WORST_CASE(?,O(n^1)) * Step 1: Ara WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: 2nd(cons(X,X1)) -> 2nd(cons1(X,activate(X1))) 2nd(cons1(X,cons(Y,Z))) -> Y activate(X) -> X activate(n__from(X)) -> from(X) from(X) -> cons(X,n__from(s(X))) from(X) -> n__from(X) - Signature: {2nd/1,activate/1,from/1} / {cons/2,cons1/2,n__from/1,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {2nd,activate,from} and constructors {cons,cons1,n__from ,s} + Applied Processor: Ara {heuristics_ = NoHeuristics, minDegree = 1, maxDegree = 3, araTimeout = 60, araFindStrictRules = Nothing, araSmtSolver = Z3} + Details: Signatures used: ---------------- 2nd :: [A(9)] -(3)-> A(0) activate :: [A(5)] -(1)-> A(0) cons :: [A(9) x A(9)] -(9)-> A(9) cons :: [A(0) x A(0)] -(0)-> A(0) cons1 :: [A(0) x A(0)] -(0)-> A(9) cons1 :: [A(0) x A(0)] -(0)-> A(11) from :: [A(2)] -(4)-> A(0) n__from :: [A(5)] -(5)-> A(5) n__from :: [A(0)] -(0)-> A(0) n__from :: [A(2)] -(2)-> A(2) s :: [A(0)] -(0)-> A(11) Cost-free Signatures used: -------------------------- 2nd :: [A_cf(0)] -(0)-> A_cf(0) activate :: [A_cf(0)] -(0)-> A_cf(0) cons :: [A_cf(0) x A_cf(0)] -(0)-> A_cf(0) cons1 :: [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: --------------------------------- cons1_A :: [A(0) x A(0)] -(0)-> A(1) cons_A :: [A(1) x A(1)] -(1)-> A(1) n__from_A :: [A(0)] -(1)-> A(1) s_A :: [A(0)] -(0)-> A(1) * Step 2: Open MAYBE - Strict TRS: 2nd(cons(X,X1)) -> 2nd(cons1(X,activate(X1))) 2nd(cons1(X,cons(Y,Z))) -> Y activate(X) -> X activate(n__from(X)) -> from(X) from(X) -> cons(X,n__from(s(X))) from(X) -> n__from(X) - Signature: {2nd/1,activate/1,from/1} / {cons/2,cons1/2,n__from/1,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {2nd,activate,from} and constructors {cons,cons1,n__from ,s} Following problems could not be solved: - Strict TRS: 2nd(cons(X,X1)) -> 2nd(cons1(X,activate(X1))) 2nd(cons1(X,cons(Y,Z))) -> Y activate(X) -> X activate(n__from(X)) -> from(X) from(X) -> cons(X,n__from(s(X))) from(X) -> n__from(X) - Signature: {2nd/1,activate/1,from/1} / {cons/2,cons1/2,n__from/1,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {2nd,activate,from} and constructors {cons,cons1,n__from ,s} WORST_CASE(?,O(n^1))