WORST_CASE(?,O(n^1)) * Step 1: Ara WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: activate(X) -> X activate(n__from(X)) -> from(X) after(0(),XS) -> XS after(s(N),cons(X,XS)) -> after(N,activate(XS)) from(X) -> cons(X,n__from(s(X))) from(X) -> n__from(X) - Signature: {activate/1,after/2,from/1} / {0/0,cons/2,n__from/1,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {activate,after,from} and constructors {0,cons,n__from,s} + Applied Processor: Ara {heuristics_ = NoHeuristics, minDegree = 1, maxDegree = 3, araTimeout = 60, araFindStrictRules = Nothing, araSmtSolver = MiniSMT} + Details: Signatures used: ---------------- 0 :: [] -(0)-> A(12) activate :: [A(0)] -(9)-> A(0) after :: [A(12) x A(0)] -(2)-> A(0) cons :: [A(0) x A(0)] -(0)-> A(0) from :: [A(0)] -(1)-> A(0) n__from :: [A(0)] -(0)-> A(0) s :: [A(12)] -(12)-> A(12) s :: [A(0)] -(0)-> A(0) Cost-free Signatures used: -------------------------- 0 :: [] -(0)-> A_cf(0) activate :: [A_cf(0)] -(0)-> A_cf(0) after :: [A_cf(0) x A_cf(0)] -(0)-> A_cf(0) cons :: [A_cf(0) x A_cf(0)] -(0)-> A_cf(0) from :: [A_cf(0)] -(0)-> A_cf(0) n__from :: [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(1) x A(0)] -(0)-> A(1) n__from_A :: [A(0)] -(0)-> A(1) s_A :: [A(1)] -(1)-> A(1) * Step 2: Open MAYBE - Strict TRS: activate(X) -> X activate(n__from(X)) -> from(X) after(0(),XS) -> XS after(s(N),cons(X,XS)) -> after(N,activate(XS)) from(X) -> cons(X,n__from(s(X))) from(X) -> n__from(X) - Signature: {activate/1,after/2,from/1} / {0/0,cons/2,n__from/1,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {activate,after,from} and constructors {0,cons,n__from,s} Following problems could not be solved: - Strict TRS: activate(X) -> X activate(n__from(X)) -> from(X) after(0(),XS) -> XS after(s(N),cons(X,XS)) -> after(N,activate(XS)) from(X) -> cons(X,n__from(s(X))) from(X) -> n__from(X) - Signature: {activate/1,after/2,from/1} / {0/0,cons/2,n__from/1,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {activate,after,from} and constructors {0,cons,n__from,s} WORST_CASE(?,O(n^1))