A :: [A(0)] -(0)-> A(1) s_A :: [A(0)] -(1)-> A(1) * Step 2: Open MAYBE - Strict TRS: f(0()) -> cons(0()) f(s(0())) -> f(p(s(0()))) p(s(0())) -> 0() - 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(0())) -> 0() - 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^1))