WORST_CASE(?,O(n^1)) * Step 1: Ara WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: 2nd(cons(X,n__cons(Y,Z))) -> activate(Y) activate(X) -> X activate(n__cons(X1,X2)) -> cons(X1,X2) activate(n__from(X)) -> from(X) cons(X1,X2) -> n__cons(X1,X2) from(X) -> cons(X,n__from(s(X))) from(X) -> n__from(X) - Signature: {2nd/1,activate/1,cons/2,from/1} / {n__cons/2,n__from/1,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {2nd,activate,cons,from} and constructors {n__cons,n__from ,s} + Applied Processor: Ara {heuristics_ = NoHeuristics, minDegree = 1, maxDegree = 3, araTimeout = 60, araFindStrictRules = Nothing, araSmtSolver = Z3} + Details: Signatures used: ---------------- 2nd :: [A(0)] -(8)-> A(0) activate :: [A(3)] -(7)-> A(0) cons :: [A(0) x A(3)] -(1)-> A(0) from :: [A(0)] -(3)-> A(0) n__cons :: [A(3) x A(3)] -(3)-> A(3) n__cons :: [A(0) x A(0)] -(0)-> A(0) n__from :: [A(0)] -(0)-> A(3) n__from :: [A(0)] -(0)-> A(8) n__from :: [A(0)] -(0)-> A(14) s :: [A(0)] -(0)-> A(14) Cost-free Signatures used: -------------------------- Base Constructor Signatures used: --------------------------------- n__cons_A :: [A(0) x A(0)] -(1)-> A(1) n__from_A :: [A(0)] -(0)-> A(1) s_A :: [A(0)] -(0)-> A(1) * Step 2: Open MAYBE - Strict TRS: 2nd(cons(X,n__cons(Y,Z))) -> activate(Y) activate(X) -> X activate(n__cons(X1,X2)) -> cons(X1,X2) activate(n__from(X)) -> from(X) cons(X1,X2) -> n__cons(X1,X2) from(X) -> cons(X,n__from(s(X))) from(X) -> n__from(X) - Signature: {2nd/1,activate/1,cons/2,from/1} / {n__cons/2,n__from/1,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {2nd,activate,cons,from} and constructors {n__cons,n__from ,s} Following problems could not be solved: - Strict TRS: 2nd(cons(X,n__cons(Y,Z))) -> activate(Y) activate(X) -> X activate(n__cons(X1,X2)) -> cons(X1,X2) activate(n__from(X)) -> from(X) cons(X1,X2) -> n__cons(X1,X2) from(X) -> cons(X,n__from(s(X))) from(X) -> n__from(X) - Signature: {2nd/1,activate/1,cons/2,from/1} / {n__cons/2,n__from/1,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {2nd,activate,cons,from} and constructors {n__cons,n__from ,s} WORST_CASE(?,O(n^1))