WORST_CASE(?,O(n^1)) * Step 1: Ara WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: activate(X) -> X activate(n__f(X)) -> f(X) f(X) -> n__f(X) f(0()) -> cons(0(),n__f(s(0()))) f(s(0())) -> f(p(s(0()))) p(s(0())) -> 0() - Signature: {activate/1,f/1,p/1} / {0/0,cons/2,n__f/1,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {activate,f,p} and constructors {0,cons,n__f,s} + Applied Processor: Ara {heuristics_ = NoHeuristics, minDegree = 1, maxDegree = 3, araTimeout = 60, araFindStrictRules = Nothing, araSmtSolver = Z3} + Details: Signatures used: ---------------- 0 :: [] -(0)-> A(7) 0 :: [] -(0)-> A(0) 0 :: [] -(0)-> A(15) 0 :: [] -(0)-> A(14) activate :: [A(7)] -(4)-> A(1) cons :: [A(0) x A(0)] -(0)-> A(11) f :: [A(7)] -(7)-> A(4) n__f :: [A(7)] -(7)-> A(7) n__f :: [A(6)] -(6)-> A(6) n__f :: [A(1)] -(1)-> A(1) p :: [A(1)] -(0)-> A(14) s :: [A(0)] -(7)-> A(7) s :: [A(0)] -(1)-> A(1) s :: [A(0)] -(3)-> A(3) Cost-free Signatures used: -------------------------- 0 :: [] -(0)-> A_cf(0) cons :: [A_cf(0) x A_cf(0)] -(0)-> A_cf(0) f :: [A_cf(0)] -(0)-> A_cf(0) n__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) x A(0)] -(0)-> A(1) n__f_A :: [A(0)] -(1)-> A(1) s_A :: [A(0)] -(1)-> A(1) * Step 2: Open MAYBE - Strict TRS: activate(X) -> X activate(n__f(X)) -> f(X) f(X) -> n__f(X) f(0()) -> cons(0(),n__f(s(0()))) f(s(0())) -> f(p(s(0()))) p(s(0())) -> 0() - Signature: {activate/1,f/1,p/1} / {0/0,cons/2,n__f/1,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {activate,f,p} and constructors {0,cons,n__f,s} Following problems could not be solved: - Strict TRS: activate(X) -> X activate(n__f(X)) -> f(X) f(X) -> n__f(X) f(0()) -> cons(0(),n__f(s(0()))) f(s(0())) -> f(p(s(0()))) p(s(0())) -> 0() - Signature: {activate/1,f/1,p/1} / {0/0,cons/2,n__f/1,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {activate,f,p} and constructors {0,cons,n__f,s} WORST_CASE(?,O(n^1))